LMFDB - Embedded newform 465.2.w.c.29.7

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [465,2,Mod(29,465)] 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("465.29"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(465, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([5, 5, 3])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 465 = 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	465.w (of order $10$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [224,0,0,-52,0,0,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(8)] == traces)

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

Self dual:	no
Analytic conductor:	$3.71304369399$
Analytic rank:	$0$
Dimension:	$224$
Relative dimension:	$56$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			29.7
Character	$\chi$	$=$	465.29
Dual form			465.2.w.c.449.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.80416 - 1.31080i) q^{2} +(-1.70077 - 0.327670i) q^{3} +(0.918771 + 2.82769i) q^{4} +(0.118368 - 2.23293i) q^{5} +(2.63896 + 2.82055i) q^{6} +(0.687565 - 0.223404i) q^{7} +(0.670664 - 2.06409i) q^{8} +(2.78527 + 1.11458i) q^{9} +(-3.14049 + 3.87342i) q^{10} +(0.309847 + 0.953612i) q^{11} +(-0.636075 - 5.11031i) q^{12} +(3.23082 - 2.34733i) q^{13} +(-1.53332 - 0.498205i) q^{14} +(-0.932981 + 3.75893i) q^{15} +(0.895148 - 0.650363i) q^{16} +(1.97792 + 0.642665i) q^{17} +(-3.56407 - 5.66182i) q^{18} +(5.11289 + 3.71473i) q^{19} +(6.42279 - 1.71685i) q^{20} +(-1.24260 + 0.154665i) q^{21} +(0.690980 - 2.12662i) q^{22} +(7.97229 + 2.59035i) q^{23} +(-1.81699 + 3.29080i) q^{24} +(-4.97198 - 0.528615i) q^{25} -8.90581 q^{26} +(-4.37189 - 2.80830i) q^{27} +(1.26343 + 1.73896i) q^{28} +(-6.83768 - 4.96787i) q^{29} +(6.61046 - 5.55877i) q^{30} +(1.76693 - 5.27996i) q^{31} -6.80811 q^{32} +(-0.214511 - 1.72341i) q^{33} +(-2.72608 - 3.75213i) q^{34} +(-0.417459 - 1.56173i) q^{35} +(-0.592673 + 8.89990i) q^{36} -3.83425 q^{37} +(-4.35521 - 13.4040i) q^{38} +(-6.26405 + 2.93364i) q^{39} +(-4.52959 - 1.74187i) q^{40} +(1.46661 - 2.01861i) q^{41} +(2.44458 + 1.34976i) q^{42} +(3.70761 + 2.69373i) q^{43} +(-2.41184 + 1.75230i) q^{44} +(2.81848 - 6.08738i) q^{45} +(-10.9879 - 15.1235i) q^{46} +(1.43030 - 1.03917i) q^{47} +(-1.73555 + 0.812808i) q^{48} +(-5.24028 + 3.80729i) q^{49} +(8.27735 + 7.47098i) q^{50} +(-3.15341 - 1.74113i) q^{51} +(9.60590 + 6.97909i) q^{52} +(0.269157 + 0.0874544i) q^{53} +(4.20648 + 10.7973i) q^{54} +(2.16603 - 0.578991i) q^{55} -1.56903i q^{56} +(-7.47866 - 7.99325i) q^{57} +(5.82441 + 17.9257i) q^{58} +(-5.81130 - 7.99856i) q^{59} +(-11.4863 + 0.815416i) q^{60} -2.89516i q^{61} +(-10.1088 + 7.20981i) q^{62} +(2.16405 + 0.144111i) q^{63} +(10.4927 + 7.62336i) q^{64} +(-4.85900 - 7.49206i) q^{65} +(-1.87203 + 3.39049i) q^{66} -7.14597i q^{67} +6.18339i q^{68} +(-12.7103 - 7.01788i) q^{69} +(-1.29395 + 3.36482i) q^{70} +(7.11760 + 2.31265i) q^{71} +(4.16858 - 5.00153i) q^{72} +(-3.14087 - 9.66659i) q^{73} +(6.91761 + 5.02594i) q^{74} +(8.28300 + 2.52822i) q^{75} +(-5.80652 + 17.8706i) q^{76} +(0.426081 + 0.586450i) q^{77} +(15.1468 + 2.91816i) q^{78} +(8.91881 + 2.89790i) q^{79} +(-1.34626 - 2.07579i) q^{80} +(6.51541 + 6.20882i) q^{81} +(-5.29200 + 1.71948i) q^{82} +(-2.22328 + 3.06008i) q^{83} +(-1.57900 - 3.37157i) q^{84} +(1.66915 - 4.34049i) q^{85} +(-3.15818 - 9.71987i) q^{86} +(10.0015 + 10.6897i) q^{87} +2.17614 q^{88} +(3.59967 + 11.0787i) q^{89} +(-13.0643 + 7.28816i) q^{90} +(1.69700 - 2.33572i) q^{91} +24.9231i q^{92} +(-4.73523 + 8.40105i) q^{93} -3.94265 q^{94} +(8.89994 - 10.9770i) q^{95} +(11.5791 + 2.23081i) q^{96} +(0.579245 - 0.188208i) q^{97} +14.4449 q^{98} +(-0.199874 + 3.00141i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 224 q - 52 q^{4} - 14 q^{9} - 2 q^{10} - 15 q^{15} - 76 q^{16} + 32 q^{19} - 10 q^{21} + 90 q^{24} - 80 q^{25} + 56 q^{31} - 40 q^{34} + 68 q^{36} + 2 q^{39} - 74 q^{40} - 42 q^{45} - 40 q^{46} + 8 q^{49}+ \cdots - 90 q^{96}+O(q^{100}) $ 224 * q - 52 * q^4 - 14 * q^9 - 2 * q^10 - 15 * q^15 - 76 * q^16 + 32 * q^19 - 10 * q^21 + 90 * q^24 - 80 * q^25 + 56 * q^31 - 40 * q^34 + 68 * q^36 + 2 * q^39 - 74 * q^40 - 42 * q^45 - 40 * q^46 + 8 * q^49 - 22 * q^51 + 80 * q^54 + 40 * q^55 - 85 * q^60 - 116 * q^64 - 124 * q^66 - 18 * q^69 - 52 * q^70 + 20 * q^75 + 24 * q^76 + 40 * q^79 + 62 * q^81 - 140 * q^84 - 20 * q^85 - 28 * q^90 - 40 * q^91 + 104 * q^94 - 90 * q^96

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/465\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$406$
$\chi(n)$	$-1$	$-1$	$e\left(\frac{3}{10}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.80416	−	1.31080i	−1.27574	−	0.926876i	−0.276321	−	0.961066i	$-0.589115\pi$
$2$	−1.80416	−	1.31080i	−1.27574	−	0.926876i	−0.999415	+	0.0341890i	$0.989115\pi$
$3$	−1.70077	−	0.327670i	−0.981942	−	0.189180i
$3$	−1.70077	−	0.327670i	−0.981942	−	0.189180i
$4$	0.918771	+	2.82769i	0.459385	+	1.41384i
$5$	0.118368	−	2.23293i	0.0529357	−	0.998598i
$5$	0.118368	−	2.23293i	0.0529357	−	0.998598i
$6$	2.63896	+	2.82055i	1.07735	+	1.15148i
$7$	0.687565	−	0.223404i	0.259875	−	0.0844386i	−0.176182	−	0.984358i	$-0.556375\pi$
$7$	0.687565	−	0.223404i	0.259875	−	0.0844386i	0.436057	+	0.899919i	$0.356375\pi$
$8$	0.670664	−	2.06409i	0.237115	−	0.729766i
$9$	2.78527	+	1.11458i	0.928422	+	0.371528i
$10$	−3.14049	+	3.87342i	−0.993109	+	1.22488i
$11$	0.309847	+	0.953612i	0.0934225	+	0.287525i	0.986839	−	0.161704i	$-0.0516989\pi$
$11$	0.309847	+	0.953612i	0.0934225	+	0.287525i	−0.893417	+	0.449229i	$0.851699\pi$
$12$	−0.636075	−	5.11031i	−0.183619	−	1.47522i
$13$	3.23082	−	2.34733i	0.896069	−	0.651032i	−0.0413844	−	0.999143i	$-0.513177\pi$
$13$	3.23082	−	2.34733i	0.896069	−	0.651032i	0.937453	+	0.348111i	$0.113177\pi$
$14$	−1.53332	−	0.498205i	−0.409796	−	0.133151i
$15$	−0.932981	+	3.75893i	−0.240895	+	0.970551i
$16$	0.895148	−	0.650363i	0.223787	−	0.162591i
$17$	1.97792	+	0.642665i	0.479716	+	0.155869i	0.538886	−	0.842379i	$-0.318845\pi$
$17$	1.97792	+	0.642665i	0.479716	+	0.155869i	−0.0591700	+	0.998248i	$0.518845\pi$
$18$	−3.56407	−	5.66182i	−0.840061	−	1.33450i
$19$	5.11289	+	3.71473i	1.17298	+	0.852217i	0.991362	−	0.131152i	$-0.0418677\pi$
$19$	5.11289	+	3.71473i	1.17298	+	0.852217i	0.181614	+	0.983370i	$0.441868\pi$
$20$	6.42279	−	1.71685i	1.43618	−	0.383898i
$21$	−1.24260	+	0.154665i	−0.271157	+	0.0337506i
$22$	0.690980	−	2.12662i	0.147318	−	0.453397i
$23$	7.97229	+	2.59035i	1.66234	+	0.540126i	0.981360	−	0.192178i	$-0.0615552\pi$
$23$	7.97229	+	2.59035i	1.66234	+	0.540126i	0.680977	+	0.732305i	$0.261555\pi$
$24$	−1.81699	+	3.29080i	−0.370891	+	0.671731i
$25$	−4.97198	−	0.528615i	−0.994396	−	0.105723i
$26$	−8.90581			−1.74657
$27$	−4.37189	−	2.80830i	−0.841371	−	0.540458i
$28$	1.26343	+	1.73896i	0.238766	+	0.328633i
$29$	−6.83768	−	4.96787i	−1.26973	−	0.922510i	−0.270534	−	0.962710i	$-0.587200\pi$
$29$	−6.83768	−	4.96787i	−1.26973	−	0.922510i	−0.999192	+	0.0402009i	$0.987200\pi$
$30$	6.61046	−	5.55877i	1.20690	−	1.01489i
$31$	1.76693	−	5.27996i	0.317350	−	0.948308i
$31$	1.76693	−	5.27996i	0.317350	−	0.948308i
$32$	−6.80811			−1.20352
$33$	−0.214511	−	1.72341i	−0.0373415	−	0.300006i
$34$	−2.72608	−	3.75213i	−0.467519	−	0.643485i
$35$	−0.417459	−	1.56173i	−0.0705635	−	0.263981i
$36$	−0.592673	+	8.89990i	−0.0987788	+	1.48332i
$37$	−3.83425			−0.630347			−0.315173	−	0.949034i	$-0.602063\pi$
$37$	−3.83425			−0.630347			−0.315173	+	0.949034i	$0.602063\pi$
$38$	−4.35521	−	13.4040i	−0.706508	−	2.17441i
$39$	−6.26405	+	2.93364i	−1.00305	+	0.469758i
$40$	−4.52959	−	1.74187i	−0.716191	−	0.275414i
$41$	1.46661	−	2.01861i	0.229046	−	0.315254i	−0.678990	−	0.734148i	$-0.737582\pi$
$41$	1.46661	−	2.01861i	0.229046	−	0.315254i	0.908035	+	0.418893i	$0.137582\pi$
$42$	2.44458	+	1.34976i	0.377207	+	0.208272i
$43$	3.70761	+	2.69373i	0.565405	+	0.410791i	0.833433	−	0.552620i	$-0.186372\pi$
$43$	3.70761	+	2.69373i	0.565405	+	0.410791i	−0.268028	+	0.963411i	$0.586372\pi$
$44$	−2.41184	+	1.75230i	−0.363598	+	0.264169i
$45$	2.81848	−	6.08738i	0.420154	−	0.907453i
$46$	−10.9879	−	15.1235i	−1.62007	−	2.22984i
$47$	1.43030	−	1.03917i	0.208631	−	0.151579i	−0.478563	−	0.878053i	$-0.658842\pi$
$47$	1.43030	−	1.03917i	0.208631	−	0.151579i	0.687194	+	0.726474i	$0.258842\pi$
$48$	−1.73555	+	0.812808i	−0.250505	+	0.117319i
$49$	−5.24028	+	3.80729i	−0.748612	+	0.543898i
$50$	8.27735	+	7.47098i	1.17059	+	1.05656i
$51$	−3.15341	−	1.74113i	−0.441566	−	0.243807i
$52$	9.60590	+	6.97909i	1.33210	+	0.967826i
$53$	0.269157	+	0.0874544i	0.0369716	+	0.0120128i	0.327444	−	0.944870i	$-0.393813\pi$
$53$	0.269157	+	0.0874544i	0.0369716	+	0.0120128i	−0.290473	+	0.956883i	$0.593813\pi$
$54$	4.20648	+	10.7973i	0.572429	+	1.46933i
$55$	2.16603	−	0.578991i	0.292067	−	0.0780711i
$56$		−	1.56903i		−	0.209670i
$57$	−7.47866	−	7.99325i	−0.990573	−	1.05873i
$58$	5.82441	+	17.9257i	0.764782	+	2.35376i
$59$	−5.81130	−	7.99856i	−0.756566	−	1.04132i	−0.997492	−	0.0707805i	$-0.977451\pi$
$59$	−5.81130	−	7.99856i	−0.756566	−	1.04132i	0.240926	−	0.970544i	$-0.422549\pi$
$60$	−11.4863	+	0.815416i	−1.48287	+	0.105270i
$61$		−	2.89516i		−	0.370687i	−0.982674	−	0.185344i	$-0.940660\pi$
$61$		−	2.89516i		−	0.370687i	0.982674	−	0.185344i	$-0.0593398\pi$
