LMFDB - Embedded newform 230.5.f.a.47.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,5,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, 5, names="a")

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

chi := DirichletCharacter("230.47");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 5 $
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:	$23.7750915093$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			47.17
Character	$\chi$	$=$	230.47
Dual form			230.5.f.a.93.17

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.00000 - 2.00000i) q^{2} +(6.64524 - 6.64524i) q^{3} +8.00000i q^{4} +(-21.5847 - 12.6135i) q^{5} -26.5810 q^{6} +(27.2438 + 27.2438i) q^{7} +(16.0000 - 16.0000i) q^{8} -7.31852i q^{9} +O(q^{10})$	\(q+(-2.00000 - 2.00000i) q^{2} +(6.64524 - 6.64524i) q^{3} +8.00000i q^{4} +(-21.5847 - 12.6135i) q^{5} -26.5810 q^{6} +(27.2438 + 27.2438i) q^{7} +(16.0000 - 16.0000i) q^{8} -7.31852i q^{9} +(17.9425 + 68.3964i) q^{10} +37.9502 q^{11} +(53.1619 + 53.1619i) q^{12} +(-142.665 + 142.665i) q^{13} -108.975i q^{14} +(-227.255 + 59.6162i) q^{15} -64.0000 q^{16} +(245.191 + 245.191i) q^{17} +(-14.6370 + 14.6370i) q^{18} +52.3582i q^{19} +(100.908 - 172.678i) q^{20} +362.084 q^{21} +(-75.9003 - 75.9003i) q^{22} +(77.9968 - 77.9968i) q^{23} -212.648i q^{24} +(306.801 + 544.516i) q^{25} +570.660 q^{26} +(489.631 + 489.631i) q^{27} +(-217.951 + 217.951i) q^{28} +529.976i q^{29} +(573.743 + 335.278i) q^{30} +291.283 q^{31} +(128.000 + 128.000i) q^{32} +(252.188 - 252.188i) q^{33} -980.765i q^{34} +(-244.412 - 931.690i) q^{35} +58.5482 q^{36} +(-1114.16 - 1114.16i) q^{37} +(104.716 - 104.716i) q^{38} +1896.09i q^{39} +(-547.171 + 143.540i) q^{40} +1609.52 q^{41} +(-724.167 - 724.167i) q^{42} +(-1529.16 + 1529.16i) q^{43} +303.601i q^{44} +(-92.3119 + 157.968i) q^{45} -311.987 q^{46} +(358.184 + 358.184i) q^{47} +(-425.296 + 425.296i) q^{48} -916.548i q^{49} +(475.431 - 1702.63i) q^{50} +3258.71 q^{51} +(-1141.32 - 1141.32i) q^{52} +(2469.97 - 2469.97i) q^{53} -1958.53i q^{54} +(-819.144 - 478.683i) q^{55} +871.802 q^{56} +(347.933 + 347.933i) q^{57} +(1059.95 - 1059.95i) q^{58} +6450.63i q^{59} +(-476.930 - 1818.04i) q^{60} +4440.02 q^{61} +(-582.566 - 582.566i) q^{62} +(199.384 - 199.384i) q^{63} -512.000i q^{64} +(4878.88 - 1279.88i) q^{65} -1008.75 q^{66} +(-150.312 - 150.312i) q^{67} +(-1961.53 + 1961.53i) q^{68} -1036.62i q^{69} +(-1374.56 + 2352.20i) q^{70} +4530.32 q^{71} +(-117.096 - 117.096i) q^{72} +(4998.60 - 4998.60i) q^{73} +4456.64i q^{74} +(5657.21 + 1579.68i) q^{75} -418.866 q^{76} +(1033.91 + 1033.91i) q^{77} +(3792.17 - 3792.17i) q^{78} -4226.17i q^{79} +(1381.42 + 807.262i) q^{80} +7100.24 q^{81} +(-3219.04 - 3219.04i) q^{82} +(-1216.26 + 1216.26i) q^{83} +2896.67i q^{84} +(-2199.68 - 8385.10i) q^{85} +6116.62 q^{86} +(3521.82 + 3521.82i) q^{87} +(607.203 - 607.203i) q^{88} +11123.6i q^{89} +(500.560 - 131.313i) q^{90} -7773.48 q^{91} +(623.974 + 623.974i) q^{92} +(1935.64 - 1935.64i) q^{93} -1432.74i q^{94} +(660.419 - 1130.14i) q^{95} +1701.18 q^{96} +(3437.40 + 3437.40i) q^{97} +(-1833.10 + 1833.10i) q^{98} -277.739i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8}+O(q^{10}) $ 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8	$ 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) $ 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8 - 184 * q^10 + 8 * q^11 + 20 * q^13 + 396 * q^15 - 2816 * q^16 + 1080 * q^17 - 2648 * q^18 + 544 * q^20 - 3096 * q^21 - 16 * q^22 - 1884 * q^25 - 80 * q^26 - 3828 * q^27 + 640 * q^28 - 2520 * q^30 - 1580 * q^31 + 5632 * q^32 + 3644 * q^33 + 8208 * q^35 + 10592 * q^36 + 3104 * q^37 - 4064 * q^38 - 704 * q^40 + 4124 * q^41 + 6192 * q^42 - 960 * q^43 - 11316 * q^45 + 2424 * q^47 + 7832 * q^50 + 14840 * q^51 + 160 * q^52 - 3116 * q^53 - 2572 * q^55 - 2560 * q^56 - 9408 * q^57 - 3928 * q^58 + 6912 * q^60 + 19136 * q^61 + 3160 * q^62 + 4564 * q^63 - 9220 * q^65 - 14576 * q^66 - 5152 * q^67 - 8640 * q^68 - 23672 * q^70 + 7900 * q^71 - 21184 * q^72 + 16424 * q^73 + 24156 * q^75 + 16256 * q^76 - 27012 * q^77 - 1808 * q^78 - 1536 * q^80 - 116684 * q^81 - 8248 * q^82 + 11184 * q^83 - 14620 * q^85 + 3840 * q^86 + 8312 * q^87 + 128 * q^88 + 14544 * q^90 + 10296 * q^91 - 7488 * q^93 + 19536 * q^95 + 41292 * q^97 + 51024 * 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 $

$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$2$	−2.00000	−	2.00000i	−0.500000	−	0.500000i
$3$	6.64524	−	6.64524i	0.738360	−	0.738360i	−0.233900	−	0.972261i	$-0.575149\pi$
$3$	6.64524	−	6.64524i	0.738360	−	0.738360i	0.972261	+	0.233900i	$0.0751489\pi$
$4$			8.00000i			0.500000i
$5$	−21.5847	−	12.6135i	−0.863389	−	0.504539i
$5$	−21.5847	−	12.6135i	−0.863389	−	0.504539i
$6$	−26.5810			−0.738360
$7$	27.2438	+	27.2438i	0.555996	+	0.555996i	0.928165	−	0.372169i	$-0.121386\pi$
$7$	27.2438	+	27.2438i	0.555996	+	0.555996i	−0.372169	+	0.928165i	$0.621386\pi$
$8$	16.0000	−	16.0000i	0.250000	−	0.250000i
$9$		−	7.31852i		−	0.0903521i
$10$	17.9425	+	68.3964i	0.179425	+	0.683964i
$11$	37.9502			0.313638			0.156819	−	0.987627i	$-0.449876\pi$
$11$	37.9502			0.313638			0.156819	+	0.987627i	$0.449876\pi$
$12$	53.1619	+	53.1619i	0.369180	+	0.369180i
$13$	−142.665	+	142.665i	−0.844171	+	0.844171i	−0.989398	−	0.145227i	$-0.953609\pi$
$13$	−142.665	+	142.665i	−0.844171	+	0.844171i	0.145227	+	0.989398i	$0.453609\pi$
$14$		−	108.975i		−	0.555996i
$15$	−227.255	+	59.6162i	−1.01002	+	0.264961i
$16$	−64.0000			−0.250000
$17$	245.191	+	245.191i	0.848413	+	0.848413i	0.989935	−	0.141522i	$-0.0451996\pi$
$17$	245.191	+	245.191i	0.848413	+	0.848413i	−0.141522	+	0.989935i	$0.545200\pi$
$18$	−14.6370	+	14.6370i	−0.0451760	+	0.0451760i
$19$			52.3582i			0.145037i	0.997367	+	0.0725183i	$0.0231036\pi$
$19$			52.3582i			0.145037i	−0.997367	+	0.0725183i	$0.976896\pi$
$20$	100.908	−	172.678i	0.252269	−	0.431695i
$21$	362.084			0.821052
$22$	−75.9003	−	75.9003i	−0.156819	−	0.156819i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$23$	77.9968	−	77.9968i	0.147442	−	0.147442i
$24$		−	212.648i		−	0.369180i
$25$	306.801	+	544.516i	0.490882	+	0.871226i
$26$	570.660			0.844171
$27$	489.631	+	489.631i	0.671648	+	0.671648i
$28$	−217.951	+	217.951i	−0.277998	+	0.277998i
$29$			529.976i			0.630174i	0.949063	+	0.315087i	$0.102034\pi$
$29$			529.976i			0.630174i	−0.949063	+	0.315087i	$0.897966\pi$
$30$	573.743	+	335.278i	0.637492	+	0.372531i
$31$	291.283			0.303104			0.151552	−	0.988449i	$-0.451573\pi$
$31$	291.283			0.303104			0.151552	+	0.988449i	$0.451573\pi$
$32$	128.000	+	128.000i	0.125000	+	0.125000i
$33$	252.188	−	252.188i	0.231578	−	0.231578i
$34$		−	980.765i		−	0.848413i
$35$	−244.412	−	931.690i	−0.199520	−	0.760563i
$36$	58.5482			0.0451760
$37$	−1114.16	−	1114.16i	−0.813849	−	0.813849i	0.171359	−	0.985209i	$-0.445184\pi$
$37$	−1114.16	−	1114.16i	−0.813849	−	0.813849i	−0.985209	+	0.171359i	$0.945184\pi$
$38$	104.716	−	104.716i	0.0725183	−	0.0725183i
$39$			1896.09i			1.24660i
$40$	−547.171	+	143.540i	−0.341982	+	0.0897126i
$41$	1609.52			0.957478			0.478739	−	0.877957i	$-0.341094\pi$
$41$	1609.52			0.957478			0.478739	+	0.877957i	$0.341094\pi$
$42$	−724.167	−	724.167i	−0.410526	−	0.410526i
$43$	−1529.16	+	1529.16i	−0.827018	+	0.827018i	−0.987103	−	0.160086i	$-0.948823\pi$
$43$	−1529.16	+	1529.16i	−0.827018	+	0.827018i	0.160086	+	0.987103i	$0.448823\pi$
$44$			303.601i			0.156819i
$45$	−92.3119	+	157.968i	−0.0455861	+	0.0780090i
$46$	−311.987			−0.147442
$47$	358.184	+	358.184i	0.162148	+	0.162148i	0.783517	−	0.621370i	$-0.213424\pi$
$47$	358.184	+	358.184i	0.162148	+	0.162148i	−0.621370	+	0.783517i	$0.713424\pi$
$48$	−425.296	+	425.296i	−0.184590	+	0.184590i
$49$		−	916.548i		−	0.381736i
$50$	475.431	−	1702.63i	0.190172	−	0.681054i
$51$	3258.71			1.25287
$52$	−1141.32	−	1141.32i	−0.422086	−	0.422086i
$53$	2469.97	−	2469.97i	0.879306	−	0.879306i	−0.114157	−	0.993463i	$-0.536417\pi$
$53$	2469.97	−	2469.97i	0.879306	−	0.879306i	0.993463	+	0.114157i	$0.0364166\pi$
$54$		−	1958.53i		−	0.671648i
$55$	−819.144	−	478.683i	−0.270791	−	0.158242i
$56$	871.802			0.277998
$57$	347.933	+	347.933i	0.107089	+	0.107089i
$58$	1059.95	−	1059.95i	0.315087	−	0.315087i
$59$			6450.63i			1.85310i	0.376176	+	0.926548i	$0.377239\pi$
$59$			6450.63i			1.85310i	−0.376176	+	0.926548i	$0.622761\pi$
$60$	−476.930	−	1818.04i	−0.132480	−	0.505012i
$61$	4440.02			1.19323			0.596617	−	0.802526i	$-0.296511\pi$
$61$	4440.02			1.19323			0.596617	+	0.802526i	$0.296511\pi$
