LMFDB - Embedded newform 867.2.h.k.712.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [867,2,Mod(688,867)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(867, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("867.688"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 867 = 3 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	867.h (of order $8$, degree $4$, not minimal)

Newform invariants

comment:select newform

sage:traces = [16,8,0,0,0,0,0,-32,0,0,0,0,0,0,-8,-24] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(16)] == traces)

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

Self dual:	no
Analytic conductor:	$6.92302985525$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8x^{14} + 32x^{12} + 296x^{10} + 1057x^{8} + 1184x^{6} + 512x^{4} - 512x^{2} + 256 $ x^16 - 8x^14 + 32x^12 + 296x^10 + 1057x^8 + 1184x^6 + 512x^4 - 512*x^2 + 256
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 51)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			712.1
Root			$-0.626225 - 1.51184i$ of defining polynomial
Character	$\chi$	$=$	867.712
Dual form			867.2.h.k.688.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.157113 - 0.157113i) q^{2} +(-0.382683 - 0.923880i) q^{3} -1.95063i q^{4} +(0.587961 - 0.243542i) q^{5} +(-0.0850290 + 0.205278i) q^{6} +(1.59687 + 0.661445i) q^{7} +(-0.620696 + 0.620696i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-0.130640 - 0.0541128i) q^{10} +(1.89452 - 4.57379i) q^{11} +(-1.80215 + 0.746474i) q^{12} -2.50625i q^{13} +(-0.146967 - 0.354811i) q^{14} +(-0.450006 - 0.450006i) q^{15} -3.70622 q^{16} +0.222191 q^{18} +(0.672198 + 0.672198i) q^{19} +(-0.475060 - 1.14690i) q^{20} -1.72844i q^{21} +(-1.01626 + 0.420947i) q^{22} +(0.812132 - 1.96066i) q^{23} +(0.810978 + 0.335918i) q^{24} +(-3.24915 + 3.24915i) q^{25} +(-0.393764 + 0.393764i) q^{26} +(0.923880 + 0.382683i) q^{27} +(1.29024 - 3.11490i) q^{28} +(8.85727 - 3.66880i) q^{29} +0.141404i q^{30} +(2.01782 + 4.87144i) q^{31} +(1.82369 + 1.82369i) q^{32} -4.95063 q^{33} +1.09999 q^{35} +(1.37930 + 1.37930i) q^{36} +(-3.24785 - 7.84101i) q^{37} -0.211222i q^{38} +(-2.31547 + 0.959100i) q^{39} +(-0.213780 + 0.516110i) q^{40} +(-6.39483 - 2.64882i) q^{41} +(-0.271560 + 0.271560i) q^{42} +(-5.05624 + 5.05624i) q^{43} +(-8.92177 - 3.69552i) q^{44} +(-0.243542 + 0.587961i) q^{45} +(-0.435642 + 0.180449i) q^{46} -8.10124i q^{47} +(1.41831 + 3.42410i) q^{48} +(-2.83726 - 2.83726i) q^{49} +1.02097 q^{50} -4.88877 q^{52} +(4.55687 + 4.55687i) q^{53} +(-0.0850290 - 0.205278i) q^{54} -3.15061i q^{55} +(-1.40173 + 0.580614i) q^{56} +(0.363791 - 0.878269i) q^{57} +(-1.96801 - 0.815176i) q^{58} +(-7.15061 + 7.15061i) q^{59} +(-0.877796 + 0.877796i) q^{60} +(2.74377 + 1.13651i) q^{61} +(0.448342 - 1.08239i) q^{62} +(-1.59687 + 0.661445i) q^{63} +6.83940i q^{64} +(-0.610376 - 1.47358i) q^{65} +(0.777809 + 0.777809i) q^{66} -7.70129 q^{67} -2.12220 q^{69} +(-0.172822 - 0.172822i) q^{70} +(0.146967 + 0.354811i) q^{71} -0.877796i q^{72} +(-6.01834 + 2.49288i) q^{73} +(-0.721645 + 1.74220i) q^{74} +(4.24522 + 1.75843i) q^{75} +(1.31121 - 1.31121i) q^{76} +(6.05062 - 6.05062i) q^{77} +(0.514478 + 0.213104i) q^{78} +(-0.908030 + 2.19218i) q^{79} +(-2.17912 + 0.902620i) q^{80} -1.00000i q^{81} +(0.588546 + 1.42088i) q^{82} +(-9.44563 - 9.44563i) q^{83} -3.37155 q^{84} +1.58880 q^{86} +(-6.77906 - 6.77906i) q^{87} +(1.66301 + 4.01485i) q^{88} -1.98875i q^{89} +(0.130640 - 0.0541128i) q^{90} +(1.65775 - 4.00215i) q^{91} +(-3.82453 - 1.58417i) q^{92} +(3.72844 - 3.72844i) q^{93} +(-1.27281 + 1.27281i) q^{94} +(0.558934 + 0.231518i) q^{95} +(0.986972 - 2.38276i) q^{96} +(2.80990 - 1.16390i) q^{97} +0.891542i q^{98} +(1.89452 + 4.57379i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{2} - 32 q^{8} - 8 q^{15} - 24 q^{16} - 8 q^{18} - 32 q^{25} - 40 q^{26} - 16 q^{32} - 24 q^{33} + 16 q^{35} - 48 q^{42} - 48 q^{43} - 32 q^{49} + 120 q^{50} - 32 q^{52} - 16 q^{53} - 56 q^{59}+ \cdots + 48 q^{94}+O(q^{100}) $ 16 * q + 8 * q^2 - 32 * q^8 - 8 * q^15 - 24 * q^16 - 8 * q^18 - 32 * q^25 - 40 * q^26 - 16 * q^32 - 24 * q^33 + 16 * q^35 - 48 * q^42 - 48 * q^43 - 32 * q^49 + 120 * q^50 - 32 * q^52 - 16 * q^53 - 56 * q^59 - 24 * q^60 + 24 * q^66 - 16 * q^67 - 24 * q^69 + 64 * q^70 + 64 * q^76 + 40 * q^77 - 16 * q^83 - 96 * q^84 - 16 * q^86 - 8 * q^87 + 16 * q^93 + 48 * q^94

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

$n$	$290$	$292$
$\chi(n)$	$1$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	−0.157113	−	0.157113i	−0.111096	−	0.111096i	0.649374	−	0.760469i	$-0.275031\pi$
$2$	−0.157113	−	0.157113i	−0.111096	−	0.111096i	−0.760469	+	0.649374i	$0.775031\pi$
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$3$	−0.382683	−	0.923880i	−0.220942	−	0.533402i
$4$		−	1.95063i		−	0.975315i
$5$	0.587961	−	0.243542i	0.262944	−	0.108915i	−0.247317	−	0.968935i	$-0.579549\pi$
$5$	0.587961	−	0.243542i	0.262944	−	0.108915i	0.510261	+	0.860020i	$0.329549\pi$
$6$	−0.0850290	+	0.205278i	−0.0347129	+	0.0838044i
$7$	1.59687	+	0.661445i	0.603560	+	0.250003i	0.663472	−	0.748201i	$-0.269082\pi$
$7$	1.59687	+	0.661445i	0.603560	+	0.250003i	−0.0599122	+	0.998204i	$0.519082\pi$
$8$	−0.620696	+	0.620696i	−0.219449	+	0.219449i
$9$	−0.707107	+	0.707107i	−0.235702	+	0.235702i
$10$	−0.130640	−	0.0541128i	−0.0413120	−	0.0171120i
$11$	1.89452	−	4.57379i	0.571221	−	1.37905i	−0.329296	−	0.944227i	$-0.606811\pi$
$11$	1.89452	−	4.57379i	0.571221	−	1.37905i	0.900517	−	0.434822i	$-0.143189\pi$
$12$	−1.80215	+	0.746474i	−0.520235	+	0.215489i
$13$		−	2.50625i		−	0.695108i	−0.937660	−	0.347554i	$-0.887012\pi$
$13$		−	2.50625i		−	0.695108i	0.937660	−	0.347554i	$-0.112988\pi$
$14$	−0.146967	−	0.354811i	−0.0392787	−	0.0948272i
$15$	−0.450006	−	0.450006i	−0.116191	−	0.116191i
$16$	−3.70622			−0.926556
$17$		0			0
$17$		0			0
$18$	0.222191			0.0523710
$19$	0.672198	+	0.672198i	0.154213	+	0.154213i	0.779997	−	0.625784i	$-0.215221\pi$
$19$	0.672198	+	0.672198i	0.154213	+	0.154213i	−0.625784	+	0.779997i	$0.715221\pi$
$20$	−0.475060	−	1.14690i	−0.106227	−	0.256454i
$21$		−	1.72844i		−	0.377176i
$22$	−1.01626	+	0.420947i	−0.216666	+	0.0897462i
$23$	0.812132	−	1.96066i	0.169341	−	0.408826i	−0.816311	−	0.577612i	$-0.803985\pi$
$23$	0.812132	−	1.96066i	0.169341	−	0.408826i	0.985653	+	0.168786i	$0.0539847\pi$
$24$	0.810978	+	0.335918i	0.165540	+	0.0685690i
$25$	−3.24915	+	3.24915i	−0.649830	+	0.649830i
$26$	−0.393764	+	0.393764i	−0.0772235	+	0.0772235i
$27$	0.923880	+	0.382683i	0.177801	+	0.0736475i
$28$	1.29024	−	3.11490i	0.243832	−	0.588662i
$29$	8.85727	−	3.66880i	1.64475	−	0.681279i	0.647988	−	0.761650i	$-0.275611\pi$
$29$	8.85727	−	3.66880i	1.64475	−	0.681279i	0.996765	+	0.0803715i	$0.0256107\pi$
$30$			0.141404i			0.0258167i
$31$	2.01782	+	4.87144i	0.362411	+	0.874937i	0.994947	+	0.100406i	$0.0320141\pi$
$31$	2.01782	+	4.87144i	0.362411	+	0.874937i	−0.632536	+	0.774531i	$0.717986\pi$
$32$	1.82369	+	1.82369i	0.322385	+	0.322385i
$33$	−4.95063			−0.861794
$34$		0			0
$35$	1.09999			0.185932
$36$	1.37930	+	1.37930i	0.229884	+	0.229884i
$37$	−3.24785	−	7.84101i	−0.533944	−	1.28905i	−0.928892	−	0.370351i	$-0.879237\pi$
$37$	−3.24785	−	7.84101i	−0.533944	−	1.28905i	0.394948	−	0.918703i	$-0.370763\pi$
$38$		−	0.211222i		−	0.0342647i
$39$	−2.31547	+	0.959100i	−0.370772	+	0.153579i
$40$	−0.213780	+	0.516110i	−0.0338016	+	0.0816042i
$41$	−6.39483	−	2.64882i	−0.998704	−	0.413677i	−0.177382	−	0.984142i	$-0.556763\pi$
$41$	−6.39483	−	2.64882i	−0.998704	−	0.413677i	−0.821322	+	0.570465i	$0.806763\pi$
$42$	−0.271560	+	0.271560i	−0.0419027	+	0.0419027i
$43$	−5.05624	+	5.05624i	−0.771070	+	0.771070i	−0.978294	−	0.207224i	$-0.933557\pi$
$43$	−5.05624	+	5.05624i	−0.771070	+	0.771070i	0.207224	+	0.978294i	$0.433557\pi$
$44$	−8.92177	−	3.69552i	−1.34501	−	0.557120i
$45$	−0.243542	+	0.587961i	−0.0363050	+	0.0876481i
$46$	−0.435642	+	0.180449i	−0.0642319	+	0.0266057i
$47$		−	8.10124i		−	1.18169i	−0.806786	−	0.590843i	$-0.798795\pi$
$47$		−	8.10124i		−	1.18169i	0.806786	−	0.590843i	$-0.201205\pi$
$48$	1.41831	+	3.42410i	0.204715	+	0.494227i
$49$	−2.83726	−	2.83726i	−0.405323	−	0.405323i
$50$	1.02097			0.144387
$51$		0			0
$52$	−4.88877			−0.677950
$53$	4.55687	+	4.55687i	0.625934	+	0.625934i	0.947042	−	0.321109i	$-0.104055\pi$
$53$	4.55687	+	4.55687i	0.625934	+	0.625934i	−0.321109	+	0.947042i	$0.604055\pi$
$54$	−0.0850290	−	0.205278i	−0.0115710	−	0.0279348i
$55$		−	3.15061i		−	0.424828i
$56$	−1.40173	+	0.580614i	−0.187314	+	0.0775878i
$57$	0.363791	−	0.878269i	0.0481853	−	0.116330i
$58$	−1.96801	−	0.815176i	−0.258412	−	0.107038i
$59$	−7.15061	+	7.15061i	−0.930930	+	0.930930i	−0.997764	−	0.0668345i	$-0.978710\pi$
$59$	−7.15061	+	7.15061i	−0.930930	+	0.930930i	0.0668345	+	0.997764i	$0.478710\pi$
$60$	−0.877796	+	0.877796i	−0.113323	+	0.113323i
$61$	2.74377	+	1.13651i	0.351303	+	0.145515i	0.551355	−	0.834271i	$-0.314111\pi$
