LMFDB - Embedded newform 510.2.bi.a.283.6

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [510,2,Mod(37,510)] 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, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("510.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 510 = 2 \cdot 3 \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	510.bi (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			283.6
Character	$\chi$	$=$	510.283
Dual form			510.2.bi.a.337.6

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.923880 + 0.382683i) q^{2} +(0.555570 - 0.831470i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-1.07422 + 1.96114i) q^{5} +(-0.195090 + 0.980785i) q^{6} +(-0.251826 + 1.26601i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(-0.382683 - 0.923880i) q^{9} +(0.241955 - 2.22294i) q^{10} +(-6.22909 - 1.23904i) q^{11} +(-0.195090 - 0.980785i) q^{12} -0.969145 q^{13} +(-0.251826 - 1.26601i) q^{14} +(1.03382 + 1.98273i) q^{15} -1.00000i q^{16} +(-3.91770 - 1.28517i) q^{17} +(0.707107 + 0.707107i) q^{18} +(0.720439 - 1.73929i) q^{19} +(0.627144 + 2.14632i) q^{20} +(0.912745 + 0.912745i) q^{21} +(6.22909 - 1.23904i) q^{22} +(2.44851 - 1.63604i) q^{23} +(0.555570 + 0.831470i) q^{24} +(-2.69211 - 4.21338i) q^{25} +(0.895374 - 0.370876i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(0.717139 + 1.07327i) q^{28} +(-1.47287 - 0.984138i) q^{29} +(-1.71388 - 1.43618i) q^{30} +(-8.50337 + 1.69143i) q^{31} +(0.382683 + 0.923880i) 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} +(6.78281 + 4.53213i) q^{37} +1.88260i q^{38} +(-0.538428 + 0.805815i) q^{39} +(-1.40077 - 1.74294i) q^{40} +(-8.11534 + 5.42250i) q^{41} +(-1.19256 - 0.493974i) q^{42} +(-3.41130 - 1.41301i) q^{43} +(-5.28076 + 3.52849i) q^{44} +(2.22294 + 0.241955i) q^{45} +(-1.63604 + 2.44851i) q^{46} -3.12264i q^{47} +(-0.831470 - 0.555570i) 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} +(4.27629 + 10.3239i) q^{53} +(0.980785 - 0.195090i) q^{54} +(9.12133 - 10.8851i) q^{55} +(-1.07327 - 0.717139i) q^{56} +(-1.04592 - 1.56532i) q^{57} +(1.73737 + 0.345583i) q^{58} +(-7.80760 + 3.23401i) q^{59} +(2.13302 + 0.670980i) q^{60} +(-8.24678 - 12.3422i) q^{61} +(7.20881 - 4.81677i) q^{62} +(1.26601 - 0.251826i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(1.04107 - 1.90063i) q^{65} +(2.43047 - 5.86767i) q^{66} +(-6.33649 - 6.33649i) q^{67} +(-3.67898 + 1.86148i) q^{68} -2.94479i q^{69} +(2.75334 + 0.866112i) q^{70} +(1.19231 + 5.99416i) q^{71} +1.00000 q^{72} +(1.92584 + 9.68185i) q^{73} +(-8.00087 - 1.59147i) q^{74} +(-4.99895 - 0.102425i) q^{75} +(-0.720439 - 1.73929i) q^{76} +(3.13729 - 7.57409i) q^{77} +(0.189071 - 0.950524i) q^{78} +(-0.614353 + 3.08856i) q^{79} +(1.96114 + 1.07422i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(5.42250 - 8.11534i) q^{82} +(15.9163 - 6.59275i) q^{83} +1.29082 q^{84} +(6.72885 - 6.30258i) q^{85} +3.69237 q^{86} +(-1.63656 + 0.677886i) q^{87} +(3.52849 - 5.28076i) q^{88} +(-0.492642 + 0.492642i) q^{89} +(-2.14632 + 0.627144i) q^{90} +(0.244056 - 1.22695i) q^{91} +(0.574501 - 2.88821i) q^{92} +(-3.31785 + 8.01000i) q^{93} +(1.19498 + 2.88495i) q^{94} +(2.63708 + 3.28126i) q^{95} +(0.980785 + 0.195090i) q^{96} +(1.77401 + 8.91855i) q^{97} -5.33379 q^{98} +(1.23904 + 6.22909i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q + 16 q^{10} - 16 q^{25} + 16 q^{28} - 32 q^{29} - 16 q^{30} + 16 q^{31} - 16 q^{33} + 32 q^{35} - 16 q^{37} + 48 q^{41} - 32 q^{43} - 16 q^{44} + 64 q^{49} + 16 q^{50} + 32 q^{51} + 16 q^{52} - 32 q^{53}+ \cdots - 48 q^{97}+O(q^{100}) $ 64 * q + 16 * q^10 - 16 * q^25 + 16 * q^28 - 32 * q^29 - 16 * q^30 + 16 * q^31 - 16 * q^33 + 32 * q^35 - 16 * q^37 + 48 * q^41 - 32 * q^43 - 16 * q^44 + 64 * q^49 + 16 * q^50 + 32 * q^51 + 16 * q^52 - 32 * q^53 + 16 * q^55 + 16 * q^56 + 32 * q^57 - 32 * q^58 - 64 * q^59 + 16 * q^60 - 48 * q^61 - 32 * q^62 + 32 * q^65 - 16 * q^67 - 16 * q^70 - 64 * q^71 + 64 * q^72 - 48 * q^74 - 64 * q^75 - 48 * q^77 - 32 * q^78 + 64 * q^79 - 16 * q^80 + 32 * q^82 - 32 * q^83 - 64 * q^85 - 64 * q^86 - 48 * q^87 - 16 * q^88 + 32 * q^89 - 48 * q^93 + 16 * q^94 + 96 * q^95 - 48 * q^97

Character values

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

$n$	$241$	$307$	$341$
$\chi(n)$	$e\left(\frac{7}{16}\right)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	−0.923880	+	0.382683i	−0.653281	+	0.270598i
$2$	−0.923880	+	0.382683i	−0.653281	+	0.270598i
$3$	0.555570	−	0.831470i	0.320759	−	0.480049i
$3$	0.555570	−	0.831470i	0.320759	−	0.480049i
$4$	0.707107	−	0.707107i	0.353553	−	0.353553i
$5$	−1.07422	+	1.96114i	−0.480406	+	0.877046i
$5$	−1.07422	+	1.96114i	−0.480406	+	0.877046i
$6$	−0.195090	+	0.980785i	−0.0796453	+	0.400404i
$7$	−0.251826	+	1.26601i	−0.0951812	+	0.478508i	0.903565	+	0.428451i	$0.140940\pi$
$7$	−0.251826	+	1.26601i	−0.0951812	+	0.478508i	−0.998746	+	0.0500575i	$0.984060\pi$
$8$	−0.382683	+	0.923880i	−0.135299	+	0.326641i
$9$	−0.382683	−	0.923880i	−0.127561	−	0.307960i
$10$	0.241955	−	2.22294i	0.0765130	−	0.702955i
$11$	−6.22909	−	1.23904i	−1.87814	−	0.373585i	−0.882778	−	0.469790i	$-0.844330\pi$
$11$	−6.22909	−	1.23904i	−1.87814	−	0.373585i	−0.995362	+	0.0962045i	$0.969330\pi$
$12$	−0.195090	−	0.980785i	−0.0563177	−	0.283128i
$13$	−0.969145			−0.268793			−0.134396	−	0.990928i	$-0.542910\pi$
$13$	−0.969145			−0.268793			−0.134396	+	0.990928i	$0.542910\pi$
$14$	−0.251826	−	1.26601i	−0.0673033	−	0.338357i
$15$	1.03382	+	1.98273i	0.266931	+	0.511939i
$16$		−	1.00000i		−	0.250000i
$17$	−3.91770	−	1.28517i	−0.950181	−	0.311699i
$17$	−3.91770	−	1.28517i	−0.950181	−	0.311699i
$18$	0.707107	+	0.707107i	0.166667	+	0.166667i
$19$	0.720439	−	1.73929i	0.165280	−	0.399021i	−0.819440	−	0.573165i	$-0.805716\pi$
$19$	0.720439	−	1.73929i	0.165280	−	0.399021i	0.984720	+	0.174143i	$0.0557156\pi$
$20$	0.627144	+	2.14632i	0.140234	+	0.479932i
$21$	0.912745	+	0.912745i	0.199177	+	0.199177i
$22$	6.22909	−	1.23904i	1.32805	−	0.264165i
$23$	2.44851	−	1.63604i	0.510549	−	0.341138i	−0.273464	−	0.961882i	$-0.588170\pi$
$23$	2.44851	−	1.63604i	0.510549	−	0.341138i	0.784013	+	0.620744i	$0.213170\pi$
$24$	0.555570	+	0.831470i	0.113405	+	0.169723i
$25$	−2.69211	−	4.21338i	−0.538421	−	0.842676i
$26$	0.895374	−	0.370876i	0.175597	−	0.0727347i
$27$	−0.980785	−	0.195090i	−0.188752	−	0.0375451i
$28$	0.717139	+	1.07327i	0.135527	+	0.202830i
$29$	−1.47287	−	0.984138i	−0.273505	−	0.182750i	0.411252	−	0.911522i	$-0.365092\pi$
$29$	−1.47287	−	0.984138i	−0.273505	−	0.182750i	−0.684757	+	0.728772i	$0.740092\pi$
$30$	−1.71388	−	1.43618i	−0.312911	−	0.262209i
$31$	−8.50337	+	1.69143i	−1.52725	+	0.303789i	−0.886052	−	0.463586i	$-0.846562\pi$
$31$	−8.50337	+	1.69143i	−1.52725	+	0.303789i	−0.641198	+	0.767375i	$0.721562\pi$
$32$	0.382683	+	0.923880i	0.0676495	+	0.163320i
$33$	−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
$37$	6.78281	+	4.53213i	1.11509	+	0.745078i	0.969700	−	0.244297i	$-0.0785572\pi$
$37$	6.78281	+	4.53213i	1.11509	+	0.745078i	0.145387	+	0.989375i	$0.453557\pi$
$38$			1.88260i			0.305398i
$39$	−0.538428	+	0.805815i	−0.0862175	+	0.129034i
$40$	−1.40077	−	1.74294i	−0.221481	−	0.275584i
$41$	−8.11534	+	5.42250i	−1.26740	+	0.846852i	−0.993380	−	0.114872i	$-0.963354\pi$
$41$	−8.11534	+	5.42250i	−1.26740	+	0.846852i	−0.274023	+	0.961723i	$0.588354\pi$
$42$	−1.19256	−	0.493974i	−0.184016	−	0.0762219i
$43$	−3.41130	−	1.41301i	−0.520219	−	0.215482i	0.107094	−	0.994249i	$-0.465845\pi$
$43$	−3.41130	−	1.41301i	−0.520219	−	0.215482i	−0.627313	+	0.778767i	$0.715845\pi$
$44$	−5.28076	+	3.52849i	−0.796105	+	0.531940i
$45$	2.22294	+	0.241955i	0.331376	+	0.0360686i
$46$	−1.63604	+	2.44851i	−0.241221	+	0.361012i
$47$		−	3.12264i		−	0.455484i	−0.973721	−	0.227742i	$-0.926866\pi$
$47$		−	3.12264i		−	0.455484i	0.973721	−	0.227742i	$-0.0731343\pi$
$48$	−0.831470	−	0.555570i	−0.120012	−	0.0801897i
$49$	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
$53$	4.27629	+	10.3239i	0.587393	+	1.41809i	0.885986	+	0.463713i	$0.153483\pi$
$53$	4.27629	+	10.3239i	0.587393	+	1.41809i	−0.298592	+	0.954381i	$0.596517\pi$
$54$	0.980785	−	0.195090i	0.133468	−	0.0265484i
$55$	9.12133	−	10.8851i	1.22992	−	1.46774i
$56$	−1.07327	−	0.717139i	−0.143422	−	0.0958318i
$57$	−1.04592	−	1.56532i	−0.138535	−	0.207332i
$58$	1.73737	+	0.345583i	0.228127	+	0.0453773i
$59$	−7.80760	+	3.23401i	−1.01646	+	0.421033i	−0.827808	−	0.561011i	$-0.810413\pi$
$59$	−7.80760	+	3.23401i	−1.01646	+	0.421033i	−0.188654	+	0.982044i	$0.560413\pi$
$60$	2.13302	+	0.670980i	0.275372	+	0.0866231i
$61$	−8.24678	−	12.3422i	−1.05589	−	1.58025i	−0.786869	−	0.617120i	$-0.788299\pi$
$61$	−8.24678	−	12.3422i	−1.05589	−	1.58025i	−0.269023	−	0.963134i	$-0.586701\pi$
$62$	7.20881	−	4.81677i	0.915519	−	0.611731i
$63$	1.26601	−	0.251826i	0.159503	−	0.0317271i
$64$	−0.707107	−	0.707107i	−0.0883883	−	0.0883883i
