LMFDB - Embedded newform 230.3.f.b.47.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(47,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 0]))

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

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.f (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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.8
Character	$\chi$	$=$	230.47
Dual form			230.3.f.b.93.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.74954 - 1.74954i) q^{3} +2.00000i q^{4} +(-3.63965 + 3.42826i) q^{5} +3.49907 q^{6} +(4.68530 + 4.68530i) q^{7} +(-2.00000 + 2.00000i) q^{8} +2.87825i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.74954 - 1.74954i) q^{3} +2.00000i q^{4} +(-3.63965 + 3.42826i) q^{5} +3.49907 q^{6} +(4.68530 + 4.68530i) q^{7} +(-2.00000 + 2.00000i) q^{8} +2.87825i q^{9} +(-7.06791 - 0.211383i) q^{10} +7.34415 q^{11} +(3.49907 + 3.49907i) q^{12} +(-0.802148 + 0.802148i) q^{13} +9.37061i q^{14} +(-0.369822 + 12.3656i) q^{15} -4.00000 q^{16} +(2.03445 + 2.03445i) q^{17} +(-2.87825 + 2.87825i) q^{18} +12.6979i q^{19} +(-6.85652 - 7.27929i) q^{20} +16.3942 q^{21} +(7.34415 + 7.34415i) q^{22} +(3.39116 - 3.39116i) q^{23} +6.99814i q^{24} +(1.49404 - 24.9553i) q^{25} -1.60430 q^{26} +(20.7814 + 20.7814i) q^{27} +(-9.37061 + 9.37061i) q^{28} -18.2947i q^{29} +(-12.7354 + 11.9957i) q^{30} +32.9458 q^{31} +(-4.00000 - 4.00000i) q^{32} +(12.8489 - 12.8489i) q^{33} +4.06891i q^{34} +(-33.1153 - 0.990394i) q^{35} -5.75651 q^{36} +(-22.1338 - 22.1338i) q^{37} +(-12.6979 + 12.6979i) q^{38} +2.80677i q^{39} +(0.422766 - 14.1358i) q^{40} -16.8120 q^{41} +(16.3942 + 16.3942i) q^{42} +(15.6643 - 15.6643i) q^{43} +14.6883i q^{44} +(-9.86741 - 10.4758i) q^{45} +6.78233 q^{46} +(-53.7739 - 53.7739i) q^{47} +(-6.99814 + 6.99814i) q^{48} -5.09584i q^{49} +(26.4494 - 23.4613i) q^{50} +7.11869 q^{51} +(-1.60430 - 1.60430i) q^{52} +(-15.1999 + 15.1999i) q^{53} +41.5628i q^{54} +(-26.7301 + 25.1777i) q^{55} -18.7412 q^{56} +(22.2155 + 22.2155i) q^{57} +(18.2947 - 18.2947i) q^{58} +8.32600i q^{59} +(-24.7311 - 0.739644i) q^{60} +16.1313 q^{61} +(32.9458 + 32.9458i) q^{62} +(-13.4855 + 13.4855i) q^{63} -8.00000i q^{64} +(0.169561 - 5.66951i) q^{65} +25.6977 q^{66} +(21.8813 + 21.8813i) q^{67} +(-4.06891 + 4.06891i) q^{68} -11.8659i q^{69} +(-32.1249 - 34.1057i) q^{70} -105.543 q^{71} +(-5.75651 - 5.75651i) q^{72} +(63.5112 - 63.5112i) q^{73} -44.2677i q^{74} +(-41.0463 - 46.2741i) q^{75} -25.3959 q^{76} +(34.4096 + 34.4096i) q^{77} +(-2.80677 + 2.80677i) q^{78} -19.7472i q^{79} +(14.5586 - 13.7130i) q^{80} +46.8114 q^{81} +(-16.8120 - 16.8120i) q^{82} +(105.262 - 105.262i) q^{83} +32.7884i q^{84} +(-14.3793 - 0.430049i) q^{85} +31.3285 q^{86} +(-32.0072 - 32.0072i) q^{87} +(-14.6883 + 14.6883i) q^{88} -131.803i q^{89} +(0.608414 - 20.3432i) q^{90} -7.51662 q^{91} +(6.78233 + 6.78233i) q^{92} +(57.6398 - 57.6398i) q^{93} -107.548i q^{94} +(-43.5319 - 46.2160i) q^{95} -13.9963 q^{96} +(101.232 + 101.232i) q^{97} +(5.09584 - 5.09584i) q^{98} +21.1383i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) $ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8	$ 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) $ 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$2$	1.00000	+	1.00000i	0.500000	+	0.500000i
$3$	1.74954	−	1.74954i	0.583178	−	0.583178i	−0.352597	−	0.935775i	$-0.614701\pi$
$3$	1.74954	−	1.74954i	0.583178	−	0.583178i	0.935775	+	0.352597i	$0.114701\pi$
$4$			2.00000i			0.500000i
$5$	−3.63965	+	3.42826i	−0.727929	+	0.685652i
$5$	−3.63965	+	3.42826i	−0.727929	+	0.685652i
$6$	3.49907			0.583178
$7$	4.68530	+	4.68530i	0.669329	+	0.669329i	0.957561	−	0.288232i	$-0.0930673\pi$
$7$	4.68530	+	4.68530i	0.669329	+	0.669329i	−0.288232	+	0.957561i	$0.593067\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$			2.87825i			0.319806i
$10$	−7.06791	−	0.211383i	−0.706791	−	0.0211383i
$11$	7.34415			0.667650			0.333825	−	0.942635i	$-0.391660\pi$
$11$	7.34415			0.667650			0.333825	+	0.942635i	$0.391660\pi$
$12$	3.49907	+	3.49907i	0.291589	+	0.291589i
$13$	−0.802148	+	0.802148i	−0.0617037	+	0.0617037i	−0.737285	−	0.675582i	$-0.763893\pi$
$13$	−0.802148	+	0.802148i	−0.0617037	+	0.0617037i	0.675582	+	0.737285i	$0.263893\pi$
$14$			9.37061i			0.669329i
$15$	−0.369822	+	12.3656i	−0.0246548	+	0.824370i
$16$	−4.00000			−0.250000
$17$	2.03445	+	2.03445i	0.119674	+	0.119674i	0.764407	−	0.644734i	$-0.223032\pi$
$17$	2.03445	+	2.03445i	0.119674	+	0.119674i	−0.644734	+	0.764407i	$0.723032\pi$
$18$	−2.87825	+	2.87825i	−0.159903	+	0.159903i
$19$			12.6979i			0.668313i	0.942518	+	0.334156i	$0.108451\pi$
$19$			12.6979i			0.668313i	−0.942518	+	0.334156i	$0.891549\pi$
$20$	−6.85652	−	7.27929i	−0.342826	−	0.363965i
$21$	16.3942			0.780677
$22$	7.34415	+	7.34415i	0.333825	+	0.333825i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$23$	3.39116	−	3.39116i	0.147442	−	0.147442i
$24$			6.99814i			0.291589i
$25$	1.49404	−	24.9553i	0.0597614	−	0.998213i
$26$	−1.60430			−0.0617037
$27$	20.7814	+	20.7814i	0.769682	+	0.769682i
$28$	−9.37061	+	9.37061i	−0.334665	+	0.334665i
$29$		−	18.2947i		−	0.630851i	−0.948950	−	0.315426i	$-0.897853\pi$
$29$		−	18.2947i		−	0.630851i	0.948950	−	0.315426i	$-0.102147\pi$
$30$	−12.7354	+	11.9957i	−0.424512	+	0.399858i
$31$	32.9458			1.06277			0.531384	−	0.847131i	$-0.321672\pi$
$31$	32.9458			1.06277			0.531384	+	0.847131i	$0.321672\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	12.8489	−	12.8489i	0.389359	−	0.389359i
$34$			4.06891i			0.119674i
$35$	−33.1153	−	0.990394i	−0.946151	−	0.0282970i
$36$	−5.75651			−0.159903
$37$	−22.1338	−	22.1338i	−0.598212	−	0.598212i	0.341625	−	0.939836i	$-0.389023\pi$
$37$	−22.1338	−	22.1338i	−0.598212	−	0.598212i	−0.939836	+	0.341625i	$0.889023\pi$
$38$	−12.6979	+	12.6979i	−0.334156	+	0.334156i
$39$			2.80677i			0.0719686i
$40$	0.422766	−	14.1358i	0.0105691	−	0.353395i
$41$	−16.8120			−0.410049			−0.205024	−	0.978757i	$-0.565727\pi$
$41$	−16.8120			−0.410049			−0.205024	+	0.978757i	$0.565727\pi$
$42$	16.3942	+	16.3942i	0.390338	+	0.390338i
$43$	15.6643	−	15.6643i	0.364285	−	0.364285i	−0.501103	−	0.865388i	$-0.667072\pi$
$43$	15.6643	−	15.6643i	0.364285	−	0.364285i	0.865388	+	0.501103i	$0.167072\pi$
$44$			14.6883i			0.333825i
$45$	−9.86741	−	10.4758i	−0.219276	−	0.232796i
$46$	6.78233			0.147442
$47$	−53.7739	−	53.7739i	−1.14412	−	1.14412i	−0.987688	−	0.156437i	$-0.949999\pi$
$47$	−53.7739	−	53.7739i	−1.14412	−	1.14412i	−0.156437	−	0.987688i	$-0.550001\pi$
$48$	−6.99814	+	6.99814i	−0.145795	+	0.145795i
$49$		−	5.09584i		−	0.103997i
$50$	26.4494	−	23.4613i	0.528987	−	0.469226i
$51$	7.11869			0.139582
$52$	−1.60430	−	1.60430i	−0.0308519	−	0.0308519i
$53$	−15.1999	+	15.1999i	−0.286790	+	0.286790i	−0.835809	−	0.549020i	$-0.815001\pi$
$53$	−15.1999	+	15.1999i	−0.286790	+	0.286790i	0.549020	+	0.835809i	$0.315001\pi$
$54$			41.5628i			0.769682i
$55$	−26.7301	+	25.1777i	−0.486002	+	0.457776i
$56$	−18.7412			−0.334665
$57$	22.2155	+	22.2155i	0.389745	+	0.389745i
$58$	18.2947	−	18.2947i	0.315426	−	0.315426i
$59$			8.32600i			0.141119i	0.997508	+	0.0705593i	$0.0224784\pi$
$59$			8.32600i			0.141119i	−0.997508	+	0.0705593i	$0.977522\pi$
$60$	−24.7311	−	0.739644i	−0.412185	−	0.0123274i
$61$	16.1313			0.264448			0.132224	−	0.991220i	$-0.457788\pi$
$61$	16.1313			0.264448			0.132224	+	0.991220i	$0.457788\pi$
$62$	32.9458	+	32.9458i	0.531384	+	0.531384i
$63$	−13.4855	+	13.4855i	−0.214055	+	0.214055i
$64$		−	8.00000i		−	0.125000i
$65$	0.169561	−	5.66951i	0.00260862	−	0.0872233i
$66$	25.6977			0.389359
$67$	21.8813	+	21.8813i	0.326587	+	0.326587i	0.851287	−	0.524700i	$-0.175823\pi$
$67$	21.8813	+	21.8813i	0.326587	+	0.326587i	−0.524700	+	0.851287i	$0.675823\pi$
$68$	−4.06891	+	4.06891i	−0.0598368	+	0.0598368i
$69$		−	11.8659i		−	0.171970i
$70$	−32.1249	−	34.1057i	−0.458927	−	0.487224i
$71$	−105.543			−1.48652			−0.743258	−	0.669005i	$-0.766721\pi$
$71$	−105.543			−1.48652			−0.743258	+	0.669005i	$0.766721\pi$
$72$	−5.75651	−	5.75651i	−0.0799515	−	0.0799515i
$73$	63.5112	−	63.5112i	0.870017	−	0.870017i	−0.122457	−	0.992474i	$-0.539077\pi$
$73$	63.5112	−	63.5112i	0.870017	−	0.870017i	0.992474	+	0.122457i	$0.0390773\pi$
$74$		−	44.2677i		−	0.598212i
$75$	−41.0463	−	46.2741i	−0.547285	−	0.616988i
$76$	−25.3959			−0.334156