$61$	2.74377	+	1.13651i	0.351303	+	0.145515i	−0.200052	+	0.979785i	$0.564111\pi$
$62$	0.448342	−	1.08239i	0.0569394	−	0.137464i
$63$	−1.59687	+	0.661445i	−0.201187	+	0.0833343i
$64$			6.83940i			0.854925i
$65$	−0.610376	−	1.47358i	−0.0757078	−	0.182775i
$66$	0.777809	+	0.777809i	0.0957416	+	0.0957416i
$67$	−7.70129			−0.940862			−0.470431	−	0.882437i	$-0.655902\pi$
$67$	−7.70129			−0.940862			−0.470431	+	0.882437i	$0.655902\pi$
$68$		0			0
$69$	−2.12220			−0.255483
$70$	−0.172822	−	0.172822i	−0.0206562	−	0.0206562i
$71$	0.146967	+	0.354811i	0.0174418	+	0.0421083i	0.932361	−	0.361530i	$-0.117745\pi$
$71$	0.146967	+	0.354811i	0.0174418	+	0.0421083i	−0.914919	+	0.403638i	$0.867745\pi$
$72$		−	0.877796i		−	0.103449i
$73$	−6.01834	+	2.49288i	−0.704393	+	0.291769i	−0.705982	−	0.708230i	$-0.749494\pi$
$73$	−6.01834	+	2.49288i	−0.704393	+	0.291769i	0.00158913	+	0.999999i	$0.499494\pi$
$74$	−0.721645	+	1.74220i	−0.0838895	+	0.202527i
$75$	4.24522	+	1.75843i	0.490195	+	0.203046i
$76$	1.31121	−	1.31121i	0.150406	−	0.150406i
$77$	6.05062	−	6.05062i	0.689532	−	0.689532i
$78$	0.514478	+	0.213104i	0.0582531	+	0.0241292i
$79$	−0.908030	+	2.19218i	−0.102161	+	0.246639i	−0.966693	−	0.255939i	$-0.917615\pi$
$79$	−0.908030	+	2.19218i	−0.102161	+	0.246639i	0.864531	+	0.502579i	$0.167615\pi$
$80$	−2.17912	+	0.902620i	−0.243633	+	0.100916i
$81$		−	1.00000i		−	0.111111i
$82$	0.588546	+	1.42088i	0.0649940	+	0.156909i
$83$	−9.44563	−	9.44563i	−1.03679	−	1.03679i	−0.999297	−	0.0374961i	$-0.988062\pi$
$83$	−9.44563	−	9.44563i	−1.03679	−	1.03679i	−0.0374961	−	0.999297i	$-0.511938\pi$
$84$	−3.37155			−0.367866
$85$		0			0
$86$	1.58880			0.171325
$87$	−6.77906	−	6.77906i	−0.726791	−	0.726791i
$88$	1.66301	+	4.01485i	0.177277	+	0.427985i
$89$		−	1.98875i		−	0.210807i	−0.994430	−	0.105404i	$-0.966387\pi$
$89$		−	1.98875i		−	0.210807i	0.994430	−	0.105404i	$-0.0336135\pi$
$90$	0.130640	−	0.0541128i	0.0137707	−	0.00570400i
$91$	1.65775	−	4.00215i	0.173779	−	0.419540i
$92$	−3.82453	−	1.58417i	−0.398734	−	0.165161i
$93$	3.72844	−	3.72844i	0.386621	−	0.386621i
$94$	−1.27281	+	1.27281i	−0.131280	+	0.131280i
$95$	0.558934	+	0.231518i	0.0573455	+	0.0237533i
$96$	0.986972	−	2.38276i	0.100732	−	0.243190i
$97$	2.80990	−	1.16390i	0.285302	−	0.118176i	−0.235443	−	0.971888i	$-0.575654\pi$
$97$	2.80990	−	1.16390i	0.285302	−	0.118176i	0.520745	+	0.853712i	$0.325654\pi$
$98$			0.891542i			0.0900594i
$99$	1.89452	+	4.57379i	0.190407	+	0.459683i
$100$	6.33789	+	6.33789i	0.633789	+	0.633789i
$101$	18.5456			1.84536			0.922679	−	0.385569i	$-0.125995\pi$
$101$	18.5456			1.84536			0.922679	+	0.385569i	$0.125995\pi$
$102$		0			0
$103$	3.39501			0.334521			0.167260	−	0.985913i	$-0.446508\pi$
$103$	3.39501			0.334521			0.167260	+	0.985913i	$0.446508\pi$
$104$	1.55562	+	1.55562i	0.152541	+	0.152541i
$105$	−0.420947	−	1.01626i	−0.0410802	−	0.0991764i
$106$		−	1.43189i		−	0.139077i
$107$	12.1519	−	5.03348i	1.17477	−	0.486604i	0.292001	−	0.956418i	$-0.405679\pi$
$107$	12.1519	−	5.03348i	1.17477	−	0.486604i	0.882766	+	0.469813i	$0.155679\pi$
$108$	0.746474	−	1.80215i	0.0718295	−	0.173412i
$109$	16.0659	+	6.65470i	1.53883	+	0.637404i	0.981254	−	0.192721i	$-0.0617313\pi$
$109$	16.0659	+	6.65470i	1.53883	+	0.637404i	0.557577	+	0.830125i	$0.311731\pi$
$110$	−0.495001	+	0.495001i	−0.0471965	+	0.0471965i
$111$	−6.00125	+	6.00125i	−0.569613	+	0.569613i
$112$	−5.91836	−	2.45146i	−0.559232	−	0.231642i
$113$	0.296978	−	0.716969i	0.0279374	−	0.0674468i	−0.909295	−	0.416152i	$-0.863378\pi$
$113$	0.296978	−	0.716969i	0.0279374	−	0.0674468i	0.937233	+	0.348705i	$0.113378\pi$
$114$	−0.195144	+	0.0808312i	−0.0182769	+	0.00757053i
$115$		−	1.35058i		−	0.125942i
$116$	−7.15647	−	17.2773i	−0.664462	−	1.60415i
$117$	1.77219	+	1.77219i	0.163839	+	0.163839i
$118$	2.24691			0.206845
$119$		0			0
$120$	0.558634			0.0509961
$121$	−9.55213	−	9.55213i	−0.868375	−	0.868375i
$122$	−0.252522	−	0.609641i	−0.0228622	−	0.0551943i
$123$			6.92171i			0.624110i
$124$	9.50238	−	3.93602i	0.853339	−	0.353465i
$125$	−2.33678	+	5.64148i	−0.209008	+	0.504590i
$126$	0.354811	+	0.146967i	0.0316091	+	0.0130929i
$127$	7.67345	−	7.67345i	0.680908	−	0.680908i	−0.279297	−	0.960205i	$-0.590101\pi$
$127$	7.67345	−	7.67345i	0.680908	−	0.680908i	0.960205	+	0.279297i	$0.0901013\pi$
$128$	4.72193	−	4.72193i	0.417364	−	0.417364i
$129$	6.60630	+	2.73642i	0.581652	+	0.240928i
$130$	−0.135620	+	0.327416i	−0.0118947	+	0.0287163i
$131$	0.652465	−	0.270260i	0.0570062	−	0.0236127i	−0.353998	−	0.935246i	$-0.615178\pi$
$131$	0.652465	−	0.270260i	0.0570062	−	0.0236127i	0.411004	+	0.911633i	$0.365178\pi$
$132$			9.65685i			0.840521i
$133$	0.628790	+	1.51803i	0.0545230	+	0.131630i
$134$	1.20997	+	1.20997i	0.104526	+	0.104526i
$135$	0.636405			0.0547730
$136$		0			0
$137$	12.3125			1.05192			0.525962	−	0.850508i	$-0.323705\pi$
$137$	12.3125			1.05192			0.525962	+	0.850508i	$0.323705\pi$
$138$	0.333426	+	0.333426i	0.0283831	+	0.0283831i
$139$	5.10668	+	12.3286i	0.433143	+	1.04570i	0.978268	+	0.207345i	$0.0664822\pi$
$139$	5.10668	+	12.3286i	0.433143	+	1.04570i	−0.545125	+	0.838355i	$0.683518\pi$
$140$		−	2.14567i		−	0.181342i
$141$	−7.48457	+	3.10021i	−0.630314	+	0.261085i
$142$	0.0326549	−	0.0788359i	0.00274034	−	0.00661576i
$143$	−11.4630	−	4.74815i	−0.958588	−	0.397060i
$144$	2.62070	−	2.62070i	0.218391	−	0.218391i
$145$	4.31423	−	4.31423i	0.358277	−	0.358277i
$146$	1.33722	+	0.553896i	0.110669	+	0.0458407i
$147$	−1.53552	+	3.70706i	−0.126647	+	0.305753i
$148$	−15.2949	+	6.33536i	−1.25723	+	0.520764i
$149$		−	0.356892i		−	0.0292377i	−0.999893	−	0.0146189i	$-0.995347\pi$
$149$		−	0.356892i		−	0.0292377i	0.999893	−	0.0146189i	$-0.00465349\pi$
$150$	−0.390707	−	0.943250i	−0.0319011	−	0.0770161i
$151$	6.45813	+	6.45813i	0.525555	+	0.525555i	0.919244	−	0.393689i	$-0.128801\pi$
$151$	6.45813	+	6.45813i	0.525555	+	0.525555i	−0.393689	+	0.919244i	$0.628801\pi$
$152$	−0.834460			−0.0676837
$153$		0			0
$154$	−1.90126			−0.153208
$155$	2.37280	+	2.37280i	0.190588	+	0.190588i
$156$	1.87085	+	4.51663i	0.149788	+	0.361620i
$157$			17.5975i			1.40443i	0.711964	+	0.702216i	$0.247806\pi$
$157$			17.5975i			1.40443i	−0.711964	+	0.702216i	$0.752194\pi$
$158$	0.487083	−	0.201756i	0.0387503	−	0.0160509i
$159$	2.46616	−	5.95383i	0.195579	−	0.472170i
$160$	1.51640	+	0.628114i	0.119882	+	0.0496568i
$161$	2.59374	−	2.59374i	0.204415	−	0.204415i
$162$	−0.157113	+	0.157113i	−0.0123440	+	0.0123440i
$163$	15.3272	+	6.34874i	1.20052	+	0.497272i	0.891167	−	0.453676i	$-0.149888\pi$
$163$	15.3272	+	6.34874i	1.20052	+	0.497272i	0.309353	+	0.950947i	$0.399888\pi$
$164$	−5.16688	+	12.4739i	−0.403465	+	0.974052i
$165$	−2.91078	+	1.20568i	−0.226604	+	0.0938624i
$166$			2.96806i			0.230366i
$167$	−5.44308	−	13.1407i	−0.421198	−	1.01686i	−0.981995	−	0.188908i	$-0.939505\pi$
$167$	−5.44308	−	13.1407i	−0.421198	−	1.01686i	0.560797	−	0.827953i	$-0.310495\pi$
$168$	1.07283	+	1.07283i	0.0827710	+	0.0827710i
$169$	6.71872			0.516825
$170$		0			0
$171$	−0.950631			−0.0726966
$172$	9.86286	+	9.86286i	0.752036	+	0.752036i
$173$	0.724538	+	1.74919i	0.0550856	+	0.132988i	0.949026	−	0.315197i	$-0.102071\pi$
$173$	0.724538	+	1.74919i	0.0550856	+	0.132988i	−0.893941	+	0.448185i	$0.852071\pi$
$174$			2.13016i			0.161487i
$175$	−7.33760	+	3.03933i	−0.554670	+	0.229752i
$176$	−7.02153	+	16.9515i	−0.529268	+	1.27777i
$177$	9.34272	+	3.86988i	0.702242	+	0.290878i
$178$	−0.312459	+	0.312459i	−0.0234198	+	0.0234198i
$179$	15.7309	−	15.7309i	1.17579	−	1.17579i	0.194978	−	0.980808i	$-0.437536\pi$
$179$	15.7309	−	15.7309i	1.17579	−	1.17579i	0.980808	−	0.194978i	$-0.0624635\pi$
$180$	1.14690	+	0.475060i	0.0854846	+	0.0354089i
$181$	−4.44456	+	10.7301i	−0.330361	+	0.797563i	0.668202	+	0.743980i	$0.267064\pi$
$181$	−4.44456	+	10.7301i	−0.330361	+	0.797563i	−0.998563	+	0.0535830i	$0.982936\pi$
$182$	−0.889244	+	0.368337i	−0.0659151	+	0.0273029i
$183$		−	2.96983i		−	0.219536i
$184$	0.712887	+	1.72106i	0.0525547	+	0.126878i
$185$	−3.81922	−	3.81922i	−0.280795	−	0.280795i
$186$	−1.17157			−0.0859039
$187$		0			0
$188$	−15.8025			−1.15252
$189$	1.22219	+	1.22219i	0.0889013	+	0.0889013i
$190$	−0.0514414	−	0.124190i	−0.00373195	−	0.00900972i
$191$			6.63311i			0.479955i	0.970778	+	0.239978i	$0.0771401\pi$
$191$			6.63311i			0.479955i	−0.970778	+	0.239978i	$0.922860\pi$
$192$	6.31878	−	2.61732i	0.456019	−	0.188889i
$193$	−1.11655	+	2.69559i	−0.0803710	+	0.194033i	−0.958957	−	0.283551i	$-0.908487\pi$
$193$	−1.11655	+	2.69559i	−0.0803710	+	0.194033i	0.878586	+	0.477584i	$0.158487\pi$
$194$	−0.624336	−	0.258608i	−0.0448247	−	0.0185670i
$195$	−1.12783	+	1.12783i	−0.0807654	+	0.0807654i
$196$	−5.53445	+	5.53445i	−0.395318	+	0.395318i
$197$	4.18995	+	1.73553i	0.298521	+	0.123652i	0.526917	−	0.849917i	$-0.323348\pi$
$197$	4.18995	+	1.73553i	0.298521	+	0.123652i	−0.228395	+	0.973568i	$0.573348\pi$
