LMFDB - Embedded newform 230.3.f.b.93.9

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			93.9
Character	$\chi$	$=$	230.93
Dual form			230.3.f.b.47.9

$q$-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 $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

Coefficient data

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

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

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

$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$2$	1.00000	−	1.00000i	0.500000	−	0.500000i
$3$	1.83776	+	1.83776i	0.612587	+	0.612587i	0.943619	−	0.331032i	$-0.107397\pi$
$3$	1.83776	+	1.83776i	0.612587	+	0.612587i	−0.331032	+	0.943619i	$0.607397\pi$
$4$		−	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	−0.241131	−	0.970493i	$-0.577518\pi$
$7$	5.10553	−	5.10553i	0.729361	−	0.729361i	0.970493	+	0.241131i	$0.0775184\pi$
$8$	−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	0.996577	+	0.0826745i	$0.0263462\pi$
$13$	14.0303	+	14.0303i	1.07925	+	1.07925i	0.0826745	+	0.996577i	$0.473654\pi$
$14$		−	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	−0.631508	−	0.775369i	$-0.717564\pi$
$17$	2.44563	−	2.44563i	0.143861	−	0.143861i	0.775369	+	0.631508i	$0.217564\pi$
$18$	−2.24526	−	2.24526i	−0.124737	−	0.124737i
$19$			9.65125i			0.507961i	0.967209	+	0.253980i	$0.0817398\pi$
$19$			9.65125i			0.507961i	−0.967209	+	0.253980i	$0.918260\pi$
$20$	−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	$0.0135747\pi$
$29$			2.47273i			0.0852666i	−0.999091	+	0.0426333i	$0.986425\pi$
$30$	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	−0.0298846	+	0.999553i	$0.509514\pi$
$37$	−38.0892	+	38.0892i	−1.02944	+	1.02944i	−0.999553	+	0.0298846i	$0.990486\pi$
$38$	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	0.514508	−	0.857485i	$-0.327974\pi$
$43$	−14.7480	−	14.7480i	−0.342977	−	0.342977i	−0.857485	+	0.514508i	$0.827974\pi$
$44$			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	−0.913158	−	0.407605i	$-0.866364\pi$
$47$	−23.7610	+	23.7610i	−0.505553	+	0.505553i	0.407605	+	0.913158i	$0.366364\pi$
$48$	−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	0.999772	−	0.0213348i	$-0.00679160\pi$
$53$	51.8572	+	51.8572i	0.978438	+	0.978438i	−0.0213348	+	0.999772i	$0.506792\pi$
$54$		−	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	$-0.954226\pi$
$59$		−	16.9105i		−	0.286619i	0.989678	−	0.143309i	$-0.0457744\pi$
$60$	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	−0.288821	−	0.957383i	$-0.593263\pi$
$67$	44.7937	−	44.7937i	0.668562	−	0.668562i	0.957383	+	0.288821i	$0.0932632\pi$
$68$	−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	0.590819	−	0.806804i	$-0.298805\pi$
$73$	−15.7669	−	15.7669i	−0.215985	−	0.215985i	−0.806804	+	0.590819i	$0.798805\pi$
$74$			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	$0.0314081\pi$
$79$			15.5648i			0.197023i	−0.995136	+	0.0985115i	$0.968592\pi$
$80$	−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	−0.984410	−	0.175887i	$-0.943721\pi$
$83$	−96.3047	−	96.3047i	−1.16030	−	1.16030i	−0.175887	−	0.984410i	$-0.556279\pi$
$84$		−	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	$-0.952451\pi$
$89$		−	26.4910i		−	0.297651i	0.988863	−	0.148826i	$-0.0475493\pi$
$90$	−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	−0.999786	−	0.0207078i	$-0.993408\pi$
$97$	−94.9705	+	94.9705i	−0.979078	+	0.979078i	0.0207078	+	0.999786i	$0.493408\pi$
$98$	−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	0.628061	−	0.778164i	$-0.283849\pi$
$103$	−15.4607	−	15.4607i	−0.150104	−	0.150104i	−0.778164	+	0.628061i	$0.783849\pi$
$104$		−	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	−0.276672	+	0.960965i	$0.589231\pi$
