LMFDB - Embedded newform 60.4.j.a.43.3

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			43.3
Root			$0.581861 - 1.28897i$ of defining polynomial
Character	$\chi$	$=$	60.43
Dual form			60.4.j.a.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.16372 - 2.57794i) q^{2} +(-2.12132 + 2.12132i) q^{3} +(-5.29150 - 6.00000i) q^{4} +(-8.61249 - 7.12917i) q^{5} +(3.00000 + 7.93725i) q^{6} +(-8.98612 - 8.98612i) q^{7} +(-21.6255 + 6.65882i) q^{8} -9.00000i q^{9} +O(q^{10})$	\(q+(1.16372 - 2.57794i) 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} +(-21.6255 + 6.65882i) q^{8} -9.00000i q^{9} +(-28.4011 + 13.9061i) q^{10} -38.8201i q^{11} +(23.9529 + 1.50295i) 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} +(-23.2014 - 10.4735i) q^{18} -15.7801 q^{19} +(2.79796 + 89.3989i) q^{20} +38.1249 q^{21} +(-100.076 - 45.1758i) 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} +(-6.36664 + 101.467i) q^{28} -208.958i q^{29} +(30.7486 - 89.7470i) q^{30} -243.881i q^{31} +(154.384 + 94.5175i) 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} +(-18.3637 + 40.6801i) q^{38} -122.082 q^{39} +(233.721 + 96.8225i) q^{40} +25.7503 q^{41} +(44.3667 - 98.2834i) 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} +(-117.729 - 151.670i) q^{48} -181.499i q^{49} +(343.743 + 82.7104i) q^{50} +47.9067i q^{51} +(20.3870 - 324.913i) 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} +(-538.680 - 243.169i) q^{58} -646.366 q^{59} +(-195.579 - 183.708i) q^{60} +527.249 q^{61} +(-628.710 - 283.810i) 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} +(-127.500 - 8.00015i) q^{68} +450.749i q^{69} +(380.177 + 130.254i) q^{70} -611.293i q^{71} +(59.9294 + 194.629i) 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} +(-142.070 + 314.720i) q^{78} +551.355 q^{79} +(521.588 - 489.843i) q^{80} -81.0000 q^{81} +(29.9662 - 66.3826i) 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} +(258.496 + 839.502i) q^{88} +740.166i q^{89} +(125.155 + 255.610i) q^{90} -517.151i q^{91} +(-1199.64 - 75.2726i) 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} +(-467.894 - 211.215i) 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 $

$2$	1.16372	−	2.57794i	0.411438	−	0.911438i
$2$	1.16372	−	2.57794i	0.411438	−	0.911438i
$3$	−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	$-0.361474\pi$
$7$	−8.98612	−	8.98612i	−0.485205	−	0.485205i	−0.906789	+	0.421584i	$0.861474\pi$
$8$	−21.6255	+	6.65882i	−0.955719	+	0.294281i
$9$		−	9.00000i		−	0.333333i
$10$	−28.4011	+	13.9061i	−0.898121	+	0.439748i
$11$		−	38.8201i		−	1.06406i	−0.846724	−	0.532032i	$-0.821429\pi$
$11$		−	38.8201i		−	1.06406i	0.846724	−	0.532032i	$-0.178571\pi$
$12$	23.9529	+	1.50295i	0.576217	+	0.0361554i
$13$	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	$0.213662\pi$
$18$	−23.2014	−	10.4735i	−0.303813	−	0.137146i
$19$	−15.7801			−0.190537			−0.0952686	−	0.995452i	$-0.530371\pi$
$19$	−15.7801			−0.190537			−0.0952686	+	0.995452i	$0.530371\pi$
$20$	2.79796	+	89.3989i	0.0312822	+	0.999511i
$21$	38.1249			0.396168
$22$	−100.076	−	45.1758i	−0.969827	−	0.437796i
$23$	106.243	−	106.243i	0.963179	−	0.963179i	−0.0361669	−	0.999346i	$-0.511515\pi$
$23$	106.243	−	106.243i	0.963179	−	0.963179i	0.999346	+	0.0361669i	$0.0115148\pi$
$24$	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
$28$	−6.36664	+	101.467i	−0.0429708	+	0.684836i
$29$		−	208.958i		−	1.33802i	−0.743254	−	0.669009i	$-0.766719\pi$
$29$		−	208.958i		−	1.33802i	0.743254	−	0.669009i	$-0.233281\pi$
$30$	30.7486	−	89.7470i	0.187130	−	0.546183i
$31$		−	243.881i		−	1.41298i	−0.707724	−	0.706489i	$-0.750278\pi$
$31$		−	243.881i		−	1.41298i	0.707724	−	0.706489i	$-0.249722\pi$
$32$	154.384	+	94.5175i	0.852859	+	0.522141i
$33$	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	$0.470769\pi$
$38$	−18.3637	+	40.6801i	−0.0783942	+	0.173663i
$39$	−122.082			−0.501251
$40$	233.721	+	96.8225i	0.923862	+	0.382725i
$41$	25.7503			0.0980858			0.0490429	−	0.998797i	$-0.484383\pi$
$41$	25.7503			0.0980858			0.0490429	+	0.998797i	$0.484383\pi$
$42$	44.3667	−	98.2834i	0.162998	−	0.361082i
$43$	−253.557	+	253.557i	−0.899234	+	0.899234i	−0.995368	−	0.0961347i	$-0.969352\pi$
$43$	−253.557	+	253.557i	−0.899234	+	0.899234i	0.0961347	+	0.995368i	$0.469352\pi$
$44$	−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	$0.0480276\pi$
$47$	366.988	+	366.988i	1.13895	+	1.13895i	0.150311	+	0.988639i	$0.451972\pi$
$48$	−117.729	−	151.670i	−0.354015	−	0.456077i
$49$		−	181.499i		−	0.529153i
$50$	343.743	+	82.7104i	0.972251	+	0.233940i
$51$			47.9067i			0.131535i
$52$	20.3870	−	324.913i	0.0543687	−	0.866488i
$53$	−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
$58$	−538.680	−	243.169i	−1.21952	−	0.550511i
$59$	−646.366			−1.42626			−0.713132	−	0.701029i	$-0.752724\pi$
$59$	−646.366			−1.42626			−0.713132	+	0.701029i	$0.752724\pi$
$60$	−195.579	−	183.708i	−0.420819	−	0.395278i
$61$	527.249			1.10668			0.553338	−	0.832957i	$-0.313354\pi$
$61$	527.249			1.10668			0.553338	+	0.832957i	$0.313354\pi$
$62$	−628.710	−	283.810i	−1.28784	−	0.581353i
$63$	−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	$-0.0811521\pi$
$67$	392.384	+	392.384i	0.715483	+	0.715483i	−0.252194	+	0.967677i	$0.581152\pi$
$68$	−127.500	−	8.00015i	−0.227378	−	0.0142671i
$69$			450.749i			0.786432i
$70$	380.177	+	130.254i	0.649140	+	0.222405i
$71$		−	611.293i		−	1.02179i	−0.859643	−	0.510896i	$-0.829314\pi$
$71$		−	611.293i		−	1.02179i	0.859643	−	0.510896i	$-0.170686\pi$
$72$	59.9294	+	194.629i	0.0980937	+	0.318573i