$62$	−10.1088	+	7.20981i	−1.28382	+	0.915647i
$63$	2.16405	+	0.144111i	0.272645	+	0.0181563i
$64$	10.4927	+	7.62336i	1.31158	+	0.952920i
$65$	−4.85900	−	7.49206i	−0.602685	−	0.929275i
$66$	−1.87203	+	3.39049i	−0.230431	+	0.417340i
$67$		−	7.14597i		−	0.873019i	−0.899700	−	0.436509i	$-0.856215\pi$
$67$		−	7.14597i		−	0.873019i	0.899700	−	0.436509i	$-0.143785\pi$
$68$			6.18339i			0.749847i
$69$	−12.7103	−	7.01788i	−1.53014	−	0.844854i
$70$	−1.29395	+	3.36482i	−0.154657	+	0.402173i
$71$	7.11760	+	2.31265i	0.844703	+	0.274461i	0.699226	−	0.714901i	$-0.253528\pi$
$71$	7.11760	+	2.31265i	0.844703	+	0.274461i	0.145478	+	0.989362i	$0.453528\pi$
$72$	4.16858	−	5.00153i	0.491272	−	0.589436i
$73$	−3.14087	−	9.66659i	−0.367610	−	1.13139i	−0.948330	−	0.317285i	$-0.897229\pi$
$73$	−3.14087	−	9.66659i	−0.367610	−	1.13139i	0.580720	−	0.814104i	$-0.302771\pi$
$74$	6.91761	+	5.02594i	0.804156	+	0.584254i
$75$	8.28300	+	2.52822i	0.956439	+	0.291934i
$76$	−5.80652	+	17.8706i	−0.666053	+	2.04990i
$77$	0.426081	+	0.586450i	0.0485564	+	0.0668321i
$78$	15.1468	+	2.91816i	1.71503	+	0.330417i
$79$	8.91881	+	2.89790i	1.00345	+	0.326039i	0.764241	−	0.644930i	$-0.223114\pi$
$79$	8.91881	+	2.89790i	1.00345	+	0.326039i	0.239204	+	0.970969i	$0.423114\pi$
$80$	−1.34626	−	2.07579i	−0.150516	−	0.232080i
$81$	6.51541	+	6.20882i	0.723934	+	0.689869i
$82$	−5.29200	+	1.71948i	−0.584404	+	0.189884i
$83$	−2.22328	+	3.06008i	−0.244036	+	0.335887i	−0.913411	−	0.407037i	$-0.866562\pi$
$83$	−2.22328	+	3.06008i	−0.244036	+	0.335887i	0.669375	+	0.742924i	$0.266562\pi$
$84$	−1.57900	−	3.37157i	−0.172283	−	0.367868i
$85$	1.66915	−	4.34049i	0.181045	−	0.470792i
$86$	−3.15818	−	9.71987i	−0.340555	−	1.04812i
$87$	10.0015	+	10.6897i	1.07228	+	1.14606i
$88$	2.17614			0.231978
$89$	3.59967	+	11.0787i	0.381564	+	1.17433i	0.938942	+	0.344075i	$0.111808\pi$
$89$	3.59967	+	11.0787i	0.381564	+	1.17433i	−0.557378	+	0.830259i	$0.688192\pi$
$90$	−13.0643	+	7.28816i	−1.37710	+	0.768240i
$91$	1.69700	−	2.33572i	0.177894	−	0.244850i
$92$			24.9231i			2.59841i
$93$	−4.73523	+	8.40105i	−0.491021	+	0.871148i
$94$	−3.94265			−0.406653
$95$	8.89994	−	10.9770i	0.913115	−	1.12622i
$96$	11.5791	+	2.23081i	1.18178	+	0.227681i
$97$	0.579245	−	0.188208i	0.0588134	−	0.0191096i	−0.279463	−	0.960157i	$-0.590156\pi$
$97$	0.579245	−	0.188208i	0.0588134	−	0.0191096i	0.338276	+	0.941047i	$0.390156\pi$
$98$	14.4449			1.45916
$99$	−0.199874	+	3.00141i	−0.0200881	+	0.301653i
$100$	−3.07335	−	14.5449i	−0.307335	−	1.45449i
$101$	6.48677	+	2.10768i	0.645458	+	0.209722i	0.613410	−	0.789764i	$-0.289797\pi$
$101$	6.48677	+	2.10768i	0.645458	+	0.209722i	0.0320477	+	0.999486i	$0.489797\pi$
$102$	3.40699	+	7.27478i	0.337342	+	0.720311i
$103$	9.60589	−	13.2214i	0.946497	−	1.30274i	−0.00656904	−	0.999978i	$-0.502091\pi$
$103$	9.60589	−	13.2214i	0.946497	−	1.30274i	0.953066	−	0.302763i	$-0.0979090\pi$
$104$	−2.67831	−	8.24298i	−0.262629	−	0.808290i
$105$	0.198272	+	2.79294i	0.0193494	+	0.272563i
$106$	−0.370968	−	0.510593i	−0.0360316	−	0.0495932i
$107$	−2.03459	+	6.26183i	−0.196691	+	0.605354i	0.803261	+	0.595627i	$0.203096\pi$
$107$	−2.03459	+	6.26183i	−0.196691	+	0.605354i	−0.999953	+	0.00972721i	$0.996904\pi$
$108$	3.92423	−	14.9425i	0.377609	−	1.43784i
$109$	−2.07114	+	1.50477i	−0.198380	+	0.144131i	−0.682541	−	0.730848i	$-0.739125\pi$
$109$	−2.07114	+	1.50477i	−0.198380	+	0.144131i	0.484161	+	0.874979i	$0.339125\pi$
$110$	−4.66681	−	1.79464i	−0.444963	−	0.171112i
$111$	6.52119	+	1.25637i	0.618964	+	0.119249i
$112$	0.470179	−	0.647146i	0.0444278	−	0.0611496i
$113$	−4.62720	−	14.2411i	−0.435290	−	1.33969i	−0.892789	−	0.450476i	$-0.851254\pi$
$113$	−4.62720	−	14.2411i	−0.435290	−	1.33969i	0.457498	−	0.889211i	$-0.348746\pi$
$114$	3.01516	+	24.2242i	0.282395	+	2.26880i
$115$	6.72775	−	17.4950i	0.627366	−	1.63141i
$116$	7.76530	−	23.8991i	0.720990	−	2.21898i
$117$	11.6150	−	2.93691i	1.07381	−	0.271518i
$118$			22.0482i			2.02970i
$119$	1.50352			0.137828
$120$	7.13305	+	4.44673i	0.651156	+	0.405929i
$121$	8.08582	−	5.87469i	0.735074	−	0.534063i
$122$	−3.79498	+	5.22334i	−0.343581	+	0.472899i
$123$	−3.15581	+	2.95264i	−0.284550	+	0.266231i
$124$	16.5535	+	0.145253i	1.48655	+	0.0130441i
$125$	−1.76888	+	11.0395i	−0.158214	+	0.987405i
$126$	−3.71541	−	3.09665i	−0.330995	−	0.275871i
$127$	−7.86899	+	5.71715i	−0.698260	+	0.507315i	−0.879365	−	0.476148i	$-0.842033\pi$
$127$	−7.86899	+	5.71715i	−0.698260	+	0.507315i	0.181105	+	0.983464i	$0.442033\pi$
$128$	−4.73010	−	14.5578i	−0.418086	−	1.28674i
$129$	−5.42315	−	5.79630i	−0.477482	−	0.510336i
$130$	−1.05416	+	19.8861i	−0.0924562	+	1.74412i
$131$	4.54943	−	1.47820i	0.397485	−	0.129151i	−0.103452	−	0.994634i	$-0.532989\pi$
$131$	4.54943	−	1.47820i	0.397485	−	0.129151i	0.500937	+	0.865484i	$0.332989\pi$
$132$	4.67616	−	2.18998i	0.407008	−	0.190614i
$133$	4.34533	+	1.41188i	0.376788	+	0.122426i
$134$	−9.36694	+	12.8925i	−0.809181	+	1.11374i
$135$	−6.78824	+	9.42973i	−0.584239	+	0.811582i
$136$	2.65304	−	3.65159i	0.227496	−	0.313121i
$137$	7.69146	+	10.5864i	0.657126	+	0.904456i	0.999382	−	0.0351503i	$-0.0111910\pi$
$137$	7.69146	+	10.5864i	0.657126	+	0.904456i	−0.342256	+	0.939607i	$0.611191\pi$
$138$	13.7324	+	29.3221i	1.16898	+	2.49606i
$139$	−1.50958	−	2.07776i	−0.128041	−	0.176233i	0.740183	−	0.672405i	$-0.234739\pi$
$139$	−1.50958	−	2.07776i	−0.128041	−	0.176233i	−0.868224	+	0.496172i	$0.834739\pi$
$140$	4.03254	−	2.61532i	0.340811	−	0.221035i
$141$	−2.77313	+	1.29874i	−0.233539	+	0.109373i
$142$	−9.80989	−	13.5021i	−0.823227	−	1.13308i
$143$	3.23950	+	2.35364i	0.270901	+	0.196821i
$144$	3.21811	−	0.813716i	0.268176	−	0.0678096i
$145$	−11.9023	+	14.6800i	−0.988430	+	1.21911i
$146$	−7.00434	+	21.5572i	−0.579684	+	1.78408i
$147$	10.1601	−	4.75826i	0.837988	−	0.392454i
$148$	−3.52280	−	10.8421i	−0.289572	−	0.891212i
$149$		−	16.2503i		−	1.33127i	−0.746276	−	0.665636i	$-0.768160\pi$
$149$		−	16.2503i		−	1.33127i	0.746276	−	0.665636i	$-0.231840\pi$
$150$	−11.6299	−	15.4187i	−0.949576	−	1.25893i
$151$	−4.94817	+	1.60776i	−0.402676	+	0.130838i	−0.503351	−	0.864082i	$-0.667900\pi$
$151$	−4.94817	+	1.60776i	−0.402676	+	0.130838i	0.100675	+	0.994919i	$0.467900\pi$
$152$	11.0966	−	8.06213i	0.900050	−	0.653925i
$153$	4.79273	+	3.99455i	0.387469	+	0.322940i
$154$		−	1.61656i		−	0.130266i
$155$	−11.5806	−	4.57041i	−0.930180	−	0.367105i
$156$	−14.0506	−	15.0174i	−1.12495	−	1.20236i
$157$	−3.20681	+	4.41380i	−0.255932	+	0.352260i	−0.917578	−	0.397557i	$-0.869858\pi$
$157$	−3.20681	+	4.41380i	−0.255932	+	0.352260i	0.661646	+	0.749816i	$0.269858\pi$
$158$	−12.2924	−	16.9191i	−0.977933	−	1.34601i
$159$	−0.429119	−	0.236935i	−0.0340314	−	0.0187901i
$160$	−0.805862	+	15.2021i	−0.0637090	+	1.20183i
$161$	6.06017			0.477608
$162$	−3.61632	−	19.7421i	−0.284125	−	1.55109i
$163$	−15.4512	−	5.02041i	−1.21023	−	0.393229i	−0.366718	−	0.930332i	$-0.619519\pi$
$163$	−15.4512	−	5.02041i	−1.21023	−	0.393229i	−0.843516	+	0.537103i	$0.819519\pi$
$164$	7.05548	+	2.29246i	0.550940	+	0.179011i
$165$	−3.87364	+	0.274992i	−0.301562	+	0.0214081i
$166$	8.02230	−	2.60660i	0.622652	−	0.202312i
$167$	−7.23115	+	9.95282i	−0.559563	+	0.770173i	−0.991271	−	0.131841i	$-0.957911\pi$
$167$	−7.23115	+	9.95282i	−0.559563	+	0.770173i	0.431708	+	0.902014i	$0.357911\pi$
$168$	−0.514122	+	2.66856i	−0.0396654	+	0.205884i
$169$	0.911035	−	2.80388i	0.0700796	−	0.215683i
$170$	−8.70094	+	5.64303i	−0.667331	+	0.432800i
$171$	10.1004	+	16.0452i	0.772394	+	1.22701i
$172$	−4.21059	+	12.9589i	−0.321055	+	0.988105i
$173$	16.6720	−	12.1129i	1.26755	−	0.920925i	0.268443	−	0.963296i	$-0.413491\pi$
$173$	16.6720	−	12.1129i	1.26755	−	0.920925i	0.999102	+	0.0423701i	$0.0134909\pi$
$174$	−4.03230	−	32.3960i	−0.305688	−	2.45594i
$175$	−3.53666	+	0.747300i	−0.267346	+	0.0564906i
$176$	0.897553	+	0.652110i	0.0676556	+	0.0491546i
$177$	7.26282	+	15.5079i	0.545907	+	1.16565i
$178$	8.02751	−	24.7061i	0.601688	−	1.85180i
$179$	−2.91826	−	8.98148i	−0.218121	−	0.671307i	−0.998917	−	0.0465217i	$-0.985186\pi$
$179$	−2.91826	−	8.98148i	−0.218121	−	0.671307i	0.780796	−	0.624786i	$-0.214814\pi$
$180$	19.8027	+	2.37686i	1.47601	+	0.177161i
$181$		−	5.35333i		−	0.397910i	−0.980009	−	0.198955i	$-0.936245\pi$
$181$		−	5.35333i		−	0.397910i	0.980009	−	0.198955i	$-0.0637547\pi$
$182$	−6.12333	+	1.98959i	−0.453891	+	0.147478i
$183$	−0.948656	+	4.92401i	−0.0701267	+	0.363994i
$184$	10.6934	−	14.7183i	0.788332	−	1.08505i
$185$	−0.453852	+	8.56162i	−0.0333679	+	0.629463i
$186$	19.5552	−	8.94991i	1.43386	−	0.656239i
$187$			2.08529i			0.152492i
$188$	4.25258	+	3.08968i	0.310151	+	0.225338i
$189$	−3.63335	−	0.954196i	−0.264287	−	0.0694075i
$190$	−30.4457	+	8.13829i	−2.20876	+	0.590414i
$191$			11.9260i			0.862937i	0.902128	+	0.431469i	$0.142004\pi$
$191$			11.9260i			0.862937i	−0.902128	+	0.431469i	$0.857996\pi$
$192$	−15.3477	−	16.4037i	−1.10762	−	1.18384i
$193$	−11.6354	+	3.78058i	−0.837536	+	0.272132i	−0.696216	−	0.717832i	$-0.745135\pi$
$193$	−11.6354	+	3.78058i	−0.837536	+	0.272132i	−0.141320	+	0.989964i	$0.545135\pi$
$194$	−1.29176	−	0.419717i	−0.0927427	−	0.0301339i
$195$	5.80915	+	14.3344i	0.416002	+	1.02651i
$196$	−15.5804	−	11.3198i	−1.11289	−	0.808560i
$197$	−7.61192	+	2.47326i	−0.542327	+	0.176213i	−0.567354	−	0.823474i	$-0.692033\pi$
