LMFDB - Embedded newform 1000.2.o.a.949.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1000,2,Mod(149,1000)] 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("1000.149"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1000, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 5, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 1000 = 2^{3} \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1000.o (of order $10$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [112] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$7.98504020213$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$28$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 200)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			949.5
Character	$\chi$	$=$	1000.949
Dual form			1000.2.o.a.549.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.22823 - 0.701037i) q^{2} +(-0.970606 + 2.98722i) q^{3} +(1.01709 + 1.72207i) q^{4} +(3.28628 - 2.98856i) q^{6} -1.71800i q^{7} +(-0.0419895 - 2.82812i) q^{8} +(-5.55435 - 4.03547i) q^{9} +(-1.35234 - 1.86134i) q^{11} +(-6.13139 + 1.36683i) q^{12} +(4.80828 + 3.49342i) q^{13} +(-1.20438 + 2.11009i) q^{14} +(-1.93104 + 3.50301i) q^{16} +(2.53693 - 0.824300i) q^{17} +(3.99300 + 8.85029i) q^{18} +(5.48112 - 1.78092i) q^{19} +(5.13203 + 1.66750i) q^{21} +(0.356118 + 3.23419i) q^{22} +(0.393834 + 0.542066i) q^{23} +(8.48896 + 2.61955i) q^{24} +(-3.45665 - 7.66150i) q^{26} +(9.82268 - 7.13660i) q^{27} +(2.95851 - 1.74736i) q^{28} +(1.22579 + 0.398283i) q^{29} +(0.362926 + 1.11697i) q^{31} +(4.82750 - 2.94877i) q^{32} +(6.87282 - 2.23312i) q^{33} +(-3.69380 - 0.766057i) q^{34} +(1.30007 - 13.6694i) q^{36} +(2.95345 + 2.14581i) q^{37} +(-7.98057 - 1.65509i) q^{38} +(-15.1026 + 10.9726i) q^{39} +(6.21636 + 4.51645i) q^{41} +(-5.13434 - 5.64582i) q^{42} -3.75396 q^{43} +(1.82990 - 4.22198i) q^{44} +(-0.103710 - 0.941873i) q^{46} +(-8.51974 - 2.76823i) q^{47} +(-8.58998 - 9.16849i) q^{48} +4.04848 q^{49} +8.37845i q^{51} +(-1.12544 + 11.8333i) q^{52} +(1.09116 - 3.35825i) q^{53} +(-17.0675 + 1.87931i) q^{54} +(-4.85870 + 0.0721379i) q^{56} +18.1019i q^{57} +(-1.22634 - 1.34851i) q^{58} +(-3.58141 + 4.92938i) q^{59} +(-0.542140 - 0.746192i) q^{61} +(0.337282 - 1.62632i) q^{62} +(-6.93293 + 9.54236i) q^{63} +(-7.99647 + 0.237503i) q^{64} +(-10.0069 - 2.07533i) q^{66} +(4.74089 + 14.5910i) q^{67} +(3.99980 + 3.53039i) q^{68} +(-2.00153 + 0.650336i) q^{69} +(1.92683 - 5.93017i) q^{71} +(-11.1796 + 15.8778i) q^{72} +(-3.14398 - 4.32732i) q^{73} +(-2.12322 - 4.70603i) q^{74} +(8.64169 + 7.62750i) q^{76} +(-3.19778 + 2.32332i) q^{77} +(26.2416 - 2.88947i) q^{78} +(-0.125628 + 0.386644i) q^{79} +(5.41990 + 16.6807i) q^{81} +(-4.46891 - 9.90513i) q^{82} +(-0.356893 - 1.09840i) q^{83} +(2.34821 + 10.5337i) q^{84} +(4.61072 + 2.63166i) q^{86} +(-2.37952 + 3.27513i) q^{87} +(-5.20730 + 3.90274i) q^{88} +(3.34918 - 2.43332i) q^{89} +(6.00168 - 8.26061i) q^{91} +(-0.532909 + 1.22954i) q^{92} -3.68890 q^{93} +(8.52356 + 9.37268i) q^{94} +(4.12301 + 17.2829i) q^{96} +(14.4383 + 4.69127i) q^{97} +(-4.97247 - 2.83814i) q^{98} +15.7959i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36}+ \cdots - 90 q^{98}+O(q^{100}) $ 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1000\mathbb{Z}\right)^\times$.

$n$	$377$	$501$	$751$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$-1$	$1$

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 $

$2$	−1.22823	−	0.701037i	−0.868489	−	0.495708i
$2$	−1.22823	−	0.701037i	−0.868489	−	0.495708i
$3$	−0.970606	+	2.98722i	−0.560380	+	1.72467i	0.120915	+	0.992663i	$0.461417\pi$
$3$	−0.970606	+	2.98722i	−0.560380	+	1.72467i	−0.681295	+	0.732009i	$0.738583\pi$
$4$	1.01709	+	1.72207i	0.508547	+	0.861034i
$5$		0			0
$5$		0			0
$6$	3.28628	−	2.98856i	1.34162	−	1.22007i
$7$		−	1.71800i		−	0.649342i	−0.945827	−	0.324671i	$-0.894746\pi$
$7$		−	1.71800i		−	0.649342i	0.945827	−	0.324671i	$-0.105254\pi$
$8$	−0.0419895	−	2.82812i	−0.0148455	−	0.999890i
$9$	−5.55435	−	4.03547i	−1.85145	−	1.34516i
$10$		0			0
$11$	−1.35234	−	1.86134i	−0.407747	−	0.561215i	0.554920	−	0.831903i	$-0.312749\pi$
$11$	−1.35234	−	1.86134i	−0.407747	−	0.561215i	−0.962667	+	0.270688i	$0.912749\pi$
$12$	−6.13139	+	1.36683i	−1.76998	+	0.394570i
$13$	4.80828	+	3.49342i	1.33358	+	0.968900i	0.999654	+	0.0262994i	$0.00837233\pi$
$13$	4.80828	+	3.49342i	1.33358	+	0.968900i	0.333922	+	0.942601i	$0.391628\pi$
$14$	−1.20438	+	2.11009i	−0.321884	+	0.563947i
$15$		0			0
$16$	−1.93104	+	3.50301i	−0.482760	+	0.875752i
$17$	2.53693	−	0.824300i	0.615297	−	0.199922i	0.0152459	−	0.999884i	$-0.495147\pi$
$17$	2.53693	−	0.824300i	0.615297	−	0.199922i	0.600051	+	0.799962i	$0.295147\pi$
$18$	3.99300	+	8.85029i	0.941159	+	2.08603i
$19$	5.48112	−	1.78092i	1.25746	−	0.408572i	0.396868	−	0.917876i	$-0.370097\pi$
$19$	5.48112	−	1.78092i	1.25746	−	0.408572i	0.860587	+	0.509304i	$0.170097\pi$
$20$		0			0
$21$	5.13203	+	1.66750i	1.11990	+	0.363878i
$22$	0.356118	+	3.23419i	0.0759246	+	0.689533i
$23$	0.393834	+	0.542066i	0.0821200	+	0.113029i	0.848101	−	0.529835i	$-0.177746\pi$
$23$	0.393834	+	0.542066i	0.0821200	+	0.113029i	−0.765981	+	0.642864i	$0.777746\pi$
$24$	8.48896	+	2.61955i	1.73280	+	0.534714i
$25$		0			0
$26$	−3.45665	−	7.66150i	−0.677905	−	1.50254i
$27$	9.82268	−	7.13660i	1.89038	−	1.37344i
$28$	2.95851	−	1.74736i	0.559106	−	0.330221i
$29$	1.22579	+	0.398283i	0.227624	+	0.0739594i	0.420608	−	0.907242i	$-0.361817\pi$
$29$	1.22579	+	0.398283i	0.227624	+	0.0739594i	−0.192985	+	0.981202i	$0.561817\pi$
$30$		0			0
$31$	0.362926	+	1.11697i	0.0651834	+	0.200614i	0.978344	−	0.206986i	$-0.0663656\pi$
$31$	0.362926	+	1.11697i	0.0651834	+	0.200614i	−0.913160	+	0.407600i	$0.866366\pi$
$32$	4.82750	−	2.94877i	0.853390	−	0.521273i
$33$	6.87282	−	2.23312i	1.19640	−	0.388735i
$34$	−3.69380	−	0.766057i	−0.633482	−	0.131378i
$35$		0			0
$36$	1.30007	−	13.6694i	0.216678	−	2.27824i
$37$	2.95345	+	2.14581i	0.485545	+	0.352769i	0.803468	−	0.595347i	$-0.202986\pi$
$37$	2.95345	+	2.14581i	0.485545	+	0.352769i	−0.317924	+	0.948116i	$0.602986\pi$
$38$	−7.98057	−	1.65509i	−1.29462	−	0.268491i
$39$	−15.1026	+	10.9726i	−2.41834	+	1.75703i
$40$		0			0
$41$	6.21636	+	4.51645i	0.970832	+	0.705351i	0.955641	−	0.294534i	$-0.0951643\pi$
$41$	6.21636	+	4.51645i	0.970832	+	0.705351i	0.0151912	+	0.999885i	$0.495164\pi$
$42$	−5.13434	−	5.64582i	−0.792245	−	0.871169i
$43$	−3.75396			−0.572473			−0.286236	−	0.958159i	$-0.592404\pi$
$43$	−3.75396			−0.572473			−0.286236	+	0.958159i	$0.592404\pi$
$44$	1.82990	−	4.22198i	0.275867	−	0.636488i
$45$		0			0
$46$	−0.103710	−	0.941873i	−0.0152912	−	0.138872i
$47$	−8.51974	−	2.76823i	−1.24273	−	0.403788i	−0.387421	−	0.921903i	$-0.626634\pi$
$47$	−8.51974	−	2.76823i	−1.24273	−	0.403788i	−0.855311	+	0.518115i	$0.826634\pi$
$48$	−8.58998	−	9.16849i	−1.23986	−	1.32336i
$49$	4.04848			0.578355
$50$		0			0
$51$			8.37845i			1.17322i
$52$	−1.12544	+	11.8333i	−0.156070	+	1.64099i
$53$	1.09116	−	3.35825i	0.149882	−	0.461291i	−0.847724	−	0.530438i	$-0.822028\pi$
$53$	1.09116	−	3.35825i	0.149882	−	0.461291i	0.997607	+	0.0691467i	$0.0220277\pi$
$54$	−17.0675	+	1.87931i	−2.32260	+	0.255742i
$55$		0			0
$56$	−4.85870	+	0.0721379i	−0.649270	+	0.00963984i
$57$			18.1019i			2.39765i
$58$	−1.22634	−	1.34851i	−0.161026	−	0.177068i
$59$	−3.58141	+	4.92938i	−0.466259	+	0.641751i	−0.975792	−	0.218700i	$-0.929818\pi$
$59$	−3.58141	+	4.92938i	−0.466259	+	0.641751i	0.509533	+	0.860451i	$0.329818\pi$
$60$		0			0
$61$	−0.542140	−	0.746192i	−0.0694139	−	0.0955401i	0.772898	−	0.634530i	$-0.218806\pi$
$61$	−0.542140	−	0.746192i	−0.0694139	−	0.0955401i	−0.842312	+	0.538990i	$0.818806\pi$
$62$	0.337282	−	1.62632i	0.0428349	−	0.206543i
$63$	−6.93293	+	9.54236i	−0.873467	+	1.20222i
$64$	−7.99647	+	0.237503i	−0.999559	+	0.0296878i
$65$		0			0
$66$	−10.0069	−	2.07533i	−1.23176	−	0.255455i
$67$	4.74089	+	14.5910i	0.579192	+	1.78257i	0.621440	+	0.783462i	$0.286548\pi$
$67$	4.74089	+	14.5910i	0.579192	+	1.78257i	−0.0422481	+	0.999107i	$0.513452\pi$
$68$	3.99980	+	3.53039i	0.485047	+	0.428122i
$69$	−2.00153	+	0.650336i	−0.240956	+	0.0782912i
$70$		0			0
$71$	1.92683	−	5.93017i	0.228673	−	0.703782i	−0.769225	−	0.638978i	$-0.779358\pi$
$71$	1.92683	−	5.93017i	0.228673	−	0.703782i	0.997898	−	0.0648044i	$-0.0206424\pi$
$72$	−11.1796	+	15.8778i	−1.31752	+	1.87122i
