LMFDB - Embedded newform 828.2.c.d.323.8

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [828,2,Mod(323,828)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("828.323"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(828, base_ring=CyclotomicField(2)) chi = DirichletCharacter(H, H._module([1, 1, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 828 = 2^{2} \cdot 3^{2} \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	828.c (of order $2$, degree $1$, minimal)

Newform invariants

comment:select newform

sage:traces = [8,4,0,0,0,0,0,4,0,8,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$6.61161328736$
Analytic rank:	$0$
Dimension:	$8$
Coefficient field:	8.0.18939904.2
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 14x^{6} - 28x^{5} + 43x^{4} - 44x^{3} + 30x^{2} - 12x + 2 $ x^8 - 4x^7 + 14x^6 - 28x^5 + 43x^4 - 44x^3 + 30x^2 - 12*x + 2
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			323.8
Root			$0.500000 - 0.0297061i$ of defining polynomial
Character	$\chi$	$=$	828.323
Dual form			828.2.c.d.323.7

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.37456 + 0.332548i) q^{2} +(1.77882 + 0.914214i) q^{4} +1.74912i q^{5} +2.80853i q^{7} +(2.14108 + 1.84818i) q^{8} +(-0.581666 + 2.40426i) q^{10} -2.82843 q^{11} -1.88784 q^{13} +(-0.933971 + 3.86049i) q^{14} +(2.32843 + 3.25245i) q^{16} -2.25088i q^{17} +2.80853i q^{19} +(-1.59907 + 3.11137i) q^{20} +(-3.88784 - 0.940588i) q^{22} -1.00000 q^{23} +1.94059 q^{25} +(-2.59495 - 0.627797i) q^{26} +(-2.56760 + 4.99588i) q^{28} -3.41421i q^{29} -0.382941i q^{31} +(2.11896 + 5.24500i) q^{32} +(0.748526 - 3.09397i) q^{34} -4.91245 q^{35} +5.14343 q^{37} +(-0.933971 + 3.86049i) q^{38} +(-3.23269 + 3.74500i) q^{40} -7.15010i q^{41} +0.780391i q^{43} +(-5.03127 - 2.58579i) q^{44} +(-1.37456 - 0.332548i) q^{46} +9.30872 q^{47} -0.887839 q^{49} +(2.66745 + 0.645339i) q^{50} +(-3.35813 - 1.72589i) q^{52} +5.27549i q^{53} -4.94725i q^{55} +(-5.19068 + 6.01328i) q^{56} +(1.13539 - 4.69304i) q^{58} -4.58579 q^{59} +12.9191 q^{61} +(0.127346 - 0.526374i) q^{62} +(1.16843 + 7.91421i) q^{64} -3.30205i q^{65} +8.18794i q^{67} +(2.05779 - 4.00392i) q^{68} +(-6.75245 - 1.63363i) q^{70} -4.16804 q^{71} +12.6041 q^{73} +(7.06995 + 1.71044i) q^{74} +(-2.56760 + 4.99588i) q^{76} -7.94372i q^{77} +8.50295i q^{79} +(-5.68892 + 4.07269i) q^{80} +(2.37775 - 9.82823i) q^{82} -0.501765 q^{83} +3.93706 q^{85} +(-0.259517 + 1.07269i) q^{86} +(-6.05588 - 5.22746i) q^{88} -1.98509i q^{89} -5.30205i q^{91} +(-1.77882 - 0.914214i) q^{92} +(12.7954 + 3.09560i) q^{94} -4.91245 q^{95} -6.13048 q^{97} +(-1.22039 - 0.295249i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{2} + 4 q^{8} + 8 q^{10} + 8 q^{13} - 4 q^{16} - 8 q^{20} - 8 q^{22} - 8 q^{23} + 16 q^{25} + 8 q^{26} + 12 q^{28} + 4 q^{32} + 24 q^{34} + 24 q^{37} + 4 q^{40} - 4 q^{46} + 16 q^{47} + 16 q^{49}+ \cdots + 12 q^{98}+O(q^{100}) $ 8 * q + 4 * q^2 + 4 * q^8 + 8 * q^10 + 8 * q^13 - 4 * q^16 - 8 * q^20 - 8 * q^22 - 8 * q^23 + 16 * q^25 + 8 * q^26 + 12 * q^28 + 4 * q^32 + 24 * q^34 + 24 * q^37 + 4 * q^40 - 4 * q^46 + 16 * q^47 + 16 * q^49 + 20 * q^50 - 4 * q^52 - 20 * q^56 + 12 * q^58 - 48 * q^59 + 40 * q^61 + 24 * q^62 - 24 * q^68 - 28 * q^70 + 32 * q^73 + 20 * q^74 + 12 * q^76 + 4 * q^80 + 12 * q^82 - 32 * q^83 - 24 * q^85 + 36 * q^86 + 8 * q^88 - 20 * q^94 + 8 * q^97 + 12 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/828\mathbb{Z}\right)^\times$.

