LMFDB - Embedded newform 175.2.x.a.108.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [175,2,Mod(3,175)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(175, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([21, 10]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("175.3");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$N$	$=$	$175 = 5^{2} \cdot 7$
Weight:	$k$	$=$	$2$
Character orbit:	$[\chi]$	$=$	175.x (of order $60$ , degree $16$ , minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$1.39738203537$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			108.13
Character	$\chi$	$=$	175.108
Dual form			175.2.x.a.47.13

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.0691326 + 1.31913i) q^{2} +(1.21688 + 0.985411i) q^{3} +(0.253721 - 0.0266672i) q^{4} +(-0.928288 - 2.03428i) q^{5} +(-1.21576 + 1.67335i) q^{6} +(0.569615 + 2.58371i) q^{7} +(0.465999 + 2.94220i) q^{8} +(-0.113970 - 0.536187i) q^{9} +(2.61930 - 1.36517i) q^{10} +(0.468564 + 0.0995964i) q^{11} +(0.335027 + 0.217569i) q^{12} +(0.0993879 + 0.195060i) q^{13} +(-3.36886 + 0.930015i) q^{14} +(0.874983 - 3.39022i) q^{15} +(-3.34984 + 0.712030i) q^{16} +(-4.48096 - 1.72008i) q^{17} +(0.699421 - 0.187409i) q^{18} +(0.561217 - 5.33963i) q^{19} +(-0.289775 - 0.491385i) q^{20} +(-1.85286 + 3.70537i) q^{21} +(-0.0989874 + 0.624982i) q^{22} +(0.532247 - 0.0278939i) q^{23} +(-2.33221 + 4.03951i) q^{24} +(-3.27656 + 3.77679i) q^{25} +(-0.250438 + 0.144591i) q^{26} +(2.52230 - 4.95029i) q^{27} +(0.213424 + 0.640352i) q^{28} +(-2.22883 - 3.06772i) q^{29} +(4.53263 + 0.919840i) q^{30} +(1.36200 + 3.05910i) q^{31} +(0.371137 + 1.38510i) q^{32} +(0.472043 + 0.582925i) q^{33} +(1.95922 - 6.02987i) q^{34} +(4.72721 - 3.55718i) q^{35} +(-0.0432152 - 0.133003i) q^{36} +(4.15075 - 6.39160i) q^{37} +(7.08245 + 0.371176i) q^{38} +(-0.0712708 + 0.335303i) q^{39} +(5.55267 - 3.67918i) q^{40} +(-2.67924 - 0.870538i) q^{41} +(-5.01595 - 2.18800i) q^{42} +(6.03300 + 6.03300i) q^{43} +(0.121541 + 0.0127744i) q^{44} +(-0.984956 + 0.729582i) q^{45} +(0.0735913 + 0.700174i) q^{46} +(-2.68148 - 6.98550i) q^{47} +(-4.77800 - 2.43451i) q^{48} +(-6.35108 + 2.94344i) q^{49} +(-5.20859 - 4.06111i) q^{50} +(-3.75781 - 6.50871i) q^{51} +(0.0304185 + 0.0468405i) q^{52} +(-3.04833 + 3.76438i) q^{53} +(6.70444 + 2.98501i) q^{54} +(-0.232356 - 1.04564i) q^{55} +(-7.33634 + 2.87993i) q^{56} +(5.94466 - 5.94466i) q^{57} +(3.89263 - 3.15219i) q^{58} +(-3.58205 - 3.97827i) q^{59} +(0.131594 - 0.883504i) q^{60} +(6.61519 + 5.95635i) q^{61} +(-3.94119 + 2.00814i) q^{62} +(1.32043 - 0.599885i) q^{63} +(-8.31559 + 2.70190i) q^{64} +(0.304545 - 0.383254i) q^{65} +(-0.736320 + 0.662985i) q^{66} +(-4.65578 + 12.1287i) q^{67} +(-1.18278 - 0.316926i) q^{68} +(0.675168 + 0.490538i) q^{69} +(5.01918 + 5.98988i) q^{70} +(3.80548 - 2.76485i) q^{71} +(1.52446 - 0.585185i) q^{72} +(11.0005 - 7.14378i) q^{73} +(8.71829 + 5.03351i) q^{74} +(-7.70888 + 1.36714i) q^{75} -1.36974i q^{76} +(0.00957352 + 1.26736i) q^{77} +(-0.447234 - 0.0708350i) q^{78} +(-3.76871 + 8.46467i) q^{79} +(4.55808 + 6.15353i) q^{80} +(6.44508 - 2.86953i) q^{81} +(0.963129 - 3.59445i) q^{82} +(-9.38322 + 1.48616i) q^{83} +(-0.371298 + 0.989542i) q^{84} +(0.660503 + 10.7122i) q^{85} +(-7.54123 + 8.37538i) q^{86} +(0.310744 - 5.92936i) q^{87} +(-0.0746822 + 1.42502i) q^{88} +(-3.91910 + 4.35260i) q^{89} +(-1.03051 - 1.24885i) q^{90} +(-0.447364 + 0.367898i) q^{91} +(0.134299 - 0.0212708i) q^{92} +(-1.35708 + 5.06469i) q^{93} +(9.02940 - 4.02015i) q^{94} +(-11.3832 + 3.81504i) q^{95} +(-0.913264 + 2.05122i) q^{96} +(-9.51421 - 1.50690i) q^{97} +(-4.32184 - 8.17440i) q^{98} -0.262589i q^{99} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$288 q - 8 q^{2} - 24 q^{3} - 10 q^{4} - 30 q^{5} - 10 q^{7} - 36 q^{8} - 10 q^{9} - 36 q^{10} - 6 q^{11} - 36 q^{12} - 20 q^{14} - 28 q^{15} - 30 q^{16} - 42 q^{17} - 14 q^{18} - 30 q^{19} - 12 q^{21} + 32 q^{22}+ \cdots + 222 q^{98}+O(q^{100})$ 288 * q - 8 * q^2 - 24 * q^3 - 10 * q^4 - 30 * q^5 - 10 * q^7 - 36 * q^8 - 10 * q^9 - 36 * q^10 - 6 * q^11 - 36 * q^12 - 20 * q^14 - 28 * q^15 - 30 * q^16 - 42 * q^17 - 14 * q^18 - 30 * q^19 - 12 * q^21 + 32 * q^22 - 40 * q^23 + 2 * q^25 - 48 * q^26 + 22 * q^28 - 58 * q^30 - 18 * q^31 + 8 * q^32 - 30 * q^33 - 2 * q^35 + 40 * q^36 - 10 * q^37 + 72 * q^38 + 30 * q^39 - 48 * q^40 + 6 * q^42 - 108 * q^43 - 10 * q^44 + 186 * q^45 - 6 * q^46 - 54 * q^47 - 248 * q^50 - 16 * q^51 + 216 * q^52 + 50 * q^53 - 30 * q^54 + 4 * q^56 - 216 * q^57 - 4 * q^58 + 90 * q^59 + 96 * q^60 - 18 * q^61 - 66 * q^63 - 100 * q^64 + 14 * q^65 - 90 * q^66 + 4 * q^67 + 342 * q^68 - 60 * q^70 - 24 * q^71 + 58 * q^72 - 6 * q^73 + 216 * q^75 - 80 * q^77 - 132 * q^78 - 10 * q^79 - 6 * q^80 - 10 * q^81 + 216 * q^82 + 20 * q^84 - 48 * q^85 - 6 * q^86 - 48 * q^87 - 122 * q^88 + 120 * q^89 - 12 * q^91 - 4 * q^92 + 106 * q^93 - 30 * q^94 - 98 * q^95 - 90 * q^96 + 222 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/175\mathbb{Z}\right)^\times$ .

$n$	$101$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{20}\right)$

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

)

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

$2$	0.0691326	+	1.31913i	0.0488842	+	0.932765i	0.907476	+	0.420105i	$0.138007\pi$
$2$	0.0691326	+	1.31913i	0.0488842	+	0.932765i	−0.858591	+	0.512660i	$0.828660\pi$
$3$	1.21688	+	0.985411i	0.702567	+	0.568927i	0.912643	−	0.408758i	$-0.134038\pi$
$3$	1.21688	+	0.985411i	0.702567	+	0.568927i	−0.210076	+	0.977685i	$0.567371\pi$
$4$	0.253721	−	0.0266672i	0.126861	−	0.0133336i
$5$	−0.928288	−	2.03428i	−0.415143	−	0.909756i
$5$	−0.928288	−	2.03428i	−0.415143	−	0.909756i
$6$	−1.21576	+	1.67335i	−0.496331	+	0.683141i
$7$	0.569615	+	2.58371i	0.215294	+	0.976549i
$7$	0.569615	+	2.58371i	0.215294	+	0.976549i
$8$	0.465999	+	2.94220i	0.164755	+	1.04023i
$9$	−0.113970	−	0.536187i	−0.0379900	−	0.178729i
$10$	2.61930	−	1.36517i	0.828295	−	0.431704i
$11$	0.468564	+	0.0995964i	0.141277	+	0.0300294i	0.278008	−	0.960579i	$-0.410326\pi$
$11$	0.468564	+	0.0995964i	0.141277	+	0.0300294i	−0.136730	+	0.990608i	$0.543659\pi$
$12$	0.335027	+	0.217569i	0.0967140	+	0.0628068i
$13$	0.0993879	+	0.195060i	0.0275653	+	0.0540999i	0.904378	−	0.426731i	$-0.140335\pi$
$13$	0.0993879	+	0.195060i	0.0275653	+	0.0540999i	−0.876813	+	0.480831i	$0.840335\pi$
$14$	−3.36886	+	0.930015i	−0.900367	+	0.248557i
$15$	0.874983	−	3.39022i	0.225920	−	0.875351i
$16$	−3.34984	+	0.712030i	−0.837460	+	0.178008i
$17$	−4.48096	−	1.72008i	−1.08679	−	0.417180i	−0.251989	−	0.967730i	$-0.581085\pi$
$17$	−4.48096	−	1.72008i	−1.08679	−	0.417180i	−0.834802	+	0.550550i	$0.814418\pi$
$18$	0.699421	−	0.187409i	0.164855	−	0.0441728i
$19$	0.561217	−	5.33963i	0.128752	−	1.22499i	−0.719155	−	0.694849i	$-0.755471\pi$
$19$	0.561217	−	5.33963i	0.128752	−	1.22499i	0.847907	−	0.530145i	$-0.177862\pi$
$20$	−0.289775	−	0.491385i	−0.0647957	−	0.109877i
$21$	−1.85286	+	3.70537i	−0.404327	+	0.808578i
$22$	−0.0989874	+	0.624982i	−0.0211042	+	0.133247i
$23$	0.532247	−	0.0278939i	0.110981	−	0.00581628i	0.00323548	−	0.999995i	$-0.498970\pi$
$23$	0.532247	−	0.0278939i	0.110981	−	0.00581628i	0.107746	+	0.994178i	$0.465637\pi$
$24$	−2.33221	+	4.03951i	−0.476061	+	0.824561i
$25$	−3.27656	+	3.77679i	−0.655313	+	0.755358i
$26$	−0.250438	+	0.144591i	−0.0491150	+	0.0283565i
$27$	2.52230	−	4.95029i	0.485416	−	0.952683i
$28$	0.213424	+	0.640352i	0.0403333	+	0.121015i
$29$	−2.22883	−	3.06772i	−0.413883	−	0.569661i	0.550277	−	0.834982i	$-0.314522\pi$
$29$	−2.22883	−	3.06772i	−0.413883	−	0.569661i	−0.964160	+	0.265321i	$0.914522\pi$
$30$	4.53263	+	0.919840i	0.827540	+	0.167939i
$31$	1.36200	+	3.05910i	0.244622	+	0.549431i	0.993573	−	0.113195i	$-0.0361086\pi$
$31$	1.36200	+	3.05910i	0.244622	+	0.549431i	−0.748950	+	0.662626i	$0.769442\pi$
$32$	0.371137	+	1.38510i	0.0656083	+	0.244853i
$33$	0.472043	+	0.582925i	0.0821722	+	0.101474i
$34$	1.95922	−	6.02987i	0.336004	−	1.03411i
$35$	4.72721	−	3.55718i	0.799044	−	0.601273i
$36$	−0.0432152	−	0.133003i	−0.00720254	−	0.0221671i
$37$	4.15075	−	6.39160i	0.682379	−	1.05077i	−0.312521	−	0.949911i	$-0.601174\pi$
$37$	4.15075	−	6.39160i	0.682379	−	1.05077i	0.994901	−	0.100861i	$-0.0321598\pi$
$38$	7.08245	+	0.371176i	1.14893	+	0.0602126i
$39$	−0.0712708	+	0.335303i	−0.0114125	+	0.0536914i
$40$	5.55267	−	3.67918i	0.877954	−	0.581729i
$41$	−2.67924	−	0.870538i	−0.418427	−	0.135955i	0.0922339	−	0.995737i	$-0.470599\pi$
$41$	−2.67924	−	0.870538i	−0.418427	−	0.135955i	−0.510661	+	0.859782i	$0.670599\pi$
$42$	−5.01595	−	2.18800i	−0.773978	−	0.337615i
$43$	6.03300	+	6.03300i	0.920024	+	0.920024i	0.997031	−	0.0770067i	$-0.0245363\pi$
$43$	6.03300	+	6.03300i	0.920024	+	0.920024i	−0.0770067	+	0.997031i	$0.524536\pi$
$44$	0.121541	+	0.0127744i	0.0183229	+	0.00192582i
$45$	−0.984956	+	0.729582i	−0.146828	+	0.108760i
$46$	0.0735913	+	0.700174i	0.0108504	+	0.103235i
$47$	−2.68148	−	6.98550i	−0.391135	−	1.01894i	−0.977880	−	0.209169i	$-0.932924\pi$
$47$	−2.68148	−	6.98550i	−0.391135	−	1.01894i	0.586745	−	0.809772i	$-0.300409\pi$
$48$	−4.77800	−	2.43451i	−0.689645	−	0.351391i
$49$	−6.35108	+	2.94344i	−0.907297	+	0.420491i
$50$	−5.20859	−	4.06111i	−0.736606	−	0.574328i
$51$	−3.75781	−	6.50871i	−0.526198	−	0.911402i
$52$	0.0304185	+	0.0468405i	0.00421829	+	0.00649560i