$65$	1.04107	−	1.90063i	0.129129	−	0.235744i
$66$	2.43047	−	5.86767i	0.299170	−	0.722260i
$67$	−6.33649	−	6.33649i	−0.774125	−	0.774125i	0.204700	−	0.978825i	$-0.434378\pi$
$67$	−6.33649	−	6.33649i	−0.774125	−	0.774125i	−0.978825	+	0.204700i	$0.934378\pi$
$68$	−3.67898	+	1.86148i	−0.446142	+	0.225737i
$69$		−	2.94479i		−	0.354511i
$70$	2.75334	+	0.866112i	0.329087	+	0.103520i
$71$	1.19231	+	5.99416i	0.141501	+	0.711376i	0.984767	+	0.173879i	$0.0556301\pi$
$71$	1.19231	+	5.99416i	0.141501	+	0.711376i	−0.843266	+	0.537497i	$0.819370\pi$
$72$	1.00000			0.117851
$73$	1.92584	+	9.68185i	0.225402	+	1.13317i	0.913275	+	0.407343i	$0.133545\pi$
$73$	1.92584	+	9.68185i	0.225402	+	1.13317i	−0.687873	+	0.725831i	$0.741455\pi$
$74$	−8.00087	−	1.59147i	−0.930083	−	0.185005i
$75$	−4.99895	−	0.102425i	−0.577229	−	0.0118270i
$76$	−0.720439	−	1.73929i	−0.0826400	−	0.199511i
$77$	3.13729	−	7.57409i	0.357527	−	0.863147i
$78$	0.189071	−	0.950524i	0.0214081	−	0.107626i
$79$	−0.614353	+	3.08856i	−0.0691202	+	0.347491i	−0.999833	−	0.0182595i	$-0.994187\pi$
$79$	−0.614353	+	3.08856i	−0.0691202	+	0.347491i	0.930713	+	0.365750i	$0.119187\pi$
$80$	1.96114	+	1.07422i	0.219262	+	0.120101i
$81$	−0.707107	+	0.707107i	−0.0785674	+	0.0785674i
$82$	5.42250	−	8.11534i	0.598815	−	0.896189i
$83$	15.9163	−	6.59275i	1.74704	−	0.723648i	0.748901	−	0.662682i	$-0.230582\pi$
$83$	15.9163	−	6.59275i	1.74704	−	0.723648i	0.998140	−	0.0609655i	$-0.0194180\pi$
$84$	1.29082			0.140840
$85$	6.72885	−	6.30258i	0.729847	−	0.683611i
$86$	3.69237			0.398158
$87$	−1.63656	+	0.677886i	−0.175458	+	0.0726770i
$88$	3.52849	−	5.28076i	0.376139	−	0.562931i
$89$	−0.492642	+	0.492642i	−0.0522199	+	0.0522199i	−0.732735	−	0.680515i	$-0.761756\pi$
$89$	−0.492642	+	0.492642i	−0.0522199	+	0.0522199i	0.680515	+	0.732735i	$0.261756\pi$
$90$	−2.14632	+	0.627144i	−0.226242	+	0.0661068i
$91$	0.244056	−	1.22695i	0.0255840	−	0.128619i
$92$	0.574501	−	2.88821i	0.0598958	−	0.301117i
$93$	−3.31785	+	8.01000i	−0.344045	+	0.830598i
$94$	1.19498	+	2.88495i	0.123253	+	0.297559i
$95$	2.63708	+	3.28126i	0.270559	+	0.336650i
$96$	0.980785	+	0.195090i	0.100101	+	0.0199113i
$97$	1.77401	+	8.91855i	0.180123	+	0.905541i	0.960084	+	0.279712i	$0.0902391\pi$
$97$	1.77401	+	8.91855i	0.180123	+	0.905541i	−0.779960	+	0.625829i	$0.784761\pi$
$98$	−5.33379			−0.538794
$99$	1.23904	+	6.22909i	0.124528	+	0.626047i
$100$	−4.88292	−	1.07570i	−0.488292	−	0.107570i
$101$		−	6.89492i		−	0.686070i	−0.939323	−	0.343035i	$-0.888545\pi$
$101$		−	6.89492i		−	0.686070i	0.939323	−	0.343035i	$-0.111455\pi$
$102$	2.02478	−	3.59169i	0.200483	−	0.355631i
$103$	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
$105$	−2.77051	+	0.809529i	−0.270374	+	0.0790019i
$106$	−7.90155	−	7.90155i	−0.767467	−	0.767467i
$107$	−7.86811	+	1.56507i	−0.760639	+	0.151301i	−0.560145	−	0.828394i	$-0.689255\pi$
$107$	−7.86811	+	1.56507i	−0.760639	+	0.151301i	−0.200494	+	0.979695i	$0.564255\pi$
$108$	−0.831470	+	0.555570i	−0.0800082	+	0.0534598i
$109$	−4.52732	−	6.77562i	−0.433639	−	0.648987i	0.548717	−	0.836008i	$-0.315117\pi$
$109$	−4.52732	−	6.77562i	−0.433639	−	0.648987i	−0.982356	+	0.187022i	$0.940117\pi$
$110$	−4.26147	+	13.5471i	−0.406316	+	1.29166i
$111$	7.53666	−	3.12179i	0.715348	−	0.296307i
$112$	1.26601	+	0.251826i	0.119627	+	0.0237953i
$113$	2.04917	+	3.06679i	0.192769	+	0.288500i	0.915246	−	0.402896i	$-0.131996\pi$
$113$	2.04917	+	3.06679i	0.192769	+	0.288500i	−0.722477	+	0.691395i	$0.756996\pi$
$114$	1.56532	+	1.04592i	0.146606	+	0.0979590i
$115$	0.578262	+	6.55932i	0.0539232	+	0.611659i
$116$	−1.73737	+	0.345583i	−0.161310	+	0.0320866i
$117$	0.370876	+	0.895374i	0.0342875	+	0.0827773i
$118$	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
$122$	12.3422	+	8.24678i	1.11741	+	0.746628i
$123$			9.76024i			0.880051i
$124$	−4.81677	+	7.20881i	−0.432559	+	0.647370i
$125$	11.1549	−	0.753489i	0.997726	−	0.0673941i
$126$	−1.07327	+	0.717139i	−0.0956149	+	0.0638879i
$127$	5.15367	+	2.13472i	0.457314	+	0.189426i	0.599435	−	0.800424i	$-0.295392\pi$
$127$	5.15367	+	2.13472i	0.457314	+	0.189426i	−0.142121	+	0.989849i	$0.545392\pi$
$128$	0.923880	+	0.382683i	0.0816602	+	0.0338248i
$129$	−3.07009	+	2.05137i	−0.270307	+	0.180613i
$130$	−0.234490	+	2.15435i	−0.0205661	+	0.188949i
$131$	8.75317	−	13.1001i	0.764768	−	1.14456i	−0.220807	−	0.975318i	$-0.570869\pi$
$131$	8.75317	−	13.1001i	0.764768	−	1.14456i	0.985575	−	0.169239i	$-0.0541310\pi$
$132$			6.35112i			0.552794i
$133$	2.02055	+	1.35009i	0.175204	+	0.117067i
$134$	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	$0.347908\pi$
$138$	1.12692	+	2.72063i	0.0959301	+	0.231596i
$139$	0.987484	−	0.196423i	0.0837573	−	0.0166604i	−0.153034	−	0.988221i	$-0.548904\pi$
$139$	0.987484	−	0.196423i	0.0837573	−	0.0166604i	0.236791	+	0.971561i	$0.423904\pi$
$140$	−2.87520	+	0.253475i	−0.242999	+	0.0214225i
$141$	−2.59638	−	1.73485i	−0.218655	−	0.146101i
$142$	−3.39542	−	5.08160i	−0.284937	−	0.426439i
$143$	6.03689	+	1.20081i	0.504830	+	0.100417i
$144$	−0.923880	+	0.382683i	−0.0769900	+	0.0318903i
$145$	3.51221	−	1.83131i	0.291673	−	0.152082i
$146$	−5.48433	−	8.20787i	−0.453886	−	0.679288i
$147$	4.43489	−	2.96330i	0.365783	−	0.244409i
$148$	8.00087	−	1.59147i	0.657668	−	0.130818i
$149$	14.7453	+	14.7453i	1.20798	+	1.20798i	0.971679	+	0.236306i	$0.0759369\pi$
$149$	14.7453	+	14.7453i	1.20798	+	1.20798i	0.236306	+	0.971679i	$0.424063\pi$
$150$	4.65762	−	1.81839i	0.380293	−	0.148471i
$151$	−2.22383	+	5.36880i	−0.180973	+	0.436907i	−0.988168	−	0.153378i	$-0.950985\pi$
$151$	−2.22383	+	5.36880i	−0.180973	+	0.436907i	0.807195	+	0.590285i	$0.200985\pi$
$152$	1.33120	+	1.33120i	0.107974	+	0.107974i
$153$	0.311896	+	4.11129i	0.0252153	+	0.332378i
$154$			8.19813i			0.660624i
$155$	5.81737	−	18.4932i	0.467262	−	1.48541i
$156$	0.189071	+	0.950524i	0.0151378	+	0.0761028i
$157$	−10.0895			−0.805232			−0.402616	−	0.915369i	$-0.631899\pi$
$157$	−10.0895			−0.805232			−0.402616	+	0.915369i	$0.631899\pi$
$158$	−0.614353	−	3.08856i	−0.0488753	−	0.245713i
$159$	10.9598	+	2.18003i	0.869166	+	0.172888i
$160$	−2.22294	−	0.241955i	−0.175739	−	0.0191282i
$161$	1.45465	+	3.51184i	0.114643	+	0.276772i
$162$	0.382683	−	0.923880i	0.0300665	−	0.0725868i
$163$	1.15695	−	5.81636i	0.0906190	−	0.455572i	−0.908658	−	0.417542i	$-0.862892\pi$
$163$	1.15695	−	5.81636i	0.0906190	−	0.455572i	0.999277	−	0.0380303i	$-0.0121083\pi$
$164$	−1.90413	+	9.57269i	−0.148687	+	0.747502i
$165$	−3.98307	−	13.6315i	−0.310082	−	1.06121i
$166$	−12.1818	+	12.1818i	−0.945491	+	0.945491i
$167$	9.15829	−	13.7063i	0.708690	−	1.06063i	−0.286052	−	0.958214i	$-0.592343\pi$
$167$	9.15829	−	13.7063i	0.708690	−	1.06063i	0.994742	−	0.102415i	$-0.0326570\pi$
$168$	−1.19256	+	0.493974i	−0.0920079	+	0.0381109i
$169$	−12.0608			−0.927751
$170$	−3.80476	+	8.39785i	−0.291812	+	0.644085i
$171$	−1.88260			−0.143966
$172$	−3.41130	+	1.41301i	−0.260109	+	0.107741i
$173$	−4.15708	+	6.22152i	−0.316057	+	0.473013i	−0.955152	−	0.296115i	$-0.904309\pi$
$173$	−4.15708	+	6.22152i	−0.316057	+	0.473013i	0.639095	+	0.769128i	$0.279309\pi$
$174$	1.25257	−	1.25257i	0.0949571	−	0.0949571i
$175$	6.01214	−	2.34721i	0.454475	−	0.177432i
$176$	−1.23904	+	6.22909i	−0.0933963	+	0.469535i
$177$	−1.64869	+	8.28850i	−0.123923	+	0.623002i
$178$	0.266616	−	0.643668i	0.0199837	−	0.0482449i
$179$	−4.53244	−	10.9423i	−0.338770	−	0.817864i	−0.997834	−	0.0657770i	$-0.979047\pi$
$179$	−4.53244	−	10.9423i	−0.338770	−	0.817864i	0.659064	−	0.752087i	$-0.270953\pi$
$180$	1.74294	−	1.40077i	0.129911	−	0.104407i
$181$	−6.14411	−	1.22214i	−0.456688	−	0.0908408i	−0.0386145	−	0.999254i	$-0.512294\pi$
$181$	−6.14411	−	1.22214i	−0.456688	−	0.0908408i	−0.418073	+	0.908413i	$0.637294\pi$
$182$	0.244056	+	1.22695i	0.0180906	+	0.0909477i
$183$	−14.8438			−1.09729
$184$	0.574501	+	2.88821i	0.0423527	+	0.212922i
$185$	−16.1744	+	8.43351i	−1.18916	+	0.620044i
$186$		−	8.66996i		−	0.635712i
$187$	22.8113	+	12.8596i	1.66813	+	0.940388i
$188$	−2.20804	−	2.20804i	−0.161038	−	0.161038i
$189$	0.493974	−	1.19256i	0.0359313	−	0.0867459i
$190$	−3.69203	−	2.02232i	−0.267848	−	0.146715i
$191$	−11.1834	−	11.1834i	−0.809204	−	0.809204i	0.175309	−	0.984513i	$-0.443908\pi$
$191$	−11.1834	−	11.1834i	−0.809204	−	0.809204i	−0.984513	+	0.175309i	$0.943908\pi$
$192$	−0.980785	+	0.195090i	−0.0707821	+	0.0140794i
$193$	−11.1271	+	7.43487i	−0.800944	+	0.535174i	−0.887356	−	0.461086i	$-0.847460\pi$
$193$	−11.1271	+	7.43487i	−0.800944	+	0.535174i	0.0864113	+	0.996260i	$0.472460\pi$
$194$	−5.05195	−	7.56078i	−0.362709	−	0.542832i
$195$	−1.00192	−	1.92155i	−0.0717491	−	0.137605i
$196$	4.92778	−	2.04115i	0.351984	−	0.145797i
$197$	−12.4938	−	2.48516i	−0.890143	−	0.177061i	−0.271225	−	0.962516i	$-0.587429\pi$
$197$	−12.4938	−	2.48516i	−0.890143	−	0.177061i	−0.618918	+	0.785455i	$0.712429\pi$