$n$	$415$	$461$	$649$
$\chi(n)$	$-1$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.37456	+	0.332548i	0.971960	+	0.235147i
$2$	1.37456	+	0.332548i	0.971960	+	0.235147i
$3$		0			0
$3$		0			0
$4$	1.77882	+	0.914214i	0.889412	+	0.457107i
$5$			1.74912i			0.782229i	0.920342	+	0.391115i	$0.127910\pi$
$5$			1.74912i			0.782229i	−0.920342	+	0.391115i	$0.872090\pi$
$6$		0			0
$7$			2.80853i			1.06152i	0.847521	+	0.530762i	$0.178094\pi$
$7$			2.80853i			1.06152i	−0.847521	+	0.530762i	$0.821906\pi$
$8$	2.14108	+	1.84818i	0.756985	+	0.653432i
$9$		0			0
$10$	−0.581666	+	2.40426i	−0.183939	+	0.760295i
$11$	−2.82843			−0.852803			−0.426401	−	0.904534i	$-0.640219\pi$
$11$	−2.82843			−0.852803			−0.426401	+	0.904534i	$0.640219\pi$
$12$		0			0
$13$	−1.88784			−0.523592			−0.261796	−	0.965123i	$-0.584315\pi$
$13$	−1.88784			−0.523592			−0.261796	+	0.965123i	$0.584315\pi$
$14$	−0.933971	+	3.86049i	−0.249614	+	1.03176i
$15$		0			0
$16$	2.32843	+	3.25245i	0.582107	+	0.813112i
$17$		−	2.25088i		−	0.545919i	−0.962025	−	0.272960i	$-0.911997\pi$
$17$		−	2.25088i		−	0.545919i	0.962025	−	0.272960i	$-0.0880025\pi$
$18$		0			0
$19$			2.80853i			0.644321i	0.946685	+	0.322160i	$0.104409\pi$
$19$			2.80853i			0.644321i	−0.946685	+	0.322160i	$0.895591\pi$
$20$	−1.59907	+	3.11137i	−0.357562	+	0.695724i
$21$		0			0
$22$	−3.88784	−	0.940588i	−0.828890	−	0.200534i
$23$	−1.00000			−0.208514
$23$	−1.00000			−0.208514
$24$		0			0
$25$	1.94059			0.388118
$26$	−2.59495	−	0.627797i	−0.508911	−	0.123121i
$27$		0			0
$28$	−2.56760	+	4.99588i	−0.485230	+	0.944132i
$29$		−	3.41421i		−	0.634004i	−0.948425	−	0.317002i	$-0.897324\pi$
$29$		−	3.41421i		−	0.634004i	0.948425	−	0.317002i	$-0.102676\pi$
$30$		0			0
$31$		−	0.382941i		−	0.0687781i	−0.999409	−	0.0343891i	$-0.989051\pi$
$31$		−	0.382941i		−	0.0687781i	0.999409	−	0.0343891i	$-0.0109485\pi$
$32$	2.11896	+	5.24500i	0.374584	+	0.927193i
$33$		0			0
$34$	0.748526	−	3.09397i	0.128371	−	0.530612i
$35$	−4.91245			−0.830355
$36$		0			0
$37$	5.14343			0.845575			0.422788	−	0.906229i	$-0.361052\pi$
$37$	5.14343			0.845575			0.422788	+	0.906229i	$0.361052\pi$
$38$	−0.933971	+	3.86049i	−0.151510	+	0.626254i
$39$		0			0
$40$	−3.23269	+	3.74500i	−0.511133	+	0.592136i
$41$		−	7.15010i		−	1.11666i	−0.829620	−	0.558329i	$-0.811443\pi$
$41$		−	7.15010i		−	1.11666i	0.829620	−	0.558329i	$-0.188557\pi$
$42$		0			0
$43$			0.780391i			0.119008i	0.998228	+	0.0595042i	$0.0189520\pi$
$43$			0.780391i			0.119008i	−0.998228	+	0.0595042i	$0.981048\pi$
$44$	−5.03127	−	2.58579i	−0.758493	−	0.389822i
$45$		0			0
$46$	−1.37456	−	0.332548i	−0.202668	−	0.0490315i