$53$	−3.04833	+	3.76438i	−0.418721	+	0.517077i	−0.942241	−	0.334936i	$-0.891285\pi$
$53$	−3.04833	+	3.76438i	−0.418721	+	0.517077i	0.523520	+	0.852013i	$0.324619\pi$
$54$	6.70444	+	2.98501i	0.912359	+	0.406208i
$55$	−0.232356	−	1.04564i	−0.0313308	−	0.140994i
$56$	−7.33634	+	2.87993i	−0.980360	+	0.384846i
$57$	5.94466	−	5.94466i	0.787389	−	0.787389i
$58$	3.89263	−	3.15219i	0.511127	−	0.413903i
$59$	−3.58205	−	3.97827i	−0.466343	−	0.517927i	0.463393	−	0.886153i	$-0.346632\pi$
$59$	−3.58205	−	3.97827i	−0.466343	−	0.517927i	−0.929736	+	0.368226i	$0.879965\pi$
$60$	0.131594	−	0.883504i	0.0169887	−	0.114060i
$61$	6.61519	+	5.95635i	0.846989	+	0.762632i	0.973343	−	0.229353i	$-0.0736611\pi$
$61$	6.61519	+	5.95635i	0.846989	+	0.762632i	−0.126355	+	0.991985i	$0.540328\pi$
$62$	−3.94119	+	2.00814i	−0.500532	+	0.255034i
$63$	1.32043	−	0.599885i	0.166359	−	0.0755785i
$64$	−8.31559	+	2.70190i	−1.03945	+	0.337737i
$65$	0.304545	−	0.383254i	0.0377742	−	0.0475368i
$66$	−0.736320	+	0.662985i	−0.0906347	+	0.0816079i
$67$	−4.65578	+	12.1287i	−0.568794	+	1.48176i	0.283644	+	0.958930i	$0.408457\pi$
$67$	−4.65578	+	12.1287i	−0.568794	+	1.48176i	−0.852437	+	0.522829i	$0.824877\pi$
$68$	−1.18278	−	0.316926i	−0.143434	−	0.0384329i
$69$	0.675168	+	0.490538i	0.0812807	+	0.0590539i
$70$	5.01918	+	5.98988i	0.599907	+	0.715927i
$71$	3.80548	−	2.76485i	0.451628	−	0.328127i	−0.338610	−	0.940927i	$-0.609957\pi$
$71$	3.80548	−	2.76485i	0.451628	−	0.328127i	0.790238	+	0.612800i	$0.209957\pi$
$72$	1.52446	−	0.585185i	0.179659	−	0.0689647i
$73$	11.0005	−	7.14378i	1.28751	−	0.836117i	0.294670	−	0.955599i	$-0.404790\pi$
$73$	11.0005	−	7.14378i	1.28751	−	0.836117i	0.992836	+	0.119482i	$0.0381235\pi$
$74$	8.71829	+	5.03351i	1.01348	+	0.585133i
$75$	−7.70888	+	1.36714i	−0.890144	+	0.157864i
$76$		−	1.36974i		−	0.157120i
$77$	0.00957352	+	1.26736i	0.00109100	+	0.144429i
$78$	−0.447234	−	0.0708350i	−0.0506393	−	0.00802048i
$79$	−3.76871	+	8.46467i	−0.424013	+	0.952349i	0.567623	+	0.823288i	$0.307863\pi$
$79$	−3.76871	+	8.46467i	−0.424013	+	0.952349i	−0.991637	+	0.129061i	$0.958804\pi$
$80$	4.55808	+	6.15353i	0.509609	+	0.687986i
$81$	6.44508	−	2.86953i	0.716120	−	0.318837i
$82$	0.963129	−	3.59445i	0.106360	−	0.396940i
$83$	−9.38322	+	1.48616i	−1.02994	+	0.163127i	−0.648459	−	0.761249i	$-0.724586\pi$
$83$	−9.38322	+	1.48616i	−1.02994	+	0.163127i	−0.381482	+	0.924376i	$0.624586\pi$
$84$	−0.371298	+	0.989542i	−0.0405119	+	0.107968i
$85$	0.660503	+	10.7122i	0.0716416	+	1.16190i
$86$	−7.54123	+	8.37538i	−0.813192	+	0.903141i
$87$	0.310744	−	5.92936i	0.0333153	−	0.635694i
$88$	−0.0746822	+	1.42502i	−0.00796115	+	0.151908i
$89$	−3.91910	+	4.35260i	−0.415424	+	0.461375i	−0.914145	−	0.405388i	$-0.867136\pi$
$89$	−3.91910	+	4.35260i	−0.415424	+	0.461375i	0.498721	+	0.866762i	$0.333803\pi$
$90$	−1.03051	−	1.24885i	−0.108625	−	0.131640i
$91$	−0.447364	+	0.367898i	−0.0468965	+	0.0385662i
$92$	0.134299	−	0.0212708i	0.0140016	−	0.00221764i
$93$	−1.35708	+	5.06469i	−0.140723	+	0.525184i
$94$	9.02940	−	4.02015i	0.931312	−	0.414647i
$95$	−11.3832	+	3.81504i	−1.16790	+	0.391415i
$96$	−0.913264	+	2.05122i	−0.0932096	+	0.209352i
$97$	−9.51421	−	1.50690i	−0.966022	−	0.153003i	−0.346558	−	0.938028i	$-0.612650\pi$
$97$	−9.51421	−	1.50690i	−0.966022	−	0.153003i	−0.619463	+	0.785026i	$0.712650\pi$
$98$	−4.32184	−	8.17440i	−0.436572	−	0.825739i
$99$		−	0.262589i		−	0.0263912i
$100$	−0.730618	+	1.04563i	−0.0730618	+	0.104563i
$101$	15.0410	+	8.68390i	1.49663	+	0.864080i	0.999992	−	0.00387741i	$-0.00123422\pi$
$101$	15.0410	+	8.68390i	1.49663	+	0.864080i	0.496638	+	0.867958i	$0.334568\pi$
$102$	8.32605	−	5.40700i	0.824402	−	0.535373i
$103$	−7.32748	+	2.81276i	−0.721998	+	0.277149i	−0.691491	−	0.722386i	$-0.743046\pi$
$103$	−7.32748	+	2.81276i	−0.721998	+	0.277149i	−0.0305073	+	0.999535i	$0.509712\pi$
$104$	−0.527590	+	0.383317i	−0.0517345	+	0.0375873i
$105$	9.25773	+	0.329578i	0.903462	+	0.0321635i
$106$	−5.17644	−	3.76090i	−0.502780	−	0.365291i
$107$	2.07579	+	0.556205i	0.200674	+	0.0537704i	0.357756	−	0.933815i	$-0.383542\pi$
$107$	2.07579	+	0.556205i	0.200674	+	0.0537704i	−0.157082	+	0.987586i	$0.550209\pi$
$108$	0.507951	−	1.32326i	0.0488776	−	0.127330i
$109$	−8.12435	+	7.31520i	−0.778171	+	0.700669i	−0.959175	−	0.282814i	$-0.908732\pi$
$109$	−8.12435	+	7.31520i	−0.778171	+	0.700669i	0.181003	+	0.983482i	$0.442065\pi$
$110$	1.36327	−	0.378795i	0.129983	−	0.0361167i
$111$	11.3493	−	3.68762i	1.07723	−	0.350013i
$112$	−3.74780	−	8.24942i	−0.354133	−	0.779497i
$113$	−15.8409	+	8.07135i	−1.49019	+	0.759289i	−0.994047	−	0.108952i	$-0.965250\pi$
$113$	−15.8409	+	8.07135i	−1.49019	+	0.759289i	−0.496142	+	0.868241i	$0.665250\pi$
$114$	8.25274	+	7.43080i	0.772940	+	0.695959i
$115$	−0.550822	−	1.05684i	−0.0513644	−	0.0985512i
$116$	−0.647308	−	0.718909i	−0.0601011	−	0.0667490i
$117$	0.0932613	−	0.0755215i	0.00862201	−	0.00698196i
$118$	5.00022	−	5.00022i	0.460307	−	0.460307i
$119$	1.89175	−	12.5573i	0.173417	−	1.15112i
$120$	10.3824	+	0.994537i	0.947783	+	0.0907884i
$121$	−9.83937	−	4.38077i	−0.894488	−	0.398252i
$122$	−7.39986	+	9.13807i	−0.669952	+	0.827322i
$123$	−2.40248	−	3.69949i	−0.216624	−	0.333572i
$124$	0.427146	+	0.739839i	0.0383589	+	0.0664395i
$125$	10.7246	+	3.15949i	0.959240	+	0.282593i
$126$	0.882611	+	1.70035i	0.0786293	+	0.151479i
$127$	16.6373	+	8.47711i	1.47632	+	0.752222i	0.992419	−	0.122902i	$-0.0392200\pi$
$127$	16.6373	+	8.47711i	1.47632	+	0.752222i	0.483899	+	0.875124i	$0.339220\pi$
$128$	−3.11126	−	8.10511i	−0.274999	−	0.716397i
$129$	1.39646	+	13.2864i	0.122951	+	1.16980i
$130$	0.526616	+	0.375239i	0.0461873	+	0.0329106i
$131$	0.505966	+	0.0531792i	0.0442064	+	0.00464628i	0.126606	−	0.991953i	$-0.459592\pi$
$131$	0.505966	+	0.0531792i	0.0442064	+	0.00464628i	−0.0823994	+	0.996599i	$0.526258\pi$
$132$	0.135313	+	0.135313i	0.0117774	+	0.0117774i
$133$	14.1157	−	1.59151i	1.22399	−	0.138002i
$134$	−16.3212	−	5.30308i	−1.40994	−	0.458117i
$135$	−12.4117	−	0.535759i	−1.06823	−	0.0461108i
$136$	2.97269	−	13.9854i	0.254906	−	1.19924i
$137$	4.34468	+	0.227695i	0.371191	+	0.0194533i	0.237020	−	0.971505i	$-0.423829\pi$
$137$	4.34468	+	0.227695i	0.371191	+	0.0194533i	0.134171	+	0.990958i	$0.457163\pi$
$138$	−0.600407	+	0.924546i	−0.0511101	+	0.0787026i
$139$	−6.71334	−	20.6615i	−0.569418	−	1.75249i	−0.654444	−	0.756111i	$-0.727097\pi$
$139$	−6.71334	−	20.6615i	−0.569418	−	1.75249i	0.0850255	−	0.996379i	$-0.472903\pi$
$140$	1.10453	−	1.02859i	0.0933501	−	0.0869320i
$141$	3.62054	−	11.1429i	0.304905	−	0.938401i
$142$	3.91027	+	4.82878i	0.328143	+	0.405222i
$143$	0.0271424	+	0.101297i	0.00226976	+	0.00847085i
$144$	0.763563	+	1.71499i	0.0636302	+	0.142916i
$145$	−4.17159	+	7.38177i	−0.346432	+	0.613023i
$146$	10.1841	+	14.0172i	0.842839	+	1.16007i
$147$	−10.6290	−	2.67661i	−0.876665	−	0.220763i
$148$	0.882688	−	1.73237i	0.0725565	−	0.142400i
$149$	10.0097	−	5.77912i	0.820030	−	0.473444i	−0.0303970	−	0.999538i	$-0.509677\pi$
$149$	10.0097	−	5.77912i	0.820030	−	0.473444i	0.850427	+	0.526094i	$0.176344\pi$
$150$	−2.33637	−	10.0745i	−0.190764	−	0.822579i
$151$	8.08621	−	14.0057i	0.658046	−	1.13977i	−0.323075	−	0.946373i	$-0.604716\pi$
$151$	8.08621	−	14.0057i	0.658046	−	1.13977i	0.981121	−	0.193396i	$-0.0619502\pi$
$152$	15.9718	−	0.837045i	1.29548	−	0.0678933i
$153$	−0.411589	+	2.59867i	−0.0332750	+	0.210090i
$154$	−1.67115	+	0.100245i	−0.134665	+	0.00807796i
$155$	4.95873	−	5.61041i	0.398295	−	0.450639i
$156$	−0.00914134	+	0.0869740i	−0.000731893	+	0.00696350i
$157$	−3.90339	+	1.04591i	−0.311525	+	0.0834728i	−0.411194	−	0.911548i	$-0.634888\pi$
$157$	−3.90339	+	1.04591i	−0.311525	+	0.0834728i	0.0996695	+	0.995021i	$0.468221\pi$
$158$	−11.4265	−	4.38623i	−0.909046	−	0.348950i
$159$	−7.41892	+	1.57694i	−0.588359	+	0.125059i
$160$	2.47316	−	2.04077i	0.195520	−	0.161337i
$161$	0.375246	+	1.35928i	0.0295735	+	0.107126i
$162$	4.23085	+	8.30351i	0.332407	+	0.652386i
$163$	−14.0036	−	9.09407i	−1.09685	−	0.712303i	−0.136372	−	0.990658i	$-0.543544\pi$
$163$	−14.0036	−	9.09407i	−1.09685	−	0.712303i	−0.960478	+	0.278355i	$0.910211\pi$
$164$	−0.702996	−	0.149426i	−0.0548947	−	0.0116682i
$165$	0.747639	−	1.50139i	0.0582036	−	0.116883i
$166$	−2.60912	−	12.2749i	−0.202507	−	0.952719i
$167$	3.73076	+	23.5551i	0.288695	+	1.82275i	0.525039	+	0.851078i	$0.324051\pi$
$167$	3.73076	+	23.5551i	0.288695	+	1.82275i	−0.236344	+	0.971669i	$0.575949\pi$
$168$	−11.7654	−	3.72478i	−0.907718	−	0.287373i
$169$	7.61304	−	10.4784i	0.585618	−	0.806034i
$170$	−14.0852	+	1.61185i	−1.08028	+	0.123624i
$171$	−2.92700	+	0.307640i	−0.223833	+	0.0235258i
$172$	1.69158	+	1.36982i	0.128982	+	0.104448i
$173$	1.28106	+	24.4441i	0.0973971	+	1.85845i	0.414492	+	0.910053i	$0.363959\pi$
$173$	1.28106	+	24.4441i	0.0973971	+	1.85845i	−0.317095	+	0.948394i	$0.602707\pi$
$174$	7.84307			0.594581
$175$	−11.6245	−	6.31436i	−0.878729	−	0.477321i
$176$	−1.64053			−0.123660
$177$	−0.438699	−	8.37088i	−0.0329746	−	0.629194i
$178$	−6.01258	−	4.86889i	−0.450662	−	0.364939i
$179$	17.6041	−	1.85027i	1.31579	−	0.138295i	0.579507	−	0.814967i	$-0.303245\pi$
$179$	17.6041	−	1.85027i	1.31579	−	0.138295i	0.736285	+	0.676672i	$0.236578\pi$
$180$	−0.230448	+	0.211377i	−0.0171766	+	0.0157551i
$181$	0.557581	−	0.767444i	0.0414447	−	0.0570437i	−0.787792	−	0.615942i	$-0.788776\pi$
$181$	0.557581	−	0.767444i	0.0414447	−	0.0570437i	0.829236	+	0.558898i	$0.188776\pi$
