LMFDB - Embedded newform 930.2.j.h.497.11

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			497.11
Character	$\chi$	$=$	930.497
Dual form			930.2.j.h.683.11

$q$-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 $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

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

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	0.338622	−	0.940922i	$-0.390039\pi$
$7$	−1.59354	−	1.59354i	−0.602300	−	0.602300i	−0.940922	+	0.338622i	$0.890039\pi$
$8$	−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	$-0.811430\pi$
$11$		−	3.70376i		−	1.11672i	0.829597	−	0.558362i	$-0.188570\pi$
$12$	−0.0980849	+	1.72927i	−0.0283147	+	0.499198i
$13$	−1.02541	+	1.02541i	−0.284399	+	0.284399i	−0.834860	−	0.550462i	$-0.814452\pi$
$13$	−1.02541	+	1.02541i	−0.284399	+	0.284399i	0.550462	+	0.834860i	$0.314452\pi$
$14$	−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	−0.762887	−	0.646532i	$-0.776219\pi$
$17$	−0.479745	+	0.479745i	−0.116355	+	0.116355i	0.646532	+	0.762887i	$0.276219\pi$
$18$	2.34759	−	1.86784i	0.553332	−	0.440255i
$19$		−	0.296019i		−	0.0679115i	−0.999423	−	0.0339558i	$-0.989189\pi$
$19$		−	0.296019i		−	0.0679115i	0.999423	−	0.0339558i	$-0.0108105\pi$
$20$	−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	0.845538	−	0.533915i	$-0.179280\pi$
$23$	1.49449	+	1.49449i	0.311623	+	0.311623i	−0.533915	+	0.845538i	$0.679280\pi$
$24$	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	0.498484	−	0.866899i	$-0.333890\pi$
$37$	−2.24098	−	2.24098i	−0.368414	−	0.368414i	−0.866899	+	0.498484i	$0.833890\pi$
$38$	−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	$0.128181\pi$
$41$			5.01872i			0.783792i	−0.920010	+	0.391896i	$0.871819\pi$
$42$	3.89709	+	0.221044i	0.601334	+	0.0341079i
$43$	−7.37080	+	7.37080i	−1.12404	+	1.12404i	−0.132907	+	0.991128i	$0.542431\pi$
$43$	−7.37080	+	7.37080i	−1.12404	+	1.12404i	−0.991128	+	0.132907i	$0.957569\pi$
$44$	−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	−0.690078	−	0.723735i	$-0.742424\pi$
$47$	0.230740	−	0.230740i	0.0336569	−	0.0336569i	0.723735	+	0.690078i	$0.242424\pi$
$48$	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	0.726263	−	0.687417i	$-0.241256\pi$
$53$	0.282801	+	0.282801i	0.0388457	+	0.0388457i	−0.687417	+	0.726263i	$0.741256\pi$
$54$	−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	−0.986326	−	0.164803i	$-0.947301\pi$
$67$	−9.42240	−	9.42240i	−1.15113	−	1.15113i	−0.164803	−	0.986326i	$-0.552699\pi$
$68$	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	$-0.875307\pi$
$71$		−	6.43406i		−	0.763582i	0.924249	−	0.381791i	$-0.124693\pi$
$72$	−1.86784	−	2.34759i	−0.220127	−	0.276666i
$73$	−5.91592	+	5.91592i	−0.692407	+	0.692407i	−0.962761	−	0.270354i	$-0.912859\pi$
$73$	−5.91592	+	5.91592i	−0.692407	+	0.692407i	0.270354	+	0.962761i	$0.412859\pi$
$74$	−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	$-0.935714\pi$
$79$		−	3.56575i		−	0.401178i	0.979675	−	0.200589i	$-0.0642856\pi$
$80$	−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	0.806200	−	0.591642i	$-0.201520\pi$
$83$	1.95472	+	1.95472i	0.214558	+	0.214558i	−0.591642	+	0.806200i	$0.701520\pi$
$84$	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	0.915895	−	0.401419i	$-0.131483\pi$
$97$	5.06700	+	5.06700i	0.514476	+	0.514476i	−0.401419	+	0.915895i	$0.631483\pi$