$47$	9.30872			1.35782			0.678908	−	0.734223i	$-0.262454\pi$
$47$	9.30872			1.35782			0.678908	+	0.734223i	$0.262454\pi$
$48$		0			0
$49$	−0.887839			−0.126834
$50$	2.66745	+	0.645339i	0.377235	+	0.0912647i
$51$		0			0
$52$	−3.35813	−	1.72589i	−0.465689	−	0.239338i
$53$			5.27549i			0.724645i	0.932053	+	0.362322i	$0.118016\pi$
$53$			5.27549i			0.724645i	−0.932053	+	0.362322i	$0.881984\pi$
$54$		0			0
$55$		−	4.94725i		−	0.667087i
$56$	−5.19068	+	6.01328i	−0.693634	+	0.803558i
$57$		0			0
$58$	1.13539	−	4.69304i	0.149084	−	0.616226i
$59$	−4.58579			−0.597019			−0.298509	−	0.954407i	$-0.596489\pi$
$59$	−4.58579			−0.597019			−0.298509	+	0.954407i	$0.596489\pi$
$60$		0			0
$61$	12.9191			1.65412			0.827061	−	0.562112i	$-0.190011\pi$
$61$	12.9191			1.65412			0.827061	+	0.562112i	$0.190011\pi$
$62$	0.127346	−	0.526374i	0.0161730	−	0.0668496i
$63$		0			0
$64$	1.16843	+	7.91421i	0.146053	+	0.989277i
$65$		−	3.30205i		−	0.409569i
$66$		0			0
$67$			8.18794i			1.00032i	0.865934	+	0.500158i	$0.166725\pi$
$67$			8.18794i			1.00032i	−0.865934	+	0.500158i	$0.833275\pi$
$68$	2.05779	−	4.00392i	0.249543	−	0.485547i
$69$		0			0
$70$	−6.75245	−	1.63363i	−0.807072	−	0.195256i
$71$	−4.16804			−0.494656			−0.247328	−	0.968932i	$-0.579552\pi$
$71$	−4.16804			−0.494656			−0.247328	+	0.968932i	$0.579552\pi$
$72$		0			0
$73$	12.6041			1.47520			0.737599	−	0.675238i	$-0.235959\pi$
$73$	12.6041			1.47520			0.737599	+	0.675238i	$0.235959\pi$
$74$	7.06995	+	1.71044i	0.821865	+	0.198834i
$75$		0			0
$76$	−2.56760	+	4.99588i	−0.294523	+	0.573067i
$77$		−	7.94372i		−	0.905271i
$78$		0			0
$79$			8.50295i			0.956656i	0.878181	+	0.478328i	$0.158757\pi$
$79$			8.50295i			0.956656i	−0.878181	+	0.478328i	$0.841243\pi$
$80$	−5.68892	+	4.07269i	−0.636040	+	0.455341i
$81$		0			0
$82$	2.37775	−	9.82823i	0.262579	−	1.08535i
$83$	−0.501765			−0.0550759			−0.0275379	−	0.999621i	$-0.508767\pi$
$83$	−0.501765			−0.0550759			−0.0275379	+	0.999621i	$0.508767\pi$
$84$		0			0
$85$	3.93706			0.427034
$86$	−0.259517	+	1.07269i	−0.0279845	+	0.115671i
$87$		0			0
$88$	−6.05588	−	5.22746i	−0.645559	−	0.557249i
$89$		−	1.98509i		−	0.210420i	−0.994450	−	0.105210i	$-0.966449\pi$
$89$		−	1.98509i		−	0.210420i	0.994450	−	0.105210i	$-0.0335514\pi$
$90$		0			0
$91$		−	5.30205i		−	0.555806i
$92$	−1.77882	−	0.914214i	−0.185455	−	0.0953134i
$93$		0			0
$94$	12.7954	+	3.09560i	1.31974	+	0.319286i
$95$	−4.91245			−0.504007
$96$		0			0
$97$	−6.13048			−0.622456			−0.311228	−	0.950335i	$-0.600740\pi$
$97$	−6.13048			−0.622456			−0.311228	+	0.950335i	$0.600740\pi$