$198$	−3.52849	−	5.28076i	−0.250759	−	0.375288i
$199$	−0.437174	−	0.292110i	−0.0309904	−	0.0207072i	0.539979	−	0.841679i	$-0.318432\pi$
$199$	−0.437174	−	0.292110i	−0.0309904	−	0.0207072i	−0.570969	+	0.820972i	$0.693432\pi$
$200$	4.92288	−	0.874790i	0.348100	−	0.0618570i
$201$	−8.78896	+	1.74823i	−0.619926	+	0.123311i
$202$	2.63857	+	6.37007i	0.185649	+	0.448197i
$203$	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
$207$	−2.44851	−	1.63604i	−0.170183	−	0.113713i
$208$			0.969145i			0.0671981i
$209$	−6.64274	+	9.94156i	−0.459488	+	0.687672i
$210$	2.24982	−	1.80813i	0.155252	−	0.124773i
$211$	3.10928	−	2.07755i	0.214052	−	0.143025i	−0.443923	−	0.896065i	$-0.646414\pi$
$211$	3.10928	−	2.07755i	0.214052	−	0.143025i	0.657974	+	0.753040i	$0.271414\pi$
$212$	10.3239	+	4.27629i	0.709047	+	0.293697i
$213$	5.64637	+	2.33880i	0.386883	+	0.160252i
$214$	6.67027	−	4.45693i	0.455970	−	0.304669i
$215$	6.43559	−	5.17215i	0.438903	−	0.352738i
$216$	0.555570	−	0.831470i	0.0378018	−	0.0565743i
$217$		−	11.1913i		−	0.759717i
$218$	6.77562	+	4.52732i	0.458903	+	0.306629i
$219$	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
$223$	−0.622511	−	1.50288i	−0.0416864	−	0.100640i	0.901665	−	0.432435i	$-0.142346\pi$
$223$	−0.622511	−	1.50288i	−0.0416864	−	0.100640i	−0.943351	+	0.331795i	$0.892346\pi$
$224$	−1.26601	+	0.251826i	−0.0845891	+	0.0168258i
$225$	−2.86243	+	4.09957i	−0.190829	+	0.273305i
$226$	−3.06679	−	2.04917i	−0.204000	−	0.136308i
$227$	−5.67837	−	8.49828i	−0.376887	−	0.564051i	0.593735	−	0.804660i	$-0.297653\pi$
$227$	−5.67837	−	8.49828i	−0.376887	−	0.564051i	−0.970622	+	0.240610i	$0.922653\pi$
$228$	−1.84642	−	0.367277i	−0.122282	−	0.0243235i
$229$	−19.1718	+	7.94120i	−1.26691	+	0.524770i	−0.912022	−	0.410141i	$-0.865480\pi$
$229$	−19.1718	+	7.94120i	−1.26691	+	0.524770i	−0.354884	+	0.934910i	$0.615480\pi$
$230$	−3.04439	−	5.83873i	−0.200741	−	0.384994i
$231$	−4.55464	−	6.81650i	−0.299673	−	0.448493i
$232$	1.47287	−	0.984138i	0.0966985	−	0.0646118i
$233$	7.42270	−	1.47647i	0.486277	−	0.0967266i	0.0541381	−	0.998533i	$-0.482759\pi$
$233$	7.42270	−	1.47647i	0.486277	−	0.0967266i	0.432139	+	0.901807i	$0.357759\pi$
$234$	−0.685289	−	0.685289i	−0.0447988	−	0.0447988i
$235$	6.12393	+	3.35440i	0.399481	+	0.218817i
$236$	−3.23401	+	7.80760i	−0.210516	+	0.508231i
$237$	2.22673	+	2.22673i	0.144642	+	0.144642i
$238$	−0.640464	+	5.28350i	−0.0415151	+	0.342478i
$239$		−	27.7718i		−	1.79641i	−0.439578	−	0.898204i	$-0.644872\pi$
$239$		−	27.7718i		−	1.79641i	0.439578	−	0.898204i	$-0.355128\pi$
$240$	1.98273	−	1.03382i	0.127985	−	0.0667328i
$241$	0.988575	+	4.96990i	0.0636797	+	0.320140i	0.999475	−	0.0324048i	$-0.0103166\pi$
$241$	0.988575	+	4.96990i	0.0636797	+	0.320140i	−0.935795	+	0.352544i	$0.885317\pi$
$242$	−29.3367			−1.88584
$243$	0.195090	+	0.980785i	0.0125150	+	0.0629174i
$244$	−14.5586	−	2.89588i	−0.932018	−	0.185390i
$245$	−9.29650	+	7.47140i	−0.593931	+	0.477330i
$246$	−3.73508	−	9.01728i	−0.238140	−	0.574921i
$247$	−0.698210	+	1.68563i	−0.0444261	+	0.107254i
$248$	1.69143	−	8.50337i	0.107406	−	0.539964i
$249$	3.36095	−	16.8967i	0.212992	−	1.07078i
$250$	−10.0175	+	4.96494i	−0.633559	+	0.314010i
$251$	−7.87714	+	7.87714i	−0.497201	+	0.497201i	−0.910566	−	0.413365i	$-0.864353\pi$
$251$	−7.87714	+	7.87714i	−0.497201	+	0.497201i	0.413365	+	0.910566i	$0.364353\pi$
$252$	0.717139	−	1.07327i	0.0451755	−	0.0676100i
$253$	−17.2791	+	7.15723i	−1.08633	+	0.449971i
$254$	−5.57829			−0.350013
$255$	−1.50205	−	9.09636i	−0.0940622	−	0.569636i
$256$	−1.00000			−0.0625000
$257$	17.9131	−	7.41985i	1.11739	−	0.462837i	0.253912	−	0.967227i	$-0.418283\pi$
$257$	17.9131	−	7.41985i	1.11739	−	0.462837i	0.863476	+	0.504390i	$0.168283\pi$
$258$	2.05137	−	3.07009i	0.127713	−	0.191136i
$259$	−7.44583	+	7.44583i	−0.462661	+	0.462661i
$260$	−0.607794	−	2.08010i	−0.0376938	−	0.129002i
$261$	−0.345583	+	1.73737i	−0.0213911	+	0.107540i
$262$	−3.07371	+	15.4526i	−0.189894	+	0.954663i
$263$	9.23187	−	22.2877i	0.569261	−	1.37432i	−0.332917	−	0.942956i	$-0.608033\pi$
$263$	9.23187	−	22.2877i	0.569261	−	1.37432i	0.902179	−	0.431362i	$-0.141967\pi$
$264$	−2.43047	−	5.86767i	−0.149585	−	0.361130i
$265$	−24.8402	−	2.70372i	−1.52592	−	0.166088i
$266$	−2.38340	−	0.474087i	−0.146135	−	0.0290681i
$267$	0.135920	+	0.683314i	0.00831814	+	0.0418181i
$268$	−8.96115			−0.547389
$269$	0.959349	+	4.82298i	0.0584926	+	0.294062i	0.998948	−	0.0458547i	$-0.0146011\pi$
$269$	0.959349	+	4.82298i	0.0584926	+	0.294062i	−0.940456	+	0.339917i	$0.889601\pi$
$270$	−0.670980	+	2.13302i	−0.0408345	+	0.129812i
$271$			2.37742i			0.144418i	0.997390	+	0.0722089i	$0.0230048\pi$
$271$			2.37742i			0.144418i	−0.997390	+	0.0722089i	$0.976995\pi$
$272$	−1.28517	+	3.91770i	−0.0779248	+	0.237545i
$273$	−0.884583	−	0.884583i	−0.0535374	−	0.0535374i
$274$	2.71224	−	6.54792i	0.163852	−	0.395574i
$275$	11.5488	+	29.5811i	0.696419	+	1.78381i
$276$	−2.08228	−	2.08228i	−0.125339	−	0.125339i
$277$	0.0318567	−	0.00633669i	0.00191408	−	0.000380735i	−0.194133	−	0.980975i	$-0.562189\pi$
$277$	0.0318567	−	0.00633669i	0.00191408	−	0.000380735i	0.196047	+	0.980594i	$0.437189\pi$
$278$	−0.837149	+	0.559365i	−0.0502088	+	0.0335485i
$279$	4.81677	+	7.20881i	0.288373	+	0.431580i
$280$	2.55934	−	1.33447i	0.152950	−	0.0797500i
$281$	−19.3455	+	8.01315i	−1.15405	+	0.478025i	−0.875891	−	0.482509i	$-0.839725\pi$
$281$	−19.3455	+	8.01315i	−1.15405	+	0.478025i	−0.278163	+	0.960534i	$0.589725\pi$
$282$	3.06264	+	0.609197i	0.182378	+	0.0362772i
$283$	0.177573	+	0.265757i	0.0105556	+	0.0157976i	0.836710	−	0.547646i	$-0.184476\pi$
$283$	0.177573	+	0.265757i	0.0105556	+	0.0157976i	−0.826154	+	0.563444i	$0.809476\pi$
$284$	5.08160	+	3.39542i	0.301538	+	0.201481i
$285$	4.19335	−	0.369682i	0.248393	−	0.0218981i
$286$	−6.03689	+	1.20081i	−0.356969	+	0.0710055i
$287$	−4.82130	−	11.6397i	−0.284593	−	0.687067i
$288$	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
$292$	8.20787	+	5.48433i	0.480329	+	0.320946i
$293$		−	29.4273i		−	1.71916i	−0.511001	−	0.859580i	$-0.670725\pi$
$293$		−	29.4273i		−	1.71916i	0.511001	−	0.859580i	$-0.329275\pi$
$294$	−2.96330	+	4.43489i	−0.172823	+	0.258648i
$295$	2.04474	−	18.7858i	0.119049	−	1.09375i
$296$	−6.78281	+	4.53213i	−0.394243	+	0.263425i
$297$	5.86767	+	2.43047i	0.340477	+	0.141030i
$298$	−19.2657	−	7.98012i	−1.11603	−	0.462276i
$299$	−2.37296	+	1.58556i	−0.137232	+	0.0916953i
$300$	−3.60722	+	3.46237i	−0.208263	+	0.199900i
$301$	2.64794	−	3.96293i	0.152625	−	0.228419i
$302$		−	5.81115i		−	0.334394i
$303$	−5.73292	−	3.83061i	−0.329347	−	0.220063i
$304$	−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	$0.485865\pi$
$308$	−3.13729	−	7.57409i	−0.178764	−	0.431574i
$309$	6.93513	−	1.37948i	0.394526	−	0.0784761i
$310$	1.70250	+	19.3117i	0.0966955	+	1.09683i
$311$	12.3300	+	8.23867i	0.699173	+	0.467172i	0.853666	−	0.520822i	$-0.174374\pi$
$311$	12.3300	+	8.23867i	0.699173	+	0.467172i	−0.154493	+	0.987994i	$0.549374\pi$
$312$	−0.538428	−	0.805815i	−0.0304825	−	0.0456203i
$313$	−20.2782	−	4.03359i	−1.14619	−	0.227992i	−0.414776	−	0.909923i	$-0.636140\pi$
$313$	−20.2782	−	4.03359i	−1.14619	−	0.227992i	−0.731416	+	0.681932i	$0.761140\pi$
$314$	9.32151	−	3.86109i	0.526043	−	0.217894i
$315$	−0.866112	+	2.75334i	−0.0487999	+	0.155133i
$316$	1.74953	+	2.61836i	0.0984188	+	0.147294i
$317$	−18.4321	+	12.3159i	−1.03525	+	0.691733i	−0.952407	−	0.304830i	$-0.901400\pi$
$317$	−18.4321	+	12.3159i	−1.03525	+	0.691733i	−0.0828443	+	0.996563i	$0.526400\pi$
$318$	−10.9598	+	2.18003i	−0.614593	+	0.122250i
$319$	7.95523	+	7.95523i	0.445407	+	0.445407i
$320$	2.14632	−	0.627144i	0.119983	−	0.0350584i
$321$	−3.06999	+	7.41160i	−0.171350	+	0.413675i
$322$	−2.68785	−	2.68785i	−0.149788	−	0.149788i
$323$	−5.05775	+	5.88814i	−0.281421	+	0.327625i
$324$			1.00000i			0.0555556i
$325$	2.60904	+	4.08338i	0.144724	+	0.226505i
$326$	1.15695	+	5.81636i	0.0640773	+	0.322138i
$327$	−8.14897			−0.450639
$328$	−1.90413	−	9.57269i	−0.105138	−	0.528564i
$329$	3.95331	+	0.786362i	0.217953	+	0.0433536i
$330$	8.89644	+	11.0696i	0.489733	+	0.609364i
$331$	0.340359	+	0.821700i	0.0187078	+	0.0451647i	0.932957	−	0.359987i	$-0.117219\pi$
$331$	0.340359	+	0.821700i	0.0187078	+	0.0451647i	−0.914250	+	0.405151i	$0.867219\pi$
$332$	6.59275	−	15.9163i	0.361824	−	0.873520i
$333$	1.59147	−	8.00087i	0.0872122	−	0.438445i
$334$	−3.21596	+	16.1677i	−0.175970	+	0.884659i
$335$	19.2335	−	5.61993i	1.05084	−	0.307050i
$336$	0.912745	−	0.912745i	0.0497943	−	0.0497943i
$337$	−10.0309	+	15.0123i	−0.546417	+	0.817771i	−0.997194	−	0.0748657i	$-0.976147\pi$
$337$	−10.0309	+	15.0123i	−0.546417	+	0.817771i	0.450776	+	0.892637i	$0.351147\pi$
$338$	11.1427	−	4.61545i	0.606082	−	0.251047i
$339$	3.68840			0.200326
$340$	0.301422	−	9.21462i	0.0163469	−	0.499733i
$341$	55.0640			2.98188
$342$	1.73929	−	0.720439i	0.0940503	−	0.0389569i
