LMFDB - Embedded newform 230.3.f.b.47.9

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			47.9
Character	$\chi$	$=$	230.47
Dual form			230.3.f.b.93.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.00000i) q^{2} +(1.83776 - 1.83776i) q^{3} +2.00000i q^{4} +(4.99936 + 0.0803026i) q^{5} +3.67552 q^{6} +(5.10553 + 5.10553i) q^{7} +(-2.00000 + 2.00000i) q^{8} +2.24526i q^{9} +O(q^{10})$	\(q+(1.00000 + 1.00000i) q^{2} +(1.83776 - 1.83776i) q^{3} +2.00000i q^{4} +(4.99936 + 0.0803026i) q^{5} +3.67552 q^{6} +(5.10553 + 5.10553i) q^{7} +(-2.00000 + 2.00000i) q^{8} +2.24526i q^{9} +(4.91905 + 5.07966i) q^{10} -18.3030 q^{11} +(3.67552 + 3.67552i) q^{12} +(14.0303 - 14.0303i) q^{13} +10.2111i q^{14} +(9.33520 - 9.04005i) q^{15} -4.00000 q^{16} +(2.44563 + 2.44563i) q^{17} +(-2.24526 + 2.24526i) q^{18} -9.65125i q^{19} +(-0.160605 + 9.99871i) q^{20} +18.7655 q^{21} +(-18.3030 - 18.3030i) q^{22} +(-3.39116 + 3.39116i) q^{23} +7.35105i q^{24} +(24.9871 + 0.802922i) q^{25} +28.0605 q^{26} +(20.6661 + 20.6661i) q^{27} +(-10.2111 + 10.2111i) q^{28} -2.47273i q^{29} +(18.3752 + 0.295154i) q^{30} -6.19311 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-33.6366 + 33.6366i) q^{33} +4.89127i q^{34} +(25.1144 + 25.9343i) q^{35} -4.49053 q^{36} +(-38.0892 - 38.0892i) q^{37} +(9.65125 - 9.65125i) q^{38} -51.5686i q^{39} +(-10.1593 + 9.83811i) q^{40} -50.7049 q^{41} +(18.7655 + 18.7655i) q^{42} +(-14.7480 + 14.7480i) q^{43} -36.6061i q^{44} +(-0.180300 + 11.2249i) q^{45} -6.78233 q^{46} +(-23.7610 - 23.7610i) q^{47} +(-7.35105 + 7.35105i) q^{48} +3.13285i q^{49} +(24.1842 + 25.7900i) q^{50} +8.98898 q^{51} +(28.0605 + 28.0605i) q^{52} +(51.8572 - 51.8572i) q^{53} +41.3322i q^{54} +(-91.5034 - 1.46978i) q^{55} -20.4221 q^{56} +(-17.7367 - 17.7367i) q^{57} +(2.47273 - 2.47273i) q^{58} +16.9105i q^{59} +(18.0801 + 18.6704i) q^{60} -25.6655 q^{61} +(-6.19311 - 6.19311i) q^{62} +(-11.4633 + 11.4633i) q^{63} -8.00000i q^{64} +(71.2689 - 69.0156i) q^{65} -67.2733 q^{66} +(44.7937 + 44.7937i) q^{67} +(-4.89127 + 4.89127i) q^{68} +12.4643i q^{69} +(-0.819974 + 51.0487i) q^{70} -36.0845 q^{71} +(-4.49053 - 4.49053i) q^{72} +(-15.7669 + 15.7669i) q^{73} -76.1784i q^{74} +(47.3959 - 44.4448i) q^{75} +19.3025 q^{76} +(-93.4467 - 93.4467i) q^{77} +(51.5686 - 51.5686i) q^{78} -15.5648i q^{79} +(-19.9974 - 0.321210i) q^{80} +55.7514 q^{81} +(-50.7049 - 50.7049i) q^{82} +(-96.3047 + 96.3047i) q^{83} +37.5310i q^{84} +(12.0302 + 12.4230i) q^{85} -29.4960 q^{86} +(-4.54429 - 4.54429i) q^{87} +(36.6061 - 36.6061i) q^{88} +26.4910i q^{89} +(-11.4052 + 11.0446i) q^{90} +143.264 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-11.3815 + 11.3815i) q^{93} -47.5220i q^{94} +(0.775021 - 48.2500i) q^{95} -14.7021 q^{96} +(-94.9705 - 94.9705i) q^{97} +(-3.13285 + 3.13285i) q^{98} -41.0951i 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
$3$	1.83776	−	1.83776i	0.612587	−	0.612587i	−0.331032	−	0.943619i	$-0.607397\pi$
$3$	1.83776	−	1.83776i	0.612587	−	0.612587i	0.943619	+	0.331032i	$0.107397\pi$
$4$			2.00000i			0.500000i
$5$	4.99936	+	0.0803026i	0.999871	+	0.0160605i
$5$	4.99936	+	0.0803026i	0.999871	+	0.0160605i
$6$	3.67552			0.612587
$7$	5.10553	+	5.10553i	0.729361	+	0.729361i	0.970493	−	0.241131i	$-0.0775184\pi$
$7$	5.10553	+	5.10553i	0.729361	+	0.729361i	−0.241131	+	0.970493i	$0.577518\pi$
$8$	−2.00000	+	2.00000i	−0.250000	+	0.250000i
$9$			2.24526i			0.249474i
$10$	4.91905	+	5.07966i	0.491905	+	0.507966i
$11$	−18.3030			−1.66391			−0.831957	−	0.554841i	$-0.812779\pi$
$11$	−18.3030			−1.66391			−0.831957	+	0.554841i	$0.812779\pi$
$12$	3.67552	+	3.67552i	0.306294	+	0.306294i
$13$	14.0303	−	14.0303i	1.07925	−	1.07925i	0.0826745	−	0.996577i	$-0.473654\pi$
$13$	14.0303	−	14.0303i	1.07925	−	1.07925i	0.996577	−	0.0826745i	$-0.0263462\pi$
$14$			10.2111i			0.729361i
$15$	9.33520	−	9.04005i	0.622347	−	0.602670i
$16$	−4.00000			−0.250000
$17$	2.44563	+	2.44563i	0.143861	+	0.143861i	0.775369	−	0.631508i	$-0.217564\pi$
$17$	2.44563	+	2.44563i	0.143861	+	0.143861i	−0.631508	+	0.775369i	$0.717564\pi$
$18$	−2.24526	+	2.24526i	−0.124737	+	0.124737i
$19$		−	9.65125i		−	0.507961i	−0.967209	−	0.253980i	$-0.918260\pi$
$19$		−	9.65125i		−	0.507961i	0.967209	−	0.253980i	$-0.0817398\pi$
$20$	−0.160605	+	9.99871i	−0.00803026	+	0.499936i
$21$	18.7655			0.893595
$22$	−18.3030	−	18.3030i	−0.831957	−	0.831957i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$23$	−3.39116	+	3.39116i	−0.147442	+	0.147442i
$24$			7.35105i			0.306294i
$25$	24.9871	+	0.802922i	0.999484	+	0.0321169i
$26$	28.0605			1.07925
$27$	20.6661	+	20.6661i	0.765412	+	0.765412i
$28$	−10.2111	+	10.2111i	−0.364681	+	0.364681i
$29$		−	2.47273i		−	0.0852666i	−0.999091	−	0.0426333i	$-0.986425\pi$
$29$		−	2.47273i		−	0.0852666i	0.999091	−	0.0426333i	$-0.0135747\pi$
$30$	18.3752	+	0.295154i	0.612508	+	0.00983847i
$31$	−6.19311			−0.199778			−0.0998888	−	0.994999i	$-0.531849\pi$
$31$	−6.19311			−0.199778			−0.0998888	+	0.994999i	$0.531849\pi$
$32$	−4.00000	−	4.00000i	−0.125000	−	0.125000i
$33$	−33.6366	+	33.6366i	−1.01929	+	1.01929i
$34$			4.89127i			0.143861i
$35$	25.1144	+	25.9343i	0.717553	+	0.740981i
$36$	−4.49053			−0.124737
$37$	−38.0892	−	38.0892i	−1.02944	−	1.02944i	−0.999553	−	0.0298846i	$-0.990486\pi$
$37$	−38.0892	−	38.0892i	−1.02944	−	1.02944i	−0.0298846	−	0.999553i	$-0.509514\pi$
$38$	9.65125	−	9.65125i	0.253980	−	0.253980i
$39$		−	51.5686i		−	1.32227i
$40$	−10.1593	+	9.83811i	−0.253983	+	0.245953i
$41$	−50.7049			−1.23670			−0.618352	−	0.785901i	$-0.712199\pi$
$41$	−50.7049			−1.23670			−0.618352	+	0.785901i	$0.712199\pi$
$42$	18.7655	+	18.7655i	0.446797	+	0.446797i
$43$	−14.7480	+	14.7480i	−0.342977	+	0.342977i	−0.857485	−	0.514508i	$-0.827974\pi$
$43$	−14.7480	+	14.7480i	−0.342977	+	0.342977i	0.514508	+	0.857485i	$0.327974\pi$
$44$		−	36.6061i		−	0.831957i
$45$	−0.180300	+	11.2249i	−0.00400668	+	0.249441i
$46$	−6.78233			−0.147442
$47$	−23.7610	−	23.7610i	−0.505553	−	0.505553i	0.407605	−	0.913158i	$-0.366364\pi$
$47$	−23.7610	−	23.7610i	−0.505553	−	0.505553i	−0.913158	+	0.407605i	$0.866364\pi$
$48$	−7.35105	+	7.35105i	−0.153147	+	0.153147i
$49$			3.13285i			0.0639357i
$50$	24.1842	+	25.7900i	0.483684	+	0.515801i
$51$	8.98898			0.176255
$52$	28.0605	+	28.0605i	0.539626	+	0.539626i
$53$	51.8572	−	51.8572i	0.978438	−	0.978438i	−0.0213348	−	0.999772i	$-0.506792\pi$
$53$	51.8572	−	51.8572i	0.978438	−	0.978438i	0.999772	+	0.0213348i	$0.00679160\pi$
$54$			41.3322i			0.765412i
$55$	−91.5034	−	1.46978i	−1.66370	−	0.0267233i
$56$	−20.4221			−0.364681
$57$	−17.7367	−	17.7367i	−0.311170	−	0.311170i
$58$	2.47273	−	2.47273i	0.0426333	−	0.0426333i
$59$			16.9105i			0.286619i	0.989678	+	0.143309i	$0.0457744\pi$
$59$			16.9105i			0.286619i	−0.989678	+	0.143309i	$0.954226\pi$
$60$	18.0801	+	18.6704i	0.301335	+	0.311173i
$61$	−25.6655			−0.420746			−0.210373	−	0.977621i	$-0.567468\pi$
$61$	−25.6655			−0.420746			−0.210373	+	0.977621i	$0.567468\pi$
$62$	−6.19311	−	6.19311i	−0.0998888	−	0.0998888i
$63$	−11.4633	+	11.4633i	−0.181956	+	0.181956i
$64$		−	8.00000i		−	0.125000i
$65$	71.2689	−	69.0156i	1.09645	−	1.06178i
$66$	−67.2733			−1.01929
$67$	44.7937	+	44.7937i	0.668562	+	0.668562i	0.957383	−	0.288821i	$-0.0932632\pi$
$67$	44.7937	+	44.7937i	0.668562	+	0.668562i	−0.288821	+	0.957383i	$0.593263\pi$
$68$	−4.89127	+	4.89127i	−0.0719304	+	0.0719304i
$69$			12.4643i			0.180642i
$70$	−0.819974	+	51.0487i	−0.0117139	+	0.729267i
$71$	−36.0845			−0.508232			−0.254116	−	0.967174i	$-0.581785\pi$
$71$	−36.0845			−0.508232			−0.254116	+	0.967174i	$0.581785\pi$
$72$	−4.49053	−	4.49053i	−0.0623684	−	0.0623684i
$73$	−15.7669	+	15.7669i	−0.215985	+	0.215985i	−0.806804	−	0.590819i	$-0.798805\pi$
$73$	−15.7669	+	15.7669i	−0.215985	+	0.215985i	0.590819	+	0.806804i	$0.298805\pi$
$74$		−	76.1784i		−	1.02944i
$75$	47.3959	−	44.4448i	0.631946	−	0.592597i
$76$	19.3025			0.253980
$77$	−93.4467	−	93.4467i	−1.21359	−	1.21359i
$78$	51.5686	−	51.5686i	0.661135	−	0.661135i
$79$		−	15.5648i		−	0.197023i	−0.995136	−	0.0985115i	$-0.968592\pi$
