LMFDB - Embedded newform 230.3.c.a.229.9

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [230,3,Mod(229,230)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("230.229"); S:= CuspForms(chi, 3); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(230, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1])) N = Newforms(chi, 3, names="a")

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$24$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			229.9
Character	$\chi$	$=$	230.229
Dual form			230.3.c.a.229.15

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q-1.41421i q^{2} +3.00625i q^{3} -2.00000 q^{4} +(-3.95888 - 3.05405i) q^{5} +4.25149 q^{6} +7.53698 q^{7} +2.82843i q^{8} -0.0375672 q^{9} +(-4.31908 + 5.59871i) q^{10} +2.07922i q^{11} -6.01251i q^{12} +19.5532i q^{13} -10.6589i q^{14} +(9.18126 - 11.9014i) q^{15} +4.00000 q^{16} +22.4321 q^{17} +0.0531281i q^{18} -7.65196i q^{19} +(7.91777 + 6.10811i) q^{20} +22.6581i q^{21} +2.94046 q^{22} +(18.5661 + 13.5757i) q^{23} -8.50297 q^{24} +(6.34551 + 24.1813i) q^{25} +27.6524 q^{26} +26.9434i q^{27} -15.0740 q^{28} +36.7226 q^{29} +(-16.8311 - 12.9843i) q^{30} -9.27717 q^{31} -5.65685i q^{32} -6.25066 q^{33} -31.7237i q^{34} +(-29.8380 - 23.0183i) q^{35} +0.0751344 q^{36} -8.26365 q^{37} -10.8215 q^{38} -58.7820 q^{39} +(8.63817 - 11.1974i) q^{40} +29.3484 q^{41} +32.0433 q^{42} -48.5714 q^{43} -4.15843i q^{44} +(0.148724 + 0.114732i) q^{45} +(19.1989 - 26.2565i) q^{46} -77.5525i q^{47} +12.0250i q^{48} +7.80601 q^{49} +(34.1975 - 8.97391i) q^{50} +67.4365i q^{51} -39.1064i q^{52} -39.4826 q^{53} +38.1037 q^{54} +(6.35004 - 8.23138i) q^{55} +21.3178i q^{56} +23.0038 q^{57} -51.9337i q^{58} -19.3611 q^{59} +(-18.3625 + 23.8028i) q^{60} -11.9413i q^{61} +13.1199i q^{62} -0.283143 q^{63} -8.00000 q^{64} +(59.7166 - 77.4089i) q^{65} +8.83976i q^{66} +23.2991 q^{67} -44.8641 q^{68} +(-40.8120 + 55.8145i) q^{69} +(-32.5528 + 42.1973i) q^{70} -9.60115 q^{71} -0.106256i q^{72} -28.4073i q^{73} +11.6866i q^{74} +(-72.6951 + 19.0762i) q^{75} +15.3039i q^{76} +15.6710i q^{77} +83.1302i q^{78} +88.7761i q^{79} +(-15.8355 - 12.2162i) q^{80} -81.3367 q^{81} -41.5049i q^{82} -70.8309 q^{83} -45.3161i q^{84} +(-88.8060 - 68.5088i) q^{85} +68.6903i q^{86} +110.398i q^{87} -5.88092 q^{88} -130.974i q^{89} +(0.162256 - 0.210328i) q^{90} +147.372i q^{91} +(-37.1322 - 27.1514i) q^{92} -27.8895i q^{93} -109.676 q^{94} +(-23.3695 + 30.2932i) q^{95} +17.0059 q^{96} -169.233 q^{97} -11.0394i q^{98} -0.0781104i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9} + 96 q^{16} - 16 q^{24} - 48 q^{25} - 32 q^{26} + 100 q^{29} - 124 q^{31} - 28 q^{35} + 192 q^{36} + 192 q^{39} - 116 q^{41} + 148 q^{46} - 76 q^{49} - 144 q^{50} - 16 q^{54}+ \cdots + 32 q^{96}+O(q^{100}) $ 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9 + 96 * q^16 - 16 * q^24 - 48 * q^25 - 32 * q^26 + 100 * q^29 - 124 * q^31 - 28 * q^35 + 192 * q^36 + 192 * q^39 - 116 * q^41 + 148 * q^46 - 76 * q^49 - 144 * q^50 - 16 * q^54 - 224 * q^55 + 84 * q^59 - 192 * q^64 - 340 * q^69 + 328 * q^70 + 196 * q^71 - 496 * q^75 + 1360 * q^81 + 316 * q^85 - 376 * q^94 - 368 * q^95 + 32 * q^96

Character values

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

$n$	$47$	$51$
$\chi(n)$	$-1$	$-1$

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 $

$2$		−	1.41421i		−	0.707107i
$2$		−	1.41421i		−	0.707107i
$3$			3.00625i			1.00208i	0.865423	+	0.501042i	$0.167050\pi$
$3$			3.00625i			1.00208i	−0.865423	+	0.501042i	$0.832950\pi$
$4$	−2.00000			−0.500000
$5$	−3.95888	−	3.05405i	−0.791777	−	0.610811i
$5$	−3.95888	−	3.05405i	−0.791777	−	0.610811i
$6$	4.25149			0.708581
$7$	7.53698			1.07671			0.538355	−	0.842718i	$-0.319046\pi$
$7$	7.53698			1.07671			0.538355	+	0.842718i	$0.319046\pi$
$8$			2.82843i			0.353553i
$9$	−0.0375672			−0.00417413
$10$	−4.31908	+	5.59871i	−0.431908	+	0.559871i
$11$			2.07922i			0.189020i	0.995524	+	0.0945099i	$0.0301284\pi$
$11$			2.07922i			0.189020i	−0.995524	+	0.0945099i	$0.969872\pi$
$12$		−	6.01251i		−	0.501042i
$13$			19.5532i			1.50409i	0.659110	+	0.752047i	$0.270933\pi$
$13$			19.5532i			1.50409i	−0.659110	+	0.752047i	$0.729067\pi$
$14$		−	10.6589i		−	0.761350i
$15$	9.18126	−	11.9014i	0.612084	−	0.793427i
$16$	4.00000			0.250000
$17$	22.4321			1.31953			0.659767	−	0.751470i	$-0.270655\pi$
$17$	22.4321			1.31953			0.659767	+	0.751470i	$0.270655\pi$
$18$			0.0531281i			0.00295156i
$19$		−	7.65196i		−	0.402735i	−0.979516	−	0.201367i	$-0.935461\pi$
$19$		−	7.65196i		−	0.402735i	0.979516	−	0.201367i	$-0.0645385\pi$
$20$	7.91777	+	6.10811i	0.395888	+	0.305405i
$21$			22.6581i			1.07896i
$22$	2.94046			0.133657
$23$	18.5661	+	13.5757i	0.807223	+	0.590247i
$23$	18.5661	+	13.5757i	0.807223	+	0.590247i
$24$	−8.50297			−0.354291
$25$	6.34551	+	24.1813i	0.253820	+	0.967251i
$26$	27.6524			1.06355
$27$			26.9434i			0.997902i
$28$	−15.0740			−0.538355
$29$	36.7226			1.26630			0.633149	−	0.774030i	$-0.281762\pi$
$29$	36.7226			1.26630			0.633149	+	0.774030i	$0.281762\pi$
$30$	−16.8311	−	12.9843i	−0.561038	−	0.432809i
$31$	−9.27717			−0.299263			−0.149632	−	0.988742i	$-0.547809\pi$
$31$	−9.27717			−0.299263			−0.149632	+	0.988742i	$0.547809\pi$
$32$		−	5.65685i		−	0.176777i
$33$	−6.25066			−0.189414
$34$		−	31.7237i		−	0.933051i
$35$	−29.8380	−	23.0183i	−0.852514	−	0.657667i
$36$	0.0751344			0.00208707
$37$	−8.26365			−0.223342			−0.111671	−	0.993745i	$-0.535620\pi$
$37$	−8.26365			−0.223342			−0.111671	+	0.993745i	$0.535620\pi$
$38$	−10.8215			−0.284777
$39$	−58.7820			−1.50723
$40$	8.63817	−	11.1974i	0.215954	−	0.279935i
$41$	29.3484			0.715814			0.357907	−	0.933757i	$-0.383491\pi$
$41$	29.3484			0.715814			0.357907	+	0.933757i	$0.383491\pi$
$42$	32.0433			0.762937
$43$	−48.5714			−1.12957			−0.564784	−	0.825239i	$-0.691040\pi$
$43$	−48.5714			−1.12957			−0.564784	+	0.825239i	$0.691040\pi$
$44$		−	4.15843i		−	0.0945099i
$45$	0.148724	+	0.114732i	0.00330498	+	0.00254961i
$46$	19.1989	−	26.2565i	0.417368	−	0.570793i
$47$		−	77.5525i		−	1.65005i	−0.565094	−	0.825027i	$-0.691160\pi$
$47$		−	77.5525i		−	1.65005i	0.565094	−	0.825027i	$-0.308840\pi$
$48$			12.0250i			0.250521i
$49$	7.80601			0.159306
$50$	34.1975	−	8.97391i	0.683950	−	0.179478i
$51$			67.4365i			1.32228i
$52$		−	39.1064i		−	0.752047i
$53$	−39.4826			−0.744955			−0.372478	−	0.928041i	$-0.621492\pi$
$53$	−39.4826			−0.744955			−0.372478	+	0.928041i	$0.621492\pi$
$54$	38.1037			0.705623
$55$	6.35004	−	8.23138i	0.115455	−	0.149661i
$56$			21.3178i			0.380675i
$57$	23.0038			0.403575
$58$		−	51.9337i		−	0.895408i
$59$	−19.3611			−0.328154			−0.164077	−	0.986448i	$-0.552465\pi$
$59$	−19.3611			−0.328154			−0.164077	+	0.986448i	$0.552465\pi$
$60$	−18.3625	+	23.8028i	−0.306042	+	0.396714i
$61$		−	11.9413i		−	0.195760i	−0.995198	−	0.0978798i	$-0.968794\pi$
$61$		−	11.9413i		−	0.195760i	0.995198	−	0.0978798i	$-0.0312061\pi$
$62$			13.1199i			0.211611i
$63$	−0.283143			−0.00449434
$64$	−8.00000			−0.125000
$65$	59.7166	−	77.4089i	0.918717	−	1.19091i
$66$			8.83976i			0.133936i
$67$	23.2991			0.347748			0.173874	−	0.984768i	$-0.444372\pi$
