LMFDB - Embedded newform 510.2.bd.a.133.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [510,2,Mod(7,510)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(510, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 4, 11])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("510.7"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.bd (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [64] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(1)] == traces)

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

Self dual:	no
Analytic conductor:	$4.07237050309$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$8$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			133.3
Character	$\chi$	$=$	510.133
Dual form			510.2.bd.a.487.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.382683 + 0.923880i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(1.40077 + 1.74294i) q^{5} +(-0.195090 - 0.980785i) q^{6} +(-1.26601 + 0.251826i) q^{7} +(0.923880 - 0.382683i) q^{8} +(0.382683 - 0.923880i) q^{9} +(-2.14632 + 0.627144i) q^{10} +(-6.22909 + 1.23904i) q^{11} +(0.980785 + 0.195090i) q^{12} -0.969145i q^{13} +(0.251826 - 1.26601i) q^{14} +(-2.13302 - 0.670980i) q^{15} +1.00000i q^{16} +(1.28517 + 3.91770i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-0.720439 - 1.73929i) q^{19} +(0.241955 - 2.22294i) q^{20} +(0.912745 - 0.912745i) q^{21} +(1.23904 - 6.22909i) q^{22} +(-1.63604 + 2.44851i) q^{23} +(-0.555570 + 0.831470i) q^{24} +(-1.07570 + 4.88292i) q^{25} +(0.895374 + 0.370876i) q^{26} +(0.195090 + 0.980785i) q^{27} +(1.07327 + 0.717139i) q^{28} +(1.47287 - 0.984138i) q^{29} +(1.43618 - 1.71388i) q^{30} +(-8.50337 - 1.69143i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(4.49092 - 4.49092i) q^{33} +(-4.11129 - 0.311896i) q^{34} +(-2.21231 - 1.85384i) q^{35} +(-0.923880 + 0.382683i) q^{36} +(-4.53213 - 6.78281i) q^{37} +1.88260 q^{38} +(0.538428 + 0.805815i) q^{39} +(1.96114 + 1.07422i) q^{40} +(-8.11534 - 5.42250i) q^{41} +(0.493974 + 1.19256i) q^{42} +(-1.41301 - 3.41130i) q^{43} +(5.28076 + 3.52849i) q^{44} +(2.14632 - 0.627144i) q^{45} +(-1.63604 - 2.44851i) q^{46} +3.12264 q^{47} +(-0.555570 - 0.831470i) q^{48} +(-4.92778 + 2.04115i) q^{49} +(-4.09957 - 2.86243i) q^{50} +(-3.24513 - 2.54344i) q^{51} +(-0.685289 + 0.685289i) q^{52} +(10.3239 + 4.27629i) q^{53} +(-0.980785 - 0.195090i) q^{54} +(-10.8851 - 9.12133i) q^{55} +(-1.07327 + 0.717139i) q^{56} +(1.56532 + 1.04592i) q^{57} +(0.345583 + 1.73737i) q^{58} +(7.80760 + 3.23401i) q^{59} +(1.03382 + 1.98273i) q^{60} +(-8.24678 + 12.3422i) q^{61} +(4.81677 - 7.20881i) q^{62} +(-0.251826 + 1.26601i) q^{63} +(0.707107 - 0.707107i) q^{64} +(1.68917 - 1.35755i) q^{65} +(2.43047 + 5.86767i) q^{66} +(6.33649 + 6.33649i) q^{67} +(1.86148 - 3.67898i) q^{68} -2.94479i q^{69} +(2.55934 - 1.33447i) q^{70} +(1.19231 - 5.99416i) q^{71} -1.00000i q^{72} +(9.68185 + 1.92584i) q^{73} +(8.00087 - 1.59147i) q^{74} +(-1.81839 - 4.65762i) q^{75} +(-0.720439 + 1.73929i) q^{76} +(7.57409 - 3.13729i) q^{77} +(-0.950524 + 0.189071i) q^{78} +(0.614353 + 3.08856i) q^{79} +(-1.74294 + 1.40077i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(8.11534 - 5.42250i) q^{82} +(-6.59275 + 15.9163i) q^{83} -1.29082 q^{84} +(-5.02810 + 7.72776i) q^{85} +3.69237 q^{86} +(-0.677886 + 1.63656i) q^{87} +(-5.28076 + 3.52849i) q^{88} +(0.492642 + 0.492642i) q^{89} +(-0.241955 + 2.22294i) q^{90} +(0.244056 + 1.22695i) q^{91} +(2.88821 - 0.574501i) q^{92} +(8.01000 - 3.31785i) q^{93} +(-1.19498 + 2.88495i) q^{94} +(2.02232 - 3.69203i) q^{95} +(0.980785 - 0.195090i) q^{96} +(-8.91855 - 1.77401i) q^{97} -5.33379i q^{98} +(-1.23904 + 6.22909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 16 q^{15} + 16 q^{20} + 16 q^{25} - 16 q^{28} + 32 q^{29} + 16 q^{31} + 16 q^{33} + 32 q^{35} - 16 q^{37} - 16 q^{40} + 48 q^{41} + 16 q^{44} + 32 q^{47} - 64 q^{49} - 16 q^{50} + 32 q^{51} + 16 q^{52}+ \cdots - 80 q^{97}+O(q^{100}) $ 64 * q - 16 * q^15 + 16 * q^20 + 16 * q^25 - 16 * q^28 + 32 * q^29 + 16 * q^31 + 16 * q^33 + 32 * q^35 - 16 * q^37 - 16 * q^40 + 48 * q^41 + 16 * q^44 + 32 * q^47 - 64 * q^49 - 16 * q^50 + 32 * q^51 + 16 * q^52 + 80 * q^53 - 16 * q^55 + 16 * q^56 - 32 * q^57 + 64 * q^59 - 48 * q^61 + 32 * q^65 + 16 * q^67 - 48 * q^68 - 64 * q^71 + 16 * q^73 + 48 * q^74 - 32 * q^75 - 80 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 48 * q^82 - 32 * q^83 - 16 * q^85 - 64 * q^86 - 32 * q^87 - 16 * q^88 - 32 * q^89 - 16 * q^90 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 112 * q^95 - 80 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/510\mathbb{Z}\right)^\times$.

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{9}{16}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.382683	+	0.923880i	−0.270598	+	0.653281i
$2$	−0.382683	+	0.923880i	−0.270598	+	0.653281i
$3$	−0.831470	+	0.555570i	−0.480049	+	0.320759i
$3$	−0.831470	+	0.555570i	−0.480049	+	0.320759i
$4$	−0.707107	−	0.707107i	−0.353553	−	0.353553i
$5$	1.40077	+	1.74294i	0.626442	+	0.779468i
$5$	1.40077	+	1.74294i	0.626442	+	0.779468i
$6$	−0.195090	−	0.980785i	−0.0796453	−	0.400404i
$7$	−1.26601	+	0.251826i	−0.478508	+	0.0951812i	−0.428451	−	0.903565i	$-0.640940\pi$
$7$	−1.26601	+	0.251826i	−0.478508	+	0.0951812i	−0.0500575	+	0.998746i	$0.515940\pi$
$8$	0.923880	−	0.382683i	0.326641	−	0.135299i
$9$	0.382683	−	0.923880i	0.127561	−	0.307960i
$10$	−2.14632	+	0.627144i	−0.678726	+	0.198320i
$11$	−6.22909	+	1.23904i	−1.87814	+	0.373585i	−0.995362	−	0.0962045i	$-0.969330\pi$
$11$	−6.22909	+	1.23904i	−1.87814	+	0.373585i	−0.882778	+	0.469790i	$0.844330\pi$
$12$	0.980785	+	0.195090i	0.283128	+	0.0563177i
$13$		−	0.969145i		−	0.268793i	−0.990928	−	0.134396i	$-0.957090\pi$
$13$		−	0.969145i		−	0.268793i	0.990928	−	0.134396i	$-0.0429095\pi$
$14$	0.251826	−	1.26601i	0.0673033	−	0.338357i
$15$	−2.13302	−	0.670980i	−0.550744	−	0.173246i
$16$			1.00000i			0.250000i
$17$	1.28517	+	3.91770i	0.311699	+	0.950181i
$17$	1.28517	+	3.91770i	0.311699	+	0.950181i
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	−0.720439	−	1.73929i	−0.165280	−	0.399021i	0.819440	−	0.573165i	$-0.194284\pi$
$19$	−0.720439	−	1.73929i	−0.165280	−	0.399021i	−0.984720	+	0.174143i	$0.944284\pi$
$20$	0.241955	−	2.22294i	0.0541028	−	0.497064i
$21$	0.912745	−	0.912745i	0.199177	−	0.199177i
$22$	1.23904	−	6.22909i	0.264165	−	1.32805i
$23$	−1.63604	+	2.44851i	−0.341138	+	0.510549i	−0.961882	−	0.273464i	$-0.911830\pi$
$23$	−1.63604	+	2.44851i	−0.341138	+	0.510549i	0.620744	+	0.784013i	$0.286830\pi$
$24$	−0.555570	+	0.831470i	−0.113405	+	0.169723i
$25$	−1.07570	+	4.88292i	−0.215141	+	0.976583i
$26$	0.895374	+	0.370876i	0.175597	+	0.0727347i
$27$	0.195090	+	0.980785i	0.0375451	+	0.188752i
$28$	1.07327	+	0.717139i	0.202830	+	0.135527i
$29$	1.47287	−	0.984138i	0.273505	−	0.182750i	−0.411252	−	0.911522i	$-0.634908\pi$
$29$	1.47287	−	0.984138i	0.273505	−	0.182750i	0.684757	+	0.728772i	$0.259908\pi$
$30$	1.43618	−	1.71388i	0.262209	−	0.312911i
$31$	−8.50337	−	1.69143i	−1.52725	−	0.303789i	−0.641198	−	0.767375i	$-0.721562\pi$
$31$	−8.50337	−	1.69143i	−1.52725	−	0.303789i	−0.886052	+	0.463586i	$0.846562\pi$
$32$	−0.923880	−	0.382683i	−0.163320	−	0.0676495i
$33$	4.49092	−	4.49092i	0.781769	−	0.781769i
$34$	−4.11129	−	0.311896i	−0.705081	−	0.0534898i
$35$	−2.21231	−	1.85384i	−0.373948	−	0.313356i
$36$	−0.923880	+	0.382683i	−0.153980	+	0.0637806i
$37$	−4.53213	−	6.78281i	−0.745078	−	1.11509i	−0.989375	−	0.145387i	$-0.953557\pi$
$37$	−4.53213	−	6.78281i	−0.745078	−	1.11509i	0.244297	−	0.969700i	$-0.421443\pi$
$38$	1.88260			0.305398
$39$	0.538428	+	0.805815i	0.0862175	+	0.129034i
$40$	1.96114	+	1.07422i	0.310083	+	0.169849i
$41$	−8.11534	−	5.42250i	−1.26740	−	0.846852i	−0.274023	−	0.961723i	$-0.588354\pi$
$41$	−8.11534	−	5.42250i	−1.26740	−	0.846852i	−0.993380	+	0.114872i	$0.963354\pi$
$42$	0.493974	+	1.19256i	0.0762219	+	0.184016i
$43$	−1.41301	−	3.41130i	−0.215482	−	0.520219i	0.778767	−	0.627313i	$-0.215845\pi$
$43$	−1.41301	−	3.41130i	−0.215482	−	0.520219i	−0.994249	+	0.107094i	$0.965845\pi$
$44$	5.28076	+	3.52849i	0.796105	+	0.531940i
$45$	2.14632	−	0.627144i	0.319955	−	0.0934892i
$46$	−1.63604	−	2.44851i	−0.241221	−	0.361012i
$47$	3.12264			0.455484			0.227742	−	0.973721i	$-0.426866\pi$
$47$	3.12264			0.455484			0.227742	+	0.973721i	$0.426866\pi$
$48$	−0.555570	−	0.831470i	−0.0801897	−	0.120012i
$49$	−4.92778	+	2.04115i	−0.703969	+	0.291593i
$50$	−4.09957	−	2.86243i	−0.579767	−	0.404809i
$51$	−3.24513	−	2.54344i	−0.454410	−	0.356153i
$52$	−0.685289	+	0.685289i	−0.0950325	+	0.0950325i
$53$	10.3239	+	4.27629i	1.41809	+	0.587393i	0.954381	−	0.298592i	$-0.0965171\pi$
$53$	10.3239	+	4.27629i	1.41809	+	0.587393i	0.463713	+	0.885986i	$0.346517\pi$
$54$	−0.980785	−	0.195090i	−0.133468	−	0.0265484i
$55$	−10.8851	−	9.12133i	−1.46774	−	1.22992i
$56$	−1.07327	+	0.717139i	−0.143422	+	0.0958318i
$57$	1.56532	+	1.04592i	0.207332	+	0.138535i
$58$	0.345583	+	1.73737i	0.0453773	+	0.228127i
$59$	7.80760	+	3.23401i	1.01646	+	0.421033i	0.827808	−	0.561011i	$-0.189587\pi$
$59$	7.80760	+	3.23401i	1.01646	+	0.421033i	0.188654	+	0.982044i	$0.439587\pi$
$60$	1.03382	+	1.98273i	0.133466	+	0.255969i
$61$	−8.24678	+	12.3422i	−1.05589	+	1.58025i	−0.269023	+	0.963134i	$0.586701\pi$
$61$	−8.24678	+	12.3422i	−1.05589	+	1.58025i	−0.786869	+	0.617120i	$0.788299\pi$
$62$	4.81677	−	7.20881i	0.611731	−	0.915519i