$73$	−3.14398	−	4.32732i	−0.367975	−	0.506475i	0.584374	−	0.811485i	$-0.301340\pi$
$73$	−3.14398	−	4.32732i	−0.367975	−	0.506475i	−0.952349	+	0.305010i	$0.901340\pi$
$74$	−2.12322	−	4.70603i	−0.246820	−	0.547064i
$75$		0			0
$76$	8.64169	+	7.62750i	0.991269	+	0.874934i
$77$	−3.19778	+	2.32332i	−0.364421	+	0.264767i
$78$	26.2416	−	2.88947i	2.97128	−	0.327168i
$79$	−0.125628	+	0.386644i	−0.0141343	+	0.0435008i	−0.957875	−	0.287186i	$-0.907280\pi$
$79$	−0.125628	+	0.386644i	−0.0141343	+	0.0435008i	0.943741	+	0.330687i	$0.107280\pi$
$80$		0			0
$81$	5.41990	+	16.6807i	0.602211	+	1.85342i
$82$	−4.46891	−	9.90513i	−0.493509	−	1.09384i
$83$	−0.356893	−	1.09840i	−0.0391741	−	0.120565i	0.929557	−	0.368678i	$-0.120190\pi$
$83$	−0.356893	−	1.09840i	−0.0391741	−	0.120565i	−0.968731	+	0.248113i	$0.920190\pi$
$84$	2.34821	+	10.5337i	0.256211	+	1.14932i
$85$		0			0
$86$	4.61072	+	2.63166i	0.497186	+	0.283779i
$87$	−2.37952	+	3.27513i	−0.255111	+	0.351131i
$88$	−5.20730	+	3.90274i	−0.555100	+	0.416033i
$89$	3.34918	−	2.43332i	0.355013	−	0.257932i	−0.395956	−	0.918269i	$-0.629587\pi$
$89$	3.34918	−	2.43332i	0.355013	−	0.257932i	0.750969	+	0.660338i	$0.229587\pi$
$90$		0			0
$91$	6.00168	−	8.26061i	0.629148	−	0.865947i
$92$	−0.532909	+	1.22954i	−0.0555596	+	0.128188i
$93$	−3.68890			−0.382521
$94$	8.52356	+	9.37268i	0.879138	+	0.966718i
$95$		0			0
$96$	4.12301	+	17.2829i	0.420803	+	1.76393i
$97$	14.4383	+	4.69127i	1.46598	+	0.476327i	0.929892	−	0.367833i	$-0.119900\pi$
$97$	14.4383	+	4.69127i	1.46598	+	0.476327i	0.536091	+	0.844160i	$0.319900\pi$
$98$	−4.97247	−	2.83814i	−0.502295	−	0.286695i
$99$			15.7959i			1.58754i
$100$		0			0
$101$			13.7524i			1.36842i	0.729286	+	0.684209i	$0.239852\pi$
$101$			13.7524i			1.36842i	−0.729286	+	0.684209i	$0.760148\pi$
$102$	5.87361	−	10.2907i	0.581574	−	1.01893i
$103$	−8.32817	−	2.70599i	−0.820599	−	0.266629i	−0.131519	−	0.991314i	$-0.541985\pi$
$103$	−8.32817	−	2.70599i	−0.820599	−	0.266629i	−0.689081	+	0.724685i	$0.741985\pi$
$104$	9.67789	−	13.7451i	0.948996	−	1.34781i
$105$		0			0
$106$	−3.69445	+	3.35975i	−0.358837	+	0.326328i
$107$	−3.49350			−0.337729			−0.168865	−	0.985639i	$-0.554010\pi$
$107$	−3.49350			−0.337729			−0.168865	+	0.985639i	$0.554010\pi$
$108$	22.2803	+	9.65675i	2.14392	+	0.929221i
$109$	−2.56568	+	3.53135i	−0.245747	+	0.338242i	−0.914016	−	0.405678i	$-0.867036\pi$
$109$	−2.56568	+	3.53135i	−0.245747	+	0.338242i	0.668269	+	0.743920i	$0.267036\pi$
$110$		0			0
$111$	−9.27664	+	6.73988i	−0.880500	+	0.639721i
$112$	6.01816	+	3.31752i	0.568663	+	0.313477i
$113$	0.895884	−	1.23308i	0.0842776	−	0.115998i	−0.764796	−	0.644272i	$-0.777161\pi$
$113$	0.895884	−	1.23308i	0.0842776	−	0.115998i	0.849074	+	0.528274i	$0.177161\pi$
$114$	12.6901	−	22.2333i	1.18854	−	2.08234i
$115$		0			0
$116$	0.560872	+	2.51599i	0.0520757	+	0.233604i
$117$	−12.6093	−	38.8073i	−1.16573	−	3.58774i
$118$	7.85447	−	3.54371i	0.723062	−	0.326225i
$119$	−1.41615	−	4.35845i	−0.129818	−	0.399538i
$120$		0			0
$121$	1.76343	−	5.42728i	0.160312	−	0.493389i
$122$	0.142764	+	1.29656i	0.0129252	+	0.117385i
$123$	−19.5253	+	14.1859i	−1.76053	+	1.27910i
$124$	−1.55437	+	1.76105i	−0.139587	+	0.158147i
$125$		0			0
$126$	15.2048	−	6.85996i	1.35455	−	0.611134i
$127$	9.99210	+	13.7529i	0.886655	+	1.22038i	0.974533	+	0.224245i	$0.0719915\pi$
$127$	9.99210	+	13.7529i	0.886655	+	1.22038i	−0.0878777	+	0.996131i	$0.528008\pi$
$128$	9.98800	+	5.31412i	0.882823	+	0.469706i
$129$	3.64361	−	11.2139i	0.320802	−	0.987328i
$130$		0			0
$131$	5.71604	−	1.85725i	0.499413	−	0.162269i	−0.0484693	−	0.998825i	$-0.515434\pi$
$131$	5.71604	−	1.85725i	0.499413	−	0.162269i	0.547882	+	0.836556i	$0.315434\pi$
$132$	10.8359	+	9.56419i	0.943142	+	0.832455i
$133$	−3.05962	−	9.41655i	−0.265303	−	0.816519i
$134$	4.40591	−	21.2446i	0.380612	−	1.83525i
$135$		0			0
$136$	−2.43774	−	7.14013i	−0.209035	−	0.612261i
$137$	2.43382	−	3.34986i	0.207935	−	0.286198i	−0.692293	−	0.721616i	$-0.743400\pi$
$137$	2.43382	−	3.34986i	0.207935	−	0.286198i	0.900228	+	0.435418i	$0.143400\pi$
$138$	2.91424	+	0.604384i	0.248077	+	0.0514486i
$139$	−5.91784	−	8.14520i	−0.501944	−	0.690867i	0.480591	−	0.876945i	$-0.340422\pi$
$139$	−5.91784	−	8.14520i	−0.501944	−	0.690867i	−0.982535	+	0.186078i	$0.940422\pi$
$140$		0			0
$141$	16.5386	−	22.7635i	1.39280	−	1.91703i
$142$	−6.52386	+	5.93283i	−0.547470	+	0.497872i
$143$		−	13.6741i		−	1.14349i
$144$	24.8620	−	11.6643i	2.07183	−	0.972023i
$145$		0			0
$146$	0.827918	+	7.51899i	0.0685190	+	0.622276i
$147$	−3.92948	+	12.0937i	−0.324098	+	0.997472i
$148$	−0.691293	+	7.26854i	−0.0568239	+	0.597470i
$149$			13.6951i			1.12195i	0.827834	+	0.560973i	$0.189573\pi$
$149$			13.6951i			1.12195i	−0.827834	+	0.560973i	$0.810427\pi$
$150$		0			0
$151$	−12.0927			−0.984088			−0.492044	−	0.870570i	$-0.663750\pi$
$151$	−12.0927			−0.984088			−0.492044	+	0.870570i	$0.663750\pi$
$152$	−5.26681	−	15.4265i	−0.427195	−	1.25125i
$153$	−17.4175	−	5.65928i	−1.40812	−	0.457525i
$154$	5.55634	−	0.611810i	0.447742	−	0.0493010i
$155$		0			0
$156$	−34.2564	−	14.8474i	−2.74270	−	1.18875i
$157$	12.6051			1.00599			0.502997	−	0.864288i	$-0.332231\pi$
$157$	12.6051			1.00599			0.502997	+	0.864288i	$0.332231\pi$
$158$	0.425352	−	0.386817i	0.0338392	−	0.0307735i
$159$	8.97273	+	6.51907i	0.711584	+	0.516996i
$160$		0			0
$161$	0.931268	−	0.676606i	0.0733942	−	0.0533240i
$162$	5.03694	−	24.2873i	0.395739	−	1.90819i
$163$	9.55541	+	6.94241i	0.748438	+	0.543772i	0.895342	−	0.445379i	$-0.146931\pi$
$163$	9.55541	+	6.94241i	0.748438	+	0.543772i	−0.146904	+	0.989151i	$0.546931\pi$
$164$	−1.45502	+	15.2987i	−0.113618	+	1.19462i
$165$		0			0
$166$	−0.331676	+	1.59929i	−0.0257430	+	0.124129i
$167$	−10.4420	+	3.39280i	−0.808023	+	0.262543i	−0.683760	−	0.729707i	$-0.739657\pi$
$167$	−10.4420	+	3.39280i	−0.808023	+	0.262543i	−0.124263	+	0.992249i	$0.539657\pi$
$168$	4.50039	−	14.5840i	0.347213	−	1.12518i
$169$	6.89835	+	21.2309i	0.530642	+	1.63315i
$170$		0			0
$171$	−37.6309	−	12.2270i	−2.87771	−	0.935024i
$172$	−3.81812	−	6.46457i	−0.291129	−	0.492919i
$173$	12.2681	−	8.91328i	0.932725	−	0.677664i	−0.0139334	−	0.999903i	$-0.504435\pi$
$173$	12.2681	−	8.91328i	0.932725	−	0.677664i	0.946659	+	0.322238i	$0.104435\pi$
$174$	5.21858	−	2.35448i	0.395620	−	0.178492i
$175$		0			0
$176$	9.13172	−	1.14294i	0.688329	−	0.0861527i
$177$	−11.2490	−	15.4829i	−0.845527	−	1.16377i
$178$	−5.81941	+	0.640777i	−0.436183	+	0.0480283i
$179$	20.5530	+	6.67808i	1.53620	+	0.499143i	0.950326	−	0.311256i	$-0.100750\pi$
$179$	20.5530	+	6.67808i	1.53620	+	0.499143i	0.585878	+	0.810399i	$0.300750\pi$
$180$		0			0
$181$	8.26366	−	2.68502i	0.614233	−	0.199576i	0.0146547	−	0.999893i	$-0.495335\pi$
$181$	8.26366	−	2.68502i	0.614233	−	0.199576i	0.599578	+	0.800316i	$0.295335\pi$
$182$	−13.1624	+	5.93852i	−0.975665	+	0.440192i
$183$	2.75524	−	0.895233i	0.203673	−	0.0661775i
$184$	1.51649	−	1.13657i	0.111797	−	0.0837890i
$185$		0			0
$186$	4.53081	+	2.58605i	0.332215	+	0.189619i
$187$	−4.96511	−	3.60736i	−0.363085	−	0.263796i
$188$	−3.89829	−	17.4871i	−0.284312	−	1.27538i
$189$	−12.2607	−	16.8753i	−0.891831	−	1.22750i
$190$		0			0
$191$	0.689197	+	0.500731i	0.0498686	+	0.0362316i	0.612440	−	0.790517i	$-0.290188\pi$
$191$	0.689197	+	0.500731i	0.0498686	+	0.0362316i	−0.562572	+	0.826748i	$0.690188\pi$
$192$	7.05196	−	24.1177i	0.508931	−	1.74055i
$193$			10.7404i			0.773113i	0.922266	+	0.386557i	$0.126336\pi$
$193$			10.7404i			0.773113i	−0.922266	+	0.386557i	$0.873664\pi$
$194$	−14.4447	−	15.8837i	−1.03707	−	1.14038i
$195$		0			0
$196$	4.11769	+	6.97177i	0.294121	+	0.497983i
$197$	−6.98882	+	21.5094i	−0.497933	+	1.53248i	0.314403	+	0.949290i	$0.398196\pi$
$197$	−6.98882	+	21.5094i	−0.497933	+	1.53248i	−0.812336	+	0.583190i	$0.801804\pi$
$198$	11.0735	−	19.4010i	0.786959	−	1.37877i
$199$	0.706769			0.0501015			0.0250508	−	0.999686i	$-0.492025\pi$
$199$	0.706769			0.0501015			0.0250508	+	0.999686i	$0.492025\pi$
$200$		0			0
$201$	−48.1879			−3.39891
$202$	9.64096	−	16.8911i	0.678336	−	1.18846i
$203$	0.684250	−	2.10590i	0.0480249	−	0.147806i
$204$	−14.4283	+	8.52167i	−1.01018	+	0.596636i
$205$		0			0
$206$	8.33191	+	9.16193i	0.580511	+	0.638342i
$207$		−	4.60013i		−	0.319731i
$208$	−21.5225	+	10.0975i	−1.49231	+	0.700136i
$209$	−10.7273	−	7.79381i	−0.742020	−	0.539109i
$210$		0			0
$211$	10.7903	+	14.8516i	0.742834	+	1.02242i	0.998451	+	0.0556452i	$0.0177216\pi$