$107$	−132.427	+	132.427i	−1.23764	+	1.23764i	−0.960965	+	0.276672i	$0.910769\pi$
$108$	−41.3322	−	41.3322i	−0.382706	−	0.382706i
$109$			131.307i			1.20465i	0.798249	+	0.602327i	$0.205760\pi$
$109$			131.307i			1.20465i	−0.798249	+	0.602327i	$0.794240\pi$
$110$	−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	−0.878221	−	0.478256i	$-0.841269\pi$
$113$	−153.282	−	153.282i	−1.35648	−	1.35648i	−0.478256	−	0.878221i	$-0.658731\pi$
$114$			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	−0.757128	−	0.653267i	$-0.773398\pi$
$127$	−13.1904	+	13.1904i	−0.103861	+	0.103861i	0.653267	+	0.757128i	$0.273398\pi$
$128$	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	0.398502	−	0.917167i	$-0.369530\pi$
$137$	180.247	−	180.247i	1.31567	−	1.31567i	0.917167	−	0.398502i	$-0.130470\pi$
$138$	−12.4643	−	12.4643i	−0.0903211	−	0.0903211i
$139$		−	136.072i		−	0.978932i	−0.872022	−	0.489466i	$-0.837192\pi$
$139$		−	136.072i		−	0.978932i	0.872022	−	0.489466i	$-0.162808\pi$
$140$	−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	$-0.634666\pi$
$149$		−	271.727i		−	1.82367i	0.410557	−	0.911835i	$-0.365334\pi$
$150$	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	−0.490937	−	0.871195i	$-0.663346\pi$
$157$	59.7004	−	59.7004i	0.380257	−	0.380257i	0.871195	+	0.490937i	$0.163346\pi$
$158$	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	0.810808	−	0.585312i	$-0.199028\pi$
$163$	36.7559	+	36.7559i	0.225496	+	0.225496i	−0.585312	+	0.810808i	$0.699028\pi$
$164$			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	0.0488887	−	0.998804i	$-0.484432\pi$
$167$	174.965	−	174.965i	1.04769	−	1.04769i	0.998804	−	0.0488887i	$-0.0155680\pi$
$168$	−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	0.912326	−	0.409466i	$-0.134285\pi$
$173$	86.9948	+	86.9948i	0.502860	+	0.502860i	−0.409466	+	0.912326i	$0.634285\pi$
$174$			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	$0.349692\pi$
$179$			318.823i			1.78113i	−0.454852	+	0.890567i	$0.650308\pi$
$180$	−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	0.992324	−	0.123662i	$-0.0394639\pi$
$193$	167.652	+	167.652i	0.868662	+	0.868662i	−0.123662	+	0.992324i	$0.539464\pi$
$194$			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	−0.685711	−	0.727874i	$-0.740508\pi$
$197$	8.30626	−	8.30626i	0.0421637	−	0.0421637i	0.727874	+	0.685711i	$0.240508\pi$
$198$	41.0951	+	41.0951i	0.207551	+	0.207551i
$199$		−	165.150i		−	0.829897i	−0.909845	−	0.414949i	$-0.863800\pi$
$199$		−	165.150i		−	0.829897i	0.909845	−	0.414949i	$-0.136200\pi$
$200$	−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	0.254764	−	0.967003i	$-0.418002\pi$
$223$	−158.829	−	158.829i	−0.712240	−	0.712240i	−0.967003	+	0.254764i	$0.918002\pi$
$224$			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	−0.999839	−	0.0179518i	$-0.994285\pi$
$227$	−222.888	+	222.888i	−0.981887	+	0.981887i	0.0179518	+	0.999839i	$0.494285\pi$
$228$	35.4734	+	35.4734i	0.155585	+	0.155585i
$229$		−	28.9066i		−	0.126230i	−0.998006	−	0.0631148i	$-0.979897\pi$
$229$		−	28.9066i		−	0.126230i	0.998006	−	0.0631148i	$-0.0201034\pi$
$230$	−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	0.992663	+	0.120918i	$0.0385837\pi$
$233$	259.464	+	259.464i	1.11358	+	1.11358i	0.120918	+	0.992663i	$0.461416\pi$
$234$		−	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	$-0.993881\pi$
$239$		−	9.18860i		−	0.0384460i	0.999815	−	0.0192230i	$-0.00611925\pi$
$240$	−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	0.0838088	−	0.996482i	$-0.473291\pi$
$257$	277.635	−	277.635i	1.08029	−	1.08029i	0.996482	−	0.0838088i	$-0.0267085\pi$
$258$	−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	−0.840960	−	0.541097i	$-0.818009\pi$
$263$	−363.481	−	363.481i	−1.38206	−	1.38206i	−0.541097	−	0.840960i	$-0.681991\pi$