$63$	−0.251826	+	1.26601i	−0.0317271	+	0.159503i
$64$	0.707107	−	0.707107i	0.0883883	−	0.0883883i
$65$	1.68917	−	1.35755i	0.209515	−	0.168383i
$66$	2.43047	+	5.86767i	0.299170	+	0.722260i
$67$	6.33649	+	6.33649i	0.774125	+	0.774125i	0.978825	−	0.204700i	$-0.0656217\pi$
$67$	6.33649	+	6.33649i	0.774125	+	0.774125i	−0.204700	+	0.978825i	$0.565622\pi$
$68$	1.86148	−	3.67898i	0.225737	−	0.446142i
$69$		−	2.94479i		−	0.354511i
$70$	2.55934	−	1.33447i	0.305900	−	0.159500i
$71$	1.19231	−	5.99416i	0.141501	−	0.711376i	−0.843266	−	0.537497i	$-0.819370\pi$
$71$	1.19231	−	5.99416i	0.141501	−	0.711376i	0.984767	−	0.173879i	$-0.0556301\pi$
$72$		−	1.00000i		−	0.117851i
$73$	9.68185	+	1.92584i	1.13317	+	0.225402i	0.725831	−	0.687873i	$-0.241455\pi$
$73$	9.68185	+	1.92584i	1.13317	+	0.225402i	0.407343	+	0.913275i	$0.366455\pi$
$74$	8.00087	−	1.59147i	0.930083	−	0.185005i
$75$	−1.81839	−	4.65762i	−0.209969	−	0.537816i
$76$	−0.720439	+	1.73929i	−0.0826400	+	0.199511i
$77$	7.57409	−	3.13729i	0.863147	−	0.357527i
$78$	−0.950524	+	0.189071i	−0.107626	+	0.0214081i
$79$	0.614353	+	3.08856i	0.0691202	+	0.347491i	0.999833	−	0.0182595i	$-0.00581251\pi$
$79$	0.614353	+	3.08856i	0.0691202	+	0.347491i	−0.930713	+	0.365750i	$0.880813\pi$
$80$	−1.74294	+	1.40077i	−0.194867	+	0.156611i
$81$	−0.707107	−	0.707107i	−0.0785674	−	0.0785674i
$82$	8.11534	−	5.42250i	0.896189	−	0.598815i
$83$	−6.59275	+	15.9163i	−0.723648	+	1.74704i	−0.0609655	+	0.998140i	$0.519418\pi$
$83$	−6.59275	+	15.9163i	−0.723648	+	1.74704i	−0.662682	+	0.748901i	$0.730582\pi$
$84$	−1.29082			−0.140840
$85$	−5.02810	+	7.72776i	−0.545374	+	0.838193i
$86$	3.69237			0.398158
$87$	−0.677886	+	1.63656i	−0.0726770	+	0.175458i
$88$	−5.28076	+	3.52849i	−0.562931	+	0.376139i
$89$	0.492642	+	0.492642i	0.0522199	+	0.0522199i	0.732735	−	0.680515i	$-0.238244\pi$
$89$	0.492642	+	0.492642i	0.0522199	+	0.0522199i	−0.680515	+	0.732735i	$0.738244\pi$
$90$	−0.241955	+	2.22294i	−0.0255043	+	0.234318i
$91$	0.244056	+	1.22695i	0.0255840	+	0.128619i
$92$	2.88821	−	0.574501i	0.301117	−	0.0598958i
$93$	8.01000	−	3.31785i	0.830598	−	0.344045i
$94$	−1.19498	+	2.88495i	−0.123253	+	0.297559i
$95$	2.02232	−	3.69203i	0.207486	−	0.378794i
$96$	0.980785	−	0.195090i	0.100101	−	0.0199113i
$97$	−8.91855	−	1.77401i	−0.905541	−	0.180123i	−0.279712	−	0.960084i	$-0.590239\pi$
$97$	−8.91855	−	1.77401i	−0.905541	−	0.180123i	−0.625829	+	0.779960i	$0.715239\pi$
$98$		−	5.33379i		−	0.538794i
$99$	−1.23904	+	6.22909i	−0.124528	+	0.626047i
$100$	4.21338	−	2.69211i	0.421338	−	0.269211i
$101$			6.89492i			0.686070i	0.939323	+	0.343035i	$0.111455\pi$
$101$			6.89492i			0.686070i	−0.939323	+	0.343035i	$0.888545\pi$
$102$	3.59169	−	2.02478i	0.355631	−	0.200483i
$103$	4.99995	+	4.99995i	0.492660	+	0.492660i	0.909143	−	0.416483i	$-0.136738\pi$
$103$	4.99995	+	4.99995i	0.492660	+	0.492660i	−0.416483	+	0.909143i	$0.636738\pi$
$104$	−0.370876	−	0.895374i	−0.0363674	−	0.0877986i
$105$	2.86941	+	0.312320i	0.280025	+	0.0304793i
$106$	−7.90155	+	7.90155i	−0.767467	+	0.767467i
$107$	−1.56507	+	7.86811i	−0.151301	+	0.760639i	0.828394	+	0.560145i	$0.189255\pi$
$107$	−1.56507	+	7.86811i	−0.151301	+	0.760639i	−0.979695	+	0.200494i	$0.935745\pi$
$108$	0.555570	−	0.831470i	0.0534598	−	0.0800082i
$109$	4.52732	−	6.77562i	0.433639	−	0.648987i	−0.548717	−	0.836008i	$-0.684883\pi$
$109$	4.52732	−	6.77562i	0.433639	−	0.648987i	0.982356	+	0.187022i	$0.0598835\pi$
$110$	12.5926	−	6.56592i	1.20065	−	0.626036i
$111$	7.53666	+	3.12179i	0.715348	+	0.296307i
$112$	−0.251826	−	1.26601i	−0.0237953	−	0.119627i
$113$	3.06679	+	2.04917i	0.288500	+	0.192769i	0.691395	−	0.722477i	$-0.256996\pi$
$113$	3.06679	+	2.04917i	0.288500	+	0.192769i	−0.402896	+	0.915246i	$0.631996\pi$
$114$	−1.56532	+	1.04592i	−0.146606	+	0.0979590i
$115$	−6.55932	+	0.578262i	−0.611659	+	0.0539232i
$116$	−1.73737	−	0.345583i	−0.161310	−	0.0320866i
$117$	−0.895374	−	0.370876i	−0.0827773	−	0.0342875i
$118$	−5.97568	+	5.97568i	−0.550106	+	0.550106i
$119$	−2.61362	−	4.63622i	−0.239590	−	0.425002i
$120$	−2.22743	+	0.196368i	−0.203336	+	0.0179258i
$121$	27.1036	−	11.2267i	2.46396	−	1.02061i
$122$	−8.24678	−	12.3422i	−0.746628	−	1.11741i
$123$	9.76024			0.880051
$124$	4.81677	+	7.20881i	0.432559	+	0.647370i
$125$	−10.0175	+	4.96494i	−0.895988	+	0.444077i
$126$	−1.07327	−	0.717139i	−0.0956149	−	0.0638879i
$127$	−2.13472	−	5.15367i	−0.189426	−	0.457314i	0.800424	−	0.599435i	$-0.204608\pi$
$127$	−2.13472	−	5.15367i	−0.189426	−	0.457314i	−0.989849	+	0.142121i	$0.954608\pi$
$128$	0.382683	+	0.923880i	0.0338248	+	0.0816602i
$129$	3.07009	+	2.05137i	0.270307	+	0.180613i
$130$	0.607794	+	2.08010i	0.0533071	+	0.182437i
$131$	8.75317	+	13.1001i	0.764768	+	1.14456i	0.985575	+	0.169239i	$0.0541310\pi$
$131$	8.75317	+	13.1001i	0.764768	+	1.14456i	−0.220807	+	0.975318i	$0.570869\pi$
$132$	−6.35112			−0.552794
$133$	1.35009	+	2.02055i	0.117067	+	0.175204i
$134$	−8.27902	+	3.42928i	−0.715199	+	0.296245i
$135$	−1.43618	+	1.71388i	−0.123606	+	0.147508i
$136$	2.68658	+	3.12767i	0.230372	+	0.268195i
$137$	−5.01156	+	5.01156i	−0.428167	+	0.428167i	−0.888003	−	0.459837i	$-0.847908\pi$
$137$	−5.01156	+	5.01156i	−0.428167	+	0.428167i	0.459837	+	0.888003i	$0.347908\pi$
$138$	2.72063	+	1.12692i	0.231596	+	0.0959301i
$139$	−0.987484	−	0.196423i	−0.0837573	−	0.0166604i	0.153034	−	0.988221i	$-0.451096\pi$
$139$	−0.987484	−	0.196423i	−0.0837573	−	0.0166604i	−0.236791	+	0.971561i	$0.576096\pi$
$140$	0.253475	+	2.87520i	0.0214225	+	0.242999i
$141$	−2.59638	+	1.73485i	−0.218655	+	0.146101i
$142$	5.08160	+	3.39542i	0.426439	+	0.284937i
$143$	1.20081	+	6.03689i	0.100417	+	0.504830i
$144$	0.923880	+	0.382683i	0.0769900	+	0.0318903i
$145$	3.77844	+	1.18858i	0.313782	+	0.0987058i
$146$	−5.48433	+	8.20787i	−0.453886	+	0.679288i
$147$	2.96330	−	4.43489i	0.244409	−	0.365783i
$148$	−1.59147	+	8.00087i	−0.130818	+	0.657668i
$149$	−14.7453	+	14.7453i	−1.20798	+	1.20798i	−0.236306	+	0.971679i	$0.575937\pi$
$149$	−14.7453	+	14.7453i	−1.20798	+	1.20798i	−0.971679	+	0.236306i	$0.924063\pi$
$150$	4.99895	+	0.102425i	0.408163	+	0.00836293i
$151$	−2.22383	−	5.36880i	−0.180973	−	0.436907i	0.807195	−	0.590285i	$-0.200985\pi$
$151$	−2.22383	−	5.36880i	−0.180973	−	0.436907i	−0.988168	+	0.153378i	$0.950985\pi$
$152$	−1.33120	−	1.33120i	−0.107974	−	0.107974i
$153$	4.11129	+	0.311896i	0.332378	+	0.0252153i
$154$			8.19813i			0.660624i
$155$	−8.96318	−	17.1902i	−0.719940	−	1.38075i
$156$	0.189071	−	0.950524i	0.0151378	−	0.0761028i
$157$			10.0895i			0.805232i	0.915369	+	0.402616i	$0.131899\pi$
$157$			10.0895i			0.805232i	−0.915369	+	0.402616i	$0.868101\pi$
$158$	−3.08856	−	0.614353i	−0.245713	−	0.0488753i
$159$	−10.9598	+	2.18003i	−0.869166	+	0.172888i
$160$	−0.627144	−	2.14632i	−0.0495801	−	0.169682i
$161$	1.45465	−	3.51184i	0.114643	−	0.276772i
$162$	0.923880	−	0.382683i	0.0725868	−	0.0300665i
$163$	−5.81636	+	1.15695i	−0.455572	+	0.0906190i	−0.417542	−	0.908658i	$-0.637108\pi$
$163$	−5.81636	+	1.15695i	−0.455572	+	0.0906190i	−0.0380303	+	0.999277i	$0.512108\pi$
$164$	1.90413	+	9.57269i	0.148687	+	0.747502i
$165$	14.1182	+	1.53669i	1.09910	+	0.119631i
$166$	−12.1818	−	12.1818i	−0.945491	−	0.945491i
$167$	13.7063	−	9.15829i	1.06063	−	0.708690i	0.102415	−	0.994742i	$-0.467343\pi$
$167$	13.7063	−	9.15829i	1.06063	−	0.708690i	0.958214	+	0.286052i	$0.0923430\pi$
$168$	0.493974	−	1.19256i	0.0381109	−	0.0920079i
$169$	12.0608			0.927751
$170$	−5.21534	−	7.60264i	−0.399999	−	0.583096i
$171$	−1.88260			−0.143966
$172$	−1.41301	+	3.41130i	−0.107741	+	0.260109i
$173$	6.22152	−	4.15708i	0.473013	−	0.316057i	−0.296115	−	0.955152i	$-0.595691\pi$
$173$	6.22152	−	4.15708i	0.473013	−	0.316057i	0.769128	+	0.639095i	$0.220691\pi$
$174$	−1.25257	−	1.25257i	−0.0949571	−	0.0949571i
$175$	0.132211	−	6.45273i	0.00999423	−	0.487781i
$176$	−1.23904	−	6.22909i	−0.0933963	−	0.469535i
$177$	−8.28850	+	1.64869i	−0.623002	+	0.123923i
$178$	−0.643668	+	0.266616i	−0.0482449	+	0.0199837i
$179$	4.53244	−	10.9423i	0.338770	−	0.817864i	−0.659064	−	0.752087i	$-0.729047\pi$
$179$	4.53244	−	10.9423i	0.338770	−	0.817864i	0.997834	−	0.0657770i	$-0.0209526\pi$
$180$	−1.96114	−	1.07422i	−0.146174	−	0.0800676i
$181$	−6.14411	+	1.22214i	−0.456688	+	0.0908408i	−0.418073	−	0.908413i	$-0.637294\pi$
$181$	−6.14411	+	1.22214i	−0.456688	+	0.0908408i	−0.0386145	+	0.999254i	$0.512294\pi$
$182$	−1.22695	−	0.244056i	−0.0909477	−	0.0180906i
$183$		−	14.8438i		−	1.09729i
$184$	−0.574501	+	2.88821i	−0.0423527	+	0.212922i
$185$	5.47360	−	17.4004i	0.402427	−	1.27930i
$186$			8.66996i			0.635712i
$187$	−12.8596	−	22.8113i	−0.940388	−	1.66813i
$188$	−2.20804	−	2.20804i	−0.161038	−	0.161038i
$189$	−0.493974	−	1.19256i	−0.0359313	−	0.0867459i
$190$	2.63708	+	3.28126i	0.191314	+	0.238048i
$191$	−11.1834	+	11.1834i	−0.809204	+	0.809204i	−0.984513	−	0.175309i	$-0.943908\pi$
$191$	−11.1834	+	11.1834i	−0.809204	+	0.809204i	0.175309	+	0.984513i	$0.443908\pi$
$192$	−0.195090	+	0.980785i	−0.0140794	+	0.0707821i
$193$	7.43487	−	11.1271i	0.535174	−	0.800944i	−0.461086	−	0.887356i	$-0.652540\pi$
$193$	7.43487	−	11.1271i	0.535174	−	0.800944i	0.996260	+	0.0864113i	$0.0275399\pi$
$194$	5.05195	−	7.56078i	0.362709	−	0.542832i
$195$	−0.650277	+	2.06721i	−0.0465673	+	0.148036i
$196$	4.92778	+	2.04115i	0.351984	+	0.145797i
$197$	2.48516	+	12.4938i	0.177061	+	0.890143i	0.962516	+	0.271225i	$0.0874288\pi$