$182$	−0.516233	−	0.564698i	−0.0382657	−	0.0418582i
$183$	2.18045	+	13.7668i	0.161184	+	1.01767i
$184$	0.330096	+	1.55298i	0.0243350	+	0.114487i
$185$	−16.8554	−	2.51053i	−1.23923	−	0.184578i
$186$	−6.77480	−	1.44003i	−0.496753	−	0.105588i
$187$	−1.92830	−	1.25225i	−0.141011	−	0.0915739i
$188$	−0.866634	−	1.70086i	−0.0632058	−	0.124048i
$189$	14.2268	+	3.69712i	1.03485	+	0.268926i
$190$	−5.81948	−	14.7522i	−0.422190	−	1.07024i
$191$	10.2434	−	2.17730i	0.741184	−	0.157544i	0.178180	−	0.983998i	$-0.442979\pi$
$191$	10.2434	−	2.17730i	0.741184	−	0.157544i	0.563004	+	0.826454i	$0.309646\pi$
$192$	−12.7816	−	4.90638i	−0.922430	−	0.354088i
$193$	19.0203	−	5.09648i	1.36911	−	0.366852i	0.501957	−	0.864892i	$-0.332613\pi$
$193$	19.0203	−	5.09648i	1.36911	−	0.366852i	0.867154	+	0.498040i	$0.165947\pi$
$194$	1.33006	−	12.6546i	0.0954925	−	0.908551i
$195$	0.748258	−	0.166273i	0.0535839	−	0.0119070i
$196$	−1.53291	+	0.916179i	−0.109494	+	0.0654413i
$197$	−2.23453	+	14.1083i	−0.159204	+	1.00517i	0.770654	+	0.637254i	$0.219930\pi$
$197$	−2.23453	+	14.1083i	−0.159204	+	1.00517i	−0.929858	+	0.367920i	$0.880070\pi$
$198$	0.346389	−	0.0181535i	0.0246168	−	0.00129011i
$199$	−3.58928	+	6.21681i	−0.254437	+	0.440698i	−0.964742	−	0.263196i	$-0.915223\pi$
$199$	−3.58928	+	6.21681i	−0.254437	+	0.440698i	0.710305	+	0.703894i	$0.248557\pi$
$200$	−12.6389	−	7.88033i	−0.893708	−	0.557223i
$201$	−17.6173	+	10.1714i	−1.24263	+	0.717432i
$202$	−10.4154	+	20.4413i	−0.732822	+	1.43824i
$203$	6.65650	−	7.50605i	0.467195	−	0.526821i
$204$	−1.12701	−	1.55119i	−0.0789062	−	0.108605i
$205$	0.716191	+	6.25843i	0.0500210	+	0.437108i
$206$	−4.21696	−	9.47144i	−0.293809	−	0.659906i
$207$	−0.0756165	−	0.282205i	−0.00525571	−	0.0196146i
$208$	−0.471822	−	0.582652i	−0.0327150	−	0.0403996i
$209$	0.794773	−	2.44606i	0.0549756	−	0.169198i
$210$	0.205256	+	12.2349i	0.0141640	+	0.844290i
$211$	−1.17257	−	3.60880i	−0.0807231	−	0.248440i	0.902548	−	0.430590i	$-0.141694\pi$
$211$	−1.17257	−	3.60880i	−0.0807231	−	0.248440i	−0.983271	+	0.182150i	$0.941694\pi$
$212$	−0.673042	+	1.03639i	−0.0462247	+	0.0711798i
$213$	7.35533	+	0.385476i	0.503979	+	0.0264124i
$214$	−0.590202	+	2.77668i	−0.0403454	+	0.189810i
$215$	6.67243	−	17.8732i	0.455056	−	1.21894i
$216$	15.7401	+	5.11428i	1.07098	+	0.347982i
$217$	−7.12800	+	5.26152i	−0.483880	+	0.357175i
$218$	−10.2113	−	10.2113i	−0.691600	−	0.691600i
$219$	20.4258	+	2.14684i	1.38025	+	0.145070i
$220$	−0.0868380	−	0.259106i	−0.00585462	−	0.0174689i
$221$	−0.109835	−	1.04501i	−0.00738830	−	0.0702949i
$222$	5.64905	+	14.7163i	0.379139	+	0.987692i
$223$	−3.42142	−	1.74330i	−0.229115	−	0.116740i	0.335665	−	0.941981i	$-0.391039\pi$
$223$	−3.42142	−	1.74330i	−0.229115	−	0.116740i	−0.564780	+	0.825242i	$0.691039\pi$
$224$	−3.36729	+	1.74788i	−0.224986	+	0.116785i
$225$	2.39849	+	1.32641i	0.159900	+	0.0884273i
$226$	−11.7423	−	20.3382i	−0.781085	−	1.35288i
$227$	1.06338	+	1.63746i	0.0705788	+	0.108682i	0.872198	−	0.489154i	$-0.162694\pi$
$227$	1.06338	+	1.63746i	0.0705788	+	0.108682i	−0.801619	+	0.597836i	$0.796028\pi$
$228$	1.34976	−	1.66682i	0.0893901	−	0.110388i
$229$	10.0729	+	4.48475i	0.665637	+	0.296361i	0.711603	−	0.702582i	$-0.247970\pi$
$229$	10.0729	+	4.48475i	0.665637	+	0.296361i	−0.0459653	+	0.998943i	$0.514636\pi$
$230$	1.35603	−	0.799668i	0.0894142	−	0.0527286i
$231$	−1.23722	+	1.55166i	−0.0814034	+	0.102092i
$232$	7.98721	−	7.98721i	0.524386	−	0.524386i
$233$	15.1967	−	12.3061i	0.995571	−	0.806198i	0.0145098	−	0.999895i	$-0.495381\pi$
$233$	15.1967	−	12.3061i	0.995571	−	0.806198i	0.981061	+	0.193697i	$0.0620479\pi$
$234$	0.106070	+	0.117803i	0.00693401	+	0.00770100i
$235$	−11.7213	+	11.9394i	−0.764610	+	0.778843i
$236$	−1.01493	−	0.913849i	−0.0660665	−	0.0594865i
$237$	−12.9273	+	6.58676i	−0.839715	+	0.427856i
$238$	16.6954	+	1.62735i	1.08220	+	0.105486i
$239$	9.20533	−	2.99099i	0.595443	−	0.193471i	0.00423616	−	0.999991i	$-0.498652\pi$
$239$	9.20533	−	2.99099i	0.595443	−	0.193471i	0.591207	+	0.806520i	$0.298652\pi$
$240$	−0.517113	+	11.9797i	−0.0333795	+	0.773286i
$241$	−9.32794	+	8.39891i	−0.600865	+	0.541021i	−0.912445	−	0.409198i	$-0.865808\pi$
$241$	−9.32794	+	8.39891i	−0.600865	+	0.541021i	0.311580	+	0.950220i	$0.399142\pi$
$242$	5.09858	−	13.2822i	0.327749	−	0.853815i
$243$	−5.42901	−	1.45470i	−0.348271	−	0.0933190i
$244$	1.83726	+	1.33484i	0.117618	+	0.0854546i
$245$	11.8834	+	10.1875i	0.759202	+	0.650855i
$246$	4.71402	−	3.42494i	0.300555	−	0.218366i
$247$	1.09732	−	0.421223i	0.0698211	−	0.0268018i
$248$	−8.36580	+	5.43281i	−0.531229	+	0.344984i
$249$	−12.8827	−	7.43785i	−0.816410	−	0.471354i
$250$	−3.42635	+	14.3656i	−0.216702	+	0.908560i
$251$			15.3215i			0.967086i	0.875321	+	0.483543i	$0.160650\pi$
$251$			15.3215i			0.967086i	−0.875321	+	0.483543i	$0.839350\pi$
$252$	0.319024	−	0.187416i	0.0200966	−	0.0118061i
$253$	0.252170	+	0.0399398i	0.0158538	+	0.00251099i
$254$	−10.0322	+	22.5327i	−0.629478	+	1.41383i
$255$	−9.75220	+	13.6864i	−0.610706	+	0.857074i
$256$	−5.49862	+	2.44814i	−0.343664	+	0.153009i
$257$	1.35339	−	5.05092i	0.0844221	−	0.315068i	−0.910782	−	0.412888i	$-0.864520\pi$
$257$	1.35339	−	5.05092i	0.0844221	−	0.315068i	0.995204	+	0.0978199i	$0.0311869\pi$
$258$	−17.4300	+	2.76064i	−1.08514	+	0.171870i
$259$	18.8783	+	7.08357i	1.17304	+	0.440152i
$260$	0.0670493	−	0.105361i	0.00415822	−	0.00653422i
$261$	−1.39085	+	1.54470i	−0.0860914	+	0.0956142i
$262$	−0.0351714	+	0.671111i	−0.00217290	+	0.0414614i
$263$	0.609132	−	11.6229i	0.0375607	−	0.716701i	−0.913339	−	0.407201i	$-0.866505\pi$
$263$	0.609132	−	11.6229i	0.0375607	−	0.716701i	0.950899	−	0.309500i	$-0.100162\pi$
$264$	−1.49511	+	1.66049i	−0.0920177	+	0.102196i
$265$	10.4875	+	2.70673i	0.644243	+	0.166273i
$266$	3.07527	+	18.5104i	0.188557	+	1.13495i
$267$	−9.05817	+	1.43467i	−0.554351	+	0.0878006i
$268$	−0.857832	+	3.20147i	−0.0524004	+	0.195561i
$269$	11.0120	−	4.90285i	0.671412	−	0.298932i	−0.0425725	−	0.999093i	$-0.513555\pi$
$269$	11.0120	−	4.90285i	0.671412	−	0.298932i	0.713984	+	0.700162i	$0.246889\pi$
$270$	−0.151316	−	16.4096i	−0.00920879	−	0.998659i
$271$	5.95538	−	13.3760i	0.361764	−	0.812535i	−0.637355	−	0.770570i	$-0.719972\pi$
$271$	5.95538	−	13.3760i	0.361764	−	0.812535i	0.999119	−	0.0419648i	$-0.0133617\pi$
$272$	16.2352	+	2.57141i	0.984405	+	0.155915i
$273$	−0.906920	+	0.00685078i	−0.0548893	+	0.000414628i
$274$			5.74694i			0.347185i
$275$	−1.91143	+	1.44333i	−0.115264	+	0.0870363i
$276$	0.184386	+	0.106455i	0.0110987	+	0.00640785i
$277$	−5.08305	+	3.30097i	−0.305411	+	0.198336i	−0.688240	−	0.725483i	$-0.741616\pi$
$277$	−5.08305	+	3.30097i	−0.305411	+	0.198336i	0.382829	+	0.923819i	$0.374950\pi$
$278$	26.7911	−	10.2842i	1.60683	−	0.616803i
$279$	1.48502	−	1.07893i	0.0889060	−	0.0645940i
$280$	12.6688	+	12.2507i	0.757106	+	0.732122i
$281$	−3.73577	−	2.71420i	−0.222857	−	0.161915i	0.470755	−	0.882264i	$-0.343982\pi$
$281$	−3.73577	−	2.71420i	−0.222857	−	0.161915i	−0.693612	+	0.720349i	$0.743982\pi$
$282$	14.9492	+	4.00563i	0.890212	+	0.238532i
$283$	1.38731	−	3.61407i	0.0824672	−	0.214834i	−0.886147	−	0.463405i	$-0.846628\pi$
$283$	1.38731	−	3.61407i	0.0824672	−	0.214834i	0.968614	+	0.248571i	$0.0799608\pi$
$284$	0.891802	−	0.802982i	0.0529187	−	0.0476482i
$285$	−17.6114	−	6.57473i	−1.04321	−	0.389453i
$286$	−0.131747	+	0.0428072i	−0.00779036	+	0.00253124i
$287$	0.723078	−	7.41824i	0.0426820	−	0.437885i
$288$	0.700374	−	0.356858i	0.0412699	−	0.0210281i
$289$	4.48684	+	4.03997i	0.263932	+	0.237645i
$290$	−10.0259	−	4.99255i	−0.588741	−	0.293172i
$291$	−10.0927	−	11.2091i	−0.591647	−	0.657091i
$292$	2.60055	−	2.10588i	0.152186	−	0.123237i
$293$	−10.8232	+	10.8232i	−0.632300	+	0.632300i	−0.948644	−	0.316344i	$-0.897545\pi$
$293$	−10.8232	+	10.8232i	−0.632300	+	0.632300i	0.316344	+	0.948644i	$0.397545\pi$
$294$	2.79598	−	14.2061i	0.163065	−	0.828515i
$295$	−4.76773	+	10.9799i	−0.277588	+	0.639272i
$296$	20.7396	+	9.23387i	1.20546	+	0.536708i
$297$	1.67489	−	2.06831i	0.0971869	−	0.120016i
$298$	8.31541	+	12.8046i	0.481699	+	0.741751i
$299$	0.0583399	+	0.101048i	0.00337388	+	0.00584374i
$300$	−1.91945	+	0.552447i	−0.110819	+	0.0318956i
$301$	−12.1510	+	19.0240i	−0.700373	+	1.09652i
$302$	19.0344	+	9.69850i	1.09531	+	0.558086i
$303$	9.74584	+	25.3888i	0.559884	+	1.45855i
$304$	1.92199	+	18.2865i	0.110234	+	1.04880i
$305$	5.97605	−	18.9863i	0.342188	−	1.08715i
$306$	−3.45643	−	0.363286i	−0.197591	−	0.0207677i
$307$	−3.99596	−	3.99596i	−0.228061	−	0.228061i	0.583821	−	0.811882i	$-0.301557\pi$
$307$	−3.99596	−	3.99596i	−0.228061	−	0.228061i	−0.811882	+	0.583821i	$0.801557\pi$
$308$	0.0362260	+	0.321302i	0.00206417	+	0.0183079i
$309$	−11.6884	−	3.79779i	−0.664929	−	0.216049i
$310$	7.74367	+	6.15334i	0.439811	+	0.349486i
$311$	0.200656	−	0.944012i	0.0113782	−	0.0535300i	−0.972092	−	0.234599i	$-0.924622\pi$
$311$	0.200656	−	0.944012i	0.0113782	−	0.0535300i	0.983470	+	0.181069i	$0.0579557\pi$
$312$	−1.01974	−	0.0534423i	−0.0577314	−	0.00302557i
$313$	0.212615	−	0.327398i	0.0120177	−	0.0185056i	−0.832611	−	0.553859i	$-0.813155\pi$
$313$	0.212615	−	0.327398i	0.0120177	−	0.0185056i	0.844628	+	0.535353i	$0.179821\pi$
$314$	−1.64954	−	5.07677i	−0.0930891	−	0.286499i
$315$	−2.44607	−	2.12925i	−0.137821	−	0.119970i
$316$	−0.730474	+	2.24817i	−0.0410924	+	0.126469i