$197$	−7.61192	+	2.47326i	−0.542327	+	0.176213i	0.0250269	+	0.999687i	$0.492033\pi$
$198$	4.29486	−	5.15304i	0.305222	−	0.366211i
$199$	−13.4119	−	18.4599i	−0.950742	−	1.30858i	−0.951197	−	0.308585i	$-0.900145\pi$
$199$	−13.4119	−	18.4599i	−0.950742	−	1.30858i	0.000454686	−	1.00000i	$-0.499855\pi$
$200$	−4.42563	+	9.90809i	−0.312940	+	0.700608i
$201$	−2.34152	+	12.1537i	−0.165158	+	0.857254i
$202$	−8.94045	−	12.3055i	−0.629048	−	0.865810i
$203$	−5.81119	−	1.88817i	−0.407866	−	0.132524i
$204$	2.02611	−	10.5166i	0.141856	−	0.736306i
$205$	−4.33383	−	3.51378i	−0.302688	−	0.245413i
$206$	−34.6612	+	11.2621i	−2.41496	+	0.784668i
$207$	19.3178	+	16.1006i	1.34268	+	1.11907i
$208$	1.36545	−	4.20241i	0.0946767	−	0.291385i
$209$	−1.95820	+	6.02671i	−0.135451	+	0.416876i
$210$	3.30327	−	5.29882i	0.227948	−	0.365653i
$211$	5.26273			0.362301			0.181151	−	0.983455i	$-0.442018\pi$
$211$	5.26273			0.362301			0.181151	+	0.983455i	$0.442018\pi$
$212$			0.841442i			0.0577905i
$213$	−11.3476	−	6.26551i	−0.777528	−	0.429306i
$214$	11.8788	−	8.63042i	0.812015	−	0.589963i
$215$	6.45379	−	7.95999i	0.440145	−	0.542867i
$216$	−8.72866	+	7.14055i	−0.593910	+	0.485853i
$217$	0.0353189	−	4.02506i	0.00239760	−	0.273239i
$218$	5.70914			0.386672
$219$	2.17445	+	17.4699i	0.146936	+	1.18050i
$220$	3.62729	+	5.59288i	0.244552	+	0.377072i
$221$	7.89885	−	2.56649i	0.531334	−	0.172641i
$222$	−10.1185	−	10.8147i	−0.679106	−	0.725834i
$223$	8.19295			0.548641			0.274320	−	0.961638i	$-0.411547\pi$
$223$	8.19295			0.548641			0.274320	+	0.961638i	$0.411547\pi$
$224$	−4.68102	+	1.52096i	−0.312764	+	0.101623i
$225$	−13.2591	−	7.01402i	−0.883939	−	0.467601i
$226$	−10.3190	+	31.7585i	−0.686408	+	2.11255i
$227$	4.90059	+	3.56048i	0.325263	+	0.236318i	0.738418	−	0.674343i	$-0.235573\pi$
$227$	4.90059	+	3.56048i	0.325263	+	0.236318i	−0.413155	+	0.910661i	$0.635573\pi$
$228$	15.7312	−	28.4913i	1.04183	−	1.88688i
$229$	−8.33147	+	11.4673i	−0.550559	+	0.757779i	−0.990088	−	0.140449i	$-0.955145\pi$
$229$	−8.33147	+	11.4673i	−0.550559	+	0.757779i	0.439529	+	0.898228i	$0.355145\pi$
$230$	−35.0704	+	22.7450i	−2.31247	+	1.49976i
$231$	−0.532505	−	1.13703i	−0.0350363	−	0.0748112i
$232$	−14.8399	+	10.7818i	−0.974288	+	0.707861i
$233$	−8.42382	+	6.12026i	−0.551863	+	0.400952i	−0.828472	−	0.560031i	$-0.810789\pi$
$233$	−8.42382	+	6.12026i	−0.551863	+	0.400952i	0.276609	+	0.960983i	$0.410789\pi$
$234$	−24.8051	−	9.92628i	−1.62156	−	0.648901i
$235$	−2.15111	−	3.31677i	−0.140323	−	0.216362i
$236$	17.2782	−	23.7814i	1.12471	−	1.54803i
$237$	−14.2193	−	7.85110i	−0.923645	−	0.509983i
$238$	−2.71260	−	1.97082i	−0.175832	−	0.127749i
$239$	−1.16475	+	3.58473i	−0.0753413	+	0.231877i	−0.981634	−	0.190774i	$-0.938900\pi$
$239$	−1.16475	+	3.58473i	−0.0753413	+	0.231877i	0.906293	+	0.422651i	$0.138900\pi$
$240$	1.60951	+	3.97157i	0.103894	+	0.256364i
$241$	−12.2895	+	3.99312i	−0.791639	+	0.257219i	−0.676802	−	0.736165i	$-0.736635\pi$
$241$	−12.2895	+	3.99312i	−0.791639	+	0.257219i	−0.114837	+	0.993384i	$0.536635\pi$
$242$	−22.2887			−1.43277
$243$	−9.04679	−	12.6947i	−0.580352	−	0.814366i
$244$	8.18660	−	2.65999i	0.524094	−	0.170288i
$245$	7.88114	+	12.1519i	0.503507	+	0.776354i
$246$	9.56392	−	1.19041i	0.609773	−	0.0758979i
$247$	25.2385			1.60589
$248$	−9.71329	−	7.18818i	−0.616795	−	0.456450i
$249$	4.78398	−	4.47600i	0.303173	−	0.283655i
$250$	17.6620	−	17.5984i	1.11704	−	1.11302i
$251$	−20.8001	+	15.1122i	−1.31289	+	0.953871i	−0.312899	+	0.949786i	$0.601300\pi$
$251$	−20.8001	+	15.1122i	−1.31289	+	0.953871i	−0.999992	+	0.00408494i	$0.998700\pi$
$252$	1.58077	+	6.25167i	0.0995791	+	0.393818i
$253$			8.40508i			0.528423i
$254$	21.6910			1.36101
$255$	−4.26109	+	6.83526i	−0.266840	+	0.428041i
$256$	−2.53278	+	7.79510i	−0.158299	+	0.487194i
$257$	5.63919	−	17.3556i	0.351763	−	1.08262i	−0.606100	−	0.795389i	$-0.707267\pi$
$257$	5.63919	−	17.3556i	0.351763	−	1.08262i	0.957863	−	0.287226i	$-0.0927332\pi$
$258$	2.18644	+	17.5661i	0.136122	+	1.09362i
$259$	−2.63630	+	0.856585i	−0.163812	+	0.0532256i
$260$	16.7209	−	20.6232i	1.03698	−	1.27900i
$261$	−13.5077	−	21.4580i	−0.836103	−	1.32822i
$262$	−10.1455	−	3.29648i	−0.626793	−	0.203657i
$263$	13.7748	+	18.9594i	0.849389	+	1.16908i	0.983997	+	0.178185i	$0.0570226\pi$
$263$	13.7748	+	18.9594i	0.849389	+	1.16908i	−0.134607	+	0.990899i	$0.542977\pi$
$264$	−3.70113	−	0.713056i	−0.227789	−	0.0438856i
$265$	0.227139	−	0.590658i	0.0139531	−	0.0362838i
$266$	−5.98898	−	8.24313i	−0.367208	−	0.505419i
$267$	−2.49209	−	20.0218i	−0.152514	−	1.22531i
$268$	20.2065	−	6.56551i	1.23431	−	0.401052i
$269$	23.9315	+	17.3873i	1.45913	+	1.06012i	0.983588	+	0.180428i	$0.0577481\pi$
$269$	23.9315	+	17.3873i	1.45913	+	1.06012i	0.475542	+	0.879693i	$0.342252\pi$
$270$	24.6076	−	8.11473i	1.49757	−	0.493847i
$271$	28.9096	+	9.39331i	1.75614	+	0.570603i	0.996788	−	0.0800818i	$-0.0255182\pi$
$271$	28.9096	+	9.39331i	1.75614	+	0.570603i	0.759348	+	0.650685i	$0.225518\pi$
$272$	2.18849	−	0.711085i	0.132697	−	0.0431159i
$273$	−3.65156	+	3.41648i	−0.221002	+	0.206775i
$274$		−	29.1816i		−	1.76292i
$275$	−1.03646	−	4.90513i	−0.0625009	−	0.295790i
$276$	8.16653	−	42.3885i	0.491568	−	2.55149i
$277$	−17.0107	−	12.3590i	−1.02208	−	0.742581i	−0.0553683	−	0.998466i	$-0.517633\pi$
$277$	−17.0107	−	12.3590i	−1.02208	−	0.742581i	−0.966707	+	0.255885i	$0.917633\pi$
$278$			5.72738i			0.343505i
$279$	10.8063	−	12.7367i	0.646958	−	0.762526i
$280$	−3.50353	−	0.185722i	−0.209376	−	0.0110990i
$281$	19.0495	−	26.2194i	1.13640	−	1.56412i	0.361096	−	0.932528i	$-0.382403\pi$
$281$	19.0495	−	26.2194i	1.13640	−	1.56412i	0.775302	−	0.631590i	$-0.217597\pi$
$282$	6.70556	+	1.29189i	0.399310	+	0.0769307i
$283$	8.86882	−	2.88165i	0.527197	−	0.171297i	−0.0333123	−	0.999445i	$-0.510606\pi$
$283$	8.86882	−	2.88165i	0.527197	−	0.171297i	0.560509	+	0.828148i	$0.310606\pi$
$284$			22.2511i			1.32036i
$285$	−18.7336	+	15.7532i	−1.10968	+	0.933139i
$286$	−2.75944	−	8.49269i	−0.163169	−	0.502183i
$287$	0.557424	−	1.71557i	0.0329037	−	0.101267i
$288$	−18.9624	−	7.58822i	−1.11737	−	0.447140i
$289$	−10.2541	−	7.45007i	−0.603185	−	0.438239i
$290$	40.7163	−	10.8837i	2.39094	−	0.639112i
$291$	−1.04684	+	0.130299i	−0.0613666	+	0.00763823i
$292$	24.4483	−	17.7628i	1.43073	−	1.03949i
$293$	8.31476	−	25.5902i	0.485754	−	1.49500i	−0.345133	−	0.938554i	$-0.612166\pi$
$293$	8.31476	−	25.5902i	0.485754	−	1.49500i	0.830886	−	0.556442i	$-0.187834\pi$
$294$	−24.5675	−	4.73316i	−1.43281	−	0.276044i
$295$	−18.5481	+	12.0295i	−1.07991	+	0.700382i
$296$	−2.57149	+	7.91424i	−0.149465	+	0.460006i
$297$	1.32341	−	5.03923i	0.0767921	−	0.292406i
$298$	−21.3009	+	29.3181i	−1.23393	+	1.69835i
$299$	31.8375	−	10.3446i	1.84121	−	0.598245i
$300$	0.461164	+	25.7446i	0.0266253	+	1.48636i
$301$	3.15101	+	1.02383i	0.181621	+	0.0590124i
$302$	11.0348	+	3.58541i	0.634979	+	0.206317i
$303$	−10.3419	−	5.71021i	−0.594127	−	0.328043i
$304$	6.99271			0.401059
$305$	−6.46470	−	0.342694i	−0.370168	−	0.0196226i
$306$	−3.41080	−	13.4891i	−0.194982	−	0.771122i
$307$	11.7949	+	16.2343i	0.673172	+	0.926541i	0.999827	−	0.0186021i	$-0.00592158\pi$
$307$	11.7949	+	16.2343i	0.673172	+	0.926541i	−0.326655	+	0.945144i	$0.605922\pi$
$308$	−1.26682	+	1.74363i	−0.0721840	+	0.0993528i
$309$	−20.6697	+	19.3390i	−1.17586	+	1.10016i
$310$	14.9025	+	23.4257i	0.846403	+	1.33049i
$311$			21.1397i			1.19872i	0.800479	+	0.599360i	$0.204578\pi$
$311$			21.1397i			1.19872i	−0.800479	+	0.599360i	$0.795422\pi$
$312$	1.85422	+	14.8970i	0.104975	+	0.843379i
$313$	−0.608471	+	0.442080i	−0.0343928	+	0.0249879i	−0.604849	−	0.796340i	$-0.706766\pi$
$313$	−0.608471	+	0.442080i	−0.0343928	+	0.0249879i	0.570456	+	0.821328i	$0.306766\pi$
$314$	11.5712	−	3.75972i	0.653002	−	0.212173i
$315$	0.577945	−	4.81513i	0.0325635	−	0.271302i
$316$			27.8821i			1.56849i
$317$	−8.72383	−	26.8492i	−0.489979	−	1.50800i	−0.824638	−	0.565661i	$-0.808621\pi$
$317$	−8.72383	−	26.8492i	−0.489979	−	1.50800i	0.334659	−	0.942339i	$-0.391379\pi$
$318$	0.463626	+	0.989959i	0.0259989	+	0.0555141i
$319$	2.61878	−	8.05977i	0.146623	−	0.451261i
$320$	18.2644	−	22.5270i	1.02101	−	1.25930i
$321$	5.51219	−	9.98329i	0.307661	−	0.557213i
$322$	−10.9335	−	7.94367i	−0.609302	−	0.442684i
$323$	7.72555	+	10.6333i	0.429861	+	0.591653i
$324$	−11.5704	+	24.1280i	−0.642802	+	1.34044i
$325$	−17.3044	+	9.96301i	−0.959876	+	0.552648i
$326$	21.2958	+	29.3111i	1.17946	+	1.62339i
$327$	4.01562	−	1.88063i	0.222064	−	0.103999i
$328$	−3.18300	−	4.38102i	−0.175752	−	0.241901i
$329$	0.751271	−	1.03404i	0.0414189	−	0.0570082i
$330$	7.34914	+	4.58144i	0.404557	+	0.252200i
$331$	−9.70199	+	13.3536i	−0.533270	+	0.733983i	−0.987624	−	0.156838i	$-0.949870\pi$
$331$	−9.70199	+	13.3536i	−0.533270	+	0.733983i	0.454355	+	0.890821i	$0.349870\pi$
$332$	−10.6956	−	3.47522i	−0.586998	−	0.190727i
$333$	−10.6794	−	4.27359i	−0.585228	−	0.234192i
$334$	26.0923	−	8.47792i	1.42771	−	0.463891i
$335$	−15.9565	−	0.845853i	−0.871795	−	0.0462139i
$336$	−1.01172	+	0.946586i	−0.0551938	+	0.0516405i
$337$	7.50873	+	23.1095i	0.409026	+	1.25885i	0.917486	+	0.397768i	$0.130215\pi$
$337$	7.50873	+	23.1095i	0.409026	+	1.25885i	−0.508459	+	0.861086i	$0.669785\pi$
$338$	−5.31898	+	3.86447i	−0.289315	+	0.210199i