$197$	2.48516	+	12.4938i	0.177061	+	0.890143i	−0.785455	+	0.618918i	$0.787571\pi$
$198$	−5.28076	−	3.52849i	−0.375288	−	0.250759i
$199$	0.437174	−	0.292110i	0.0309904	−	0.0207072i	−0.539979	−	0.841679i	$-0.681568\pi$
$199$	0.437174	−	0.292110i	0.0309904	−	0.0207072i	0.570969	+	0.820972i	$0.306568\pi$
$200$	0.874790	+	4.92288i	0.0618570	+	0.348100i
$201$	−8.78896	−	1.74823i	−0.619926	−	0.123311i
$202$	−6.37007	−	2.63857i	−0.448197	−	0.185649i
$203$	−1.61684	+	1.61684i	−0.113480	+	0.113480i
$204$	0.496170	+	4.09314i	0.0347388	+	0.286577i
$205$	−1.91660	−	21.7402i	−0.133861	−	1.51840i
$206$	−6.53275	+	2.70595i	−0.455158	+	0.188533i
$207$	1.63604	+	2.44851i	0.113713	+	0.170183i
$208$	0.969145			0.0671981
$209$	6.64274	+	9.94156i	0.459488	+	0.687672i
$210$	−1.38662	+	2.53147i	−0.0956859	+	0.174688i
$211$	3.10928	+	2.07755i	0.214052	+	0.143025i	0.657974	−	0.753040i	$-0.271414\pi$
$211$	3.10928	+	2.07755i	0.214052	+	0.143025i	−0.443923	+	0.896065i	$0.646414\pi$
$212$	−4.27629	−	10.3239i	−0.293697	−	0.709047i
$213$	2.33880	+	5.64637i	0.160252	+	0.386883i
$214$	−6.67027	−	4.45693i	−0.455970	−	0.304669i
$215$	3.96641	−	7.24123i	0.270507	−	0.493848i
$216$	0.555570	+	0.831470i	0.0378018	+	0.0565743i
$217$	11.1913			0.759717
$218$	4.52732	+	6.77562i	0.306629	+	0.458903i
$219$	−9.12010	+	3.77767i	−0.616279	+	0.255271i
$220$	1.24716	+	14.1467i	0.0840832	+	0.953768i
$221$	3.79682	−	1.24552i	0.255402	−	0.0837824i
$222$	−5.76831	+	5.76831i	−0.387144	+	0.387144i
$223$	−1.50288	−	0.622511i	−0.100640	−	0.0416864i	0.331795	−	0.943351i	$-0.392346\pi$
$223$	−1.50288	−	0.622511i	−0.100640	−	0.0416864i	−0.432435	+	0.901665i	$0.642346\pi$
$224$	1.26601	+	0.251826i	0.0845891	+	0.0168258i
$225$	4.09957	+	2.86243i	0.273305	+	0.190829i
$226$	−3.06679	+	2.04917i	−0.204000	+	0.136308i
$227$	8.49828	+	5.67837i	0.564051	+	0.376887i	0.804660	−	0.593735i	$-0.202347\pi$
$227$	8.49828	+	5.67837i	0.564051	+	0.376887i	−0.240610	+	0.970622i	$0.577347\pi$
$228$	−0.367277	−	1.84642i	−0.0243235	−	0.122282i
$229$	19.1718	+	7.94120i	1.26691	+	0.524770i	0.912022	−	0.410141i	$-0.134520\pi$
$229$	19.1718	+	7.94120i	1.26691	+	0.524770i	0.354884	+	0.934910i	$0.384520\pi$
$230$	1.97590	−	6.28131i	0.130287	−	0.414177i
$231$	−4.55464	+	6.81650i	−0.299673	+	0.448493i
$232$	0.984138	−	1.47287i	0.0646118	−	0.0966985i
$233$	−1.47647	+	7.42270i	−0.0967266	+	0.486277i	0.901807	+	0.432139i	$0.142241\pi$
$233$	−1.47647	+	7.42270i	−0.0967266	+	0.486277i	−0.998533	+	0.0541381i	$0.982759\pi$
$234$	0.685289	−	0.685289i	0.0447988	−	0.0447988i
$235$	4.37410	+	5.44259i	0.285335	+	0.355035i
$236$	−3.23401	−	7.80760i	−0.210516	−	0.508231i
$237$	−2.22673	−	2.22673i	−0.144642	−	0.144642i
$238$	5.28350	−	0.640464i	0.342478	−	0.0415151i
$239$		−	27.7718i		−	1.79641i	−0.439578	−	0.898204i	$-0.644872\pi$
$239$		−	27.7718i		−	1.79641i	0.439578	−	0.898204i	$-0.355128\pi$
$240$	0.670980	−	2.13302i	0.0433116	−	0.137686i
$241$	0.988575	−	4.96990i	0.0636797	−	0.320140i	−0.935795	−	0.352544i	$-0.885317\pi$
$241$	0.988575	−	4.96990i	0.0636797	−	0.320140i	0.999475	+	0.0324048i	$0.0103166\pi$
$242$			29.3367i			1.88584i
$243$	0.980785	+	0.195090i	0.0629174	+	0.0125150i
$244$	14.5586	−	2.89588i	0.932018	−	0.185390i
$245$	−10.4603	−	5.72966i	−0.668283	−	0.366055i
$246$	−3.73508	+	9.01728i	−0.238140	+	0.574921i
$247$	−1.68563	+	0.698210i	−0.107254	+	0.0444261i
$248$	−8.50337	+	1.69143i	−0.539964	+	0.107406i
$249$	−3.36095	−	16.8967i	−0.212992	−	1.07078i
$250$	−0.753489	−	11.1549i	−0.0476549	−	0.705499i
$251$	−7.87714	−	7.87714i	−0.497201	−	0.497201i	0.413365	−	0.910566i	$-0.364353\pi$
$251$	−7.87714	−	7.87714i	−0.497201	−	0.497201i	−0.910566	+	0.413365i	$0.864353\pi$
$252$	1.07327	−	0.717139i	0.0676100	−	0.0451755i
$253$	7.15723	−	17.2791i	0.449971	−	1.08633i
$254$	5.57829			0.350013
$255$	−0.112598	−	9.21886i	−0.00705116	−	0.577307i
$256$	−1.00000			−0.0625000
$257$	7.41985	−	17.9131i	0.462837	−	1.11739i	−0.504390	−	0.863476i	$-0.668283\pi$
$257$	7.41985	−	17.9131i	0.462837	−	1.11739i	0.967227	−	0.253912i	$-0.0817175\pi$
$258$	−3.07009	+	2.05137i	−0.191136	+	0.127713i
$259$	7.44583	+	7.44583i	0.462661	+	0.462661i
$260$	−2.15435	−	0.234490i	−0.133607	−	0.0145424i
$261$	−0.345583	−	1.73737i	−0.0213911	−	0.107540i
$262$	−15.4526	+	3.07371i	−0.954663	+	0.189894i
$263$	−22.2877	+	9.23187i	−1.37432	+	0.569261i	−0.942956	−	0.332917i	$-0.891967\pi$
$263$	−22.2877	+	9.23187i	−1.37432	+	0.569261i	−0.431362	+	0.902179i	$0.641967\pi$
$264$	2.43047	−	5.86767i	0.149585	−	0.361130i
$265$	7.00801	+	23.9840i	0.430499	+	1.47333i
$266$	−2.38340	+	0.474087i	−0.146135	+	0.0290681i
$267$	−0.683314	−	0.135920i	−0.0418181	−	0.00831814i
$268$		−	8.96115i		−	0.547389i
$269$	−0.959349	+	4.82298i	−0.0584926	+	0.294062i	−0.998948	−	0.0458547i	$-0.985399\pi$
$269$	−0.959349	+	4.82298i	−0.0584926	+	0.294062i	0.940456	+	0.339917i	$0.110399\pi$
$270$	−1.03382	−	1.98273i	−0.0629163	−	0.120665i
$271$		−	2.37742i		−	0.144418i	−0.997390	−	0.0722089i	$-0.976995\pi$
$271$		−	2.37742i		−	0.144418i	0.997390	−	0.0722089i	$-0.0230048\pi$
$272$	−3.91770	+	1.28517i	−0.237545	+	0.0779248i
$273$	−0.884583	−	0.884583i	−0.0535374	−	0.0535374i
$274$	−2.71224	−	6.54792i	−0.163852	−	0.395574i
$275$	0.650510	−	31.7489i	0.0392273	−	1.91453i
$276$	−2.08228	+	2.08228i	−0.125339	+	0.125339i
$277$	0.00633669	−	0.0318567i	0.000380735	−	0.00191408i	−0.980594	−	0.196047i	$-0.937189\pi$
$277$	0.00633669	−	0.0318567i	0.000380735	−	0.00191408i	0.980975	+	0.194133i	$0.0621894\pi$
$278$	0.559365	−	0.837149i	0.0335485	−	0.0502088i
$279$	−4.81677	+	7.20881i	−0.288373	+	0.431580i
$280$	−2.75334	−	0.866112i	−0.164544	−	0.0517601i
$281$	−19.3455	−	8.01315i	−1.15405	−	0.478025i	−0.278163	−	0.960534i	$-0.589725\pi$
$281$	−19.3455	−	8.01315i	−1.15405	−	0.478025i	−0.875891	+	0.482509i	$0.839725\pi$
$282$	−0.609197	−	3.06264i	−0.0362772	−	0.182378i
$283$	0.265757	+	0.177573i	0.0157976	+	0.0105556i	0.563444	−	0.826154i	$-0.309476\pi$
$283$	0.265757	+	0.177573i	0.0157976	+	0.0105556i	−0.547646	+	0.836710i	$0.684476\pi$
$284$	−5.08160	+	3.39542i	−0.301538	+	0.201481i
$285$	0.369682	+	4.19335i	0.0218981	+	0.248393i
$286$	−6.03689	−	1.20081i	−0.356969	−	0.0710055i
$287$	11.6397	+	4.82130i	0.687067	+	0.284593i
$288$	−0.707107	+	0.707107i	−0.0416667	+	0.0416667i
$289$	−13.6967	+	10.0698i	−0.805687	+	0.592341i
$290$	−2.54405	+	3.03598i	−0.149392	+	0.178279i
$291$	8.40109	−	3.47984i	0.492480	−	0.203992i
$292$	−5.48433	−	8.20787i	−0.320946	−	0.480329i
$293$	−29.4273			−1.71916			−0.859580	−	0.511001i	$-0.829275\pi$
$293$	−29.4273			−1.71916			−0.859580	+	0.511001i	$0.829275\pi$
$294$	2.96330	+	4.43489i	0.172823	+	0.258648i
$295$	5.29993	+	18.1383i	0.308574	+	1.05605i
$296$	−6.78281	−	4.53213i	−0.394243	−	0.263425i
$297$	−2.43047	−	5.86767i	−0.141030	−	0.340477i
$298$	−7.98012	−	19.2657i	−0.462276	−	1.11603i
$299$	2.37296	+	1.58556i	0.137232	+	0.0916953i
$300$	−2.00764	+	4.57923i	−0.115911	+	0.264382i
$301$	2.64794	+	3.96293i	0.152625	+	0.228419i
$302$	5.81115			0.334394
$303$	−3.83061	−	5.73292i	−0.220063	−	0.329347i
$304$	1.73929	−	0.720439i	0.0997554	−	0.0413200i
$305$	−33.0635	+	2.91485i	−1.89321	+	0.166904i
$306$	−1.86148	+	3.67898i	−0.106414	+	0.210313i
$307$	−16.7263	+	16.7263i	−0.954622	+	0.954622i	−0.999014	−	0.0443924i	$-0.985865\pi$
$307$	−16.7263	+	16.7263i	−0.954622	+	0.954622i	0.0443924	+	0.999014i	$0.485865\pi$
$308$	−7.57409	−	3.13729i	−0.431574	−	0.178764i
$309$	−6.93513	−	1.37948i	−0.394526	−	0.0784761i
$310$	19.3117	−	1.70250i	1.09683	−	0.0966955i
$311$	12.3300	−	8.23867i	0.699173	−	0.467172i	−0.154493	−	0.987994i	$-0.549374\pi$
$311$	12.3300	−	8.23867i	0.699173	−	0.467172i	0.853666	+	0.520822i	$0.174374\pi$
$312$	0.805815	+	0.538428i	0.0456203	+	0.0304825i
$313$	−4.03359	−	20.2782i	−0.227992	−	1.14619i	−0.909923	−	0.414776i	$-0.863860\pi$
$313$	−4.03359	−	20.2782i	−0.227992	−	1.14619i	0.681932	−	0.731416i	$-0.261140\pi$
$314$	−9.32151	−	3.86109i	−0.526043	−	0.217894i
$315$	−2.55934	+	1.33447i	−0.144202	+	0.0751890i
$316$	1.74953	−	2.61836i	0.0984188	−	0.147294i
$317$	−12.3159	+	18.4321i	−0.691733	+	1.03525i	0.304830	+	0.952407i	$0.401400\pi$
$317$	−12.3159	+	18.4321i	−0.691733	+	1.03525i	−0.996563	+	0.0828443i	$0.973600\pi$
$318$	2.18003	−	10.9598i	0.122250	−	0.614593i
$319$	−7.95523	+	7.95523i	−0.445407	+	0.445407i
$320$	2.22294	+	0.241955i	0.124266	+	0.0135257i
$321$	−3.06999	−	7.41160i	−0.171350	−	0.413675i
$322$	2.68785	+	2.68785i	0.149788	+	0.149788i
$323$	5.88814	−	5.05775i	0.327625	−	0.281421i
$324$			1.00000i			0.0555556i
$325$	4.73225	+	1.04251i	0.262498	+	0.0578282i
$326$	1.15695	−	5.81636i	0.0640773	−	0.322138i
$327$			8.14897i			0.450639i
$328$	−9.57269	−	1.90413i	−0.528564	−	0.105138i
$329$	−3.95331	+	0.786362i	−0.217953	+	0.0433536i
$330$	−6.82250	+	12.4554i	−0.375566	+	0.685648i
$331$	0.340359	−	0.821700i	0.0187078	−	0.0451647i	−0.914250	−	0.405151i	$-0.867219\pi$
$331$	0.340359	−	0.821700i	0.0187078	−	0.0451647i	0.932957	+	0.359987i	$0.117219\pi$
$332$	15.9163	−	6.59275i	0.873520	−	0.361824i
$333$	−8.00087	+	1.59147i	−0.438445	+	0.0872122i
$334$	3.21596	+	16.1677i	0.175970	+	0.884659i
$335$	−2.16820	+	19.9201i	−0.118461	+	1.08835i
$336$	0.912745	+	0.912745i	0.0497943	+	0.0497943i
$337$	−15.0123	+	10.0309i	−0.817771	+	0.546417i	−0.892637	−	0.450776i	$-0.851147\pi$
$337$	−15.0123	+	10.0309i	−0.817771	+	0.546417i	0.0748657	+	0.997194i	$0.476147\pi$
