LMFDB - Embedded newform 60.4.j.a.43.4

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			43.4
Root			$1.28897 - 0.581861i$ of defining polynomial
Character	$\chi$	$=$	60.43
Dual form			60.4.j.a.7.4

$q$-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 $\left(\mathbb{Z}/60\mathbb{Z}\right)^\times$.

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

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 $

$2$	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	0.906789	−	0.421584i	$-0.138526\pi$
$7$	8.98612	+	8.98612i	0.485205	+	0.485205i	−0.421584	+	0.906789i	$0.638526\pi$
$8$	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	$0.178571\pi$
$11$			38.8201i			1.06406i	−0.846724	+	0.532032i	$0.821429\pi$
$12$	−1.50295	−	23.9529i	−0.0361554	−	0.576217i
$13$	28.7750	+	28.7750i	0.613904	+	0.613904i	0.943961	−	0.330057i	$-0.107068\pi$
$13$	28.7750	+	28.7750i	0.613904	+	0.613904i	−0.330057	+	0.943961i	$0.607068\pi$
$14$	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	−0.621956	−	0.783052i	$-0.713662\pi$
$17$	11.2917	−	11.2917i	0.161097	−	0.161097i	0.783052	+	0.621956i	$0.213662\pi$
$18$	−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	−0.999346	−	0.0361669i	$-0.988485\pi$
$23$	−106.243	+	106.243i	−0.963179	+	0.963179i	0.0361669	+	0.999346i	$0.488485\pi$
$24$	−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	$-0.766719\pi$
$29$		−	208.958i		−	1.33802i	0.743254	−	0.669009i	$-0.233281\pi$
$30$	−82.4235	+	46.9720i	−0.501613	+	0.285862i
$31$			243.881i			1.41298i	0.707724	+	0.706489i	$0.249722\pi$
$31$			243.881i			1.41298i	−0.707724	+	0.706489i	$0.750278\pi$
$32$	−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	−0.995786	−	0.0917043i	$-0.970769\pi$
$37$	−203.475	+	203.475i	−0.904082	+	0.904082i	0.0917043	+	0.995786i	$0.470769\pi$
$38$	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	−0.0961347	−	0.995368i	$-0.530648\pi$
$43$	253.557	−	253.557i	0.899234	−	0.899234i	0.995368	+	0.0961347i	$0.0306480\pi$
$44$	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	−0.988639	−	0.150311i	$-0.951972\pi$
$47$	−366.988	−	366.988i	−1.13895	−	1.13895i	−0.150311	−	0.988639i	$-0.548028\pi$
$48$	−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	−0.928187	−	0.372114i	$-0.878633\pi$
$53$	−501.716	−	501.716i	−1.30030	−	1.30030i	−0.372114	−	0.928187i	$-0.621367\pi$
$54$	−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	0.252194	−	0.967677i	$-0.418848\pi$
$67$	−392.384	−	392.384i	−0.715483	−	0.715483i	−0.967677	+	0.252194i	$0.918848\pi$
$68$	−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	$0.170686\pi$
$71$			611.293i			1.02179i	−0.859643	+	0.510896i	$0.829314\pi$
$72$	−194.629	−	59.9294i	−0.318573	−	0.0980937i
$73$	144.800	+	144.800i	0.232158	+	0.232158i	0.813593	−	0.581435i	$-0.197509\pi$
$73$	144.800	+	144.800i	0.232158	+	0.232158i	−0.581435	+	0.813593i	$0.697509\pi$
$74$	−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	−0.953981	−	0.299866i	$-0.903058\pi$
$83$	−494.620	+	494.620i	−0.654116	+	0.654116i	0.299866	+	0.953981i	$0.403058\pi$
$84$	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	$0.145295\pi$
$89$			740.166i			0.881544i	−0.897619	+	0.440772i	$0.854705\pi$
$90$	−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	−0.661331	−	0.750095i	$-0.730008\pi$