$211$	10.7903	+	14.8516i	0.742834	+	1.02242i	−0.255616	+	0.966778i	$0.582278\pi$
$212$	6.89295	−	1.53660i	0.473409	−	0.105534i
$213$	15.8445	+	11.5117i	1.08565	+	0.788770i
$214$	4.29082	+	2.44907i	0.293314	+	0.167415i
$215$		0			0
$216$	−20.5956	−	27.4800i	−1.40135	−	1.86978i
$217$	1.91895	−	0.623506i	0.130267	−	0.0423263i
$218$	5.62685	−	2.53868i	0.381098	−	0.171941i
$219$	15.9782	−	5.19164i	1.07971	−	0.350818i
$220$		0			0
$221$	15.0779	+	4.89911i	1.01425	+	0.329550i
$222$	16.1187	−	1.77484i	1.08182	−	0.119119i
$223$	4.51123	+	6.20918i	0.302094	+	0.415797i	0.932895	−	0.360147i	$-0.117274\pi$
$223$	4.51123	+	6.20918i	0.302094	+	0.415797i	−0.630801	+	0.775945i	$0.717274\pi$
$224$	−5.06597	−	8.29364i	−0.338485	−	0.554142i
$225$		0			0
$226$	−1.96478	+	0.886455i	−0.130695	+	0.0589661i
$227$	9.47829	−	6.88638i	0.629096	−	0.457065i	−0.226991	−	0.973897i	$-0.572889\pi$
$227$	9.47829	−	6.88638i	0.629096	−	0.457065i	0.856087	+	0.516832i	$0.172889\pi$
$228$	−31.1727	+	18.4113i	−2.06446	+	1.21932i
$229$	−25.6372	−	8.33003i	−1.69415	−	0.550464i	−0.706582	−	0.707631i	$-0.749764\pi$
$229$	−25.6372	−	8.33003i	−1.69415	−	0.550464i	−0.987572	+	0.157167i	$0.949764\pi$
$230$		0			0
$231$	−3.83649	−	11.8075i	−0.252422	−	0.776876i
$232$	1.07492	−	3.48340i	0.0705720	−	0.228696i
$233$	−13.2560	+	4.30712i	−0.868426	+	0.282169i	−0.709144	−	0.705064i	$-0.750918\pi$
$233$	−13.2560	+	4.30712i	−0.868426	+	0.282169i	−0.159283	+	0.987233i	$0.550918\pi$
$234$	−11.7183	+	56.5039i	−0.766050	+	3.69377i
$235$		0			0
$236$	−12.1314	−	1.15378i	−0.789684	−	0.0751049i
$237$	−1.03305	−	0.750558i	−0.0671041	−	0.0487540i
$238$	−1.31608	+	6.34594i	−0.0853090	+	0.411346i
$239$	7.73830	−	5.62220i	0.500549	−	0.363670i	−0.308678	−	0.951167i	$-0.599886\pi$
$239$	7.73830	−	5.62220i	0.500549	−	0.363670i	0.809227	+	0.587497i	$0.199886\pi$
$240$		0			0
$241$	20.3460	+	14.7823i	1.31060	+	0.952210i	0.999999	+	0.00167085i	$0.000531849\pi$
$241$	20.3460	+	14.7823i	1.31060	+	0.952210i	0.310606	+	0.950539i	$0.399468\pi$
$242$	−5.97063	+	5.42972i	−0.383806	+	0.349035i
$243$	−18.6651			−1.19737
$244$	0.733587	−	1.69255i	0.0469631	−	0.108354i
$245$		0			0
$246$	33.9264	−	3.73564i	2.16307	−	0.238176i
$247$	32.5763	+	10.5847i	2.07278	+	0.673486i
$248$	3.14369	−	1.07330i	0.199624	−	0.0681545i
$249$	3.62757			0.229888
$250$		0			0
$251$		−	6.91776i		−	0.436645i	−0.975877	−	0.218323i	$-0.929941\pi$
$251$		−	6.91776i		−	0.436645i	0.975877	−	0.218323i	$-0.0700585\pi$
$252$	−23.4840	−	2.23351i	−1.47936	−	0.140698i
$253$	0.476370	−	1.46612i	0.0299492	−	0.0921740i
$254$	−2.63126	−	23.8966i	−0.165100	−	1.49941i
$255$		0			0
$256$	−8.54216	−	13.5289i	−0.533885	−	0.845557i
$257$		−	29.8090i		−	1.85943i	−0.368277	−	0.929716i	$-0.620052\pi$
$257$		−	29.8090i		−	1.85943i	0.368277	−	0.929716i	$-0.379948\pi$
$258$	−12.3365	+	11.2189i	−0.768040	+	0.698459i
$259$	3.68650	−	5.07403i	0.229068	−	0.315285i
$260$		0			0
$261$	−5.20121	−	7.15885i	−0.321947	−	0.443122i
$262$	−8.32261	−	1.72602i	−0.514173	−	0.106634i
$263$	15.5573	−	21.4128i	0.959304	−	1.32037i	0.0120353	−	0.999928i	$-0.496169\pi$
$263$	15.5573	−	21.4128i	0.959304	−	1.32037i	0.947269	−	0.320441i	$-0.103831\pi$
$264$	−6.60409	−	19.3434i	−0.406454	−	1.19050i
$265$		0			0
$266$	−2.84344	+	13.7106i	−0.174342	+	0.840650i
$267$	4.01813	+	12.3665i	0.245906	+	0.756820i
$268$	−20.3047	+	23.0045i	−1.24031	+	1.40522i
$269$	−7.64014	+	2.48243i	−0.465827	+	0.151357i	−0.532521	−	0.846417i	$-0.678755\pi$
$269$	−7.64014	+	2.48243i	−0.465827	+	0.151357i	0.0666932	+	0.997774i	$0.478755\pi$
$270$		0			0
$271$	2.87827	−	8.85842i	0.174843	−	0.538111i	−0.824784	−	0.565449i	$-0.808703\pi$
$271$	2.87827	−	8.85842i	0.174843	−	0.538111i	0.999626	+	0.0273381i	$0.00870306\pi$
$272$	−2.01140	+	10.4787i	−0.121959	+	0.635362i
$273$	18.8510	+	25.9461i	1.14091	+	1.57033i
$274$	−5.33766	+	2.40820i	−0.322460	+	0.145485i
$275$		0			0
$276$	−3.15566	−	2.78531i	−0.189949	−	0.167656i
$277$	−3.05174	+	2.21722i	−0.183361	+	0.133220i	−0.675679	−	0.737196i	$-0.736150\pi$
$277$	−3.05174	+	2.21722i	−0.183361	+	0.133220i	0.492318	+	0.870415i	$0.336150\pi$
$278$	1.55837	+	14.1528i	0.0934647	+	0.848829i
$279$	2.49169	−	7.66863i	0.149173	−	0.459109i
$280$		0			0
$281$	−6.62409	−	20.3869i	−0.395160	−	1.21618i	−0.928837	−	0.370489i	$-0.879190\pi$
$281$	−6.62409	−	20.3869i	−0.395160	−	1.21618i	0.533676	−	0.845689i	$-0.320810\pi$
$282$	−36.2713	+	16.3646i	−2.15992	+	0.974495i
$283$	0.286114	+	0.880568i	0.0170077	+	0.0523443i	0.959200	−	0.282728i	$-0.0912393\pi$
$283$	0.286114	+	0.880568i	0.0170077	+	0.0523443i	−0.942192	+	0.335072i	$0.891239\pi$
$284$	12.1719	−	2.71341i	0.722271	−	0.161011i
$285$		0			0
$286$	−9.58608	+	16.7950i	−0.566837	+	0.993108i
$287$	7.75925	−	10.6797i	0.458014	−	0.630402i
$288$	−38.7133	−	3.10276i	−2.28120	−	0.182832i
$289$	−7.99672	+	5.80996i	−0.470395	+	0.341762i
$290$		0			0
$291$	−28.0277	+	38.5769i	−1.64301	+	2.26142i
$292$	4.25422	−	9.81544i	0.248959	−	0.574405i
$293$	−13.3571			−0.780332			−0.390166	−	0.920744i	$-0.627582\pi$
$293$	−13.3571			−0.780332			−0.390166	+	0.920744i	$0.627582\pi$
$294$	13.3044	−	12.0991i	0.775931	−	0.705636i
$295$		0			0
$296$	5.94458	−	8.44281i	0.345522	−	0.490728i
$297$	−26.5673	−	8.63223i	−1.54159	−	0.500893i
$298$	9.60077	−	16.8207i	0.556157	−	0.974397i
$299$			3.98223i			0.230298i
$300$		0			0
$301$			6.44929i			0.371731i
$302$	14.8526	+	8.47742i	0.854670	+	0.487821i
$303$	−41.0815	−	13.3482i	−2.36007	−	0.766833i
$304$	−4.34568	+	22.6395i	−0.249242	+	1.29846i
$305$		0			0
$306$	17.4253	+	19.1612i	0.996137	+	1.09537i
$307$	−14.1781			−0.809186			−0.404593	−	0.914497i	$-0.632587\pi$
$307$	−14.1781			−0.809186			−0.404593	+	0.914497i	$0.632587\pi$
$308$	−7.25336	−	3.14376i	−0.413298	−	0.179132i
$309$	16.1668	−	22.2516i	0.919695	−	1.26585i
$310$		0			0
$311$	0.386936	−	0.281125i	0.0219411	−	0.0159412i	−0.576761	−	0.816913i	$-0.695683\pi$
$311$	0.386936	−	0.281125i	0.0219411	−	0.0159412i	0.598702	+	0.800972i	$0.295683\pi$
$312$	31.6661	+	42.2510i	1.79274	+	2.39199i
$313$	6.67701	−	9.19012i	0.377407	−	0.519456i	−0.577488	−	0.816399i	$-0.695967\pi$
$313$	6.67701	−	9.19012i	0.377407	−	0.519456i	0.954895	+	0.296943i	$0.0959671\pi$
$314$	−15.4819	−	8.83662i	−0.873695	−	0.498679i
$315$		0			0
$316$	−0.793603	+	0.176913i	−0.0446436	+	0.00995211i
$317$	−4.27173	−	13.1470i	−0.239924	−	0.738411i	−0.996430	−	0.0844241i	$-0.973095\pi$
$317$	−4.27173	−	13.1470i	−0.239924	−	0.738411i	0.756505	−	0.653987i	$-0.226905\pi$
$318$	−6.45046	−	14.2971i	−0.361724	−	0.801744i
$319$	−0.916348	−	2.82023i	−0.0513056	−	0.157902i
$320$		0			0
$321$	3.39081	−	10.4358i	0.189257	−	0.582472i
$322$	−1.61814	+	0.178173i	−0.0901752	+	0.00992921i
$323$	12.4372	−	9.03618i	0.692026	−	0.502786i
$324$	−23.2128	+	26.2993i	−1.28960	+	1.46107i
$325$		0			0
$326$	−6.86935	−	15.2256i	−0.380458	−	0.843267i
$327$	−8.05866	−	11.0918i	−0.445645	−	0.613378i
$328$	12.5120	−	17.7702i	0.690861	−	0.981197i
$329$	−4.75581	+	14.6369i	−0.262197	+	0.806958i
$330$		0			0
$331$	6.42804	−	2.08860i	0.353317	−	0.114800i	−0.126981	−	0.991905i	$-0.540529\pi$
$331$	6.42804	−	2.08860i	0.353317	−	0.114800i	0.480298	+	0.877105i	$0.340529\pi$
$332$	1.52853	−	1.73177i	0.0838891	−	0.0950434i
$333$	−7.74516	−	23.8372i	−0.424432	−	1.30627i
$334$	15.2036	+	3.15307i	0.831904	+	0.172528i
$335$		0			0
$336$	−15.7514	+	14.7576i	−0.859311	+	0.805091i
$337$	9.77379	−	13.4525i	0.532412	−	0.732803i	−0.455083	−	0.890449i	$-0.650391\pi$
$337$	9.77379	−	13.4525i	0.532412	−	0.732803i	0.987496	+	0.157646i	$0.0503905\pi$
$338$	6.41092	−	30.9124i	0.348708	−	1.68141i
$339$	2.81392	+	3.87303i	0.152831	+	0.210354i
$340$		0			0
$341$	1.58826	−	2.18606i	0.0860093	−	0.118382i
$342$	37.6478	+	41.3983i	2.03576	+	2.23856i
$343$		−	18.9813i		−	1.02489i
$344$	0.157627	+	10.6166i	0.00849867	+	0.572410i
$345$		0			0
$346$	−21.3166	+	2.34717i	−1.14599	+	0.126185i
$347$	0.155098	−	0.477342i	0.00832608	−	0.0256250i	−0.946807	−	0.321801i	$-0.895712\pi$
$347$	0.155098	−	0.477342i	0.00832608	−	0.0256250i	0.955133	+	0.296176i	$0.0957116\pi$
$348$	−8.06019	−	0.766585i	−0.432072	−	0.0410933i
$349$			1.38740i			0.0742660i	0.999310	+	0.0371330i	$0.0118225\pi$
$349$			1.38740i			0.0742660i	−0.999310	+	0.0371330i	$0.988177\pi$
$350$		0			0
$351$	72.1613			3.85169
$352$	−12.0171	−	4.99788i	−0.640513	−	0.266388i
$353$	27.1323	+	8.81582i	1.44411	+	0.469218i	0.923175	−	0.384380i	$-0.125585\pi$