$338$	−4.61545	+	11.1427i	−0.251047	+	0.606082i
$339$	−3.68840			−0.200326
$340$	9.01975	−	1.90894i	0.489165	−	0.103527i
$341$	55.0640			2.98188
$342$	0.720439	−	1.73929i	0.0389569	−	0.0940503i
$343$	13.2375	−	8.84505i	0.714761	−	0.477588i
$344$	−2.61090	−	2.61090i	−0.140770	−	0.140770i
$345$	5.13261	−	4.12497i	0.276330	−	0.222081i
$346$	1.45977	+	7.33878i	0.0784779	+	0.394535i
$347$	−31.5380	+	6.27330i	−1.69305	+	0.336768i	−0.945049	−	0.326930i	$-0.893986\pi$
$347$	−31.5380	+	6.27330i	−1.69305	+	0.336768i	−0.748001	+	0.663698i	$0.768986\pi$
$348$	1.63656	−	0.677886i	0.0877289	−	0.0363385i
$349$	4.43969	−	10.7184i	0.237651	−	0.573740i	−0.759388	−	0.650638i	$-0.774502\pi$
$349$	4.43969	−	10.7184i	0.237651	−	0.573740i	0.997039	+	0.0768977i	$0.0245015\pi$
$350$	5.91095	+	2.59150i	0.315954	+	0.138522i
$351$	0.950524	−	0.189071i	0.0507352	−	0.0100919i
$352$	6.22909	+	1.23904i	0.332011	+	0.0660412i
$353$		−	7.14466i		−	0.380272i	−0.981758	−	0.190136i	$-0.939107\pi$
$353$		−	7.14466i		−	0.380272i	0.981758	−	0.190136i	$-0.0608929\pi$
$354$	1.64869	−	8.28850i	0.0876267	−	0.440529i
$355$	12.1176	−	6.31829i	0.643137	−	0.335340i
$356$		−	0.696701i		−	0.0369251i
$357$	4.74889	+	2.40283i	0.251338	+	0.127171i
$358$	8.37485	+	8.37485i	0.442625	+	0.442625i
$359$	5.20627	+	12.5690i	0.274776	+	0.663368i	0.999675	−	0.0254868i	$-0.00811357\pi$
$359$	5.20627	+	12.5690i	0.274776	+	0.663368i	−0.724899	+	0.688855i	$0.758114\pi$
$360$	1.74294	−	1.40077i	0.0918612	−	0.0738269i
$361$	10.9289	−	10.9289i	0.575206	−	0.575206i
$362$	1.22214	−	6.14411i	0.0642342	−	0.322927i
$363$	−16.2986	+	24.3926i	−0.855455	+	1.28028i
$364$	0.695012	−	1.04016i	0.0364285	−	0.0545192i
$365$	10.2054	+	19.5726i	0.534174	+	1.02447i
$366$	13.7139	+	5.68048i	0.716837	+	0.296923i
$367$	1.96783	+	9.89297i	0.102720	+	0.516409i	0.997547	+	0.0699962i	$0.0222987\pi$
$367$	1.96783	+	9.89297i	0.102720	+	0.516409i	−0.894827	+	0.446413i	$0.852701\pi$
$368$	−2.44851	−	1.63604i	−0.127637	−	0.0852844i
$369$	−8.11534	+	5.42250i	−0.422468	+	0.282284i
$370$	13.9812	+	11.7158i	0.726848	+	0.609075i
$371$	−14.1471	−	2.81402i	−0.734478	−	0.146097i
$372$	−8.01000	−	3.31785i	−0.415299	−	0.172022i
$373$	12.1318	−	12.1318i	0.628159	−	0.628159i	−0.319446	−	0.947604i	$-0.603497\pi$
$373$	12.1318	−	12.1318i	0.628159	−	0.628159i	0.947604	+	0.319446i	$0.103497\pi$
$374$	25.9960	−	3.15123i	1.34422	−	0.162946i
$375$	5.57084	−	9.69359i	0.287677	−	0.500575i
$376$	2.88495	−	1.19498i	0.148780	−	0.0616266i
$377$	−0.953773	−	1.42742i	−0.0491218	−	0.0735160i
$378$	1.29082			0.0663925
$379$	−5.92310	−	8.86455i	−0.304249	−	0.455342i	0.647568	−	0.762008i	$-0.275786\pi$
$379$	−5.92310	−	8.86455i	−0.304249	−	0.455342i	−0.951817	+	0.306667i	$0.900786\pi$
$380$	−4.04066	+	1.18066i	−0.207281	+	0.0605666i
$381$	4.63818	+	3.09913i	0.237621	+	0.158773i
$382$	−6.05243	−	14.6119i	−0.309669	−	0.747607i
$383$	4.59901	+	11.1030i	0.234998	+	0.567336i	0.996752	−	0.0805306i	$-0.0256615\pi$
$383$	4.59901	+	11.1030i	0.234998	+	0.567336i	−0.761754	+	0.647866i	$0.775661\pi$
$384$	−0.831470	−	0.555570i	−0.0424308	−	0.0283513i
$385$	16.0776	+	8.80659i	0.819393	+	0.448826i
$386$	7.43487	+	11.1271i	0.378425	+	0.566353i
$387$	−3.69237			−0.187694
$388$	5.05195	+	7.56078i	0.256474	+	0.383840i
$389$	14.4743	−	5.99546i	0.733877	−	0.303982i	0.0157327	−	0.999876i	$-0.494992\pi$
$389$	14.4743	−	5.99546i	0.733877	−	0.303982i	0.718144	+	0.695895i	$0.244992\pi$
$390$	−1.66100	−	1.39186i	−0.0841081	−	0.0704798i
$391$	−11.6951	−	3.26276i	−0.591446	−	0.165005i
$392$	−3.77156	+	3.77156i	−0.190493	+	0.190493i
$393$	−14.5560	−	6.02929i	−0.734253	−	0.304138i
$394$	−12.4938	−	2.48516i	−0.629426	−	0.125201i
$395$	−4.52262	+	5.39714i	−0.227558	+	0.271560i
$396$	5.28076	−	3.52849i	0.265368	−	0.177313i
$397$	11.0113	+	7.35749i	0.552639	+	0.369262i	0.800314	−	0.599582i	$-0.204666\pi$
$397$	11.0113	+	7.35749i	0.552639	+	0.369262i	−0.247675	+	0.968843i	$0.579666\pi$
$398$	0.102576	+	0.515682i	0.00514165	+	0.0258488i
$399$	−2.24511	−	0.929955i	−0.112396	−	0.0465560i
$400$	−4.88292	−	1.07570i	−0.244146	−	0.0537852i
$401$	11.1371	−	16.6679i	0.556161	−	0.832353i	−0.441738	−	0.897144i	$-0.645638\pi$
$401$	11.1371	−	16.6679i	0.556161	−	0.832353i	0.997899	+	0.0647907i	$0.0206380\pi$
$402$	4.97855	−	7.45092i	0.248307	−	0.371618i
$403$	−1.63924	+	8.24100i	−0.0816562	+	0.410513i
$404$	4.87544	−	4.87544i	0.242562	−	0.242562i
$405$	0.241955	−	2.22294i	0.0120229	−	0.110459i
$406$	−0.875027	−	2.11250i	−0.0434269	−	0.104842i
$407$	36.6352	+	36.6352i	1.81594	+	1.81594i
$408$	−3.97145	−	1.10798i	−0.196616	−	0.0548530i
$409$		−	35.7325i		−	1.76686i	−0.468563	−	0.883430i	$-0.655228\pi$
$409$		−	35.7325i		−	1.76686i	0.468563	−	0.883430i	$-0.344772\pi$
$410$	20.8188	+	6.54892i	1.02817	+	0.323428i
$411$	1.38269	−	6.95123i	0.0682029	−	0.342879i
$412$		−	7.07100i		−	0.348363i
$413$	−10.6989	−	2.12815i	−0.526460	−	0.104719i
$414$	−2.88821	+	0.574501i	−0.141948	+	0.0282352i
$415$	−36.9761	+	10.8042i	−1.81509	+	0.530359i
$416$	−0.370876	+	0.895374i	−0.0181837	+	0.0438993i
$417$	0.930190	−	0.385297i	0.0455516	−	0.0188681i
$418$	−11.7269	+	2.33262i	−0.573580	+	0.114092i
$419$	−3.70095	−	18.6060i	−0.180803	−	0.908960i	−0.959532	−	0.281599i	$-0.909135\pi$
$419$	−3.70095	−	18.6060i	−0.180803	−	0.908960i	0.778729	−	0.627361i	$-0.215865\pi$
$420$	−1.80813	−	2.24982i	−0.0882279	−	0.109780i
$421$	10.1724	+	10.1724i	0.495770	+	0.495770i	0.910118	−	0.414348i	$-0.135990\pi$
$421$	10.1724	+	10.1724i	0.495770	+	0.495770i	−0.414348	+	0.910118i	$0.635990\pi$
$422$	−3.10928	+	2.07755i	−0.151357	+	0.101134i
$423$	1.19498	−	2.88495i	0.0581021	−	0.140271i
$424$	11.1745			0.542681
$425$	−20.5122	+	2.06109i	−0.994990	+	0.0999776i
$426$	−6.11159			−0.296108
$427$	7.33246	−	17.7021i	0.354843	−	0.856666i
$428$	6.67027	−	4.45693i	0.322419	−	0.215434i
$429$	−4.35235	−	4.35235i	−0.210134	−	0.210134i
$430$	5.17215	+	6.43559i	0.249423	+	0.310352i
$431$	−3.33880	−	16.7853i	−0.160824	−	0.808519i	−0.974008	−	0.226512i	$-0.927268\pi$
$431$	−3.33880	−	16.7853i	−0.160824	−	0.808519i	0.813184	−	0.582007i	$-0.197732\pi$
$432$	−0.980785	+	0.195090i	−0.0471881	+	0.00938629i
$433$	11.6817	−	4.83872i	0.561387	−	0.232534i	−0.0839001	−	0.996474i	$-0.526738\pi$
$433$	11.6817	−	4.83872i	0.561387	−	0.232534i	0.645287	+	0.763940i	$0.276738\pi$
$434$	−4.28274	+	10.3394i	−0.205578	+	0.496309i
$435$	−3.80200	+	1.11093i	−0.182292	+	0.0532648i
$436$	−7.99239	+	1.58978i	−0.382766	+	0.0761369i
$437$	5.43734	+	1.08155i	0.260103	+	0.0517377i
$438$		−	9.87152i		−	0.471680i
$439$	−2.63591	+	13.2516i	−0.125805	+	0.632466i	0.865503	+	0.500904i	$0.166999\pi$
$439$	−2.63591	+	13.2516i	−0.125805	+	0.632466i	−0.991308	+	0.131562i	$0.958001\pi$
$440$	−13.5471	−	4.26147i	−0.645832	−	0.203158i
$441$			5.33379i			0.253990i
$442$	−0.302273	+	3.98444i	−0.0143777	+	0.189520i
$443$	4.04523	+	4.04523i	0.192195	+	0.192195i	0.796644	−	0.604449i	$-0.206607\pi$
$443$	4.04523	+	4.04523i	0.192195	+	0.192195i	−0.604449	+	0.796644i	$0.706607\pi$
$444$	−3.12179	−	7.53666i	−0.148153	−	0.357674i
$445$	−0.168570	+	1.54872i	−0.00799100	+	0.0734165i
$446$	1.15025	−	1.15025i	0.0544660	−	0.0544660i
$447$	4.06823	−	20.4524i	0.192421	−	0.967364i
$448$	−0.717139	+	1.07327i	−0.0338817	+	0.0507075i
$449$	−17.6959	+	26.4838i	−0.835121	+	1.24985i	0.130903	+	0.991395i	$0.458212\pi$
$449$	−17.6959	+	26.4838i	−0.835121	+	1.24985i	−0.966024	+	0.258452i	$0.916788\pi$
$450$	−4.21338	+	2.69211i	−0.198621	+	0.126907i
$451$	57.2698	+	23.7219i	2.69673	+	1.11702i
$452$	−0.719571	−	3.61753i	−0.0338458	−	0.170154i
$453$	4.83180	+	3.22850i	0.227018	+	0.151688i
$454$	−8.49828	+	5.67837i	−0.398844	+	0.266499i
$455$	−1.79664	+	2.14405i	−0.0842279	+	0.100515i
$456$	1.84642	+	0.367277i	0.0864668	+	0.0171993i
$457$	−7.30168	−	3.02446i	−0.341558	−	0.141478i	0.205309	−	0.978697i	$-0.434180\pi$
$457$	−7.30168	−	3.02446i	−0.341558	−	0.141478i	−0.546868	+	0.837219i	$0.684180\pi$
$458$	−14.6734	+	14.6734i	−0.685645	+	0.685645i
$459$	−3.59169	+	2.02478i	−0.167646	+	0.0945086i
$460$	5.04703	+	4.22924i	0.235319	+	0.197190i
$461$	11.2432	−	4.65708i	0.523647	−	0.216902i	−0.105171	−	0.994454i	$-0.533539\pi$
$461$	11.2432	−	4.65708i	0.523647	−	0.216902i	0.628818	+	0.777553i	$0.283539\pi$
$462$	−4.55464	−	6.81650i	−0.211901	−	0.317132i
$463$	18.9460			0.880495			0.440248	−	0.897876i	$-0.354891\pi$
$463$	18.9460			0.880495			0.440248	+	0.897876i	$0.354891\pi$
$464$	0.984138	+	1.47287i	0.0456875	+	0.0683761i
$465$	17.0030	+	9.31344i	0.788494	+	0.431900i
$466$	−6.29266	−	4.20462i	−0.291502	−	0.194775i
$467$	13.9956	+	33.7883i	0.647639	+	1.56354i	0.816151	+	0.577839i	$0.196104\pi$
$467$	13.9956	+	33.7883i	0.647639	+	1.56354i	−0.168512	+	0.985700i	$0.553896\pi$
$468$	0.370876	+	0.895374i	0.0171437	+	0.0413887i
$469$	−9.61778	−	6.42639i	−0.444108	−	0.296743i
$470$	−6.70219	+	1.95835i	−0.309149	+	0.0903319i
$471$	−5.60544	−	8.38914i	−0.258285	−	0.386551i
$472$	8.45089			0.388984
$473$	13.0285	+	19.4985i	0.599051	+	0.896543i
$474$	2.90936	−	1.20510i	0.133631	−	0.0553520i
$475$	9.26781	−	1.64688i	0.425236	−	0.0755640i
$476$	−1.43019	+	5.12641i	−0.0655529	+	0.234969i
$477$	7.90155	−	7.90155i	0.361787	−	0.361787i
$478$	25.6578	+	10.6278i	1.17356	+	0.486105i
$479$	26.8712	+	5.34501i	1.22778	+	0.244220i	0.766037	−	0.642797i	$-0.222226\pi$
$479$	26.8712	+	5.34501i	1.22778	+	0.244220i	0.461738	+	0.887016i	$0.347226\pi$