$79$		−	15.5648i		−	0.197023i	0.995136	−	0.0985115i	$-0.0314081\pi$
$80$	−19.9974	−	0.321210i	−0.249968	−	0.00401513i
$81$	55.7514			0.688289
$82$	−50.7049	−	50.7049i	−0.618352	−	0.618352i
$83$	−96.3047	+	96.3047i	−1.16030	+	1.16030i	−0.175887	+	0.984410i	$0.556279\pi$
$83$	−96.3047	+	96.3047i	−1.16030	+	1.16030i	−0.984410	+	0.175887i	$0.943721\pi$
$84$			37.5310i			0.446797i
$85$	12.0302	+	12.4230i	0.141532	+	0.146153i
$86$	−29.4960			−0.342977
$87$	−4.54429	−	4.54429i	−0.0522332	−	0.0522332i
$88$	36.6061	−	36.6061i	0.415978	−	0.415978i
$89$			26.4910i			0.297651i	0.988863	+	0.148826i	$0.0475493\pi$
$89$			26.4910i			0.297651i	−0.988863	+	0.148826i	$0.952451\pi$
$90$	−11.4052	+	11.0446i	−0.126724	+	0.122717i
$91$	143.264			1.57433
$92$	−6.78233	−	6.78233i	−0.0737210	−	0.0737210i
$93$	−11.3815	+	11.3815i	−0.122381	+	0.122381i
$94$		−	47.5220i		−	0.505553i
$95$	0.775021	−	48.2500i	0.00815811	−	0.507895i
$96$	−14.7021			−0.153147
$97$	−94.9705	−	94.9705i	−0.979078	−	0.979078i	0.0207078	−	0.999786i	$-0.493408\pi$
$97$	−94.9705	−	94.9705i	−0.979078	−	0.979078i	−0.999786	+	0.0207078i	$0.993408\pi$
$98$	−3.13285	+	3.13285i	−0.0319679	+	0.0319679i
$99$		−	41.0951i		−	0.415102i
$100$	−1.60584	+	49.9742i	−0.0160584	+	0.499742i
$101$	128.681			1.27407			0.637033	−	0.770837i	$-0.280162\pi$
$101$	128.681			1.27407			0.637033	+	0.770837i	$0.280162\pi$
$102$	8.98898	+	8.98898i	0.0881273	+	0.0881273i
$103$	−15.4607	+	15.4607i	−0.150104	+	0.150104i	−0.778164	−	0.628061i	$-0.783849\pi$
$103$	−15.4607	+	15.4607i	−0.150104	+	0.150104i	0.628061	+	0.778164i	$0.283849\pi$
$104$			56.1211i			0.539626i
$105$	93.8154	+	1.50692i	0.893480	+	0.0143516i
$106$	103.714			0.978438
$107$	−132.427	−	132.427i	−1.23764	−	1.23764i	−0.960965	−	0.276672i	$-0.910769\pi$
$107$	−132.427	−	132.427i	−1.23764	−	1.23764i	−0.276672	−	0.960965i	$-0.589231\pi$
$108$	−41.3322	+	41.3322i	−0.382706	+	0.382706i
$109$		−	131.307i		−	1.20465i	−0.798249	−	0.602327i	$-0.794240\pi$
$109$		−	131.307i		−	1.20465i	0.798249	−	0.602327i	$-0.205760\pi$
$110$	−90.0336	−	92.9732i	−0.818488	−	0.845211i
$111$	−139.998			−1.26124
$112$	−20.4221	−	20.4221i	−0.182340	−	0.182340i
$113$	−153.282	+	153.282i	−1.35648	+	1.35648i	−0.478256	+	0.878221i	$0.658731\pi$
$113$	−153.282	+	153.282i	−1.35648	+	1.35648i	−0.878221	+	0.478256i	$0.841269\pi$
$114$		−	35.4734i		−	0.311170i
$115$	−17.2260	+	16.6813i	−0.149791	+	0.145055i
$116$	4.94546			0.0426333
$117$	31.5016	+	31.5016i	0.269245	+	0.269245i
$118$	−16.9105	+	16.9105i	−0.143309	+	0.143309i
$119$			24.9725i			0.209853i
$120$	−0.590308	+	36.7505i	−0.00491923	+	0.306254i
$121$	214.001			1.76861
$122$	−25.6655	−	25.6655i	−0.210373	−	0.210373i
$123$	−93.1835	+	93.1835i	−0.757589	+	0.757589i
$124$		−	12.3862i		−	0.0998888i
$125$	124.855	+	6.02062i	0.998839	+	0.0481650i
$126$	−22.9265			−0.181956
$127$	−13.1904	−	13.1904i	−0.103861	−	0.103861i	0.653267	−	0.757128i	$-0.273398\pi$
$127$	−13.1904	−	13.1904i	−0.103861	−	0.103861i	−0.757128	+	0.653267i	$0.773398\pi$
$128$	8.00000	−	8.00000i	0.0625000	−	0.0625000i
$129$			54.2067i			0.420207i
$130$	140.285	+	2.25333i	1.07911	+	0.0173333i
$131$	88.7690			0.677626			0.338813	−	0.940854i	$-0.389975\pi$
$131$	88.7690			0.677626			0.338813	+	0.940854i	$0.389975\pi$
$132$	−67.2733	−	67.2733i	−0.509646	−	0.509646i
$133$	49.2747	−	49.2747i	0.370487	−	0.370487i
$134$			89.5874i			0.668562i
$135$	101.658	+	104.977i	0.753020	+	0.777606i
$136$	−9.78253			−0.0719304
$137$	180.247	+	180.247i	1.31567	+	1.31567i	0.917167	+	0.398502i	$0.130470\pi$
$137$	180.247	+	180.247i	1.31567	+	1.31567i	0.398502	+	0.917167i	$0.369530\pi$
$138$	−12.4643	+	12.4643i	−0.0903211	+	0.0903211i
$139$			136.072i			0.978932i	0.872022	+	0.489466i	$0.162808\pi$
$139$			136.072i			0.978932i	−0.872022	+	0.489466i	$0.837192\pi$
$140$	−51.8687	+	50.2287i	−0.370491	+	0.358777i
$141$	−87.3341			−0.619391
$142$	−36.0845	−	36.0845i	−0.254116	−	0.254116i
$143$	−256.797	+	256.797i	−1.79578	+	1.79578i
$144$		−	8.98105i		−	0.0623684i
$145$	0.198567	−	12.3621i	0.00136943	−	0.0852556i
$146$	−31.5339			−0.215985
$147$	5.75743	+	5.75743i	0.0391662	+	0.0391662i
$148$	76.1784	−	76.1784i	0.514719	−	0.514719i
$149$			271.727i			1.82367i	0.410557	+	0.911835i	$0.365334\pi$
$149$			271.727i			1.82367i	−0.410557	+	0.911835i	$0.634666\pi$
$150$	91.8407	+	2.95116i	0.612271	+	0.0196744i
$151$	93.7692			0.620988			0.310494	−	0.950575i	$-0.399505\pi$
$151$	93.7692			0.620988			0.310494	+	0.950575i	$0.399505\pi$
$152$	19.3025	+	19.3025i	0.126990	+	0.126990i
$153$	−5.49109	+	5.49109i	−0.0358895	+	0.0358895i
$154$		−	186.893i		−	1.21359i
$155$	−30.9615	−	0.497323i	−0.199752	−	0.00320853i
$156$	103.137			0.661135
$157$	59.7004	+	59.7004i	0.380257	+	0.380257i	0.871195	−	0.490937i	$-0.163346\pi$
$157$	59.7004	+	59.7004i	0.380257	+	0.380257i	−0.490937	+	0.871195i	$0.663346\pi$
$158$	15.5648	−	15.5648i	0.0985115	−	0.0985115i
$159$		−	190.602i		−	1.19876i
$160$	−19.6762	−	20.3186i	−0.122976	−	0.126991i
$161$	−34.6274			−0.215077
$162$	55.7514	+	55.7514i	0.344145	+	0.344145i
$163$	36.7559	−	36.7559i	0.225496	−	0.225496i	−0.585312	−	0.810808i	$-0.699028\pi$
$163$	36.7559	−	36.7559i	0.225496	−	0.225496i	0.810808	+	0.585312i	$0.199028\pi$
$164$		−	101.410i		−	0.618352i
$165$	−170.863	+	165.460i	−1.03553	+	1.00279i
$166$	−192.609			−1.16030
$167$	174.965	+	174.965i	1.04769	+	1.04769i	0.998804	+	0.0488887i	$0.0155680\pi$
$167$	174.965	+	174.965i	1.04769	+	1.04769i	0.0488887	+	0.998804i	$0.484432\pi$
$168$	−37.5310	+	37.5310i	−0.223399	+	0.223399i
$169$		−	224.697i		−	1.32957i
$170$	−0.392781	+	24.4532i	−0.00231048	+	0.143842i
$171$	21.6696			0.126723
$172$	−29.4960	−	29.4960i	−0.171489	−	0.171489i
$173$	86.9948	−	86.9948i	0.502860	−	0.502860i	−0.409466	−	0.912326i	$-0.634285\pi$
$173$	86.9948	−	86.9948i	0.502860	−	0.502860i	0.912326	+	0.409466i	$0.134285\pi$
$174$		−	9.08858i		−	0.0522332i
$175$	123.473	+	131.672i	0.705560	+	0.752410i
$176$	73.2122			0.415978
$177$	31.0775	+	31.0775i	0.175579	+	0.175579i
$178$	−26.4910	+	26.4910i	−0.148826	+	0.148826i
$179$		−	318.823i		−	1.78113i	−0.454852	−	0.890567i	$-0.650308\pi$
$179$		−	318.823i		−	1.78113i	0.454852	−	0.890567i	$-0.349692\pi$
$180$	−22.4497	−	0.360601i	−0.124721	−	0.00200334i
$181$	345.259			1.90751			0.953754	−	0.300589i	$-0.0971832\pi$
$181$	345.259			1.90751			0.953754	+	0.300589i	$0.0971832\pi$
$182$	143.264	+	143.264i	0.787164	+	0.787164i
$183$	−47.1670	+	47.1670i	−0.257743	+	0.257743i
$184$		−	13.5647i		−	0.0737210i
$185$	−187.363	−	193.480i	−1.01277	−	1.04584i
$186$	−22.7629			−0.122381
$187$	−44.7625	−	44.7625i	−0.239372	−	0.239372i
$188$	47.5220	−	47.5220i	0.252777	−	0.252777i
$189$			211.023i			1.11652i
$190$	49.0251	−	47.4750i	0.258027	−	0.249869i
$191$	−81.7982			−0.428263			−0.214131	−	0.976805i	$-0.568692\pi$
$191$	−81.7982			−0.428263			−0.214131	+	0.976805i	$0.568692\pi$
$192$	−14.7021	−	14.7021i	−0.0765734	−	0.0765734i
$193$	167.652	−	167.652i	0.868662	−	0.868662i	−0.123662	−	0.992324i	$-0.539464\pi$
$193$	167.652	−	167.652i	0.868662	−	0.868662i	0.992324	+	0.123662i	$0.0394639\pi$
$194$		−	189.941i		−	0.979078i
$195$	4.14109	−	257.810i	0.0212364	−	1.32210i
$196$	−6.26570			−0.0319679
$197$	8.30626	+	8.30626i	0.0421637	+	0.0421637i	0.727874	−	0.685711i	$-0.240508\pi$
$197$	8.30626	+	8.30626i	0.0421637	+	0.0421637i	−0.685711	+	0.727874i	$0.740508\pi$
$198$	41.0951	−	41.0951i	0.207551	−	0.207551i
$199$			165.150i			0.829897i	0.909845	+	0.414949i	$0.136200\pi$
$199$			165.150i			0.829897i	−0.909845	+	0.414949i	$0.863800\pi$
$200$	−51.5801	+	48.3684i	−0.257900	+	0.241842i
$201$	164.640			0.819106
$202$	128.681	+	128.681i	0.637033	+	0.637033i
$203$	12.6246	−	12.6246i	0.0621901	−	0.0621901i
$204$			17.9780i			0.0881273i
$205$	−253.492	−	4.07173i	−1.23654	−	0.0198621i
$206$	−30.9214			−0.150104
$207$	−7.61406	−	7.61406i	−0.0367829	−	0.0367829i
$208$	−56.1211	+	56.1211i	−0.269813	+	0.269813i
$209$			176.647i			0.845202i
$210$	92.3084	+	95.3223i	0.439564	+	0.453916i
$211$	311.748			1.47748			0.738740	−	0.673990i	$-0.235421\pi$