$353$	27.1323	+	8.81582i	1.44411	+	0.469218i	0.520931	+	0.853599i	$0.325585\pi$
$354$	2.96225	+	26.9026i	0.157442	+	1.42985i
$355$		0			0
$356$	7.59678	+	3.29260i	0.402629	+	0.174508i
$357$	14.3942			0.761820
$358$	−20.5622	−	22.6106i	−1.08675	−	1.19501i
$359$	−18.7073	−	13.5917i	−0.987336	−	0.717342i	−0.0279998	−	0.999608i	$-0.508914\pi$
$359$	−18.7073	−	13.5917i	−0.987336	−	0.717342i	−0.959336	+	0.282266i	$0.908914\pi$
$360$		0			0
$361$	11.4997	−	8.35500i	0.605246	−	0.439737i
$362$	−12.0320	−	2.49531i	−0.632386	−	0.131150i
$363$	14.5009	+	10.5355i	0.761099	+	0.552971i
$364$	20.3296	+	1.93350i	1.06556	+	0.101343i
$365$		0			0
$366$	−4.01166	−	0.831977i	−0.209693	−	0.0434881i
$367$	−26.8195	+	8.71417i	−1.39996	+	0.454876i	−0.909179	−	0.416405i	$-0.863290\pi$
$367$	−26.8195	+	8.71417i	−1.39996	+	0.454876i	−0.490785	+	0.871281i	$0.663290\pi$
$368$	−2.65937	+	0.332852i	−0.138629	+	0.0173511i
$369$	−16.3018	−	50.1719i	−0.848640	−	2.61184i
$370$		0			0
$371$	−5.76946	−	1.87461i	−0.299535	−	0.0973250i
$372$	−3.75195	−	6.35253i	−0.194530	−	0.329364i
$373$	−14.5528	+	10.5732i	−0.753515	+	0.547461i	−0.896914	−	0.442204i	$-0.854197\pi$
$373$	−14.5528	+	10.5732i	−0.753515	+	0.547461i	0.143399	+	0.989665i	$0.454197\pi$
$374$	3.56939	+	7.91139i	0.184569	+	0.409088i
$375$		0			0
$376$	−7.47114	+	24.2110i	−0.385295	+	1.24859i
$377$	4.50257	+	6.19726i	0.231894	+	0.319175i
$378$	3.22865	+	29.3220i	0.166064	+	1.50816i
$379$	−5.18753	−	1.68553i	−0.266466	−	0.0865799i	0.172737	−	0.984968i	$-0.444739\pi$
$379$	−5.18753	−	1.68553i	−0.266466	−	0.0865799i	−0.439203	+	0.898388i	$0.644739\pi$
$380$		0			0
$381$	−50.7814	+	16.4999i	−2.60161	+	0.845315i
$382$	−0.495461	−	1.09817i	−0.0253500	−	0.0561870i
$383$	13.2382	−	4.30135i	0.676440	−	0.219789i	0.0494042	−	0.998779i	$-0.484268\pi$
$383$	13.2382	−	4.30135i	0.676440	−	0.219789i	0.627036	+	0.778990i	$0.284268\pi$
$384$	−25.5689	+	24.6784i	−1.30480	+	1.25937i
$385$		0			0
$386$	7.52944	−	13.1917i	0.383239	−	0.671441i
$387$	20.8508	+	15.1490i	1.05990	+	0.770066i
$388$	6.60636	+	29.6351i	0.335387	+	1.50450i
$389$	−21.7230	−	29.8991i	−1.10140	−	1.51594i	−0.833518	−	0.552492i	$-0.813677\pi$
$389$	−21.7230	−	29.8991i	−1.10140	−	1.51594i	−0.267880	−	0.963452i	$-0.586323\pi$
$390$		0			0
$391$	1.44596	+	1.05055i	0.0731251	+	0.0531285i
$392$	−0.169994	−	11.4496i	−0.00858599	−	0.578291i
$393$			18.8777i			0.952255i
$394$	23.6627	−	21.5190i	1.19211	−	1.08411i
$395$		0			0
$396$	−27.2016	+	16.0659i	−1.36693	+	0.807341i
$397$	7.32490	−	22.5437i	0.367626	−	1.13144i	−0.580694	−	0.814122i	$-0.697219\pi$
$397$	7.32490	−	22.5437i	0.367626	−	1.13144i	0.948320	−	0.317315i	$-0.102781\pi$
$398$	−0.868074	−	0.495471i	−0.0435126	−	0.0248357i
$399$	31.0990			1.55690
$400$		0			0
$401$	−0.881338			−0.0440119			−0.0220060	−	0.999758i	$-0.507005\pi$
$401$	−0.881338			−0.0440119			−0.0220060	+	0.999758i	$0.507005\pi$
$402$	59.1858	+	33.7815i	2.95192	+	1.68487i
$403$	−2.15700	+	6.63856i	−0.107448	+	0.330690i
$404$	−23.6826	+	13.9875i	−1.17825	+	0.695904i
$405$		0			0
$406$	−2.31673	+	2.10685i	−0.114978	+	0.104561i
$407$		−	8.39925i		−	0.416335i
$408$	23.6952	−	0.351807i	1.17309	−	0.0174171i
$409$	28.9714	+	21.0489i	1.43254	+	1.04080i	0.989536	+	0.144283i	$0.0460876\pi$
$409$	28.9714	+	21.0489i	1.43254	+	1.04080i	0.443005	+	0.896519i	$0.353912\pi$
$410$		0			0
$411$	7.64449	+	10.5217i	0.377075	+	0.518999i
$412$	−3.81063	−	17.0939i	−0.187737	−	0.842158i
$413$	8.46866	+	6.15285i	0.416716	+	0.302762i
$414$	−3.22486	+	5.65001i	−0.158493	+	0.277683i
$415$		0			0
$416$	33.5132	+	2.68599i	1.64312	+	0.131692i
$417$	30.0754	−	9.77209i	1.47280	−	0.478541i
$418$	7.71178	+	17.0928i	0.377196	+	0.836036i
$419$	−18.1069	+	5.88329i	−0.884581	+	0.287418i	−0.715858	−	0.698246i	$-0.753964\pi$
$419$	−18.1069	+	5.88329i	−0.884581	+	0.287418i	−0.168723	+	0.985664i	$0.553964\pi$
$420$		0			0
$421$	8.42477	+	2.73737i	0.410598	+	0.133411i	0.507031	−	0.861928i	$-0.330743\pi$
$421$	8.42477	+	2.73737i	0.410598	+	0.133411i	−0.0964323	+	0.995340i	$0.530743\pi$
$422$	−2.84145	−	25.8055i	−0.138320	−	1.25619i
$423$	36.1505	+	49.7569i	1.75770	+	2.41926i
$424$	−9.54333	−	2.94492i	−0.463465	−	0.143018i
$425$		0			0
$426$	−11.3906	−	25.2466i	−0.551875	−	1.22320i
$427$	−1.28196	+	0.931395i	−0.0620382	+	0.0450734i
$428$	−3.55322	−	6.01605i	−0.171751	−	0.290797i
$429$	40.8476	+	13.2722i	1.97214	+	0.640788i
$430$		0			0
$431$	0.956566	+	2.94401i	0.0460762	+	0.141808i	0.971448	−	0.237253i	$-0.0762471\pi$
$431$	0.956566	+	2.94401i	0.0460762	+	0.141808i	−0.925372	+	0.379061i	$0.876247\pi$
$432$	6.03156	+	48.1900i	0.290194	+	2.31854i
$433$	−8.67407	+	2.81837i	−0.416849	+	0.135442i	−0.509930	−	0.860216i	$-0.670329\pi$
$433$	−8.67407	+	2.81837i	−0.416849	+	0.135442i	0.0930806	+	0.995659i	$0.470329\pi$
$434$	−2.79402	−	0.579450i	−0.134117	−	0.0278145i
$435$		0			0
$436$	−8.69077	−	0.826558i	−0.416212	−	0.0395849i
$437$	3.12403	+	2.26974i	0.149443	+	0.108576i
$438$	−23.2645	−	4.82481i	−1.11162	−	0.230538i
$439$	31.0958	−	22.5924i	1.48412	−	1.07828i	0.507920	−	0.861404i	$-0.330415\pi$
$439$	31.0958	−	22.5924i	1.48412	−	1.07828i	0.976200	−	0.216872i	$-0.0695854\pi$
$440$		0			0
$441$	−22.4867	−	16.3375i	−1.07080	−	0.777978i
$442$	−15.0847	−	16.5874i	−0.717505	−	0.788983i
$443$	33.8214			1.60690			0.803451	−	0.595371i	$-0.202995\pi$
$443$	33.8214			1.60690			0.803451	+	0.595371i	$0.202995\pi$
$444$	−21.0417	−	9.11993i	−0.998597	−	0.432813i
$445$		0			0
$446$	−1.18796	−	10.7888i	−0.0562516	−	0.510866i
$447$	−40.9102	−	13.2925i	−1.93499	−	0.628715i
$448$	0.408029	+	13.7379i	0.0192775	+	0.649056i
$449$	11.7494			0.554489			0.277245	−	0.960799i	$-0.410579\pi$
$449$	11.7494			0.554489			0.277245	+	0.960799i	$0.410579\pi$
$450$		0			0
$451$		−	17.6785i		−	0.832450i
$452$	3.03464	+	0.288618i	0.142738	+	0.0135754i
$453$	11.7372	−	36.1235i	0.551463	−	1.69723i
$454$	−16.4691	+	1.81342i	−0.772934	+	0.0851080i
$455$		0			0
$456$	51.1942	−	0.760090i	2.39739	−	0.0355945i
$457$			12.5132i			0.585342i	0.956213	+	0.292671i	$0.0945441\pi$
$457$			12.5132i			0.585342i	−0.956213	+	0.292671i	$0.905456\pi$
$458$	25.6487	+	28.2038i	1.19848	+	1.31788i
$459$	19.0368	−	26.2019i	0.888562	−	1.22300i
$460$		0			0
$461$	7.24736	+	9.97513i	0.337543	+	0.464588i	0.943722	−	0.330740i	$-0.107298\pi$
$461$	7.24736	+	9.97513i	0.337543	+	0.464588i	−0.606179	+	0.795328i	$0.707298\pi$
$462$	−3.56541	+	17.1918i	−0.165878	+	0.799836i
$463$	9.71829	−	13.3761i	0.451647	−	0.621639i	−0.521103	−	0.853494i	$-0.674479\pi$
$463$	9.71829	−	13.3761i	0.451647	−	0.621639i	0.972751	+	0.231854i	$0.0744793\pi$
$464$	−3.76224	+	3.52485i	−0.174658	+	0.163637i
$465$		0			0
$466$	19.3008	+	4.00279i	0.894092	+	0.185426i
$467$	4.96826	+	15.2907i	0.229904	+	0.707571i	0.997757	+	0.0669450i	$0.0213252\pi$
$467$	4.96826	+	15.2907i	0.229904	+	0.707571i	−0.767853	+	0.640626i	$0.778675\pi$
$468$	54.0041	−	61.1847i	2.49634	−	2.82826i
$469$	25.0672	−	8.14484i	1.15750	−	0.376094i
$470$		0			0
$471$	−12.2346	+	37.6541i	−0.563739	+	1.73501i
$472$	14.0912	+	9.92164i	0.648602	+	0.456681i
$473$	5.07663	+	6.98739i	0.233424	+	0.321280i
$474$	0.742658	+	1.64607i	0.0341114	+	0.0756063i
$475$		0			0
$476$	6.06519	−	6.87165i	0.277998	−	0.314962i
$477$	−19.6128	+	14.2495i	−0.898008	+	0.652441i
$478$	−13.4458	+	1.48052i	−0.614995	+	0.0677173i
$479$	−6.65413	+	20.4793i	−0.304035	+	0.935723i	0.676001	+	0.736901i	$0.263712\pi$
$479$	−6.65413	+	20.4793i	−0.304035	+	0.935723i	−0.980036	+	0.198822i	$0.936288\pi$
$480$		0			0
$481$	6.70481	+	20.6353i	0.305713	+	0.940889i
$482$	−14.6267	−	32.4194i	−0.666227	−	1.47666i
$483$	1.11727	+	3.43862i	0.0508378	+	0.156463i
$484$	11.1397	−	2.48330i	0.506351	−	0.112877i
$485$		0			0
$486$	22.9250	+	13.0849i	1.03990	+	0.593545i
$487$	−15.7256	+	21.6444i	−0.712593	+	0.980800i	0.287144	+	0.957887i	$0.407294\pi$
$487$	−15.7256	+	21.6444i	−0.712593	+	0.980800i	−0.999737	+	0.0229129i	$0.992706\pi$
$488$	−2.08755	+	1.56457i	−0.0944991	+	0.0708246i
$489$	−30.0131	+	21.8058i	−1.35724	+	0.986091i
$490$		0			0
$491$	−0.191575	+	0.263680i	−0.00864564	+	0.0118997i	−0.813318	−	0.581820i	$-0.802341\pi$
$491$	−0.191575	+	0.263680i	−0.00864564	+	0.0118997i	0.804672	+	0.593719i	$0.202341\pi$
$492$	−44.2882	−	19.1954i	−1.99666	−	0.865397i
$493$	3.43806			0.154842
$494$	−32.5909	−	35.8376i	−1.46633	−	1.61241i
$495$		0			0