$480$	1.71388	+	1.43618i	0.0782277	+	0.0655522i
$481$	−6.57353	+	4.39229i	−0.299727	+	0.200271i
$482$	4.21328	+	2.81522i	0.191910	+	0.128230i
$483$	0.741575	+	3.72815i	0.0337428	+	0.169637i
$484$	−27.1036	−	11.2267i	−1.23198	−	0.510304i
$485$	−9.40081	−	18.0295i	−0.426869	−	0.818677i
$486$	−0.555570	+	0.831470i	−0.0252012	+	0.0377162i
$487$	5.09357	−	7.62306i	0.230812	−	0.345434i	−0.697927	−	0.716169i	$-0.745894\pi$
$487$	5.09357	−	7.62306i	0.230812	−	0.345434i	0.928739	+	0.370735i	$0.120894\pi$
$488$	−2.89588	+	14.5586i	−0.131090	+	0.659036i
$489$	4.19336	−	4.19336i	0.189630	−	0.189630i
$490$	9.29650	−	7.47140i	0.419973	−	0.337523i
$491$	−0.193181	−	0.466380i	−0.00871814	−	0.0210475i	0.919461	−	0.393182i	$-0.128626\pi$
$491$	−0.193181	−	0.466380i	−0.00871814	−	0.0210475i	−0.928179	+	0.372135i	$0.878626\pi$
$492$	−6.90153	−	6.90153i	−0.311145	−	0.311145i
$493$	5.74844	+	4.50546i	0.258897	+	0.202916i
$494$		−	1.82451i		−	0.0820887i
$495$	−12.5926	+	6.56592i	−0.565993	+	0.295116i
$496$	1.69143	−	8.50337i	0.0759472	−	0.381812i
$497$			7.88895i			0.353868i
$498$	16.8967	+	3.36095i	0.757157	+	0.150608i
$499$	−11.3111	+	2.24993i	−0.506356	+	0.100720i	−0.441656	−	0.897184i	$-0.645609\pi$
$499$	−11.3111	+	2.24993i	−0.506356	+	0.100720i	−0.0646997	+	0.997905i	$0.520609\pi$
$500$	10.5942	+	3.57267i	0.473785	+	0.159775i
$501$	−6.30834	+	15.2297i	−0.281836	+	0.680412i
$502$	10.2920	−	4.26308i	0.459354	−	0.190271i
$503$	6.75145	−	1.34295i	0.301032	−	0.0598791i	−0.0422631	−	0.999107i	$-0.513457\pi$
$503$	6.75145	−	1.34295i	0.301032	−	0.0598791i	0.343295	+	0.939227i	$0.388457\pi$
$504$	0.251826	+	1.26601i	0.0112172	+	0.0563928i
$505$	−12.0175	+	9.65818i	−0.534770	+	0.429783i
$506$	13.2248	+	13.2248i	0.587915	+	0.587915i
$507$	−10.0282	+	6.70060i	−0.445366	+	0.297584i
$508$	−2.13472	+	5.15367i	−0.0947129	+	0.228657i
$509$	−18.2532			−0.809061			−0.404530	−	0.914525i	$-0.632565\pi$
$509$	−18.2532			−0.809061			−0.404530	+	0.914525i	$0.632565\pi$
$510$	8.56020	+	3.42388i	0.379052	+	0.151612i
$511$	−12.7423			−0.563687
$512$	0.382683	−	0.923880i	0.0169124	−	0.0408301i
$513$	1.56532	−	1.04592i	0.0691107	−	0.0461783i
$514$	13.7101	+	13.7101i	0.604726	+	0.604726i
$515$	−1.71087	+	15.7184i	−0.0753897	+	0.692635i
$516$	−0.720345	−	3.62142i	−0.0317114	−	0.159424i
$517$	−19.4512	+	3.86909i	−0.855463	+	0.170162i
$518$	−9.72844	+	4.02965i	−0.427443	+	0.177053i
$519$	−2.86345	+	6.91298i	−0.125691	+	0.303446i
$520$	1.04107	−	1.90063i	0.0456541	−	0.0833479i
$521$	−41.0026	+	8.15592i	−1.79636	+	0.357317i	−0.976544	−	0.215317i	$-0.930922\pi$
$521$	−41.0026	+	8.15592i	−1.79636	+	0.357317i	−0.819811	+	0.572634i	$0.805922\pi$
$522$	1.73737	+	0.345583i	0.0760424	+	0.0151258i
$523$		−	22.6931i		−	0.992298i	−0.868237	−	0.496149i	$-0.834747\pi$
$523$		−	22.6931i		−	0.992298i	0.868237	−	0.496149i	$-0.165253\pi$
$524$	3.07371	−	15.4526i	0.134275	−	0.675048i
$525$	3.47501	+	5.43870i	0.151662	+	0.237364i
$526$		−	24.1240i		−	1.05186i
$527$	−4.30177	−	35.4874i	−0.187388	−	1.54585i
$528$	4.49092	+	4.49092i	0.195442	+	0.195442i
$529$	5.48316	+	13.2375i	0.238398	+	0.575545i
$530$	−24.8402	−	2.70372i	−1.07899	−	0.117442i
$531$	5.97568	−	5.97568i	0.259322	−	0.259322i
$532$	0.474087	−	2.38340i	0.0205543	−	0.103333i
$533$	−5.25519	+	7.86494i	−0.227627	+	0.340669i
$534$	0.387066	−	0.579286i	0.0167500	−	0.0250681i
$535$	−15.9060	+	8.29358i	−0.687675	+	0.358563i
$536$	8.27902	+	3.42928i	0.357599	+	0.148122i
$537$	2.31062	+	11.6163i	0.0997105	+	0.501278i
$538$	−4.08872	−	2.73200i	−0.176277	−	0.117785i
$539$	28.1665	−	18.8202i	1.21322	−	0.810646i
$540$	2.22743	−	0.196368i	0.0958533	−	0.00845032i
$541$	26.1253	+	5.19664i	1.12321	+	0.223421i	0.721548	−	0.692365i	$-0.243431\pi$
$541$	26.1253	+	5.19664i	1.12321	+	0.223421i	0.401666	+	0.915786i	$0.368431\pi$
$542$	2.19645	+	0.909798i	0.0943455	+	0.0390792i
$543$	4.42965	−	4.42965i	0.190095	−	0.190095i
$544$	0.311896	−	4.11129i	0.0133724	−	0.176270i
$545$	18.1512	−	1.60019i	0.777514	−	0.0685448i
$546$	1.15576	−	0.478733i	0.0494621	−	0.0204879i
$547$	9.99266	+	14.9551i	0.427255	+	0.639433i	0.981171	−	0.193140i	$-0.0618671\pi$
$547$	9.99266	+	14.9551i	0.427255	+	0.639433i	−0.553916	+	0.832573i	$0.686867\pi$
$548$	7.08742			0.302759
$549$	8.24678	+	12.3422i	0.351964	+	0.526751i
$550$	29.0833	+	12.7508i	1.24011	+	0.543695i
$551$	−2.77282	−	1.85274i	−0.118126	−	0.0789293i
$552$	−1.12692	−	2.72063i	−0.0479650	−	0.115798i
$553$	−1.55556	−	3.75545i	−0.0661492	−	0.159698i
$554$	0.0270068	+	0.0180454i	0.00114741	+	0.000766675i
$555$	5.11601	+	17.5089i	0.217162	+	0.743210i
$556$	0.559365	+	0.837149i	0.0237224	+	0.0355030i
$557$	−2.40807			−0.102033			−0.0510165	−	0.998698i	$-0.516246\pi$
$557$	−2.40807			−0.102033			−0.0510165	+	0.998698i	$0.516246\pi$
$558$	−4.81677	−	7.20881i	−0.203910	−	0.305173i
$559$	−3.30605	+	1.36941i	−0.139831	+	0.0579199i
$560$	1.85384	−	2.21231i	0.0783391	−	0.0934871i
$561$	23.3656	+	11.8225i	0.986499	+	0.499145i
$562$	14.8064	−	14.8064i	0.624569	−	0.624569i
$563$	−13.3462	−	5.52819i	−0.562477	−	0.232985i	0.0832834	−	0.996526i	$-0.473459\pi$
$563$	−13.3462	−	5.52819i	−0.562477	−	0.232985i	−0.645760	+	0.763540i	$0.723459\pi$
$564$	3.06264	+	0.609197i	0.128961	+	0.0256518i
$565$	0.724283	+	8.21565i	0.0304708	+	0.345635i
$566$	−0.265757	+	0.177573i	−0.0111706	+	0.00746395i
$567$	1.07327	+	0.717139i	0.0450733	+	0.0301170i
$568$	−1.19231	−	5.99416i	−0.0500283	−	0.251509i
$569$	−37.2485	−	15.4288i	−1.56154	−	0.646810i	−0.576182	−	0.817322i	$-0.695458\pi$
$569$	−37.2485	−	15.4288i	−1.56154	−	0.646810i	−0.985356	+	0.170512i	$0.945458\pi$
$570$	−4.01563	−	1.26319i	−0.168196	−	0.0529090i
$571$	−16.6671	+	24.9440i	−0.697496	+	1.04388i	0.298494	+	0.954411i	$0.403516\pi$
$571$	−16.6671	+	24.9440i	−0.697496	+	1.04388i	−0.995990	+	0.0894646i	$0.971484\pi$
$572$	3.41962	−	5.11783i	0.142982	−	0.213987i
$573$	3.08550	−	15.5119i	0.128899	−	0.648017i
$574$	−8.90861	+	8.90861i	−0.371838	+	0.371838i
$575$	−10.1960	−	10.6225i	−0.425201	−	0.442989i
$576$	−0.382683	−	0.923880i	−0.0159451	−	0.0384950i
$577$	−1.69249	−	1.69249i	−0.0704591	−	0.0704591i	0.670999	−	0.741458i	$-0.265865\pi$
$577$	−1.69249	−	1.69249i	−0.0704591	−	0.0704591i	−0.741458	+	0.670999i	$0.765865\pi$
$578$	−4.06179	−	16.5076i	−0.168948	−	0.686627i
$579$			13.3824i			0.556154i
$580$	−1.83131	−	3.51221i	−0.0760411	−	0.145837i
$581$	4.33837	−	21.8105i	0.179986	−	0.904851i
$582$			9.09327i			0.376928i
$583$	−69.6068	−	13.8457i	−2.88282	−	0.573428i
$584$	9.68185	−	1.92584i	0.400638	−	0.0796918i
$585$	−0.607794	−	2.08010i	−0.0251292	−	0.0860014i
$586$	11.2613	−	27.1873i	0.465201	−	1.12310i
$587$	−10.9797	+	4.54792i	−0.453179	+	0.187713i	−0.597585	−	0.801806i	$-0.703873\pi$
$587$	−10.9797	+	4.54792i	−0.453179	+	0.187713i	0.144406	+	0.989519i	$0.453873\pi$
$588$	−5.23130	+	1.04057i	−0.215735	+	0.0429124i
$589$	3.18427	+	16.0084i	0.131206	+	0.659616i
$590$	−18.7858	−	2.04474i	−0.773399	−	0.0841804i
$591$	−9.00750	−	9.00750i	−0.370519	−	0.370519i
$592$	6.78281	−	4.53213i	0.278772	−	0.186269i
$593$	4.75609	−	11.4822i	0.195309	−	0.471518i	−0.795638	−	0.605773i	$-0.792864\pi$
$593$	4.75609	−	11.4822i	0.195309	−	0.471518i	0.990947	+	0.134255i	$0.0428640\pi$
$594$	6.35112			0.260590
$595$	4.41960	−	11.0497i	0.181186	−	0.452992i
$596$	20.8531			0.854174
$597$	−0.201209	+	0.485762i	−0.00823494	+	0.0198809i
$598$	−2.37296	+	1.58556i	−0.0970375	+	0.0648384i
$599$	−3.89710	−	3.89710i	−0.159231	−	0.159231i	0.622995	−	0.782226i	$-0.285916\pi$
$599$	−3.89710	−	3.89710i	−0.159231	−	0.159231i	−0.782226	+	0.622995i	$0.785916\pi$
$600$	−3.46237	−	3.60722i	−0.141351	−	0.147264i
$601$	−0.699020	−	3.51421i	−0.0285136	−	0.143348i	0.963906	−	0.266243i	$-0.0857822\pi$
$601$	−0.699020	−	3.51421i	−0.0285136	−	0.143348i	−0.992420	+	0.122895i	$0.960782\pi$
$602$	−4.67459	+	0.929834i	−0.190522	+	0.0378972i
$603$	8.27902	−	3.42928i	0.337148	−	0.139651i
$604$	−2.22383	+	5.36880i	−0.0904864	+	0.218454i
$605$	57.5333	+	31.5141i	2.33906	+	1.28123i
$606$	6.76244	−	1.34513i	0.274705	−	0.0546423i
$607$	24.6773	+	4.90862i	1.00162	+	0.199235i	0.668550	−	0.743667i	$-0.266915\pi$
$607$	24.6773	+	4.90862i	1.00162	+	0.199235i	0.333070	+	0.942902i	$0.391915\pi$
$608$			1.88260i			0.0763494i
$609$	0.446085	−	2.24262i	0.0180763	−	0.0908756i
$610$	9.95990	−	31.6622i	0.403265	−	1.28196i
$611$		−	3.02629i		−	0.122431i
$612$	−2.68658	−	3.12767i	−0.108598	−	0.126428i
$613$	4.13558	+	4.13558i	0.167034	+	0.167034i	0.785675	−	0.618640i	$-0.212316\pi$
$613$	4.13558	+	4.13558i	0.167034	+	0.167034i	−0.618640	+	0.785675i	$0.712316\pi$
$614$	−9.05222	−	21.8540i	−0.365318	−	0.881956i
$615$	13.6718	+	17.0115i	0.551301	+	0.685971i
$616$	5.79696	−	5.79696i	0.233566	−	0.233566i
$617$	1.72188	−	8.65646i	0.0693202	−	0.348496i	−0.930523	−	0.366235i	$-0.880647\pi$
$617$	1.72188	−	8.65646i	0.0693202	−	0.348496i	0.999843	+	0.0177388i	$0.00564672\pi$
$618$	3.92844	−	5.87932i	0.158025	−	0.236501i
$619$	26.6751	−	39.9221i	1.07216	−	1.60460i	0.317786	−	0.948162i	$-0.397061\pi$
$619$	26.6751	−	39.9221i	1.07216	−	1.60460i	0.754376	−	0.656442i	$-0.227939\pi$
$620$	−5.81737	+	18.4932i	−0.233631	+	0.742706i
$621$	−2.72063	−	1.12692i	−0.109175	−	0.0452219i
$622$	2.89304	+	14.5443i	0.116000	+	0.583173i
$623$	−0.747752	−	0.499632i	−0.0299580	−	0.0200173i
$624$	−0.805815	+	0.538428i	−0.0322584	+	0.0215544i
$625$	−22.6857	−	10.5051i	−0.907429	−	0.420205i
