LMFDB - Embedded newform 867.2.h.i.757.3

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			757.3
Root			$0.626225 - 1.51184i$ of defining polynomial
Character	$\chi$	$=$	867.757
Dual form			867.2.h.i.733.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.157113 - 0.157113i) q^{2} +(-0.923880 - 0.382683i) q^{3} +1.95063i q^{4} +(-0.243542 + 0.587961i) q^{5} +(-0.205278 + 0.0850290i) q^{6} +(-0.661445 - 1.59687i) q^{7} +(0.620696 + 0.620696i) q^{8} +(0.707107 + 0.707107i) q^{9} +(0.0541128 + 0.130640i) q^{10} +(4.57379 - 1.89452i) q^{11} +(0.746474 - 1.80215i) q^{12} +2.50625i q^{13} +(-0.354811 - 0.146967i) q^{14} +(0.450006 - 0.450006i) q^{15} -3.70622 q^{16} +0.222191 q^{18} +(-0.672198 + 0.672198i) q^{19} +(-1.14690 - 0.475060i) q^{20} +1.72844i q^{21} +(0.420947 - 1.01626i) q^{22} +(1.96066 - 0.812132i) q^{23} +(-0.335918 - 0.810978i) q^{24} +(3.24915 + 3.24915i) q^{25} +(0.393764 + 0.393764i) q^{26} +(-0.382683 - 0.923880i) q^{27} +(3.11490 - 1.29024i) q^{28} +(-3.66880 + 8.85727i) q^{29} -0.141404i q^{30} +(4.87144 + 2.01782i) q^{31} +(-1.82369 + 1.82369i) q^{32} -4.95063 q^{33} +1.09999 q^{35} +(-1.37930 + 1.37930i) q^{36} +(-7.84101 - 3.24785i) q^{37} +0.211222i q^{38} +(0.959100 - 2.31547i) q^{39} +(-0.516110 + 0.213780i) q^{40} +(2.64882 + 6.39483i) q^{41} +(0.271560 + 0.271560i) q^{42} +(5.05624 + 5.05624i) q^{43} +(3.69552 + 8.92177i) q^{44} +(-0.587961 + 0.243542i) q^{45} +(0.180449 - 0.435642i) q^{46} +8.10124i q^{47} +(3.42410 + 1.41831i) q^{48} +(2.83726 - 2.83726i) q^{49} +1.02097 q^{50} -4.88877 q^{52} +(-4.55687 + 4.55687i) q^{53} +(-0.205278 - 0.0850290i) q^{54} +3.15061i q^{55} +(0.580614 - 1.40173i) q^{56} +(0.878269 - 0.363791i) q^{57} +(0.815176 + 1.96801i) q^{58} +(7.15061 + 7.15061i) q^{59} +(0.877796 + 0.877796i) q^{60} +(-1.13651 - 2.74377i) q^{61} +(1.08239 - 0.448342i) q^{62} +(0.661445 - 1.59687i) q^{63} -6.83940i q^{64} +(-1.47358 - 0.610376i) q^{65} +(-0.777809 + 0.777809i) q^{66} -7.70129 q^{67} -2.12220 q^{69} +(0.172822 - 0.172822i) q^{70} +(0.354811 + 0.146967i) q^{71} +0.877796i q^{72} +(2.49288 - 6.01834i) q^{73} +(-1.74220 + 0.721645i) q^{74} +(-1.75843 - 4.24522i) q^{75} +(-1.31121 - 1.31121i) q^{76} +(-6.05062 - 6.05062i) q^{77} +(-0.213104 - 0.514478i) q^{78} +(-2.19218 + 0.908030i) q^{79} +(0.902620 - 2.17912i) q^{80} +1.00000i q^{81} +(1.42088 + 0.588546i) q^{82} +(9.44563 - 9.44563i) q^{83} -3.37155 q^{84} +1.58880 q^{86} +(6.77906 - 6.77906i) q^{87} +(4.01485 + 1.66301i) q^{88} +1.98875i q^{89} +(-0.0541128 + 0.130640i) q^{90} +(4.00215 - 1.65775i) q^{91} +(1.58417 + 3.82453i) q^{92} +(-3.72844 - 3.72844i) q^{93} +(1.27281 + 1.27281i) q^{94} +(-0.231518 - 0.558934i) q^{95} +(2.38276 - 0.986972i) q^{96} +(-1.16390 + 2.80990i) q^{97} -0.891542i q^{98} +(4.57379 + 1.89452i) 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 $\left(\mathbb{Z}/867\mathbb{Z}\right)^\times$.

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

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	$-0.724969\pi$
$2$	0.157113	−	0.157113i	0.111096	−	0.111096i	0.760469	+	0.649374i	$0.224969\pi$
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$3$	−0.923880	−	0.382683i	−0.533402	−	0.220942i
$4$			1.95063i			0.975315i
$5$	−0.243542	+	0.587961i	−0.108915	+	0.262944i	−0.968935	−	0.247317i	$-0.920451\pi$
$5$	−0.243542	+	0.587961i	−0.108915	+	0.262944i	0.860020	+	0.510261i	$0.170451\pi$
$6$	−0.205278	+	0.0850290i	−0.0838044	+	0.0347129i
$7$	−0.661445	−	1.59687i	−0.250003	−	0.603560i	0.748201	−	0.663472i	$-0.230918\pi$
$7$	−0.661445	−	1.59687i	−0.250003	−	0.603560i	−0.998204	+	0.0599122i	$0.980918\pi$
$8$	0.620696	+	0.620696i	0.219449	+	0.219449i
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$	0.0541128	+	0.130640i	0.0171120	+	0.0413120i
$11$	4.57379	−	1.89452i	1.37905	−	0.571221i	0.434822	−	0.900517i	$-0.356811\pi$
$11$	4.57379	−	1.89452i	1.37905	−	0.571221i	0.944227	+	0.329296i	$0.106811\pi$
$12$	0.746474	−	1.80215i	0.215489	−	0.520235i
$13$			2.50625i			0.695108i	0.937660	+	0.347554i	$0.112988\pi$
$13$			2.50625i			0.695108i	−0.937660	+	0.347554i	$0.887012\pi$
$14$	−0.354811	−	0.146967i	−0.0948272	−	0.0392787i
$15$	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	$-0.784779\pi$
$19$	−0.672198	+	0.672198i	−0.154213	+	0.154213i	0.625784	+	0.779997i	$0.284779\pi$
$20$	−1.14690	−	0.475060i	−0.256454	−	0.106227i
$21$			1.72844i			0.377176i
$22$	0.420947	−	1.01626i	0.0897462	−	0.216666i
$23$	1.96066	−	0.812132i	0.408826	−	0.169341i	−0.168786	−	0.985653i	$-0.553985\pi$
$23$	1.96066	−	0.812132i	0.408826	−	0.169341i	0.577612	+	0.816311i	$0.303985\pi$
$24$	−0.335918	−	0.810978i	−0.0685690	−	0.165540i
$25$	3.24915	+	3.24915i	0.649830	+	0.649830i
$26$	0.393764	+	0.393764i	0.0772235	+	0.0772235i
$27$	−0.382683	−	0.923880i	−0.0736475	−	0.177801i
$28$	3.11490	−	1.29024i	0.588662	−	0.243832i
$29$	−3.66880	+	8.85727i	−0.681279	+	1.64475i	0.0803715	+	0.996765i	$0.474389\pi$
$29$	−3.66880	+	8.85727i	−0.681279	+	1.64475i	−0.761650	+	0.647988i	$0.775611\pi$
$30$		−	0.141404i		−	0.0258167i
$31$	4.87144	+	2.01782i	0.874937	+	0.362411i	0.774531	−	0.632536i	$-0.217986\pi$
$31$	4.87144	+	2.01782i	0.874937	+	0.362411i	0.100406	+	0.994947i	$0.467986\pi$
$32$	−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
$37$	−7.84101	−	3.24785i	−1.28905	−	0.533944i	−0.370351	−	0.928892i	$-0.620763\pi$
$37$	−7.84101	−	3.24785i	−1.28905	−	0.533944i	−0.918703	+	0.394948i	$0.870763\pi$
$38$			0.211222i			0.0342647i
$39$	0.959100	−	2.31547i	0.153579	−	0.370772i
$40$	−0.516110	+	0.213780i	−0.0816042	+	0.0338016i
$41$	2.64882	+	6.39483i	0.413677	+	0.998704i	0.984142	+	0.177382i	$0.0567630\pi$
$41$	2.64882	+	6.39483i	0.413677	+	0.998704i	−0.570465	+	0.821322i	$0.693237\pi$
$42$	0.271560	+	0.271560i	0.0419027	+	0.0419027i
$43$	5.05624	+	5.05624i	0.771070	+	0.771070i	0.978294	−	0.207224i	$-0.0664429\pi$
$43$	5.05624	+	5.05624i	0.771070	+	0.771070i	−0.207224	+	0.978294i	$0.566443\pi$
$44$	3.69552	+	8.92177i	0.557120	+	1.34501i
$45$	−0.587961	+	0.243542i	−0.0876481	+	0.0363050i
$46$	0.180449	−	0.435642i	0.0266057	−	0.0642319i
$47$			8.10124i			1.18169i	0.806786	+	0.590843i	$0.201205\pi$
$47$			8.10124i			1.18169i	−0.806786	+	0.590843i	$0.798795\pi$
$48$	3.42410	+	1.41831i	0.494227	+	0.204715i
$49$	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	$-0.895945\pi$
$53$	−4.55687	+	4.55687i	−0.625934	+	0.625934i	0.321109	+	0.947042i	$0.395945\pi$
$54$	−0.205278	−	0.0850290i	−0.0279348	−	0.0115710i
$55$			3.15061i			0.424828i
$56$	0.580614	−	1.40173i	0.0775878	−	0.187314i
$57$	0.878269	−	0.363791i	0.116330	−	0.0481853i
$58$	0.815176	+	1.96801i	0.107038	+	0.258412i
$59$	7.15061	+	7.15061i	0.930930	+	0.930930i	0.997764	−	0.0668345i	$-0.0212899\pi$
$59$	7.15061	+	7.15061i	0.930930	+	0.930930i	−0.0668345	+	0.997764i	$0.521290\pi$
$60$	0.877796	+	0.877796i	0.113323	+	0.113323i
$61$	−1.13651	−	2.74377i	−0.145515	−	0.351303i	0.834271	−	0.551355i	$-0.185889\pi$
$61$	−1.13651	−	2.74377i	−0.145515	−	0.351303i	−0.979785	+	0.200052i	$0.935889\pi$
$62$	1.08239	−	0.448342i	0.137464	−	0.0569394i
$63$	0.661445	−	1.59687i	0.0833343	−	0.201187i
$64$		−	6.83940i		−	0.854925i
$65$	−1.47358	−	0.610376i	−0.182775	−	0.0757078i
$66$	−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
$71$	0.354811	+	0.146967i	0.0421083	+	0.0174418i	0.403638	−	0.914919i	$-0.367745\pi$
$71$	0.354811	+	0.146967i	0.0421083	+	0.0174418i	−0.361530	+	0.932361i	$0.617745\pi$
$72$			0.877796i			0.103449i
$73$	2.49288	−	6.01834i	0.291769	−	0.704393i	−0.708230	−	0.705982i	$-0.750506\pi$
$73$	2.49288	−	6.01834i	0.291769	−	0.704393i	0.999999	+	0.00158913i	$0.000505836\pi$
$74$	−1.74220	+	0.721645i	−0.202527	+	0.0838895i