$98$	−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	$-0.964878\pi$
$101$		−	2.21327i		−	0.220229i	0.993919	−	0.110115i	$-0.0351218\pi$
$102$	0.0665468	−	1.17324i	0.00658911	−	0.116168i
$103$	−4.54917	+	4.54917i	−0.448243	+	0.448243i	−0.894770	−	0.446527i	$-0.852661\pi$
$103$	−4.54917	+	4.54917i	−0.448243	+	0.448243i	0.446527	+	0.894770i	$0.352661\pi$
$104$	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	0.0733937	−	0.997303i	$-0.476617\pi$
$107$	11.0754	−	11.0754i	1.07070	−	1.07070i	0.997303	−	0.0733937i	$-0.0233830\pi$
$108$	−0.878989	+	5.12127i	−0.0845808	+	0.492794i
$109$		−	9.99461i		−	0.957310i	−0.878003	−	0.478655i	$-0.841125\pi$
$109$		−	9.99461i		−	0.957310i	0.878003	−	0.478655i	$-0.158875\pi$
$110$	−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	0.854676	−	0.519161i	$-0.173756\pi$
$113$	3.56657	+	3.56657i	0.335515	+	0.335515i	−0.519161	+	0.854676i	$0.673756\pi$
$114$	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	0.358695	−	0.933455i	$-0.383222\pi$
$127$	−6.47722	−	6.47722i	−0.574760	−	0.574760i	−0.933455	+	0.358695i	$0.883222\pi$
$128$	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	$-0.741937\pi$
$131$		−	16.5912i		−	1.44958i	0.688970	−	0.724790i	$-0.258063\pi$
$132$	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	−0.0162416	−	0.999868i	$-0.505170\pi$
$137$	11.5131	−	11.5131i	0.983626	−	0.983626i	0.999868	+	0.0162416i	$0.00517010\pi$
$138$	−3.65486	−	0.207305i	−0.311123	−	0.0176470i
$139$		−	1.69987i		−	0.144181i	−0.997398	−	0.0720907i	$-0.977033\pi$
$139$		−	1.69987i		−	0.144181i	0.997398	−	0.0720907i	$-0.0229671\pi$
$140$	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	0.319193	−	0.947690i	$-0.396588\pi$
$157$	−7.87504	−	7.87504i	−0.628497	−	0.628497i	−0.947690	+	0.319193i	$0.896588\pi$
$158$	−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	−0.612447	−	0.790511i	$-0.709815\pi$
$163$	2.27337	−	2.27337i	0.178064	−	0.178064i	0.790511	+	0.612447i	$0.209815\pi$
$164$	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	−0.281204	−	0.959648i	$-0.590734\pi$
$167$	8.76742	−	8.76742i	0.678444	−	0.678444i	0.959648	+	0.281204i	$0.0907339\pi$
$168$	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	0.417438	−	0.908705i	$-0.362928\pi$
$173$	−6.46161	−	6.46161i	−0.491267	−	0.491267i	−0.908705	+	0.417438i	$0.862928\pi$
$174$	−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	$-0.695524\pi$
$191$		−	22.5879i		−	1.63440i	0.576351	−	0.817202i	$-0.304476\pi$
$192$	0.0980849	−	1.72927i	0.00707867	−	0.124799i
$193$	7.24548	−	7.24548i	0.521541	−	0.521541i	−0.396496	−	0.918037i	$-0.629774\pi$
$193$	7.24548	−	7.24548i	0.521541	−	0.521541i	0.918037	+	0.396496i	$0.129774\pi$
$194$	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	−0.582279	−	0.812989i	$-0.697839\pi$
$197$	3.23816	−	3.23816i	0.230709	−	0.230709i	0.812989	+	0.582279i	$0.197839\pi$
$198$	−6.91803	−	8.69489i	−0.491643	−	0.617919i
$199$			17.2659i			1.22394i	0.790879	+	0.611972i	$0.209623\pi$
$199$			17.2659i			1.22394i	−0.790879	+	0.611972i	$0.790377\pi$
$200$	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	−0.863703	−	0.504001i	$-0.831861\pi$
$223$	−5.37150	+	5.37150i	−0.359702	+	0.359702i	0.504001	+	0.863703i	$0.331861\pi$
$224$	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	−0.156118	−	0.987738i	$-0.549898\pi$
