LMFDB - Embedded newform 875.2.bb.c.257.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [875,2,Mod(82,875)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(875, base_ring=CyclotomicField(60))

chi = DirichletCharacter(H, H._module([27, 50]))

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

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

chi := DirichletCharacter("875.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 875 = 5^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	875.bb (of order $60$, degree $16$, not 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:	$6.98691017686$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$18$ over $\Q(\zeta_{60})$
Twist minimal:	no (minimal twist has level 175)
Sato-Tate group:	$\mathrm{SU}(2)[C_{60}]$

Embedding invariants

Embedding label			257.6
Character	$\chi$	$=$	875.257
Dual form			875.2.bb.c.143.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/875\mathbb{Z}\right)^\times$.

$n$	$127$	$626$
$\chi(n)$	$e\left(\frac{17}{20}\right)$	$e\left(\frac{5}{6}\right)$

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	0.858591	+	0.512660i	$0.171340\pi$
$2$	−0.0691326	+	1.31913i	−0.0488842	+	0.932765i	−0.907476	+	0.420105i	$0.861993\pi$
$3$	−1.21688	+	0.985411i	−0.702567	+	0.568927i	−0.912643	−	0.408758i	$-0.865962\pi$
$3$	−1.21688	+	0.985411i	−0.702567	+	0.568927i	0.210076	+	0.977685i	$0.432629\pi$
$4$	0.253721	+	0.0266672i	0.126861	+	0.0133336i
$5$		0			0
$5$		0			0
$6$	−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
$10$		0			0
$11$	0.468564	−	0.0995964i	0.141277	−	0.0300294i	−0.136730	−	0.990608i	$-0.543659\pi$
$11$	0.468564	−	0.0995964i	0.141277	−	0.0300294i	0.278008	+	0.960579i	$0.410326\pi$
$12$	−0.335027	+	0.217569i	−0.0967140	+	0.0628068i
$13$	−0.0993879	+	0.195060i	−0.0275653	+	0.0540999i	−0.904378	−	0.426731i	$-0.859665\pi$
$13$	−0.0993879	+	0.195060i	−0.0275653	+	0.0540999i	0.876813	+	0.480831i	$0.159665\pi$
$14$	−3.36886	−	0.930015i	−0.900367	−	0.248557i
$15$		0			0
$16$	−3.34984	−	0.712030i	−0.837460	−	0.178008i
$17$	4.48096	−	1.72008i	1.08679	−	0.417180i	0.251989	−	0.967730i	$-0.418915\pi$
$17$	4.48096	−	1.72008i	1.08679	−	0.417180i	0.834802	+	0.550550i	$0.185582\pi$
$18$	−0.699421	−	0.187409i	−0.164855	−	0.0441728i
$19$	0.561217	+	5.33963i	0.128752	+	1.22499i	0.847907	+	0.530145i	$0.177862\pi$
$19$	0.561217	+	5.33963i	0.128752	+	1.22499i	−0.719155	+	0.694849i	$0.755471\pi$
$20$		0			0
$21$	−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	$-0.501030\pi$
$23$	−0.532247	−	0.0278939i	−0.110981	−	0.00581628i	−0.107746	+	0.994178i	$0.534363\pi$
$24$	−2.33221	−	4.03951i	−0.476061	−	0.824561i
$25$		0			0
$26$	−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	−0.964160	−	0.265321i	$-0.914522\pi$
$29$	−2.22883	+	3.06772i	−0.413883	+	0.569661i	0.550277	+	0.834982i	$0.314522\pi$
$30$		0			0
$31$	1.36200	−	3.05910i	0.244622	−	0.549431i	−0.748950	−	0.662626i	$-0.769442\pi$
$31$	1.36200	−	3.05910i	0.244622	−	0.549431i	0.993573	+	0.113195i	$0.0361086\pi$
$32$	−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
$35$		0			0
$36$	−0.0432152	+	0.133003i	−0.00720254	+	0.0221671i
$37$	−4.15075	−	6.39160i	−0.682379	−	1.05077i	−0.994901	−	0.100861i	$-0.967840\pi$
$37$	−4.15075	−	6.39160i	−0.682379	−	1.05077i	0.312521	−	0.949911i	$-0.398826\pi$
$38$	−7.08245	+	0.371176i	−1.14893	+	0.0602126i
$39$	−0.0712708	−	0.335303i	−0.0114125	−	0.0536914i
$40$		0			0
$41$	−2.67924	+	0.870538i	−0.418427	+	0.135955i	−0.510661	−	0.859782i	$-0.670599\pi$
$41$	−2.67924	+	0.870538i	−0.418427	+	0.135955i	0.0922339	+	0.995737i	$0.470599\pi$
$42$	5.01595	−	2.18800i	0.773978	−	0.337615i
$43$	−6.03300	+	6.03300i	−0.920024	+	0.920024i	−0.997031	−	0.0770067i	$-0.975464\pi$
$43$	−6.03300	+	6.03300i	−0.920024	+	0.920024i	0.0770067	+	0.997031i	$0.475464\pi$
$44$	0.121541	−	0.0127744i	0.0183229	−	0.00192582i
$45$		0			0
$46$	0.0735913	−	0.700174i	0.0108504	−	0.103235i
$47$	2.68148	−	6.98550i	0.391135	−	1.01894i	−0.586745	−	0.809772i	$-0.699591\pi$
$47$	2.68148	−	6.98550i	0.391135	−	1.01894i	0.977880	−	0.209169i	$-0.0670757\pi$
$48$	4.77800	−	2.43451i	0.689645	−	0.351391i
$49$	−6.35108	−	2.94344i	−0.907297	−	0.420491i
$50$		0			0
$51$	−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	$-0.108715\pi$
$53$	3.04833	+	3.76438i	0.418721	+	0.517077i	−0.523520	+	0.852013i	$0.675381\pi$
$54$	6.70444	−	2.98501i	0.912359	−	0.406208i
$55$		0			0
$56$	−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	−0.929736	−	0.368226i	$-0.879965\pi$
$59$	−3.58205	+	3.97827i	−0.466343	+	0.517927i	0.463393	+	0.886153i	$0.346632\pi$
$60$		0			0
$61$	6.61519	−	5.95635i	0.846989	−	0.762632i	−0.126355	−	0.991985i	$-0.540328\pi$
$61$	6.61519	−	5.95635i	0.846989	−	0.762632i	0.973343	+	0.229353i	$0.0736611\pi$
$62$	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			0
$66$	−0.736320	−	0.662985i	−0.0906347	−	0.0816079i
$67$	4.65578	+	12.1287i	0.568794	+	1.48176i	0.852437	+	0.522829i	$0.175123\pi$
$67$	4.65578	+	12.1287i	0.568794	+	1.48176i	−0.283644	+	0.958930i	$0.591543\pi$
$68$	1.18278	−	0.316926i	0.143434	−	0.0384329i
$69$	0.675168	−	0.490538i	0.0812807	−	0.0590539i
$70$		0			0
$71$	3.80548	+	2.76485i	0.451628	+	0.328127i	0.790238	−	0.612800i	$-0.209957\pi$
$71$	3.80548	+	2.76485i	0.451628	+	0.328127i	−0.338610	+	0.940927i	$0.609957\pi$
$72$	−1.52446	−	0.585185i	−0.179659	−	0.0689647i
$73$	−11.0005	−	7.14378i	−1.28751	−	0.836117i	−0.294670	−	0.955599i	$-0.595210\pi$
$73$	−11.0005	−	7.14378i	−1.28751	−	0.836117i	−0.992836	+	0.119482i	$0.961876\pi$
$74$	8.71829	−	5.03351i	1.01348	−	0.585133i
$75$		0			0
$76$			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	−0.991637	−	0.129061i	$-0.958804\pi$
$79$	−3.76871	−	8.46467i	−0.424013	−	0.952349i	0.567623	−	0.823288i	$-0.307863\pi$
$80$		0			0
$81$	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	$-0.275414\pi$