$211$	311.748			1.47748			0.738740	+	0.673990i	$0.235421\pi$
$212$	103.714	+	103.714i	0.489219	+	0.489219i
$213$	−66.3147	+	66.3147i	−0.311337	+	0.311337i
$214$		−	264.854i		−	1.23764i
$215$	−74.9149	+	72.5463i	−0.348441	+	0.337425i
$216$	−82.6645			−0.382706
$217$	−31.6191	−	31.6191i	−0.145710	−	0.145710i
$218$	131.307	−	131.307i	0.602327	−	0.602327i
$219$			57.9517i			0.264620i
$220$	2.93956	−	183.007i	0.0133617	−	0.831849i
$221$	68.6257			0.310524
$222$	−139.998	−	139.998i	−0.630621	−	0.630621i
$223$	−158.829	+	158.829i	−0.712240	+	0.712240i	−0.967003	−	0.254764i	$-0.918002\pi$
$223$	−158.829	+	158.829i	−0.712240	+	0.712240i	0.254764	+	0.967003i	$0.418002\pi$
$224$		−	40.8442i		−	0.182340i
$225$	−1.80277	+	56.1026i	−0.00801232	+	0.249345i
$226$	−306.564			−1.35648
$227$	−222.888	−	222.888i	−0.981887	−	0.981887i	0.0179518	−	0.999839i	$-0.494285\pi$
$227$	−222.888	−	222.888i	−0.981887	−	0.981887i	−0.999839	+	0.0179518i	$0.994285\pi$
$228$	35.4734	−	35.4734i	0.155585	−	0.155585i
$229$			28.9066i			0.126230i	0.998006	+	0.0631148i	$0.0201034\pi$
$229$			28.9066i			0.126230i	−0.998006	+	0.0631148i	$0.979897\pi$
$230$	−33.9073	−	0.544639i	−0.147423	−	0.00236799i
$231$	−343.466			−1.48686
$232$	4.94546	+	4.94546i	0.0213166	+	0.0213166i
$233$	259.464	−	259.464i	1.11358	−	1.11358i	0.120918	−	0.992663i	$-0.461416\pi$
$233$	259.464	−	259.464i	1.11358	−	1.11358i	0.992663	−	0.120918i	$-0.0385837\pi$
$234$			63.0033i			0.269245i
$235$	−116.882	−	120.698i	−0.497369	−	0.513608i
$236$	−33.8210			−0.143309
$237$	−28.6044	−	28.6044i	−0.120694	−	0.120694i
$238$	−24.9725	+	24.9725i	−0.104926	+	0.104926i
$239$			9.18860i			0.0384460i	0.999815	+	0.0192230i	$0.00611925\pi$
$239$			9.18860i			0.0384460i	−0.999815	+	0.0192230i	$0.993881\pi$
$240$	−37.3408	+	36.1602i	−0.155587	+	0.150667i
$241$	−67.4055			−0.279691			−0.139845	−	0.990173i	$-0.544661\pi$
$241$	−67.4055			−0.279691			−0.139845	+	0.990173i	$0.544661\pi$
$242$	214.001	+	214.001i	0.884303	+	0.884303i
$243$	−83.5372	+	83.5372i	−0.343774	+	0.343774i
$244$		−	51.3310i		−	0.210373i
$245$	−0.251576	+	15.6622i	−0.00102684	+	0.0639275i
$246$	−186.367			−0.757589
$247$	−135.410	−	135.410i	−0.548217	−	0.548217i
$248$	12.3862	−	12.3862i	0.0499444	−	0.0499444i
$249$			353.970i			1.42157i
$250$	118.834	+	130.876i	0.475337	+	0.523502i
$251$	−77.9583			−0.310591			−0.155295	−	0.987868i	$-0.549633\pi$
$251$	−77.9583			−0.310591			−0.155295	+	0.987868i	$0.549633\pi$
$252$	−22.9265	−	22.9265i	−0.0909782	−	0.0909782i
$253$	62.0686	−	62.0686i	0.245331	−	0.245331i
$254$		−	26.3807i		−	0.103861i
$255$	44.9391	+	0.721838i	0.176232	+	0.00283074i
$256$	16.0000			0.0625000
$257$	277.635	+	277.635i	1.08029	+	1.08029i	0.996482	+	0.0838088i	$0.0267085\pi$
$257$	277.635	+	277.635i	1.08029	+	1.08029i	0.0838088	+	0.996482i	$0.473291\pi$
$258$	−54.2067	+	54.2067i	−0.210103	+	0.210103i
$259$		−	388.931i		−	1.50166i
$260$	138.031	+	142.538i	0.530889	+	0.548223i
$261$	5.55193			0.0212718
$262$	88.7690	+	88.7690i	0.338813	+	0.338813i
$263$	−363.481	+	363.481i	−1.38206	+	1.38206i	−0.541097	+	0.840960i	$0.681991\pi$
$263$	−363.481	+	363.481i	−1.38206	+	1.38206i	−0.840960	+	0.541097i	$0.818009\pi$
$264$		−	134.547i		−	0.509646i
$265$	263.417	−	255.088i	0.994026	−	0.962597i
$266$	98.5495			0.370487
$267$	48.6841	+	48.6841i	0.182337	+	0.182337i
$268$	−89.5874	+	89.5874i	−0.334281	+	0.334281i
$269$		−	95.2110i		−	0.353944i	−0.984216	−	0.176972i	$-0.943370\pi$
$269$		−	95.2110i		−	0.353944i	0.984216	−	0.176972i	$-0.0566303\pi$
$270$	−3.31909	+	206.634i	−0.0122929	+	0.765313i
$271$	313.682			1.15750			0.578749	−	0.815506i	$-0.303541\pi$
$271$	313.682			1.15750			0.578749	+	0.815506i	$0.303541\pi$
$272$	−9.78253	−	9.78253i	−0.0359652	−	0.0359652i
$273$	263.285	−	263.285i	0.964413	−	0.964413i
$274$			360.493i			1.31567i
$275$	−457.340	−	14.6959i	−1.66305	−	0.0534397i
$276$	−24.9286			−0.0903211
$277$	191.916	+	191.916i	0.692836	+	0.692836i	0.962855	−	0.270019i	$-0.0870299\pi$
$277$	191.916	+	191.916i	0.692836	+	0.692836i	−0.270019	+	0.962855i	$0.587030\pi$
$278$	−136.072	+	136.072i	−0.489466	+	0.489466i
$279$		−	13.9052i		−	0.0498393i
$280$	−102.097	−	1.63995i	−0.364634	−	0.00585696i
$281$	−196.577			−0.699561			−0.349781	−	0.936832i	$-0.613744\pi$
$281$	−196.577			−0.699561			−0.349781	+	0.936832i	$0.613744\pi$
$282$	−87.3341	−	87.3341i	−0.309696	−	0.309696i
$283$	29.9409	−	29.9409i	0.105798	−	0.105798i	−0.652226	−	0.758024i	$-0.726165\pi$
$283$	29.9409	−	29.9409i	0.105798	−	0.105798i	0.758024	+	0.652226i	$0.226165\pi$
$284$		−	72.1690i		−	0.254116i
$285$	−87.2478	−	90.0964i	−0.306133	−	0.316128i
$286$	−513.593			−1.79578
$287$	−258.875	−	258.875i	−0.902004	−	0.902004i
$288$	8.98105	−	8.98105i	0.0311842	−	0.0311842i
$289$		−	277.038i		−	0.958608i
$290$	12.5606	−	12.1635i	0.0433125	−	0.0419431i
$291$	−349.066			−1.19954
$292$	−31.5339	−	31.5339i	−0.107993	−	0.107993i
$293$	160.923	−	160.923i	0.549227	−	0.549227i	−0.376990	−	0.926217i	$-0.623041\pi$
$293$	160.923	−	160.923i	0.549227	−	0.549227i	0.926217	+	0.376990i	$0.123041\pi$
$294$			11.5149i			0.0391662i
$295$	−1.35796	+	84.5416i	−0.00460324	+	0.286582i
$296$	152.357			0.514719
$297$	−378.253	−	378.253i	−1.27358	−	1.27358i
$298$	−271.727	+	271.727i	−0.911835	+	0.911835i
$299$			95.1579i			0.318254i
$300$	88.8895	+	94.7918i	0.296298	+	0.315973i
$301$	−150.593			−0.500309
$302$	93.7692	+	93.7692i	0.310494	+	0.310494i
$303$	236.484	−	236.484i	0.780476	−	0.780476i
$304$			38.6050i			0.126990i
$305$	−128.311	−	2.06100i	−0.420691	−	0.00675739i
$306$	−10.9822			−0.0358895
$307$	−173.652	−	173.652i	−0.565643	−	0.565643i	0.365262	−	0.930905i	$-0.380979\pi$
$307$	−173.652	−	173.652i	−0.565643	−	0.565643i	−0.930905	+	0.365262i	$0.880979\pi$
$308$	186.893	−	186.893i	0.606797	−	0.606797i
$309$			56.8262i			0.183903i
$310$	−30.4642	−	31.4589i	−0.0982717	−	0.101480i
$311$	−549.290			−1.76621			−0.883103	−	0.469179i	$-0.844550\pi$
$311$	−549.290			−1.76621			−0.883103	+	0.469179i	$0.844550\pi$
$312$	103.137	+	103.137i	0.330568	+	0.330568i
$313$	199.770	−	199.770i	0.638244	−	0.638244i	−0.311878	−	0.950122i	$-0.600958\pi$
$313$	199.770	−	199.770i	0.638244	−	0.638244i	0.950122	+	0.311878i	$0.100958\pi$
$314$			119.401i			0.380257i
$315$	−58.2294	+	56.3883i	−0.184855	+	0.179011i
$316$	31.1296			0.0985115
$317$	−5.02560	−	5.02560i	−0.0158536	−	0.0158536i	0.699136	−	0.714989i	$-0.253568\pi$
$317$	−5.02560	−	5.02560i	−0.0158536	−	0.0158536i	−0.714989	+	0.699136i	$0.753568\pi$
$318$	190.602	−	190.602i	0.599378	−	0.599378i
$319$			45.2585i			0.141876i
$320$	0.642421	−	39.9948i	0.00200756	−	0.124984i
$321$	−486.739			−1.51632
$322$	−34.6274	−	34.6274i	−0.107538	−	0.107538i
$323$	23.6034	−	23.6034i	0.0730756	−	0.0730756i
$324$			111.503i			0.344145i
$325$	361.841	−	339.310i	1.11336	−	1.04403i
$326$	73.5118			0.225496
$327$	−241.312	−	241.312i	−0.737956	−	0.737956i
$328$	101.410	−	101.410i	0.309176	−	0.309176i
$329$		−	242.625i		−	0.737462i
$330$	−336.323	−	5.40222i	−1.01916	−	0.0163704i
$331$	−89.5027			−0.270401			−0.135200	−	0.990818i	$-0.543168\pi$
$331$	−89.5027			−0.270401			−0.135200	+	0.990818i	$0.543168\pi$
$332$	−192.609	−	192.609i	−0.580149	−	0.580149i
$333$	85.5203	−	85.5203i	0.256818	−	0.256818i
$334$			349.929i			1.04769i
$335$	220.342	+	227.537i	0.657739	+	0.679214i
$336$	−75.0620			−0.223399
$337$	−119.687	−	119.687i	−0.355156	−	0.355156i	0.506868	−	0.862024i	$-0.330803\pi$
$337$	−119.687	−	119.687i	−0.355156	−	0.355156i	−0.862024	+	0.506868i	$0.830803\pi$
$338$	224.697	−	224.697i	0.664783	−	0.664783i
$339$			563.391i			1.66192i
$340$	−24.8460	+	24.0604i	−0.0730763	+	0.0707659i
$341$	113.353			0.332413
$342$	21.6696	+	21.6696i	0.0633614	+	0.0633614i
$343$	234.176	−	234.176i	0.682729	−	0.682729i
$344$		−	58.9921i		−	0.171489i
$345$	−1.00092	+	62.3135i	−0.00290121	+	0.180619i
$346$	173.990			0.502860
$347$	234.971	+	234.971i	0.677148	+	0.677148i	0.959354	−	0.282206i	$-0.0910660\pi$
$347$	234.971	+	234.971i	0.677148	+	0.677148i	−0.282206	+	0.959354i	$0.591066\pi$
$348$	9.08858	−	9.08858i	0.0261166	−	0.0261166i