$264$			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	$0.0566303\pi$
$269$			95.2110i			0.353944i	−0.984216	+	0.176972i	$0.943370\pi$
$270$	−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	−0.270019	−	0.962855i	$-0.587030\pi$
$277$	191.916	−	191.916i	0.692836	−	0.692836i	0.962855	+	0.270019i	$0.0870299\pi$
$278$	−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	0.758024	−	0.652226i	$-0.226165\pi$
$283$	29.9409	+	29.9409i	0.105798	+	0.105798i	−0.652226	+	0.758024i	$0.726165\pi$
$284$			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	0.926217	−	0.376990i	$-0.123041\pi$
$293$	160.923	+	160.923i	0.549227	+	0.549227i	−0.376990	+	0.926217i	$0.623041\pi$
$294$		−	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	−0.930905	−	0.365262i	$-0.880979\pi$
$307$	−173.652	+	173.652i	−0.565643	+	0.565643i	0.365262	+	0.930905i	$0.380979\pi$
$308$	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	0.950122	−	0.311878i	$-0.100958\pi$
$313$	199.770	+	199.770i	0.638244	+	0.638244i	−0.311878	+	0.950122i	$0.600958\pi$
$314$		−	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	−0.714989	−	0.699136i	$-0.753568\pi$
$317$	−5.02560	+	5.02560i	−0.0158536	+	0.0158536i	0.699136	+	0.714989i	$0.253568\pi$
$318$	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	−0.862024	−	0.506868i	$-0.830803\pi$
$337$	−119.687	+	119.687i	−0.355156	+	0.355156i	0.506868	+	0.862024i	$0.330803\pi$
$338$	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	−0.282206	−	0.959354i	$-0.591066\pi$
$347$	234.971	−	234.971i	0.677148	−	0.677148i	0.959354	+	0.282206i	$0.0910660\pi$
$348$	9.08858	+	9.08858i	0.0261166	+	0.0261166i
$349$			67.9780i			0.194779i	0.995246	+	0.0973896i	$0.0310493\pi$
$349$			67.9780i			0.194779i	−0.995246	+	0.0973896i	$0.968951\pi$
$350$	−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	0.150876	−	0.988553i	$-0.451790\pi$
$353$	−295.700	−	295.700i	−0.837676	−	0.837676i	−0.988553	+	0.150876i	$0.951790\pi$
$354$		−	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	$-0.903569\pi$
$359$		−	214.204i		−	0.596670i	0.954461	−	0.298335i	$-0.0964312\pi$
$360$	−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	−0.311166	−	0.950355i	$-0.600720\pi$
$367$	234.582	−	234.582i	0.639189	−	0.639189i	0.950355	+	0.311166i	$0.100720\pi$
$368$	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	−0.997861	−	0.0653653i	$-0.979179\pi$
$373$	−396.584	−	396.584i	−1.06323	−	1.06323i	−0.0653653	−	0.997861i	$-0.520821\pi$
$374$			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	$-0.825047\pi$
$379$		−	395.959i		−	1.04475i	0.852717	−	0.522374i	$-0.174953\pi$
$380$	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	0.996884	−	0.0788876i	$-0.0251368\pi$
$383$	351.592	+	351.592i	0.917996	+	0.917996i	−0.0788876	+	0.996884i	$0.525137\pi$
$384$			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	$-0.744290\pi$
$389$		−	559.908i		−	1.43935i	0.694310	−	0.719676i	$-0.255710\pi$
$390$	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	−0.863341	−	0.504621i	$-0.831632\pi$
$397$	−142.412	+	142.412i	−0.358720	+	0.358720i	0.504621	+	0.863341i	$0.331632\pi$
$398$	−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	$-0.859438\pi$
$409$		−	349.594i		−	0.854753i	0.904074	−	0.427376i	$-0.140562\pi$
$410$	−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	$0.0484929\pi$
$419$			127.172i			0.303513i	−0.988418	+	0.151756i	$0.951507\pi$
$420$	−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	0.107354	−	0.994221i	$-0.465762\pi$
$433$	−384.013	−	384.013i	−0.886867	−	0.886867i	−0.994221	+	0.107354i	$0.965762\pi$
$434$			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	$0.321964\pi$
$439$			744.209i			1.69524i	−0.530607	+	0.847618i	$0.678036\pi$