$77$	34.4096	+	34.4096i	0.446878	+	0.446878i
$78$	−2.80677	+	2.80677i	−0.0359843	+	0.0359843i
$79$		−	19.7472i		−	0.249964i	−0.992159	−	0.124982i	$-0.960113\pi$
$79$		−	19.7472i		−	0.249964i	0.992159	−	0.124982i	$-0.0398874\pi$
$80$	14.5586	−	13.7130i	0.181982	−	0.171413i
$81$	46.8114			0.577918
$82$	−16.8120	−	16.8120i	−0.205024	−	0.205024i
$83$	105.262	−	105.262i	1.26822	−	1.26822i	0.321214	−	0.947007i	$-0.395909\pi$
$83$	105.262	−	105.262i	1.26822	−	1.26822i	0.947007	−	0.321214i	$-0.104091\pi$
$84$			32.7884i			0.390338i
$85$	−14.3793	−	0.430049i	−0.169169	−	0.00505940i
$86$	31.3285			0.364285
$87$	−32.0072	−	32.0072i	−0.367899	−	0.367899i
$88$	−14.6883	+	14.6883i	−0.166913	+	0.166913i
$89$		−	131.803i		−	1.48093i	−0.672092	−	0.740467i	$-0.734604\pi$
$89$		−	131.803i		−	1.48093i	0.672092	−	0.740467i	$-0.265396\pi$
$90$	0.608414	−	20.3432i	0.00676015	−	0.226036i
$91$	−7.51662			−0.0826002
$92$	6.78233	+	6.78233i	0.0737210	+	0.0737210i
$93$	57.6398	−	57.6398i	0.619783	−	0.619783i
$94$		−	107.548i		−	1.14412i
$95$	−43.5319	−	46.2160i	−0.458230	−	0.486484i
$96$	−13.9963			−0.145795
$97$	101.232	+	101.232i	1.04362	+	1.04362i	0.999004	+	0.0446199i	$0.0142077\pi$
$97$	101.232	+	101.232i	1.04362	+	1.04362i	0.0446199	+	0.999004i	$0.485792\pi$
$98$	5.09584	−	5.09584i	0.0519984	−	0.0519984i
$99$			21.1383i			0.213519i
$100$	49.9106	+	2.98807i	0.499106	+	0.0298807i
$101$	−33.1423			−0.328141			−0.164071	−	0.986449i	$-0.552463\pi$
$101$	−33.1423			−0.328141			−0.164071	+	0.986449i	$0.552463\pi$
$102$	7.11869	+	7.11869i	0.0697911	+	0.0697911i
$103$	63.5710	−	63.5710i	0.617194	−	0.617194i	−0.327616	−	0.944811i	$-0.606245\pi$
$103$	63.5710	−	63.5710i	0.617194	−	0.617194i	0.944811	+	0.327616i	$0.106245\pi$
$104$		−	3.20859i		−	0.0308519i
$105$	−59.6691	+	56.2037i	−0.568277	+	0.535273i
$106$	−30.3997			−0.286790
$107$	49.0182	+	49.0182i	0.458114	+	0.458114i	0.898036	−	0.439922i	$-0.144994\pi$
$107$	49.0182	+	49.0182i	0.458114	+	0.458114i	−0.439922	+	0.898036i	$0.644994\pi$
$108$	−41.5628	+	41.5628i	−0.384841	+	0.384841i
$109$			192.423i			1.76534i	0.469989	+	0.882672i	$0.344258\pi$
$109$			192.423i			1.76534i	−0.469989	+	0.882672i	$0.655742\pi$
$110$	−51.9078	−	1.55243i	−0.471889	−	0.0141130i
$111$	−77.4478			−0.697728
$112$	−18.7412	−	18.7412i	−0.167332	−	0.167332i
$113$	68.6393	−	68.6393i	0.607428	−	0.607428i	−0.334845	−	0.942273i	$-0.608684\pi$
$113$	68.6393	−	68.6393i	0.607428	−	0.607428i	0.942273	+	0.334845i	$0.108684\pi$
$114$			44.4310i			0.389745i
$115$	−0.716834	+	23.9684i	−0.00623334	+	0.208421i
$116$	36.5894			0.315426
$117$	−2.30879	−	2.30879i	−0.0197332	−	0.0197332i
$118$	−8.32600	+	8.32600i	−0.0705593	+	0.0705593i
$119$			19.0641i			0.160202i
$120$	−23.9915	−	25.4707i	−0.199929	−	0.212256i
$121$	−67.0634			−0.554243
$122$	16.1313	+	16.1313i	0.132224	+	0.132224i
$123$	−29.4132	+	29.4132i	−0.239131	+	0.239131i
$124$			65.8916i			0.531384i
$125$	80.1156	+	95.9504i	0.640925	+	0.767604i
$126$	−26.9710			−0.214055
$127$	39.6115	+	39.6115i	0.311901	+	0.311901i	0.845646	−	0.533744i	$-0.179216\pi$
$127$	39.6115	+	39.6115i	0.311901	+	0.311901i	−0.533744	+	0.845646i	$0.679216\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$		−	54.8103i		−	0.424886i
$130$	5.83907	−	5.49995i	0.0449159	−	0.0423073i
$131$	−151.732			−1.15826			−0.579130	−	0.815236i	$-0.696607\pi$
$131$	−151.732			−1.15826			−0.579130	+	0.815236i	$0.696607\pi$
$132$	25.6977	+	25.6977i	0.194680	+	0.194680i
$133$	−59.4937	+	59.4937i	−0.447321	+	0.447321i
$134$			43.7626i			0.326587i
$135$	−146.881	−	4.39284i	−1.08801	−	0.0325395i
$136$	−8.13781			−0.0598368
$137$	115.031	+	115.031i	0.839642	+	0.839642i	0.988812	−	0.149169i	$-0.0476600\pi$
$137$	115.031	+	115.031i	0.839642	+	0.839642i	−0.149169	+	0.988812i	$0.547660\pi$
$138$	11.8659	−	11.8659i	0.0859850	−	0.0859850i
$139$		−	8.87351i		−	0.0638382i	−0.999490	−	0.0319191i	$-0.989838\pi$
$139$		−	8.87351i		−	0.0638382i	0.999490	−	0.0319191i	$-0.0101619\pi$
$140$	1.98079	−	66.2306i	0.0141485	−	0.473076i
$141$	−188.159			−1.33446
$142$	−105.543	−	105.543i	−0.743258	−	0.743258i
$143$	−5.89110	+	5.89110i	−0.0411965	+	0.0411965i
$144$		−	11.5130i		−	0.0799515i
$145$	62.7190	+	66.5862i	0.432545	+	0.459215i
$146$	127.022			0.870017
$147$	−8.91535	−	8.91535i	−0.0606487	−	0.0606487i
$148$	44.2677	−	44.2677i	0.299106	−	0.299106i
$149$			98.3865i			0.660312i	0.943926	+	0.330156i	$0.107101\pi$
$149$			98.3865i			0.660312i	−0.943926	+	0.330156i	$0.892899\pi$
$150$	5.22773	−	87.3204i	0.0348516	−	0.582136i
$151$	−74.3468			−0.492363			−0.246181	−	0.969224i	$-0.579176\pi$
$151$	−74.3468			−0.492363			−0.246181	+	0.969224i	$0.579176\pi$
$152$	−25.3959	−	25.3959i	−0.167078	−	0.167078i
$153$	−5.85567	+	5.85567i	−0.0382724	+	0.0382724i
$154$			68.8192i			0.446878i
$155$	−119.911	+	112.947i	−0.773620	+	0.728689i
$156$	−5.61355			−0.0359843
$157$	102.456	+	102.456i	0.652587	+	0.652587i	0.953615	−	0.301028i	$-0.0973298\pi$
$157$	102.456	+	102.456i	0.652587	+	0.652587i	−0.301028	+	0.953615i	$0.597330\pi$
$158$	19.7472	−	19.7472i	0.124982	−	0.124982i
$159$			53.1853i			0.334499i
$160$	28.2716	+	0.845532i	0.176698	+	0.00528457i
$161$	31.7773			0.197374
$162$	46.8114	+	46.8114i	0.288959	+	0.288959i
$163$	69.6921	−	69.6921i	0.427559	−	0.427559i	−0.460237	−	0.887796i	$-0.652236\pi$
$163$	69.6921	−	69.6921i	0.427559	−	0.427559i	0.887796	+	0.460237i	$0.152236\pi$
$164$		−	33.6240i		−	0.205024i
$165$	−2.71603	+	90.8145i	−0.0164608	+	0.550391i
$166$	210.525			1.26822
$167$	−134.667	−	134.667i	−0.806391	−	0.806391i	0.177695	−	0.984086i	$-0.443136\pi$
$167$	−134.667	−	134.667i	−0.806391	−	0.806391i	−0.984086	+	0.177695i	$0.943136\pi$
$168$	−32.7884	+	32.7884i	−0.195169	+	0.195169i
$169$			167.713i			0.992385i
$170$	−13.9493	−	14.8094i	−0.0820546	−	0.0871140i
$171$	−36.5479			−0.213730
$172$	31.3285	+	31.3285i	0.182143	+	0.182143i
$173$	−54.9807	+	54.9807i	−0.317808	+	0.317808i	−0.847925	−	0.530117i	$-0.822148\pi$
$173$	−54.9807	+	54.9807i	−0.317808	+	0.317808i	0.530117	+	0.847925i	$0.322148\pi$
$174$		−	64.0144i		−	0.367899i
$175$	123.923	−	109.923i	0.708133	−	0.628133i
$176$	−29.3766			−0.166913
$177$	14.5666	+	14.5666i	0.0822974	+	0.0822974i
$178$	131.803	−	131.803i	0.740467	−	0.740467i
$179$			151.781i			0.847941i	0.905676	+	0.423970i	$0.139364\pi$
$179$			151.781i			0.847941i	−0.905676	+	0.423970i	$0.860636\pi$
$180$	20.9516	−	19.7348i	0.116398	−	0.109638i
$181$	−13.6959			−0.0756682			−0.0378341	−	0.999284i	$-0.512046\pi$
$181$	−13.6959			−0.0756682			−0.0378341	+	0.999284i	$0.512046\pi$
$182$	−7.51662	−	7.51662i	−0.0413001	−	0.0413001i
$183$	28.2223	−	28.2223i	0.154220	−	0.154220i
$184$			13.5647i			0.0737210i
$185$	156.440	+	4.67871i	0.845621	+	0.0252903i
$186$	115.280			0.619783
$187$	14.9413	+	14.9413i	0.0799002	+	0.0799002i
$188$	107.548	−	107.548i	0.572062	−	0.572062i
$189$			194.735i			1.03034i
$190$	2.68413	−	89.7479i	0.0141270	−	0.472357i
$191$	−222.336			−1.16406			−0.582032	−	0.813166i	$-0.697742\pi$
$191$	−222.336			−1.16406			−0.582032	+	0.813166i	$0.697742\pi$
$192$	−13.9963	−	13.9963i	−0.0728973	−	0.0728973i
$193$	107.725	−	107.725i	0.558158	−	0.558158i	−0.370625	−	0.928783i	$-0.620856\pi$
$193$	107.725	−	107.725i	0.558158	−	0.558158i	0.928783	+	0.370625i	$0.120856\pi$
$194$			202.463i			1.04362i
$195$	−9.62236	−	10.2157i	−0.0493454	−	0.0523880i
$196$	10.1917			0.0519984
$197$	−5.03748	−	5.03748i	−0.0255709	−	0.0255709i	0.694206	−	0.719777i	$-0.255756\pi$
$197$	−5.03748	−	5.03748i	−0.0255709	−	0.0255709i	−0.719777	+	0.694206i	$0.755756\pi$
$198$	−21.1383	+	21.1383i	−0.106759	+	0.106759i
$199$			127.303i			0.639711i	0.947466	+	0.319856i	$0.103634\pi$
$199$			127.303i			0.639711i	−0.947466	+	0.319856i	$0.896366\pi$
$200$	46.9226	+	52.8987i	0.234613	+	0.264494i
$201$	76.5642			0.380916
$202$	−33.1423	−	33.1423i	−0.164071	−	0.164071i
$203$	85.7162	−	85.7162i	0.422247	−	0.422247i
$204$			14.2374i			0.0697911i
$205$	61.1897	−	57.6359i	0.298486	−	0.281151i
$206$	127.142			0.617194
$207$	9.76063	+	9.76063i	0.0471528	+	0.0471528i
$208$	3.20859	−	3.20859i	0.0154259	−	0.0154259i
$209$			93.2556i			0.446199i
$210$	−115.873	−	3.46546i	−0.551775	−	0.0165022i
$211$	9.59463			0.0454722			0.0227361	−	0.999742i	$-0.492762\pi$
$211$	9.59463			0.0454722			0.0227361	+	0.999742i	$0.492762\pi$
$212$	−30.3997	−	30.3997i	−0.143395	−	0.143395i