$62$	−582.566	−	582.566i	−0.151552	−	0.151552i
$63$	199.384	−	199.384i	0.0502354	−	0.0502354i
$64$		−	512.000i		−	0.125000i
$65$	4878.88	−	1279.88i	1.15477	−	0.302931i
$66$	−1008.75			−0.231578
$67$	−150.312	−	150.312i	−0.0334845	−	0.0334845i	0.690166	−	0.723651i	$-0.257537\pi$
$67$	−150.312	−	150.312i	−0.0334845	−	0.0334845i	−0.723651	+	0.690166i	$0.757537\pi$
$68$	−1961.53	+	1961.53i	−0.424207	+	0.424207i
$69$		−	1036.62i		−	0.217731i
$70$	−1374.56	+	2352.20i	−0.280522	+	0.480041i
$71$	4530.32			0.898694			0.449347	−	0.893357i	$-0.351657\pi$
$71$	4530.32			0.898694			0.449347	+	0.893357i	$0.351657\pi$
$72$	−117.096	−	117.096i	−0.0225880	−	0.0225880i
$73$	4998.60	−	4998.60i	0.938000	−	0.938000i	−0.0601871	−	0.998187i	$-0.519170\pi$
$73$	4998.60	−	4998.60i	0.938000	−	0.938000i	0.998187	+	0.0601871i	$0.0191697\pi$
$74$			4456.64i			0.813849i
$75$	5657.21	+	1579.68i	1.00573	+	0.280832i
$76$	−418.866			−0.0725183
$77$	1033.91	+	1033.91i	0.174382	+	0.174382i
$78$	3792.17	−	3792.17i	0.623302	−	0.623302i
$79$		−	4226.17i		−	0.677162i	−0.940937	−	0.338581i	$-0.890053\pi$
$79$		−	4226.17i		−	0.677162i	0.940937	−	0.338581i	$-0.109947\pi$
$80$	1381.42	+	807.262i	0.215847	+	0.126135i
$81$	7100.24			1.08219
$82$	−3219.04	−	3219.04i	−0.478739	−	0.478739i
$83$	−1216.26	+	1216.26i	−0.176551	+	0.176551i	−0.789850	−	0.613300i	$-0.789842\pi$
$83$	−1216.26	+	1216.26i	−0.176551	+	0.176551i	0.613300	+	0.789850i	$0.289842\pi$
$84$			2896.67i			0.410526i
$85$	−2199.68	−	8385.10i	−0.304453	−	1.16057i
$86$	6116.62			0.827018
$87$	3521.82	+	3521.82i	0.465296	+	0.465296i
$88$	607.203	−	607.203i	0.0784094	−	0.0784094i
$89$			11123.6i			1.40431i	0.712022	+	0.702157i	$0.247780\pi$
$89$			11123.6i			1.40431i	−0.712022	+	0.702157i	$0.752220\pi$
$90$	500.560	−	131.313i	0.0617976	−	0.0162114i
$91$	−7773.48			−0.938712
$92$	623.974	+	623.974i	0.0737210	+	0.0737210i
$93$	1935.64	−	1935.64i	0.223800	−	0.223800i
$94$		−	1432.74i		−	0.162148i
$95$	660.419	−	1130.14i	0.0731766	−	0.125223i
$96$	1701.18			0.184590
$97$	3437.40	+	3437.40i	0.365331	+	0.365331i	0.865771	−	0.500440i	$-0.166828\pi$
$97$	3437.40	+	3437.40i	0.365331	+	0.365331i	−0.500440	+	0.865771i	$0.666828\pi$
$98$	−1833.10	+	1833.10i	−0.190868	+	0.190868i
$99$		−	277.739i		−	0.0283378i
$100$	−4356.13	+	2454.41i	−0.435613	+	0.245441i
$101$	−15588.8			−1.52817			−0.764083	−	0.645118i	$-0.776808\pi$
$101$	−15588.8			−1.52817			−0.764083	+	0.645118i	$0.776808\pi$
$102$	−6517.42	−	6517.42i	−0.626435	−	0.626435i
$103$	−5202.52	+	5202.52i	−0.490388	+	0.490388i	−0.908428	−	0.418041i	$-0.862717\pi$
$103$	−5202.52	+	5202.52i	−0.490388	+	0.490388i	0.418041	+	0.908428i	$0.362717\pi$
$104$			4565.28i			0.422086i
$105$	−7815.48	−	4567.13i	−0.708887	−	0.414252i
$106$	−9879.88			−0.879306
$107$	3029.84	+	3029.84i	0.264638	+	0.264638i	0.826935	−	0.562297i	$-0.190082\pi$
$107$	3029.84	+	3029.84i	0.264638	+	0.264638i	−0.562297	+	0.826935i	$0.690082\pi$
$108$	−3917.05	+	3917.05i	−0.335824	+	0.335824i
$109$			18617.0i			1.56696i	0.621419	+	0.783478i	$0.286556\pi$
$109$			18617.0i			1.56696i	−0.621419	+	0.783478i	$0.713444\pi$
$110$	680.922	+	2595.65i	0.0562745	+	0.214517i
$111$	−14807.7			−1.20183
$112$	−1743.60	−	1743.60i	−0.138999	−	0.138999i
$113$	−3319.45	+	3319.45i	−0.259961	+	0.259961i	−0.825038	−	0.565077i	$-0.808846\pi$
$113$	−3319.45	+	3319.45i	−0.259961	+	0.259961i	0.565077	+	0.825038i	$0.308846\pi$
$114$		−	1391.73i		−	0.107089i
$115$	−2667.35	+	699.730i	−0.201690	+	0.0529096i
$116$	−4239.81			−0.315087
$117$	1044.10	+	1044.10i	0.0762726	+	0.0762726i
$118$	12901.3	−	12901.3i	0.926548	−	0.926548i
$119$			13359.9i			0.943429i
$120$	−2682.23	+	4589.94i	−0.186266	+	0.318746i
$121$	−13200.8			−0.901631
$122$	−8880.05	−	8880.05i	−0.596617	−	0.596617i
$123$	10695.7	−	10695.7i	0.706964	−	0.706964i
$124$			2330.26i			0.151552i
$125$	246.024	−	15623.1i	0.0157456	−	0.999876i
$126$	−797.538			−0.0502354
$127$	−17675.5	−	17675.5i	−1.09588	−	1.09588i	−0.994887	−	0.100996i	$-0.967797\pi$
$127$	−17675.5	−	17675.5i	−1.09588	−	1.09588i	−0.100996	−	0.994887i	$-0.532203\pi$
$128$	−1024.00	+	1024.00i	−0.0625000	+	0.0625000i
$129$			20323.2i			1.22127i
$130$	−12317.5	−	7198.00i	−0.728848	−	0.425917i
$131$	−4980.57			−0.290226			−0.145113	−	0.989415i	$-0.546355\pi$
$131$	−4980.57			−0.290226			−0.145113	+	0.989415i	$0.546355\pi$
$132$	2017.51	+	2017.51i	0.115789	+	0.115789i
$133$	−1426.44	+	1426.44i	−0.0806399	+	0.0806399i
$134$			601.248i			0.0334845i
$135$	−4392.61	−	16744.5i	−0.241021	−	0.918766i
$136$	7846.12			0.424207
$137$	4323.96	+	4323.96i	0.230378	+	0.230378i	0.812850	−	0.582473i	$-0.197915\pi$
$137$	4323.96	+	4323.96i	0.230378	+	0.230378i	−0.582473	+	0.812850i	$0.697915\pi$
$138$	−2073.23	+	2073.23i	−0.108865	+	0.108865i
$139$			12334.2i			0.638386i	0.947690	+	0.319193i	$0.103412\pi$
$139$			12334.2i			0.638386i	−0.947690	+	0.319193i	$0.896588\pi$
$140$	7453.52	−	1955.29i	0.380282	−	0.0997598i
$141$	4760.44			0.239447
$142$	−9060.63	−	9060.63i	−0.449347	−	0.449347i
$143$	−5414.16	+	5414.16i	−0.264764	+	0.264764i
$144$			468.385i			0.0225880i
$145$	6684.84	−	11439.4i	0.317947	−	0.544086i
$146$	−19994.4			−0.938000
$147$	−6090.68	−	6090.68i	−0.281859	−	0.281859i
$148$	8913.28	−	8913.28i	0.406925	−	0.406925i
$149$			2187.32i			0.0985233i	0.998786	+	0.0492616i	$0.0156868\pi$
$149$			2187.32i			0.0985233i	−0.998786	+	0.0492616i	$0.984313\pi$
$150$	−8155.07	−	14473.8i	−0.362447	−	0.643279i
$151$	2291.65			0.100507			0.0502534	−	0.998737i	$-0.483997\pi$
$151$	2291.65			0.100507			0.0502534	+	0.998737i	$0.483997\pi$
$152$	837.732	+	837.732i	0.0362592	+	0.0362592i
$153$	1794.44	−	1794.44i	0.0766559	−	0.0766559i
$154$		−	4135.63i		−	0.174382i
$155$	−6287.26	−	3674.09i	−0.261697	−	0.152928i
$156$	−15168.7			−0.623302
$157$	25514.2	+	25514.2i	1.03510	+	1.03510i	0.999361	+	0.0357386i	$0.0113784\pi$
$157$	25514.2	+	25514.2i	1.03510	+	1.03510i	0.0357386	+	0.999361i	$0.488622\pi$
$158$	−8452.34	+	8452.34i	−0.338581	+	0.338581i
$159$		−	32827.1i		−	1.29849i
$160$	−1148.32	−	4377.37i	−0.0448563	−	0.170991i
$161$	4249.86			0.163954
$162$	−14200.5	−	14200.5i	−0.541094	−	0.541094i
$163$	−33276.6	+	33276.6i	−1.25246	+	1.25246i	−0.297843	+	0.954615i	$0.596267\pi$
$163$	−33276.6	+	33276.6i	−1.25246	+	1.25246i	−0.954615	+	0.297843i	$0.903733\pi$
$164$			12876.2i			0.478739i
$165$	−8624.38	+	2262.45i	−0.316782	+	0.0831018i
$166$	4865.03			0.176551
$167$	−3480.54	−	3480.54i	−0.124800	−	0.124800i	0.641948	−	0.766748i	$-0.278126\pi$
$167$	−3480.54	−	3480.54i	−0.124800	−	0.124800i	−0.766748	+	0.641948i	$0.778126\pi$
$168$	5793.34	−	5793.34i	0.205263	−	0.205263i
$169$		−	12145.6i		−	0.425250i
$170$	−12370.9	+	21169.6i	−0.428057	+	0.732511i
$171$	383.185			0.0131044
$172$	−12233.2	−	12233.2i	−0.413509	−	0.413509i
$173$	20130.4	−	20130.4i	0.672605	−	0.672605i	−0.285711	−	0.958316i	$-0.592230\pi$
$173$	20130.4	−	20130.4i	0.672605	−	0.672605i	0.958316	+	0.285711i	$0.0922296\pi$
$174$		−	14087.3i		−	0.465296i
$175$	−6476.28	+	23193.1i	−0.211470	+	0.757327i
$176$	−2428.81			−0.0784094
$177$	42866.0	+	42866.0i	1.36825	+	1.36825i
$178$	22247.2	−	22247.2i	0.702157	−	0.702157i
$179$			15961.6i			0.498163i	0.968483	+	0.249081i	$0.0801287\pi$
$179$			15961.6i			0.498163i	−0.968483	+	0.249081i	$0.919871\pi$
$180$	−1263.75	−	738.495i	−0.0390045	−	0.0227931i
$181$	−36537.9			−1.11529			−0.557643	−	0.830081i	$-0.688294\pi$
$181$	−36537.9			−1.11529			−0.557643	+	0.830081i	$0.688294\pi$
$182$	15547.0	+	15547.0i	0.469356	+	0.469356i
$183$	29505.0	−	29505.0i	0.881037	−	0.881037i
$184$		−	2495.90i		−	0.0737210i
$185$	9995.42	+	38102.3i	0.292050	+	1.11329i
$186$	−7742.58			−0.223800
$187$	9305.05	+	9305.05i	0.266094	+	0.266094i
$188$	−2865.47	+	2865.47i	−0.0810738	+	0.0810738i
$189$			26678.9i			0.746868i
$190$	−3581.11	+	939.439i	−0.0991998	+	0.0260232i
$191$	36818.7			1.00926			0.504629	−	0.863336i	$-0.331629\pi$
$191$	36818.7			1.00926			0.504629	+	0.863336i	$0.331629\pi$
$192$	−3402.36	−	3402.36i	−0.0922950	−	0.0922950i
$193$	−22602.3	+	22602.3i	−0.606789	+	0.606789i	−0.942106	−	0.335316i	$-0.891157\pi$
$193$	−22602.3	+	22602.3i	−0.606789	+	0.606789i	0.335316	+	0.942106i	$0.391157\pi$
$194$		−	13749.6i		−	0.365331i
$195$	23916.2	−	40926.5i	0.628960	−	1.07631i
$196$	7332.38			0.190868
$197$	291.404	+	291.404i	0.00750867	+	0.00750867i	0.710851	−	0.703342i	$-0.248310\pi$
$197$	291.404	+	291.404i	0.00750867	+	0.00750867i	−0.703342	+	0.710851i	$0.748310\pi$
$198$	−555.478	+	555.478i	−0.0141689	+	0.0141689i