$440$	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	0.640779	−	0.767726i	$-0.278612\pi$
$443$	−56.2374	−	56.2374i	−0.126947	−	0.126947i	−0.767726	+	0.640779i	$0.778612\pi$
$444$			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	$0.122856\pi$
$449$			338.053i			0.752903i	−0.926436	+	0.376452i	$0.877144\pi$
$450$	−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	−0.868223	−	0.496175i	$-0.834737\pi$
$457$	−170.026	+	170.026i	−0.372048	+	0.372048i	0.496175	+	0.868223i	$0.334737\pi$
$458$	−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	0.597996	−	0.801499i	$-0.295964\pi$
$463$	−94.2218	−	94.2218i	−0.203503	−	0.203503i	−0.801499	+	0.597996i	$0.795964\pi$
$464$		−	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	−0.205451	−	0.978667i	$-0.565866\pi$
$467$	361.092	−	361.092i	0.773216	−	0.773216i	0.978667	+	0.205451i	$0.0658661\pi$
$468$	−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	$0.223045\pi$
$479$			617.686i			1.28953i	−0.764380	+	0.644766i	$0.776955\pi$
$480$	−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	−0.984186	−	0.177139i	$-0.943316\pi$
$487$	−393.032	+	393.032i	−0.807047	+	0.807047i	0.177139	+	0.984186i	$0.443316\pi$
$488$	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	$-0.752558\pi$
$499$		−	699.998i		−	1.40280i	0.712767	−	0.701401i	$-0.247442\pi$
$500$	−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	0.0614321	−	0.998111i	$-0.480433\pi$
$503$	−471.150	−	471.150i	−0.936679	−	0.936679i	−0.998111	+	0.0614321i	$0.980433\pi$
$504$			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	$-0.809286\pi$
$509$		−	574.088i		−	1.12787i	0.825818	−	0.563937i	$-0.190714\pi$
$510$	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	0.887072	+	0.461632i	$0.152736\pi$
$523$	705.372	+	705.372i	1.34870	+	1.34870i	0.461632	+	0.887072i	$0.347264\pi$
$524$		−	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	−0.422430	−	0.906395i	$-0.638823\pi$
$547$	264.729	−	264.729i	0.483965	−	0.483965i	0.906395	+	0.422430i	$0.138823\pi$
$548$	−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	−0.941405	−	0.337279i	$-0.890493\pi$
$557$	−336.498	+	336.498i	−0.604125	+	0.604125i	0.337279	+	0.941405i	$0.390493\pi$
$558$	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	0.669797	−	0.742544i	$-0.266381\pi$
$563$	−40.9563	−	40.9563i	−0.0727465	−	0.0727465i	−0.742544	+	0.669797i	$0.766381\pi$
$564$			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	$-0.990558\pi$
$569$		−	33.7512i		−	0.0593168i	0.999560	−	0.0296584i	$-0.00944194\pi$
$570$	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	−0.724025	−	0.689774i	$-0.757710\pi$
$577$	−19.7627	+	19.7627i	−0.0342508	+	0.0342508i	0.689774	+	0.724025i	$0.257710\pi$
$578$	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	0.329262	−	0.944239i	$-0.393200\pi$
$587$	747.545	−	747.545i	1.27350	−	1.27350i	0.944239	−	0.329262i	$-0.106800\pi$
$588$	−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	0.931416	−	0.363957i	$-0.118574\pi$
$593$	336.503	+	336.503i	0.567459	+	0.567459i	−0.363957	+	0.931416i	$0.618574\pi$
$594$			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	$0.265843\pi$
$599$			888.211i			1.48282i	−0.671050	+	0.741412i	$0.734157\pi$
$600$	−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	−0.861618	−	0.507557i	$-0.830549\pi$
$607$	−214.915	+	214.915i	−0.354061	+	0.354061i	0.507557	+	0.861618i	$0.330549\pi$
$608$	−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	0.499554	−	0.866283i	$-0.333497\pi$
$613$	−224.804	−	224.804i	−0.366728	−	0.366728i	−0.866283	+	0.499554i	$0.833497\pi$
$614$			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	−0.743209	−	0.669060i	$-0.766697\pi$