$83$	9.38322	+	1.48616i	1.02994	+	0.163127i	0.381482	+	0.924376i	$0.375414\pi$
$84$	−0.371298	−	0.989542i	−0.0405119	−	0.107968i
$85$		0			0
$86$	−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	0.498721	−	0.866762i	$-0.333803\pi$
$89$	−3.91910	−	4.35260i	−0.415424	−	0.461375i	−0.914145	+	0.405388i	$0.867136\pi$
$90$		0			0
$91$	−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
$95$		0			0
$96$	−0.913264	−	2.05122i	−0.0932096	−	0.209352i
$97$	9.51421	−	1.50690i	0.966022	−	0.153003i	0.346558	−	0.938028i	$-0.387350\pi$
$97$	9.51421	−	1.50690i	0.966022	−	0.153003i	0.619463	+	0.785026i	$0.287350\pi$
$98$	4.32184	−	8.17440i	0.436572	−	0.825739i
$99$			0.262589i			0.0263912i
$100$		0			0
$101$	15.0410	−	8.68390i	1.49663	−	0.864080i	0.496638	−	0.867958i	$-0.334568\pi$
$101$	15.0410	−	8.68390i	1.49663	−	0.864080i	0.999992	+	0.00387741i	$0.00123422\pi$
$102$	−8.32605	−	5.40700i	−0.824402	−	0.535373i
$103$	7.32748	+	2.81276i	0.721998	+	0.277149i	0.691491	−	0.722386i	$-0.256954\pi$
$103$	7.32748	+	2.81276i	0.721998	+	0.277149i	0.0305073	+	0.999535i	$0.490288\pi$
$104$	−0.527590	−	0.383317i	−0.0517345	−	0.0375873i
$105$		0			0
$106$	−5.17644	+	3.76090i	−0.502780	+	0.365291i
$107$	−2.07579	+	0.556205i	−0.200674	+	0.0537704i	−0.357756	−	0.933815i	$-0.616458\pi$
$107$	−2.07579	+	0.556205i	−0.200674	+	0.0537704i	0.157082	+	0.987586i	$0.449791\pi$
$108$	−0.507951	−	1.32326i	−0.0488776	−	0.127330i
$109$	−8.12435	−	7.31520i	−0.778171	−	0.700669i	0.181003	−	0.983482i	$-0.442065\pi$
$109$	−8.12435	−	7.31520i	−0.778171	−	0.700669i	−0.959175	+	0.282814i	$0.908732\pi$
$110$		0			0
$111$	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	$-0.0347496\pi$
$113$	15.8409	+	8.07135i	1.49019	+	0.759289i	0.496142	+	0.868241i	$0.334750\pi$
$114$	8.25274	−	7.43080i	0.772940	−	0.695959i
$115$		0			0
$116$	−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
$120$		0			0
$121$	−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
$125$		0			0
$126$	0.882611	−	1.70035i	0.0786293	−	0.151479i
$127$	−16.6373	+	8.47711i	−1.47632	+	0.752222i	−0.992419	−	0.122902i	$-0.960780\pi$
$127$	−16.6373	+	8.47711i	−1.47632	+	0.752222i	−0.483899	+	0.875124i	$0.660780\pi$
$128$	3.11126	−	8.10511i	0.274999	−	0.716397i
$129$	1.39646	−	13.2864i	0.122951	−	1.16980i
$130$		0			0
$131$	0.505966	−	0.0531792i	0.0442064	−	0.00464628i	−0.0823994	−	0.996599i	$-0.526258\pi$
$131$	0.505966	−	0.0531792i	0.0442064	−	0.00464628i	0.126606	+	0.991953i	$0.459592\pi$
$132$	−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
$135$		0			0
$136$	2.97269	+	13.9854i	0.254906	+	1.19924i
$137$	−4.34468	+	0.227695i	−0.371191	+	0.0194533i	−0.237020	−	0.971505i	$-0.576171\pi$
$137$	−4.34468	+	0.227695i	−0.371191	+	0.0194533i	−0.134171	+	0.990958i	$0.542837\pi$
$138$	0.600407	+	0.924546i	0.0511101	+	0.0787026i
$139$	−6.71334	+	20.6615i	−0.569418	+	1.75249i	0.0850255	+	0.996379i	$0.472903\pi$
$139$	−6.71334	+	20.6615i	−0.569418	+	1.75249i	−0.654444	+	0.756111i	$0.727097\pi$
$140$		0			0
$141$	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
$145$		0			0
$146$	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	0.850427	−	0.526094i	$-0.176344\pi$
$149$	10.0097	+	5.77912i	0.820030	+	0.473444i	−0.0303970	+	0.999538i	$0.509677\pi$
$150$		0			0
$151$	8.08621	+	14.0057i	0.658046	+	1.13977i	0.981121	+	0.193396i	$0.0619502\pi$
$151$	8.08621	+	14.0057i	0.658046	+	1.13977i	−0.323075	+	0.946373i	$0.604716\pi$
$152$	−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
$155$		0			0
$156$	−0.00914134	−	0.0869740i	−0.000731893	−	0.00696350i
$157$	3.90339	+	1.04591i	0.311525	+	0.0834728i	0.411194	−	0.911548i	$-0.365112\pi$
$157$	3.90339	+	1.04591i	0.311525	+	0.0834728i	−0.0996695	+	0.995021i	$0.531779\pi$
$158$	11.4265	−	4.38623i	0.909046	−	0.348950i
$159$	−7.41892	−	1.57694i	−0.588359	−	0.125059i
$160$		0			0
$161$	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	$-0.456456\pi$
$163$	14.0036	−	9.09407i	1.09685	−	0.712303i	0.960478	+	0.278355i	$0.0897892\pi$
$164$	−0.702996	+	0.149426i	−0.0548947	+	0.0116682i
$165$		0			0
$166$	−2.60912	+	12.2749i	−0.202507	+	0.952719i
$167$	−3.73076	+	23.5551i	−0.288695	+	1.82275i	0.236344	+	0.971669i	$0.424051\pi$
$167$	−3.73076	+	23.5551i	−0.288695	+	1.82275i	−0.525039	+	0.851078i	$0.675949\pi$
$168$	11.7654	−	3.72478i	0.907718	−	0.287373i
$169$	7.61304	+	10.4784i	0.585618	+	0.806034i
$170$		0			0
$171$	−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	0.317095	+	0.948394i	$0.397293\pi$
$173$	−1.28106	+	24.4441i	−0.0973971	+	1.85845i	−0.414492	+	0.910053i	$0.636041\pi$
$174$	7.84307			0.594581
$175$		0			0
$176$	−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	0.736285	−	0.676672i	$-0.236578\pi$
$179$	17.6041	+	1.85027i	1.31579	+	0.138295i	0.579507	+	0.814967i	$0.303245\pi$
$180$		0			0
$181$	0.557581	+	0.767444i	0.0414447	+	0.0570437i	0.829236	−	0.558898i	$-0.188776\pi$
$181$	0.557581	+	0.767444i	0.0414447	+	0.0570437i	−0.787792	+	0.615942i	$0.788776\pi$
$182$	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
$185$		0			0
$186$	−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
$190$		0			0
$191$	10.2434	+	2.17730i	0.741184	+	0.157544i	0.563004	−	0.826454i	$-0.309646\pi$
$191$	10.2434	+	2.17730i	0.741184	+	0.157544i	0.178180	+	0.983998i	$0.442979\pi$
$192$	12.7816	−	4.90638i	0.922430	−	0.354088i
$193$	−19.0203	−	5.09648i	−1.36911	−	0.366852i	−0.501957	−	0.864892i	$-0.667387\pi$
$193$	−19.0203	−	5.09648i	−1.36911	−	0.366852i	−0.867154	+	0.498040i	$0.834053\pi$
$194$	1.33006	+	12.6546i	0.0954925	+	0.908551i
$195$		0			0
$196$	−1.53291	−	0.916179i	−0.109494	−	0.0654413i
$197$	2.23453	+	14.1083i	0.159204	+	1.00517i	0.929858	+	0.367920i	$0.119930\pi$
$197$	2.23453	+	14.1083i	0.159204	+	1.00517i	−0.770654	+	0.637254i	$0.780070\pi$
$198$	−0.346389	−	0.0181535i	−0.0246168	−	0.00129011i
$199$	−3.58928	−	6.21681i	−0.254437	−	0.440698i	0.710305	−	0.703894i	$-0.248557\pi$