$626$	20.2782	+	4.03359i	0.810480	+	0.161215i
$627$	−11.0465	−	4.57560i	−0.441153	−	0.182732i
$628$	7.13437	−	7.13437i	0.284692	−	0.284692i
$629$	20.7484	−	26.4726i	0.827295	−	1.05553i
$630$	−0.253475	−	2.87520i	−0.0100987	−	0.114551i
$631$	5.05556	−	2.09408i	0.201259	−	0.0833640i	−0.279777	−	0.960065i	$-0.590261\pi$
$631$	5.05556	−	2.09408i	0.201259	−	0.0833640i	0.481036	+	0.876701i	$0.340261\pi$
$632$	1.74953	+	2.61836i	0.0695926	+	0.104153i
$633$	−3.73950			−0.148632
$634$	−12.3159	−	18.4321i	−0.489129	−	0.732033i
$635$	5.99231	−	10.9398i	0.237797	−	0.434132i
$636$	9.29124	+	6.20821i	0.368422	+	0.246172i
$637$	1.97817	+	4.77574i	0.0783781	+	0.189222i
$638$	−4.30534	−	10.3940i	−0.170450	−	0.411503i
$639$	−5.08160	−	3.39542i	−0.201025	−	0.134321i
$640$	−1.07422	+	1.96114i	−0.0424622	+	0.0775207i
$641$	−4.14094	−	6.19736i	−0.163557	−	0.244781i	0.740634	−	0.671909i	$-0.234525\pi$
$641$	−4.14094	−	6.19736i	−0.163557	−	0.244781i	−0.904191	+	0.427128i	$0.859525\pi$
$642$	8.02226			0.316613
$643$	20.1484	+	30.1541i	0.794574	+	1.18916i	0.978505	+	0.206224i	$0.0661176\pi$
$643$	20.1484	+	30.1541i	0.794574	+	1.18916i	−0.183931	+	0.982939i	$0.558882\pi$
$644$	−3.51184	+	1.45465i	−0.138386	+	0.0573213i
$645$	0.725062	+	8.22449i	0.0285493	+	0.323839i
$646$	2.41946	+	7.37545i	0.0951922	+	0.290183i
$647$	19.6435	−	19.6435i	0.772267	−	0.772267i	−0.206235	−	0.978502i	$-0.566121\pi$
$647$	19.6435	−	19.6435i	0.772267	−	0.772267i	0.978502	+	0.206235i	$0.0661212\pi$
$648$	−0.923880	−	0.382683i	−0.0362934	−	0.0150332i
$649$	−52.6413	−	10.4710i	−2.06635	−	0.411023i
$650$	−2.77411	+	3.97308i	−0.108810	+	0.155837i
$651$	−9.30525	+	6.21757i	−0.364701	+	0.243686i
$652$	4.93087	+	3.29470i	0.193108	+	0.129030i
$653$	7.45548	+	37.4812i	0.291756	+	1.46675i	0.797106	+	0.603840i	$0.206363\pi$
$653$	7.45548	+	37.4812i	0.291756	+	1.46675i	−0.505350	+	0.862914i	$0.668637\pi$
$654$	−7.52866	−	3.11847i	−0.294394	−	0.121942i
$655$	−10.5715	+	33.6064i	−0.413062	+	1.31311i
$656$	5.42250	−	8.11534i	0.211713	−	0.316851i
$657$	5.48433	−	8.20787i	0.213964	−	0.320220i
$658$	0.786362	−	3.95331i	0.0306556	−	0.154116i
$659$	−9.22638	+	9.22638i	−0.359409	+	0.359409i	−0.863595	−	0.504186i	$-0.831792\pi$
$659$	−9.22638	+	9.22638i	−0.359409	+	0.359409i	0.504186	+	0.863595i	$0.331792\pi$
$660$	−8.89644	−	11.0696i	−0.346293	−	0.430885i
$661$	6.04675	+	14.5981i	0.235191	+	0.567802i	0.996773	−	0.0802665i	$-0.0255771\pi$
$661$	6.04675	+	14.5981i	0.235191	+	0.567802i	−0.761582	+	0.648068i	$0.775577\pi$
$662$	0.628902	+	0.628902i	0.0244430	+	0.0244430i
$663$	−2.46497	+	3.14501i	−0.0957314	+	0.122142i
$664$			17.2277i			0.668563i
$665$	−1.63054	+	5.18344i	−0.0632297	+	0.201005i
$666$	1.59147	−	8.00087i	0.0616683	−	0.310028i
$667$			5.21641i			0.201980i
$668$	−16.1677	−	3.21596i	−0.625549	−	0.124429i
$669$	1.59544	−	0.317353i	0.0616834	−	0.0122696i
$670$	−17.5740	−	9.62624i	−0.678944	−	0.371894i
$671$	36.0774	−	87.0986i	1.39275	−	3.36240i
$672$	−1.19256	+	0.493974i	−0.0460040	+	0.0190555i
$673$	−46.7527	+	9.29969i	−1.80218	+	0.358477i	−0.978123	−	0.208026i	$-0.933296\pi$
$673$	−46.7527	+	9.29969i	−1.80218	+	0.358477i	−0.824060	+	0.566502i	$0.808296\pi$
$674$	−3.52238	−	17.7082i	−0.135677	−	0.682094i
$675$	−4.99895	−	0.102425i	−0.192410	−	0.00394232i
$676$	−8.52824	−	8.52824i	−0.328009	−	0.328009i
$677$	−14.9271	+	9.97394i	−0.573693	+	0.383330i	−0.808309	−	0.588759i	$-0.799617\pi$
$677$	−14.9271	+	9.97394i	−0.573693	+	0.383330i	0.234616	+	0.972088i	$0.424617\pi$
$678$	1.41149	−	3.40764i	0.0542079	−	0.130870i
$679$	11.7377			0.450453
$680$	−1.68808	+	9.06369i	−0.0647347	+	0.347576i
$681$	−10.2208			−0.391662
$682$	−21.0721	+	50.8725i	−0.806891	+	1.94801i
$683$	9.33294	−	6.23607i	0.357115	−	0.238617i	−0.364051	−	0.931379i	$-0.618607\pi$
$683$	9.33294	−	6.23607i	0.357115	−	0.238617i	0.721166	+	0.692762i	$0.243607\pi$
$684$	1.33120	+	1.33120i	0.0508996	+	0.0508996i
$685$	−15.7549	−	1.71484i	−0.601964	−	0.0655206i
$686$	3.10597	+	15.6148i	0.118586	+	0.596174i
$687$	−20.3526	+	4.04839i	−0.776502	+	0.154456i
$688$	3.41130	−	1.41301i	0.130055	−	0.0538704i
$689$	4.14435	−	10.0053i	0.157887	−	0.381173i
$690$	1.84681	+	6.32047i	0.0703069	+	0.240616i
$691$	−11.5897	+	2.30534i	−0.440894	+	0.0876993i	−0.410546	−	0.911840i	$-0.634662\pi$
$691$	−11.5897	+	2.30534i	−0.440894	+	0.0876993i	−0.0303486	+	0.999539i	$0.509662\pi$
$692$	−7.33878	−	1.45977i	−0.278978	−	0.0554923i
$693$		−	8.19813i		−	0.311421i
$694$	6.27330	−	31.5380i	0.238131	−	1.19717i
$695$	−1.04088	−	1.99627i	−0.0394829	−	0.0757229i
$696$			1.77140i			0.0671448i
$697$	10.8141	−	38.7623i	0.409614	−	1.46822i
$698$	8.20347	+	8.20347i	0.310506	+	0.310506i
$699$	−2.89619	−	6.99203i	−0.109544	−	0.264463i
$700$	−4.65626	+	4.46928i	−0.175990	+	0.168923i
$701$	−30.2444	+	30.2444i	−1.14232	+	1.14232i	−0.154290	+	0.988026i	$0.549309\pi$
$701$	−30.2444	+	30.2444i	−1.14232	+	1.14232i	−0.988026	+	0.154290i	$0.950691\pi$
$702$	−0.189071	+	0.950524i	−0.00713602	+	0.0358752i
$703$	−8.53218	+	12.7693i	−0.321797	+	0.481604i
$704$	−3.52849	+	5.28076i	−0.132985	+	0.199026i
$705$	−6.66067	−	2.09523i	−0.250855	−	0.0789110i
$706$	6.60080	+	2.73414i	0.248425	+	0.102901i
$707$	−1.73632	−	8.72906i	−0.0653010	−	0.328290i
$708$	7.02665	+	4.69506i	0.264078	+	0.176451i
$709$	10.6544	−	7.11906i	0.400135	−	0.267362i	−0.339180	−	0.940722i	$-0.610149\pi$
$709$	10.6544	−	7.11906i	0.400135	−	0.267362i	0.739315	+	0.673360i	$0.235149\pi$
$710$	1.20012	+	13.6131i	0.0450397	+	0.510892i
$711$	3.08856	+	0.614353i	0.115830	+	0.0230401i
$712$	0.643668	+	0.266616i	0.0241225	+	0.00999185i
$713$	18.0533	−	18.0533i	0.676102	−	0.676102i
$714$	−4.03724	+	3.46788i	−0.151090	+	0.129782i
$715$	−8.83990	+	10.5492i	−0.330593	+	0.394519i
$716$	−10.9423	+	4.53244i	−0.408932	+	0.169385i
$717$	15.4292	+	23.0914i	0.576214	+	0.862364i
$718$	−13.6046			−0.507720
$719$	22.3812	+	33.4958i	0.834676	+	1.24918i	0.966181	+	0.257866i	$0.0830193\pi$
$719$	22.3812	+	33.4958i	0.834676	+	1.24918i	−0.131504	+	0.991316i	$0.541981\pi$
$720$	0.627144	+	2.14632i	0.0233723	+	0.0799886i
$721$	−7.58913	−	5.07089i	−0.282634	−	0.188850i
$722$	5.91469	+	14.2793i	0.220122	+	0.531421i
$723$	1.93916	+	4.68155i	0.0721181	+	0.174109i
$724$	5.20872	+	3.48036i	0.193581	+	0.129346i
$725$	3.22110	+	8.25053i	0.119629	+	0.306417i
$726$	−16.2986	−	24.3926i	−0.604898	−	0.905294i
$727$	−34.5928			−1.28298			−0.641489	−	0.767132i	$-0.721683\pi$
$727$	−34.5928			−1.28298			−0.641489	+	0.767132i	$0.721683\pi$
$728$	0.695012	+	1.04016i	0.0257589	+	0.0385509i
$729$	−0.923880	+	0.382683i	−0.0342178	+	0.0141735i
$730$	−21.9881	+	1.93845i	−0.813817	+	0.0717452i
$731$	11.5485	−	9.91984i	0.427137	−	0.366898i
$732$	−10.4962	+	10.4962i	−0.387949	+	0.387949i
$733$	−31.2591	−	12.9480i	−1.15458	−	0.478244i	−0.278515	−	0.960432i	$-0.589842\pi$
$733$	−31.2591	−	12.9480i	−1.15458	−	0.478244i	−0.876068	+	0.482188i	$0.839842\pi$
$734$	−9.89297	−	1.96783i	−0.365156	−	0.0726341i
$735$	11.8806	−	1.04738i	0.438224	−	0.0386334i
$736$	2.44851	−	1.63604i	0.0902531	−	0.0603052i
$737$	−47.3217	−	31.6194i	−1.74312	−	1.16471i
$738$	−1.90413	−	9.57269i	−0.0700919	−	0.352376i
$739$	9.58712	+	3.97111i	0.352668	+	0.146080i	0.551982	−	0.833856i	$-0.313872\pi$
$739$	9.58712	+	3.97111i	0.352668	+	0.146080i	−0.199315	+	0.979936i	$0.563872\pi$
$740$	−16.1744	+	8.43351i	−0.594581	+	0.310022i
$741$	1.01364	−	1.51703i	0.0372372	−	0.0557293i
$742$	8.01366	−	11.9933i	0.294191	−	0.440288i
$743$	7.02404	−	35.3122i	0.257687	−	1.29548i	−0.607616	−	0.794231i	$-0.707874\pi$
$743$	7.02404	−	35.3122i	0.257687	−	1.29548i	0.865303	−	0.501249i	$-0.167126\pi$
$744$	6.13059	−	6.13059i	0.224758	−	0.224758i
$745$	−46.3551	−	5.04550i	−1.69832	−	0.184853i
$746$	6.56566	+	15.8509i	0.240386	+	0.580343i
$747$	12.1818	+	12.1818i	0.445709	+	0.445709i
$748$	−7.03689	+	25.2231i	−0.257294	+	0.922249i
$749$		−	10.3553i		−	0.378373i
$750$	6.82385	+	8.85636i	0.249172	+	0.323389i
$751$	−3.32985	+	16.7403i	−0.121508	+	0.610862i	0.871261	+	0.490820i	$0.163303\pi$
$751$	−3.32985	+	16.7403i	−0.121508	+	0.610862i	−0.992769	+	0.120042i	$0.961697\pi$
$752$			3.12264i			0.113871i
$753$	10.9259	+	2.17330i	0.398162	+	0.0791994i
$754$	1.68376	−	0.334921i	0.0613189	−	0.0121971i
$755$	6.24245	−	11.3965i	0.227186	−	0.414760i
$756$	−0.493974	+	1.19256i	−0.0179657	+	0.0433730i
$757$	17.8788	−	7.40565i	0.649817	−	0.269163i	−0.0333296	−	0.999444i	$-0.510611\pi$
$757$	17.8788	−	7.40565i	0.649817	−	0.269163i	0.683146	+	0.730282i	$0.260611\pi$
$758$	10.4565	−	2.07992i	0.379795	−	0.0755460i
$759$	3.64872	+	18.3434i	0.132440	+	0.665822i
$760$	0.455505	−	4.18490i	0.0165229	−	0.151802i
$761$	0.114457	+	0.114457i	0.00414906	+	0.00414906i	0.709178	−	0.705029i	$-0.249066\pi$
$761$	0.114457	+	0.114457i	0.00414906	+	0.00414906i	−0.705029	+	0.709178i	$0.749066\pi$
$762$	−4.63818	+	3.09913i	−0.168023	+	0.112270i
$763$	−4.02538	+	9.71813i	−0.145729	+	0.351820i
$764$	15.8158			0.572194
$765$	5.21534	+	7.60264i	0.188561	+	0.274874i
$766$	−12.0178			−0.434220
$767$	3.13423	−	7.56670i	0.113170	−	0.273218i
$768$	0.831470	−	0.555570i	0.0300031	−	0.0200474i
$769$	−24.1686	−	24.1686i	−0.871542	−	0.871542i	0.121098	−	0.992641i	$-0.461358\pi$
$769$	−24.1686	−	24.1686i	−0.871542	−	0.871542i	−0.992641	+	0.121098i	$0.961358\pi$
$770$	−14.2889	+	11.4837i	−0.514936	+	0.413843i
$771$	3.78261	+	19.0164i	0.136227	+	0.684860i