$339$	3.20346	+	25.7370i	0.173988	+	1.39784i
$340$	13.8071	+	0.731916i	0.748795	+	0.0396937i
$341$	5.58251	+	0.0489852i	0.302310	+	0.00265270i
$342$	2.80942	−	42.1878i	0.151916	−	2.28126i
$343$	−5.72705	+	7.88260i	−0.309231	+	0.425621i
$344$	8.04667	−	5.84625i	0.433847	−	0.315209i
$345$	−17.1750	+	27.5505i	−0.924668	+	1.48327i
$346$	−45.9565			−2.47064
$347$		−	9.05946i		−	0.486338i	−0.969984	−	0.243169i	$-0.921813\pi$
$347$		−	9.05946i		−	0.486338i	0.969984	−	0.243169i	$-0.0781869\pi$
$348$	−21.0380	+	38.1026i	−1.12776	+	2.04251i
$349$	1.09317	−	3.36442i	0.0585158	−	0.180093i	−0.917526	−	0.397675i	$-0.869817\pi$
$349$	1.09317	−	3.36442i	0.0585158	−	0.180093i	0.976042	+	0.217582i	$0.0698170\pi$
$350$	7.36026	+	3.28760i	0.393423	+	0.175730i
$351$	−20.7168	+	1.18915i	−1.10578	+	0.0634719i
$352$	−2.10948	−	6.49230i	−0.112435	−	0.346041i
$353$	−8.29541	+	11.4177i	−0.441520	+	0.607700i	−0.970549	−	0.240903i	$-0.922556\pi$
$353$	−8.29541	+	11.4177i	−0.441520	+	0.607700i	0.529029	+	0.848604i	$0.322556\pi$
$354$	7.22451	−	37.4989i	0.383979	−	1.99305i
$355$	6.00648	−	15.6194i	0.318791	−	0.828990i
$356$	−28.0197	+	20.3575i	−1.48504	+	1.07894i
$357$	−2.55715	−	0.492659i	−0.135339	−	0.0260743i
$358$	−6.50792	+	20.0293i	−0.343954	+	1.05858i
$359$	−19.1380	−	26.3413i	−1.01007	−	1.39024i	−0.918939	−	0.394399i	$-0.870953\pi$
$359$	−19.1380	−	26.3413i	−1.01007	−	1.39024i	−0.0911278	−	0.995839i	$-0.529047\pi$
$360$	−10.6747	−	9.90017i	−0.562603	−	0.521785i
$361$	6.47107	+	19.9159i	0.340583	+	1.04821i
$362$	−7.01715	+	9.65827i	−0.368813	+	0.507628i
$363$	−15.6771	+	7.34204i	−0.822835	+	0.385357i
$364$	8.16384	+	2.65259i	0.427901	+	0.139034i
$365$	−21.9566	+	5.86913i	−1.14926	+	0.307204i
$366$	8.16593	−	7.64023i	0.426840	−	0.399361i
$367$	29.3803			1.53364			0.766819	−	0.641864i	$-0.221839\pi$
$367$	29.3803			1.53364			0.766819	+	0.641864i	$0.221839\pi$
$368$	8.82105	−	2.86613i	0.459829	−	0.149407i
$369$	6.33481	−	3.98771i	0.329777	−	0.207592i
$370$	12.0414	−	14.8517i	0.626003	−	0.772101i
$371$	0.204601			0.0106223
$372$	−28.1061	−	5.67111i	−1.45723	−	0.294033i
$373$			34.9589i			1.81011i	0.425299	+	0.905053i	$0.360169\pi$
$373$			34.9589i			1.81011i	−0.425299	+	0.905053i	$0.639831\pi$
$374$	2.73341	−	3.76221i	0.141341	−	0.194539i
$375$	6.62579	−	18.1961i	0.342154	−	0.939644i
$376$	−1.18570	−	3.64921i	−0.0611478	−	0.188194i
$377$	−33.7526			−1.73834
$378$	5.30439	+	6.48412i	0.272828	+	0.333507i
$379$	−4.59427	−	14.1397i	−0.235992	−	0.726308i	−0.996988	−	0.0775518i	$-0.975290\pi$
$379$	−4.59427	−	14.1397i	−0.235992	−	0.726308i	0.760997	−	0.648756i	$-0.224710\pi$
$380$	39.2166	+	15.0809i	2.01177	+	0.773632i
$381$	15.2567	−	7.14516i	0.781625	−	0.366058i
$382$	15.6327	−	21.5165i	0.799836	−	1.10088i
$383$	−4.81112	+	1.56323i	−0.245837	+	0.0798772i	−0.429344	−	0.903141i	$-0.641255\pi$
$383$	−4.81112	+	1.56323i	−0.245837	+	0.0798772i	0.183507	+	0.983018i	$0.441255\pi$
$384$	3.27470	+	26.3094i	0.167111	+	1.34260i
$385$	1.35994	−	0.881992i	0.0693088	−	0.0449505i
$386$	25.9478	+	8.43095i	1.32071	+	0.429124i
$387$	7.32428	+	11.6352i	0.372314	+	0.591451i
$388$	1.06439	+	1.46500i	0.0540361	+	0.0743743i
$389$	1.88117	−	5.78965i	0.0953792	−	0.293547i	−0.891973	−	0.452088i	$-0.850679\pi$
$389$	1.88117	−	5.78965i	0.0953792	−	0.293547i	0.987352	+	0.158542i	$0.0506792\pi$
$390$	8.30896	−	33.4763i	0.420740	−	1.69514i
$391$	14.1038	+	10.2470i	0.713261	+	0.518214i
$392$	4.34412	+	13.3698i	0.219411	+	0.675278i
$393$	−8.22191	+	1.02337i	−0.414740	+	0.0516223i
$394$	16.9751	+	5.51555i	0.855194	+	0.277869i
$395$	7.52651	−	19.5721i	0.378700	−	0.984779i
$396$	−8.67069	+	2.19243i	−0.435719	+	0.110174i
$397$		−	2.79654i		−	0.140354i	−0.997535	−	0.0701772i	$-0.977644\pi$
$397$		−	2.79654i		−	0.140354i	0.997535	−	0.0701772i	$-0.0223565\pi$
$398$			50.8849i			2.55063i
$399$	−6.92779	−	3.82513i	−0.346823	−	0.191496i
$400$	−4.79445	+	2.76040i	−0.239722	+	0.138020i
$401$	−8.36811	−	6.07979i	−0.417883	−	0.303610i	0.358902	−	0.933375i	$-0.383151\pi$
$401$	−8.36811	−	6.07979i	−0.417883	−	0.303610i	−0.776786	+	0.629765i	$0.783151\pi$
$402$	20.1555	−	18.8580i	1.00527	−	0.940549i
$403$	−6.68517	−	21.2062i	−0.333012	−	1.05635i
$404$			20.2790i			1.00892i
$405$	14.6351	−	13.8135i	0.727224	−	0.686400i
$406$	8.00932	+	11.0239i	0.397496	+	0.547106i
$407$	−1.18803	−	3.65639i	−0.0588886	−	0.181240i
$408$	−5.70873	+	5.34121i	−0.282624	+	0.264429i
$409$			21.0248i			1.03961i	0.854285	+	0.519805i	$0.173995\pi$
$409$			21.0248i			1.03961i	−0.854285	+	0.519805i	$0.826005\pi$
$410$	3.21307	+	12.0202i	0.158682	+	0.593636i
$411$	−9.61260	−	20.5253i	−0.474155	−	1.01244i
$412$	46.2115	+	15.0150i	2.27668	+	0.739738i
$413$	−5.78255	−	4.20127i	−0.284541	−	0.206731i
$414$	−13.7477	−	54.3699i	−0.675663	−	2.67213i
$415$	6.56978	+	5.32664i	0.322498	+	0.261475i
$416$	−21.9958	+	15.9809i	−1.07843	+	0.783528i
$417$	1.88664	+	4.02844i	0.0923891	+	0.197274i
$418$	11.4327	−	8.30636i	0.559193	−	0.406277i
$419$	4.24348	+	5.84065i	0.207307	+	0.285334i	0.899992	−	0.435906i	$-0.143572\pi$
$419$	4.24348	+	5.84065i	0.207307	+	0.285334i	−0.692685	+	0.721241i	$0.743572\pi$
$420$	−7.71539	+	3.12672i	−0.376473	+	0.152569i
$421$	18.0432	−	13.1091i	0.879370	−	0.638900i	−0.0537145	−	0.998556i	$-0.517106\pi$
$421$	18.0432	−	13.1091i	0.879370	−	0.638900i	0.933085	+	0.359656i	$0.117106\pi$
$422$	−9.49482	−	6.89839i	−0.462201	−	0.335808i
$423$	5.14202	−	1.30019i	0.250013	−	0.0632172i
$424$	0.361028	−	0.496912i	0.0175330	−	0.0241322i
$425$	−9.49445	−	4.24087i	−0.460548	−	0.205713i
$426$	12.2602	+	26.1785i	0.594006	+	1.26835i
$427$	−0.646789	−	1.99061i	−0.0313003	−	0.0963325i
$428$	−19.5758			−0.946233
$429$	−4.73845	−	5.06449i	−0.228774	−	0.244516i
$430$	−22.0777	+	5.90148i	−1.06468	+	0.284595i
$431$	6.12092	+	8.42472i	0.294834	+	0.405804i	0.930577	−	0.366097i	$-0.119306\pi$
$431$	6.12092	+	8.42472i	0.294834	+	0.405804i	−0.635743	+	0.771901i	$0.719306\pi$
$432$	−5.73990	+	0.329471i	−0.276161	+	0.0158517i
$433$	−17.3456			−0.833578			−0.416789	−	0.909003i	$-0.636845\pi$
$433$	−17.3456			−0.833578			−0.416789	+	0.909003i	$0.636845\pi$
$434$	−5.33977	+	7.21556i	−0.256317	+	0.346358i
$435$	25.0533	−	21.0674i	1.20121	−	1.01011i
$436$	−6.15794	−	4.47400i	−0.294912	−	0.214266i
$437$	31.1389	+	42.8591i	1.48958	+	2.05023i
$438$	18.9764	−	34.3687i	0.906729	−	1.64220i
$439$	4.72274			0.225404			0.112702	−	0.993629i	$-0.464049\pi$
$439$	4.72274			0.225404			0.112702	+	0.993629i	$0.464049\pi$
$440$	0.257586	−	4.85918i	0.0122799	−	0.231652i
$441$	−18.8391	+	4.76357i	−0.897101	+	0.226837i
$442$	−17.6150	−	5.72345i	−0.837859	−	0.272237i
$443$	−7.49677	+	23.0727i	−0.356182	+	1.09622i	0.599139	+	0.800645i	$0.295510\pi$
$443$	−7.49677	+	23.0727i	−0.356182	+	1.09622i	−0.955321	+	0.295571i	$0.904490\pi$
$444$	2.43887	+	19.5942i	0.115744	+	0.929900i
$445$	25.1640	−	6.72647i	1.19289	−	0.318865i
$446$	−14.7814	−	10.7393i	−0.699921	−	0.508522i
$447$	−5.32471	+	27.6380i	−0.251850	+	1.30723i
$448$	8.91747	+	2.89746i	0.421311	+	0.136892i
$449$	6.70791	−	4.87358i	0.316566	−	0.229998i	−0.418143	−	0.908381i	$-0.637319\pi$
$449$	6.70791	−	4.87358i	0.316566	−	0.229998i	0.734709	+	0.678383i	$0.237319\pi$
$450$	14.7276	+	30.0345i	0.694265	+	1.41584i
$451$	2.37940	+	0.773113i	0.112041	+	0.0364045i
$452$	36.0179	−	26.1685i	1.69414	−	1.23086i
$453$	8.94254	−	1.11307i	0.420157	−	0.0522965i
$454$	−4.17437	−	12.8474i	−0.195913	−	0.602958i
$455$	−5.01464	−	4.06576i	−0.235090	−	0.190606i
$456$	−21.5145	+	10.0758i	−1.00751	+	0.471845i
$457$	2.42093	−	7.45085i	0.113246	−	0.348536i	−0.878331	−	0.478053i	$-0.841343\pi$
$457$	2.42093	−	7.45085i	0.113246	−	0.348536i	0.991577	+	0.129517i	$0.0413427\pi$
$458$	30.0627	−	9.76795i	1.40474	−	0.456426i
$459$	−6.84245	−	8.36426i	−0.319378	−	0.390410i
$460$	55.6515	+	2.95009i	2.59477	+	0.137549i
$461$	−0.507927	−	1.56324i	−0.0236565	−	0.0728073i	0.938531	−	0.345194i	$-0.112187\pi$
$461$	−0.507927	−	1.56324i	−0.0236565	−	0.0728073i	−0.962188	+	0.272387i	$0.912187\pi$
$462$	−0.529697	+	2.74940i	−0.0246437	+	0.127914i
$463$	19.6634	+	14.2863i	0.913834	+	0.663940i	0.941982	−	0.335664i	$-0.108961\pi$
$463$	19.6634	+	14.2863i	0.913834	+	0.663940i	−0.0281473	+	0.999604i	$0.508961\pi$
$464$	−9.35165			−0.434139
$465$	18.1985	+	11.5679i	0.843934	+	0.536447i
$466$	23.2204			1.07566
$467$	21.0305	+	15.2795i	0.973175	+	0.707053i	0.956173	−	0.292802i	$-0.0945878\pi$
$467$	21.0305	+	15.2795i	0.973175	+	0.707053i	0.0170021	+	0.999855i	$0.494588\pi$
$468$	18.9762	+	30.1452i	0.877174	+	1.39346i
$469$	−1.59643	−	4.91332i	−0.0737165	−	0.226876i
$470$	−0.466683	+	8.80367i	−0.0215265	+	0.406083i
$471$	6.90033	−	6.45610i	0.317951	−	0.297481i
$472$	−20.4072	+	6.63069i	−0.939317	+	0.305202i
$473$	−1.41998	+	4.37026i	−0.0652910	+	0.200945i
$474$	15.3628	+	32.8034i	0.705636	+	1.50671i
$475$	−23.4575	−	21.1723i	−1.07630	−	0.971452i
$476$	1.38139	+	4.25149i	0.0633160	+	0.194867i
$477$	0.652198	+	0.543582i	0.0298621	+	0.0248889i
$478$	6.80026	−	4.94068i	0.311037	−	0.225981i
$479$	−24.3570	−	7.91408i	−1.11290	−	0.361603i	−0.305847	−	0.952081i	$-0.598939\pi$
$479$	−24.3570	−	7.91408i	−1.11290	−	0.361603i	−0.807054	+	0.590477i	$0.798939\pi$
$480$	6.35184	−	25.5912i	0.289921	−	1.16807i