$317$	−18.9350	−	23.3828i	−1.06350	−	1.31331i	−0.947393	−	0.320073i	$-0.896293\pi$
$317$	−18.9350	−	23.3828i	−1.06350	−	1.31331i	−0.116105	−	0.993237i	$-0.537041\pi$
$318$	−2.59308	−	9.67749i	−0.145413	−	0.542687i
$319$	−0.738814	−	1.65940i	−0.0413657	−	0.0929088i
$320$	13.2157	+	14.4081i	0.738778	+	0.805436i
$321$	1.97789	+	2.72234i	0.110395	+	0.151946i
$322$	−1.76713	+	0.588968i	−0.0984781	+	0.0328219i
$323$	−11.6994	+	22.9613i	−0.650970	+	1.27760i
$324$	1.55873	−	0.899935i	0.0865962	−	0.0499964i
$325$	−1.06235	−	0.263759i	−0.0589286	−	0.0146307i
$326$	11.0281	−	19.1013i	0.610792	−	1.05792i
$327$	−17.0948	+	0.895903i	−0.945347	+	0.0495435i
$328$	1.31277	−	8.28853i	0.0724859	−	0.457658i
$329$	16.5211	−	10.9072i	0.910836	−	0.601334i
$330$	2.03221	+	0.882437i	0.111870	+	0.0485766i
$331$	0.925838	−	8.80876i	0.0508887	−	0.484173i	−0.939163	−	0.343471i	$-0.888397\pi$
$331$	0.925838	−	8.80876i	0.0508887	−	0.484173i	0.990052	−	0.140702i	$-0.0449360\pi$
$332$	−2.34109	+	0.627294i	−0.128484	+	0.0344272i
$333$	−3.90015	−	1.49713i	−0.213727	−	0.0820421i
$334$	−30.8143	+	6.54978i	−1.68608	+	0.358388i
$335$	28.9951	−	1.78780i	1.58417	−	0.0976779i
$336$	3.56844	−	13.7317i	0.194674	−	0.749125i
$337$	−9.00124	−	17.6659i	−0.490329	−	0.962324i	−0.995081	−	0.0990602i	$-0.968416\pi$
$337$	−9.00124	−	17.6659i	−0.490329	−	0.962324i	0.504753	−	0.863264i	$-0.331584\pi$
$338$	14.3487	+	9.31818i	0.780468	+	0.506842i
$339$	−27.2301	−	5.78794i	−1.47894	−	0.314358i
$340$	0.453249	+	2.70031i	0.0245809	+	0.146445i
$341$	0.333509	+	1.56903i	0.0180605	+	0.0849680i
$342$	−0.608168	−	3.83982i	−0.0328860	−	0.207634i
$343$	−11.2226	−	14.7327i	−0.605966	−	0.795490i
$344$	−14.9389	+	20.5617i	−0.805453	+	1.10861i
$345$	0.371140	−	1.82884i	0.0199815	−	0.0984614i
$346$	−32.1563	+	3.37976i	−1.72873	+	0.181697i
$347$	0.780769	+	0.632254i	0.0419139	+	0.0339412i	0.650048	−	0.759893i	$-0.274749\pi$
$347$	0.780769	+	0.632254i	0.0419139	+	0.0339412i	−0.608135	+	0.793834i	$0.708082\pi$
$348$	−0.0792768	−	1.51269i	−0.00424968	−	0.0810888i
$349$	−22.8601			−1.22367			−0.611835	−	0.790985i	$-0.709569\pi$
$349$	−22.8601			−1.22367			−0.611835	+	0.790985i	$0.709569\pi$
$350$	7.52583	−	15.7707i	0.402272	−	0.842981i
$351$	1.21629			0.0649206
$352$	0.0359503	+	0.685972i	0.00191616	+	0.0365624i
$353$	−13.6401	−	11.0455i	−0.725988	−	0.587893i	0.193459	−	0.981108i	$-0.438029\pi$
$353$	−13.6401	−	11.0455i	−0.725988	−	0.587893i	−0.919447	+	0.393215i	$0.871363\pi$
$354$	11.0119	−	1.15740i	0.585278	−	0.0615152i
$355$	−9.15704	−	5.17483i	−0.486005	−	0.274652i
$356$	−0.878288	+	1.20886i	−0.0465491	+	0.0640694i
$357$	14.6761	−	13.4165i	0.776742	−	0.710078i
$358$	3.65776	+	23.0942i	0.193318	+	1.22056i
$359$	−6.02179	−	28.3303i	−0.317818	−	1.49522i	−0.789666	−	0.613537i	$-0.789746\pi$
$359$	−6.02179	−	28.3303i	−0.317818	−	1.49522i	0.471848	−	0.881680i	$-0.343587\pi$
$360$	−2.60557	−	2.55795i	−0.137325	−	0.134816i
$361$	−9.61183	−	2.04306i	−0.505886	−	0.107529i
$362$	1.05091	+	0.682466i	0.0552344	+	0.0358696i
$363$	−7.65648	−	15.0267i	−0.401861	−	0.788697i
$364$	−0.103695	+	0.105274i	−0.00543510	+	0.00551784i
$365$	−24.7440	−	15.7465i	−1.29516	−	0.824209i
$366$	−18.0095	+	3.82804i	−0.941372	+	0.200095i
$367$	15.4802	+	5.94229i	0.808060	+	0.310185i	0.727099	−	0.686532i	$-0.240868\pi$
$367$	15.4802	+	5.94229i	0.808060	+	0.310185i	0.0809605	+	0.996717i	$0.474201\pi$
$368$	−1.76308	+	0.472416i	−0.0919069	+	0.0246264i
$369$	−0.161418	+	1.53579i	−0.00840308	+	0.0799500i
$370$	2.14646	−	22.4080i	0.111589	−	1.16493i
$371$	−11.4624	−	5.73175i	−0.595100	−	0.297578i
$372$	−0.209259	+	1.32121i	−0.0108496	+	0.0685016i
$373$	29.2838	−	1.53470i	1.51626	−	0.0794637i	0.724064	−	0.689733i	$-0.242272\pi$
$373$	29.2838	−	1.53470i	1.51626	−	0.0794637i	0.792194	+	0.610269i	$0.208939\pi$
$374$	1.51858	−	2.63025i	0.0785237	−	0.136007i
$375$	9.93720	+	14.4129i	0.513155	+	0.744278i
$376$	19.3032	−	11.1447i	0.995486	−	0.574744i
$377$	0.376870	−	0.739648i	0.0194098	−	0.0380938i
$378$	−3.89343	+	19.0226i	−0.200257	+	0.978418i
$379$	−10.6445	−	14.6509i	−0.546773	−	0.752568i	0.442797	−	0.896622i	$-0.353986\pi$
$379$	−10.6445	−	14.6509i	−0.546773	−	0.752568i	−0.989570	+	0.144054i	$0.953986\pi$
$380$	−2.78644	+	1.27152i	−0.142941	+	0.0652274i
$381$	11.8921	+	26.7102i	0.609253	+	1.36840i
$382$	3.58028	+	13.3618i	0.183183	+	0.683649i
$383$	−18.7744	−	23.1844i	−0.959326	−	1.18467i	−0.982749	−	0.184944i	$-0.940790\pi$
$383$	−18.7744	−	23.1844i	−0.959326	−	1.18467i	0.0234230	−	0.999726i	$-0.492544\pi$
$384$	4.20083	−	12.9288i	0.214373	−	0.659771i
$385$	2.56928	−	1.19595i	0.130943	−	0.0609514i
$386$	8.03783	+	24.7379i	0.409115	+	1.25913i
$387$	2.54723	−	3.92240i	0.129483	−	0.199387i
$388$	−2.45414	−	0.128616i	−0.124590	−	0.00652950i
$389$	−2.34616	+	11.0378i	−0.118955	+	0.559639i	0.877792	+	0.479042i	$0.159016\pi$
$389$	−2.34616	+	11.0378i	−0.118955	+	0.559639i	−0.996747	+	0.0805966i	$0.974317\pi$
$390$	0.271064	+	0.975554i	0.0137259	+	0.0493991i
$391$	−2.43296	−	0.790515i	−0.123040	−	0.0399781i
$392$	−11.6198	−	17.3145i	−0.586887	−	0.874515i
$393$	0.563297	+	0.563297i	0.0284146	+	0.0284146i
$394$	−18.7651	−	1.97230i	−0.945374	−	0.0993628i
$395$	20.7179	−	0.191043i	1.04243	−	0.00961243i
$396$	−0.00700251	−	0.0666244i	−0.000351889	−	0.00334800i
$397$	−1.77857	−	4.63333i	−0.0892638	−	0.232540i	0.881680	−	0.471848i	$-0.156413\pi$
$397$	−1.77857	−	4.63333i	−0.0892638	−	0.232540i	−0.970944	+	0.239308i	$0.923080\pi$
$398$	−8.44891	−	4.30493i	−0.423505	−	0.215787i
$399$	18.7454	+	11.9731i	0.938445	+	0.599404i
$400$	8.28677	−	14.9846i	0.414339	−	0.749232i
$401$	2.20052	+	3.81142i	0.109889	+	0.190333i	0.915725	−	0.401805i	$-0.131617\pi$
$401$	2.20052	+	3.81142i	0.109889	+	0.190333i	−0.805836	+	0.592139i	$0.798284\pi$
$402$	−14.6353	−	22.5363i	−0.729940	−	1.12401i
$403$	−0.461341	+	0.569709i	−0.0229810	+	0.0283792i
$404$	4.04779	+	1.80219i	0.201385	+	0.0896624i
$405$	−11.8203	−	10.4473i	−0.587356	−	0.519132i
$406$	10.3616	+	8.26188i	0.514239	+	0.410030i
$407$	2.58147	−	2.58147i	0.127959	−	0.127959i
$408$	17.3988	−	14.0893i	0.861369	−	0.697523i
$409$	0.144146	+	0.160091i	0.00712759	+	0.00791599i	0.746698	−	0.665163i	$-0.231638\pi$
$409$	0.144146	+	0.160091i	0.00712759	+	0.00791599i	−0.739570	+	0.673079i	$0.764971\pi$
$410$	−8.20616	+	1.37741i	−0.405273	+	0.0680254i
$411$	5.06259	+	4.55837i	0.249719	+	0.224848i
$412$	−1.78413	+	0.909060i	−0.0878978	+	0.0447862i
$413$	8.23829	−	11.5211i	0.405380	−	0.566914i
$414$	0.367037	−	0.119258i	0.0180389	−	0.00586119i
$415$	11.7336	+	17.7085i	0.575979	+	0.869275i
$416$	−0.233291	+	0.210056i	−0.0114380	+	0.0102988i
$417$	12.1908	−	31.7580i	0.596985	−	1.55520i
$418$	3.28162	+	0.879306i	0.160509	+	0.0430083i
$419$	28.0621	+	20.3883i	1.37092	+	0.996034i	0.997664	+	0.0683067i	$0.0217596\pi$
$419$	28.0621	+	20.3883i	1.37092	+	0.996034i	0.373259	+	0.927727i	$0.378240\pi$
$420$	2.35767	−	0.163257i	0.115043	−	0.00796612i
$421$	24.3135	−	17.6648i	1.18497	−	0.860928i	0.192243	−	0.981347i	$-0.438424\pi$
$421$	24.3135	−	17.6648i	1.18497	−	0.860928i	0.992723	+	0.120419i	$0.0384239\pi$
$422$	4.67942	−	1.79626i	0.227790	−	0.0874405i
$423$	−3.43993	+	2.23391i	−0.167255	+	0.108617i
$424$	−12.4961	−	7.21461i	−0.606863	−	0.350373i
$425$	21.1785	−	11.2877i	1.02731	−	0.547533i
$426$			9.72928i			0.471385i
$427$	−11.6213	+	20.4845i	−0.562396	+	0.991316i
$428$	0.541504	+	0.0857658i	0.0261746	+	0.00414565i
$429$	−0.0667898	+	0.150012i	−0.00322464	+	0.00724267i
$430$	24.0383	+	7.56618i	1.15923	+	0.364874i
$431$	31.9852	−	14.2407i	1.54067	−	0.685952i	0.551699	−	0.834043i	$-0.313980\pi$
$431$	31.9852	−	14.2407i	1.54067	−	0.685952i	0.988974	+	0.148092i	$0.0473130\pi$
$432$	−4.92453	+	18.3786i	−0.236932	+	0.884241i
$433$	−5.71937	+	0.905859i	−0.274855	+	0.0435328i	−0.292340	−	0.956314i	$-0.594434\pi$
$433$	−5.71937	+	0.905859i	−0.274855	+	0.0435328i	0.0174852	+	0.999847i	$0.494434\pi$
$434$	−7.43340	−	9.03901i	−0.356815	−	0.433887i
$435$	−12.3504	+	4.87201i	−0.592157	+	0.233595i
$436$	−1.86625	+	2.07268i	−0.0893770	+	0.0992632i
$437$	0.149763	−	2.85765i	0.00716415	−	0.136700i
$438$	−1.41987	+	27.0927i	−0.0678439	+	1.29454i
$439$	−12.8713	+	14.2950i	−0.614312	+	0.682263i	−0.967379	−	0.253335i	$-0.918472\pi$
$439$	−12.8713	+	14.2950i	−0.614312	+	0.682263i	0.353066	+	0.935598i	$0.385139\pi$
$440$	2.96821	−	1.17091i	0.141504	−	0.0558207i
$441$	2.30207	+	3.06990i	0.109622	+	0.146186i
$442$	1.37091	−	0.217131i	0.0652075	−	0.0103279i
$443$	−3.99023	+	14.8917i	−0.189581	+	0.707527i	0.804022	+	0.594600i	$0.202689\pi$
$443$	−3.99023	+	14.8917i	−0.189581	+	0.707527i	−0.993603	+	0.112928i	$0.963977\pi$
$444$	2.78123	−	1.23828i	0.131991	−	0.0587663i
$445$	12.4924	+	3.93206i	0.592199	+	0.186398i
$446$	2.06310	−	4.63381i	0.0976908	−	0.219417i
$447$	17.8755	+	2.83120i	0.845481	+	0.133911i
$448$	−11.7176	−	19.9460i	−0.553605	−	0.942360i
$449$			14.1182i			0.666281i	0.942877	+	0.333140i	$0.108108\pi$
$449$			14.1182i			0.666281i	−0.942877	+	0.333140i	$0.891892\pi$
$450$	−1.58389	+	3.25562i	−0.0746654	+	0.153472i
$451$	−1.16869	−	0.674745i	−0.0550316	−	0.0317725i
$452$	−3.80394	+	2.47031i	−0.178922	+	0.116194i
$453$	23.6413	−	9.07506i	1.11077	−	0.426384i
$454$	−2.08650	+	1.51593i	−0.0979245	+	0.0711463i
$455$	1.16369	+	0.568547i	0.0545546	+	0.0266539i
$456$	20.2606	+	14.7202i	0.948789	+	0.689335i
$457$	−27.9738	−	7.49556i	−1.30856	−	0.350627i	−0.463879	−	0.885899i	$-0.653543\pi$
