LMFDB - Embedded newform 930.2.j.h.683.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [930,2,Mod(497,930)] 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("930.497"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(930, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.j (of order $4$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [40,0,-4,0,0,8,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			683.11
Character	$\chi$	$=$	930.683
Dual form			930.2.j.h.497.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.707107 + 0.707107i) q^{2} +(-1.72927 + 0.0980849i) q^{3} +1.00000i q^{4} +(0.278761 + 2.21862i) q^{5} +(-1.29214 - 1.15342i) q^{6} +(-1.59354 + 1.59354i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98076 - 0.339231i) q^{9} +(-1.37169 + 1.76592i) q^{10} +3.70376i q^{11} +(-0.0980849 - 1.72927i) q^{12} +(-1.02541 - 1.02541i) q^{13} -2.25360 q^{14} +(-0.699666 - 3.80926i) q^{15} -1.00000 q^{16} +(-0.479745 - 0.479745i) q^{17} +(2.34759 + 1.86784i) q^{18} +0.296019i q^{19} +(-2.21862 + 0.278761i) q^{20} +(2.59936 - 2.91196i) q^{21} +(-2.61895 + 2.61895i) q^{22} +(1.49449 - 1.49449i) q^{23} +(1.15342 - 1.29214i) q^{24} +(-4.84458 + 1.23693i) q^{25} -1.45015i q^{26} +(-5.12127 + 0.878989i) q^{27} +(-1.59354 - 1.59354i) q^{28} +1.30186 q^{29} +(2.19882 - 3.18829i) q^{30} -1.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.363282 - 6.40480i) q^{33} -0.678461i q^{34} +(-3.97967 - 3.09124i) q^{35} +(0.339231 + 2.98076i) q^{36} +(-2.24098 + 2.24098i) q^{37} +(-0.209317 + 0.209317i) q^{38} +(1.87380 + 1.67264i) q^{39} +(-1.76592 - 1.37169i) q^{40} -5.01872i q^{41} +(3.89709 - 0.221044i) q^{42} +(-7.37080 - 7.37080i) q^{43} -3.70376 q^{44} +(1.58354 + 6.51862i) q^{45} +2.11353 q^{46} +(0.230740 + 0.230740i) q^{47} +(1.72927 - 0.0980849i) q^{48} +1.92128i q^{49} +(-4.30028 - 2.55100i) q^{50} +(0.876664 + 0.782553i) q^{51} +(1.02541 - 1.02541i) q^{52} +(0.282801 - 0.282801i) q^{53} +(-4.24282 - 2.99974i) q^{54} +(-8.21724 + 1.03246i) q^{55} -2.25360i q^{56} +(-0.0290350 - 0.511898i) q^{57} +(0.920553 + 0.920553i) q^{58} -12.3141 q^{59} +(3.80926 - 0.699666i) q^{60} +11.1031 q^{61} +(-0.707107 - 0.707107i) q^{62} +(-4.20937 + 5.29053i) q^{63} -1.00000i q^{64} +(1.98916 - 2.56085i) q^{65} +(4.27200 - 4.78576i) q^{66} +(-9.42240 + 9.42240i) q^{67} +(0.479745 - 0.479745i) q^{68} +(-2.43779 + 2.73097i) q^{69} +(-0.628216 - 4.99989i) q^{70} +6.43406i q^{71} +(-1.86784 + 2.34759i) q^{72} +(-5.91592 - 5.91592i) q^{73} -3.16922 q^{74} +(8.25628 - 2.61417i) q^{75} -0.296019 q^{76} +(-5.90207 - 5.90207i) q^{77} +(0.142238 + 2.50771i) q^{78} +3.56575i q^{79} +(-0.278761 - 2.21862i) q^{80} +(8.76985 - 2.02233i) q^{81} +(3.54877 - 3.54877i) q^{82} +(1.95472 - 1.95472i) q^{83} +(2.91196 + 2.59936i) q^{84} +(0.930639 - 1.19811i) q^{85} -10.4239i q^{86} +(-2.25127 + 0.127693i) q^{87} +(-2.61895 - 2.61895i) q^{88} +10.7601 q^{89} +(-3.48962 + 5.72909i) q^{90} +3.26807 q^{91} +(1.49449 + 1.49449i) q^{92} +(1.72927 - 0.0980849i) q^{93} +0.326316i q^{94} +(-0.656756 + 0.0825186i) q^{95} +(1.29214 + 1.15342i) q^{96} +(5.06700 - 5.06700i) q^{97} +(-1.35855 + 1.35855i) q^{98} +(1.25643 + 11.0400i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) $ 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

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 $

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$	−1.72927	+	0.0980849i	−0.998395	+	0.0566293i
$3$	−1.72927	+	0.0980849i	−0.998395	+	0.0566293i
$4$			1.00000i			0.500000i
$5$	0.278761	+	2.21862i	0.124666	+	0.992199i
$5$	0.278761	+	2.21862i	0.124666	+	0.992199i
$6$	−1.29214	−	1.15342i	−0.527512	−	0.470883i
$7$	−1.59354	+	1.59354i	−0.602300	+	0.602300i	−0.940922	−	0.338622i	$-0.890039\pi$
$7$	−1.59354	+	1.59354i	−0.602300	+	0.602300i	0.338622	+	0.940922i	$0.390039\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.98076	−	0.339231i	0.993586	−	0.113077i
$10$	−1.37169	+	1.76592i	−0.433767	+	0.558432i
$11$			3.70376i			1.11672i	0.829597	+	0.558362i	$0.188570\pi$
$11$			3.70376i			1.11672i	−0.829597	+	0.558362i	$0.811430\pi$
$12$	−0.0980849	−	1.72927i	−0.0283147	−	0.499198i
$13$	−1.02541	−	1.02541i	−0.284399	−	0.284399i	0.550462	−	0.834860i	$-0.314452\pi$
$13$	−1.02541	−	1.02541i	−0.284399	−	0.284399i	−0.834860	+	0.550462i	$0.814452\pi$
$14$	−2.25360			−0.602300
$15$	−0.699666	−	3.80926i	−0.180653	−	0.983547i
$16$	−1.00000			−0.250000
$17$	−0.479745	−	0.479745i	−0.116355	−	0.116355i	0.646532	−	0.762887i	$-0.276219\pi$
$17$	−0.479745	−	0.479745i	−0.116355	−	0.116355i	−0.762887	+	0.646532i	$0.776219\pi$
$18$	2.34759	+	1.86784i	0.553332	+	0.440255i
$19$			0.296019i			0.0679115i	0.999423	+	0.0339558i	$0.0108105\pi$
$19$			0.296019i			0.0679115i	−0.999423	+	0.0339558i	$0.989189\pi$
$20$	−2.21862	+	0.278761i	−0.496099	+	0.0623328i
$21$	2.59936	−	2.91196i	0.567226	−	0.635442i
$22$	−2.61895	+	2.61895i	−0.558362	+	0.558362i
$23$	1.49449	−	1.49449i	0.311623	−	0.311623i	−0.533915	−	0.845538i	$-0.679280\pi$
$23$	1.49449	−	1.49449i	0.311623	−	0.311623i	0.845538	+	0.533915i	$0.179280\pi$
$24$	1.15342	−	1.29214i	0.235441	−	0.263756i
$25$	−4.84458	+	1.23693i	−0.968917	+	0.247386i
$26$		−	1.45015i		−	0.284399i
$27$	−5.12127	+	0.878989i	−0.985588	+	0.169162i
$28$	−1.59354	−	1.59354i	−0.301150	−	0.301150i
$29$	1.30186			0.241749			0.120875	−	0.992668i	$-0.461430\pi$
$29$	1.30186			0.241749			0.120875	+	0.992668i	$0.461430\pi$
$30$	2.19882	−	3.18829i	0.401447	−	0.582100i
$31$	−1.00000			−0.179605
$31$	−1.00000			−0.179605
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$	−0.363282	−	6.40480i	−0.0632393	−	1.11493i
$34$		−	0.678461i		−	0.116355i
$35$	−3.97967	−	3.09124i	−0.672688	−	0.522516i
$36$	0.339231	+	2.98076i	0.0565384	+	0.496793i
$37$	−2.24098	+	2.24098i	−0.368414	+	0.368414i	−0.866899	−	0.498484i	$-0.833890\pi$
$37$	−2.24098	+	2.24098i	−0.368414	+	0.368414i	0.498484	+	0.866899i	$0.333890\pi$
$38$	−0.209317	+	0.209317i	−0.0339558	+	0.0339558i
$39$	1.87380	+	1.67264i	0.300047	+	0.267837i
$40$	−1.76592	−	1.37169i	−0.279216	−	0.216883i
$41$		−	5.01872i		−	0.783792i	−0.920010	−	0.391896i	$-0.871819\pi$
$41$		−	5.01872i		−	0.783792i	0.920010	−	0.391896i	$-0.128181\pi$
$42$	3.89709	−	0.221044i	0.601334	−	0.0341079i
$43$	−7.37080	−	7.37080i	−1.12404	−	1.12404i	−0.991128	−	0.132907i	$-0.957569\pi$
$43$	−7.37080	−	7.37080i	−1.12404	−	1.12404i	−0.132907	−	0.991128i	$-0.542431\pi$
$44$	−3.70376			−0.558362
$45$	1.58354	+	6.51862i	0.236061	+	0.971738i
$46$	2.11353			0.311623
$47$	0.230740	+	0.230740i	0.0336569	+	0.0336569i	0.723735	−	0.690078i	$-0.242424\pi$
$47$	0.230740	+	0.230740i	0.0336569	+	0.0336569i	−0.690078	+	0.723735i	$0.742424\pi$
$48$	1.72927	−	0.0980849i	0.249599	−	0.0141573i
$49$			1.92128i			0.274469i
$50$	−4.30028	−	2.55100i	−0.608152	−	0.360765i
$51$	0.876664	+	0.782553i	0.122758	+	0.109579i
$52$	1.02541	−	1.02541i	0.142199	−	0.142199i
$53$	0.282801	−	0.282801i	0.0388457	−	0.0388457i	−0.687417	−	0.726263i	$-0.741256\pi$
$53$	0.282801	−	0.282801i	0.0388457	−	0.0388457i	0.726263	+	0.687417i	$0.241256\pi$
$54$	−4.24282	−	2.99974i	−0.577375	−	0.408213i
$55$	−8.21724	+	1.03246i	−1.10801	+	0.139217i
$56$		−	2.25360i		−	0.301150i
$57$	−0.0290350	−	0.511898i	−0.00384578	−	0.0678025i
$58$	0.920553	+	0.920553i	0.120875	+	0.120875i
$59$	−12.3141			−1.60316			−0.801581	−	0.597886i	$-0.796008\pi$
$59$	−12.3141			−1.60316			−0.801581	+	0.597886i	$0.796008\pi$
$60$	3.80926	−	0.699666i	0.491773	−	0.0903265i
$61$	11.1031			1.42160			0.710801	−	0.703393i	$-0.248333\pi$
$61$	11.1031			1.42160			0.710801	+	0.703393i	$0.248333\pi$
$62$	−0.707107	−	0.707107i	−0.0898027	−	0.0898027i
$63$	−4.20937	+	5.29053i	−0.530331	+	0.666544i
$64$		−	1.00000i		−	0.125000i
$65$	1.98916	−	2.56085i	0.246725	−	0.317635i
$66$	4.27200	−	4.78576i	0.525846	−	0.589086i
$67$	−9.42240	+	9.42240i	−1.15113	+	1.15113i	−0.164803	+	0.986326i	$0.552699\pi$
$67$	−9.42240	+	9.42240i	−1.15113	+	1.15113i	−0.986326	+	0.164803i	$0.947301\pi$
$68$	0.479745	−	0.479745i	0.0581776	−	0.0581776i
$69$	−2.43779	+	2.73097i	−0.293476	+	0.328770i
$70$	−0.628216	−	4.99989i	−0.0750861	−	0.597602i
$71$			6.43406i			0.763582i	0.924249	+	0.381791i	$0.124693\pi$
$71$			6.43406i			0.763582i	−0.924249	+	0.381791i	$0.875307\pi$
$72$	−1.86784	+	2.34759i	−0.220127	+	0.276666i
$73$	−5.91592	−	5.91592i	−0.692407	−	0.692407i	0.270354	−	0.962761i	$-0.412859\pi$
$73$	−5.91592	−	5.91592i	−0.692407	−	0.692407i	−0.962761	+	0.270354i	$0.912859\pi$
$74$	−3.16922			−0.368414
$75$	8.25628	−	2.61417i	0.953353	−	0.301858i
$76$	−0.296019			−0.0339558
$77$	−5.90207	−	5.90207i	−0.672603	−	0.672603i