$97$	84.7998	−	84.7998i	0.0887641	−	0.0887641i	0.750095	+	0.661331i	$0.230008\pi$
$98$	−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	−0.283508	+	0.958970i	$0.591498\pi$
$103$	−1298.81	+	1298.81i	−1.24248	+	1.24248i	−0.958970	+	0.283508i	$0.908502\pi$
$104$	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	0.852455	−	0.522801i	$-0.175113\pi$
$107$	364.866	+	364.866i	0.329653	+	0.329653i	−0.522801	+	0.852455i	$0.675113\pi$
$108$	−215.576	+	13.5265i	−0.192072	+	0.0120518i
$109$		−	1210.25i		−	1.06349i	−0.846903	−	0.531747i	$-0.821536\pi$
$109$		−	1210.25i		−	1.06349i	0.846903	−	0.531747i	$-0.178464\pi$
$110$	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	0.901885	−	0.431977i	$-0.142184\pi$
$113$	564.456	+	564.456i	0.469908	+	0.469908i	−0.431977	+	0.901885i	$0.642184\pi$
$114$	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	0.637313	−	0.770605i	$-0.280046\pi$
$127$	−190.770	−	190.770i	−0.133292	−	0.133292i	−0.770605	+	0.637313i	$0.780046\pi$
$128$	−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	$-0.806676\pi$
$131$		−	1711.34i		−	1.14138i	0.821166	−	0.570689i	$-0.193324\pi$
$132$	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	−0.667864	−	0.744283i	$-0.732791\pi$
$137$	122.540	−	122.540i	0.0764184	−	0.0764184i	0.744283	+	0.667864i	$0.232791\pi$
$138$	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	$0.234843\pi$
$149$			2446.79i			1.34529i	−0.739964	+	0.672647i	$0.765157\pi$
$150$	1044.74	+	183.066i	0.568686	+	0.0996484i
$151$		−	905.413i		−	0.487957i	−0.969781	−	0.243978i	$-0.921547\pi$
$151$		−	905.413i		−	0.487957i	0.969781	−	0.243978i	$-0.0784526\pi$
$152$	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	−0.714747	−	0.699383i	$-0.753458\pi$
$157$	−30.2239	+	30.2239i	−0.0153639	+	0.0153639i	0.699383	+	0.714747i	$0.253458\pi$
$158$	−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	−0.439219	−	0.898380i	$-0.644745\pi$
$163$	955.533	−	955.533i	0.459160	−	0.459160i	0.898380	+	0.439219i	$0.144745\pi$
$164$	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	0.665787	−	0.746142i	$-0.268096\pi$
$167$	−173.415	−	173.415i	−0.0803550	−	0.0803550i	−0.746142	+	0.665787i	$0.768096\pi$
$168$	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	0.931141	−	0.364660i	$-0.118815\pi$
$173$	1289.00	+	1289.00i	0.566480	+	0.566480i	−0.364660	+	0.931141i	$0.618815\pi$
$174$	−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	$0.0565180\pi$
$191$			932.465i			0.353250i	−0.984278	+	0.176625i	$0.943482\pi$
$192$	−1508.94	+	287.058i	−0.567178	+	0.107899i
$193$	−2205.49	−	2205.49i	−0.822565	−	0.822565i	0.163910	−	0.986475i	$-0.447589\pi$
$193$	−2205.49	−	2205.49i	−0.822565	−	0.822565i	−0.986475	+	0.163910i	$0.947589\pi$
$194$	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	−0.957751	−	0.287600i	$-0.907143\pi$
$197$	−1852.98	+	1852.98i	−0.670150	+	0.670150i	0.287600	+	0.957751i	$0.407143\pi$
$198$	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	$-0.757274\pi$
$211$		−	4234.33i		−	1.38153i	0.723078	−	0.690766i	$-0.242726\pi$
$212$	−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	−0.630080	−	0.776531i	$-0.716978\pi$
$223$	487.697	−	487.697i	0.146451	−	0.146451i	0.776531	+	0.630080i	$0.216978\pi$