$213$	−184.651	+	184.651i	−0.866904	+	0.866904i
$214$			98.0363i			0.458114i
$215$	−3.31116	+	110.714i	−0.0154007	+	0.514947i
$216$	−83.1257			−0.384841
$217$	154.361	+	154.361i	0.711342	+	0.711342i
$218$	−192.423	+	192.423i	−0.882672	+	0.882672i
$219$		−	222.230i		−	1.01475i
$220$	−50.3554	−	53.4602i	−0.228888	−	0.243001i
$221$	−3.26387			−0.0147686
$222$	−77.4478	−	77.4478i	−0.348864	−	0.348864i
$223$	231.304	−	231.304i	1.03724	−	1.03724i	0.0379566	−	0.999279i	$-0.487915\pi$
$223$	231.304	−	231.304i	1.03724	−	1.03724i	0.999279	−	0.0379566i	$-0.0120849\pi$
$224$		−	37.4824i		−	0.167332i
$225$	71.8277	+	4.30021i	0.319234	+	0.0191121i
$226$	137.279			0.607428
$227$	−295.186	−	295.186i	−1.30038	−	1.30038i	−0.928134	−	0.372247i	$-0.878588\pi$
$227$	−295.186	−	295.186i	−1.30038	−	1.30038i	−0.372247	−	0.928134i	$-0.621412\pi$
$228$	−44.4310	+	44.4310i	−0.194873	+	0.194873i
$229$		−	441.791i		−	1.92922i	−0.263687	−	0.964608i	$-0.584939\pi$
$229$		−	441.791i		−	1.92922i	0.263687	−	0.964608i	$-0.415061\pi$
$230$	−24.6853	+	23.2516i	−0.107327	+	0.101094i
$231$	120.402			0.521219
$232$	36.5894	+	36.5894i	0.157713	+	0.157713i
$233$	−142.357	+	142.357i	−0.610974	+	0.610974i	−0.943200	−	0.332226i	$-0.892200\pi$
$233$	−142.357	+	142.357i	−0.610974	+	0.610974i	0.332226	+	0.943200i	$0.392200\pi$
$234$		−	4.61757i		−	0.0197332i
$235$	380.069	+	11.3669i	1.61731	+	0.0483697i
$236$	−16.6520			−0.0705593
$237$	−34.5484	−	34.5484i	−0.145774	−	0.145774i
$238$	−19.0641	+	19.0641i	−0.0801011	+	0.0801011i
$239$			103.472i			0.432938i	0.976289	+	0.216469i	$0.0694541\pi$
$239$			103.472i			0.432938i	−0.976289	+	0.216469i	$0.930546\pi$
$240$	1.47929	−	49.4622i	0.00616370	−	0.206093i
$241$	11.4659			0.0475762			0.0237881	−	0.999717i	$-0.492427\pi$
$241$	11.4659			0.0475762			0.0237881	+	0.999717i	$0.492427\pi$
$242$	−67.0634	−	67.0634i	−0.277122	−	0.277122i
$243$	−105.135	+	105.135i	−0.432653	+	0.432653i
$244$			32.2626i			0.132224i
$245$	17.4699	+	18.5471i	0.0713056	+	0.0757023i
$246$	−58.8263			−0.239131
$247$	−10.1856	−	10.1856i	−0.0412374	−	0.0412374i
$248$	−65.8916	+	65.8916i	−0.265692	+	0.265692i
$249$		−	368.320i		−	1.47920i
$250$	−15.8348	+	176.066i	−0.0633393	+	0.704264i
$251$	46.6849			0.185996			0.0929978	−	0.995666i	$-0.470355\pi$
$251$	46.6849			0.185996			0.0929978	+	0.995666i	$0.470355\pi$
$252$	−26.9710	−	26.9710i	−0.107028	−	0.107028i
$253$	24.9052	−	24.9052i	0.0984397	−	0.0984397i
$254$			79.2229i			0.311901i
$255$	−25.9095	+	24.4047i	−0.101606	+	0.0957049i
$256$	16.0000			0.0625000
$257$	−309.876	−	309.876i	−1.20574	−	1.20574i	−0.972393	−	0.233351i	$-0.925031\pi$
$257$	−309.876	−	309.876i	−1.20574	−	1.20574i	−0.233351	−	0.972393i	$-0.574969\pi$
$258$	54.8103	−	54.8103i	0.212443	−	0.212443i
$259$		−	207.407i		−	0.800801i
$260$	11.3390	+	0.339121i	0.0436116	+	0.00130431i
$261$	52.6567			0.201750
$262$	−151.732	−	151.732i	−0.579130	−	0.579130i
$263$	−45.9507	+	45.9507i	−0.174718	+	0.174718i	−0.789048	−	0.614331i	$-0.789426\pi$
$263$	−45.9507	+	45.9507i	−0.174718	+	0.174718i	0.614331	+	0.789048i	$0.289426\pi$
$264$			51.3954i			0.194680i
$265$	3.21299	−	107.431i	0.0121245	−	0.405401i
$266$	−118.987			−0.447321
$267$	−230.594	−	230.594i	−0.863649	−	0.863649i
$268$	−43.7626	+	43.7626i	−0.163293	+	0.163293i
$269$		−	138.967i		−	0.516606i	−0.966064	−	0.258303i	$-0.916837\pi$
$269$		−	138.967i		−	0.516606i	0.966064	−	0.258303i	$-0.0831632\pi$
$270$	−142.488	−	151.274i	−0.527735	−	0.560274i
$271$	−373.516			−1.37829			−0.689143	−	0.724625i	$-0.742013\pi$
$271$	−373.516			−1.37829			−0.689143	+	0.724625i	$0.742013\pi$
$272$	−8.13781	−	8.13781i	−0.0299184	−	0.0299184i
$273$	−13.1506	+	13.1506i	−0.0481707	+	0.0481707i
$274$			230.062i			0.839642i
$275$	10.9724	−	183.276i	0.0398997	−	0.666457i
$276$	23.7318			0.0859850
$277$	329.820	+	329.820i	1.19069	+	1.19069i	0.976875	+	0.213813i	$0.0685882\pi$
$277$	329.820	+	329.820i	1.19069	+	1.19069i	0.213813	+	0.976875i	$0.431412\pi$
$278$	8.87351	−	8.87351i	0.0319191	−	0.0319191i
$279$			94.8264i			0.339880i
$280$	68.2114	−	64.2498i	0.243612	−	0.229464i
$281$	433.168			1.54152			0.770761	−	0.637124i	$-0.219876\pi$
$281$	433.168			1.54152			0.770761	+	0.637124i	$0.219876\pi$
$282$	−188.159	−	188.159i	−0.667229	−	0.667229i
$283$	−112.199	+	112.199i	−0.396462	+	0.396462i	−0.876983	−	0.480521i	$-0.840448\pi$
$283$	−112.199	+	112.199i	−0.396462	+	0.396462i	0.480521	+	0.876983i	$0.340448\pi$
$284$		−	211.085i		−	0.743258i
$285$	−157.017	−	4.69598i	−0.550937	−	0.0164771i
$286$	−11.7822			−0.0411965
$287$	−78.7693	−	78.7693i	−0.274457	−	0.274457i
$288$	11.5130	−	11.5130i	0.0399757	−	0.0399757i
$289$		−	280.722i		−	0.971356i
$290$	−3.86719	+	129.305i	−0.0133351	+	0.445880i
$291$	354.216			1.21724
$292$	127.022	+	127.022i	0.435008	+	0.435008i
$293$	−157.692	+	157.692i	−0.538196	+	0.538196i	−0.922999	−	0.384803i	$-0.874270\pi$
$293$	−157.692	+	157.692i	−0.538196	+	0.538196i	0.384803	+	0.922999i	$0.374270\pi$
$294$		−	17.8307i		−	0.0606487i
$295$	−28.5437	−	30.3037i	−0.0967584	−	0.102724i
$296$	88.5353			0.299106
$297$	152.622	+	152.622i	0.513879	+	0.513879i
$298$	−98.3865	+	98.3865i	−0.330156	+	0.330156i
$299$			5.44044i			0.0181954i
$300$	92.5481	−	82.0927i	0.308494	−	0.273642i
$301$	146.784			0.487653
$302$	−74.3468	−	74.3468i	−0.246181	−	0.246181i
$303$	−57.9836	+	57.9836i	−0.191365	+	0.191365i
$304$		−	50.7918i		−	0.167078i
$305$	−58.7122	+	55.3023i	−0.192499	+	0.181319i
$306$	−11.7113			−0.0382724
$307$	157.847	+	157.847i	0.514159	+	0.514159i	0.915798	−	0.401639i	$-0.131559\pi$
$307$	157.847	+	157.847i	0.514159	+	0.514159i	−0.401639	+	0.915798i	$0.631559\pi$
$308$	−68.8192	+	68.8192i	−0.223439	+	0.223439i
$309$		−	222.440i		−	0.719869i
$310$	−232.858	−	6.96418i	−0.751155	−	0.0224651i
$311$	−543.283			−1.74689			−0.873445	−	0.486923i	$-0.838119\pi$
$311$	−543.283			−1.74689			−0.873445	+	0.486923i	$0.838119\pi$
$312$	−5.61355	−	5.61355i	−0.0179921	−	0.0179921i
$313$	30.7142	−	30.7142i	0.0981286	−	0.0981286i	−0.656338	−	0.754467i	$-0.727896\pi$
$313$	30.7142	−	30.7142i	0.0981286	−	0.0981286i	0.754467	+	0.656338i	$0.227896\pi$
$314$			204.912i			0.652587i
$315$	2.85060	−	95.3142i	0.00904954	−	0.302585i
$316$	39.4944			0.124982
$317$	−370.911	−	370.911i	−1.17007	−	1.17007i	−0.982193	−	0.187873i	$-0.939841\pi$
$317$	−370.911	−	370.911i	−1.17007	−	1.17007i	−0.187873	−	0.982193i	$-0.560159\pi$
$318$	−53.1853	+	53.1853i	−0.167250	+	0.167250i
$319$		−	134.359i		−	0.421188i
$320$	27.4261	+	29.1172i	0.0857066	+	0.0909911i
$321$	171.518			0.534324
$322$	31.7773	+	31.7773i	0.0986872	+	0.0986872i
$323$	−25.8334	+	25.8334i	−0.0799794	+	0.0799794i
$324$			93.6228i			0.288959i
$325$	18.8194	+	21.2163i	0.0579059	+	0.0652809i
$326$	139.384			0.427559
$327$	336.650	+	336.650i	1.02951	+	1.02951i
$328$	33.6240	−	33.6240i	0.102512	−	0.102512i
$329$		−	503.894i		−	1.53159i
$330$	−93.5305	+	88.0985i	−0.283426	+	0.266965i
$331$	−334.223			−1.00974			−0.504869	−	0.863196i	$-0.668459\pi$
$331$	−334.223			−1.00974			−0.504869	+	0.863196i	$0.668459\pi$
$332$	210.525	+	210.525i	0.634110	+	0.634110i
$333$	63.7068	−	63.7068i	0.191312	−	0.191312i
$334$		−	269.335i		−	0.806391i
$335$	−154.655	−	4.62533i	−0.461657	−	0.0138070i
$336$	−65.5768			−0.195169
$337$	−280.330	−	280.330i	−0.831841	−	0.831841i	0.155927	−	0.987769i	$-0.450163\pi$
$337$	−280.330	−	280.330i	−0.831841	−	0.831841i	−0.987769	+	0.155927i	$0.950163\pi$
$338$	−167.713	+	167.713i	−0.496193	+	0.496193i
$339$		−	240.174i		−	0.708477i
$340$	0.860097	−	28.7586i	0.00252970	−	0.0845843i
$341$	241.959			0.709557
$342$	−36.5479	−	36.5479i	−0.106865	−	0.106865i
$343$	253.455	−	253.455i	0.738937	−	0.738937i
$344$			62.6570i			0.182143i
$345$	40.6795	+	43.1878i	0.117912	+	0.125182i
$346$	−109.961			−0.317808
$347$	433.965	+	433.965i	1.25062	+	1.25062i	0.955443	+	0.295176i	$0.0953782\pi$
$347$	433.965	+	433.965i	1.25062	+	1.25062i	0.295176	+	0.955443i	$0.404622\pi$
$348$	64.0144	−	64.0144i	0.183949	−	0.183949i
$349$		−	221.072i		−	0.633443i	−0.948519	−	0.316721i	$-0.897418\pi$
$349$		−	221.072i		−	0.633443i	0.948519	−	0.316721i	$-0.102582\pi$
$350$	233.847	+	14.0000i	0.668133	+	0.0400001i
$351$	−33.3396			−0.0949845
$352$	−29.3766	−	29.3766i	−0.0834563	−	0.0834563i
$353$	−10.4152	+	10.4152i	−0.0295049	+	0.0295049i	−0.721705	−	0.692200i	$-0.756641\pi$