$199$	−3.58928	−	6.21681i	−0.254437	−	0.440698i	−0.964742	+	0.263196i	$0.915223\pi$
$200$		0			0
$201$	−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			0
$206$	−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			0
$211$	−1.17257	+	3.60880i	−0.0807231	+	0.248440i	−0.983271	−	0.182150i	$-0.941694\pi$
$211$	−1.17257	+	3.60880i	−0.0807231	+	0.248440i	0.902548	+	0.430590i	$0.141694\pi$
$212$	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
$215$		0			0
$216$	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			0
$221$	−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	$-0.608961\pi$
$223$	3.42142	−	1.74330i	0.229115	−	0.116740i	0.564780	+	0.825242i	$0.308961\pi$
$224$	−3.36729	−	1.74788i	−0.224986	−	0.116785i
$225$		0			0
$226$	−11.7423	+	20.3382i	−0.781085	+	1.35288i
$227$	−1.06338	+	1.63746i	−0.0705788	+	0.108682i	−0.872198	−	0.489154i	$-0.837306\pi$
$227$	−1.06338	+	1.63746i	−0.0705788	+	0.108682i	0.801619	+	0.597836i	$0.203972\pi$
$228$	−1.34976	−	1.66682i	−0.0893901	−	0.110388i
$229$	10.0729	−	4.48475i	0.665637	−	0.296361i	−0.0459653	−	0.998943i	$-0.514636\pi$
$229$	10.0729	−	4.48475i	0.665637	−	0.296361i	0.711603	+	0.702582i	$0.247970\pi$
$230$		0			0
$231$	−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	$-0.504619\pi$
$233$	−15.1967	−	12.3061i	−0.995571	−	0.806198i	−0.981061	+	0.193697i	$0.937952\pi$
$234$	0.106070	−	0.117803i	0.00693401	−	0.00770100i
$235$		0			0
$236$	−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	0.591207	−	0.806520i	$-0.298652\pi$
$239$	9.20533	+	2.99099i	0.595443	+	0.193471i	0.00423616	+	0.999991i	$0.498652\pi$
$240$		0			0
$241$	−9.32794	−	8.39891i	−0.600865	−	0.541021i	0.311580	−	0.950220i	$-0.399142\pi$
$241$	−9.32794	−	8.39891i	−0.600865	−	0.541021i	−0.912445	+	0.409198i	$0.865808\pi$
$242$	−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
$245$		0			0
$246$	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
$250$		0			0
$251$		−	15.3215i		−	0.967086i	−0.875321	−	0.483543i	$-0.839350\pi$
$251$		−	15.3215i		−	0.967086i	0.875321	−	0.483543i	$-0.160650\pi$
$252$	−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
$255$		0			0
$256$	−5.49862	−	2.44814i	−0.343664	−	0.153009i
$257$	−1.35339	−	5.05092i	−0.0844221	−	0.315068i	0.910782	−	0.412888i	$-0.135480\pi$
$257$	−1.35339	−	5.05092i	−0.0844221	−	0.315068i	−0.995204	+	0.0978199i	$0.968813\pi$
$258$	17.4300	+	2.76064i	1.08514	+	0.171870i
$259$	18.8783	−	7.08357i	1.17304	−	0.440152i
$260$		0			0
$261$	−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	−0.950899	−	0.309500i	$-0.899838\pi$
$263$	−0.609132	−	11.6229i	−0.0375607	−	0.716701i	0.913339	−	0.407201i	$-0.133495\pi$
$264$	−1.49511	−	1.66049i	−0.0920177	−	0.102196i
$265$		0			0
$266$	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	0.713984	−	0.700162i	$-0.246889\pi$
$269$	11.0120	+	4.90285i	0.671412	+	0.298932i	−0.0425725	+	0.999093i	$0.513555\pi$
$270$		0			0
$271$	5.95538	+	13.3760i	0.361764	+	0.812535i	0.999119	+	0.0419648i	$0.0133617\pi$
$271$	5.95538	+	13.3760i	0.361764	+	0.812535i	−0.637355	+	0.770570i	$0.719972\pi$
$272$	−16.2352	+	2.57141i	−0.984405	+	0.155915i
$273$	0.906920	+	0.00685078i	0.0548893	+	0.000414628i
$274$		−	5.74694i		−	0.347185i
$275$		0			0
$276$	0.184386	−	0.106455i	0.0110987	−	0.00640785i
$277$	5.08305	+	3.30097i	0.305411	+	0.198336i	0.688240	−	0.725483i	$-0.258384\pi$
$277$	5.08305	+	3.30097i	0.305411	+	0.198336i	−0.382829	+	0.923819i	$0.625050\pi$
$278$	−26.7911	−	10.2842i	−1.60683	−	0.616803i
$279$	1.48502	+	1.07893i	0.0889060	+	0.0645940i
$280$		0			0
$281$	−3.73577	+	2.71420i	−0.222857	+	0.161915i	−0.693612	−	0.720349i	$-0.743982\pi$
$281$	−3.73577	+	2.71420i	−0.222857	+	0.161915i	0.470755	+	0.882264i	$0.343982\pi$
$282$	−14.9492	+	4.00563i	−0.890212	+	0.238532i
$283$	−1.38731	−	3.61407i	−0.0824672	−	0.214834i	0.886147	−	0.463405i	$-0.153372\pi$
$283$	−1.38731	−	3.61407i	−0.0824672	−	0.214834i	−0.968614	+	0.248571i	$0.920039\pi$
$284$	0.891802	+	0.802982i	0.0529187	+	0.0476482i
$285$		0			0
$286$	−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
$290$		0			0
$291$	−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	$-0.102455\pi$
$293$	10.8232	+	10.8232i	0.632300	+	0.632300i	−0.316344	+	0.948644i	$0.602455\pi$
$294$	2.79598	+	14.2061i	0.163065	+	0.828515i
$295$		0			0
$296$	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
$300$		0			0
$301$	−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
$305$		0			0
$306$	−3.45643	+	0.363286i	−0.197591	+	0.0207677i
$307$	3.99596	−	3.99596i	0.228061	−	0.228061i	−0.583821	−	0.811882i	$-0.698443\pi$
$307$	3.99596	−	3.99596i	0.228061	−	0.228061i	0.811882	+	0.583821i	$0.198443\pi$
$308$	−0.0362260	+	0.321302i	−0.00206417	+	0.0183079i
$309$	−11.6884	+	3.79779i	−0.664929	+	0.216049i
$310$		0			0
$311$	0.200656	+	0.944012i	0.0113782	+	0.0535300i	0.983470	−	0.181069i	$-0.0579557\pi$
$311$	0.200656	+	0.944012i	0.0113782	+	0.0535300i	−0.972092	+	0.234599i	$0.924622\pi$
$312$	1.01974	−	0.0534423i	0.0577314	−	0.00302557i
$313$	−0.212615	−	0.327398i	−0.0120177	−	0.0185056i	0.832611	−	0.553859i	$-0.186845\pi$
$313$	−0.212615	−	0.327398i	−0.0120177	−	0.0185056i	−0.844628	+	0.535353i	$0.820179\pi$
$314$	−1.64954	+	5.07677i	−0.0930891	+	0.286499i
$315$		0			0
$316$	−0.730474	−	2.24817i	−0.0410924	−	0.126469i
$317$	18.9350	−	23.3828i	1.06350	−	1.31331i	0.116105	−	0.993237i	$-0.462959\pi$
$317$	18.9350	−	23.3828i	1.06350	−	1.31331i	0.947393	−	0.320073i	$-0.103707\pi$
$318$	2.59308	−	9.67749i	0.145413	−	0.542687i
$319$	−0.738814	+	1.65940i	−0.0413657	+	0.0929088i
$320$		0			0
$321$	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
$325$		0			0
$326$	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
$330$		0			0
$331$	0.925838	+	8.80876i	0.0508887	+	0.484173i	0.990052	+	0.140702i	$0.0449360\pi$
$331$	0.925838	+	8.80876i	0.0508887	+	0.484173i	−0.939163	+	0.343471i	$0.888397\pi$