$224$	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	0.949788	−	0.312895i	$-0.101299\pi$
$227$	2178.24	+	2178.24i	0.636892	+	0.636892i	−0.312895	+	0.949788i	$0.601299\pi$
$228$	−23.7167	−	377.980i	−0.00688894	−	0.109791i
$229$		−	3797.50i		−	1.09583i	−0.836533	−	0.547916i	$-0.815421\pi$
$229$		−	3797.50i		−	1.09583i	0.836533	−	0.547916i	$-0.184579\pi$
$230$	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	0.353003	−	0.935622i	$-0.385161\pi$
$233$	−2072.14	−	2072.14i	−0.582620	−	0.582620i	−0.935622	+	0.353003i	$0.885161\pi$
$234$	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	$0.165448\pi$
$251$			3950.18i			0.993359i	−0.867934	+	0.496679i	$0.834552\pi$
$252$	−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	0.0112693	−	0.999936i	$-0.496413\pi$
$257$	4166.19	−	4166.19i	1.01121	−	1.01121i	0.999936	−	0.0112693i	$-0.00358721\pi$
$258$	−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	−0.428064	−	0.903748i	$-0.640804\pi$
$263$	2028.86	−	2028.86i	0.475684	−	0.475684i	0.903748	+	0.428064i	$0.140804\pi$
$264$	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	$0.0141380\pi$
$269$			391.791i			0.0888027i	−0.999014	+	0.0444014i	$0.985862\pi$
$270$	422.748	+	741.812i	0.0952874	+	0.167204i
$271$			2030.42i			0.455127i	0.973763	+	0.227563i	$0.0730759\pi$
$271$			2030.42i			0.455127i	−0.973763	+	0.227563i	$0.926924\pi$
$272$	−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	−0.00477858	−	0.999989i	$-0.501521\pi$
$277$	4588.12	−	4588.12i	0.995210	−	0.995210i	0.999989	+	0.00477858i	$0.00152108\pi$
$278$	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	−0.876015	−	0.482283i	$-0.839808\pi$
$283$	−1874.48	+	1874.48i	−0.393732	+	0.393732i	0.482283	+	0.876015i	$0.339808\pi$
$284$	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	0.792803	−	0.609478i	$-0.208621\pi$
$293$	919.438	+	919.438i	0.183325	+	0.183325i	−0.609478	+	0.792803i	$0.708621\pi$
$294$	−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	0.868407	−	0.495852i	$-0.165144\pi$
$307$	2004.00	+	2004.00i	0.372555	+	0.372555i	−0.495852	+	0.868407i	$0.665144\pi$
$308$	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	$-0.886496\pi$
$311$		−	3829.04i		−	0.698151i	0.937095	−	0.349075i	$-0.113504\pi$
$312$	812.923	−	2640.08i	0.147509	−	0.479055i
$313$	706.908	+	706.908i	0.127657	+	0.127657i	0.768049	−	0.640391i	$-0.221228\pi$
$313$	706.908	+	706.908i	0.127657	+	0.127657i	−0.640391	+	0.768049i	$0.721228\pi$
$314$	−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	−0.638307	−	0.769782i	$-0.720365\pi$
$317$	742.045	−	742.045i	0.131475	−	0.131475i	0.769782	+	0.638307i	$0.220365\pi$
$318$	−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	$-0.791638\pi$
$331$		−	7332.79i		−	1.21766i	0.793299	−	0.608832i	$-0.208362\pi$
$332$	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	−0.997413	−	0.0718830i	$-0.977099\pi$
$337$	−5725.79	+	5725.79i	−0.925530	+	0.925530i	0.0718830	+	0.997413i	$0.477099\pi$
$338$	−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	0.841339	−	0.540507i	$-0.181768\pi$
$347$	1944.55	+	1944.55i	0.300832	+	0.300832i	−0.540507	+	0.841339i	$0.681768\pi$
$348$	−5005.15	+	314.053i	−0.770989	+	0.0483765i
$349$		−	9581.22i		−	1.46954i	−0.678314	−	0.734772i	$-0.737289\pi$
$349$		−	9581.22i		−	1.46954i	0.678314	−	0.734772i	$-0.262711\pi$