$67$	23.2991			0.347748			0.173874	+	0.984768i	$0.444372\pi$
$68$	−44.8641			−0.659767
$69$	−40.8120	+	55.8145i	−0.591478	+	0.808906i
$70$	−32.5528	+	42.1973i	−0.465041	+	0.602819i
$71$	−9.60115			−0.135228			−0.0676138	−	0.997712i	$-0.521539\pi$
$71$	−9.60115			−0.135228			−0.0676138	+	0.997712i	$0.521539\pi$
$72$		−	0.106256i		−	0.00147578i
$73$		−	28.4073i		−	0.389140i	−0.980889	−	0.194570i	$-0.937669\pi$
$73$		−	28.4073i		−	0.389140i	0.980889	−	0.194570i	$-0.0623312\pi$
$74$			11.6866i			0.157927i
$75$	−72.6951	+	19.0762i	−0.969268	+	0.254350i
$76$			15.3039i			0.201367i
$77$			15.6710i			0.203520i
$78$			83.1302i			1.06577i
$79$			88.7761i			1.12375i	0.827223	+	0.561874i	$0.189919\pi$
$79$			88.7761i			1.12375i	−0.827223	+	0.561874i	$0.810081\pi$
$80$	−15.8355	−	12.2162i	−0.197944	−	0.152703i
$81$	−81.3367			−1.00416
$82$		−	41.5049i		−	0.506157i
$83$	−70.8309			−0.853385			−0.426692	−	0.904397i	$-0.640321\pi$
$83$	−70.8309			−0.853385			−0.426692	+	0.904397i	$0.640321\pi$
$84$		−	45.3161i		−	0.539478i
$85$	−88.8060	−	68.5088i	−1.04478	−	0.805985i
$86$			68.6903i			0.798725i
$87$			110.398i			1.26894i
$88$	−5.88092			−0.0668286
$89$		−	130.974i		−	1.47162i	−0.677189	−	0.735809i	$-0.736802\pi$
$89$		−	130.974i		−	1.47162i	0.677189	−	0.735809i	$-0.263198\pi$
$90$	0.162256	−	0.210328i	0.00180284	−	0.00233698i
$91$			147.372i			1.61947i
$92$	−37.1322	−	27.1514i	−0.403611	−	0.295123i
$93$		−	27.8895i		−	0.299887i
$94$	−109.676			−1.16676
$95$	−23.3695	+	30.2932i	−0.245995	+	0.318876i
$96$	17.0059			0.177145
$97$	−169.233			−1.74467			−0.872336	−	0.488907i	$-0.837396\pi$
$97$	−169.233			−1.74467			−0.872336	+	0.488907i	$0.837396\pi$
$98$		−	11.0394i		−	0.112647i
$99$		−	0.0781104i		−	0.000788994i
$100$	−12.6910	−	48.3626i	−0.126910	−	0.483626i
$101$	146.128			1.44681			0.723406	−	0.690423i	$-0.242575\pi$
$101$	146.128			1.44681			0.723406	+	0.690423i	$0.242575\pi$
$102$	95.3697			0.934997
$103$	135.502			1.31556			0.657778	−	0.753212i	$-0.271497\pi$
$103$	135.502			1.31556			0.657778	+	0.753212i	$0.271497\pi$
$104$	−55.3049			−0.531777
$105$	69.1990	−	89.7006i	0.659038	−	0.854292i
$106$			55.8369i			0.526763i
$107$	−112.264			−1.04920			−0.524599	−	0.851349i	$-0.675785\pi$
$107$	−112.264			−1.04920			−0.524599	+	0.851349i	$0.675785\pi$
$108$		−	53.8867i		−	0.498951i
$109$			155.964i			1.43086i	0.698685	+	0.715429i	$0.253769\pi$
$109$			155.964i			1.43086i	−0.698685	+	0.715429i	$0.746231\pi$
$110$	−11.6409	−	8.98032i	−0.105827	−	0.0816392i
$111$		−	24.8426i		−	0.223808i
$112$	30.1479			0.269178
$113$	176.113			1.55852			0.779260	−	0.626701i	$-0.215595\pi$
$113$	176.113			1.55852			0.779260	+	0.626701i	$0.215595\pi$
$114$		−	32.5322i		−	0.285370i
$115$	−32.0402	−	110.446i	−0.278611	−	0.960404i
$116$	−73.4453			−0.633149
$117$		−	0.734560i		−	0.00627829i
$118$			27.3807i			0.232040i
$119$	169.070			1.42076
$120$	33.6623	+	25.9685i	0.280519	+	0.216404i
$121$	116.677			0.964272
$122$	−16.8876			−0.138423
$123$			88.2287i			0.717306i
$124$	18.5543			0.149632
$125$	48.7298	−	115.110i	0.389838	−	0.920883i
$126$			0.400425i			0.00317798i
$127$			41.7240i			0.328535i	0.986416	+	0.164268i	$0.0525260\pi$
$127$			41.7240i			0.328535i	−0.986416	+	0.164268i	$0.947474\pi$
$128$			11.3137i			0.0883883i
$129$		−	146.018i		−	1.13192i
$130$	−109.473	−	84.4520i	−0.842098	−	0.649631i
$131$	119.975			0.915840			0.457920	−	0.888993i	$-0.348595\pi$
$131$	119.975			0.915840			0.457920	+	0.888993i	$0.348595\pi$
$132$	12.5013			0.0947069
$133$		−	57.6727i		−	0.433629i
$134$		−	32.9499i		−	0.245895i
$135$	82.2865	−	106.666i	0.609529	−	0.790116i
$136$			63.4475i			0.466526i
$137$	−230.549			−1.68284			−0.841418	−	0.540385i	$-0.818279\pi$
$137$	−230.549			−1.68284			−0.841418	+	0.540385i	$0.818279\pi$
$138$	78.9336	+	57.7168i	0.571983	+	0.418238i
$139$	91.6204			0.659139			0.329570	−	0.944131i	$-0.393096\pi$
$139$	91.6204			0.659139			0.329570	+	0.944131i	$0.393096\pi$
$140$	59.6760	+	46.0367i	0.426257	+	0.328833i
$141$	233.143			1.65349
$142$			13.5781i			0.0956203i
$143$	−40.6554			−0.284303
$144$	−0.150269			−0.00104353
$145$	−145.381	−	112.153i	−1.00263	−	0.773468i
$146$	−40.1739			−0.275164
$147$			23.4668i			0.159638i
$148$	16.5273			0.111671
$149$		−	202.520i		−	1.35920i	−0.733584	−	0.679599i	$-0.762154\pi$
$149$		−	202.520i		−	1.35920i	0.733584	−	0.679599i	$-0.237846\pi$
$150$	26.9778	+	102.806i	0.179852	+	0.685376i
$151$	−130.456			−0.863944			−0.431972	−	0.901887i	$-0.642182\pi$
$151$	−130.456			−0.863944			−0.431972	+	0.901887i	$0.642182\pi$
$152$	21.6430			0.142388
$153$	−0.842711			−0.00550791
$154$	22.1622			0.143910
$155$	36.7272	+	28.3330i	0.236950	+	0.182793i
$156$	117.564			0.753615
$157$	96.1669			0.612528			0.306264	−	0.951947i	$-0.400921\pi$
$157$	96.1669			0.612528			0.306264	+	0.951947i	$0.400921\pi$
$158$	125.548			0.794610
$159$		−	118.695i		−	0.746508i
$160$	−17.2763	+	22.3948i	−0.107977	+	0.139968i
$161$	139.932	+	102.320i	0.869145	+	0.635525i
$162$			115.027i			0.710046i
$163$		−	166.567i		−	1.02189i	−0.859614	−	0.510943i	$-0.829296\pi$
$163$		−	166.567i		−	1.02189i	0.859614	−	0.510943i	$-0.170704\pi$
$164$	−58.6967			−0.357907
$165$	24.7456	+	19.0898i	0.149973	+	0.115696i
$166$			100.170i			0.603434i
$167$			193.754i			1.16020i	0.814545	+	0.580100i	$0.196987\pi$
$167$			193.754i			1.16020i	−0.814545	+	0.580100i	$0.803013\pi$
$168$	−64.0867			−0.381468
$169$	−213.328			−1.26230
$170$	−96.8860	+	125.591i	−0.569918	+	0.738768i
$171$			0.287463i			0.00168107i
$172$	97.1428			0.564784
$173$		−	6.29236i		−	0.0363720i	−0.999835	−	0.0181860i	$-0.994211\pi$
$173$		−	6.29236i		−	0.0363720i	0.999835	−	0.0181860i	$-0.00578910\pi$
$174$	156.126			0.897275
$175$	47.8260	+	182.254i	0.273291	+	1.04145i
$176$			8.31687i			0.0472549i
$177$		−	58.2044i		−	0.328838i
$178$	−185.225			−1.04059
$179$	−127.641			−0.713077			−0.356539	−	0.934281i	$-0.616043\pi$
$179$	−127.641			−0.713077			−0.356539	+	0.934281i	$0.616043\pi$
$180$	−0.297448	−	0.229465i	−0.00165249	−	0.00127480i
$181$		−	175.172i		−	0.967799i	−0.875124	−	0.483899i	$-0.839220\pi$
$181$		−	175.172i		−	0.967799i	0.875124	−	0.483899i	$-0.160780\pi$
$182$	208.416			1.14514
$183$	35.8987			0.196168
$184$	−38.3978	+	52.5129i	−0.208684	+	0.285396i
$185$	32.7148	+	25.2376i	0.176837	+	0.136420i
$186$	−39.4417			−0.212052
$187$			46.6412i			0.249418i
$188$			155.105i			0.825027i
$189$			203.071i			1.07445i
$190$	42.8411	+	33.0495i	0.225479	+	0.173945i
$191$		−	33.1238i		−	0.173423i	−0.996233	−	0.0867116i	$-0.972364\pi$
$191$		−	33.1238i		−	0.173423i	0.996233	−	0.0867116i	$-0.0276359\pi$
$192$		−	24.0500i		−	0.125261i
$193$		−	312.691i		−	1.62016i	−0.586318	−	0.810081i	$-0.699423\pi$
$193$		−	312.691i		−	1.62016i	0.586318	−	0.810081i	$-0.300577\pi$
$194$			239.332i			1.23367i
$195$	232.711	+	179.523i	1.19339	+	0.920632i
$196$	−15.6120			−0.0796531
$197$			241.945i			1.22815i	0.789249	+	0.614073i	$0.210470\pi$
$197$			241.945i			1.22815i	−0.789249	+	0.614073i	$0.789530\pi$
$198$	−0.110465			−0.000557903
$199$		−	194.994i		−	0.979870i	−0.871759	−	0.489935i	$-0.837020\pi$