$199$			32361.5i			0.817188i	0.912716	+	0.408594i	$0.133981\pi$
$199$			32361.5i			0.817188i	−0.912716	+	0.408594i	$0.866019\pi$
$200$	13621.1	+	3803.45i	0.340527	+	0.0950862i
$201$	−1997.72			−0.0494473
$202$	31177.7	+	31177.7i	0.764083	+	0.764083i
$203$	−14438.6	+	14438.6i	−0.350375	+	0.350375i
$204$			26069.7i			0.626435i
$205$	−34741.1	−	20301.6i	−0.826676	−	0.483085i
$206$	20810.1			0.490388
$207$	−570.821	−	570.821i	−0.0133217	−	0.0133217i
$208$	9130.55	−	9130.55i	0.211043	−	0.211043i
$209$			1987.00i			0.0454890i
$210$	6496.70	+	24765.2i	0.147317	+	0.561570i
$211$	−63479.1			−1.42582			−0.712911	−	0.701254i	$-0.752624\pi$
$211$	−63479.1			−1.42582			−0.712911	+	0.701254i	$0.752624\pi$
$212$	19759.8	+	19759.8i	0.439653	+	0.439653i
$213$	30105.1	−	30105.1i	0.663560	−	0.663560i
$214$		−	12119.4i		−	0.264638i
$215$	52294.4	−	13718.5i	1.13130	−	0.296776i
$216$	15668.2			0.335824
$217$	7935.66	+	7935.66i	0.168525	+	0.168525i
$218$	37234.0	−	37234.0i	0.783478	−	0.783478i
$219$		−	66433.9i		−	1.38516i
$220$	3829.47	−	6553.15i	0.0791212	−	0.135396i
$221$	−69960.4			−1.43241
$222$	29615.5	+	29615.5i	0.600914	+	0.600914i
$223$	67930.2	−	67930.2i	1.36601	−	1.36601i	0.499960	−	0.866048i	$-0.333348\pi$
$223$	67930.2	−	67930.2i	1.36601	−	1.36601i	0.866048	−	0.499960i	$-0.166652\pi$
$224$			6974.42i			0.138999i
$225$	3985.05	−	2245.33i	0.0787171	−	0.0443522i
$226$	13277.8			0.259961
$227$	7072.59	+	7072.59i	0.137255	+	0.137255i	0.772396	−	0.635141i	$-0.219058\pi$
$227$	7072.59	+	7072.59i	0.137255	+	0.137255i	−0.635141	+	0.772396i	$0.719058\pi$
$228$	−2783.47	+	2783.47i	−0.0535447	+	0.0535447i
$229$		−	48107.1i		−	0.917357i	−0.888602	−	0.458679i	$-0.848323\pi$
$229$		−	48107.1i		−	0.917357i	0.888602	−	0.458679i	$-0.151677\pi$
$230$	6734.16	+	3935.24i	0.127300	+	0.0743902i
$231$	13741.1			0.257513
$232$	8479.62	+	8479.62i	0.157544	+	0.157544i
$233$	20958.7	−	20958.7i	0.386059	−	0.386059i	−0.487220	−	0.873279i	$-0.661989\pi$
$233$	20958.7	−	20958.7i	0.386059	−	0.386059i	0.873279	+	0.487220i	$0.161989\pi$
$234$		−	4176.38i		−	0.0762726i
$235$	−3213.36	−	12249.2i	−0.0581867	−	0.221806i
$236$	−51605.0			−0.926548
$237$	−28083.9	−	28083.9i	−0.499990	−	0.499990i
$238$	26719.8	−	26719.8i	0.471715	−	0.471715i
$239$		−	26411.0i		−	0.462369i	−0.972910	−	0.231184i	$-0.925740\pi$
$239$		−	26411.0i		−	0.462369i	0.972910	−	0.231184i	$-0.0742601\pi$
$240$	14544.3	−	3815.44i	0.252506	−	0.0662402i
$241$	60300.2			1.03821			0.519104	−	0.854711i	$-0.326266\pi$
$241$	60300.2			1.03821			0.519104	+	0.854711i	$0.326266\pi$
$242$	26401.6	+	26401.6i	0.450816	+	0.450816i
$243$	7522.68	−	7522.68i	0.127397	−	0.127397i
$244$			35520.2i			0.596617i
$245$	−11560.8	+	19783.4i	−0.192600	+	0.329587i
$246$	−42782.6			−0.706964
$247$	−7469.68	−	7469.68i	−0.122436	−	0.122436i
$248$	4660.52	−	4660.52i	0.0757760	−	0.0757760i
$249$			16164.6i			0.260716i
$250$	−31738.2	+	30754.1i	−0.507811	+	0.492065i
$251$	−38653.5			−0.613538			−0.306769	−	0.951784i	$-0.599248\pi$
$251$	−38653.5			−0.613538			−0.306769	+	0.951784i	$0.599248\pi$
$252$	1595.08	+	1595.08i	0.0251177	+	0.0251177i
$253$	2959.99	−	2959.99i	0.0462434	−	0.0462434i
$254$			70702.0i			1.09588i
$255$	−70338.4	−	41103.7i	−1.08171	−	0.632121i
$256$	4096.00			0.0625000
$257$	−41324.3	−	41324.3i	−0.625662	−	0.625662i	0.321312	−	0.946973i	$-0.395876\pi$
$257$	−41324.3	−	41324.3i	−0.625662	−	0.625662i	−0.946973	+	0.321312i	$0.895876\pi$
$258$	40646.4	−	40646.4i	0.610637	−	0.610637i
$259$		−	60708.0i		−	0.904995i
$260$	10239.1	+	39031.1i	0.151466	+	0.577383i
$261$	3878.64			0.0569376
$262$	9961.14	+	9961.14i	0.145113	+	0.145113i
$263$	40828.6	−	40828.6i	0.590273	−	0.590273i	−0.347432	−	0.937705i	$-0.612946\pi$
$263$	40828.6	−	40828.6i	0.590273	−	0.590273i	0.937705	+	0.347432i	$0.112946\pi$
$264$		−	8070.02i		−	0.115789i
$265$	−84468.5	+	22158.8i	−1.20283	+	0.315539i
$266$	5705.75			0.0806399
$267$	73918.9	+	73918.9i	1.03689	+	1.03689i
$268$	1202.50	−	1202.50i	0.0167423	−	0.0167423i
$269$			95883.5i			1.32507i	0.749030	+	0.662536i	$0.230520\pi$
$269$			95883.5i			1.32507i	−0.749030	+	0.662536i	$0.769480\pi$
$270$	−24703.8	+	42274.2i	−0.338872	+	0.579894i
$271$	67685.2			0.921626			0.460813	−	0.887497i	$-0.347558\pi$
$271$	67685.2			0.921626			0.460813	+	0.887497i	$0.347558\pi$
$272$	−15692.2	−	15692.2i	−0.212103	−	0.212103i
$273$	−51656.6	+	51656.6i	−0.693108	+	0.693108i
$274$		−	17295.8i		−	0.230378i
$275$	11643.1	+	20664.5i	0.153959	+	0.273250i
$276$	8292.92			0.108865
$277$	−23268.7	−	23268.7i	−0.303258	−	0.303258i	0.539029	−	0.842287i	$-0.318791\pi$
$277$	−23268.7	−	23268.7i	−0.303258	−	0.303258i	−0.842287	+	0.539029i	$0.818791\pi$
$278$	24668.5	−	24668.5i	0.319193	−	0.319193i
$279$		−	2131.76i		−	0.0273861i
$280$	−18817.6	−	10996.5i	−0.240021	−	0.140261i
$281$	−15597.7			−0.197537			−0.0987684	−	0.995110i	$-0.531490\pi$
$281$	−15597.7			−0.197537			−0.0987684	+	0.995110i	$0.531490\pi$
$282$	−9520.88	−	9520.88i	−0.119723	−	0.119723i
$283$	79901.2	−	79901.2i	0.997655	−	0.997655i	−0.00234263	−	0.999997i	$-0.500746\pi$
$283$	79901.2	−	79901.2i	0.997655	−	0.997655i	0.999997	+	0.00234263i	$0.000745682\pi$
$284$			36242.5i			0.449347i
$285$	−3121.40	−	11898.7i	−0.0384291	−	0.146490i
$286$	21656.6			0.264764
$287$	43849.5	+	43849.5i	0.532354	+	0.532354i
$288$	936.770	−	936.770i	0.0112940	−	0.0112940i
$289$			36716.6i			0.439609i
$290$	−36248.5	+	9509.12i	−0.431016	+	0.113069i
$291$	45684.7			0.539492
$292$	39988.8	+	39988.8i	0.469000	+	0.469000i
$293$	35980.8	−	35980.8i	0.419118	−	0.419118i	−0.465782	−	0.884900i	$-0.654227\pi$
$293$	35980.8	−	35980.8i	0.419118	−	0.419118i	0.884900	+	0.465782i	$0.154227\pi$
$294$			24362.7i			0.281859i
$295$	81364.8	−	139235.i	0.934959	−	1.59994i
$296$	−35653.1			−0.406925
$297$	18581.6	+	18581.6i	0.210654	+	0.210654i
$298$	4374.63	−	4374.63i	0.0492616	−	0.0492616i
$299$			22254.8i			0.248932i
$300$	−12637.4	+	45257.7i	−0.140416	+	0.502863i
$301$	−83320.1			−0.919638
$302$	−4583.31	−	4583.31i	−0.0502534	−	0.0502534i
$303$	−103592.	+	103592.i	−1.12834	+	1.12834i
$304$		−	3350.93i		−	0.0362592i
$305$	−95836.7	−	56004.1i	−1.03023	−	0.602033i
$306$	−7177.75			−0.0766559
$307$	−39959.9	−	39959.9i	−0.423982	−	0.423982i	0.462590	−	0.886572i	$-0.346920\pi$
$307$	−39959.9	−	39959.9i	−0.423982	−	0.423982i	−0.886572	+	0.462590i	$0.846920\pi$
$308$	−8271.26	+	8271.26i	−0.0871908	+	0.0871908i
$309$			69144.1i			0.724166i
$310$	5226.35	+	19922.7i	0.0543845	+	0.207312i
$311$	−50867.2			−0.525917			−0.262959	−	0.964807i	$-0.584698\pi$
$311$	−50867.2			−0.525917			−0.262959	+	0.964807i	$0.584698\pi$
$312$	30337.4	+	30337.4i	0.311651	+	0.311651i
$313$	26030.7	−	26030.7i	0.265704	−	0.265704i	−0.561663	−	0.827366i	$-0.689838\pi$
$313$	26030.7	−	26030.7i	0.265704	−	0.265704i	0.827366	+	0.561663i	$0.189838\pi$
$314$		−	102057.i		−	1.03510i
$315$	−6818.59	+	1788.73i	−0.0687185	+	0.0180270i
$316$	33809.4			0.338581
$317$	56633.1	+	56633.1i	0.563575	+	0.563575i	0.930321	−	0.366746i	$-0.119528\pi$
$317$	56633.1	+	56633.1i	0.563575	+	0.563575i	−0.366746	+	0.930321i	$0.619528\pi$
$318$	−65654.2	+	65654.2i	−0.649245	+	0.649245i
$319$			20112.7i			0.197646i
$320$	−6458.09	+	11051.4i	−0.0630673	+	0.107924i
$321$	40268.1			0.390797
$322$	−8499.72	−	8499.72i	−0.0819772	−	0.0819772i
$323$	−12837.8	+	12837.8i	−0.123051	+	0.123051i
$324$			56801.9i			0.541094i
$325$	−121453.	−	33913.7i	−1.14985	−	0.321076i
$326$	133106.			1.25246
$327$	123715.	+	123715.i	1.15698	+	1.15698i
$328$	25752.3	−	25752.3i	0.239370	−	0.239370i
$329$			19516.6i			0.180307i
$330$	21773.6	+	12723.9i	0.199942	+	0.116840i
$331$	109493.			0.999377			0.499688	−	0.866205i	$-0.333448\pi$
$331$	109493.			0.999377			0.499688	+	0.866205i	$0.333448\pi$
$332$	−9730.05	−	9730.05i	−0.0882753	−	0.0882753i
$333$	−8154.00	+	8154.00i	−0.0735330	+	0.0735330i
$334$			13922.2i			0.124800i
$335$	1348.49	+	5140.40i	0.0120159	+	0.0458044i
$336$	−23173.4			−0.205263
$337$	−121614.	−	121614.i	−1.07084	−	1.07084i	−0.997292	−	0.0735499i	$-0.976567\pi$
$337$	−121614.	−	121614.i	−1.07084	−	1.07084i	−0.0735499	−	0.997292i	$-0.523433\pi$
$338$	−24291.1	+	24291.1i	−0.212625	+	0.212625i
$339$			44117.1i			0.383890i
$340$	67080.8	−	17597.4i	0.580284	−	0.152227i
$341$	11054.2			0.0950648
$342$	−766.369	−	766.369i	−0.00655218	−	0.00655218i
$343$	90382.7	−	90382.7i	0.768240	−	0.768240i
$344$			48933.0i			0.413509i
$345$	−13075.3	+	22375.1i	−0.109853	+	0.187986i
$346$	−80521.6			−0.672605
$347$	14527.7	+	14527.7i	0.120653	+	0.120653i	0.764855	−	0.644202i	$-0.222811\pi$