$98$	−1.22039	−	0.295249i	−0.123278	−	0.0298247i
$99$		0			0
$100$	3.45196	+	1.77411i	0.345196	+	0.177411i
$101$		−	13.7409i		−	1.36727i	−0.729825	−	0.683634i	$-0.760398\pi$
$101$		−	13.7409i		−	1.36727i	0.729825	−	0.683634i	$-0.239602\pi$
$102$		0			0
$103$		−	15.7769i		−	1.55454i	−0.629167	−	0.777270i	$-0.716604\pi$
$103$		−	15.7769i		−	1.55454i	0.629167	−	0.777270i	$-0.283396\pi$
$104$	−4.04201	−	3.48908i	−0.396352	−	0.342132i
$105$		0			0
$106$	−1.75435	+	7.25147i	−0.170398	+	0.704325i
$107$	−12.9870			−1.25551			−0.627753	−	0.778413i	$-0.716025\pi$
$107$	−12.9870			−1.25551			−0.627753	+	0.778413i	$0.716025\pi$
$108$		0			0
$109$	14.3892			1.37824			0.689118	−	0.724649i	$-0.257998\pi$
$109$	14.3892			1.37824			0.689118	+	0.724649i	$0.257998\pi$
$110$	1.64520	−	6.80029i	0.156864	−	0.648382i
$111$		0			0
$112$	−9.13460	+	6.53946i	−0.863139	+	0.617921i
$113$		−	17.0114i		−	1.60030i	−0.599803	−	0.800148i	$-0.704754\pi$
$113$		−	17.0114i		−	1.60030i	0.599803	−	0.800148i	$-0.295246\pi$
$114$		0			0
$115$		−	1.74912i		−	0.163106i
$116$	3.12132	−	6.07328i	0.289807	−	0.563890i
$117$		0			0
$118$	−6.30343	−	1.52499i	−0.580278	−	0.140387i
$119$	6.32167			0.579507
$120$		0			0
$121$	−3.00000			−0.272727
$122$	17.7581	+	4.29623i	1.60774	+	0.388962i
$123$		0			0
$124$	0.350089	−	0.681184i	0.0314390	−	0.0611721i
$125$			12.1399i			1.08583i
$126$		0			0
$127$		−	5.22470i		−	0.463617i	−0.972761	−	0.231808i	$-0.925536\pi$
$127$		−	5.22470i		−	0.463617i	0.972761	−	0.231808i	$-0.0744642\pi$
$128$	−1.02578	+	11.2671i	−0.0906673	+	0.995881i
$129$		0			0
$130$	1.09809	−	4.53887i	0.0963090	−	0.398085i
$131$	−12.9004			−1.12711			−0.563556	−	0.826078i	$-0.690567\pi$
$131$	−12.9004			−1.12711			−0.563556	+	0.826078i	$0.690567\pi$
$132$		0			0
$133$	−7.88784			−0.683962
$134$	−2.72288	+	11.2548i	−0.235221	+	0.972267i
$135$		0			0
$136$	4.16005	−	4.81931i	0.356721	−	0.413253i
$137$		−	3.68342i		−	0.314695i	−0.987543	−	0.157348i	$-0.949706\pi$
$137$		−	3.68342i		−	0.314695i	0.987543	−	0.157348i	$-0.0502943\pi$
$138$		0			0
$139$		−	13.4514i		−	1.14093i	−0.821321	−	0.570466i	$-0.806763\pi$
$139$		−	13.4514i		−	1.14093i	0.821321	−	0.570466i	$-0.193237\pi$
$140$	−8.73838	−	4.49103i	−0.738528	−	0.379561i
$141$		0			0
$142$	−5.72922	−	1.38607i	−0.480785	−	0.116317i
$143$	5.33962			0.446521
$144$		0			0
$145$	5.97186			0.495936
$146$	17.3251	+	4.19147i	1.43383	+	0.346889i
$147$		0			0
$148$	9.14926	+	4.70220i	0.752065	+	0.386518i
$149$			10.3908i			0.851246i	0.904900	+	0.425623i	$0.139945\pi$
$149$			10.3908i			0.851246i	−0.904900	+	0.425623i	$0.860055\pi$
$150$		0			0