$75$	−1.75843	−	4.24522i	−0.203046	−	0.490195i
$76$	−1.31121	−	1.31121i	−0.150406	−	0.150406i
$77$	−6.05062	−	6.05062i	−0.689532	−	0.689532i
$78$	−0.213104	−	0.514478i	−0.0241292	−	0.0582531i
$79$	−2.19218	+	0.908030i	−0.246639	+	0.102161i	−0.502579	−	0.864531i	$-0.667615\pi$
$79$	−2.19218	+	0.908030i	−0.246639	+	0.102161i	0.255939	+	0.966693i	$0.417615\pi$
$80$	0.902620	−	2.17912i	0.100916	−	0.243633i
$81$			1.00000i			0.111111i
$82$	1.42088	+	0.588546i	0.156909	+	0.0649940i
$83$	9.44563	−	9.44563i	1.03679	−	1.03679i	0.0374961	−	0.999297i	$-0.488062\pi$
$83$	9.44563	−	9.44563i	1.03679	−	1.03679i	0.999297	−	0.0374961i	$-0.0119382\pi$
$84$	−3.37155			−0.367866
$85$		0			0
$86$	1.58880			0.171325
$87$	6.77906	−	6.77906i	0.726791	−	0.726791i
$88$	4.01485	+	1.66301i	0.427985	+	0.177277i
$89$			1.98875i			0.210807i	0.994430	+	0.105404i	$0.0336135\pi$
$89$			1.98875i			0.210807i	−0.994430	+	0.105404i	$0.966387\pi$
$90$	−0.0541128	+	0.130640i	−0.00570400	+	0.0137707i
$91$	4.00215	−	1.65775i	0.419540	−	0.173779i
$92$	1.58417	+	3.82453i	0.165161	+	0.398734i
$93$	−3.72844	−	3.72844i	−0.386621	−	0.386621i
$94$	1.27281	+	1.27281i	0.131280	+	0.131280i
$95$	−0.231518	−	0.558934i	−0.0237533	−	0.0573455i
$96$	2.38276	−	0.986972i	0.243190	−	0.100732i
$97$	−1.16390	+	2.80990i	−0.118176	+	0.285302i	−0.971888	−	0.235443i	$-0.924346\pi$
$97$	−1.16390	+	2.80990i	−0.118176	+	0.285302i	0.853712	+	0.520745i	$0.174346\pi$
$98$		−	0.891542i		−	0.0900594i
$99$	4.57379	+	1.89452i	0.459683	+	0.190407i
$100$	−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
$105$	−1.01626	−	0.420947i	−0.0991764	−	0.0410802i
$106$			1.43189i			0.139077i
$107$	−5.03348	+	12.1519i	−0.486604	+	1.17477i	0.469813	+	0.882766i	$0.344321\pi$
$107$	−5.03348	+	12.1519i	−0.486604	+	1.17477i	−0.956418	+	0.292001i	$0.905679\pi$
$108$	1.80215	−	0.746474i	0.173412	−	0.0718295i
$109$	−6.65470	−	16.0659i	−0.637404	−	1.53883i	−0.830125	−	0.557577i	$-0.811731\pi$
$109$	−6.65470	−	16.0659i	−0.637404	−	1.53883i	0.192721	−	0.981254i	$-0.438269\pi$
$110$	0.495001	+	0.495001i	0.0471965	+	0.0471965i
$111$	6.00125	+	6.00125i	0.569613	+	0.569613i
$112$	2.45146	+	5.91836i	0.231642	+	0.559232i
$113$	0.716969	−	0.296978i	0.0674468	−	0.0279374i	−0.348705	−	0.937233i	$-0.613378\pi$
$113$	0.716969	−	0.296978i	0.0674468	−	0.0279374i	0.416152	+	0.909295i	$0.363378\pi$
$114$	0.0808312	−	0.195144i	0.00757053	−	0.0182769i
$115$			1.35058i			0.125942i
$116$	−17.2773	−	7.15647i	−1.60415	−	0.664462i
$117$	−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
$122$	−0.609641	−	0.252522i	−0.0551943	−	0.0228622i
$123$		−	6.92171i		−	0.624110i
$124$	−3.93602	+	9.50238i	−0.353465	+	0.853339i
$125$	−5.64148	+	2.33678i	−0.504590	+	0.209008i
$126$	−0.146967	−	0.354811i	−0.0130929	−	0.0316091i
$127$	−7.67345	−	7.67345i	−0.680908	−	0.680908i	0.279297	−	0.960205i	$-0.409899\pi$
$127$	−7.67345	−	7.67345i	−0.680908	−	0.680908i	−0.960205	+	0.279297i	$0.909899\pi$
$128$	−4.72193	−	4.72193i	−0.417364	−	0.417364i
$129$	−2.73642	−	6.60630i	−0.240928	−	0.581652i
$130$	−0.327416	+	0.135620i	−0.0287163	+	0.0118947i
$131$	−0.270260	+	0.652465i	−0.0236127	+	0.0570062i	−0.935246	−	0.353998i	$-0.884822\pi$
$131$	−0.270260	+	0.652465i	−0.0236127	+	0.0570062i	0.911633	+	0.411004i	$0.134822\pi$
$132$		−	9.65685i		−	0.840521i
$133$	1.51803	+	0.628790i	0.131630	+	0.0545230i
$134$	−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
$139$	12.3286	+	5.10668i	1.04570	+	0.433143i	0.838355	−	0.545125i	$-0.183518\pi$
$139$	12.3286	+	5.10668i	1.04570	+	0.433143i	0.207345	+	0.978268i	$0.433518\pi$
$140$			2.14567i			0.181342i
$141$	3.10021	−	7.48457i	0.261085	−	0.630314i
$142$	0.0788359	−	0.0326549i	0.00661576	−	0.00274034i
$143$	4.74815	+	11.4630i	0.397060	+	0.958588i
$144$	−2.62070	−	2.62070i	−0.218391	−	0.218391i
$145$	−4.31423	−	4.31423i	−0.358277	−	0.358277i
$146$	−0.553896	−	1.33722i	−0.0458407	−	0.110669i
$147$	−3.70706	+	1.53552i	−0.305753	+	0.126647i
$148$	6.33536	−	15.2949i	0.520764	−	1.25723i
$149$			0.356892i			0.0292377i	0.999893	+	0.0146189i	$0.00465349\pi$
$149$			0.356892i			0.0292377i	−0.999893	+	0.0146189i	$0.995347\pi$
$150$	−0.943250	−	0.390707i	−0.0770161	−	0.0319011i
$151$	−6.45813	+	6.45813i	−0.525555	+	0.525555i	−0.919244	−	0.393689i	$-0.871199\pi$
$151$	−6.45813	+	6.45813i	−0.525555	+	0.525555i	0.393689	+	0.919244i	$0.371199\pi$
$152$	−0.834460			−0.0676837
$153$		0			0
$154$	−1.90126			−0.153208
$155$	−2.37280	+	2.37280i	−0.190588	+	0.190588i
$156$	4.51663	+	1.87085i	0.361620	+	0.149788i
$157$		−	17.5975i		−	1.40443i	−0.711964	−	0.702216i	$-0.752194\pi$
$157$		−	17.5975i		−	1.40443i	0.711964	−	0.702216i	$-0.247806\pi$
$158$	−0.201756	+	0.487083i	−0.0160509	+	0.0387503i
$159$	5.95383	−	2.46616i	0.472170	−	0.195579i
$160$	−0.628114	−	1.51640i	−0.0496568	−	0.119882i
$161$	−2.59374	−	2.59374i	−0.204415	−	0.204415i
$162$	0.157113	+	0.157113i	0.0123440	+	0.0123440i
$163$	−6.34874	−	15.3272i	−0.497272	−	1.20052i	−0.950947	−	0.309353i	$-0.899888\pi$
$163$	−6.34874	−	15.3272i	−0.497272	−	1.20052i	0.453676	−	0.891167i	$-0.350112\pi$
$164$	−12.4739	+	5.16688i	−0.974052	+	0.403465i
$165$	1.20568	−	2.91078i	0.0938624	−	0.226604i
$166$		−	2.96806i		−	0.230366i
$167$	−13.1407	−	5.44308i	−1.01686	−	0.421198i	−0.188908	−	0.981995i	$-0.560495\pi$
$167$	−13.1407	−	5.44308i	−1.01686	−	0.421198i	−0.827953	+	0.560797i	$0.810495\pi$
$168$	−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
$173$	1.74919	+	0.724538i	0.132988	+	0.0550856i	0.448185	−	0.893941i	$-0.352071\pi$
$173$	1.74919	+	0.724538i	0.132988	+	0.0550856i	−0.315197	+	0.949026i	$0.602071\pi$
$174$		−	2.13016i		−	0.161487i
$175$	3.03933	−	7.33760i	0.229752	−	0.554670i
$176$	−16.9515	+	7.02153i	−1.27777	+	0.529268i
$177$	−3.86988	−	9.34272i	−0.290878	−	0.702242i
$178$	0.312459	+	0.312459i	0.0234198	+	0.0234198i
$179$	−15.7309	−	15.7309i	−1.17579	−	1.17579i	−0.980808	−	0.194978i	$-0.937536\pi$
$179$	−15.7309	−	15.7309i	−1.17579	−	1.17579i	−0.194978	−	0.980808i	$-0.562464\pi$
$180$	−0.475060	−	1.14690i	−0.0354089	−	0.0854846i
$181$	−10.7301	+	4.44456i	−0.797563	+	0.330361i	−0.743980	−	0.668202i	$-0.767064\pi$
$181$	−10.7301	+	4.44456i	−0.797563	+	0.330361i	−0.0535830	+	0.998563i	$0.517064\pi$
$182$	0.368337	−	0.889244i	0.0273029	−	0.0659151i
$183$			2.96983i			0.219536i
$184$	1.72106	+	0.712887i	0.126878	+	0.0525547i
$185$	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
$190$	−0.124190	−	0.0514414i	−0.00900972	−	0.00373195i
$191$		−	6.63311i		−	0.479955i	−0.970778	−	0.239978i	$-0.922860\pi$
$191$		−	6.63311i		−	0.479955i	0.970778	−	0.239978i	$-0.0771401\pi$
$192$	−2.61732	+	6.31878i	−0.188889	+	0.456019i
$193$	−2.69559	+	1.11655i	−0.194033	+	0.0803710i	−0.477584	−	0.878586i	$-0.658487\pi$
$193$	−2.69559	+	1.11655i	−0.194033	+	0.0803710i	0.283551	+	0.958957i	$0.408487\pi$
$194$	0.258608	+	0.624336i	0.0185670	+	0.0448247i
$195$	1.12783	+	1.12783i	0.0807654	+	0.0807654i
$196$	5.53445	+	5.53445i	0.395318	+	0.395318i
$197$	−1.73553	−	4.18995i	−0.123652	−	0.298521i	0.849917	−	0.526917i	$-0.176652\pi$
$197$	−1.73553	−	4.18995i	−0.123652	−	0.298521i	−0.973568	+	0.228395i	$0.926652\pi$
$198$	1.01626	−	0.420947i	0.0722222	−	0.0299154i
$199$	−0.941512	+	2.27301i	−0.0667420	+	0.161129i	−0.953731	−	0.300661i	$-0.902793\pi$
$199$	−0.941512	+	2.27301i	−0.0667420	+	0.161129i	0.886989	+	0.461790i	$0.152793\pi$
$200$			4.03346i			0.285209i
$201$	7.11506	+	2.94715i	0.501858	+	0.207876i
$202$	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
$207$	1.96066	+	0.812132i	0.136275	+	0.0564471i
$208$		−	9.28872i		−	0.644057i
$209$	−1.80099	+	4.34798i	−0.124577	+	0.300756i
$210$	−0.225803	+	0.0935308i	−0.0155819	+	0.00645424i