$347$	14527.7	+	14527.7i	0.120653	+	0.120653i	−0.644202	+	0.764855i	$0.722811\pi$
$348$	−28174.6	+	28174.6i	−0.232648	+	0.232648i
$349$			161924.i			1.32941i	0.747105	+	0.664706i	$0.231443\pi$
$349$			161924.i			1.32941i	−0.747105	+	0.664706i	$0.768557\pi$
$350$	59338.8	−	33433.7i	0.484399	−	0.272928i
$351$	−139706.			−1.13397
$352$	4857.62	+	4857.62i	0.0392047	+	0.0392047i
$353$	98066.9	−	98066.9i	0.786997	−	0.786997i	−0.194004	−	0.981001i	$-0.562147\pi$
$353$	98066.9	−	98066.9i	0.786997	−	0.786997i	0.981001	+	0.194004i	$0.0621474\pi$
$354$		−	171464.i		−	1.36825i
$355$	−97785.6	−	57143.0i	−0.775923	−	0.453426i
$356$	−88988.6			−0.702157
$357$	88779.8	+	88779.8i	0.696591	+	0.696591i
$358$	31923.3	−	31923.3i	0.249081	−	0.249081i
$359$			94626.7i			0.734218i	0.930178	+	0.367109i	$0.119652\pi$
$359$			94626.7i			0.734218i	−0.930178	+	0.367109i	$0.880348\pi$
$360$	1050.50	+	4004.48i	0.00810572	+	0.0308988i
$361$	127580.			0.978964
$362$	73075.8	+	73075.8i	0.557643	+	0.557643i
$363$	−87722.4	+	87722.4i	−0.665729	+	0.665729i
$364$		−	62187.8i		−	0.469356i
$365$	−170943.	+	44843.8i	−1.28312	+	0.336602i
$366$	−118020.			−0.881037
$367$	−74774.9	−	74774.9i	−0.555167	−	0.555167i	0.372761	−	0.927928i	$-0.378411\pi$
$367$	−74774.9	−	74774.9i	−0.555167	−	0.555167i	−0.927928	+	0.372761i	$0.878411\pi$
$368$	−4991.79	+	4991.79i	−0.0368605	+	0.0368605i
$369$		−	11779.3i		−	0.0865101i
$370$	56213.7	−	96195.3i	0.410618	−	0.702669i
$371$	134583.			0.977782
$372$	15485.2	+	15485.2i	0.111900	+	0.111900i
$373$	−45063.6	+	45063.6i	−0.323898	+	0.323898i	−0.850260	−	0.526362i	$-0.823556\pi$
$373$	−45063.6	+	45063.6i	−0.323898	+	0.323898i	0.526362	+	0.850260i	$0.323556\pi$
$374$		−	37220.2i		−	0.266094i
$375$	−102184.	−	105454.i	−0.726643	−	0.749895i
$376$	11461.9			0.0810738
$377$	−75609.1	−	75609.1i	−0.531975	−	0.531975i
$378$	53357.7	−	53357.7i	0.373434	−	0.373434i
$379$		−	130867.i		−	0.911072i	−0.890217	−	0.455536i	$-0.849448\pi$
$379$		−	130867.i		−	0.911072i	0.890217	−	0.455536i	$-0.150552\pi$
$380$	9041.11	+	5283.35i	0.0626115	+	0.0365883i
$381$	−234916.			−1.61831
$382$	−73637.5	−	73637.5i	−0.504629	−	0.504629i
$383$	122263.	−	122263.i	0.833487	−	0.833487i	−0.154505	−	0.987992i	$-0.549378\pi$
$383$	122263.	−	122263.i	0.833487	−	0.833487i	0.987992	+	0.154505i	$0.0493782\pi$
$384$			13609.5i			0.0922950i
$385$	−9275.46	−	35357.8i	−0.0625769	−	0.238541i
$386$	90409.2			0.606789
$387$	11191.2	+	11191.2i	0.0747228	+	0.0747228i
$388$	−27499.2	+	27499.2i	−0.182666	+	0.182666i
$389$		−	41424.9i		−	0.273755i	−0.990588	−	0.136877i	$-0.956293\pi$
$389$		−	41424.9i		−	0.273755i	0.990588	−	0.136877i	$-0.0437066\pi$
$390$	−129685.	+	34020.6i	−0.852633	+	0.223672i
$391$	38248.3			0.250183
$392$	−14664.8	−	14664.8i	−0.0954340	−	0.0954340i
$393$	−33097.1	+	33097.1i	−0.214291	+	0.214291i
$394$		−	1165.62i		−	0.00750867i
$395$	−53306.7	+	91220.8i	−0.341655	+	0.584655i
$396$	2221.91			0.0141689
$397$	−213830.	−	213830.i	−1.35671	−	1.35671i	−0.877938	−	0.478774i	$-0.841082\pi$
$397$	−213830.	−	213830.i	−1.35671	−	1.35671i	−0.478774	−	0.877938i	$-0.658918\pi$
$398$	64722.9	−	64722.9i	0.408594	−	0.408594i
$399$			18958.1i			0.119083i
$400$	−19635.3	−	34849.1i	−0.122720	−	0.217807i
$401$	81156.5			0.504702			0.252351	−	0.967636i	$-0.418796\pi$
$401$	81156.5			0.504702			0.252351	+	0.967636i	$0.418796\pi$
$402$	3995.44	+	3995.44i	0.0247236	+	0.0247236i
$403$	−41555.8	+	41555.8i	−0.255871	+	0.255871i
$404$		−	124711.i		−	0.764083i
$405$	−153257.	−	89558.6i	−0.934350	−	0.546006i
$406$	57754.4			0.350375
$407$	−42282.6	−	42282.6i	−0.255254	−	0.255254i
$408$	52139.4	−	52139.4i	0.313217	−	0.313217i
$409$		−	105048.i		−	0.627972i	−0.949428	−	0.313986i	$-0.898335\pi$
$409$		−	105048.i		−	0.627972i	0.949428	−	0.313986i	$-0.101665\pi$
$410$	28878.9	+	110085.i	0.171796	+	0.654880i
$411$	57467.5			0.340203
$412$	−41620.2	−	41620.2i	−0.245194	−	0.245194i
$413$	−175740.	+	175740.i	−1.03032	+	1.03032i
$414$			2283.28i			0.0133217i
$415$	41593.8	−	10911.4i	0.241508	−	0.0633553i
$416$	−36522.2			−0.211043
$417$	81964.1	+	81964.1i	0.471359	+	0.471359i
$418$	3974.01	−	3974.01i	0.0227445	−	0.0227445i
$419$		−	71694.4i		−	0.408373i	−0.978932	−	0.204187i	$-0.934545\pi$
$419$		−	71694.4i		−	0.408373i	0.978932	−	0.204187i	$-0.0654550\pi$
$420$	36537.0	−	62523.8i	0.207126	−	0.354443i
$421$	174799.			0.986222			0.493111	−	0.869967i	$-0.335860\pi$
$421$	174799.			0.986222			0.493111	+	0.869967i	$0.335860\pi$
$422$	126958.	+	126958.i	0.712911	+	0.712911i
$423$	2621.38	−	2621.38i	0.0146504	−	0.0146504i
$424$		−	79039.1i		−	0.439653i
$425$	−58285.8	+	208736.i	−0.322689	+	1.15563i
$426$	−120420.			−0.663560
$427$	120963.	+	120963.i	0.663434	+	0.663434i
$428$	−24238.7	+	24238.7i	−0.132319	+	0.132319i
$429$			71956.8i			0.390982i
$430$	−132026.	−	77151.8i	−0.714038	−	0.417262i
$431$	209036.			1.12530			0.562648	−	0.826696i	$-0.309783\pi$
$431$	209036.			1.12530			0.562648	+	0.826696i	$0.309783\pi$
$432$	−31336.4	−	31336.4i	−0.167912	−	0.167912i
$433$	−130839.	+	130839.i	−0.697851	+	0.697851i	−0.963947	−	0.266096i	$-0.914266\pi$
$433$	−130839.	+	130839.i	−0.697851	+	0.697851i	0.266096	+	0.963947i	$0.414266\pi$
$434$		−	31742.6i		−	0.168525i
$435$	−31595.2	−	120440.i	−0.166972	−	0.636491i
$436$	−148936.			−0.783478
$437$	4083.77	+	4083.77i	0.0213845	+	0.0213845i
$438$	−132868.	+	132868.i	−0.692582	+	0.692582i
$439$		−	253039.i		−	1.31298i	−0.754335	−	0.656490i	$-0.772040\pi$
$439$		−	253039.i		−	1.31298i	0.754335	−	0.656490i	$-0.227960\pi$
$440$	−20765.2	+	5447.38i	−0.107258	+	0.0281373i
$441$	−6707.77			−0.0344906
$442$	139921.	+	139921.i	0.716206	+	0.716206i
$443$	−172616.	+	172616.i	−0.879579	+	0.879579i	−0.993491	−	0.113912i	$-0.963662\pi$
$443$	−172616.	+	172616.i	−0.879579	+	0.879579i	0.113912	+	0.993491i	$0.463662\pi$
$444$		−	118462.i		−	0.600914i
$445$	140307.	−	240099.i	0.708531	−	1.21247i
$446$	−271721.			−1.36601
$447$	14535.2	+	14535.2i	0.0727457	+	0.0727457i
$448$	13948.8	−	13948.8i	0.0694996	−	0.0694996i
$449$			301429.i			1.49517i	0.664164	+	0.747587i	$0.268788\pi$
$449$			301429.i			1.49517i	−0.664164	+	0.747587i	$0.731212\pi$
$450$	−12460.8	−	3479.45i	−0.0615346	−	0.0171825i
$451$	61081.6			0.300301
$452$	−26555.6	−	26555.6i	−0.129981	−	0.129981i
$453$	15228.6	−	15228.6i	0.0742102	−	0.0742102i
$454$		−	28290.4i		−	0.137255i
$455$	167788.	+	98050.5i	0.810474	+	0.473617i
$456$	11133.9			0.0535447
$457$	−196252.	−	196252.i	−0.939683	−	0.939683i	0.0585983	−	0.998282i	$-0.481337\pi$
$457$	−196252.	−	196252.i	−0.939683	−	0.939683i	−0.998282	+	0.0585983i	$0.981337\pi$
$458$	−96214.3	+	96214.3i	−0.458679	+	0.458679i
$459$			240107.i			1.13967i
$460$	−5597.84	−	21338.8i	−0.0264548	−	0.100845i
$461$	−161672.			−0.760733			−0.380367	−	0.924836i	$-0.624202\pi$
$461$	−161672.			−0.760733			−0.380367	+	0.924836i	$0.624202\pi$
$462$	−27482.3	−	27482.3i	−0.128756	−	0.128756i
$463$	−172838.	+	172838.i	−0.806266	+	0.806266i	−0.984067	−	0.177801i	$-0.943102\pi$
$463$	−172838.	+	172838.i	−0.806266	+	0.806266i	0.177801	+	0.984067i	$0.443102\pi$
$464$		−	33918.5i		−	0.157544i
$465$	−66195.6	+	17365.2i	−0.306142	+	0.0803107i
$466$	−83835.0			−0.386059
$467$	−71031.6	−	71031.6i	−0.325700	−	0.325700i	0.525249	−	0.850949i	$-0.323972\pi$
$467$	−71031.6	−	71031.6i	−0.325700	−	0.325700i	−0.850949	+	0.525249i	$0.823972\pi$
$468$	−8352.77	+	8352.77i	−0.0381363	+	0.0381363i
$469$		−	8190.15i		−	0.0372345i
$470$	−18071.8	+	30925.2i	−0.0818097	+	0.139996i
$471$	339096.			1.52855
$472$	103210.	+	103210.i	0.463274	+	0.463274i
$473$	−58031.7	+	58031.7i	−0.259384	+	0.259384i
$474$			112336.i			0.499990i
$475$	−28509.9	+	16063.6i	−0.126360	+	0.0711958i
$476$	−106879.			−0.471715
$477$	−18076.5	−	18076.5i	−0.0794471	−	0.0794471i
$478$	−52821.9	+	52821.9i	−0.231184	+	0.231184i
$479$		−	202244.i		−	0.881464i	−0.897639	−	0.440732i	$-0.854719\pi$
$479$		−	202244.i		−	0.881464i	0.897639	−	0.440732i	$-0.145281\pi$
$480$	−36719.6	−	21457.8i	−0.159373	−	0.0931328i
$481$	317903.			1.37406
$482$	−120600.	−	120600.i	−0.519104	−	0.519104i
$483$	28241.4	−	28241.4i	0.121057	−	0.121057i
$484$		−	105606.i		−	0.450816i
$485$	−30837.8	−	117553.i	−0.131099	−	0.499747i
$486$	−30090.7			−0.127397
$487$	−196464.	−	196464.i	−0.828369	−	0.828369i	0.158922	−	0.987291i	$-0.449198\pi$
$487$	−196464.	−	196464.i	−0.828369	−	0.828369i	−0.987291	+	0.158922i	$0.949198\pi$
$488$	71040.4	−	71040.4i	0.298308	−	0.298308i
$489$			442262.i			1.84953i
$490$	62688.6	−	16445.2i	0.261094	−	0.0684930i