$78$	0.142238	+	2.50771i	0.0161053	+	0.283942i
$79$			3.56575i			0.401178i	0.979675	+	0.200589i	$0.0642856\pi$
$79$			3.56575i			0.401178i	−0.979675	+	0.200589i	$0.935714\pi$
$80$	−0.278761	−	2.21862i	−0.0311664	−	0.248050i
$81$	8.76985	−	2.02233i	0.974427	−	0.224703i
$82$	3.54877	−	3.54877i	0.391896	−	0.391896i
$83$	1.95472	−	1.95472i	0.214558	−	0.214558i	−0.591642	−	0.806200i	$-0.701520\pi$
$83$	1.95472	−	1.95472i	0.214558	−	0.214558i	0.806200	+	0.591642i	$0.201520\pi$
$84$	2.91196	+	2.59936i	0.317721	+	0.283613i
$85$	0.930639	−	1.19811i	0.100942	−	0.129953i
$86$		−	10.4239i		−	1.12404i
$87$	−2.25127	+	0.127693i	−0.241361	+	0.0136901i
$88$	−2.61895	−	2.61895i	−0.279181	−	0.279181i
$89$	10.7601			1.14057			0.570283	−	0.821448i	$-0.306834\pi$
$89$	10.7601			1.14057			0.570283	+	0.821448i	$0.306834\pi$
$90$	−3.48962	+	5.72909i	−0.367839	+	0.603900i
$91$	3.26807			0.342587
$92$	1.49449	+	1.49449i	0.155811	+	0.155811i
$93$	1.72927	−	0.0980849i	0.179317	−	0.0101709i
$94$			0.326316i			0.0336569i
$95$	−0.656756	+	0.0825186i	−0.0673817	+	0.00846623i
$96$	1.29214	+	1.15342i	0.131878	+	0.117721i
$97$	5.06700	−	5.06700i	0.514476	−	0.514476i	−0.401419	−	0.915895i	$-0.631483\pi$
$97$	5.06700	−	5.06700i	0.514476	−	0.514476i	0.915895	+	0.401419i	$0.131483\pi$
$98$	−1.35855	+	1.35855i	−0.137234	+	0.137234i
$99$	1.25643	+	11.0400i	0.126276	+	1.10956i
$100$	−1.23693	−	4.84458i	−0.123693	−	0.484458i
$101$			2.21327i			0.220229i	0.993919	+	0.110115i	$0.0351218\pi$
$101$			2.21327i			0.220229i	−0.993919	+	0.110115i	$0.964878\pi$
$102$	0.0665468	+	1.17324i	0.00658911	+	0.116168i
$103$	−4.54917	−	4.54917i	−0.448243	−	0.448243i	0.446527	−	0.894770i	$-0.352661\pi$
$103$	−4.54917	−	4.54917i	−0.448243	−	0.448243i	−0.894770	+	0.446527i	$0.852661\pi$
$104$	1.45015			0.142199
$105$	7.18514	+	4.95525i	0.701198	+	0.483583i
$106$	0.399941			0.0388457
$107$	11.0754	+	11.0754i	1.07070	+	1.07070i	0.997303	+	0.0733937i	$0.0233830\pi$
$107$	11.0754	+	11.0754i	1.07070	+	1.07070i	0.0733937	+	0.997303i	$0.476617\pi$
$108$	−0.878989	−	5.12127i	−0.0845808	−	0.492794i
$109$			9.99461i			0.957310i	0.878003	+	0.478655i	$0.158875\pi$
$109$			9.99461i			0.957310i	−0.878003	+	0.478655i	$0.841125\pi$
$110$	−6.54053	−	5.08041i	−0.623615	−	0.484398i
$111$	3.65545	−	4.09506i	0.346960	−	0.388686i
$112$	1.59354	−	1.59354i	0.150575	−	0.150575i
$113$	3.56657	−	3.56657i	0.335515	−	0.335515i	−0.519161	−	0.854676i	$-0.673756\pi$
$113$	3.56657	−	3.56657i	0.335515	−	0.335515i	0.854676	+	0.519161i	$0.173756\pi$
$114$	0.341436	−	0.382497i	0.0319784	−	0.0358242i
$115$	3.73232	+	2.89911i	0.348040	+	0.270343i
$116$			1.30186i			0.120875i
$117$	−3.40436	−	2.70866i	−0.314733	−	0.250416i
$118$	−8.70740	−	8.70740i	−0.801581	−	0.801581i
$119$	1.52898			0.140162
$120$	3.18829	+	2.19882i	0.291050	+	0.200723i
$121$	−2.71780			−0.247073
$122$	7.85106	+	7.85106i	0.710801	+	0.710801i
$123$	0.492260	+	8.67872i	0.0443856	+	0.782534i
$124$		−	1.00000i		−	0.0898027i
$125$	−4.09476	−	10.4035i	−0.366247	−	0.930518i
$126$	−6.71744	+	0.764491i	−0.598437	+	0.0681063i
$127$	−6.47722	+	6.47722i	−0.574760	+	0.574760i	−0.933455	−	0.358695i	$-0.883222\pi$
$127$	−6.47722	+	6.47722i	−0.574760	+	0.574760i	0.358695	+	0.933455i	$0.383222\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$	13.4691	+	12.0231i	1.18589	+	1.05858i
$130$	3.21735	−	0.404246i	0.282180	−	0.0354547i
$131$			16.5912i			1.44958i	0.688970	+	0.724790i	$0.258063\pi$
$131$			16.5912i			1.44958i	−0.688970	+	0.724790i	$0.741937\pi$
$132$	6.40480	−	0.363282i	0.557466	−	0.0316197i
$133$	−0.471718	−	0.471718i	−0.0409031	−	0.0409031i
$134$	−13.3253			−1.15113
$135$	−3.37775	−	11.1171i	−0.290711	−	0.956811i
$136$	0.678461			0.0581776
$137$	11.5131	+	11.5131i	0.983626	+	0.983626i	0.999868	−	0.0162416i	$-0.00517010\pi$
$137$	11.5131	+	11.5131i	0.983626	+	0.983626i	−0.0162416	+	0.999868i	$0.505170\pi$
$138$	−3.65486	+	0.207305i	−0.311123	+	0.0176470i
$139$			1.69987i			0.144181i	0.997398	+	0.0720907i	$0.0229671\pi$
$139$			1.69987i			0.144181i	−0.997398	+	0.0720907i	$0.977033\pi$
$140$	3.09124	−	3.97967i	0.261258	−	0.336344i
$141$	−0.421645	−	0.376380i	−0.0355089	−	0.0316969i
$142$	−4.54956	+	4.54956i	−0.381791	+	0.381791i
$143$	3.79788	−	3.79788i	0.317595	−	0.317595i
$144$	−2.98076	+	0.339231i	−0.248397	+	0.0282692i
$145$	0.362907	+	2.88834i	0.0301378	+	0.239863i
$146$		−	8.36638i		−	0.692407i
$147$	−0.188449	−	3.32241i	−0.0155430	−	0.274028i
$148$	−2.24098	−	2.24098i	−0.184207	−	0.184207i
$149$	−11.1620			−0.914429			−0.457214	−	0.889357i	$-0.651153\pi$
$149$	−11.1620			−0.914429			−0.457214	+	0.889357i	$0.651153\pi$
$150$	7.68657	+	3.98957i	0.627606	+	0.325747i
$151$	−2.13427			−0.173684			−0.0868422	−	0.996222i	$-0.527678\pi$
$151$	−2.13427			−0.173684			−0.0868422	+	0.996222i	$0.527678\pi$
$152$	−0.209317	−	0.209317i	−0.0169779	−	0.0169779i
$153$	−1.59275	−	1.26726i	−0.128766	−	0.102452i
$154$		−	8.34679i		−	0.672603i
$155$	−0.278761	−	2.21862i	−0.0223906	−	0.178204i
$156$	−1.67264	+	1.87380i	−0.133918	+	0.150024i
$157$	−7.87504	+	7.87504i	−0.628497	+	0.628497i	−0.947690	−	0.319193i	$-0.896588\pi$
$157$	−7.87504	+	7.87504i	−0.628497	+	0.628497i	0.319193	+	0.947690i	$0.396588\pi$
$158$	−2.52136	+	2.52136i	−0.200589	+	0.200589i
$159$	−0.461301	+	0.516778i	−0.0365835	+	0.0409831i
$160$	1.37169	−	1.76592i	0.108442	−	0.139608i
$161$			4.76305i			0.375381i
$162$	7.63122	+	4.77121i	0.599565	+	0.374862i
$163$	2.27337	+	2.27337i	0.178064	+	0.178064i	0.790511	−	0.612447i	$-0.209815\pi$
$163$	2.27337	+	2.27337i	0.178064	+	0.178064i	−0.612447	+	0.790511i	$0.709815\pi$
$164$	5.01872			0.391896
$165$	14.1086	−	2.59139i	1.09835	−	0.201740i
$166$	2.76439			0.214558
$167$	8.76742	+	8.76742i	0.678444	+	0.678444i	0.959648	−	0.281204i	$-0.0907339\pi$
$167$	8.76742	+	8.76742i	0.678444	+	0.678444i	−0.281204	+	0.959648i	$0.590734\pi$
$168$	0.221044	+	3.89709i	0.0170539	+	0.300667i
$169$		−	10.8971i		−	0.838235i
$170$	1.50525	−	0.189128i	0.115447	−	0.0145055i
$171$	0.100419	+	0.882362i	0.00767922	+	0.0674759i
$172$	7.37080	−	7.37080i	0.562018	−	0.562018i
$173$	−6.46161	+	6.46161i	−0.491267	+	0.491267i	−0.908705	−	0.417438i	$-0.862928\pi$
$173$	−6.46161	+	6.46161i	−0.491267	+	0.491267i	0.417438	+	0.908705i	$0.362928\pi$
$174$	−1.68218	−	1.50159i	−0.127526	−	0.113836i
$175$	5.74893	−	9.69112i	0.434578	−	0.732580i
$176$		−	3.70376i		−	0.279181i
$177$	21.2945	−	1.20783i	1.60059	−	0.0907860i
$178$	7.60852	+	7.60852i	0.570283	+	0.570283i
$179$	18.6584			1.39459			0.697297	−	0.716782i	$-0.254386\pi$
$179$	18.6584			1.39459			0.697297	+	0.716782i	$0.254386\pi$
$180$	−6.51862	+	1.58354i	−0.485869	+	0.118030i
$181$	20.5221			1.52539			0.762697	−	0.646756i	$-0.223875\pi$
$181$	20.5221			1.52539			0.762697	+	0.646756i	$0.223875\pi$
$182$	2.31087	+	2.31087i	0.171293	+	0.171293i
$183$	−19.2002	+	1.08904i	−1.41932	+	0.0805044i
$184$			2.11353i			0.155811i
$185$	−5.59658	−	4.34719i	−0.411469	−	0.319612i
$186$	1.29214	+	1.15342i	0.0947440	+	0.0845731i
$187$	1.77686	−	1.77686i	0.129937	−	0.129937i
$188$	−0.230740	+	0.230740i	−0.0168285	+	0.0168285i
$189$	6.76023	−	9.56163i	0.491734	−	0.695506i
$190$	−0.522746	−	0.406047i	−0.0379240	−	0.0294577i
$191$			22.5879i			1.63440i	0.576351	+	0.817202i	$0.304476\pi$
$191$			22.5879i			1.63440i	−0.576351	+	0.817202i	$0.695524\pi$
$192$	0.0980849	+	1.72927i	0.00707867	+	0.124799i
$193$	7.24548	+	7.24548i	0.521541	+	0.521541i	0.918037	−	0.396496i	$-0.129774\pi$
$193$	7.24548	+	7.24548i	0.521541	+	0.521541i	−0.396496	+	0.918037i	$0.629774\pi$
$194$	7.16582			0.514476
$195$	−3.18862	+	4.62352i	−0.228342	+	0.331097i
$196$	−1.92128			−0.137234
$197$	3.23816	+	3.23816i	0.230709	+	0.230709i	0.812989	−	0.582279i	$-0.197839\pi$
$197$	3.23816	+	3.23816i	0.230709	+	0.230709i	−0.582279	+	0.812989i	$0.697839\pi$
$198$	−6.91803	+	8.69489i	−0.491643	+	0.617919i
$199$		−	17.2659i		−	1.22394i	−0.790879	−	0.611972i	$-0.790377\pi$
$199$		−	17.2659i		−	1.22394i	0.790879	−	0.611972i	$-0.209623\pi$
$200$	2.55100	−	4.30028i	0.180383	−	0.304076i
$201$	15.3697	−	17.2181i	1.08409	−	1.21447i
$202$	−1.56502	+	1.56502i	−0.110115	+	0.110115i
$203$	−2.07456	+	2.07456i	−0.145606	+	0.145606i
$204$	−0.782553	+	0.876664i	−0.0547897	+	0.0613788i
$205$	11.1346	−	1.39902i	0.777677	−	0.0977119i
$206$		−	6.43350i		−	0.448243i
$207$	3.94774	−	4.96169i	0.274387	−	0.344861i
$208$	1.02541	+	1.02541i	0.0710996	+	0.0710996i
$209$	−1.09638			−0.0758384
$210$	1.57677	+	8.58456i	0.108807	+	0.592391i
$211$	−21.7612			−1.49810			−0.749050	−	0.662513i	$-0.769490\pi$
$211$	−21.7612			−1.49810			−0.749050	+	0.662513i	$0.769490\pi$