$496$	−4.61359	−	0.885585i	−0.207156	−	0.0397639i
$497$	−10.1880	−	3.31029i	−0.456995	−	0.148487i
$498$	−4.45549	−	2.54306i	−0.199655	−	0.113957i
$499$			23.2206i			1.03950i	0.854320	+	0.519748i	$0.173974\pi$
$499$			23.2206i			1.03950i	−0.854320	+	0.519748i	$0.826026\pi$
$500$		0			0
$501$		−	34.4855i		−	1.54070i
$502$	−4.84961	+	8.49660i	−0.216449	+	0.379222i
$503$	8.85545	+	2.87731i	0.394845	+	0.128293i	0.499708	−	0.866194i	$-0.333441\pi$
$503$	8.85545	+	2.87731i	0.394845	+	0.128293i	−0.104863	+	0.994487i	$0.533441\pi$
$504$	27.2780	+	19.2064i	1.21506	+	0.855523i
$505$		0			0
$506$	−1.61289	+	1.46677i	−0.0717019	+	0.0652061i
$507$	−70.1170			−3.11401
$508$	−13.5206	+	31.1951i	−0.599880	+	1.38406i
$509$	−11.8276	+	16.2793i	−0.524249	+	0.721567i	−0.986240	−	0.165318i	$-0.947135\pi$
$509$	−11.8276	+	16.2793i	−0.524249	+	0.721567i	0.461992	+	0.886884i	$0.347135\pi$
$510$		0			0
$511$	−7.43433	+	5.40135i	−0.328875	+	0.238942i
$512$	1.00745	+	22.6050i	0.0445236	+	0.999008i
$513$	41.1296	−	56.6100i	1.81592	−	2.49939i
$514$	−20.8972	+	36.6122i	−0.921736	+	1.61490i
$515$		0			0
$516$	23.0170	−	5.13102i	1.01327	−	0.225881i
$517$	6.36899	+	19.6017i	0.280108	+	0.862083i
$518$	−8.08494	+	3.64770i	−0.355232	+	0.160271i
$519$	14.7185	+	45.2987i	0.646068	+	1.98839i
$520$		0			0
$521$	5.18227	−	15.9494i	0.227039	−	0.698755i	−0.771039	−	0.636788i	$-0.780263\pi$
$521$	5.18227	−	15.9494i	0.227039	−	0.698755i	0.998078	−	0.0619670i	$-0.0197373\pi$
$522$	1.36966	+	12.4389i	0.0599482	+	0.544438i
$523$	0.0366350	−	0.0266169i	0.00160194	−	0.00116388i	−0.586984	−	0.809599i	$-0.699685\pi$
$523$	0.0366350	−	0.0266169i	0.00160194	−	0.00116388i	0.588586	+	0.808435i	$0.299685\pi$
$524$	9.01207	+	7.95441i	0.393694	+	0.347490i
$525$		0			0
$526$	−34.1191	+	15.3936i	−1.48766	+	0.671191i
$527$	1.84144	+	2.53452i	0.0802144	+	0.110406i
$528$	−5.44908	+	28.3878i	−0.237141	+	1.23542i
$529$	6.96866	−	21.4473i	0.302985	−	0.932493i
$530$		0			0
$531$	39.7848	−	12.9268i	1.72651	−	0.560978i
$532$	13.1040	−	14.8464i	0.568132	−	0.643673i
$533$	14.1121	+	43.4327i	0.611265	+	1.88128i
$534$	3.73422	−	18.0058i	0.161595	−	0.779187i
$535$		0			0
$536$	41.0658	−	14.0204i	1.77377	−	0.605591i
$537$	−39.8978	+	54.9146i	−1.72172	+	2.36974i
$538$	11.1241	+	2.30703i	0.479595	+	0.0994630i
$539$	−5.47494	−	7.53561i	−0.235822	−	0.324582i
$540$		0			0
$541$	10.3777	−	14.2837i	0.446173	−	0.614104i	−0.525397	−	0.850857i	$-0.676083\pi$
$541$	10.3777	−	14.2837i	0.446173	−	0.614104i	0.971570	+	0.236753i	$0.0760832\pi$
$542$	−9.74526	+	8.86239i	−0.418595	+	0.380672i
$543$			27.2915i			1.17119i
$544$	9.81639	−	11.4601i	0.420874	−	0.491349i
$545$		0			0
$546$	−4.96411	−	45.0831i	−0.212444	−	1.92938i
$547$	10.9369	−	33.6604i	0.467630	−	1.43922i	−0.388015	−	0.921653i	$-0.626839\pi$
$547$	10.9369	−	33.6604i	0.467630	−	1.43922i	0.855645	−	0.517563i	$-0.173161\pi$
$548$	8.24411	+	0.784077i	0.352171	+	0.0334941i
$549$			6.33240i			0.270260i
$550$		0			0
$551$	7.42802			0.316444
$552$	1.92327	+	5.63324i	0.0818597	+	0.239767i
$553$	0.664253	+	0.215829i	0.0282469	+	0.00917798i
$554$	5.30259	−	0.583869i	0.225285	−	0.0248062i
$555$		0			0
$556$	8.00761	−	18.4754i	0.339598	−	0.783530i
$557$	−27.7529			−1.17593			−0.587964	−	0.808887i	$-0.700070\pi$
$557$	−27.7529			−1.17593			−0.587964	+	0.808887i	$0.700070\pi$
$558$	−8.43636	+	7.67207i	−0.357140	+	0.324784i
$559$	−18.0501	−	13.1141i	−0.763436	−	0.554669i
$560$		0			0
$561$	15.5951	−	11.3305i	0.658428	−	0.478376i
$562$	−6.15605	+	29.6835i	−0.259677	+	1.25212i
$563$	−23.5565	−	17.1148i	−0.992788	−	0.721303i	−0.0322580	−	0.999480i	$-0.510270\pi$
$563$	−23.5565	−	17.1148i	−0.992788	−	0.721303i	−0.960530	+	0.278177i	$0.910270\pi$
$564$	56.0216	+	5.32808i	2.35893	+	0.224353i
$565$		0			0
$566$	0.265897	−	1.28212i	0.0111765	−	0.0538913i
$567$	28.6575	−	9.31138i	1.20350	−	0.391041i
$568$	−16.8521	−	5.20029i	−0.707099	−	0.218199i
$569$	5.68191	+	17.4871i	0.238198	+	0.733098i	0.996681	+	0.0814052i	$0.0259408\pi$
$569$	5.68191	+	17.4871i	0.238198	+	0.733098i	−0.758483	+	0.651693i	$0.774059\pi$
$570$		0			0
$571$	−20.4740	−	6.65241i	−0.856811	−	0.278395i	−0.152515	−	0.988301i	$-0.548737\pi$
$571$	−20.4740	−	6.65241i	−0.856811	−	0.278395i	−0.704296	+	0.709906i	$0.748737\pi$
$572$	23.5478	−	13.9079i	0.984583	−	0.581518i
$573$	−2.16473	+	1.57277i	−0.0904330	+	0.0657034i
$574$	−17.0170	+	7.67758i	−0.710276	+	0.320456i
$575$		0			0
$576$	45.3736	+	30.9504i	1.89057	+	1.28960i
$577$	−1.65018	−	2.27128i	−0.0686978	−	0.0945545i	0.773285	−	0.634058i	$-0.218612\pi$
$577$	−1.65018	−	2.27128i	−0.0686978	−	0.0945545i	−0.841983	+	0.539504i	$0.818612\pi$
$578$	13.8948	−	1.52996i	0.577948	−	0.0636379i
$579$	−32.0840	−	10.4247i	−1.33337	−	0.433237i
$580$		0			0
$581$	−1.88705	+	0.613141i	−0.0782882	+	0.0254374i
$582$	61.4683	−	27.7327i	2.54794	−	1.14956i
$583$	−7.72646	+	2.51048i	−0.319997	+	0.103973i
$584$	−12.1061	+	9.07325i	−0.500956	+	0.375454i
$585$		0			0
$586$	16.4056	+	9.36385i	0.677710	+	0.386817i
$587$	−9.41724	−	6.84202i	−0.388691	−	0.282401i	0.376228	−	0.926527i	$-0.377221\pi$
$587$	−9.41724	−	6.84202i	−0.388691	−	0.282401i	−0.764919	+	0.644127i	$0.777221\pi$
$588$	−24.8229	+	5.53359i	−1.02368	+	0.228201i
$589$	3.97848	+	5.47591i	0.163931	+	0.225631i
$590$		0			0
$591$	−57.4698	−	41.7543i	−2.36399	−	1.71754i
$592$	−13.2200	+	6.20233i	−0.543340	+	0.254914i
$593$			12.6560i			0.519720i	0.965646	+	0.259860i	$0.0836765\pi$
$593$			12.6560i			0.519720i	−0.965646	+	0.259860i	$0.916324\pi$
$594$	26.5792	+	29.2270i	1.09056	+	1.19920i
$595$		0			0
$596$	−23.5839	+	13.9292i	−0.966033	+	0.570562i
$597$	−0.685994	+	2.11127i	−0.0280759	+	0.0864087i
$598$	2.79169	−	4.89109i	0.114161	−	0.200012i
$599$	−20.9771			−0.857101			−0.428550	−	0.903518i	$-0.640976\pi$
$599$	−20.9771			−0.857101			−0.428550	+	0.903518i	$0.640976\pi$
$600$		0			0
$601$	23.0207			0.939032			0.469516	−	0.882924i	$-0.344428\pi$
$601$	23.0207			0.939032			0.469516	+	0.882924i	$0.344428\pi$
$602$	4.52119	−	7.92120i	0.184270	−	0.322844i
$603$	32.5488	−	100.175i	1.32549	−	4.07944i
$604$	−12.2994	−	20.8244i	−0.500455	−	0.847334i
$605$		0			0
$606$	41.0999	+	45.1943i	1.66957	+	1.83589i
$607$			26.0419i			1.05701i	0.848931	+	0.528504i	$0.177247\pi$
$607$			26.0419i			1.05701i	−0.848931	+	0.528504i	$0.822753\pi$
$608$	21.2086	−	24.7600i	0.860122	−	1.00415i
$609$	5.62666	+	4.08801i	0.228004	+	0.165654i
$610$		0			0
$611$	−31.2947	−	43.0734i	−1.26605	−	1.74257i
$612$	−7.96953	−	35.7501i	−0.322149	−	1.44511i
$613$	−13.6825	−	9.94089i	−0.552629	−	0.401509i	0.276125	−	0.961122i	$-0.410950\pi$
$613$	−13.6825	−	9.94089i	−0.552629	−	0.401509i	−0.828754	+	0.559613i	$0.810950\pi$
$614$	17.4139	+	9.93937i	0.702770	+	0.401120i
$615$		0			0
$616$	6.70489	+	8.94613i	0.270148	+	0.360450i
$617$	−5.20768	+	1.69208i	−0.209653	+	0.0681205i	−0.411961	−	0.911202i	$-0.635156\pi$
$617$	−5.20768	+	1.69208i	−0.209653	+	0.0681205i	0.202308	+	0.979322i	$0.435156\pi$
$618$	−35.4557	+	15.9966i	−1.42624	+	0.643478i
$619$	−15.1429	+	4.92021i	−0.608643	+	0.197760i	−0.597091	−	0.802173i	$-0.703677\pi$
$619$	−15.1429	+	4.92021i	−0.608643	+	0.197760i	−0.0115514	+	0.999933i	$0.503677\pi$
$620$		0			0
$621$	7.73701	+	2.51391i	0.310476	+	0.100880i
$622$	−0.672325	+	0.0740299i	−0.0269578	+	0.00296833i
$623$	−4.18044	−	5.75389i	−0.167486	−	0.230525i
$624$	−9.27363	−	74.0930i	−0.371242	−	2.96609i
$625$		0			0
$626$	−14.6435	+	6.60673i	−0.585272	+	0.264058i
$627$	33.6938	−	24.4799i	1.34560	−	0.977635i
$628$	12.8205	+	21.7068i	0.511595	+	0.866195i
$629$	9.26151	+	3.00925i	0.369281	+	0.119987i
$630$		0			0
$631$	−15.0147	−	46.2106i	−0.597727	−	1.83961i	−0.540654	−	0.841245i	$-0.681823\pi$
$631$	−15.0147	−	46.2106i	−0.597727	−	1.83961i	−0.0570726	−	0.998370i	$-0.518177\pi$
$632$	1.09875	+	0.339056i	0.0437059	+	0.0134869i
$633$	−54.8380	+	17.8179i	−2.17961	+	0.708200i
$634$	−3.96990	+	19.1422i	−0.157665	+	0.760235i
$635$		0			0
$636$	−2.10018	+	22.0822i	−0.0832776	+	0.875615i
$637$	19.4662	+	14.1431i	0.771280	+	0.560368i
$638$	−0.851600	+	4.10628i	−0.0337152	+	0.162569i
$639$	−34.6333	+	25.1626i	−1.37007	+	0.995417i
$640$		0			0
$641$	15.1755	+	11.0256i	0.599396	+	0.435486i	0.845664	−	0.533715i	$-0.179205\pi$
$641$	15.1755	+	11.0256i	0.599396	+	0.435486i	−0.246269	+	0.969202i	$0.579205\pi$
$642$	−11.4806	+	10.4405i	−0.453104	+	0.412055i
$643$	−37.8673			−1.49334			−0.746669	−	0.665195i	$-0.768348\pi$