$343$	−8.84505	+	13.2375i	−0.477588	+	0.714761i
$344$	2.61090	−	2.61090i	0.140770	−	0.140770i
$345$	5.77514	+	3.16335i	0.310923	+	0.170309i
$346$	1.45977	−	7.33878i	0.0784779	−	0.394535i
$347$	−6.27330	+	31.5380i	−0.336768	+	1.69305i	0.326930	+	0.945049i	$0.393986\pi$
$347$	−6.27330	+	31.5380i	−0.336768	+	1.69305i	−0.663698	+	0.748001i	$0.731014\pi$
$348$	−0.677886	+	1.63656i	−0.0363385	+	0.0877289i
$349$	−4.43969	−	10.7184i	−0.237651	−	0.573740i	0.759388	−	0.650638i	$-0.225498\pi$
$349$	−4.43969	−	10.7184i	−0.237651	−	0.573740i	−0.997039	+	0.0768977i	$0.975498\pi$
$350$	−4.65626	+	4.46928i	−0.248887	+	0.238893i
$351$	0.950524	+	0.189071i	0.0507352	+	0.0100919i
$352$	−1.23904	−	6.22909i	−0.0660412	−	0.332011i
$353$	−7.14466			−0.380272			−0.190136	−	0.981758i	$-0.560893\pi$
$353$	−7.14466			−0.380272			−0.190136	+	0.981758i	$0.560893\pi$
$354$	−1.64869	−	8.28850i	−0.0876267	−	0.440529i
$355$	−13.0362	−	4.10076i	−0.691888	−	0.217646i
$356$			0.696701i			0.0369251i
$357$	−2.40283	−	4.74889i	−0.127171	−	0.251338i
$358$	8.37485	+	8.37485i	0.442625	+	0.442625i
$359$	−5.20627	+	12.5690i	−0.274776	+	0.663368i	−0.999675	−	0.0254868i	$-0.991886\pi$
$359$	−5.20627	+	12.5690i	−0.274776	+	0.663368i	0.724899	+	0.688855i	$0.241886\pi$
$360$	−1.07422	+	1.96114i	−0.0566163	+	0.103361i
$361$	10.9289	+	10.9289i	0.575206	+	0.575206i
$362$	6.14411	−	1.22214i	0.322927	−	0.0642342i
$363$	24.3926	−	16.2986i	1.28028	−	0.855455i
$364$	−0.695012	−	1.04016i	−0.0364285	−	0.0545192i
$365$	−21.0562	−	6.62360i	−1.10213	−	0.346695i
$366$	13.7139	−	5.68048i	0.716837	−	0.296923i
$367$	−9.89297	−	1.96783i	−0.516409	−	0.102720i	−0.0699962	−	0.997547i	$-0.522299\pi$
$367$	−9.89297	−	1.96783i	−0.516409	−	0.102720i	−0.446413	+	0.894827i	$0.647299\pi$
$368$	−1.63604	−	2.44851i	−0.0852844	−	0.127637i
$369$	8.11534	+	5.42250i	0.422468	+	0.282284i
$370$	11.7158	−	13.9812i	0.609075	−	0.726848i
$371$	−14.1471	+	2.81402i	−0.734478	+	0.146097i
$372$	3.31785	+	8.01000i	0.172022	+	0.415299i
$373$	−12.1318	+	12.1318i	−0.628159	+	0.628159i	−0.947604	−	0.319446i	$-0.896503\pi$
$373$	−12.1318	+	12.1318i	−0.628159	+	0.628159i	0.319446	+	0.947604i	$0.396503\pi$
$374$	−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
$377$	1.42742	+	0.953773i	0.0735160	+	0.0491218i
$378$			1.29082i			0.0663925i
$379$	5.92310	−	8.86455i	0.304249	−	0.455342i	−0.647568	−	0.762008i	$-0.724214\pi$
$379$	5.92310	−	8.86455i	0.304249	−	0.455342i	0.951817	+	0.306667i	$0.0992136\pi$
$380$	4.18490	+	0.455505i	0.214681	+	0.0233669i
$381$	4.63818	−	3.09913i	0.237621	−	0.158773i
$382$	14.6119	+	6.05243i	0.747607	+	0.309669i
$383$	11.1030	+	4.59901i	0.567336	+	0.234998i	0.647866	−	0.761754i	$-0.275661\pi$
$383$	11.1030	+	4.59901i	0.567336	+	0.234998i	−0.0805306	+	0.996752i	$0.525661\pi$
$384$	0.831470	−	0.555570i	0.0424308	−	0.0283513i
$385$	11.4837	+	14.2889i	0.585262	+	0.728229i
$386$	7.43487	−	11.1271i	0.378425	−	0.566353i
$387$			3.69237i			0.187694i
$388$	7.56078	+	5.05195i	0.383840	+	0.256474i
$389$	−14.4743	−	5.99546i	−0.733877	−	0.303982i	−0.0157327	−	0.999876i	$-0.505008\pi$
$389$	−14.4743	−	5.99546i	−0.733877	−	0.303982i	−0.718144	+	0.695895i	$0.755008\pi$
$390$	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
$393$	−6.02929	−	14.5560i	−0.304138	−	0.734253i
$394$	12.4938	−	2.48516i	0.629426	−	0.125201i
$395$	−5.39714	−	4.52262i	−0.271560	−	0.227558i
$396$	5.28076	+	3.52849i	0.265368	+	0.177313i
$397$	−7.35749	−	11.0113i	−0.369262	−	0.552639i	0.599582	−	0.800314i	$-0.295334\pi$
$397$	−7.35749	−	11.0113i	−0.369262	−	0.552639i	−0.968843	+	0.247675i	$0.920334\pi$
$398$	0.515682	+	0.102576i	0.0258488	+	0.00514165i
$399$	2.24511	−	0.929955i	0.112396	−	0.0465560i
$400$	−4.21338	+	2.69211i	−0.210669	+	0.134605i
$401$	11.1371	+	16.6679i	0.556161	+	0.832353i	0.997899	−	0.0647907i	$-0.0206380\pi$
$401$	11.1371	+	16.6679i	0.556161	+	0.832353i	−0.441738	+	0.897144i	$0.645638\pi$
$402$	7.45092	−	4.97855i	0.371618	−	0.248307i
$403$	8.24100	−	1.63924i	0.410513	−	0.0816562i
$404$	−4.87544	−	4.87544i	−0.242562	−	0.242562i
$405$	−0.627144	−	2.14632i	−0.0311631	−	0.106652i
$406$	−0.875027	+	2.11250i	−0.0434269	+	0.104842i
$407$	−36.6352	−	36.6352i	−1.81594	−	1.81594i
$408$	−1.10798	−	3.97145i	−0.0548530	−	0.196616i
$409$		−	35.7325i		−	1.76686i	−0.468563	−	0.883430i	$-0.655228\pi$
$409$		−	35.7325i		−	1.76686i	0.468563	−	0.883430i	$-0.344772\pi$
$410$	10.0903	+	19.3519i	0.498326	+	0.955722i
$411$	1.38269	+	6.95123i	0.0682029	+	0.342879i
$412$	7.07100			0.348363
$413$	−2.12815	−	10.6989i	−0.104719	−	0.526460i
$414$	2.88821	+	0.574501i	0.141948	+	0.0282352i
$415$	−4.16833	+	38.2961i	−0.204615	+	1.87988i
$416$	−0.370876	−	0.895374i	−0.0181837	−	0.0438993i
$417$	0.385297	−	0.930190i	0.0188681	−	0.0455516i
$418$	2.33262	−	11.7269i	0.114092	−	0.573580i
$419$	3.70095	−	18.6060i	0.180803	−	0.908960i	−0.778729	−	0.627361i	$-0.784135\pi$
$419$	3.70095	−	18.6060i	0.180803	−	0.908960i	0.959532	−	0.281599i	$-0.0908649\pi$
$420$	−1.38662	+	2.53147i	−0.0676601	+	0.123523i
$421$	10.1724	−	10.1724i	0.495770	−	0.495770i	−0.414348	−	0.910118i	$-0.635990\pi$
$421$	10.1724	−	10.1724i	0.495770	−	0.495770i	0.910118	+	0.414348i	$0.135990\pi$
$422$	−2.07755	+	3.10928i	−0.101134	+	0.151357i
$423$	−2.88495	+	1.19498i	−0.140271	+	0.0581021i
$424$	−11.1745			−0.542681
$425$	5.13195	+	19.9665i	0.248936	+	0.968520i
$426$	−6.11159			−0.296108
$427$	17.7021	−	7.33246i	0.856666	−	0.354843i
$428$	−4.45693	+	6.67027i	−0.215434	+	0.322419i
$429$	4.35235	−	4.35235i	0.210134	−	0.210134i
$430$	−3.96641	+	7.24123i	−0.191277	+	0.349203i
$431$	−3.33880	+	16.7853i	−0.160824	+	0.808519i	0.813184	+	0.582007i	$0.197732\pi$
$431$	−3.33880	+	16.7853i	−0.160824	+	0.808519i	−0.974008	+	0.226512i	$0.927268\pi$
$432$	−0.195090	+	0.980785i	−0.00938629	+	0.0471881i
$433$	−4.83872	+	11.6817i	−0.232534	+	0.561387i	−0.996474	−	0.0839001i	$-0.973262\pi$
$433$	−4.83872	+	11.6817i	−0.232534	+	0.561387i	0.763940	+	0.645287i	$0.223262\pi$
$434$	4.28274	+	10.3394i	0.205578	+	0.496309i
$435$	0.428600	−	3.93772i	0.0205498	−	0.188799i
$436$	−7.99239	−	1.58978i	−0.382766	−	0.0761369i
$437$	−1.08155	−	5.43734i	−0.0517377	−	0.260103i
$438$	−9.87152			−0.471680
$439$	2.63591	+	13.2516i	0.125805	+	0.632466i	0.991308	+	0.131562i	$0.0419991\pi$
$439$	2.63591	+	13.2516i	0.125805	+	0.632466i	−0.865503	+	0.500904i	$0.833001\pi$
$440$	6.56592	+	12.5926i	0.313018	+	0.600326i
$441$		−	5.33379i		−	0.253990i
$442$	−3.98444	+	0.302273i	−0.189520	+	0.0143777i
$443$	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
$445$	−0.436932	−	1.49534i	−0.0207126	−	0.0708861i
$446$	1.15025	+	1.15025i	0.0544660	+	0.0544660i
$447$	20.4524	−	4.06823i	0.967364	−	0.192421i
$448$	1.07327	−	0.717139i	0.0507075	−	0.0338817i
$449$	17.6959	+	26.4838i	0.835121	+	1.24985i	0.966024	+	0.258452i	$0.0832124\pi$
$449$	17.6959	+	26.4838i	0.835121	+	1.24985i	−0.130903	+	0.991395i	$0.541788\pi$
$450$	1.07570	−	4.88292i	0.0507091	−	0.230183i
$451$	57.2698	−	23.7219i	2.69673	−	1.11702i
$452$	3.61753	+	0.719571i	0.170154	+	0.0338458i
$453$	3.22850	+	4.83180i	0.151688	+	0.227018i
$454$	8.49828	+	5.67837i	0.398844	+	0.266499i
$455$	2.14405	+	1.79664i	0.100515	+	0.0842279i
$456$	1.84642	−	0.367277i	0.0864668	−	0.0171993i
$457$	3.02446	+	7.30168i	0.141478	+	0.341558i	0.978697	−	0.205309i	$-0.0658200\pi$
$457$	3.02446	+	7.30168i	0.141478	+	0.341558i	−0.837219	+	0.546868i	$0.815820\pi$
$458$	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	0.628818	−	0.777553i	$-0.283539\pi$
$461$	11.2432	+	4.65708i	0.523647	+	0.216902i	−0.105171	+	0.994454i	$0.533539\pi$
$462$	6.81650	+	4.55464i	0.317132	+	0.211901i
$463$			18.9460i			0.880495i	0.897876	+	0.440248i	$0.145109\pi$
$463$			18.9460i			0.880495i	−0.897876	+	0.440248i	$0.854891\pi$
$464$	−0.984138	+	1.47287i	−0.0456875	+	0.0683761i
$465$	−12.1446	−	15.1112i	−0.563192	−	0.700767i
$466$	−6.29266	+	4.20462i	−0.291502	+	0.194775i
$467$	−33.7883	−	13.9956i	−1.56354	−	0.647639i	−0.577839	−	0.816151i	$-0.696104\pi$
$467$	−33.7883	−	13.9956i	−1.56354	−	0.647639i	−0.985700	+	0.168512i	$0.946104\pi$
$468$	0.895374	+	0.370876i	0.0413887	+	0.0171437i
$469$	9.61778	−	6.42639i	0.444108	−	0.296743i
$470$	−6.94144	−	0.755540i	−0.320185	−	0.0348505i
$471$	−5.60544	+	8.38914i	−0.258285	+	0.386551i
$472$		−	8.45089i		−	0.388984i
$473$	19.4985	+	13.0285i	0.896543	+	0.599051i
$474$	−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
$478$	10.6278	+	25.6578i	0.486105	+	1.17356i
$479$	−26.8712	+	5.34501i	−1.22778	+	0.244220i	−0.766037	−	0.642797i	$-0.777774\pi$
$479$	−26.8712	+	5.34501i	−1.22778	+	0.244220i	−0.461738	+	0.887016i	$0.652774\pi$
$480$	−1.43618	+	1.71388i	−0.0655522	+	0.0782277i
$481$	−6.57353	−	4.39229i	−0.299727	−	0.200271i
$482$	−2.81522	−	4.21328i	−0.128230	−	0.191910i
$483$	3.72815	+	0.741575i	0.169637	+	0.0337428i