$353$	−10.4152	+	10.4152i	−0.0295049	+	0.0295049i	0.692200	+	0.721705i	$0.256641\pi$
$354$			29.1333i			0.0822974i
$355$	384.138	−	361.828i	1.08208	−	1.01923i
$356$	263.606			0.740467
$357$	33.3532	+	33.3532i	0.0934265	+	0.0934265i
$358$	−151.781	+	151.781i	−0.423970	+	0.423970i
$359$			92.8731i			0.258699i	0.991599	+	0.129350i	$0.0412890\pi$
$359$			92.8731i			0.258699i	−0.991599	+	0.129350i	$0.958711\pi$
$360$	40.6865	+	1.21683i	0.113018	+	0.00338008i
$361$	199.762			0.553358
$362$	−13.6959	−	13.6959i	−0.0378341	−	0.0378341i
$363$	−117.330	+	117.330i	−0.323223	+	0.323223i
$364$		−	15.0332i		−	0.0413001i
$365$	−13.4252	+	448.892i	−0.0367814	+	1.22984i
$366$	56.4446			0.154220
$367$	−42.3293	−	42.3293i	−0.115339	−	0.115339i	0.647082	−	0.762421i	$-0.275989\pi$
$367$	−42.3293	−	42.3293i	−0.115339	−	0.115339i	−0.762421	+	0.647082i	$0.775989\pi$
$368$	−13.5647	+	13.5647i	−0.0368605	+	0.0368605i
$369$		−	48.3892i		−	0.131136i
$370$	151.761	+	161.119i	0.410165	+	0.435456i
$371$	−142.432			−0.383913
$372$	115.280	+	115.280i	0.309892	+	0.309892i
$373$	−99.0976	+	99.0976i	−0.265677	+	0.265677i	−0.827356	−	0.561678i	$-0.810156\pi$
$373$	−99.0976	+	99.0976i	−0.265677	+	0.265677i	0.561678	+	0.827356i	$0.310156\pi$
$374$			29.8827i			0.0799002i
$375$	308.034	+	27.7036i	0.821423	+	0.0738763i
$376$	215.095			0.572062
$377$	14.6751	+	14.6751i	0.0389259	+	0.0389259i
$378$	−194.735	+	194.735i	−0.515171	+	0.515171i
$379$			267.871i			0.706784i	0.935475	+	0.353392i	$0.114972\pi$
$379$			267.871i			0.706784i	−0.935475	+	0.353392i	$0.885028\pi$
$380$	92.4320	−	87.0637i	0.243242	−	0.229115i
$381$	138.603			0.363788
$382$	−222.336	−	222.336i	−0.582032	−	0.582032i
$383$	193.931	−	193.931i	0.506347	−	0.506347i	−0.407056	−	0.913403i	$-0.633445\pi$
$383$	193.931	−	193.931i	0.506347	−	0.506347i	0.913403	+	0.407056i	$0.133445\pi$
$384$		−	27.9926i		−	0.0728973i
$385$	−243.204	−	7.27360i	−0.631698	−	0.0188925i
$386$	215.449			0.558158
$387$	45.0857	+	45.0857i	0.116501	+	0.116501i
$388$	−202.463	+	202.463i	−0.521812	+	0.521812i
$389$			582.596i			1.49768i	0.662753	+	0.748838i	$0.269388\pi$
$389$			582.596i			1.49768i	−0.662753	+	0.748838i	$0.730612\pi$
$390$	0.593304	−	19.8380i	0.00152129	−	0.0508667i
$391$	13.7983			0.0352898
$392$	10.1917	+	10.1917i	0.0259992	+	0.0259992i
$393$	−265.460	+	265.460i	−0.675472	+	0.675472i
$394$		−	10.0750i		−	0.0255709i
$395$	67.6985	+	71.8728i	0.171389	+	0.181956i
$396$	−42.2767			−0.106759
$397$	325.494	+	325.494i	0.819885	+	0.819885i	0.986091	−	0.166206i	$-0.0531518\pi$
$397$	325.494	+	325.494i	0.819885	+	0.819885i	−0.166206	+	0.986091i	$0.553152\pi$
$398$	−127.303	+	127.303i	−0.319856	+	0.319856i
$399$			208.173i			0.521736i
$400$	−5.97614	+	99.8213i	−0.0149404	+	0.249553i
$401$	101.242			0.252474			0.126237	−	0.992000i	$-0.459710\pi$
$401$	101.242			0.252474			0.126237	+	0.992000i	$0.459710\pi$
$402$	76.5642	+	76.5642i	0.190458	+	0.190458i
$403$	−26.4274	+	26.4274i	−0.0655767	+	0.0655767i
$404$		−	66.2845i		−	0.164071i
$405$	−170.377	+	160.482i	−0.420683	+	0.396251i
$406$	171.432			0.422247
$407$	−162.554	−	162.554i	−0.399396	−	0.399396i
$408$	−14.2374	+	14.2374i	−0.0348956	+	0.0348956i
$409$		−	348.881i		−	0.853011i	−0.904485	−	0.426505i	$-0.859745\pi$
$409$		−	348.881i		−	0.853011i	0.904485	−	0.426505i	$-0.140255\pi$
$410$	118.826	+	3.55377i	0.289819	+	0.00866773i
$411$	402.501			0.979322
$412$	127.142	+	127.142i	0.308597	+	0.308597i
$413$	−39.0098	+	39.0098i	−0.0944548	+	0.0944548i
$414$			19.5213i			0.0471528i
$415$	−22.2507	+	743.984i	−0.0536161	+	1.79273i
$416$	6.41719			0.0154259
$417$	−15.5245	−	15.5245i	−0.0372291	−	0.0372291i
$418$	−93.2556	+	93.2556i	−0.223100	+	0.223100i
$419$			120.421i			0.287401i	0.989621	+	0.143700i	$0.0459002\pi$
$419$			120.421i			0.287401i	−0.989621	+	0.143700i	$0.954100\pi$
$420$	−112.407	−	119.338i	−0.267636	−	0.284139i
$421$	−703.519			−1.67107			−0.835534	−	0.549439i	$-0.814841\pi$
$421$	−703.519			−1.67107			−0.835534	+	0.549439i	$0.814841\pi$
$422$	9.59463	+	9.59463i	0.0227361	+	0.0227361i
$423$	154.775	−	154.775i	0.365898	−	0.365898i
$424$		−	60.7994i		−	0.143395i
$425$	53.8100	−	47.7309i	0.126612	−	0.112308i
$426$	−369.301			−0.866904
$427$	75.5801	+	75.5801i	0.177002	+	0.177002i
$428$	−98.0363	+	98.0363i	−0.229057	+	0.229057i
$429$			20.6134i			0.0480498i
$430$	−114.025	+	107.402i	−0.265174	+	0.249773i
$431$	−309.307			−0.717650			−0.358825	−	0.933405i	$-0.616823\pi$
$431$	−309.307			−0.717650			−0.358825	+	0.933405i	$0.616823\pi$
$432$	−83.1257	−	83.1257i	−0.192421	−	0.192421i
$433$	−88.2644	+	88.2644i	−0.203844	+	0.203844i	−0.801645	−	0.597801i	$-0.796041\pi$
$433$	−88.2644	+	88.2644i	−0.203844	+	0.203844i	0.597801	+	0.801645i	$0.296041\pi$
$434$			308.722i			0.711342i
$435$	226.224	+	6.76578i	0.520055	+	0.0155535i
$436$	−384.845			−0.882672
$437$	43.0608	+	43.0608i	0.0985373	+	0.0985373i
$438$	222.230	−	222.230i	0.507375	−	0.507375i
$439$			231.130i			0.526492i	0.964729	+	0.263246i	$0.0847931\pi$
$439$			231.130i			0.526492i	−0.964729	+	0.263246i	$0.915207\pi$
$440$	3.10486	−	103.816i	0.00705649	−	0.235945i
$441$	14.6671			0.0332588
$442$	−3.26387	−	3.26387i	−0.00738431	−	0.00738431i
$443$	−572.899	+	572.899i	−1.29322	+	1.29322i	−0.360444	+	0.932781i	$0.617375\pi$
$443$	−572.899	+	572.899i	−1.29322	+	1.29322i	−0.932781	+	0.360444i	$0.882625\pi$
$444$		−	154.896i		−	0.348864i
$445$	451.856	+	479.717i	1.01541	+	1.07802i
$446$	462.607			1.03724
$447$	172.131	+	172.131i	0.385080	+	0.385080i
$448$	37.4824	−	37.4824i	0.0836662	−	0.0836662i
$449$		−	58.7939i		−	0.130944i	−0.997854	−	0.0654721i	$-0.979145\pi$
$449$		−	58.7939i		−	0.130944i	0.997854	−	0.0654721i	$-0.0208553\pi$
$450$	67.5275	+	76.1279i	0.150061	+	0.169173i
$451$	−123.470			−0.273769
$452$	137.279	+	137.279i	0.303714	+	0.303714i
$453$	−130.072	+	130.072i	−0.287135	+	0.287135i
$454$		−	590.373i		−	1.30038i
$455$	27.3578	−	25.7689i	0.0601271	−	0.0566350i
$456$	−88.8620			−0.194873
$457$	−146.469	−	146.469i	−0.320501	−	0.320501i	0.528458	−	0.848959i	$-0.322770\pi$
$457$	−146.469	−	146.469i	−0.320501	−	0.320501i	−0.848959	+	0.528458i	$0.822770\pi$
$458$	441.791	−	441.791i	0.964608	−	0.964608i
$459$			84.5576i			0.184221i
$460$	−47.9369	−	1.43367i	−0.104211	−	0.00311667i
$461$	532.088			1.15420			0.577102	−	0.816672i	$-0.304183\pi$
$461$	532.088			1.15420			0.577102	+	0.816672i	$0.304183\pi$
$462$	120.402	+	120.402i	0.260609	+	0.260609i
$463$	−97.3256	+	97.3256i	−0.210206	+	0.210206i	−0.804355	−	0.594149i	$-0.797489\pi$
$463$	−97.3256	+	97.3256i	−0.210206	+	0.210206i	0.594149	+	0.804355i	$0.297489\pi$
$464$			73.1788i			0.157713i
$465$	−12.1841	+	407.393i	−0.0262023	+	0.876114i
$466$	−284.714			−0.610974
$467$	−648.867	−	648.867i	−1.38944	−	1.38944i	−0.826501	−	0.562935i	$-0.809672\pi$
$467$	−648.867	−	648.867i	−1.38944	−	1.38944i	−0.562935	−	0.826501i	$-0.690328\pi$
$468$	4.61757	−	4.61757i	0.00986661	−	0.00986661i
$469$			205.041i			0.437188i
$470$	368.702	+	391.436i	0.784472	+	0.832842i
$471$	358.501			0.761149
$472$	−16.6520	−	16.6520i	−0.0352797	−	0.0352797i
$473$	115.041	−	115.041i	0.243215	−	0.243215i
$474$		−	69.0968i		−	0.145774i
$475$	316.881	+	18.9712i	0.667118	+	0.0399393i
$476$	−38.1281			−0.0801011
$477$	−43.7490	−	43.7490i	−0.0917170	−	0.0917170i
$478$	−103.472	+	103.472i	−0.216469	+	0.216469i
$479$		−	67.3465i		−	0.140598i	−0.997526	−	0.0702991i	$-0.977605\pi$
$479$		−	67.3465i		−	0.140598i	0.997526	−	0.0702991i	$-0.0223954\pi$
$480$	50.9415	−	47.9829i	0.106128	−	0.0999644i
$481$	35.5092			0.0738238
$482$	11.4659	+	11.4659i	0.0237881	+	0.0237881i
$483$	55.5955	−	55.5955i	0.115104	−	0.115104i
$484$		−	134.127i		−	0.277122i
$485$	−715.495	−	21.3986i	−1.47525	−	0.0441209i
$486$	−210.269			−0.432653
$487$	74.4495	+	74.4495i	0.152874	+	0.152874i	0.779400	−	0.626526i	$-0.215524\pi$
$487$	74.4495	+	74.4495i	0.152874	+	0.152874i	−0.626526	+	0.779400i	$0.715524\pi$
$488$	−32.2626	+	32.2626i	−0.0661119	+	0.0661119i
$489$		−	243.858i		−	0.498687i
$490$	−1.07717	+	36.0169i	−0.00219831	+	0.0735039i
$491$	767.159			1.56244			0.781221	−	0.624255i	$-0.214597\pi$
$491$	767.159			1.56244			0.781221	+	0.624255i	$0.214597\pi$
$492$	−58.8263	−	58.8263i	−0.119566	−	0.119566i
$493$	37.2197	−	37.2197i	0.0754963	−	0.0754963i
$494$		−	20.3713i		−	0.0412374i
$495$	−72.4678	−	76.9360i	−0.146399	−	0.155426i
$496$	−131.783			−0.265692