$349$		−	67.9780i		−	0.194779i	−0.995246	−	0.0973896i	$-0.968951\pi$
$349$		−	67.9780i		−	0.194779i	0.995246	−	0.0973896i	$-0.0310493\pi$
$350$	−8.19869	+	255.145i	−0.0234248	+	0.728985i
$351$	579.902			1.65214
$352$	73.2122	+	73.2122i	0.207989	+	0.207989i
$353$	−295.700	+	295.700i	−0.837676	+	0.837676i	−0.988553	−	0.150876i	$-0.951790\pi$
$353$	−295.700	+	295.700i	−0.837676	+	0.837676i	0.150876	+	0.988553i	$0.451790\pi$
$354$			62.1549i			0.175579i
$355$	−180.399	−	2.89768i	−0.508167	−	0.00816248i
$356$	−52.9819			−0.148826
$357$	45.8935	+	45.8935i	0.128553	+	0.128553i
$358$	318.823	−	318.823i	0.890567	−	0.890567i
$359$			214.204i			0.596670i	0.954461	+	0.298335i	$0.0964312\pi$
$359$			214.204i			0.596670i	−0.954461	+	0.298335i	$0.903569\pi$
$360$	−22.0891	−	22.8103i	−0.0613587	−	0.0633620i
$361$	267.853			0.741976
$362$	345.259	+	345.259i	0.953754	+	0.953754i
$363$	393.284	−	393.284i	1.08343	−	1.08343i
$364$			286.528i			0.787164i
$365$	−80.0906	+	77.5584i	−0.219426	+	0.212489i
$366$	−94.3341			−0.257743
$367$	234.582	+	234.582i	0.639189	+	0.639189i	0.950355	−	0.311166i	$-0.100720\pi$
$367$	234.582	+	234.582i	0.639189	+	0.639189i	−0.311166	+	0.950355i	$0.600720\pi$
$368$	13.5647	−	13.5647i	0.0368605	−	0.0368605i
$369$		−	113.846i		−	0.308525i
$370$	6.11732	−	380.843i	0.0165333	−	1.02931i
$371$	529.517			1.42727
$372$	−22.7629	−	22.7629i	−0.0611906	−	0.0611906i
$373$	−396.584	+	396.584i	−1.06323	+	1.06323i	−0.0653653	+	0.997861i	$0.520821\pi$
$373$	−396.584	+	396.584i	−1.06323	+	1.06323i	−0.997861	+	0.0653653i	$0.979179\pi$
$374$		−	89.5251i		−	0.239372i
$375$	240.518	−	218.389i	0.641382	−	0.582371i
$376$	95.0440			0.252777
$377$	−34.6931	−	34.6931i	−0.0920240	−	0.0920240i
$378$	−211.023	+	211.023i	−0.558262	+	0.558262i
$379$			395.959i			1.04475i	0.852717	+	0.522374i	$0.174953\pi$
$379$			395.959i			1.04475i	−0.852717	+	0.522374i	$0.825047\pi$
$380$	96.5001	+	1.55004i	0.253948	+	0.00407906i
$381$	−48.4815			−0.127248
$382$	−81.7982	−	81.7982i	−0.214131	−	0.214131i
$383$	351.592	−	351.592i	0.917996	−	0.917996i	−0.0788876	−	0.996884i	$-0.525137\pi$
$383$	351.592	−	351.592i	0.917996	−	0.917996i	0.996884	+	0.0788876i	$0.0251368\pi$
$384$		−	29.4042i		−	0.0765734i
$385$	−459.669	−	474.677i	−1.19395	−	1.23293i
$386$	335.304			0.868662
$387$	−33.1132	−	33.1132i	−0.0855638	−	0.0855638i
$388$	189.941	−	189.941i	0.489539	−	0.489539i
$389$			559.908i			1.43935i	0.694310	+	0.719676i	$0.255710\pi$
$389$			559.908i			1.43935i	−0.694310	+	0.719676i	$0.744290\pi$
$390$	261.951	−	253.668i	0.671668	−	0.650432i
$391$	−16.5871			−0.0424222
$392$	−6.26570	−	6.26570i	−0.0159839	−	0.0159839i
$393$	163.136	−	163.136i	0.415105	−	0.415105i
$394$			16.6125i			0.0421637i
$395$	1.24990	−	77.8140i	0.00316429	−	0.196998i
$396$	82.1903			0.207551
$397$	−142.412	−	142.412i	−0.358720	−	0.358720i	0.504621	−	0.863341i	$-0.331632\pi$
$397$	−142.412	−	142.412i	−0.358720	−	0.358720i	−0.863341	+	0.504621i	$0.831632\pi$
$398$	−165.150	+	165.150i	−0.414949	+	0.414949i
$399$		−	181.111i		−	0.453911i
$400$	−99.9484	−	3.21169i	−0.249871	−	0.00802922i
$401$	−677.211			−1.68881			−0.844403	−	0.535708i	$-0.820045\pi$
$401$	−677.211			−1.68881			−0.844403	+	0.535708i	$0.820045\pi$
$402$	164.640	+	164.640i	0.409553	+	0.409553i
$403$	−86.8909	+	86.8909i	−0.215610	+	0.215610i
$404$			257.361i			0.637033i
$405$	278.721	+	4.47698i	0.688200	+	0.0110543i
$406$	25.2492			0.0621901
$407$	697.148	+	697.148i	1.71290	+	1.71290i
$408$	−17.9780	+	17.9780i	−0.0440636	+	0.0440636i
$409$			349.594i			0.854753i	0.904074	+	0.427376i	$0.140562\pi$
$409$			349.594i			0.854753i	−0.904074	+	0.427376i	$0.859438\pi$
$410$	−249.420	−	257.563i	−0.608341	−	0.628203i
$411$	662.501			1.61192
$412$	−30.9214	−	30.9214i	−0.0750519	−	0.0750519i
$413$	−86.3370	+	86.3370i	−0.209048	+	0.209048i
$414$		−	15.2281i		−	0.0367829i
$415$	−489.195	+	473.728i	−1.17878	+	1.14151i
$416$	−112.242			−0.269813
$417$	250.067	+	250.067i	0.599681	+	0.599681i
$418$	−176.647	+	176.647i	−0.422601	+	0.422601i
$419$		−	127.172i		−	0.303513i	−0.988418	−	0.151756i	$-0.951507\pi$
$419$		−	127.172i		−	0.303513i	0.988418	−	0.151756i	$-0.0484929\pi$
$420$	−3.01384	+	187.631i	−0.00717580	+	0.446740i
$421$	123.176			0.292580			0.146290	−	0.989242i	$-0.453267\pi$
$421$	123.176			0.292580			0.146290	+	0.989242i	$0.453267\pi$
$422$	311.748	+	311.748i	0.738740	+	0.738740i
$423$	53.3497	−	53.3497i	0.126122	−	0.126122i
$424$			207.429i			0.489219i
$425$	59.1456	+	63.0729i	0.139166	+	0.148407i
$426$	−132.629			−0.311337
$427$	−131.036	−	131.036i	−0.306876	−	0.306876i
$428$	264.854	−	264.854i	0.618818	−	0.618818i
$429$			943.862i			2.20014i
$430$	−147.461	−	2.36861i	−0.342933	−	0.00550839i
$431$	158.451			0.367636			0.183818	−	0.982960i	$-0.441154\pi$
$431$	158.451			0.367636			0.183818	+	0.982960i	$0.441154\pi$
$432$	−82.6645	−	82.6645i	−0.191353	−	0.191353i
$433$	−384.013	+	384.013i	−0.886867	+	0.886867i	−0.994221	−	0.107354i	$-0.965762\pi$
$433$	−384.013	+	384.013i	−0.886867	+	0.886867i	0.107354	+	0.994221i	$0.465762\pi$
$434$		−	63.2382i		−	0.145710i
$435$	−22.3536	−	23.0834i	−0.0513876	−	0.0530654i
$436$	262.615			0.602327
$437$	32.7290	+	32.7290i	0.0748947	+	0.0748947i
$438$	−57.9517	+	57.9517i	−0.132310	+	0.132310i
$439$		−	744.209i		−	1.69524i	−0.530607	−	0.847618i	$-0.678036\pi$
$439$		−	744.209i		−	1.69524i	0.530607	−	0.847618i	$-0.321964\pi$
$440$	185.946	−	180.067i	0.422605	−	0.409244i
$441$	−7.03407			−0.0159503
$442$	68.6257	+	68.6257i	0.155262	+	0.155262i
$443$	−56.2374	+	56.2374i	−0.126947	+	0.126947i	−0.767726	−	0.640779i	$-0.778612\pi$
$443$	−56.2374	+	56.2374i	−0.126947	+	0.126947i	0.640779	+	0.767726i	$0.278612\pi$
$444$		−	279.996i		−	0.630621i
$445$	−2.12729	+	132.438i	−0.00478043	+	0.297613i
$446$	−317.659			−0.712240
$447$	499.369	+	499.369i	1.11716	+	1.11716i
$448$	40.8442	−	40.8442i	0.0911702	−	0.0911702i
$449$		−	338.053i		−	0.752903i	−0.926436	−	0.376452i	$-0.877144\pi$
$449$		−	338.053i		−	0.752903i	0.926436	−	0.376452i	$-0.122856\pi$
$450$	−57.9054	+	54.2998i	−0.128679	+	0.120666i
$451$	928.053			2.05777
$452$	−306.564	−	306.564i	−0.678238	−	0.678238i
$453$	172.326	−	172.326i	0.380410	−	0.380410i
$454$		−	445.777i		−	0.981887i
$455$	716.227	+	11.5045i	1.57412	+	0.0252845i
$456$	70.9468			0.155585
$457$	−170.026	−	170.026i	−0.372048	−	0.372048i	0.496175	−	0.868223i	$-0.334737\pi$
$457$	−170.026	−	170.026i	−0.372048	−	0.372048i	−0.868223	+	0.496175i	$0.834737\pi$
$458$	−28.9066	+	28.9066i	−0.0631148	+	0.0631148i
$459$			101.083i			0.220225i
$460$	−33.3626	−	34.4519i	−0.0725275	−	0.0748955i
$461$	−645.832			−1.40094			−0.700469	−	0.713683i	$-0.747026\pi$
$461$	−645.832			−1.40094			−0.700469	+	0.713683i	$0.747026\pi$
$462$	−343.466	−	343.466i	−0.743432	−	0.743432i
$463$	−94.2218	+	94.2218i	−0.203503	+	0.203503i	−0.801499	−	0.597996i	$-0.795964\pi$
$463$	−94.2218	+	94.2218i	−0.203503	+	0.203503i	0.597996	+	0.801499i	$0.295964\pi$
$464$			9.89092i			0.0213166i
$465$	−57.8139	+	55.9860i	−0.124331	+	0.120400i
$466$	518.928			1.11358
$467$	361.092	+	361.092i	0.773216	+	0.773216i	0.978667	−	0.205451i	$-0.0658661\pi$
$467$	361.092	+	361.092i	0.773216	+	0.773216i	−0.205451	+	0.978667i	$0.565866\pi$
$468$	−63.0033	+	63.0033i	−0.134622	+	0.134622i
$469$			457.391i			0.975247i
$470$	3.81614	−	237.579i	0.00811945	−	0.505488i
$471$	219.430			0.465882
$472$	−33.8210	−	33.8210i	−0.0716546	−	0.0716546i
$473$	269.934	−	269.934i	0.570684	−	0.570684i
$474$		−	57.2089i		−	0.120694i
$475$	7.74921	−	241.157i	0.0163141	−	0.507699i
$476$	−49.9450			−0.104926
$477$	116.433	+	116.433i	0.244094	+	0.244094i
$478$	−9.18860	+	9.18860i	−0.0192230	+	0.0192230i
$479$		−	617.686i		−	1.28953i	−0.764380	−	0.644766i	$-0.776955\pi$
$479$		−	617.686i		−	1.28953i	0.764380	−	0.644766i	$-0.223045\pi$
$480$	−73.5010	−	1.18062i	−0.153127	−	0.00245962i
$481$	−1068.80			−2.22204
$482$	−67.4055	−	67.4055i	−0.139845	−	0.139845i
$483$	−63.6369	+	63.6369i	−0.131753	+	0.131753i
$484$			428.003i			0.884303i
$485$	−467.165	−	482.418i	−0.963227	−	0.994676i