$211$	7.61684	+	18.3887i	0.524365	+	1.26593i	0.935168	+	0.354205i	$0.115248\pi$
$211$	7.61684	+	18.3887i	0.524365	+	1.26593i	−0.410803	+	0.911724i	$0.634752\pi$
$212$	−8.88877	−	8.88877i	−0.610483	−	0.610483i
$213$	−0.271560	−	0.271560i	−0.0186070	−	0.0186070i
$214$	1.11839	+	2.70004i	0.0764519	+	0.184571i
$215$	−4.20428	+	1.74147i	−0.286730	+	0.118767i
$216$	0.335918	−	0.810978i	0.0228563	−	0.0551801i
$217$		−	9.11373i		−	0.618681i
$218$	−3.56970	−	1.47862i	−0.241770	−	0.100145i
$219$	−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	$-0.590306\pi$
$223$	10.1562	−	10.1562i	0.680111	−	0.680111i	0.960025	+	0.279914i	$0.0903059\pi$
$224$	4.11846	+	1.70592i	0.275176	+	0.113982i
$225$			4.59499i			0.306333i
$226$	0.0659860	−	0.159304i	0.00438932	−	0.0105968i
$227$	10.0466	−	4.16145i	0.666818	−	0.276205i	−0.0234865	−	0.999724i	$-0.507477\pi$
$227$	10.0466	−	4.16145i	0.666818	−	0.276205i	0.690304	+	0.723519i	$0.257477\pi$
$228$	0.709621	+	1.71318i	0.0469958	+	0.113458i
$229$	−13.4280	−	13.4280i	−0.887345	−	0.887345i	0.106923	−	0.994267i	$-0.465900\pi$
$229$	−13.4280	−	13.4280i	−0.887345	−	0.887345i	−0.994267	+	0.106923i	$0.965900\pi$
$230$	0.212194	+	0.212194i	0.0139916	+	0.0139916i
$231$	3.27457	+	7.90551i	0.215451	+	0.520145i
$232$	−7.77487	+	3.22046i	−0.510445	+	0.211433i
$233$	−2.70970	+	6.54179i	−0.177518	+	0.428567i	−0.987445	−	0.157964i	$-0.949507\pi$
$233$	−2.70970	+	6.54179i	−0.177518	+	0.428567i	0.809926	+	0.586531i	$0.199507\pi$
$234$			0.556867i			0.0364035i
$235$	−4.76322	−	1.97299i	−0.310718	−	0.128704i
$236$	−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
$241$	−5.35689	−	2.21890i	−0.345068	−	0.142932i	0.203417	−	0.979092i	$-0.434795\pi$
$241$	−5.35689	−	2.21890i	−0.345068	−	0.142932i	−0.548485	+	0.836160i	$0.684795\pi$
$242$		−	3.00153i		−	0.192945i
$243$	0.382683	−	0.923880i	0.0245492	−	0.0592669i
$244$	5.35207	−	2.21690i	0.342631	−	0.141923i
$245$	0.977210	+	2.35919i	0.0624317	+	0.150723i
$246$	−1.08749	−	1.08749i	−0.0693359	−	0.0693359i
$247$	−1.68469	−	1.68469i	−0.107195	−	0.107195i
$248$	1.77123	+	4.27613i	0.112473	+	0.271535i
$249$	−12.3413	+	5.11194i	−0.782099	+	0.323956i
$250$	−0.519212	+	1.25349i	−0.0328379	+	0.0792776i
$251$		−	8.33190i		−	0.525905i	−0.964809	−	0.262952i	$-0.915304\pi$
$251$		−	8.33190i		−	0.525905i	0.964809	−	0.262952i	$-0.0846962\pi$
$252$	3.11490	+	1.29024i	0.196221	+	0.0812772i
$253$	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	$-0.792374\pi$
$257$	−3.00920	+	3.00920i	−0.187709	+	0.187709i	0.606996	+	0.794705i	$0.292374\pi$
$258$	−1.46786	−	0.608009i	−0.0913851	−	0.0378530i
$259$			14.6694i			0.911509i
$260$	1.19062	−	2.87441i	0.0738390	−	0.178263i
$261$	−8.85727	+	3.66880i	−0.548251	+	0.227093i
$262$	0.0600494	+	0.144972i	0.00370987	+	0.00895641i
$263$	6.43466	+	6.43466i	0.396778	+	0.396778i	0.877095	−	0.480317i	$-0.159478\pi$
$263$	6.43466	+	6.43466i	0.396778	+	0.396778i	−0.480317	+	0.877095i	$0.659478\pi$
$264$	−3.07283	−	3.07283i	−0.189120	−	0.189120i
$265$	−1.56948	−	3.78905i	−0.0964121	−	0.232759i
$266$	0.337294	−	0.139712i	0.0206808	−	0.00856628i
$267$	0.761063	−	1.83737i	0.0465763	−	0.112445i
$268$		−	15.0224i		−	0.917637i
$269$	19.7544	+	8.18254i	1.20445	+	0.498898i	0.892433	−	0.451180i	$-0.148997\pi$
$269$	19.7544	+	8.18254i	1.20445	+	0.498898i	0.312013	+	0.950078i	$0.398997\pi$
$270$	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
$275$	21.0165	+	8.70532i	1.26734	+	0.524950i
$276$		−	4.13964i		−	0.249177i
$277$	1.27821	−	3.08588i	0.0768003	−	0.185412i	−0.880816	−	0.473458i	$-0.843006\pi$
$277$	1.27821	−	3.08588i	0.0768003	−	0.185412i	0.957617	+	0.288046i	$0.0930055\pi$
$278$	2.73931	−	1.13466i	0.164293	−	0.0680524i
$279$	2.01782	+	4.87144i	0.120804	+	0.291646i
$280$	0.682757	+	0.682757i	0.0408026	+	0.0408026i
$281$	3.30752	+	3.30752i	0.197310	+	0.197310i	0.798846	−	0.601536i	$-0.205444\pi$
$281$	3.30752	+	3.30752i	0.197310	+	0.197310i	−0.601536	+	0.798846i	$0.705444\pi$
$282$	−0.688840	−	1.66301i	−0.0410198	−	0.0990306i
$283$	9.29255	−	3.84910i	0.552384	−	0.228805i	−0.0889908	−	0.996032i	$-0.528364\pi$
$283$	9.29255	−	3.84910i	0.552384	−	0.228805i	0.641375	+	0.767227i	$0.278364\pi$
$284$	−0.286679	+	0.692105i	−0.0170113	+	0.0410689i
$285$			0.604986i			0.0358363i
$286$	2.54699	+	1.05500i	0.150607	+	0.0623833i
$287$	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
$292$	11.7396	+	4.86268i	0.687005	+	0.284567i
$293$		−	5.76934i		−	0.337048i	−0.985698	−	0.168524i	$-0.946100\pi$
$293$		−	5.76934i		−	0.337048i	0.985698	−	0.168524i	$-0.0539001\pi$
$294$	−0.341178	+	0.823678i	−0.0198979	+	0.0480378i
$295$	−5.94575	+	2.46281i	−0.346175	+	0.143390i
$296$	−2.85095	−	6.88281i	−0.165708	−	0.400055i
$297$	−3.50062	−	3.50062i	−0.203127	−	0.203127i
$298$	0.0560723	+	0.0560723i	0.00324818	+	0.00324818i
$299$	2.03541	+	4.91390i	0.117711	+	0.284178i
$300$	8.28085	−	3.43004i	0.478095	−	0.198033i
$301$	4.72973	−	11.4186i	0.272617	−	0.658156i
$302$			2.02931i			0.116774i
$303$	−17.1339	−	7.09710i	−0.984318	−	0.407718i
$304$	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
$309$	−3.13658	−	1.29922i	−0.178434	−	0.0739098i
$310$			0.745595i			0.0423469i
$311$	−0.495691	+	1.19670i	−0.0281081	+	0.0678589i	−0.937310	−	0.348496i	$-0.886693\pi$
$311$	−0.495691	+	1.19670i	−0.0281081	+	0.0678589i	0.909202	+	0.416355i	$0.136693\pi$
$312$	2.03251	−	0.841894i	0.115068	−	0.0476629i
$313$	−7.30953	−	17.6468i	−0.413159	−	0.997454i	−0.984284	−	0.176591i	$-0.943493\pi$
$313$	−7.30953	−	17.6468i	−0.413159	−	0.997454i	0.571125	−	0.820863i	$-0.306507\pi$
$314$	−2.76479	−	2.76479i	−0.156026	−	0.156026i
$315$	0.777809	+	0.777809i	0.0438246	+	0.0438246i
$316$	−1.77123	−	4.27613i	−0.0996396	−	0.240551i
$317$	13.9545	−	5.78015i	0.783763	−	0.324645i	0.0453302	−	0.998972i	$-0.485566\pi$
$317$	13.9545	−	5.78015i	0.783763	−	0.324645i	0.738433	+	0.674327i	$0.235566\pi$
$318$	0.547959	−	1.32289i	0.0307280	−	0.0741840i
$319$			47.4619i			2.65735i
$320$	4.02130	+	1.66568i	0.224798	+	0.0931142i
$321$	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
$326$	−3.40557	−	1.41063i	−0.188617	−	0.0781278i
$327$			17.3896i			0.961645i
$328$	−2.32513	+	5.61335i	−0.128384	+	0.309946i
$329$	12.9366	−	5.35852i	0.713219	−	0.295425i
$330$	−0.267893	−	0.646750i	−0.0147470	−	0.0356024i
$331$	16.0350	+	16.0350i	0.881363	+	0.881363i	0.993673	−	0.112310i	$-0.0358250\pi$
$331$	16.0350	+	16.0350i	0.881363	+	0.881363i	−0.112310	+	0.993673i	$0.535825\pi$
$332$	18.4249	+	18.4249i	1.01120	+	1.01120i
$333$	−3.24785	−	7.84101i	−0.177981	−	0.429685i
$334$	−2.91976	+	1.20940i	−0.159762	+	0.0661757i
$335$	1.87558	−	4.52806i	0.102474	−	0.247394i
$336$		−	6.40598i		−	0.349475i
$337$	−1.49362	−	0.618680i	−0.0813629	−	0.0337016i	0.341631	−	0.939834i	$-0.389021\pi$
$337$	−1.49362	−	0.618680i	−0.0813629	−	0.0337016i	−0.422994	+	0.906133i	$0.639021\pi$
$338$	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
$343$	−17.5855	−	7.28416i	−0.949529	−	0.393308i
$344$			6.27677i			0.338421i
$345$	0.516845	−	1.24777i	0.0278260	−	0.0671779i
$346$	0.388655	−	0.160986i	0.0208942	−	0.00865467i
$347$	−5.87826	−	14.1914i	−0.315562	−	0.761833i	−0.999479	−	0.0322738i	$-0.989725\pi$
$347$	−5.87826	−	14.1914i	−0.315562	−	0.761833i	0.683917	−	0.729559i	$-0.260275\pi$
$348$	13.2234	+	13.2234i	0.708851	+	0.708851i
$349$	−10.6834	−	10.6834i	−0.571872	−	0.571872i	0.360779	−	0.932651i	$-0.382511\pi$
$349$	−10.6834	−	10.6834i	−0.571872	−	0.571872i	−0.932651	+	0.360779i	$0.882511\pi$
$350$	−0.675314	−	1.63035i	−0.0360970	−	0.0871459i
$351$	2.31547	−	0.959100i	0.123591	−	0.0511930i
$352$	−4.88614	+	11.7962i	−0.260432	+	0.628738i
$353$		−	31.2482i		−	1.66317i	−0.555396	−	0.831586i	$-0.687433\pi$