$73$	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
$78$	−142.070	+	314.720i	−0.206234	+	0.456859i
$79$	551.355			0.785218			0.392609	−	0.919705i	$-0.371573\pi$
$79$	551.355			0.785218			0.392609	+	0.919705i	$0.371573\pi$
$80$	521.588	−	489.843i	0.728942	−	0.684576i
$81$	−81.0000			−0.111111
$82$	29.9662	−	66.3826i	0.0403562	−	0.0893991i
$83$	494.620	−	494.620i	0.654116	−	0.654116i	−0.299866	−	0.953981i	$-0.596942\pi$
$83$	494.620	−	494.620i	0.654116	−	0.654116i	0.953981	+	0.299866i	$0.0969419\pi$
$84$	−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
$88$	258.496	+	839.502i	0.313134	+	1.01695i
$89$			740.166i			0.881544i	0.897619	+	0.440772i	$0.145295\pi$
$89$			740.166i			0.881544i	−0.897619	+	0.440772i	$0.854705\pi$
$90$	125.155	+	255.610i	0.146583	+	0.299374i
$91$		−	517.151i		−	0.595739i
$92$	−1199.64	−	75.2726i	−1.35947	−	0.0853012i
$93$	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	$0.230008\pi$
$98$	−467.894	−	211.215i	−0.482290	−	0.217714i
$99$	−349.381			−0.354688
$100$	613.243	−	789.894i	0.613243	−	0.789894i
$101$	573.126			0.564635			0.282318	−	0.959321i	$-0.408897\pi$
$101$	573.126			0.564635			0.282318	+	0.959321i	$0.408897\pi$
$102$	123.500	+	55.7501i	0.119886	+	0.0541184i
$103$	1298.81	−	1298.81i	1.24248	−	1.24248i	0.283508	−	0.958970i	$-0.408502\pi$
$103$	1298.81	−	1298.81i	1.24248	−	1.24248i	0.958970	−	0.283508i	$-0.0914983\pi$
$104$	−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	$-0.324887\pi$
$107$	−364.866	−	364.866i	−0.329653	−	0.329653i	−0.852455	+	0.522801i	$0.824887\pi$
$108$	13.5265	−	215.576i	0.0120518	−	0.192072i
$109$		−	1210.25i		−	1.06349i	−0.846903	−	0.531747i	$-0.821536\pi$
$109$		−	1210.25i		−	1.06349i	0.846903	−	0.531747i	$-0.178464\pi$
$110$	539.834	+	1102.53i	0.467920	+	0.955658i
$111$		−	863.270i		−	0.738180i
$112$	642.490	−	498.712i	0.542050	−	0.420748i
$113$	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
$118$	−752.190	+	1666.29i	−0.586819	+	1.29995i
$119$	−202.937			−0.156330
$120$	−701.188	+	290.405i	−0.533412	+	0.220919i
$121$	−175.999			−0.132231
$122$	613.571	−	1359.21i	0.455329	−	1.00867i
$123$	−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	$-0.219954\pi$
$127$	190.770	+	190.770i	0.133292	+	0.133292i	−0.637313	+	0.770605i	$0.719954\pi$
$128$	−249.818	−	1426.44i	−0.172508	−	0.985008i
$129$		−	1075.75i		−	0.734221i
$130$	−1217.39	−	417.095i	−0.821324	−	0.281397i
$131$			1711.34i			1.14138i	0.821166	+	0.570689i	$0.193324\pi$
$131$			1711.34i			1.14138i	−0.821166	+	0.570689i	$0.806676\pi$
$132$	58.3446	−	929.853i	0.0384716	−	0.613131i
$133$	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	$0.232791\pi$
$138$	1162.00	+	524.547i	0.716784	+	0.323568i
$139$	−799.394			−0.487797			−0.243898	−	0.969801i	$-0.578426\pi$
$139$	−799.394			−0.487797			−0.243898	+	0.969801i	$0.578426\pi$
$140$	778.206	−	828.492i	0.469789	−	0.500145i
$141$	−1557.00			−0.929949
$142$	−1575.87	−	711.376i	−0.931299	−	0.420404i
$143$	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
$148$	2297.54	+	144.161i	1.27606	+	0.0800675i
$149$			2446.79i			1.34529i	0.739964	+	0.672647i	$0.234843\pi$
$149$			2446.79i			1.34529i	−0.739964	+	0.672647i	$0.765157\pi$
$150$	−904.644	+	553.733i	−0.492426	+	0.301414i
$151$			905.413i			0.487957i	0.969781	+	0.243978i	$0.0784526\pi$
$151$			905.413i			0.487957i	−0.969781	+	0.243978i	$0.921547\pi$
$152$	341.252	−	105.077i	0.182100	−	0.0560715i
$153$	−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	$0.253458\pi$
$158$	641.623	−	1421.36i	0.323068	−	0.715677i
$159$	2128.60			1.06169
$160$	−655.799	−	1914.66i	−0.324034	−	0.946045i
$161$	−1909.42			−0.934678
$162$	−94.2615	+	208.813i	−0.0457153	+	0.101271i
$163$	−955.533	+	955.533i	−0.459160	+	0.459160i	−0.898380	−	0.439219i	$-0.855255\pi$
$163$	−955.533	+	955.533i	−0.459160	+	0.459160i	0.439219	+	0.898380i	$0.355255\pi$
$164$	−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	$-0.231904\pi$
$167$	173.415	+	173.415i	0.0803550	+	0.0803550i	−0.665787	+	0.746142i	$0.731904\pi$
$168$	−824.467	+	253.867i	−0.378625	+	0.116585i
$169$		−	540.996i		−	0.246243i
$170$	−163.674	+	477.720i	−0.0738423	+	0.215526i
$171$			142.021i			0.0635124i
$172$	2863.04	+	179.644i	1.26921	+	0.0796381i
$173$	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
$178$	1908.10	+	861.347i	0.803473	+	0.362701i
$179$	−826.182			−0.344982			−0.172491	−	0.985011i	$-0.555182\pi$
$179$	−826.182			−0.344982			−0.172491	+	0.985011i	$0.555182\pi$
$180$	804.591	−	25.1817i	0.333170	−	0.0104274i
$181$	1414.74			0.580979			0.290489	−	0.956878i	$-0.406182\pi$
$181$	1414.74			0.580979			0.290489	+	0.956878i	$0.406182\pi$
$182$	−1333.18	−	601.820i	−0.542979	−	0.245109i
$183$	−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
$188$	260.010	−	4143.84i	0.100868	−	1.60756i
$189$		−	343.124i		−	0.132056i
$190$	448.173	−	219.439i	0.171126	−	0.0837884i
$191$		−	932.465i		−	0.353250i	−0.984278	−	0.176625i	$-0.943482\pi$
$191$		−	932.465i		−	0.353250i	0.984278	−	0.176625i	$-0.0565180\pi$
$192$	−287.058	+	1508.94i	−0.107899	+	0.567178i
$193$	−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	$0.407143\pi$
$198$	−406.582	+	900.681i	−0.145932	+	0.323276i
$199$	1633.75			0.581978			0.290989	−	0.956726i	$-0.406016\pi$
$199$	1633.75			0.581978			0.290989	+	0.956726i	$0.406016\pi$
$200$	−1322.65	−	2500.12i	−0.467628	−	0.883925i
$201$	−1664.74			−0.584189
$202$	666.959	−	1477.48i	0.232312	−	0.514630i
$203$	−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
$208$	−2057.36	+	1596.96i	−0.685827	+	0.532351i