$486$	−167.074			−0.343774
$487$	−393.032	−	393.032i	−0.807047	−	0.807047i	0.177139	−	0.984186i	$-0.443316\pi$
$487$	−393.032	−	393.032i	−0.807047	−	0.807047i	−0.984186	+	0.177139i	$0.943316\pi$
$488$	51.3310	−	51.3310i	0.105186	−	0.105186i
$489$		−	135.097i		−	0.276273i
$490$	−15.9138	+	15.4107i	−0.0324772	+	0.0314503i
$491$	−896.627			−1.82612			−0.913062	−	0.407821i	$-0.866289\pi$
$491$	−896.627			−1.82612			−0.913062	+	0.407821i	$0.866289\pi$
$492$	−186.367	−	186.367i	−0.378795	−	0.378795i
$493$	6.04739	−	6.04739i	0.0122665	−	0.0122665i
$494$		−	270.819i		−	0.548217i
$495$	3.30005	−	205.449i	0.00666676	−	0.415049i
$496$	24.7724			0.0499444
$497$	−184.230	−	184.230i	−0.370685	−	0.370685i
$498$	−353.970	+	353.970i	−0.710783	+	0.710783i
$499$			699.998i			1.40280i	0.712767	+	0.701401i	$0.247442\pi$
$499$			699.998i			1.40280i	−0.712767	+	0.701401i	$0.752558\pi$
$500$	−12.0412	+	249.710i	−0.0240825	+	0.499420i
$501$	643.087			1.28361
$502$	−77.9583	−	77.9583i	−0.155295	−	0.155295i
$503$	−471.150	+	471.150i	−0.936679	+	0.936679i	−0.998111	−	0.0614321i	$-0.980433\pi$
$503$	−471.150	+	471.150i	−0.936679	+	0.936679i	0.0614321	+	0.998111i	$0.480433\pi$
$504$		−	45.8530i		−	0.0909782i
$505$	643.320	+	10.3334i	1.27390	+	0.0204621i
$506$	124.137			0.245331
$507$	−412.939	−	412.939i	−0.814475	−	0.814475i
$508$	26.3807	−	26.3807i	0.0519305	−	0.0519305i
$509$			574.088i			1.12787i	0.825818	+	0.563937i	$0.190714\pi$
$509$			574.088i			1.12787i	−0.825818	+	0.563937i	$0.809286\pi$
$510$	44.2173	+	45.6609i	0.0867005	+	0.0895313i
$511$	−160.997			−0.315063
$512$	16.0000	+	16.0000i	0.0312500	+	0.0312500i
$513$	199.454	−	199.454i	0.388799	−	0.388799i
$514$			555.269i			1.08029i
$515$	−78.5351	+	76.0520i	−0.152495	+	0.147674i
$516$	−108.413			−0.210103
$517$	434.899	+	434.899i	0.841197	+	0.841197i
$518$	388.931	−	388.931i	0.750832	−	0.750832i
$519$		−	319.751i		−	0.616091i
$520$	−4.50667	+	280.569i	−0.00866667	+	0.539556i
$521$	−468.012			−0.898296			−0.449148	−	0.893457i	$-0.648272\pi$
$521$	−468.012			−0.898296			−0.449148	+	0.893457i	$0.648272\pi$
$522$	5.55193	+	5.55193i	0.0106359	+	0.0106359i
$523$	705.372	−	705.372i	1.34870	−	1.34870i	0.461632	−	0.887072i	$-0.347264\pi$
$523$	705.372	−	705.372i	1.34870	−	1.34870i	0.887072	−	0.461632i	$-0.152736\pi$
$524$			177.538i			0.338813i
$525$	468.895	+	15.0672i	0.893134	+	0.0286995i
$526$	−726.962			−1.38206
$527$	−15.1461	−	15.1461i	−0.0287402	−	0.0287402i
$528$	134.547	−	134.547i	0.254823	−	0.254823i
$529$		−	23.0000i		−	0.0434783i
$530$	518.505	+	8.32853i	0.978311	+	0.0157142i
$531$	−37.9685			−0.0715038
$532$	98.5495	+	98.5495i	0.185243	+	0.185243i
$533$	−711.403	+	711.403i	−1.33471	+	1.33471i
$534$			97.3681i			0.182337i
$535$	−651.416	−	672.684i	−1.21760	−	1.25735i
$536$	−179.175			−0.334281
$537$	−585.921	−	585.921i	−1.09110	−	1.09110i
$538$	95.2110	−	95.2110i	0.176972	−	0.176972i
$539$		−	57.3407i		−	0.106383i
$540$	−209.954	+	203.315i	−0.388803	+	0.376510i
$541$	277.505			0.512947			0.256474	−	0.966551i	$-0.417439\pi$
$541$	277.505			0.512947			0.256474	+	0.966551i	$0.417439\pi$
$542$	313.682	+	313.682i	0.578749	+	0.578749i
$543$	634.504	−	634.504i	1.16851	−	1.16851i
$544$		−	19.5651i		−	0.0359652i
$545$	10.5443	−	656.452i	0.0193474	−	1.20450i
$546$	526.570			0.964413
$547$	264.729	+	264.729i	0.483965	+	0.483965i	0.906395	−	0.422430i	$-0.138823\pi$
$547$	264.729	+	264.729i	0.483965	+	0.483965i	−0.422430	+	0.906395i	$0.638823\pi$
$548$	−360.493	+	360.493i	−0.657835	+	0.657835i
$549$		−	57.6258i		−	0.104965i
$550$	−442.644	−	472.036i	−0.804808	−	0.858247i
$551$	−23.8649			−0.0433121
$552$	−24.9286	−	24.9286i	−0.0451605	−	0.0451605i
$553$	79.4666	−	79.4666i	0.143701	−	0.143701i
$554$			383.831i			0.692836i
$555$	−699.899	−	11.2422i	−1.26108	−	0.0202562i
$556$	−272.143			−0.489466
$557$	−336.498	−	336.498i	−0.604125	−	0.604125i	0.337279	−	0.941405i	$-0.390493\pi$
$557$	−336.498	−	336.498i	−0.604125	−	0.604125i	−0.941405	+	0.337279i	$0.890493\pi$
$558$	13.9052	−	13.9052i	0.0249196	−	0.0249196i
$559$			413.837i			0.740317i
$560$	−100.457	−	103.737i	−0.179388	−	0.185245i
$561$	−164.526			−0.293272
$562$	−196.577	−	196.577i	−0.349781	−	0.349781i
$563$	−40.9563	+	40.9563i	−0.0727465	+	0.0727465i	−0.742544	−	0.669797i	$-0.766381\pi$
$563$	−40.9563	+	40.9563i	−0.0727465	+	0.0727465i	0.669797	+	0.742544i	$0.266381\pi$
$564$		−	174.668i		−	0.309696i
$565$	−778.619	+	754.001i	−1.37809	+	1.33452i
$566$	59.8819			0.105798
$567$	284.641	+	284.641i	0.502012	+	0.502012i
$568$	72.1690	−	72.1690i	0.127058	−	0.127058i
$569$			33.7512i			0.0593168i	0.999560	+	0.0296584i	$0.00944194\pi$
$569$			33.7512i			0.0593168i	−0.999560	+	0.0296584i	$0.990558\pi$
$570$	2.84861	−	177.344i	0.00499756	−	0.311130i
$571$	669.004			1.17164			0.585818	−	0.810443i	$-0.300773\pi$
$571$	669.004			1.17164			0.585818	+	0.810443i	$0.300773\pi$
$572$	−513.593	−	513.593i	−0.897890	−	0.897890i
$573$	−150.326	+	150.326i	−0.262348	+	0.262348i
$574$		−	517.750i		−	0.902004i
$575$	−87.4582	+	82.0125i	−0.152101	+	0.142631i
$576$	17.9621			0.0311842
$577$	−19.7627	−	19.7627i	−0.0342508	−	0.0342508i	0.689774	−	0.724025i	$-0.257710\pi$
$577$	−19.7627	−	19.7627i	−0.0342508	−	0.0342508i	−0.724025	+	0.689774i	$0.757710\pi$
$578$	277.038	−	277.038i	0.479304	−	0.479304i
$579$		−	616.208i		−	1.06426i
$580$	24.7241	+	0.397133i	0.0426278	+	0.000684713i
$581$	−983.372			−1.69255
$582$	−349.066	−	349.066i	−0.599771	−	0.599771i
$583$	−949.144	+	949.144i	−1.62804	+	1.62804i
$584$		−	63.0677i		−	0.107993i
$585$	154.958	+	160.017i	0.264886	+	0.273534i
$586$	321.847			0.549227
$587$	747.545	+	747.545i	1.27350	+	1.27350i	0.944239	+	0.329262i	$0.106800\pi$
$587$	747.545	+	747.545i	1.27350	+	1.27350i	0.329262	+	0.944239i	$0.393200\pi$
$588$	−11.5149	+	11.5149i	−0.0195831	+	0.0195831i
$589$			59.7712i			0.101479i
$590$	−85.8995	+	83.1836i	−0.145592	+	0.140989i
$591$	30.5298			0.0516579
$592$	152.357	+	152.357i	0.257359	+	0.257359i
$593$	336.503	−	336.503i	0.567459	−	0.567459i	−0.363957	−	0.931416i	$-0.618574\pi$
$593$	336.503	−	336.503i	0.567459	−	0.567459i	0.931416	+	0.363957i	$0.118574\pi$
$594$		−	756.506i		−	1.27358i
$595$	−2.00536	+	124.846i	−0.00337035	+	0.209826i
$596$	−543.454			−0.911835
$597$	303.505	+	303.505i	0.508384	+	0.508384i
$598$	−95.1579	+	95.1579i	−0.159127	+	0.159127i
$599$		−	888.211i		−	1.48282i	−0.671050	−	0.741412i	$-0.734157\pi$
$599$		−	888.211i		−	1.48282i	0.671050	−	0.741412i	$-0.265843\pi$
$600$	−5.90232	+	183.681i	−0.00983720	+	0.306136i
$601$	−337.568			−0.561676			−0.280838	−	0.959755i	$-0.590612\pi$
$601$	−337.568			−0.561676			−0.280838	+	0.959755i	$0.590612\pi$
$602$	−150.593	−	150.593i	−0.250154	−	0.250154i
$603$	−100.574	+	100.574i	−0.166789	+	0.166789i
$604$			187.538i			0.310494i
$605$	1069.87	+	17.1849i	1.76838	+	0.0284047i
$606$	472.969			0.780476
$607$	−214.915	−	214.915i	−0.354061	−	0.354061i	0.507557	−	0.861618i	$-0.330549\pi$
$607$	−214.915	−	214.915i	−0.354061	−	0.354061i	−0.861618	+	0.507557i	$0.830549\pi$
$608$	−38.6050	+	38.6050i	−0.0634951	+	0.0634951i
$609$		−	46.4020i		−	0.0761938i
$610$	−126.250	−	130.372i	−0.206967	−	0.213724i
$611$	−666.746			−1.09124
$612$	−10.9822	−	10.9822i	−0.0179447	−	0.0179447i
$613$	−224.804	+	224.804i	−0.366728	+	0.366728i	−0.866283	−	0.499554i	$-0.833497\pi$
$613$	−224.804	+	224.804i	−0.366728	+	0.366728i	0.499554	+	0.866283i	$0.333497\pi$
$614$		−	347.305i		−	0.565643i
$615$	−473.340	+	458.374i	−0.769659	+	0.745324i
$616$	373.787			0.606797
$617$	−45.7498	−	45.7498i	−0.0741487	−	0.0741487i	0.669060	−	0.743209i	$-0.266697\pi$
$617$	−45.7498	−	45.7498i	−0.0741487	−	0.0741487i	−0.743209	+	0.669060i	$0.766697\pi$
$618$	−56.8262	+	56.8262i	−0.0919517	+	0.0919517i
$619$			984.136i			1.58988i	0.606688	+	0.794940i	$0.292498\pi$
$619$			984.136i			1.58988i	−0.606688	+	0.794940i	$0.707502\pi$
$620$	0.994645	−	61.9231i	0.00160427	−	0.0998759i
$621$	−140.164			−0.225708
$622$	−549.290	−	549.290i	−0.883103	−	0.883103i
$623$	−135.250	+	135.250i	−0.217095	+	0.217095i
$624$			206.274i			0.330568i