$481$	−12.3878	+	9.00025i	−0.564834	+	0.410376i
$482$	27.4065	+	8.90492i	1.24833	+	0.405608i
$483$	−10.3070	−	1.98573i	−0.468983	−	0.0903539i
$484$	24.0408	+	17.4667i	1.09276	+	0.793939i
$485$	−0.351692	−	1.31569i	−0.0159695	−	0.0597425i
$486$	−0.318354	+	34.7619i	−0.0144408	+	1.57683i
$487$	−12.5102	+	38.5025i	−0.566893	+	1.74472i	0.0953666	+	0.995442i	$0.469598\pi$
$487$	−12.5102	+	38.5025i	−0.566893	+	1.74472i	−0.662259	+	0.749275i	$0.730402\pi$
$488$	−5.97587	−	1.94168i	−0.270515	−	0.0878957i
$489$	24.6340	+	13.6015i	1.11399	+	0.615080i
$490$	1.70982	−	32.2545i	0.0772416	−	1.45711i
$491$	−5.46573			−0.246665			−0.123332	−	0.992365i	$-0.539358\pi$
$491$	−5.46573			−0.246665			−0.123332	+	0.992365i	$0.539358\pi$
$492$	−11.2486	−	6.21083i	−0.507126	−	0.280006i
$493$	−10.3317	−	14.2204i	−0.465317	−	0.640453i
$494$	−45.5344	−	33.0827i	−2.04869	−	1.48846i
$495$	6.67829	+	0.801575i	0.300167	+	0.0360281i
$496$	−1.85222	−	5.87549i	−0.0831673	−	0.263817i
$497$	5.41047			0.242693
$498$	−14.4982	+	1.80458i	−0.649681	+	0.0808652i
$499$	−13.9222	−	19.1622i	−0.623242	−	0.857819i	0.374342	−	0.927291i	$-0.377869\pi$
$499$	−13.9222	−	19.1622i	−0.623242	−	0.857819i	−0.997584	+	0.0694715i	$0.977869\pi$
$500$	−32.8415	+	5.14094i	−1.46872	+	0.229910i
$501$	15.5598	−	14.5581i	0.695160	−	0.650407i
$502$	57.3358			2.55902
$503$	6.45522	+	19.8671i	0.287824	+	0.885831i	0.985538	+	0.169454i	$0.0542006\pi$
$503$	6.45522	+	19.8671i	0.287824	+	0.885831i	−0.697714	+	0.716376i	$0.745799\pi$
$504$	1.74881	−	4.37015i	0.0778982	−	0.194662i
$505$	5.47414	−	14.2350i	0.243596	−	0.633451i
$506$	11.0174	−	15.1641i	0.489783	−	0.674128i
$507$	−2.46821	+	4.47024i	−0.109617	+	0.198531i
$508$	−23.3961	−	16.9983i	−1.03803	−	0.754176i
$509$	−31.9972	+	23.2473i	−1.41825	+	1.03042i	−0.426195	+	0.904632i	$0.640146\pi$
$509$	−31.9972	+	23.2473i	−1.41825	+	1.03042i	−0.992057	+	0.125789i	$0.959854\pi$
$510$	16.6474	−	6.74648i	0.737158	−	0.298739i
$511$	−4.31910	−	5.94473i	−0.191066	−	0.262979i
$512$	−9.97977	+	7.25073i	−0.441048	+	0.320440i
$513$	−11.9209	−	30.5989i	−0.526321	−	1.35098i
$514$	−32.9238	+	23.9206i	−1.45221	+	1.05509i
$515$	−28.3854	−	23.0143i	−1.25081	−	1.01413i
$516$	11.4075	−	20.6604i	0.502187	−	0.909525i
$517$	1.43414	+	1.04197i	0.0630736	+	0.0458256i
$518$	5.87913	+	1.91024i	0.258314	+	0.0839313i
$519$	−32.3242	+	15.1384i	−1.41888	+	0.664501i
$520$	−18.7230	+	5.00477i	−0.821060	+	0.219474i
$521$			6.91967i			0.303156i	0.988445	+	0.151578i	$0.0484355\pi$
$521$			6.91967i			0.303156i	−0.988445	+	0.151578i	$0.951565\pi$
$522$	−3.75716	+	56.4196i	−0.164446	+	2.46942i
$523$	4.24251	+	13.0571i	0.185512	+	0.570948i	0.999957	−	0.00929357i	$-0.00295828\pi$
$523$	4.24251	+	13.0571i	0.185512	+	0.570948i	−0.814445	+	0.580241i	$0.802958\pi$
$524$	8.35976	+	11.5062i	0.365198	+	0.502652i
$525$	6.25992	−	0.112134i	0.273205	−	0.00489394i
$526$		−	52.2618i		−	2.27872i
$527$	6.88809	−	9.30779i	0.300050	−	0.405453i
$528$	−1.31286	−	1.40319i	−0.0571348	−	0.0610661i
$529$	38.2401	+	27.7830i	1.66261	+	1.20796i
$530$	−1.18403	+	0.767908i	−0.0514310	+	0.0333558i
$531$	−7.27093	−	28.7553i	−0.315532	−	1.24787i
$532$			13.5844i			0.588959i
$533$		−	9.96439i		−	0.431606i
$534$	−21.7484	+	39.3892i	−0.941147	+	1.70454i
$535$	13.7414	+	5.28431i	0.594093	+	0.228461i
$536$	−14.7499	−	4.79254i	−0.637100	−	0.207006i
$537$	2.02034	+	16.2317i	0.0871842	+	0.700449i
$538$	−20.3851	−	62.7389i	−0.878865	−	2.70487i
$539$	−5.25436	−	3.81752i	−0.226321	−	0.164432i
$540$	−32.9011	−	10.5313i	−1.41584	−	0.453193i
$541$	7.40812	−	22.7999i	0.318500	−	0.980242i	−0.655790	−	0.754944i	$-0.727664\pi$
$541$	7.40812	−	22.7999i	0.318500	−	0.980242i	0.974290	−	0.225299i	$-0.0723358\pi$
$542$	−39.8450	−	54.8419i	−1.71149	−	2.35566i
$543$	−1.75412	+	9.10480i	−0.0752766	+	0.390724i
$544$	−13.4659	−	4.37534i	−0.577346	−	0.187591i
$545$	3.11490	+	4.80284i	0.133428	+	0.205731i
$546$	11.0663	−	1.37742i	0.473595	−	0.0589479i
$547$	−9.93358	+	3.22762i	−0.424729	+	0.138003i	−0.513579	−	0.858042i	$-0.671681\pi$
$547$	−9.93358	+	3.22762i	−0.424729	+	0.138003i	0.0888502	+	0.996045i	$0.471681\pi$
$548$	−22.8683	+	31.4755i	−0.976885	+	1.34457i
$549$	3.22690	−	8.06379i	0.137721	−	0.344154i
$550$	−4.55970	+	10.2082i	−0.194426	+	0.435281i
$551$	−16.5060	−	50.8003i	−0.703180	−	2.16416i
$552$	−23.0099	+	21.5285i	−0.979365	+	0.916315i
$553$	6.77967			0.288301
$554$	14.4899	+	44.5954i	0.615617	+	1.89468i
$555$	3.57728	−	14.4127i	0.151847	−	0.611784i
$556$	4.48829	−	6.17761i	0.190346	−	0.261989i
$557$		−	41.2206i		−	1.74657i	−0.487209	−	0.873286i	$-0.661985\pi$
$557$		−	41.2206i		−	1.74657i	0.487209	−	0.873286i	$-0.338015\pi$
$558$	−36.1916	+	8.81412i	−1.53211	+	0.373132i
$559$	18.3017			0.774080
$560$	−1.38938	−	1.12648i	−0.0587120	−	0.0476025i
$561$	0.683288	−	3.54662i	0.0288484	−	0.149738i
$562$	−68.7369	+	22.3340i	−2.89949	+	0.942101i
$563$	−11.4701			−0.483408			−0.241704	−	0.970350i	$-0.577706\pi$
$563$	−11.4701			−0.483408			−0.241704	+	0.970350i	$0.577706\pi$
$564$	−6.22028	−	6.64829i	−0.261921	−	0.279943i
$565$	−32.3470	+	8.64654i	−1.36085	+	0.363763i
$566$	−19.7781	−	6.42629i	−0.831334	−	0.270117i
$567$	5.86684	+	2.81341i	0.246384	+	0.118152i
$568$	9.54703	−	13.1404i	0.400584	−	0.551357i
$569$	4.21255	+	12.9649i	0.176599	+	0.543517i	0.999703	−	0.0243744i	$-0.00775938\pi$
$569$	4.21255	+	12.9649i	0.176599	+	0.543517i	−0.823104	+	0.567891i	$0.807759\pi$
$570$	54.4478	−	3.86528i	2.28057	−	0.161899i
$571$	7.18971	+	9.89579i	0.300880	+	0.414126i	0.932510	−	0.361144i	$-0.117614\pi$
$571$	7.18971	+	9.89579i	0.300880	+	0.414126i	−0.631630	+	0.775270i	$0.717614\pi$
$572$	−3.67898	+	11.3227i	−0.153826	+	0.473428i
$573$	3.90780	−	20.2835i	0.163251	−	0.847355i
$574$	−3.25446	+	2.36450i	−0.135839	+	0.0986925i
$575$	−38.2687	−	17.0935i	−1.59592	−	0.712846i
$576$	20.7280	+	32.9280i	0.863665	+	1.37200i
$577$	−20.7730	+	28.5916i	−0.864791	+	1.19028i	0.115614	+	0.993294i	$0.463116\pi$
$577$	−20.7730	+	28.5916i	−0.864791	+	1.19028i	−0.980406	+	0.196989i	$0.936884\pi$
$578$	8.73458	+	26.8823i	0.363311	+	1.11816i
$579$	21.0280	−	2.61734i	0.873895	−	0.108773i
$580$	−52.4460	−	20.1683i	−2.17770	−	0.837443i
$581$	−0.845016	+	2.60069i	−0.0350572	+	0.107895i
$582$	2.05946	+	1.13711i	0.0853672	+	0.0471349i
$583$			0.283769i			0.0117525i
$584$	−22.0592			−0.912815
$585$	−5.18309	−	26.2831i	−0.214294	−	1.08667i
$586$	−48.5449	+	35.2699i	−2.00537	+	1.45699i
$587$	9.13941	−	12.5793i	0.377224	−	0.519204i	−0.577623	−	0.816304i	$-0.696019\pi$
$587$	9.13941	−	12.5793i	0.377224	−	0.519204i	0.954846	+	0.297100i	$0.0960194\pi$
$588$	22.7896	+	24.3577i	0.939828	+	1.00450i
$589$	28.6477	−	20.4322i	1.18041	−	0.841892i
$590$	49.2321	+	2.60980i	2.02685	+	0.107444i
$591$	13.7566	−	1.71227i	0.565870	−	0.0704332i
$592$	−3.43222	+	2.49365i	−0.141063	+	0.102489i
$593$	2.60050	+	8.00352i	0.106790	+	0.328665i	0.990146	−	0.140036i	$-0.0447220\pi$
$593$	2.60050	+	8.00352i	0.106790	+	0.328665i	−0.883357	+	0.468702i	$0.844722\pi$
$594$	−8.99308	+	7.35687i	−0.368991	+	0.301856i
$595$	0.177969	−	3.35726i	0.00729601	−	0.137634i
$596$	45.9506	−	14.9303i	1.88221	−	0.611567i
$597$	16.7618	+	35.7907i	0.686016	+	1.46482i
$598$	−70.9997	−	23.0692i	−2.90339	−	0.943370i
$599$	−12.8532	+	17.6909i	−0.525166	+	0.722829i	−0.986384	−	0.164458i	$-0.947413\pi$
$599$	−12.8532	+	17.6909i	−0.525166	+	0.722829i	0.461218	+	0.887287i	$0.347413\pi$
$600$	10.7736	−	15.4013i	0.439830	−	0.628754i
$601$	−7.55631	+	10.4004i	−0.308228	+	0.424240i	−0.934828	−	0.355102i	$-0.884446\pi$
$601$	−7.55631	+	10.4004i	−0.308228	+	0.424240i	0.626599	+	0.779342i	$0.284446\pi$
$602$	−4.34291	−	5.97750i	−0.177004	−	0.243625i
$603$	7.96478	−	19.9034i	0.324351	−	0.810530i
$604$	−9.09247	−	12.5147i	−0.369967	−	0.509216i
$605$	−12.1607	−	18.7505i	−0.494402	−	0.762315i
$606$	11.1736	+	23.8583i	0.453895	+	0.969179i
$607$	23.4889	+	32.3298i	0.953387	+	1.31222i	0.950006	+	0.312230i	$0.101076\pi$
$607$	23.4889	+	32.3298i	0.953387	+	1.31222i	0.00338057	+	0.999994i	$0.498924\pi$
$608$	−34.8091	−	25.2903i	−1.41170	−	1.02566i
$609$	9.26483	+	5.11550i	0.375430	+	0.207291i
$610$	11.2142	+	9.09221i	0.454048	+	0.368133i
$611$	2.18176	−	6.71478i	0.0882647	−	0.271651i
$612$	−6.89191	+	17.2224i	−0.278589	+	0.696174i
$613$	−12.5852	−	38.7333i	−0.508312	−	1.56442i	−0.795131	−	0.606437i	$-0.792598\pi$
$613$	−12.5852	−	38.7333i	−0.508312	−	1.56442i	0.286820	−	0.957985i	$-0.407402\pi$
$614$		−	44.7502i		−	1.80597i
$615$	6.21950	+	7.39620i	0.250795	+	0.298244i
$616$	1.49624	−	0.486158i	0.0602853	−	0.0195879i
$617$	4.21296	−	3.06089i	0.169607	−	0.123227i	−0.499743	−	0.866173i	$-0.666572\pi$
$617$	4.21296	−	3.06089i	0.169607	−	0.123227i	0.669351	+	0.742947i	$0.266572\pi$
$618$	62.6411	−	7.79688i	2.51980	−	0.313636i
$619$			9.44414i			0.379592i	0.981824	+	0.189796i	$0.0607826\pi$
$619$			9.44414i			0.379592i	−0.981824	+	0.189796i	$0.939217\pi$
$620$	2.28374	−	36.9456i	0.0917172	−	1.48377i
$621$	−27.5795	−	33.7133i	−1.10673	−	1.35287i
$622$	27.7099	−	38.1394i	1.11107	−	1.52925i
$623$	4.95002	+	6.81312i	0.198318	+	0.272962i
$624$	−3.69932	+	6.69994i	−0.148091	+	0.268212i
$625$	24.4411	+	5.25653i	0.977645	+	0.210261i
$626$	1.67726			0.0670368
$627$	5.30522	−	9.60843i	0.211870	−	0.383724i