$209$			612.586i			0.202744i
$210$	−1082.79	+	530.167i	−0.355807	+	0.174214i
$211$			4234.33i			1.38153i	0.723078	+	0.690766i	$0.242726\pi$
$211$			4234.33i			1.38153i	−0.723078	+	0.690766i	$0.757274\pi$
$212$	−355.464	+	5665.13i	−0.115158	+	1.83529i
$213$	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
$218$	−3119.95	−	1408.39i	−0.969309	−	0.437562i
$219$	−614.333			−0.189556
$220$	3470.47	−	108.617i	1.06354	−	0.0332862i
$221$	649.839			0.197796
$222$	−2225.45	−	1004.61i	−0.672805	−	0.303715i
$223$	−487.697	+	487.697i	−0.146451	+	0.146451i	−0.776531	−	0.630080i	$-0.783022\pi$
$223$	−487.697	+	487.697i	−0.146451	+	0.146451i	0.630080	+	0.776531i	$0.283022\pi$
$224$	−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	$-0.398701\pi$
$227$	−2178.24	−	2178.24i	−0.636892	−	0.636892i	−0.949788	+	0.312895i	$0.898701\pi$
$228$	−377.980	−	23.7167i	−0.109791	−	0.00688894i
$229$		−	3797.50i		−	1.09583i	−0.836533	−	0.547916i	$-0.815421\pi$
$229$		−	3797.50i		−	1.09583i	0.836533	−	0.547916i	$-0.184579\pi$
$230$	−1539.99	+	4494.82i	−0.441495	+	1.28861i
$231$		−	1480.01i		−	0.421548i
$232$	1391.41	+	4518.81i	0.393753	+	1.27877i
$233$	−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
$238$	−236.163	+	523.159i	−0.0643199	+	0.142485i
$239$	−1188.51			−0.321665			−0.160833	−	0.986982i	$-0.551418\pi$
$239$	−1188.51			−0.321665			−0.160833	+	0.986982i	$0.551418\pi$
$240$	−67.3428	+	2145.57i	−0.0181123	+	0.577066i
$241$	6989.98			1.86832			0.934159	−	0.356858i	$-0.116152\pi$
$241$	6989.98			1.86832			0.934159	+	0.356858i	$0.116152\pi$
$242$	−204.814	+	453.714i	−0.0544047	+	0.120520i
$243$	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
$248$	1623.96	+	5274.04i	0.415813	+	1.35041i
$249$			2098.49i			0.534083i
$250$	−2370.82	−	3162.94i	−0.599776	−	0.800168i
$251$		−	3950.18i		−	0.993359i	−0.867934	−	0.496679i	$-0.834552\pi$
$251$		−	3950.18i		−	0.993359i	0.867934	−	0.496679i	$-0.165448\pi$
$252$	913.201	+	57.2998i	0.228279	+	0.0143236i
$253$	−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	$-0.00358721\pi$
$258$	−2773.21	−	1251.87i	−0.669197	−	0.302086i
$259$	3656.89			0.877330
$260$	−2491.95	+	2652.97i	−0.594400	+	0.632808i
$261$	−1880.62			−0.446006
$262$	4411.72	+	1991.52i	1.04029	+	0.469606i
$263$	−2028.86	+	2028.86i	−0.475684	+	0.475684i	−0.903748	−	0.428064i	$-0.859196\pi$
$263$	−2028.86	+	2028.86i	−0.475684	+	0.475684i	0.428064	+	0.903748i	$0.359196\pi$
$264$	−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
$268$	278.003	−	4430.61i	0.0633647	−	1.00986i
$269$			391.791i			0.0888027i	0.999014	+	0.0444014i	$0.0141380\pi$
$269$			391.791i			0.0888027i	−0.999014	+	0.0444014i	$0.985862\pi$
$270$	−807.723	−	276.737i	−0.182061	−	0.0623766i
$271$		−	2030.42i		−	0.455127i	−0.973763	−	0.227563i	$-0.926924\pi$
$271$		−	2030.42i		−	0.455127i	0.973763	−	0.227563i	$-0.0730759\pi$
$272$	626.668	+	807.335i	0.139696	+	0.179970i
$273$	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	$0.00152108\pi$
$278$	−930.273	+	2060.79i	−0.200698	+	0.444596i
$279$	−2194.93			−0.470993
$280$	−1230.18	−	2970.30i	−0.262563	−	0.633962i
$281$	−2401.75			−0.509880			−0.254940	−	0.966957i	$-0.582056\pi$
$281$	−2401.75			−0.509880			−0.254940	+	0.966957i	$0.582056\pi$
$282$	−1811.91	+	4013.84i	−0.382616	+	0.847590i
$283$	1874.48	−	1874.48i	0.393732	−	0.393732i	−0.482283	−	0.876015i	$-0.660192\pi$
$283$	1874.48	−	1874.48i	0.393732	−	0.393732i	0.876015	+	0.482283i	$0.160192\pi$
$284$	−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
$288$	850.658	−	1389.46i	0.174047	−	0.284286i
$289$			4657.99i			0.948096i
$290$	2905.78	+	5934.63i	0.588391	+	1.20170i
$291$			359.775i			0.0724755i
$292$	102.590	−	1635.01i	0.0205604	−	0.327677i
$293$	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
$298$	6307.66	+	2847.38i	1.22615	+	0.553504i
$299$	6114.27			1.18260
$300$	374.734	+	2976.50i	0.0721176	+	0.572828i
$301$	4556.98			0.872625
$302$	2334.10	+	1053.65i	0.444742	+	0.200764i
$303$	−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	$-0.334856\pi$
$307$	−2004.00	−	2004.00i	−0.372555	−	0.372555i	−0.868407	+	0.495852i	$0.834856\pi$
$308$	3938.95	+	247.153i	0.728709	+	0.0457236i
$309$			5510.37i			1.01448i
$310$	3391.42	+	6926.49i	0.621355	+	1.26903i
$311$			3829.04i			0.698151i	0.937095	+	0.349075i	$0.113504\pi$
$311$			3829.04i			0.698151i	−0.937095	+	0.349075i	$0.886496\pi$
$312$	2640.08	−	812.923i	0.479055	−	0.147509i
$313$	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	$0.220365\pi$
$318$	2477.10	−	5487.39i	0.436820	−	0.967666i
$319$	−8111.77			−1.42374
$320$	−5699.04	−	537.526i	−0.995581	−	0.0939020i
$321$	1547.99			0.269161
$322$	−2222.03	+	4922.35i	−0.384562	+	0.851901i
$323$	−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
$328$	−556.861	+	171.466i	−0.0937425	+	0.0288648i
$329$		−	6595.59i		−	1.10525i
$330$	−3483.99	−	1193.66i	−0.581173	−	0.199118i
$331$			7332.79i			1.21766i	0.793299	+	0.608832i	$0.208362\pi$
$331$			7332.79i			1.21766i	−0.793299	+	0.608832i	$0.791638\pi$
$332$	−5585.00	−	350.437i	−0.923244	−	0.0579299i
$333$	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	$0.477099\pi$
$338$	−1394.65	−	629.568i	−0.224435	−	0.101314i
$339$	−2394.79			−0.383678
$340$	1041.06	+	977.873i	0.166057	+	0.155978i
$341$	−9467.48			−1.50350
$342$	366.121	+	165.273i	0.0578876	+	0.0261314i
$343$	−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	$-0.318232\pi$
$347$	−1944.55	−	1944.55i	−0.300832	−	0.300832i	−0.841339	+	0.540507i	$0.818232\pi$
$348$	314.053	−	5005.15i	0.0483765	−	0.770989i