$350$	−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	0.680507	−	0.732742i	$-0.261760\pi$
$353$	−346.439	−	346.439i	−0.0522354	−	0.0522354i	−0.732742	+	0.680507i	$0.761760\pi$
$354$	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	0.968632	−	0.248501i	$-0.0799380\pi$
$367$	5063.03	+	5063.03i	0.720130	+	0.720130i	−0.248501	+	0.968632i	$0.579938\pi$
$368$	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	0.656803	−	0.754062i	$-0.271908\pi$
$373$	−700.635	−	700.635i	−0.0972588	−	0.0972588i	−0.754062	+	0.656803i	$0.771908\pi$
$374$	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	−0.100345	−	0.994953i	$-0.531995\pi$
$383$	6705.49	−	6705.49i	0.894608	−	0.894608i	0.994953	+	0.100345i	$0.0319947\pi$
$384$	−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	$-0.974978\pi$
$389$		−	1204.96i		−	0.157053i	0.996912	−	0.0785267i	$-0.0250216\pi$
$390$	−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	−0.999675	−	0.0254910i	$-0.991885\pi$
$397$	−7705.96	+	7705.96i	−0.974184	+	0.974184i	0.0254910	+	0.999675i	$0.491885\pi$
$398$	−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	$0.214473\pi$
$409$			10322.0i			1.24790i	−0.781465	+	0.623949i	$0.785527\pi$
$410$	−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	$0.327140\pi$
$431$			15321.0i			1.71227i	−0.516756	+	0.856133i	$0.672860\pi$
$432$	−1059.56	+	1365.03i	−0.118005	+	0.152026i
$433$	−192.550	−	192.550i	−0.0213704	−	0.0213704i	0.696341	−	0.717711i	$-0.254810\pi$
$433$	−192.550	−	192.550i	−0.0213704	−	0.0213704i	−0.717711	+	0.696341i	$0.754810\pi$
$434$	−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	−0.233729	+	0.972302i	$0.575093\pi$
$443$	−11245.1	+	11245.1i	−1.20603	+	1.20603i	−0.972302	+	0.233729i	$0.924907\pi$
$444$	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	$0.0786581\pi$
$449$			4654.40i			0.489209i	−0.969623	+	0.244604i	$0.921342\pi$
$450$	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	−0.712471	−	0.701702i	$-0.752424\pi$
$457$	−105.211	+	105.211i	−0.0107693	+	0.0107693i	0.701702	+	0.712471i	$0.252424\pi$
$458$	−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	−0.861100	−	0.508436i	$-0.830224\pi$
$463$	−3513.45	+	3513.45i	−0.352665	+	0.352665i	0.508436	+	0.861100i	$0.330224\pi$
$464$	−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	0.113662	−	0.993519i	$-0.463742\pi$
$467$	−8879.48	−	8879.48i	−0.879857	−	0.879857i	−0.993519	+	0.113662i	$0.963742\pi$
$468$	−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	0.431142	−	0.902284i	$-0.358111\pi$
$487$	−5063.44	−	5063.44i	−0.471142	−	0.471142i	−0.902284	+	0.431142i	$0.858111\pi$
$488$	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	$0.168939\pi$
$491$			11014.1i			1.01234i	−0.862434	+	0.506169i	$0.831061\pi$
$492$	−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	−0.250091	−	0.968222i	$-0.580460\pi$
$503$	8101.33	−	8101.33i	0.718132	−	0.718132i	0.968222	+	0.250091i	$0.0804604\pi$
$504$	−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	$0.210111\pi$
$509$			14083.0i			1.22637i	−0.789941	+	0.613183i	$0.789889\pi$
$510$	−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	−0.996299	−	0.0859510i	$-0.972607\pi$
$523$	−10888.3	+	10888.3i	−0.910348	+	0.910348i	0.0859510	+	0.996299i	$0.472607\pi$