$198$	0.420947	−	1.01626i	0.0299154	−	0.0722222i
$199$	2.27301	−	0.941512i	0.161129	−	0.0667420i	−0.300661	−	0.953731i	$-0.597207\pi$
$199$	2.27301	−	0.941512i	0.161129	−	0.0667420i	0.461790	+	0.886989i	$0.347207\pi$
$200$		−	4.03346i		−	0.285209i
$201$	2.94715	+	7.11506i	0.207876	+	0.501858i
$202$	−2.91376	−	2.91376i	−0.205011	−	0.205011i
$203$	16.5706			1.16303
$204$		0			0
$205$	−4.40501			−0.307659
$206$	−0.533401	−	0.533401i	−0.0371638	−	0.0371638i
$207$	0.812132	+	1.96066i	0.0564471	+	0.136275i
$208$			9.28872i			0.644057i
$209$	4.34798	−	1.80099i	0.300756	−	0.124577i
$210$	−0.0935308	+	0.225803i	−0.00645424	+	0.0155819i
$211$	−18.3887	−	7.61684i	−1.26593	−	0.524365i	−0.354205	−	0.935168i	$-0.615248\pi$
$211$	−18.3887	−	7.61684i	−1.26593	−	0.524365i	−0.911724	+	0.410803i	$0.865248\pi$
$212$	8.88877	−	8.88877i	0.610483	−	0.610483i
$213$	0.271560	−	0.271560i	0.0186070	−	0.0186070i
$214$	−2.70004	−	1.11839i	−0.184571	−	0.0764519i
$215$	−1.74147	+	4.20428i	−0.118767	+	0.286730i
$216$	−0.810978	+	0.335918i	−0.0551801	+	0.0228563i
$217$			9.11373i			0.618681i
$218$	−1.47862	−	3.56970i	−0.100145	−	0.241770i
$219$	4.60624	+	4.60624i	0.311261	+	0.311261i
$220$	−6.14567			−0.414341
$221$		0			0
$222$	1.88575			0.126563
$223$	−10.1562	−	10.1562i	−0.680111	−	0.680111i	0.279914	−	0.960025i	$-0.409694\pi$
$223$	−10.1562	−	10.1562i	−0.680111	−	0.680111i	−0.960025	+	0.279914i	$0.909694\pi$
$224$	1.70592	+	4.11846i	0.113982	+	0.275176i
$225$		−	4.59499i		−	0.306333i
$226$	−0.159304	+	0.0659860i	−0.0105968	+	0.00438932i
$227$	4.16145	−	10.0466i	0.276205	−	0.666818i	−0.723519	−	0.690304i	$-0.757477\pi$
$227$	4.16145	−	10.0466i	0.276205	−	0.666818i	0.999724	+	0.0234865i	$0.00747666\pi$
$228$	−1.71318	−	0.709621i	−0.113458	−	0.0469958i
$229$	13.4280	−	13.4280i	0.887345	−	0.887345i	−0.106923	−	0.994267i	$-0.534100\pi$
$229$	13.4280	−	13.4280i	0.887345	−	0.887345i	0.994267	+	0.106923i	$0.0340998\pi$
$230$	−0.212194	+	0.212194i	−0.0139916	+	0.0139916i
$231$	−7.90551	−	3.27457i	−0.520145	−	0.215451i
$232$	−3.22046	+	7.77487i	−0.211433	+	0.510445i
$233$	6.54179	−	2.70970i	0.428567	−	0.177518i	−0.157964	−	0.987445i	$-0.550493\pi$
$233$	6.54179	−	2.70970i	0.428567	−	0.177518i	0.586531	+	0.809926i	$0.300493\pi$
$234$		−	0.556867i		−	0.0364035i
$235$	−1.97299	−	4.76322i	−0.128704	−	0.310718i
$236$	13.9482	+	13.9482i	0.907950	+	0.907950i
$237$	2.37280			0.154130
$238$		0			0
$239$	−5.28872			−0.342099			−0.171049	−	0.985262i	$-0.554716\pi$
$239$	−5.28872			−0.342099			−0.171049	+	0.985262i	$0.554716\pi$
$240$	1.66782	+	1.66782i	0.107658	+	0.107658i
$241$	−2.21890	−	5.35689i	−0.142932	−	0.345068i	0.836160	−	0.548485i	$-0.184795\pi$
$241$	−2.21890	−	5.35689i	−0.142932	−	0.345068i	−0.979092	+	0.203417i	$0.934795\pi$
$242$			3.00153i			0.192945i
$243$	−0.923880	+	0.382683i	−0.0592669	+	0.0245492i
$244$	2.21690	−	5.35207i	0.141923	−	0.342631i
$245$	−2.35919	−	0.977210i	−0.150723	−	0.0624317i
$246$	1.08749	−	1.08749i	0.0693359	−	0.0693359i
$247$	1.68469	−	1.68469i	0.107195	−	0.107195i
$248$	−4.27613	−	1.77123i	−0.271535	−	0.112473i
$249$	−5.11194	+	12.3413i	−0.323956	+	0.782099i
$250$	1.25349	−	0.519212i	0.0792776	−	0.0328379i
$251$			8.33190i			0.525905i	0.964809	+	0.262952i	$0.0846962\pi$
$251$			8.33190i			0.525905i	−0.964809	+	0.262952i	$0.915304\pi$
$252$	1.29024	+	3.11490i	0.0812772	+	0.196221i
$253$	−7.42904	−	7.42904i	−0.467060	−	0.467060i
$254$	−2.41120			−0.151292
$255$		0			0
$256$	12.1950			0.762190
$257$	3.00920	+	3.00920i	0.187709	+	0.187709i	0.794705	−	0.606996i	$-0.207626\pi$
$257$	3.00920	+	3.00920i	0.187709	+	0.187709i	−0.606996	+	0.794705i	$0.707626\pi$
$258$	−0.608009	−	1.46786i	−0.0378530	−	0.0913851i
$259$		−	14.6694i		−	0.911509i
$260$	−2.87441	+	1.19062i	−0.178263	+	0.0738390i
$261$	−3.66880	+	8.85727i	−0.227093	+	0.548251i
$262$	−0.144972	−	0.0600494i	−0.00895641	−	0.00370987i
$263$	−6.43466	+	6.43466i	−0.396778	+	0.396778i	−0.877095	−	0.480317i	$-0.840522\pi$
$263$	−6.43466	+	6.43466i	−0.396778	+	0.396778i	0.480317	+	0.877095i	$0.340522\pi$
$264$	3.07283	−	3.07283i	0.189120	−	0.189120i
$265$	3.78905	+	1.56948i	0.232759	+	0.0964121i
$266$	0.139712	−	0.337294i	0.00856628	−	0.0206808i
$267$	−1.83737	+	0.761063i	−0.112445	+	0.0465763i
$268$			15.0224i			0.917637i
$269$	8.18254	+	19.7544i	0.498898	+	1.20445i	0.950078	+	0.312013i	$0.101003\pi$
$269$	8.18254	+	19.7544i	0.498898	+	1.20445i	−0.451180	+	0.892433i	$0.648997\pi$
$270$	−0.0999875	−	0.0999875i	−0.00608505	−	0.00608505i
$271$	19.3213			1.17368			0.586842	−	0.809702i	$-0.300371\pi$
$271$	19.3213			1.17368			0.586842	+	0.809702i	$0.300371\pi$
$272$		0			0
$273$	−4.33190			−0.262178
$274$	−1.93445	−	1.93445i	−0.116864	−	0.116864i
$275$	8.70532	+	21.0165i	0.524950	+	1.26734i
$276$			4.13964i			0.249177i
$277$	−3.08588	+	1.27821i	−0.185412	+	0.0768003i	−0.473458	−	0.880816i	$-0.656994\pi$
$277$	−3.08588	+	1.27821i	−0.185412	+	0.0768003i	0.288046	+	0.957617i	$0.406994\pi$
$278$	1.13466	−	2.73931i	0.0680524	−	0.164293i
$279$	−4.87144	−	2.01782i	−0.291646	−	0.120804i
$280$	−0.682757	+	0.682757i	−0.0408026	+	0.0408026i
$281$	−3.30752	+	3.30752i	−0.197310	+	0.197310i	−0.798846	−	0.601536i	$-0.794556\pi$
$281$	−3.30752	+	3.30752i	−0.197310	+	0.197310i	0.601536	+	0.798846i	$0.294556\pi$
$282$	1.66301	+	0.688840i	0.0990306	+	0.0410198i
$283$	3.84910	−	9.29255i	0.228805	−	0.552384i	−0.767227	−	0.641375i	$-0.778364\pi$
$283$	3.84910	−	9.29255i	0.228805	−	0.552384i	0.996032	+	0.0889908i	$0.0283642\pi$
$284$	0.692105	−	0.286679i	0.0410689	−	0.0170113i
$285$		−	0.604986i		−	0.0358363i
$286$	1.05500	+	2.54699i	0.0623833	+	0.150607i
$287$	−8.45966	−	8.45966i	−0.499358	−	0.499358i
$288$	−2.57908			−0.151974
$289$		0			0
$290$	−1.35564			−0.0796061
$291$	−2.15061	−	2.15061i	−0.126071	−	0.126071i
$292$	4.86268	+	11.7396i	0.284567	+	0.687005i
$293$			5.76934i			0.337048i	0.985698	+	0.168524i	$0.0539001\pi$
$293$			5.76934i			0.337048i	−0.985698	+	0.168524i	$0.946100\pi$
$294$	0.823678	−	0.341178i	0.0480378	−	0.0198979i
$295$	−2.46281	+	5.94575i	−0.143390	+	0.346175i
$296$	6.88281	+	2.85095i	0.400055	+	0.165708i
$297$	3.50062	−	3.50062i	0.203127	−	0.203127i
$298$	−0.0560723	+	0.0560723i	−0.00324818	+	0.00324818i
$299$	−4.91390	−	2.03541i	−0.284178	−	0.117711i
$300$	3.43004	−	8.28085i	0.198033	−	0.478095i
$301$	−11.4186	+	4.72973i	−0.658156	+	0.272617i
$302$		−	2.02931i		−	0.116774i
$303$	−7.09710	−	17.1339i	−0.407718	−	0.984318i
$304$	−2.49131	−	2.49131i	−0.142887	−	0.142887i
$305$	1.89001			0.108222
$306$		0			0
$307$	−13.2375			−0.755502			−0.377751	−	0.925907i	$-0.623302\pi$
$307$	−13.2375			−0.755502			−0.377751	+	0.925907i	$0.623302\pi$
$308$	−11.8025	−	11.8025i	−0.672511	−	0.672511i
$309$	−1.29922	−	3.13658i	−0.0739098	−	0.178434i
$310$		−	0.745595i		−	0.0423469i
$311$	1.19670	−	0.495691i	0.0678589	−	0.0281081i	−0.348496	−	0.937310i	$-0.613307\pi$
$311$	1.19670	−	0.495691i	0.0678589	−	0.0281081i	0.416355	+	0.909202i	$0.363307\pi$
$312$	0.841894	−	2.03251i	0.0476629	−	0.115068i
$313$	17.6468	+	7.30953i	0.997454	+	0.413159i	0.820863	−	0.571125i	$-0.193493\pi$
$313$	17.6468	+	7.30953i	0.997454	+	0.413159i	0.176591	+	0.984284i	$0.443493\pi$
$314$	2.76479	−	2.76479i	0.156026	−	0.156026i
$315$	−0.777809	+	0.777809i	−0.0438246	+	0.0438246i
$316$	4.27613	+	1.77123i	0.240551	+	0.0996396i
$317$	5.78015	−	13.9545i	0.324645	−	0.783763i	−0.674327	−	0.738433i	$-0.735566\pi$
$317$	5.78015	−	13.9545i	0.324645	−	0.783763i	0.998972	−	0.0453302i	$-0.0144340\pi$
$318$	−1.32289	+	0.547959i	−0.0741840	+	0.0307280i
$319$		−	47.4619i		−	2.65735i
$320$	1.66568	+	4.02130i	0.0931142	+	0.224798i
$321$	−9.30065	−	9.30065i	−0.519112	−	0.519112i
$322$	−0.815020			−0.0454193
$323$		0			0
$324$	−1.95063			−0.108368
$325$	8.14317	+	8.14317i	0.451702	+	0.451702i
$326$	−1.41063	−	3.40557i	−0.0781278	−	0.188617i
$327$		−	17.3896i		−	0.961645i
$328$	5.61335	−	2.32513i	0.309946	−	0.128384i
$329$	5.35852	−	12.9366i	0.295425	−	0.713219i
$330$	0.646750	+	0.267893i	0.0356024	+	0.0147470i
$331$	−16.0350	+	16.0350i	−0.881363	+	0.881363i	−0.993673	−	0.112310i	$-0.964175\pi$
$331$	−16.0350	+	16.0350i	−0.881363	+	0.881363i	0.112310	+	0.993673i	$0.464175\pi$
$332$	−18.4249	+	18.4249i	−1.01120	+	1.01120i
$333$	7.84101	+	3.24785i	0.429685	+	0.177981i
$334$	−1.20940	+	2.91976i	−0.0661757	+	0.159762i
$335$	−4.52806	+	1.87558i	−0.247394	+	0.102474i
$336$			6.40598i			0.349475i
$337$	−0.618680	−	1.49362i	−0.0337016	−	0.0813629i	0.906133	−	0.422994i	$-0.139021\pi$
$337$	−0.618680	−	1.49362i	−0.0337016	−	0.0813629i	−0.939834	+	0.341631i	$0.889021\pi$
$338$	−1.05560	−	1.05560i	−0.0574170	−	0.0574170i
$339$	−0.776042			−0.0421488
$340$		0			0
$341$	26.1037			1.41360
$342$	0.149357	+	0.149357i	0.00807628	+	0.00807628i
$343$	−7.28416	−	17.5855i	−0.393308	−	0.949529i
$344$		−	6.27677i		−	0.338421i