$199$		−	194.994i		−	0.979870i	0.871759	−	0.489935i	$-0.162980\pi$
$200$	−68.3950	+	17.9478i	−0.341975	+	0.0897391i
$201$			70.0430i			0.348473i
$202$		−	206.656i		−	1.02305i
$203$	276.778			1.36344
$204$		−	134.873i		−	0.661142i
$205$	−116.187	−	89.6315i	−0.566765	−	0.437227i
$206$		−	191.629i		−	0.930238i
$207$	−0.697477	−	0.510000i	−0.00336946	−	0.00246377i
$208$			78.2129i			0.376023i
$209$	15.9101			0.0761249
$210$	−126.856	−	97.8621i	−0.604076	−	0.466010i
$211$	−392.823			−1.86172			−0.930861	−	0.365375i	$-0.880941\pi$
$211$	−392.823			−1.86172			−0.930861	+	0.365375i	$0.880941\pi$
$212$	78.9652			0.372478
$213$		−	28.8635i		−	0.135509i
$214$			158.766i			0.741895i
$215$	192.288	+	148.340i	0.894365	+	0.689952i
$216$	−76.2073			−0.352812
$217$	−69.9218			−0.322220
$218$	220.566			1.01177
$219$	85.3994			0.389952
$220$	−12.7001	+	16.4628i	−0.0577277	+	0.0748307i
$221$			438.619i			1.98470i
$222$	−35.1328			−0.158256
$223$			294.817i			1.32205i	0.750364	+	0.661025i	$0.229878\pi$
$223$			294.817i			1.32205i	−0.750364	+	0.661025i	$0.770122\pi$
$224$		−	42.6356i		−	0.190337i
$225$	−0.238383	−	0.908423i	−0.00105948	−	0.00403744i
$226$		−	249.061i		−	1.10204i
$227$	−279.401			−1.23084			−0.615421	−	0.788198i	$-0.711014\pi$
$227$	−279.401			−1.23084			−0.615421	+	0.788198i	$0.711014\pi$
$228$	−46.0075			−0.201787
$229$		−	19.5785i		−	0.0854956i	−0.999086	−	0.0427478i	$-0.986389\pi$
$229$		−	19.5785i		−	0.0854956i	0.999086	−	0.0427478i	$-0.0136112\pi$
$230$	−156.195	+	45.3118i	−0.679108	+	0.197008i
$231$	−47.1111			−0.203944
$232$			103.867i			0.447704i
$233$		−	202.249i		−	0.868022i	−0.900908	−	0.434011i	$-0.857098\pi$
$233$		−	202.249i		−	0.868022i	0.900908	−	0.434011i	$-0.142902\pi$
$234$	−1.03882			−0.00443942
$235$	−236.850	+	307.021i	−1.00787	+	1.30647i
$236$	38.7222			0.164077
$237$	−266.884			−1.12609
$238$		−	239.101i		−	1.00463i
$239$	−116.074			−0.485667			−0.242834	−	0.970068i	$-0.578077\pi$
$239$	−116.074			−0.485667			−0.242834	+	0.970068i	$0.578077\pi$
$240$	36.7251	−	47.6056i	0.153021	−	0.198357i
$241$			127.761i			0.530130i	0.964231	+	0.265065i	$0.0853935\pi$
$241$			127.761i			0.530130i	−0.964231	+	0.265065i	$0.914607\pi$
$242$		−	165.006i		−	0.681843i
$243$		−	2.02862i		−	0.00834822i
$244$			23.8827i			0.0978798i
$245$	−30.9031	−	23.8400i	−0.126135	−	0.0973060i
$246$	124.774			0.507212
$247$	149.621			0.605751
$248$		−	26.2398i		−	0.105806i
$249$		−	212.936i		−	0.855164i
$250$	−162.791	−	68.9144i	−0.651163	−	0.275657i
$251$		−	391.496i		−	1.55975i	−0.625937	−	0.779873i	$-0.715283\pi$
$251$		−	391.496i		−	1.55975i	0.625937	−	0.779873i	$-0.284717\pi$
$252$	0.566286			0.00224717
$253$	−28.2268	+	38.6030i	−0.111568	+	0.152581i
$254$	59.0066			0.232309
$255$	205.955	−	266.973i	0.807666	−	1.04695i
$256$	16.0000			0.0625000
$257$		−	442.554i		−	1.72200i	−0.508605	−	0.861000i	$-0.669839\pi$
$257$		−	442.554i		−	1.72200i	0.508605	−	0.861000i	$-0.330161\pi$
$258$	−206.501			−0.800390
$259$	−62.2829			−0.240475
$260$	−119.433	+	154.818i	−0.459358	+	0.595453i
$261$	−1.37957			−0.00528570
$262$		−	169.670i		−	0.647597i
$263$	104.907			0.398885			0.199443	−	0.979910i	$-0.436087\pi$
$263$	104.907			0.398885			0.199443	+	0.979910i	$0.436087\pi$
$264$		−	17.6795i		−	0.0669679i
$265$	156.307	+	120.582i	0.589838	+	0.455027i
$266$	−81.5615			−0.306622
$267$	393.741			1.47469
$268$	−46.5982			−0.173874
$269$	38.9402			0.144759			0.0723795	−	0.997377i	$-0.476941\pi$
$269$	38.9402			0.144759			0.0723795	+	0.997377i	$0.476941\pi$
$270$	−150.848	−	116.371i	−0.558696	−	0.431002i
$271$	−275.239			−1.01564			−0.507822	−	0.861462i	$-0.669549\pi$
$271$	−275.239			−1.01564			−0.507822	+	0.861462i	$0.669549\pi$
$272$	89.7283			0.329883
$273$	−443.038			−1.62285
$274$			326.045i			1.18994i
$275$	−50.2781	+	13.1937i	−0.182830	+	0.0479771i
$276$	81.6239	−	111.629i	0.295739	−	0.404453i
$277$			25.9384i			0.0936406i	0.998903	+	0.0468203i	$0.0149088\pi$
$277$			25.9384i			0.0936406i	−0.998903	+	0.0468203i	$0.985091\pi$
$278$		−	129.571i		−	0.466082i
$279$	0.348517			0.00124917
$280$	65.1057	−	84.3946i	0.232520	−	0.301409i
$281$			235.636i			0.838563i	0.907856	+	0.419281i	$0.137718\pi$
$281$			235.636i			0.838563i	−0.907856	+	0.419281i	$0.862282\pi$
$282$		−	329.713i		−	1.16920i
$283$	−375.709			−1.32759			−0.663797	−	0.747913i	$-0.731056\pi$
$283$	−375.709			−1.32759			−0.663797	+	0.747913i	$0.731056\pi$
$284$	19.2023			0.0676138
$285$	−91.0692	−	70.2547i	−0.319541	−	0.246508i
$286$			57.4954i			0.201033i
$287$	221.198			0.770725
$288$			0.212512i			0.000737890i
$289$	214.198			0.741169
$290$	−158.608	+	205.599i	−0.546925	+	0.708963i
$291$		−	508.758i		−	1.74831i
$292$			56.8145i			0.194570i
$293$	376.743			1.28581			0.642906	−	0.765945i	$-0.277729\pi$
$293$	376.743			1.28581			0.642906	+	0.765945i	$0.277729\pi$
$294$	33.1871			0.112881
$295$	76.6483	+	59.1298i	0.259825	+	0.200440i
$296$		−	23.3731i		−	0.0789633i
$297$	−56.0211			−0.188623
$298$	−286.407			−0.961098
$299$	−265.448	+	363.027i	−0.887787	+	1.21414i
$300$	145.390	−	38.1524i	0.484634	−	0.127175i
$301$	−366.081			−1.21622
$302$			184.492i			0.610901i
$303$			439.298i			1.44983i
$304$		−	30.6079i		−	0.100684i
$305$	−36.4695	+	47.2743i	−0.119572	+	0.154998i
$306$			1.19177i			0.00389468i
$307$		−	371.158i		−	1.20898i	−0.796612	−	0.604491i	$-0.793376\pi$
$307$		−	371.158i		−	1.20898i	0.796612	−	0.604491i	$-0.206624\pi$
$308$		−	31.3420i		−	0.101760i
$309$			407.354i			1.31830i
$310$	40.0689	−	51.9401i	0.129254	−	0.167549i
$311$	304.788			0.980025			0.490013	−	0.871715i	$-0.336992\pi$
$311$	304.788			0.980025			0.490013	+	0.871715i	$0.336992\pi$
$312$		−	166.260i		−	0.532886i
$313$	440.377			1.40696			0.703478	−	0.710717i	$-0.251629\pi$
$313$	440.377			1.40696			0.703478	+	0.710717i	$0.251629\pi$
$314$		−	136.001i		−	0.433123i
$315$	1.12093	+	0.864735i	0.00355851	+	0.00274519i
$316$		−	177.552i		−	0.561874i
$317$		−	86.1647i		−	0.271813i	−0.990722	−	0.135907i	$-0.956605\pi$
$317$		−	86.1647i		−	0.271813i	0.990722	−	0.135907i	$-0.0433947\pi$
$318$	−167.860			−0.527861
$319$			76.3544i			0.239355i
$320$	31.6711	+	24.4324i	0.0989721	+	0.0763513i
$321$		−	337.495i		−	1.05139i
$322$	144.702	−	197.894i	0.449384	−	0.614579i
$323$		−	171.649i		−	0.531422i
$324$	162.673			0.502078
$325$	−472.822	+	124.075i	−1.45484	+	0.381770i
$326$	−235.562			−0.722583
$327$	−468.866			−1.43384
$328$			83.0097i			0.253078i
$329$		−	584.511i		−	1.77663i
$330$	26.9971	−	34.9956i	0.0818094	−	0.106047i
$331$	−28.8280			−0.0870936			−0.0435468	−	0.999051i	$-0.513866\pi$
$331$	−28.8280			−0.0870936			−0.0435468	+	0.999051i	$0.513866\pi$
$332$	141.662			0.426692
$333$	0.310442			0.000932259
$334$	274.009			0.820386
$335$	−92.2383	−	71.1567i	−0.275338	−	0.212408i
$336$			90.6323i			0.269739i
$337$	314.690			0.933799			0.466900	−	0.884310i	$-0.345371\pi$
$337$	314.690			0.933799			0.466900	+	0.884310i	$0.345371\pi$
$338$			301.692i			0.892580i
$339$			529.440i			1.56177i
$340$	177.612	+	137.018i	0.522388	+	0.402993i
$341$		−	19.2892i		−	0.0565667i