$151$			4.40569i			0.358530i	0.983801	+	0.179265i	$0.0573720\pi$
$151$			4.40569i			0.358530i	−0.983801	+	0.179265i	$0.942628\pi$
$152$	−5.19068	+	6.01328i	−0.421020	+	0.487741i
$153$		0			0
$154$	2.64167	−	10.9191i	0.212872	−	0.879887i
$155$	0.669808			0.0538003
$156$		0			0
$157$	−17.0474			−1.36053			−0.680264	−	0.732967i	$-0.738135\pi$
$157$	−17.0474			−1.36053			−0.680264	+	0.732967i	$0.738135\pi$
$158$	−2.82764	+	11.6878i	−0.224955	+	0.929831i
$159$		0			0
$160$	−9.17412	+	3.70632i	−0.725278	+	0.293010i
$161$		−	2.80853i		−	0.221343i
$162$		0			0
$163$		−	12.5643i		−	0.984113i	−0.870563	−	0.492056i	$-0.836245\pi$
$163$		−	12.5643i		−	0.984113i	0.870563	−	0.492056i	$-0.163755\pi$
$164$	6.53672	−	12.7188i	0.510432	−	0.993168i
$165$		0			0
$166$	−0.689705	−	0.166861i	−0.0535315	−	0.0129509i
$167$	21.0496			1.62887			0.814433	−	0.580257i	$-0.197048\pi$
$167$	21.0496			1.62887			0.814433	+	0.580257i	$0.197048\pi$
$168$		0			0
$169$	−9.43606			−0.725851
$170$	5.41172	+	1.30926i	0.415060	+	0.100416i
$171$		0			0
$172$	−0.713444	+	1.38818i	−0.0543996	+	0.105848i
$173$		−	1.12735i		−	0.0857105i	−0.999081	−	0.0428553i	$-0.986355\pi$
$173$		−	1.12735i		−	0.0857105i	0.999081	−	0.0428553i	$-0.0136454\pi$
$174$		0			0
$175$			5.45020i			0.411996i
$176$	−6.58579	−	9.19932i	−0.496422	−	0.693425i
$177$		0			0
$178$	0.660139	−	2.72863i	0.0494795	−	0.204519i
$179$	20.9585			1.56651			0.783256	−	0.621699i	$-0.213557\pi$
$179$	20.9585			1.56651			0.783256	+	0.621699i	$0.213557\pi$
$180$		0			0
$181$	−11.6006			−0.862264			−0.431132	−	0.902289i	$-0.641886\pi$
$181$	−11.6006			−0.862264			−0.431132	+	0.902289i	$0.641886\pi$
$182$	1.76319	−	7.28798i	0.130696	−	0.540221i
$183$		0			0
$184$	−2.14108	−	1.84818i	−0.157842	−	0.136250i
$185$			8.99647i			0.661434i
$186$		0			0
$187$			6.36646i			0.465561i
$188$	16.5586	+	8.51015i	1.20766	+	0.620667i
$189$		0			0
$190$	−6.75245	−	1.63363i	−0.489874	−	0.118516i
$191$	1.77345			0.128322			0.0641611	−	0.997940i	$-0.479563\pi$
$191$	1.77345			0.128322			0.0641611	+	0.997940i	$0.479563\pi$
$192$		0			0
$193$	−22.7977			−1.64101			−0.820506	−	0.571638i	$-0.806308\pi$
$193$	−22.7977			−1.64101			−0.820506	+	0.571638i	$0.806308\pi$
$194$	−8.42671	−	2.03868i	−0.605002	−	0.146369i
$195$		0			0
$196$	−1.57931	−	0.811675i	−0.112808	−	0.0579768i
$197$		−	15.1430i		−	1.07890i	−0.842019	−	0.539448i	$-0.818633\pi$
$197$		−	15.1430i		−	1.07890i	0.842019	−	0.539448i	$-0.181367\pi$
$198$		0			0
$199$		−	18.0660i		−	1.28066i	−0.768099	−	0.640331i	$-0.778797\pi$
$199$		−	18.0660i		−	1.28066i	0.768099	−	0.640331i	$-0.221203\pi$