$345$	−1.24777	+	0.516845i	−0.0671779	+	0.0278260i
$346$	0.160986	−	0.388655i	0.00865467	−	0.0208942i
$347$	14.1914	+	5.87826i	0.761833	+	0.315562i	0.729559	−	0.683917i	$-0.239725\pi$
$347$	14.1914	+	5.87826i	0.761833	+	0.315562i	0.0322738	+	0.999479i	$0.489725\pi$
$348$	−13.2234	+	13.2234i	−0.708851	+	0.708851i
$349$	10.6834	−	10.6834i	0.571872	−	0.571872i	−0.360779	−	0.932651i	$-0.617489\pi$
$349$	10.6834	−	10.6834i	0.571872	−	0.571872i	0.932651	+	0.360779i	$0.117489\pi$
$350$	1.63035	+	0.675314i	0.0871459	+	0.0360970i
$351$	0.959100	−	2.31547i	0.0511930	−	0.123591i
$352$	11.7962	−	4.88614i	0.628738	−	0.260432i
$353$			31.2482i			1.66317i	0.555396	+	0.831586i	$0.312567\pi$
$353$			31.2482i			1.66317i	−0.555396	+	0.831586i	$0.687433\pi$
$354$	−0.859854	−	2.07587i	−0.0457007	−	0.110331i
$355$	0.172822	+	0.172822i	0.00917246	+	0.00917246i
$356$	−3.87932			−0.205604
$357$		0			0
$358$	−4.94307			−0.261249
$359$	−1.92689	−	1.92689i	−0.101697	−	0.101697i	0.654428	−	0.756125i	$-0.272910\pi$
$359$	−1.92689	−	1.92689i	−0.101697	−	0.101697i	−0.756125	+	0.654428i	$0.772910\pi$
$360$	−0.213780	−	0.516110i	−0.0112672	−	0.0272014i
$361$		−	18.0963i		−	0.952437i
$362$	2.38414	−	0.987542i	0.125308	−	0.0519041i
$363$	−5.16957	+	12.4805i	−0.271332	+	0.655054i
$364$	−7.80672	−	3.23365i	−0.409183	−	0.169489i
$365$	−2.93143	+	2.93143i	−0.153438	+	0.153438i
$366$	−0.466599	+	0.466599i	−0.0243895	+	0.0243895i
$367$	−17.0470	−	7.06110i	−0.889846	−	0.368586i	−0.109539	−	0.993983i	$-0.534937\pi$
$367$	−17.0470	−	7.06110i	−0.889846	−	0.368586i	−0.780307	+	0.625396i	$0.784937\pi$
$368$	−3.00994	+	7.26665i	−0.156904	+	0.378800i
$369$	6.39483	−	2.64882i	0.332901	−	0.137892i
$370$			1.20010i			0.0623902i
$371$	4.26261	+	10.2908i	0.221303	+	0.534274i
$372$	−7.27281	−	7.27281i	−0.377078	−	0.377078i
$373$	−24.4049			−1.26364			−0.631820	−	0.775115i	$-0.717692\pi$
$373$	−24.4049			−1.26364			−0.631820	+	0.775115i	$0.717692\pi$
$374$		0			0
$375$	6.10630			0.315328
$376$	5.02840	+	5.02840i	0.259320	+	0.259320i
$377$	−9.19492	−	22.1985i	−0.473563	−	1.14328i
$378$		−	0.384044i		−	0.0197531i
$379$	5.44218	−	2.25422i	0.279546	−	0.115792i	−0.238506	−	0.971141i	$-0.576658\pi$
$379$	5.44218	−	2.25422i	0.279546	−	0.115792i	0.518052	+	0.855349i	$0.326658\pi$
$380$	0.451607	−	1.09027i	0.0231669	−	0.0559299i
$381$	−10.0258	−	4.15284i	−0.513639	−	0.212756i
$382$	1.04215	−	1.04215i	0.0533209	−	0.0533209i
$383$	−21.7616	+	21.7616i	−1.11197	+	1.11197i	−0.119083	+	0.992884i	$0.537995\pi$
$383$	−21.7616	+	21.7616i	−1.11197	+	1.11197i	−0.992884	+	0.119083i	$0.962005\pi$
$384$	−6.16950	−	2.55549i	−0.314836	−	0.130409i
$385$	2.08395	−	5.03111i	0.106208	−	0.256409i
$386$	0.598937	−	0.248088i	0.0304851	−	0.0126273i
$387$		−	7.15061i		−	0.363486i
$388$	−2.27034	−	5.48108i	−0.115259	−	0.278260i
$389$	13.8058	+	13.8058i	0.699983	+	0.699983i	0.964407	−	0.264424i	$-0.0851818\pi$
$389$	13.8058	+	13.8058i	0.699983	+	0.699983i	−0.264424	+	0.964407i	$0.585182\pi$
$390$	0.354393			0.0179454
$391$		0			0
$392$	3.52215			0.177896
$393$	−0.499375	−	0.499375i	−0.0251901	−	0.0251901i
$394$	−0.385621	−	0.930970i	−0.0194273	−	0.0469016i
$395$			1.51006i			0.0759794i
$396$	8.92177	−	3.69552i	0.448336	−	0.185707i
$397$	0.346052	−	0.835444i	0.0173679	−	0.0419298i	−0.914958	−	0.403550i	$-0.867776\pi$
$397$	0.346052	−	0.835444i	0.0173679	−	0.0419298i	0.932326	+	0.361620i	$0.117776\pi$
$398$	−0.505043	−	0.209196i	−0.0253155	−	0.0104860i
$399$	1.16185	−	1.16185i	0.0581654	−	0.0581654i
$400$	12.0421	−	12.0421i	0.602103	−	0.602103i
$401$	1.16858	+	0.484040i	0.0583559	+	0.0241718i	0.411670	−	0.911333i	$-0.364945\pi$
$401$	1.16858	+	0.484040i	0.0583559	+	0.0241718i	−0.353315	+	0.935505i	$0.614945\pi$
$402$	0.654832	−	1.58091i	0.0326601	−	0.0788484i
$403$	12.2090	−	5.05715i	0.608176	−	0.251915i
$404$		−	36.1757i		−	1.79981i
$405$	−0.243542	−	0.587961i	−0.0121017	−	0.0292160i
$406$	−2.60346	−	2.60346i	−0.129208	−	0.129208i
$407$	−42.0162			−2.08267
$408$		0			0
$409$	28.6350			1.41591			0.707954	−	0.706258i	$-0.249618\pi$
$409$	28.6350			1.41591			0.707954	+	0.706258i	$0.249618\pi$
$410$	0.692085	+	0.692085i	0.0341796	+	0.0341796i
$411$	−4.71177	−	11.3752i	−0.232415	−	0.561099i
$412$		−	6.62242i		−	0.326263i
$413$	−16.1483	+	6.68885i	−0.794607	+	0.329137i
$414$	0.180449	−	0.435642i	0.00886857	−	0.0214106i
$415$	−7.85407	−	3.25326i	−0.385541	−	0.159696i
$416$	4.57061	−	4.57061i	0.224093	−	0.224093i
$417$	9.43591	−	9.43591i	0.462079	−	0.462079i
$418$	−0.966084	−	0.400165i	−0.0472527	−	0.0195727i
$419$	9.16836	−	22.1344i	0.447903	−	1.08133i	−0.525203	−	0.850977i	$-0.676010\pi$
$419$	9.16836	−	22.1344i	0.447903	−	1.08133i	0.973106	−	0.230357i	$-0.0739895\pi$
$420$	−1.98234	+	0.821112i	−0.0967283	+	0.0400662i
$421$			12.5312i			0.610735i	0.952235	+	0.305368i	$0.0987794\pi$
$421$			12.5312i			0.610735i	−0.952235	+	0.305368i	$0.901221\pi$
$422$	1.69240	+	4.08581i	0.0823846	+	0.198894i
$423$	5.72844	+	5.72844i	0.278526	+	0.278526i
$424$	−5.65685			−0.274721
$425$		0			0
$426$	−0.0853313			−0.00413432
$427$	3.62970	+	3.62970i	0.175654	+	0.175654i
$428$	−9.81845	−	23.7038i	−0.474593	−	1.14577i
$429$			12.4075i			0.599040i
$430$	0.934155	−	0.386940i	0.0450490	−	0.0186599i
$431$	6.76307	−	16.3275i	0.325766	−	0.786468i	−0.673132	−	0.739523i	$-0.735051\pi$
$431$	6.76307	−	16.3275i	0.325766	−	0.786468i	0.998897	−	0.0469454i	$-0.0149487\pi$
$432$	−3.42410	−	1.41831i	−0.164742	−	0.0682385i
$433$	−9.90484	+	9.90484i	−0.475996	+	0.475996i	−0.903849	−	0.427852i	$-0.859270\pi$
$433$	−9.90484	+	9.90484i	−0.475996	+	0.475996i	0.427852	+	0.903849i	$0.359270\pi$
$434$	1.43189	−	1.43189i	0.0687327	−	0.0687327i
$435$	−5.63681	−	2.33484i	−0.270264	−	0.111947i
$436$	12.9809	−	31.3386i	0.621670	−	1.50084i
$437$	1.86386	−	0.772038i	0.0891607	−	0.0369316i
$438$		−	1.44740i		−	0.0691594i
$439$	−4.42919	−	10.6930i	−0.211394	−	0.510349i	0.782244	−	0.622972i	$-0.214075\pi$
$439$	−4.42919	−	10.6930i	−0.211394	−	0.510349i	−0.993638	+	0.112623i	$0.964075\pi$
$440$	1.95557	+	1.95557i	0.0932280	+	0.0932280i
$441$	4.01250			0.191071
$442$		0			0
$443$	−35.6174			−1.69223			−0.846117	−	0.532997i	$-0.821066\pi$
$443$	−35.6174			−1.69223			−0.846117	+	0.532997i	$0.821066\pi$
$444$	11.7062	+	11.7062i	0.555553	+	0.555553i
$445$	−0.484344	−	1.16931i	−0.0229601	−	0.0554306i
$446$			3.19135i			0.151115i
$447$	−0.329725	+	0.136577i	−0.0155955	+	0.00645985i
$448$	−4.52389	+	10.9216i	−0.213734	+	0.515998i
$449$	20.4603	+	8.47493i	0.965581	+	0.399957i	0.809065	−	0.587719i	$-0.199974\pi$
$449$	20.4603	+	8.47493i	0.965581	+	0.399957i	0.156516	+	0.987675i	$0.449974\pi$
$450$	−0.721933	+	0.721933i	−0.0340322	+	0.0340322i
$451$	−24.2303	+	24.2303i	−1.14096	+	1.14096i
$452$	−1.39854	−	0.579295i	−0.0657819	−	0.0272477i
$453$	3.49511	−	8.43795i	0.164215	−	0.396450i
$454$	−2.23227	+	0.924638i	−0.104766	+	0.0433954i
$455$		−	2.75684i		−	0.129243i
$456$	0.319334	+	0.770941i	0.0149542	+	0.0361026i
$457$	7.00483	+	7.00483i	0.327672	+	0.327672i	0.851701	−	0.524029i	$-0.175572\pi$
$457$	7.00483	+	7.00483i	0.327672	+	0.327672i	−0.524029	+	0.851701i	$0.675572\pi$
$458$	−4.21941			−0.197160
$459$		0			0
$460$	−2.63449			−0.122834
$461$	6.80496	+	6.80496i	0.316939	+	0.316939i	0.847590	−	0.530651i	$-0.178053\pi$
$461$	6.80496	+	6.80496i	0.316939	+	0.316939i	−0.530651	+	0.847590i	$0.678053\pi$
$462$	0.727581	+	1.75654i	0.0338502	+	0.0817215i
$463$			15.3013i			0.711113i	0.934655	+	0.355557i	$0.115709\pi$
$463$			15.3013i			0.711113i	−0.934655	+	0.355557i	$0.884291\pi$
$464$	−32.8270	+	13.5974i	−1.52396	+	0.631243i
$465$	1.28415	−	3.10021i	0.0595510	−	0.143769i
$466$	−1.45353	−	0.602072i	−0.0673335	−	0.0278904i
$467$	−15.7791	+	15.7791i	−0.730168	+	0.730168i	−0.970653	−	0.240485i	$-0.922693\pi$
$467$	−15.7791	+	15.7791i	−0.730168	+	0.730168i	0.240485	+	0.970653i	$0.422693\pi$
$468$	3.45688	−	3.45688i	0.159794	−	0.159794i
$469$	−12.2980	−	5.09398i	−0.567867	−	0.235218i
$470$	−0.438381	+	1.05835i	−0.0202210	+	0.0488178i
$471$	16.2580	−	6.73427i	0.749127	−	0.310299i
$472$		−	8.87670i		−	0.408583i
$473$	13.5470	+	32.7053i	0.622892	+	1.50379i
$474$	−0.372797	−	0.372797i	−0.0171232	−	0.0171232i
$475$	−4.36814			−0.200424
$476$		0			0
$477$	−6.44438			−0.295068
$478$	0.830926	+	0.830926i	0.0380057	+	0.0380057i
$479$	5.95346	+	14.3729i	0.272021	+	0.656716i	0.999569	−	0.0293400i	$-0.00934056\pi$
$479$	5.95346	+	14.3729i	0.272021	+	0.656716i	−0.727549	+	0.686056i	$0.759341\pi$
$480$		−	1.64134i		−	0.0749166i
$481$	−19.6515	+	8.13993i	−0.896032	+	0.371149i
$482$	−0.493020	+	1.19026i	−0.0224564	+	0.0542146i
$483$	−3.38888	−	1.40372i	−0.154200	−	0.0638715i
$484$	−18.6327	+	18.6327i	−0.846940	+	0.846940i
$485$	1.36866	−	1.36866i	0.0621475	−	0.0621475i
$486$	0.205278	+	0.0850290i	0.00931160	+	0.00385699i
$487$	−0.0113472	+	0.0273945i	−0.000514190	+	0.00124136i	−0.924136	−	0.382063i	$-0.875214\pi$