$497$	−494.500	−	494.500i	−0.994969	−	0.994969i
$498$	368.320	−	368.320i	0.739599	−	0.739599i
$499$		−	530.092i		−	1.06231i	−0.847275	−	0.531154i	$-0.821759\pi$
$499$		−	530.092i		−	1.06231i	0.847275	−	0.531154i	$-0.178241\pi$
$500$	−191.901	+	160.231i	−0.383802	+	0.320462i
$501$	−471.210			−0.940539
$502$	46.6849	+	46.6849i	0.0929978	+	0.0929978i
$503$	−145.546	+	145.546i	−0.289355	+	0.289355i	−0.836825	−	0.547470i	$-0.815591\pi$
$503$	−145.546	+	145.546i	−0.289355	+	0.289355i	0.547470	+	0.836825i	$0.315591\pi$
$504$		−	53.9420i		−	0.107028i
$505$	120.626	−	113.620i	0.238864	−	0.224991i
$506$	49.8105			0.0984397
$507$	293.420	+	293.420i	0.578738	+	0.578738i
$508$	−79.2229	+	79.2229i	−0.155951	+	0.155951i
$509$		−	771.820i		−	1.51635i	−0.652054	−	0.758173i	$-0.726092\pi$
$509$		−	771.820i		−	1.51635i	0.652054	−	0.758173i	$-0.273908\pi$
$510$	−50.3143	−	1.50477i	−0.0986554	−	0.00295053i
$511$	595.139			1.16466
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	−263.881	+	263.881i	−0.514388	+	0.514388i
$514$		−	619.752i		−	1.20574i
$515$	−13.4378	+	449.314i	−0.0260929	+	0.872455i
$516$	109.621			0.212443
$517$	−394.923	−	394.923i	−0.763875	−	0.763875i
$518$	207.407	−	207.407i	0.400400	−	0.400400i
$519$			192.381i			0.370677i
$520$	10.9999	+	11.6781i	0.0211537	+	0.0224580i
$521$	−61.1677			−0.117404			−0.0587022	−	0.998276i	$-0.518696\pi$
$521$	−61.1677			−0.117404			−0.0587022	+	0.998276i	$0.518696\pi$
$522$	52.6567	+	52.6567i	0.100875	+	0.100875i
$523$	471.652	−	471.652i	0.901819	−	0.901819i	−0.0937741	−	0.995593i	$-0.529893\pi$
$523$	471.652	−	471.652i	0.901819	−	0.901819i	0.995593	+	0.0937741i	$0.0298932\pi$
$524$		−	303.464i		−	0.579130i
$525$	24.4935	−	409.123i	0.0466543	−	0.779281i
$526$	−91.9014			−0.174718
$527$	67.0267	+	67.0267i	0.127185	+	0.127185i
$528$	−51.3954	+	51.3954i	−0.0973398	+	0.0973398i
$529$		−	23.0000i		−	0.0434783i
$530$	110.644	−	104.218i	0.208763	−	0.196638i
$531$	−23.9643			−0.0451306
$532$	−118.987	−	118.987i	−0.223661	−	0.223661i
$533$	13.4857	−	13.4857i	0.0253015	−	0.0253015i
$534$		−	461.189i		−	0.863649i
$535$	−346.456	−	10.3616i	−0.647581	−	0.0193675i
$536$	−87.5252			−0.163293
$537$	265.547	+	265.547i	0.494501	+	0.494501i
$538$	138.967	−	138.967i	0.258303	−	0.258303i
$539$		−	37.4246i		−	0.0694335i
$540$	8.78568	−	293.762i	0.0162698	−	0.544004i
$541$	−721.465			−1.33358			−0.666789	−	0.745247i	$-0.732332\pi$
$541$	−721.465			−1.33358			−0.666789	+	0.745247i	$0.732332\pi$
$542$	−373.516	−	373.516i	−0.689143	−	0.689143i
$543$	−23.9615	+	23.9615i	−0.0441280	+	0.0441280i
$544$		−	16.2756i		−	0.0299184i
$545$	−659.675	−	700.350i	−1.21041	−	1.28505i
$546$	−26.3012			−0.0481707
$547$	−574.163	−	574.163i	−1.04966	−	1.04966i	−0.998701	−	0.0509573i	$-0.983773\pi$
$547$	−574.163	−	574.163i	−1.04966	−	1.04966i	−0.0509573	−	0.998701i	$-0.516227\pi$
$548$	−230.062	+	230.062i	−0.419821	+	0.419821i
$549$			46.4300i			0.0845719i
$550$	194.248	−	172.303i	0.353178	−	0.313279i
$551$	232.305			0.421606
$552$	23.7318	+	23.7318i	0.0429925	+	0.0429925i
$553$	92.5216	−	92.5216i	0.167308	−	0.167308i
$554$			659.641i			1.19069i
$555$	281.883	−	265.511i	0.507897	−	0.478399i
$556$	17.7470			0.0319191
$557$	−337.658	−	337.658i	−0.606209	−	0.606209i	0.335744	−	0.941953i	$-0.391012\pi$
$557$	−337.658	−	337.658i	−0.606209	−	0.606209i	−0.941953	+	0.335744i	$0.891012\pi$
$558$	−94.8264	+	94.8264i	−0.169940	+	0.169940i
$559$			25.1301i			0.0449555i
$560$	132.461	+	3.96157i	0.236538	+	0.00707424i
$561$	52.2808			0.0931921
$562$	433.168	+	433.168i	0.770761	+	0.770761i
$563$	−42.8665	+	42.8665i	−0.0761394	+	0.0761394i	−0.744151	−	0.668012i	$-0.767146\pi$
$563$	−42.8665	+	42.8665i	−0.0761394	+	0.0761394i	0.668012	+	0.744151i	$0.267146\pi$
$564$		−	376.317i		−	0.667229i
$565$	−14.5092	+	485.136i	−0.0256800	+	0.858648i
$566$	−224.398			−0.396462
$567$	219.326	+	219.326i	0.386818	+	0.386818i
$568$	211.085	−	211.085i	0.371629	−	0.371629i
$569$			428.539i			0.753145i	0.926387	+	0.376572i	$0.122897\pi$
$569$			428.539i			0.753145i	−0.926387	+	0.376572i	$0.877103\pi$
$570$	−152.321	−	161.713i	−0.267230	−	0.283707i
$571$	−1067.35			−1.86926			−0.934628	−	0.355626i	$-0.884268\pi$
$571$	−1067.35			−1.86926			−0.934628	+	0.355626i	$0.884268\pi$
$572$	−11.7822	−	11.7822i	−0.0205983	−	0.0205983i
$573$	−388.985	+	388.985i	−0.678857	+	0.678857i
$574$		−	157.539i		−	0.274457i
$575$	−79.5611	−	89.6941i	−0.138367	−	0.155990i
$576$	23.0260			0.0399757
$577$	−308.950	−	308.950i	−0.535442	−	0.535442i	0.386745	−	0.922187i	$-0.373599\pi$
$577$	−308.950	−	308.950i	−0.535442	−	0.535442i	−0.922187	+	0.386745i	$0.873599\pi$
$578$	280.722	−	280.722i	0.485678	−	0.485678i
$579$		−	376.936i		−	0.651011i
$580$	−133.172	+	125.438i	−0.229607	+	0.216272i
$581$	986.372			1.69771
$582$	354.216	+	354.216i	0.608619	+	0.608619i
$583$	−111.630	+	111.630i	−0.191475	+	0.191475i
$584$			254.045i			0.435008i
$585$	16.3183	+	0.488038i	0.0278945	+	0.000834253i
$586$	−315.383			−0.538196
$587$	348.585	+	348.585i	0.593842	+	0.593842i	0.938667	−	0.344825i	$-0.112062\pi$
$587$	348.585	+	348.585i	0.593842	+	0.593842i	−0.344825	+	0.938667i	$0.612062\pi$
$588$	17.8307	−	17.8307i	0.0303243	−	0.0303243i
$589$			418.344i			0.710261i
$590$	1.75997	−	58.8474i	0.00298301	−	0.0997414i
$591$	−17.6265			−0.0298248
$592$	88.5353	+	88.5353i	0.149553	+	0.149553i
$593$	483.268	−	483.268i	0.814954	−	0.814954i	−0.170418	−	0.985372i	$-0.554512\pi$
$593$	483.268	−	483.268i	0.814954	−	0.814954i	0.985372	+	0.170418i	$0.0545118\pi$
$594$			305.244i			0.513879i
$595$	−65.3566	−	69.3864i	−0.109843	−	0.116616i
$596$	−196.773			−0.330156
$597$	222.720	+	222.720i	0.373066	+	0.373066i
$598$	−5.44044	+	5.44044i	−0.00909772	+	0.00909772i
$599$			879.264i			1.46789i	0.679211	+	0.733943i	$0.262322\pi$
$599$			879.264i			1.46789i	−0.679211	+	0.733943i	$0.737678\pi$
$600$	174.641	+	10.4555i	0.291068	+	0.0174258i
$601$	−462.938			−0.770279			−0.385139	−	0.922858i	$-0.625847\pi$
$601$	−462.938			−0.770279			−0.385139	+	0.922858i	$0.625847\pi$
$602$	146.784	+	146.784i	0.243827	+	0.243827i
$603$	−62.9799	+	62.9799i	−0.104444	+	0.104444i
$604$		−	148.694i		−	0.246181i
$605$	244.087	−	229.911i	0.403450	−	0.380018i
$606$	−115.967			−0.191365
$607$	523.602	+	523.602i	0.862606	+	0.862606i	0.991640	−	0.129034i	$-0.0411877\pi$
$607$	523.602	+	523.602i	0.862606	+	0.862606i	−0.129034	+	0.991640i	$0.541188\pi$
$608$	50.7918	−	50.7918i	0.0835391	−	0.0835391i
$609$		−	299.927i		−	0.492491i
$610$	−114.015	−	3.40988i	−0.186909	−	0.00558997i
$611$	86.2692			0.141194
$612$	−11.7113	−	11.7113i	−0.0191362	−	0.0191362i
$613$	−625.075	+	625.075i	−1.01970	+	1.01970i	−0.0198960	+	0.999802i	$0.506334\pi$
$613$	−625.075	+	625.075i	−1.01970	+	1.01970i	−0.999802	+	0.0198960i	$0.993666\pi$
$614$			315.694i			0.514159i
$615$	6.21744	−	207.890i	0.0101097	−	0.338032i
$616$	−137.638			−0.223439
$617$	−267.604	−	267.604i	−0.433719	−	0.433719i	0.456173	−	0.889891i	$-0.349220\pi$
$617$	−267.604	−	267.604i	−0.433719	−	0.433719i	−0.889891	+	0.456173i	$0.849220\pi$
$618$	222.440	−	222.440i	0.359934	−	0.359934i
$619$			1088.11i			1.75785i	0.476960	+	0.878925i	$0.341739\pi$
$619$			1088.11i			1.75785i	−0.476960	+	0.878925i	$0.658261\pi$
$620$	−225.894	−	239.822i	−0.364345	−	0.386810i
$621$	140.946			0.226967
$622$	−543.283	−	543.283i	−0.873445	−	0.873445i
$623$	617.538	−	617.538i	0.991233	−	0.991233i
$624$		−	11.2271i		−	0.0179921i
$625$	−620.536	−	74.5682i	−0.992857	−	0.119309i
$626$	61.4285			0.0981286
$627$	163.154	+	163.154i	0.260214	+	0.260214i
$628$	−204.912	+	204.912i	−0.326293	+	0.326293i
$629$		−	90.0605i		−	0.143180i
$630$	98.1648	−	92.4636i	0.155817	−	0.146768i
$631$	742.234			1.17628			0.588141	−	0.808759i	$-0.299860\pi$
$631$	742.234			1.17628			0.588141	+	0.808759i	$0.299860\pi$
$632$	39.4944	+	39.4944i	0.0624911	+	0.0624911i
$633$	16.7861	−	16.7861i	0.0265184	−	0.0265184i
$634$		−	741.822i		−	1.17007i
$635$	−279.970	−	8.37319i	−0.440898	−	0.0131861i
$636$	−106.371			−0.167250
$637$	4.08762	+	4.08762i	0.00641699	+	0.00641699i
$638$	134.359	−	134.359i	0.210594	−	0.210594i
$639$		−	303.779i		−	0.475397i
$640$	−1.69106	+	56.5433i	−0.00264229	+	0.0883488i
$641$	799.585			1.24740			0.623702	−	0.781663i	$-0.285628\pi$
$641$	799.585			1.24740			0.623702	+	0.781663i	$0.285628\pi$
$642$	171.518	+	171.518i	0.267162	+	0.267162i