$643$	−37.8673			−1.49334			−0.746669	+	0.665195i	$0.768348\pi$
$644$	2.11235	+	0.915536i	0.0832382	+	0.0360772i
$645$		0			0
$646$	−21.6105	+	2.37953i	−0.850252	+	0.0936215i
$647$	37.5073	+	12.1869i	1.47456	+	0.479115i	0.932484	−	0.361212i	$-0.117637\pi$
$647$	37.5073	+	12.1869i	1.47456	+	0.479115i	0.542080	+	0.840327i	$0.317637\pi$
$648$	46.9475	−	16.0285i	1.84427	−	0.629660i
$649$	14.0185			0.550276
$650$		0			0
$651$			6.33752i			0.248387i
$652$	−2.23657	+	23.5162i	−0.0875907	+	0.920964i
$653$	−6.71891	+	20.6787i	−0.262931	+	0.809219i	0.729232	+	0.684267i	$0.239878\pi$
$653$	−6.71891	+	20.6787i	−0.262931	+	0.809219i	−0.992163	+	0.124952i	$0.960122\pi$
$654$	2.12212	+	19.2727i	0.0829815	+	0.753622i
$655$		0			0
$656$	−27.8252	+	13.0545i	−1.08639	+	0.509693i
$657$			36.7229i			1.43270i
$658$	16.1022	−	14.6435i	0.627731	−	0.570861i
$659$	−3.19947	+	4.40369i	−0.124634	+	0.171543i	−0.866774	−	0.498701i	$-0.833811\pi$
$659$	−3.19947	+	4.40369i	−0.124634	+	0.171543i	0.742141	+	0.670244i	$0.233811\pi$
$660$		0			0
$661$	−26.8362	−	36.9368i	−1.04381	−	1.43668i	−0.894058	−	0.447951i	$-0.852154\pi$
$661$	−26.8362	−	36.9368i	−1.04381	−	1.43668i	−0.149747	−	0.988724i	$-0.547846\pi$
$662$	−9.35929	−	1.94102i	−0.363759	−	0.0754399i
$663$	−29.2694	+	40.2859i	−1.13673	+	1.56458i
$664$	−3.09143	+	1.05546i	−0.119971	+	0.0409596i
$665$		0			0
$666$	−7.19790	+	34.7071i	−0.278913	+	1.34487i
$667$	0.266862	+	0.821317i	0.0103329	+	0.0318015i
$668$	−16.4631	−	14.5310i	−0.636976	−	0.562221i
$669$	−22.9268	+	7.44937i	−0.886402	+	0.288009i
$670$		0			0
$671$	−0.655758	+	2.01821i	−0.0253152	+	0.0779123i
$672$	29.6920	−	7.08332i	1.14539	−	0.273245i
$673$	−25.2847	−	34.8014i	−0.974654	−	1.34150i	−0.939661	−	0.342108i	$-0.888859\pi$
$673$	−25.2847	−	34.8014i	−0.974654	−	1.34150i	−0.0349929	−	0.999388i	$-0.511141\pi$
$674$	−21.4351	+	9.67092i	−0.825651	+	0.372510i
$675$		0			0
$676$	−29.5448	+	33.4733i	−1.13634	+	1.28743i
$677$	−37.8808	+	27.5220i	−1.45588	+	1.05776i	−0.471466	+	0.881884i	$0.656275\pi$
$677$	−37.8808	+	27.5220i	−1.45588	+	1.05776i	−0.984413	+	0.175873i	$0.943725\pi$
$678$	−0.741002	−	6.72964i	−0.0284580	−	0.258450i
$679$	8.05960	−	24.8049i	0.309299	−	0.951924i
$680$		0			0
$681$	11.3714	+	34.9977i	0.435755	+	1.34111i
$682$	−3.48326	+	1.57155i	−0.133381	+	0.0601776i
$683$	−0.331130	−	1.01911i	−0.0126703	−	0.0389953i	0.944521	−	0.328450i	$-0.106526\pi$
$683$	−0.331130	−	1.01911i	−0.0126703	−	0.0389953i	−0.957192	+	0.289454i	$0.906526\pi$
$684$	−17.2184	−	77.2391i	−0.658362	−	2.95331i
$685$		0			0
$686$	−13.3066	+	23.3133i	−0.508047	+	0.890108i
$687$	49.7673	−	68.4988i	1.89874	−	2.61339i
$688$	7.24904	−	13.1501i	0.276367	−	0.501345i
$689$	16.9784	−	12.3355i	0.646824	−	0.469945i
$690$		0			0
$691$	8.71658	−	11.9973i	0.331595	−	0.456401i	−0.610368	−	0.792118i	$-0.708979\pi$
$691$	8.71658	−	11.9973i	0.331595	−	0.456401i	0.941963	+	0.335717i	$0.108979\pi$
$692$	27.8271	+	12.0608i	1.05783	+	0.458484i
$693$	27.1373			1.03086
$694$	−0.525130	+	0.477556i	−0.0199337	+	0.0181278i
$695$		0			0
$696$	9.36235	+	6.59204i	0.354879	+	0.249870i
$697$	19.4934	+	6.33379i	0.738366	+	0.239910i
$698$	0.972622	−	1.70405i	0.0368143	−	0.0644992i
$699$		−	43.7790i		−	1.65587i
$700$		0			0
$701$		−	6.33651i		−	0.239327i	−0.992815	−	0.119663i	$-0.961818\pi$
$701$		−	6.33651i		−	0.239327i	0.992815	−	0.119663i	$-0.0381815\pi$
$702$	−88.6306	−	50.5878i	−3.34515	−	1.90931i
$703$	20.0098	+	6.50156i	0.754682	+	0.245211i
$704$	11.2560	+	14.5630i	0.424228	+	0.548863i
$705$		0			0
$706$	−27.1445	−	29.8486i	−1.02159	−	1.12337i
$707$	23.6266			0.888571
$708$	15.2214	−	35.1192i	0.572054	−	1.31986i
$709$	−25.4810	+	35.0716i	−0.956960	+	1.31714i	−0.00859395	+	0.999963i	$0.502736\pi$
$709$	−25.4810	+	35.0716i	−0.956960	+	1.31714i	−0.948366	+	0.317179i	$0.897264\pi$
$710$		0			0
$711$	2.25807	−	1.64059i	0.0846843	−	0.0615268i
$712$	−7.02235	−	9.36970i	−0.263174	−	0.351144i
$713$	−0.462540	+	0.636631i	−0.0173222	+	0.0238420i
$714$	−17.6793	−	10.0908i	−0.661632	−	0.377640i
$715$		0			0
$716$	9.40423	+	42.1859i	0.351452	+	1.57656i
$717$	9.28391	+	28.5729i	0.346714	+	1.06708i
$718$	13.4486	+	29.8082i	0.501898	+	1.11243i
$719$	2.82195	+	8.68507i	0.105241	+	0.323898i	0.989787	−	0.142555i	$-0.0455316\pi$
$719$	2.82195	+	8.68507i	0.105241	+	0.323898i	−0.884546	+	0.466453i	$0.845532\pi$
$720$		0			0
$721$	−4.64888	+	14.3078i	−0.173133	+	0.532850i
$722$	−19.9814	+	2.20016i	−0.743631	+	0.0818814i
$723$	−63.9059	+	46.4303i	−2.37669	+	1.72676i
$724$	13.0287	+	11.4997i	0.484208	+	0.427382i
$725$		0			0
$726$	−10.4246	−	23.1057i	−0.386894	−	0.857532i
$727$	−24.3866	−	33.5653i	−0.904449	−	1.24487i	−0.969027	−	0.246955i	$-0.920570\pi$
$727$	−24.3866	−	33.5653i	−0.904449	−	1.24487i	0.0645777	−	0.997913i	$-0.479430\pi$
$728$	−23.6140	−	16.6266i	−0.875192	−	0.616223i
$729$	1.85677	−	5.71454i	0.0687691	−	0.211649i
$730$		0			0
$731$	−9.52354	+	3.09439i	−0.352241	+	0.114450i
$732$	4.34399	+	3.83418i	0.160559	+	0.141715i
$733$	−11.2254	−	34.5481i	−0.414619	−	1.27606i	−0.912592	−	0.408872i	$-0.865922\pi$
$733$	−11.2254	−	34.5481i	−0.414619	−	1.27606i	0.497973	−	0.867193i	$-0.334078\pi$
$734$	39.0494	+	8.09844i	1.44134	+	0.298919i
$735$		0			0
$736$	3.49966	+	1.45550i	0.128999	+	0.0536504i
$737$	20.7474	−	28.5564i	0.764241	−	1.05189i
$738$	−15.1500	+	73.0508i	−0.557678	+	2.68904i
$739$	−27.2866	−	37.5567i	−1.00375	−	1.38155i	−0.922995	−	0.384813i	$-0.874266\pi$
$739$	−27.2866	−	37.5567i	−1.00375	−	1.38155i	−0.0807577	−	0.996734i	$-0.525734\pi$
$740$		0			0
$741$	−63.2375	+	87.0389i	−2.32309	+	3.19745i
$742$	5.77205	+	6.34706i	0.211899	+	0.233008i
$743$			43.8156i			1.60744i	0.595008	+	0.803720i	$0.297149\pi$
$743$			43.8156i			1.60744i	−0.595008	+	0.803720i	$0.702851\pi$
$744$	0.154895	+	10.4326i	0.00567873	+	0.382479i
$745$		0			0
$746$	25.2864	−	2.78429i	0.925801	−	0.101940i
$747$	−2.45027	+	7.54115i	−0.0896506	+	0.275916i
$748$	1.16215	−	12.2193i	0.0424923	−	0.446781i
$749$			6.00182i			0.219302i
$750$		0			0
$751$	0.0692442			0.00252676			0.00126338	−	0.999999i	$-0.499598\pi$
$751$	0.0692442			0.00252676			0.00126338	+	0.999999i	$0.499598\pi$
$752$	26.1491	−	24.4992i	0.953560	−	0.893393i
$753$	20.6649	+	6.71442i	0.753070	+	0.244687i
$754$	−1.18568	−	10.7681i	−0.0431799	−	0.392152i
$755$		0			0
$756$	16.5903	−	38.2775i	0.603382	−	1.39214i
$757$	17.1602			0.623700			0.311850	−	0.950131i	$-0.399051\pi$
$757$	17.1602			0.623700			0.311850	+	0.950131i	$0.399051\pi$
$758$	5.18986	+	5.70687i	0.188504	+	0.207283i
$759$	3.91725	+	2.84605i	0.142187	+	0.103305i
$760$		0			0
$761$	8.77922	−	6.37847i	0.318246	−	0.231220i	−0.417180	−	0.908824i	$-0.636982\pi$
$761$	8.77922	−	6.37847i	0.318246	−	0.231220i	0.735427	+	0.677604i	$0.236982\pi$
$762$	73.9383	+	15.3340i	2.67850	+	0.555493i
$763$	6.06686	+	4.40783i	0.219635	+	0.159574i
$764$	−0.161315	+	1.69614i	−0.00583618	+	0.0613640i
$765$		0			0
$766$	−19.2750	−	3.99743i	−0.696432	−	0.144433i
$767$	−34.4408	+	11.1905i	−1.24358	+	0.404065i
$768$	48.7049	−	12.3860i	1.75749	−	0.446943i
$769$	5.30296	+	16.3208i	0.191230	+	0.588545i	1.00000		0.000419828i	$0.000133635\pi$
$769$	5.30296	+	16.3208i	0.191230	+	0.588545i	−0.808770	+	0.588125i	$0.799866\pi$
$770$		0			0
$771$	89.0459	+	28.9328i	3.20691	+	1.04199i
$772$	−18.4958	+	10.9240i	−0.665677	+	0.393164i
$773$	−29.9036	+	21.7262i	−1.07556	+	0.781437i	−0.976903	−	0.213685i	$-0.931454\pi$
$773$	−29.9036	+	21.7262i	−1.07556	+	0.781437i	−0.0986535	+	0.995122i	$0.531454\pi$
$774$	−14.9895	−	33.2236i	−0.538788	−	1.19420i
$775$		0			0
$776$	12.6612	−	41.0300i	0.454511	−	1.47289i
$777$	11.5791	+	15.9372i	0.415398	+	0.571746i
$778$	5.72040	+	51.9516i	0.205086	+	1.86255i
$779$	42.1161	+	13.6843i	1.50896	+	0.490292i
$780$		0			0
$781$	−13.6438	+	4.43314i	−0.488214	+	0.158630i
$782$	−1.03949	−	2.30398i	−0.0371721	−	0.0823903i
$783$	14.8829	−	4.83576i	0.531873	−	0.172816i
$784$	−7.81779	+	14.1819i	−0.279207	+	0.506496i
$785$		0			0
$786$	13.2340	−	23.1862i	0.472041	−	0.827023i
$787$	−19.5842	−	14.2288i	−0.698102	−	0.507201i	0.181212	−	0.983444i	$-0.441998\pi$
$787$	−19.5842	−	14.2288i	−0.698102	−	0.507201i	−0.879313	+	0.476244i	$0.841998\pi$
$788$	−44.1489	+	9.84182i	−1.57274	+	0.350600i
$789$	48.8646	+	67.2564i	1.73963	+	2.39439i
$790$		0			0
$791$	−2.11843	−	1.53913i	−0.0753225	−	0.0547250i
$792$	44.6726	−	0.663261i	1.58737	−	0.0235680i