$487$	−0.0113472	+	0.0273945i	−0.000514190	+	0.00124136i	0.923622	+	0.383304i	$0.125214\pi$
$488$	−2.40847	+	0.997620i	−0.109026	+	0.0451601i
$489$		−	16.5901i		−	0.750228i
$490$	0.217128	+	0.524192i	0.00980883	+	0.0236806i
$491$	4.71594	+	4.71594i	0.212828	+	0.212828i	0.805467	−	0.592640i	$-0.201914\pi$
$491$	4.71594	+	4.71594i	0.212828	+	0.212828i	−0.592640	+	0.805467i	$0.701914\pi$
$492$	13.5017			0.608704
$493$		0			0
$494$	−0.529375			−0.0238177
$495$	2.22781	+	2.22781i	0.100133	+	0.100133i
$496$	−7.47848	−	18.0546i	−0.335794	−	0.810678i
$497$			0.663798i			0.0297754i
$498$	2.74213	−	1.13583i	0.122878	−	0.0508977i
$499$	7.13584	−	17.2274i	0.319444	−	0.771207i	−0.679839	−	0.733361i	$-0.737951\pi$
$499$	7.13584	−	17.2274i	0.319444	−	0.771207i	0.999284	−	0.0378455i	$-0.0120495\pi$
$500$	11.0045	+	4.55819i	0.492134	+	0.203849i
$501$	−10.0575	+	10.0575i	−0.449336	+	0.449336i
$502$	1.30905	−	1.30905i	0.0584258	−	0.0584258i
$503$	23.7803	+	9.85013i	1.06031	+	0.439195i	0.843562	−	0.537032i	$-0.180454\pi$
$503$	23.7803	+	9.85013i	1.06031	+	0.439195i	0.216750	+	0.976227i	$0.430454\pi$
$504$	0.580614	−	1.40173i	0.0258626	−	0.0624379i
$505$	10.9041	−	4.51663i	0.485227	−	0.200987i
$506$			2.33440i			0.103777i
$507$	−2.57114	−	6.20729i	−0.114188	−	0.275675i
$508$	−14.9681	−	14.9681i	−0.664100	−	0.664100i
$509$	−41.1950			−1.82594			−0.912968	−	0.408032i	$-0.866215\pi$
$509$	−41.1950			−1.82594			−0.912968	+	0.408032i	$0.866215\pi$
$510$		0			0
$511$	−11.2594			−0.498087
$512$	−11.3599	−	11.3599i	−0.502040	−	0.502040i
$513$	0.363791	+	0.878269i	0.0160618	+	0.0387765i
$514$		−	0.945570i		−	0.0417073i
$515$	1.99614	−	0.826827i	0.0879603	−	0.0364344i
$516$	5.33774	−	12.8865i	0.234981	−	0.567294i
$517$	−37.0533	−	15.3480i	−1.62960	−	0.675004i
$518$	−2.30475	+	2.30475i	−0.101265	+	0.101265i
$519$	1.33877	−	1.33877i	0.0587656	−	0.0587656i
$520$	1.29350	+	0.535785i	0.0567238	+	0.0234957i
$521$	3.43728	−	8.29833i	0.150590	−	0.363557i	−0.830525	−	0.556981i	$-0.811960\pi$
$521$	3.43728	−	8.29833i	0.150590	−	0.363557i	0.981115	+	0.193425i	$0.0619595\pi$
$522$	1.96801	−	0.815176i	0.0861374	−	0.0356793i
$523$			5.38995i			0.235686i	0.993032	+	0.117843i	$0.0375980\pi$
$523$			5.38995i			0.235686i	−0.993032	+	0.117843i	$0.962402\pi$
$524$	−0.527177	−	1.27272i	−0.0230299	−	0.0555990i
$525$	5.61596	+	5.61596i	0.245100	+	0.245100i
$526$	2.02194			0.0881607
$527$		0			0
$528$	18.3481			0.798500
$529$	13.0788	+	13.0788i	0.568645	+	0.568645i
$530$	−0.348724	−	0.841894i	−0.0151476	−	0.0365695i
$531$		−	10.1125i		−	0.438844i
$532$	2.96112	−	1.22654i	0.128381	−	0.0531772i
$533$	−6.63861	+	16.0270i	−0.287550	+	0.694208i
$534$	0.408247	+	0.169102i	0.0176666	+	0.00731774i
$535$	5.91898	−	5.91898i	0.255900	−	0.255900i
$536$	4.78015	−	4.78015i	0.206471	−	0.206471i
$537$	−20.5535	−	8.51352i	−0.886947	−	0.367386i
$538$	1.81809	−	4.38926i	0.0783834	−	0.189234i
$539$	−18.3523	+	7.60177i	−0.790490	+	0.327432i
$540$		−	1.24139i		−	0.0534210i
$541$	0.469799	+	1.13420i	0.0201983	+	0.0487629i	0.933657	−	0.358169i	$-0.116599\pi$
$541$	0.469799	+	1.13420i	0.0201983	+	0.0487629i	−0.913459	+	0.406932i	$0.866599\pi$
$542$	−3.03562	−	3.03562i	−0.130391	−	0.130391i
$543$	11.6142			0.498413
$544$		0			0
$545$	11.0668			0.474050
$546$	0.680598	+	0.680598i	0.0291269	+	0.0291269i
$547$	−5.17672	−	12.4977i	−0.221341	−	0.534364i	0.773732	−	0.633513i	$-0.218388\pi$
$547$	−5.17672	−	12.4977i	−0.221341	−	0.534364i	−0.995073	+	0.0991495i	$0.968388\pi$
$548$		−	24.0171i		−	1.02596i
$549$	−2.74377	+	1.13651i	−0.117101	+	0.0485049i
$550$	1.93425	−	4.66968i	0.0824766	−	0.199116i
$551$	8.41999	+	3.48767i	0.358704	+	0.148580i
$552$	1.31724	−	1.31724i	0.0560656	−	0.0560656i
$553$	−2.90001	+	2.90001i	−0.123321	+	0.123321i
$554$	0.685655	+	0.284008i	0.0291307	+	0.0120663i
$555$	−2.06695	+	4.99006i	−0.0877371	+	0.211816i
$556$	24.0486	−	9.96125i	1.01989	−	0.422451i
$557$			18.3599i			0.777936i	0.921251	+	0.388968i	$0.127168\pi$
$557$			18.3599i			0.777936i	−0.921251	+	0.388968i	$0.872832\pi$
$558$	0.448342	+	1.08239i	0.0189798	+	0.0458213i
$559$	12.6722	+	12.6722i	0.535977	+	0.535977i
$560$	−4.07680			−0.172276
$561$		0			0
$562$	1.03931			0.0438406
$563$	−2.35689	−	2.35689i	−0.0993311	−	0.0993311i	0.655695	−	0.755026i	$-0.272376\pi$
$563$	−2.35689	−	2.35689i	−0.0993311	−	0.0993311i	−0.755026	+	0.655695i	$0.772376\pi$
$564$	6.04736	+	14.5996i	0.254640	+	0.614755i
$565$		−	0.493877i		−	0.0207775i
$566$	−2.06472	+	0.855236i	−0.0867868	+	0.0359483i
$567$	0.661445	−	1.59687i	0.0277781	−	0.0670622i
$568$	−0.311451	−	0.129007i	−0.0130682	−	0.00541303i
$569$	20.8150	−	20.8150i	0.872611	−	0.872611i	−0.120145	−	0.992756i	$-0.538336\pi$
$569$	20.8150	−	20.8150i	0.872611	−	0.872611i	0.992756	+	0.120145i	$0.0383360\pi$
$570$	−0.0950512	+	0.0950512i	−0.00398126	+	0.00398126i
$571$	−23.8615	−	9.88376i	−0.998573	−	0.413623i	−0.177300	−	0.984157i	$-0.556736\pi$
$571$	−23.8615	−	9.88376i	−0.998573	−	0.413623i	−0.821274	+	0.570534i	$0.806736\pi$
$572$	−9.26189	+	22.3602i	−0.387259	+	0.934926i
$573$	6.12820	−	2.53838i	0.256009	−	0.106042i
$574$			2.65824i			0.110953i
$575$	3.73174	+	9.00921i	0.155624	+	0.375710i
$576$	−4.83618	−	4.83618i	−0.201508	−	0.201508i
$577$	22.1850			0.923575			0.461788	−	0.886990i	$-0.347208\pi$
$577$	22.1850			0.923575			0.461788	+	0.886990i	$0.347208\pi$
$578$		0			0
$579$	2.91769			0.121255
$580$	−8.41546	−	8.41546i	−0.349433	−	0.349433i
$581$	−8.83568	−	21.3312i	−0.366566	−	0.884968i
$582$			0.675776i			0.0280118i
$583$	29.4752	−	12.2090i	1.22074	−	0.505647i
$584$	2.18824	−	5.28287i	0.0905499	−	0.218607i
$585$	1.47358	+	0.610376i	0.0609249	+	0.0252359i
$586$	0.906438	−	0.906438i	0.0374446	−	0.0374446i
$587$	−22.7322	+	22.7322i	−0.938258	+	0.938258i	−0.998202	−	0.0599439i	$-0.980908\pi$
$587$	−22.7322	+	22.7322i	−0.938258	+	0.938258i	0.0599439	+	0.998202i	$0.480908\pi$
$588$	7.23111	+	2.99522i	0.298206	+	0.123521i
$589$	−1.91820	+	4.63094i	−0.0790380	+	0.190815i
$590$	1.32109	−	0.547215i	0.0543886	−	0.0225285i
$591$		−	4.53517i		−	0.186552i
$592$	12.0373	+	29.0605i	0.494729	+	1.19438i
$593$	−20.7470	−	20.7470i	−0.851976	−	0.851976i	0.138400	−	0.990376i	$-0.455804\pi$
$593$	−20.7470	−	20.7470i	−0.851976	−	0.851976i	−0.990376	+	0.138400i	$0.955804\pi$
$594$	−1.09999			−0.0451330
$595$		0			0
$596$	−0.696164			−0.0285160
$597$	−1.73969	−	1.73969i	−0.0712006	−	0.0712006i
$598$	0.452249	+	1.09183i	0.0184939	+	0.0446481i
$599$		−	36.2632i		−	1.48167i	−0.671686	−	0.740836i	$-0.734430\pi$
$599$		−	36.2632i		−	1.48167i	0.671686	−	0.740836i	$-0.265570\pi$
$600$	−3.72643	+	1.54354i	−0.152131	+	0.0630147i
$601$	−17.5033	+	42.2566i	−0.713973	+	1.72368i	−0.0241482	+	0.999708i	$0.507687\pi$
$601$	−17.5033	+	42.2566i	−0.713973	+	1.72368i	−0.689825	+	0.723976i	$0.742313\pi$
$602$	2.53711	+	1.05091i	0.103405	+	0.0428317i
$603$	5.44563	−	5.44563i	0.221763	−	0.221763i
$604$	12.5974	−	12.5974i	0.512582	−	0.512582i
$605$	−7.94262	−	3.28994i	−0.322914	−	0.133755i
$606$	−1.57691	+	3.80701i	−0.0640578	+	0.154649i
$607$	−31.1015	+	12.8827i	−1.26237	+	0.522891i	−0.910636	−	0.413209i	$-0.864408\pi$
$607$	−31.1015	+	12.8827i	−1.26237	+	0.522891i	−0.351734	+	0.936100i	$0.614408\pi$
$608$			2.45176i			0.0994318i
$609$	−6.34130	−	15.3092i	−0.256962	−	0.620362i
$610$	−0.296946	−	0.296946i	−0.0120230	−	0.0120230i
$611$	−20.3037			−0.821400
$612$		0			0
$613$	−5.89120			−0.237943			−0.118972	−	0.992898i	$-0.537960\pi$
$613$	−5.89120			−0.237943			−0.118972	+	0.992898i	$0.537960\pi$
$614$	2.07978	+	2.07978i	0.0839330	+	0.0839330i
$615$	1.68572	+	4.06970i	0.0679750	+	0.164106i
$616$			7.51118i			0.302634i
$617$	32.5371	−	13.4773i	1.30989	−	0.542575i	0.385040	−	0.922900i	$-0.374188\pi$
$617$	32.5371	−	13.4773i	1.30989	−	0.542575i	0.924853	+	0.380325i	$0.124188\pi$
$618$	−0.288674	+	0.696922i	−0.0116122	+	0.0280343i
$619$	30.3298	+	12.5630i	1.21906	+	0.504951i	0.897110	−	0.441807i	$-0.145662\pi$
$619$	30.3298	+	12.5630i	1.21906	+	0.504951i	0.321948	+	0.946757i	$0.395662\pi$
$620$	4.62845	−	4.62845i	0.185883	−	0.185883i
$621$	1.50062	−	1.50062i	0.0602180	−	0.0602180i
$622$	−0.265897	−	0.110138i	−0.0106615	−	0.00441615i
$623$	1.31545	−	3.17578i	0.0527024	−	0.127235i
$624$	8.58165	−	3.55464i	0.343541	−	0.142299i
$625$		−	19.0889i		−	0.763555i
$626$	−1.62411	−	3.92096i	−0.0649127	−	0.156713i
$627$	−3.32780	−	3.32780i	−0.132900	−	0.132900i
$628$	34.3262			1.36976
$629$		0			0
$630$	0.244408			0.00973744
$631$	−7.57005	−	7.57005i	−0.301359	−	0.301359i	0.540186	−	0.841545i	$-0.318354\pi$
$631$	−7.57005	−	7.57005i	−0.301359	−	0.301359i	−0.841545	+	0.540186i	$0.818354\pi$
$632$	−0.797065	−	1.92429i	−0.0317056	−	0.0765440i
$633$			19.9038i			0.791103i
$634$	−3.10057	+	1.28430i	−0.123139	+	0.0510060i
$635$	2.64289	−	6.38050i	0.104880	−	0.253202i
$636$	−11.6137	−	4.81057i	−0.460514	−	0.190751i
$637$	−7.11089	+	7.11089i	−0.281744	+	0.281744i