$457$	−27.9738	−	7.49556i	−1.30856	−	0.350627i	−0.844680	+	0.535271i	$0.820209\pi$
$458$	−5.21960	+	13.5975i	−0.243896	+	0.635371i
$459$	−19.8172	+	17.8435i	−0.924987	+	0.832862i
$460$	−0.167938	−	0.253455i	−0.00783017	−	0.0118174i
$461$	−30.3418	+	9.85863i	−1.41316	+	0.459162i	−0.913421	−	0.407016i	$-0.866569\pi$
$461$	−30.3418	+	9.85863i	−1.41316	+	0.459162i	−0.499735	+	0.866178i	$0.666569\pi$
$462$	−2.13238	−	1.52479i	−0.0992072	−	0.0709395i
$463$	3.31433	−	1.68874i	0.154030	−	0.0784822i	−0.375276	−	0.926913i	$-0.622452\pi$
$463$	3.31433	−	1.68874i	0.154030	−	0.0784822i	0.529306	+	0.848431i	$0.322452\pi$
$464$	9.65052	+	8.68936i	0.448014	+	0.403394i
$465$	11.5627	−	1.94082i	0.536209	−	0.0900032i
$466$	17.2839	+	19.1957i	0.800661	+	0.889224i
$467$	5.52562	−	4.47456i	0.255695	−	0.207058i	−0.492899	−	0.870087i	$-0.664063\pi$
$467$	5.52562	−	4.47456i	0.255695	−	0.207058i	0.748594	+	0.663029i	$0.230729\pi$
$468$	0.0216484	−	0.0216484i	0.00100070	−	0.00100070i
$469$	−33.9891	−	5.12046i	−1.56947	−	0.236441i
$470$	−16.5600	−	14.6364i	−0.763855	−	0.675129i
$471$	−5.78062	−	2.57370i	−0.266357	−	0.118590i
$472$	10.0356	−	12.3930i	0.461928	−	0.570433i
$473$	2.22598	+	3.42771i	0.102351	+	0.157606i
$474$	−9.58249	−	16.5974i	−0.440138	−	0.762342i
$475$	18.3278	+	19.6152i	0.840936	+	0.900008i
$476$	0.145112	−	3.23649i	0.00665119	−	0.148344i
$477$	2.36583	+	1.20545i	0.108324	+	0.0551938i
$478$	4.58189	+	11.9362i	0.209571	+	0.545951i
$479$	−1.20444	−	11.4595i	−0.0550324	−	0.523598i	−0.986961	−	0.160957i	$-0.948542\pi$
$479$	−1.20444	−	11.4595i	−0.0550324	−	0.523598i	0.931929	−	0.362641i	$-0.118125\pi$
$480$	5.02053	−	0.0462951i	0.229155	−	0.00211307i
$481$	1.65928	+	0.174397i	0.0756566	+	0.00795182i
$482$	−11.7241	−	11.7241i	−0.534019	−	0.534019i
$483$	−0.882821	+	2.02385i	−0.0401697	+	0.0920886i
$484$	−2.61328	−	0.849107i	−0.118786	−	0.0385958i
$485$	5.76647	+	20.7534i	0.261842	+	0.942362i
$486$	1.54361	−	7.26214i	0.0700198	−	0.329417i
$487$	−4.36966	−	0.229004i	−0.198008	−	0.0103772i	−0.0469259	−	0.998898i	$-0.514942\pi$
$487$	−4.36966	−	0.229004i	−0.198008	−	0.0103772i	−0.151082	+	0.988521i	$0.548276\pi$
$488$	−14.4421	+	22.2389i	−0.653763	+	1.00671i
$489$	−8.07937	−	24.8657i	−0.365362	−	1.12447i
$490$	−12.6171	+	16.3800i	−0.569982	+	0.739974i
$491$	2.98502	−	9.18693i	0.134712	−	0.414600i	−0.860833	−	0.508887i	$-0.830057\pi$
$491$	2.98502	−	9.18693i	0.134712	−	0.414600i	0.995545	+	0.0942867i	$0.0300570\pi$
$492$	−0.708216	−	0.874574i	−0.0319288	−	0.0394288i
$493$	4.71056	+	17.5801i	0.212153	+	0.791766i
$494$	0.631509	+	1.41839i	0.0284129	+	0.0638165i
$495$	−0.534178	+	0.243758i	−0.0240095	+	0.0109561i
$496$	−6.74065	−	9.27771i	−0.302664	−	0.416582i
$497$	9.31121	+	8.25735i	0.417665	+	0.370393i
$498$	8.92087	−	17.5082i	0.399754	−	0.784561i
$499$	−4.09112	+	2.36201i	−0.183144	+	0.105738i	−0.588769	−	0.808301i	$-0.700387\pi$
$499$	−4.09112	+	2.36201i	−0.183144	+	0.105738i	0.405625	+	0.914040i	$0.367054\pi$
$500$	2.80532	+	0.515634i	0.125458	+	0.0230599i
$501$	−18.6716	+	32.3401i	−0.834184	+	1.44485i
$502$	−20.2111	+	1.05922i	−0.902064	+	0.0472752i
$503$	−0.623100	+	3.93410i	−0.0277826	+	0.175413i	−0.997678	−	0.0681101i	$-0.978303\pi$
$503$	−0.623100	+	3.93410i	−0.0277826	+	0.175413i	0.969895	+	0.243523i	$0.0783031\pi$
$504$	2.38030	+	3.60543i	0.106027	+	0.160598i
$505$	3.70312	−	38.6586i	0.164787	−	1.72029i
$506$	−0.0352526	+	0.335406i	−0.00156717	+	0.0149106i
$507$	19.5897	−	5.24905i	0.870011	−	0.233119i
$508$	4.44729	+	1.70716i	0.197317	+	0.0757428i
$509$	2.23882	−	0.475875i	0.0992337	−	0.0210928i	−0.158027	−	0.987435i	$-0.550513\pi$
$509$	2.23882	−	0.475875i	0.0992337	−	0.0210928i	0.257261	+	0.966342i	$0.417180\pi$
$510$	−18.7283	−	11.9182i	−0.829303	−	0.527748i
$511$	24.7235	+	24.3528i	1.09370	+	1.07730i
$512$	−11.4924	−	22.5551i	−0.507898	−	0.996806i
$513$	−25.0171	−	16.2463i	−1.10453	−	0.717292i
$514$	6.75638	+	1.43611i	0.298011	+	0.0633442i
$515$	12.5239	+	12.2951i	0.551870	+	0.541786i
$516$	0.708624	+	3.33381i	0.0311954	+	0.146763i
$517$	−0.560716	−	3.54022i	−0.0246603	−	0.155699i
$518$	−8.03903	+	25.3927i	−0.353215	+	1.11569i
$519$	−22.5285	+	31.0079i	−0.988893	+	1.36109i
$520$	1.26953	+	0.717436i	0.0556725	+	0.0314617i
$521$	−13.4075	+	1.40918i	−0.587391	+	0.0617373i	−0.393562	−	0.919298i	$-0.628757\pi$
$521$	−13.4075	+	1.40918i	−0.587391	+	0.0617373i	−0.193829	+	0.981035i	$0.562091\pi$
$522$	−2.13381	−	1.72792i	−0.0933941	−	0.0756291i
$523$	−0.357203	−	6.81583i	−0.0156194	−	0.298036i	−0.995258	−	0.0972678i	$-0.968990\pi$
$523$	−0.357203	−	6.81583i	−0.0156194	−	0.298036i	0.979639	−	0.200768i	$-0.0643437\pi$
$524$	0.129793			0.00567001
$525$	−7.92339	−	19.1387i	−0.345805	−	0.835283i
$526$	15.3743			0.670350
$527$	−0.841168	−	16.0504i	−0.0366419	−	0.699168i
$528$	−1.99633	−	1.61660i	−0.0868791	−	0.0703533i
$529$	−22.5915	+	2.37446i	−0.982239	+	0.103237i
$530$	−2.84549	+	14.0215i	−0.123600	+	0.609056i
$531$	−1.72485	+	2.37405i	−0.0748521	+	0.103025i
$532$	3.53902	−	0.780227i	0.153436	−	0.0338271i
$533$	−0.0964772	−	0.609133i	−0.00417889	−	0.0263845i
$534$	−2.51874	−	11.8497i	−0.108996	−	0.512788i
$535$	−0.795452	−	4.73904i	−0.0343904	−	0.204887i
$536$	−37.8547	−	8.04627i	−1.63507	−	0.347546i
$537$	23.2454	+	15.0957i	1.00311	+	0.651428i
$538$	7.22877	+	14.1873i	0.311655	+	0.611657i
$539$	−3.26904	+	0.746645i	−0.140808	+	0.0321603i
$540$	−3.16339	+	0.195051i	−0.136131	+	0.00839365i
$541$	7.46757	−	1.58728i	0.321056	−	0.0682425i	−0.0445647	−	0.999006i	$-0.514190\pi$
$541$	7.46757	−	1.58728i	0.321056	−	0.0682425i	0.365621	+	0.930764i	$0.380857\pi$
$542$	18.0564	+	6.93120i	0.775589	+	0.297721i
$543$	1.43476	−	0.384442i	0.0615714	−	0.0164980i
$544$	0.719434	−	6.84496i	0.0308455	−	0.293475i
$545$	22.4229	+	9.73656i	0.960490	+	0.417069i
$546$	−0.0717348	−	1.19587i	−0.00306997	−	0.0511786i
$547$	−6.49848	+	41.0298i	−0.277855	+	1.75431i	0.315089	+	0.949062i	$0.397966\pi$
$547$	−6.49848	+	41.0298i	−0.277855	+	1.75431i	−0.592944	+	0.805244i	$0.702034\pi$
$548$	1.10841	−	0.0580893i	0.0473490	−	0.00248145i
$549$	2.43978	−	4.22582i	0.104127	−	0.180354i
$550$	−2.03609	−	2.42165i	−0.0868190	−	0.103259i
$551$	−17.6313	+	10.1794i	−0.751119	+	0.433659i
$552$	−1.12863	+	2.21507i	−0.0480379	+	0.0942797i
$553$	−24.0169	−	4.91564i	−1.02130	−	0.209034i
$554$	−4.70581	−	6.47699i	−0.199931	−	0.275181i
$555$	−18.0371	−	19.6645i	−0.765631	−	0.834711i
$556$	−2.25430	−	5.06325i	−0.0956038	−	0.214730i
$557$	−3.67322	−	13.7087i	−0.155640	−	0.580855i	−0.999050	−	0.0435845i	$-0.986122\pi$
$557$	−3.67322	−	13.7087i	−0.155640	−	0.580855i	0.843410	−	0.537270i	$-0.180544\pi$
$558$	1.52591	+	1.88435i	0.0645971	+	0.0797708i
$559$	−0.577188	+	1.77640i	−0.0244125	+	0.0751338i
$560$	−13.3026	+	15.2819i	−0.562136	+	0.645778i
$561$	−1.11253	−	3.42401i	−0.0469710	−	0.144562i
$562$	3.32211	−	5.11560i	0.140135	−	0.215789i
$563$	41.9397	+	2.19797i	1.76755	+	0.0926332i	0.908142	−	0.418662i	$-0.137501\pi$
$563$	41.9397	+	2.19797i	1.76755	+	0.0926332i	0.859405	+	0.511295i	$0.170834\pi$
$564$	0.621460	−	2.92374i	0.0261682	−	0.123112i
$565$	31.1243	+	24.7323i	1.30941	+	1.04050i
$566$	4.86334	+	1.58019i	0.204421	+	0.0664205i
$567$	11.0852	+	15.0177i	0.465537	+	0.630682i
$568$	9.90808	+	9.90808i	0.415734	+	0.415734i
$569$	−23.3390	−	2.45303i	−0.978423	−	0.102836i	−0.398204	−	0.917297i	$-0.630366\pi$
$569$	−23.3390	−	2.45303i	−0.978423	−	0.102836i	−0.580219	+	0.814460i	$0.697033\pi$
$570$	7.45539	−	23.6863i	0.312272	−	0.992109i
$571$	1.01109	+	9.61986i	0.0423127	+	0.402579i	0.995095	+	0.0989242i	$0.0315401\pi$
$571$	1.01109	+	9.61986i	0.0423127	+	0.402579i	−0.952782	+	0.303654i	$0.901793\pi$
$572$	0.00958790	+	0.0249773i	0.000400890	+	0.00104435i
$573$	14.6105	+	7.44442i	0.610362	+	0.310995i
$574$	9.83561	+	0.440991i	0.410530	+	0.0184066i
$575$	−1.63859	+	2.10158i	−0.0683340	+	0.0876420i
$576$	2.39645	+	4.15077i	0.0998521	+	0.172949i
$577$	0.910483	+	1.40202i	0.0379039	+	0.0583669i	0.857115	−	0.515126i	$-0.172255\pi$
$577$	0.910483	+	1.40202i	0.0379039	+	0.0583669i	−0.819211	+	0.573493i	$0.805588\pi$
$578$	−5.01906	+	6.19802i	−0.208765	+	0.257804i
$579$	28.1676	+	12.5410i	1.17060	+	0.521187i
$580$	−0.861571	+	1.98416i	−0.0357748	+	0.0823877i
$581$	−9.18461	−	23.3969i	−0.381042	−	0.970668i
$582$	14.0886	−	14.0886i	0.583989	−	0.583989i
$583$	−1.80326	+	1.46025i	−0.0746833	+	0.0604774i
$584$	26.1446	+	29.0366i	1.08187	+	1.20154i
$585$	−0.240205	−	0.119614i	−0.00993125	−	0.00494541i
$586$	−15.0255	−	13.5290i	−0.620697	−	0.558878i
$587$	0.544273	−	0.277321i	0.0224646	−	0.0114463i	−0.442722	−	0.896659i	$-0.645987\pi$
$587$	0.544273	−	0.277321i	0.0224646	−	0.0114463i	0.465187	+	0.885213i	$0.345987\pi$
$588$	−2.76818	−	0.395667i	−0.114158	−	0.0163170i
$589$	17.0988	−	5.55575i	0.704545	−	0.228921i
$590$	−14.8135	−	5.53018i	−0.609861	−	0.227674i
$591$	−16.6216	+	14.9662i	−0.683722	+	0.615626i
$592$	−9.35334	+	24.3663i	−0.384420	+	1.00145i
$593$	24.4672	+	6.55597i	1.00475	+	0.269221i	0.723433	−	0.690394i	$-0.242563\pi$
$593$	24.4672	+	6.55597i	1.00475	+	0.269221i	0.281314	+	0.959616i	$0.409230\pi$
$594$	2.84416	+	2.06641i	0.116697	+	0.0847857i
$595$	−27.3010	+	7.80840i	−1.11923	+	0.320113i
$596$	2.38557	−	1.73322i	0.0977168	−	0.0709954i
$597$	−10.4938	+	4.02820i	−0.429484	+	0.164863i
$598$	−0.129262	+	0.0839435i	−0.00528591	+	0.00343271i