$524$	−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	−0.876216	−	0.481918i	$-0.839940\pi$
$547$	−17375.0	−	17375.0i	−1.35813	−	1.35813i	−0.481918	−	0.876216i	$-0.660060\pi$
$548$	−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	−0.701788	−	0.712386i	$-0.747615\pi$
$557$	139.313	−	139.313i	0.0105976	−	0.0105976i	0.712386	+	0.701788i	$0.247615\pi$
$558$	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	−0.776785	−	0.629766i	$-0.783151\pi$
$563$	−1963.98	+	1963.98i	−0.147020	+	0.147020i	0.629766	+	0.776785i	$0.283151\pi$
$564$	−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	$-0.807516\pi$
$569$		−	15432.8i		−	1.13704i	0.822668	−	0.568522i	$-0.192484\pi$
$570$	−1300.65	+	741.223i	−0.0955761	+	0.0544674i
$571$			7847.00i			0.575108i	0.957764	+	0.287554i	$0.0928421\pi$
$571$			7847.00i			0.575108i	−0.957764	+	0.287554i	$0.907158\pi$
$572$	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	−0.964784	−	0.263043i	$-0.915274\pi$
$577$	−9726.14	+	9726.14i	−0.701741	+	0.701741i	0.263043	+	0.964784i	$0.415274\pi$
$578$	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	0.879517	−	0.475868i	$-0.157866\pi$
$587$	5740.65	+	5740.65i	0.403649	+	0.403649i	−0.475868	+	0.879517i	$0.657866\pi$
$588$	−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	0.934657	−	0.355550i	$-0.115706\pi$
$593$	8362.60	+	8362.60i	0.579107	+	0.579107i	−0.355550	+	0.934657i	$0.615706\pi$
$594$	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	−0.977153	−	0.212538i	$-0.931827\pi$
$607$	−17791.7	−	17791.7i	−1.18969	−	1.18969i	−0.212538	−	0.977153i	$-0.568173\pi$
$608$	−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	0.727447	−	0.686163i	$-0.240707\pi$
$613$	626.573	+	626.573i	0.0412839	+	0.0412839i	−0.686163	+	0.727447i	$0.740707\pi$
$614$	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	−0.882721	−	0.469897i	$-0.844291\pi$
$617$	−6326.92	+	6326.92i	−0.412824	+	0.412824i	0.469897	+	0.882721i	$0.344291\pi$
$618$	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	$0.134849\pi$
$631$			13031.7i			0.822161i	−0.911599	+	0.411081i	$0.865151\pi$
$632$	−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	−0.837126	−	0.547010i	$-0.815766\pi$
$643$	−4730.31	+	4730.31i	−0.290117	+	0.290117i	0.547010	+	0.837126i	$0.315766\pi$
$644$	−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	0.450901	−	0.892574i	$-0.351103\pi$
$647$	−7268.71	−	7268.71i	−0.441673	−	0.441673i	−0.892574	+	0.450901i	$0.851103\pi$
$648$	−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	−0.961068	−	0.276313i	$-0.910887\pi$
$653$	−20647.8	−	20647.8i	−1.23738	−	1.23738i	−0.276313	−	0.961068i	$-0.589113\pi$
$654$	−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	0.936187	+	0.351502i	$0.114329\pi$
$673$	22481.9	+	22481.9i	1.28769	+	1.28769i	0.351502	+	0.936187i	$0.385671\pi$
$674$	−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	−0.877447	−	0.479673i	$-0.840755\pi$
$677$	−7006.79	+	7006.79i	−0.397774	+	0.397774i	0.479673	+	0.877447i	$0.340755\pi$
$678$	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	−0.442652	−	0.896693i	$-0.645962\pi$
$683$	8104.50	−	8104.50i	0.454041	−	0.454041i	0.896693	+	0.442652i	$0.145962\pi$
$684$	−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	$-0.834998\pi$