$638$	−7.45688	+	7.45688i	−0.295221	+	0.295221i
$639$	−0.354811	−	0.146967i	−0.0140361	−	0.00581394i
$640$	1.62633	−	3.92630i	0.0642862	−	0.155201i
$641$	−34.1315	+	14.1377i	−1.34811	+	0.558406i	−0.935766	−	0.352621i	$-0.885291\pi$
$641$	−34.1315	+	14.1377i	−1.34811	+	0.558406i	−0.412346	+	0.911027i	$0.635291\pi$
$642$			2.92251i			0.115342i
$643$	−15.0447	−	36.3211i	−0.593305	−	1.43237i	−0.880293	−	0.474431i	$-0.842654\pi$
$643$	−15.0447	−	36.3211i	−0.593305	−	1.43237i	0.286987	−	0.957934i	$-0.407346\pi$
$644$	−5.05943	−	5.05943i	−0.199369	−	0.199369i
$645$	4.55068			0.179183
$646$		0			0
$647$	−14.8806			−0.585016			−0.292508	−	0.956263i	$-0.594490\pi$
$647$	−14.8806			−0.585016			−0.292508	+	0.956263i	$0.594490\pi$
$648$	0.620696	+	0.620696i	0.0243832	+	0.0243832i
$649$	19.1583	+	46.2523i	0.752031	+	1.81556i
$650$		−	2.55880i		−	0.100364i
$651$	8.41999	−	3.48767i	0.330005	−	0.136693i
$652$	12.3840	−	29.8977i	0.484997	−	1.17089i
$653$	−22.4417	−	9.29567i	−0.878213	−	0.363768i	−0.102410	−	0.994742i	$-0.532655\pi$
$653$	−22.4417	−	9.29567i	−0.878213	−	0.363768i	−0.775803	+	0.630975i	$0.782655\pi$
$654$	−2.73213	+	2.73213i	−0.106835	+	0.106835i
$655$	0.317805	−	0.317805i	0.0124177	−	0.0124177i
$656$	23.7007	+	9.81713i	0.925355	+	0.383295i
$657$	2.49288	−	6.01834i	0.0972564	−	0.234798i
$658$	−2.87441	+	1.19062i	−0.112056	+	0.0464151i
$659$			9.14192i			0.356119i	0.984020	+	0.178059i	$0.0569819\pi$
$659$			9.14192i			0.356119i	−0.984020	+	0.178059i	$0.943018\pi$
$660$	2.35185	+	5.67786i	0.0915455	+	0.221010i
$661$	−11.8759	−	11.8759i	−0.461920	−	0.461920i	0.437365	−	0.899284i	$-0.355912\pi$
$661$	−11.8759	−	11.8759i	−0.461920	−	0.461920i	−0.899284	+	0.437365i	$0.855912\pi$
$662$	5.03861			0.195831
$663$		0			0
$664$	11.7257			0.455046
$665$	0.739409	+	0.739409i	0.0286731	+	0.0286731i
$666$	−0.721645	−	1.74220i	−0.0279632	−	0.0675091i
$667$		−	20.3456i		−	0.787787i
$668$	−25.6327	+	10.6174i	−0.991761	+	0.410801i
$669$	−5.49651	+	13.2698i	−0.212507	+	0.513038i
$670$	1.00610	+	0.416739i	0.0388689	+	0.0161000i
$671$	10.3963	−	10.3963i	0.401343	−	0.401343i
$672$	3.15213	−	3.15213i	0.121596	−	0.121596i
$673$	17.2131	+	7.12991i	0.663517	+	0.274838i	0.688918	−	0.724840i	$-0.258086\pi$
$673$	17.2131	+	7.12991i	0.663517	+	0.274838i	−0.0254007	+	0.999677i	$0.508086\pi$
$674$	−0.137465	+	0.331870i	−0.00529496	+	0.0127832i
$675$	−4.24522	+	1.75843i	−0.163398	+	0.0676819i
$676$		−	13.1057i		−	0.504067i
$677$	4.13338	+	9.97885i	0.158859	+	0.383519i	0.983189	−	0.182590i	$-0.0584482\pi$
$677$	4.13338	+	9.97885i	0.158859	+	0.383519i	−0.824331	+	0.566109i	$0.808448\pi$
$678$	0.121926	+	0.121926i	0.00468255	+	0.00468255i
$679$	5.25690			0.201741
$680$		0			0
$681$	−10.8744			−0.416707
$682$	−4.10124	−	4.10124i	−0.157044	−	0.157044i
$683$	8.50319	+	20.5285i	0.325366	+	0.785502i	0.998924	+	0.0463683i	$0.0147648\pi$
$683$	8.50319	+	20.5285i	0.325366	+	0.785502i	−0.673559	+	0.739134i	$0.735235\pi$
$684$			1.85433i			0.0709021i
$685$	7.23925	−	2.99860i	0.276598	−	0.114570i
$686$	−1.61848	+	3.90735i	−0.0617938	+	0.149183i
$687$	−17.5445	−	7.26716i	−0.669363	−	0.277259i
$688$	18.7396	−	18.7396i	0.714439	−	0.714439i
$689$	11.4206	−	11.4206i	0.435092	−	0.435092i
$690$	0.277245	+	0.114838i	0.0105545	+	0.00437183i
$691$	−14.7491	+	35.6075i	−0.561083	+	1.35457i	0.347818	+	0.937562i	$0.386923\pi$
$691$	−14.7491	+	35.6075i	−0.561083	+	1.35457i	−0.908901	+	0.417012i	$0.863077\pi$
$692$	3.41202	−	1.41331i	0.129706	−	0.0537258i
$693$			8.55687i			0.325048i
$694$	−1.30610	−	3.15320i	−0.0495788	−	0.119694i
$695$	6.00506	+	6.00506i	0.227785	+	0.227785i
$696$	8.41546			0.318987
$697$		0			0
$698$	−3.35702			−0.127065
$699$	−5.00687	−	5.00687i	−0.189377	−	0.189377i
$700$	5.92862	+	14.3129i	0.224081	+	0.540979i
$701$			18.0843i			0.683034i	0.939876	+	0.341517i	$0.110941\pi$
$701$			18.0843i			0.683034i	−0.939876	+	0.341517i	$0.889059\pi$
$702$	−0.514478	+	0.213104i	−0.0194177	+	0.00804308i
$703$	3.08751	−	7.45391i	0.116448	−	0.281129i
$704$	31.2819	+	12.9574i	1.17898	+	0.488351i
$705$	−3.64561	+	3.64561i	−0.137302	+	0.137302i
$706$	4.90949	−	4.90949i	0.184771	−	0.184771i
$707$	29.6149	+	12.2669i	1.11378	+	0.461345i
$708$	7.54871	−	18.2242i	0.283698	−	0.684907i
$709$	48.2832	−	19.9996i	1.81331	−	0.751099i	0.833111	−	0.553105i	$-0.186557\pi$
$709$	48.2832	−	19.9996i	1.81331	−	0.751099i	0.980203	−	0.197994i	$-0.0634427\pi$
$710$		−	0.0543053i		−	0.00203804i
$711$	−0.908030	−	2.19218i	−0.0340538	−	0.0822131i
$712$	1.23441	+	1.23441i	0.0462615	+	0.0462615i
$713$	11.1900			0.419068
$714$		0			0
$715$	−7.89620			−0.295301
$716$	−30.6853	−	30.6853i	−1.14676	−	1.14676i
$717$	2.02390	+	4.88614i	0.0755841	+	0.182476i
$718$			0.605478i			0.0225962i
$719$	−2.08640	+	0.864216i	−0.0778097	+	0.0322298i	−0.421249	−	0.906945i	$-0.638408\pi$
$719$	−2.08640	+	0.864216i	−0.0778097	+	0.0322298i	0.343439	+	0.939175i	$0.388408\pi$
$720$	0.902620	−	2.17912i	0.0336386	−	0.0812109i
$721$	5.42140	+	2.24562i	0.201903	+	0.0836311i
$722$	−2.84316	+	2.84316i	−0.105812	+	0.105812i
$723$	−4.09999	+	4.09999i	−0.152480	+	0.152480i
$724$	20.9305	+	8.66969i	0.777875	+	0.322207i
$725$	−16.8581	+	40.6990i	−0.626094	+	1.51152i
$726$	2.77305	−	1.14863i	0.102918	−	0.0426298i
$727$			39.5601i			1.46720i	0.679581	+	0.733601i	$0.262162\pi$
$727$			39.5601i			1.46720i	−0.679581	+	0.733601i	$0.737838\pi$
$728$	1.45516	+	3.51307i	0.0539319	+	0.130203i
$729$	0.707107	+	0.707107i	0.0261891	+	0.0261891i
$730$	0.921132			0.0340926
$731$		0			0
$732$	−5.79304			−0.214117
$733$	9.55562	+	9.55562i	0.352945	+	0.352945i	0.861204	−	0.508259i	$-0.169711\pi$
$733$	9.55562	+	9.55562i	0.352945	+	0.352945i	−0.508259	+	0.861204i	$0.669711\pi$
$734$	1.56892	+	3.78770i	0.0579097	+	0.139806i
$735$			2.55357i			0.0941899i
$736$	5.05671	−	2.09456i	0.186393	−	0.0772064i
$737$	−14.5903	+	35.2240i	−0.537440	+	1.29749i
$738$	−1.42088	−	0.588546i	−0.0523031	−	0.0216647i
$739$	−7.58596	+	7.58596i	−0.279054	+	0.279054i	−0.832731	−	0.553677i	$-0.813224\pi$
$739$	−7.58596	+	7.58596i	−0.279054	+	0.279054i	0.553677	+	0.832731i	$0.313224\pi$
$740$	−7.44990	+	7.44990i	−0.273864	+	0.273864i
$741$	−2.20116	−	0.911750i	−0.0808616	−	0.0334940i
$742$	0.947114	−	2.28654i	0.0347697	−	0.0839414i
$743$	−40.6434	+	16.8351i	−1.49106	+	0.617619i	−0.971548	−	0.236843i	$-0.923887\pi$
$743$	−40.6434	+	16.8351i	−1.49106	+	0.617619i	−0.519515	+	0.854461i	$0.673887\pi$
$744$			4.62845i			0.169687i
$745$	−0.0869180	−	0.209839i	−0.00318443	−	0.00768789i
$746$	3.83434	+	3.83434i	0.140385	+	0.140385i
$747$	13.3581			0.488749
$748$		0			0
$749$	22.7343			0.830695
$750$	−0.959379	−	0.959379i	−0.0350316	−	0.0350316i
$751$	4.78535	+	11.5529i	0.174620	+	0.421570i	0.986823	−	0.161806i	$-0.0517317\pi$
$751$	4.78535	+	11.5529i	0.174620	+	0.421570i	−0.812203	+	0.583375i	$0.801732\pi$
$752$			30.0250i			1.09490i
$753$	7.69767	−	3.18848i	0.280519	−	0.116195i
$754$	−2.04303	+	4.93232i	−0.0744029	+	0.179624i
$755$	5.36995	+	2.22431i	0.195433	+	0.0809509i
$756$	2.38404	−	2.38404i	0.0867069	−	0.0867069i
$757$	25.3480	−	25.3480i	0.921288	−	0.921288i	−0.0758328	−	0.997121i	$-0.524162\pi$
$757$	25.3480	−	25.3480i	0.921288	−	0.921288i	0.997121	+	0.0758328i	$0.0241615\pi$
$758$	−1.20920	−	0.500869i	−0.0439203	−	0.0181924i
$759$	−4.02057	+	9.70651i	−0.145937	+	0.352324i
$760$	−0.490630	+	0.203226i	−0.0177970	+	0.00737177i
$761$			23.4468i			0.849944i	0.905206	+	0.424972i	$0.139716\pi$
$761$			23.4468i			0.849944i	−0.905206	+	0.424972i	$0.860284\pi$
$762$	0.922725	+	2.22766i	0.0334268	+	0.0806994i
$763$	21.2534	+	21.2534i	0.769424	+	0.769424i
$764$	12.9388			0.468108
$765$		0			0
$766$	6.83807			0.247070
$767$	17.9212	+	17.9212i	0.647097	+	0.647097i
$768$	−4.66684	−	11.2667i	−0.168400	−	0.406554i
$769$			22.8938i			0.825573i	0.910828	+	0.412786i	$0.135444\pi$
$769$			22.8938i			0.825573i	−0.910828	+	0.412786i	$0.864556\pi$
$770$	−1.11787	+	0.463036i	−0.0402852	+	0.0166867i
$771$	1.62857	−	3.93171i	0.0586515	−	0.141597i
$772$	5.25810	+	2.17798i	0.189243	+	0.0783871i
$773$	24.1327	−	24.1327i	0.867991	−	0.867991i	−0.124259	−	0.992250i	$-0.539655\pi$
$773$	24.1327	−	24.1327i	0.867991	−	0.867991i	0.992250	+	0.124259i	$0.0396552\pi$
$774$	−1.12345	+	1.12345i	−0.0403817	+	0.0403817i
$775$	−22.3842	−	9.27185i	−0.804065	−	0.333055i
$776$	−1.02167	+	2.46652i	−0.0366757	+	0.0885430i
$777$	−13.5527	+	5.61372i	−0.486201	+	0.201391i
$778$		−	4.33815i		−	0.155530i
$779$	−2.51805	−	6.07912i	−0.0902187	−	0.217807i
$780$	2.19998	+	2.19998i	0.0787717	+	0.0787717i
$781$	1.90126			0.0680325
$782$		0			0
$783$	9.58704			0.342613
$784$	10.5155	+	10.5155i	0.375555	+	0.375555i
$785$	4.28572	+	10.3466i	0.152964	+	0.369288i
$786$			0.156917i			0.00559703i
$787$	−12.1703	+	5.04110i	−0.433824	+	0.179696i	−0.588899	−	0.808207i	$-0.700438\pi$
$787$	−12.1703	+	5.04110i	−0.433824	+	0.179696i	0.155074	+	0.987903i	$0.450438\pi$