$484$	27.1036	−	11.2267i	1.23198	−	0.510304i
$485$	−19.3962	−	6.10140i	−0.880734	−	0.277050i
$486$	−0.555570	−	0.831470i	−0.0252012	−	0.0377162i
$487$	7.62306	−	5.09357i	0.345434	−	0.230812i	−0.370735	−	0.928739i	$-0.620894\pi$
$487$	7.62306	−	5.09357i	0.345434	−	0.230812i	0.716169	+	0.697927i	$0.245894\pi$
$488$	14.5586	−	2.89588i	0.659036	−	0.131090i
$489$	−4.19336	−	4.19336i	−0.189630	−	0.189630i
$490$	5.72966	−	10.4603i	0.258840	−	0.472548i
$491$	−0.193181	+	0.466380i	−0.00871814	+	0.0210475i	−0.928179	−	0.372135i	$-0.878626\pi$
$491$	−0.193181	+	0.466380i	−0.00871814	+	0.0210475i	0.919461	+	0.393182i	$0.128626\pi$
$492$	6.90153	+	6.90153i	0.311145	+	0.311145i
$493$	4.50546	+	5.74844i	0.202916	+	0.258897i
$494$		−	1.82451i		−	0.0820887i
$495$	−13.5471	−	4.26147i	−0.608896	−	0.191539i
$496$	1.69143	+	8.50337i	0.0759472	+	0.381812i
$497$	−7.88895			−0.353868
$498$	3.36095	+	16.8967i	0.150608	+	0.757157i
$499$	11.3111	+	2.24993i	0.506356	+	0.100720i	0.441656	−	0.897184i	$-0.354391\pi$
$499$	11.3111	+	2.24993i	0.506356	+	0.100720i	0.0646997	+	0.997905i	$0.479391\pi$
$500$	7.35492	−	8.42052i	0.328922	−	0.376577i
$501$	−6.30834	−	15.2297i	−0.281836	−	0.680412i
$502$	4.26308	−	10.2920i	0.190271	−	0.459354i
$503$	−1.34295	+	6.75145i	−0.0598791	+	0.301032i	−0.999107	−	0.0422631i	$-0.986543\pi$
$503$	−1.34295	+	6.75145i	−0.0598791	+	0.301032i	0.939227	+	0.343295i	$0.111543\pi$
$504$	−0.251826	+	1.26601i	−0.0112172	+	0.0563928i
$505$	13.5219	+	7.40666i	0.601715	+	0.329592i
$506$	13.2248	−	13.2248i	0.587915	−	0.587915i
$507$	−6.70060	+	10.0282i	−0.297584	+	0.445366i
$508$	5.15367	−	2.13472i	0.228657	−	0.0947129i
$509$	18.2532			0.809061			0.404530	−	0.914525i	$-0.367435\pi$
$509$	18.2532			0.809061			0.404530	+	0.914525i	$0.367435\pi$
$510$	4.86874	+	7.82913i	0.215592	+	0.346680i
$511$	−12.7423			−0.563687
$512$	0.923880	−	0.382683i	0.0408301	−	0.0169124i
$513$	−1.04592	+	1.56532i	−0.0461783	+	0.0691107i
$514$	−13.7101	+	13.7101i	−0.604726	+	0.604726i
$515$	−15.1766	+	4.43454i	−0.668762	+	0.195409i
$516$	−0.720345	+	3.62142i	−0.0317114	+	0.159424i
$517$	−3.86909	+	19.4512i	−0.170162	+	0.855463i
$518$	4.02965	−	9.72844i	0.177053	−	0.427443i
$519$	2.86345	+	6.91298i	0.125691	+	0.303446i
$520$	1.35755	+	1.68917i	0.0595324	+	0.0740748i
$521$	−41.0026	−	8.15592i	−1.79636	−	0.357317i	−0.819811	−	0.572634i	$-0.805922\pi$
$521$	−41.0026	−	8.15592i	−1.79636	−	0.357317i	−0.976544	+	0.215317i	$0.930922\pi$
$522$	−0.345583	−	1.73737i	−0.0151258	−	0.0760424i
$523$	−22.6931			−0.992298			−0.496149	−	0.868237i	$-0.665253\pi$
$523$	−22.6931			−0.992298			−0.496149	+	0.868237i	$0.665253\pi$
$524$	−3.07371	−	15.4526i	−0.134275	−	0.675048i
$525$	1.38854	−	6.30295i	0.0606007	−	0.275083i
$526$			24.1240i			1.05186i
$527$	35.4874	+	4.30177i	1.54585	+	0.187388i
$528$	4.49092	+	4.49092i	0.195442	+	0.195442i
$529$	−5.48316	+	13.2375i	−0.238398	+	0.575545i
$530$	23.9840	−	7.00801i	1.04180	−	0.304409i
$531$	5.97568	+	5.97568i	0.259322	+	0.259322i
$532$	2.38340	−	0.474087i	0.103333	−	0.0205543i
$533$	7.86494	−	5.25519i	0.340669	−	0.227627i
$534$	−0.387066	−	0.579286i	−0.0167500	−	0.0250681i
$535$	5.38278	−	17.1117i	0.232718	−	0.739802i
$536$	8.27902	−	3.42928i	0.357599	−	0.148122i
$537$	−11.6163	−	2.31062i	−0.501278	−	0.0997105i
$538$	−2.73200	−	4.08872i	−0.117785	−	0.176277i
$539$	−28.1665	−	18.8202i	−1.21322	−	0.810646i
$540$	−0.196368	−	2.22743i	−0.00845032	−	0.0958533i
$541$	26.1253	−	5.19664i	1.12321	−	0.223421i	0.401666	−	0.915786i	$-0.368431\pi$
$541$	26.1253	−	5.19664i	1.12321	−	0.223421i	0.721548	+	0.692365i	$0.243431\pi$
$542$	−0.909798	−	2.19645i	−0.0390792	−	0.0943455i
$543$	−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
$547$	−14.9551	−	9.99266i	−0.639433	−	0.427255i	0.193140	−	0.981171i	$-0.438133\pi$
$547$	−14.9551	−	9.99266i	−0.639433	−	0.427255i	−0.832573	+	0.553916i	$0.813133\pi$
$548$			7.08742i			0.302759i
$549$	−8.24678	+	12.3422i	−0.351964	+	0.526751i
$550$	−21.9899	−	22.9099i	−0.937653	−	0.976880i
$551$	−2.77282	+	1.85274i	−0.118126	+	0.0789293i
$552$	2.72063	+	1.12692i	0.115798	+	0.0479650i
$553$	−3.75545	−	1.55556i	−0.159698	−	0.0661492i
$554$	−0.0270068	+	0.0180454i	−0.00114741	+	0.000766675i
$555$	−1.97378	+	18.1339i	−0.0837822	+	0.769741i
$556$	0.559365	−	0.837149i	0.0237224	−	0.0355030i
$557$			2.40807i			0.102033i	0.998698	+	0.0510165i	$0.0162461\pi$
$557$			2.40807i			0.102033i	−0.998698	+	0.0510165i	$0.983754\pi$
$558$	−7.20881	−	4.81677i	−0.305173	−	0.203910i
$559$	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
$563$	−5.52819	−	13.3462i	−0.232985	−	0.562477i	0.763540	−	0.645760i	$-0.223459\pi$
$563$	−5.52819	−	13.3462i	−0.232985	−	0.562477i	−0.996526	+	0.0832834i	$0.973459\pi$
$564$	−3.06264	+	0.609197i	−0.128961	+	0.0256518i
$565$	−8.21565	+	0.724283i	−0.345635	+	0.0304708i
$566$	−0.265757	−	0.177573i	−0.0111706	−	0.00746395i
$567$	−0.717139	−	1.07327i	−0.0301170	−	0.0450733i
$568$	−5.99416	−	1.19231i	−0.251509	−	0.0500283i
$569$	37.2485	−	15.4288i	1.56154	−	0.646810i	0.576182	−	0.817322i	$-0.304542\pi$
$569$	37.2485	−	15.4288i	1.56154	−	0.646810i	0.985356	+	0.170512i	$0.0545421\pi$
$570$	−3.73268	+	1.94627i	−0.156345	+	0.0815202i
$571$	−16.6671	−	24.9440i	−0.697496	−	1.04388i	−0.995990	−	0.0894646i	$-0.971484\pi$
$571$	−16.6671	−	24.9440i	−0.697496	−	1.04388i	0.298494	−	0.954411i	$-0.403516\pi$
$572$	5.11783	−	3.41962i	0.213987	−	0.142982i
$573$	−15.5119	+	3.08550i	−0.648017	+	0.128899i
$574$	8.90861	+	8.90861i	0.371838	+	0.371838i
$575$	−13.4849	−	5.91209i	−0.562359	−	0.246551i
$576$	−0.382683	+	0.923880i	−0.0159451	+	0.0384950i
$577$	1.69249	+	1.69249i	0.0704591	+	0.0704591i	0.741458	−	0.670999i	$-0.234135\pi$
$577$	1.69249	+	1.69249i	0.0704591	+	0.0704591i	−0.670999	+	0.741458i	$0.734135\pi$
$578$	−16.5076	−	4.06179i	−0.686627	−	0.168948i
$579$			13.3824i			0.556154i
$580$	1.18858	−	3.77844i	0.0493529	−	0.156891i
$581$	4.33837	+	21.8105i	0.179986	+	0.904851i
$582$	−9.09327			−0.376928
$583$	−13.8457	−	69.6068i	−0.573428	−	2.88282i
$584$	−9.68185	−	1.92584i	−0.400638	−	0.0796918i
$585$	−2.15435	−	0.234490i	−0.0890715	−	0.00969496i
$586$	11.2613	+	27.1873i	0.465201	+	1.12310i
$587$	−4.54792	+	10.9797i	−0.187713	+	0.453179i	−0.989519	−	0.144406i	$-0.953873\pi$
$587$	−4.54792	+	10.9797i	−0.187713	+	0.453179i	0.801806	+	0.597585i	$0.203873\pi$
$588$	1.04057	−	5.23130i	0.0429124	−	0.215735i
$589$	−3.18427	+	16.0084i	−0.131206	+	0.659616i
$590$	5.29993	+	18.1383i	0.218194	+	0.746742i
$591$	−9.00750	+	9.00750i	−0.370519	+	0.370519i
$592$	4.53213	−	6.78281i	0.186269	−	0.278772i
$593$	−11.4822	+	4.75609i	−0.471518	+	0.195309i	−0.605773	−	0.795638i	$-0.707136\pi$
$593$	−11.4822	+	4.75609i	−0.471518	+	0.195309i	0.134255	+	0.990947i	$0.457136\pi$
$594$	−6.35112			−0.260590
$595$	6.28466	+	10.1060i	0.257646	+	0.414305i
$596$	20.8531			0.854174
$597$	−0.485762	+	0.201209i	−0.0198809	+	0.00823494i
$598$	1.58556	−	2.37296i	0.0648384	−	0.0970375i
$599$	3.89710	−	3.89710i	0.159231	−	0.159231i	−0.622995	−	0.782226i	$-0.714084\pi$
$599$	3.89710	−	3.89710i	0.159231	−	0.159231i	0.782226	+	0.622995i	$0.214084\pi$
$600$	2.00764	−	4.57923i	0.0819617	−	0.186946i
$601$	−0.699020	+	3.51421i	−0.0285136	+	0.143348i	−0.992420	−	0.122895i	$-0.960782\pi$
$601$	−0.699020	+	3.51421i	−0.0285136	+	0.143348i	0.963906	+	0.266243i	$0.0857822\pi$
$602$	−0.929834	+	4.67459i	−0.0378972	+	0.190522i
$603$	−3.42928	+	8.27902i	−0.139651	+	0.337148i
$604$	2.22383	+	5.36880i	0.0904864	+	0.218454i
$605$	−51.1323	+	41.0939i	−2.07882	+	1.67071i
$606$	6.76244	+	1.34513i	0.274705	+	0.0546423i
$607$	−4.90862	−	24.6773i	−0.199235	−	1.00162i	−0.942902	−	0.333070i	$-0.891915\pi$
$607$	−4.90862	−	24.6773i	−0.199235	−	1.00162i	0.743667	−	0.668550i	$-0.233085\pi$
$608$	1.88260			0.0763494
$609$	−0.446085	−	2.24262i	−0.0180763	−	0.0908756i
$610$	−29.4313	+	15.3458i	−1.19164	+	0.621335i
$611$			3.02629i			0.122431i
$612$	3.12767	+	2.68658i	0.126428	+	0.108598i
$613$	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
$615$	−19.1411	−	10.4846i	−0.771845	−	0.422781i
$616$	5.79696	+	5.79696i	0.233566	+	0.233566i
$617$	8.65646	−	1.72188i	0.348496	−	0.0693202i	−0.0177388	−	0.999843i	$-0.505647\pi$
$617$	8.65646	−	1.72188i	0.348496	−	0.0693202i	0.366235	+	0.930523i	$0.380647\pi$
$618$	−5.87932	+	3.92844i	−0.236501	+	0.158025i
$619$	−26.6751	−	39.9221i	−1.07216	−	1.60460i	−0.754376	−	0.656442i	$-0.772061\pi$
$619$	−26.6751	−	39.9221i	−1.07216	−	1.60460i	−0.317786	−	0.948162i	$-0.602939\pi$
$620$	−8.96318	−	17.1902i	−0.359970	−	0.690374i
$621$	−2.72063	+	1.12692i	−0.109175	+	0.0452219i
$622$	−14.5443	−	2.89304i	−0.583173	−	0.116000i
$623$	−0.499632	−	0.747752i	−0.0200173	−	0.0299580i
$624$	0.805815	+	0.538428i	0.0322584	+	0.0215544i
$625$	−10.5051	+	22.6857i	−0.420205	+	0.907429i
$626$	20.2782	−	4.03359i	0.810480	−	0.161215i