$212$	0.282801	+	0.282801i	0.0194228	+	0.0194228i
$213$	−0.631083	−	11.1262i	−0.0432411	−	0.762357i
$214$			15.6629i			1.07070i
$215$	14.2983	−	18.4077i	0.975138	−	1.25540i
$216$	2.99974	−	4.24282i	0.204107	−	0.288687i
$217$	1.59354	−	1.59354i	0.108176	−	0.108176i
$218$	−7.06726	+	7.06726i	−0.478655	+	0.478655i
$219$	10.8105	+	9.64998i	0.730506	+	0.652085i
$220$	−1.03246	−	8.21724i	−0.0696085	−	0.554006i
$221$			0.983873i			0.0661825i
$222$	5.48044	−	0.310853i	0.367823	−	0.0208631i
$223$	−5.37150	−	5.37150i	−0.359702	−	0.359702i	0.504001	−	0.863703i	$-0.331861\pi$
$223$	−5.37150	−	5.37150i	−0.359702	−	0.359702i	−0.863703	+	0.504001i	$0.831861\pi$
$224$	2.25360			0.150575
$225$	−14.0209	+	5.33042i	−0.934729	+	0.355362i
$226$	5.04389			0.335515
$227$	12.5296	+	12.5296i	0.831620	+	0.831620i	0.987738	−	0.156118i	$-0.0498981\pi$
$227$	12.5296	+	12.5296i	0.831620	+	0.831620i	−0.156118	+	0.987738i	$0.549898\pi$
$228$	0.511898	−	0.0290350i	0.0339013	−	0.00192289i
$229$		−	7.68865i		−	0.508081i	−0.967194	−	0.254040i	$-0.918240\pi$
$229$		−	7.68865i		−	0.508081i	0.967194	−	0.254040i	$-0.0817596\pi$
$230$	0.589168	+	4.68912i	0.0388486	+	0.309192i
$231$	10.7852	+	9.62738i	0.709613	+	0.633435i
$232$	−0.920553	+	0.920553i	−0.0604373	+	0.0604373i
$233$	−6.41781	+	6.41781i	−0.420445	+	0.420445i	−0.885357	−	0.464912i	$-0.846086\pi$
$233$	−6.41781	+	6.41781i	−0.420445	+	0.420445i	0.464912	+	0.885357i	$0.346086\pi$
$234$	−0.491937	−	4.32256i	−0.0321589	−	0.282575i
$235$	−0.447604	+	0.576247i	−0.0291985	+	0.0375902i
$236$		−	12.3141i		−	0.801581i
$237$	−0.349746	−	6.16614i	−0.0227184	−	0.400534i
$238$	1.08115	+	1.08115i	0.0700808	+	0.0700808i
$239$	23.1583			1.49799			0.748994	−	0.662577i	$-0.230537\pi$
$239$	23.1583			1.49799			0.748994	+	0.662577i	$0.230537\pi$
$240$	0.699666	+	3.80926i	0.0451633	+	0.245887i
$241$	−24.6719			−1.58926			−0.794628	−	0.607097i	$-0.792334\pi$
$241$	−24.6719			−1.58926			−0.794628	+	0.607097i	$0.792334\pi$
$242$	−1.92178	−	1.92178i	−0.123537	−	0.123537i
$243$	−14.9671	+	4.35735i	−0.960139	+	0.279524i
$244$			11.1031i			0.710801i
$245$	−4.26260	+	0.535577i	−0.272327	+	0.0342168i
$246$	−5.78870	+	6.48486i	−0.369074	+	0.413460i
$247$	0.303542	−	0.303542i	0.0193139	−	0.0193139i
$248$	0.707107	−	0.707107i	0.0449013	−	0.0449013i
$249$	−3.18851	+	3.57196i	−0.202063	+	0.226364i
$250$	4.46095	−	10.2518i	0.282136	−	0.648382i
$251$			18.6979i			1.18020i	0.807330	+	0.590100i	$0.200912\pi$
$251$			18.6979i			1.18020i	−0.807330	+	0.590100i	$0.799088\pi$
$252$	−5.29053	−	4.20937i	−0.333272	−	0.265166i
$253$	5.53522	+	5.53522i	0.347997	+	0.347997i
$254$	−9.16017			−0.574760
$255$	−1.49181	+	2.16313i	−0.0934208	+	0.135461i
$256$	1.00000			0.0625000
$257$	−7.29634	−	7.29634i	−0.455133	−	0.455133i	0.441921	−	0.897054i	$-0.354297\pi$
$257$	−7.29634	−	7.29634i	−0.455133	−	0.455133i	−0.897054	+	0.441921i	$0.854297\pi$
$258$	1.02242	+	18.0257i	0.0636534	+	1.12223i
$259$		−	7.14216i		−	0.443792i
$260$	2.56085	+	1.98916i	0.158817	+	0.123363i
$261$	3.88053	−	0.441631i	0.240199	−	0.0273362i
$262$	−11.7317	+	11.7317i	−0.724790	+	0.724790i
$263$	−11.3678	+	11.3678i	−0.700968	+	0.700968i	−0.964618	−	0.263650i	$-0.915074\pi$
$263$	−11.3678	+	11.3678i	−0.700968	+	0.700968i	0.263650	+	0.964618i	$0.415074\pi$
$264$	4.78576	+	4.27200i	0.294543	+	0.262923i
$265$	0.706262	+	0.548595i	0.0433854	+	0.0336999i
$266$		−	0.667110i		−	0.0409031i
$267$	−18.6071	+	1.05540i	−1.13874	+	0.0645894i
$268$	−9.42240	−	9.42240i	−0.575565	−	0.575565i
$269$	5.71888			0.348687			0.174343	−	0.984685i	$-0.444220\pi$
$269$	5.71888			0.348687			0.174343	+	0.984685i	$0.444220\pi$
$270$	5.47257	−	10.2494i	0.333050	−	0.623761i
$271$	−14.6399			−0.889311			−0.444656	−	0.895702i	$-0.646674\pi$
$271$	−14.6399			−0.889311			−0.444656	+	0.895702i	$0.646674\pi$
$272$	0.479745	+	0.479745i	0.0290888	+	0.0290888i
$273$	−5.65138	+	0.320548i	−0.342037	+	0.0194005i
$274$			16.2819i			0.983626i
$275$	−4.58129	−	17.9432i	−0.276262	−	1.08201i
$276$	−2.73097	−	2.43779i	−0.164385	−	0.146738i
$277$	−0.510362	+	0.510362i	−0.0306647	+	0.0306647i	−0.722273	−	0.691608i	$-0.756903\pi$
$277$	−0.510362	+	0.510362i	−0.0306647	+	0.0306647i	0.691608	+	0.722273i	$0.256903\pi$
$278$	−1.20199	+	1.20199i	−0.0720907	+	0.0720907i
$279$	−2.98076	+	0.339231i	−0.178453	+	0.0203092i
$280$	4.99989	−	0.628216i	0.298801	−	0.0375431i
$281$			29.3698i			1.75206i	0.482260	+	0.876028i	$0.339816\pi$
$281$			29.3698i			1.75206i	−0.482260	+	0.876028i	$0.660184\pi$
$282$	−0.0320067	−	0.564289i	−0.00190597	−	0.0336029i
$283$	−1.77470	−	1.77470i	−0.105495	−	0.105495i	0.652389	−	0.757884i	$-0.273767\pi$
$283$	−1.77470	−	1.77470i	−0.105495	−	0.105495i	−0.757884	+	0.652389i	$0.773767\pi$
$284$	−6.43406			−0.381791
$285$	1.12762	−	0.207115i	0.0667942	−	0.0122684i
$286$	5.37102			0.317595
$287$	7.99751	+	7.99751i	0.472078	+	0.472078i
$288$	−2.34759	−	1.86784i	−0.138333	−	0.110064i
$289$		−	16.5397i		−	0.972923i
$290$	−1.78575	+	2.29898i	−0.104863	+	0.135001i
$291$	−8.26522	+	9.25921i	−0.484516	+	0.542785i
$292$	5.91592	−	5.91592i	0.346203	−	0.346203i
$293$	−14.2801	+	14.2801i	−0.834255	+	0.834255i	−0.988096	−	0.153841i	$-0.950836\pi$
$293$	−14.2801	+	14.2801i	−0.834255	+	0.834255i	0.153841	+	0.988096i	$0.450836\pi$
$294$	2.21605	−	2.48256i	0.129243	−	0.144786i
$295$	−3.43269	−	27.3204i	−0.199859	−	1.59066i
$296$		−	3.16922i		−	0.184207i
$297$	−3.25556	−	18.9679i	−0.188907	−	1.10063i
$298$	−7.89274	−	7.89274i	−0.457214	−	0.457214i
$299$	−3.06494			−0.177250
$300$	2.61417	+	8.25628i	0.150929	+	0.476676i
$301$	23.4913			1.35401
$302$	−1.50916	−	1.50916i	−0.0868422	−	0.0868422i
$303$	−0.217089	−	3.82735i	−0.0124714	−	0.219876i
$304$		−	0.296019i		−	0.0169779i
$305$	3.09510	+	24.6335i	0.177225	+	1.41051i
$306$	−0.230155	−	2.02233i	−0.0131571	−	0.115609i
$307$	0.577798	−	0.577798i	0.0329767	−	0.0329767i	−0.690426	−	0.723403i	$-0.742577\pi$
$307$	0.577798	−	0.577798i	0.0329767	−	0.0329767i	0.723403	+	0.690426i	$0.242577\pi$
$308$	5.90207	−	5.90207i	0.336302	−	0.336302i
$309$	8.31296	+	7.42055i	0.472908	+	0.422140i
$310$	1.37169	−	1.76592i	0.0779068	−	0.100297i
$311$		−	29.9949i		−	1.70086i	−0.526091	−	0.850429i	$-0.676343\pi$
$311$		−	29.9949i		−	1.70086i	0.526091	−	0.850429i	$-0.323657\pi$
$312$	−2.50771	+	0.142238i	−0.141971	+	0.00805265i
$313$	−6.71881	−	6.71881i	−0.379769	−	0.379769i	0.491250	−	0.871019i	$-0.336540\pi$
$313$	−6.71881	−	6.71881i	−0.379769	−	0.379769i	−0.871019	+	0.491250i	$0.836540\pi$
$314$	−11.1370			−0.628497
$315$	−12.9111	−	7.86422i	−0.727458	−	0.443099i
$316$	−3.56575			−0.200589
$317$	−17.6706	−	17.6706i	−0.992478	−	0.992478i	0.00749364	−	0.999972i	$-0.497615\pi$
$317$	−17.6706	−	17.6706i	−0.992478	−	0.992478i	−0.999972	+	0.00749364i	$0.997615\pi$
$318$	−0.691606	+	0.0392281i	−0.0387833	+	0.00219980i
$319$			4.82177i			0.269967i
$320$	2.21862	−	0.278761i	0.124025	−	0.0155832i
$321$	−20.2387	−	18.0660i	−1.12961	−	1.00835i
$322$	−3.36798	+	3.36798i	−0.187690	+	0.187690i
$323$	0.142014	−	0.142014i	0.00790185	−	0.00790185i
$324$	2.02233	+	8.76985i	0.112352	+	0.487214i
$325$	6.23607	+	3.69934i	0.345915	+	0.205202i
$326$			3.21503i			0.178064i
$327$	−0.980320	−	17.2834i	−0.0542118	−	0.955774i
$328$	3.54877	+	3.54877i	0.195948	+	0.195948i
$329$	−0.735386			−0.0405431
$330$	11.8087	+	8.14387i	0.650045	+	0.448306i
$331$	15.4781			0.850755			0.425377	−	0.905016i	$-0.360141\pi$
$331$	15.4781			0.850755			0.425377	+	0.905016i	$0.360141\pi$
$332$	1.95472	+	1.95472i	0.107279	+	0.107279i
$333$	−5.91961	+	7.44002i	−0.324392	+	0.407711i
$334$			12.3990i			0.678444i
$335$	−23.5314	−	18.2782i	−1.28566	−	0.998643i
$336$	−2.59936	+	2.91196i	−0.141806	+	0.158860i
$337$	−18.1620	+	18.1620i	−0.989349	+	0.989349i	−0.999944	−	0.0105948i	$-0.996627\pi$
$337$	−18.1620	+	18.1620i	−0.989349	+	0.989349i	0.0105948	+	0.999944i	$0.496627\pi$
$338$	7.70538	−	7.70538i	0.419117	−	0.419117i
$339$	−5.81774	+	6.51740i	−0.315976	+	0.353976i
$340$	1.19811	+	0.930639i	0.0649765	+	0.0504710i
$341$		−	3.70376i		−	0.200570i
$342$	−0.552918	+	0.694931i	−0.0298984	+	0.0375776i
$343$	−14.2164	−	14.2164i	−0.767613	−	0.767613i
$344$	10.4239			0.562018
$345$	−6.73855	−	4.64726i	−0.362791	−	0.250200i
$346$	−9.13810			−0.491267
$347$	−12.9136	−	12.9136i	−0.693239	−	0.693239i	0.269704	−	0.962943i	$-0.413074\pi$
$347$	−12.9136	−	12.9136i	−0.693239	−	0.693239i	−0.962943	+	0.269704i	$0.913074\pi$
$348$	−0.127693	−	2.25127i	−0.00684505	−	0.120681i
$349$			30.6701i			1.64173i	0.571119	+	0.820867i	$0.306510\pi$
$349$			30.6701i			1.64173i	−0.571119	+	0.820867i	$0.693490\pi$