$342$	0.406534			0.00118870
$343$	−310.478			−0.905184
$344$		−	137.381i		−	0.399362i
$345$	332.030	−	96.3211i	0.962406	−	0.279192i
$346$	−8.89874			−0.0257189
$347$			318.146i			0.916847i	0.888734	+	0.458424i	$0.151586\pi$
$347$			318.146i			0.916847i	−0.888734	+	0.458424i	$0.848414\pi$
$348$		−	220.795i		−	0.634469i
$349$	−161.289			−0.462147			−0.231074	−	0.972936i	$-0.574224\pi$
$349$	−161.289			−0.462147			−0.231074	+	0.972936i	$0.574224\pi$
$350$	257.746	−	67.6361i	0.736416	−	0.193246i
$351$	−526.829			−1.50094
$352$	11.7618			0.0334143
$353$		−	10.7788i		−	0.0305349i	−0.999883	−	0.0152675i	$-0.995140\pi$
$353$		−	10.7788i		−	0.0305349i	0.999883	−	0.0152675i	$-0.00485998\pi$
$354$	−82.3134			−0.232524
$355$	38.0098	+	29.3224i	0.107070	+	0.0825984i
$356$			261.948i			0.735809i
$357$			508.268i			1.42372i
$358$			180.511i			0.504222i
$359$			310.640i			0.865292i	0.901564	+	0.432646i	$0.142420\pi$
$359$			310.640i			0.865292i	−0.901564	+	0.432646i	$0.857580\pi$
$360$	−0.324512	+	0.420656i	−0.000901422	+	0.00116849i
$361$	302.447			0.837805
$362$	−247.730			−0.684337
$363$			350.760i			0.966282i
$364$		−	294.744i		−	0.809737i
$365$	−86.7573	+	112.461i	−0.237691	+	0.308112i
$366$		−	50.7684i		−	0.138711i
$367$	−132.239			−0.360324			−0.180162	−	0.983637i	$-0.557662\pi$
$367$	−132.239			−0.360324			−0.180162	+	0.983637i	$0.557662\pi$
$368$	74.2645	+	54.3027i	0.201806	+	0.147562i
$369$	−1.10254			−0.00298790
$370$	35.6914	−	46.2658i	0.0964633	−	0.125043i
$371$	−297.580			−0.802101
$372$			55.7790i			0.149944i
$373$	324.296			0.869426			0.434713	−	0.900569i	$-0.356850\pi$
$373$	324.296			0.869426			0.434713	+	0.900569i	$0.356850\pi$
$374$	65.9606			0.176365
$375$	346.051	+	146.494i	0.922803	+	0.390651i
$376$	219.352			0.583382
$377$			718.046i			1.90463i
$378$	287.186			0.759752
$379$			274.491i			0.724252i	0.932129	+	0.362126i	$0.117949\pi$
$379$			274.491i			0.724252i	−0.932129	+	0.362126i	$0.882051\pi$
$380$	46.7390	−	60.5865i	0.122997	−	0.159438i
$381$	−125.433			−0.329220
$382$	−46.8442			−0.122629
$383$	−336.100			−0.877545			−0.438772	−	0.898598i	$-0.644587\pi$
$383$	−336.100			−0.877545			−0.438772	+	0.898598i	$0.644587\pi$
$384$	−34.0119			−0.0885726
$385$	47.8601	−	62.0397i	0.124312	−	0.161142i
$386$	−442.212			−1.14563
$387$	1.82469			0.00471497
$388$	338.466			0.872336
$389$		−	46.7493i		−	0.120178i	−0.998193	−	0.0600891i	$-0.980862\pi$
$389$		−	46.7493i		−	0.120178i	0.998193	−	0.0600891i	$-0.0191385\pi$
$390$	253.884	−	329.103i	0.650985	−	0.843854i
$391$	416.477	+	304.531i	1.06516	+	0.778851i
$392$			22.0787i			0.0563233i
$393$			360.676i			0.917750i
$394$	342.161			0.868430
$395$	271.127	−	351.454i	0.686397	−	0.889758i
$396$			0.156221i			0.000394497i
$397$		−	210.518i		−	0.530273i	−0.964211	−	0.265137i	$-0.914583\pi$
$397$		−	210.518i		−	0.530273i	0.964211	−	0.265137i	$-0.0854171\pi$
$398$	−275.763			−0.692873
$399$	173.379			0.434533
$400$	25.3820	+	96.7251i	0.0634551	+	0.241813i
$401$		−	263.085i		−	0.656073i	−0.944665	−	0.328036i	$-0.893613\pi$
$401$		−	263.085i		−	0.656073i	0.944665	−	0.328036i	$-0.106387\pi$
$402$	99.0557			0.246407
$403$		−	181.398i		−	0.450120i
$404$	−292.256			−0.723406
$405$	322.002	+	248.407i	0.795068	+	0.613350i
$406$		−	391.423i		−	0.964095i
$407$		−	17.1819i		−	0.0422160i
$408$	−190.739			−0.467498
$409$	719.544			1.75928			0.879638	−	0.475644i	$-0.157785\pi$
$409$	719.544			1.75928			0.879638	+	0.475644i	$0.157785\pi$
$410$	−126.758	+	164.313i	−0.309166	+	0.400763i
$411$		−	693.088i		−	1.68634i
$412$	−271.004			−0.657778
$413$	−145.924			−0.353327
$414$	−0.721250	+	0.986382i	−0.00174215	+	0.00238257i
$415$	280.411	+	216.321i	0.675690	+	0.521256i
$416$	110.610			0.265889
$417$			275.434i			0.660514i
$418$		−	22.5003i		−	0.0538284i
$419$		−	566.267i		−	1.35147i	−0.737143	−	0.675737i	$-0.763826\pi$
$419$		−	566.267i		−	1.35147i	0.737143	−	0.675737i	$-0.236174\pi$
$420$	−138.398	+	179.401i	−0.329519	+	0.427146i
$421$		−	506.544i		−	1.20319i	−0.798800	−	0.601596i	$-0.794532\pi$
$421$		−	506.544i		−	1.20319i	0.798800	−	0.601596i	$-0.205468\pi$
$422$			555.536i			1.31644i
$423$			2.91343i			0.00688755i
$424$		−	111.674i		−	0.263381i
$425$	142.343	+	542.436i	0.334925	+	1.27632i
$426$	−40.8192			−0.0958197
$427$		−	90.0015i		−	0.210776i
$428$	224.528			0.524599
$429$		−	122.220i		−	0.284896i
$430$	209.784	−	271.937i	0.487870	−	0.632411i
$431$		−	174.935i		−	0.405883i	−0.979191	−	0.202941i	$-0.934950\pi$
$431$		−	174.935i		−	0.405883i	0.979191	−	0.202941i	$-0.0650501\pi$
$432$			107.773i			0.249476i
$433$	−162.574			−0.375460			−0.187730	−	0.982221i	$-0.560113\pi$
$433$	−162.574			−0.375460			−0.187730	+	0.982221i	$0.560113\pi$
$434$			98.8843i			0.227844i
$435$	337.160	−	437.051i	0.775081	−	1.00472i
$436$		−	311.927i		−	0.715429i
$437$	103.881	−	142.067i	0.237713	−	0.325097i
$438$		−	120.773i		−	0.275738i
$439$	88.5661			0.201745			0.100873	−	0.994899i	$-0.467837\pi$
$439$	88.5661			0.201745			0.100873	+	0.994899i	$0.467837\pi$
$440$	23.2819	+	17.9606i	0.0529133	+	0.0408196i
$441$	−0.293250			−0.000664966
$442$	620.301			1.40340
$443$		−	299.756i		−	0.676650i	−0.941029	−	0.338325i	$-0.890140\pi$
$443$		−	299.756i		−	0.676650i	0.941029	−	0.338325i	$-0.109860\pi$
$444$			49.6853i			0.111904i
$445$	−400.001	+	518.511i	−0.898880	+	1.16519i
$446$	416.934			0.934830
$447$	608.828			1.36203
$448$	−60.2958			−0.134589
$449$	−475.804			−1.05970			−0.529849	−	0.848092i	$-0.677751\pi$
$449$	−475.804			−1.05970			−0.529849	+	0.848092i	$0.677751\pi$
$450$	−1.28470	+	0.337125i	−0.00285490	+	0.000749166i
$451$			61.0216i			0.135303i
$452$	−352.225			−0.779260
$453$		−	392.183i		−	0.865746i
$454$			395.133i			0.870337i
$455$	450.082	−	583.429i	0.989192	−	1.28226i
$456$			65.0644i			0.142685i
$457$	−632.889			−1.38488			−0.692438	−	0.721477i	$-0.743463\pi$
$457$	−632.889			−1.38488			−0.692438	+	0.721477i	$0.743463\pi$
$458$	−27.6882			−0.0604545
$459$			604.395i			1.31677i
$460$	64.0805	+	220.893i	0.139305	+	0.480202i
$461$	−389.815			−0.845587			−0.422793	−	0.906226i	$-0.638950\pi$
$461$	−389.815			−0.845587			−0.422793	+	0.906226i	$0.638950\pi$
$462$			66.6251i			0.144210i
$463$		−	146.564i		−	0.316554i	−0.987395	−	0.158277i	$-0.949406\pi$
$463$		−	146.564i		−	0.316554i	0.987395	−	0.158277i	$-0.0505939\pi$
$464$	146.891			0.316575
$465$	−85.1761	+	110.411i	−0.183174	+	0.237444i
$466$	−286.023			−0.613784
$467$	−114.522			−0.245228			−0.122614	−	0.992454i	$-0.539128\pi$
$467$	−114.522			−0.245228			−0.122614	+	0.992454i	$0.539128\pi$
$468$			1.46912i			0.00313915i
$469$	175.605			0.374424
$470$	434.194	+	334.956i	0.923817	+	0.712672i
$471$			289.102i			0.613805i
$472$		−	54.7614i		−	0.116020i
$473$		−	100.990i		−	0.213511i
$474$			377.430i			0.796267i
$475$	185.034	−	48.5556i	0.389546	−	0.102222i
$476$	−338.140			−0.710378
$477$	1.48325			0.00310954
$478$			164.154i			0.343419i
$479$		−	572.110i		−	1.19438i	−0.802098	−	0.597192i	$-0.796283\pi$
$479$		−	572.110i		−	1.19438i	0.802098	−	0.597192i	$-0.203717\pi$
$480$	−67.3245	−	51.9371i	−0.140259	−	0.108202i
$481$		−	161.581i		−	0.335927i