$627$	4.57560	+	11.0465i	0.182732	+	0.441153i
$628$	−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	0.481036	−	0.876701i	$-0.340261\pi$
$631$	5.05556	+	2.09408i	0.201259	+	0.0833640i	−0.279777	+	0.960065i	$0.590261\pi$
$632$	−2.61836	−	1.74953i	−0.104153	−	0.0695926i
$633$		−	3.73950i		−	0.148632i
$634$	12.3159	−	18.4321i	0.489129	−	0.732033i
$635$	−9.72264	+	7.81389i	−0.385831	+	0.310085i
$636$	9.29124	−	6.20821i	0.368422	−	0.246172i
$637$	−4.77574	−	1.97817i	−0.189222	−	0.0783781i
$638$	−10.3940	−	4.30534i	−0.411503	−	0.170450i
$639$	5.08160	−	3.39542i	0.201025	−	0.134321i
$640$	−1.74294	+	1.40077i	−0.0688959	+	0.0553702i
$641$	−4.14094	+	6.19736i	−0.163557	+	0.244781i	−0.904191	−	0.427128i	$-0.859525\pi$
$641$	−4.14094	+	6.19736i	−0.163557	+	0.244781i	0.740634	+	0.671909i	$0.234525\pi$
$642$		−	8.02226i		−	0.316613i
$643$	30.1541	+	20.1484i	1.18916	+	0.794574i	0.982939	−	0.183931i	$-0.0588824\pi$
$643$	30.1541	+	20.1484i	1.18916	+	0.794574i	0.206224	+	0.978505i	$0.433882\pi$
$644$	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	$0.0661212\pi$
$648$	−0.382683	−	0.923880i	−0.0150332	−	0.0362934i
$649$	52.6413	−	10.4710i	2.06635	−	0.411023i
$650$	−3.97308	−	2.77411i	−0.155837	−	0.108810i
$651$	−9.30525	−	6.21757i	−0.364701	−	0.243686i
$652$	−3.29470	−	4.93087i	−0.129030	−	0.193108i
$653$	37.4812	+	7.45548i	1.46675	+	0.291756i	0.862914	−	0.505350i	$-0.168637\pi$
$653$	37.4812	+	7.45548i	1.46675	+	0.291756i	0.603840	+	0.797106i	$0.293637\pi$
$654$	7.52866	−	3.11847i	0.294394	−	0.121942i
$655$	16.2881	+	31.2385i	0.636431	+	1.22059i
$656$	5.42250	+	8.11534i	0.211713	+	0.316851i
$657$	8.20787	−	5.48433i	0.320220	−	0.213964i
$658$	−3.95331	+	0.786362i	−0.154116	+	0.0306556i
$659$	9.22638	+	9.22638i	0.359409	+	0.359409i	0.863595	−	0.504186i	$-0.168208\pi$
$659$	9.22638	+	9.22638i	0.359409	+	0.359409i	−0.504186	+	0.863595i	$0.668208\pi$
$660$	−12.4554	−	6.82250i	−0.484826	−	0.265565i
$661$	6.04675	−	14.5981i	0.235191	−	0.567802i	−0.761582	−	0.648068i	$-0.775577\pi$
$661$	6.04675	−	14.5981i	0.235191	−	0.567802i	0.996773	+	0.0802665i	$0.0255771\pi$
$662$	−0.628902	−	0.628902i	−0.0244430	−	0.0244430i
$663$	3.14501	−	2.46497i	0.122142	−	0.0957314i
$664$			17.2277i			0.668563i
$665$	−4.81821	+	2.51228i	−0.186842	+	0.0974219i
$666$	1.59147	+	8.00087i	0.0616683	+	0.310028i
$667$	−5.21641			−0.201980
$668$	−3.21596	−	16.1677i	−0.124429	−	0.625549i
$669$	−1.59544	−	0.317353i	−0.0616834	−	0.0122696i
$670$	−15.6188	+	12.5525i	−0.603406	+	0.484945i
$671$	36.0774	+	87.0986i	1.39275	+	3.36240i
$672$	−0.493974	+	1.19256i	−0.0190555	+	0.0460040i
$673$	9.29969	−	46.7527i	0.358477	−	1.80218i	−0.208026	−	0.978123i	$-0.566704\pi$
$673$	9.29969	−	46.7527i	0.358477	−	1.80218i	0.566502	−	0.824060i	$-0.308296\pi$
$674$	3.52238	−	17.7082i	0.135677	−	0.682094i
$675$	1.81839	+	4.65762i	0.0699898	+	0.179272i
$676$	−8.52824	+	8.52824i	−0.328009	+	0.328009i
$677$	−9.97394	+	14.9271i	−0.383330	+	0.573693i	−0.972088	−	0.234616i	$-0.924617\pi$
$677$	−9.97394	+	14.9271i	−0.383330	+	0.573693i	0.588759	+	0.808309i	$0.299617\pi$
$678$	−3.40764	+	1.41149i	−0.130870	+	0.0542079i
$679$	−11.7377			−0.450453
$680$	3.24780	+	8.62854i	0.124548	+	0.330890i
$681$	−10.2208			−0.391662
$682$	−50.8725	+	21.0721i	−1.94801	+	0.806891i
$683$	−6.23607	+	9.33294i	−0.238617	+	0.357115i	−0.931379	−	0.364051i	$-0.881393\pi$
$683$	−6.23607	+	9.33294i	−0.238617	+	0.357115i	0.692762	+	0.721166i	$0.256393\pi$
$684$	−1.33120	+	1.33120i	−0.0508996	+	0.0508996i
$685$	−4.44483	−	15.2119i	−0.169828	−	0.581215i
$686$	3.10597	−	15.6148i	0.118586	−	0.596174i
$687$	−4.04839	+	20.3526i	−0.154456	+	0.776502i
$688$	−1.41301	+	3.41130i	−0.0538704	+	0.130055i
$689$	−4.14435	−	10.0053i	−0.157887	−	0.381173i
$690$	−6.54609	−	0.712508i	−0.249206	−	0.0271247i
$691$	−11.5897	−	2.30534i	−0.440894	−	0.0876993i	−0.0303486	−	0.999539i	$-0.509662\pi$
$691$	−11.5897	−	2.30534i	−0.440894	−	0.0876993i	−0.410546	+	0.911840i	$0.634662\pi$
$692$	1.45977	+	7.33878i	0.0554923	+	0.278978i
$693$	−8.19813			−0.311421
$694$	−6.27330	−	31.5380i	−0.238131	−	1.19717i
$695$	−0.675563	+	2.14759i	−0.0256256	+	0.0814628i
$696$		−	1.77140i		−	0.0671448i
$697$	38.7623	−	10.8141i	1.46822	−	0.409614i
$698$	8.20347	+	8.20347i	0.310506	+	0.310506i
$699$	2.89619	−	6.99203i	0.109544	−	0.264463i
$700$	2.59150	−	5.91095i	0.0979495	−	0.223413i
$701$	−30.2444	−	30.2444i	−1.14232	−	1.14232i	−0.988026	−	0.154290i	$-0.950691\pi$
$701$	−30.2444	−	30.2444i	−1.14232	−	1.14232i	−0.154290	−	0.988026i	$-0.549309\pi$
$702$	−0.950524	+	0.189071i	−0.0358752	+	0.00713602i
$703$	12.7693	−	8.53218i	0.481604	−	0.321797i
$704$	3.52849	+	5.28076i	0.132985	+	0.199026i
$705$	6.19136	−	3.22825i	0.233180	−	0.121583i
$706$	6.60080	−	2.73414i	0.248425	−	0.102901i
$707$	8.72906	+	1.73632i	0.328290	+	0.0653010i
$708$	4.69506	+	7.02665i	0.176451	+	0.264078i
$709$	−10.6544	−	7.11906i	−0.400135	−	0.267362i	0.339180	−	0.940722i	$-0.389851\pi$
$709$	−10.6544	−	7.11906i	−0.400135	−	0.267362i	−0.739315	+	0.673360i	$0.764851\pi$
$710$	13.6131	−	1.20012i	0.510892	−	0.0450397i
$711$	3.08856	−	0.614353i	0.115830	−	0.0230401i
$712$	−0.266616	−	0.643668i	−0.00999185	−	0.0241225i
$713$	−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
$717$	−23.0914	−	15.4292i	−0.862364	−	0.576214i
$718$		−	13.6046i		−	0.507720i
$719$	−22.3812	+	33.4958i	−0.834676	+	1.24918i	0.131504	+	0.991316i	$0.458019\pi$
$719$	−22.3812	+	33.4958i	−0.834676	+	1.24918i	−0.966181	+	0.257866i	$0.916981\pi$
$720$	0.241955	−	2.22294i	0.00901714	−	0.0828440i
$721$	−7.58913	+	5.07089i	−0.282634	+	0.188850i
$722$	−14.2793	−	5.91469i	−0.531421	−	0.220122i
$723$	4.68155	+	1.93916i	0.174109	+	0.0721181i
$724$	−5.20872	+	3.48036i	−0.193581	+	0.129346i
$725$	−0.181435	+	8.85515i	−0.00673833	+	0.328872i
$726$	−16.2986	+	24.3926i	−0.604898	+	0.905294i
$727$			34.5928i			1.28298i	0.767132	+	0.641489i	$0.221683\pi$
$727$			34.5928i			1.28298i	−0.767132	+	0.641489i	$0.778317\pi$
$728$	1.04016	+	0.695012i	0.0385509	+	0.0257589i
$729$	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
$733$	−12.9480	−	31.2591i	−0.478244	−	1.15458i	−0.960432	−	0.278515i	$-0.910158\pi$
$733$	−12.9480	−	31.2591i	−0.478244	−	1.15458i	0.482188	−	0.876068i	$-0.339842\pi$
$734$	9.89297	−	1.96783i	0.365156	−	0.0726341i
$735$	1.04738	+	11.8806i	0.0386334	+	0.438224i
$736$	2.44851	+	1.63604i	0.0902531	+	0.0603052i
$737$	31.6194	+	47.3217i	1.16471	+	1.74312i
$738$	−9.57269	−	1.90413i	−0.352376	−	0.0700919i
$739$	−9.58712	+	3.97111i	−0.352668	+	0.146080i	−0.551982	−	0.833856i	$-0.686128\pi$
$739$	−9.58712	+	3.97111i	−0.352668	+	0.146080i	0.199315	+	0.979936i	$0.436128\pi$
$740$	−5.47360	+	17.4004i	−0.201214	+	0.639651i
$741$	1.01364	+	1.51703i	0.0372372	+	0.0557293i
$742$	11.9933	−	8.01366i	0.440288	−	0.294191i
$743$	−35.3122	+	7.02404i	−1.29548	+	0.257687i	−0.794231	−	0.607616i	$-0.792126\pi$
$743$	−35.3122	+	7.02404i	−1.29548	+	0.257687i	−0.501249	+	0.865303i	$0.667126\pi$
$744$	−6.13059	−	6.13059i	−0.224758	−	0.224758i
$745$	−44.7573	+	13.0779i	−1.63978	+	0.479136i
$746$	6.56566	−	15.8509i	0.240386	−	0.580343i
$747$	−12.1818	−	12.1818i	−0.445709	−	0.445709i
$748$	25.2231	−	7.03689i	0.922249	−	0.257294i
$749$		−	10.3553i		−	0.378373i
$750$	−1.43721	+	11.0876i	−0.0524793	+	0.404861i
$751$	−3.32985	−	16.7403i	−0.121508	−	0.610862i	−0.992769	−	0.120042i	$-0.961697\pi$
$751$	−3.32985	−	16.7403i	−0.121508	−	0.610862i	0.871261	−	0.490820i	$-0.163303\pi$
$752$	−3.12264			−0.113871
$753$	2.17330	+	10.9259i	0.0791994	+	0.398162i
$754$	−1.68376	−	0.334921i	−0.0613189	−	0.0121971i
$755$	−8.14007	−	10.1285i	−0.296248	−	0.368614i
$756$	−0.493974	−	1.19256i	−0.0179657	−	0.0433730i
$757$	7.40565	−	17.8788i	0.269163	−	0.649817i	−0.730282	−	0.683146i	$-0.760611\pi$
$757$	7.40565	−	17.8788i	0.269163	−	0.649817i	0.999444	+	0.0333296i	$0.0106111\pi$
$758$	−2.07992	+	10.4565i	−0.0755460	+	0.379795i
$759$	−3.64872	+	18.3434i	−0.132440	+	0.665822i
$760$	−4.04066	+	1.18066i	−0.146570	+	0.0428271i
$761$	0.114457	−	0.114457i	0.00414906	−	0.00414906i	−0.705029	−	0.709178i	$-0.749066\pi$
$761$	0.114457	−	0.114457i	0.00414906	−	0.00414906i	0.709178	+	0.705029i	$0.249066\pi$
$762$	−3.09913	+	4.63818i	−0.112270	+	0.168023i
$763$	9.71813	−	4.02538i	0.351820	−	0.145729i
$764$	−15.8158			−0.572194
$765$	−8.39785	−	3.80476i	−0.303625	−	0.137561i
$766$	−12.0178			−0.434220
$767$	7.56670	−	3.13423i	0.273218	−	0.113170i
$768$	−0.555570	+	0.831470i	−0.0200474	+	0.0300031i
$769$	24.1686	−	24.1686i	0.871542	−	0.871542i	−0.121098	−	0.992641i	$-0.538642\pi$
$769$	24.1686	−	24.1686i	0.871542	−	0.871542i	0.992641	+	0.121098i	$0.0386417\pi$
$770$	−16.0776	−	8.80659i	−0.579398	−	0.317368i
$771$	3.78261	−	19.0164i	0.136227	−	0.684860i
$772$	−2.61078	+	13.1253i	−0.0939640	+	0.472389i
$773$	9.78154	−	23.6147i	0.351818	−	0.849363i	−0.644578	−	0.764538i	$-0.722967\pi$