$332$	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
$335$		0			0
$336$	3.56844	+	13.7317i	0.194674	+	0.749125i
$337$	9.00124	−	17.6659i	0.490329	−	0.962324i	−0.504753	−	0.863264i	$-0.668416\pi$
$337$	9.00124	−	17.6659i	0.490329	−	0.962324i	0.995081	−	0.0990602i	$-0.0315836\pi$
$338$	−14.3487	+	9.31818i	−0.780468	+	0.506842i
$339$	−27.2301	+	5.78794i	−1.47894	+	0.314358i
$340$		0			0
$341$	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			0
$346$	−32.1563	−	3.37976i	−1.72873	−	0.181697i
$347$	−0.780769	+	0.632254i	−0.0419139	+	0.0339412i	−0.650048	−	0.759893i	$-0.725251\pi$
$347$	−0.780769	+	0.632254i	−0.0419139	+	0.0339412i	0.608135	+	0.793834i	$0.291918\pi$
$348$	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	$0.709569\pi$
$350$		0			0
$351$	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	$-0.561971\pi$
$353$	13.6401	−	11.0455i	0.725988	−	0.587893i	0.919447	+	0.393215i	$0.128637\pi$
$354$	11.0119	+	1.15740i	0.585278	+	0.0615152i
$355$		0			0
$356$	−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	0.471848	+	0.881680i	$0.343587\pi$
$359$	−6.02179	+	28.3303i	−0.317818	+	1.49522i	−0.789666	+	0.613537i	$0.789746\pi$
$360$		0			0
$361$	−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
$365$		0			0
$366$	−18.0095	−	3.82804i	−0.941372	−	0.200095i
$367$	−15.4802	+	5.94229i	−0.808060	+	0.310185i	−0.727099	−	0.686532i	$-0.759132\pi$
$367$	−15.4802	+	5.94229i	−0.808060	+	0.310185i	−0.0809605	+	0.996717i	$0.525799\pi$
$368$	1.76308	+	0.472416i	0.0919069	+	0.0246264i
$369$	−0.161418	−	1.53579i	−0.00840308	−	0.0799500i
$370$		0			0
$371$	−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	$-0.757728\pi$
$373$	−29.2838	−	1.53470i	−1.51626	−	0.0794637i	−0.792194	+	0.610269i	$0.791061\pi$
$374$	1.51858	+	2.63025i	0.0785237	+	0.136007i
$375$		0			0
$376$	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	−0.989570	−	0.144054i	$-0.953986\pi$
$379$	−10.6445	+	14.6509i	−0.546773	+	0.752568i	0.442797	+	0.896622i	$0.353986\pi$
$380$		0			0
$381$	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	−0.0234230	−	0.999726i	$-0.507456\pi$
$383$	18.7744	−	23.1844i	0.959326	−	1.18467i	0.982749	−	0.184944i	$-0.0592102\pi$
$384$	4.20083	+	12.9288i	0.214373	+	0.659771i
$385$		0			0
$386$	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	−0.996747	−	0.0805966i	$-0.974317\pi$
$389$	−2.34616	−	11.0378i	−0.118955	−	0.559639i	0.877792	−	0.479042i	$-0.159016\pi$
$390$		0			0
$391$	−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
$395$		0			0
$396$	−0.00700251	+	0.0666244i	−0.000351889	+	0.00334800i
$397$	1.77857	−	4.63333i	0.0892638	−	0.232540i	−0.881680	−	0.471848i	$-0.843587\pi$
$397$	1.77857	−	4.63333i	0.0892638	−	0.232540i	0.970944	+	0.239308i	$0.0769205\pi$
$398$	8.44891	−	4.30493i	0.423505	−	0.215787i
$399$	18.7454	−	11.9731i	0.938445	−	0.599404i
$400$		0			0
$401$	2.20052	−	3.81142i	0.109889	−	0.190333i	−0.805836	−	0.592139i	$-0.798284\pi$
$401$	2.20052	−	3.81142i	0.109889	−	0.190333i	0.915725	+	0.401805i	$0.131617\pi$
$402$	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
$405$		0			0
$406$	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	−0.739570	−	0.673079i	$-0.764971\pi$
$409$	0.144146	−	0.160091i	0.00712759	−	0.00791599i	0.746698	+	0.665163i	$0.231638\pi$
$410$		0			0
$411$	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
$415$		0			0
$416$	−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	0.373259	−	0.927727i	$-0.378240\pi$
$419$	28.0621	−	20.3883i	1.37092	−	0.996034i	0.997664	−	0.0683067i	$-0.0217596\pi$
$420$		0			0
$421$	24.3135	+	17.6648i	1.18497	+	0.860928i	0.992723	−	0.120419i	$-0.0384239\pi$
$421$	24.3135	+	17.6648i	1.18497	+	0.860928i	0.192243	+	0.981347i	$0.438424\pi$
$422$	−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
$425$		0			0
$426$		−	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
$430$		0			0
$431$	31.9852	+	14.2407i	1.54067	+	0.685952i	0.988974	−	0.148092i	$-0.0473130\pi$
$431$	31.9852	+	14.2407i	1.54067	+	0.685952i	0.551699	+	0.834043i	$0.313980\pi$
$432$	4.92453	+	18.3786i	0.236932	+	0.884241i
$433$	5.71937	+	0.905859i	0.274855	+	0.0435328i	0.292340	−	0.956314i	$-0.405566\pi$
$433$	5.71937	+	0.905859i	0.274855	+	0.0435328i	−0.0174852	+	0.999847i	$0.505566\pi$
$434$	−7.43340	+	9.03901i	−0.356815	+	0.433887i
$435$		0			0
$436$	−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	0.353066	−	0.935598i	$-0.385139\pi$
$439$	−12.8713	−	14.2950i	−0.614312	−	0.682263i	−0.967379	+	0.253335i	$0.918472\pi$
$440$		0			0
$441$	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	0.993603	+	0.112928i	$0.0360228\pi$
$443$	3.99023	+	14.8917i	0.189581	+	0.707527i	−0.804022	+	0.594600i	$0.797311\pi$
$444$	2.78123	+	1.23828i	0.131991	+	0.0587663i
$445$		0			0
$446$	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	$-0.891892\pi$
$449$		−	14.1182i		−	0.666281i	0.942877	−	0.333140i	$-0.108108\pi$
$450$		0			0
$451$	−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
$455$		0			0
$456$	20.2606	−	14.7202i	0.948789	−	0.689335i
$457$	27.9738	−	7.49556i	1.30856	−	0.350627i	0.463879	−	0.885899i	$-0.346457\pi$
$457$	27.9738	−	7.49556i	1.30856	−	0.350627i	0.844680	+	0.535271i	$0.179791\pi$
$458$	5.21960	+	13.5975i	0.243896	+	0.635371i
$459$	−19.8172	−	17.8435i	−0.924987	−	0.832862i
$460$		0			0
$461$	−30.3418	−	9.85863i	−1.41316	−	0.459162i	−0.499735	−	0.866178i	$-0.666569\pi$
$461$	−30.3418	−	9.85863i	−1.41316	−	0.459162i	−0.913421	+	0.407016i	$0.866569\pi$
$462$	2.13238	−	1.52479i	0.0992072	−	0.0709395i
$463$	−3.31433	−	1.68874i	−0.154030	−	0.0784822i	0.375276	−	0.926913i	$-0.377548\pi$
$463$	−3.31433	−	1.68874i	−0.154030	−	0.0784822i	−0.529306	+	0.848431i	$0.677548\pi$
$464$	9.65052	−	8.68936i	0.448014	−	0.403394i
$465$		0			0
$466$	17.2839	−	19.1957i	0.800661	−	0.889224i
$467$	−5.52562	−	4.47456i	−0.255695	−	0.207058i	0.492899	−	0.870087i	$-0.335937\pi$