$349$		−	9581.22i		−	1.46954i	−0.678314	−	0.734772i	$-0.737289\pi$
$349$		−	9581.22i		−	1.46954i	0.678314	−	0.734772i	$-0.262711\pi$
$350$	−2345.67	−	3832.16i	−0.358232	−	0.585250i
$351$			1098.74i			0.167084i
$352$	3669.18	−	5993.20i	0.555591	−	0.907496i
$353$	−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
$358$	−961.446	+	2129.84i	−0.141939	+	0.314430i
$359$	−2196.06			−0.322852			−0.161426	−	0.986885i	$-0.551609\pi$
$359$	−2196.06			−0.322852			−0.161426	+	0.986885i	$0.551609\pi$
$360$	871.403	−	2103.49i	0.127575	−	0.307954i
$361$	−6609.99			−0.963696
$362$	1646.37	−	3647.12i	0.239037	−	0.529526i
$363$	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	$-0.420062\pi$
$367$	−5063.03	−	5063.03i	−0.720130	−	0.720130i	−0.968632	+	0.248501i	$0.920062\pi$
$368$	5896.25	+	7596.14i	0.835227	+	1.07602i
$369$		−	231.753i		−	0.0326953i
$370$	2949.37	−	8608.43i	0.414407	−	1.20954i
$371$			9016.95i			1.26182i
$372$	366.541	−	5841.66i	0.0510867	−	0.814182i
$373$	−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
$378$	−884.551	−	399.301i	−0.120361	−	0.0543328i
$379$	7182.07			0.973398			0.486699	−	0.873570i	$-0.338201\pi$
$379$	7182.07			0.973398			0.486699	+	0.873570i	$0.338201\pi$
$380$	−44.1522	−	1410.73i	−0.00596042	−	0.190444i
$381$	−809.367			−0.108832
$382$	−2403.83	−	1085.13i	−0.321966	−	0.145340i
$383$	−6705.49	+	6705.49i	−0.894608	+	0.894608i	−0.994953	−	0.100345i	$-0.968005\pi$
$383$	−6705.49	+	6705.49i	−0.894608	+	0.894608i	0.100345	+	0.994953i	$0.468005\pi$
$384$	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
$388$	−957.517	−	60.0804i	−0.125285	−	0.00786114i
$389$		−	1204.96i		−	0.157053i	−0.996912	−	0.0785267i	$-0.974978\pi$
$389$		−	1204.96i		−	0.157053i	0.996912	−	0.0785267i	$-0.0250216\pi$
$390$	3467.26	−	1697.68i	0.450184	−	0.220424i
$391$		−	2399.32i		−	0.310330i
$392$	1208.57	+	3925.01i	0.155720	+	0.505721i
$393$	−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	$0.491885\pi$
$398$	1901.23	−	4211.71i	0.239448	−	0.530437i
$399$	−601.615			−0.0754848
$400$	−7984.34	+	500.270i	−0.998043	+	0.0625338i
$401$	−2779.99			−0.346200			−0.173100	−	0.984904i	$-0.555378\pi$
$401$	−2779.99			−0.346200			−0.173100	+	0.984904i	$0.555378\pi$
$402$	−1937.30	+	4291.60i	−0.240358	+	0.532452i
$403$	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
$408$	−319.002	−	1036.00i	−0.0387082	−	0.125710i
$409$			10322.0i			1.24790i	0.781465	+	0.623949i	$0.214473\pi$
$409$			10322.0i			1.24790i	−0.781465	+	0.623949i	$0.785527\pi$
$410$	−731.336	+	358.085i	−0.0880929	+	0.0431331i
$411$			519.895i			0.0623954i
$412$	−14665.5	−	920.201i	−1.75368	−	0.110037i
$413$	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
$418$	1579.21	+	712.879i	0.184788	+	0.0834164i
$419$	10705.0			1.24815			0.624075	−	0.781365i	$-0.285476\pi$
$419$	10705.0			1.24815			0.624075	+	0.781365i	$0.285476\pi$
$420$	106.672	+	3408.32i	0.0123930	+	0.395974i
$421$	14290.0			1.65428			0.827140	−	0.561996i	$-0.189966\pi$
$421$	14290.0			1.65428			0.827140	+	0.561996i	$0.189966\pi$
$422$	10915.8	+	4927.58i	1.25918	+	0.568414i
$423$	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
$428$	−258.506	+	4119.88i	−0.0291948	+	0.465285i
$429$			4739.24i			0.533363i
$430$	3675.31	−	10727.3i	0.412184	−	1.20306i
$431$		−	15321.0i		−	1.71227i	−0.516756	−	0.856133i	$-0.672860\pi$
$431$		−	15321.0i		−	1.71227i	0.516756	−	0.856133i	$-0.327140\pi$
$432$	−1365.03	+	1059.56i	−0.152026	+	0.118005i
$433$	−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
$438$	−714.913	+	1583.71i	−0.0779906	+	0.172769i
$439$	5728.97			0.622845			0.311423	−	0.950272i	$-0.399195\pi$
$439$	5728.97			0.622845			0.311423	+	0.950272i	$0.399195\pi$
$440$	3758.66	−	9073.06i	0.407243	−	0.983048i
$441$	−1633.49			−0.176384
$442$	756.232	−	1675.24i	0.0813807	−	0.180279i
$443$	11245.1	−	11245.1i	1.20603	−	1.20603i	0.233729	−	0.972302i	$-0.424907\pi$
$443$	11245.1	−	11245.1i	1.20603	−	1.20603i	0.972302	−	0.233729i	$-0.0750930\pi$
$444$	−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
$448$	−6392.01	−	1216.00i	−0.674094	−	0.128238i
$449$			4654.40i			0.489209i	0.969623	+	0.244604i	$0.0786581\pi$
$449$			4654.40i			0.489209i	−0.969623	+	0.244604i	$0.921342\pi$
$450$	744.394	−	3093.68i	0.0779801	−	0.324084i
$451$		−	999.628i		−	0.104369i
$452$	399.916	−	6373.56i	0.0416161	−	0.663246i
$453$	−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	$0.252424\pi$
$458$	−9789.70	−	4419.23i	−0.998783	−	0.450867i
$459$	431.160			0.0438449
$460$	9795.24	+	9200.71i	0.992838	+	0.932577i
$461$	5834.36			0.589443			0.294721	−	0.955583i	$-0.404773\pi$
$461$	5834.36			0.589443			0.294721	+	0.955583i	$0.404773\pi$
$462$	−3815.37	−	1722.32i	−0.384215	−	0.173441i
$463$	3513.45	−	3513.45i	0.352665	−	0.352665i	−0.508436	−	0.861100i	$-0.669776\pi$
$463$	3513.45	−	3513.45i	0.352665	−	0.352665i	0.861100	+	0.508436i	$0.169776\pi$
$464$	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	$-0.0362582\pi$
$467$	8879.48	+	8879.48i	0.879857	+	0.879857i	−0.113662	+	0.993519i	$0.536258\pi$
$468$	−2924.22	−	183.483i	−0.288829	−	0.0181229i
$469$		−	7052.02i		−	0.694311i
$470$	−15526.2	−	5319.49i	−1.52377	−	0.522064i
$471$		−	128.229i		−	0.0125445i
$472$	13977.9	−	4304.03i	1.36311	−	0.419723i
$473$	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
$478$	−1383.09	+	3063.89i	−0.132345	+	0.293178i
$479$	−14862.9			−1.41775			−0.708875	−	0.705335i	$-0.750797\pi$
$479$	−14862.9			−1.41775			−0.708875	+	0.705335i	$0.750797\pi$
$480$	5452.77	+	2670.45i	0.518508	+	0.253935i