$793$		−	5.48182i		−	0.194665i
$794$	−24.8006	+	22.5538i	−0.880142	+	0.800405i
$795$		0			0
$796$	0.718850	+	1.21710i	0.0254790	+	0.0431391i
$797$	−0.311905	+	0.959946i	−0.0110483	+	0.0340030i	−0.956429	−	0.291966i	$-0.905691\pi$
$797$	−0.311905	+	0.959946i	−0.0110483	+	0.0340030i	0.945380	+	0.325969i	$0.105691\pi$
$798$	−38.1967	−	21.8016i	−1.35215	−	0.771767i
$799$	−23.8959			−0.845375
$800$		0			0
$801$	−28.4221			−1.00425
$802$	1.08249	+	0.617851i	0.0382239	+	0.0218171i
$803$	−3.80287	+	11.7040i	−0.134200	+	0.413027i
$804$	−49.0116	−	82.9829i	−1.72851	−	2.92658i
$805$		0			0
$806$	7.30317	−	6.64154i	0.257243	−	0.233938i
$807$		−	25.2322i		−	0.888217i
$808$	38.8934	−	0.577458i	1.36827	−	0.0203149i
$809$	−14.0834	−	10.2322i	−0.495147	−	0.359745i	0.312013	−	0.950078i	$-0.398997\pi$
$809$	−14.0834	−	10.2322i	−0.495147	−	0.359745i	−0.807160	+	0.590332i	$0.798997\pi$
$810$		0			0
$811$	4.13632	+	5.69316i	0.145246	+	0.199914i	0.875441	−	0.483325i	$-0.160571\pi$
$811$	4.13632	+	5.69316i	0.145246	+	0.199914i	−0.730195	+	0.683238i	$0.760571\pi$
$812$	4.32246	−	0.963577i	0.151689	−	0.0338149i
$813$	23.6684	+	17.1961i	0.830086	+	0.603093i
$814$	−5.88819	+	10.3162i	−0.206381	+	0.361583i
$815$		0			0
$816$	−29.3498	−	16.1791i	−1.02745	−	0.566383i
$817$	−20.5759	+	6.68551i	−0.719859	+	0.233896i
$818$	−20.8274	−	46.1629i	−0.728212	−	1.61405i
$819$	−66.6709	+	21.6627i	−2.32967	+	0.756956i
$820$		0			0
$821$	24.4826	+	7.95489i	0.854450	+	0.277628i	0.703309	−	0.710884i	$-0.251705\pi$
$821$	24.4826	+	7.95489i	0.854450	+	0.277628i	0.151141	+	0.988512i	$0.451705\pi$
$822$	−2.01305	−	18.2822i	−0.0702134	−	0.637664i
$823$	−24.5580	−	33.8012i	−0.856038	−	1.17823i	−0.982500	−	0.186264i	$-0.940362\pi$
$823$	−24.5580	−	33.8012i	−0.856038	−	1.17823i	0.126462	−	0.991971i	$-0.459638\pi$
$824$	−7.30315	+	23.6667i	−0.254417	+	0.824467i
$825$		0			0
$826$	−6.08809	−	13.4940i	−0.211832	−	0.469515i
$827$	−21.0719	+	15.3096i	−0.732741	+	0.532368i	−0.890429	−	0.455121i	$-0.849596\pi$
$827$	−21.0719	+	15.3096i	−0.732741	+	0.532368i	0.157688	+	0.987489i	$0.449596\pi$
$828$	7.92174	−	4.67876i	0.275299	−	0.162598i
$829$	−3.94736	−	1.28257i	−0.137097	−	0.0445457i	0.239665	−	0.970856i	$-0.422963\pi$
$829$	−3.94736	−	1.28257i	−0.137097	−	0.0445457i	−0.376762	+	0.926310i	$0.622963\pi$
$830$		0			0
$831$	−3.66128	−	11.2683i	−0.127008	−	0.390892i
$832$	−39.2790	−	26.7931i	−1.36175	−	0.928882i
$833$	10.2707	−	3.33717i	0.355860	−	0.115626i
$834$	−43.7901	−	9.08161i	−1.51633	−	0.314470i
$835$		0			0
$836$	2.51085	−	26.4001i	0.0868396	−	0.913067i
$837$	11.5363	+	8.38160i	0.398752	+	0.289710i
$838$	26.3639	+	5.46759i	0.910724	+	0.188875i
$839$	−31.5974	+	22.9568i	−1.09086	+	0.792557i	−0.979545	−	0.201227i	$-0.935507\pi$
$839$	−31.5974	+	22.9568i	−1.09086	+	0.792557i	−0.111317	+	0.993785i	$0.535507\pi$
$840$		0			0
$841$	−22.1176	−	16.0693i	−0.762674	−	0.554115i
$842$	−8.42855	−	9.26820i	−0.290467	−	0.319403i
$843$	67.3294			2.31895
$844$	−14.6007	+	33.6870i	−0.502576	+	1.15956i
$845$		0			0
$846$	−9.51966	−	86.4557i	−0.327293	−	2.97241i
$847$	−9.32406	−	3.02957i	−0.320378	−	0.104097i
$848$	9.65690	+	10.3073i	0.331619	+	0.353953i
$849$	−2.90815			−0.0998075
$850$		0			0
$851$			2.44606i			0.0838498i
$852$	−3.70861	+	38.9939i	−0.127055	+	1.33591i
$853$	3.09392	−	9.52211i	0.105934	−	0.326031i	−0.884015	−	0.467459i	$-0.845169\pi$
$853$	3.09392	−	9.52211i	0.105934	−	0.326031i	0.989948	+	0.141428i	$0.0451695\pi$
$854$	2.22748	−	0.245268i	0.0762227	−	0.00839290i
$855$		0			0
$856$	0.146690	+	9.88002i	0.00501378	+	0.337692i
$857$		−	31.6591i		−	1.08146i	−0.841198	−	0.540728i	$-0.818149\pi$
$857$		−	31.6591i		−	1.08146i	0.841198	−	0.540728i	$-0.181851\pi$
$858$	−40.8660	−	44.9370i	−1.39514	−	1.53412i
$859$	10.6822	−	14.7028i	0.364473	−	0.501654i	−0.586915	−	0.809649i	$-0.699658\pi$
$859$	10.6822	−	14.7028i	0.364473	−	0.501654i	0.951388	+	0.307994i	$0.0996577\pi$
$860$		0			0
$861$	24.3714	+	33.5444i	0.830575	+	1.14319i
$862$	0.888977	−	4.28651i	0.0302787	−	0.145999i
$863$	−1.06034	+	1.45943i	−0.0360944	+	0.0496797i	−0.826683	−	0.562668i	$-0.809775\pi$
$863$	−1.06034	+	1.45943i	−0.0360944	+	0.0496797i	0.790588	+	0.612348i	$0.209775\pi$
$864$	26.3749	−	63.4167i	0.897291	−	2.15748i
$865$		0			0
$866$	12.6295	+	2.61923i	0.429169	+	0.0890052i
$867$	−9.59395	−	29.5271i	−0.325828	−	1.00279i
$868$	3.02548	+	2.67041i	0.102691	+	0.0906395i
$869$	0.889568	−	0.289038i	0.0301765	−	0.00980495i
$870$		0			0
$871$	−28.1768	+	86.7193i	−0.954735	+	2.93837i
$872$	10.0948	+	7.10776i	0.341853	+	0.240699i
$873$	−61.2636	−	84.3221i	−2.07346	−	2.85387i
$874$	−2.24585	−	4.97782i	−0.0759671	−	0.168377i
$875$		0			0
$876$	25.1917	+	22.2352i	0.851149	+	0.751258i
$877$	25.8054	−	18.7487i	0.871387	−	0.633100i	−0.0595719	−	0.998224i	$-0.518974\pi$
$877$	25.8054	−	18.7487i	0.871387	−	0.633100i	0.930959	+	0.365124i	$0.118974\pi$
$878$	−54.0308	+	5.94935i	−1.82345	+	0.200781i
$879$	12.9645	−	39.9007i	0.437282	−	1.34582i
$880$		0			0
$881$	5.46376	+	16.8157i	0.184079	+	0.566536i	0.999931	−	0.0117237i	$-0.00373186\pi$
$881$	5.46376	+	16.8157i	0.184079	+	0.566536i	−0.815852	+	0.578260i	$0.803732\pi$
$882$	16.1656	+	35.8303i	0.544324	+	1.20647i
$883$	3.19347	+	9.82850i	0.107469	+	0.330755i	0.990302	−	0.138932i	$-0.0443668\pi$
$883$	3.19347	+	9.82850i	0.107469	+	0.330755i	−0.882833	+	0.469687i	$0.844367\pi$
$884$	6.89904	+	30.9481i	0.232040	+	1.04090i
$885$		0			0
$886$	−41.5404	−	23.7101i	−1.39558	−	0.796555i
$887$	−18.9891	+	26.1362i	−0.637591	+	0.877568i	−0.998484	−	0.0550388i	$-0.982472\pi$
$887$	−18.9891	+	26.1362i	−0.637591	+	0.877568i	0.360894	+	0.932607i	$0.382472\pi$
$888$	19.4507	+	25.9524i	0.652722	+	0.870906i
$889$	23.6275	−	17.1664i	0.792442	−	0.575742i
$890$		0			0
$891$	23.7190	−	32.6464i	0.794615	−	1.09369i
$892$	−6.10429	+	14.0840i	−0.204387	+	0.471566i
$893$	−51.6277			−1.72766
$894$	40.9286	+	45.0059i	1.36886	+	1.50522i
$895$		0			0
$896$	9.12964	−	17.1594i	0.305000	−	0.573254i
$897$	−11.8958	−	3.86518i	−0.397189	−	0.129055i
$898$	−14.4310	−	8.23678i	−0.481568	−	0.274865i
$899$			1.51372i			0.0504854i
$900$		0			0
$901$		−	9.41910i		−	0.313796i
$902$	−12.3933	+	21.7133i	−0.412652	+	0.722974i
$903$	−19.2654	−	6.25972i	−0.641113	−	0.208310i
$904$	−3.52490	−	2.48189i	−0.117237	−	0.0825463i
$905$		0			0
$906$	−39.7399	+	36.1397i	−1.32027	+	1.20066i
$907$	38.2694			1.27071			0.635357	−	0.772219i	$-0.280853\pi$
$907$	38.2694			1.27071			0.635357	+	0.772219i	$0.280853\pi$
$908$	21.4991	+	9.31817i	0.713474	+	0.309234i
$909$	55.4975	−	76.3858i	1.84074	−	2.53356i
$910$		0			0
$911$	−39.1122	+	28.4167i	−1.29584	+	0.941486i	−0.999906	−	0.0137212i	$-0.995632\pi$
$911$	−39.1122	+	28.4167i	−1.29584	+	0.941486i	−0.295938	+	0.955207i	$0.595632\pi$
$912$	−63.4111	−	34.9555i	−2.09975	−	1.15749i
$913$	−1.56186	+	2.14972i	−0.0516901	+	0.0711453i
$914$	8.77221	−	15.3691i	0.290159	−	0.508363i
$915$		0			0
$916$	−11.7305	−	52.6214i	−0.387588	−	1.73866i
$917$	−3.19076	−	9.82014i	−0.105368	−	0.324290i
$918$	−41.7501	+	18.8364i	−1.37796	+	0.621695i
$919$	−2.97260	−	9.14872i	−0.0980570	−	0.301788i	0.889981	−	0.455997i	$-0.150717\pi$
$919$	−2.97260	−	9.14872i	−0.0980570	−	0.301788i	−0.988038	+	0.154209i	$0.950717\pi$
$920$		0			0
$921$	13.7613	−	42.3531i	0.453452	−	1.39558i
$922$	−1.90848	−	17.3324i	−0.0628523	−	0.570813i
$923$	29.9813	−	21.7827i	0.986847	−	0.716986i
$924$	16.4312	−	18.6160i	0.540548	−	0.612422i
$925$		0			0
$926$	−21.3134	+	9.61601i	−0.700403	+	0.316002i
$927$	35.3377	+	48.6381i	1.16064	+	1.59749i
$928$	7.09195	−	1.69186i	0.232805	−	0.0555379i
$929$	5.02685	−	15.4710i	0.164926	−	0.507589i	−0.834105	−	0.551605i	$-0.814015\pi$
$929$	5.02685	−	15.4710i	0.164926	−	0.507589i	0.999031	+	0.0440168i	$0.0140155\pi$
$930$		0			0
$931$	22.1902	−	7.21004i	0.727255	−	0.236300i
$932$	−20.8997	−	18.4469i	−0.684593	−	0.604249i
$933$	0.464221	+	1.42872i	0.0151979	+	0.0467743i
$934$	4.61722	−	22.2635i	0.151080	−	0.728483i
$935$		0			0
$936$	−109.222	+	37.2900i	−3.57004	+	1.21886i
$937$	−2.13418	+	2.93745i	−0.0697207	+	0.0959623i	−0.842453	−	0.538769i	$-0.818889\pi$
$937$	−2.13418	+	2.93745i	−0.0697207	+	0.0959623i	0.772733	+	0.634732i	$0.218889\pi$
$938$	−36.4981	−	7.56934i	−1.19171	−	0.247148i
$939$	20.9721	+	28.8657i	0.684400	+	0.941996i
$940$		0			0
$941$	−23.9722	+	32.9948i	−0.781470	+	1.07560i	0.213648	+	0.976911i	$0.431465\pi$