$353$		−	31.2482i		−	1.66317i	0.555396	−	0.831586i	$-0.312567\pi$
$354$	−2.07587	−	0.859854i	−0.110331	−	0.0457007i
$355$	−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	$-0.727090\pi$
$359$	1.92689	−	1.92689i	0.101697	−	0.101697i	0.756125	+	0.654428i	$0.227090\pi$
$360$	−0.516110	−	0.213780i	−0.0272014	−	0.0112672i
$361$			18.0963i			0.952437i
$362$	−0.987542	+	2.38414i	−0.0519041	+	0.125308i
$363$	−12.4805	+	5.16957i	−0.655054	+	0.271332i
$364$	3.23365	+	7.80672i	0.169489	+	0.409183i
$365$	2.93143	+	2.93143i	0.153438	+	0.153438i
$366$	0.466599	+	0.466599i	0.0243895	+	0.0243895i
$367$	7.06110	+	17.0470i	0.368586	+	0.889846i	0.993983	+	0.109539i	$0.0349374\pi$
$367$	7.06110	+	17.0470i	0.368586	+	0.889846i	−0.625396	+	0.780307i	$0.715063\pi$
$368$	−7.26665	+	3.00994i	−0.378800	+	0.156904i
$369$	−2.64882	+	6.39483i	−0.137892	+	0.332901i
$370$		−	1.20010i		−	0.0623902i
$371$	10.2908	+	4.26261i	0.534274	+	0.221303i
$372$	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
$377$	−22.1985	−	9.19492i	−1.14328	−	0.473563i
$378$			0.384044i			0.0197531i
$379$	−2.25422	+	5.44218i	−0.115792	+	0.279546i	−0.971141	−	0.238506i	$-0.923342\pi$
$379$	−2.25422	+	5.44218i	−0.115792	+	0.279546i	0.855349	+	0.518052i	$0.173342\pi$
$380$	1.09027	−	0.451607i	0.0559299	−	0.0231669i
$381$	4.15284	+	10.0258i	0.212756	+	0.513639i
$382$	−1.04215	−	1.04215i	−0.0533209	−	0.0533209i
$383$	21.7616	+	21.7616i	1.11197	+	1.11197i	0.992884	+	0.119083i	$0.0379954\pi$
$383$	21.7616	+	21.7616i	1.11197	+	1.11197i	0.119083	+	0.992884i	$0.462005\pi$
$384$	2.55549	+	6.16950i	0.130409	+	0.314836i
$385$	5.03111	−	2.08395i	0.256409	−	0.106208i
$386$	−0.248088	+	0.598937i	−0.0126273	+	0.0304851i
$387$			7.15061i			0.363486i
$388$	−5.48108	−	2.27034i	−0.278260	−	0.115259i
$389$	−13.8058	+	13.8058i	−0.699983	+	0.699983i	−0.964407	−	0.264424i	$-0.914818\pi$
$389$	−13.8058	+	13.8058i	−0.699983	+	0.699983i	0.264424	+	0.964407i	$0.414818\pi$
$390$	0.354393			0.0179454
$391$		0			0
$392$	3.52215			0.177896
$393$	0.499375	−	0.499375i	0.0251901	−	0.0251901i
$394$	−0.930970	−	0.385621i	−0.0469016	−	0.0194273i
$395$		−	1.51006i		−	0.0759794i
$396$	−3.69552	+	8.92177i	−0.185707	+	0.448336i
$397$	0.835444	−	0.346052i	0.0419298	−	0.0173679i	−0.361620	−	0.932326i	$-0.617776\pi$
$397$	0.835444	−	0.346052i	0.0419298	−	0.0173679i	0.403550	+	0.914958i	$0.367776\pi$
$398$	0.209196	+	0.505043i	0.0104860	+	0.0253155i
$399$	−1.16185	−	1.16185i	−0.0581654	−	0.0581654i
$400$	−12.0421	−	12.0421i	−0.602103	−	0.602103i
$401$	−0.484040	−	1.16858i	−0.0241718	−	0.0583559i	0.911333	−	0.411670i	$-0.135055\pi$
$401$	−0.484040	−	1.16858i	−0.0241718	−	0.0583559i	−0.935505	+	0.353315i	$0.885055\pi$
$402$	1.58091	−	0.654832i	0.0788484	−	0.0326601i
$403$	−5.05715	+	12.2090i	−0.251915	+	0.608176i
$404$			36.1757i			1.79981i
$405$	−0.587961	−	0.243542i	−0.0292160	−	0.0121017i
$406$	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
$411$	−11.3752	−	4.71177i	−0.561099	−	0.232415i
$412$			6.62242i			0.326263i
$413$	6.68885	−	16.1483i	0.329137	−	0.794607i
$414$	0.435642	−	0.180449i	0.0214106	−	0.00886857i
$415$	3.25326	+	7.85407i	0.159696	+	0.385541i
$416$	−4.57061	−	4.57061i	−0.224093	−	0.224093i
$417$	−9.43591	−	9.43591i	−0.462079	−	0.462079i
$418$	0.400165	+	0.966084i	0.0195727	+	0.0472527i
$419$	22.1344	−	9.16836i	1.08133	−	0.447903i	0.230357	−	0.973106i	$-0.426010\pi$
$419$	22.1344	−	9.16836i	1.08133	−	0.447903i	0.850977	+	0.525203i	$0.176010\pi$
$420$	0.821112	−	1.98234i	0.0400662	−	0.0967283i
$421$		−	12.5312i		−	0.610735i	−0.952235	−	0.305368i	$-0.901221\pi$
$421$		−	12.5312i		−	0.610735i	0.952235	−	0.305368i	$-0.0987794\pi$
$422$	4.08581	+	1.69240i	0.198894	+	0.0823846i
$423$	−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
$428$	−23.7038	−	9.81845i	−1.14577	−	0.474593i
$429$		−	12.4075i		−	0.599040i
$430$	−0.386940	+	0.934155i	−0.0186599	+	0.0450490i
$431$	16.3275	−	6.76307i	0.786468	−	0.325766i	0.0469454	−	0.998897i	$-0.485051\pi$
$431$	16.3275	−	6.76307i	0.786468	−	0.325766i	0.739523	+	0.673132i	$0.235051\pi$
$432$	1.41831	+	3.42410i	0.0682385	+	0.164742i
$433$	9.90484	+	9.90484i	0.475996	+	0.475996i	0.903849	−	0.427852i	$-0.140730\pi$
$433$	9.90484	+	9.90484i	0.475996	+	0.475996i	−0.427852	+	0.903849i	$0.640730\pi$
$434$	−1.43189	−	1.43189i	−0.0687327	−	0.0687327i
$435$	2.33484	+	5.63681i	0.111947	+	0.270264i
$436$	31.3386	−	12.9809i	1.50084	−	0.621670i
$437$	−0.772038	+	1.86386i	−0.0369316	+	0.0891607i
$438$			1.44740i			0.0691594i
$439$	−10.6930	−	4.42919i	−0.510349	−	0.211394i	0.112623	−	0.993638i	$-0.464075\pi$
$439$	−10.6930	−	4.42919i	−0.510349	−	0.211394i	−0.622972	+	0.782244i	$0.714075\pi$
$440$	−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
$445$	−1.16931	−	0.484344i	−0.0554306	−	0.0229601i
$446$		−	3.19135i		−	0.151115i
$447$	0.136577	−	0.329725i	0.00645985	−	0.0155955i
$448$	−10.9216	+	4.52389i	−0.515998	+	0.213734i
$449$	−8.47493	−	20.4603i	−0.399957	−	0.965581i	−0.987675	−	0.156516i	$-0.949974\pi$
$449$	−8.47493	−	20.4603i	−0.399957	−	0.965581i	0.587719	−	0.809065i	$-0.300026\pi$
$450$	0.721933	+	0.721933i	0.0340322	+	0.0340322i
$451$	24.2303	+	24.2303i	1.14096	+	1.14096i
$452$	0.579295	+	1.39854i	0.0272477	+	0.0657819i
$453$	8.43795	−	3.49511i	0.396450	−	0.164215i
$454$	0.924638	−	2.23227i	0.0433954	−	0.104766i
$455$			2.75684i			0.129243i
$456$	0.770941	+	0.319334i	0.0361026	+	0.0149542i
$457$	−7.00483	+	7.00483i	−0.327672	+	0.327672i	−0.851701	−	0.524029i	$-0.824428\pi$
$457$	−7.00483	+	7.00483i	−0.327672	+	0.327672i	0.524029	+	0.851701i	$0.324428\pi$
$458$	−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	$-0.821947\pi$
$461$	−6.80496	+	6.80496i	−0.316939	+	0.316939i	0.530651	+	0.847590i	$0.321947\pi$
$462$	1.75654	+	0.727581i	0.0817215	+	0.0338502i
$463$		−	15.3013i		−	0.711113i	−0.934655	−	0.355557i	$-0.884291\pi$
$463$		−	15.3013i		−	0.711113i	0.934655	−	0.355557i	$-0.115709\pi$
$464$	13.5974	−	32.8270i	0.631243	−	1.52396i
$465$	3.10021	−	1.28415i	0.143769	−	0.0595510i
$466$	0.602072	+	1.45353i	0.0278904	+	0.0673335i
$467$	15.7791	+	15.7791i	0.730168	+	0.730168i	0.970653	−	0.240485i	$-0.0773065\pi$
$467$	15.7791	+	15.7791i	0.730168	+	0.730168i	−0.240485	+	0.970653i	$0.577307\pi$
$468$	−3.45688	−	3.45688i	−0.159794	−	0.159794i
$469$	5.09398	+	12.2980i	0.235218	+	0.567867i
$470$	−1.05835	+	0.438381i	−0.0488178	+	0.0202210i
$471$	−6.73427	+	16.2580i	−0.310299	+	0.749127i
$472$			8.87670i			0.408583i
$473$	32.7053	+	13.5470i	1.50379	+	0.622892i
$474$	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
$479$	14.3729	+	5.95346i	0.656716	+	0.272021i	0.686056	−	0.727549i	$-0.259341\pi$
$479$	14.3729	+	5.95346i	0.656716	+	0.272021i	−0.0293400	+	0.999569i	$0.509341\pi$
$480$			1.64134i			0.0749166i
$481$	8.13993	−	19.6515i	0.371149	−	0.896032i
$482$	−1.19026	+	0.493020i	−0.0542146	+	0.0224564i
$483$	1.40372	+	3.38888i	0.0638715	+	0.154200i
$484$	18.6327	+	18.6327i	0.846940	+	0.846940i
$485$	−1.36866	−	1.36866i	−0.0621475	−	0.0621475i
$486$	−0.0850290	−	0.205278i	−0.00385699	−	0.00931160i
$487$	−0.0273945	+	0.0113472i	−0.00124136	+	0.000514190i	−0.383304	−	0.923622i	$-0.625214\pi$
$487$	−0.0273945	+	0.0113472i	−0.00124136	+	0.000514190i	0.382063	+	0.924136i	$0.375214\pi$
$488$	0.997620	−	2.40847i	0.0451601	−	0.109026i
$489$			16.5901i			0.750228i
$490$	0.524192	+	0.217128i	0.0236806	+	0.00980883i
$491$	−4.71594	+	4.71594i	−0.212828	+	0.212828i	−0.805467	−	0.592640i	$-0.798086\pi$
$491$	−4.71594	+	4.71594i	−0.212828	+	0.212828i	0.592640	+	0.805467i	$0.298086\pi$
$492$	13.5017			0.608704
$493$		0			0
$494$	−0.529375			−0.0238177
$495$	−2.22781	+	2.22781i	−0.100133	+	0.100133i