$491$	273192.			1.13320			0.566599	−	0.823994i	$-0.308259\pi$
$491$	273192.			1.13320			0.566599	+	0.823994i	$0.308259\pi$
$492$	85565.3	+	85565.3i	0.353482	+	0.353482i
$493$	−129946.	+	129946.i	−0.534648	+	0.534648i
$494$			29878.7i			0.122436i
$495$	−3503.25	+	5994.92i	−0.0142975	+	0.0244666i
$496$	−18642.1			−0.0757760
$497$	123423.	+	123423.i	0.499671	+	0.499671i
$498$	32329.3	−	32329.3i	0.130358	−	0.130358i
$499$			411097.i			1.65098i	0.564414	+	0.825492i	$0.309102\pi$
$499$			411097.i			1.65098i	−0.564414	+	0.825492i	$0.690898\pi$
$500$	124985.	+	1968.19i	0.499938	+	0.00787278i
$501$	−46258.1			−0.184294
$502$	77307.0	+	77307.0i	0.306769	+	0.306769i
$503$	230936.	−	230936.i	0.912759	−	0.912759i	−0.0837299	−	0.996488i	$-0.526683\pi$
$503$	230936.	−	230936.i	0.912759	−	0.912759i	0.996488	+	0.0837299i	$0.0266833\pi$
$504$		−	6380.30i		−	0.0251177i
$505$	336481.	+	196629.i	1.31940	+	0.771019i
$506$	−11840.0			−0.0462434
$507$	−80710.2	−	80710.2i	−0.313988	−	0.313988i
$508$	141404.	−	141404.i	0.547941	−	0.547941i
$509$			128837.i			0.497285i	0.968595	+	0.248642i	$0.0799844\pi$
$509$			128837.i			0.497285i	−0.968595	+	0.248642i	$0.920016\pi$
$510$	58469.5	+	222884.i	0.224796	+	0.856917i
$511$	272362.			1.04305
$512$	−8192.00	−	8192.00i	−0.0312500	−	0.0312500i
$513$	−25636.2	+	25636.2i	−0.0974136	+	0.0974136i
$514$			165297.i			0.625662i
$515$	177917.	−	46673.2i	0.670815	−	0.175976i
$516$	−162586.			−0.610637
$517$	13593.1	+	13593.1i	0.0508556	+	0.0508556i
$518$	−121416.	+	121416.i	−0.452497	+	0.452497i
$519$		−	267543.i		−	0.993250i
$520$	57584.0	−	98540.3i	0.212958	−	0.364424i
$521$	99025.7			0.364815			0.182407	−	0.983223i	$-0.441611\pi$
$521$	99025.7			0.364815			0.182407	+	0.983223i	$0.441611\pi$
$522$	−7757.29	−	7757.29i	−0.0284688	−	0.0284688i
$523$	257545.	−	257545.i	0.941563	−	0.941563i	−0.0568215	−	0.998384i	$-0.518097\pi$
$523$	257545.	−	257545.i	0.941563	−	0.941563i	0.998384	+	0.0568215i	$0.0180966\pi$
$524$		−	39844.6i		−	0.145113i
$525$	111088.	+	197161.i	0.403039	+	0.715322i
$526$	−163314.			−0.590273
$527$	71420.0	+	71420.0i	0.257157	+	0.257157i
$528$	−16140.0	+	16140.0i	−0.0578944	+	0.0578944i
$529$		−	12167.0i		−	0.0434783i
$530$	213255.	+	124620.i	0.759183	+	0.443644i
$531$	47209.0			0.167431
$532$	−11411.5	−	11411.5i	−0.0403199	−	0.0403199i
$533$	−229622.	+	229622.i	−0.808275	+	0.808275i
$534$		−	295676.i		−	1.03689i
$535$	−27181.5	−	103615.i	−0.0949656	−	0.362006i
$536$	−4809.98			−0.0167423
$537$	106069.	+	106069.i	0.367824	+	0.367824i
$538$	191767.	−	191767.i	0.662536	−	0.662536i
$539$		−	34783.1i		−	0.119727i
$540$	133956.	−	35140.9i	0.459383	−	0.120511i
$541$	−390200.			−1.33319			−0.666595	−	0.745420i	$-0.732249\pi$
$541$	−390200.			−1.33319			−0.666595	+	0.745420i	$0.732249\pi$
$542$	−135370.	−	135370.i	−0.460813	−	0.460813i
$543$	−242803.	+	242803.i	−0.823484	+	0.823484i
$544$			62769.0i			0.212103i
$545$	234825.	−	401843.i	0.790590	−	1.35289i
$546$	206627.			0.693108
$547$	18117.5	+	18117.5i	0.0605515	+	0.0605515i	0.736734	−	0.676183i	$-0.236367\pi$
$547$	18117.5	+	18117.5i	0.0605515	+	0.0605515i	−0.676183	+	0.736734i	$0.736367\pi$
$548$	−34591.7	+	34591.7i	−0.115189	+	0.115189i
$549$		−	32494.4i		−	0.107811i
$550$	18042.7	−	64615.3i	0.0596452	−	0.213604i
$551$	−27748.6			−0.0913984
$552$	−16585.8	−	16585.8i	−0.0544326	−	0.0544326i
$553$	115137.	−	115137.i	0.376500	−	0.376500i
$554$			93074.8i			0.303258i
$555$	319621.	+	186777.i	1.03765	+	0.606369i
$556$	−98674.0			−0.319193
$557$	82819.6	+	82819.6i	0.266946	+	0.266946i	0.827868	−	0.560923i	$-0.189554\pi$
$557$	82819.6	+	82819.6i	0.266946	+	0.266946i	−0.560923	+	0.827868i	$0.689554\pi$
$558$	−4263.52	+	4263.52i	−0.0136930	+	0.0136930i
$559$		−	436314.i		−	1.39629i
$560$	15642.3	+	59628.1i	0.0498799	+	0.190141i
$561$	123669.			0.392947
$562$	31195.4	+	31195.4i	0.0987684	+	0.0987684i
$563$	−20066.6	+	20066.6i	−0.0633079	+	0.0633079i	−0.738052	−	0.674744i	$-0.764254\pi$
$563$	−20066.6	+	20066.6i	−0.0633079	+	0.0633079i	0.674744	+	0.738052i	$0.264254\pi$
$564$			38083.5i			0.119723i
$565$	113519.	−	29779.6i	0.355608	−	0.0932873i
$566$	−319605.			−0.997655
$567$	193438.	+	193438.i	0.601693	+	0.601693i
$568$	72485.1	−	72485.1i	0.224673	−	0.224673i
$569$			246358.i			0.760926i	0.924796	+	0.380463i	$0.124235\pi$
$569$			246358.i			0.760926i	−0.924796	+	0.380463i	$0.875765\pi$
$570$	−17554.6	+	30040.2i	−0.0540307	+	0.0924598i
$571$	305093.			0.935752			0.467876	−	0.883794i	$-0.345019\pi$
$571$	305093.			0.935752			0.467876	+	0.883794i	$0.345019\pi$
$572$	−43313.3	−	43313.3i	−0.132382	−	0.132382i
$573$	244670.	−	244670.i	0.745196	−	0.745196i
$574$		−	175398.i		−	0.532354i
$575$	66400.0	+	18541.0i	0.200832	+	0.0560788i
$576$	−3747.08			−0.0112940
$577$	−103024.	−	103024.i	−0.309447	−	0.309447i	0.535248	−	0.844695i	$-0.320218\pi$
$577$	−103024.	−	103024.i	−0.309447	−	0.309447i	−0.844695	+	0.535248i	$0.820218\pi$
$578$	73433.2	−	73433.2i	0.219805	−	0.219805i
$579$			300395.i			0.896058i
$580$	91515.2	+	53478.7i	0.272043	+	0.158974i
$581$	−66271.0			−0.196323
$582$	−91369.4	−	91369.4i	−0.269746	−	0.269746i
$583$	93735.8	−	93735.8i	0.275784	−	0.275784i
$584$		−	159955.i		−	0.469000i
$585$	−9366.86	−	35706.2i	−0.0273705	−	0.104335i
$586$	−143923.			−0.419118
$587$	−84518.3	−	84518.3i	−0.245287	−	0.245287i	0.573746	−	0.819033i	$-0.305490\pi$
$587$	−84518.3	−	84518.3i	−0.245287	−	0.245287i	−0.819033	+	0.573746i	$0.805490\pi$
$588$	48725.5	−	48725.5i	0.140929	−	0.140929i
$589$			15251.1i			0.0439612i
$590$	−441200.	+	115741.i	−1.26745	+	0.332492i
$591$	3872.90			0.0110882
$592$	71306.2	+	71306.2i	0.203462	+	0.203462i
$593$	94583.9	−	94583.9i	0.268972	−	0.268972i	−0.559714	−	0.828686i	$-0.689089\pi$
$593$	94583.9	−	94583.9i	0.268972	−	0.268972i	0.828686	+	0.559714i	$0.189089\pi$
$594$		−	74326.4i		−	0.210654i
$595$	168515.	−	288370.i	0.475997	−	0.814547i
$596$	−17498.5			−0.0492616
$597$	215050.	+	215050.i	0.603379	+	0.603379i
$598$	44509.6	−	44509.6i	0.124466	−	0.124466i
$599$		−	556653.i		−	1.55143i	−0.631086	−	0.775713i	$-0.717390\pi$
$599$		−	556653.i		−	1.55143i	0.631086	−	0.775713i	$-0.282610\pi$
$600$	115790.	−	65240.5i	0.321639	−	0.181224i
$601$	−490933.			−1.35917			−0.679584	−	0.733597i	$-0.737840\pi$
$601$	−490933.			−1.35917			−0.679584	+	0.733597i	$0.737840\pi$
$602$	166640.	+	166640.i	0.459819	+	0.459819i
$603$	−1100.06	+	1100.06i	−0.00302540	+	0.00302540i
$604$			18333.2i			0.0502534i
$605$	284935.	+	166508.i	0.778459	+	0.454908i
$606$	414366.			1.12834
$607$	−437517.	−	437517.i	−1.18746	−	1.18746i	−0.977769	−	0.209687i	$-0.932756\pi$
$607$	−437517.	−	437517.i	−1.18746	−	1.18746i	−0.209687	−	0.977769i	$-0.567244\pi$
$608$	−6701.85	+	6701.85i	−0.0181296	+	0.0181296i
$609$			191896.i			0.517405i
$610$	79665.2	+	303682.i	0.214096	+	0.816129i
$611$	−102201.			−0.273761
$612$	14355.5	+	14355.5i	0.0383279	+	0.0383279i
$613$	351107.	−	351107.i	0.934370	−	0.934370i	−0.0636050	−	0.997975i	$-0.520260\pi$
$613$	351107.	−	351107.i	0.934370	−	0.934370i	0.997975	+	0.0636050i	$0.0202598\pi$
$614$			159840.i			0.423982i
$615$	−365772.	+	95953.5i	−0.967075	+	0.253694i
$616$	33085.1			0.0871908
$617$	−161031.	−	161031.i	−0.423000	−	0.423000i	0.463235	−	0.886235i	$-0.346688\pi$
$617$	−161031.	−	161031.i	−0.423000	−	0.423000i	−0.886235	+	0.463235i	$0.846688\pi$
$618$	138288.	−	138288.i	0.362083	−	0.362083i
$619$			470793.i			1.22871i	0.789031	+	0.614353i	$0.210583\pi$
$619$			470793.i			1.22871i	−0.789031	+	0.614353i	$0.789417\pi$
$620$	29392.7	−	50298.1i	0.0764638	−	0.130848i
$621$	76379.4			0.198058
$622$	101734.	+	101734.i	0.262959	+	0.262959i
$623$	−303049.	+	303049.i	−0.780794	+	0.780794i
$624$		−	121350.i		−	0.311651i
$625$	−202371.	+	334116.i	−0.518071	+	0.855338i
$626$	−104123.			−0.265704
$627$	13204.1	+	13204.1i	0.0335873	+	0.0335873i
$628$	−204113.	+	204113.i	−0.517550	+	0.517550i
$629$		−	546365.i		−	1.38096i
$630$	17214.6	+	10059.7i	0.0433727	+	0.0253457i
$631$	−68406.1			−0.171805			−0.0859026	−	0.996304i	$-0.527377\pi$
$631$	−68406.1			−0.171805			−0.0859026	+	0.996304i	$0.527377\pi$
$632$	−67618.7	−	67618.7i	−0.169291	−	0.169291i
$633$	−421834.	+	421834.i	−1.05277	+	1.05277i
$634$		−	226532.i		−	0.563575i
$635$	158571.	+	604470.i	0.393258	+	1.49909i
$636$	262617.			0.649245
$637$	130759.	+	130759.i	0.322250	+	0.322250i
$638$	40225.4	−	40225.4i	0.0988232	−	0.0988232i
$639$		−	33155.2i		−	0.0811989i
$640$	35019.0	−	9186.57i	0.0854955	−	0.0224282i
$641$	534988.			1.30205			0.651025	−	0.759056i	$-0.274339\pi$