$481$	−11710.0			−1.11004
$482$	8134.40	−	18019.7i	0.768696	−	1.70286i
$483$	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	$-0.141889\pi$
$487$	5063.44	+	5063.44i	0.471142	+	0.471142i	−0.431142	+	0.902284i	$0.641889\pi$
$488$	−11402.0	+	3510.85i	−1.05767	+	0.325674i
$489$		−	4053.98i		−	0.374903i
$490$	2523.94	+	5154.78i	0.232694	+	0.475243i
$491$		−	11014.1i		−	1.01234i	−0.862434	−	0.506169i	$-0.831061\pi$
$491$		−	11014.1i		−	1.01234i	0.862434	−	0.506169i	$-0.168939\pi$
$492$	616.794	+	38.7014i	0.0565187	+	0.00354633i
$493$	−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
$498$	5409.78	+	2442.06i	0.486784	+	0.219742i
$499$	3339.95			0.299633			0.149816	−	0.988714i	$-0.452132\pi$
$499$	3339.95			0.299633			0.149816	+	0.988714i	$0.452132\pi$
$500$	−10912.8	+	2431.04i	−0.976074	+	0.217439i
$501$	−735.739			−0.0656096
$502$	−10183.3	−	4596.91i	−0.905385	−	0.408705i
$503$	−8101.33	+	8101.33i	−0.718132	+	0.718132i	−0.968222	−	0.250091i	$-0.919540\pi$
$503$	−8101.33	+	8101.33i	−0.718132	+	0.718132i	0.250091	+	0.968222i	$0.419540\pi$
$504$	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
$508$	135.160	−	2154.08i	0.0118046	−	0.188133i
$509$			14083.0i			1.22637i	0.789941	+	0.613183i	$0.210111\pi$
$509$			14083.0i			1.22637i	−0.789941	+	0.613183i	$0.789889\pi$
$510$	−666.193	−	1360.60i	−0.0578422	−	0.118134i
$511$		−	2602.38i		−	0.225288i
$512$	−7236.75	+	9046.94i	−0.624653	+	0.780903i
$513$	−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
$518$	4255.61	−	9427.24i	0.360967	−	0.799631i
$519$	−5468.78			−0.462529
$520$	3939.25	+	9511.39i	0.332207	+	0.802120i
$521$	9152.23			0.769610			0.384805	−	0.922998i	$-0.374269\pi$
$521$	9152.23			0.769610			0.384805	+	0.922998i	$0.374269\pi$
$522$	−2188.52	+	4848.12i	−0.183504	+	0.406507i
$523$	10888.3	−	10888.3i	0.910348	−	0.910348i	−0.0859510	−	0.996299i	$-0.527393\pi$
$523$	10888.3	−	10888.3i	0.910348	−	0.910348i	0.996299	+	0.0859510i	$0.0273928\pi$
$524$	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
$528$	−5887.85	+	4570.25i	−0.485295	+	0.376695i
$529$		−	10408.0i		−	0.855427i
$530$	21226.2	+	7272.38i	1.73963	+	0.596023i
$531$			5817.29i			0.475422i
$532$	100.466	−	1601.16i	0.00818753	−	0.130487i
$533$	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
$538$	1010.01	+	455.936i	0.0809381	+	0.0365368i
$539$	−7045.82			−0.563052
$540$	−1653.38	+	1760.21i	−0.131759	+	0.140273i
$541$	−9855.75			−0.783238			−0.391619	−	0.920127i	$-0.628085\pi$
$541$	−9855.75			−0.783238			−0.391619	+	0.920127i	$0.628085\pi$
$542$	−5234.29	−	2362.85i	−0.414820	−	0.187256i
$543$	−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	$0.160060\pi$
$547$	17375.0	+	17375.0i	1.35813	+	1.35813i	0.481918	+	0.876216i	$0.339940\pi$
$548$	−1383.66	−	86.8195i	−0.107860	−	0.00676778i
$549$		−	4745.24i		−	0.368892i
$550$	3210.83	−	13344.1i	0.248927	−	1.03454i
$551$			3297.38i			0.254942i
$552$	−3001.46	−	9747.65i	−0.231432	−	0.751608i
$553$	−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	$0.247615\pi$
$558$	−2554.29	+	5658.39i	−0.193784	+	0.429281i
$559$	−14592.2			−1.10409
$560$	−9088.83	−	285.270i	−0.685845	−	0.0215266i
$561$	1859.74			0.139961
$562$	−2794.97	+	6191.56i	−0.209784	+	0.464724i
$563$	1963.98	−	1963.98i	0.147020	−	0.147020i	−0.629766	−	0.776785i	$-0.716849\pi$
$563$	1963.98	−	1963.98i	0.147020	−	0.147020i	0.776785	+	0.629766i	$0.216849\pi$
$564$	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
$568$	4070.49	+	13219.5i	0.300694	+	0.976545i
$569$		−	15432.8i		−	1.13704i	−0.822668	−	0.568522i	$-0.807516\pi$
$569$		−	15432.8i		−	1.13704i	0.822668	−	0.568522i	$-0.192484\pi$
$570$	−485.216	+	1416.22i	−0.0356552	+	0.104068i
$571$		−	7847.00i		−	0.575108i	−0.957764	−	0.287554i	$-0.907158\pi$
$571$		−	7847.00i		−	0.575108i	0.957764	−	0.287554i	$-0.0928421\pi$
$572$	−12613.2	−	791.426i	−0.921998	−	0.0578517i
$573$	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	$0.415274\pi$
$578$	12008.0	+	5420.61i	0.864130	+	0.390082i
$579$	9357.12			0.671621
$580$	18680.6	−	584.657i	1.33736	−	0.0418562i
$581$	−8889.43			−0.634760
$582$	927.477	+	418.678i	0.0660570	+	0.0298192i
$583$	−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	$-0.342134\pi$
$587$	−5740.65	−	5740.65i	−0.403649	−	0.403649i	−0.879517	+	0.475868i	$0.842134\pi$
$588$	272.785	−	4347.44i	0.0191317	−	0.304907i
$589$			3848.47i			0.269225i
$590$	18357.5	−	8988.40i	1.28096	−	0.627198i
$591$		−	7861.54i		−	0.547176i
$592$	−11292.4	−	14548.0i	−0.783981	−	1.01000i
$593$	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
$598$	7115.31	−	15762.2i	0.486566	−	1.07787i
$599$	−6073.61			−0.414292			−0.207146	−	0.978310i	$-0.566417\pi$
$599$	−6073.61			−0.414292			−0.207146	+	0.978310i	$0.566417\pi$
$600$	8109.32	+	2497.78i	0.551769	+	0.169953i
$601$	26636.5			1.80786			0.903931	−	0.427679i	$-0.140669\pi$
$601$	26636.5			1.80786			0.903931	+	0.427679i	$0.140669\pi$
$602$	5303.06	−	11747.6i	0.359031	−	0.795343i
$603$	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	$0.0681730\pi$
$607$	17791.7	+	17791.7i	1.18969	+	1.18969i	0.212538	+	0.977153i	$0.431827\pi$
$608$	−2436.20	−	1491.50i	−0.162502	−	0.0994872i
$609$		−	7966.49i		−	0.530080i
$610$	−14974.4	+	7331.95i	−0.993930	+	0.486659i
$611$			21120.2i			1.39841i
$612$	−72.0013	+	1147.50i	−0.00475569	+	0.0757926i
$613$	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	$0.344291\pi$
$618$	14205.4	+	6412.54i	0.924635	+	0.417395i
$619$	−19250.8			−1.25001			−0.625005	−	0.780621i	$-0.714903\pi$
$619$	−19250.8			−1.25001			−0.625005	+	0.780621i	$0.714903\pi$