$496$	−18.0546	−	7.47848i	−0.810678	−	0.335794i
$497$		−	0.663798i		−	0.0297754i
$498$	−1.13583	+	2.74213i	−0.0508977	+	0.122878i
$499$	17.2274	−	7.13584i	0.771207	−	0.319444i	0.0378455	−	0.999284i	$-0.487951\pi$
$499$	17.2274	−	7.13584i	0.771207	−	0.319444i	0.733361	+	0.679839i	$0.237951\pi$
$500$	−4.55819	−	11.0045i	−0.203849	−	0.492134i
$501$	10.0575	+	10.0575i	0.449336	+	0.449336i
$502$	−1.30905	−	1.30905i	−0.0584258	−	0.0584258i
$503$	−9.85013	−	23.7803i	−0.439195	−	1.06031i	−0.976227	−	0.216750i	$-0.930454\pi$
$503$	−9.85013	−	23.7803i	−0.439195	−	1.06031i	0.537032	−	0.843562i	$-0.319546\pi$
$504$	1.40173	−	0.580614i	0.0624379	−	0.0258626i
$505$	−4.51663	+	10.9041i	−0.200987	+	0.485227i
$506$		−	2.33440i		−	0.103777i
$507$	−6.20729	−	2.57114i	−0.275675	−	0.114188i
$508$	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
$513$	0.878269	+	0.363791i	0.0387765	+	0.0160618i
$514$			0.945570i			0.0417073i
$515$	−0.826827	+	1.99614i	−0.0364344	+	0.0879603i
$516$	12.8865	−	5.33774i	0.567294	−	0.234981i
$517$	15.3480	+	37.0533i	0.675004	+	1.62960i
$518$	2.30475	+	2.30475i	0.101265	+	0.101265i
$519$	−1.33877	−	1.33877i	−0.0587656	−	0.0587656i
$520$	−0.535785	−	1.29350i	−0.0234957	−	0.0567238i
$521$	8.29833	−	3.43728i	0.363557	−	0.150590i	−0.193425	−	0.981115i	$-0.561960\pi$
$521$	8.29833	−	3.43728i	0.363557	−	0.150590i	0.556981	+	0.830525i	$0.311960\pi$
$522$	−0.815176	+	1.96801i	−0.0356793	+	0.0861374i
$523$		−	5.38995i		−	0.235686i	−0.993032	−	0.117843i	$-0.962402\pi$
$523$		−	5.38995i		−	0.235686i	0.993032	−	0.117843i	$-0.0375980\pi$
$524$	−1.27272	−	0.527177i	−0.0555990	−	0.0230299i
$525$	−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
$530$	−0.841894	−	0.348724i	−0.0365695	−	0.0151476i
$531$			10.1125i			0.438844i
$532$	−1.22654	+	2.96112i	−0.0531772	+	0.128381i
$533$	−16.0270	+	6.63861i	−0.694208	+	0.287550i
$534$	−0.169102	−	0.408247i	−0.00731774	−	0.0176666i
$535$	−5.91898	−	5.91898i	−0.255900	−	0.255900i
$536$	−4.78015	−	4.78015i	−0.206471	−	0.206471i
$537$	8.51352	+	20.5535i	0.367386	+	0.886947i
$538$	4.38926	−	1.81809i	0.189234	−	0.0783834i
$539$	7.60177	−	18.3523i	0.327432	−	0.790490i
$540$			1.24139i			0.0534210i
$541$	1.13420	+	0.469799i	0.0487629	+	0.0201983i	0.406932	−	0.913459i	$-0.366599\pi$
$541$	1.13420	+	0.469799i	0.0487629	+	0.0201983i	−0.358169	+	0.933657i	$0.616599\pi$
$542$	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
$547$	−12.4977	−	5.17672i	−0.534364	−	0.221341i	0.0991495	−	0.995073i	$-0.468388\pi$
$547$	−12.4977	−	5.17672i	−0.534364	−	0.221341i	−0.633513	+	0.773732i	$0.718388\pi$
$548$			24.0171i			1.02596i
$549$	1.13651	−	2.74377i	0.0485049	−	0.117101i
$550$	4.66968	−	1.93425i	0.199116	−	0.0824766i
$551$	−3.48767	−	8.41999i	−0.148580	−	0.358704i
$552$	−1.31724	−	1.31724i	−0.0560656	−	0.0560656i
$553$	2.90001	+	2.90001i	0.123321	+	0.123321i
$554$	−0.284008	−	0.685655i	−0.0120663	−	0.0291307i
$555$	−4.99006	+	2.06695i	−0.211816	+	0.0877371i
$556$	−9.96125	+	24.0486i	−0.422451	+	1.01989i
$557$		−	18.3599i		−	0.777936i	−0.921251	−	0.388968i	$-0.872832\pi$
$557$		−	18.3599i		−	0.777936i	0.921251	−	0.388968i	$-0.127168\pi$
$558$	1.08239	+	0.448342i	0.0458213	+	0.0189798i
$559$	−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	$-0.727624\pi$
$563$	2.35689	−	2.35689i	0.0993311	−	0.0993311i	0.755026	+	0.655695i	$0.227624\pi$
$564$	14.5996	+	6.04736i	0.614755	+	0.254640i
$565$			0.493877i			0.0207775i
$566$	0.855236	−	2.06472i	0.0359483	−	0.0867868i
$567$	1.59687	−	0.661445i	0.0670622	−	0.0277781i
$568$	0.129007	+	0.311451i	0.00541303	+	0.0130682i
$569$	−20.8150	−	20.8150i	−0.872611	−	0.872611i	0.120145	−	0.992756i	$-0.461664\pi$
$569$	−20.8150	−	20.8150i	−0.872611	−	0.872611i	−0.992756	+	0.120145i	$0.961664\pi$
$570$	0.0950512	+	0.0950512i	0.00398126	+	0.00398126i
$571$	9.88376	+	23.8615i	0.413623	+	0.998573i	0.984157	+	0.177300i	$0.0567361\pi$
$571$	9.88376	+	23.8615i	0.413623	+	0.998573i	−0.570534	+	0.821274i	$0.693264\pi$
$572$	−22.3602	+	9.26189i	−0.934926	+	0.387259i
$573$	−2.53838	+	6.12820i	−0.106042	+	0.256009i
$574$		−	2.65824i		−	0.110953i
$575$	9.00921	+	3.73174i	0.375710	+	0.155624i
$576$	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
$581$	−21.3312	−	8.83568i	−0.884968	−	0.366566i
$582$		−	0.675776i		−	0.0280118i
$583$	−12.2090	+	29.4752i	−0.505647	+	1.22074i
$584$	5.28287	−	2.18824i	0.218607	−	0.0905499i
$585$	−0.610376	−	1.47358i	−0.0252359	−	0.0609249i
$586$	−0.906438	−	0.906438i	−0.0374446	−	0.0374446i
$587$	22.7322	+	22.7322i	0.938258	+	0.938258i	0.998202	−	0.0599439i	$-0.0190922\pi$
$587$	22.7322	+	22.7322i	0.938258	+	0.938258i	−0.0599439	+	0.998202i	$0.519092\pi$
$588$	−2.99522	−	7.23111i	−0.123521	−	0.298206i
$589$	−4.63094	+	1.91820i	−0.190815	+	0.0790380i
$590$	−0.547215	+	1.32109i	−0.0225285	+	0.0543886i
$591$			4.53517i			0.186552i
$592$	29.0605	+	12.0373i	1.19438	+	0.494729i
$593$	20.7470	−	20.7470i	0.851976	−	0.851976i	−0.138400	−	0.990376i	$-0.544196\pi$
$593$	20.7470	−	20.7470i	0.851976	−	0.851976i	0.990376	+	0.138400i	$0.0441961\pi$
$594$	−1.09999			−0.0451330
$595$		0			0
$596$	−0.696164			−0.0285160
$597$	1.73969	−	1.73969i	0.0712006	−	0.0712006i
$598$	1.09183	+	0.452249i	0.0446481	+	0.0184939i
$599$			36.2632i			1.48167i	0.671686	+	0.740836i	$0.265570\pi$
$599$			36.2632i			1.48167i	−0.671686	+	0.740836i	$0.734430\pi$
$600$	1.54354	−	3.72643i	0.0630147	−	0.152131i
$601$	−42.2566	+	17.5033i	−1.72368	+	0.713973i	−0.723976	+	0.689825i	$0.757687\pi$
$601$	−42.2566	+	17.5033i	−1.72368	+	0.713973i	−0.999708	+	0.0241482i	$0.992313\pi$
$602$	−1.05091	−	2.53711i	−0.0428317	−	0.103405i
$603$	−5.44563	−	5.44563i	−0.221763	−	0.221763i
$604$	−12.5974	−	12.5974i	−0.512582	−	0.512582i
$605$	3.28994	+	7.94262i	0.133755	+	0.322914i
$606$	−3.80701	+	1.57691i	−0.154649	+	0.0640578i
$607$	12.8827	−	31.1015i	0.522891	−	1.26237i	−0.413209	−	0.910636i	$-0.635592\pi$
$607$	12.8827	−	31.1015i	0.522891	−	1.26237i	0.936100	−	0.351734i	$-0.114408\pi$
$608$		−	2.45176i		−	0.0994318i
$609$	−15.3092	−	6.34130i	−0.620362	−	0.256962i
$610$	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
$615$	4.06970	+	1.68572i	0.164106	+	0.0679750i
$616$		−	7.51118i		−	0.302634i
$617$	−13.4773	+	32.5371i	−0.542575	+	1.30989i	0.380325	+	0.924853i	$0.375812\pi$
$617$	−13.4773	+	32.5371i	−0.542575	+	1.30989i	−0.922900	+	0.385040i	$0.874188\pi$
$618$	−0.696922	+	0.288674i	−0.0280343	+	0.0116122i
$619$	−12.5630	−	30.3298i	−0.504951	−	1.21906i	−0.946757	−	0.321948i	$-0.895662\pi$
$619$	−12.5630	−	30.3298i	−0.504951	−	1.21906i	0.441807	−	0.897110i	$-0.354338\pi$
$620$	−4.62845	−	4.62845i	−0.185883	−	0.185883i
$621$	−1.50062	−	1.50062i	−0.0602180	−	0.0602180i
$622$	0.110138	+	0.265897i	0.00441615	+	0.0106615i
$623$	3.17578	−	1.31545i	0.127235	−	0.0527024i
$624$	−3.55464	+	8.58165i	−0.142299	+	0.343541i
$625$			19.0889i			0.763555i
$626$	−3.92096	−	1.62411i	−0.156713	−	0.0649127i
$627$	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	$-0.681646\pi$
$631$	7.57005	−	7.57005i	0.301359	−	0.301359i	0.841545	+	0.540186i	$0.181646\pi$
$632$	−1.92429	−	0.797065i	−0.0765440	−	0.0317056i
$633$		−	19.9038i		−	0.791103i
$634$	1.28430	−	3.10057i	0.0510060	−	0.123139i
$635$	6.38050	−	2.64289i	0.253202	−	0.104880i
$636$	4.81057	+	11.6137i	0.190751	+	0.460514i
$637$	7.11089	+	7.11089i	0.281744	+	0.281744i
$638$	7.45688	+	7.45688i	0.295221	+	0.295221i
$639$	0.146967	+	0.354811i	0.00581394	+	0.0140361i
$640$	3.92630	−	1.62633i	0.155201	−	0.0642862i
$641$	14.1377	−	34.1315i	0.558406	−	1.34811i	−0.352621	−	0.935766i	$-0.614709\pi$
$641$	14.1377	−	34.1315i	0.558406	−	1.34811i	0.911027	−	0.412346i	$-0.135291\pi$
$642$		−	2.92251i		−	0.115342i