$482$	180.682			0.374859
$483$	−307.599	+	420.672i	−0.636850	+	0.870958i
$484$	−233.354			−0.482136
$485$	669.974	+	516.847i	1.38139	+	1.06566i
$486$	−2.86890			−0.00590308
$487$		−	288.653i		−	0.592716i	−0.955077	−	0.296358i	$-0.904228\pi$
$487$		−	288.653i		−	0.592716i	0.955077	−	0.296358i	$-0.0957722\pi$
$488$	33.7752			0.0692114
$489$	500.744			1.02402
$490$	−33.7148	+	43.7035i	−0.0688057	+	0.0891909i
$491$	665.833			1.35608			0.678038	−	0.735027i	$-0.262830\pi$
$491$	665.833			1.35608			0.678038	+	0.735027i	$0.262830\pi$
$492$		−	176.457i		−	0.358653i
$493$	823.765			1.67092
$494$		−	211.595i		−	0.428331i
$495$	−0.238553	+	0.309230i	−0.000481926	+	0.000624707i
$496$	−37.1087			−0.0748158
$497$	−72.3637			−0.145601
$498$	−301.137			−0.604692
$499$	−118.165			−0.236805			−0.118402	−	0.992966i	$-0.537777\pi$
$499$	−118.165			−0.236805			−0.118402	+	0.992966i	$0.537777\pi$
$500$	−97.4596	+	230.221i	−0.194919	+	0.460442i
$501$	−582.472			−1.16262
$502$	−553.660			−1.10291
$503$	−814.476			−1.61924			−0.809618	−	0.586957i	$-0.800326\pi$
$503$	−814.476			−1.61924			−0.809618	+	0.586957i	$0.800326\pi$
$504$		−	0.800850i		−	0.00158899i
$505$	−578.504	−	446.283i	−1.14555	−	0.883728i
$506$	54.5929	+	39.9187i	0.107891	+	0.0788907i
$507$		−	641.320i		−	1.26493i
$508$		−	83.4479i		−	0.164268i
$509$	−221.229			−0.434635			−0.217318	−	0.976101i	$-0.569731\pi$
$509$	−221.229			−0.434635			−0.217318	+	0.976101i	$0.569731\pi$
$510$	−377.557	−	291.264i	−0.740308	−	0.571106i
$511$		−	214.105i		−	0.418992i
$512$		−	22.6274i		−	0.0441942i
$513$	206.170			0.401890
$514$	−625.866			−1.21764
$515$	−536.437	−	413.831i	−1.04163	−	0.803555i
$516$			292.036i			0.565961i
$517$	161.249			0.311893
$518$			88.0814i			0.170041i
$519$	18.9164			0.0364478
$520$	218.945	+	168.904i	0.421049	+	0.324815i
$521$		−	92.1604i		−	0.176891i	−0.996081	−	0.0884457i	$-0.971810\pi$
$521$		−	92.1604i		−	0.176891i	0.996081	−	0.0884457i	$-0.0281900\pi$
$522$			1.95100i			0.00373755i
$523$	62.0002			0.118547			0.0592736	−	0.998242i	$-0.481122\pi$
$523$	62.0002			0.118547			0.0592736	+	0.998242i	$0.481122\pi$
$524$	−239.950			−0.457920
$525$	−547.901	+	143.777i	−1.04362	+	0.273861i
$526$		−	148.361i		−	0.282054i
$527$	−208.106			−0.394888
$528$	−25.0026			−0.0473535
$529$	160.402	+	504.095i	0.303217	+	0.952922i
$530$	170.529	−	221.052i	0.321752	−	0.417078i
$531$	0.727342			0.00136976
$532$			115.345i			0.216815i
$533$			573.855i			1.07665i
$534$		−	556.834i		−	1.04276i
$535$	444.441	+	342.861i	0.830730	+	0.640861i
$536$			65.8998i			0.122947i
$537$		−	383.721i		−	0.714564i
$538$		−	55.0697i		−	0.102360i
$539$			16.2304i			0.0301120i
$540$	−164.573	+	213.331i	−0.304765	+	0.395058i
$541$	−93.7470			−0.173285			−0.0866424	−	0.996239i	$-0.527614\pi$
$541$	−93.7470			−0.173285			−0.0866424	+	0.996239i	$0.527614\pi$
$542$			389.247i			0.718168i
$543$	526.610			0.969817
$544$		−	126.895i		−	0.233263i
$545$	476.321	−	617.442i	0.873984	−	1.13292i
$546$			626.551i			1.14753i
$547$			748.011i			1.36748i	0.729726	+	0.683739i	$0.239647\pi$
$547$			748.011i			1.36748i	−0.729726	+	0.683739i	$0.760353\pi$
$548$	461.097			0.841418
$549$			0.448602i			0.000817127i
$550$	18.6587	+	71.1040i	0.0339249	+	0.129280i
$551$		−	281.000i		−	0.509982i
$552$	−157.867	−	115.434i	−0.285991	−	0.209119i
$553$			669.103i			1.20995i
$554$	36.6825			0.0662139
$555$	−75.8708	+	98.3491i	−0.136704	+	0.177206i
$556$	−183.241			−0.329570
$557$	417.310			0.749209			0.374605	−	0.927185i	$-0.377778\pi$
$557$	417.310			0.749209			0.374605	+	0.927185i	$0.377778\pi$
$558$		−	0.492878i		−	0.000883294i
$559$		−	949.727i		−	1.69897i
$560$	−119.352	−	92.0733i	−0.213129	−	0.164417i
$561$	−140.215			−0.249938
$562$	333.240			0.592953
$563$	−931.244			−1.65407			−0.827037	−	0.562147i	$-0.809975\pi$
$563$	−931.244			−1.65407			−0.827037	+	0.562147i	$0.809975\pi$
$564$	−466.285			−0.826747
$565$	−697.209	−	537.858i	−1.23400	−	0.951960i
$566$			531.333i			0.938751i
$567$	−613.033			−1.08119
$568$		−	27.1562i		−	0.0478101i
$569$			342.848i			0.602546i	0.953538	+	0.301273i	$0.0974115\pi$
$569$			342.848i			0.602546i	−0.953538	+	0.301273i	$0.902589\pi$
$570$	−99.3552	+	128.791i	−0.174307	+	0.225950i
$571$			50.5137i			0.0884653i	0.999021	+	0.0442327i	$0.0140843\pi$
$571$			50.5137i			0.0884653i	−0.999021	+	0.0442327i	$0.985916\pi$
$572$	81.3108			0.142152
$573$	99.5786			0.173785
$574$		−	312.821i		−	0.544985i
$575$	−210.466	+	535.097i	−0.366028	+	0.930604i
$576$	0.300538			0.000521767
$577$		−	7.96828i		−	0.0138099i	−0.999976	−	0.00690493i	$-0.997802\pi$
$577$		−	7.96828i		−	0.0138099i	0.999976	−	0.00690493i	$-0.00219792\pi$
$578$		−	302.922i		−	0.524086i
$579$	940.030			1.62354
$580$	290.761	+	224.306i	0.501313	+	0.386734i
$581$	−533.851			−0.918848
$582$	−719.492			−1.23624
$583$		−	82.0929i		−	0.140811i
$584$	80.3478			0.137582
$585$	−2.24339	+	2.90804i	−0.00383485	+	0.00497100i
$586$		−	532.795i		−	0.909206i
$587$		−	992.708i		−	1.69115i	−0.533853	−	0.845577i	$-0.679256\pi$
$587$		−	992.708i		−	1.69115i	0.533853	−	0.845577i	$-0.320744\pi$
$588$		−	46.9337i		−	0.0798192i
$589$			70.9885i			0.120524i
$590$	83.6222	−	108.397i	0.141732	−	0.183724i
$591$	−727.347			−1.23071
$592$	−33.0546			−0.0558355
$593$		−	1040.58i		−	1.75477i	−0.479792	−	0.877383i	$-0.659288\pi$
$593$		−	1040.58i		−	1.75477i	0.479792	−	0.877383i	$-0.340712\pi$
$594$			79.2258i			0.133377i
$595$	−669.328	−	516.349i	−1.12492	−	0.867813i
$596$			405.041i			0.679599i
$597$	586.202			0.981913
$598$	513.398	+	375.401i	0.858526	+	0.627760i
$599$	−194.575			−0.324832			−0.162416	−	0.986722i	$-0.551929\pi$
$599$	−194.575			−0.324832			−0.162416	+	0.986722i	$0.551929\pi$
$600$	−53.9557	−	205.613i	−0.0899262	−	0.342688i
$601$	841.243			1.39974			0.699869	−	0.714271i	$-0.253242\pi$
$601$	841.243			1.39974			0.699869	+	0.714271i	$0.253242\pi$
$602$			517.717i			0.859995i
$603$	−0.875282			−0.00145155
$604$	260.911			0.431972
$605$	−461.910	−	356.337i	−0.763488	−	0.588987i
$606$	621.261			1.02518
$607$		−	590.121i		−	0.972192i	−0.873905	−	0.486096i	$-0.838421\pi$
$607$		−	590.121i		−	0.972192i	0.873905	−	0.486096i	$-0.161579\pi$
$608$	−43.2860			−0.0711942
$609$			832.064i			1.36628i
$610$	66.8560	+	51.5756i	0.109600	+	0.0845502i
$611$	1516.40			2.48184
$612$	1.68542			0.00275396
$613$	773.706			1.26216			0.631081	−	0.775717i	$-0.282611\pi$
$613$	773.706			1.26216			0.631081	+	0.775717i	$0.282611\pi$
$614$	−524.896			−0.854880
$615$	269.455	−	349.287i	0.438138	−	0.567946i
$616$	−44.3243			−0.0719551
$617$	−642.187			−1.04082			−0.520411	−	0.853916i	$-0.674221\pi$
$617$	−642.187			−1.04082			−0.520411	+	0.853916i	$0.674221\pi$
$618$	576.086			0.932177
$619$			1036.23i			1.67405i	0.547168	+	0.837023i	$0.315706\pi$
$619$			1036.23i			1.67405i	−0.547168	+	0.837023i	$0.684294\pi$
$620$	−73.4544	−	56.6659i	−0.118475	−	0.0913967i
$621$	−365.774	+	500.234i	−0.589009	+	0.805529i
$622$		−	431.035i		−	0.692982i
$623$		−	987.148i		−	1.58451i
$624$	−235.128			−0.376807
$625$	−544.469	+	306.885i	−0.871150	+	0.491016i
$626$		−	622.788i		−	0.994868i