$620$	21802.7	−	682.371i	1.41229	−	0.0442011i
$621$	4056.74			0.262144
$622$	9871.01	+	4455.94i	0.636321	+	0.287246i
$623$	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
$628$	341.273	+	21.4135i	0.0216851	+	0.00136066i
$629$			4595.16i			0.291289i
$630$	1172.29	−	3421.59i	0.0741349	−	0.216380i
$631$		−	13031.7i		−	0.822161i	−0.911599	−	0.411081i	$-0.865151\pi$
$631$		−	13031.7i		−	0.822161i	0.911599	−	0.411081i	$-0.134849\pi$
$632$	−11923.3	+	3671.37i	−0.750448	+	0.231075i
$633$	−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
$638$	−9439.84	+	20911.6i	−0.585779	+	1.29765i
$639$	−5501.64			−0.340597
$640$	−8017.81	+	14066.2i	−0.495206	+	0.868776i
$641$	20195.0			1.24439			0.622195	−	0.782863i	$-0.286241\pi$
$641$	20195.0			1.24439			0.622195	+	0.782863i	$0.286241\pi$
$642$	1801.43	−	3990.63i	0.110743	−	0.245323i
$643$	4730.31	−	4730.31i	0.290117	−	0.290117i	−0.547010	−	0.837126i	$-0.684234\pi$
$643$	4730.31	−	4730.31i	0.290117	−	0.290117i	0.837126	+	0.547010i	$0.184234\pi$
$644$	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	$-0.148897\pi$
$647$	7268.71	+	7268.71i	0.441673	+	0.441673i	−0.450901	+	0.892574i	$0.648897\pi$
$648$	1751.66	−	539.364i	0.106191	−	0.0326979i
$649$			25092.0i			1.51764i
$650$	7511.21	+	12271.2i	0.453252	+	0.740486i
$651$		−	9297.93i		−	0.559777i
$652$	10789.4	+	676.993i	0.648076	+	0.0406642i
$653$	−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
$658$	−17003.0	−	7675.43i	−1.00736	−	0.454741i
$659$	24317.2			1.43742			0.718712	−	0.695307i	$-0.244732\pi$
$659$	24317.2			1.43742			0.718712	+	0.695307i	$0.244732\pi$
$660$	−7131.58	+	7592.40i	−0.420600	+	0.447778i
$661$	−14423.7			−0.848742			−0.424371	−	0.905488i	$-0.639505\pi$
$661$	−14423.7			−0.848742			−0.424371	+	0.905488i	$0.639505\pi$
$662$	18903.5	+	8533.33i	1.10982	+	0.500993i
$663$	−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
$668$	122.864	−	1958.12i	0.00711641	−	0.113416i
$669$		−	2069.12i		−	0.119577i
$670$	−16600.6	−	5687.62i	−0.957222	−	0.327958i
$671$		−	20467.8i		−	1.17757i
$672$	5885.87	+	3603.47i	0.337876	+	0.206855i
$673$	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	$0.340755\pi$
$678$	−2786.86	+	6173.60i	−0.157860	+	0.349699i
$679$	−1524.04			−0.0861375
$680$	3732.40	−	1545.82i	0.210487	−	0.0871755i
$681$	9241.47			0.520021
$682$	−11017.5	+	24406.6i	−0.618596	+	1.37035i
$683$	−8104.50	+	8104.50i	−0.454041	+	0.454041i	−0.896693	−	0.442652i	$-0.854038\pi$
$683$	−8104.50	+	8104.50i	−0.454041	+	0.454041i	0.442652	+	0.896693i	$0.354038\pi$
$684$	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
$688$	−14071.9	−	18128.8i	−0.779776	−	1.00458i
$689$		−	28873.8i		−	1.59652i
$690$	−6268.15	−	12801.8i	−0.345832	−	0.706311i
$691$			17999.5i			0.990928i	0.868628	+	0.495464i	$0.165002\pi$
$691$			17999.5i			0.990928i	−0.868628	+	0.495464i	$0.834998\pi$
$692$	913.255	−	14554.8i	0.0501687	−	0.799552i
$693$	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
$698$	−24699.8	−	11149.9i	−1.33940	−	0.604626i
$699$	8791.34			0.475707
$700$	−12608.8	+	1587.41i	−0.680809	+	0.0857121i
$701$	18730.1			1.00917			0.504584	−	0.863362i	$-0.331646\pi$
$701$	18730.1			1.00917			0.504584	+	0.863362i	$0.331646\pi$
$702$	2832.48	+	1278.63i	0.152286	+	0.0687445i
$703$	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
$708$	−15482.3	−	971.455i	−0.821838	−	0.0515671i
$709$			6597.00i			0.349443i	0.984618	+	0.174722i	$0.0559026\pi$
$709$			6597.00i			0.349443i	−0.984618	+	0.174722i	$0.944097\pi$
$710$	8500.68	+	17361.4i	0.449331	+	0.917692i
$711$		−	4962.19i		−	0.261739i
$712$	−4928.63	−	16006.4i	−0.259422	−	0.842508i
$713$	−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
$718$	−2555.61	+	5661.31i	−0.132833	+	0.294259i
$719$	−2093.70			−0.108598			−0.0542989	−	0.998525i	$-0.517292\pi$
$719$	−2093.70			−0.108598			−0.0542989	+	0.998525i	$0.517292\pi$
$720$	−4408.58	−	4694.29i	−0.228192	−	0.242981i
$721$	−23342.5			−1.20571
$722$	−7692.19	+	17040.1i	−0.396501	+	0.878349i
$723$	−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	$-0.263955\pi$
$727$	−1214.94	−	1214.94i	−0.0619801	−	0.0619801i	−0.737417	+	0.675437i	$0.763955\pi$
$728$	3443.62	+	11183.6i	0.175315	+	0.569359i
$729$			729.000i			0.0370370i
$730$	−6126.06	−	2098.88i	−0.310597	−	0.106415i
$731$			5726.18i			0.289727i
$732$	12629.1	+	792.428i	0.637686	+	0.0400123i
$733$	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
$738$	−597.443	−	269.695i	−0.0297997	−	0.0134521i
$739$	−7751.58			−0.385854			−0.192927	−	0.981213i	$-0.561798\pi$
$739$	−7751.58			−0.385854			−0.192927	+	0.981213i	$0.561798\pi$
$740$	−18759.7	−	17621.1i	−0.931921	−	0.875358i
$741$	1926.47			0.0955070
$742$	23245.1	+	10493.2i	1.15007	+	0.519162i
$743$	15280.2	−	15280.2i	0.754477	−	0.754477i	−0.220834	−	0.975311i	$-0.570878\pi$
$743$	15280.2	−	15280.2i	0.754477	−	0.754477i	0.975311	+	0.220834i	$0.0708780\pi$
$744$	−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
$748$	−310.566	+	4949.58i	−0.0151811	+	0.241944i
$749$			6557.45i			0.319898i
$750$	11738.9	+	1680.34i	0.571525	+	0.0818099i
$751$		−	39607.5i		−	1.92450i	−0.272171	−	0.962249i	$-0.587742\pi$
$751$		−	39607.5i		−	1.92450i	0.272171	−	0.962249i	$-0.412258\pi$
$752$	−26238.9	+	20367.1i	−1.27239	+	0.987648i
$753$	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	$0.192301\pi$
$758$	8357.93	−	18514.9i	0.400493	−	0.887192i
$759$	17498.1			0.836814
$760$	−3688.14	−	1527.87i	−0.176030	−	0.0729233i
$761$	−22046.7			−1.05019			−0.525094	−	0.851044i	$-0.675970\pi$