$625$	623.711	+	40.1254i	0.997937	+	0.0642006i
$626$	399.541			0.638244
$627$	324.636	+	324.636i	0.517760	+	0.517760i
$628$	−119.401	+	119.401i	−0.190129	+	0.190129i
$629$		−	186.304i		−	0.296191i
$630$	−114.618	−	1.84106i	−0.181933	−	0.00292231i
$631$	496.798			0.787318			0.393659	−	0.919257i	$-0.371209\pi$
$631$	496.798			0.787318			0.393659	+	0.919257i	$0.371209\pi$
$632$	31.1296	+	31.1296i	0.0492558	+	0.0492558i
$633$	572.919	−	572.919i	0.905086	−	0.905086i
$634$		−	10.0512i		−	0.0158536i
$635$	−64.8841	−	67.0025i	−0.102180	−	0.105516i
$636$	381.205			0.599378
$637$	43.9547	+	43.9547i	0.0690027	+	0.0690027i
$638$	−45.2585	+	45.2585i	−0.0709381	+	0.0709381i
$639$		−	81.0192i		−	0.126791i
$640$	40.6373	−	39.3524i	0.0634957	−	0.0614882i
$641$	549.603			0.857415			0.428708	−	0.903443i	$-0.358969\pi$
$641$	549.603			0.857415			0.428708	+	0.903443i	$0.358969\pi$
$642$	−486.739	−	486.739i	−0.758160	−	0.758160i
$643$	−175.464	+	175.464i	−0.272883	+	0.272883i	−0.830260	−	0.557377i	$-0.811808\pi$
$643$	−175.464	+	175.464i	−0.272883	+	0.272883i	0.557377	+	0.830260i	$0.311808\pi$
$644$		−	69.2548i		−	0.107538i
$645$	−4.35294	+	270.998i	−0.00674874	+	0.420153i
$646$	47.2068			0.0730756
$647$	453.474	+	453.474i	0.700886	+	0.700886i	0.964601	−	0.263714i	$-0.0849476\pi$
$647$	453.474	+	453.474i	0.700886	+	0.700886i	−0.263714	+	0.964601i	$0.584948\pi$
$648$	−111.503	+	111.503i	−0.172072	+	0.172072i
$649$		−	309.514i		−	0.476908i
$650$	701.151	+	22.5304i	1.07869	+	0.0346622i
$651$	−116.217			−0.178520
$652$	73.5118	+	73.5118i	0.112748	+	0.112748i
$653$	−108.171	+	108.171i	−0.165652	+	0.165652i	−0.785065	−	0.619413i	$-0.787371\pi$
$653$	−108.171	+	108.171i	−0.165652	+	0.165652i	0.619413	+	0.785065i	$0.287371\pi$
$654$		−	482.623i		−	0.737956i
$655$	443.788	+	7.12838i	0.677539	+	0.0108830i
$656$	202.819			0.309176
$657$	−35.4009	−	35.4009i	−0.0538827	−	0.0538827i
$658$	242.625	−	242.625i	0.368731	−	0.368731i
$659$		−	746.059i		−	1.13211i	−0.824368	−	0.566054i	$-0.808469\pi$
$659$		−	746.059i		−	1.13211i	0.824368	−	0.566054i	$-0.191531\pi$
$660$	−330.921	−	341.725i	−0.501395	−	0.517765i
$661$	−129.940			−0.196580			−0.0982902	−	0.995158i	$-0.531337\pi$
$661$	−129.940			−0.196580			−0.0982902	+	0.995158i	$0.531337\pi$
$662$	−89.5027	−	89.5027i	−0.135200	−	0.135200i
$663$	126.118	−	126.118i	0.190223	−	0.190223i
$664$		−	385.219i		−	0.580149i
$665$	250.299	−	242.385i	0.376389	−	0.364489i
$666$	171.041			0.256818
$667$	8.38544	+	8.38544i	0.0125719	+	0.0125719i
$668$	−349.929	+	349.929i	−0.523846	+	0.523846i
$669$			583.781i			0.872618i
$670$	−7.19410	+	447.879i	−0.0107375	+	0.668476i
$671$	469.756			0.700084
$672$	−75.0620	−	75.0620i	−0.111699	−	0.111699i
$673$	−343.345	+	343.345i	−0.510171	+	0.510171i	−0.914579	−	0.404408i	$-0.867478\pi$
$673$	−343.345	+	343.345i	−0.510171	+	0.510171i	0.404408	+	0.914579i	$0.367478\pi$
$674$		−	239.375i		−	0.355156i
$675$	499.793	+	532.980i	0.740434	+	0.789599i
$676$	449.393			0.664783
$677$	−334.906	−	334.906i	−0.494691	−	0.494691i	0.415089	−	0.909781i	$-0.363750\pi$
$677$	−334.906	−	334.906i	−0.494691	−	0.494691i	−0.909781	+	0.415089i	$0.863750\pi$
$678$	−563.391	+	563.391i	−0.830960	+	0.830960i
$679$		−	969.750i		−	1.42820i
$680$	−48.9063	−	0.785563i	−0.0719211	−	0.00115524i
$681$	−819.231			−1.20298
$682$	113.353	+	113.353i	0.166206	+	0.166206i
$683$	242.992	−	242.992i	0.355772	−	0.355772i	−0.506480	−	0.862252i	$-0.669054\pi$
$683$	242.992	−	242.992i	0.355772	−	0.355772i	0.862252	+	0.506480i	$0.169054\pi$
$684$			43.3392i			0.0633614i
$685$	886.643	+	915.592i	1.29437	+	1.33663i
$686$	468.352			0.682729
$687$	53.1234	+	53.1234i	0.0773267	+	0.0773267i
$688$	58.9921	−	58.9921i	0.0857443	−	0.0857443i
$689$		−	1455.14i		−	2.11196i
$690$	−63.3144	+	61.3126i	−0.0917600	+	0.0888588i
$691$	−369.702			−0.535025			−0.267512	−	0.963554i	$-0.586202\pi$
$691$	−369.702			−0.535025			−0.267512	+	0.963554i	$0.586202\pi$
$692$	173.990	+	173.990i	0.251430	+	0.251430i
$693$	209.812	−	209.812i	0.302760	−	0.302760i
$694$			469.941i			0.677148i
$695$	−10.9269	+	680.270i	−0.0157222	+	0.978806i
$696$	18.1772			0.0261166
$697$	−124.005	−	124.005i	−0.177913	−	0.177913i
$698$	67.9780	−	67.9780i	0.0973896	−	0.0973896i
$699$		−	953.667i		−	1.36433i
$700$	−263.343	+	246.946i	−0.376205	+	0.352780i
$701$	−72.5797			−0.103537			−0.0517687	−	0.998659i	$-0.516486\pi$
$701$	−72.5797			−0.103537			−0.0517687	+	0.998659i	$0.516486\pi$
$702$	579.902	+	579.902i	0.826071	+	0.826071i
$703$	−367.609	+	367.609i	−0.522914	+	0.522914i
$704$			146.424i			0.207989i
$705$	−436.614	−	7.01316i	−0.619311	−	0.00994774i
$706$	−591.399			−0.837676
$707$	656.982	+	656.982i	0.929254	+	0.929254i
$708$	−62.1549	+	62.1549i	−0.0877894	+	0.0877894i
$709$		−	171.177i		−	0.241435i	−0.992687	−	0.120718i	$-0.961480\pi$
$709$		−	171.177i		−	0.241435i	0.992687	−	0.120718i	$-0.0385195\pi$
$710$	−177.502	−	183.297i	−0.250002	−	0.258165i
$711$	34.9471			0.0491520
$712$	−52.9819	−	52.9819i	−0.0744128	−	0.0744128i
$713$	21.0018	−	21.0018i	0.0294556	−	0.0294556i
$714$			91.7870i			0.128553i
$715$	−1304.44	+	1263.20i	−1.82439	+	1.76671i
$716$	637.646			0.890567
$717$	16.8865	+	16.8865i	0.0235515	+	0.0235515i
$718$	−214.204	+	214.204i	−0.298335	+	0.298335i
$719$		−	880.854i		−	1.22511i	−0.790428	−	0.612555i	$-0.790142\pi$
$719$		−	880.854i		−	1.22511i	0.790428	−	0.612555i	$-0.209858\pi$
$720$	0.721202	−	44.8995i	0.00100167	−	0.0623604i
$721$	−157.870			−0.218960
$722$	267.853	+	267.853i	0.370988	+	0.370988i
$723$	−123.875	+	123.875i	−0.171335	+	0.171335i
$724$			690.518i			0.953754i
$725$	1.98541	−	61.7864i	0.00273850	−	0.0852226i
$726$	786.567			1.08343
$727$	−448.270	−	448.270i	−0.616603	−	0.616603i	0.328056	−	0.944658i	$-0.393607\pi$
$727$	−448.270	−	448.270i	−0.616603	−	0.616603i	−0.944658	+	0.328056i	$0.893607\pi$
$728$	−286.528	+	286.528i	−0.393582	+	0.393582i
$729$			808.806i			1.10947i
$730$	−157.649	−	2.53225i	−0.215958	−	0.00346884i
$731$	−72.1365			−0.0986819
$732$	−94.3341	−	94.3341i	−0.128872	−	0.128872i
$733$	−270.164	+	270.164i	−0.368573	+	0.368573i	−0.866957	−	0.498383i	$-0.833927\pi$
$733$	−270.164	+	270.164i	−0.368573	+	0.368573i	0.498383	+	0.866957i	$0.333927\pi$
$734$			469.165i			0.639189i
$735$	28.3211	+	29.2458i	0.0385321	+	0.0397902i
$736$	27.1293			0.0368605
$737$	−819.861	−	819.861i	−1.11243	−	1.11243i
$738$	113.846	−	113.846i	0.154263	−	0.154263i
$739$		−	1322.07i		−	1.78900i	−0.447067	−	0.894501i	$-0.647531\pi$
$739$		−	1322.07i		−	1.78900i	0.447067	−	0.894501i	$-0.352469\pi$
$740$	386.960	−	374.726i	0.522919	−	0.506386i
$741$	−497.701			−0.671662
$742$	529.517	+	529.517i	0.713634	+	0.713634i
$743$	83.1674	−	83.1674i	0.111935	−	0.111935i	−0.648921	−	0.760856i	$-0.724779\pi$
$743$	83.1674	−	83.1674i	0.111935	−	0.111935i	0.760856	+	0.648921i	$0.224779\pi$
$744$		−	45.5258i		−	0.0611906i
$745$	−21.8204	+	1358.46i	−0.0292891	+	1.82343i
$746$	−793.167			−1.06323
$747$	−216.229	−	216.229i	−0.289464	−	0.289464i
$748$	89.5251	−	89.5251i	0.119686	−	0.119686i
$749$		−	1352.22i		−	1.80537i
$750$	458.907	+	22.1289i	0.611876	+	0.0295053i
$751$	−60.0818			−0.0800025			−0.0400012	−	0.999200i	$-0.512736\pi$
$751$	−60.0818			−0.0800025			−0.0400012	+	0.999200i	$0.512736\pi$
$752$	95.0440	+	95.0440i	0.126388	+	0.126388i
$753$	−143.269	+	143.269i	−0.190264	+	0.190264i
$754$		−	69.3861i		−	0.0920240i
$755$	468.786	+	7.52991i	0.620908	+	0.00997339i
$756$	−422.046			−0.558262
$757$	628.103	+	628.103i	0.829727	+	0.829727i	0.987479	−	0.157752i	$-0.0504246\pi$
$757$	628.103	+	628.103i	0.829727	+	0.829727i	−0.157752	+	0.987479i	$0.550425\pi$
$758$	−395.959	+	395.959i	−0.522374	+	0.522374i
$759$		−	228.135i		−	0.300573i
$760$	94.9500	+	98.0501i	0.124934	+	0.129013i
$761$	1236.91			1.62537			0.812684	−	0.582704i	$-0.198005\pi$
$761$	1236.91			1.62537			0.812684	+	0.582704i	$0.198005\pi$
$762$	−48.4815	−	48.4815i	−0.0636240	−	0.0636240i
$763$	670.393	−	670.393i	0.878628	−	0.878628i
$764$		−	163.596i		−	0.214131i
$765$	−27.8928	+	27.0110i	−0.0364612	+	0.0353084i
$766$	703.185			0.917996