$617$	−45.7498	+	45.7498i	−0.0741487	+	0.0741487i	0.669060	+	0.743209i	$0.266697\pi$
$618$	−56.8262	−	56.8262i	−0.0919517	−	0.0919517i
$619$		−	984.136i		−	1.58988i	−0.606688	−	0.794940i	$-0.707502\pi$
$619$		−	984.136i		−	1.58988i	0.606688	−	0.794940i	$-0.292498\pi$
$620$	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	0.557377	−	0.830260i	$-0.311808\pi$
$643$	−175.464	−	175.464i	−0.272883	−	0.272883i	−0.830260	+	0.557377i	$0.811808\pi$
$644$			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	−0.263714	−	0.964601i	$-0.584948\pi$
$647$	453.474	−	453.474i	0.700886	−	0.700886i	0.964601	+	0.263714i	$0.0849476\pi$
$648$	−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	0.619413	−	0.785065i	$-0.287371\pi$
$653$	−108.171	−	108.171i	−0.165652	−	0.165652i	−0.785065	+	0.619413i	$0.787371\pi$
$654$			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	$0.191531\pi$
$659$			746.059i			1.13211i	−0.824368	+	0.566054i	$0.808469\pi$
$660$	−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	0.404408	−	0.914579i	$-0.367478\pi$
$673$	−343.345	−	343.345i	−0.510171	−	0.510171i	−0.914579	+	0.404408i	$0.867478\pi$
$674$			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	−0.909781	−	0.415089i	$-0.863750\pi$
$677$	−334.906	+	334.906i	−0.494691	+	0.494691i	0.415089	+	0.909781i	$0.363750\pi$
$678$	−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	0.862252	−	0.506480i	$-0.169054\pi$
$683$	242.992	+	242.992i	0.355772	+	0.355772i	−0.506480	+	0.862252i	$0.669054\pi$
$684$		−	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	$0.0385195\pi$
$709$			171.177i			0.241435i	−0.992687	+	0.120718i	$0.961480\pi$
$710$	−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	$0.209858\pi$
$719$			880.854i			1.22511i	−0.790428	+	0.612555i	$0.790142\pi$
$720$	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	−0.944658	−	0.328056i	$-0.893607\pi$
$727$	−448.270	+	448.270i	−0.616603	+	0.616603i	0.328056	+	0.944658i	$0.393607\pi$
$728$	−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	0.498383	−	0.866957i	$-0.333927\pi$
$733$	−270.164	−	270.164i	−0.368573	−	0.368573i	−0.866957	+	0.498383i	$0.833927\pi$
$734$		−	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	$0.352469\pi$
$739$			1322.07i			1.78900i	−0.447067	+	0.894501i	$0.647531\pi$
$740$	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	0.760856	−	0.648921i	$-0.224779\pi$
$743$	83.1674	+	83.1674i	0.111935	+	0.111935i	−0.648921	+	0.760856i	$0.724779\pi$
$744$			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	−0.157752	−	0.987479i	$-0.550425\pi$
$757$	628.103	−	628.103i	0.829727	−	0.829727i	0.987479	+	0.157752i	$0.0504246\pi$
$758$	−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	$-0.930076\pi$
$769$		−	335.147i		−	0.435822i	0.975969	−	0.217911i	$-0.0699242\pi$
$770$	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	0.864691	−	0.502305i	$-0.167514\pi$
$773$	280.124	+	280.124i	0.362386	+	0.362386i	−0.502305	+	0.864691i	$0.667514\pi$
$774$			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	−0.968836	−	0.247704i	$-0.920324\pi$
$787$	−567.531	+	567.531i	−0.721132	+	0.721132i	0.247704	+	0.968836i	$0.420324\pi$
$788$	−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	−0.600947	−	0.799289i	$-0.705210\pi$
$797$	158.078	−	158.078i	0.198341	−	0.198341i	0.799289	+	0.600947i	$0.205210\pi$
$798$	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	$0.130951\pi$
$809$			647.019i			0.799776i	−0.916564	+	0.399888i	$0.869049\pi$
$810$	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	0.365136	−	0.930954i	$-0.381022\pi$
$823$	−465.668	−	465.668i	−0.565818	−	0.565818i	−0.930954	+	0.365136i	$0.881022\pi$
$824$			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	−0.967838	−	0.251573i	$-0.919052\pi$