$200$	4.15495	+	3.58656i	0.293799	+	0.253608i
$201$		0			0
$202$	4.56950	−	18.8876i	0.321509	−	1.32893i
$203$	9.58892			0.673010
$204$		0			0
$205$	12.5064			0.873482
$206$	5.24656	−	21.6862i	0.365545	−	1.51095i
$207$		0			0
$208$	−4.39570	−	6.14010i	−0.304787	−	0.425739i
$209$		−	7.94372i		−	0.549479i
$210$		0			0
$211$			12.9378i			0.890677i	0.895362	+	0.445338i	$0.146917\pi$
$211$			12.9378i			0.890677i	−0.895362	+	0.445338i	$0.853083\pi$
$212$	−4.82293	+	9.38417i	−0.331240	+	0.644507i
$213$		0			0
$214$	−17.8515	−	4.31882i	−1.22030	−	0.295228i
$215$	−1.36499			−0.0930919
$216$		0			0
$217$	1.07550			0.0730097
$218$	19.7788	+	4.78510i	1.33959	+	0.324088i
$219$		0			0
$220$	4.52284	−	8.80029i	0.304930	−	0.593315i
$221$			4.24930i			0.285839i
$222$		0			0
$223$			4.77215i			0.319567i	0.987152	+	0.159783i	$0.0510796\pi$
$223$			4.77215i			0.319567i	−0.987152	+	0.159783i	$0.948920\pi$
$224$	−14.7307	+	5.95117i	−0.984238	+	0.397630i
$225$		0			0
$226$	5.65710	−	23.3831i	0.376305	−	1.55542i
$227$	9.47952			0.629178			0.314589	−	0.949228i	$-0.398133\pi$
$227$	9.47952			0.629178			0.314589	+	0.949228i	$0.398133\pi$
$228$		0			0
$229$	−9.97019			−0.658849			−0.329424	−	0.944182i	$-0.606855\pi$
$229$	−9.97019			−0.658849			−0.329424	+	0.944182i	$0.606855\pi$
$230$	0.581666	−	2.40426i	0.0383539	−	0.158533i
$231$		0			0
$232$	6.31010	−	7.31010i	0.414278	−	0.479931i
$233$			23.8034i			1.55941i	0.626145	+	0.779707i	$0.284632\pi$
$233$			23.8034i			1.55941i	−0.626145	+	0.779707i	$0.715368\pi$
$234$		0			0
$235$			16.2820i			1.06212i
$236$	−8.15731	−	4.19239i	−0.530995	−	0.272901i
$237$		0			0
$238$	8.68951	+	2.10226i	0.563257	+	0.136269i
$239$	−10.8745			−0.703412			−0.351706	−	0.936110i	$-0.614398\pi$
$239$	−10.8745			−0.703412			−0.351706	+	0.936110i	$0.614398\pi$
$240$		0			0
$241$	−11.5983			−0.747115			−0.373558	−	0.927607i	$-0.621862\pi$
$241$	−11.5983			−0.747115			−0.373558	+	0.927607i	$0.621862\pi$
$242$	−4.12368	−	0.997644i	−0.265080	−	0.0641310i
$243$		0			0
$244$	22.9808	+	11.8108i	1.47120	+	0.756111i
$245$		−	1.55294i		−	0.0992134i
$246$		0			0
$247$		−	5.30205i		−	0.337362i
$248$	0.707745	−	0.819905i	0.0449418	−	0.0520640i
$249$		0			0
$250$	−4.03710	+	16.6870i	−0.255329	+	1.05538i
$251$	−14.1791			−0.894979			−0.447490	−	0.894289i	$-0.647682\pi$
$251$	−14.1791			−0.894979			−0.447490	+	0.894289i	$0.647682\pi$
$252$		0			0
$253$	2.82843			0.177822
$254$	1.73746	−	7.18165i	0.109018	−	0.450617i
$255$		0			0
$256$	−5.15685	+	15.1462i	−0.322303	+	0.946636i
$257$		−	1.19932i		−	0.0748113i	−0.999300	−	0.0374056i	$-0.988091\pi$