$643$	−36.3211	−	15.0447i	−1.43237	−	0.593305i	−0.474431	−	0.880293i	$-0.657346\pi$
$643$	−36.3211	−	15.0447i	−1.43237	−	0.593305i	−0.957934	+	0.286987i	$0.907346\pi$
$644$	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
$649$	46.2523	+	19.1583i	1.81556	+	0.752031i
$650$			2.55880i			0.100364i
$651$	−3.48767	+	8.41999i	−0.136693	+	0.330005i
$652$	29.8977	−	12.3840i	1.17089	−	0.484997i
$653$	9.29567	+	22.4417i	0.363768	+	0.878213i	0.994742	+	0.102410i	$0.0326552\pi$
$653$	9.29567	+	22.4417i	0.363768	+	0.878213i	−0.630975	+	0.775803i	$0.717345\pi$
$654$	2.73213	+	2.73213i	0.106835	+	0.106835i
$655$	−0.317805	−	0.317805i	−0.0124177	−	0.0124177i
$656$	−9.81713	−	23.7007i	−0.383295	−	0.925355i
$657$	6.01834	−	2.49288i	0.234798	−	0.0972564i
$658$	1.19062	−	2.87441i	0.0464151	−	0.112056i
$659$		−	9.14192i		−	0.356119i	−0.984020	−	0.178059i	$-0.943018\pi$
$659$		−	9.14192i		−	0.356119i	0.984020	−	0.178059i	$-0.0569819\pi$
$660$	5.67786	+	2.35185i	0.221010	+	0.0915455i
$661$	11.8759	−	11.8759i	0.461920	−	0.461920i	−0.437365	−	0.899284i	$-0.644088\pi$
$661$	11.8759	−	11.8759i	0.461920	−	0.461920i	0.899284	+	0.437365i	$0.144088\pi$
$662$	5.03861			0.195831
$663$		0			0
$664$	11.7257			0.455046
$665$	−0.739409	+	0.739409i	−0.0286731	+	0.0286731i
$666$	−1.74220	−	0.721645i	−0.0675091	−	0.0279632i
$667$			20.3456i			0.787787i
$668$	10.6174	−	25.6327i	0.410801	−	0.991761i
$669$	−13.2698	+	5.49651i	−0.513038	+	0.212507i
$670$	−0.416739	−	1.00610i	−0.0161000	−	0.0388689i
$671$	−10.3963	−	10.3963i	−0.401343	−	0.401343i
$672$	−3.15213	−	3.15213i	−0.121596	−	0.121596i
$673$	−7.12991	−	17.2131i	−0.274838	−	0.663517i	0.724840	−	0.688918i	$-0.241914\pi$
$673$	−7.12991	−	17.2131i	−0.274838	−	0.663517i	−0.999677	+	0.0254007i	$0.991914\pi$
$674$	−0.331870	+	0.137465i	−0.0127832	+	0.00529496i
$675$	1.75843	−	4.24522i	0.0676819	−	0.163398i
$676$			13.1057i			0.504067i
$677$	9.97885	+	4.13338i	0.383519	+	0.158859i	0.566109	−	0.824331i	$-0.308448\pi$
$677$	9.97885	+	4.13338i	0.383519	+	0.158859i	−0.182590	+	0.983189i	$0.558448\pi$
$678$	−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
$683$	20.5285	+	8.50319i	0.785502	+	0.325366i	0.739134	−	0.673559i	$-0.235235\pi$
$683$	20.5285	+	8.50319i	0.785502	+	0.325366i	0.0463683	+	0.998924i	$0.485235\pi$
$684$		−	1.85433i		−	0.0709021i
$685$	−2.99860	+	7.23925i	−0.114570	+	0.276598i
$686$	−3.90735	+	1.61848i	−0.149183	+	0.0617938i
$687$	7.26716	+	17.5445i	0.277259	+	0.669363i
$688$	−18.7396	−	18.7396i	−0.714439	−	0.714439i
$689$	−11.4206	−	11.4206i	−0.435092	−	0.435092i
$690$	−0.114838	−	0.277245i	−0.00437183	−	0.0105545i
$691$	−35.6075	+	14.7491i	−1.35457	+	0.561083i	−0.937562	−	0.347818i	$-0.886923\pi$
$691$	−35.6075	+	14.7491i	−1.35457	+	0.561083i	−0.417012	+	0.908901i	$0.636923\pi$
$692$	−1.41331	+	3.41202i	−0.0537258	+	0.129706i
$693$		−	8.55687i		−	0.325048i
$694$	−3.15320	−	1.30610i	−0.119694	−	0.0495788i
$695$	−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
$700$	14.3129	+	5.92862i	0.540979	+	0.224081i
$701$		−	18.0843i		−	0.683034i	−0.939876	−	0.341517i	$-0.889059\pi$
$701$		−	18.0843i		−	0.683034i	0.939876	−	0.341517i	$-0.110941\pi$
$702$	0.213104	−	0.514478i	0.00804308	−	0.0194177i
$703$	7.45391	−	3.08751i	0.281129	−	0.116448i
$704$	−12.9574	−	31.2819i	−0.488351	−	1.17898i
$705$	3.64561	+	3.64561i	0.137302	+	0.137302i
$706$	−4.90949	−	4.90949i	−0.184771	−	0.184771i
$707$	−12.2669	−	29.6149i	−0.461345	−	1.11378i
$708$	18.2242	−	7.54871i	0.684907	−	0.283698i
$709$	−19.9996	+	48.2832i	−0.751099	+	1.81331i	−0.197994	+	0.980203i	$0.563443\pi$
$709$	−19.9996	+	48.2832i	−0.751099	+	1.81331i	−0.553105	+	0.833111i	$0.686557\pi$
$710$			0.0543053i			0.00203804i
$711$	−2.19218	−	0.908030i	−0.0822131	−	0.0340538i
$712$	−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
$717$	4.88614	+	2.02390i	0.182476	+	0.0755841i
$718$		−	0.605478i		−	0.0225962i
$719$	0.864216	−	2.08640i	0.0322298	−	0.0778097i	−0.906945	−	0.421249i	$-0.861592\pi$
$719$	0.864216	−	2.08640i	0.0322298	−	0.0778097i	0.939175	+	0.343439i	$0.111592\pi$
$720$	2.17912	−	0.902620i	0.0812109	−	0.0336386i
$721$	−2.24562	−	5.42140i	−0.0836311	−	0.201903i
$722$	2.84316	+	2.84316i	0.105812	+	0.105812i
$723$	4.09999	+	4.09999i	0.152480	+	0.152480i
$724$	−8.66969	−	20.9305i	−0.322207	−	0.777875i
$725$	−40.6990	+	16.8581i	−1.51152	+	0.626094i
$726$	−1.14863	+	2.77305i	−0.0426298	+	0.102918i
$727$		−	39.5601i		−	1.46720i	−0.679581	−	0.733601i	$-0.737838\pi$
$727$		−	39.5601i		−	1.46720i	0.679581	−	0.733601i	$-0.262162\pi$
$728$	3.51307	+	1.45516i	0.130203	+	0.0539319i
$729$	−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	$-0.830289\pi$
$733$	−9.55562	+	9.55562i	−0.352945	+	0.352945i	0.508259	+	0.861204i	$0.330289\pi$
$734$	3.78770	+	1.56892i	0.139806	+	0.0579097i
$735$		−	2.55357i		−	0.0941899i
$736$	−2.09456	+	5.05671i	−0.0772064	+	0.186393i
$737$	−35.2240	+	14.5903i	−1.29749	+	0.537440i
$738$	0.588546	+	1.42088i	0.0216647	+	0.0523031i
$739$	7.58596	+	7.58596i	0.279054	+	0.279054i	0.832731	−	0.553677i	$-0.186776\pi$
$739$	7.58596	+	7.58596i	0.279054	+	0.279054i	−0.553677	+	0.832731i	$0.686776\pi$
$740$	7.44990	+	7.44990i	0.273864	+	0.273864i
$741$	0.911750	+	2.20116i	0.0334940	+	0.0808616i
$742$	2.28654	−	0.947114i	0.0839414	−	0.0347697i
$743$	16.8351	−	40.6434i	0.617619	−	1.49106i	−0.236843	−	0.971548i	$-0.576113\pi$
$743$	16.8351	−	40.6434i	0.617619	−	1.49106i	0.854461	−	0.519515i	$-0.173887\pi$
$744$		−	4.62845i		−	0.169687i
$745$	−0.209839	−	0.0869180i	−0.00768789	−	0.00318443i
$746$	−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
$751$	11.5529	+	4.78535i	0.421570	+	0.174620i	0.583375	−	0.812203i	$-0.301732\pi$
$751$	11.5529	+	4.78535i	0.421570	+	0.174620i	−0.161806	+	0.986823i	$0.551732\pi$
$752$		−	30.0250i		−	1.09490i
$753$	−3.18848	+	7.69767i	−0.116195	+	0.280519i
$754$	−4.93232	+	2.04303i	−0.179624	+	0.0744029i
$755$	−2.22431	−	5.36995i	−0.0809509	−	0.195433i
$756$	−2.38404	−	2.38404i	−0.0867069	−	0.0867069i
$757$	−25.3480	−	25.3480i	−0.921288	−	0.921288i	0.0758328	−	0.997121i	$-0.475838\pi$
$757$	−25.3480	−	25.3480i	−0.921288	−	0.921288i	−0.997121	+	0.0758328i	$0.975838\pi$
$758$	0.500869	+	1.20920i	0.0181924	+	0.0439203i
$759$	−9.70651	+	4.02057i	−0.352324	+	0.145937i
$760$	0.203226	−	0.490630i	0.00737177	−	0.0177970i
$761$		−	23.4468i		−	0.849944i	−0.905206	−	0.424972i	$-0.860284\pi$
$761$		−	23.4468i		−	0.849944i	0.905206	−	0.424972i	$-0.139716\pi$
$762$	2.22766	+	0.922725i	0.0806994	+	0.0334268i
$763$	−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
$768$	−11.2667	−	4.66684i	−0.406554	−	0.168400i
$769$		−	22.8938i		−	0.825573i	−0.910828	−	0.412786i	$-0.864556\pi$
$769$		−	22.8938i		−	0.825573i	0.910828	−	0.412786i	$-0.135444\pi$
$770$	0.463036	−	1.11787i	0.0166867	−	0.0402852i
$771$	3.93171	−	1.62857i	0.141597	−	0.0586515i
$772$	−2.17798	−	5.25810i	−0.0783871	−	0.189243i
$773$	−24.1327	−	24.1327i	−0.867991	−	0.867991i	0.124259	−	0.992250i	$-0.460345\pi$
$773$	−24.1327	−	24.1327i	−0.867991	−	0.867991i	−0.992250	+	0.124259i	$0.960345\pi$
$774$	1.12345	+	1.12345i	0.0403817	+	0.0403817i
$775$	9.27185	+	22.3842i	0.333055	+	0.804065i
$776$	−2.46652	+	1.02167i	−0.0885430	+	0.0366757i
$777$	5.61372	−	13.5527i	0.201391	−	0.486201i
$778$			4.33815i			0.155530i
$779$	−6.07912	−	2.51805i	−0.217807	−	0.0902187i
$780$	−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
$785$	10.3466	+	4.28572i	0.369288	+	0.152964i
$786$		−	0.156917i		−	0.00559703i
$787$	5.04110	−	12.1703i	0.179696	−	0.433824i	−0.808207	−	0.588899i	$-0.799562\pi$
$787$	5.04110	−	12.1703i	0.179696	−	0.433824i	0.987903	+	0.155074i	$0.0495617\pi$
$788$	8.17304	−	3.38539i	0.291153	−	0.120599i
$789$	−3.48241	−	8.40729i	−0.123977	−	0.299308i