$227$	12.5296	−	12.5296i	0.831620	−	0.831620i	0.987738	+	0.156118i	$0.0498981\pi$
$228$	0.511898	+	0.0290350i	0.0339013	+	0.00192289i
$229$			7.68865i			0.508081i	0.967194	+	0.254040i	$0.0817596\pi$
$229$			7.68865i			0.508081i	−0.967194	+	0.254040i	$0.918240\pi$
$230$	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	0.464912	−	0.885357i	$-0.346086\pi$
$233$	−6.41781	−	6.41781i	−0.420445	−	0.420445i	−0.885357	+	0.464912i	$0.846086\pi$
$234$	−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	$-0.799088\pi$
$251$		−	18.6979i		−	1.18020i	0.807330	−	0.590100i	$-0.200912\pi$
$252$	−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	−0.897054	−	0.441921i	$-0.854297\pi$
$257$	−7.29634	+	7.29634i	−0.455133	+	0.455133i	0.441921	+	0.897054i	$0.354297\pi$
$258$	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	0.263650	−	0.964618i	$-0.415074\pi$
$263$	−11.3678	−	11.3678i	−0.700968	−	0.700968i	−0.964618	+	0.263650i	$0.915074\pi$
$264$	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	0.691608	−	0.722273i	$-0.256903\pi$
$277$	−0.510362	−	0.510362i	−0.0306647	−	0.0306647i	−0.722273	+	0.691608i	$0.756903\pi$
$278$	−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	$-0.660184\pi$
$281$		−	29.3698i		−	1.75206i	0.482260	−	0.876028i	$-0.339816\pi$
$282$	−0.0320067	+	0.564289i	−0.00190597	+	0.0336029i
$283$	−1.77470	+	1.77470i	−0.105495	+	0.105495i	−0.757884	−	0.652389i	$-0.773767\pi$
$283$	−1.77470	+	1.77470i	−0.105495	+	0.105495i	0.652389	+	0.757884i	$0.273767\pi$
$284$	−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	0.153841	−	0.988096i	$-0.450836\pi$
$293$	−14.2801	−	14.2801i	−0.834255	−	0.834255i	−0.988096	+	0.153841i	$0.950836\pi$
$294$	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	0.723403	−	0.690426i	$-0.242577\pi$
$307$	0.577798	+	0.577798i	0.0329767	+	0.0329767i	−0.690426	+	0.723403i	$0.742577\pi$
$308$	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	$0.323657\pi$
$311$			29.9949i			1.70086i	−0.526091	+	0.850429i	$0.676343\pi$
$312$	−2.50771	−	0.142238i	−0.141971	−	0.00805265i
$313$	−6.71881	+	6.71881i	−0.379769	+	0.379769i	−0.871019	−	0.491250i	$-0.836540\pi$
$313$	−6.71881	+	6.71881i	−0.379769	+	0.379769i	0.491250	+	0.871019i	$0.336540\pi$
$314$	−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	−0.999972	−	0.00749364i	$-0.997615\pi$
$317$	−17.6706	+	17.6706i	−0.992478	+	0.992478i	0.00749364	+	0.999972i	$0.497615\pi$
$318$	−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	0.0105948	−	0.999944i	$-0.496627\pi$
$337$	−18.1620	−	18.1620i	−0.989349	−	0.989349i	−0.999944	+	0.0105948i	$0.996627\pi$
$338$	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	−0.962943	−	0.269704i	$-0.913074\pi$
$347$	−12.9136	+	12.9136i	−0.693239	+	0.693239i	0.269704	+	0.962943i	$0.413074\pi$
$348$	−0.127693	+	2.25127i	−0.00684505	+	0.120681i
$349$		−	30.6701i		−	1.64173i	−0.571119	−	0.820867i	$-0.693490\pi$
$349$		−	30.6701i		−	1.64173i	0.571119	−	0.820867i	$-0.306510\pi$
$350$	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	0.945246	−	0.326359i	$-0.105822\pi$
$353$	11.6278	+	11.6278i	0.618886	+	0.618886i	−0.326359	+	0.945246i	$0.605822\pi$
$354$	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	0.825038	−	0.565077i	$-0.191154\pi$