$628$	−15.4272	−	5.01259i	−0.615611	−	0.200024i
$629$	−7.58384	−	2.46414i	−0.302387	−	0.0982516i
$630$	−7.35439	+	7.92971i	−0.293006	+	0.315927i
$631$	−43.8729	+	14.2552i	−1.74655	+	0.567489i	−0.995671	−	0.0929497i	$-0.970370\pi$
$631$	−43.8729	+	14.2552i	−1.74655	+	0.567489i	−0.750880	+	0.660439i	$0.770370\pi$
$632$	11.9630	−	16.4657i	0.475865	−	0.654971i
$633$	−8.95071	−	1.72444i	−0.355759	−	0.0685402i
$634$	−19.4547	+	59.8755i	−0.772646	+	2.37796i
$635$	11.8346	+	18.2476i	0.469641	+	0.724136i
$636$	0.275715	−	1.43110i	0.0109328	−	0.0567469i
$637$	−7.99346	+	24.6013i	−0.316712	+	0.974741i
$638$	−15.2895	+	11.1084i	−0.605316	+	0.439788i
$639$	17.2468	+	14.3745i	0.682271	+	0.568646i
$640$	−33.0664	+	8.83883i	−1.30706	+	0.349386i
$641$	15.4180	+	11.2018i	0.608974	+	0.442445i	0.849053	−	0.528308i	$-0.177173\pi$
$641$	15.4180	+	11.2018i	0.608974	+	0.442445i	−0.240079	+	0.970753i	$0.577173\pi$
$642$	−23.0310	+	10.7861i	−0.908961	+	0.425693i
$643$	−2.78189	+	8.56177i	−0.109707	+	0.337643i	−0.990806	−	0.135288i	$-0.956804\pi$
$643$	−2.78189	+	8.56177i	−0.109707	+	0.337643i	0.881099	+	0.472931i	$0.156804\pi$
$644$	5.56790	+	17.1362i	0.219406	+	0.675263i
$645$	−13.5847	+	11.4234i	−0.534896	+	0.449797i
$646$		−	29.3109i		−	1.15322i
$647$	8.09151	−	2.62909i	0.318110	−	0.103360i	−0.145610	−	0.989342i	$-0.546514\pi$
$647$	8.09151	−	2.62909i	0.318110	−	0.103360i	0.463720	+	0.885982i	$0.346514\pi$
$648$	17.1852	−	9.28435i	0.675099	−	0.364724i
$649$	5.82691	−	8.02005i	0.228726	−	0.314815i
$650$	44.2795	+	4.70775i	1.73679	+	0.184653i
$651$	−1.37896	+	6.83414i	−0.0540456	+	0.267851i
$652$		−	48.3038i		−	1.89172i
$653$	−6.96587	−	5.06100i	−0.272595	−	0.198052i	0.443086	−	0.896479i	$-0.353884\pi$
$653$	−6.96587	−	5.06100i	−0.272595	−	0.198052i	−0.715681	+	0.698427i	$0.753884\pi$
$654$	−9.70996	−	1.87071i	−0.379690	−	0.0731507i
$655$	−2.76221	−	10.3335i	−0.107929	−	0.403765i
$656$		−	2.76078i		−	0.107790i
$657$	2.02608	−	30.4248i	0.0790450	−	1.18698i
$658$	−2.71083	+	0.880802i	−0.105679	+	0.0343372i
$659$	11.9057	+	3.86839i	0.463779	+	0.150691i	0.531580	−	0.847008i	$-0.321598\pi$
$659$	11.9057	+	3.86839i	0.463779	+	0.150691i	−0.0678012	+	0.997699i	$0.521598\pi$
$660$	−4.33658	−	10.7008i	−0.168801	−	0.416527i
$661$	15.1750	+	11.0253i	0.590238	+	0.428833i	0.842400	−	0.538852i	$-0.181142\pi$
$661$	15.1750	+	11.0253i	0.590238	+	0.428833i	−0.252163	+	0.967685i	$0.581142\pi$
$662$	35.0080	−	11.3748i	1.36062	−	0.442093i
$663$	−14.2751	+	1.77681i	−0.554400	+	0.0690056i
$664$	4.82520	+	6.64132i	0.187254	+	0.257733i
$665$	3.66699	−	9.53570i	0.142200	−	0.369779i
$666$	13.6656	+	21.7088i	0.529530	+	0.841200i
$667$	−41.6434	−	57.3173i	−1.61244	−	2.21933i
$668$	−34.7872	−	11.3031i	−1.34596	−	0.437328i
$669$	−13.9344	−	2.68458i	−0.538733	−	0.103792i
$670$	27.6793	+	22.4418i	1.06935	+	0.867003i
$671$	2.76086	−	0.897057i	0.106582	−	0.0346305i
$672$	8.45974	−	1.05297i	0.326341	−	0.0406194i
$673$	−6.67674	+	20.5489i	−0.257369	+	0.792102i	0.735984	+	0.676999i	$0.236720\pi$
$673$	−6.67674	+	20.5489i	−0.257369	+	0.792102i	−0.993354	+	0.115103i	$0.963280\pi$
$674$	16.7450	−	51.5357i	0.644992	−	1.98508i
$675$	20.2524	+	16.2739i	0.779517	+	0.626381i
$676$	8.76552			0.337135
$677$			17.8508i			0.686063i	0.939324	+	0.343031i	$0.111454\pi$
$677$			17.8508i			0.686063i	−0.939324	+	0.343031i	$0.888546\pi$
$678$	27.9566	−	50.6329i	1.07366	−	1.94454i
$679$	0.356223	−	0.258811i	0.0136706	−	0.00993225i
$680$	−7.83972	−	6.35628i	−0.300640	−	0.243752i
$681$	−7.16813	−	7.66135i	−0.274683	−	0.293584i
$682$	−10.0075	−	7.40594i	−0.383209	−	0.283588i
$683$	37.1942			1.42320			0.711598	−	0.702587i	$-0.247972\pi$
$683$	37.1942			1.42320			0.711598	+	0.702587i	$0.247972\pi$
$684$	−36.0910	+	43.3026i	−1.37997	+	1.65572i
$685$	24.5491	−	15.9214i	0.937974	−	0.608327i
$686$	20.6651	−	6.71448i	0.788995	−	0.256360i
$687$	17.9274	−	16.7733i	0.683974	−	0.639941i
$688$	5.07076			0.193321
$689$	1.07488	−	0.349251i	0.0409498	−	0.0133054i
$690$	67.0997	−	27.1927i	2.55444	−	1.03521i
$691$	−6.23767	+	19.1976i	−0.237292	+	0.730310i	0.759517	+	0.650488i	$0.225435\pi$
$691$	−6.23767	+	19.1976i	−0.237292	+	0.730310i	−0.996809	+	0.0798228i	$0.974565\pi$
$692$	49.5691	+	36.0141i	1.88434	+	1.36905i
$693$	0.533100	+	2.10832i	0.0202508	+	0.0800885i
$694$	−11.8752	+	16.3448i	−0.450775	+	0.620438i
$695$	−4.81819	+	3.12485i	−0.182764	+	0.118532i
$696$	28.7722	−	13.4749i	1.09061	−	0.510763i
$697$	4.19812	−	3.05012i	0.159015	−	0.115531i
$698$	−6.38233	+	4.63704i	−0.241575	+	0.175514i
$699$	16.3324	−	7.64895i	0.617749	−	0.289310i
$700$	−5.36251	−	9.31395i	−0.202684	−	0.352034i
$701$	−9.77198	+	13.4500i	−0.369083	+	0.507999i	−0.952651	−	0.304065i	$-0.901656\pi$
$701$	−9.77198	+	13.4500i	−0.369083	+	0.507999i	0.583569	+	0.812064i	$0.301656\pi$
$702$	38.9353	+	25.0102i	1.46952	+	0.943950i
$703$	−19.6041	−	14.2432i	−0.739382	−	0.537193i
$704$	−4.01861	+	12.3680i	−0.151457	+	0.466136i
$705$	2.57174	+	6.34593i	0.0968573	+	0.239002i
$706$	29.9325	−	9.72567i	1.12653	−	0.366031i
$707$	4.93095			0.185447
$708$	−37.1787	+	34.7852i	−1.39726	+	1.30731i
$709$	14.4452	−	4.69353i	0.542501	−	0.176269i	−0.0249314	−	0.999689i	$-0.507937\pi$
$709$	14.4452	−	4.69353i	0.542501	−	0.176269i	0.567433	+	0.823420i	$0.307937\pi$
$710$	−31.3106	+	20.3066i	−1.17506	+	0.762093i
$711$	21.6113	+	18.0122i	0.810488	+	0.675510i
$712$	25.2815			0.947464
$713$	27.7634	−	37.5164i	1.03975	−	1.40500i
$714$	3.96774	+	4.24075i	0.148489	+	0.158706i
$715$	5.63897	−	6.95500i	0.210885	−	0.260102i
$716$	22.7156	−	16.5038i	0.848922	−	0.616778i
$717$	3.15558	−	5.71516i	0.117847	−	0.213437i
$718$			72.6101i			2.70978i
$719$	29.7549			1.10967			0.554836	−	0.831960i	$-0.312781\pi$
$719$	29.7549			1.10967			0.554836	+	0.831960i	$0.312781\pi$
$720$	−1.43605	−	7.28214i	−0.0535185	−	0.271389i
$721$	3.65098	−	11.2366i	0.135970	−	0.418471i
$722$	14.4309	−	44.4138i	0.537064	−	1.65291i
$723$	22.2102	−	2.76448i	0.826005	−	0.102812i
$724$	15.1375	−	4.91848i	0.562582	−	0.182794i
$725$	31.3707	+	28.3146i	1.16508	+	1.05158i
$726$	37.9080	+	7.30332i	1.40690	+	0.271052i
$727$	−44.2887	−	14.3903i	−1.64258	−	0.533706i	−0.665465	−	0.746429i	$-0.731767\pi$
$727$	−44.2887	−	14.3903i	−1.64258	−	0.533706i	−0.977112	+	0.212724i	$0.931767\pi$
$728$	−3.68302	−	5.06924i	−0.136502	−	0.187879i
$729$	11.2269	+	24.5552i	0.415810	+	0.909451i
$730$	47.3066	+	18.1919i	1.75090	+	0.673313i
$731$	5.60218	+	7.71074i	0.207204	+	0.285192i
$732$	−14.7952	+	1.84154i	−0.546845	+	0.0680652i
$733$	51.0511	−	16.5875i	1.88562	−	0.612674i	0.902199	−	0.431321i	$-0.141952\pi$
$733$	51.0511	−	16.5875i	1.88562	−	0.612674i	0.983418	−	0.181353i	$-0.0580477\pi$
$734$	−53.0068	−	38.5117i	−1.95652	−	1.42149i
$735$	−9.42224	−	23.2500i	−0.347544	−	0.857588i
$736$	−54.2763	−	17.6354i	−2.00065	−	0.650050i
$737$	6.81448	−	2.21416i	0.251015	−	0.0815596i
$738$	−16.6561	−	1.10918i	−0.613120	−	0.0408296i
$739$			42.2956i			1.55587i	0.628346	+	0.777934i	$0.283732\pi$
$739$			42.2956i			1.55587i	−0.628346	+	0.777934i	$0.716268\pi$
$740$	−24.6266	+	6.58282i	−0.905291	+	0.241989i
$741$	−42.9250	−	8.26990i	−1.57689	−	0.303802i
$742$	−0.369133	−	0.268191i	−0.0135513	−	0.00984559i
$743$			5.13102i			0.188239i	0.995561	+	0.0941194i	$0.0300036\pi$
$743$			5.13102i			0.188239i	−0.995561	+	0.0941194i	$0.969996\pi$
$744$	14.1648	+	15.4082i	0.519306	+	0.564893i
$745$	−36.2857	−	1.92351i	−1.32941	−	0.0704719i
$746$	45.8242	−	63.0716i	1.67774	−	2.30922i
$747$	−9.60313	+	6.04510i	−0.351360	+	0.221179i
$748$	−5.89656	+	1.91591i	−0.215600	+	0.0700525i
$749$			4.75995i			0.173925i
$750$	−35.8055	+	24.1437i	−1.30743	+	0.881603i
$751$	−9.20420	−	28.3276i	−0.335866	−	1.03369i	−0.966294	−	0.257441i	$-0.917121\pi$
$751$	−9.20420	−	28.3276i	−0.335866	−	1.03369i	0.630428	−	0.776248i	$-0.282879\pi$
$752$	0.604490	−	1.86043i	0.0220435	−	0.0678429i
$753$	40.3281	−	18.8868i	1.46964	−	0.688274i
$754$	60.8951	+	44.2429i	2.21767	+	1.61123i
$755$	3.00431	+	11.2392i	0.109338	+	0.409038i
$756$	−0.640048	−	11.1506i	−0.0232783	−	0.405545i
$757$	6.30868	−	4.58352i	0.229293	−	0.166591i	−0.467207	−	0.884148i	$-0.654740\pi$
$757$	6.30868	−	4.58352i	0.229293	−	0.166591i	0.696500	+	0.717557i	$0.254740\pi$
$758$	−10.2455	+	31.5325i	−0.372134	+	1.14531i
$759$	2.75409	−	14.2951i	0.0999671	−	0.518881i
$760$	−16.6887	−	25.7322i	−0.605363	−	0.933404i
$761$	6.12955	−	18.8648i	0.222196	−	0.683849i	−0.776368	−	0.630280i	$-0.782940\pi$
$761$	6.12955	−	18.8648i	0.222196	−	0.683849i	0.998564	−	0.0535694i	$-0.0170599\pi$
$762$	−36.8915	−	7.10748i	−1.33644	−	0.257477i
$763$	−1.08788	+	1.49733i	−0.0393837	+	0.0542071i
$764$	−33.7231	+	10.9573i	−1.22006	+	0.396421i
$765$	9.48686	−	10.2290i	0.342998	−	0.369831i
$766$	10.7291	+	3.48611i	0.387659	+	0.125958i
$767$	−37.5505	−	12.2009i	−1.35587	−	0.440549i
$768$	6.86191	−	12.4278i	0.247608	−	0.448449i
$769$	−40.8329			−1.47247			−0.736237	−	0.676724i	$-0.763399\pi$
$769$	−40.8329			−1.47247			−0.736237	+	0.676724i	$0.763399\pi$
$770$	−3.60966	−	0.191349i	−0.130083	−	0.00689572i
$771$	−15.2779	+	27.6702i	−0.550220	+	0.996519i
$772$	−21.3806	−	29.4278i	−0.769504	−	1.05913i
$773$	−11.9515	+	16.4499i	−0.429867	+	0.591661i	−0.967923	−	0.251249i	$-0.919159\pi$