$790$	−0.237250	−	0.237250i	−0.00844098	−	0.00844098i
$791$	−0.948471	−	0.948471i	−0.0337238	−	0.0337238i
$792$	1.66301	+	4.01485i	0.0590924	+	0.142662i
$793$	6.87656	−	2.84836i	0.244194	−	0.101148i
$794$	0.0768899	−	0.185629i	0.00272872	−	0.00658771i
$795$			4.10124i			0.145456i
$796$	−4.43380	−	1.83654i	−0.157152	−	0.0650945i
$797$	−25.7038	+	25.7038i	−0.910475	+	0.910475i	−0.996309	−	0.0858346i	$-0.972644\pi$
$797$	−25.7038	+	25.7038i	−0.910475	+	0.910475i	0.0858346	+	0.996309i	$0.472644\pi$
$798$	−0.365084			−0.0129239
$799$		0			0
$800$	−11.8509			−0.418991
$801$	−1.40626	+	1.40626i	−0.0496878	+	0.0496878i
$802$	−0.259647	−	0.107549i	−0.00916847	−	0.00379770i
$803$		−	32.2494i		−	1.13806i
$804$	−5.74881	+	13.8789i	−0.202745	+	0.489470i
$805$	2.15670	−	0.893335i	0.0760138	−	0.0314859i
$806$	1.12366	+	2.71274i	0.0395791	+	0.0955523i
$807$	−15.1194	−	15.1194i	−0.532227	−	0.532227i
$808$	11.5112	+	11.5112i	0.404962	+	0.404962i
$809$	17.2692	+	41.6916i	0.607154	+	1.46580i	0.866082	+	0.499903i	$0.166631\pi$
$809$	17.2692	+	41.6916i	0.607154	+	1.46580i	−0.258928	+	0.965897i	$0.583369\pi$
$810$	−0.130640	+	0.0541128i	−0.00459022	+	0.00190133i
$811$	1.27363	−	3.07481i	0.0447231	−	0.107971i	−0.899939	−	0.436015i	$-0.856389\pi$
$811$	1.27363	−	3.07481i	0.0447231	−	0.107971i	0.944662	+	0.328044i	$0.106389\pi$
$812$			32.3232i			1.13432i
$813$	−17.8505	−	7.39393i	−0.626045	−	0.259316i
$814$	−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
$819$	4.00215	+	1.65775i	0.139847	+	0.0579263i
$820$		−	8.59255i		−	0.300065i
$821$	−2.85858	+	6.90122i	−0.0997651	+	0.240854i	−0.965880	−	0.258991i	$-0.916610\pi$
$821$	−2.85858	+	6.90122i	−0.0997651	+	0.240854i	0.866115	+	0.499846i	$0.166610\pi$
$822$	−2.52748	+	1.04692i	−0.0881559	+	0.0365154i
$823$	20.7351	+	50.0589i	0.722779	+	1.74494i	0.665275	+	0.746599i	$0.268314\pi$
$823$	20.7351	+	50.0589i	0.722779	+	1.74494i	0.0575047	+	0.998345i	$0.481686\pi$
$824$	2.10727	+	2.10727i	0.0734102	+	0.0734102i
$825$	−16.0853	−	16.0853i	−0.560019	−	0.560019i
$826$	−1.48621	−	3.58802i	−0.0517117	−	0.124843i
$827$	−4.57379	+	1.89452i	−0.159046	+	0.0658791i	−0.460786	−	0.887511i	$-0.652433\pi$
$827$	−4.57379	+	1.89452i	−0.159046	+	0.0658791i	0.301740	+	0.953390i	$0.402433\pi$
$828$	−1.58417	+	3.82453i	−0.0550537	+	0.132911i
$829$		−	0.0762440i		−	0.00264806i	−0.999999	−	0.00132403i	$-0.999579\pi$
$829$		−	0.0762440i		−	0.00264806i	0.999999	−	0.00132403i	$-0.000421453\pi$
$830$	1.74511	+	0.722847i	0.0605736	+	0.0250904i
$831$	−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
$836$	−8.48131	−	3.51307i	−0.293332	−	0.121502i
$837$		−	5.27281i		−	0.182255i
$838$	2.03713	−	4.91807i	0.0703715	−	0.169892i
$839$	33.6734	−	13.9480i	1.16254	−	0.481538i	0.283817	−	0.958878i	$-0.408399\pi$
$839$	33.6734	−	13.9480i	1.16254	−	0.481538i	0.878719	+	0.477340i	$0.158399\pi$
$840$	−0.369506	−	0.892066i	−0.0127492	−	0.0307792i
$841$	−44.4850	−	44.4850i	−1.53396	−	1.53396i
$842$	−1.96882	−	1.96882i	−0.0678501	−	0.0678501i
$843$	−1.79002	−	4.32149i	−0.0616515	−	0.148840i
$844$	−35.8695	+	14.8576i	−1.23468	+	0.511421i
$845$	−1.63629	+	3.95035i	−0.0562900	+	0.135896i
$846$			1.80002i			0.0618861i
$847$	−21.5717	−	8.93530i	−0.741213	−	0.307020i
$848$	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
$853$	−36.9260	−	15.2952i	−1.26432	−	0.523699i	−0.353088	−	0.935590i	$-0.614868\pi$
$853$	−36.9260	−	15.2952i	−1.26432	−	0.523699i	−0.911233	+	0.411891i	$0.864868\pi$
$854$			1.14055i			0.0390287i
$855$	0.231518	−	0.558934i	0.00791776	−	0.0191152i
$856$	−10.6669	+	4.41837i	−0.364586	+	0.151017i
$857$	−1.13260	−	2.73433i	−0.0386888	−	0.0934030i	0.903354	−	0.428896i	$-0.141097\pi$
$857$	−1.13260	−	2.73433i	−0.0386888	−	0.0934030i	−0.942043	+	0.335493i	$0.891097\pi$
$858$	−1.94938	−	1.94938i	−0.0665508	−	0.0665508i
$859$	−15.8741	−	15.8741i	−0.541618	−	0.541618i	0.382385	−	0.924003i	$-0.375103\pi$
$859$	−15.8741	−	15.8741i	−0.541618	−	0.541618i	−0.924003	+	0.382385i	$0.875103\pi$
$860$	−3.39697	−	8.20100i	−0.115836	−	0.279652i
$861$	−11.0531	+	4.57833i	−0.376688	+	0.156029i
$862$	1.50270	−	3.62783i	0.0511820	−	0.123564i
$863$		−	27.8981i		−	0.949661i	−0.880077	−	0.474831i	$-0.842509\pi$
$863$		−	27.8981i		−	0.949661i	0.880077	−	0.474831i	$-0.157491\pi$
$864$	2.38276	+	0.986972i	0.0810632	+	0.0335775i
$865$	−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
$870$	1.25245	+	0.518782i	0.0424620	+	0.0175884i
$871$		−	19.3013i		−	0.654001i
$872$	5.84147	−	14.1025i	0.197817	−	0.477573i
$873$	−2.80990	+	1.16390i	−0.0951008	+	0.0393920i
$874$	0.171540	+	0.414135i	0.00580243	+	0.0140083i
$875$	7.46307	+	7.46307i	0.252298	+	0.252298i
$876$	−8.98507	−	8.98507i	−0.303577	−	0.303577i
$877$	−7.92006	−	19.1207i	−0.267441	−	0.645661i	0.731920	−	0.681390i	$-0.238624\pi$
$877$	−7.92006	−	19.1207i	−0.267441	−	0.645661i	−0.999361	+	0.0357299i	$0.988624\pi$
$878$	−2.37589	+	0.984127i	−0.0801825	+	0.0332127i
$879$	−2.20783	+	5.33017i	−0.0744683	+	0.179782i
$880$		−	11.6768i		−	0.393627i
$881$	−20.5470	−	8.51085i	−0.692246	−	0.286738i	0.00868935	−	0.999962i	$-0.497234\pi$
$881$	−20.5470	−	8.51085i	−0.692246	−	0.286738i	−0.700936	+	0.713224i	$0.747234\pi$
$882$	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
$887$	33.5412	+	13.8932i	1.12620	+	0.466488i	0.866488	−	0.499198i	$-0.166372\pi$
$887$	33.5412	+	13.8932i	1.12620	+	0.466488i	0.259714	+	0.965686i	$0.416372\pi$
$888$			7.44990i			0.250002i
$889$	−7.17793	+	17.3291i	−0.240740	+	0.581198i
$890$	−0.259811	+	0.107617i	−0.00870887	+	0.00360733i
$891$	1.89452	+	4.57379i	0.0634690	+	0.153228i
$892$	19.8111	+	19.8111i	0.663323	+	0.663323i
$893$	−5.44563	−	5.44563i	−0.182231	−	0.182231i
$894$	−0.0303461	−	0.0732620i	−0.00101493	−	0.00245025i
$895$	13.0803	−	5.41805i	0.437227	−	0.181105i
$896$	−4.41701	+	10.6636i	−0.147562	+	0.356246i
$897$		−	5.31877i		−	0.177589i
$898$	−4.54610	−	1.88306i	−0.151705	−	0.0628384i
$899$	−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
$904$	0.629353	+	0.260686i	0.0209320	+	0.00867030i
$905$		−	7.39133i		−	0.245696i
$906$	0.776584	−	1.87484i	0.0258003	−	0.0622874i
$907$	−22.5166	+	9.32667i	−0.747651	+	0.309687i	−0.723783	−	0.690028i	$-0.757598\pi$
$907$	−22.5166	+	9.32667i	−0.747651	+	0.309687i	−0.0238680	+	0.999715i	$0.507598\pi$
$908$	8.11745	+	19.5973i	0.269387	+	0.650358i
$909$	13.1137	+	13.1137i	0.434955	+	0.434955i
$910$	0.433136	+	0.433136i	0.0143583	+	0.0143583i
$911$	−10.3010	−	24.8688i	−0.341287	−	0.823940i	−0.997586	−	0.0694390i	$-0.977879\pi$
$911$	−10.3010	−	24.8688i	−0.341287	−	0.823940i	0.656299	−	0.754501i	$-0.272121\pi$
$912$	−3.25506	+	1.34829i	−0.107786	+	0.0446463i
$913$	25.3073	−	61.0973i	0.837550	−	2.02203i
$914$			2.20110i			0.0728059i
$915$	−1.74615	−	0.723277i	−0.0577258	−	0.0239108i
$916$	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
$921$	12.2298	+	5.06576i	0.402986	+	0.166922i
$922$			2.13830i			0.0704210i
$923$	−0.368337	+	0.889244i	−0.0121240	+	0.0292698i
$924$	−15.4207	+	6.38748i	−0.507305	+	0.210133i
$925$	−14.9238	−	36.0294i	−0.490693	−	1.18464i
$926$	−2.40404	−	2.40404i	−0.0790016	−	0.0790016i
$927$	2.40064	+	2.40064i	0.0788473	+	0.0788473i
$928$	−9.46214	−	22.8436i	−0.310610	−	0.749879i
$929$	−5.38383	+	2.23006i	−0.176638	+	0.0731658i	−0.469250	−	0.883066i	$-0.655476\pi$
$929$	−5.38383	+	2.23006i	−0.176638	+	0.0731658i	0.292612	+	0.956231i	$0.405476\pi$
$930$	0.285327	−	0.688840i	0.00935623	−	0.0225879i
$931$			3.81440i			0.125012i
$932$	−12.7606	−	5.28563i	−0.417988	−	0.173136i
$933$	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	0.340477	−	0.940253i	$-0.389411\pi$
$937$	39.2037	−	39.2037i	1.28073	−	1.28073i	0.940253	−	0.340477i	$-0.110589\pi$