$367$	4.98013	+	4.98013i	0.259961	+	0.259961i	−0.565077	+	0.825038i	$0.691154\pi$
$368$	−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	−0.145146	−	0.989410i	$-0.546365\pi$
$373$	16.3054	−	16.3054i	0.844264	−	0.844264i	0.989410	+	0.145146i	$0.0463653\pi$
$374$	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	$-0.851107\pi$
$379$		−	17.5558i		−	0.901780i	0.892579	−	0.450890i	$-0.148893\pi$
$380$	−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	0.511785	−	0.859113i	$-0.328984\pi$
$383$	−6.79735	−	6.79735i	−0.347328	−	0.347328i	−0.859113	+	0.511785i	$0.828984\pi$
$384$	−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	0.925243	−	0.379374i	$-0.123861\pi$
$397$	10.8764	+	10.8764i	0.545869	+	0.545869i	−0.379374	+	0.925243i	$0.623861\pi$
$398$	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	$-0.935929\pi$
$401$		−	8.00715i		−	0.399858i	0.979810	−	0.199929i	$-0.0640711\pi$
$402$	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	$-0.965187\pi$
$409$		−	4.41491i		−	0.218303i	0.994025	−	0.109152i	$-0.0348134\pi$
$410$	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	$0.160857\pi$
$431$			20.1008i			0.968224i	−0.875006	+	0.484112i	$0.839143\pi$
$432$	5.12127	+	0.878989i	0.246397	+	0.0422904i
$433$	17.4620	−	17.4620i	0.839169	−	0.839169i	−0.149581	−	0.988750i	$-0.547792\pi$
$433$	17.4620	−	17.4620i	0.839169	−	0.839169i	0.988750	+	0.149581i	$0.0477924\pi$
$434$	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	$0.335615\pi$
$439$			36.4397i			1.73917i	−0.493781	+	0.869587i	$0.664385\pi$
$440$	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	0.573106	−	0.819481i	$-0.305738\pi$
$443$	−5.18559	−	5.18559i	−0.246375	−	0.246375i	−0.819481	+	0.573106i	$0.805738\pi$
$444$	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	0.620965	−	0.783838i	$-0.286741\pi$
$457$	−3.48182	−	3.48182i	−0.162873	−	0.162873i	−0.783838	+	0.620965i	$0.786741\pi$
$458$	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	$0.104711\pi$
$461$			13.8727i			0.646117i	−0.946379	+	0.323059i	$0.895289\pi$
$462$	0.818694	−	14.4339i	0.0380891	−	0.671524i
$463$	−2.51704	+	2.51704i	−0.116977	+	0.116977i	−0.763172	−	0.646195i	$-0.776359\pi$
$463$	−2.51704	+	2.51704i	−0.116977	+	0.116977i	0.646195	+	0.763172i	$0.276359\pi$
$464$	−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	0.564836	−	0.825204i	$-0.308940\pi$
$467$	30.0390	−	30.0390i	1.39004	−	1.39004i	0.825204	−	0.564836i	$-0.191060\pi$
$468$	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	0.972557	−	0.232666i	$-0.0747448\pi$
$487$	16.3280	+	16.3280i	0.739891	+	0.739891i	−0.232666	+	0.972557i	$0.574745\pi$
$488$	−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	$0.0925432\pi$
$491$			12.7037i			0.573309i	−0.958034	+	0.286655i	$0.907457\pi$
$492$	−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	$0.0773521\pi$
$499$			10.7503i			0.481248i	−0.970618	+	0.240624i	$0.922648\pi$
$500$	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	0.994520	−	0.104551i	$-0.0333406\pi$
$503$	19.9599	+	19.9599i	0.889968	+	0.889968i	−0.104551	+	0.994520i	$0.533341\pi$
$504$	−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	$0.188598\pi$
$521$			25.4930i			1.11687i	−0.829548	+	0.558435i	$0.811402\pi$
$522$	3.05623	−	2.43167i	0.133767	−	0.106431i
$523$	−11.2546	+	11.2546i	−0.492128	+	0.492128i	−0.908976	−	0.416848i	$-0.863135\pi$