$827$	−592.352	+	592.352i	−0.716266	+	0.716266i	0.251573	+	0.967838i	$0.419052\pi$
$828$	15.2281	+	15.2281i	0.0183914	+	0.0183914i
$829$		−	1358.47i		−	1.63869i	−0.573304	−	0.819343i	$-0.694338\pi$
$829$		−	1358.47i		−	1.63869i	0.573304	−	0.819343i	$-0.305662\pi$
$830$	−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	$0.111069\pi$
$839$			573.703i			0.683794i	−0.939737	+	0.341897i	$0.888931\pi$
$840$	−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	0.446171	−	0.894948i	$-0.352787\pi$
$853$	−382.807	−	382.807i	−0.448777	−	0.448777i	−0.894948	+	0.446171i	$0.852787\pi$
$854$			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	−0.889793	−	0.456364i	$-0.849152\pi$
$857$	−371.449	+	371.449i	−0.433430	+	0.433430i	0.456364	+	0.889793i	$0.349152\pi$
$858$	−943.862	−	943.862i	−1.10007	−	1.10007i
$859$		−	200.800i		−	0.233760i	−0.993146	−	0.116880i	$-0.962711\pi$
$859$		−	200.800i		−	0.233760i	0.993146	−	0.116880i	$-0.0372893\pi$
$860$	−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	0.964946	−	0.262447i	$-0.0845295\pi$
$863$	606.257	+	606.257i	0.702499	+	0.702499i	−0.262447	+	0.964946i	$0.584530\pi$
$864$			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	−0.225277	+	0.974295i	$0.572329\pi$
$877$	−1052.02	+	1052.02i	−1.19957	+	1.19957i	−0.974295	+	0.225277i	$0.927671\pi$
$878$	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	0.573876	−	0.818942i	$-0.305439\pi$
$883$	−216.393	−	216.393i	−0.245066	−	0.245066i	−0.818942	+	0.573876i	$0.805439\pi$
$884$		−	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	−0.441908	−	0.897060i	$-0.645698\pi$
$887$	403.720	−	403.720i	0.455153	−	0.455153i	0.897060	+	0.441908i	$0.145698\pi$
$888$	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	−0.606472	−	0.795105i	$-0.707416\pi$
$907$	171.091	−	171.091i	0.188633	−	0.188633i	0.795105	+	0.606472i	$0.207416\pi$
$908$	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	$-0.967876\pi$
$919$		−	185.175i		−	0.201497i	0.994912	−	0.100748i	$-0.0321237\pi$
$920$	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	$-0.982578\pi$
$929$		−	101.644i		−	0.109412i	0.998502	−	0.0547061i	$-0.0174222\pi$
$930$	−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	−0.695551	−	0.718477i	$-0.744840\pi$
$937$	21.4820	−	21.4820i	0.0229263	−	0.0229263i	0.718477	+	0.695551i	$0.244840\pi$
$938$	−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	−0.607410	−	0.794388i	$-0.707792\pi$
$947$	177.068	−	177.068i	0.186978	−	0.186978i	0.794388	+	0.607410i	$0.207792\pi$
$948$	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	−0.967345	−	0.253464i	$-0.918430\pi$
$953$	−1163.43	−	1163.43i	−1.22081	−	1.22081i	−0.253464	−	0.967345i	$-0.581570\pi$
$954$		−	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	−0.978821	−	0.204720i	$-0.934372\pi$
$967$	−748.555	+	748.555i	−0.774101	+	0.774101i	0.204720	+	0.978821i	$0.434372\pi$
$968$	−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	−0.128859	+	0.991663i	$0.541132\pi$
$977$	−1094.75	+	1094.75i	−1.12052	+	1.12052i	−0.991663	+	0.128859i	$0.958868\pi$
$978$	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	0.478864	−	0.877889i	$-0.341049\pi$
$983$	−392.242	−	392.242i	−0.399026	−	0.399026i	−0.877889	+	0.478864i	$0.841049\pi$
$984$			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	−0.0594004	+	0.998234i	$0.518919\pi$
$997$	−1054.46	+	1054.46i	−1.05763	+	1.05763i	−0.998234	+	0.0594004i	$0.981081\pi$
$998$	−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.93.9	yes	24
5.2	odd	4	inner	230.3.f.b.47.9	✓	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.f.b.47.9	✓	24	5.2	odd	4	inner
230.3.f.b.93.9	yes	24	1.1	even	1	trivial

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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