$599$	−2.55964	−	1.47781i	−0.104584	−	0.0603816i	0.446796	−	0.894636i	$-0.352565\pi$
$599$	−2.55964	−	1.47781i	−0.104584	−	0.0603816i	−0.551380	+	0.834254i	$0.685898\pi$
$600$	−7.61473	−	22.0440i	−0.310870	−	0.899942i
$601$		−	2.33505i		−	0.0952489i	−0.998865	−	0.0476244i	$-0.984835\pi$
$601$		−	2.33505i		−	0.0952489i	0.998865	−	0.0476244i	$-0.0151651\pi$
$602$	−25.9351	−	14.7136i	−1.05704	−	0.599681i
$603$	7.03388	+	1.11406i	0.286442	+	0.0453679i
$604$	1.67815	−	3.76919i	0.0682830	−	0.153366i
$605$	0.222070	+	24.0826i	0.00902841	+	0.979097i
$606$	−32.8173	+	14.6112i	−1.33311	+	0.593540i
$607$	−4.99555	+	18.6437i	−0.202763	+	0.756723i	0.787356	+	0.616498i	$0.211449\pi$
$607$	−4.99555	+	18.6437i	−0.202763	+	0.756723i	−0.990120	+	0.140225i	$0.955218\pi$
$608$	7.60420	−	1.20439i	0.308391	−	0.0488444i
$609$	15.4967	−	2.57458i	0.627959	−	0.104327i
$610$	25.4586	+	6.57061i	1.03079	+	0.266036i
$611$	1.09608	−	1.21732i	0.0443428	−	0.0492477i
$612$	−0.0351296	+	0.670314i	−0.00142003	+	0.0270958i
$613$	0.518264	−	9.88907i	0.0209325	−	0.399416i	−0.967991	−	0.250987i	$-0.919245\pi$
$613$	0.518264	−	9.88907i	0.0209325	−	0.399416i	0.988923	−	0.148429i	$-0.0474217\pi$
$614$	4.99493	−	5.54743i	0.201579	−	0.223876i
$615$	−5.29560	+	8.32150i	−0.213539	+	0.335555i
$616$	−3.72438	+	0.618757i	−0.150059	+	0.0249304i
$617$	5.48345	−	0.868493i	0.220755	−	0.0349642i	−0.0450769	−	0.998984i	$-0.514353\pi$
$617$	5.48345	−	0.868493i	0.220755	−	0.0349642i	0.265832	+	0.964019i	$0.414353\pi$
$618$	4.20172	−	15.6810i	0.169018	−	0.630784i
$619$	34.8010	−	15.4944i	1.39877	−	0.622772i	0.437710	−	0.899116i	$-0.355790\pi$
$619$	34.8010	−	15.4944i	1.39877	−	0.622772i	0.961059	+	0.276344i	$0.0891228\pi$
$620$	1.10852	−	1.55572i	0.0445193	−	0.0624791i
$621$	1.20440	−	2.70513i	0.0483310	−	0.108553i
$622$	1.25915	+	0.199429i	0.0504872	+	0.00799638i
$623$	−13.4782	−	7.64649i	−0.539993	−	0.306350i
$624$		−	1.17396i		−	0.0469959i
$625$	−3.52826	−	24.7498i	−0.141131	−	0.989991i
$626$	0.446579	+	0.257833i	0.0178489	+	0.0103051i
$627$	3.37752	−	2.19339i	0.134885	−	0.0875954i
$628$	−0.962483	+	0.369462i	−0.0384072	+	0.0147432i
$629$	−29.5934	+	21.5008i	−1.17997	+	0.857295i
$630$	2.63966	−	3.37389i	0.105166	−	0.134419i
$631$	−11.4331	−	8.30661i	−0.455143	−	0.330681i	0.336480	−	0.941691i	$-0.390764\pi$
$631$	−11.4331	−	8.30661i	−0.455143	−	0.330681i	−0.791623	+	0.611010i	$0.790764\pi$
$632$	−26.6610	−	7.14378i	−1.06052	−	0.284164i
$633$	2.12927	−	5.54695i	0.0846311	−	0.220471i
$634$	29.5359	−	26.5943i	1.17302	−	1.05619i
$635$	1.80062	−	41.7140i	0.0714553	−	1.65537i
$636$	−1.84029	+	0.597945i	−0.0729721	+	0.0237101i
$637$	−1.20537	−	0.946298i	−0.0477584	−	0.0374937i
$638$	2.13789	−	1.08931i	0.0846400	−	0.0431262i
$639$	−1.91618	−	1.72534i	−0.0758031	−	0.0682534i
$640$	−13.5999	+	13.8530i	−0.537583	+	0.547590i
$641$	5.18908	+	5.76306i	0.204956	+	0.227627i	0.836856	−	0.547423i	$-0.184391\pi$
$641$	5.18908	+	5.76306i	0.204956	+	0.227627i	−0.631900	+	0.775050i	$0.717724\pi$
$642$	−3.45438	+	2.79730i	−0.136333	+	0.110401i
$643$	16.8674	−	16.8674i	0.665185	−	0.665185i	−0.291412	−	0.956598i	$-0.594125\pi$
$643$	16.8674	−	16.8674i	0.665185	−	0.665185i	0.956598	+	0.291412i	$0.0941251\pi$
$644$	0.131456	+	0.334872i	0.00518010	+	0.0131958i
$645$	25.7320	−	15.1744i	1.01319	−	0.597492i
$646$	−31.0977	−	13.8456i	−1.22352	−	0.544748i
$647$	19.0469	−	23.5210i	0.748811	−	0.924704i	−0.250244	−	0.968183i	$-0.580511\pi$
$647$	19.0469	−	23.5210i	0.748811	−	0.924704i	0.999054	+	0.0434786i	$0.0138440\pi$
$648$	11.4461	+	17.6255i	0.449647	+	0.692396i
$649$	−1.28220	−	2.22083i	−0.0503307	−	0.0871754i
$650$	0.274489	−	1.41961i	0.0107663	−	0.0556818i
$651$	−13.8587	−	0.621370i	−0.543165	−	0.0243534i
$652$	−3.79554	−	1.93392i	−0.148645	−	0.0757383i
$653$	12.0313	+	31.3427i	0.470823	+	1.22654i	0.939311	+	0.343066i	$0.111465\pi$
$653$	12.0313	+	31.3427i	0.470823	+	1.22654i	−0.468488	+	0.883470i	$0.655201\pi$
$654$	−2.36362	−	22.4884i	−0.0924250	−	0.879365i
$655$	−0.361501	−	1.07864i	−0.0141250	−	0.0421460i
$656$	9.59487	+	1.00846i	0.374617	+	0.0393738i
$657$	−5.08413	−	5.08413i	−0.198351	−	0.198351i
$658$	15.5302	+	21.0394i	0.605429	+	0.820201i
$659$	45.9853	+	14.9415i	1.79133	+	0.582039i	0.999585	−	0.0288108i	$-0.00917203\pi$
$659$	45.9853	+	14.9415i	1.79133	+	0.582039i	0.791747	+	0.610850i	$0.209172\pi$
$660$	0.149654	−	0.400872i	0.00582528	−	0.0156039i
$661$	1.42228	−	6.69130i	0.0553203	−	0.260262i	−0.941793	−	0.336194i	$-0.890860\pi$
$661$	1.42228	−	6.69130i	0.0553203	−	0.260262i	0.997113	+	0.0759328i	$0.0241934\pi$
$662$	11.6839	+	0.612327i	0.454108	+	0.0237988i
$663$	0.896108	−	1.37988i	0.0348019	−	0.0535903i
$664$	−8.74513	−	26.9148i	−0.339377	−	1.04450i
$665$	−16.3410	−	27.2379i	−0.633677	−	1.05624i
$666$	1.70528	−	5.24830i	0.0660781	−	0.203368i
$667$	−1.27186	−	1.57061i	−0.0492465	−	0.0608143i
$668$	1.57472	+	5.87694i	0.0609278	+	0.227386i
$669$	−2.44559	−	5.49289i	−0.0945520	−	0.212367i
$670$	4.36284	+	38.1247i	0.168551	+	1.47288i
$671$	2.50641	+	3.44978i	0.0967589	+	0.133177i
$672$	−5.81997	−	1.19120i	−0.224510	−	0.0459514i
$673$	12.8780	−	25.2746i	0.496412	−	0.974263i	−0.497847	−	0.867265i	$-0.665876\pi$
$673$	12.8780	−	25.2746i	0.496412	−	0.974263i	0.994259	−	0.106999i	$-0.0341240\pi$
$674$	22.6814	−	13.0951i	0.873653	−	0.504404i
$675$	10.4317	+	25.7461i	0.401517	+	0.990968i
$676$	1.65216	−	2.86163i	0.0635446	−	0.110063i
$677$	−12.5876	+	0.659688i	−0.483780	+	0.0253539i	−0.292668	−	0.956214i	$-0.594543\pi$
$677$	−12.5876	+	0.659688i	−0.483780	+	0.0253539i	−0.191113	+	0.981568i	$0.561210\pi$
$678$	5.75255	−	36.3202i	0.220925	−	1.39487i
$679$	−1.52605	−	25.4403i	−0.0585643	−	0.976308i
$680$	−31.2097	+	6.93522i	−1.19684	+	0.265954i
$681$	−0.319565	+	3.04046i	−0.0122457	+	0.116510i
$682$	−2.04670	+	0.548413i	−0.0783723	+	0.0209998i
$683$	4.75634	+	1.82579i	0.181996	+	0.0698619i	0.447660	−	0.894204i	$-0.352258\pi$
$683$	4.75634	+	1.82579i	0.181996	+	0.0698619i	−0.265663	+	0.964066i	$0.585591\pi$
$684$	−0.734439	+	0.156110i	−0.0280820	+	0.00596900i
$685$	−3.56992	−	9.04965i	−0.136400	−	0.345769i
$686$	18.6585	−	15.8226i	0.712384	−	0.604111i
$687$	7.83822	+	15.3834i	0.299047	+	0.586912i
$688$	−24.5053	−	15.9139i	−0.934254	−	0.606712i
$689$	−1.03725	−	0.220474i	−0.0395159	−	0.00839937i
$690$	2.43813	+	0.363150i	0.0928182	+	0.0138249i
$691$	2.60404	+	12.2510i	0.0990622	+	0.466051i	0.999516	+	0.0310999i	$0.00990101\pi$
$691$	2.60404	+	12.2510i	0.0990622	+	0.466051i	−0.900454	+	0.434951i	$0.856766\pi$
$692$	0.976886	+	6.16782i	0.0371356	+	0.234465i
$693$	0.678453	−	0.149575i	0.0257723	−	0.00568187i
$694$	−0.780048	+	1.07364i	−0.0296102	+	0.0407550i
$695$	−35.7994	+	32.8367i	−1.35795	+	1.24557i
$696$	17.5902	−	1.84880i	0.666753	−	0.0700786i
$697$	10.5082	+	8.50935i	0.398025	+	0.322315i
$698$	−1.58038	−	30.1554i	−0.0598181	−	1.14140i
$699$	30.6192			1.15812
$700$	−3.11777	−	1.29210i	−0.117841	−	0.0488366i
$701$	−38.5281			−1.45519			−0.727594	−	0.686008i	$-0.759361\pi$
$701$	−38.5281			−1.45519			−0.727594	+	0.686008i	$0.759361\pi$
$702$	0.0840852	+	1.60444i	0.00317359	+	0.0605557i
$703$	−31.7993	−	25.7505i	−1.19933	−	0.971199i
$704$	−4.16549	+	0.437810i	−0.156993	+	0.0165006i
$705$	−26.0286	+	2.97862i	−0.980295	+	0.112181i
$706$	13.6275	−	18.7566i	0.512877	−	0.705915i
$707$	−13.8691	+	43.8079i	−0.521601	+	1.64757i
$708$	−0.334535	−	2.11217i	−0.0125726	−	0.0793803i
$709$	7.37634	+	34.7029i	0.277024	+	1.30330i	0.867983	+	0.496594i	$0.165416\pi$
$709$	7.37634	+	34.7029i	0.277024	+	1.30330i	−0.590959	+	0.806702i	$0.701250\pi$
$710$	6.19322	−	12.4371i	0.232428	−	0.466755i
$711$	4.96816	+	1.05602i	0.186321	+	0.0396037i
$712$	−14.6325	−	9.50247i	−0.548377	−	0.356120i
$713$	0.810250	+	1.59021i	0.0303441	+	0.0595537i
$714$	18.7127	+	18.4322i	0.700307	+	0.689806i
$715$	0.180870	−	0.149248i	0.00676414	−	0.00558154i
$716$	4.41720	−	0.938904i	0.165078	−	0.0350885i
$717$	14.1491	+	5.43135i	0.528410	+	0.202837i
$718$	36.9550	−	9.90207i	1.37915	−	0.369542i
$719$	−1.43210	+	13.6255i	−0.0534082	+	0.508145i	0.934816	+	0.355132i	$0.115564\pi$
$719$	−1.43210	+	13.6255i	−0.0534082	+	0.508145i	−0.988224	+	0.153013i	$0.951102\pi$
$720$	2.77996	−	3.14530i	0.103603	−	0.117218i
$721$	−11.4412	−	17.3299i	−0.426092	−	0.645398i
$722$	2.03057	−	12.8205i	0.0755698	−	0.477129i
$723$	−19.6274	+	1.02863i	−0.729950	+	0.0382550i
$724$	0.121005	−	0.209586i	0.00449710	−	0.00778921i
$725$	18.8890	+	1.63376i	0.701520	+	0.0606764i
$726$	19.2928	−	11.1387i	0.716024	−	0.413397i
$727$	18.6979	−	36.6967i	0.693467	−	1.36101i	−0.228425	−	0.973561i	$-0.573358\pi$
$727$	18.6979	−	36.6967i	0.693467	−	1.36101i	0.921893	−	0.387445i	$-0.126642\pi$
$728$	−1.29090	−	1.14480i	−0.0478440	−	0.0424289i
$729$	−17.6135	−	24.2429i	−0.652352	−	0.897885i
$730$	19.0610	−	33.7292i	0.705481	−	1.24837i
$731$	−16.6564	−	37.4108i	−0.616058	−	1.38369i
$732$	0.920351	+	3.43480i	0.0340172	+	0.126954i
$733$	−18.1721	−	22.4407i	−0.671203	−	0.828867i	0.321818	−	0.946802i	$-0.395706\pi$
$733$	−18.1721	−	22.4407i	−0.671203	−	0.828867i	−0.993021	+	0.117934i	$0.962373\pi$
$734$	−6.76846	+	20.8312i	−0.249829	+	0.768893i
$735$	4.42181	+	24.1070i	0.163101	+	0.889200i
$736$	0.236172	+	0.726863i	0.00870542	+	0.0267925i
$737$	−3.38951	+	5.21938i	−0.124854	+	0.192258i
$738$	−2.03706	−	0.106758i	−0.0749853	−	0.00392982i