$523$	−11.2546	+	11.2546i	−0.492128	+	0.492128i	0.416848	+	0.908976i	$0.363135\pi$
$524$	−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	0.895538	−	0.444985i	$-0.146791\pi$
$547$	10.5375	+	10.5375i	0.450553	+	0.450553i	−0.444985	+	0.895538i	$0.646791\pi$
$548$	−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	−0.726948	−	0.686692i	$-0.759062\pi$
$557$	−0.950084	+	0.950084i	−0.0402563	+	0.0402563i	0.686692	+	0.726948i	$0.259062\pi$
$558$	−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	0.729560	−	0.683916i	$-0.239725\pi$
$563$	1.08303	+	1.08303i	0.0456442	+	0.0456442i	−0.683916	+	0.729560i	$0.739725\pi$
$564$	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	0.00911207	−	0.999958i	$-0.497099\pi$
$577$	−23.8009	−	23.8009i	−0.990846	−	0.990846i	−0.999958	+	0.00911207i	$0.997099\pi$
$578$	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	−0.541157	−	0.840922i	$-0.682013\pi$
$587$	7.26273	−	7.26273i	0.299765	−	0.299765i	0.840922	+	0.541157i	$0.182013\pi$
$588$	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	0.969370	−	0.245606i	$-0.0789871\pi$
$593$	17.6248	+	17.6248i	0.723763	+	0.723763i	−0.245606	+	0.969370i	$0.578987\pi$
$594$	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	0.711396	−	0.702791i	$-0.248063\pi$
$607$	0.212009	+	0.212009i	0.00860518	+	0.00860518i	−0.702791	+	0.711396i	$0.748063\pi$
$608$	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	−0.0334327	−	0.999441i	$-0.510644\pi$
$613$	23.9172	−	23.9172i	0.966008	−	0.966008i	0.999441	+	0.0334327i	$0.0106439\pi$
$614$	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	−0.531145	−	0.847281i	$-0.678238\pi$
$617$	7.85266	−	7.85266i	0.316136	−	0.316136i	0.847281	+	0.531145i	$0.178238\pi$
$618$	0.631029	−	11.1253i	0.0253837	−	0.447524i
$619$		−	7.62713i		−	0.306560i	−0.988183	−	0.153280i	$-0.951016\pi$
$619$		−	7.62713i		−	0.306560i	0.988183	−	0.153280i	$-0.0489837\pi$
$620$	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	$-0.761630\pi$
$641$		−	34.4732i		−	1.36161i	0.732464	−	0.680805i	$-0.238370\pi$
$642$	−1.53630	+	27.0855i	−0.0606328	+	1.06898i
$643$	25.0469	−	25.0469i	0.987752	−	0.987752i	−0.0121735	−	0.999926i	$-0.503875\pi$
$643$	25.0469	−	25.0469i	0.987752	−	0.987752i	0.999926	+	0.0121735i	$0.00387503\pi$
$644$	−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	−0.775489	−	0.631361i	$-0.782496\pi$
$647$	−3.66605	+	3.66605i	−0.144127	+	0.144127i	0.631361	+	0.775489i	$0.282496\pi$
$648$	−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	−0.954322	−	0.298780i	$-0.903420\pi$
$653$	−32.0216	−	32.0216i	−1.25310	−	1.25310i	−0.298780	−	0.954322i	$-0.596580\pi$
$654$	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	0.0765405	−	0.997066i	$-0.475613\pi$
$673$	27.8518	−	27.8518i	1.07361	−	1.07361i	0.997066	−	0.0765405i	$-0.0243874\pi$
$674$	−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	−0.719898	−	0.694079i	$-0.755812\pi$
$677$	−0.671792	+	0.671792i	−0.0258191	+	0.0258191i	0.694079	+	0.719898i	$0.255812\pi$
$678$	−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	0.584778	−	0.811193i	$-0.301182\pi$
$683$	−5.91720	−	5.91720i	−0.226415	−	0.226415i	−0.811193	+	0.584778i	$0.801182\pi$
$684$	−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	$0.0858977\pi$