$772$	−13.1253	+	2.61078i	−0.472389	+	0.0939640i
$773$	−23.6147	+	9.78154i	−0.849363	+	0.351818i	−0.764538	−	0.644578i	$-0.777033\pi$
$773$	−23.6147	+	9.78154i	−0.849363	+	0.351818i	−0.0848245	+	0.996396i	$0.527033\pi$
$774$	1.41301	−	3.41130i	0.0507895	−	0.122617i
$775$	17.4062	−	39.7018i	0.625249	−	1.42613i
$776$	−8.91855	+	1.77401i	−0.320157	+	0.0636832i
$777$	−10.3277	−	2.05430i	−0.370503	−	0.0736976i
$778$			15.6669i			0.561685i
$779$	−3.58471	+	18.0215i	−0.128435	+	0.645689i
$780$	1.92155	−	1.00192i	0.0688026	−	0.0358746i
$781$			38.8155i			1.38893i
$782$	7.48992	−	9.55625i	0.267839	−	0.341731i
$783$	1.25257	+	1.25257i	0.0447632	+	0.0447632i
$784$	−2.04115	−	4.92778i	−0.0728984	−	0.175992i
$785$	−17.5855	+	14.1331i	−0.627652	+	0.504431i
$786$	11.1407	−	11.1407i	0.397375	−	0.397375i
$787$	−7.35381	+	36.9701i	−0.262135	+	1.31784i	0.595405	+	0.803426i	$0.296992\pi$
$787$	−7.35381	+	36.9701i	−0.262135	+	1.31784i	−0.857540	+	0.514417i	$0.828008\pi$
$788$	7.07715	−	10.5917i	0.252113	−	0.377314i
$789$	13.4026	−	20.0584i	0.477145	−	0.714098i
$790$	−3.25557	−	6.24376i	−0.115828	−	0.222143i
$791$	−4.39864	−	1.82197i	−0.156397	−	0.0647820i
$792$	1.23904	+	6.22909i	0.0440274	+	0.221341i
$793$	11.9614	+	7.99233i	0.424760	+	0.283816i
$794$	−11.0113	+	7.35749i	−0.390775	+	0.261107i
$795$	−19.1518	−	16.0485i	−0.679243	−	0.569183i
$796$	−0.515682	−	0.102576i	−0.0182779	−	0.00363569i
$797$	−28.4456	−	11.7825i	−1.00759	−	0.417359i	−0.183018	−	0.983110i	$-0.558587\pi$
$797$	−28.4456	−	11.7825i	−1.00759	−	0.417359i	−0.824576	+	0.565751i	$0.808587\pi$
$798$	1.71833	−	1.71833i	0.0608283	−	0.0608283i
$799$	4.01312	+	12.2336i	0.141974	+	0.432792i
$800$	2.86243	−	4.09957i	0.101202	−	0.144942i
$801$	0.643668	−	0.266616i	0.0227429	−	0.00942041i
$802$	11.1371	+	16.6679i	0.393265	+	0.588563i
$803$	−62.6952			−2.21247
$804$	4.97855	+	7.45092i	0.175580	+	0.262774i
$805$	8.15857	−	2.38389i	0.287552	−	0.0840212i
$806$	−6.98638	−	4.66815i	−0.246085	−	0.164429i
$807$	−1.88183	−	4.54314i	−0.0662436	−	0.159926i
$808$	2.63857	+	6.37007i	0.0928246	+	0.224098i
$809$	−15.8678	−	10.6025i	−0.557882	−	0.372765i	0.244433	−	0.969666i	$-0.421398\pi$
$809$	−15.8678	−	10.6025i	−0.557882	−	0.372765i	−0.802315	+	0.596901i	$0.796398\pi$
$810$	1.96114	+	1.07422i	0.0689073	+	0.0377442i
$811$	−23.1205	−	34.6023i	−0.811872	−	1.21505i	−0.973610	−	0.228218i	$-0.926710\pi$
$811$	−23.1205	−	34.6023i	−0.811872	−	1.21505i	0.161738	−	0.986834i	$-0.448290\pi$
$812$	2.28656			0.0802424
$813$	1.32082	+	1.97675i	0.0463233	+	0.0693277i
$814$	−47.8662	+	19.8268i	−1.67771	+	0.694930i
$815$	−10.1639	−	8.51697i	−0.356024	−	0.298336i
$816$	2.54344	−	3.24513i	0.0890383	−	0.113602i
$817$	−4.91527	+	4.91527i	−0.171964	+	0.171964i
$818$	33.0125	+	13.6742i	1.15426	+	0.478109i
$819$	1.22695	+	0.244056i	0.0428732	+	0.00852800i
$820$	−14.0174	+	16.7279i	−0.489510	+	0.584164i
$821$	−11.6571	+	7.78902i	−0.406836	+	0.271839i	−0.742105	−	0.670283i	$-0.766173\pi$
$821$	−11.6571	+	7.78902i	−0.406836	+	0.271839i	0.335270	+	0.942122i	$0.391173\pi$
$822$	5.89297	+	3.93756i	0.205541	+	0.137338i
$823$	5.32707	+	26.7810i	0.185690	+	0.933526i	0.955441	+	0.295182i	$0.0953803\pi$
$823$	5.32707	+	26.7810i	0.185690	+	0.933526i	−0.769751	+	0.638344i	$0.779620\pi$
$824$	6.53275	+	2.70595i	0.227579	+	0.0942664i
$825$	17.0979	+	26.7597i	0.595272	+	0.931653i
$826$	6.06046	−	9.07012i	0.210870	−	0.315590i
$827$	18.6452	−	27.9045i	0.648357	−	0.970335i	−0.351065	−	0.936351i	$-0.614180\pi$
$827$	18.6452	−	27.9045i	0.648357	−	0.970335i	0.999422	−	0.0339842i	$-0.0108196\pi$
$828$	0.574501	−	2.88821i	0.0199653	−	0.100372i
$829$	−32.8754	+	32.8754i	−1.14181	+	1.14181i	−0.153689	+	0.988119i	$0.549115\pi$
$829$	−32.8754	+	32.8754i	−1.14181	+	1.14181i	−0.988119	+	0.153689i	$0.950885\pi$
$830$	4.16833	−	38.2961i	0.144685	−	1.32928i
$831$	0.0124299	+	0.0300084i	0.000431187	+	0.00104098i
$832$	−0.685289	−	0.685289i	−0.0237581	−	0.0237581i
$833$	−14.3296	−	16.6823i	−0.496493	−	0.578008i
$834$			1.00683i			0.0348637i
$835$	35.1618	+	11.0608i	1.21682	+	0.382773i
$836$	2.33262	−	11.7269i	0.0806753	−	0.405582i
$837$		−	8.66996i		−	0.299678i
$838$	18.6060	+	3.70095i	0.642732	+	0.127847i
$839$	53.2083	−	10.5838i	1.83696	−	0.365393i	0.850052	−	0.526699i	$-0.176571\pi$
$839$	53.2083	−	10.5838i	1.83696	−	0.365393i	0.986904	+	0.161306i	$0.0515706\pi$
$840$	2.77051	−	0.809529i	0.0955915	−	0.0279314i
$841$	−9.89701	+	23.8935i	−0.341276	+	0.823914i
$842$	−13.2908	+	5.50524i	−0.458032	+	0.189723i
$843$	20.5370	−	4.08507i	0.707333	−	0.140697i
$844$	−0.729540	−	3.66764i	−0.0251118	−	0.126246i
$845$	16.8943	+	21.0212i	0.581182	+	0.723152i
$846$	2.20804	+	2.20804i	0.0759140	+	0.0759140i
$847$	−31.4864	+	21.0385i	−1.08188	+	0.722892i
$848$	−4.27629	+	10.3239i	−0.146848	+	0.354523i
$849$	−0.319623			−0.0109694
$850$	5.94549	−	19.7396i	0.203929	−	0.677062i
$851$	24.0225			0.823481
$852$	2.33880	−	5.64637i	0.0801261	−	0.193442i
$853$	−0.0210551	+	0.0140686i	−0.000720912	+	0.000481698i	−0.555931	−	0.831229i	$-0.687638\pi$
$853$	−0.0210551	+	0.0140686i	−0.000720912	+	0.000481698i	0.555210	+	0.831710i	$0.312638\pi$
$854$	13.5486	+	13.5486i	0.463624	+	0.463624i
$855$	−2.63708	−	3.28126i	−0.0901863	−	0.112217i
$856$	1.56507	+	7.86811i	0.0534928	+	0.268927i
$857$	28.9993	−	5.76832i	0.990597	−	0.197042i	0.326912	−	0.945055i	$-0.393992\pi$
$857$	28.9993	−	5.76832i	0.990597	−	0.197042i	0.663684	+	0.748013i	$0.268992\pi$
$858$	5.68663	−	2.35548i	0.194138	−	0.0804147i
$859$	19.3336	−	46.6754i	0.659653	−	1.59254i	−0.138686	−	0.990336i	$-0.544288\pi$
$859$	19.3336	−	46.6754i	0.659653	−	1.59254i	0.798340	−	0.602208i	$-0.205712\pi$
$860$	−7.92500	+	2.31565i	−0.270240	+	0.0789629i
$861$	−12.3566	+	2.45788i	−0.421112	+	0.0837643i
$862$	16.7853	+	3.33880i	0.571709	+	0.113720i
$863$			26.2240i			0.892675i	0.894865	+	0.446338i	$0.147272\pi$
$863$			26.2240i			0.892675i	−0.894865	+	0.446338i	$0.852728\pi$
$864$	0.195090	−	0.980785i	0.00663711	−	0.0333670i
$865$	15.9605	+	5.02064i	0.542672	+	0.170707i
$866$			12.6442i			0.429667i
$867$	5.79390	−	15.9822i	0.196771	−	0.542784i
$868$	−7.91346	−	7.91346i	−0.268600	−	0.268600i
$869$	−7.65372	−	18.4777i	−0.259635	−	0.626814i
$870$	0.428600	−	3.93772i	0.0145309	−	0.133501i
$871$	6.14098	−	6.14098i	0.208079	−	0.208079i
$872$	1.58978	−	7.99239i	0.0538369	−	0.270656i
$873$	−5.05195	+	7.56078i	−0.170983	+	0.255894i
$874$	−3.08001	+	4.60955i	−0.104183	+	0.155920i
$875$	11.4319	−	8.80833i	0.386470	−	0.297776i
$876$	9.12010	+	3.77767i	0.308140	+	0.127636i
$877$	−1.91570	−	9.63086i	−0.0646885	−	0.325211i	0.934868	−	0.354996i	$-0.115518\pi$
$877$	−1.91570	−	9.63086i	−0.0646885	−	0.325211i	−0.999556	+	0.0297849i	$0.990518\pi$
$878$	−11.2342	−	7.50645i	−0.379136	−	0.253330i
$879$	24.4679	−	16.3489i	0.825281	−	0.551435i
$880$	9.12133	−	10.8851i	0.307480	−	0.366936i
$881$	−31.2221	−	6.21047i	−1.05190	−	0.209236i	−0.361283	−	0.932456i	$-0.617661\pi$
$881$	−31.2221	−	6.21047i	−1.05190	−	0.209236i	−0.690618	+	0.723220i	$0.742661\pi$
$882$	−4.92778	−	2.04115i	−0.165927	−	0.0687292i
$883$	−3.56802	+	3.56802i	−0.120074	+	0.120074i	−0.764590	−	0.644517i	$-0.777059\pi$
$883$	−3.56802	+	3.56802i	−0.120074	+	0.120074i	0.644517	+	0.764590i	$0.277059\pi$
$884$	−3.56547	−	1.80404i	−0.119920	−	0.0606765i
$885$	−14.4838	−	12.1370i	−0.486869	−	0.407980i
$886$	−5.28535	+	2.18926i	−0.177565	+	0.0735497i
$887$	29.9479	+	44.8202i	1.00555	+	1.50491i	0.856542	+	0.516078i	$0.172608\pi$
$887$	29.9479	+	44.8202i	1.00555	+	1.50491i	0.149009	+	0.988836i	$0.452392\pi$
$888$	8.15762			0.273752
$889$	4.00041	+	5.98704i	0.134170	+	0.200799i
$890$	−1.36632	−	0.748410i	−0.0457993	−	0.0250867i
$891$	5.28076	+	3.52849i	0.176912	+	0.118209i
$892$	0.622511	+	1.50288i	0.0208432	+	0.0503200i
$893$	−2.24967	−	5.43119i	−0.0752825	−	0.181748i
$894$	17.3387	+	11.5853i	0.579892	+	0.387472i
$895$	25.4207	−	7.42779i	0.849719	−	0.248284i
$896$	−0.717139	−	1.07327i	−0.0239579	−	0.0358556i
$897$	−2.85393			−0.0952900
$898$	−17.6959	−	26.4838i	−0.590520	−	0.883775i
$899$	−14.1889	+	5.87725i	−0.473227	+	0.196017i
$900$	−0.874790	−	4.92288i	−0.0291597	−	0.164096i
$901$	−3.48528	+	45.9416i	−0.116112	+	1.53054i
$902$	−43.8324	+	43.8324i	−1.45946	+	1.45946i
$903$	−4.40337	−	1.82393i	−0.146535	−	0.0606967i
$904$	3.61753	+	0.719571i	0.120317	+	0.0239326i
$905$	−10.7366	−	8.99690i	−0.356896	−	0.299067i
$906$	−4.83180	+	3.22850i	−0.160526	+	0.107260i
$907$	−27.4379	−	18.3334i	−0.911059	−	0.608750i	0.00924346	−	0.999957i	$-0.497058\pi$
$907$	−27.4379	−	18.3334i	−0.911059	−	0.608750i	−0.920303	+	0.391207i	$0.872058\pi$
$908$	−1.99398	−	10.0244i	−0.0661725	−	0.332672i
$909$	6.37007	+	2.63857i	0.211282	+	0.0875159i
$910$	−1.29330	−	2.48037i	−0.0428724	−	0.0822236i
$911$	−2.36178	+	3.53465i	−0.0782493	+	0.117108i	−0.868530	−	0.495637i	$-0.834935\pi$
$911$	−2.36178	+	3.53465i	−0.0782493	+	0.117108i	0.790281	+	0.612745i	$0.209935\pi$
$912$	−1.04592	+	1.56532i	−0.0346337	+	0.0518330i
$913$	21.3458	−	107.313i	0.706443	−	3.55153i
$914$	5.58847	−	5.58847i	0.184850	−	0.184850i
$915$	25.8719	−	20.7927i	0.855299	−	0.687386i
$916$	−7.94120	−	19.1718i	−0.262385	−	0.633453i
$917$	−14.3806	−	14.3806i	−0.474888	−	0.474888i
$918$	−0.496170	−	4.09314i	−0.0163760	−	0.135094i
$919$		−	52.2065i		−	1.72213i	−0.508491	−	0.861067i	$-0.669797\pi$
$919$		−	52.2065i		−	1.72213i	0.508491	−	0.861067i	$-0.330203\pi$
$920$	−5.83873	+	3.04439i	−0.192497	+	0.100370i