$467$	−5.52562	−	4.47456i	−0.255695	−	0.207058i	−0.748594	+	0.663029i	$0.769271\pi$
$468$	−0.0216484	−	0.0216484i	−0.00100070	−	0.00100070i
$469$	−33.9891	+	5.12046i	−1.56947	+	0.236441i
$470$		0			0
$471$	−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
$475$		0			0
$476$	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	0.931929	+	0.362641i	$0.118125\pi$
$479$	−1.20444	+	11.4595i	−0.0550324	+	0.523598i	−0.986961	+	0.160957i	$0.948542\pi$
$480$		0			0
$481$	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
$485$		0			0
$486$	1.54361	+	7.26214i	0.0700198	+	0.329417i
$487$	4.36966	−	0.229004i	0.198008	−	0.0103772i	0.0469259	−	0.998898i	$-0.485058\pi$
$487$	4.36966	−	0.229004i	0.198008	−	0.0103772i	0.151082	+	0.988521i	$0.451724\pi$
$488$	14.4421	+	22.2389i	0.653763	+	1.00671i
$489$	−8.07937	+	24.8657i	−0.365362	+	1.12447i
$490$		0			0
$491$	2.98502	+	9.18693i	0.134712	+	0.414600i	0.995545	−	0.0942867i	$-0.0300570\pi$
$491$	2.98502	+	9.18693i	0.134712	+	0.414600i	−0.860833	+	0.508887i	$0.830057\pi$
$492$	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			0
$496$	−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	0.405625	−	0.914040i	$-0.367054\pi$
$499$	−4.09112	−	2.36201i	−0.183144	−	0.105738i	−0.588769	+	0.808301i	$0.700387\pi$
$500$		0			0
$501$	−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	$-0.0216969\pi$
$503$	0.623100	+	3.93410i	0.0277826	+	0.175413i	−0.969895	+	0.243523i	$0.921697\pi$
$504$	2.38030	−	3.60543i	0.106027	−	0.160598i
$505$		0			0
$506$	−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	0.257261	−	0.966342i	$-0.417180\pi$
$509$	2.23882	+	0.475875i	0.0992337	+	0.0210928i	−0.158027	+	0.987435i	$0.550513\pi$
$510$		0			0
$511$	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
$515$		0			0
$516$	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
$520$		0			0
$521$	−13.4075	−	1.40918i	−0.587391	−	0.0617373i	−0.193829	−	0.981035i	$-0.562091\pi$
$521$	−13.4075	−	1.40918i	−0.587391	−	0.0617373i	−0.393562	+	0.919298i	$0.628757\pi$
$522$	2.13381	−	1.72792i	0.0933941	−	0.0756291i
$523$	0.357203	−	6.81583i	0.0156194	−	0.298036i	−0.979639	−	0.200768i	$-0.935656\pi$
$523$	0.357203	−	6.81583i	0.0156194	−	0.298036i	0.995258	−	0.0972678i	$-0.0310103\pi$
$524$	0.129793			0.00567001
$525$		0			0
$526$	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
$530$		0			0
$531$	−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			0
$536$	−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
$540$		0			0
$541$	7.46757	+	1.58728i	0.321056	+	0.0682425i	0.365621	−	0.930764i	$-0.380857\pi$
$541$	7.46757	+	1.58728i	0.321056	+	0.0682425i	−0.0445647	+	0.999006i	$0.514190\pi$
$542$	−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
$545$		0			0
$546$	−0.0717348	+	1.19587i	−0.00306997	+	0.0511786i
$547$	6.49848	+	41.0298i	0.277855	+	1.75431i	0.592944	+	0.805244i	$0.297966\pi$
$547$	6.49848	+	41.0298i	0.277855	+	1.75431i	−0.315089	+	0.949062i	$0.602034\pi$
$548$	−1.10841	−	0.0580893i	−0.0473490	−	0.00248145i
$549$	2.43978	+	4.22582i	0.104127	+	0.180354i
$550$		0			0
$551$	−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
$555$		0			0
$556$	−2.25430	+	5.06325i	−0.0956038	+	0.214730i
$557$	3.67322	−	13.7087i	0.155640	−	0.580855i	−0.843410	−	0.537270i	$-0.819456\pi$
$557$	3.67322	−	13.7087i	0.155640	−	0.580855i	0.999050	−	0.0435845i	$-0.0138778\pi$
$558$	−1.52591	+	1.88435i	−0.0645971	+	0.0797708i
$559$	−0.577188	−	1.77640i	−0.0244125	−	0.0751338i
$560$		0			0
$561$	−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	$-0.862499\pi$
$563$	−41.9397	+	2.19797i	−1.76755	+	0.0926332i	−0.859405	+	0.511295i	$0.829166\pi$
$564$	0.621460	+	2.92374i	0.0261682	+	0.123112i
$565$		0			0
$566$	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	−0.580219	−	0.814460i	$-0.697033\pi$
$569$	−23.3390	+	2.45303i	−0.978423	+	0.102836i	−0.398204	+	0.917297i	$0.630366\pi$
$570$		0			0
$571$	1.01109	−	9.61986i	0.0423127	−	0.402579i	−0.952782	−	0.303654i	$-0.901793\pi$
$571$	1.01109	−	9.61986i	0.0423127	−	0.402579i	0.995095	−	0.0989242i	$-0.0315401\pi$
$572$	−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
$575$		0			0
$576$	2.39645	−	4.15077i	0.0998521	−	0.172949i
$577$	−0.910483	+	1.40202i	−0.0379039	+	0.0583669i	−0.857115	−	0.515126i	$-0.827745\pi$
$577$	−0.910483	+	1.40202i	−0.0379039	+	0.0583669i	0.819211	+	0.573493i	$0.194412\pi$
$578$	5.01906	+	6.19802i	0.208765	+	0.257804i
$579$	28.1676	−	12.5410i	1.17060	−	0.521187i
$580$		0			0
$581$	−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			0
$586$	−15.0255	+	13.5290i	−0.620697	+	0.558878i
$587$	−0.544273	−	0.277321i	−0.0224646	−	0.0114463i	0.442722	−	0.896659i	$-0.354013\pi$
$587$	−0.544273	−	0.277321i	−0.0224646	−	0.0114463i	−0.465187	+	0.885213i	$0.654013\pi$
$588$	2.76818	−	0.395667i	0.114158	−	0.0163170i
$589$	17.0988	+	5.55575i	0.704545	+	0.228921i
$590$		0			0
$591$	−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	$-0.757437\pi$
$593$	−24.4672	+	6.55597i	−1.00475	+	0.269221i	−0.281314	+	0.959616i	$0.590770\pi$
$594$	2.84416	−	2.06641i	0.116697	−	0.0847857i
$595$		0			0
$596$	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	−0.551380	−	0.834254i	$-0.685898\pi$
$599$	−2.55964	+	1.47781i	−0.104584	+	0.0603816i	0.446796	+	0.894636i	$0.352565\pi$
$600$		0			0
$601$			2.33505i			0.0952489i	0.998865	+	0.0476244i	$0.0151651\pi$
$601$			2.33505i			0.0952489i	−0.998865	+	0.0476244i	$0.984835\pi$
$602$	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			0
$606$	−32.8173	−	14.6112i	−1.33311	−	0.593540i
$607$	4.99555	+	18.6437i	0.202763	+	0.756723i	0.990120	+	0.140225i	$0.0447825\pi$
$607$	4.99555	+	18.6437i	0.202763	+	0.756723i	−0.787356	+	0.616498i	$0.788551\pi$
$608$	−7.60420	−	1.20439i	−0.308391	−	0.0488444i
$609$	15.4967	+	2.57458i	0.627959	+	0.104327i
$610$		0			0