$627$			47.8298i			0.0762836i
$628$	−192.334			−0.306264
$629$	−185.371			−0.294707
$630$	1.22292	−	1.58524i	0.00194114	−	0.00251625i
$631$			1106.65i			1.75381i	0.480668	+	0.876903i	$0.340394\pi$
$631$			1106.65i			1.75381i	−0.480668	+	0.876903i	$0.659606\pi$
$632$	−251.097			−0.397305
$633$		−	1180.93i		−	1.86560i
$634$	−121.855			−0.192201
$635$	127.427	−	165.180i	0.200673	−	0.260126i
$636$			237.390i			0.373254i
$637$			152.633i			0.239612i
$638$	107.981			0.169250
$639$	0.360689			0.000564458
$640$	34.5527	−	44.7896i	0.0539886	−	0.0699838i
$641$			862.461i			1.34549i	0.739873	+	0.672746i	$0.234885\pi$
$641$			862.461i			1.34549i	−0.739873	+	0.672746i	$0.765115\pi$
$642$	−477.290			−0.743442
$643$	353.637			0.549980			0.274990	−	0.961447i	$-0.411326\pi$
$643$	353.637			0.549980			0.274990	+	0.961447i	$0.411326\pi$
$644$	−279.865	−	204.639i	−0.434573	−	0.317763i
$645$	−445.947	+	578.068i	−0.691390	+	0.896230i
$646$	−242.749			−0.375772
$647$		−	521.182i		−	0.805536i	−0.915302	−	0.402768i	$-0.868048\pi$
$647$		−	521.182i		−	0.805536i	0.915302	−	0.402768i	$-0.131952\pi$
$648$		−	230.055i		−	0.355023i
$649$		−	40.2559i		−	0.0620276i
$650$	175.469	+	668.671i	0.269952	+	1.02872i
$651$		−	210.203i		−	0.322892i
$652$			333.135i			0.510943i
$653$			875.693i			1.34103i	0.741896	+	0.670515i	$0.233927\pi$
$653$			875.693i			1.34103i	−0.741896	+	0.670515i	$0.766073\pi$
$654$			663.077i			1.01388i
$655$	−474.967	−	366.410i	−0.725141	−	0.559405i
$656$	117.393			0.178953
$657$			1.06718i			0.00162432i
$658$	−826.624			−1.25627
$659$		−	1148.81i		−	1.74326i	−0.490165	−	0.871630i	$-0.663063\pi$
$659$		−	1148.81i		−	1.74326i	0.490165	−	0.871630i	$-0.336937\pi$
$660$	−49.4912	−	38.1797i	−0.0749867	−	0.0578480i
$661$			231.297i			0.349920i	0.984576	+	0.174960i	$0.0559796\pi$
$661$			231.297i			0.349920i	−0.984576	+	0.174960i	$0.944020\pi$
$662$			40.7689i			0.0615845i
$663$	−1318.60			−1.98884
$664$		−	200.340i		−	0.301717i
$665$	−176.135	+	228.319i	−0.264865	+	0.343337i
$666$		−	0.439032i		−	0.000659207i
$667$	681.797	+	498.535i	1.02218	+	0.747429i
$668$		−	387.507i		−	0.580100i
$669$	−886.295			−1.32481
$670$	−100.631	+	130.445i	−0.150195	+	0.194694i
$671$	24.8286			0.0370024
$672$	128.173			0.190734
$673$		−	538.439i		−	0.800058i	−0.916503	−	0.400029i	$-0.869000\pi$
$673$		−	538.439i		−	0.800058i	0.916503	−	0.400029i	$-0.131000\pi$
$674$		−	445.039i		−	0.660296i
$675$	−651.525	+	170.969i	−0.965222	+	0.253288i
$676$	426.657			0.631149
$677$	−139.261			−0.205703			−0.102852	−	0.994697i	$-0.532797\pi$
$677$	−139.261			−0.205703			−0.102852	+	0.994697i	$0.532797\pi$
$678$	748.741			1.10434
$679$	−1275.51			−1.87851
$680$	193.772	−	251.181i	0.284959	−	0.369384i
$681$		−	839.951i		−	1.23341i
$682$	−27.2791			−0.0399987
$683$			1045.84i			1.53124i	0.643294	+	0.765619i	$0.277567\pi$
$683$			1045.84i			1.53124i	−0.643294	+	0.765619i	$0.722433\pi$
$684$		−	0.574926i		−	0.000840535i
$685$	912.715	+	704.108i	1.33243	+	1.02789i
$686$			439.082i			0.640062i
$687$	58.8579			0.0856738
$688$	−194.286			−0.282392
$689$		−	772.012i		−	1.12048i
$690$	−136.219	−	469.562i	−0.197418	−	0.680524i
$691$	−38.1323			−0.0551842			−0.0275921	−	0.999619i	$-0.508784\pi$
$691$	−38.1323			−0.0551842			−0.0275921	+	0.999619i	$0.508784\pi$
$692$			12.5847i			0.0181860i
$693$		−	0.588716i		−	0.000849518i
$694$	449.926			0.648309
$695$	−362.714	−	279.814i	−0.521891	−	0.402609i
$696$	−312.252			−0.448637
$697$	658.345			0.944541
$698$			228.098i			0.326787i
$699$	608.012			0.869832
$700$	−95.6519	−	364.508i	−0.136646	−	0.520725i
$701$			1257.67i			1.79410i	0.441925	+	0.897052i	$0.354296\pi$
$701$			1257.67i			1.79410i	−0.441925	+	0.897052i	$0.645704\pi$
$702$			745.049i			1.06132i
$703$			63.2332i			0.0899476i
$704$		−	16.6337i		−	0.0236275i
$705$	−922.984	−	712.030i	−1.30920	−	1.00997i
$706$	−15.2436			−0.0215915
$707$	1101.36			1.55780
$708$			116.409i			0.164419i
$709$			109.672i			0.154685i	0.997005	+	0.0773426i	$0.0246435\pi$
$709$			109.672i			0.154685i	−0.997005	+	0.0773426i	$0.975356\pi$
$710$	41.4682	−	53.7540i	0.0584059	−	0.0757099i
$711$		−	3.33507i		−	0.00469068i
$712$	370.450			0.520295
$713$	−172.241	−	125.944i	−0.241572	−	0.176639i
$714$	718.799			1.00672
$715$	160.950	+	124.164i	0.225105	+	0.173656i
$716$	255.282			0.356539
$717$		−	348.949i		−	0.486680i
$718$	439.311			0.611854
$719$	805.978			1.12097			0.560485	−	0.828164i	$-0.310615\pi$
$719$	805.978			1.12097			0.560485	+	0.828164i	$0.310615\pi$
$720$	0.594897	+	0.458929i	0.000826246	+	0.000637402i
$721$	1021.28			1.41647
$722$		−	427.725i		−	0.592417i
$723$	−384.083			−0.531236
$724$			350.343i			0.483899i
$725$	233.024	+	888.001i	0.321412	+	1.22483i
$726$	496.050			0.683265
$727$	1088.51			1.49726			0.748631	−	0.662986i	$-0.230711\pi$
$727$	1088.51			1.49726			0.748631	+	0.662986i	$0.230711\pi$
$728$	−416.831			−0.572571
$729$	−725.932			−0.995791
$730$	159.044	+	122.693i	0.217868	+	0.168073i
$731$	−1089.56			−1.49050
$732$	−71.7974			−0.0980838
$733$	−1168.31			−1.59388			−0.796938	−	0.604061i	$-0.793548\pi$
$733$	−1168.31			−1.59388			−0.796938	+	0.604061i	$0.793548\pi$
$734$			187.014i			0.254788i
$735$	71.6690	−	92.9025i	0.0975089	−	0.126398i
$736$	76.7956	−	105.026i	0.104342	−	0.142698i
$737$			48.4439i			0.0657312i
$738$			1.55922i			0.00211277i
$739$	1476.43			1.99788			0.998941	−	0.0460187i	$-0.0146534\pi$
$739$	1476.43			1.99788			0.998941	+	0.0460187i	$0.0146534\pi$
$740$	−65.4297	−	50.4753i	−0.0884185	−	0.0682098i
$741$			449.797i			0.607014i
$742$			420.841i			0.567171i
$743$	874.658			1.17720			0.588599	−	0.808425i	$-0.299680\pi$
$743$	874.658			1.17720			0.588599	+	0.808425i	$0.299680\pi$
$744$	78.8835			0.106026
$745$	−618.508	+	801.754i	−0.830212	+	1.07618i
$746$		−	458.624i		−	0.614777i
$747$	2.66092			0.00356214
$748$		−	93.2823i		−	0.124709i
$749$	−846.132			−1.12968
$750$	207.174	−	489.390i	0.276232	−	0.652520i
$751$			23.7157i			0.0315788i	0.999875	+	0.0157894i	$0.00502613\pi$
$751$			23.7157i			0.0315788i	−0.999875	+	0.0157894i	$0.994974\pi$
$752$		−	310.210i		−	0.412513i
$753$	1176.94			1.56300
$754$	1015.47			1.34678
$755$	516.458	+	398.418i	0.684051	+	0.527707i
$756$		−	406.143i		−	0.537226i
$757$	353.307			0.466720			0.233360	−	0.972390i	$-0.425028\pi$
$757$	353.307			0.466720			0.233360	+	0.972390i	$0.425028\pi$
$758$	388.190			0.512123
$759$	−116.050	−	84.8569i	−0.152899	−	0.111801i
$760$	−85.6822	−	66.0990i	−0.112740	−	0.0869723i
$761$	−984.853			−1.29416			−0.647078	−	0.762423i	$-0.724009\pi$
$761$	−984.853			−1.29416			−0.647078	+	0.762423i	$0.724009\pi$
$762$			177.389i			0.232794i
$763$			1175.49i			1.54062i
$764$			66.2476i			0.0867116i
$765$	3.33619	+	2.57368i	0.00436104	+	0.00336429i
$766$			475.317i			0.620518i
$767$		−	378.572i		−	0.493574i
$768$			48.1001i			0.0626303i
$769$			590.079i			0.767333i	0.923472	+	0.383666i	$0.125339\pi$
$769$			590.079i			0.767333i	−0.923472	+	0.383666i	$0.874661\pi$
$770$	−87.7374	−	67.6844i	−0.113945	−	0.0879018i
$771$	1330.43			1.72559
$772$			625.383i			0.810081i
$773$	960.379			1.24241			0.621203	−	0.783650i	$-0.286644\pi$