$773$	9.78154	−	23.6147i	0.351818	−	0.849363i	0.996396	−	0.0848245i	$-0.0270330\pi$
$774$	−1.41301	−	3.41130i	−0.0507895	−	0.122617i
$775$	30.0186	+	31.2744i	1.07830	+	1.12341i
$776$	−8.91855	−	1.77401i	−0.320157	−	0.0636832i
$777$	2.05430	+	10.3277i	0.0736976	+	0.370503i
$778$	15.6669			0.561685
$779$	3.58471	+	18.0215i	0.128435	+	0.645689i
$780$	−2.06721	−	0.650277i	−0.0740180	−	0.0232837i
$781$		−	38.8155i		−	1.38893i
$782$	9.55625	−	7.48992i	0.341731	−	0.267839i
$783$	1.25257	+	1.25257i	0.0447632	+	0.0447632i
$784$	2.04115	−	4.92778i	0.0728984	−	0.175992i
$785$	10.8384	−	19.7869i	0.386838	−	0.706226i
$786$	11.1407	+	11.1407i	0.397375	+	0.397375i
$787$	−36.9701	+	7.35381i	−1.31784	+	0.262135i	−0.803426	−	0.595405i	$-0.796992\pi$
$787$	−36.9701	+	7.35381i	−1.31784	+	0.262135i	−0.514417	+	0.857540i	$0.671992\pi$
$788$	−10.5917	+	7.07715i	−0.377314	+	0.252113i
$789$	−13.4026	−	20.0584i	−0.477145	−	0.714098i
$790$	6.71704	+	2.11296i	0.238982	+	0.0751759i
$791$	−4.39864	+	1.82197i	−0.156397	+	0.0647820i
$792$	−6.22909	−	1.23904i	−0.221341	−	0.0440274i
$793$	7.99233	+	11.9614i	0.283816	+	0.424760i
$794$	11.0113	+	7.35749i	0.390775	+	0.261107i
$795$	−16.0485	+	19.1518i	−0.569183	+	0.679243i
$796$	−0.515682	+	0.102576i	−0.0182779	+	0.00363569i
$797$	11.7825	+	28.4456i	0.417359	+	1.00759i	0.983110	+	0.183018i	$0.0585865\pi$
$797$	11.7825	+	28.4456i	0.417359	+	1.00759i	−0.565751	+	0.824576i	$0.691413\pi$
$798$	−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
$802$	−16.6679	−	11.1371i	−0.588563	−	0.393265i
$803$		−	62.6952i		−	2.21247i
$804$	−4.97855	+	7.45092i	−0.175580	+	0.262774i
$805$	−8.44981	−	0.919717i	−0.297817	−	0.0324158i
$806$	−6.98638	+	4.66815i	−0.246085	+	0.164429i
$807$	4.54314	+	1.88183i	0.159926	+	0.0662436i
$808$	6.37007	+	2.63857i	0.224098	+	0.0928246i
$809$	15.8678	−	10.6025i	0.557882	−	0.372765i	−0.244433	−	0.969666i	$-0.578602\pi$
$809$	15.8678	−	10.6025i	0.557882	−	0.372765i	0.802315	+	0.596901i	$0.203602\pi$
$810$	1.40077	+	1.74294i	0.0492179	+	0.0612408i
$811$	−23.1205	+	34.6023i	−0.811872	+	1.21505i	0.161738	+	0.986834i	$0.448290\pi$
$811$	−23.1205	+	34.6023i	−0.811872	+	1.21505i	−0.973610	+	0.228218i	$0.926710\pi$
$812$		−	2.28656i		−	0.0802424i
$813$	1.97675	+	1.32082i	0.0693277	+	0.0463233i
$814$	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
$818$	13.6742	+	33.0125i	0.478109	+	1.15426i
$819$	−1.22695	+	0.244056i	−0.0428732	+	0.00852800i
$820$	−16.7279	−	14.0174i	−0.584164	−	0.489510i
$821$	−11.6571	−	7.78902i	−0.406836	−	0.271839i	0.335270	−	0.942122i	$-0.391173\pi$
$821$	−11.6571	−	7.78902i	−0.406836	−	0.271839i	−0.742105	+	0.670283i	$0.766173\pi$
$822$	−3.93756	−	5.89297i	−0.137338	−	0.205541i
$823$	26.7810	+	5.32707i	0.933526	+	0.185690i	0.638344	−	0.769751i	$-0.279620\pi$
$823$	26.7810	+	5.32707i	0.933526	+	0.185690i	0.295182	+	0.955441i	$0.404620\pi$
$824$	−6.53275	+	2.70595i	−0.227579	+	0.0942664i
$825$	31.0120	+	6.83192i	1.07970	+	0.237857i
$826$	6.06046	+	9.07012i	0.210870	+	0.315590i
$827$	27.9045	−	18.6452i	0.970335	−	0.648357i	0.0339842	−	0.999422i	$-0.489180\pi$
$827$	27.9045	−	18.6452i	0.970335	−	0.648357i	0.936351	+	0.351065i	$0.114180\pi$
$828$	−2.88821	+	0.574501i	−0.100372	+	0.0199653i
$829$	32.8754	+	32.8754i	1.14181	+	1.14181i	0.988119	+	0.153689i	$0.0491154\pi$
$829$	32.8754	+	32.8754i	1.14181	+	1.14181i	0.153689	+	0.988119i	$0.450885\pi$
$830$	−10.8042	−	36.9761i	−0.375021	−	1.28346i
$831$	0.0124299	−	0.0300084i	0.000431187	−	0.00104098i
$832$	0.685289	+	0.685289i	0.0237581	+	0.0237581i
$833$	−16.6823	−	14.3296i	−0.578008	−	0.496493i
$834$			1.00683i			0.0348637i
$835$	17.0420	+	32.6843i	0.589763	+	1.13109i
$836$	2.33262	+	11.7269i	0.0806753	+	0.405582i
$837$	8.66996			0.299678
$838$	3.70095	+	18.6060i	0.127847	+	0.642732i
$839$	−53.2083	−	10.5838i	−1.83696	−	0.365393i	−0.850052	−	0.526699i	$-0.823429\pi$
$839$	−53.2083	−	10.5838i	−1.83696	−	0.365393i	−0.986904	+	0.161306i	$0.948429\pi$
$840$	0.312320	−	2.86941i	0.0107761	−	0.0990039i
$841$	−9.89701	−	23.8935i	−0.341276	−	0.823914i
$842$	−5.50524	+	13.2908i	−0.189723	+	0.458032i
$843$	−4.08507	+	20.5370i	−0.140697	+	0.707333i
$844$	0.729540	−	3.66764i	0.0251118	−	0.126246i
$845$	12.9559	−	23.6528i	0.445696	−	0.813680i
$846$	2.20804	−	2.20804i	0.0759140	−	0.0759140i
$847$	−21.0385	+	31.4864i	−0.722892	+	1.08188i
$848$	10.3239	−	4.27629i	0.354523	−	0.146848i
$849$	0.319623			0.0109694
$850$	−12.3822	−	16.4828i	−0.424705	−	0.565355i
$851$	24.0225			0.823481
$852$	5.64637	−	2.33880i	0.193442	−	0.0801261i
$853$	0.0140686	−	0.0210551i	0.000481698	−	0.000720912i	−0.831229	−	0.555931i	$-0.812362\pi$
$853$	0.0140686	−	0.0210551i	0.000481698	−	0.000720912i	0.831710	+	0.555210i	$0.187362\pi$
$854$	−13.5486	+	13.5486i	−0.463624	+	0.463624i
$855$	2.02232	−	3.69203i	0.0691620	−	0.126265i
$856$	1.56507	−	7.86811i	0.0534928	−	0.268927i
$857$	5.76832	−	28.9993i	0.197042	−	0.990597i	−0.748013	−	0.663684i	$-0.768992\pi$
$857$	5.76832	−	28.9993i	0.197042	−	0.990597i	0.945055	−	0.326912i	$-0.106008\pi$
$858$	−2.35548	+	5.68663i	−0.0804147	+	0.194138i
$859$	−19.3336	−	46.6754i	−0.659653	−	1.59254i	−0.798340	−	0.602208i	$-0.794288\pi$
$859$	−19.3336	−	46.6754i	−0.659653	−	1.59254i	0.138686	−	0.990336i	$-0.455712\pi$
$860$	0.893388	−	8.20791i	0.0304643	−	0.279887i
$861$	−12.3566	−	2.45788i	−0.421112	−	0.0837643i
$862$	−3.33880	−	16.7853i	−0.113720	−	0.571709i
$863$	26.2240			0.892675			0.446338	−	0.894865i	$-0.352728\pi$
$863$	26.2240			0.892675			0.446338	+	0.894865i	$0.352728\pi$
$864$	−0.195090	−	0.980785i	−0.00663711	−	0.0333670i
$865$	−7.73561	−	14.8359i	−0.263019	−	0.504435i
$866$		−	12.6442i		−	0.429667i
$867$	15.9822	−	5.79390i	0.542784	−	0.196771i
$868$	−7.91346	−	7.91346i	−0.268600	−	0.268600i
$869$	7.65372	−	18.4777i	0.259635	−	0.626814i
$870$	1.11093	+	3.80200i	0.0376639	+	0.128900i
$871$	6.14098	+	6.14098i	0.208079	+	0.208079i
$872$	7.99239	−	1.58978i	0.270656	−	0.0538369i
$873$	7.56078	−	5.05195i	0.255894	−	0.170983i
$874$	3.08001	+	4.60955i	0.104183	+	0.155920i
$875$	−1.85517	+	14.3120i	−0.0627162	+	0.483835i
$876$	9.12010	−	3.77767i	0.308140	−	0.127636i
$877$	9.63086	+	1.91570i	0.325211	+	0.0646885i	0.354996	−	0.934868i	$-0.384482\pi$
$877$	9.63086	+	1.91570i	0.325211	+	0.0646885i	−0.0297849	+	0.999556i	$0.509482\pi$
$878$	−7.50645	−	11.2342i	−0.253330	−	0.379136i
$879$	−24.4679	−	16.3489i	−0.825281	−	0.551435i
$880$	−10.8851	−	9.12133i	−0.366936	−	0.307480i
$881$	−31.2221	+	6.21047i	−1.05190	+	0.209236i	−0.690618	−	0.723220i	$-0.742661\pi$
$881$	−31.2221	+	6.21047i	−1.05190	+	0.209236i	−0.361283	+	0.932456i	$0.617661\pi$
$882$	2.04115	+	4.92778i	0.0687292	+	0.165927i
$883$	3.56802	−	3.56802i	0.120074	−	0.120074i	−0.644517	−	0.764590i	$-0.722941\pi$
$883$	3.56802	−	3.56802i	0.120074	−	0.120074i	0.764590	+	0.644517i	$0.222941\pi$
$884$	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
$887$	−44.8202	−	29.9479i	−1.50491	−	1.00555i	−0.988836	−	0.149009i	$-0.952392\pi$
$887$	−44.8202	−	29.9479i	−1.50491	−	1.00555i	−0.516078	−	0.856542i	$-0.672608\pi$
$888$			8.15762i			0.273752i
$889$	−4.00041	+	5.98704i	−0.134170	+	0.200799i
$890$	0.975916	+	1.21431i	0.0327128	+	0.0407038i
$891$	5.28076	−	3.52849i	0.176912	−	0.118209i
$892$	−1.50288	−	0.622511i	−0.0503200	−	0.0208432i
$893$	−5.43119	−	2.24967i	−0.181748	−	0.0752825i
$894$	−17.3387	+	11.5853i	−0.579892	+	0.387472i
$895$	26.3281	+	2.86568i	0.880052	+	0.0957890i
$896$	−0.717139	+	1.07327i	−0.0239579	+	0.0358556i
$897$			2.85393i			0.0952900i
$898$	−26.4838	−	17.6959i	−0.883775	−	0.590520i
$899$	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
$903$	−1.82393	−	4.40337i	−0.0606967	−	0.146535i
$904$	−3.61753	+	0.719571i	−0.120317	+	0.0239326i
$905$	8.99690	−	10.7366i	0.299067	−	0.356896i
$906$	−4.83180	−	3.22850i	−0.160526	−	0.107260i
$907$	18.3334	+	27.4379i	0.608750	+	0.911059i	0.999957	−	0.00924346i	$-0.00294233\pi$
$907$	18.3334	+	27.4379i	0.608750	+	0.911059i	−0.391207	+	0.920303i	$0.627942\pi$
$908$	−10.0244	−	1.99398i	−0.332672	−	0.0661725i
$909$	−6.37007	+	2.63857i	−0.211282	+	0.0875159i
$910$	−2.66839	−	0.839389i	−0.0884562	−	0.0278255i
$911$	−2.36178	−	3.53465i	−0.0782493	−	0.117108i	0.790281	−	0.612745i	$-0.209935\pi$
$911$	−2.36178	−	3.53465i	−0.0782493	−	0.117108i	−0.868530	+	0.495637i	$0.834935\pi$
$912$	−1.56532	+	1.04592i	−0.0518330	+	0.0346337i
$913$	−107.313	+	21.3458i	−3.55153	+	0.706443i
$914$	−5.58847	−	5.58847i	−0.184850	−	0.184850i
$915$	15.9455	−	29.1107i	0.527142	−	0.962371i
$916$	−7.94120	+	19.1718i	−0.262385	+	0.633453i
$917$	14.3806	+	14.3806i	0.474888	+	0.474888i
$918$	−4.09314	−	0.496170i	−0.135094	−	0.0163760i
$919$		−	52.2065i		−	1.72213i	−0.508491	−	0.861067i	$-0.669797\pi$
$919$		−	52.2065i		−	1.72213i	0.508491	−	0.861067i	$-0.330203\pi$