$611$	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	−0.988923	−	0.148429i	$-0.952578\pi$
$613$	−0.518264	−	9.88907i	−0.0209325	−	0.399416i	0.967991	−	0.250987i	$-0.0807550\pi$
$614$	4.99493	+	5.54743i	0.201579	+	0.223876i
$615$		0			0
$616$	−3.72438	−	0.618757i	−0.150059	−	0.0249304i
$617$	−5.48345	−	0.868493i	−0.220755	−	0.0349642i	0.0450769	−	0.998984i	$-0.485647\pi$
$617$	−5.48345	−	0.868493i	−0.220755	−	0.0349642i	−0.265832	+	0.964019i	$0.585647\pi$
$618$	−4.20172	−	15.6810i	−0.169018	−	0.630784i
$619$	34.8010	+	15.4944i	1.39877	+	0.622772i	0.961059	−	0.276344i	$-0.0891228\pi$
$619$	34.8010	+	15.4944i	1.39877	+	0.622772i	0.437710	+	0.899116i	$0.355790\pi$
$620$		0			0
$621$	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
$625$		0			0
$626$	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
$630$		0			0
$631$	−11.4331	+	8.30661i	−0.455143	+	0.330681i	−0.791623	−	0.611010i	$-0.790764\pi$
$631$	−11.4331	+	8.30661i	−0.455143	+	0.330681i	0.336480	+	0.941691i	$0.390764\pi$
$632$	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
$635$		0			0
$636$	−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
$640$		0			0
$641$	5.18908	−	5.76306i	0.204956	−	0.227627i	−0.631900	−	0.775050i	$-0.717724\pi$
$641$	5.18908	−	5.76306i	0.204956	−	0.227627i	0.836856	+	0.547423i	$0.184391\pi$
$642$	3.45438	+	2.79730i	0.136333	+	0.110401i
$643$	−16.8674	−	16.8674i	−0.665185	−	0.665185i	0.291412	−	0.956598i	$-0.405875\pi$
$643$	−16.8674	−	16.8674i	−0.665185	−	0.665185i	−0.956598	+	0.291412i	$0.905875\pi$
$644$	0.131456	−	0.334872i	0.00518010	−	0.0131958i
$645$		0			0
$646$	−31.0977	+	13.8456i	−1.22352	+	0.544748i
$647$	−19.0469	−	23.5210i	−0.748811	−	0.924704i	0.250244	−	0.968183i	$-0.419489\pi$
$647$	−19.0469	−	23.5210i	−0.748811	−	0.924704i	−0.999054	+	0.0434786i	$0.986156\pi$
$648$	−11.4461	+	17.6255i	−0.449647	+	0.692396i
$649$	−1.28220	+	2.22083i	−0.0503307	+	0.0871754i
$650$		0			0
$651$	−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	0.468488	+	0.883470i	$0.344799\pi$
$653$	−12.0313	+	31.3427i	−0.470823	+	1.22654i	−0.939311	+	0.343066i	$0.888535\pi$
$654$	−2.36362	+	22.4884i	−0.0924250	+	0.879365i
$655$		0			0
$656$	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	0.791747	−	0.610850i	$-0.209172\pi$
$659$	45.9853	−	14.9415i	1.79133	−	0.582039i	0.999585	+	0.0288108i	$0.00917203\pi$
$660$		0			0
$661$	1.42228	+	6.69130i	0.0553203	+	0.260262i	0.997113	−	0.0759328i	$-0.0241934\pi$
$661$	1.42228	+	6.69130i	0.0553203	+	0.260262i	−0.941793	+	0.336194i	$0.890860\pi$
$662$	−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
$665$		0			0
$666$	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
$670$		0			0
$671$	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	−0.994259	−	0.106999i	$-0.965876\pi$
$673$	−12.8780	−	25.2746i	−0.496412	−	0.974263i	0.497847	−	0.867265i	$-0.334124\pi$
$674$	22.6814	+	13.0951i	0.873653	+	0.504404i
$675$		0			0
$676$	1.65216	+	2.86163i	0.0635446	+	0.110063i
$677$	12.5876	+	0.659688i	0.483780	+	0.0253539i	0.292668	−	0.956214i	$-0.405457\pi$
$677$	12.5876	+	0.659688i	0.483780	+	0.0253539i	0.191113	+	0.981568i	$0.438790\pi$
$678$	−5.75255	−	36.3202i	−0.220925	−	1.39487i
$679$	−1.52605	+	25.4403i	−0.0585643	+	0.976308i
$680$		0			0
$681$	−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	$-0.647742\pi$
$683$	−4.75634	+	1.82579i	−0.181996	+	0.0698619i	0.265663	+	0.964066i	$0.414409\pi$
$684$	−0.734439	−	0.156110i	−0.0280820	−	0.00596900i
$685$		0			0
$686$	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
$690$		0			0
$691$	2.60404	−	12.2510i	0.0990622	−	0.466051i	−0.900454	−	0.434951i	$-0.856766\pi$
$691$	2.60404	−	12.2510i	0.0990622	−	0.466051i	0.999516	−	0.0310999i	$-0.00990101\pi$
$692$	−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
$695$		0			0
$696$	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
$700$		0			0
$701$	−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
$705$		0			0
$706$	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	−0.590959	−	0.806702i	$-0.701250\pi$
$709$	7.37634	−	34.7029i	0.277024	−	1.30330i	0.867983	−	0.496594i	$-0.165416\pi$
$710$		0			0
$711$	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			0
$716$	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	−0.988224	−	0.153013i	$-0.951102\pi$
$719$	−1.43210	−	13.6255i	−0.0534082	−	0.508145i	0.934816	−	0.355132i	$-0.115564\pi$
$720$		0			0
$721$	−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
$725$		0			0
$726$	19.2928	+	11.1387i	0.716024	+	0.413397i
$727$	−18.6979	−	36.6967i	−0.693467	−	1.36101i	−0.921893	−	0.387445i	$-0.873358\pi$
$727$	−18.6979	−	36.6967i	−0.693467	−	1.36101i	0.228425	−	0.973561i	$-0.426642\pi$
$728$	1.29090	−	1.14480i	0.0478440	−	0.0424289i
$729$	−17.6135	+	24.2429i	−0.652352	+	0.897885i
$730$		0			0
$731$	−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	$-0.604294\pi$
$733$	18.1721	−	22.4407i	0.671203	−	0.828867i	0.993021	+	0.117934i	$0.0376272\pi$
$734$	−6.76846	−	20.8312i	−0.249829	−	0.768893i
$735$		0			0
$736$	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	−0.991081	−	0.133263i	$-0.957455\pi$
$739$	−3.80274	−	17.8905i	−0.139886	−	0.658113i	0.851195	−	0.524850i	$-0.175879\pi$
$740$		0			0
$741$	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	$-0.588822\pi$
$743$	18.6958	−	18.6958i	0.685883	−	0.685883i	0.961319	+	0.275437i	$0.0888224\pi$
$744$	−15.5337	+	1.63266i	−0.569494	+	0.0598563i
$745$		0			0
$746$	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
$750$		0			0
$751$	14.6728	−	25.4141i	0.535418	−	0.927372i	−0.463724	−	0.885979i	$-0.653487\pi$
$751$	14.6728	−	25.4141i	0.535418	−	0.927372i	0.999143	−	0.0413925i	$-0.0131794\pi$
$752$	−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
$755$		0			0
$756$	3.70824	−	0.558648i	0.134867	−	0.0203178i
$757$	26.5318	+	26.5318i	0.964316	+	0.964316i	0.999385	−	0.0350687i	$-0.0111650\pi$