$739$	−3.80274	+	17.8905i	−0.139886	+	0.658113i	0.851195	+	0.524850i	$0.175879\pi$
$739$	−3.80274	+	17.8905i	−0.139886	+	0.658113i	−0.991081	+	0.133263i	$0.957455\pi$
$740$	−4.34352	−	0.187491i	−0.159671	−	0.00689231i
$741$	1.75039	+	0.568737i	0.0643022	+	0.0208931i
$742$	6.76849	−	15.5167i	0.248479	−	0.569635i
$743$	−18.6958	−	18.6958i	−0.685883	−	0.685883i	0.275437	−	0.961319i	$-0.411178\pi$
$743$	−18.6958	−	18.6958i	−0.685883	−	0.685883i	−0.961319	+	0.275437i	$0.911178\pi$
$744$	−15.5337	−	1.63266i	−0.569494	−	0.0598563i
$745$	−21.0483	−	14.9979i	−0.771148	−	0.549480i
$746$	4.04893	+	38.5230i	0.148242	+	1.41043i
$747$	1.86626	+	4.86178i	0.0682830	+	0.177883i
$748$	−0.522646	−	0.266301i	−0.0191098	−	0.00973694i
$749$	−0.254671	+	5.68005i	−0.00930549	+	0.207544i
$750$	−18.3255	+	14.1049i	−0.669152	+	0.515036i
$751$	14.6728	+	25.4141i	0.535418	+	0.927372i	0.999143	+	0.0413925i	$0.0131794\pi$
$751$	14.6728	+	25.4141i	0.535418	+	0.927372i	−0.463724	+	0.885979i	$0.653487\pi$
$752$	13.9564	+	21.4910i	0.508938	+	0.783697i
$753$	−15.0980	+	18.6445i	−0.550201	+	0.679442i
$754$	1.00175	+	0.446006i	0.0364814	+	0.0162426i
$755$	−35.9978	−	3.44824i	−1.31010	−	0.125494i
$756$	3.70824	+	0.558648i	0.134867	+	0.0203178i
$757$	−26.5318	+	26.5318i	−0.964316	+	0.964316i	−0.999385	−	0.0350687i	$-0.988835\pi$
$757$	−26.5318	+	26.5318i	−0.964316	+	0.964316i	0.0350687	+	0.999385i	$0.488835\pi$
$758$	18.5906	−	15.0544i	0.675241	−	0.546799i
$759$	0.267504	+	0.297093i	0.00970977	+	0.0107838i
$760$	−16.5292	−	31.7140i	−0.599577	−	1.15039i
$761$	−0.760199	−	0.684487i	−0.0275572	−	0.0248126i	0.655237	−	0.755423i	$-0.272569\pi$
$761$	−0.760199	−	0.684487i	−0.0275572	−	0.0248126i	−0.682794	+	0.730611i	$0.739235\pi$
$762$	−34.4120	+	17.5338i	−1.24662	+	0.635183i
$763$	−23.5281	−	16.8241i	−0.851773	−	0.609073i
$764$	2.54090	−	0.825588i	0.0919265	−	0.0298687i
$765$	5.66848	−	1.57503i	0.204944	−	0.0569452i
$766$	29.2853	−	26.3686i	1.05812	−	0.952738i
$767$	0.419988	−	1.09411i	0.0151649	−	0.0395059i
$768$	−9.10360	−	2.43930i	−0.328498	−	0.0880207i
$769$	−16.8522	−	12.2439i	−0.607708	−	0.441525i	0.240899	−	0.970550i	$-0.422558\pi$
$769$	−16.8522	−	12.2439i	−0.607708	−	0.441525i	−0.848606	+	0.529025i	$0.822558\pi$
$770$	1.75524	+	3.30653i	0.0632544	+	0.119159i
$771$	6.62415	−	4.81272i	0.238563	−	0.173326i
$772$	4.68995	−	1.80030i	0.168795	−	0.0647943i
$773$	−21.8018	+	14.1583i	−0.784158	+	0.509238i	−0.873536	−	0.486760i	$-0.838179\pi$
$773$	−21.8018	+	14.1583i	−0.784158	+	0.509238i	0.0893781	+	0.995998i	$0.471512\pi$
$774$	5.35024	+	3.08897i	0.192311	+	0.111031i
$775$	−16.0163	−	4.87935i	−0.575321	−	0.175272i
$776$		−	28.6949i		−	1.03009i
$777$	15.9925	+	27.2228i	0.573726	+	0.976612i
$778$	−14.7225	−	2.33181i	−0.527827	−	0.0835995i
$779$	−6.15198	+	13.8176i	−0.220418	+	0.495066i
$780$	0.185415	−	0.0621409i	0.00663892	−	0.00222500i
$781$	2.05848	−	0.916495i	0.0736582	−	0.0327948i
$782$	0.874595	−	3.26403i	0.0312754	−	0.116722i
$783$	−20.8078	+	3.29564i	−0.743611	+	0.117776i
$784$	19.1793	−	14.3822i	0.684974	−	0.513650i
$785$	5.75114	+	6.96967i	0.205267	+	0.248758i
$786$	−0.704119	+	0.782004i	−0.0251151	+	0.0278931i
$787$	−2.54078	+	48.4809i	−0.0905689	+	1.72816i	0.455343	+	0.890316i	$0.349517\pi$
$787$	−2.54078	+	48.4809i	−0.0905689	+	1.72816i	−0.545912	+	0.837842i	$0.683817\pi$
$788$	−0.190721	+	3.63916i	−0.00679414	+	0.129640i
$789$	12.1946	−	13.5435i	0.434140	−	0.482161i
$790$	1.68430	+	27.3164i	0.0599245	+	0.971874i
$791$	−29.8772	−	36.3307i	−1.06231	−	1.29177i
$792$	0.772589	−	0.122366i	0.0274528	−	0.00434809i
$793$	−0.504373	+	1.88235i	−0.0179108	+	0.0668441i
$794$	5.98900	−	2.66647i	0.212542	−	0.0946296i
$795$	10.0948	+	13.6283i	0.358027	+	0.483345i
$796$	−0.744891	+	1.67305i	−0.0264020	+	0.0592998i
$797$	−10.1052	−	1.60051i	−0.357945	−	0.0566929i	−0.0251277	−	0.999684i	$-0.507999\pi$
$797$	−10.1052	−	1.60051i	−0.357945	−	0.0566929i	−0.332817	+	0.942991i	$0.607999\pi$
$798$	−14.4981	+	25.5554i	−0.513228	+	0.904650i
$799$			35.9141i			1.27055i
$800$	−6.44728	−	3.13666i	−0.227946	−	0.110898i
$801$	2.78047	+	1.60530i	0.0982429	+	0.0567206i
$802$	−4.87563	+	3.16627i	−0.172164	+	0.111805i
$803$	5.86591	−	2.25171i	0.207004	−	0.0794613i
$804$	−4.19865	+	3.05049i	−0.148075	+	0.107583i
$805$	2.41682	−	2.02516i	0.0851816	−	0.0713774i
$806$	−0.783414	−	0.569183i	−0.0275946	−	0.0200486i
$807$	18.2316	+	4.88514i	0.641782	+	0.171965i
$808$	−18.5407	+	48.3002i	−0.652260	+	1.69919i
$809$	−31.3375	+	28.2164i	−1.10177	+	0.992036i	−0.999996	−	0.00277189i	$-0.999118\pi$
$809$	−31.3375	+	28.2164i	−1.10177	+	0.992036i	−0.101771	+	0.994808i	$0.532451\pi$
$810$	12.9642	−	16.3148i	0.455515	−	0.573243i
$811$	30.4344	−	9.88872i	1.06869	−	0.347240i	0.278716	−	0.960374i	$-0.410091\pi$
$811$	30.4344	−	9.88872i	1.06869	−	0.347240i	0.789979	+	0.613134i	$0.210091\pi$
$812$	1.48873	−	2.08196i	0.0522443	−	0.0730623i
$813$	20.4279	−	10.4085i	0.716436	−	0.365043i
$814$	3.58376	+	3.22683i	0.125611	+	0.113100i
$815$	−5.50045	+	36.9292i	−0.192672	+	1.29357i
$816$	17.2225	+	19.1275i	0.602906	+	0.669595i
$817$	35.5998	−	28.8281i	1.24548	−	1.00857i
$818$	−0.201215	+	0.201215i	−0.00703533	+	0.00703533i
$819$	0.248248	+	0.197942i	0.00867450	+	0.00691664i
$820$	0.348608	+	1.56880i	0.0121739	+	0.0547848i
$821$	44.4213	+	19.7776i	1.55031	+	0.690244i	0.990390	−	0.138300i	$-0.0441638\pi$
$821$	44.4213	+	19.7776i	1.55031	+	0.690244i	0.559924	+	0.828544i	$0.310830\pi$
$822$	−5.66309	+	6.99334i	−0.197523	+	0.243921i
$823$	0.978707	+	1.50708i	0.0341156	+	0.0525334i	0.855317	−	0.518105i	$-0.173362\pi$
$823$	0.978707	+	1.50708i	0.0341156	+	0.0525334i	−0.821201	+	0.570639i	$0.806696\pi$
$824$	−11.6903	−	20.2482i	−0.407250	−	0.705378i
$825$	−3.74826	−	0.127183i	−0.130498	−	0.00442793i
$826$	15.7673	+	10.0709i	0.548614	+	0.350411i
$827$	−15.8538	−	8.07790i	−0.551290	−	0.280896i	0.156075	−	0.987745i	$-0.450116\pi$
$827$	−15.8538	−	8.07790i	−0.551290	−	0.280896i	−0.707364	+	0.706849i	$0.750116\pi$
$828$	−0.0267111	−	0.0695849i	−0.000928277	−	0.00241824i
$829$	−5.29689	−	50.3966i	−0.183969	−	1.75035i	−0.564369	−	0.825523i	$-0.690880\pi$
$829$	−5.29689	−	50.3966i	−0.183969	−	1.75035i	0.380400	−	0.924822i	$-0.375786\pi$
$830$	−22.5486	+	16.7023i	−0.782673	+	0.579747i
$831$	−9.43827	−	0.992002i	−0.327410	−	0.0344122i
$832$	−1.35350	−	1.35350i	−0.0469242	−	0.0469242i
$833$	33.5218	−	2.26507i	1.16146	−	0.0784800i
$834$	42.7357	+	13.8857i	1.47982	+	0.480822i
$835$	44.4544	−	29.4553i	1.53841	−	1.01934i
$836$	0.136421	−	0.641813i	0.00471824	−	0.0221976i
$837$	18.5788	+	0.973673i	0.642177	+	0.0336551i
$838$	−24.9548	+	38.4270i	−0.862049	+	1.32744i
$839$	2.38981	+	7.35507i	0.0825053	+	0.253925i	0.983797	−	0.179288i	$-0.0573795\pi$
$839$	2.38981	+	7.35507i	0.0825053	+	0.253925i	−0.901291	+	0.433214i	$0.857380\pi$
$840$	3.34441	+	27.3917i	0.115393	+	0.945103i
$841$	4.51828	−	13.9058i	0.155803	−	0.479511i
$842$	24.9830	+	30.8514i	0.860970	+	1.06321i
$843$	−1.87139	−	6.98412i	−0.0644541	−	0.240546i
$844$	−0.393743	−	0.884362i	−0.0135532	−	0.0304410i
$845$	−28.3832	−	5.76001i	−0.976410	−	0.198150i
$846$	−3.18463	−	4.38327i	−0.109490	−	0.150700i
$847$	5.71396	−	27.9174i	0.196334	−	0.959253i
$848$	7.53108	−	14.7806i	0.258618	−	0.507567i
$849$	5.24954	−	3.03082i	0.180164	−	0.104018i
$850$	16.3540	+	27.1568i	0.560939	+	0.931472i
$851$	2.03094	−	3.51769i	0.0696197	−	0.120585i
$852$	1.87648	−	0.0983424i	0.0642873	−	0.00336915i
$853$	−1.83983	+	11.6162i	−0.0629946	+	0.397732i	0.935964	+	0.352097i	$0.114531\pi$
$853$	−1.83983	+	11.6162i	−0.0629946	+	0.397732i	−0.998958	+	0.0456353i	$0.985469\pi$
$854$	−27.8252	−	13.9139i	−0.952158	−	0.476124i
$855$	3.34292	+	5.66875i	0.114326	+	0.193867i
$856$	−0.669154	+	6.36657i	−0.0228712	+	0.217605i
$857$	−0.368054	+	0.0986197i	−0.0125725	+	0.00336878i	−0.265100	−	0.964221i	$-0.585405\pi$
$857$	−0.368054	+	0.0986197i	−0.0125725	+	0.00336878i	0.252527	+	0.967590i	$0.418738\pi$
$858$	−0.202503	−	0.0777336i	−0.00691334	−	0.00265378i
$859$	9.45007	−	2.00867i	0.322432	−	0.0685351i	−0.0438522	−	0.999038i	$-0.513963\pi$
$859$	9.45007	−	2.00867i	0.322432	−	0.0685351i	0.366284	+	0.930503i	$0.380630\pi$
$860$	1.21631	−	4.71274i	0.0414759	−	0.160703i
$861$	8.18992	−	8.31459i	0.279112	−	0.283361i
$862$	20.9966	+	41.2081i	0.715146	+	1.40355i
$863$	4.21948	+	2.74016i	0.143633	+	0.0932762i	0.614455	−	0.788952i	$-0.289376\pi$
$863$	4.21948	+	2.74016i	0.143633	+	0.0932762i	−0.470822	+	0.882228i	$0.656043\pi$
$864$	7.79276	+	1.65640i	0.265115	+	0.0563519i
$865$	48.5368	−	25.2971i	1.65030	−	0.860129i
$866$	−1.59034	−	7.48196i	−0.0540419	−	0.254247i
$867$	1.47892	+	9.33755i	0.0502268	+	0.317120i
$868$	−1.66822	+	1.52504i	−0.0566230	+	0.0517634i
$869$	−2.60893	+	3.59089i	−0.0885020	+	0.121813i
$870$	−7.28063	−	15.9550i	−0.246836	−	0.540924i
$871$	−2.82855	+	0.297293i	−0.0958419	+	0.0100734i
$872$	−25.3087	−	20.4946i	−0.857061	−	0.694034i
$873$	0.276353	+	5.27314i	0.00935315	+	0.178469i
$874$	3.77997			0.127859
$875$	−2.05428	+	29.5090i	−0.0694474	+	0.997586i
$876$	5.23972			0.177034
$877$	1.13176	+	21.5953i	0.0382169	+	0.729223i	0.948796	+	0.315888i	$0.102303\pi$
$877$	1.13176	+	21.5953i	0.0382169	+	0.729223i	−0.910579	+	0.413334i	$0.864364\pi$
$878$	−19.7468	−	15.9906i	−0.666421	−	0.539657i
$879$	−23.8359	+	2.50526i	−0.803966	+	0.0845002i
$880$	1.52288	+	3.33729i	0.0513364	+	0.112500i