$788$	3.38539	−	8.17304i	0.120599	−	0.291153i
$789$	8.40729	+	3.48241i	0.299308	+	0.123977i
$790$	0.237250	−	0.237250i	0.00844098	−	0.00844098i
$791$	0.948471	−	0.948471i	0.0337238	−	0.0337238i
$792$	−4.01485	−	1.66301i	−0.142662	−	0.0590924i
$793$	2.84836	−	6.87656i	0.101148	−	0.244194i
$794$	−0.185629	+	0.0768899i	−0.00658771	+	0.00272872i
$795$		−	4.10124i		−	0.145456i
$796$	−1.83654	−	4.43380i	−0.0650945	−	0.157152i
$797$	25.7038	+	25.7038i	0.910475	+	0.910475i	0.996309	−	0.0858346i	$-0.0273557\pi$
$797$	25.7038	+	25.7038i	0.910475	+	0.910475i	−0.0858346	+	0.996309i	$0.527356\pi$
$798$	−0.365084			−0.0129239
$799$		0			0
$800$	−11.8509			−0.418991
$801$	1.40626	+	1.40626i	0.0496878	+	0.0496878i
$802$	−0.107549	−	0.259647i	−0.00379770	−	0.00916847i
$803$			32.2494i			1.13806i
$804$	13.8789	−	5.74881i	0.489470	−	0.202745i
$805$	0.893335	−	2.15670i	0.0314859	−	0.0760138i
$806$	−2.71274	−	1.12366i	−0.0955523	−	0.0395791i
$807$	15.1194	−	15.1194i	0.532227	−	0.532227i
$808$	−11.5112	+	11.5112i	−0.404962	+	0.404962i
$809$	−41.6916	−	17.2692i	−1.46580	−	0.607154i	−0.499903	−	0.866082i	$-0.666631\pi$
$809$	−41.6916	−	17.2692i	−1.46580	−	0.607154i	−0.965897	+	0.258928i	$0.916631\pi$
$810$	−0.0541128	+	0.130640i	−0.00190133	+	0.00459022i
$811$	−3.07481	+	1.27363i	−0.107971	+	0.0447231i	−0.436015	−	0.899939i	$-0.643611\pi$
$811$	−3.07481	+	1.27363i	−0.107971	+	0.0447231i	0.328044	+	0.944662i	$0.393611\pi$
$812$		−	32.3232i		−	1.13432i
$813$	−7.39393	−	17.8505i	−0.259316	−	0.626045i
$814$	6.60130	+	6.60130i	0.231375	+	0.231375i
$815$	10.5580			0.369830
$816$		0			0
$817$	−6.79759			−0.237817
$818$	−4.49893	−	4.49893i	−0.157301	−	0.157301i
$819$	1.65775	+	4.00215i	0.0579263	+	0.139847i
$820$			8.59255i			0.300065i
$821$	6.90122	−	2.85858i	0.240854	−	0.0997651i	−0.258991	−	0.965880i	$-0.583390\pi$
$821$	6.90122	−	2.85858i	0.240854	−	0.0997651i	0.499846	+	0.866115i	$0.333390\pi$
$822$	−1.04692	+	2.52748i	−0.0365154	+	0.0881559i
$823$	−50.0589	−	20.7351i	−1.74494	−	0.722779i	−0.998345	−	0.0575047i	$-0.981686\pi$
$823$	−50.0589	−	20.7351i	−1.74494	−	0.722779i	−0.746599	−	0.665275i	$-0.768314\pi$
$824$	−2.10727	+	2.10727i	−0.0734102	+	0.0734102i
$825$	16.0853	−	16.0853i	0.560019	−	0.560019i
$826$	3.58802	+	1.48621i	0.124843	+	0.0517117i
$827$	−1.89452	+	4.57379i	−0.0658791	+	0.159046i	−0.953390	−	0.301740i	$-0.902433\pi$
$827$	−1.89452	+	4.57379i	−0.0658791	+	0.159046i	0.887511	+	0.460786i	$0.152433\pi$
$828$	3.82453	−	1.58417i	0.132911	−	0.0550537i
$829$			0.0762440i			0.00264806i	0.999999	+	0.00132403i	$0.000421453\pi$
$829$			0.0762440i			0.00264806i	−0.999999	+	0.00132403i	$0.999579\pi$
$830$	0.722847	+	1.74511i	0.0250904	+	0.0605736i
$831$	2.36183	+	2.36183i	0.0819309	+	0.0819309i
$832$	17.1412			0.594265
$833$		0			0
$834$	−2.96501			−0.102670
$835$	−6.40064	−	6.40064i	−0.221503	−	0.221503i
$836$	−3.51307	−	8.48131i	−0.121502	−	0.293332i
$837$			5.27281i			0.182255i
$838$	−4.91807	+	2.03713i	−0.169892	+	0.0703715i
$839$	13.9480	−	33.6734i	0.481538	−	1.16254i	−0.477340	−	0.878719i	$-0.658399\pi$
$839$	13.9480	−	33.6734i	0.481538	−	1.16254i	0.958878	−	0.283817i	$-0.0916009\pi$
$840$	0.892066	+	0.369506i	0.0307792	+	0.0127492i
$841$	44.4850	−	44.4850i	1.53396	−	1.53396i
$842$	1.96882	−	1.96882i	0.0678501	−	0.0678501i
$843$	4.32149	+	1.79002i	0.148840	+	0.0616515i
$844$	−14.8576	+	35.8695i	−0.511421	+	1.23468i
$845$	3.95035	−	1.63629i	0.135896	−	0.0562900i
$846$		−	1.80002i		−	0.0618861i
$847$	−8.93530	−	21.5717i	−0.307020	−	0.741213i
$848$	−16.8888	−	16.8888i	−0.579963	−	0.579963i
$849$	−10.0582			−0.345196
$850$		0			0
$851$	−18.0112			−0.617418
$852$	−0.529714	−	0.529714i	−0.0181477	−	0.0181477i
$853$	−15.2952	−	36.9260i	−0.523699	−	1.26432i	−0.935590	−	0.353088i	$-0.885132\pi$
$853$	−15.2952	−	36.9260i	−0.523699	−	1.26432i	0.411891	−	0.911233i	$-0.364868\pi$
$854$		−	1.14055i		−	0.0390287i
$855$	−0.558934	+	0.231518i	−0.0191152	+	0.00791776i
$856$	−4.41837	+	10.6669i	−0.151017	+	0.364586i
$857$	2.73433	+	1.13260i	0.0934030	+	0.0386888i	0.428896	−	0.903354i	$-0.358903\pi$
$857$	2.73433	+	1.13260i	0.0934030	+	0.0386888i	−0.335493	+	0.942043i	$0.608903\pi$
$858$	1.94938	−	1.94938i	0.0665508	−	0.0665508i
$859$	15.8741	−	15.8741i	0.541618	−	0.541618i	−0.382385	−	0.924003i	$-0.624897\pi$
$859$	15.8741	−	15.8741i	0.541618	−	0.541618i	0.924003	+	0.382385i	$0.124897\pi$
$860$	8.20100	+	3.39697i	0.279652	+	0.115836i
$861$	−4.57833	+	11.0531i	−0.156029	+	0.376688i
$862$	−3.62783	+	1.50270i	−0.123564	+	0.0511820i
$863$			27.8981i			0.949661i	0.880077	+	0.474831i	$0.157491\pi$
$863$			27.8981i			0.949661i	−0.880077	+	0.474831i	$0.842509\pi$
$864$	0.986972	+	2.38276i	0.0335775	+	0.0810632i
$865$	0.852001	+	0.852001i	0.0289689	+	0.0289689i
$866$	3.11236			0.105762
$867$		0			0
$868$	17.7775			0.603409
$869$	8.30627	+	8.30627i	0.281771	+	0.281771i
$870$	0.518782	+	1.25245i	0.0175884	+	0.0424620i
$871$			19.3013i			0.654001i
$872$	−14.1025	+	5.84147i	−0.477573	+	0.197817i
$873$	−1.16390	+	2.80990i	−0.0393920	+	0.0951008i
$874$	−0.414135	−	0.171540i	−0.0140083	−	0.00580243i
$875$	−7.46307	+	7.46307i	−0.252298	+	0.252298i
$876$	8.98507	−	8.98507i	0.303577	−	0.303577i
$877$	19.1207	+	7.92006i	0.645661	+	0.267441i	0.681390	−	0.731920i	$-0.261376\pi$
$877$	19.1207	+	7.92006i	0.645661	+	0.267441i	−0.0357299	+	0.999361i	$0.511376\pi$
$878$	−0.984127	+	2.37589i	−0.0332127	+	0.0801825i
$879$	5.33017	−	2.20783i	0.179782	−	0.0744683i
$880$			11.6768i			0.393627i
$881$	−8.51085	−	20.5470i	−0.286738	−	0.692246i	0.713224	−	0.700936i	$-0.247234\pi$
$881$	−8.51085	−	20.5470i	−0.286738	−	0.692246i	−0.999962	+	0.00868935i	$0.997234\pi$
$882$	−0.630415	−	0.630415i	−0.0212272	−	0.0212272i
$883$	−4.23253			−0.142436			−0.0712180	−	0.997461i	$-0.522689\pi$
$883$	−4.23253			−0.142436			−0.0712180	+	0.997461i	$0.522689\pi$
$884$		0			0
$885$	6.43563			0.216331
$886$	5.59596	+	5.59596i	0.188000	+	0.188000i
$887$	13.8932	+	33.5412i	0.466488	+	1.12620i	0.965686	+	0.259714i	$0.0836282\pi$
$887$	13.8932	+	33.5412i	0.466488	+	1.12620i	−0.499198	+	0.866488i	$0.666372\pi$
$888$		−	7.44990i		−	0.250002i
$889$	17.3291	−	7.17793i	0.581198	−	0.240740i
$890$	−0.107617	+	0.259811i	−0.00360733	+	0.00870887i
$891$	−4.57379	−	1.89452i	−0.153228	−	0.0634690i
$892$	−19.8111	+	19.8111i	−0.663323	+	0.663323i
$893$	5.44563	−	5.44563i	0.182231	−	0.182231i
$894$	0.0732620	+	0.0303461i	0.00245025	+	0.00101493i
$895$	5.41805	−	13.0803i	0.181105	−	0.437227i
$896$	10.6636	−	4.41701i	0.356246	−	0.147562i
$897$			5.31877i			0.177589i
$898$	−1.88306	−	4.54610i	−0.0628384	−	0.151705i
$899$	35.7447	+	35.7447i	1.19215	+	1.19215i
$900$	−8.96313			−0.298771
$901$		0			0
$902$	7.61380			0.253512
$903$	8.73941	+	8.73941i	0.290829	+	0.290829i
$904$	0.260686	+	0.629353i	0.00867030	+	0.0209320i
$905$			7.39133i			0.245696i
$906$	−1.87484	+	0.776584i	−0.0622874	+	0.0258003i
$907$	−9.32667	+	22.5166i	−0.309687	+	0.747651i	0.690028	+	0.723783i	$0.257598\pi$
$907$	−9.32667	+	22.5166i	−0.309687	+	0.747651i	−0.999715	+	0.0238680i	$0.992402\pi$
$908$	−19.5973	−	8.11745i	−0.650358	−	0.269387i
$909$	−13.1137	+	13.1137i	−0.434955	+	0.434955i
$910$	−0.433136	+	0.433136i	−0.0143583	+	0.0143583i
$911$	24.8688	+	10.3010i	0.823940	+	0.341287i	0.754501	−	0.656299i	$-0.227879\pi$
$911$	24.8688	+	10.3010i	0.823940	+	0.341287i	0.0694390	+	0.997586i	$0.477879\pi$
$912$	−1.34829	+	3.25506i	−0.0446463	+	0.107786i
$913$	−61.0973	+	25.3073i	−2.02203	+	0.837550i
$914$		−	2.20110i		−	0.0728059i
$915$	−0.723277	−	1.74615i	−0.0239108	−	0.0577258i
$916$	−26.1930	−	26.1930i	−0.865441	−	0.865441i
$917$	1.22066			0.0403099
$918$		0			0
$919$	−23.8000			−0.785088			−0.392544	−	0.919733i	$-0.628405\pi$
$919$	−23.8000			−0.785088			−0.392544	+	0.919733i	$0.628405\pi$
$920$	0.838300	+	0.838300i	0.0276379	+	0.0276379i
$921$	5.06576	+	12.2298i	0.166922	+	0.402986i
$922$		−	2.13830i		−	0.0704210i
$923$	0.889244	−	0.368337i	0.0292698	−	0.0121240i
$924$	−6.38748	+	15.4207i	−0.210133	+	0.507305i
$925$	36.0294	+	14.9238i	1.18464	+	0.490693i
$926$	2.40404	−	2.40404i	0.0790016	−	0.0790016i
$927$	−2.40064	+	2.40064i	−0.0788473	+	0.0788473i
$928$	22.8436	+	9.46214i	0.749879	+	0.310610i
$929$	−2.23006	+	5.38383i	−0.0731658	+	0.176638i	−0.956231	−	0.292612i	$-0.905476\pi$
$929$	−2.23006	+	5.38383i	−0.0731658	+	0.176638i	0.883066	+	0.469250i	$0.155476\pi$
$930$	−0.688840	+	0.285327i	−0.0225879	+	0.00935623i
$931$		−	3.81440i		−	0.125012i
$932$	−5.28563	−	12.7606i	−0.173136	−	0.417988i
$933$	−0.915918	−	0.915918i	−0.0299858	−	0.0299858i
$934$	4.95819			0.162237
$935$		0			0
$936$	−2.19998			−0.0719084
$937$	−39.2037	−	39.2037i	−1.28073	−	1.28073i	−0.940253	−	0.340477i	$-0.889411\pi$
$937$	−39.2037	−	39.2037i	−1.28073	−	1.28073i	−0.340477	−	0.940253i	$-0.610589\pi$
$938$	1.13184	+	2.73250i	0.0369558	+	0.0892193i