$757$	26.5318	+	26.5318i	0.964316	+	0.964316i	−0.0350687	+	0.999385i	$0.511165\pi$
$758$	−18.5906	−	15.0544i	−0.675241	−	0.546799i
$759$	0.267504	−	0.297093i	0.00970977	−	0.0107838i
$760$		0			0
$761$	−0.760199	+	0.684487i	−0.0275572	+	0.0248126i	−0.682794	−	0.730611i	$-0.739235\pi$
$761$	−0.760199	+	0.684487i	−0.0275572	+	0.0248126i	0.655237	+	0.755423i	$0.272569\pi$
$762$	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
$765$		0			0
$766$	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	−0.848606	−	0.529025i	$-0.822558\pi$
$769$	−16.8522	+	12.2439i	−0.607708	+	0.441525i	0.240899	+	0.970550i	$0.422558\pi$
$770$		0			0
$771$	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	$-0.161821\pi$
$773$	21.8018	+	14.1583i	0.784158	+	0.509238i	−0.0893781	+	0.995998i	$0.528488\pi$
$774$	5.35024	−	3.08897i	0.192311	−	0.111031i
$775$		0			0
$776$			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			0
$781$	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
$785$		0			0
$786$	−0.704119	−	0.782004i	−0.0251151	−	0.0278931i
$787$	2.54078	+	48.4809i	0.0905689	+	1.72816i	0.545912	+	0.837842i	$0.316183\pi$
$787$	2.54078	+	48.4809i	0.0905689	+	1.72816i	−0.455343	+	0.890316i	$0.650483\pi$
$788$	0.190721	+	3.63916i	0.00679414	+	0.129640i
$789$	12.1946	+	13.5435i	0.434140	+	0.482161i
$790$		0			0
$791$	−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
$795$		0			0
$796$	−0.744891	−	1.67305i	−0.0264020	−	0.0592998i
$797$	10.1052	−	1.60051i	0.357945	−	0.0566929i	0.0251277	−	0.999684i	$-0.492001\pi$
$797$	10.1052	−	1.60051i	0.357945	−	0.0566929i	0.332817	+	0.942991i	$0.392001\pi$
$798$	14.4981	+	25.5554i	0.513228	+	0.904650i
$799$		−	35.9141i		−	1.27055i
$800$		0			0
$801$	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
$805$		0			0
$806$	−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	−0.101771	−	0.994808i	$-0.532451\pi$
$809$	−31.3375	−	28.2164i	−1.10177	−	0.992036i	−0.999996	+	0.00277189i	$0.999118\pi$
$810$		0			0
$811$	30.4344	+	9.88872i	1.06869	+	0.347240i	0.789979	−	0.613134i	$-0.210091\pi$
$811$	30.4344	+	9.88872i	1.06869	+	0.347240i	0.278716	+	0.960374i	$0.410091\pi$
$812$	−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
$815$		0			0
$816$	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			0
$821$	44.4213	−	19.7776i	1.55031	−	0.690244i	0.559924	−	0.828544i	$-0.310830\pi$
$821$	44.4213	−	19.7776i	1.55031	−	0.690244i	0.990390	+	0.138300i	$0.0441638\pi$
$822$	5.66309	+	6.99334i	0.197523	+	0.243921i
$823$	−0.978707	+	1.50708i	−0.0341156	+	0.0525334i	−0.855317	−	0.518105i	$-0.826638\pi$
$823$	−0.978707	+	1.50708i	−0.0341156	+	0.0525334i	0.821201	+	0.570639i	$0.193304\pi$
$824$	−11.6903	+	20.2482i	−0.407250	+	0.705378i
$825$		0			0
$826$	15.7673	−	10.0709i	0.548614	−	0.350411i
$827$	15.8538	−	8.07790i	0.551290	−	0.280896i	−0.156075	−	0.987745i	$-0.549884\pi$
$827$	15.8538	−	8.07790i	0.551290	−	0.280896i	0.707364	+	0.706849i	$0.249884\pi$
$828$	0.0267111	−	0.0695849i	0.000928277	−	0.00241824i
$829$	−5.29689	+	50.3966i	−0.183969	+	1.75035i	0.380400	+	0.924822i	$0.375786\pi$
$829$	−5.29689	+	50.3966i	−0.183969	+	1.75035i	−0.564369	+	0.825523i	$0.690880\pi$
$830$		0			0
$831$	−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
$835$		0			0
$836$	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	−0.901291	−	0.433214i	$-0.857380\pi$
$839$	2.38981	−	7.35507i	0.0825053	−	0.253925i	0.983797	+	0.179288i	$0.0573795\pi$
$840$		0			0
$841$	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
$845$		0			0
$846$	−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
$850$		0			0
$851$	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	0.998958	+	0.0456353i	$0.0145312\pi$
$853$	1.83983	+	11.6162i	0.0629946	+	0.397732i	−0.935964	+	0.352097i	$0.885469\pi$
$854$	−27.8252	+	13.9139i	−0.952158	+	0.476124i
$855$		0			0
$856$	−0.669154	−	6.36657i	−0.0228712	−	0.217605i
$857$	0.368054	+	0.0986197i	0.0125725	+	0.00336878i	0.265100	−	0.964221i	$-0.414595\pi$
$857$	0.368054	+	0.0986197i	0.0125725	+	0.00336878i	−0.252527	+	0.967590i	$0.581262\pi$
$858$	0.202503	−	0.0777336i	0.00691334	−	0.00265378i
$859$	9.45007	+	2.00867i	0.322432	+	0.0685351i	0.366284	−	0.930503i	$-0.380630\pi$
$859$	9.45007	+	2.00867i	0.322432	+	0.0685351i	−0.0438522	+	0.999038i	$0.513963\pi$
$860$		0			0
$861$	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	$-0.710624\pi$
$863$	−4.21948	+	2.74016i	−0.143633	+	0.0932762i	0.470822	+	0.882228i	$0.343957\pi$
$864$	7.79276	−	1.65640i	0.265115	−	0.0563519i
$865$		0			0
$866$	−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
$870$		0			0
$871$	−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
$875$		0			0
$876$	5.23972			0.177034
$877$	−1.13176	+	21.5953i	−0.0382169	+	0.729223i	0.910579	+	0.413334i	$0.135636\pi$
$877$	−1.13176	+	21.5953i	−0.0382169	+	0.729223i	−0.948796	+	0.315888i	$0.897697\pi$
$878$	19.7468	−	15.9906i	0.666421	−	0.539657i
$879$	−23.8359	−	2.50526i	−0.803966	−	0.0845002i
$880$		0			0
$881$	−15.8503	−	21.8160i	−0.534009	−	0.735001i	0.453725	−	0.891142i	$-0.350095\pi$
$881$	−15.8503	−	21.8160i	−0.534009	−	0.735001i	−0.987735	+	0.156141i	$0.950095\pi$
$882$	3.89045	+	3.24895i	0.130998	+	0.109398i
$883$	−0.103976	+	0.656476i	−0.00349906	+	0.0220922i	−0.989376	−	0.145379i	$-0.953560\pi$
$883$	−0.103976	+	0.656476i	−0.00349906	+	0.0220922i	0.985877	+	0.167471i	$0.0535600\pi$
$884$	−0.0557349	+	0.262212i	−0.00187457	+	0.00881915i
$885$		0			0
$886$	−19.9200	+	4.23412i	−0.669224	+	0.142248i
$887$	−25.6659	+	16.6676i	−0.861775	+	0.559644i	−0.898147	−	0.439695i	$-0.855087\pi$
$887$	−25.6659	+	16.6676i	−0.861775	+	0.559644i	0.0363718	+	0.999338i	$0.488420\pi$
$888$	−16.1385	+	31.6735i	−0.541572	+	1.06289i
$889$	−12.4255	−	47.8145i	−0.416739	−	1.60365i
$890$		0			0
$891$	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
$895$		0			0
$896$	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			0