$350$	10.9178	−	2.78755i	0.583579	−	0.149001i
$351$	6.15274	+	4.35009i	0.328409	+	0.232191i
$352$	2.61895	−	2.61895i	0.139591	−	0.139591i
$353$	11.6278	−	11.6278i	0.618886	−	0.618886i	−0.326359	−	0.945246i	$-0.605822\pi$
$353$	11.6278	−	11.6278i	0.618886	−	0.618886i	0.945246	+	0.326359i	$0.105822\pi$
$354$	15.9115	+	14.2034i	0.845688	+	0.754902i
$355$	−14.2748	+	1.79356i	−0.757625	+	0.0951924i
$356$			10.7601i			0.570283i
$357$	−2.64402	+	0.149970i	−0.139937	+	0.00793725i
$358$	13.1935	+	13.1935i	0.697297	+	0.697297i
$359$	−14.2862			−0.753998			−0.376999	−	0.926214i	$-0.623044\pi$
$359$	−14.2862			−0.753998			−0.376999	+	0.926214i	$0.623044\pi$
$360$	−5.72909	−	3.48962i	−0.301950	−	0.183919i
$361$	18.9124			0.995388
$362$	14.5113	+	14.5113i	0.762697	+	0.762697i
$363$	4.69982	−	0.266575i	0.246677	−	0.0139916i
$364$			3.26807i			0.171293i
$365$	11.4761	−	14.7743i	0.600686	−	0.773324i
$366$	−14.3467	−	12.8065i	−0.749913	−	0.669408i
$367$	4.98013	−	4.98013i	0.259961	−	0.259961i	−0.565077	−	0.825038i	$-0.691154\pi$
$367$	4.98013	−	4.98013i	0.259961	−	0.259961i	0.825038	+	0.565077i	$0.191154\pi$
$368$	−1.49449	+	1.49449i	−0.0779057	+	0.0779057i
$369$	−1.70250	−	14.9596i	−0.0886288	−	0.778765i
$370$	−0.883454	−	7.03131i	−0.0459286	−	0.365540i
$371$			0.901307i			0.0467935i
$372$	0.0980849	+	1.72927i	0.00508546	+	0.0896585i
$373$	16.3054	+	16.3054i	0.844264	+	0.844264i	0.989410	−	0.145146i	$-0.0463653\pi$
$373$	16.3054	+	16.3054i	0.844264	+	0.844264i	−0.145146	+	0.989410i	$0.546365\pi$
$374$	2.51285			0.129937
$375$	8.10138	+	17.5888i	0.418354	+	0.908284i
$376$	−0.326316			−0.0168285
$377$	−1.33494	−	1.33494i	−0.0687531	−	0.0687531i
$378$	11.5413	−	1.98089i	0.593620	−	0.101886i
$379$			17.5558i			0.901780i	0.892579	+	0.450890i	$0.148893\pi$
$379$			17.5558i			0.901780i	−0.892579	+	0.450890i	$0.851107\pi$
$380$	−0.0825186	−	0.656756i	−0.00423311	−	0.0336909i
$381$	10.5655	−	11.8362i	0.541289	−	0.606386i
$382$	−15.9721	+	15.9721i	−0.817202	+	0.817202i
$383$	−6.79735	+	6.79735i	−0.347328	+	0.347328i	−0.859113	−	0.511785i	$-0.828984\pi$
$383$	−6.79735	+	6.79735i	−0.347328	+	0.347328i	0.511785	+	0.859113i	$0.328984\pi$
$384$	−1.15342	+	1.29214i	−0.0588604	+	0.0659390i
$385$	11.4492	−	14.7397i	0.583506	−	0.751207i
$386$			10.2467i			0.521541i
$387$	−24.4710	−	19.4702i	−1.24393	−	0.989724i
$388$	5.06700	+	5.06700i	0.257238	+	0.257238i
$389$	9.51345			0.482351			0.241175	−	0.970482i	$-0.422467\pi$
$389$	9.51345			0.482351			0.241175	+	0.970482i	$0.422467\pi$
$390$	−5.52401	+	1.01462i	−0.279719	+	0.0513775i
$391$	−1.43395			−0.0725178
$392$	−1.35855	−	1.35855i	−0.0686172	−	0.0686172i
$393$	−1.62735	−	28.6907i	−0.0820887	−	1.44725i
$394$			4.57945i			0.230709i
$395$	−7.91105	+	0.993990i	−0.398048	+	0.0500131i
$396$	−11.0400	+	1.25643i	−0.554781	+	0.0631379i
$397$	10.8764	−	10.8764i	0.545869	−	0.545869i	−0.379374	−	0.925243i	$-0.623861\pi$
$397$	10.8764	−	10.8764i	0.545869	−	0.545869i	0.925243	+	0.379374i	$0.123861\pi$
$398$	12.2088	−	12.2088i	0.611972	−	0.611972i
$399$	0.861997	+	0.769460i	0.0431538	+	0.0385212i
$400$	4.84458	−	1.23693i	0.242229	−	0.0618465i
$401$			8.00715i			0.399858i	0.979810	+	0.199929i	$0.0640711\pi$
$401$			8.00715i			0.399858i	−0.979810	+	0.199929i	$0.935929\pi$
$402$	23.0430	−	1.30701i	1.14928	−	0.0651877i
$403$	1.02541	+	1.02541i	0.0510795	+	0.0510795i
$404$	−2.21327			−0.110115
$405$	6.93148	+	18.8932i	0.344428	+	0.938813i
$406$	−2.93387			−0.145606
$407$	−8.30003	−	8.30003i	−0.411417	−	0.411417i
$408$	−1.17324	+	0.0665468i	−0.0580842	+	0.00329456i
$409$			4.41491i			0.218303i	0.994025	+	0.109152i	$0.0348134\pi$
$409$			4.41491i			0.218303i	−0.994025	+	0.109152i	$0.965187\pi$
$410$	8.86264	+	6.88413i	0.437695	+	0.339983i
$411$	−21.0384	−	18.7799i	−1.03775	−	0.926346i
$412$	4.54917	−	4.54917i	0.224122	−	0.224122i
$413$	19.6230	−	19.6230i	0.965585	−	0.965585i
$414$	6.29992	−	0.716973i	0.309624	−	0.0352373i
$415$	4.88168	+	3.79188i	0.239632	+	0.186136i
$416$			1.45015i			0.0710996i
$417$	−0.166732	−	2.93954i	−0.00816490	−	0.143950i
$418$	−0.775260	−	0.775260i	−0.0379192	−	0.0379192i
$419$	2.07061			0.101156			0.0505780	−	0.998720i	$-0.483894\pi$
$419$	2.07061			0.101156			0.0505780	+	0.998720i	$0.483894\pi$
$420$	−4.95525	+	7.18514i	−0.241792	+	0.350599i
$421$	−28.7331			−1.40036			−0.700182	−	0.713964i	$-0.746898\pi$
$421$	−28.7331			−1.40036			−0.700182	+	0.713964i	$0.746898\pi$
$422$	−15.3875	−	15.3875i	−0.749050	−	0.749050i
$423$	0.766055	+	0.609507i	0.0372469	+	0.0296352i
$424$			0.399941i			0.0194228i
$425$	2.91757	+	1.73075i	0.141523	+	0.0839539i
$426$	7.42119	−	8.31367i	0.359558	−	0.402799i
$427$	−17.6931	+	17.6931i	−0.856232	+	0.856232i
$428$	−11.0754	+	11.0754i	−0.535348	+	0.535348i
$429$	−6.19505	+	6.94008i	−0.299100	+	0.335070i
$430$	23.1267	−	2.90577i	1.11527	−	0.140129i
$431$		−	20.1008i		−	0.968224i	−0.875006	−	0.484112i	$-0.839143\pi$
$431$		−	20.1008i		−	0.968224i	0.875006	−	0.484112i	$-0.160857\pi$
$432$	5.12127	−	0.878989i	0.246397	−	0.0422904i
$433$	17.4620	+	17.4620i	0.839169	+	0.839169i	0.988750	−	0.149581i	$-0.0477924\pi$
$433$	17.4620	+	17.4620i	0.839169	+	0.839169i	−0.149581	+	0.988750i	$0.547792\pi$
$434$	2.25360			0.108176
$435$	−0.910867	−	4.95912i	−0.0436727	−	0.237772i
$436$	−9.99461			−0.478655
$437$	0.442398	+	0.442398i	0.0211628	+	0.0211628i
$438$	0.820615	+	14.4677i	0.0392105	+	0.691295i
$439$		−	36.4397i		−	1.73917i	−0.493781	−	0.869587i	$-0.664385\pi$
$439$		−	36.4397i		−	1.73917i	0.493781	−	0.869587i	$-0.335615\pi$
$440$	5.08041	−	6.54053i	0.242199	−	0.311807i
$441$	0.651757	+	5.72687i	0.0310361	+	0.272708i
$442$	−0.695704	+	0.695704i	−0.0330912	+	0.0330912i
$443$	−5.18559	+	5.18559i	−0.246375	+	0.246375i	−0.819481	−	0.573106i	$-0.805738\pi$
$443$	−5.18559	+	5.18559i	−0.246375	+	0.246375i	0.573106	+	0.819481i	$0.305738\pi$
$444$	4.09506	+	3.65545i	0.194343	+	0.173480i
$445$	2.99949	+	23.8726i	0.142189	+	1.13167i
$446$		−	7.59645i		−	0.359702i
$447$	19.3022	−	1.09483i	0.912961	−	0.0517835i
$448$	1.59354	+	1.59354i	0.0752875	+	0.0752875i
$449$	−38.7024			−1.82648			−0.913240	−	0.407423i	$-0.866427\pi$
$449$	−38.7024			−1.82648			−0.913240	+	0.407423i	$0.866427\pi$
$450$	−13.6835	−	6.14512i	−0.645045	−	0.289684i
$451$	18.5881			0.875279
$452$	3.56657	+	3.56657i	0.167757	+	0.167757i
$453$	3.69073	−	0.209340i	0.173406	−	0.00983563i
$454$			17.7196i			0.831620i
$455$	0.911009	+	7.25062i	0.0427088	+	0.339914i
$456$	0.382497	+	0.341436i	0.0179121	+	0.0159892i
$457$	−3.48182	+	3.48182i	−0.162873	+	0.162873i	−0.783838	−	0.620965i	$-0.786741\pi$
$457$	−3.48182	+	3.48182i	−0.162873	+	0.162873i	0.620965	+	0.783838i	$0.286741\pi$
$458$	5.43670	−	5.43670i	0.254040	−	0.254040i
$459$	2.87859	+	2.03521i	0.134361	+	0.0949955i
$460$	−2.89911	+	3.73232i	−0.135172	+	0.174020i
$461$		−	13.8727i		−	0.646117i	−0.946379	−	0.323059i	$-0.895289\pi$
$461$		−	13.8727i		−	0.646117i	0.946379	−	0.323059i	$-0.104711\pi$
$462$	0.818694	+	14.4339i	0.0380891	+	0.671524i
$463$	−2.51704	−	2.51704i	−0.116977	−	0.116977i	0.646195	−	0.763172i	$-0.276359\pi$
$463$	−2.51704	−	2.51704i	−0.116977	−	0.116977i	−0.763172	+	0.646195i	$0.776359\pi$
$464$	−1.30186			−0.0604373
$465$	0.699666	+	3.80926i	0.0324462	+	0.176650i
$466$	−9.07616			−0.420445
$467$	30.0390	+	30.0390i	1.39004	+	1.39004i	0.825204	+	0.564836i	$0.191060\pi$
$467$	30.0390	+	30.0390i	1.39004	+	1.39004i	0.564836	+	0.825204i	$0.308940\pi$
$468$	2.70866	−	3.40436i	0.125208	−	0.157367i
$469$		−	30.0299i		−	1.38665i
$470$	−0.723972	+	0.0909641i	−0.0333944	+	0.00419586i
$471$	12.8457	−	14.3905i	0.591897	−	0.663079i
$472$	8.70740	−	8.70740i	0.400791	−	0.400791i
$473$	27.2996	−	27.2996i	1.25524	−	1.25524i
$474$	4.11281	−	4.60743i	0.188908	−	0.211626i
$475$	−0.366155	−	1.43409i	−0.0168004	−	0.0658006i
$476$			1.52898i			0.0700808i
$477$	0.747026	−	0.938896i	0.0342040	−	0.0429891i
$478$	16.3754	+	16.3754i	0.748994	+	0.748994i
$479$	24.4251			1.11601			0.558005	−	0.829837i	$-0.311567\pi$
$479$	24.4251			1.11601			0.558005	+	0.829837i	$0.311567\pi$
$480$	−2.19882	+	3.18829i	−0.100362	+	0.145525i
$481$	4.59586			0.209553
$482$	−17.4457	−	17.4457i	−0.794628	−	0.794628i
$483$	−0.467183	−	8.23660i	−0.0212576	−	0.374778i
$484$		−	2.71780i		−	0.123537i
$485$	12.6542	+	9.82929i	0.574600	+	0.446325i
$486$	−13.6644	−	7.50222i	−0.619831	−	0.340307i
$487$	16.3280	−	16.3280i	0.739891	−	0.739891i	−0.232666	−	0.972557i	$-0.574745\pi$
$487$	16.3280	−	16.3280i	0.739891	−	0.739891i	0.972557	+	0.232666i	$0.0747448\pi$
$488$	−7.85106	+	7.85106i	−0.355401	+	0.355401i
$489$	−4.15426	−	3.70829i	−0.187862	−	0.167695i