$761$	−22046.7			−1.05019			−0.525094	+	0.851044i	$0.675970\pi$
$762$	−941.878	+	2086.50i	−0.0447777	+	0.0991939i
$763$	−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
$768$	10572.6	−	6262.20i	0.496752	−	0.294229i
$769$			9309.49i			0.436552i	0.975887	+	0.218276i	$0.0700433\pi$
$769$			9309.49i			0.436552i	−0.975887	+	0.218276i	$0.929957\pi$
$770$	5056.47	−	14758.5i	0.236653	−	0.690726i
$771$			17675.7i			0.825646i
$772$	−1562.59	+	24903.4i	−0.0728481	+	1.16100i
$773$	−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
$778$	−3106.30	−	1402.24i	−0.143144	−	0.0646177i
$779$	−406.343			−0.0186890
$780$	−341.581	−	10914.0i	−0.0156802	−	0.501006i
$781$	−23730.5			−1.08725
$782$	−6185.30	−	2792.14i	−0.282846	−	0.127681i
$783$	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	$-0.230070\pi$
$787$	1953.67	+	1953.67i	0.0884888	+	0.0884888i	−0.661477	+	0.749966i	$0.730070\pi$
$788$	20923.0	+	1312.83i	0.945876	+	0.0593500i
$789$		−	8607.73i		−	0.388394i
$790$	−15659.1	+	7667.17i	−0.705221	+	0.345298i
$791$		−	10144.5i		−	0.456003i
$792$	7555.52	−	2326.46i	0.338982	−	0.104378i
$793$	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	$0.449106\pi$
$798$	−700.113	+	1550.92i	−0.0310573	+	0.0687997i
$799$	8287.84			0.366962
$800$	−8001.89	+	21165.3i	−0.353637	+	0.935383i
$801$	6661.49			0.293848
$802$	−3235.13	+	7166.63i	−0.142440	+	0.315539i
$803$	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
$808$	−12394.1	+	3816.34i	−0.539633	+	0.166161i
$809$			17520.6i			0.761425i	0.924693	+	0.380712i	$0.124321\pi$
$809$			17520.6i			0.761425i	−0.924693	+	0.380712i	$0.875679\pi$
$810$	2300.49	−	1126.39i	0.0997912	−	0.0488609i
$811$			39421.8i			1.70689i	0.521183	+	0.853445i	$0.325491\pi$
$811$			39421.8i			1.70689i	−0.521183	+	0.853445i	$0.674509\pi$
$812$	21202.3	+	1330.36i	0.916323	+	0.0574957i
$813$	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
$818$	26609.5	+	12011.9i	1.13738	+	0.513432i
$819$	−4654.36			−0.198580
$820$	72.0484	+	2302.05i	0.00306834	+	0.0980378i
$821$	−1985.12			−0.0843864			−0.0421932	−	0.999109i	$-0.513434\pi$
$821$	−1985.12			−0.0843864			−0.0421932	+	0.999109i	$0.513434\pi$
$822$	1340.25	+	605.013i	0.0568695	+	0.0256718i
$823$	−11773.8	+	11773.8i	−0.498674	+	0.498674i	−0.911025	−	0.412351i	$-0.864708\pi$
$823$	−11773.8	+	11773.8i	−0.498674	+	0.498674i	0.412351	+	0.911025i	$0.364708\pi$
$824$	−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	$-0.394090\pi$
$827$	−14710.3	−	14710.3i	−0.618534	−	0.618534i	−0.945155	+	0.326622i	$0.894090\pi$
$828$	−677.453	+	10796.7i	−0.0284337	+	0.453156i
$829$			514.236i			0.0215442i	0.999942	+	0.0107721i	$0.00342894\pi$
$829$			514.236i			0.0215442i	−0.999942	+	0.0107721i	$0.996571\pi$
$830$	−7169.53	+	20926.0i	−0.299829	+	0.875121i
$831$			19465.7i			0.812586i
$832$	20468.3	+	3893.84i	0.852896	+	0.162253i
$833$	−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
$838$	12457.7	−	27596.9i	0.513536	−	1.13761i
$839$	27918.0			1.14879			0.574396	−	0.818577i	$-0.305237\pi$
$839$	27918.0			1.14879			0.574396	+	0.818577i	$0.305237\pi$
$840$	8910.57	+	3691.35i	0.366005	+	0.151623i
$841$	−19274.4			−0.790293
$842$	16629.6	−	36838.7i	0.680633	−	1.50777i
$843$	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
$848$	35871.7	−	27844.2i	1.45264	−	1.12756i
$849$			7952.73i			0.321481i
$850$	4815.39	−	2947.50i	0.194313	−	0.118939i
$851$			43235.4i			1.74159i
$852$	918.743	−	14642.2i	0.0369432	−	0.588774i
$853$	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	$0.296105\pi$
$858$	12217.4	+	5515.15i	0.486127	+	0.219446i
$859$	47092.3			1.87051			0.935255	−	0.353975i	$-0.115170\pi$
$859$	47092.3			1.87051			0.935255	+	0.353975i	$0.115170\pi$
$860$	−23377.2	−	21958.3i	−0.926924	−	0.870664i
$861$	981.726			0.0388584
$862$	−39496.5	−	17829.4i	−1.56062	−	0.704491i
$863$	−7615.70	+	7615.70i	−0.300396	+	0.300396i	−0.841169	−	0.540773i	$-0.818132\pi$
$863$	−7615.70	+	7615.70i	−0.300396	+	0.300396i	0.540773	+	0.841169i	$0.318132\pi$
$864$	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
$868$	24745.8	+	1552.70i	0.967659	+	0.0607168i
$869$		−	21403.6i		−	0.835522i
$870$	−18753.4	−	6425.16i	−0.730803	−	0.250383i
$871$			22581.7i			0.878476i
$872$	8058.84	+	26172.2i	0.312966	+	1.01640i
$873$	−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	$-0.134733\pi$
$878$	6666.93	−	14768.9i	0.256262	−	0.567685i
$879$	−3900.85			−0.149684
$880$	−19015.7	−	20248.1i	−0.728432	−	0.775640i
$881$	4007.97			0.153271			0.0766355	−	0.997059i	$-0.475582\pi$
$881$	4007.97			0.153271			0.0766355	+	0.997059i	$0.475582\pi$
$882$	−1900.93	+	4211.04i	−0.0725712	+	0.160763i
$883$	−18107.5	+	18107.5i	−0.690108	+	0.690108i	−0.962255	−	0.272148i	$-0.912266\pi$
$883$	−18107.5	+	18107.5i	−0.690108	+	0.690108i	0.272148	+	0.962255i	$0.412266\pi$
$884$	−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	$-0.178726\pi$
$887$	8295.62	+	8295.62i	0.314024	+	0.314024i	−0.532442	+	0.846466i	$0.678726\pi$
$888$	5748.36	+	18668.6i	0.217232	+	0.705492i
$889$		−	3428.56i		−	0.129348i
$890$	−10292.8	−	21021.5i	−0.387657	−	0.791733i
$891$			3144.43i			0.118229i
$892$	5506.83	+	345.532i	0.206707	+	0.0129700i
$893$	−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
$898$	11998.7	+	5416.43i	0.445883	+	0.201279i
$899$	−50960.9			−1.89059
$900$	−7109.05	−	5519.19i	−0.263298	−	0.204414i
$901$	−11330.5			−0.418948
$902$	−2576.98	−	1163.29i	−0.0951263	−	0.0429416i
$903$	−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	$-0.857033\pi$