$921$	4.61478	−	23.2001i	0.152062	−	0.764469i
$922$			12.1695i			0.400782i
$923$	−5.80921	−	1.15552i	−0.191213	−	0.0380345i
$924$	8.04061	−	1.59938i	0.264517	−	0.0526156i
$925$	37.9951	−	14.8337i	1.24927	−	0.487730i
$926$	−7.25032	+	17.5038i	−0.238260	+	0.575211i
$927$	6.53275	−	2.70595i	0.214564	−	0.0888752i
$928$	−1.73737	+	0.345583i	−0.0570318	+	0.0113443i
$929$	8.97586	+	45.1247i	0.294489	+	1.48049i	0.790653	+	0.612265i	$0.209741\pi$
$929$	8.97586	+	45.1247i	0.294489	+	1.48049i	−0.496164	+	0.868229i	$0.665259\pi$
$930$	−15.1112	+	12.1446i	−0.495517	+	0.398237i
$931$	7.10033	+	7.10033i	0.232704	+	0.232704i
$932$	6.29266	−	4.20462i	0.206123	−	0.137727i
$933$	−5.67490	+	13.7004i	−0.185788	+	0.448531i
$934$	−36.5722			−1.19668
$935$	21.7455	−	54.3669i	0.711152	−	1.77799i
$936$	−0.969145			−0.0316775
$937$	3.92262	−	9.47003i	0.128146	−	0.309372i	−0.846765	−	0.531968i	$-0.821453\pi$
$937$	3.92262	−	9.47003i	0.128146	−	0.309372i	0.974911	+	0.222595i	$0.0714528\pi$
$938$	9.61778	−	6.42639i	0.314032	−	0.209829i
$939$	14.6198	+	14.6198i	0.477098	+	0.477098i
$940$	0.755540	−	6.94144i	0.0246430	−	0.226405i
$941$	1.93627	+	9.73431i	0.0631207	+	0.317329i	0.999427	−	0.0338559i	$-0.0107787\pi$
$941$	1.93627	+	9.73431i	0.0631207	+	0.317329i	−0.936306	+	0.351185i	$0.885779\pi$
$942$	9.89566	−	1.96837i	0.322418	−	0.0641329i
$943$	26.5540	−	10.9990i	0.864718	−	0.358178i
$944$	−3.23401	+	7.80760i	−0.105258	+	0.254116i
$945$	1.38662	−	2.53147i	0.0451068	−	0.0823486i
$946$	−23.0001	+	4.57500i	−0.747797	+	0.148746i
$947$	17.2196	+	3.42519i	0.559562	+	0.111304i	0.466765	−	0.884381i	$-0.345419\pi$
$947$	17.2196	+	3.42519i	0.559562	+	0.111304i	0.0927970	+	0.995685i	$0.470419\pi$
$948$			3.14907i			0.102277i
$949$	1.86642	−	9.38312i	0.0605865	−	0.304589i
$950$	−2.02512	+	9.19257i	−0.0657035	+	0.298246i
$951$		−	22.1681i		−	0.718851i
$952$	−4.18887	−	3.28312i	−0.135762	−	0.106407i
$953$	28.5046	+	28.5046i	0.923355	+	0.923355i	0.997265	−	0.0739096i	$-0.0235476\pi$
$953$	28.5046	+	28.5046i	0.923355	+	0.923355i	−0.0739096	+	0.997265i	$0.523548\pi$
$954$	4.27629	+	10.3239i	0.138450	+	0.334248i
$955$	−35.1575	−	3.82670i	−1.13767	−	0.123829i
$956$	−19.6376	+	19.6376i	−0.635126	+	0.635126i
$957$	2.19484	−	11.0342i	0.0709492	−	0.356686i
$958$	−15.2213	+	22.7803i	−0.491778	+	0.735997i
$959$	5.08267	−	7.60675i	0.164128	−	0.245635i
$960$	−1.98273	+	1.03382i	−0.0639923	+	0.0333664i
$961$	40.8061	+	16.9024i	1.31633	+	0.545240i
$962$	−1.54237	−	7.75401i	−0.0497280	−	0.249999i
$963$	6.67027	+	4.45693i	0.214946	+	0.143623i
$964$	−4.21328	+	2.81522i	−0.135701	+	0.0906723i
$965$	29.8084	−	2.62788i	0.959566	−	0.0845943i
$966$	−3.72815	−	0.741575i	−0.119951	−	0.0238598i
$967$	−4.49794	−	1.86311i	−0.144644	−	0.0599136i	0.309187	−	0.951001i	$-0.399943\pi$
$967$	−4.49794	−	1.86311i	−0.144644	−	0.0599136i	−0.453831	+	0.891088i	$0.649943\pi$
$968$	20.7442	−	20.7442i	0.666744	−	0.666744i
$969$	−2.08588	+	7.47664i	−0.0670080	+	0.240184i
$970$	20.2546	−	1.78563i	0.650336	−	0.0573330i
$971$	−26.9513	+	11.1636i	−0.864910	+	0.358257i	−0.770626	−	0.637288i	$-0.780056\pi$
$971$	−26.9513	+	11.1636i	−0.864910	+	0.358257i	−0.0942840	+	0.995545i	$0.530056\pi$
$972$	−0.555570	−	0.831470i	−0.0178199	−	0.0266694i
$973$	1.29963			0.0416643
$974$	5.09357	+	7.62306i	0.163208	+	0.244259i
$975$	−4.51392	+	1.76228i	−0.144561	+	0.0564382i
$976$	−12.3422	−	8.24678i	−0.395063	−	0.263973i
$977$	3.20893	+	7.74704i	0.102663	+	0.247850i	0.966862	−	0.255300i	$-0.0821743\pi$
$977$	3.20893	+	7.74704i	0.102663	+	0.247850i	−0.864199	+	0.503150i	$0.832174\pi$
$978$	2.26943	+	5.47889i	0.0725684	+	0.175196i
$979$	−3.67911	−	2.45830i	−0.117585	−	0.0785678i
$980$	3.34506	+	11.4480i	0.106854	+	0.365694i
$981$	−4.52732	−	6.77562i	−0.144546	−	0.216329i
$982$	0.504807			0.0161090
$983$	34.3157	+	51.3571i	1.09450	+	1.63804i	0.690604	+	0.723233i	$0.257345\pi$
$983$	34.3157	+	51.3571i	1.09450	+	1.63804i	0.403897	+	0.914804i	$0.367655\pi$
$984$	9.01728	−	3.73508i	0.287460	−	0.119070i
$985$	−18.2948	+	21.8323i	−0.582920	+	0.695636i
$986$	−6.36234	+	3.58670i	−0.202618	+	0.114224i
$987$	2.85018	−	2.85018i	0.0907222	−	0.0907222i
$988$	1.68563	+	0.698210i	0.0536270	+	0.0222130i
$989$	10.6643	+	2.12127i	0.339106	+	0.0674524i
$990$	−1.24716	−	14.1467i	−0.0396372	−	0.449611i
$991$	−34.5776	+	23.1040i	−1.09839	+	0.733923i	−0.966327	−	0.257318i	$-0.917161\pi$
$991$	−34.5776	+	23.1040i	−1.09839	+	0.733923i	−0.132067	+	0.991241i	$0.542161\pi$
$992$	7.20881	+	4.81677i	0.228880	+	0.152933i
$993$	0.173514	+	0.872312i	0.00550629	+	0.0276820i
$994$	−7.28844	−	3.01897i	−0.231175	−	0.0957559i
$995$	1.12151	+	0.352791i	0.0355543	+	0.0111842i
$996$	−9.57118	+	14.3243i	−0.303275	+	0.453882i
$997$	21.4241	−	32.0634i	0.678508	−	1.01546i	−0.319193	−	0.947690i	$-0.603412\pi$
$997$	21.4241	−	32.0634i	0.678508	−	1.01546i	0.997701	−	0.0677692i	$-0.0215882\pi$
$998$	2.24993	−	11.3111i	0.0712201	−	0.358048i
$999$	5.76831	−	5.76831i	0.182501	−	0.182501i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	510.2.bd.a.133.3	✓	64
5.2	odd	4		510.2.bi.a.337.6	yes	64
17.11	odd	16		510.2.bi.a.283.6	yes	64
85.62	even	16	inner	510.2.bd.a.487.3	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.bd.a.133.3	✓	64	1.1	even	1	trivial
510.2.bd.a.487.3	yes	64	85.62	even	16	inner
510.2.bi.a.283.6	yes	64	17.11	odd	16
510.2.bi.a.337.6	yes	64	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.bd (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.382683 + 0.923880i) q^{2} +(-0.831470 + 0.555570i) q^{3} +(-0.707107 - 0.707107i) q^{4} +(1.40077 + 1.74294i) q^{5} +(-0.195090 - 0.980785i) q^{6} +(-1.26601 + 0.251826i) q^{7} +(0.923880 - 0.382683i) q^{8} +(0.382683 - 0.923880i) q^{9} +(-2.14632 + 0.627144i) q^{10} +(-6.22909 + 1.23904i) q^{11} +(0.980785 + 0.195090i) q^{12} -0.969145i q^{13} +(0.251826 - 1.26601i) q^{14} +(-2.13302 - 0.670980i) q^{15} +1.00000i q^{16} +(1.28517 + 3.91770i) q^{17} +(0.707107 + 0.707107i) q^{18} +(-0.720439 - 1.73929i) q^{19} +(0.241955 - 2.22294i) q^{20} +(0.912745 - 0.912745i) q^{21} +(1.23904 - 6.22909i) q^{22} +(-1.63604 + 2.44851i) q^{23} +(-0.555570 + 0.831470i) q^{24} +(-1.07570 + 4.88292i) q^{25} +(0.895374 + 0.370876i) q^{26} +(0.195090 + 0.980785i) q^{27} +(1.07327 + 0.717139i) q^{28} +(1.47287 - 0.984138i) q^{29} +(1.43618 - 1.71388i) q^{30} +(-8.50337 - 1.69143i) q^{31} +(-0.923880 - 0.382683i) q^{32} +(4.49092 - 4.49092i) q^{33} +(-4.11129 - 0.311896i) q^{34} +(-2.21231 - 1.85384i) q^{35} +(-0.923880 + 0.382683i) q^{36} +(-4.53213 - 6.78281i) q^{37} +1.88260 q^{38} +(0.538428 + 0.805815i) q^{39} +(1.96114 + 1.07422i) q^{40} +(-8.11534 - 5.42250i) q^{41} +(0.493974 + 1.19256i) q^{42} +(-1.41301 - 3.41130i) q^{43} +(5.28076 + 3.52849i) q^{44} +(2.14632 - 0.627144i) q^{45} +(-1.63604 - 2.44851i) q^{46} +3.12264 q^{47} +(-0.555570 - 0.831470i) q^{48} +(-4.92778 + 2.04115i) q^{49} +(-4.09957 - 2.86243i) q^{50} +(-3.24513 - 2.54344i) q^{51} +(-0.685289 + 0.685289i) q^{52} +(10.3239 + 4.27629i) q^{53} +(-0.980785 - 0.195090i) q^{54} +(-10.8851 - 9.12133i) q^{55} +(-1.07327 + 0.717139i) q^{56} +(1.56532 + 1.04592i) q^{57} +(0.345583 + 1.73737i) q^{58} +(7.80760 + 3.23401i) q^{59} +(1.03382 + 1.98273i) q^{60} +(-8.24678 + 12.3422i) q^{61} +(4.81677 - 7.20881i) q^{62} +(-0.251826 + 1.26601i) q^{63} +(0.707107 - 0.707107i) q^{64} +(1.68917 - 1.35755i) q^{65} +(2.43047 + 5.86767i) q^{66} +(6.33649 + 6.33649i) q^{67} +(1.86148 - 3.67898i) q^{68} -2.94479i q^{69} +(2.55934 - 1.33447i) q^{70} +(1.19231 - 5.99416i) q^{71} -1.00000i q^{72} +(9.68185 + 1.92584i) q^{73} +(8.00087 - 1.59147i) q^{74} +(-1.81839 - 4.65762i) q^{75} +(-0.720439 + 1.73929i) q^{76} +(7.57409 - 3.13729i) q^{77} +(-0.950524 + 0.189071i) q^{78} +(0.614353 + 3.08856i) q^{79} +(-1.74294 + 1.40077i) q^{80} +(-0.707107 - 0.707107i) q^{81} +(8.11534 - 5.42250i) q^{82} +(-6.59275 + 15.9163i) q^{83} -1.29082 q^{84} +(-5.02810 + 7.72776i) q^{85} +3.69237 q^{86} +(-0.677886 + 1.63656i) q^{87} +(-5.28076 + 3.52849i) q^{88} +(0.492642 + 0.492642i) q^{89} +(-0.241955 + 2.22294i) q^{90} +(0.244056 + 1.22695i) q^{91} +(2.88821 - 0.574501i) q^{92} +(8.01000 - 3.31785i) q^{93} +(-1.19498 + 2.88495i) q^{94} +(2.02232 - 3.69203i) q^{95} +(0.980785 - 0.195090i) q^{96} +(-8.91855 - 1.77401i) q^{97} -5.33379i q^{98} +(-1.23904 + 6.22909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 16 q^{15} + 16 q^{20} + 16 q^{25} - 16 q^{28} + 32 q^{29} + 16 q^{31} + 16 q^{33} + 32 q^{35} - 16 q^{37} - 16 q^{40} + 48 q^{41} + 16 q^{44} + 32 q^{47} - 64 q^{49} - 16 q^{50} + 32 q^{51} + 16 q^{52}+ \cdots - 80 q^{97}+O(q^{100}) \) 64 * q - 16 * q^15 + 16 * q^20 + 16 * q^25 - 16 * q^28 + 32 * q^29 + 16 * q^31 + 16 * q^33 + 32 * q^35 - 16 * q^37 - 16 * q^40 + 48 * q^41 + 16 * q^44 + 32 * q^47 - 64 * q^49 - 16 * q^50 + 32 * q^51 + 16 * q^52 + 80 * q^53 - 16 * q^55 + 16 * q^56 - 32 * q^57 + 64 * q^59 - 48 * q^61 + 32 * q^65 + 16 * q^67 - 48 * q^68 - 64 * q^71 + 16 * q^73 + 48 * q^74 - 32 * q^75 - 80 * q^77 - 32 * q^78 - 64 * q^79 - 16 * q^80 - 48 * q^82 - 32 * q^83 - 16 * q^85 - 64 * q^86 - 32 * q^87 - 16 * q^88 - 32 * q^89 - 16 * q^90 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 112 * q^95 - 80 * q^97

Introduction

L-functions

Modular forms

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Database

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