$701$			14.1168i			0.533184i	−0.963809	+	0.266592i	$0.914102\pi$
$702$	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	$0.158188\pi$
$709$			25.3893i			0.953514i	−0.879035	+	0.476757i	$0.841812\pi$
$710$	−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	0.997606	+	0.0691526i	$0.0220295\pi$
$727$	28.7629	+	28.7629i	1.06676	+	1.06676i	0.0691526	+	0.997606i	$0.477970\pi$
$728$	−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	−0.607835	−	0.794063i	$-0.707962\pi$
$733$	5.04195	−	5.04195i	0.186229	−	0.186229i	0.794063	+	0.607835i	$0.207962\pi$
$734$	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	$0.285152\pi$
$739$			42.4476i			1.56146i	−0.624869	+	0.780730i	$0.714848\pi$
$740$	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	0.651540	−	0.758614i	$-0.274123\pi$
$743$	−2.91864	−	2.91864i	−0.107074	−	0.107074i	−0.758614	+	0.651540i	$0.774123\pi$
$744$	−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	0.999943	+	0.0106944i	$0.00340420\pi$
$757$	27.8063	+	27.8063i	1.01064	+	1.01064i	0.0106944	+	0.999943i	$0.496596\pi$
$758$	−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	$-0.990454\pi$
$761$		−	1.65428i		−	0.0599675i	0.999550	−	0.0299838i	$-0.00954556\pi$
$762$	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	$-0.762347\pi$
$769$		−	37.6670i		−	1.35831i	0.733997	−	0.679153i	$-0.237653\pi$
$770$	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	0.768760	−	0.639538i	$-0.220874\pi$
$773$	3.59275	+	3.59275i	0.129222	+	0.129222i	−0.639538	+	0.768760i	$0.720874\pi$
$774$	−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	0.450078	−	0.892989i	$-0.351396\pi$
$787$	−12.4252	−	12.4252i	−0.442911	−	0.442911i	−0.892989	+	0.450078i	$0.851396\pi$
$788$	−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	−0.499277	−	0.866442i	$-0.666401\pi$
$797$	10.3655	−	10.3655i	0.367165	−	0.367165i	0.866442	+	0.499277i	$0.166401\pi$
$798$	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	$-0.684998\pi$
$821$		−	47.8971i		−	1.67162i	0.549018	−	0.835811i	$-0.315002\pi$
$822$	−1.59701	+	28.1558i	−0.0557021	+	0.982048i
$823$	7.06755	−	7.06755i	0.246359	−	0.246359i	−0.573115	−	0.819475i	$-0.694265\pi$
$823$	7.06755	−	7.06755i	0.246359	−	0.246359i	0.819475	+	0.573115i	$0.194265\pi$
$824$	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	0.108391	−	0.994108i	$-0.465430\pi$
$827$	31.7052	−	31.7052i	1.10250	−	1.10250i	0.994108	−	0.108391i	$-0.0345699\pi$
$828$	4.96169	−	3.94774i	0.172431	−	0.137193i
$829$			56.5372i			1.96362i	0.189867	+	0.981810i	$0.439194\pi$
$829$			56.5372i			1.96362i	−0.189867	+	0.981810i	$0.560806\pi$
$830$	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	−0.494398	−	0.869235i	$-0.664612\pi$
$853$	10.9476	−	10.9476i	0.374837	−	0.374837i	0.869235	+	0.494398i	$0.164612\pi$
$854$	−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	−0.0695640	−	0.997577i	$-0.522161\pi$
$857$	27.1672	−	27.1672i	0.928013	−	0.928013i	0.997577	+	0.0695640i	$0.0221608\pi$
$858$	−9.28794	−	0.526815i	−0.317085	−	0.0179852i
$859$		−	27.0450i		−	0.922764i	−0.887201	−	0.461382i	$-0.847354\pi$
$859$		−	27.0450i		−	0.922764i	0.887201	−	0.461382i	$-0.152646\pi$
$860$	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	0.947636	+	0.319352i	$0.103465\pi$
$863$	37.2201	+	37.2201i	1.26699	+	1.26699i	0.319352	+	0.947636i	$0.396535\pi$