$881$	−15.8503	+	21.8160i	−0.534009	+	0.735001i	−0.987735	−	0.156141i	$-0.950095\pi$
$881$	−15.8503	+	21.8160i	−0.534009	+	0.735001i	0.453725	+	0.891142i	$0.350095\pi$
$882$	−3.89045	+	3.24895i	−0.130998	+	0.109398i
$883$	0.103976	+	0.656476i	0.00349906	+	0.0220922i	0.989376	−	0.145379i	$-0.0464400\pi$
$883$	0.103976	+	0.656476i	0.00349906	+	0.0220922i	−0.985877	+	0.167471i	$0.946440\pi$
$884$	−0.0557349	−	0.262212i	−0.00187457	−	0.00881915i
$885$	−16.6214	+	8.66302i	−0.558724	+	0.291204i
$886$	−19.9200	−	4.23412i	−0.669224	−	0.142248i
$887$	25.6659	+	16.6676i	0.861775	+	0.559644i	0.898147	−	0.439695i	$-0.144913\pi$
$887$	25.6659	+	16.6676i	0.861775	+	0.559644i	−0.0363718	+	0.999338i	$0.511580\pi$
$888$	16.1385	+	31.6735i	0.541572	+	1.06289i
$889$	−12.4255	+	47.8145i	−0.416739	+	1.60365i
$890$	−4.32327	+	16.7510i	−0.144916	+	0.561494i
$891$	3.30573	−	0.702654i	0.110746	−	0.0235398i
$892$	−0.914576	−	0.351073i	−0.0306223	−	0.0117548i
$893$	−38.8049	+	10.3977i	−1.29856	+	0.347947i
$894$	−2.49894	+	23.7758i	−0.0835769	+	0.795181i
$895$	−20.1056	−	34.0940i	−0.672057	−	1.13964i
$896$	19.1690	−	12.6554i	0.640391	−	0.422787i
$897$	−0.0285808	+	0.180452i	−0.000954284	+	0.00602511i
$898$	−18.6238	+	0.976031i	−0.621484	+	0.0325706i
$899$	6.34879	−	10.9964i	0.211744	−	0.366752i
$900$	0.643921	+	0.272577i	0.0214640	+	0.00908591i
$901$	20.1345	−	11.6246i	0.670777	−	0.387273i
$902$	0.809282	−	1.58830i	0.0269461	−	0.0528848i
$903$	−33.5328	+	11.1762i	−1.11590	+	0.371921i
$904$	−31.1294	−	42.8459i	−1.03535	−	1.42503i
$905$	−2.07879	−	0.421865i	−0.0691013	−	0.0140233i
$906$	13.6056	+	30.5586i	0.452015	+	1.01524i
$907$	−8.74745	−	32.6459i	−0.290454	−	1.08399i	−0.944761	−	0.327760i	$-0.893706\pi$
$907$	−8.74745	−	32.6459i	−0.290454	−	1.08399i	0.654307	−	0.756229i	$-0.272961\pi$
$908$	0.313468	+	0.387101i	0.0104028	+	0.0128464i
$909$	2.94197	−	9.05447i	0.0975791	−	0.300318i
$910$	−0.669538	+	1.57436i	−0.0221950	+	0.0521896i
$911$	6.27024	+	19.2978i	0.207742	+	0.639365i	0.999590	+	0.0286459i	$0.00911953\pi$
$911$	6.27024	+	19.2978i	0.207742	+	0.639365i	−0.791847	+	0.610719i	$0.790880\pi$
$912$	−15.6809	+	24.1464i	−0.519246	+	0.799568i
$913$	−4.54465	−	0.238175i	−0.150406	−	0.00788245i
$914$	7.95370	−	37.4192i	0.263085	−	1.23772i
$915$	25.9815	−	17.2152i	0.858922	−	0.569119i
$916$	2.67531	+	0.869261i	0.0883948	+	0.0287212i
$917$	0.150807	+	1.33756i	0.00498007	+	0.0441701i
$918$	−24.9079	−	24.9079i	−0.822082	−	0.822082i
$919$	31.8299	+	3.34546i	1.04997	+	0.110357i	0.613764	−	0.789489i	$-0.289654\pi$
$919$	31.8299	+	3.34546i	1.04997	+	0.110357i	0.436208	+	0.899846i	$0.356321\pi$
$920$	2.85276	−	2.11312i	0.0940529	−	0.0696674i
$921$	−0.924945	−	8.80026i	−0.0304780	−	0.289979i
$922$	−15.1024	−	39.3431i	−0.497372	−	1.29570i
$923$	0.917529	+	0.467504i	0.0302008	+	0.0153881i
$924$	−0.272532	+	0.426684i	−0.00896563	+	0.0140369i
$925$	10.5395	+	36.6190i	0.346537	+	1.20402i
$926$	2.45679	+	4.25528i	0.0807351	+	0.139837i
$927$	2.34328	+	3.60833i	0.0769633	+	0.118513i
$928$	3.42190	−	4.22569i	0.112329	−	0.138715i
$929$	38.4664	+	17.1263i	1.26204	+	0.561897i	0.925134	−	0.379641i	$-0.123952\pi$
$929$	38.4664	+	17.1263i	1.26204	+	0.561897i	0.336908	+	0.941538i	$0.390619\pi$
$930$	3.35955	+	15.1186i	0.110164	+	0.495758i
$931$	12.1525	+	35.5643i	0.398283	+	1.16557i
$932$	3.52757	−	3.52757i	0.115549	−	0.115549i
$933$	1.17441	−	0.951022i	0.0384486	−	0.0311351i
$934$	6.28452	+	6.97967i	0.205636	+	0.228382i
$935$	−0.757412	+	5.08515i	−0.0247700	+	0.166302i
$936$	0.265659	+	0.239200i	0.00868334	+	0.00781851i
$937$	−14.8083	+	7.54518i	−0.483765	+	0.246490i	−0.678824	−	0.734301i	$-0.737510\pi$
$937$	−14.8083	+	7.54518i	−0.483765	+	0.246490i	0.195059	+	0.980791i	$0.437510\pi$
$938$	4.40480	−	45.1899i	0.143822	−	1.47550i
$939$	0.581349	−	0.188892i	0.0189716	−	0.00616425i
$940$	−2.65554	+	3.34186i	−0.0866143	+	0.109000i
$941$	8.12267	−	7.31369i	0.264791	−	0.238419i	−0.526030	−	0.850466i	$-0.676320\pi$
$941$	8.12267	−	7.31369i	0.264791	−	0.238419i	0.790822	+	0.612047i	$0.209653\pi$
$942$	2.99541	−	7.80330i	0.0975957	−	0.254245i
$943$	−1.45030	−	0.388607i	−0.0472283	−	0.0126548i
$944$	14.8319	+	10.7760i	0.482739	+	0.350730i
$945$	−5.68563	−	32.3733i	−0.184954	−	1.05310i
$946$	−4.36771	+	3.17332i	−0.142006	+	0.103174i
$947$	30.5764	−	11.7372i	0.993599	−	0.381407i	0.193386	−	0.981123i	$-0.438053\pi$
$947$	30.5764	−	11.7372i	0.993599	−	0.381407i	0.800213	+	0.599716i	$0.204720\pi$
$948$	−3.10427	+	2.01594i	−0.100822	+	0.0654746i
$949$	2.48678	+	1.43574i	0.0807242	+	0.0466062i
$950$	−24.6080	+	25.5328i	−0.798388	+	0.828392i
$951$		−	47.1129i		−	1.52774i
$952$	37.8275	−	0.285745i	1.22600	−	0.00926105i
$953$	−30.6299	−	4.85130i	−0.992200	−	0.157149i	−0.360831	−	0.932631i	$-0.617507\pi$
$953$	−30.6299	−	4.85130i	−0.992200	−	0.157149i	−0.631369	+	0.775482i	$0.717507\pi$
$954$	−1.42659	+	3.20417i	−0.0461875	+	0.103739i
$955$	−13.9380	−	18.8167i	−0.451024	−	0.608894i
$956$	2.25583	−	1.00436i	0.0729587	−	0.0324833i
$957$	0.736146	−	2.74733i	0.0237962	−	0.0888087i
$958$	15.0333	−	2.38104i	0.485704	−	0.0769279i
$959$	1.88650	+	11.3551i	0.0609182	+	0.366675i
$960$	1.88403	+	30.5558i	0.0608068	+	0.986183i
$961$	13.2400	−	14.7045i	0.427097	−	0.474339i
$962$	−0.115342	+	2.20086i	−0.00371878	+	0.0709585i
$963$	0.0616525	−	1.17640i	0.00198673	−	0.0379090i
$964$	−2.14272	+	2.37973i	−0.0690124	+	0.0766461i
$965$	−28.0240	−	33.9616i	−0.902123	−	1.09326i
$966$	−2.73076	−	1.02464i	−0.0878607	−	0.0329673i
$967$	−32.8149	+	5.19736i	−1.05525	+	0.167136i	−0.659870	−	0.751380i	$-0.729389\pi$
$967$	−32.8149	+	5.19736i	−1.05525	+	0.167136i	−0.395385	+	0.918516i	$0.629389\pi$
$968$	8.30397	−	30.9908i	0.266900	−	0.996083i
$969$	−36.8630	+	16.4125i	−1.18421	+	0.527245i
$970$	−26.9777	+	9.04145i	−0.866203	+	0.290304i
$971$	−3.93520	+	8.83860i	−0.126287	+	0.283644i	−0.965613	−	0.259983i	$-0.916283\pi$
$971$	−3.93520	+	8.83860i	−0.126287	+	0.283644i	0.839327	+	0.543628i	$0.182950\pi$
$972$	−1.41625	−	0.224312i	−0.0454262	−	0.00719481i
$973$	49.5593	−	29.1144i	1.58880	−	0.933366i
$974$		−	5.77998i		−	0.185202i
$975$	−1.03284	−	1.36781i	−0.0330775	−	0.0438051i
$976$	−26.4009	−	15.2426i	−0.845073	−	0.487903i
$977$	−3.50951	+	2.27910i	−0.112279	+	0.0729149i	−0.599557	−	0.800332i	$-0.704657\pi$
$977$	−3.50951	+	2.27910i	−0.112279	+	0.0729149i	0.487278	+	0.873247i	$0.337990\pi$
$978$	32.2426	−	12.3768i	1.03100	−	0.395765i
$979$	−2.26985	+	1.64914i	−0.0725448	+	0.0527069i
$980$	3.28674	+	2.26789i	0.104991	+	0.0724450i
$981$	4.84824	+	3.52246i	0.154793	+	0.112463i
$982$	12.3251	+	3.30250i	0.393310	+	0.105387i
$983$	4.36704	−	11.3765i	0.139287	−	0.362855i	−0.846138	−	0.532963i	$-0.821078\pi$
$983$	4.36704	−	11.3765i	0.139287	−	0.362855i	0.985425	+	0.170108i	$0.0544118\pi$
$984$	9.76510	−	8.79254i	0.311300	−	0.280296i
$985$	30.7745	−	8.55090i	0.980556	−	0.272454i
$986$	−22.8647	+	7.42920i	−0.728161	+	0.236594i
$987$	30.8523	+	3.00726i	0.982039	+	0.0957222i
$988$	0.267182	−	0.136136i	0.00850019	−	0.00433106i
$989$	3.37933	+	3.04276i	0.107456	+	0.0967542i
$990$	−0.358478	−	0.687799i	−0.0113932	−	0.0218597i
$991$	−26.7684	−	29.7294i	−0.850327	−	0.944384i	0.148682	−	0.988885i	$-0.452497\pi$
$991$	−26.7684	−	29.7294i	−0.850327	−	0.944384i	−0.999009	+	0.0445008i	$0.985830\pi$
$992$	−3.73167	+	3.02185i	−0.118481	+	0.0959438i
$993$	9.80688	−	9.80688i	0.311212	−	0.311212i
$994$	−10.2488	+	12.8535i	−0.325072	+	0.407690i
$995$	15.9786	+	1.53059i	0.506555	+	0.0485230i
$996$	−3.46697	−	1.54360i	−0.109855	−	0.0489107i
$997$	−0.243400	+	0.300574i	−0.00770855	+	0.00951926i	−0.780986	−	0.624549i	$-0.785283\pi$
$997$	−0.243400	+	0.300574i	−0.00770855	+	0.00951926i	0.773277	+	0.634068i	$0.218616\pi$
$998$	−3.39863	−	5.23343i	−0.107582	−	0.165661i
$999$	−21.1708	−	36.6689i	−0.669815	−	1.16015i

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	175.2.x.a.108.13	yes	288
5.2	odd	4		875.2.bb.b.857.6		288
5.3	odd	4		875.2.bb.a.857.13		288
5.4	even	2		875.2.bb.c.143.6		288
7.5	odd	6	inner	175.2.x.a.33.13	✓	288
25.3	odd	20		875.2.bb.c.507.6		288
25.4	even	10		875.2.bb.a.493.6		288
25.21	even	5		875.2.bb.b.493.13		288
25.22	odd	20	inner	175.2.x.a.122.13	yes	288
35.12	even	12		875.2.bb.b.607.13		288
35.19	odd	6		875.2.bb.c.768.6		288
35.33	even	12		875.2.bb.a.607.6		288
175.47	even	60	inner	175.2.x.a.47.13	yes	288
175.54	odd	30		875.2.bb.a.243.13		288
175.96	odd	30		875.2.bb.b.243.6		288
175.103	even	60		875.2.bb.c.257.6		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.13	✓	288	7.5	odd	6	inner
175.2.x.a.47.13	yes	288	175.47	even	60	inner
175.2.x.a.108.13	yes	288	1.1	even	1	trivial
175.2.x.a.122.13	yes	288	25.22	odd	20	inner
875.2.bb.a.243.13		288	175.54	odd	30
875.2.bb.a.493.6		288	25.4	even	10
875.2.bb.a.607.6		288	35.33	even	12
875.2.bb.a.857.13		288	5.3	odd	4
875.2.bb.b.243.6		288	175.96	odd	30
875.2.bb.b.493.13		288	25.21	even	5
875.2.bb.b.607.13		288	35.12	even	12
875.2.bb.b.857.6		288	5.2	odd	4
875.2.bb.c.143.6		288	5.4	even	2
875.2.bb.c.257.6		288	175.103	even	60
875.2.bb.c.507.6		288	25.3	odd	20
875.2.bb.c.768.6		288	35.19	odd	6

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Classical	Maass
Hilbert	Bianchi

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	175.2.x.a.108.13

Level	$175$
Weight	$2$
Character	175.108
Analytic conductor	$1.397$
Analytic rank	$0$
Dimension	$288$
Inner twists	$4$