$773$	960.379			1.24241			0.621203	+	0.783650i	$0.286644\pi$
$774$		−	2.58050i		−	0.00333398i
$775$	−58.8683	−	224.334i	−0.0759592	−	0.289463i
$776$		−	478.664i		−	0.616835i
$777$		−	187.238i		−	0.240976i
$778$	−66.1135			−0.0849788
$779$		−	224.573i		−	0.288283i
$780$	−465.422	−	359.047i	−0.596695	−	0.460316i
$781$		−	19.9629i		−	0.0255607i
$782$	430.671	−	588.987i	0.550731	−	0.753180i
$783$			989.431i			1.26364i
$784$	31.2240			0.0398266
$785$	−380.714	−	293.699i	−0.484985	−	0.374139i
$786$	510.072			0.648947
$787$	557.933			0.708937			0.354468	−	0.935068i	$-0.384662\pi$
$787$	557.933			0.708937			0.354468	+	0.935068i	$0.384662\pi$
$788$		−	483.889i		−	0.614073i
$789$			315.376i			0.399717i
$790$	−497.031	−	383.431i	−0.629154	−	0.485356i
$791$	1327.36			1.67807
$792$	0.220930			0.000278952
$793$	233.491			0.294441
$794$	−297.718			−0.374960
$795$	−362.500	+	469.899i	−0.455975	+	0.591068i
$796$			389.988i			0.489935i
$797$	113.712			0.142675			0.0713377	−	0.997452i	$-0.477273\pi$
$797$	113.712			0.142675			0.0713377	+	0.997452i	$0.477273\pi$
$798$		−	245.195i		−	0.307261i
$799$		−	1739.66i		−	2.17730i
$800$	136.790	−	35.8956i	0.170987	−	0.0448695i
$801$			4.92033i			0.00614273i
$802$	−372.059			−0.463913
$803$	59.0649			0.0735552
$804$		−	140.086i		−	0.174236i
$805$	−241.487	−	832.432i	−0.299983	−	1.03408i
$806$	−256.536			−0.318283
$807$			117.064i			0.145061i
$808$			413.312i			0.511525i
$809$	638.881			0.789716			0.394858	−	0.918742i	$-0.370794\pi$
$809$	638.881			0.789716			0.394858	+	0.918742i	$0.370794\pi$
$810$	351.300	−	455.380i	0.433704	−	0.562198i
$811$	109.715			0.135284			0.0676421	−	0.997710i	$-0.478452\pi$
$811$	109.715			0.135284			0.0676421	+	0.997710i	$0.478452\pi$
$812$	−553.555			−0.681718
$813$		−	827.440i		−	1.01776i
$814$	−24.2989			−0.0298512
$815$	−508.706	+	659.421i	−0.624179	+	0.809106i
$816$			269.746i			0.330571i
$817$			371.667i			0.454916i
$818$		−	1017.59i		−	1.24400i
$819$		−	5.53636i		−	0.00675990i
$820$	232.374	+	179.263i	0.283382	+	0.218613i
$821$	1159.45			1.41224			0.706119	−	0.708093i	$-0.250444\pi$
$821$	1159.45			1.41224			0.706119	+	0.708093i	$0.250444\pi$
$822$	−980.174			−1.19243
$823$		−	239.903i		−	0.291498i	−0.989322	−	0.145749i	$-0.953441\pi$
$823$		−	239.903i		−	0.291498i	0.989322	−	0.145749i	$-0.0465593\pi$
$824$			383.258i			0.465119i
$825$	−39.6636	−	151.149i	−0.0480771	−	0.183211i
$826$			206.368i			0.249840i
$827$	−1320.07			−1.59621			−0.798105	−	0.602519i	$-0.794164\pi$
$827$	−1320.07			−1.59621			−0.798105	+	0.602519i	$0.794164\pi$
$828$	1.39495	+	1.02000i	0.00168473	+	0.00123189i
$829$	−637.640			−0.769168			−0.384584	−	0.923090i	$-0.625655\pi$
$829$	−637.640			−0.769168			−0.384584	+	0.923090i	$0.625655\pi$
$830$	305.925	−	396.562i	0.368584	−	0.477785i
$831$	−77.9775			−0.0938358
$832$		−	156.426i		−	0.188012i
$833$	175.105			0.210210
$834$	389.523			0.467054
$835$	591.734	−	767.048i	0.708663	−	0.918620i
$836$	−31.8202			−0.0380624
$837$		−	249.958i		−	0.298636i
$838$	−800.823			−0.955636
$839$		−	641.702i		−	0.764841i	−0.923988	−	0.382421i	$-0.875091\pi$
$839$		−	641.702i		−	0.764841i	0.923988	−	0.382421i	$-0.124909\pi$
$840$	253.712	+	195.724i	0.302038	+	0.233005i
$841$	507.553			0.603511
$842$	−716.361			−0.850785
$843$	−708.382			−0.840311
$844$	785.646			0.930861
$845$	844.542	+	651.516i	0.999458	+	0.771025i
$846$	4.12022			0.00487023
$847$	879.391			1.03824
$848$	−157.930			−0.186239
$849$		−	1129.48i		−	1.33036i
$850$	767.121	−	201.303i	0.902495	−	0.236827i
$851$	−153.424	−	112.185i	−0.180287	−	0.131827i
$852$			57.7270i			0.0677547i
$853$			134.906i			0.158154i	0.996869	+	0.0790771i	$0.0251973\pi$
$853$			134.906i			0.158154i	−0.996869	+	0.0790771i	$0.974803\pi$
$854$	−127.281			−0.149041
$855$	0.877927	−	1.13803i	0.00102682	−	0.00133103i
$856$		−	317.531i		−	0.370947i
$857$			479.350i			0.559335i	0.960097	+	0.279667i	$0.0902242\pi$
$857$			479.350i			0.559335i	−0.960097	+	0.279667i	$0.909776\pi$
$858$	−172.846			−0.201452
$859$	−1325.07			−1.54258			−0.771289	−	0.636485i	$-0.780388\pi$
$859$	−1325.07			−1.54258			−0.771289	+	0.636485i	$0.780388\pi$
$860$	−384.577	−	296.679i	−0.447182	−	0.344976i
$861$			664.977i			0.772331i
$862$	−247.396			−0.287002
$863$			898.018i			1.04058i	0.853991	+	0.520288i	$0.174176\pi$
$863$			898.018i			1.04058i	−0.853991	+	0.520288i	$0.825824\pi$
$864$	152.415			0.176406
$865$	−19.2172	+	24.9107i	−0.0222164	+	0.0287985i
$866$			229.914i			0.265490i
$867$			643.934i			0.742715i
$868$	139.844			0.161110
$869$	−184.585			−0.212411
$870$	−618.084	−	476.817i	−0.710441	−	0.548065i
$871$			455.572i			0.523045i
$872$	−441.132			−0.505885
$873$	6.35762			0.00728249
$874$	−200.914	−	146.909i	−0.229878	−	0.168089i
$875$	367.275	−	867.584i	0.419743	−	0.991525i
$876$	−170.799			−0.194976
$877$			1319.84i			1.50495i	0.658621	+	0.752474i	$0.271140\pi$
$877$			1319.84i			1.50495i	−0.658621	+	0.752474i	$0.728860\pi$
$878$		−	125.251i		−	0.142655i
$879$			1132.58i			1.28849i
$880$	25.4002	−	32.9255i	0.0288638	−	0.0374154i
$881$		−	1258.50i		−	1.42849i	−0.699893	−	0.714247i	$-0.746769\pi$
$881$		−	1258.50i		−	1.42849i	0.699893	−	0.714247i	$-0.253231\pi$
$882$			0.414718i			0.000470202i
$883$			852.771i			0.965765i	0.875685	+	0.482883i	$0.160410\pi$
$883$			852.771i			0.965765i	−0.875685	+	0.482883i	$0.839590\pi$
$884$		−	877.239i		−	0.992351i
$885$	−177.759	+	230.424i	−0.200858	+	0.260366i
$886$	−423.919			−0.478464
$887$			449.712i			0.507003i	0.967335	+	0.253502i	$0.0815823\pi$
$887$			449.712i			0.507003i	−0.967335	+	0.253502i	$0.918418\pi$
$888$	70.2656			0.0791279
$889$			314.472i			0.353737i
$890$	733.285	+	565.688i	0.823915	+	0.635604i
$891$		−	169.117i		−	0.189805i
$892$		−	589.634i		−	0.661025i
$893$	−593.429			−0.664534
$894$		−	861.013i		−	0.963101i
$895$	505.315	+	389.822i	0.564598	+	0.435555i
$896$			85.2712i			0.0951687i
$897$	−1091.35	−	798.005i	−1.21667	−	0.889638i
$898$			672.889i			0.749319i
$899$	−340.682			−0.378957
$900$	0.476766	+	1.81685i	0.000529740	+	0.00201872i
$901$	−885.677			−0.982993
$902$	86.2976			0.0956736
$903$		−	1100.53i		−	1.21875i
$904$			498.122i			0.551020i
$905$	−534.984	+	693.484i	−0.591142	+	0.766281i
$906$	−554.630			−0.612175
$907$	−620.317			−0.683922			−0.341961	−	0.939714i	$-0.611091\pi$
$907$	−620.317			−0.683922			−0.341961	+	0.939714i	$0.611091\pi$
$908$	558.802			0.615421
$909$	−5.48962			−0.00603919
$910$	−825.093	−	636.513i	−0.906696	−	0.699465i
$911$			1122.03i			1.23164i	0.787886	+	0.615821i	$0.211175\pi$
$911$			1122.03i			1.23164i	−0.787886	+	0.615821i	$0.788825\pi$
$912$	92.0150			0.100894
$913$		−	147.273i		−	0.161307i
$914$			895.040i			0.979256i
$915$	−142.119	−	109.637i	−0.155321	−	0.119821i
$916$			39.1570i			0.0427478i
$917$	904.249			0.986095
$918$	854.744			0.931094
$919$			192.248i			0.209192i	0.994515	+	0.104596i	$0.0333550\pi$
$919$			192.248i			0.209192i	−0.994515	+	0.104596i	$0.966645\pi$
$920$	312.390	−	90.6235i	0.339554	−	0.0985038i
$921$	1115.79			1.21150
$922$			551.282i			0.597920i
$923$		−	187.733i		−	0.203395i