$920$	−6.28131	−	1.97590i	−0.207089	−	0.0651434i
$921$	4.61478	+	23.2001i	0.152062	+	0.764469i
$922$	−12.1695			−0.400782
$923$	−1.15552	−	5.80921i	−0.0380345	−	0.191213i
$924$	−8.04061	−	1.59938i	−0.264517	−	0.0526156i
$925$	0.835540	−	40.7795i	0.0274724	−	1.34082i
$926$	−7.25032	−	17.5038i	−0.238260	−	0.575211i
$927$	2.70595	−	6.53275i	0.0888752	−	0.214564i
$928$	0.345583	−	1.73737i	0.0113443	−	0.0570318i
$929$	−8.97586	+	45.1247i	−0.294489	+	1.48049i	0.496164	+	0.868229i	$0.334741\pi$
$929$	−8.97586	+	45.1247i	−0.294489	+	1.48049i	−0.790653	+	0.612265i	$0.790259\pi$
$930$	17.0030	+	9.31344i	0.557549	+	0.305400i
$931$	7.10033	−	7.10033i	0.232704	−	0.232704i
$932$	4.20462	−	6.29266i	0.137727	−	0.206123i
$933$	13.7004	−	5.67490i	0.448531	−	0.185788i
$934$	36.5722			1.19668
$935$	−49.7238	+	30.9220i	−1.62614	+	1.01126i
$936$	−0.969145			−0.0316775
$937$	9.47003	−	3.92262i	0.309372	−	0.128146i	−0.222595	−	0.974911i	$-0.571453\pi$
$937$	9.47003	−	3.92262i	0.309372	−	0.128146i	0.531968	+	0.846765i	$0.321453\pi$
$938$	−6.42639	+	9.61778i	−0.209829	+	0.314032i
$939$	−14.6198	+	14.6198i	−0.477098	+	0.477098i
$940$	6.70219	−	1.95835i	0.218601	−	0.0638743i
$941$	1.93627	−	9.73431i	0.0631207	−	0.317329i	−0.936306	−	0.351185i	$-0.885779\pi$
$941$	1.93627	−	9.73431i	0.0631207	−	0.317329i	0.999427	+	0.0338559i	$0.0107787\pi$
$942$	1.96837	−	9.89566i	0.0641329	−	0.322418i
$943$	−10.9990	+	26.5540i	−0.358178	+	0.864718i
$944$	3.23401	+	7.80760i	0.105258	+	0.254116i
$945$	1.80813	+	2.24982i	0.0588186	+	0.0731867i
$946$	−23.0001	−	4.57500i	−0.747797	−	0.148746i
$947$	−3.42519	−	17.2196i	−0.111304	−	0.559562i	−0.995685	−	0.0927970i	$-0.970419\pi$
$947$	−3.42519	−	17.2196i	−0.111304	−	0.559562i	0.884381	−	0.466765i	$-0.154581\pi$
$948$	3.14907			0.102277
$949$	−1.86642	−	9.38312i	−0.0605865	−	0.304589i
$950$	7.93210	−	5.06815i	0.257351	−	0.164433i
$951$			22.1681i			0.718851i
$952$	3.28312	+	4.18887i	0.106407	+	0.135762i
$953$	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
$955$	33.9457	−	9.91876i	1.09846	−	0.320964i
$956$	−19.6376	−	19.6376i	−0.635126	−	0.635126i
$957$	11.0342	−	2.19484i	0.356686	−	0.0709492i
$958$	22.7803	−	15.2213i	0.735997	−	0.491778i
$959$	−5.08267	−	7.60675i	−0.164128	−	0.245635i
$960$	0.670980	−	2.13302i	0.0216558	−	0.0688430i
$961$	40.8061	−	16.9024i	1.31633	−	0.545240i
$962$	7.75401	+	1.54237i	0.249999	+	0.0497280i
$963$	4.45693	+	6.67027i	0.143623	+	0.214946i
$964$	4.21328	+	2.81522i	0.135701	+	0.0906723i
$965$	−2.62788	−	29.8084i	−0.0845943	−	0.959566i
$966$	−3.72815	+	0.741575i	−0.119951	+	0.0238598i
$967$	1.86311	+	4.49794i	0.0599136	+	0.144644i	0.951001	−	0.309187i	$-0.100057\pi$
$967$	1.86311	+	4.49794i	0.0599136	+	0.144644i	−0.891088	+	0.453831i	$0.850057\pi$
$968$	−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	−0.0942840	−	0.995545i	$-0.530056\pi$
$971$	−26.9513	−	11.1636i	−0.864910	−	0.358257i	−0.770626	+	0.637288i	$0.780056\pi$
$972$	0.831470	+	0.555570i	0.0266694	+	0.0178199i
$973$			1.29963i			0.0416643i
$974$	−5.09357	+	7.62306i	−0.163208	+	0.244259i
$975$	4.84471	+	0.0992642i	0.155155	+	0.00317900i
$976$	−12.3422	+	8.24678i	−0.395063	+	0.263973i
$977$	−7.74704	−	3.20893i	−0.247850	−	0.102663i	0.255300	−	0.966862i	$-0.417826\pi$
$977$	−7.74704	−	3.20893i	−0.247850	−	0.102663i	−0.503150	+	0.864199i	$0.667826\pi$
$978$	5.47889	+	2.26943i	0.175196	+	0.0725684i
$979$	3.67911	−	2.45830i	0.117585	−	0.0785678i
$980$	−1.29054	+	11.8567i	−0.0412248	+	0.378748i
$981$	−4.52732	+	6.77562i	−0.144546	+	0.216329i
$982$		−	0.504807i		−	0.0161090i
$983$	51.3571	+	34.3157i	1.63804	+	1.09450i	0.914804	+	0.403897i	$0.132345\pi$
$983$	51.3571	+	34.3157i	1.63804	+	1.09450i	0.723233	+	0.690604i	$0.242655\pi$
$984$	−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
$988$	0.698210	+	1.68563i	0.0222130	+	0.0536270i
$989$	−10.6643	+	2.12127i	−0.339106	+	0.0674524i
$990$	14.1467	−	1.24716i	0.449611	−	0.0396372i
$991$	−34.5776	−	23.1040i	−1.09839	−	0.733923i	−0.132067	−	0.991241i	$-0.542161\pi$
$991$	−34.5776	−	23.1040i	−1.09839	−	0.733923i	−0.966327	+	0.257318i	$0.917161\pi$
$992$	−4.81677	−	7.20881i	−0.152933	−	0.228880i
$993$	0.872312	+	0.173514i	0.0276820	+	0.00550629i
$994$	7.28844	−	3.01897i	0.231175	−	0.0957559i
$995$	1.04249	−	0.543567i	0.0330491	−	0.0172322i
$996$	−9.57118	−	14.3243i	−0.303275	−	0.453882i
$997$	32.0634	−	21.4241i	1.01546	−	0.678508i	0.0677692	−	0.997701i	$-0.478412\pi$
$997$	32.0634	−	21.4241i	1.01546	−	0.678508i	0.947690	+	0.319193i	$0.103412\pi$
$998$	−11.3111	+	2.24993i	−0.358048	+	0.0712201i
$999$	−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.bi.a.283.6	yes	64
5.2	odd	4		510.2.bd.a.487.3	yes	64
17.14	odd	16		510.2.bd.a.133.3	✓	64
85.82	even	16	inner	510.2.bi.a.337.6	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
510.2.bd.a.133.3	✓	64	17.14	odd	16
510.2.bd.a.487.3	yes	64	5.2	odd	4
510.2.bi.a.283.6	yes	64	1.1	even	1	trivial
510.2.bi.a.337.6	yes	64	85.82	even	16	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:	\( N \)	\(=\)	\( 510 = 2 \cdot 3 \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	510.bi (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.923880 + 0.382683i) q^{2} +(0.555570 - 0.831470i) q^{3} +(0.707107 - 0.707107i) q^{4} +(-1.07422 + 1.96114i) q^{5} +(-0.195090 + 0.980785i) q^{6} +(-0.251826 + 1.26601i) q^{7} +(-0.382683 + 0.923880i) q^{8} +(-0.382683 - 0.923880i) q^{9} +(0.241955 - 2.22294i) q^{10} +(-6.22909 - 1.23904i) q^{11} +(-0.195090 - 0.980785i) q^{12} -0.969145 q^{13} +(-0.251826 - 1.26601i) q^{14} +(1.03382 + 1.98273i) q^{15} -1.00000i q^{16} +(-3.91770 - 1.28517i) q^{17} +(0.707107 + 0.707107i) q^{18} +(0.720439 - 1.73929i) q^{19} +(0.627144 + 2.14632i) q^{20} +(0.912745 + 0.912745i) q^{21} +(6.22909 - 1.23904i) q^{22} +(2.44851 - 1.63604i) q^{23} +(0.555570 + 0.831470i) q^{24} +(-2.69211 - 4.21338i) q^{25} +(0.895374 - 0.370876i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(0.717139 + 1.07327i) q^{28} +(-1.47287 - 0.984138i) q^{29} +(-1.71388 - 1.43618i) q^{30} +(-8.50337 + 1.69143i) q^{31} +(0.382683 + 0.923880i) 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} +(6.78281 + 4.53213i) q^{37} +1.88260i q^{38} +(-0.538428 + 0.805815i) q^{39} +(-1.40077 - 1.74294i) q^{40} +(-8.11534 + 5.42250i) q^{41} +(-1.19256 - 0.493974i) q^{42} +(-3.41130 - 1.41301i) q^{43} +(-5.28076 + 3.52849i) q^{44} +(2.22294 + 0.241955i) q^{45} +(-1.63604 + 2.44851i) q^{46} -3.12264i q^{47} +(-0.831470 - 0.555570i) 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} +(4.27629 + 10.3239i) q^{53} +(0.980785 - 0.195090i) q^{54} +(9.12133 - 10.8851i) q^{55} +(-1.07327 - 0.717139i) q^{56} +(-1.04592 - 1.56532i) q^{57} +(1.73737 + 0.345583i) q^{58} +(-7.80760 + 3.23401i) q^{59} +(2.13302 + 0.670980i) q^{60} +(-8.24678 - 12.3422i) q^{61} +(7.20881 - 4.81677i) q^{62} +(1.26601 - 0.251826i) q^{63} +(-0.707107 - 0.707107i) q^{64} +(1.04107 - 1.90063i) q^{65} +(2.43047 - 5.86767i) q^{66} +(-6.33649 - 6.33649i) q^{67} +(-3.67898 + 1.86148i) q^{68} -2.94479i q^{69} +(2.75334 + 0.866112i) q^{70} +(1.19231 + 5.99416i) q^{71} +1.00000 q^{72} +(1.92584 + 9.68185i) q^{73} +(-8.00087 - 1.59147i) q^{74} +(-4.99895 - 0.102425i) q^{75} +(-0.720439 - 1.73929i) q^{76} +(3.13729 - 7.57409i) q^{77} +(0.189071 - 0.950524i) q^{78} +(-0.614353 + 3.08856i) q^{79} +(1.96114 + 1.07422i) q^{80} +(-0.707107 + 0.707107i) q^{81} +(5.42250 - 8.11534i) q^{82} +(15.9163 - 6.59275i) q^{83} +1.29082 q^{84} +(6.72885 - 6.30258i) q^{85} +3.69237 q^{86} +(-1.63656 + 0.677886i) q^{87} +(3.52849 - 5.28076i) q^{88} +(-0.492642 + 0.492642i) q^{89} +(-2.14632 + 0.627144i) q^{90} +(0.244056 - 1.22695i) q^{91} +(0.574501 - 2.88821i) q^{92} +(-3.31785 + 8.01000i) q^{93} +(1.19498 + 2.88495i) q^{94} +(2.63708 + 3.28126i) q^{95} +(0.980785 + 0.195090i) q^{96} +(1.77401 + 8.91855i) q^{97} -5.33379 q^{98} +(1.23904 + 6.22909i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q + 16 q^{10} - 16 q^{25} + 16 q^{28} - 32 q^{29} - 16 q^{30} + 16 q^{31} - 16 q^{33} + 32 q^{35} - 16 q^{37} + 48 q^{41} - 32 q^{43} - 16 q^{44} + 64 q^{49} + 16 q^{50} + 32 q^{51} + 16 q^{52} - 32 q^{53}+ \cdots - 48 q^{97}+O(q^{100}) \) 64 * q + 16 * q^10 - 16 * q^25 + 16 * q^28 - 32 * q^29 - 16 * q^30 + 16 * q^31 - 16 * q^33 + 32 * q^35 - 16 * q^37 + 48 * q^41 - 32 * q^43 - 16 * q^44 + 64 * q^49 + 16 * q^50 + 32 * q^51 + 16 * q^52 - 32 * q^53 + 16 * q^55 + 16 * q^56 + 32 * q^57 - 32 * q^58 - 64 * q^59 + 16 * q^60 - 48 * q^61 - 32 * q^62 + 32 * q^65 - 16 * q^67 - 16 * q^70 - 64 * q^71 + 64 * q^72 - 48 * q^74 - 64 * q^75 - 48 * q^77 - 32 * q^78 + 64 * q^79 - 16 * q^80 + 32 * q^82 - 32 * q^83 - 64 * q^85 - 64 * q^86 - 48 * q^87 - 16 * q^88 + 32 * q^89 - 48 * q^93 + 16 * q^94 + 96 * q^95 - 48 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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