$941$	−23.9722	+	32.9948i	−0.781470	+	1.07560i	−0.995118	+	0.0986904i	$0.968535\pi$
$942$	41.4238	−	37.6710i	1.34966	−	1.22739i
$943$			5.14841i			0.167655i
$944$	−10.3518	−	22.0645i	−0.336923	−	0.718140i
$945$		0			0
$946$	−1.33685	−	12.1410i	−0.0434648	−	0.394739i
$947$	7.79156	−	23.9800i	0.253192	−	0.779244i	−0.740989	−	0.671517i	$-0.765643\pi$
$947$	7.79156	−	23.9800i	0.253192	−	0.779244i	0.994181	−	0.107727i	$-0.0343572\pi$
$948$	0.241799	−	2.54238i	0.00785328	−	0.0825726i
$949$		−	31.7902i		−	1.03195i
$950$		0			0
$951$	43.4193			1.40797
$952$	−12.2667	+	4.18803i	−0.397567	+	0.135735i
$953$	−22.2071	−	7.21551i	−0.719357	−	0.233733i	−0.0736128	−	0.997287i	$-0.523453\pi$
$953$	−22.2071	−	7.21551i	−0.719357	−	0.233733i	−0.645745	+	0.763554i	$0.723453\pi$
$954$	34.0785	−	3.75239i	1.10333	−	0.121488i
$955$		0			0
$956$	17.5524	+	7.60757i	0.567685	+	0.246047i
$957$	9.31405			0.301081
$958$	22.5295	−	20.4885i	0.727897	−	0.661953i
$959$	−5.75505	−	4.18129i	−0.185840	−	0.135021i
$960$		0			0
$961$	23.9636	−	17.4106i	0.773020	−	0.561632i
$962$	6.23106	−	30.0452i	0.200898	−	0.968696i
$963$	19.4041	+	14.0979i	0.625289	+	0.454299i
$964$	−4.76225	+	50.0722i	−0.153382	+	1.61272i
$965$		0			0
$966$	1.03833	−	5.00666i	0.0334077	−	0.161087i
$967$	23.8786	−	7.75862i	0.767883	−	0.249500i	0.101225	−	0.994864i	$-0.467724\pi$
$967$	23.8786	−	7.75862i	0.767883	−	0.249500i	0.666659	+	0.745363i	$0.267724\pi$
$968$	−15.4230	−	4.75930i	−0.495715	−	0.152970i
$969$	14.9214	+	45.9233i	0.479344	+	1.47527i
$970$		0			0
$971$	9.54087	+	3.10002i	0.306181	+	0.0994843i	0.458078	−	0.888912i	$-0.348538\pi$
$971$	9.54087	+	3.10002i	0.306181	+	0.0994843i	−0.151897	+	0.988396i	$0.548538\pi$
$972$	−18.9842	−	32.1426i	−0.608917	−	1.03097i
$973$	−13.9934	+	10.1668i	−0.448609	+	0.325934i
$974$	34.4881	−	15.5600i	1.10507	−	0.498576i
$975$		0			0
$976$	3.66081	−	0.458195i	0.117180	−	0.0146665i
$977$	−12.8529	−	17.6906i	−0.411202	−	0.565971i	0.552309	−	0.833640i	$-0.313747\pi$
$977$	−12.8529	−	17.6906i	−0.411202	−	0.565971i	−0.963511	+	0.267668i	$0.913747\pi$
$978$	52.1496	−	5.74220i	1.66756	−	0.183615i
$979$	−9.05848	−	2.94328i	−0.289510	−	0.0940676i
$980$		0			0
$981$	28.5014	−	9.26065i	0.909978	−	0.295670i
$982$	0.420147	−	0.189558i	0.0134074	−	0.00604905i
$983$	17.7241	−	5.75890i	0.565311	−	0.183681i	−0.0123987	−	0.999923i	$-0.503947\pi$
$983$	17.7241	−	5.75890i	0.565311	−	0.183681i	0.577709	+	0.816243i	$0.303947\pi$
$984$	40.9393	+	54.6240i	1.30510	+	1.74135i
$985$		0			0
$986$	−4.22272	−	2.41021i	−0.134479	−	0.0767566i
$987$	−39.1076	−	28.4133i	−1.24481	−	0.904406i
$988$	14.9056	+	66.8642i	0.474210	+	2.12723i
$989$	−1.47843	−	2.03489i	−0.0470115	−	0.0647058i
$990$		0			0
$991$	29.3074	+	21.2931i	0.930981	+	0.676398i	0.946233	−	0.323486i	$-0.104855\pi$
$991$	29.3074	+	21.2931i	0.930981	+	0.676398i	−0.0152515	+	0.999884i	$0.504855\pi$
$992$	5.04571	+	4.32200i	0.160202	+	0.137224i
$993$			21.2292i			0.673688i
$994$	10.1926	+	11.2080i	0.323289	+	0.355495i
$995$		0			0
$996$	3.68958	+	6.24693i	0.116909	+	0.197942i
$997$	5.62136	−	17.3008i	0.178030	−	0.547921i	−0.821729	−	0.569879i	$-0.806990\pi$
$997$	5.62136	−	17.3008i	0.178030	−	0.547921i	0.999759	+	0.0219581i	$0.00699003\pi$
$998$	16.2785	−	28.5202i	0.515286	−	0.902791i
$999$	44.3246			1.40237

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1000.2.o.a.949.5		112
5.2	odd	4		1000.2.t.b.301.38		224
5.3	odd	4		1000.2.t.b.301.19		224
5.4	even	2		200.2.o.a.189.24	yes	112
8.5	even	2	inner	1000.2.o.a.949.12		112
20.19	odd	2		800.2.be.a.689.1		112
25.9	even	10	inner	1000.2.o.a.549.12		112
25.12	odd	20		1000.2.t.b.701.53		224
25.13	odd	20		1000.2.t.b.701.4		224
25.16	even	5		200.2.o.a.109.17	✓	112
40.13	odd	4		1000.2.t.b.301.4		224
40.19	odd	2		800.2.be.a.689.28		112
40.29	even	2		200.2.o.a.189.17	yes	112
40.37	odd	4		1000.2.t.b.301.53		224
100.91	odd	10		800.2.be.a.209.28		112
200.13	odd	20		1000.2.t.b.701.19		224
200.37	odd	20		1000.2.t.b.701.38		224
200.91	odd	10		800.2.be.a.209.1		112
200.109	even	10	inner	1000.2.o.a.549.5		112
200.141	even	10		200.2.o.a.109.24	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
200.2.o.a.109.17	✓	112	25.16	even	5
200.2.o.a.109.24	yes	112	200.141	even	10
200.2.o.a.189.17	yes	112	40.29	even	2
200.2.o.a.189.24	yes	112	5.4	even	2
800.2.be.a.209.1		112	200.91	odd	10
800.2.be.a.209.28		112	100.91	odd	10
800.2.be.a.689.1		112	20.19	odd	2
800.2.be.a.689.28		112	40.19	odd	2
1000.2.o.a.549.5		112	200.109	even	10	inner
1000.2.o.a.549.12		112	25.9	even	10	inner
1000.2.o.a.949.5		112	1.1	even	1	trivial
1000.2.o.a.949.12		112	8.5	even	2	inner
1000.2.t.b.301.4		224	40.13	odd	4
1000.2.t.b.301.19		224	5.3	odd	4
1000.2.t.b.301.38		224	5.2	odd	4
1000.2.t.b.301.53		224	40.37	odd	4
1000.2.t.b.701.4		224	25.13	odd	20
1000.2.t.b.701.19		224	200.13	odd	20
1000.2.t.b.701.38		224	200.37	odd	20
1000.2.t.b.701.53		224	25.12	odd	20

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:	\( N \)	\(=\)	\( 1000 = 2^{3} \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1000.o (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.22823 - 0.701037i) q^{2} +(-0.970606 + 2.98722i) q^{3} +(1.01709 + 1.72207i) q^{4} +(3.28628 - 2.98856i) q^{6} -1.71800i q^{7} +(-0.0419895 - 2.82812i) q^{8} +(-5.55435 - 4.03547i) q^{9} +(-1.35234 - 1.86134i) q^{11} +(-6.13139 + 1.36683i) q^{12} +(4.80828 + 3.49342i) q^{13} +(-1.20438 + 2.11009i) q^{14} +(-1.93104 + 3.50301i) q^{16} +(2.53693 - 0.824300i) q^{17} +(3.99300 + 8.85029i) q^{18} +(5.48112 - 1.78092i) q^{19} +(5.13203 + 1.66750i) q^{21} +(0.356118 + 3.23419i) q^{22} +(0.393834 + 0.542066i) q^{23} +(8.48896 + 2.61955i) q^{24} +(-3.45665 - 7.66150i) q^{26} +(9.82268 - 7.13660i) q^{27} +(2.95851 - 1.74736i) q^{28} +(1.22579 + 0.398283i) q^{29} +(0.362926 + 1.11697i) q^{31} +(4.82750 - 2.94877i) q^{32} +(6.87282 - 2.23312i) q^{33} +(-3.69380 - 0.766057i) q^{34} +(1.30007 - 13.6694i) q^{36} +(2.95345 + 2.14581i) q^{37} +(-7.98057 - 1.65509i) q^{38} +(-15.1026 + 10.9726i) q^{39} +(6.21636 + 4.51645i) q^{41} +(-5.13434 - 5.64582i) q^{42} -3.75396 q^{43} +(1.82990 - 4.22198i) q^{44} +(-0.103710 - 0.941873i) q^{46} +(-8.51974 - 2.76823i) q^{47} +(-8.58998 - 9.16849i) q^{48} +4.04848 q^{49} +8.37845i q^{51} +(-1.12544 + 11.8333i) q^{52} +(1.09116 - 3.35825i) q^{53} +(-17.0675 + 1.87931i) q^{54} +(-4.85870 + 0.0721379i) q^{56} +18.1019i q^{57} +(-1.22634 - 1.34851i) q^{58} +(-3.58141 + 4.92938i) q^{59} +(-0.542140 - 0.746192i) q^{61} +(0.337282 - 1.62632i) q^{62} +(-6.93293 + 9.54236i) q^{63} +(-7.99647 + 0.237503i) q^{64} +(-10.0069 - 2.07533i) q^{66} +(4.74089 + 14.5910i) q^{67} +(3.99980 + 3.53039i) q^{68} +(-2.00153 + 0.650336i) q^{69} +(1.92683 - 5.93017i) q^{71} +(-11.1796 + 15.8778i) q^{72} +(-3.14398 - 4.32732i) q^{73} +(-2.12322 - 4.70603i) q^{74} +(8.64169 + 7.62750i) q^{76} +(-3.19778 + 2.32332i) q^{77} +(26.2416 - 2.88947i) q^{78} +(-0.125628 + 0.386644i) q^{79} +(5.41990 + 16.6807i) q^{81} +(-4.46891 - 9.90513i) q^{82} +(-0.356893 - 1.09840i) q^{83} +(2.34821 + 10.5337i) q^{84} +(4.61072 + 2.63166i) q^{86} +(-2.37952 + 3.27513i) q^{87} +(-5.20730 + 3.90274i) q^{88} +(3.34918 - 2.43332i) q^{89} +(6.00168 - 8.26061i) q^{91} +(-0.532909 + 1.22954i) q^{92} -3.68890 q^{93} +(8.52356 + 9.37268i) q^{94} +(4.12301 + 17.2829i) q^{96} +(14.4383 + 4.69127i) q^{97} +(-4.97247 - 2.83814i) q^{98} +15.7959i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 5 q^{2} - 3 q^{4} + q^{6} - 10 q^{8} - 30 q^{9} + 5 q^{12} - 3 q^{14} - 15 q^{16} + 10 q^{17} + 30 q^{22} + 10 q^{23} - 16 q^{24} - 14 q^{26} - 15 q^{28} - 18 q^{31} + 10 q^{33} + 9 q^{34} + 41 q^{36}+ \cdots - 90 q^{98}+O(q^{100}) \) 112 * q + 5 * q^2 - 3 * q^4 + q^6 - 10 * q^8 - 30 * q^9 + 5 * q^12 - 3 * q^14 - 15 * q^16 + 10 * q^17 + 30 * q^22 + 10 * q^23 - 16 * q^24 - 14 * q^26 - 15 * q^28 - 18 * q^31 + 10 * q^33 + 9 * q^34 + 41 * q^36 - 45 * q^38 - 10 * q^39 - 10 * q^41 - 75 * q^42 - 32 * q^44 + 13 * q^46 + 10 * q^47 + 70 * q^48 - 80 * q^49 + 100 * q^52 + 43 * q^54 + 36 * q^56 + 30 * q^58 - 20 * q^62 - 60 * q^63 - 36 * q^64 + 40 * q^66 + 22 * q^71 + 65 * q^72 + 10 * q^73 + 4 * q^74 - 36 * q^76 + 55 * q^78 + 14 * q^79 - 6 * q^81 + 78 * q^84 - 59 * q^86 + 10 * q^87 - 110 * q^88 + 24 * q^89 - 90 * q^92 + 45 * q^94 + 46 * q^96 + 50 * q^97 - 90 * q^98

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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