$641$	534988.			1.30205			0.651025	+	0.759056i	$0.274339\pi$
$642$	−80536.2	−	80536.2i	−0.195398	−	0.195398i
$643$	−309818.	+	309818.i	−0.749351	+	0.749351i	−0.974357	−	0.225006i	$-0.927760\pi$
$643$	−309818.	+	309818.i	−0.749351	+	0.749351i	0.225006	+	0.974357i	$0.427760\pi$
$644$			33998.9i			0.0819772i
$645$	256346.	−	438671.i	0.616180	−	1.05443i
$646$	51351.1			0.123051
$647$	−515996.	−	515996.i	−1.23265	−	1.23265i	−0.962944	−	0.269701i	$-0.913075\pi$
$647$	−515996.	−	515996.i	−1.23265	−	1.23265i	−0.269701	−	0.962944i	$-0.586925\pi$
$648$	113604.	−	113604.i	0.270547	−	0.270547i
$649$			244802.i			0.581201i
$650$	175079.	+	310734.i	0.414388	+	0.735464i
$651$	105469.			0.248864
$652$	−266212.	−	266212.i	−0.626229	−	0.626229i
$653$	231899.	−	231899.i	0.543841	−	0.543841i	−0.380812	−	0.924653i	$-0.624355\pi$
$653$	231899.	−	231899.i	0.543841	−	0.543841i	0.924653	+	0.380812i	$0.124355\pi$
$654$		−	494858.i		−	1.15698i
$655$	107504.	+	62822.3i	0.250578	+	0.146430i
$656$	−103009.			−0.239370
$657$	−36582.4	−	36582.4i	−0.0847503	−	0.0847503i
$658$	39033.2	−	39033.2i	0.0901535	−	0.0901535i
$659$		−	420006.i		−	0.967130i	−0.875308	−	0.483565i	$-0.839342\pi$
$659$		−	420006.i		−	0.967130i	0.875308	−	0.483565i	$-0.160658\pi$
$660$	−18099.6	−	68995.0i	−0.0415509	−	0.158391i
$661$	−808866.			−1.85129			−0.925644	−	0.378396i	$-0.876476\pi$
$661$	−808866.			−1.85129			−0.925644	+	0.378396i	$0.876476\pi$
$662$	−218985.	−	218985.i	−0.499688	−	0.499688i
$663$	−464904.	+	464904.i	−1.05764	+	1.05764i
$664$			38920.2i			0.0882753i
$665$	48781.6	−	12797.0i	0.110310	−	0.0289377i
$666$	32616.0			0.0735330
$667$	41336.5	+	41336.5i	0.0929141	+	0.0929141i
$668$	27844.3	−	27844.3i	0.0623999	−	0.0623999i
$669$		−	902826.i		−	2.01721i
$670$	7583.82	−	12977.8i	0.0168942	−	0.0289102i
$671$	168500.			0.374243
$672$	46346.7	+	46346.7i	0.102631	+	0.102631i
$673$	295993.	−	295993.i	0.653509	−	0.653509i	−0.300327	−	0.953836i	$-0.597096\pi$
$673$	295993.	−	295993.i	0.653509	−	0.653509i	0.953836	+	0.300327i	$0.0970959\pi$
$674$			486458.i			1.07084i
$675$	−116393.	+	416832.i	−0.255458	+	0.914857i
$676$	97164.5			0.212625
$677$	289978.	+	289978.i	0.632685	+	0.632685i	0.948741	−	0.316056i	$-0.102359\pi$
$677$	289978.	+	289978.i	0.632685	+	0.632685i	−0.316056	+	0.948741i	$0.602359\pi$
$678$	88234.1	−	88234.1i	0.191945	−	0.191945i
$679$			187296.i			0.406246i
$680$	−169356.	−	98966.8i	−0.366255	−	0.214029i
$681$	93998.2			0.202687
$682$	−22108.5	−	22108.5i	−0.0475324	−	0.0475324i
$683$	32799.9	−	32799.9i	0.0703123	−	0.0703123i	−0.671076	−	0.741388i	$-0.734168\pi$
$683$	32799.9	−	32799.9i	0.0703123	−	0.0703123i	0.741388	+	0.671076i	$0.234168\pi$
$684$			3065.48i			0.00655218i
$685$	−38791.4	−	147872.i	−0.0826711	−	0.315140i
$686$	−361531.			−0.768240
$687$	−319684.	−	319684.i	−0.677340	−	0.677340i
$688$	97865.9	−	97865.9i	0.206754	−	0.206754i
$689$			704756.i			1.48457i
$690$	70900.7	−	18599.5i	0.148920	−	0.0390664i
$691$	391510.			0.819949			0.409975	−	0.912097i	$-0.365538\pi$
$691$	391510.			0.819949			0.409975	+	0.912097i	$0.365538\pi$
$692$	161043.	+	161043.i	0.336303	+	0.336303i
$693$	7566.67	−	7566.67i	0.0157557	−	0.0157557i
$694$		−	58110.7i		−	0.120653i
$695$	155578.	−	266231.i	0.322090	−	0.551175i
$696$	112698.			0.232648
$697$	394641.	+	394641.i	0.812337	+	0.812337i
$698$	323847.	−	323847.i	0.664706	−	0.664706i
$699$		−	278552.i		−	0.570101i
$700$	−185545.	−	51810.2i	−0.378664	−	0.105735i
$701$	802248.			1.63257			0.816287	−	0.577647i	$-0.196029\pi$
$701$	802248.			1.63257			0.816287	+	0.577647i	$0.196029\pi$
$702$	279413.	+	279413.i	0.566986	+	0.566986i
$703$	58335.4	−	58335.4i	0.118038	−	0.118038i
$704$		−	19430.5i		−	0.0392047i
$705$	−102753.	−	60045.6i	−0.206736	−	0.120810i
$706$	−392268.			−0.786997
$707$	−424699.	−	424699.i	−0.849655	−	0.849655i
$708$	−342928.	+	342928.i	−0.684126	+	0.684126i
$709$			814129.i			1.61957i	0.586724	+	0.809787i	$0.300417\pi$
$709$			814129.i			1.61957i	−0.586724	+	0.809787i	$0.699583\pi$
$710$	81285.3	+	309857.i	0.161248	+	0.614674i
$711$	−30929.3			−0.0611830
$712$	177977.	+	177977.i	0.351079	+	0.351079i
$713$	22719.1	−	22719.1i	0.0446902	−	0.0446902i
$714$		−	355119.i		−	0.696591i
$715$	185154.	−	48571.8i	0.362178	−	0.0950107i
$716$	−127693.			−0.249081
$717$	−175507.	−	175507.i	−0.341395	−	0.341395i
$718$	189253.	−	189253.i	0.367109	−	0.367109i
$719$		−	435112.i		−	0.841673i	−0.907136	−	0.420837i	$-0.861737\pi$
$719$		−	435112.i		−	0.841673i	0.907136	−	0.420837i	$-0.138263\pi$
$720$	5907.96	−	10110.0i	0.0113965	−	0.0195023i
$721$	−283473.			−0.545308
$722$	−255159.	−	255159.i	−0.489482	−	0.489482i
$723$	400709.	−	400709.i	0.766572	−	0.766572i
$724$		−	292303.i		−	0.557643i
$725$	−288581.	+	162597.i	−0.549024	+	0.309341i
$726$	350890.			0.665729
$727$	362504.	+	362504.i	0.685873	+	0.685873i	0.961317	−	0.275444i	$-0.0888250\pi$
$727$	362504.	+	362504.i	0.685873	+	0.685873i	−0.275444	+	0.961317i	$0.588825\pi$
$728$	−124376.	+	124376.i	−0.234678	+	0.234678i
$729$			475139.i			0.894059i
$730$	431574.	+	252199.i	0.809859	+	0.473257i
$731$	−749871.			−1.40330
$732$	236040.	+	236040.i	0.440518	+	0.440518i
$733$	−499774.	+	499774.i	−0.930176	+	0.930176i	−0.997717	−	0.0675402i	$-0.978485\pi$
$733$	−499774.	+	499774.i	−0.930176	+	0.930176i	0.0675402	+	0.997717i	$0.478485\pi$
$734$			299100.i			0.555167i
$735$	54641.1	+	208290.i	0.101145	+	0.385562i
$736$	19967.2			0.0368605
$737$	−5704.37	−	5704.37i	−0.0105020	−	0.0105020i
$738$	−23558.6	+	23558.6i	−0.0432551	+	0.0432551i
$739$		−	339853.i		−	0.622303i	−0.950360	−	0.311151i	$-0.899285\pi$
$739$		−	339853.i		−	0.622303i	0.950360	−	0.311151i	$-0.100715\pi$
$740$	−304818.	+	79963.4i	−0.556644	+	0.146025i
$741$	−99275.7			−0.180803
$742$	−269166.	−	269166.i	−0.488891	−	0.488891i
$743$	−586561.	+	586561.i	−1.06252	+	1.06252i	−0.0646045	+	0.997911i	$0.520579\pi$
$743$	−586561.	+	586561.i	−1.06252	+	1.06252i	−0.997911	+	0.0646045i	$0.979421\pi$
$744$		−	61940.6i		−	0.111900i
$745$	27589.6	−	47212.6i	0.0497088	−	0.0850639i
$746$	180255.			0.323898
$747$	8901.20	+	8901.20i	0.0159517	+	0.0159517i
$748$	−74440.4	+	74440.4i	−0.133047	+	0.133047i
$749$			165089.i			0.294276i
$750$	−6539.56	+	415276.i	−0.0116259	+	0.738269i
$751$	246945.			0.437845			0.218923	−	0.975742i	$-0.429746\pi$
$751$	246945.			0.437845			0.218923	+	0.975742i	$0.429746\pi$
$752$	−22923.8	−	22923.8i	−0.0405369	−	0.0405369i
$753$	−256862.	+	256862.i	−0.453012	+	0.453012i
$754$			302436.i			0.531975i
$755$	−49464.7	−	28905.7i	−0.0867764	−	0.0507095i
$756$	−213431.			−0.373434
$757$	−450335.	−	450335.i	−0.785859	−	0.785859i	0.194954	−	0.980812i	$-0.437544\pi$
$757$	−450335.	−	450335.i	−0.785859	−	0.785859i	−0.980812	+	0.194954i	$0.937544\pi$
$758$	−261735.	+	261735.i	−0.455536	+	0.455536i
$759$		−	39339.7i		−	0.0682885i
$760$	−7515.51	−	28648.9i	−0.0130116	−	0.0495999i
$761$	−322648.			−0.557134			−0.278567	−	0.960417i	$-0.589859\pi$
$761$	−322648.			−0.557134			−0.278567	+	0.960417i	$0.589859\pi$
$762$	469832.	+	469832.i	0.809156	+	0.809156i
$763$	−507199.	+	507199.i	−0.871222	+	0.871222i
$764$			294550.i			0.504629i
$765$	−61366.5	+	16098.4i	−0.104860	+	0.0275080i
$766$	−489054.			−0.833487
$767$	−920278.	−	920278.i	−1.56433	−	1.56433i
$768$	27218.9	−	27218.9i	0.0461475	−	0.0461475i
$769$		−	891399.i		−	1.50737i	−0.657237	−	0.753684i	$-0.728275\pi$
$769$		−	891399.i		−	1.50737i	0.657237	−	0.753684i	$-0.271725\pi$
$770$	−52164.6	+	89266.5i	−0.0879822	+	0.150559i
$771$	−549221.			−0.923928
$772$	−180818.	−	180818.i	−0.303395	−	0.303395i
$773$	−242345.	+	242345.i	−0.405578	+	0.405578i	−0.880193	−	0.474615i	$-0.842587\pi$
$773$	−242345.	+	242345.i	−0.405578	+	0.405578i	0.474615	+	0.880193i	$0.342587\pi$
$774$		−	44764.6i		−	0.0747228i
$775$	89365.8	+	158608.i	0.148788	+	0.264072i
$776$	109997.			0.182666
$777$	−403419.	−	403419.i	−0.668212	−	0.668212i
$778$	−82849.7	+	82849.7i	−0.136877	+	0.136877i
$779$			84271.7i			0.138869i
$780$	327412.	+	191330.i	0.538153	+	0.314480i
$781$	171926.			0.281864
$782$	−76496.6	−	76496.6i	−0.125092	−	0.125092i
$783$	−259493.	+	259493.i	−0.423255	+	0.423255i
$784$			58659.1i			0.0954340i
$785$	−228894.	−	872539.i	−0.371446	−	1.41594i
$786$	132388.			0.214291
$787$	−240838.	−	240838.i	−0.388843	−	0.388843i	0.485431	−	0.874275i	$-0.338663\pi$
$787$	−240838.	−	240838.i	−0.388843	−	0.388843i	−0.874275	+	0.485431i	$0.838663\pi$
$788$	−2331.23	+	2331.23i	−0.00375433	+	0.00375433i
$789$		−	542632.i		−	0.871668i