$643$	−647.571	+	647.571i	−1.00711	+	1.00711i	−0.00713404	+	0.999975i	$0.502271\pi$
$643$	−647.571	+	647.571i	−1.00711	+	1.00711i	−0.999975	+	0.00713404i	$0.997729\pi$
$644$			63.5546i			0.0986872i
$645$	187.904	+	199.490i	0.291324	+	0.309287i
$646$	−51.6667			−0.0799794
$647$	−710.350	−	710.350i	−1.09791	−	1.09791i	−0.994654	−	0.103259i	$-0.967073\pi$
$647$	−710.350	−	710.350i	−1.09791	−	1.09791i	−0.103259	−	0.994654i	$-0.532927\pi$
$648$	−93.6228	+	93.6228i	−0.144480	+	0.144480i
$649$			61.1474i			0.0942179i
$650$	−2.39688	+	40.0357i	−0.00368750	+	0.0615934i
$651$	540.120			0.829678
$652$	139.384	+	139.384i	0.213780	+	0.213780i
$653$	816.226	−	816.226i	1.24996	−	1.24996i	0.294228	−	0.955735i	$-0.404938\pi$
$653$	816.226	−	816.226i	1.24996	−	1.24996i	0.955735	−	0.294228i	$-0.0950624\pi$
$654$			673.300i			1.02951i
$655$	552.250	−	520.177i	0.843130	−	0.794163i
$656$	67.2480			0.102512
$657$	182.801	+	182.801i	0.278237	+	0.278237i
$658$	503.894	−	503.894i	0.765796	−	0.765796i
$659$			1221.53i			1.85361i	0.375542	+	0.926805i	$0.377457\pi$
$659$			1221.53i			1.85361i	−0.375542	+	0.926805i	$0.622543\pi$
$660$	−181.629	−	5.43206i	−0.275195	−	0.00823039i
$661$	269.209			0.407275			0.203638	−	0.979046i	$-0.434724\pi$
$661$	269.209			0.407275			0.203638	+	0.979046i	$0.434724\pi$
$662$	−334.223	−	334.223i	−0.504869	−	0.504869i
$663$	−5.71025	+	5.71025i	−0.00861274	+	0.00861274i
$664$			421.049i			0.634110i
$665$	12.5760	−	420.496i	0.0189112	−	0.632325i
$666$	127.414			0.191312
$667$	−62.0403	−	62.0403i	−0.0930139	−	0.0930139i
$668$	269.335	−	269.335i	0.403195	−	0.403195i
$669$		−	809.348i		−	1.20979i
$670$	−150.030	−	159.280i	−0.223925	−	0.237732i
$671$	118.471			0.176558
$672$	−65.5768	−	65.5768i	−0.0975846	−	0.0975846i
$673$	−19.4524	+	19.4524i	−0.0289041	+	0.0289041i	−0.721411	−	0.692507i	$-0.756506\pi$
$673$	−19.4524	+	19.4524i	−0.0289041	+	0.0289041i	0.692507	+	0.721411i	$0.256506\pi$
$674$		−	560.661i		−	0.831841i
$675$	549.655	−	487.559i	0.814304	−	0.722309i
$676$	−335.426			−0.496193
$677$	173.259	+	173.259i	0.255922	+	0.255922i	0.823393	−	0.567471i	$-0.192078\pi$
$677$	173.259	+	173.259i	0.255922	+	0.255922i	−0.567471	+	0.823393i	$0.692078\pi$
$678$	240.174	−	240.174i	0.354239	−	0.354239i
$679$			948.601i			1.39706i
$680$	29.6187	−	27.8986i	0.0435570	−	0.0410273i
$681$	−1032.88			−1.51671
$682$	241.959	+	241.959i	0.354779	+	0.354779i
$683$	155.847	−	155.847i	0.228181	−	0.228181i	−0.583752	−	0.811932i	$-0.698416\pi$
$683$	155.847	−	155.847i	0.228181	−	0.228181i	0.811932	+	0.583752i	$0.198416\pi$
$684$		−	73.0958i		−	0.106865i
$685$	−813.028	−	24.3156i	−1.18690	−	0.0354972i
$686$	506.911			0.738937
$687$	−772.928	−	772.928i	−1.12508	−	1.12508i
$688$	−62.6570	+	62.6570i	−0.0910713	+	0.0910713i
$689$		−	24.3851i		−	0.0353920i
$690$	−2.50825	+	83.8673i	−0.00363515	+	0.121547i
$691$	−834.701			−1.20796			−0.603981	−	0.796999i	$-0.706420\pi$
$691$	−834.701			−1.20796			−0.603981	+	0.796999i	$0.706420\pi$
$692$	−109.961	−	109.961i	−0.158904	−	0.158904i
$693$	−99.0395	+	99.0395i	−0.142914	+	0.142914i
$694$			867.929i			1.25062i
$695$	30.4207	+	32.2964i	0.0437708	+	0.0464697i
$696$	128.029			0.183949
$697$	−34.2032	−	34.2032i	−0.0490720	−	0.0490720i
$698$	221.072	−	221.072i	0.316721	−	0.316721i
$699$			498.117i			0.712613i
$700$	219.847	+	247.847i	0.314066	+	0.354066i
$701$	−1081.67			−1.54304			−0.771520	−	0.636205i	$-0.780503\pi$
$701$	−1081.67			−1.54304			−0.771520	+	0.636205i	$0.780503\pi$
$702$	−33.3396	−	33.3396i	−0.0474923	−	0.0474923i
$703$	281.054	−	281.054i	0.399792	−	0.399792i
$704$		−	58.7532i		−	0.0834563i
$705$	684.830	−	645.057i	0.971390	−	0.914974i
$706$	−20.8305			−0.0295049
$707$	−155.282	−	155.282i	−0.219635	−	0.219635i
$708$	−29.1333	+	29.1333i	−0.0411487	+	0.0411487i
$709$			736.698i			1.03907i	0.854450	+	0.519533i	$0.173894\pi$
$709$			736.698i			1.03907i	−0.854450	+	0.519533i	$0.826106\pi$
$710$	745.966	+	22.3099i	1.05066	+	0.0314224i
$711$	56.8374			0.0799401
$712$	263.606	+	263.606i	0.370234	+	0.370234i
$713$	111.725	−	111.725i	0.156697	−	0.156697i
$714$			66.7065i			0.0934265i
$715$	1.24528	−	41.6378i	0.00174165	−	0.0582346i
$716$	−303.563			−0.423970
$717$	181.028	+	181.028i	0.252480	+	0.252480i
$718$	−92.8731	+	92.8731i	−0.129350	+	0.129350i
$719$		−	158.393i		−	0.220297i	−0.993915	−	0.110148i	$-0.964867\pi$
$719$		−	158.393i		−	0.220297i	0.993915	−	0.110148i	$-0.0351326\pi$
$720$	39.4696	+	41.9033i	0.0548189	+	0.0581990i
$721$	595.699			0.826213
$722$	199.762	+	199.762i	0.276679	+	0.276679i
$723$	20.0599	−	20.0599i	0.0277454	−	0.0277454i
$724$		−	27.3919i		−	0.0378341i
$725$	−456.550	−	27.3329i	−0.629724	−	0.0377006i
$726$	−234.660			−0.323223
$727$	−470.451	−	470.451i	−0.647112	−	0.647112i	0.305182	−	0.952294i	$-0.401283\pi$
$727$	−470.451	−	470.451i	−0.647112	−	0.647112i	−0.952294	+	0.305182i	$0.901283\pi$
$728$	15.0332	−	15.0332i	0.0206501	−	0.0206501i
$729$			789.176i			1.08255i
$730$	−462.317	+	435.466i	−0.633311	+	0.596529i
$731$	63.7364			0.0871907
$732$	56.4446	+	56.4446i	0.0771101	+	0.0771101i
$733$	−83.7227	+	83.7227i	−0.114219	+	0.114219i	−0.761906	−	0.647687i	$-0.775736\pi$
$733$	−83.7227	+	83.7227i	−0.114219	+	0.114219i	0.647687	+	0.761906i	$0.275736\pi$
$734$		−	84.6586i		−	0.115339i
$735$	63.0129	+	1.88455i	0.0857318	+	0.00256402i
$736$	−27.1293			−0.0368605
$737$	160.700	+	160.700i	0.218046	+	0.218046i
$738$	48.3892	−	48.3892i	0.0655680	−	0.0655680i
$739$			786.751i			1.06462i	0.846551	+	0.532308i	$0.178675\pi$
$739$			786.751i			1.06462i	−0.846551	+	0.532308i	$0.821325\pi$
$740$	−9.35743	+	312.880i	−0.0126452	+	0.422810i
$741$	−35.6402			−0.0480975
$742$	−142.432	−	142.432i	−0.191957	−	0.191957i
$743$	434.532	−	434.532i	0.584834	−	0.584834i	−0.351394	−	0.936228i	$-0.614292\pi$
$743$	434.532	−	434.532i	0.584834	−	0.584834i	0.936228	+	0.351394i	$0.114292\pi$
$744$			230.559i			0.309892i
$745$	−337.295	−	358.092i	−0.452745	−	0.480661i
$746$	−198.195			−0.265677
$747$	302.972	+	302.972i	0.405585	+	0.405585i
$748$	−29.8827	+	29.8827i	−0.0399501	+	0.0399501i
$749$			459.330i			0.613258i
$750$	280.330	+	335.737i	0.373774	+	0.447650i
$751$	−36.0488			−0.0480010			−0.0240005	−	0.999712i	$-0.507640\pi$
$751$	−36.0488			−0.0480010			−0.0240005	+	0.999712i	$0.507640\pi$
$752$	215.095	+	215.095i	0.286031	+	0.286031i
$753$	81.6769	−	81.6769i	0.108469	−	0.108469i
$754$			29.3501i			0.0389259i
$755$	270.596	−	254.880i	0.358405	−	0.337590i
$756$	−389.469			−0.515171
$757$	991.601	+	991.601i	1.30991	+	1.30991i	0.921478	+	0.388431i	$0.126983\pi$
$757$	991.601	+	991.601i	1.30991	+	1.30991i	0.388431	+	0.921478i	$0.373017\pi$
$758$	−267.871	+	267.871i	−0.353392	+	0.353392i
$759$		−	87.1452i		−	0.114816i
$760$	179.496	+	5.36826i	0.236179	+	0.00706350i
$761$	1444.95			1.89875			0.949375	−	0.314145i	$-0.101718\pi$
$761$	1444.95			1.89875			0.949375	+	0.314145i	$0.101718\pi$
$762$	138.603	+	138.603i	0.181894	+	0.181894i
$763$	−901.559	+	901.559i	−1.18160	+	1.18160i
$764$		−	444.673i		−	0.582032i
$765$	1.23779	−	41.3873i	0.00161802	−	0.0541011i
$766$	387.862			0.506347
$767$	−6.67869	−	6.67869i	−0.00870755	−	0.00870755i
$768$	27.9926	−	27.9926i	0.0364486	−	0.0364486i
$769$		−	630.455i		−	0.819838i	−0.912122	−	0.409919i	$-0.865557\pi$
$769$		−	630.455i		−	0.819838i	0.912122	−	0.409919i	$-0.134443\pi$
$770$	−235.930	−	250.477i	−0.306403	−	0.325295i
$771$	−1084.28			−1.40633
$772$	215.449	+	215.449i	0.279079	+	0.279079i
$773$	−333.366	+	333.366i	−0.431262	+	0.431262i	−0.889058	−	0.457795i	$-0.848639\pi$
$773$	−333.366	+	333.366i	−0.431262	+	0.431262i	0.457795	+	0.889058i	$0.348639\pi$
$774$			90.1714i			0.116501i
$775$	49.2222	−	822.173i	0.0635125	−	1.06087i
$776$	−404.926			−0.521812
$777$	−362.867	−	362.867i	−0.467010	−	0.467010i
$778$	−582.596	+	582.596i	−0.748838	+	0.748838i
$779$		−	213.478i		−	0.274041i
$780$	20.4313	−	19.2447i	0.0261940	−	0.0246727i
$781$	−775.122			−0.992473
$782$	13.7983	+	13.7983i	0.0176449	+	0.0176449i
$783$	380.190	−	380.190i	0.485555	−	0.485555i
$784$			20.3834i			0.0259992i
$785$	−724.151	−	21.6575i	−0.922485	−	0.0275892i
$786$	−530.921			−0.675472
$787$	478.649	+	478.649i	0.608194	+	0.608194i	0.942474	−	0.334280i	$-0.108493\pi$
$787$	478.649	+	478.649i	0.608194	+	0.608194i	−0.334280	+	0.942474i	$0.608493\pi$
$788$	10.0750	−	10.0750i	0.0127855	−	0.0127855i
$789$			160.785i			0.203783i