$938$	2.73250	+	1.13184i	0.0892193	+	0.0369558i
$939$			19.1007i			0.623328i
$940$	3.84857	−	9.29128i	0.125527	−	0.303048i
$941$	19.5582	−	8.10125i	0.637577	−	0.264093i	−0.0403913	−	0.999184i	$-0.512860\pi$
$941$	19.5582	−	8.10125i	0.637577	−	0.264093i	0.677969	+	0.735091i	$0.262860\pi$
$942$	1.49630	+	3.61238i	0.0487520	+	0.117698i
$943$	10.3869	+	10.3869i	0.338244	+	0.338244i
$944$	−26.5017	−	26.5017i	−0.862558	−	0.862558i
$945$	−0.420947	−	1.01626i	−0.0136934	−	0.0330588i
$946$	7.26685	−	3.01003i	0.236266	−	0.0978644i
$947$	−14.3824	+	34.7223i	−0.467366	+	1.12832i	0.497942	+	0.867210i	$0.334089\pi$
$947$	−14.3824	+	34.7223i	−0.467366	+	1.12832i	−0.965309	+	0.261112i	$0.915911\pi$
$948$			4.62845i			0.150325i
$949$	15.0834	+	6.24777i	0.489629	+	0.202811i
$950$	−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
$955$	3.90001	+	1.61544i	0.126201	+	0.0522744i
$956$		−	10.3163i		−	0.333654i
$957$	18.1629	−	43.8491i	0.587122	−	1.41744i
$958$	3.19354	−	1.32281i	0.103179	−	0.0427380i
$959$	−8.14402	−	19.6614i	−0.262984	−	0.634900i
$960$	−3.07777	−	3.07777i	−0.0993346	−	0.0993346i
$961$	−2.26096	−	2.26096i	−0.0729341	−	0.0729341i
$962$	−1.80862	−	4.36640i	−0.0583123	−	0.140778i
$963$	−12.1519	+	5.03348i	−0.391589	+	0.162201i
$964$	4.32825	−	10.4493i	0.139404	−	0.336550i
$965$		−	1.85683i		−	0.0597734i
$966$	0.752981	+	0.311895i	0.0242268	+	0.0100351i
$967$	18.5488	−	18.5488i	0.596489	−	0.596489i	−0.342887	−	0.939377i	$-0.611405\pi$
$967$	18.5488	−	18.5488i	0.596489	−	0.596489i	0.939377	+	0.342887i	$0.111405\pi$
$968$	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	$-0.858447\pi$
$971$	−14.7250	+	14.7250i	−0.472549	+	0.472549i	0.430190	+	0.902738i	$0.358447\pi$
$972$	1.80215	+	0.746474i	0.0578039	+	0.0239432i
$973$		−	23.0650i		−	0.739429i
$974$	−0.00252125	+	0.00608683i	−8.07860e−5	+	0.000195035i
$975$	10.6396	−	4.40705i	0.340739	−	0.141139i
$976$	4.21214	+	10.1690i	0.134827	+	0.325502i
$977$	−11.5187	−	11.5187i	−0.368517	−	0.368517i	0.498419	−	0.866936i	$-0.333914\pi$
$977$	−11.5187	−	11.5187i	−0.368517	−	0.368517i	−0.866936	+	0.498419i	$0.833914\pi$
$978$	2.60651	+	2.60651i	0.0833471	+	0.0833471i
$979$	3.76774	+	9.09613i	0.120418	+	0.290714i
$980$	−4.60192	+	1.90618i	−0.147003	+	0.0608906i
$981$	6.65470	−	16.0659i	0.212468	−	0.512943i
$982$			1.48187i			0.0472884i
$983$	0.860752	+	0.356535i	0.0274537	+	0.0113717i	0.396368	−	0.918092i	$-0.370270\pi$
$983$	0.860752	+	0.356535i	0.0274537	+	0.0113717i	−0.368914	+	0.929463i	$0.620270\pi$
$984$	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
$989$	14.0199	+	5.80724i	0.445807	+	0.184659i
$990$			0.700037i			0.0222487i
$991$	−8.30316	+	20.0456i	−0.263759	+	0.636769i	−0.999165	−	0.0408568i	$-0.986991\pi$
$991$	−8.30316	+	20.0456i	−0.263759	+	0.636769i	0.735407	+	0.677626i	$0.236991\pi$
$992$	−12.5639	+	5.20412i	−0.398903	+	0.165231i
$993$	−8.67808	−	20.9507i	−0.275390	−	0.664851i
$994$	−0.104291	−	0.104291i	−0.00330792	−	0.00330792i
$995$	−1.10715	−	1.10715i	−0.0350989	−	0.0350989i
$996$	−9.97151	−	24.0733i	−0.315959	−	0.762793i
$997$	−2.98144	+	1.23495i	−0.0944232	+	0.0391114i	−0.429395	−	0.903117i	$-0.641273\pi$
$997$	−2.98144	+	1.23495i	−0.0944232	+	0.0391114i	0.334972	+	0.942228i	$0.391273\pi$
$998$	1.58552	−	3.82779i	0.0501888	−	0.121167i
$999$			8.48705i			0.268518i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	867.2.h.i.757.3		16
17.2	even	8	inner	867.2.h.i.733.3		16
17.3	odd	16		51.2.e.a.13.2	yes	8
17.4	even	4		867.2.h.k.688.1		16
17.5	odd	16		867.2.e.g.616.3		8
17.6	odd	16		867.2.a.k.1.3		4
17.7	odd	16		867.2.d.f.577.4		8
17.8	even	8		867.2.h.k.712.2		16
17.9	even	8		867.2.h.k.712.1		16
17.10	odd	16		867.2.d.f.577.3		8
17.11	odd	16		867.2.a.l.1.3		4
17.12	odd	16		51.2.e.a.4.3	✓	8
17.13	even	4		867.2.h.k.688.2		16
17.14	odd	16		867.2.e.g.829.2		8
17.15	even	8	inner	867.2.h.i.733.4		16
17.16	even	2	inner	867.2.h.i.757.4		16
51.11	even	16		2601.2.a.be.1.2		4
51.20	even	16		153.2.f.b.64.3		8
51.23	even	16		2601.2.a.bf.1.2		4
51.29	even	16		153.2.f.b.55.2		8
68.3	even	16		816.2.bd.e.625.3		8
68.63	even	16		816.2.bd.e.769.3		8
204.71	odd	16		2448.2.be.x.1441.3		8
204.131	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	17.12	odd	16
51.2.e.a.13.2	yes	8	17.3	odd	16
153.2.f.b.55.2		8	51.29	even	16
153.2.f.b.64.3		8	51.20	even	16
816.2.bd.e.625.3		8	68.3	even	16
816.2.bd.e.769.3		8	68.63	even	16
867.2.a.k.1.3		4	17.6	odd	16
867.2.a.l.1.3		4	17.11	odd	16
867.2.d.f.577.3		8	17.10	odd	16
867.2.d.f.577.4		8	17.7	odd	16
867.2.e.g.616.3		8	17.5	odd	16
867.2.e.g.829.2		8	17.14	odd	16
867.2.h.i.733.3		16	17.2	even	8	inner
867.2.h.i.733.4		16	17.15	even	8	inner
867.2.h.i.757.3		16	1.1	even	1	trivial
867.2.h.i.757.4		16	17.16	even	2	inner
867.2.h.k.688.1		16	17.4	even	4
867.2.h.k.688.2		16	17.13	even	4
867.2.h.k.712.1		16	17.9	even	8
867.2.h.k.712.2		16	17.8	even	8
2448.2.be.x.1441.3		8	204.71	odd	16
2448.2.be.x.1585.3		8	204.131	odd	16
2601.2.a.be.1.2		4	51.11	even	16
2601.2.a.bf.1.2		4	51.23	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} +(-0.923880 - 0.382683i) q^{3} +1.95063i q^{4} +(-0.243542 + 0.587961i) q^{5} +(-0.205278 + 0.0850290i) q^{6} +(-0.661445 - 1.59687i) q^{7} +(0.620696 + 0.620696i) q^{8} +(0.707107 + 0.707107i) q^{9} +(0.0541128 + 0.130640i) q^{10} +(4.57379 - 1.89452i) q^{11} +(0.746474 - 1.80215i) q^{12} +2.50625i q^{13} +(-0.354811 - 0.146967i) q^{14} +(0.450006 - 0.450006i) q^{15} -3.70622 q^{16} +0.222191 q^{18} +(-0.672198 + 0.672198i) q^{19} +(-1.14690 - 0.475060i) q^{20} +1.72844i q^{21} +(0.420947 - 1.01626i) q^{22} +(1.96066 - 0.812132i) q^{23} +(-0.335918 - 0.810978i) q^{24} +(3.24915 + 3.24915i) q^{25} +(0.393764 + 0.393764i) q^{26} +(-0.382683 - 0.923880i) q^{27} +(3.11490 - 1.29024i) q^{28} +(-3.66880 + 8.85727i) q^{29} -0.141404i q^{30} +(4.87144 + 2.01782i) q^{31} +(-1.82369 + 1.82369i) q^{32} -4.95063 q^{33} +1.09999 q^{35} +(-1.37930 + 1.37930i) q^{36} +(-7.84101 - 3.24785i) q^{37} +0.211222i q^{38} +(0.959100 - 2.31547i) q^{39} +(-0.516110 + 0.213780i) q^{40} +(2.64882 + 6.39483i) q^{41} +(0.271560 + 0.271560i) q^{42} +(5.05624 + 5.05624i) q^{43} +(3.69552 + 8.92177i) q^{44} +(-0.587961 + 0.243542i) q^{45} +(0.180449 - 0.435642i) q^{46} +8.10124i q^{47} +(3.42410 + 1.41831i) q^{48} +(2.83726 - 2.83726i) q^{49} +1.02097 q^{50} -4.88877 q^{52} +(-4.55687 + 4.55687i) q^{53} +(-0.205278 - 0.0850290i) q^{54} +3.15061i q^{55} +(0.580614 - 1.40173i) q^{56} +(0.878269 - 0.363791i) q^{57} +(0.815176 + 1.96801i) q^{58} +(7.15061 + 7.15061i) q^{59} +(0.877796 + 0.877796i) q^{60} +(-1.13651 - 2.74377i) q^{61} +(1.08239 - 0.448342i) q^{62} +(0.661445 - 1.59687i) q^{63} -6.83940i q^{64} +(-1.47358 - 0.610376i) q^{65} +(-0.777809 + 0.777809i) q^{66} -7.70129 q^{67} -2.12220 q^{69} +(0.172822 - 0.172822i) q^{70} +(0.354811 + 0.146967i) q^{71} +0.877796i q^{72} +(2.49288 - 6.01834i) q^{73} +(-1.74220 + 0.721645i) q^{74} +(-1.75843 - 4.24522i) q^{75} +(-1.31121 - 1.31121i) q^{76} +(-6.05062 - 6.05062i) q^{77} +(-0.213104 - 0.514478i) q^{78} +(-2.19218 + 0.908030i) q^{79} +(0.902620 - 2.17912i) q^{80} +1.00000i q^{81} +(1.42088 + 0.588546i) q^{82} +(9.44563 - 9.44563i) q^{83} -3.37155 q^{84} +1.58880 q^{86} +(6.77906 - 6.77906i) q^{87} +(4.01485 + 1.66301i) q^{88} +1.98875i q^{89} +(-0.0541128 + 0.130640i) q^{90} +(4.00215 - 1.65775i) q^{91} +(1.58417 + 3.82453i) q^{92} +(-3.72844 - 3.72844i) q^{93} +(1.27281 + 1.27281i) q^{94} +(-0.231518 - 0.558934i) q^{95} +(2.38276 - 0.986972i) q^{96} +(-1.16390 + 2.80990i) q^{97} -0.891542i q^{98} +(4.57379 + 1.89452i) 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

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