$790$	289055.	−	75828.2i	0.463155	−	0.121500i
$791$	−180869.			−0.289075
$792$	−4443.82	−	4443.82i	−0.00708446	−	0.00708446i
$793$	−633436.	+	633436.i	−1.00729	+	1.00729i
$794$			855320.i			1.35671i
$795$	−414064.	+	708564.i	−0.655138	+	1.12110i
$796$	−258892.			−0.408594
$797$	−223774.	−	223774.i	−0.352285	−	0.352285i	0.508674	−	0.860959i	$-0.330136\pi$
$797$	−223774.	−	223774.i	−0.352285	−	0.352285i	−0.860959	+	0.508674i	$0.830136\pi$
$798$	37916.1	−	37916.1i	0.0595413	−	0.0595413i
$799$			175647.i			0.275136i
$800$	−30427.6	+	108969.i	−0.0475431	+	0.170263i
$801$	81408.1			0.126883
$802$	−162313.	−	162313.i	−0.252351	−	0.252351i
$803$	189698.	−	189698.i	0.294192	−	0.294192i
$804$		−	15981.8i		−	0.0247236i
$805$	−91732.1	−	53605.5i	−0.141556	−	0.0827213i
$806$	166223.			0.255871
$807$	637169.	+	637169.i	0.978380	+	0.978380i
$808$	−249421.	+	249421.i	−0.382042	+	0.382042i
$809$		−	637853.i		−	0.974594i	−0.873236	−	0.487297i	$-0.837983\pi$
$809$		−	637853.i		−	0.974594i	0.873236	−	0.487297i	$-0.162017\pi$
$810$	127396.	+	485631.i	0.194172	+	0.740178i
$811$	−337009.			−0.512389			−0.256195	−	0.966625i	$-0.582469\pi$
$811$	−337009.			−0.512389			−0.256195	+	0.966625i	$0.582469\pi$
$812$	−115509.	−	115509.i	−0.175187	−	0.175187i
$813$	449784.	−	449784.i	0.680492	−	0.680492i
$814$			169130.i			0.255254i
$815$	1.13800e6	−	298533.i	1.71327	−	0.449445i
$816$	−208558.			−0.313217
$817$	−80063.9	−	80063.9i	−0.119948	−	0.119948i
$818$	−210096.	+	210096.i	−0.313986	+	0.313986i
$819$			56890.3i			0.0848146i
$820$	162413.	−	277929.i	0.241542	−	0.413338i
$821$	−1.13881e6			−1.68952			−0.844761	−	0.535143i	$-0.820258\pi$
$821$	−1.13881e6			−1.68952			−0.844761	+	0.535143i	$0.820258\pi$
$822$	−114935.	−	114935.i	−0.170102	−	0.170102i
$823$	−478404.	+	478404.i	−0.706309	+	0.706309i	−0.965757	−	0.259448i	$-0.916459\pi$
$823$	−478404.	+	478404.i	−0.706309	+	0.706309i	0.259448	+	0.965757i	$0.416459\pi$
$824$			166481.i			0.245194i
$825$	214692.	+	59949.0i	0.315434	+	0.0880794i
$826$	702959.			1.03032
$827$	−234268.	−	234268.i	−0.342533	−	0.342533i	0.514786	−	0.857319i	$-0.327871\pi$
$827$	−234268.	−	234268.i	−0.342533	−	0.342533i	−0.857319	+	0.514786i	$0.827871\pi$
$828$	4566.57	−	4566.57i	0.00666084	−	0.00666084i
$829$			970931.i			1.41280i	0.707815	+	0.706398i	$0.249681\pi$
$829$			970931.i			1.41280i	−0.707815	+	0.706398i	$0.750319\pi$
$830$	−105010.	−	61364.9i	−0.152432	−	0.0890766i
$831$	−309252.			−0.447828
$832$	73044.4	+	73044.4i	0.105521	+	0.105521i
$833$	224730.	−	224730.i	0.323870	−	0.323870i
$834$		−	327856.i		−	0.471359i
$835$	31224.8	+	119028.i	0.0447844	+	0.170717i
$836$	−15896.0			−0.0227445
$837$	142621.	+	142621.i	0.203579	+	0.203579i
$838$	−143389.	+	143389.i	−0.204187	+	0.204187i
$839$		−	372232.i		−	0.528798i	−0.964413	−	0.264399i	$-0.914826\pi$
$839$		−	372232.i		−	0.528798i	0.964413	−	0.264399i	$-0.0851736\pi$
$840$	−198122.	+	51973.6i	−0.280785	+	0.0736587i
$841$	426406.			0.602881
$842$	−349598.	−	349598.i	−0.493111	−	0.493111i
$843$	−103651.	+	103651.i	−0.145853	+	0.145853i
$844$		−	507832.i		−	0.712911i
$845$	−153198.	+	262159.i	−0.214555	+	0.367156i
$846$	−10485.5			−0.0146504
$847$	−359640.	−	359640.i	−0.501304	−	0.501304i
$848$	−158078.	+	158078.i	−0.219827	+	0.219827i
$849$		−	1.06193e6i		−	1.47326i
$850$	534043.	−	300900.i	0.739160	−	0.416470i
$851$	−173802.			−0.239991
$852$	240840.	+	240840.i	0.331780	+	0.331780i
$853$	674098.	−	674098.i	0.926456	−	0.926456i	−0.0710187	−	0.997475i	$-0.522625\pi$
$853$	674098.	−	674098.i	0.926456	−	0.926456i	0.997475	+	0.0710187i	$0.0226250\pi$
$854$		−	483853.i		−	0.663434i
$855$	−8270.94	−	4833.29i	−0.0113142	−	0.00661166i
$856$	96955.0			0.132319
$857$	330560.	+	330560.i	0.450079	+	0.450079i	0.895381	−	0.445301i	$-0.146903\pi$
$857$	330560.	+	330560.i	0.450079	+	0.450079i	−0.445301	+	0.895381i	$0.646903\pi$
$858$	143914.	−	143914.i	0.195491	−	0.195491i
$859$		−	828048.i		−	1.12220i	−0.827749	−	0.561098i	$-0.810379\pi$
$859$		−	828048.i		−	1.12220i	0.827749	−	0.561098i	$-0.189621\pi$
$860$	109748.	+	418355.i	0.148388	+	0.565650i
$861$	582781.			0.786139
$862$	−418072.	−	418072.i	−0.562648	−	0.562648i
$863$	227076.	−	227076.i	0.304894	−	0.304894i	−0.538031	−	0.842925i	$-0.680832\pi$
$863$	227076.	−	227076.i	0.304894	−	0.304894i	0.842925	+	0.538031i	$0.180832\pi$
$864$			125346.i			0.167912i
$865$	−688423.	+	180595.i	−0.920075	+	0.241365i
$866$	523357.			0.697851
$867$	243991.	+	243991.i	0.324590	+	0.324590i
$868$	−63485.3	+	63485.3i	−0.0842623	+	0.0842623i
$869$		−	160384.i		−	0.212384i
$870$	−177690.	+	304070.i	−0.234760	+	0.401731i
$871$	42888.5			0.0565333
$872$	297872.	+	297872.i	0.391739	+	0.391739i
$873$	25156.7	−	25156.7i	0.0330084	−	0.0330084i
$874$		−	16335.1i		−	0.0213845i
$875$	432335.	−	418929.i	0.564682	−	0.547173i
$876$	531471.			0.692582
$877$	65571.6	+	65571.6i	0.0852543	+	0.0852543i	0.748448	−	0.663194i	$-0.230799\pi$
$877$	65571.6	+	65571.6i	0.0852543	+	0.0852543i	−0.663194	+	0.748448i	$0.730799\pi$
$878$	−506078.	+	506078.i	−0.656490	+	0.656490i
$879$		−	478203.i		−	0.618920i
$880$	52425.2	+	30635.7i	0.0676979	+	0.0395606i
$881$	−57397.2			−0.0739501			−0.0369750	−	0.999316i	$-0.511772\pi$
$881$	−57397.2			−0.0739501			−0.0369750	+	0.999316i	$0.511772\pi$
$882$	13415.5	+	13415.5i	0.0172453	+	0.0172453i
$883$	246526.	−	246526.i	0.316185	−	0.316185i	−0.531115	−	0.847300i	$-0.678227\pi$
$883$	246526.	−	246526.i	0.316185	−	0.316185i	0.847300	+	0.531115i	$0.178227\pi$
$884$		−	559683.i		−	0.716206i
$885$	−384562.	−	1.46594e6i	−0.490998	−	1.87167i
$886$	690466.			0.879579
$887$	−391039.	−	391039.i	−0.497018	−	0.497018i	0.413490	−	0.910509i	$-0.364310\pi$
$887$	−391039.	−	391039.i	−0.497018	−	0.497018i	−0.910509	+	0.413490i	$0.864310\pi$
$888$	−236924.	+	236924.i	−0.300457	+	0.300457i
$889$		−	963096.i		−	1.21861i
$890$	−760813.	+	199585.i	−0.960501	+	0.251970i
$891$	269455.			0.339415
$892$	543442.	+	543442.i	0.683004	+	0.683004i
$893$	−18753.9	+	18753.9i	−0.0235173	+	0.0235173i
$894$		−	58141.0i		−	0.0727457i
$895$	201332.	−	344528.i	0.251342	−	0.430108i
$896$	−55795.4			−0.0694996
$897$	147889.	+	147889.i	0.183802	+	0.183802i
$898$	602857.	−	602857.i	0.747587	−	0.747587i
$899$			154373.i			0.191008i
$900$	17962.6	+	31880.4i	0.0221761	+	0.0393586i
$901$	1.21123e6			1.49203
$902$	−122163.	−	122163.i	−0.150151	−	0.150151i
$903$	−553682.	+	553682.i	−0.679024	+	0.679024i
$904$			106222.i			0.129981i
$905$	788661.	+	460870.i	0.962926	+	0.562705i
$906$	−60914.4			−0.0742102
$907$	769364.	+	769364.i	0.935228	+	0.935228i	0.998026	−	0.0627985i	$-0.0200026\pi$
$907$	769364.	+	769364.i	0.935228	+	0.935228i	−0.0627985	+	0.998026i	$0.520003\pi$
$908$	−56580.7	+	56580.7i	−0.0686273	+	0.0686273i
$909$			114087.i			0.138073i
$910$	−139476.	−	531678.i	−0.168429	−	0.642045i
$911$	643870.			0.775820			0.387910	−	0.921697i	$-0.373197\pi$
$911$	643870.			0.775820			0.387910	+	0.921697i	$0.373197\pi$
$912$	−22267.7	−	22267.7i	−0.0267723	−	0.0267723i
$913$	−46157.2	+	46157.2i	−0.0553729	+	0.0553729i
$914$			785008.i			0.939683i
$915$	−1.00902e6	+	264697.i	−1.20519	+	0.316160i
$916$	384857.			0.458679
$917$	−135690.	−	135690.i	−0.161365	−	0.161365i
$918$	480214.	−	480214.i	0.569835	−	0.569835i
$919$			820469.i			0.971474i	0.874105	+	0.485737i	$0.161449\pi$
$919$			820469.i			0.971474i	−0.874105	+	0.485737i	$0.838551\pi$
$920$	−31481.9	+	53873.3i	−0.0371951	+	0.0636499i
$921$	−531086.			−0.626103
$922$	323344.	+	323344.i	0.380367	+	0.380367i
$923$	−646317.	+	646317.i	−0.758651	+	0.758651i
$924$			109929.i			0.128756i
$925$	264853.	−	948504.i	0.309543	−	1.10855i
$926$	691354.			0.806266
$927$	38074.8	+	38074.8i	0.0443076	+	0.0443076i
$928$	−67837.0	+	67837.0i	−0.0787718	+	0.0787718i
$929$			701235.i			0.812516i	0.913758	+	0.406258i	$0.133167\pi$
$929$			701235.i			0.812516i	−0.913758	+	0.406258i	$0.866833\pi$
$930$	167121.	+	97660.8i	0.193226	+	0.112916i
$931$	47988.8			0.0553657
$932$	167670.	+	167670.i	0.193029	+	0.193029i
$933$	−338025.	+	338025.i	−0.388317	+	0.388317i
$934$			284126.i			0.325700i
$935$	−83478.1	−	318216.i	−0.0954881	−	0.363998i
$936$	33411.1			0.0381363
$937$	−5714.04	−	5714.04i	−0.00650825	−	0.00650825i	0.703845	−	0.710353i	$-0.251465\pi$
$937$	−5714.04	−	5714.04i	−0.00650825	−	0.00650825i	−0.710353	+	0.703845i	$0.751465\pi$
$938$	−16380.3	+	16380.3i	−0.0186173	+	0.0186173i
$939$		−	345961.i		−	0.392371i
$940$	97993.9	−	25706.9i	0.110903	−	0.0290934i
$941$	361320.			0.408049			0.204024	−	0.978966i	$-0.434598\pi$