$691$		−	17999.5i		−	0.990928i	0.868628	−	0.495464i	$-0.165002\pi$
$692$	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	$0.0559026\pi$
$709$			6597.00i			0.349443i	−0.984618	+	0.174722i	$0.944097\pi$
$710$	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	0.737417	−	0.675437i	$-0.236045\pi$
$727$	1214.94	+	1214.94i	0.0619801	+	0.0619801i	−0.675437	+	0.737417i	$0.736045\pi$
$728$	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	0.744798	−	0.667290i	$-0.232546\pi$
$733$	1538.15	+	1538.15i	0.0775074	+	0.0775074i	−0.667290	+	0.744798i	$0.732546\pi$
$734$	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	−0.975311	−	0.220834i	$-0.929122\pi$
$743$	−15280.2	+	15280.2i	−0.754477	+	0.754477i	0.220834	+	0.975311i	$0.429122\pi$
$744$	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	$0.412258\pi$
$751$			39607.5i			1.92450i	−0.272171	+	0.962249i	$0.587742\pi$
$752$	−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	−0.568049	−	0.822995i	$-0.692301\pi$
$757$	5309.98	−	5309.98i	0.254946	−	0.254946i	0.822995	+	0.568049i	$0.192301\pi$
$758$	−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	$0.0700433\pi$
$769$			9309.49i			0.436552i	−0.975887	+	0.218276i	$0.929957\pi$
$770$	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	0.313567	−	0.949566i	$-0.398476\pi$
$773$	−13668.6	−	13668.6i	−0.635999	−	0.635999i	−0.949566	+	0.313567i	$0.898476\pi$
$774$	−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	0.661477	−	0.749966i	$-0.269930\pi$
$787$	−1953.67	−	1953.67i	−0.0884888	−	0.0884888i	−0.749966	+	0.661477i	$0.769930\pi$
$788$	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	−0.987245	−	0.159208i	$-0.949106\pi$
$797$	−18631.1	+	18631.1i	−0.828037	+	0.828037i	0.159208	+	0.987245i	$0.449106\pi$
$798$	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	$0.124321\pi$
$809$			17520.6i			0.761425i	−0.924693	+	0.380712i	$0.875679\pi$
$810$	2470.40	+	676.836i	0.107162	+	0.0293600i
$811$		−	39421.8i		−	1.70689i	−0.521183	−	0.853445i	$-0.674509\pi$
$811$		−	39421.8i		−	1.70689i	0.521183	−	0.853445i	$-0.325491\pi$
$812$	−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	−0.412351	−	0.911025i	$-0.635292\pi$
$823$	11773.8	−	11773.8i	0.498674	−	0.498674i	0.911025	+	0.412351i	$0.135292\pi$
$824$	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	0.945155	−	0.326622i	$-0.105910\pi$
$827$	14710.3	+	14710.3i	0.618534	+	0.618534i	−0.326622	+	0.945155i	$0.605910\pi$
$828$	10796.7	−	677.453i	0.453156	−	0.0284337i
$829$			514.236i			0.0215442i	0.999942	+	0.0107721i	$0.00342894\pi$
$829$			514.236i			0.0215442i	−0.999942	+	0.0107721i	$0.996571\pi$
$830$	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	0.999838	+	0.0180228i	$0.00573714\pi$
$853$	25357.8	+	25357.8i	1.01786	+	1.01786i	0.0180228	+	0.999838i	$0.494263\pi$
$854$	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	−0.801765	−	0.597639i	$-0.796105\pi$
$857$	−5121.17	+	5121.17i	−0.204126	+	0.204126i	0.597639	+	0.801765i	$0.296105\pi$
$858$	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	−0.540773	−	0.841169i	$-0.681868\pi$
$863$	7615.70	−	7615.70i	0.300396	−	0.300396i	0.841169	+	0.540773i	$0.181868\pi$
$864$	−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	0.410749	−	0.911749i	$-0.365267\pi$