$490$	−3.39282	−	2.63540i	−0.153272	−	0.119055i
$491$		−	12.7037i		−	0.573309i	−0.958034	−	0.286655i	$-0.907457\pi$
$491$		−	12.7037i		−	0.573309i	0.958034	−	0.286655i	$-0.0925432\pi$
$492$	−8.67872	+	0.492260i	−0.391267	+	0.0221928i
$493$	−0.624560	−	0.624560i	−0.0281288	−	0.0281288i
$494$	0.429274			0.0193139
$495$	−24.1434	+	5.86506i	−1.08516	+	0.263615i
$496$	1.00000			0.0449013
$497$	−10.2529	−	10.2529i	−0.459906	−	0.459906i
$498$	−4.78037	+	0.271144i	−0.214214	+	0.0121503i
$499$		−	10.7503i		−	0.481248i	−0.970618	−	0.240624i	$-0.922648\pi$
$499$		−	10.7503i		−	0.481248i	0.970618	−	0.240624i	$-0.0773521\pi$
$500$	10.4035	−	4.09476i	0.465259	−	0.183123i
$501$	−16.0212	−	14.3013i	−0.715775	−	0.638935i
$502$	−13.2214	+	13.2214i	−0.590100	+	0.590100i
$503$	19.9599	−	19.9599i	0.889968	−	0.889968i	−0.104551	−	0.994520i	$-0.533341\pi$
$503$	19.9599	−	19.9599i	0.889968	−	0.889968i	0.994520	+	0.104551i	$0.0333406\pi$
$504$	−0.764491	−	6.71744i	−0.0340531	−	0.299219i
$505$	−4.91042	+	0.616974i	−0.218511	+	0.0274550i
$506$			7.82799i			0.347997i
$507$	1.06884	+	18.8440i	0.0474687	+	0.836890i
$508$	−6.47722	−	6.47722i	−0.287380	−	0.287380i
$509$	13.5548			0.600804			0.300402	−	0.953813i	$-0.402879\pi$
$509$	13.5548			0.600804			0.300402	+	0.953813i	$0.402879\pi$
$510$	−2.58444	+	0.474697i	−0.114441	+	0.0210199i
$511$	18.8545			0.834073
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$	−0.260198	−	1.51599i	−0.0114880	−	0.0669328i
$514$		−	10.3186i		−	0.455133i
$515$	8.82478	−	11.3610i	0.388866	−	0.500627i
$516$	−12.0231	+	13.4691i	−0.529289	+	0.592943i
$517$	−0.854605	+	0.854605i	−0.0375855	+	0.0375855i
$518$	5.05027	−	5.05027i	0.221896	−	0.221896i
$519$	10.5401	−	11.8077i	0.462659	−	0.518299i
$520$	0.404246	+	3.21735i	0.0177274	+	0.141090i
$521$		−	25.4930i		−	1.11687i	−0.829548	−	0.558435i	$-0.811402\pi$
$521$		−	25.4930i		−	1.11687i	0.829548	−	0.558435i	$-0.188598\pi$
$522$	3.05623	+	2.43167i	0.133767	+	0.106431i
$523$	−11.2546	−	11.2546i	−0.492128	−	0.492128i	0.416848	−	0.908976i	$-0.363135\pi$
$523$	−11.2546	−	11.2546i	−0.492128	−	0.492128i	−0.908976	+	0.416848i	$0.863135\pi$
$524$	−16.5912			−0.724790
$525$	−8.99091	+	17.3225i	−0.392395	+	0.756014i
$526$	−16.0765			−0.700968
$527$	0.479745	+	0.479745i	0.0208980	+	0.0208980i
$528$	0.363282	+	6.40480i	0.0158098	+	0.278733i
$529$			18.5330i			0.805783i
$530$	0.111488	+	0.887318i	0.00484272	+	0.0385426i
$531$	−36.7054	+	4.17733i	−1.59288	+	0.181281i
$532$	0.471718	−	0.471718i	0.0204516	−	0.0204516i
$533$	−5.14626	+	5.14626i	−0.222909	+	0.222909i
$534$	−13.9035	−	12.4109i	−0.601662	−	0.537073i
$535$	−21.4847	+	27.6595i	−0.928865	+	1.19582i
$536$		−	13.3253i		−	0.575565i
$537$	−32.2654	+	1.83011i	−1.39236	+	0.0789749i
$538$	4.04386	+	4.04386i	0.174343	+	0.174343i
$539$	−7.11595			−0.306506
$540$	11.1171	−	3.37775i	0.478405	−	0.145355i
$541$	33.4322			1.43736			0.718681	−	0.695340i	$-0.244746\pi$
$541$	33.4322			1.43736			0.718681	+	0.695340i	$0.244746\pi$
$542$	−10.3520	−	10.3520i	−0.444656	−	0.444656i
$543$	−35.4883	+	2.01291i	−1.52295	+	0.0863821i
$544$			0.678461i			0.0290888i
$545$	−22.1743	+	2.78610i	−0.949842	+	0.119344i
$546$	−4.22279	−	3.76947i	−0.180719	−	0.161318i
$547$	10.5375	−	10.5375i	0.450553	−	0.450553i	−0.444985	−	0.895538i	$-0.646791\pi$
$547$	10.5375	−	10.5375i	0.450553	−	0.450553i	0.895538	+	0.444985i	$0.146791\pi$
$548$	−11.5131	+	11.5131i	−0.491813	+	0.491813i
$549$	33.0956	−	3.76650i	1.41248	−	0.160750i
$550$	9.44827	−	15.9272i	0.402876	−	0.679138i
$551$			0.385376i			0.0164176i
$552$	−0.207305	−	3.65486i	−0.00882349	−	0.155561i
$553$	−5.68215	−	5.68215i	−0.241630	−	0.241630i
$554$	−0.721760			−0.0306647
$555$	10.1044	+	6.96853i	0.428908	+	0.295798i
$556$	−1.69987			−0.0720907
$557$	−0.950084	−	0.950084i	−0.0402563	−	0.0402563i	0.686692	−	0.726948i	$-0.259062\pi$
$557$	−0.950084	−	0.950084i	−0.0402563	−	0.0402563i	−0.726948	+	0.686692i	$0.759062\pi$
$558$	−2.34759	−	1.86784i	−0.0993813	−	0.0790721i
$559$			15.1162i			0.639348i
$560$	3.97967	+	3.09124i	0.168172	+	0.130629i
$561$	−2.89838	+	3.24695i	−0.122370	+	0.137086i
$562$	−20.7676	+	20.7676i	−0.876028	+	0.876028i
$563$	1.08303	−	1.08303i	0.0456442	−	0.0456442i	−0.683916	−	0.729560i	$-0.739725\pi$
$563$	1.08303	−	1.08303i	0.0456442	−	0.0456442i	0.729560	+	0.683916i	$0.239725\pi$
$564$	0.376380	−	0.421645i	0.0158485	−	0.0177544i
$565$	8.90710	+	6.91866i	0.374725	+	0.291070i
$566$		−	2.50981i		−	0.105495i
$567$	−10.7524	+	17.1977i	−0.451559	+	0.722237i
$568$	−4.54956	−	4.54956i	−0.190895	−	0.190895i
$569$	−22.3470			−0.936835			−0.468418	−	0.883507i	$-0.655176\pi$
$569$	−22.3470			−0.936835			−0.468418	+	0.883507i	$0.655176\pi$
$570$	0.943797	+	0.650892i	0.0395313	+	0.0272629i
$571$	−3.60507			−0.150867			−0.0754337	−	0.997151i	$-0.524034\pi$
$571$	−3.60507			−0.150867			−0.0754337	+	0.997151i	$0.524034\pi$
$572$	3.79788	+	3.79788i	0.158797	+	0.158797i
$573$	−2.21553	−	39.0606i	−0.0925552	−	1.63178i
$574$			11.3102i			0.472078i
$575$	−5.39160	+	9.08876i	−0.224845	+	0.379028i
$576$	−0.339231	−	2.98076i	−0.0141346	−	0.124198i
$577$	−23.8009	+	23.8009i	−0.990846	+	0.990846i	−0.999958	−	0.00911207i	$-0.997099\pi$
$577$	−23.8009	+	23.8009i	−0.990846	+	0.990846i	0.00911207	+	0.999958i	$0.497099\pi$
$578$	11.6953	−	11.6953i	0.486461	−	0.486461i
$579$	−13.2401	−	11.8187i	−0.550239	−	0.491170i
$580$	−2.88834	+	0.362907i	−0.119932	+	0.0150689i
$581$			6.22983i			0.258457i
$582$	−12.3916	+	0.702859i	−0.513650	+	0.0291344i
$583$	1.04743	+	1.04743i	0.0433799	+	0.0433799i
$584$	8.36638			0.346203
$585$	5.06049	−	8.30807i	0.209226	−	0.343496i
$586$	−20.1952			−0.834255
$587$	7.26273	+	7.26273i	0.299765	+	0.299765i	0.840922	−	0.541157i	$-0.182013\pi$
$587$	7.26273	+	7.26273i	0.299765	+	0.299765i	−0.541157	+	0.840922i	$0.682013\pi$
$588$	3.32241	−	0.188449i	0.137014	−	0.00777149i
$589$		−	0.296019i		−	0.0121973i
$590$	16.8912	−	21.7457i	0.695399	−	0.895258i
$591$	−5.91727	−	5.28204i	−0.243404	−	0.217274i
$592$	2.24098	−	2.24098i	0.0921036	−	0.0921036i
$593$	17.6248	−	17.6248i	0.723763	−	0.723763i	−0.245606	−	0.969370i	$-0.578987\pi$
$593$	17.6248	−	17.6248i	0.723763	−	0.723763i	0.969370	+	0.245606i	$0.0789871\pi$
$594$	11.1103	−	15.7144i	0.455862	−	0.644769i
$595$	0.426220	+	3.39224i	0.0174733	+	0.139068i
$596$		−	11.1620i		−	0.457214i
$597$	1.69352	+	29.8573i	0.0693111	+	1.22198i
$598$	−2.16724	−	2.16724i	−0.0886250	−	0.0886250i
$599$	−34.3921			−1.40522			−0.702612	−	0.711573i	$-0.747983\pi$
$599$	−34.3921			−1.40522			−0.702612	+	0.711573i	$0.747983\pi$
$600$	−3.98957	+	7.68657i	−0.162874	+	0.313803i
$601$	−31.0073			−1.26482			−0.632408	−	0.774636i	$-0.717933\pi$
$601$	−31.0073			−1.26482			−0.632408	+	0.774636i	$0.717933\pi$
$602$	16.6108	+	16.6108i	0.677007	+	0.677007i
$603$	−24.8895	+	31.2823i	−1.01358	+	1.27391i
$604$		−	2.13427i		−	0.0868422i
$605$	−0.757617	−	6.02978i	−0.0308015	−	0.245146i
$606$	2.55284	−	2.85985i	0.103702	−	0.116174i
$607$	0.212009	−	0.212009i	0.00860518	−	0.00860518i	−0.702791	−	0.711396i	$-0.748063\pi$
$607$	0.212009	−	0.212009i	0.00860518	−	0.00860518i	0.711396	+	0.702791i	$0.248063\pi$
$608$	0.209317	−	0.209317i	0.00848894	−	0.00848894i
$609$	3.38400	−	3.79096i	0.137126	−	0.153617i
$610$	−15.2300	+	19.6071i	−0.616644	+	0.793868i
$611$		−	0.473208i		−	0.0191440i
$612$	1.26726	−	1.59275i	0.0512259	−	0.0643830i
$613$	23.9172	+	23.9172i	0.966008	+	0.966008i	0.999441	−	0.0334327i	$-0.0106439\pi$
$613$	23.9172	+	23.9172i	0.966008	+	0.966008i	−0.0334327	+	0.999441i	$0.510644\pi$
$614$	0.817129			0.0329767
$615$	−19.1176	+	3.51143i	−0.770896	+	0.141594i
$616$	8.34679			0.336302
$617$	7.85266	+	7.85266i	0.316136	+	0.316136i	0.847281	−	0.531145i	$-0.178238\pi$
$617$	7.85266	+	7.85266i	0.316136	+	0.316136i	−0.531145	+	0.847281i	$0.678238\pi$
$618$	0.631029	+	11.1253i	0.0253837	+	0.447524i
$619$			7.62713i			0.306560i	0.988183	+	0.153280i	$0.0489837\pi$
$619$			7.62713i			0.306560i	−0.988183	+	0.153280i	$0.951016\pi$
$620$	2.21862	−	0.278761i	0.0891021	−	0.0111953i
$621$	−6.34004	+	8.96732i	−0.254417	+	0.359846i
$622$	21.2096	−	21.2096i	0.850429	−	0.850429i
$623$	−17.1466	+	17.1466i	−0.686963	+	0.686963i
$624$	−1.87380	−	1.67264i	−0.0750119	−	0.0669592i
$625$	21.9400	−	11.9848i	0.877600	−	0.479393i
$626$		−	9.50183i		−	0.379769i
$627$	1.89594	−	0.107539i	0.0757167	−	0.00429468i
$628$	−7.87504	−	7.87504i	−0.314248	−	0.314248i
$629$	2.15019			0.0857338
$630$	−3.56868	−	14.6904i	−0.142179	−	0.585278i
$631$	44.1114			1.75605			0.878024	−	0.478616i	$-0.158861\pi$
$631$	44.1114			1.75605			0.878024	+	0.478616i	$0.158861\pi$
$632$	−2.52136	−	2.52136i	−0.100294	−	0.100294i