$939$		−	19.1007i		−	0.623328i
$940$	−9.29128	+	3.84857i	−0.303048	+	0.125527i
$941$	8.10125	−	19.5582i	0.264093	−	0.637577i	−0.735091	−	0.677969i	$-0.762860\pi$
$941$	8.10125	−	19.5582i	0.264093	−	0.637577i	0.999184	+	0.0403913i	$0.0128604\pi$
$942$	−3.61238	−	1.49630i	−0.117698	−	0.0487520i
$943$	−10.3869	+	10.3869i	−0.338244	+	0.338244i
$944$	26.5017	−	26.5017i	0.862558	−	0.862558i
$945$	1.01626	+	0.420947i	0.0330588	+	0.0136934i
$946$	3.01003	−	7.26685i	0.0978644	−	0.236266i
$947$	34.7223	−	14.3824i	1.12832	−	0.467366i	0.261112	−	0.965309i	$-0.415911\pi$
$947$	34.7223	−	14.3824i	1.12832	−	0.467366i	0.867210	+	0.497942i	$0.165911\pi$
$948$		−	4.62845i		−	0.150325i
$949$	6.24777	+	15.0834i	0.202811	+	0.489629i
$950$	0.686292	+	0.686292i	0.0222662	+	0.0222662i
$951$	−15.1043			−0.489789
$952$		0			0
$953$	21.2794			0.689307			0.344654	−	0.938730i	$-0.387996\pi$
$953$	21.2794			0.689307			0.344654	+	0.938730i	$0.387996\pi$
$954$	1.01250	+	1.01250i	0.0327808	+	0.0327808i
$955$	1.61544	+	3.90001i	0.0522744	+	0.126201i
$956$			10.3163i			0.333654i
$957$	−43.8491	+	18.1629i	−1.41744	+	0.587122i
$958$	1.32281	−	3.19354i	0.0427380	−	0.103179i
$959$	19.6614	+	8.14402i	0.634900	+	0.262984i
$960$	3.07777	−	3.07777i	0.0993346	−	0.0993346i
$961$	2.26096	−	2.26096i	0.0729341	−	0.0729341i
$962$	4.36640	+	1.80862i	0.140778	+	0.0583123i
$963$	−5.03348	+	12.1519i	−0.162201	+	0.391589i
$964$	−10.4493	+	4.32825i	−0.336550	+	0.139404i
$965$			1.85683i			0.0597734i
$966$	0.311895	+	0.752981i	0.0100351	+	0.0242268i
$967$	−18.5488	−	18.5488i	−0.596489	−	0.596489i	0.342887	−	0.939377i	$-0.388595\pi$
$967$	−18.5488	−	18.5488i	−0.596489	−	0.596489i	−0.939377	+	0.342887i	$0.888595\pi$
$968$	11.8579			0.381128
$969$		0			0
$970$	−0.430067			−0.0138086
$971$	14.7250	+	14.7250i	0.472549	+	0.472549i	0.902738	−	0.430190i	$-0.141553\pi$
$971$	14.7250	+	14.7250i	0.472549	+	0.472549i	−0.430190	+	0.902738i	$0.641553\pi$
$972$	0.746474	+	1.80215i	0.0239432	+	0.0578039i
$973$			23.0650i			0.739429i
$974$	0.00608683	−	0.00252125i	0.000195035	−	8.07860e-5i
$975$	4.40705	−	10.6396i	0.141139	−	0.340739i
$976$	−10.1690	−	4.21214i	−0.325502	−	0.134827i
$977$	11.5187	−	11.5187i	0.368517	−	0.368517i	−0.498419	−	0.866936i	$-0.666086\pi$
$977$	11.5187	−	11.5187i	0.368517	−	0.368517i	0.866936	+	0.498419i	$0.166086\pi$
$978$	−2.60651	+	2.60651i	−0.0833471	+	0.0833471i
$979$	−9.09613	−	3.76774i	−0.290714	−	0.120418i
$980$	−1.90618	+	4.60192i	−0.0608906	+	0.147003i
$981$	−16.0659	+	6.65470i	−0.512943	+	0.212468i
$982$		−	1.48187i		−	0.0472884i
$983$	0.356535	+	0.860752i	0.0113717	+	0.0274537i	0.929463	−	0.368914i	$-0.120270\pi$
$983$	0.356535	+	0.860752i	0.0113717	+	0.0274537i	−0.918092	+	0.396368i	$0.870270\pi$
$984$	−4.29628	−	4.29628i	−0.136960	−	0.136960i
$985$	2.88620			0.0919621
$986$		0			0
$987$	−14.0025			−0.445704
$988$	−3.28622	−	3.28622i	−0.104548	−	0.104548i
$989$	5.80724	+	14.0199i	0.184659	+	0.445807i
$990$		−	0.700037i		−	0.0222487i
$991$	20.0456	−	8.30316i	0.636769	−	0.263759i	−0.0408568	−	0.999165i	$-0.513009\pi$
$991$	20.0456	−	8.30316i	0.636769	−	0.263759i	0.677626	+	0.735407i	$0.263009\pi$
$992$	−5.20412	+	12.5639i	−0.165231	+	0.398903i
$993$	20.9507	+	8.67808i	0.664851	+	0.275390i
$994$	0.104291	−	0.104291i	0.00330792	−	0.00330792i
$995$	1.10715	−	1.10715i	0.0350989	−	0.0350989i
$996$	24.0733	+	9.97151i	0.762793	+	0.315959i
$997$	−1.23495	+	2.98144i	−0.0391114	+	0.0944232i	−0.942228	−	0.334972i	$-0.891273\pi$
$997$	−1.23495	+	2.98144i	−0.0391114	+	0.0944232i	0.903117	+	0.429395i	$0.141273\pi$
$998$	−3.82779	+	1.58552i	−0.121167	+	0.0501888i
$999$		−	8.48705i		−	0.268518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.k.712.1		16
17.2	even	8		867.2.h.i.757.3		16
17.3	odd	16		867.2.d.f.577.3		8
17.4	even	4		867.2.h.i.733.3		16
17.5	odd	16		867.2.a.l.1.3		4
17.6	odd	16		51.2.e.a.13.2	yes	8
17.7	odd	16		51.2.e.a.4.3	✓	8
17.8	even	8	inner	867.2.h.k.688.1		16
17.9	even	8	inner	867.2.h.k.688.2		16
17.10	odd	16		867.2.e.g.616.3		8
17.11	odd	16		867.2.e.g.829.2		8
17.12	odd	16		867.2.a.k.1.3		4
17.13	even	4		867.2.h.i.733.4		16
17.14	odd	16		867.2.d.f.577.4		8
17.15	even	8		867.2.h.i.757.4		16
17.16	even	2	inner	867.2.h.k.712.2		16
51.5	even	16		2601.2.a.be.1.2		4
51.23	even	16		153.2.f.b.64.3		8
51.29	even	16		2601.2.a.bf.1.2		4
51.41	even	16		153.2.f.b.55.2		8
68.7	even	16		816.2.bd.e.769.3		8
68.23	even	16		816.2.bd.e.625.3		8
204.23	odd	16		2448.2.be.x.1441.3		8
204.143	odd	16		2448.2.be.x.1585.3		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
51.2.e.a.4.3	✓	8	17.7	odd	16
51.2.e.a.13.2	yes	8	17.6	odd	16
153.2.f.b.55.2		8	51.41	even	16
153.2.f.b.64.3		8	51.23	even	16
816.2.bd.e.625.3		8	68.23	even	16
816.2.bd.e.769.3		8	68.7	even	16
867.2.a.k.1.3		4	17.12	odd	16
867.2.a.l.1.3		4	17.5	odd	16
867.2.d.f.577.3		8	17.3	odd	16
867.2.d.f.577.4		8	17.14	odd	16
867.2.e.g.616.3		8	17.10	odd	16
867.2.e.g.829.2		8	17.11	odd	16
867.2.h.i.733.3		16	17.4	even	4
867.2.h.i.733.4		16	17.13	even	4
867.2.h.i.757.3		16	17.2	even	8
867.2.h.i.757.4		16	17.15	even	8
867.2.h.k.688.1		16	17.8	even	8	inner
867.2.h.k.688.2		16	17.9	even	8	inner
867.2.h.k.712.1		16	1.1	even	1	trivial
867.2.h.k.712.2		16	17.16	even	2	inner
2448.2.be.x.1441.3		8	204.23	odd	16
2448.2.be.x.1585.3		8	204.143	odd	16
2601.2.a.be.1.2		4	51.5	even	16
2601.2.a.bf.1.2		4	51.29	even	16

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:	\( N \)	\(=\)	\( 867 = 3 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	867.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.157113 - 0.157113i) q^{2} +(-0.382683 - 0.923880i) q^{3} -1.95063i q^{4} +(0.587961 - 0.243542i) q^{5} +(-0.0850290 + 0.205278i) q^{6} +(1.59687 + 0.661445i) q^{7} +(-0.620696 + 0.620696i) q^{8} +(-0.707107 + 0.707107i) q^{9} +(-0.130640 - 0.0541128i) q^{10} +(1.89452 - 4.57379i) q^{11} +(-1.80215 + 0.746474i) q^{12} -2.50625i q^{13} +(-0.146967 - 0.354811i) q^{14} +(-0.450006 - 0.450006i) q^{15} -3.70622 q^{16} +0.222191 q^{18} +(0.672198 + 0.672198i) q^{19} +(-0.475060 - 1.14690i) q^{20} -1.72844i q^{21} +(-1.01626 + 0.420947i) q^{22} +(0.812132 - 1.96066i) q^{23} +(0.810978 + 0.335918i) q^{24} +(-3.24915 + 3.24915i) q^{25} +(-0.393764 + 0.393764i) q^{26} +(0.923880 + 0.382683i) q^{27} +(1.29024 - 3.11490i) q^{28} +(8.85727 - 3.66880i) q^{29} +0.141404i q^{30} +(2.01782 + 4.87144i) q^{31} +(1.82369 + 1.82369i) q^{32} -4.95063 q^{33} +1.09999 q^{35} +(1.37930 + 1.37930i) q^{36} +(-3.24785 - 7.84101i) q^{37} -0.211222i q^{38} +(-2.31547 + 0.959100i) q^{39} +(-0.213780 + 0.516110i) q^{40} +(-6.39483 - 2.64882i) q^{41} +(-0.271560 + 0.271560i) q^{42} +(-5.05624 + 5.05624i) q^{43} +(-8.92177 - 3.69552i) q^{44} +(-0.243542 + 0.587961i) q^{45} +(-0.435642 + 0.180449i) q^{46} -8.10124i q^{47} +(1.41831 + 3.42410i) q^{48} +(-2.83726 - 2.83726i) q^{49} +1.02097 q^{50} -4.88877 q^{52} +(4.55687 + 4.55687i) q^{53} +(-0.0850290 - 0.205278i) q^{54} -3.15061i q^{55} +(-1.40173 + 0.580614i) q^{56} +(0.363791 - 0.878269i) q^{57} +(-1.96801 - 0.815176i) q^{58} +(-7.15061 + 7.15061i) q^{59} +(-0.877796 + 0.877796i) q^{60} +(2.74377 + 1.13651i) q^{61} +(0.448342 - 1.08239i) q^{62} +(-1.59687 + 0.661445i) q^{63} +6.83940i q^{64} +(-0.610376 - 1.47358i) q^{65} +(0.777809 + 0.777809i) q^{66} -7.70129 q^{67} -2.12220 q^{69} +(-0.172822 - 0.172822i) q^{70} +(0.146967 + 0.354811i) q^{71} -0.877796i q^{72} +(-6.01834 + 2.49288i) q^{73} +(-0.721645 + 1.74220i) q^{74} +(4.24522 + 1.75843i) q^{75} +(1.31121 - 1.31121i) q^{76} +(6.05062 - 6.05062i) q^{77} +(0.514478 + 0.213104i) q^{78} +(-0.908030 + 2.19218i) q^{79} +(-2.17912 + 0.902620i) q^{80} -1.00000i q^{81} +(0.588546 + 1.42088i) q^{82} +(-9.44563 - 9.44563i) q^{83} -3.37155 q^{84} +1.58880 q^{86} +(-6.77906 - 6.77906i) q^{87} +(1.66301 + 4.01485i) q^{88} -1.98875i q^{89} +(0.130640 - 0.0541128i) q^{90} +(1.65775 - 4.00215i) q^{91} +(-3.82453 - 1.58417i) q^{92} +(3.72844 - 3.72844i) q^{93} +(-1.27281 + 1.27281i) q^{94} +(0.558934 + 0.231518i) q^{95} +(0.986972 - 2.38276i) q^{96} +(2.80990 - 1.16390i) q^{97} +0.891542i q^{98} +(1.89452 + 4.57379i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{2} - 32 q^{8} - 8 q^{15} - 24 q^{16} - 8 q^{18} - 32 q^{25} - 40 q^{26} - 16 q^{32} - 24 q^{33} + 16 q^{35} - 48 q^{42} - 48 q^{43} - 32 q^{49} + 120 q^{50} - 32 q^{52} - 16 q^{53} - 56 q^{59}+ \cdots + 48 q^{94}+O(q^{100}) \) 16 * q + 8 * q^2 - 32 * q^8 - 8 * q^15 - 24 * q^16 - 8 * q^18 - 32 * q^25 - 40 * q^26 - 16 * q^32 - 24 * q^33 + 16 * q^35 - 48 * q^42 - 48 * q^43 - 32 * q^49 + 120 * q^50 - 32 * q^52 - 16 * q^53 - 56 * q^59 - 24 * q^60 + 24 * q^66 - 16 * q^67 - 24 * q^69 + 64 * q^70 + 64 * q^76 + 40 * q^77 - 16 * q^83 - 96 * q^84 - 16 * q^86 - 8 * q^87 + 16 * q^93 + 48 * q^94

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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