$790$	−4.17422	+	139.571i	−0.00528382	+	0.176673i
$791$	643.192			0.813138
$792$	−42.2767	−	42.2767i	−0.0533796	−	0.0533796i
$793$	−12.9397	+	12.9397i	−0.0163174	+	0.0163174i
$794$			650.988i			0.819885i
$795$	−182.333	−	193.576i	−0.229350	−	0.243492i
$796$	−254.605			−0.319856
$797$	285.605	+	285.605i	0.358350	+	0.358350i	0.863204	−	0.504855i	$-0.168454\pi$
$797$	285.605	+	285.605i	0.358350	+	0.358350i	−0.504855	+	0.863204i	$0.668454\pi$
$798$	−208.173	+	208.173i	−0.260868	+	0.260868i
$799$		−	218.801i		−	0.273843i
$800$	−105.797	+	93.8451i	−0.132247	+	0.117306i
$801$	379.363			0.473612
$802$	101.242	+	101.242i	0.126237	+	0.126237i
$803$	466.436	−	466.436i	0.580867	−	0.580867i
$804$			153.128i			0.190458i
$805$	−115.658	+	108.941i	−0.143675	+	0.135330i
$806$	−52.8549			−0.0655767
$807$	−243.127	−	243.127i	−0.301273	−	0.301273i
$808$	66.2845	−	66.2845i	0.0820353	−	0.0820353i
$809$		−	1404.45i		−	1.73603i	−0.496539	−	0.868014i	$-0.665396\pi$
$809$		−	1404.45i		−	1.73603i	0.496539	−	0.868014i	$-0.334604\pi$
$810$	−330.858	−	9.89513i	−0.408467	−	0.0122162i
$811$	−700.599			−0.863871			−0.431935	−	0.901905i	$-0.642169\pi$
$811$	−700.599			−0.863871			−0.431935	+	0.901905i	$0.642169\pi$
$812$	171.432	+	171.432i	0.211124	+	0.211124i
$813$	−653.479	+	653.479i	−0.803787	+	0.803787i
$814$		−	325.108i		−	0.399396i
$815$	−14.7317	+	492.578i	−0.0180757	+	0.604390i
$816$	−28.4748			−0.0348956
$817$	198.904	+	198.904i	0.243456	+	0.243456i
$818$	348.881	−	348.881i	0.426505	−	0.426505i
$819$		−	21.6347i		−	0.0264160i
$820$	115.272	+	122.379i	0.140575	+	0.149243i
$821$	−599.235			−0.729884			−0.364942	−	0.931030i	$-0.618911\pi$
$821$	−599.235			−0.729884			−0.364942	+	0.931030i	$0.618911\pi$
$822$	402.501	+	402.501i	0.489661	+	0.489661i
$823$	328.958	−	328.958i	0.399705	−	0.399705i	−0.478424	−	0.878129i	$-0.658792\pi$
$823$	328.958	−	328.958i	0.399705	−	0.399705i	0.878129	+	0.478424i	$0.158792\pi$
$824$			254.284i			0.308597i
$825$	−301.451	−	339.844i	−0.365395	−	0.411932i
$826$	−78.0197			−0.0944548
$827$	405.815	+	405.815i	0.490708	+	0.490708i	0.908529	−	0.417821i	$-0.137206\pi$
$827$	405.815	+	405.815i	0.490708	+	0.490708i	−0.417821	+	0.908529i	$0.637206\pi$
$828$	−19.5213	+	19.5213i	−0.0235764	+	0.0235764i
$829$			731.100i			0.881906i	0.897530	+	0.440953i	$0.145359\pi$
$829$			731.100i			0.881906i	−0.897530	+	0.440953i	$0.854641\pi$
$830$	−766.235	+	721.734i	−0.923175	+	0.869559i
$831$	1154.06			1.38877
$832$	6.41719	+	6.41719i	0.00771297	+	0.00771297i
$833$	10.3672	−	10.3672i	0.0124457	−	0.0124457i
$834$		−	31.0490i		−	0.0372291i
$835$	951.816	+	28.4664i	1.13990	+	0.0340915i
$836$	−186.511			−0.223100
$837$	684.661	+	684.661i	0.817994	+	0.817994i
$838$	−120.421	+	120.421i	−0.143700	+	0.143700i
$839$			1144.06i			1.36360i	0.731539	+	0.681800i	$0.238803\pi$
$839$			1144.06i			1.36360i	−0.731539	+	0.681800i	$0.761197\pi$
$840$	6.93091	−	231.746i	0.00825109	−	0.275888i
$841$	506.304			0.602027
$842$	−703.519	−	703.519i	−0.835534	−	0.835534i
$843$	757.842	−	757.842i	0.898983	−	0.898983i
$844$			19.1893i			0.0227361i
$845$	−574.965	−	610.416i	−0.680431	−	0.722386i
$846$	309.550			0.365898
$847$	−314.213	−	314.213i	−0.370971	−	0.370971i
$848$	60.7994	−	60.7994i	0.0716974	−	0.0716974i
$849$			392.591i			0.462416i
$850$	101.541	+	6.07909i	0.119460	+	0.00715187i
$851$	−150.119			−0.176403
$852$	−369.301	−	369.301i	−0.433452	−	0.433452i
$853$	672.838	−	672.838i	0.788790	−	0.788790i	−0.192506	−	0.981296i	$-0.561662\pi$
$853$	672.838	−	672.838i	0.788790	−	0.788790i	0.981296	+	0.192506i	$0.0616615\pi$
$854$			151.160i			0.177002i
$855$	133.021	−	125.296i	0.155581	−	0.146545i
$856$	−196.073			−0.229057
$857$	1132.64	+	1132.64i	1.32163	+	1.32163i	0.912453	+	0.409182i	$0.134186\pi$
$857$	1132.64	+	1132.64i	1.32163	+	1.32163i	0.409182	+	0.912453i	$0.365814\pi$
$858$	−20.6134	+	20.6134i	−0.0240249	+	0.0240249i
$859$		−	26.7642i		−	0.0311574i	−0.999879	−	0.0155787i	$-0.995041\pi$
$859$		−	26.7642i		−	0.0311574i	0.999879	−	0.0155787i	$-0.00495906\pi$
$860$	−221.427	−	6.62231i	−0.257473	−	0.00770037i
$861$	−275.619			−0.320115
$862$	−309.307	−	309.307i	−0.358825	−	0.358825i
$863$	151.057	−	151.057i	0.175037	−	0.175037i	−0.614151	−	0.789188i	$-0.710502\pi$
$863$	151.057	−	151.057i	0.175037	−	0.175037i	0.789188	+	0.614151i	$0.210502\pi$
$864$		−	166.251i		−	0.192421i
$865$	11.6220	−	388.599i	0.0134358	−	0.449247i
$866$	−176.529			−0.203844
$867$	−491.133	−	491.133i	−0.566474	−	0.566474i
$868$	−308.722	+	308.722i	−0.355671	+	0.355671i
$869$		−	145.026i		−	0.166889i
$870$	219.458	+	232.990i	0.252251	+	0.267804i
$871$	−35.1041			−0.0403032
$872$	−384.845	−	384.845i	−0.441336	−	0.441336i
$873$	−291.370	+	291.370i	−0.333757	+	0.333757i
$874$			86.1216i			0.0985373i
$875$	−74.1910	+	824.923i	−0.0847897	+	0.942769i
$876$	444.461			0.507375
$877$	217.435	+	217.435i	0.247930	+	0.247930i	0.820121	−	0.572191i	$-0.193906\pi$
$877$	217.435	+	217.435i	0.247930	+	0.247930i	−0.572191	+	0.820121i	$0.693906\pi$
$878$	−231.130	+	231.130i	−0.263246	+	0.263246i
$879$			551.774i			0.627729i
$880$	106.920	−	100.711i	0.121501	−	0.114444i
$881$	−238.193			−0.270367			−0.135183	−	0.990821i	$-0.543162\pi$
$881$	−238.193			−0.270367			−0.135183	+	0.990821i	$0.543162\pi$
$882$	14.6671	+	14.6671i	0.0166294	+	0.0166294i
$883$	−38.7342	+	38.7342i	−0.0438666	+	0.0438666i	−0.728700	−	0.684833i	$-0.759875\pi$
$883$	−38.7342	+	38.7342i	−0.0438666	+	0.0438666i	0.684833	+	0.728700i	$0.259875\pi$
$884$		−	6.52773i		−	0.00738431i
$885$	−102.956	−	3.07914i	−0.116334	−	0.00347925i
$886$	−1145.80			−1.29322
$887$	664.555	+	664.555i	0.749217	+	0.749217i	0.974332	−	0.225115i	$-0.0722759\pi$
$887$	664.555	+	664.555i	0.749217	+	0.749217i	−0.225115	+	0.974332i	$0.572276\pi$
$888$	154.896	−	154.896i	0.174432	−	0.174432i
$889$			371.184i			0.417529i
$890$	−27.8609	+	931.573i	−0.0313044	+	1.04671i
$891$	343.790			0.385847
$892$	462.607	+	462.607i	0.518618	+	0.518618i
$893$	682.817	−	682.817i	0.764633	−	0.764633i
$894$			344.261i			0.385080i
$895$	−520.347	−	552.431i	−0.581393	−	0.617241i
$896$	74.9649			0.0836662
$897$	9.51823	+	9.51823i	0.0106112	+	0.0106112i
$898$	58.7939	−	58.7939i	0.0654721	−	0.0654721i
$899$		−	602.733i		−	0.670449i
$900$	−8.60042	+	143.655i	−0.00955603	+	0.159617i
$901$	−61.8468			−0.0686424
$902$	−123.470	−	123.470i	−0.136885	−	0.136885i
$903$	256.803	−	256.803i	0.284389	−	0.284389i
$904$			274.557i			0.303714i
$905$	49.8484	−	46.9533i	0.0550811	−	0.0518821i
$906$	−260.145			−0.287135
$907$	−439.664	−	439.664i	−0.484746	−	0.484746i	0.421898	−	0.906643i	$-0.361364\pi$
$907$	−439.664	−	439.664i	−0.484746	−	0.484746i	−0.906643	+	0.421898i	$0.861364\pi$
$908$	590.373	−	590.373i	0.650190	−	0.650190i
$909$		−	95.3919i		−	0.104942i
$910$	53.1268	+	1.58889i	0.0583811	+	0.00174603i
$911$	636.924			0.699148			0.349574	−	0.936909i	$-0.386326\pi$
$911$	636.924			0.699148			0.349574	+	0.936909i	$0.386326\pi$
$912$	−88.8620	−	88.8620i	−0.0974364	−	0.0974364i
$913$	773.063	−	773.063i	0.846728	−	0.846728i
$914$		−	292.938i		−	0.320501i
$915$	−5.96571	+	199.472i	−0.00651990	+	0.218003i
$916$	883.581			0.964608
$917$	−710.910	−	710.910i	−0.775257	−	0.775257i
$918$	−84.5576	+	84.5576i	−0.0921107	+	0.0921107i
$919$		−	863.041i		−	0.939109i	−0.882903	−	0.469555i	$-0.844414\pi$
$919$		−	863.041i		−	0.939109i	0.882903	−	0.469555i	$-0.155586\pi$
$920$	−46.5032	−	49.3706i	−0.0505470	−	0.0536636i
$921$	552.317			0.599693
$922$	532.088	+	532.088i	0.577102	+	0.577102i
$923$	84.6609	−	84.6609i	0.0917236	−	0.0917236i
$924$			240.803i			0.260609i
$925$	−585.425	+	519.288i	−0.632892	+	0.561392i
$926$	−194.651			−0.210206
$927$	182.974	+	182.974i	0.197382	+	0.197382i
$928$	−73.1788	+	73.1788i	−0.0788564	+	0.0788564i
$929$		−	1277.97i		−	1.37564i	−0.725881	−	0.687821i	$-0.758568\pi$
$929$		−	1277.97i		−	1.37564i	0.725881	−	0.687821i	$-0.241432\pi$
$930$	−419.577	+	395.209i	−0.451158	+	0.424956i
$931$	64.7067			0.0695023
$932$	−284.714	−	284.714i	−0.305487	−	0.305487i
$933$	−950.493	+	950.493i	−1.01875	+	1.01875i
$934$		−	1297.73i		−	1.38944i
$935$	−105.604	−	3.15834i	−0.112945	−	0.00337791i
$936$	9.23515			0.00986661
$937$	1058.24	+	1058.24i	1.12939	+	1.12939i	0.990276	+	0.139116i	$0.0444261\pi$
$937$	1058.24	+	1058.24i	1.12939	+	1.12939i	0.139116	+	0.990276i	$0.455574\pi$