$773$	−11.9515	+	16.4499i	−0.429867	+	0.591661i	0.538056	+	0.842909i	$0.319159\pi$
$774$	2.03725	−	30.5925i	0.0732275	−	1.09962i
$775$	−11.5762	+	25.3178i	−0.415830	+	0.909443i
$776$		−	1.32184i		−	0.0474512i
$777$	4.76443	−	0.593023i	0.170923	−	0.0212746i
$778$	−10.9830	+	7.97963i	−0.393760	+	0.286084i
$779$	14.9972	−	4.87289i	0.537331	−	0.174589i
$780$	−35.1960	+	29.5965i	−1.26022	+	1.05973i
$781$			7.50399i			0.268514i
$782$	−12.0138	−	36.9746i	−0.429612	−	1.32221i
$783$	15.9423	+	40.9212i	0.569732	+	1.46241i
$784$	−2.21471	+	6.81617i	−0.0790967	+	0.243435i
$785$	9.47613	+	7.68305i	0.338218	+	0.274220i
$786$	16.1751	+	8.93096i	0.576947	+	0.318557i
$787$	−25.9833	−	18.8780i	−0.926204	−	0.672926i	0.0188566	−	0.999822i	$-0.493997\pi$
$787$	−25.9833	−	18.8780i	−0.926204	−	0.672926i	−0.945060	+	0.326896i	$0.893997\pi$
$788$	−13.9872	−	19.2518i	−0.498274	−	0.685816i
$789$	−17.2154	−	36.7592i	−0.612884	−	1.30866i
$790$	−39.2342	+	25.4455i	−1.39589	+	0.905310i
$791$	−6.36301	−	8.75793i	−0.226242	−	0.311396i
$792$	6.06114	+	2.42550i	0.215373	+	0.0861862i
$793$	−6.79590	−	9.35375i	−0.241329	−	0.332161i
$794$	−3.66571	+	5.04542i	−0.130091	+	0.179055i
$795$	−0.579853	+	0.930149i	−0.0205653	+	0.0329890i
$796$	39.8762	−	54.8849i	1.41338	−	1.94534i
$797$	−3.20974	−	1.04291i	−0.113695	−	0.0369417i	0.251617	−	0.967827i	$-0.419038\pi$
$797$	−3.20974	−	1.04291i	−0.113695	−	0.0369417i	−0.365312	+	0.930885i	$0.619038\pi$
$798$	7.48489	+	15.9821i	0.264962	+	0.565760i
$799$	3.49686	−	1.13620i	0.123710	−	0.0401958i
$800$	33.8498	+	3.59887i	1.19677	+	0.127239i
$801$	−2.32205	+	34.8691i	−0.0820454	+	1.23204i
$802$	7.12804	+	21.9379i	0.251700	+	0.774653i
$803$	8.24498	−	5.99033i	0.290959	−	0.211394i
$804$	−36.5181	+	4.54537i	−1.28789	+	0.160303i
$805$	0.717329	−	13.5319i	0.0252825	−	0.476938i
$806$	−15.7360	+	47.0223i	−0.554275	+	1.65629i
$807$	−35.0048	−	37.4134i	−1.23223	−	1.31702i
$808$	8.70089	−	11.9757i	0.306096	−	0.421305i
$809$	37.7760	−	27.4458i	1.32813	−	0.964945i	0.328340	−	0.944560i	$-0.393511\pi$
$809$	37.7760	−	27.4458i	1.32813	−	0.964945i	0.999792	−	0.0203851i	$-0.00648923\pi$
$810$	−44.5109	+	5.73816i	−1.56395	+	0.201619i
$811$	41.0821			1.44259			0.721295	−	0.692628i	$-0.243547\pi$
$811$	41.0821			1.44259			0.721295	+	0.692628i	$0.243547\pi$
$812$		−	18.1670i		−	0.637537i
$813$	−46.0909	−	25.4487i	−1.61648	−	0.892526i
$814$	−2.64939	+	8.15399i	−0.0928612	+	0.285797i
$815$	−13.0392	+	33.9073i	−0.456742	+	1.18772i
$816$	−3.95514	+	0.492292i	−0.138457	+	0.0172337i
$817$	8.95008	+	27.5455i	0.313124	+	0.963696i
$818$	27.5593	−	37.9322i	0.963590	−	1.32627i
$819$	7.32995	−	4.61415i	0.256129	−	0.161231i
$820$	5.95406	−	15.4831i	0.207925	−	0.540692i
$821$	10.4169	−	7.56835i	0.363554	−	0.264137i	−0.390979	−	0.920400i	$-0.627864\pi$
$821$	10.4169	−	7.56835i	0.363554	−	0.264137i	0.754533	+	0.656262i	$0.227864\pi$
$822$	−9.56191	+	49.6312i	−0.333510	+	1.73109i
$823$	−7.86642	+	24.2104i	−0.274206	+	0.843920i	0.715222	+	0.698897i	$0.246326\pi$
$823$	−7.86642	+	24.2104i	−0.274206	+	0.843920i	−0.989428	+	0.145023i	$0.953674\pi$
$824$	−20.8478	−	28.6945i	−0.726267	−	0.999621i
$825$	0.155523	+	8.68213i	0.00541463	+	0.302273i
$826$	4.92564	+	15.1596i	0.171385	+	0.527468i
$827$	13.7959	−	18.9884i	0.479729	−	0.660290i	−0.498724	−	0.866761i	$-0.666198\pi$
$827$	13.7959	−	18.9884i	0.479729	−	0.660290i	0.978453	+	0.206471i	$0.0661978\pi$
$828$	−27.7789	+	69.4174i	−0.965382	+	2.41242i
$829$	−22.7348	−	7.38700i	−0.789614	−	0.256561i	−0.113674	−	0.993518i	$-0.536262\pi$
$829$	−22.7348	−	7.38700i	−0.789614	−	0.256561i	−0.675940	+	0.736957i	$0.736262\pi$
$830$	−4.87079	−	18.2218i	−0.169068	−	0.632488i
$831$	24.8817	+	26.5938i	0.863138	+	0.922529i
$832$	51.7944			1.79565
$833$	−12.8117	+	4.16276i	−0.443898	+	0.144231i
$834$	1.87669	−	9.74098i	0.0649844	−	0.337303i
$835$	21.3681	+	17.3248i	0.739472	+	0.599548i
$836$	−18.8408			−0.651622
$837$	−22.5525	+	18.1213i	−0.779530	+	0.626365i
$838$		−	16.0998i		−	0.556160i
$839$	−15.4010	+	21.1977i	−0.531703	+	0.731826i	−0.987389	−	0.158314i	$-0.949394\pi$
$839$	−15.4010	+	21.1977i	−0.531703	+	0.731826i	0.455686	+	0.890141i	$0.349394\pi$
$840$	5.89786	+	1.46387i	0.203495	+	0.0505084i
$841$	13.1127	+	40.3567i	0.452162	+	1.39161i
$842$	−49.7363			−1.71403
$843$	−40.9902	+	38.3513i	−1.41178	+	1.32089i
$844$	4.83524	+	14.8813i	0.166436	+	0.512237i
$845$	−6.15303	−	2.36617i	−0.211671	−	0.0813987i
$846$	−10.9813	−	4.39441i	−0.377546	−	0.151083i
$847$	4.24710	−	5.84563i	0.145932	−	0.200858i
$848$	0.297812	−	0.0967651i	0.0102269	−	0.00332293i
$849$	−16.0281	+	1.99500i	−0.550083	+	0.0684682i
$850$	11.5706	+	20.0966i	0.396868	+	0.689306i
$851$	−30.5678	−	9.93207i	−1.04785	−	0.340467i
$852$	7.29102	−	37.8441i	0.249786	−	1.29652i
$853$	21.7419	+	29.9252i	0.744430	+	1.02462i	0.998352	+	0.0573950i	$0.0182794\pi$
$853$	21.7419	+	29.9252i	0.744430	+	1.02462i	−0.253922	+	0.967225i	$0.581721\pi$
$854$	−1.44238	+	4.43920i	−0.0493574	+	0.151906i
$855$	37.0235	−	20.6542i	1.26618	−	0.706359i
$856$	11.5605	+	8.39917i	0.395128	+	0.287078i
$857$	2.71670	+	8.36114i	0.0928007	+	0.285611i	0.986674	−	0.162708i	$-0.0520228\pi$
$857$	2.71670	+	8.36114i	0.0928007	+	0.285611i	−0.893874	+	0.448319i	$0.852023\pi$
$858$	1.91039	+	15.3483i	0.0652197	+	0.523983i
$859$	−11.2418	−	3.65268i	−0.383565	−	0.124628i	0.110886	−	0.993833i	$-0.464631\pi$
$859$	−11.2418	−	3.65268i	−0.383565	−	0.124628i	−0.494452	+	0.869205i	$0.664631\pi$
$860$	28.4379	+	10.9359i	0.969724	+	0.372911i
$861$	−1.51019	+	2.73515i	−0.0514673	+	0.0932138i
$862$		−	23.2229i		−	0.790974i
$863$			21.8754i			0.744648i	0.928103	+	0.372324i	$0.121439\pi$
$863$			21.8754i			0.744648i	−0.928103	+	0.372324i	$0.878561\pi$
$864$	29.7643	+	19.1192i	1.01260	+	0.650450i
$865$	−25.0738	−	38.6611i	−0.852536	−	1.31452i
$866$	31.2944	+	22.7367i	1.06343	+	0.772624i
$867$	14.9988	+	16.0309i	0.509387	+	0.544437i
$868$	11.4140	−	3.59823i	0.387418	−	0.122132i
$869$			9.40299i			0.318975i
$870$	−72.8154	+	5.16921i	−2.46867	+	0.175252i
$871$	−16.7739	−	23.0873i	−0.568363	−	0.782285i
$872$	1.71695	+	5.28423i	0.0581433	+	0.178947i
$873$	1.82312	+	0.121408i	0.0617034	+	0.00410903i
$874$		−	118.142i		−	3.99620i
$875$	1.25004	+	7.98557i	0.0422592	+	0.269962i
$876$	−47.4014	+	22.1995i	−1.60155	+	0.750050i
$877$	−3.76400	−	1.22300i	−0.127101	−	0.0412977i	0.244776	−	0.969580i	$-0.421286\pi$
$877$	−3.76400	−	1.22300i	−0.127101	−	0.0412977i	−0.371877	+	0.928282i	$0.621286\pi$
$878$	−8.52060	−	6.19058i	−0.287556	−	0.208922i
$879$	−22.5267	+	40.7987i	−0.759806	+	1.37610i
$880$	1.56236	−	1.92699i	0.0526671	−	0.0649587i
$881$	−25.6716	+	18.6515i	−0.864899	+	0.628386i	−0.929213	−	0.369544i	$-0.879514\pi$
$881$	−25.6716	+	18.6515i	−0.864899	+	0.628386i	0.0643145	+	0.997930i	$0.479514\pi$
$882$	40.2329	+	16.1001i	1.35471	+	0.542118i
$883$	−24.0499	+	17.4733i	−0.809343	+	0.588022i	−0.913640	−	0.406524i	$-0.866741\pi$
$883$	−24.0499	+	17.4733i	−0.809343	+	0.588022i	0.104297	+	0.994546i	$0.466741\pi$
$884$	14.5145	+	19.9775i	0.488174	+	0.671914i
$885$	35.4879	−	14.3817i	1.19291	−	0.483437i
$886$	43.7691	−	31.8001i	1.47045	−	1.06835i
$887$	−14.8975	−	10.8237i	−0.500210	−	0.363424i	0.308887	−	0.951099i	$-0.400044\pi$
$887$	−14.8975	−	10.8237i	−0.500210	−	0.363424i	−0.809097	+	0.587675i	$0.800044\pi$
$888$	6.96678	−	12.6177i	0.233790	−	0.423423i
$889$	−4.13321	+	5.68888i	−0.138623	+	0.190799i
$890$	−54.2170	−	20.8493i	−1.81736	−	0.698871i
$891$	−3.90203	+	8.13695i	−0.130723	+	0.272598i
$892$	7.52744	+	23.1671i	0.252037	+	0.775692i
$893$	11.1732			0.373898
$894$	45.8346	−	42.8838i	1.53294	−	1.43425i
$895$	−20.4005	+	5.45316i	−0.681913	+	0.182279i
$896$	−6.50451	−	8.95269i	−0.217301	−	0.299089i
$897$	−57.5380	+	7.16169i	−1.92114	+	0.239122i
$898$	−18.4904			−0.617034
$899$	−38.3118	+	27.3248i	−1.27777	+	0.911333i
$900$	7.65138	−	43.9368i	0.255046	−	1.46456i
$901$	0.476167	+	0.345955i	0.0158634	+	0.0115254i
$902$	−3.27942	−	4.51374i	−0.109193	−	0.150291i
$903$	−5.02368	−	2.77379i	−0.167178	−	0.0923059i
$904$	−32.4981			−1.08087
$905$	−11.9536	−	0.633662i	−0.397352	−	0.0210636i
$906$	−17.5928	−	9.71373i	−0.584482	−	0.322717i
$907$	−14.2069	−	4.61611i	−0.471733	−	0.153275i	0.0634964	−	0.997982i	$-0.479775\pi$
$907$	−14.2069	−	4.61611i	−0.471733	−	0.153275i	−0.535230	+	0.844707i	$0.679775\pi$
$908$	−5.56542	+	17.1286i	−0.184695	+	0.568432i
$909$	15.7182	+	13.1005i	0.521340	+	0.434516i
$910$	3.71782	+	13.9085i	0.123244	+	0.461062i
$911$	−17.6930	−	12.8547i	−0.586195	−	0.425896i	0.254757	−	0.967005i	$-0.418004\pi$
$911$	−17.6930	−	12.8547i	−0.586195	−	0.425896i	−0.840952	+	0.541110i	$0.818004\pi$
$912$	−11.8930	−	2.29130i	−0.393817	−	0.0758725i
$913$	−3.60700	−	1.17199i	−0.119374	−	0.0387871i
$914$	−14.1343	+	10.2692i	−0.467522	+	0.339675i
$915$	10.8827	+	2.70113i	0.359771	+	0.0892966i
$916$	−40.0806	−	13.0230i	−1.32430	−	0.430291i
$917$	2.79779	−	2.03272i	0.0923913	−	0.0671262i
$918$	1.38102	+	24.0596i	0.0455805	+	0.794084i
$919$	2.24271	+	6.90236i	0.0739803	+	0.227688i	0.981208	−	0.192951i	$-0.0618059\pi$
$919$	2.24271	+	6.90236i	0.0739803	+	0.227688i	−0.907228	+	0.420639i	$0.861806\pi$
$920$	−31.5991	−	25.6199i	−1.04179	−	0.844664i
$921$	−14.7410	−	31.4757i	−0.485733	−	1.03716i
$922$	−1.13271	+	3.48613i	−0.0373039	+	0.114810i