$864$	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	0.533333	−	0.845905i	$-0.320939\pi$
$877$	−9.25658	−	9.25658i	−0.312572	−	0.312572i	−0.845905	+	0.533333i	$0.820939\pi$
$878$	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	$-0.974215\pi$
$881$		−	4.80357i		−	0.161836i	0.996721	−	0.0809182i	$-0.0257852\pi$
$882$	−3.58865	−	4.51037i	−0.120836	−	0.151872i
$883$	20.8825	−	20.8825i	0.702751	−	0.702751i	−0.262249	−	0.965000i	$-0.584464\pi$
$883$	20.8825	−	20.8825i	0.702751	−	0.702751i	0.965000	+	0.262249i	$0.0844642\pi$
$884$	−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	−0.882436	−	0.470433i	$-0.844098\pi$
$887$	−12.2705	+	12.2705i	−0.412003	+	0.412003i	0.470433	+	0.882436i	$0.344098\pi$
$888$	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	0.876055	−	0.482211i	$-0.160166\pi$
$907$	11.8612	+	11.8612i	0.393843	+	0.393843i	−0.482211	+	0.876055i	$0.660166\pi$
$908$	−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	$-0.810259\pi$
$911$		−	33.8899i		−	1.12282i	0.827537	−	0.561411i	$-0.189741\pi$
$912$	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	$-0.606106\pi$
$919$		−	57.2926i		−	1.88991i	0.327202	−	0.944954i	$-0.393894\pi$
$920$	−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	0.905155	−	0.425081i	$-0.139755\pi$
$937$	14.6953	+	14.6953i	0.480074	+	0.480074i	−0.425081	+	0.905155i	$0.639755\pi$
$938$	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	$0.203791\pi$
$941$			36.6501i			1.19476i	−0.801959	+	0.597379i	$0.796209\pi$
$942$	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	0.159200	−	0.987246i	$-0.449109\pi$
$947$	35.2800	−	35.2800i	1.14645	−	1.14645i	0.987246	−	0.159200i	$-0.0508914\pi$
$948$	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	0.543327	−	0.839521i	$-0.317165\pi$
$953$	−9.14374	−	9.14374i	−0.296195	−	0.296195i	−0.839521	+	0.543327i	$0.817165\pi$
$954$	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	0.972258	−	0.233912i	$-0.0751527\pi$
$967$	22.9601	+	22.9601i	0.738346	+	0.738346i	−0.233912	+	0.972258i	$0.575153\pi$
$968$	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	$-0.998568\pi$
$971$		−	0.280300i		−	0.00899525i	0.999990	−	0.00449762i	$-0.00143164\pi$
$972$	−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	−0.296208	−	0.955124i	$-0.595722\pi$
$977$	20.5957	−	20.5957i	0.658916	−	0.658916i	0.955124	+	0.296208i	$0.0957221\pi$
$978$	−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	0.849848	−	0.527028i	$-0.176694\pi$
$983$	10.1213	+	10.1213i	0.322820	+	0.322820i	−0.527028	+	0.849848i	$0.676694\pi$
$984$	−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	0.143615	−	0.989634i	$-0.454127\pi$
$997$	−26.7133	−	26.7133i	−0.846019	−	0.846019i	−0.989634	+	0.143615i	$0.954127\pi$
$998$	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.497.11	yes	40
3.2	odd	2	inner	930.2.j.h.497.7	✓	40
5.3	odd	4	inner	930.2.j.h.683.7	yes	40
15.8	even	4	inner	930.2.j.h.683.11	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.j.h.497.7	✓	40	3.2	odd	2	inner
930.2.j.h.497.11	yes	40	1.1	even	1	trivial
930.2.j.h.683.7	yes	40	5.3	odd	4	inner
930.2.j.h.683.11	yes	40	15.8	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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Database

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