$767$	237.259	+	237.259i	0.309333	+	0.309333i
$768$	29.4042	−	29.4042i	0.0382867	−	0.0382867i
$769$			335.147i			0.435822i	0.975969	+	0.217911i	$0.0699242\pi$
$769$			335.147i			0.435822i	−0.975969	+	0.217911i	$0.930076\pi$
$770$	15.0080	−	934.347i	0.0194909	−	1.21344i
$771$	1020.45			1.32354
$772$	335.304	+	335.304i	0.434331	+	0.434331i
$773$	280.124	−	280.124i	0.362386	−	0.362386i	−0.502305	−	0.864691i	$-0.667514\pi$
$773$	280.124	−	280.124i	0.362386	−	0.362386i	0.864691	+	0.502305i	$0.167514\pi$
$774$		−	66.2264i		−	0.0855638i
$775$	−154.748	−	4.97258i	−0.199675	−	0.00641624i
$776$	379.882			0.489539
$777$	−714.763	−	714.763i	−0.919901	−	0.919901i
$778$	−559.908	+	559.908i	−0.719676	+	0.719676i
$779$			489.365i			0.628197i
$780$	515.619	+	8.28218i	0.661050	+	0.0106182i
$781$	660.456			0.845655
$782$	−16.5871	−	16.5871i	−0.0212111	−	0.0212111i
$783$	51.1017	−	51.1017i	0.0652640	−	0.0652640i
$784$		−	12.5314i		−	0.0159839i
$785$	293.669	+	303.258i	0.374101	+	0.386316i
$786$	326.273			0.415105
$787$	−567.531	−	567.531i	−0.721132	−	0.721132i	0.247704	−	0.968836i	$-0.420324\pi$
$787$	−567.531	−	567.531i	−0.721132	−	0.721132i	−0.968836	+	0.247704i	$0.920324\pi$
$788$	−16.6125	+	16.6125i	−0.0210819	+	0.0210819i
$789$			1335.98i			1.69326i
$790$	79.0639	−	76.5642i	0.100081	−	0.0969167i
$791$	−1565.17			−1.97872
$792$	82.1903	+	82.1903i	0.103776	+	0.103776i
$793$	−360.094	+	360.094i	−0.454090	+	0.454090i
$794$		−	284.824i		−	0.358720i
$795$	15.3059	−	952.889i	0.0192527	−	1.19860i
$796$	−330.299			−0.414949
$797$	158.078	+	158.078i	0.198341	+	0.198341i	0.799289	−	0.600947i	$-0.205210\pi$
$797$	158.078	+	158.078i	0.198341	+	0.198341i	−0.600947	+	0.799289i	$0.705210\pi$
$798$	181.111	−	181.111i	0.226956	−	0.226956i
$799$		−	116.221i		−	0.145459i
$800$	−96.7367	−	103.160i	−0.120921	−	0.128950i
$801$	−59.4791			−0.0742561
$802$	−677.211	−	677.211i	−0.844403	−	0.844403i
$803$	288.583	−	288.583i	0.359381	−	0.359381i
$804$			329.280i			0.409553i
$805$	−173.115	−	2.78067i	−0.215049	−	0.00345425i
$806$	−173.782			−0.215610
$807$	−174.975	−	174.975i	−0.216822	−	0.216822i
$808$	−257.361	+	257.361i	−0.318516	+	0.318516i
$809$		−	647.019i		−	0.799776i	−0.916564	−	0.399888i	$-0.869049\pi$
$809$		−	647.019i		−	0.799776i	0.916564	−	0.399888i	$-0.130951\pi$
$810$	274.244	+	283.198i	0.338573	+	0.349627i
$811$	−168.302			−0.207525			−0.103762	−	0.994602i	$-0.533088\pi$
$811$	−168.302			−0.207525			−0.103762	+	0.994602i	$0.533088\pi$
$812$	25.2492	+	25.2492i	0.0310951	+	0.0310951i
$813$	576.473	−	576.473i	0.709068	−	0.709068i
$814$			1394.30i			1.71290i
$815$	186.707	−	180.804i	0.229089	−	0.221846i
$816$	−35.9559			−0.0440636
$817$	142.337	+	142.337i	0.174219	+	0.174219i
$818$	−349.594	+	349.594i	−0.427376	+	0.427376i
$819$			321.665i			0.392753i
$820$	8.14346	−	506.983i	0.00993105	−	0.618272i
$821$	1095.40			1.33423			0.667114	−	0.744956i	$-0.267530\pi$
$821$	1095.40			1.33423			0.667114	+	0.744956i	$0.267530\pi$
$822$	662.501	+	662.501i	0.805962	+	0.805962i
$823$	−465.668	+	465.668i	−0.565818	+	0.565818i	−0.930954	−	0.365136i	$-0.881022\pi$
$823$	−465.668	+	465.668i	−0.565818	+	0.565818i	0.365136	+	0.930954i	$0.381022\pi$
$824$		−	61.8428i		−	0.0750519i
$825$	−867.490	+	813.474i	−1.05150	+	0.986030i
$826$	−172.674			−0.209048
$827$	−592.352	−	592.352i	−0.716266	−	0.716266i	0.251573	−	0.967838i	$-0.419052\pi$
$827$	−592.352	−	592.352i	−0.716266	−	0.716266i	−0.967838	+	0.251573i	$0.919052\pi$
$828$	15.2281	−	15.2281i	0.0183914	−	0.0183914i
$829$			1358.47i			1.63869i	0.573304	+	0.819343i	$0.305662\pi$
$829$			1358.47i			1.63869i	−0.573304	+	0.819343i	$0.694338\pi$
$830$	−962.922	−	15.4670i	−1.16015	−	0.0186350i
$831$	705.391			0.848846
$832$	−112.242	−	112.242i	−0.134906	−	0.134906i
$833$	−7.66180	+	7.66180i	−0.00919784	+	0.00919784i
$834$			500.134i			0.599681i
$835$	860.661	+	888.761i	1.03073	+	1.06438i
$836$	−353.295			−0.422601
$837$	−127.987	−	127.987i	−0.152912	−	0.152912i
$838$	127.172	−	127.172i	0.151756	−	0.151756i
$839$		−	573.703i		−	0.683794i	−0.939737	−	0.341897i	$-0.888931\pi$
$839$		−	573.703i		−	0.683794i	0.939737	−	0.341897i	$-0.111069\pi$
$840$	−190.645	+	184.617i	−0.226958	+	0.219782i
$841$	834.886			0.992730
$842$	123.176	+	123.176i	0.146290	+	0.146290i
$843$	−361.261	+	361.261i	−0.428542	+	0.428542i
$844$			623.497i			0.738740i
$845$	18.0437	−	1123.34i	0.0213535	−	1.32939i
$846$	106.699			0.126122
$847$	1092.59	+	1092.59i	1.28995	+	1.28995i
$848$	−207.429	+	207.429i	−0.244609	+	0.244609i
$849$		−	110.049i		−	0.129621i
$850$	−3.92731	+	122.219i	−0.00462036	+	0.143787i
$851$	258.334			0.303565
$852$	−132.629	−	132.629i	−0.155668	−	0.155668i
$853$	−382.807	+	382.807i	−0.448777	+	0.448777i	−0.894948	−	0.446171i	$-0.852787\pi$
$853$	−382.807	+	382.807i	−0.448777	+	0.448777i	0.446171	+	0.894948i	$0.352787\pi$
$854$		−	262.072i		−	0.306876i
$855$	108.334	+	1.74012i	0.126706	+	0.00203523i
$856$	529.708			0.618818
$857$	−371.449	−	371.449i	−0.433430	−	0.433430i	0.456364	−	0.889793i	$-0.349152\pi$
$857$	−371.449	−	371.449i	−0.433430	−	0.433430i	−0.889793	+	0.456364i	$0.849152\pi$
$858$	−943.862	+	943.862i	−1.10007	+	1.10007i
$859$			200.800i			0.233760i	0.993146	+	0.116880i	$0.0372893\pi$
$859$			200.800i			0.233760i	−0.993146	+	0.116880i	$0.962711\pi$
$860$	−145.093	−	149.830i	−0.168712	−	0.174221i
$861$	−951.502			−1.10511
$862$	158.451	+	158.451i	0.183818	+	0.183818i
$863$	606.257	−	606.257i	0.702499	−	0.702499i	−0.262447	−	0.964946i	$-0.584530\pi$
$863$	606.257	−	606.257i	0.702499	−	0.702499i	0.964946	+	0.262447i	$0.0845295\pi$
$864$		−	165.329i		−	0.191353i
$865$	441.904	−	427.932i	0.510871	−	0.494719i
$866$	−768.026			−0.886867
$867$	−509.129	−	509.129i	−0.587231	−	0.587231i
$868$	63.2382	−	63.2382i	0.0728550	−	0.0728550i
$869$			284.884i			0.327829i
$870$	0.729836	−	45.4370i	0.000838892	−	0.0522265i
$871$	1256.93			1.44309
$872$	262.615	+	262.615i	0.301164	+	0.301164i
$873$	213.234	−	213.234i	0.244254	−	0.244254i
$874$			65.4580i			0.0748947i
$875$	606.712	+	668.189i	0.693385	+	0.763644i
$876$	−115.903			−0.132310
$877$	−1052.02	−	1052.02i	−1.19957	−	1.19957i	−0.974295	−	0.225277i	$-0.927671\pi$
$877$	−1052.02	−	1052.02i	−1.19957	−	1.19957i	−0.225277	−	0.974295i	$-0.572329\pi$
$878$	744.209	−	744.209i	0.847618	−	0.847618i
$879$		−	591.478i		−	0.672899i
$880$	366.014	+	5.87913i	0.415925	+	0.00668083i
$881$	556.146			0.631267			0.315633	−	0.948881i	$-0.397783\pi$
$881$	556.146			0.631267			0.315633	+	0.948881i	$0.397783\pi$
$882$	−7.03407	−	7.03407i	−0.00797514	−	0.00797514i
$883$	−216.393	+	216.393i	−0.245066	+	0.245066i	−0.818942	−	0.573876i	$-0.805439\pi$
$883$	−216.393	+	216.393i	−0.245066	+	0.245066i	0.573876	+	0.818942i	$0.305439\pi$
$884$			137.251i			0.155262i
$885$	152.872	+	157.863i	0.172736	+	0.178376i
$886$	−112.475			−0.126947
$887$	403.720	+	403.720i	0.455153	+	0.455153i	0.897060	−	0.441908i	$-0.145698\pi$
$887$	403.720	+	403.720i	0.455153	+	0.455153i	−0.441908	+	0.897060i	$0.645698\pi$
$888$	279.996	−	279.996i	0.315310	−	0.315310i
$889$		−	134.688i		−	0.151505i
$890$	−134.565	+	130.310i	−0.151197	+	0.146416i
$891$	−1020.42			−1.14525
$892$	−317.659	−	317.659i	−0.356120	−	0.356120i
$893$	−229.323	+	229.323i	−0.256801	+	0.256801i
$894$			998.738i			1.11716i
$895$	25.6023	−	1593.91i	0.0286059	−	1.78090i
$896$	81.6885			0.0911702
$897$	174.878	+	174.878i	0.194958	+	0.194958i
$898$	338.053	−	338.053i	0.376452	−	0.376452i
$899$			15.3139i			0.0170344i
$900$	−112.205	−	3.60554i	−0.124672	−	0.00400616i
$901$	253.647			0.281518
$902$	928.053	+	928.053i	1.02888	+	1.02888i
$903$	−276.754	+	276.754i	−0.306483	+	0.306483i
$904$		−	613.127i		−	0.678238i
$905$	1726.07	+	27.7252i	1.90726	+	0.0306356i
$906$	344.651			0.380410
$907$	171.091	+	171.091i	0.188633	+	0.188633i	0.795105	−	0.606472i	$-0.207416\pi$
$907$	171.091	+	171.091i	0.188633	+	0.188633i	−0.606472	+	0.795105i	$0.707416\pi$
$908$	445.777	−	445.777i	0.490944	−	0.490944i
$909$			288.922i			0.317846i
$910$	704.722	+	727.731i	0.774420	+	0.799705i