$633$	37.6310	−	2.13444i	1.49570	−	0.0848364i
$634$		−	24.9900i		−	0.992478i
$635$	−16.1761	−	12.5649i	−0.641929	−	0.498623i
$636$	−0.516778	−	0.461301i	−0.0204916	−	0.0182918i
$637$	1.97011	−	1.97011i	0.0780585	−	0.0780585i
$638$	−3.40950	+	3.40950i	−0.134984	+	0.134984i
$639$	2.18263	+	19.1784i	0.0863435	+	0.758684i
$640$	1.76592	+	1.37169i	0.0698040	+	0.0542208i
$641$			34.4732i			1.36161i	0.732464	+	0.680805i	$0.238370\pi$
$641$			34.4732i			1.36161i	−0.732464	+	0.680805i	$0.761630\pi$
$642$	−1.53630	−	27.0855i	−0.0606328	−	1.06898i
$643$	25.0469	+	25.0469i	0.987752	+	0.987752i	0.999926	−	0.0121735i	$-0.00387503\pi$
$643$	25.0469	+	25.0469i	0.987752	+	0.987752i	−0.0121735	+	0.999926i	$0.503875\pi$
$644$	−4.76305			−0.187690
$645$	−22.9202	+	33.2344i	−0.902481	+	1.30860i
$646$	0.200838			0.00790185
$647$	−3.66605	−	3.66605i	−0.144127	−	0.144127i	0.631361	−	0.775489i	$-0.282496\pi$
$647$	−3.66605	−	3.66605i	−0.144127	−	0.144127i	−0.775489	+	0.631361i	$0.782496\pi$
$648$	−4.77121	+	7.63122i	−0.187431	+	0.299783i
$649$		−	45.6085i		−	1.79029i
$650$	1.79374	+	7.02539i	0.0703562	+	0.275559i
$651$	−2.59936	+	2.91196i	−0.101877	+	0.114129i
$652$	−2.27337	+	2.27337i	−0.0890320	+	0.0890320i
$653$	−32.0216	+	32.0216i	−1.25310	+	1.25310i	−0.298780	+	0.954322i	$0.596580\pi$
$653$	−32.0216	+	32.0216i	−1.25310	+	1.25310i	−0.954322	+	0.298780i	$0.903420\pi$
$654$	11.5280	−	12.9144i	0.450781	−	0.504993i
$655$	−36.8096	+	4.62497i	−1.43827	+	0.180713i
$656$			5.01872i			0.195948i
$657$	−19.6408	−	15.6271i	−0.766261	−	0.609670i
$658$	−0.519996	−	0.519996i	−0.0202716	−	0.0202716i
$659$	6.39570			0.249141			0.124571	−	0.992211i	$-0.460245\pi$
$659$	6.39570			0.249141			0.124571	+	0.992211i	$0.460245\pi$
$660$	2.59139	+	14.1086i	0.100870	+	0.549175i
$661$	−22.1241			−0.860528			−0.430264	−	0.902703i	$-0.641579\pi$
$661$	−22.1241			−0.860528			−0.430264	+	0.902703i	$0.641579\pi$
$662$	10.9447	+	10.9447i	0.425377	+	0.425377i
$663$	−0.0965031	−	1.70138i	−0.00374787	−	0.0660763i
$664$			2.76439i			0.107279i
$665$	0.915068	−	1.17806i	0.0354848	−	0.0456832i
$666$	−9.44668	+	1.07510i	−0.366052	+	0.0416592i
$667$	1.94562	−	1.94562i	0.0753345	−	0.0753345i
$668$	−8.76742	+	8.76742i	−0.339222	+	0.339222i
$669$	9.81565	+	8.76192i	0.379495	+	0.338755i
$670$	−3.71457	−	29.5638i	−0.143506	−	1.14215i
$671$			41.1230i			1.58754i
$672$	−3.89709	+	0.221044i	−0.150333	+	0.00852697i
$673$	27.8518	+	27.8518i	1.07361	+	1.07361i	0.997066	+	0.0765405i	$0.0243874\pi$
$673$	27.8518	+	27.8518i	1.07361	+	1.07361i	0.0765405	+	0.997066i	$0.475613\pi$
$674$	−25.6850			−0.989349
$675$	23.7232	−	10.5930i	0.913105	−	0.407724i
$676$	10.8971			0.419117
$677$	−0.671792	−	0.671792i	−0.0258191	−	0.0258191i	0.694079	−	0.719898i	$-0.255812\pi$
$677$	−0.671792	−	0.671792i	−0.0258191	−	0.0258191i	−0.719898	+	0.694079i	$0.755812\pi$
$678$	−8.72226	+	0.494730i	−0.334976	+	0.0190000i
$679$			16.1489i			0.619738i
$680$	0.189128	+	1.50525i	0.00725274	+	0.0577237i
$681$	−22.8961	−	20.4382i	−0.877380	−	0.783192i
$682$	2.61895	−	2.61895i	0.100285	−	0.100285i
$683$	−5.91720	+	5.91720i	−0.226415	+	0.226415i	−0.811193	−	0.584778i	$-0.801182\pi$
$683$	−5.91720	+	5.91720i	−0.226415	+	0.226415i	0.584778	+	0.811193i	$0.301182\pi$
$684$	−0.882362	+	0.100419i	−0.0337380	+	0.00383961i
$685$	−22.3337	+	28.7525i	−0.853329	+	1.09858i
$686$		−	20.1050i		−	0.767613i
$687$	0.754141	+	13.2958i	0.0287723	+	0.507265i
$688$	7.37080	+	7.37080i	0.281009	+	0.281009i
$689$	−0.579976			−0.0220953
$690$	−1.47876	−	8.05098i	−0.0562956	−	0.306495i
$691$	43.7242			1.66335			0.831673	−	0.555266i	$-0.187383\pi$
$691$	43.7242			1.66335			0.831673	+	0.555266i	$0.187383\pi$
$692$	−6.46161	−	6.46161i	−0.245634	−	0.245634i
$693$	−19.5948	−	15.5905i	−0.744345	−	0.592234i
$694$		−	18.2626i		−	0.693239i
$695$	−3.77138	+	0.473858i	−0.143057	+	0.0179745i
$696$	1.50159	−	1.68218i	0.0569178	−	0.0637628i
$697$	−2.40770	+	2.40770i	−0.0911982	+	0.0911982i
$698$	−21.6871	+	21.6871i	−0.820867	+	0.820867i
$699$	10.4687	−	11.7276i	0.395961	−	0.443580i
$700$	9.69112	+	5.74893i	0.366290	+	0.217289i
$701$		−	14.1168i		−	0.533184i	−0.963809	−	0.266592i	$-0.914102\pi$
$701$		−	14.1168i		−	0.533184i	0.963809	−	0.266592i	$-0.0858977\pi$
$702$	1.27467	+	7.42663i	0.0481093	+	0.280300i
$703$	−0.663373	−	0.663373i	−0.0250196	−	0.0250196i
$704$	3.70376			0.139591
$705$	0.717508	−	1.04039i	0.0270229	−	0.0391834i
$706$	16.4442			0.618886
$707$	−3.52693	−	3.52693i	−0.132644	−	0.132644i
$708$	1.20783	+	21.2945i	0.0453930	+	0.800295i
$709$		−	25.3893i		−	0.953514i	−0.879035	−	0.476757i	$-0.841812\pi$
$709$		−	25.3893i		−	0.953514i	0.879035	−	0.476757i	$-0.158188\pi$
$710$	−11.3620	−	8.82553i	−0.426409	−	0.331216i
$711$	1.20961	+	10.6286i	0.0453639	+	0.398605i
$712$	−7.60852	+	7.60852i	−0.285141	+	0.285141i
$713$	−1.49449	+	1.49449i	−0.0559691	+	0.0559691i
$714$	−1.97565	−	1.76356i	−0.0739369	−	0.0659997i
$715$	9.48477	+	7.36737i	0.354710	+	0.275524i
$716$			18.6584i			0.697297i
$717$	−40.0470	+	2.27148i	−1.49558	+	0.0848300i
$718$	−10.1019	−	10.1019i	−0.376999	−	0.376999i
$719$	−43.5310			−1.62343			−0.811716	−	0.584052i	$-0.801466\pi$
$719$	−43.5310			−1.62343			−0.811716	+	0.584052i	$0.801466\pi$
$720$	−1.58354	−	6.51862i	−0.0590152	−	0.242935i
$721$	14.4986			0.539954
$722$	13.3731	+	13.3731i	0.497694	+	0.497694i
$723$	42.6644	−	2.41994i	1.58671	−	0.0899985i
$724$			20.5221i			0.762697i
$725$	−6.30697	+	1.61031i	−0.234235	+	0.0598054i
$726$	3.51177	+	3.13478i	0.130334	+	0.116343i
$727$	28.7629	−	28.7629i	1.06676	−	1.06676i	0.0691526	−	0.997606i	$-0.477970\pi$
$727$	28.7629	−	28.7629i	1.06676	−	1.06676i	0.997606	−	0.0691526i	$-0.0220295\pi$
$728$	−2.31087	+	2.31087i	−0.0856467	+	0.0856467i
$729$	25.4548	−	9.00308i	0.942769	−	0.333447i
$730$	18.5619	−	2.33222i	0.687005	−	0.0863193i
$731$			7.07220i			0.261575i
$732$	−1.08904	−	19.2002i	−0.0402522	−	0.709660i
$733$	5.04195	+	5.04195i	0.186229	+	0.186229i	0.794063	−	0.607835i	$-0.207962\pi$
$733$	5.04195	+	5.04195i	0.186229	+	0.186229i	−0.607835	+	0.794063i	$0.707962\pi$
$734$	7.04297			0.259961
$735$	7.31866	−	1.34426i	0.269953	−	0.0495836i
$736$	−2.11353			−0.0779057
$737$	−34.8983	−	34.8983i	−1.28549	−	1.28549i
$738$	9.37417	−	11.7819i	0.345068	−	0.433697i
$739$		−	42.4476i		−	1.56146i	−0.624869	−	0.780730i	$-0.714848\pi$
$739$		−	42.4476i		−	1.56146i	0.624869	−	0.780730i	$-0.285152\pi$
$740$	4.34719	−	5.59658i	0.159806	−	0.205734i
$741$	−0.495134	+	0.554680i	−0.0181892	+	0.0203767i
$742$	−0.637320	+	0.637320i	−0.0233968	+	0.0233968i
$743$	−2.91864	+	2.91864i	−0.107074	+	0.107074i	−0.758614	−	0.651540i	$-0.774123\pi$
$743$	−2.91864	+	2.91864i	−0.107074	+	0.107074i	0.651540	+	0.758614i	$0.274123\pi$
$744$	−1.15342	+	1.29214i	−0.0422865	+	0.0473720i
$745$	−3.11153	−	24.7643i	−0.113998	−	0.907295i
$746$			23.0594i			0.844264i
$747$	5.16344	−	6.48964i	0.188920	−	0.237443i
$748$	1.77686	+	1.77686i	0.0649683	+	0.0649683i
$749$	−35.2980			−1.28976
$750$	−6.70865	+	18.1657i	−0.244965	+	0.663319i
$751$	47.4716			1.73226			0.866132	−	0.499815i	$-0.166599\pi$
$751$	47.4716			1.73226			0.866132	+	0.499815i	$0.166599\pi$
$752$	−0.230740	−	0.230740i	−0.00841423	−	0.00841423i
$753$	−1.83398	−	32.3337i	−0.0668339	−	1.17831i
$754$		−	1.88790i		−	0.0687531i
$755$	−0.594950	−	4.73514i	−0.0216525	−	0.172329i
$756$	9.56163	+	6.76023i	0.347753	+	0.245867i
$757$	27.8063	−	27.8063i	1.01064	−	1.01064i	0.0106944	−	0.999943i	$-0.496596\pi$
$757$	27.8063	−	27.8063i	1.01064	−	1.01064i	0.999943	−	0.0106944i	$-0.00340420\pi$
$758$	−12.4138	+	12.4138i	−0.450890	+	0.450890i
$759$	−10.1148	−	9.02898i	−0.367145	−	0.327731i
$760$	0.406047	−	0.522746i	0.0147289	−	0.0189620i
$761$			1.65428i			0.0599675i	0.999550	+	0.0299838i	$0.00954556\pi$
$761$			1.65428i			0.0599675i	−0.999550	+	0.0299838i	$0.990454\pi$
$762$	15.8404	−	0.898474i	0.573838	−	0.0325483i
$763$	−15.9268	−	15.9268i	−0.576588	−	0.576588i
$764$	−22.5879			−0.817202
$765$	2.36758	−	3.88697i	0.0855999	−	0.140534i
$766$	−9.61290			−0.347328
$767$	12.6271	+	12.6271i	0.455937	+	0.455937i
$768$	−1.72927	+	0.0980849i	−0.0623997	+	0.00353933i
$769$			37.6670i			1.35831i	0.733997	+	0.679153i	$0.237653\pi$
$769$			37.6670i			1.35831i	−0.733997	+	0.679153i	$0.762347\pi$
$770$	18.5184	−	2.32676i	0.667356	−	0.0838505i
$771$	13.3330	+	11.9017i	0.480177	+	0.428629i
$772$	−7.24548	+	7.24548i	−0.260771	+	0.260771i
$773$	3.59275	−	3.59275i	0.129222	−	0.129222i	−0.639538	−	0.768760i	$-0.720874\pi$
$773$	3.59275	−	3.59275i	0.129222	−	0.129222i	0.768760	+	0.639538i	$0.220874\pi$
$774$	−3.53610	−	31.0711i	−0.127102	−	1.11683i