$924$	94.2221			0.101972
$925$	−52.4371	−	199.826i	−0.0566887	−	0.216028i
$926$	−207.273			−0.223837
$927$	−5.09044			−0.00549130
$928$		−	207.735i		−	0.223852i
$929$	−403.792			−0.434652			−0.217326	−	0.976099i	$-0.569733\pi$
$929$	−403.792			−0.434652			−0.217326	+	0.976099i	$0.569733\pi$
$930$	156.145	+	120.457i	0.167898	+	0.129524i
$931$		−	59.7313i		−	0.0641582i
$932$			404.498i			0.434011i
$933$			916.270i			0.982068i
$934$			161.958i			0.173403i
$935$	142.445	−	184.647i	0.152347	−	0.197483i
$936$	2.07765			0.00221971
$937$	345.580			0.368815			0.184408	−	0.982850i	$-0.440963\pi$
$937$	345.580			0.368815			0.184408	+	0.982850i	$0.440963\pi$
$938$		−	248.342i		−	0.264757i
$939$			1323.89i			1.40989i
$940$	473.699	−	614.043i	0.503935	−	0.653237i
$941$			536.881i			0.570543i	0.958447	+	0.285272i	$0.0920838\pi$
$941$			536.881i			0.570543i	−0.958447	+	0.285272i	$0.907916\pi$
$942$	408.852			0.434026
$943$	544.885	+	398.424i	0.577821	+	0.422507i
$944$	−77.4444			−0.0820385
$945$	620.191	−	803.936i	0.656287	−	0.850726i
$946$	−142.822			−0.150975
$947$		−	1325.38i		−	1.39956i	−0.714361	−	0.699778i	$-0.753282\pi$
$947$		−	1325.38i		−	1.39956i	0.714361	−	0.699778i	$-0.246718\pi$
$948$	533.767			0.563046
$949$	555.453			0.585304
$950$	−68.6680	−	261.678i	−0.0722821	−	0.275451i
$951$	259.033			0.272380
$952$			478.202i			0.502313i
$953$	803.540			0.843169			0.421585	−	0.906789i	$-0.361474\pi$
$953$	803.540			0.843169			0.421585	+	0.906789i	$0.361474\pi$
$954$		−	2.09764i		−	0.00219878i
$955$	−101.162	+	131.133i	−0.105929	+	0.137312i
$956$	232.149			0.242834
$957$	−229.541			−0.239854
$958$	−809.086			−0.844557
$959$	−1737.64			−1.81193
$960$	−73.4501	+	95.2113i	−0.0765105	+	0.0991784i
$961$	−874.934			−0.910441
$962$	−228.510			−0.237536
$963$	4.21745			0.00437949
$964$		−	255.523i		−	0.265065i
$965$	−954.976	+	1237.91i	−0.989612	+	1.28281i
$966$	594.921	+	435.010i	0.615860	+	0.450321i
$967$		−	753.094i		−	0.778794i	−0.921070	−	0.389397i	$-0.872683\pi$
$967$		−	753.094i		−	0.778794i	0.921070	−	0.389397i	$-0.127317\pi$
$968$			330.012i			0.340921i
$969$	516.022			0.532530
$970$	730.932	−	947.487i	0.753538	−	0.976790i
$971$			1335.10i			1.37498i	0.726196	+	0.687488i	$0.241287\pi$
$971$			1335.10i			1.37498i	−0.726196	+	0.687488i	$0.758713\pi$
$972$			4.05723i			0.00417411i
$973$	690.540			0.709702
$974$	−408.217			−0.419114
$975$	−373.002	−	1421.42i	−0.382566	−	1.45787i
$976$		−	47.7653i		−	0.0489399i
$977$	−966.819			−0.989579			−0.494790	−	0.869013i	$-0.664755\pi$
$977$	−966.819			−0.989579			−0.494790	+	0.869013i	$0.664755\pi$
$978$		−	708.159i		−	0.724089i
$979$	272.323			0.278165
$980$	61.8061	+	47.6799i	0.0630675	+	0.0486530i
$981$		−	5.85912i		−	0.00597260i
$982$		−	941.631i		−	0.958891i
$983$	−1726.38			−1.75624			−0.878118	−	0.478444i	$-0.841201\pi$
$983$	−1726.38			−1.75624			−0.878118	+	0.478444i	$0.841201\pi$
$984$	−249.548			−0.253606
$985$	738.912	−	957.831i	0.750165	−	0.972417i
$986$		−	1164.98i		−	1.18152i
$987$	1757.19			1.78033
$988$	−299.241			−0.302876
$989$	−901.782	−	659.390i	−0.911812	−	0.666724i
$990$	0.437317	+	0.337365i	0.000441735	+	0.000340773i
$991$	−981.652			−0.990567			−0.495283	−	0.868732i	$-0.664936\pi$
$991$	−981.652			−0.990567			−0.495283	+	0.868732i	$0.664936\pi$
$992$			52.4796i			0.0529028i
$993$		−	86.6642i		−	0.0872752i
$994$			102.338i			0.102955i
$995$	−595.523	+	771.959i	−0.598515	+	0.775838i
$996$			425.872i			0.427582i
$997$		−	306.920i		−	0.307844i	−0.988083	−	0.153922i	$-0.950810\pi$
$997$		−	306.920i		−	0.307844i	0.988083	−	0.153922i	$-0.0491904\pi$
$998$			167.111i			0.167446i
$999$		−	222.650i		−	0.222873i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.c.a.229.9	✓	24
5.2	odd	4		1150.3.d.e.551.14		24
5.3	odd	4		1150.3.d.e.551.11		24
5.4	even	2	inner	230.3.c.a.229.16	yes	24
23.22	odd	2	inner	230.3.c.a.229.10	yes	24
115.22	even	4		1150.3.d.e.551.23		24
115.68	even	4		1150.3.d.e.551.2		24
115.114	odd	2	inner	230.3.c.a.229.15	yes	24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.c.a.229.9	✓	24	1.1	even	1	trivial
230.3.c.a.229.10	yes	24	23.22	odd	2	inner
230.3.c.a.229.15	yes	24	115.114	odd	2	inner
230.3.c.a.229.16	yes	24	5.4	even	2	inner
1150.3.d.e.551.2		24	115.68	even	4
1150.3.d.e.551.11		24	5.3	odd	4
1150.3.d.e.551.14		24	5.2	odd	4
1150.3.d.e.551.23		24	115.22	even	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421i q^{2} +3.00625i q^{3} -2.00000 q^{4} +(-3.95888 - 3.05405i) q^{5} +4.25149 q^{6} +7.53698 q^{7} +2.82843i q^{8} -0.0375672 q^{9} +(-4.31908 + 5.59871i) q^{10} +2.07922i q^{11} -6.01251i q^{12} +19.5532i q^{13} -10.6589i q^{14} +(9.18126 - 11.9014i) q^{15} +4.00000 q^{16} +22.4321 q^{17} +0.0531281i q^{18} -7.65196i q^{19} +(7.91777 + 6.10811i) q^{20} +22.6581i q^{21} +2.94046 q^{22} +(18.5661 + 13.5757i) q^{23} -8.50297 q^{24} +(6.34551 + 24.1813i) q^{25} +27.6524 q^{26} +26.9434i q^{27} -15.0740 q^{28} +36.7226 q^{29} +(-16.8311 - 12.9843i) q^{30} -9.27717 q^{31} -5.65685i q^{32} -6.25066 q^{33} -31.7237i q^{34} +(-29.8380 - 23.0183i) q^{35} +0.0751344 q^{36} -8.26365 q^{37} -10.8215 q^{38} -58.7820 q^{39} +(8.63817 - 11.1974i) q^{40} +29.3484 q^{41} +32.0433 q^{42} -48.5714 q^{43} -4.15843i q^{44} +(0.148724 + 0.114732i) q^{45} +(19.1989 - 26.2565i) q^{46} -77.5525i q^{47} +12.0250i q^{48} +7.80601 q^{49} +(34.1975 - 8.97391i) q^{50} +67.4365i q^{51} -39.1064i q^{52} -39.4826 q^{53} +38.1037 q^{54} +(6.35004 - 8.23138i) q^{55} +21.3178i q^{56} +23.0038 q^{57} -51.9337i q^{58} -19.3611 q^{59} +(-18.3625 + 23.8028i) q^{60} -11.9413i q^{61} +13.1199i q^{62} -0.283143 q^{63} -8.00000 q^{64} +(59.7166 - 77.4089i) q^{65} +8.83976i q^{66} +23.2991 q^{67} -44.8641 q^{68} +(-40.8120 + 55.8145i) q^{69} +(-32.5528 + 42.1973i) q^{70} -9.60115 q^{71} -0.106256i q^{72} -28.4073i q^{73} +11.6866i q^{74} +(-72.6951 + 19.0762i) q^{75} +15.3039i q^{76} +15.6710i q^{77} +83.1302i q^{78} +88.7761i q^{79} +(-15.8355 - 12.2162i) q^{80} -81.3367 q^{81} -41.5049i q^{82} -70.8309 q^{83} -45.3161i q^{84} +(-88.8060 - 68.5088i) q^{85} +68.6903i q^{86} +110.398i q^{87} -5.88092 q^{88} -130.974i q^{89} +(0.162256 - 0.210328i) q^{90} +147.372i q^{91} +(-37.1322 - 27.1514i) q^{92} -27.8895i q^{93} -109.676 q^{94} +(-23.3695 + 30.2932i) q^{95} +17.0059 q^{96} -169.233 q^{97} -11.0394i q^{98} -0.0781104i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{4} + 8 q^{6} - 96 q^{9} + 96 q^{16} - 16 q^{24} - 48 q^{25} - 32 q^{26} + 100 q^{29} - 124 q^{31} - 28 q^{35} + 192 q^{36} + 192 q^{39} - 116 q^{41} + 148 q^{46} - 76 q^{49} - 144 q^{50} - 16 q^{54}+ \cdots + 32 q^{96}+O(q^{100}) \) 24 * q - 48 * q^4 + 8 * q^6 - 96 * q^9 + 96 * q^16 - 16 * q^24 - 48 * q^25 - 32 * q^26 + 100 * q^29 - 124 * q^31 - 28 * q^35 + 192 * q^36 + 192 * q^39 - 116 * q^41 + 148 * q^46 - 76 * q^49 - 144 * q^50 - 16 * q^54 - 224 * q^55 + 84 * q^59 - 192 * q^64 - 340 * q^69 + 328 * q^70 + 196 * q^71 - 496 * q^75 + 1360 * q^81 + 316 * q^85 - 376 * q^94 - 368 * q^95 + 32 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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