$941$	361320.			0.408049			0.204024	+	0.978966i	$0.434598\pi$
$942$	−678192.	−	678192.i	−0.764277	−	0.764277i
$943$	125537.	−	125537.i	0.141172	−	0.141172i
$944$		−	412840.i		−	0.463274i
$945$	336513.	−	575856.i	0.376824	−	0.644838i
$946$	232127.			0.259384
$947$	839653.	+	839653.i	0.936268	+	0.936268i	0.998087	−	0.0618197i	$-0.0196904\pi$
$947$	839653.	+	839653.i	0.936268	+	0.936268i	−0.0618197	+	0.998087i	$0.519690\pi$
$948$	224671.	−	224671.i	0.249995	−	0.249995i
$949$			1.42625e6i			1.58366i
$950$	89147.0	+	24892.7i	0.0987778	+	0.0275820i
$951$	752682.			0.832243
$952$	213758.	+	213758.i	0.235857	+	0.235857i
$953$	1.15178e6	−	1.15178e6i	1.26819	−	1.26819i	0.321163	−	0.947024i	$-0.395926\pi$
$953$	1.15178e6	−	1.15178e6i	1.26819	−	1.26819i	0.947024	−	0.321163i	$-0.104074\pi$
$954$			72306.1i			0.0794471i
$955$	−794723.	−	464412.i	−0.871382	−	0.509210i
$956$	211288.			0.231184
$957$	133654.	+	133654.i	0.145934	+	0.145934i
$958$	−404488.	+	404488.i	−0.440732	+	0.440732i
$959$			235602.i			0.256178i
$960$	30523.5	+	116355.i	0.0331201	+	0.126253i
$961$	−838675.			−0.908128
$962$	−635806.	−	635806.i	−0.687028	−	0.687028i
$963$	22174.0	−	22174.0i	0.0239106	−	0.0239106i
$964$			482401.i			0.519104i
$965$	772957.	−	202771.i	0.830044	−	0.217747i
$966$	−112965.			−0.121057
$967$	549893.	+	549893.i	0.588065	+	0.588065i	0.937107	−	0.349042i	$-0.113493\pi$
$967$	549893.	+	549893.i	0.588065	+	0.588065i	−0.349042	+	0.937107i	$0.613493\pi$
$968$	−211213.	+	211213.i	−0.225408	+	0.225408i
$969$			170620.i			0.181712i
$970$	−173430.	+	296781.i	−0.184324	+	0.315423i
$971$	1.42517e6			1.51157			0.755784	−	0.654821i	$-0.227256\pi$
$971$	1.42517e6			1.51157			0.755784	+	0.654821i	$0.227256\pi$
$972$	60181.4	+	60181.4i	0.0636986	+	0.0636986i
$973$	−336032.	+	336032.i	−0.354940	+	0.354940i
$974$			785854.i			0.828369i
$975$	−1.03245e6	+	581721.i	−1.08608	+	0.611935i
$976$	−284161.			−0.298308
$977$	682208.	+	682208.i	0.714706	+	0.714706i	0.967516	−	0.252810i	$-0.0813546\pi$
$977$	682208.	+	682208.i	0.714706	+	0.714706i	−0.252810	+	0.967516i	$0.581355\pi$
$978$	884523.	−	884523.i	0.924765	−	0.924765i
$979$			422142.i			0.440446i
$980$	−158267.	−	92486.8i	−0.164793	−	0.0963002i
$981$	136249.			0.141578
$982$	−546385.	−	546385.i	−0.566599	−	0.566599i
$983$	−876914.	+	876914.i	−0.907507	+	0.907507i	−0.996071	−	0.0885634i	$-0.971772\pi$
$983$	−876914.	+	876914.i	−0.907507	+	0.907507i	0.0885634	+	0.996071i	$0.471772\pi$
$984$		−	342261.i		−	0.353482i
$985$	−2614.26	−	9965.49i	−0.00269449	−	0.0102713i
$986$	519783.			0.534648
$987$	129693.	+	129693.i	0.133131	+	0.133131i
$988$	59757.5	−	59757.5i	0.0612179	−	0.0612179i
$989$			238538.i			0.243874i
$990$	18996.3	−	4983.34i	0.0193821	−	0.00508452i
$991$	1.13459e6			1.15529			0.577646	−	0.816288i	$-0.303972\pi$
$991$	1.13459e6			1.15529			0.577646	+	0.816288i	$0.303972\pi$
$992$	37284.2	+	37284.2i	0.0378880	+	0.0378880i
$993$	727606.	−	727606.i	0.737900	−	0.737900i
$994$		−	493693.i		−	0.499671i
$995$	408190.	−	698514.i	0.412303	−	0.705551i
$996$	−129317.			−0.130358
$997$	−705341.	−	705341.i	−0.709592	−	0.709592i	0.256858	−	0.966449i	$-0.417313\pi$
$997$	−705341.	−	705341.i	−0.709592	−	0.709592i	−0.966449	+	0.256858i	$0.917313\pi$
$998$	822194.	−	822194.i	0.825492	−	0.825492i
$999$		−	1.09106e6i		−	1.09324i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.5.f.a.47.17	✓	44
5.3	odd	4	inner	230.5.f.a.93.17	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.5.f.a.47.17	✓	44	1.1	even	1	trivial
230.5.f.a.93.17	yes	44	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:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	230.f (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.00000 - 2.00000i) q^{2} +(6.64524 - 6.64524i) q^{3} +8.00000i q^{4} +(-21.5847 - 12.6135i) q^{5} -26.5810 q^{6} +(27.2438 + 27.2438i) q^{7} +(16.0000 - 16.0000i) q^{8} -7.31852i q^{9} +O(q^{10})\)	\(q+(-2.00000 - 2.00000i) q^{2} +(6.64524 - 6.64524i) q^{3} +8.00000i q^{4} +(-21.5847 - 12.6135i) q^{5} -26.5810 q^{6} +(27.2438 + 27.2438i) q^{7} +(16.0000 - 16.0000i) q^{8} -7.31852i q^{9} +(17.9425 + 68.3964i) q^{10} +37.9502 q^{11} +(53.1619 + 53.1619i) q^{12} +(-142.665 + 142.665i) q^{13} -108.975i q^{14} +(-227.255 + 59.6162i) q^{15} -64.0000 q^{16} +(245.191 + 245.191i) q^{17} +(-14.6370 + 14.6370i) q^{18} +52.3582i q^{19} +(100.908 - 172.678i) q^{20} +362.084 q^{21} +(-75.9003 - 75.9003i) q^{22} +(77.9968 - 77.9968i) q^{23} -212.648i q^{24} +(306.801 + 544.516i) q^{25} +570.660 q^{26} +(489.631 + 489.631i) q^{27} +(-217.951 + 217.951i) q^{28} +529.976i q^{29} +(573.743 + 335.278i) q^{30} +291.283 q^{31} +(128.000 + 128.000i) q^{32} +(252.188 - 252.188i) q^{33} -980.765i q^{34} +(-244.412 - 931.690i) q^{35} +58.5482 q^{36} +(-1114.16 - 1114.16i) q^{37} +(104.716 - 104.716i) q^{38} +1896.09i q^{39} +(-547.171 + 143.540i) q^{40} +1609.52 q^{41} +(-724.167 - 724.167i) q^{42} +(-1529.16 + 1529.16i) q^{43} +303.601i q^{44} +(-92.3119 + 157.968i) q^{45} -311.987 q^{46} +(358.184 + 358.184i) q^{47} +(-425.296 + 425.296i) q^{48} -916.548i q^{49} +(475.431 - 1702.63i) q^{50} +3258.71 q^{51} +(-1141.32 - 1141.32i) q^{52} +(2469.97 - 2469.97i) q^{53} -1958.53i q^{54} +(-819.144 - 478.683i) q^{55} +871.802 q^{56} +(347.933 + 347.933i) q^{57} +(1059.95 - 1059.95i) q^{58} +6450.63i q^{59} +(-476.930 - 1818.04i) q^{60} +4440.02 q^{61} +(-582.566 - 582.566i) q^{62} +(199.384 - 199.384i) q^{63} -512.000i q^{64} +(4878.88 - 1279.88i) q^{65} -1008.75 q^{66} +(-150.312 - 150.312i) q^{67} +(-1961.53 + 1961.53i) q^{68} -1036.62i q^{69} +(-1374.56 + 2352.20i) q^{70} +4530.32 q^{71} +(-117.096 - 117.096i) q^{72} +(4998.60 - 4998.60i) q^{73} +4456.64i q^{74} +(5657.21 + 1579.68i) q^{75} -418.866 q^{76} +(1033.91 + 1033.91i) q^{77} +(3792.17 - 3792.17i) q^{78} -4226.17i q^{79} +(1381.42 + 807.262i) q^{80} +7100.24 q^{81} +(-3219.04 - 3219.04i) q^{82} +(-1216.26 + 1216.26i) q^{83} +2896.67i q^{84} +(-2199.68 - 8385.10i) q^{85} +6116.62 q^{86} +(3521.82 + 3521.82i) q^{87} +(607.203 - 607.203i) q^{88} +11123.6i q^{89} +(500.560 - 131.313i) q^{90} -7773.48 q^{91} +(623.974 + 623.974i) q^{92} +(1935.64 - 1935.64i) q^{93} -1432.74i q^{94} +(660.419 - 1130.14i) q^{95} +1701.18 q^{96} +(3437.40 + 3437.40i) q^{97} +(-1833.10 + 1833.10i) q^{98} -277.739i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8}+O(q^{10}) \) 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8	\( 44 q - 88 q^{2} + 24 q^{5} - 80 q^{7} + 704 q^{8} - 184 q^{10} + 8 q^{11} + 20 q^{13} + 396 q^{15} - 2816 q^{16} + 1080 q^{17} - 2648 q^{18} + 544 q^{20} - 3096 q^{21} - 16 q^{22} - 1884 q^{25} - 80 q^{26} - 3828 q^{27} + 640 q^{28} - 2520 q^{30} - 1580 q^{31} + 5632 q^{32} + 3644 q^{33} + 8208 q^{35} + 10592 q^{36} + 3104 q^{37} - 4064 q^{38} - 704 q^{40} + 4124 q^{41} + 6192 q^{42} - 960 q^{43} - 11316 q^{45} + 2424 q^{47} + 7832 q^{50} + 14840 q^{51} + 160 q^{52} - 3116 q^{53} - 2572 q^{55} - 2560 q^{56} - 9408 q^{57} - 3928 q^{58} + 6912 q^{60} + 19136 q^{61} + 3160 q^{62} + 4564 q^{63} - 9220 q^{65} - 14576 q^{66} - 5152 q^{67} - 8640 q^{68} - 23672 q^{70} + 7900 q^{71} - 21184 q^{72} + 16424 q^{73} + 24156 q^{75} + 16256 q^{76} - 27012 q^{77} - 1808 q^{78} - 1536 q^{80} - 116684 q^{81} - 8248 q^{82} + 11184 q^{83} - 14620 q^{85} + 3840 q^{86} + 8312 q^{87} + 128 q^{88} + 14544 q^{90} + 10296 q^{91} - 7488 q^{93} + 19536 q^{95} + 41292 q^{97} + 51024 q^{98}+O(q^{100}) \) 44 * q - 88 * q^2 + 24 * q^5 - 80 * q^7 + 704 * q^8 - 184 * q^10 + 8 * q^11 + 20 * q^13 + 396 * q^15 - 2816 * q^16 + 1080 * q^17 - 2648 * q^18 + 544 * q^20 - 3096 * q^21 - 16 * q^22 - 1884 * q^25 - 80 * q^26 - 3828 * q^27 + 640 * q^28 - 2520 * q^30 - 1580 * q^31 + 5632 * q^32 + 3644 * q^33 + 8208 * q^35 + 10592 * q^36 + 3104 * q^37 - 4064 * q^38 - 704 * q^40 + 4124 * q^41 + 6192 * q^42 - 960 * q^43 - 11316 * q^45 + 2424 * q^47 + 7832 * q^50 + 14840 * q^51 + 160 * q^52 - 3116 * q^53 - 2572 * q^55 - 2560 * q^56 - 9408 * q^57 - 3928 * q^58 + 6912 * q^60 + 19136 * q^61 + 3160 * q^62 + 4564 * q^63 - 9220 * q^65 - 14576 * q^66 - 5152 * q^67 - 8640 * q^68 - 23672 * q^70 + 7900 * q^71 - 21184 * q^72 + 16424 * q^73 + 24156 * q^75 + 16256 * q^76 - 27012 * q^77 - 1808 * q^78 - 1536 * q^80 - 116684 * q^81 - 8248 * q^82 + 11184 * q^83 - 14620 * q^85 + 3840 * q^86 + 8312 * q^87 + 128 * q^88 + 14544 * q^90 + 10296 * q^91 - 7488 * q^93 + 19536 * q^95 + 41292 * q^97 + 51024 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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