$907$	−36466.7	−	36466.7i	−1.33501	−	1.33501i	−0.434195	−	0.900819i	$-0.642967\pi$
$908$	−1543.27	+	24595.6i	−0.0564046	+	0.898934i
$909$		−	5158.13i		−	0.188212i
$910$	7191.54	+	14687.7i	0.261975	+	0.535045i
$911$			36350.5i			1.32200i	0.750385	+	0.661002i	$0.229868\pi$
$911$			36350.5i			1.32200i	−0.750385	+	0.661002i	$0.770132\pi$
$912$	1857.78	+	2393.37i	0.0674531	+	0.0868997i
$913$	−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
$918$	501.750	−	1111.50i	0.0180395	−	0.0399619i
$919$	−1636.73			−0.0587495			−0.0293748	−	0.999568i	$-0.509352\pi$
$919$	−1636.73			−0.0587495			−0.0293748	+	0.999568i	$0.509352\pi$
$920$	35117.8	−	14544.4i	1.25848	−	0.521212i
$921$	8502.25			0.304190
$922$	6789.57	−	15040.6i	0.242519	−	0.537240i
$923$	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
$928$	19750.2	−	32259.8i	0.698634	−	1.14114i
$929$			12094.4i			0.427131i	0.976929	+	0.213565i	$0.0685076\pi$
$929$			12094.4i			0.427131i	−0.976929	+	0.213565i	$0.931492\pi$
$930$	−21887.6	−	7499.00i	−0.771745	−	0.264411i
$931$			2864.08i			0.100823i
$932$	−1468.11	+	23397.6i	−0.0515981	+	0.822332i
$933$	−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	$0.151920\pi$
$938$	−18179.6	−	8206.59i	−0.632821	−	0.285666i
$939$	−2999.16			−0.104232
$940$	−31781.5	+	33835.1i	−1.10276	+	1.17402i
$941$	25713.6			0.890797			0.445398	−	0.895332i	$-0.353062\pi$
$941$	25713.6			0.890797			0.445398	+	0.895332i	$0.353062\pi$
$942$	−330.566	−	149.223i	−0.0114336	−	0.00516130i
$943$	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	$-0.341762\pi$
$947$	−11717.1	−	11717.1i	−0.402064	−	0.402064i	−0.878960	+	0.476896i	$0.841762\pi$
$948$	13206.5	+	828.658i	0.452456	+	0.0283898i
$949$			8333.24i			0.285046i
$950$	−5424.30	−	1305.18i	−0.185250	−	0.0445744i
$951$			3148.23i			0.107348i
$952$	4388.61	−	1351.32i	0.149407	−	0.0460049i
$953$	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
$958$	−17296.2	+	38315.5i	−0.583316	+	1.29219i
$959$	−2202.32			−0.0741572
$960$	13229.8	−	10949.2i	0.444780	−	0.368109i
$961$	−29687.0			−0.996508
$962$	−13627.2	+	30187.6i	−0.456712	+	1.01173i
$963$	−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	$-0.218365\pi$
$967$	4219.47	+	4219.47i	0.140319	+	0.140319i	−0.633458	+	0.773777i	$0.718365\pi$
$968$	3806.06	−	1171.95i	0.126375	−	0.0389130i
$969$		−	755.973i		−	0.0250623i
$970$	−1229.17	+	3587.64i	−0.0406870	+	0.118755i
$971$			33342.1i			1.10195i	0.834520	+	0.550977i	$0.185745\pi$
$971$			33342.1i			1.10195i	−0.834520	+	0.550977i	$0.814255\pi$
$972$	−1940.18	−	121.739i	−0.0640241	−	0.00401726i
$973$	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	$0.218246\pi$
$978$	−10450.9	−	4717.71i	−0.341701	−	0.154249i
$979$	28733.3			0.938019
$980$	16225.9	−	507.829i	0.528894	−	0.0165531i
$981$	−10892.2			−0.354498
$982$	−28393.6	−	12817.3i	−0.922683	−	0.416514i
$983$	−8362.60	+	8362.60i	−0.271338	+	0.271338i	−0.829639	−	0.558301i	$-0.811454\pi$
$983$	−8362.60	+	8362.60i	−0.271338	+	0.271338i	0.558301	+	0.829639i	$0.311454\pi$
$984$	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
$988$	−321.710	+	5127.17i	−0.0103593	+	0.165098i
$989$			53877.1i			1.73225i
$990$	9922.79	−	4858.51i	0.318553	−	0.155973i
$991$		−	35928.9i		−	1.15168i	−0.817561	−	0.575842i	$-0.804674\pi$
$991$		−	35928.9i		−	1.15168i	0.817561	−	0.575842i	$-0.195326\pi$
$992$	23051.0	−	37651.3i	0.737773	−	1.20507i
$993$	−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	$0.497066\pi$
$998$	3886.78	−	8610.18i	0.123280	−	0.273097i
$999$	−7769.43			−0.246060

Twists

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

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(1.16372 - 2.57794i) q^{2} +(-2.12132 + 2.12132i) q^{3} +(-5.29150 - 6.00000i) q^{4} +(-8.61249 - 7.12917i) q^{5} +(3.00000 + 7.93725i) q^{6} +(-8.98612 - 8.98612i) q^{7} +(-21.6255 + 6.65882i) q^{8} -9.00000i q^{9} +O(q^{10})\)	\(q+(1.16372 - 2.57794i) 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} +(-21.6255 + 6.65882i) q^{8} -9.00000i q^{9} +(-28.4011 + 13.9061i) q^{10} -38.8201i q^{11} +(23.9529 + 1.50295i) 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} +(-23.2014 - 10.4735i) q^{18} -15.7801 q^{19} +(2.79796 + 89.3989i) q^{20} +38.1249 q^{21} +(-100.076 - 45.1758i) 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} +(-6.36664 + 101.467i) q^{28} -208.958i q^{29} +(30.7486 - 89.7470i) q^{30} -243.881i q^{31} +(154.384 + 94.5175i) 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} +(-18.3637 + 40.6801i) q^{38} -122.082 q^{39} +(233.721 + 96.8225i) q^{40} +25.7503 q^{41} +(44.3667 - 98.2834i) 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} +(-117.729 - 151.670i) q^{48} -181.499i q^{49} +(343.743 + 82.7104i) q^{50} +47.9067i q^{51} +(20.3870 - 324.913i) 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} +(-538.680 - 243.169i) q^{58} -646.366 q^{59} +(-195.579 - 183.708i) q^{60} +527.249 q^{61} +(-628.710 - 283.810i) 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} +(-127.500 - 8.00015i) q^{68} +450.749i q^{69} +(380.177 + 130.254i) q^{70} -611.293i q^{71} +(59.9294 + 194.629i) 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} +(-142.070 + 314.720i) q^{78} +551.355 q^{79} +(521.588 - 489.843i) q^{80} -81.0000 q^{81} +(29.9662 - 66.3826i) 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} +(258.496 + 839.502i) q^{88} +740.166i q^{89} +(125.155 + 255.610i) q^{90} -517.151i q^{91} +(-1199.64 - 75.2726i) 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} +(-467.894 - 211.215i) 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