$911$	534.110			0.586290			0.293145	−	0.956068i	$-0.405298\pi$
$911$	534.110			0.586290			0.293145	+	0.956068i	$0.405298\pi$
$912$	70.9468	+	70.9468i	0.0777926	+	0.0777926i
$913$	1762.67	−	1762.67i	1.93063	−	1.93063i
$914$		−	340.052i		−	0.372048i
$915$	−239.592	+	232.017i	−0.261850	+	0.253571i
$916$	−57.8132			−0.0631148
$917$	453.213	+	453.213i	0.494234	+	0.494234i
$918$	−101.083	+	101.083i	−0.110113	+	0.110113i
$919$			185.175i			0.201497i	0.994912	+	0.100748i	$0.0321237\pi$
$919$			185.175i			0.201497i	−0.994912	+	0.100748i	$0.967876\pi$
$920$	1.08928	−	67.8146i	0.00118400	−	0.0737115i
$921$	−638.264			−0.693012
$922$	−645.832	−	645.832i	−0.700469	−	0.700469i
$923$	−506.275	+	506.275i	−0.548510	+	0.548510i
$924$		−	686.931i		−	0.743432i
$925$	−921.156	−	982.322i	−0.995845	−	1.06197i
$926$	−188.444			−0.203503
$927$	−34.7133	−	34.7133i	−0.0374470	−	0.0374470i
$928$	−9.89092	+	9.89092i	−0.0106583	+	0.0106583i
$929$			101.644i			0.109412i	0.998502	+	0.0547061i	$0.0174222\pi$
$929$			101.644i			0.109412i	−0.998502	+	0.0547061i	$0.982578\pi$
$930$	−113.800	−	1.82792i	−0.122365	−	0.00196551i
$931$	30.2359			0.0324768
$932$	518.928	+	518.928i	0.556790	+	0.556790i
$933$	−1009.46	+	1009.46i	−1.08196	+	1.08196i
$934$			722.184i			0.773216i
$935$	−220.189	−	227.378i	−0.235496	−	0.243185i
$936$	−126.007			−0.134622
$937$	21.4820	+	21.4820i	0.0229263	+	0.0229263i	0.718477	−	0.695551i	$-0.244840\pi$
$937$	21.4820	+	21.4820i	0.0229263	+	0.0229263i	−0.695551	+	0.718477i	$0.744840\pi$
$938$	−457.391	+	457.391i	−0.487624	+	0.487624i
$939$		−	734.261i		−	0.781961i
$940$	241.396	−	233.763i	0.256804	−	0.248684i
$941$	−235.909			−0.250700			−0.125350	−	0.992113i	$-0.540005\pi$
$941$	−235.909			−0.250700			−0.125350	+	0.992113i	$0.540005\pi$
$942$	219.430	+	219.430i	0.232941	+	0.232941i
$943$	171.949	−	171.949i	0.182342	−	0.182342i
$944$		−	67.6420i		−	0.0716546i
$945$	−16.9457	+	1054.98i	−0.0179319	+	1.11638i
$946$	539.867			0.570684
$947$	177.068	+	177.068i	0.186978	+	0.186978i	0.794388	−	0.607410i	$-0.207792\pi$
$947$	177.068	+	177.068i	0.186978	+	0.186978i	−0.607410	+	0.794388i	$0.707792\pi$
$948$	57.2089	−	57.2089i	0.0603469	−	0.0603469i
$949$			442.429i			0.466205i
$950$	248.906	−	233.408i	0.262006	−	0.245692i
$951$	−18.4717			−0.0194235
$952$	−49.9450	−	49.9450i	−0.0524632	−	0.0524632i
$953$	−1163.43	+	1163.43i	−1.22081	+	1.22081i	−0.253464	+	0.967345i	$0.581570\pi$
$953$	−1163.43	+	1163.43i	−1.22081	+	1.22081i	−0.967345	+	0.253464i	$0.918430\pi$
$954$			232.866i			0.244094i
$955$	−408.938	−	6.56861i	−0.428208	−	0.00687812i
$956$	−18.3772			−0.0192230
$957$	83.1743	+	83.1743i	0.0869115	+	0.0869115i
$958$	617.686	−	617.686i	0.644766	−	0.644766i
$959$			1840.51i			1.91920i
$960$	−72.3204	−	74.6816i	−0.0753337	−	0.0777933i
$961$	−922.645			−0.960089
$962$	−1068.80	−	1068.80i	−1.11102	−	1.11102i
$963$	297.334	−	297.334i	0.308758	−	0.308758i
$964$		−	134.811i		−	0.139845i
$965$	851.614	−	824.688i	0.882501	−	0.854599i
$966$	−127.274			−0.131753
$967$	−748.555	−	748.555i	−0.774101	−	0.774101i	0.204720	−	0.978821i	$-0.434372\pi$
$967$	−748.555	−	748.555i	−0.774101	−	0.774101i	−0.978821	+	0.204720i	$0.934372\pi$
$968$	−428.003	+	428.003i	−0.442152	+	0.442152i
$969$		−	86.7549i		−	0.0895304i
$970$	15.2528	−	949.583i	0.0157245	−	0.978951i
$971$	−90.4980			−0.0932008			−0.0466004	−	0.998914i	$-0.514839\pi$
$971$	−90.4980			−0.0932008			−0.0466004	+	0.998914i	$0.514839\pi$
$972$	−167.074	−	167.074i	−0.171887	−	0.171887i
$973$	−694.717	+	694.717i	−0.713995	+	0.713995i
$974$		−	786.064i		−	0.807047i
$975$	41.4056	−	1288.55i	0.0424672	−	1.32159i
$976$	102.662			0.105186
$977$	−1094.75	−	1094.75i	−1.12052	−	1.12052i	−0.991663	−	0.128859i	$-0.958868\pi$
$977$	−1094.75	−	1094.75i	−1.12052	−	1.12052i	−0.128859	−	0.991663i	$-0.541132\pi$
$978$	135.097	−	135.097i	0.138136	−	0.138136i
$979$		−	484.865i		−	0.495266i
$980$	−31.3245	−	0.503152i	−0.0319637	−	0.000513420i
$981$	294.819			0.300529
$982$	−896.627	−	896.627i	−0.913062	−	0.913062i
$983$	−392.242	+	392.242i	−0.399026	+	0.399026i	−0.877889	−	0.478864i	$-0.841049\pi$
$983$	−392.242	+	392.242i	−0.399026	+	0.399026i	0.478864	+	0.877889i	$0.341049\pi$
$984$		−	372.734i		−	0.378795i
$985$	40.8589	+	42.1929i	0.0414811	+	0.0428355i
$986$	12.0948			0.0122665
$987$	−445.887	−	445.887i	−0.451760	−	0.451760i
$988$	270.819	−	270.819i	0.274109	−	0.274109i
$989$		−	100.026i		−	0.101138i
$990$	208.749	−	202.149i	0.210858	−	0.204191i
$991$	−70.8250			−0.0714682			−0.0357341	−	0.999361i	$-0.511377\pi$
$991$	−70.8250			−0.0714682			−0.0357341	+	0.999361i	$0.511377\pi$
$992$	24.7724	+	24.7724i	0.0249722	+	0.0249722i
$993$	−164.485	+	164.485i	−0.165644	+	0.165644i
$994$		−	368.461i		−	0.370685i
$995$	−13.2619	+	825.641i	−0.0133286	+	0.829790i
$996$	−707.940			−0.710783
$997$	−1054.46	−	1054.46i	−1.05763	−	1.05763i	−0.998234	−	0.0594004i	$-0.981081\pi$
$997$	−1054.46	−	1054.46i	−1.05763	−	1.05763i	−0.0594004	−	0.998234i	$-0.518919\pi$
$998$	−699.998	+	699.998i	−0.701401	+	0.701401i
$999$		−	1574.31i		−	1.57589i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.f.b.47.9	✓	24
5.3	odd	4	inner	230.3.f.b.93.9	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.b.47.9	✓	24	1.1	even	1	trivial
230.3.f.b.93.9	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)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.83776 - 1.83776i) q^{3} +2.00000i q^{4} +(4.99936 + 0.0803026i) q^{5} +3.67552 q^{6} +(5.10553 + 5.10553i) q^{7} +(-2.00000 + 2.00000i) q^{8} +2.24526i q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.00000i) q^{2} +(1.83776 - 1.83776i) q^{3} +2.00000i q^{4} +(4.99936 + 0.0803026i) q^{5} +3.67552 q^{6} +(5.10553 + 5.10553i) q^{7} +(-2.00000 + 2.00000i) q^{8} +2.24526i q^{9} +(4.91905 + 5.07966i) q^{10} -18.3030 q^{11} +(3.67552 + 3.67552i) q^{12} +(14.0303 - 14.0303i) q^{13} +10.2111i q^{14} +(9.33520 - 9.04005i) q^{15} -4.00000 q^{16} +(2.44563 + 2.44563i) q^{17} +(-2.24526 + 2.24526i) q^{18} -9.65125i q^{19} +(-0.160605 + 9.99871i) q^{20} +18.7655 q^{21} +(-18.3030 - 18.3030i) q^{22} +(-3.39116 + 3.39116i) q^{23} +7.35105i q^{24} +(24.9871 + 0.802922i) q^{25} +28.0605 q^{26} +(20.6661 + 20.6661i) q^{27} +(-10.2111 + 10.2111i) q^{28} -2.47273i q^{29} +(18.3752 + 0.295154i) q^{30} -6.19311 q^{31} +(-4.00000 - 4.00000i) q^{32} +(-33.6366 + 33.6366i) q^{33} +4.89127i q^{34} +(25.1144 + 25.9343i) q^{35} -4.49053 q^{36} +(-38.0892 - 38.0892i) q^{37} +(9.65125 - 9.65125i) q^{38} -51.5686i q^{39} +(-10.1593 + 9.83811i) q^{40} -50.7049 q^{41} +(18.7655 + 18.7655i) q^{42} +(-14.7480 + 14.7480i) q^{43} -36.6061i q^{44} +(-0.180300 + 11.2249i) q^{45} -6.78233 q^{46} +(-23.7610 - 23.7610i) q^{47} +(-7.35105 + 7.35105i) q^{48} +3.13285i q^{49} +(24.1842 + 25.7900i) q^{50} +8.98898 q^{51} +(28.0605 + 28.0605i) q^{52} +(51.8572 - 51.8572i) q^{53} +41.3322i q^{54} +(-91.5034 - 1.46978i) q^{55} -20.4221 q^{56} +(-17.7367 - 17.7367i) q^{57} +(2.47273 - 2.47273i) q^{58} +16.9105i q^{59} +(18.0801 + 18.6704i) q^{60} -25.6655 q^{61} +(-6.19311 - 6.19311i) q^{62} +(-11.4633 + 11.4633i) q^{63} -8.00000i q^{64} +(71.2689 - 69.0156i) q^{65} -67.2733 q^{66} +(44.7937 + 44.7937i) q^{67} +(-4.89127 + 4.89127i) q^{68} +12.4643i q^{69} +(-0.819974 + 51.0487i) q^{70} -36.0845 q^{71} +(-4.49053 - 4.49053i) q^{72} +(-15.7669 + 15.7669i) q^{73} -76.1784i q^{74} +(47.3959 - 44.4448i) q^{75} +19.3025 q^{76} +(-93.4467 - 93.4467i) q^{77} +(51.5686 - 51.5686i) q^{78} -15.5648i q^{79} +(-19.9974 - 0.321210i) q^{80} +55.7514 q^{81} +(-50.7049 - 50.7049i) q^{82} +(-96.3047 + 96.3047i) q^{83} +37.5310i q^{84} +(12.0302 + 12.4230i) q^{85} -29.4960 q^{86} +(-4.54429 - 4.54429i) q^{87} +(36.6061 - 36.6061i) q^{88} +26.4910i q^{89} +(-11.4052 + 11.0446i) q^{90} +143.264 q^{91} +(-6.78233 - 6.78233i) q^{92} +(-11.3815 + 11.3815i) q^{93} -47.5220i q^{94} +(0.775021 - 48.2500i) q^{95} -14.7021 q^{96} +(-94.9705 - 94.9705i) q^{97} +(-3.13285 + 3.13285i) q^{98} -41.0951i 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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