$877$	34347.4	−	34347.4i	1.32250	−	1.32250i	0.911749	−	0.410749i	$-0.134733\pi$
$878$	−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	−0.272148	−	0.962255i	$-0.587734\pi$
$883$	18107.5	−	18107.5i	0.690108	−	0.690108i	0.962255	+	0.272148i	$0.0877340\pi$
$884$	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	0.532442	−	0.846466i	$-0.321274\pi$
$887$	−8295.62	−	8295.62i	−0.314024	−	0.314024i	−0.846466	+	0.532442i	$0.821274\pi$
$888$	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	0.900819	+	0.434195i	$0.142967\pi$
$907$	36466.7	+	36466.7i	1.33501	+	1.33501i	0.434195	+	0.900819i	$0.357033\pi$
$908$	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	$-0.770132\pi$
$911$		−	36350.5i		−	1.32200i	0.750385	−	0.661002i	$-0.229868\pi$
$912$	−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	$0.0685076\pi$
$929$			12094.4i			0.427131i	−0.976929	+	0.213565i	$0.931492\pi$
$930$	−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	−0.459356	−	0.888252i	$-0.651920\pi$
$937$	12301.6	−	12301.6i	0.428896	−	0.428896i	0.888252	+	0.459356i	$0.151920\pi$
$938$	−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	0.878960	−	0.476896i	$-0.158238\pi$
$947$	11717.1	+	11717.1i	0.402064	+	0.402064i	−0.476896	+	0.878960i	$0.658238\pi$
$948$	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	0.893093	−	0.449872i	$-0.148530\pi$
$953$	13039.5	+	13039.5i	0.443222	+	0.443222i	−0.449872	+	0.893093i	$0.648530\pi$
$954$	−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	0.633458	−	0.773777i	$-0.281635\pi$
$967$	−4219.47	−	4219.47i	−0.140319	−	0.140319i	−0.773777	+	0.633458i	$0.781635\pi$
$968$	−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	$-0.814255\pi$
$971$		−	33342.1i		−	1.10195i	0.834520	−	0.550977i	$-0.185745\pi$
$972$	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	−0.633167	−	0.774015i	$-0.718246\pi$
$977$	4301.21	−	4301.21i	0.140847	−	0.140847i	0.774015	+	0.633167i	$0.218246\pi$
$978$	−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	−0.558301	−	0.829639i	$-0.688546\pi$
$983$	8362.60	−	8362.60i	0.271338	−	0.271338i	0.829639	+	0.558301i	$0.188546\pi$
$984$	−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	$0.195326\pi$
$991$			35928.9i			1.15168i	−0.817561	+	0.575842i	$0.804674\pi$
$992$	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	−0.999958	−	0.00921702i	$-0.997066\pi$
$997$	−31189.1	+	31189.1i	−0.990740	+	0.990740i	0.00921702	+	0.999958i	$0.497066\pi$
$998$	−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.43.4	yes	8
3.2	odd	2		180.4.k.d.163.1		8
4.3	odd	2	inner	60.4.j.a.43.3	yes	8
5.2	odd	4	inner	60.4.j.a.7.3	✓	8
12.11	even	2		180.4.k.d.163.2		8
15.2	even	4		180.4.k.d.127.2		8
20.7	even	4	inner	60.4.j.a.7.4	yes	8
60.47	odd	4		180.4.k.d.127.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
60.4.j.a.7.3	✓	8	5.2	odd	4	inner
60.4.j.a.7.4	yes	8	20.7	even	4	inner
60.4.j.a.43.3	yes	8	4.3	odd	2	inner
60.4.j.a.43.4	yes	8	1.1	even	1	trivial
180.4.k.d.127.1		8	60.47	odd	4
180.4.k.d.127.2		8	15.2	even	4
180.4.k.d.163.1		8	3.2	odd	2
180.4.k.d.163.2		8	12.11	even	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:	\( k \)	\(=\)	\( 4 \)
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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more