$775$	4.84458	−	1.23693i	0.174023	−	0.0444318i
$776$			7.16582i			0.257238i
$777$	0.700538	+	12.3507i	0.0251317	+	0.443080i
$778$	6.72702	+	6.72702i	0.241175	+	0.241175i
$779$	1.48564			0.0532285
$780$	−4.62352	−	3.18862i	−0.165548	−	0.114171i
$781$	−23.8302			−0.852710
$782$	−1.01395	−	1.01395i	−0.0362589	−	0.0362589i
$783$	−6.66717	+	1.14432i	−0.238265	+	0.0408947i
$784$		−	1.92128i		−	0.0686172i
$785$	−19.6670	−	15.2765i	−0.701946	−	0.545242i
$786$	19.1367	−	21.4381i	0.682582	−	0.764671i
$787$	−12.4252	+	12.4252i	−0.442911	+	0.442911i	−0.892989	−	0.450078i	$-0.851396\pi$
$787$	−12.4252	+	12.4252i	−0.442911	+	0.442911i	0.450078	+	0.892989i	$0.351396\pi$
$788$	−3.23816	+	3.23816i	−0.115355	+	0.115355i
$789$	18.5430	−	20.7730i	0.660148	−	0.739539i
$790$	−6.29682	−	4.89110i	−0.224031	−	0.174018i
$791$			11.3669i			0.404161i
$792$	−8.69489	−	6.91803i	−0.308959	−	0.245822i
$793$	−11.3852	−	11.3852i	−0.404302	−	0.404302i
$794$	15.3815			0.545869
$795$	−1.27513	−	0.879396i	−0.0452241	−	0.0311890i
$796$	17.2659			0.611972
$797$	10.3655	+	10.3655i	0.367165	+	0.367165i	0.866442	−	0.499277i	$-0.166401\pi$
$797$	10.3655	+	10.3655i	0.367165	+	0.367165i	−0.499277	+	0.866442i	$0.666401\pi$
$798$	0.0654334	+	1.15361i	0.00231632	+	0.0408375i
$799$		−	0.221393i		−	0.00783231i
$800$	4.30028	+	2.55100i	0.152038	+	0.0901914i
$801$	32.0732	−	3.65015i	1.13325	−	0.128972i
$802$	−5.66191	+	5.66191i	−0.199929	+	0.199929i
$803$	21.9111	−	21.9111i	0.773227	−	0.773227i
$804$	17.2181	+	15.3697i	0.607235	+	0.542047i
$805$	−10.5674	+	1.32775i	−0.372452	+	0.0467971i
$806$			1.45015i			0.0510795i
$807$	−9.88950	+	0.560936i	−0.348127	+	0.0197459i
$808$	−1.56502	−	1.56502i	−0.0550573	−	0.0550573i
$809$	18.7297			0.658500			0.329250	−	0.944243i	$-0.393204\pi$
$809$	18.7297			0.658500			0.329250	+	0.944243i	$0.393204\pi$
$810$	−8.45825	+	18.2608i	−0.297192	+	0.641620i
$811$	−20.9677			−0.736276			−0.368138	−	0.929771i	$-0.620005\pi$
$811$	−20.9677			−0.736276			−0.368138	+	0.929771i	$0.620005\pi$
$812$	−2.07456	−	2.07456i	−0.0728028	−	0.0728028i
$813$	25.3164	−	1.43595i	0.887884	−	0.0503611i
$814$		−	11.7380i		−	0.411417i
$815$	−4.41003	+	5.67748i	−0.154476	+	0.198873i
$816$	−0.876664	−	0.782553i	−0.0306894	−	0.0273948i
$817$	2.18190	−	2.18190i	0.0763350	−	0.0763350i
$818$	−3.12182	+	3.12182i	−0.109152	+	0.109152i
$819$	9.74132	−	1.10863i	0.340389	−	0.0387386i
$820$	1.39902	+	11.1346i	0.0488559	+	0.388839i
$821$			47.8971i			1.67162i	0.549018	+	0.835811i	$0.315002\pi$
$821$			47.8971i			1.67162i	−0.549018	+	0.835811i	$0.684998\pi$
$822$	−1.59701	−	28.1558i	−0.0557021	−	0.982048i
$823$	7.06755	+	7.06755i	0.246359	+	0.246359i	0.819475	−	0.573115i	$-0.194265\pi$
$823$	7.06755	+	7.06755i	0.246359	+	0.246359i	−0.573115	+	0.819475i	$0.694265\pi$
$824$	6.43350			0.224122
$825$	9.68224	+	30.5792i	0.337092	+	1.06463i
$826$	27.7511			0.965585
$827$	31.7052	+	31.7052i	1.10250	+	1.10250i	0.994108	+	0.108391i	$0.0345699\pi$
$827$	31.7052	+	31.7052i	1.10250	+	1.10250i	0.108391	+	0.994108i	$0.465430\pi$
$828$	4.96169	+	3.94774i	0.172431	+	0.137193i
$829$		−	56.5372i		−	1.96362i	−0.189867	−	0.981810i	$-0.560806\pi$
$829$		−	56.5372i		−	1.96362i	0.189867	−	0.981810i	$-0.439194\pi$
$830$	0.770602	+	6.13313i	0.0267480	+	0.212884i
$831$	0.832495	−	0.932612i	0.0288789	−	0.0323520i
$832$	−1.02541	+	1.02541i	−0.0355498	+	0.0355498i
$833$	0.921724	−	0.921724i	0.0319358	−	0.0319358i
$834$	1.96067	−	2.19647i	0.0678926	−	0.0760575i
$835$	−17.0076	+	21.8956i	−0.588572	+	0.757730i
$836$		−	1.09638i		−	0.0379192i
$837$	5.12127	−	0.878989i	0.177017	−	0.0303823i
$838$	1.46414	+	1.46414i	0.0505780	+	0.0505780i
$839$	22.1729			0.765492			0.382746	−	0.923854i	$-0.374978\pi$
$839$	22.1729			0.765492			0.382746	+	0.923854i	$0.374978\pi$
$840$	−8.58456	+	1.57677i	−0.296195	+	0.0544037i
$841$	−27.3052			−0.941557
$842$	−20.3173	−	20.3173i	−0.700182	−	0.700182i
$843$	−2.88074	−	50.7884i	−0.0992178	−	1.74925i
$844$		−	21.7612i		−	0.749050i
$845$	24.1765	−	3.03767i	0.831696	−	0.104499i
$846$	0.110696	+	0.972669i	0.00380582	+	0.0334411i
$847$	4.33092	−	4.33092i	0.148812	−	0.148812i
$848$	−0.282801	+	0.282801i	−0.00971142	+	0.00971142i
$849$	3.24302	+	2.89487i	0.111300	+	0.0993518i
$850$	0.839209	+	3.28686i	0.0287846	+	0.112738i
$851$			6.69824i			0.229613i
$852$	11.1262	−	0.631083i	0.381178	−	0.0216206i
$853$	10.9476	+	10.9476i	0.374837	+	0.374837i	0.869235	−	0.494398i	$-0.164612\pi$
$853$	10.9476	+	10.9476i	0.374837	+	0.374837i	−0.494398	+	0.869235i	$0.664612\pi$
$854$	−25.0219			−0.856232
$855$	−1.92964	+	0.468760i	−0.0659922	+	0.0160312i
$856$	−15.6629			−0.535348
$857$	27.1672	+	27.1672i	0.928013	+	0.928013i	0.997577	−	0.0695640i	$-0.0221608\pi$
$857$	27.1672	+	27.1672i	0.928013	+	0.928013i	−0.0695640	+	0.997577i	$0.522161\pi$
$858$	−9.28794	+	0.526815i	−0.317085	+	0.0179852i
$859$			27.0450i			0.922764i	0.887201	+	0.461382i	$0.152646\pi$
$859$			27.0450i			0.922764i	−0.887201	+	0.461382i	$0.847354\pi$
$860$	18.4077	+	14.2983i	0.627698	+	0.487569i
$861$	−14.6143	−	13.0454i	−0.498054	−	0.444587i
$862$	14.2134	−	14.2134i	0.484112	−	0.484112i
$863$	37.2201	−	37.2201i	1.26699	−	1.26699i	0.319352	−	0.947636i	$-0.396535\pi$
$863$	37.2201	−	37.2201i	1.26699	−	1.26699i	0.947636	−	0.319352i	$-0.103465\pi$
$864$	4.24282	+	2.99974i	0.144344	+	0.102053i
$865$	−16.1371	−	12.5346i	−0.548679	−	0.426191i
$866$			24.6950i			0.839169i
$867$	1.62229	+	28.6016i	0.0550960	+	0.971362i
$868$	1.59354	+	1.59354i	0.0540882	+	0.0540882i
$869$	−13.2067			−0.448005
$870$	2.86255	−	4.15071i	0.0970495	−	0.140722i
$871$	19.3237			0.654759
$872$	−7.06726	−	7.06726i	−0.239327	−	0.239327i
$873$	13.3846	−	16.8224i	0.453001	−	0.569352i
$874$			0.625645i			0.0211628i
$875$	23.1035	+	10.0532i	0.781042	+	0.339861i
$876$	−9.64998	+	10.8105i	−0.326042	+	0.365253i
$877$	−9.25658	+	9.25658i	−0.312572	+	0.312572i	−0.845905	−	0.533333i	$-0.820939\pi$
$877$	−9.25658	+	9.25658i	−0.312572	+	0.312572i	0.533333	+	0.845905i	$0.320939\pi$
$878$	25.7668	−	25.7668i	0.869587	−	0.869587i
$879$	23.2936	−	26.0949i	0.785673	−	0.880159i
$880$	8.21724	−	1.03246i	0.277003	−	0.0348043i
$881$			4.80357i			0.161836i	0.996721	+	0.0809182i	$0.0257852\pi$
$881$			4.80357i			0.161836i	−0.996721	+	0.0809182i	$0.974215\pi$
$882$	−3.58865	+	4.51037i	−0.120836	+	0.151872i
$883$	20.8825	+	20.8825i	0.702751	+	0.702751i	0.965000	−	0.262249i	$-0.0844642\pi$
$883$	20.8825	+	20.8825i	0.702751	+	0.702751i	−0.262249	+	0.965000i	$0.584464\pi$
$884$	−0.983873			−0.0330912
$885$	8.61578	+	46.9077i	0.289616	+	1.57679i
$886$	−7.33353			−0.246375
$887$	−12.2705	−	12.2705i	−0.412003	−	0.412003i	0.470433	−	0.882436i	$-0.344098\pi$
$887$	−12.2705	−	12.2705i	−0.412003	−	0.412003i	−0.882436	+	0.470433i	$0.844098\pi$
$888$	0.310853	+	5.48044i	0.0104315	+	0.183912i
$889$		−	20.6434i		−	0.692356i
$890$	−14.7595	+	19.0014i	−0.494739	+	0.636928i
$891$	7.49021	+	32.4814i	0.250932	+	1.08817i
$892$	5.37150	−	5.37150i	0.179851	−	0.179851i
$893$	−0.0683036	+	0.0683036i	−0.00228569	+	0.00228569i
$894$	14.4229	+	12.8745i	0.482372	+	0.430589i
$895$	5.20123	+	41.3960i	0.173858	+	1.38371i
$896$			2.25360i			0.0752875i
$897$	5.30011	−	0.300624i	0.176966	−	0.0100376i
$898$	−27.3667	−	27.3667i	−0.913240	−	0.913240i
$899$	−1.30186			−0.0434194
$900$	−5.33042	−	14.0209i	−0.177681	−	0.467364i
$901$	−0.271344			−0.00903979
$902$	13.1438	+	13.1438i	0.437640	+	0.437640i
$903$	−40.6228	+	2.30414i	−1.35184	+	0.0766769i
$904$			5.04389i			0.167757i
$905$	5.72075	+	45.5308i	0.190164	+	1.51349i
$906$	2.75777	+	2.46172i	0.0916207	+	0.0817850i
$907$	11.8612	−	11.8612i	0.393843	−	0.393843i	−0.482211	−	0.876055i	$-0.660166\pi$
$907$	11.8612	−	11.8612i	0.393843	−	0.393843i	0.876055	+	0.482211i	$0.160166\pi$
$908$	−12.5296	+	12.5296i	−0.415810	+	0.415810i
$909$	0.750811	+	6.59724i	0.0249028	+	0.218817i
$910$	−4.48278	+	5.77114i	−0.148603	+	0.191311i
$911$			33.8899i			1.12282i	0.827537	+	0.561411i	$0.189741\pi$
$911$			33.8899i			1.12282i	−0.827537	+	0.561411i	$0.810259\pi$
$912$	0.0290350	+	0.511898i	0.000961446	+	0.0169506i
$913$	7.23979	+	7.23979i	0.239602	+	0.239602i
$914$	−4.92404			−0.162873
$915$	−7.76844	−	42.2945i	−0.256817	−	1.39821i
$916$	7.68865			0.254040
$917$	−26.4387	−	26.4387i	−0.873082	−	0.873082i
$918$	0.596360	+	3.47458i	0.0196828	+	0.114678i
$919$			57.2926i			1.88991i	0.327202	+	0.944954i	$0.393894\pi$
$919$			57.2926i			1.88991i	−0.327202	+	0.944954i	$0.606106\pi$
$920$	−4.68912	+	0.589168i	−0.154596	+	0.0194243i
$921$	−0.942496	+	1.05584i	−0.0310563	+	0.0347912i
$922$	9.80950	−	9.80950i	0.323059	−	0.323059i