$923$	28.4242	−	9.23560i	0.935595	−	0.303993i
$924$	2.72592	−	2.55043i	0.0896761	−	0.0839029i
$925$	19.0638	+	2.02684i	0.626814	+	0.0666422i
$926$	−16.7495	−	51.5495i	−0.550422	−	1.69402i
$927$	41.4913	−	26.1185i	1.36275	−	0.857843i
$928$	46.5517	+	33.8218i	1.52813	+	1.11025i
$929$	39.2082			1.28638			0.643190	−	0.765707i	$-0.277611\pi$
$929$	39.2082			1.28638			0.643190	+	0.765707i	$0.277611\pi$
$930$	−17.6698	−	44.7249i	−0.579417	−	1.46659i
$931$	−40.9360			−1.34162
$932$	−25.0457	−	18.1968i	−0.820400	−	0.596056i
$933$	6.92683	−	35.9538i	0.226774	−	1.17707i
$934$	−17.9140	−	55.1336i	−0.586164	−	1.80403i
$935$	4.65632	+	0.246832i	0.152278	+	0.00807227i
$936$	1.72770	−	25.9441i	0.0564716	−	0.848009i
$937$	41.5749	−	13.5085i	1.35819	−	0.441304i	0.462754	−	0.886487i	$-0.346861\pi$
$937$	41.5749	−	13.5085i	1.35819	−	0.441304i	0.895440	+	0.445183i	$0.146861\pi$
$938$	−3.56016	+	10.9570i	−0.116243	+	0.357760i
$939$	1.17973	−	0.552501i	0.0384990	−	0.0180302i
$940$	7.40242	−	9.13000i	0.241440	−	0.297788i
$941$	13.1916	+	40.5994i	0.430033	+	1.32350i	0.898092	+	0.439807i	$0.144953\pi$
$941$	13.1916	+	40.5994i	0.430033	+	1.32350i	−0.468060	+	0.883697i	$0.655047\pi$
$942$	−20.9120	+	2.60289i	−0.681349	+	0.0848069i
$943$	16.9211	−	12.2939i	0.551028	−	0.400346i
$944$	−10.4039	−	3.38044i	−0.338619	−	0.110024i
$945$	−2.56073	+	8.00007i	−0.0833004	+	0.260242i
$946$	8.29043	−	6.02335i	0.269545	−	0.195836i
$947$	38.8521	+	12.6238i	1.26252	+	0.410218i	0.862393	−	0.506240i	$-0.168965\pi$
$947$	38.8521	+	12.6238i	1.26252	+	0.410218i	0.400130	+	0.916458i	$0.368965\pi$
$948$	9.13612	−	47.4212i	0.296727	−	1.54017i
$949$	−32.8383	−	23.8584i	−1.06597	−	0.774476i
$950$	14.5685	+	68.9464i	0.472664	+	2.23692i
$951$	6.03960	+	48.5229i	0.195847	+	1.57346i
$952$	1.00836	−	3.10341i	0.0326811	−	0.100582i
$953$	13.1509	+	4.27300i	0.426001	+	0.138416i	0.514168	−	0.857690i	$-0.328101\pi$
$953$	13.1509	+	4.27300i	0.426001	+	0.138416i	−0.0881668	+	0.996106i	$0.528101\pi$
$954$	−0.464144	−	1.83561i	−0.0150272	−	0.0594301i
$955$	26.6300	+	1.41166i	0.861727	+	0.0456802i
$956$	−11.2066			−0.362448
$957$	−7.09489	+	12.8498i	−0.229345	+	0.415374i
$958$	33.5703	+	46.2055i	1.08461	+	1.49283i
$959$	7.65342	+	5.56054i	0.247142	+	0.179559i
$960$	−38.4451	+	32.3287i	−1.24081	+	1.04340i
$961$	−24.7559	−	18.6586i	−0.798578	−	0.601892i
$962$	34.1471			1.10095
$963$	−12.6462	+	15.1731i	−0.407519	+	0.488948i
$964$	−22.5826	−	31.0822i	−0.727335	−	1.00109i
$965$	7.06452	+	26.4286i	0.227415	+	0.850768i
$966$	15.9926	+	17.0930i	0.514552	+	0.549958i
$967$	48.2241			1.55078			0.775391	−	0.631481i	$-0.217553\pi$
$967$	48.2241			1.55078			0.775391	+	0.631481i	$0.217553\pi$
$968$	−6.70303	−	20.6298i	−0.215443	−	0.663067i
$969$	−9.65520	−	20.6163i	−0.310170	−	0.662290i
$970$	−1.09010	+	2.83472i	−0.0350011	+	0.0910175i
$971$	6.97203	−	9.59617i	0.223743	−	0.307956i	−0.682357	−	0.731019i	$-0.739045\pi$
$971$	6.97203	−	9.59617i	0.223743	−	0.307956i	0.906100	+	0.423063i	$0.139045\pi$
$972$	27.5847	−	37.2450i	0.884780	−	1.19463i
$973$	−1.50212	−	1.09135i	−0.0481556	−	0.0349871i
$974$	73.0397	−	53.0664i	2.34034	−	1.70036i
$975$	32.6955	−	11.2747i	1.04709	−	0.361079i
$976$	−1.88290	−	2.59160i	−0.0602703	−	0.0829550i
$977$	5.78254	−	4.20126i	0.185000	−	0.134410i	−0.491431	−	0.870917i	$-0.663526\pi$
$977$	5.78254	−	4.20126i	0.185000	−	0.134410i	0.676431	+	0.736506i	$0.263526\pi$
$978$	−26.6150	−	56.8296i	−0.851052	−	1.81721i
$979$	−9.44938	+	6.86538i	−0.302004	+	0.219418i
$980$	−27.1207	+	33.4501i	−0.866338	+	1.06853i
$981$	−7.44589	+	1.88273i	−0.237729	+	0.0601110i
$982$	9.86107	+	7.16448i	0.314679	+	0.228628i
$983$	−18.6822	−	6.07021i	−0.595869	−	0.193610i	−0.00447202	−	0.999990i	$-0.501423\pi$
$983$	−18.6822	−	6.07021i	−0.595869	−	0.193610i	−0.591397	+	0.806380i	$0.701423\pi$
$984$	3.97803	+	8.49410i	0.126815	+	0.270782i
$985$	4.62162	+	17.2897i	0.147257	+	0.550895i
$986$			39.1987i			1.24834i
$987$	−1.61656	+	1.51249i	−0.0514558	+	0.0481431i
$988$	23.1884	+	71.3666i	0.737722	+	2.27047i
$989$	22.5804	+	31.0792i	0.718015	+	0.988263i
$990$	−10.9980	−	10.2001i	−0.349540	−	0.324180i
$991$			47.8808i			1.52098i	0.649347	+	0.760492i	$0.275042\pi$
$991$			47.8808i			1.52098i	−0.649347	+	0.760492i	$0.724958\pi$
$992$	−12.0295	+	35.9466i	−0.381936	+	1.14130i
$993$	20.8765	−	19.5325i	0.662495	−	0.619845i
$994$	−9.76137	−	7.09205i	−0.309612	−	0.224946i
$995$	−42.8072	+	27.7627i	−1.35708	+	0.880138i
$996$	17.0521	+	9.41519i	0.540317	+	0.298332i
$997$			8.25826i			0.261542i	0.991413	+	0.130771i	$0.0417452\pi$
$997$			8.25826i			0.261542i	−0.991413	+	0.130771i	$0.958255\pi$
$998$			52.8210i			1.67202i
$999$	16.7629	+	10.7677i	0.530356	+	0.340676i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	465.2.w.c.29.7	✓	224
3.2	odd	2	inner	465.2.w.c.29.49	yes	224
5.4	even	2	inner	465.2.w.c.29.50	yes	224
15.14	odd	2	inner	465.2.w.c.29.8	yes	224
31.15	odd	10	inner	465.2.w.c.449.8	yes	224
93.77	even	10	inner	465.2.w.c.449.50	yes	224
155.139	odd	10	inner	465.2.w.c.449.49	yes	224
465.449	even	10	inner	465.2.w.c.449.7	yes	224

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
465.2.w.c.29.7	✓	224	1.1	even	1	trivial
465.2.w.c.29.8	yes	224	15.14	odd	2	inner
465.2.w.c.29.49	yes	224	3.2	odd	2	inner
465.2.w.c.29.50	yes	224	5.4	even	2	inner
465.2.w.c.449.7	yes	224	465.449	even	10	inner
465.2.w.c.449.8	yes	224	31.15	odd	10	inner
465.2.w.c.449.49	yes	224	155.139	odd	10	inner
465.2.w.c.449.50	yes	224	93.77	even	10	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:	\( N \)	\(=\)	\( 465 = 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	465.w (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.80416 - 1.31080i) q^{2} +(-1.70077 - 0.327670i) q^{3} +(0.918771 + 2.82769i) q^{4} +(0.118368 - 2.23293i) q^{5} +(2.63896 + 2.82055i) q^{6} +(0.687565 - 0.223404i) q^{7} +(0.670664 - 2.06409i) q^{8} +(2.78527 + 1.11458i) q^{9} +(-3.14049 + 3.87342i) q^{10} +(0.309847 + 0.953612i) q^{11} +(-0.636075 - 5.11031i) q^{12} +(3.23082 - 2.34733i) q^{13} +(-1.53332 - 0.498205i) q^{14} +(-0.932981 + 3.75893i) q^{15} +(0.895148 - 0.650363i) q^{16} +(1.97792 + 0.642665i) q^{17} +(-3.56407 - 5.66182i) q^{18} +(5.11289 + 3.71473i) q^{19} +(6.42279 - 1.71685i) q^{20} +(-1.24260 + 0.154665i) q^{21} +(0.690980 - 2.12662i) q^{22} +(7.97229 + 2.59035i) q^{23} +(-1.81699 + 3.29080i) q^{24} +(-4.97198 - 0.528615i) q^{25} -8.90581 q^{26} +(-4.37189 - 2.80830i) q^{27} +(1.26343 + 1.73896i) q^{28} +(-6.83768 - 4.96787i) q^{29} +(6.61046 - 5.55877i) q^{30} +(1.76693 - 5.27996i) q^{31} -6.80811 q^{32} +(-0.214511 - 1.72341i) q^{33} +(-2.72608 - 3.75213i) q^{34} +(-0.417459 - 1.56173i) q^{35} +(-0.592673 + 8.89990i) q^{36} -3.83425 q^{37} +(-4.35521 - 13.4040i) q^{38} +(-6.26405 + 2.93364i) q^{39} +(-4.52959 - 1.74187i) q^{40} +(1.46661 - 2.01861i) q^{41} +(2.44458 + 1.34976i) q^{42} +(3.70761 + 2.69373i) q^{43} +(-2.41184 + 1.75230i) q^{44} +(2.81848 - 6.08738i) q^{45} +(-10.9879 - 15.1235i) q^{46} +(1.43030 - 1.03917i) q^{47} +(-1.73555 + 0.812808i) q^{48} +(-5.24028 + 3.80729i) q^{49} +(8.27735 + 7.47098i) q^{50} +(-3.15341 - 1.74113i) q^{51} +(9.60590 + 6.97909i) q^{52} +(0.269157 + 0.0874544i) q^{53} +(4.20648 + 10.7973i) q^{54} +(2.16603 - 0.578991i) q^{55} -1.56903i q^{56} +(-7.47866 - 7.99325i) q^{57} +(5.82441 + 17.9257i) q^{58} +(-5.81130 - 7.99856i) q^{59} +(-11.4863 + 0.815416i) q^{60} -2.89516i q^{61} +(-10.1088 + 7.20981i) q^{62} +(2.16405 + 0.144111i) q^{63} +(10.4927 + 7.62336i) q^{64} +(-4.85900 - 7.49206i) q^{65} +(-1.87203 + 3.39049i) q^{66} -7.14597i q^{67} +6.18339i q^{68} +(-12.7103 - 7.01788i) q^{69} +(-1.29395 + 3.36482i) q^{70} +(7.11760 + 2.31265i) q^{71} +(4.16858 - 5.00153i) q^{72} +(-3.14087 - 9.66659i) q^{73} +(6.91761 + 5.02594i) q^{74} +(8.28300 + 2.52822i) q^{75} +(-5.80652 + 17.8706i) q^{76} +(0.426081 + 0.586450i) q^{77} +(15.1468 + 2.91816i) q^{78} +(8.91881 + 2.89790i) q^{79} +(-1.34626 - 2.07579i) q^{80} +(6.51541 + 6.20882i) q^{81} +(-5.29200 + 1.71948i) q^{82} +(-2.22328 + 3.06008i) q^{83} +(-1.57900 - 3.37157i) q^{84} +(1.66915 - 4.34049i) q^{85} +(-3.15818 - 9.71987i) q^{86} +(10.0015 + 10.6897i) q^{87} +2.17614 q^{88} +(3.59967 + 11.0787i) q^{89} +(-13.0643 + 7.28816i) q^{90} +(1.69700 - 2.33572i) q^{91} +24.9231i q^{92} +(-4.73523 + 8.40105i) q^{93} -3.94265 q^{94} +(8.89994 - 10.9770i) q^{95} +(11.5791 + 2.23081i) q^{96} +(0.579245 - 0.188208i) q^{97} +14.4449 q^{98} +(-0.199874 + 3.00141i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 224 q - 52 q^{4} - 14 q^{9} - 2 q^{10} - 15 q^{15} - 76 q^{16} + 32 q^{19} - 10 q^{21} + 90 q^{24} - 80 q^{25} + 56 q^{31} - 40 q^{34} + 68 q^{36} + 2 q^{39} - 74 q^{40} - 42 q^{45} - 40 q^{46} + 8 q^{49}+ \cdots - 90 q^{96}+O(q^{100}) \) 224 * q - 52 * q^4 - 14 * q^9 - 2 * q^10 - 15 * q^15 - 76 * q^16 + 32 * q^19 - 10 * q^21 + 90 * q^24 - 80 * q^25 + 56 * q^31 - 40 * q^34 + 68 * q^36 + 2 * q^39 - 74 * q^40 - 42 * q^45 - 40 * q^46 + 8 * q^49 - 22 * q^51 + 80 * q^54 + 40 * q^55 - 85 * q^60 - 116 * q^64 - 124 * q^66 - 18 * q^69 - 52 * q^70 + 20 * q^75 + 24 * q^76 + 40 * q^79 + 62 * q^81 - 140 * q^84 - 20 * q^85 - 28 * q^90 - 40 * q^91 + 104 * q^94 - 90 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more