$938$	−205.041	+	205.041i	−0.218594	+	0.218594i
$939$		−	107.471i		−	0.114453i
$940$	−22.7338	+	760.137i	−0.0241848	+	0.808657i
$941$	812.669			0.863623			0.431812	−	0.901964i	$-0.357875\pi$
$941$	812.669			0.863623			0.431812	+	0.901964i	$0.357875\pi$
$942$	358.501	+	358.501i	0.380575	+	0.380575i
$943$	−57.0122	+	57.0122i	−0.0604584	+	0.0604584i
$944$		−	33.3040i		−	0.0352797i
$945$	−667.601	−	708.765i	−0.706456	−	0.750016i
$946$	230.081			0.243215
$947$	332.856	+	332.856i	0.351485	+	0.351485i	0.860662	−	0.509177i	$-0.170050\pi$
$947$	332.856	+	332.856i	0.351485	+	0.351485i	−0.509177	+	0.860662i	$0.670050\pi$
$948$	69.0968	−	69.0968i	0.0728869	−	0.0728869i
$949$			101.891i			0.107367i
$950$	297.910	+	335.852i	0.313589	+	0.353529i
$951$	−1297.84			−1.36472
$952$	−38.1281	−	38.1281i	−0.0400506	−	0.0400506i
$953$	54.2554	−	54.2554i	0.0569312	−	0.0569312i	−0.678068	−	0.734999i	$-0.737183\pi$
$953$	54.2554	−	54.2554i	0.0569312	−	0.0569312i	0.734999	+	0.678068i	$0.237183\pi$
$954$		−	87.4980i		−	0.0917170i
$955$	809.225	−	762.227i	0.847356	−	0.798144i
$956$	−206.945			−0.216469
$957$	−235.066	−	235.066i	−0.245628	−	0.245628i
$958$	67.3465	−	67.3465i	0.0702991	−	0.0702991i
$959$			1077.91i			1.12399i
$960$	98.9244	+	2.95858i	0.103046	+	0.00308185i
$961$	124.426			0.129476
$962$	35.5092	+	35.5092i	0.0369119	+	0.0369119i
$963$	−141.087	+	141.087i	−0.146508	+	0.146508i
$964$			22.9317i			0.0237881i
$965$	−22.7711	+	761.387i	−0.0235970	+	0.789002i
$966$	111.191			0.115104
$967$	−1089.02	−	1089.02i	−1.12619	−	1.12619i	−0.990792	−	0.135395i	$-0.956770\pi$
$967$	−1089.02	−	1089.02i	−1.12619	−	1.12619i	−0.135395	−	0.990792i	$-0.543230\pi$
$968$	134.127	−	134.127i	0.138561	−	0.138561i
$969$			90.3927i			0.0932846i
$970$	−694.096	−	736.894i	−0.715563	−	0.759684i
$971$	781.891			0.805243			0.402621	−	0.915367i	$-0.368099\pi$
$971$	781.891			0.805243			0.402621	+	0.915367i	$0.368099\pi$
$972$	−210.269	−	210.269i	−0.216326	−	0.216326i
$973$	41.5751	−	41.5751i	0.0427288	−	0.0427288i
$974$			148.899i			0.152874i
$975$	70.0439	+	4.19342i	0.0718399	+	0.00430094i
$976$	−64.5252			−0.0661119
$977$	92.3138	+	92.3138i	0.0944870	+	0.0944870i	0.752770	−	0.658283i	$-0.228717\pi$
$977$	92.3138	+	92.3138i	0.0944870	+	0.0944870i	−0.658283	+	0.752770i	$0.728717\pi$
$978$	243.858	−	243.858i	0.249343	−	0.249343i
$979$		−	967.983i		−	0.988746i
$980$	−37.0941	+	34.9398i	−0.0378511	+	0.0356528i
$981$	−553.841			−0.564568
$982$	767.159	+	767.159i	0.781221	+	0.781221i
$983$	−458.204	+	458.204i	−0.466128	+	0.466128i	−0.900658	−	0.434529i	$-0.856915\pi$
$983$	−458.204	+	458.204i	−0.466128	+	0.466128i	0.434529	+	0.900658i	$0.356915\pi$
$984$		−	117.653i		−	0.119566i
$985$	35.6044	+	1.06484i	0.0361466	+	0.00108105i
$986$	74.4394			0.0754963
$987$	−881.580	−	881.580i	−0.893191	−	0.893191i
$988$	20.3713	−	20.3713i	0.0206187	−	0.0206187i
$989$		−	106.240i		−	0.107422i
$990$	4.46828	−	149.404i	0.00451342	−	0.150913i
$991$	988.103			0.997077			0.498538	−	0.866868i	$-0.333870\pi$
$991$	988.103			0.997077			0.498538	+	0.866868i	$0.333870\pi$
$992$	−131.783	−	131.783i	−0.132846	−	0.132846i
$993$	−584.735	+	584.735i	−0.588857	+	0.588857i
$994$		−	988.999i		−	0.994969i
$995$	−436.426	−	463.336i	−0.438620	−	0.465664i
$996$	736.641			0.739599
$997$	−105.423	−	105.423i	−0.105741	−	0.105741i	0.652257	−	0.757998i	$-0.273822\pi$
$997$	−105.423	−	105.423i	−0.105741	−	0.105741i	−0.757998	+	0.652257i	$0.773822\pi$
$998$	530.092	−	530.092i	0.531154	−	0.531154i
$999$		−	919.945i		−	0.920866i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.b.47.8	✓	24
5.3	odd	4	inner	230.3.f.b.93.8	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.b.47.8	✓	24	1.1	even	1	trivial
230.3.f.b.93.8	yes	24	5.3	odd	4	inner

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.74954 - 1.74954i) q^{3} +2.00000i q^{4} +(-3.63965 + 3.42826i) q^{5} +3.49907 q^{6} +(4.68530 + 4.68530i) q^{7} +(-2.00000 + 2.00000i) q^{8} +2.87825i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.74954 - 1.74954i) q^{3} +2.00000i q^{4} +(-3.63965 + 3.42826i) q^{5} +3.49907 q^{6} +(4.68530 + 4.68530i) q^{7} +(-2.00000 + 2.00000i) q^{8} +2.87825i q^{9} +(-7.06791 - 0.211383i) q^{10} +7.34415 q^{11} +(3.49907 + 3.49907i) q^{12} +(-0.802148 + 0.802148i) q^{13} +9.37061i q^{14} +(-0.369822 + 12.3656i) q^{15} -4.00000 q^{16} +(2.03445 + 2.03445i) q^{17} +(-2.87825 + 2.87825i) q^{18} +12.6979i q^{19} +(-6.85652 - 7.27929i) q^{20} +16.3942 q^{21} +(7.34415 + 7.34415i) q^{22} +(3.39116 - 3.39116i) q^{23} +6.99814i q^{24} +(1.49404 - 24.9553i) q^{25} -1.60430 q^{26} +(20.7814 + 20.7814i) q^{27} +(-9.37061 + 9.37061i) q^{28} -18.2947i q^{29} +(-12.7354 + 11.9957i) q^{30} +32.9458 q^{31} +(-4.00000 - 4.00000i) q^{32} +(12.8489 - 12.8489i) q^{33} +4.06891i q^{34} +(-33.1153 - 0.990394i) q^{35} -5.75651 q^{36} +(-22.1338 - 22.1338i) q^{37} +(-12.6979 + 12.6979i) q^{38} +2.80677i q^{39} +(0.422766 - 14.1358i) q^{40} -16.8120 q^{41} +(16.3942 + 16.3942i) q^{42} +(15.6643 - 15.6643i) q^{43} +14.6883i q^{44} +(-9.86741 - 10.4758i) q^{45} +6.78233 q^{46} +(-53.7739 - 53.7739i) q^{47} +(-6.99814 + 6.99814i) q^{48} -5.09584i q^{49} +(26.4494 - 23.4613i) q^{50} +7.11869 q^{51} +(-1.60430 - 1.60430i) q^{52} +(-15.1999 + 15.1999i) q^{53} +41.5628i q^{54} +(-26.7301 + 25.1777i) q^{55} -18.7412 q^{56} +(22.2155 + 22.2155i) q^{57} +(18.2947 - 18.2947i) q^{58} +8.32600i q^{59} +(-24.7311 - 0.739644i) q^{60} +16.1313 q^{61} +(32.9458 + 32.9458i) q^{62} +(-13.4855 + 13.4855i) q^{63} -8.00000i q^{64} +(0.169561 - 5.66951i) q^{65} +25.6977 q^{66} +(21.8813 + 21.8813i) q^{67} +(-4.06891 + 4.06891i) q^{68} -11.8659i q^{69} +(-32.1249 - 34.1057i) q^{70} -105.543 q^{71} +(-5.75651 - 5.75651i) q^{72} +(63.5112 - 63.5112i) q^{73} -44.2677i q^{74} +(-41.0463 - 46.2741i) q^{75} -25.3959 q^{76} +(34.4096 + 34.4096i) q^{77} +(-2.80677 + 2.80677i) q^{78} -19.7472i q^{79} +(14.5586 - 13.7130i) q^{80} +46.8114 q^{81} +(-16.8120 - 16.8120i) q^{82} +(105.262 - 105.262i) q^{83} +32.7884i q^{84} +(-14.3793 - 0.430049i) q^{85} +31.3285 q^{86} +(-32.0072 - 32.0072i) q^{87} +(-14.6883 + 14.6883i) q^{88} -131.803i q^{89} +(0.608414 - 20.3432i) q^{90} -7.51662 q^{91} +(6.78233 + 6.78233i) q^{92} +(57.6398 - 57.6398i) q^{93} -107.548i q^{94} +(-43.5319 - 46.2160i) q^{95} -13.9963 q^{96} +(101.232 + 101.232i) q^{97} +(5.09584 - 5.09584i) q^{98} +21.1383i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8}+O(q^{10}) \) 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8	\( 24 q + 24 q^{2} + 4 q^{5} + 8 q^{7} - 48 q^{8} + 16 q^{10} - 8 q^{11} - 24 q^{13} - 24 q^{15} - 96 q^{16} - 12 q^{17} + 88 q^{18} + 24 q^{20} - 24 q^{21} - 8 q^{22} - 48 q^{25} - 48 q^{26} + 60 q^{27} - 16 q^{28} + 12 q^{30} + 12 q^{31} - 96 q^{32} + 92 q^{33} + 48 q^{35} + 176 q^{36} - 100 q^{37} + 56 q^{38} + 16 q^{40} + 116 q^{41} - 24 q^{42} - 120 q^{43} - 204 q^{45} + 56 q^{47} - 104 q^{50} + 176 q^{51} - 48 q^{52} - 192 q^{53} + 180 q^{55} - 32 q^{56} + 28 q^{58} + 72 q^{60} - 152 q^{61} + 12 q^{62} + 364 q^{63} + 40 q^{65} + 184 q^{66} + 72 q^{67} + 24 q^{68} - 100 q^{70} - 28 q^{71} + 176 q^{72} - 364 q^{73} + 276 q^{75} + 112 q^{76} - 92 q^{77} - 32 q^{78} - 16 q^{80} - 440 q^{81} + 116 q^{82} + 360 q^{83} + 232 q^{85} - 240 q^{86} + 176 q^{87} + 16 q^{88} - 84 q^{90} - 432 q^{91} + 192 q^{93} + 144 q^{95} - 432 q^{97} - 484 q^{98}+O(q^{100}) \) 24 * q + 24 * q^2 + 4 * q^5 + 8 * q^7 - 48 * q^8 + 16 * q^10 - 8 * q^11 - 24 * q^13 - 24 * q^15 - 96 * q^16 - 12 * q^17 + 88 * q^18 + 24 * q^20 - 24 * q^21 - 8 * q^22 - 48 * q^25 - 48 * q^26 + 60 * q^27 - 16 * q^28 + 12 * q^30 + 12 * q^31 - 96 * q^32 + 92 * q^33 + 48 * q^35 + 176 * q^36 - 100 * q^37 + 56 * q^38 + 16 * q^40 + 116 * q^41 - 24 * q^42 - 120 * q^43 - 204 * q^45 + 56 * q^47 - 104 * q^50 + 176 * q^51 - 48 * q^52 - 192 * q^53 + 180 * q^55 - 32 * q^56 + 28 * q^58 + 72 * q^60 - 152 * q^61 + 12 * q^62 + 364 * q^63 + 40 * q^65 + 184 * q^66 + 72 * q^67 + 24 * q^68 - 100 * q^70 - 28 * q^71 + 176 * q^72 - 364 * q^73 + 276 * q^75 + 112 * q^76 - 92 * q^77 - 32 * q^78 - 16 * q^80 - 440 * q^81 + 116 * q^82 + 360 * q^83 + 232 * q^85 - 240 * q^86 + 176 * q^87 + 16 * q^88 - 84 * q^90 - 432 * q^91 + 192 * q^93 + 144 * q^95 - 432 * q^97 - 484 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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