$901$	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
$905$		0			0
$906$	13.6056	−	30.5586i	0.452015	−	1.01524i
$907$	8.74745	−	32.6459i	0.290454	−	1.08399i	−0.654307	−	0.756229i	$-0.727039\pi$
$907$	8.74745	−	32.6459i	0.290454	−	1.08399i	0.944761	−	0.327760i	$-0.106294\pi$
$908$	−0.313468	+	0.387101i	−0.0104028	+	0.0128464i
$909$	2.94197	+	9.05447i	0.0975791	+	0.300318i
$910$		0			0
$911$	6.27024	−	19.2978i	0.207742	−	0.639365i	−0.791847	−	0.610719i	$-0.790880\pi$
$911$	6.27024	−	19.2978i	0.207742	−	0.639365i	0.999590	−	0.0286459i	$-0.00911953\pi$
$912$	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
$915$		0			0
$916$	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	0.436208	−	0.899846i	$-0.356321\pi$
$919$	31.8299	−	3.34546i	1.04997	−	0.110357i	0.613764	+	0.789489i	$0.289654\pi$
$920$		0			0
$921$	−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
$925$		0			0
$926$	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	0.336908	−	0.941538i	$-0.390619\pi$
$929$	38.4664	−	17.1263i	1.26204	−	0.561897i	0.925134	+	0.379641i	$0.123952\pi$
$930$		0			0
$931$	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			0
$936$	0.265659	−	0.239200i	0.00868334	−	0.00781851i
$937$	14.8083	+	7.54518i	0.483765	+	0.246490i	0.678824	−	0.734301i	$-0.262490\pi$
$937$	14.8083	+	7.54518i	0.483765	+	0.246490i	−0.195059	+	0.980791i	$0.562490\pi$
$938$	−4.40480	−	45.1899i	−0.143822	−	1.47550i
$939$	0.581349	+	0.188892i	0.0189716	+	0.00616425i
$940$		0			0
$941$	8.12267	+	7.31369i	0.264791	+	0.238419i	0.790822	−	0.612047i	$-0.209653\pi$
$941$	8.12267	+	7.31369i	0.264791	+	0.238419i	−0.526030	+	0.850466i	$0.676320\pi$
$942$	−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
$945$		0			0
$946$	−4.36771	−	3.17332i	−0.142006	−	0.103174i
$947$	−30.5764	−	11.7372i	−0.993599	−	0.381407i	−0.193386	−	0.981123i	$-0.561947\pi$
$947$	−30.5764	−	11.7372i	−0.993599	−	0.381407i	−0.800213	+	0.599716i	$0.795280\pi$
$948$	3.10427	+	2.01594i	0.100822	+	0.0654746i
$949$	2.48678	−	1.43574i	0.0807242	−	0.0466062i
$950$		0			0
$951$			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	$-0.382493\pi$
$953$	30.6299	−	4.85130i	0.992200	−	0.157149i	0.631369	+	0.775482i	$0.282493\pi$
$954$	−1.42659	−	3.20417i	−0.0461875	−	0.103739i
$955$		0			0
$956$	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
$960$		0			0
$961$	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
$965$		0			0
$966$	−2.73076	+	1.02464i	−0.0878607	+	0.0329673i
$967$	32.8149	+	5.19736i	1.05525	+	0.167136i	0.659870	−	0.751380i	$-0.270611\pi$
$967$	32.8149	+	5.19736i	1.05525	+	0.167136i	0.395385	+	0.918516i	$0.370611\pi$
$968$	−8.30397	−	30.9908i	−0.266900	−	0.996083i
$969$	−36.8630	−	16.4125i	−1.18421	−	0.527245i
$970$		0			0
$971$	−3.93520	−	8.83860i	−0.126287	−	0.283644i	0.839327	−	0.543628i	$-0.182950\pi$
$971$	−3.93520	−	8.83860i	−0.126287	−	0.283644i	−0.965613	+	0.259983i	$0.916283\pi$
$972$	1.41625	−	0.224312i	0.0454262	−	0.00719481i
$973$	−49.5593	−	29.1144i	−1.58880	−	0.933366i
$974$			5.77998i			0.185202i
$975$		0			0
$976$	−26.4009	+	15.2426i	−0.845073	+	0.487903i
$977$	3.50951	+	2.27910i	0.112279	+	0.0729149i	0.599557	−	0.800332i	$-0.295343\pi$
$977$	3.50951	+	2.27910i	0.112279	+	0.0729149i	−0.487278	+	0.873247i	$0.662010\pi$
$978$	−32.2426	−	12.3768i	−1.03100	−	0.395765i
$979$	−2.26985	−	1.64914i	−0.0725448	−	0.0527069i
$980$		0			0
$981$	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	$-0.178922\pi$
$983$	−4.36704	−	11.3765i	−0.139287	−	0.362855i	−0.985425	+	0.170108i	$0.945588\pi$
$984$	9.76510	+	8.79254i	0.311300	+	0.280296i
$985$		0			0
$986$	−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			0
$991$	−26.7684	+	29.7294i	−0.850327	+	0.944384i	−0.999009	−	0.0445008i	$-0.985830\pi$
$991$	−26.7684	+	29.7294i	−0.850327	+	0.944384i	0.148682	+	0.988885i	$0.452497\pi$
$992$	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
$995$		0			0
$996$	−3.46697	+	1.54360i	−0.109855	+	0.0489107i
$997$	0.243400	+	0.300574i	0.00770855	+	0.00951926i	0.780986	−	0.624549i	$-0.214717\pi$
$997$	0.243400	+	0.300574i	0.00770855	+	0.00951926i	−0.773277	+	0.634068i	$0.781384\pi$
$998$	3.39863	−	5.23343i	0.107582	−	0.165661i
$999$	−21.1708	+	36.6689i	−0.669815	+	1.16015i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	875.2.bb.c.257.6		288
5.2	odd	4		875.2.bb.b.243.6		288
5.3	odd	4		875.2.bb.a.243.13		288
5.4	even	2		175.2.x.a.47.13	yes	288
7.3	odd	6	inner	875.2.bb.c.507.6		288
25.6	even	5		875.2.bb.a.607.6		288
25.8	odd	20	inner	875.2.bb.c.768.6		288
25.17	odd	20		175.2.x.a.33.13	✓	288
25.19	even	10		875.2.bb.b.607.13		288
35.3	even	12		875.2.bb.a.493.6		288
35.17	even	12		875.2.bb.b.493.13		288
35.24	odd	6		175.2.x.a.122.13	yes	288
175.17	even	60		175.2.x.a.108.13	yes	288
175.31	odd	30		875.2.bb.a.857.13		288
175.94	odd	30		875.2.bb.b.857.6		288
175.108	even	60	inner	875.2.bb.c.143.6		288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
175.2.x.a.33.13	✓	288	25.17	odd	20
175.2.x.a.47.13	yes	288	5.4	even	2
175.2.x.a.108.13	yes	288	175.17	even	60
175.2.x.a.122.13	yes	288	35.24	odd	6
875.2.bb.a.243.13		288	5.3	odd	4
875.2.bb.a.493.6		288	35.3	even	12
875.2.bb.a.607.6		288	25.6	even	5
875.2.bb.a.857.13		288	175.31	odd	30
875.2.bb.b.243.6		288	5.2	odd	4
875.2.bb.b.493.13		288	35.17	even	12
875.2.bb.b.607.13		288	25.19	even	10
875.2.bb.b.857.6		288	175.94	odd	30
875.2.bb.c.143.6		288	175.108	even	60	inner
875.2.bb.c.257.6		288	1.1	even	1	trivial
875.2.bb.c.507.6		288	7.3	odd	6	inner
875.2.bb.c.768.6		288	25.8	odd	20	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 875 = 5^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	875.bb (of order \(60\), degree \(16\), not minimal)

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

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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