$923$	6.59757	−	6.59757i	0.217162	−	0.217162i
$924$	−9.62738	+	10.7852i	−0.316717	+	0.354807i
$925$	8.08467	−	13.6285i	0.265822	−	0.448104i
$926$		−	3.55963i		−	0.116977i
$927$	−15.1032	−	12.0168i	−0.496055	−	0.394683i
$928$	−0.920553	−	0.920553i	−0.0302186	−	0.0302186i
$929$	39.2239			1.28689			0.643447	−	0.765491i	$-0.277504\pi$
$929$	39.2239			1.28689			0.643447	+	0.765491i	$0.277504\pi$
$930$	−2.19882	+	3.18829i	−0.0721020	+	0.104548i
$931$	−0.568736			−0.0186396
$932$	−6.41781	−	6.41781i	−0.210223	−	0.210223i
$933$	2.94205	+	51.8694i	0.0963184	+	1.69813i
$934$			42.4816i			1.39004i
$935$	4.43749	+	3.44686i	0.145122	+	0.112724i
$936$	4.32256	−	0.491937i	0.141287	−	0.0160795i
$937$	14.6953	−	14.6953i	0.480074	−	0.480074i	−0.425081	−	0.905155i	$-0.639755\pi$
$937$	14.6953	−	14.6953i	0.480074	−	0.480074i	0.905155	+	0.425081i	$0.139755\pi$
$938$	21.2343	−	21.2343i	0.693326	−	0.693326i
$939$	12.2777	+	10.9596i	0.400666	+	0.357654i
$940$	−0.576247	−	0.447604i	−0.0187951	−	0.0145992i
$941$		−	36.6501i		−	1.19476i	−0.801959	−	0.597379i	$-0.796209\pi$
$941$		−	36.6501i		−	1.19476i	0.801959	−	0.597379i	$-0.203791\pi$
$942$	19.2589	−	1.09237i	0.627488	−	0.0355913i
$943$	−7.50042	−	7.50042i	−0.244247	−	0.244247i
$944$	12.3141			0.400791
$945$	23.0981	+	12.3330i	0.751383	+	0.401192i
$946$	38.6075			1.25524
$947$	35.2800	+	35.2800i	1.14645	+	1.14645i	0.987246	+	0.159200i	$0.0508914\pi$
$947$	35.2800	+	35.2800i	1.14645	+	1.14645i	0.159200	+	0.987246i	$0.449109\pi$
$948$	6.16614	−	0.349746i	0.200267	−	0.0113592i
$949$			12.1325i			0.393839i
$950$	0.755145	−	1.27297i	0.0245001	−	0.0413005i
$951$	32.2904	+	28.8240i	1.04709	+	0.934682i
$952$	−1.08115	+	1.08115i	−0.0350404	+	0.0350404i
$953$	−9.14374	+	9.14374i	−0.296195	+	0.296195i	−0.839521	−	0.543327i	$-0.817165\pi$
$953$	−9.14374	+	9.14374i	−0.296195	+	0.296195i	0.543327	+	0.839521i	$0.317165\pi$
$954$	1.19213	−	0.135672i	0.0385965	−	0.00439255i
$955$	−50.1141	+	6.29663i	−1.62165	+	0.203754i
$956$			23.1583i			0.748994i
$957$	−0.472942	−	8.33814i	−0.0152881	−	0.269534i
$958$	17.2711	+	17.2711i	0.558005	+	0.558005i
$959$	−36.6929			−1.18488
$960$	−3.80926	+	0.699666i	−0.122943	+	0.0225816i
$961$	1.00000			0.0322581
$962$	3.24976	+	3.24976i	0.104777	+	0.104777i
$963$	36.7701	+	29.2559i	1.18490	+	0.942758i
$964$		−	24.6719i		−	0.794628i
$965$	−14.0552	+	18.0948i	−0.452454	+	0.582491i
$966$	5.49381	−	6.15451i	0.176760	−	0.198018i
$967$	22.9601	−	22.9601i	0.738346	−	0.738346i	−0.233912	−	0.972258i	$-0.575153\pi$
$967$	22.9601	−	22.9601i	0.738346	−	0.738346i	0.972258	+	0.233912i	$0.0751527\pi$
$968$	1.92178	−	1.92178i	0.0617683	−	0.0617683i
$969$	−0.231651	+	0.259510i	−0.00744170	+	0.00833665i
$970$	1.99755	+	15.8983i	0.0641374	+	0.510462i
$971$			0.280300i			0.00899525i	0.999990	+	0.00449762i	$0.00143164\pi$
$971$			0.280300i			0.00899525i	−0.999990	+	0.00449762i	$0.998568\pi$
$972$	−4.35735	−	14.9671i	−0.139762	−	0.480069i
$973$	−2.70881	−	2.70881i	−0.0868405	−	0.0868405i
$974$	23.0912			0.739891
$975$	−11.1467	−	5.78550i	−0.356980	−	0.185284i
$976$	−11.1031			−0.355401
$977$	20.5957	+	20.5957i	0.658916	+	0.658916i	0.955124	−	0.296208i	$-0.0957221\pi$
$977$	20.5957	+	20.5957i	0.658916	+	0.658916i	−0.296208	+	0.955124i	$0.595722\pi$
$978$	−0.315346	−	5.55966i	−0.0100836	−	0.177778i
$979$			39.8527i			1.27370i
$980$	−0.535577	−	4.26260i	−0.0171084	−	0.136164i
$981$	3.39048	+	29.7915i	0.108250	+	0.951170i
$982$	8.98286	−	8.98286i	0.286655	−	0.286655i
$983$	10.1213	−	10.1213i	0.322820	−	0.322820i	−0.527028	−	0.849848i	$-0.676694\pi$
$983$	10.1213	−	10.1213i	0.322820	−	0.322820i	0.849848	+	0.527028i	$0.176694\pi$
$984$	−6.48486	−	5.78870i	−0.206730	−	0.184537i
$985$	−6.28159	+	8.08693i	−0.200148	+	0.257671i
$986$		−	0.883261i		−	0.0281288i
$987$	1.27168	−	0.0721302i	0.0404781	−	0.00229593i
$988$	0.303542	+	0.303542i	0.00965697	+	0.00965697i
$989$	−22.0312			−0.700550
$990$	−21.2192	−	12.9247i	−0.674389	−	0.410774i
$991$	−16.7627			−0.532485			−0.266243	−	0.963906i	$-0.585782\pi$
$991$	−16.7627			−0.532485			−0.266243	+	0.963906i	$0.585782\pi$
$992$	0.707107	+	0.707107i	0.0224507	+	0.0224507i
$993$	−26.7659	+	1.51817i	−0.849389	+	0.0481777i
$994$		−	14.4998i		−	0.459906i
$995$	38.3064	−	4.81304i	1.21440	−	0.152584i
$996$	−3.57196	−	3.18851i	−0.113182	−	0.101032i
$997$	−26.7133	+	26.7133i	−0.846019	+	0.846019i	−0.989634	−	0.143615i	$-0.954127\pi$
$997$	−26.7133	+	26.7133i	−0.846019	+	0.846019i	0.143615	+	0.989634i	$0.454127\pi$
$998$	7.60159	−	7.60159i	0.240624	−	0.240624i
$999$	9.50685	−	13.4464i	0.300783	−	0.425427i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.j.h.683.11	yes	40
3.2	odd	2	inner	930.2.j.h.683.7	yes	40
5.2	odd	4	inner	930.2.j.h.497.7	✓	40
15.2	even	4	inner	930.2.j.h.497.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.7	✓	40	5.2	odd	4	inner
930.2.j.h.497.11	yes	40	15.2	even	4	inner
930.2.j.h.683.7	yes	40	3.2	odd	2	inner
930.2.j.h.683.11	yes	40	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.j (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +(-1.72927 + 0.0980849i) q^{3} +1.00000i q^{4} +(0.278761 + 2.21862i) q^{5} +(-1.29214 - 1.15342i) q^{6} +(-1.59354 + 1.59354i) q^{7} +(-0.707107 + 0.707107i) q^{8} +(2.98076 - 0.339231i) q^{9} +(-1.37169 + 1.76592i) q^{10} +3.70376i q^{11} +(-0.0980849 - 1.72927i) q^{12} +(-1.02541 - 1.02541i) q^{13} -2.25360 q^{14} +(-0.699666 - 3.80926i) q^{15} -1.00000 q^{16} +(-0.479745 - 0.479745i) q^{17} +(2.34759 + 1.86784i) q^{18} +0.296019i q^{19} +(-2.21862 + 0.278761i) q^{20} +(2.59936 - 2.91196i) q^{21} +(-2.61895 + 2.61895i) q^{22} +(1.49449 - 1.49449i) q^{23} +(1.15342 - 1.29214i) q^{24} +(-4.84458 + 1.23693i) q^{25} -1.45015i q^{26} +(-5.12127 + 0.878989i) q^{27} +(-1.59354 - 1.59354i) q^{28} +1.30186 q^{29} +(2.19882 - 3.18829i) q^{30} -1.00000 q^{31} +(-0.707107 - 0.707107i) q^{32} +(-0.363282 - 6.40480i) q^{33} -0.678461i q^{34} +(-3.97967 - 3.09124i) q^{35} +(0.339231 + 2.98076i) q^{36} +(-2.24098 + 2.24098i) q^{37} +(-0.209317 + 0.209317i) q^{38} +(1.87380 + 1.67264i) q^{39} +(-1.76592 - 1.37169i) q^{40} -5.01872i q^{41} +(3.89709 - 0.221044i) q^{42} +(-7.37080 - 7.37080i) q^{43} -3.70376 q^{44} +(1.58354 + 6.51862i) q^{45} +2.11353 q^{46} +(0.230740 + 0.230740i) q^{47} +(1.72927 - 0.0980849i) q^{48} +1.92128i q^{49} +(-4.30028 - 2.55100i) q^{50} +(0.876664 + 0.782553i) q^{51} +(1.02541 - 1.02541i) q^{52} +(0.282801 - 0.282801i) q^{53} +(-4.24282 - 2.99974i) q^{54} +(-8.21724 + 1.03246i) q^{55} -2.25360i q^{56} +(-0.0290350 - 0.511898i) q^{57} +(0.920553 + 0.920553i) q^{58} -12.3141 q^{59} +(3.80926 - 0.699666i) q^{60} +11.1031 q^{61} +(-0.707107 - 0.707107i) q^{62} +(-4.20937 + 5.29053i) q^{63} -1.00000i q^{64} +(1.98916 - 2.56085i) q^{65} +(4.27200 - 4.78576i) q^{66} +(-9.42240 + 9.42240i) q^{67} +(0.479745 - 0.479745i) q^{68} +(-2.43779 + 2.73097i) q^{69} +(-0.628216 - 4.99989i) q^{70} +6.43406i q^{71} +(-1.86784 + 2.34759i) q^{72} +(-5.91592 - 5.91592i) q^{73} -3.16922 q^{74} +(8.25628 - 2.61417i) q^{75} -0.296019 q^{76} +(-5.90207 - 5.90207i) q^{77} +(0.142238 + 2.50771i) q^{78} +3.56575i q^{79} +(-0.278761 - 2.21862i) q^{80} +(8.76985 - 2.02233i) q^{81} +(3.54877 - 3.54877i) q^{82} +(1.95472 - 1.95472i) q^{83} +(2.91196 + 2.59936i) q^{84} +(0.930639 - 1.19811i) q^{85} -10.4239i q^{86} +(-2.25127 + 0.127693i) q^{87} +(-2.61895 - 2.61895i) q^{88} +10.7601 q^{89} +(-3.48962 + 5.72909i) q^{90} +3.26807 q^{91} +(1.49449 + 1.49449i) q^{92} +(1.72927 - 0.0980849i) q^{93} +0.326316i q^{94} +(-0.656756 + 0.0825186i) q^{95} +(1.29214 + 1.15342i) q^{96} +(5.06700 - 5.06700i) q^{97} +(-1.35855 + 1.35855i) q^{98} +(1.25643 + 11.0400i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q - 4 q^{3} + 8 q^{6} - 8 q^{7} + 4 q^{12} + 24 q^{13} - 12 q^{15} - 40 q^{16} - 56 q^{21} + 16 q^{22} - 48 q^{25} + 8 q^{27} - 8 q^{28} + 4 q^{30} - 40 q^{31} - 20 q^{33} - 8 q^{37} - 8 q^{40} + 12 q^{42}+ \cdots + 24 q^{97}+O(q^{100}) \) 40 * q - 4 * q^3 + 8 * q^6 - 8 * q^7 + 4 * q^12 + 24 * q^13 - 12 * q^15 - 40 * q^16 - 56 * q^21 + 16 * q^22 - 48 * q^25 + 8 * q^27 - 8 * q^28 + 4 * q^30 - 40 * q^31 - 20 * q^33 - 8 * q^37 - 8 * q^40 + 12 * q^42 - 16 * q^43 + 76 * q^45 - 8 * q^46 + 4 * q^48 + 16 * q^51 - 24 * q^52 - 48 * q^55 + 56 * q^57 - 56 * q^58 + 12 * q^60 + 128 * q^61 - 24 * q^63 + 16 * q^66 + 8 * q^67 + 32 * q^70 + 248 * q^73 - 8 * q^75 + 56 * q^76 + 8 * q^78 + 40 * q^81 - 8 * q^82 - 48 * q^85 + 12 * q^87 + 16 * q^88 + 16 * q^90 - 192 * q^91 + 4 * q^93 - 8 * q^96 + 24 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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