$257$		−	1.19932i		−	0.0748113i	0.999300	−	0.0374056i	$-0.0119094\pi$
$258$		0			0
$259$			14.4455i			0.897599i
$260$	3.01878	−	5.87377i	0.187217	−	0.364276i
$261$		0			0
$262$	−17.7324	−	4.29000i	−1.09551	−	0.265037i
$263$	30.0046			1.85016			0.925081	−	0.379769i	$-0.123997\pi$
$263$	30.0046			1.85016			0.925081	+	0.379769i	$0.123997\pi$
$264$		0			0
$265$	−9.22746			−0.566838
$266$	−10.8423	−	2.62309i	−0.664784	−	0.160832i
$267$		0			0
$268$	−7.48553	+	14.5649i	−0.457251	+	0.889693i
$269$			8.70145i			0.530537i	0.964175	+	0.265269i	$0.0854606\pi$
$269$			8.70145i			0.530537i	−0.964175	+	0.265269i	$0.914539\pi$
$270$		0			0
$271$		−	23.7029i		−	1.43985i	−0.694052	−	0.719925i	$-0.744176\pi$
$271$		−	23.7029i		−	1.43985i	0.694052	−	0.719925i	$-0.255824\pi$
$272$	7.32088	−	5.24102i	0.443894	−	0.317783i
$273$		0			0
$274$	1.22491	−	5.06307i	0.0739997	−	0.305871i
$275$	−5.48881			−0.330988
$276$		0			0
$277$	12.0929			0.726593			0.363296	−	0.931674i	$-0.381651\pi$
$277$	12.0929			0.726593			0.363296	+	0.931674i	$0.381651\pi$
$278$	4.47323	−	18.4897i	0.268286	−	1.10894i
$279$		0			0
$280$	−10.5179	−	9.07911i	−0.628567	−	0.542581i
$281$			22.2079i			1.32481i	0.749144	+	0.662407i	$0.230465\pi$
$281$			22.2079i			1.32481i	−0.749144	+	0.662407i	$0.769535\pi$
$282$		0			0
$283$			18.0636i			1.07377i	0.843656	+	0.536885i	$0.180399\pi$
$283$			18.0636i			1.07377i	−0.843656	+	0.536885i	$0.819601\pi$
$284$	−7.41421	−	3.81048i	−0.439953	−	0.226110i
$285$		0			0
$286$	7.33962	+	1.77568i	0.434001	+	0.104998i
$287$	20.0813			1.18536
$288$		0			0
$289$	11.9335			0.701972
$290$	8.20867	+	1.98593i	0.482030	+	0.116618i
$291$		0			0
$292$	22.4205	+	11.5228i	1.31206	+	0.674323i
$293$			15.3630i			0.897517i	0.893653	+	0.448759i	$0.148134\pi$
$293$			15.3630i			0.897517i	−0.893653	+	0.448759i	$0.851866\pi$
$294$		0			0
$295$		−	8.02108i		−	0.467005i
$296$	11.0125	+	9.50601i	0.640088	+	0.552526i
$297$		0			0
$298$	−3.45544	+	14.2827i	−0.200168	+	0.827377i
$299$	1.88784			0.109177
$300$		0			0
$301$	−2.19175			−0.126330
$302$	−1.46510	+	6.05588i	−0.0843073	+	0.348477i
$303$		0			0
$304$	−9.13460	+	6.53946i	−0.523905	+	0.375064i
$305$			22.5970i			1.29390i
$306$		0			0
$307$			9.78510i			0.558465i	0.960223	+	0.279233i	$0.0900801\pi$
$307$			9.78510i			0.558465i	−0.960223	+	0.279233i	$0.909920\pi$
$308$	7.26226	−	14.1305i	0.413806	−	0.805159i
$309$		0			0
$310$	0.920690	+	0.222743i	0.0522917	+	0.0126510i
$311$	−12.0013			−0.680530			−0.340265	−	0.940330i	$-0.610517\pi$
$311$	−12.0013			−0.680530			−0.340265	+	0.940330i	$0.610517\pi$
$312$		0			0
$313$	5.12472			0.289666			0.144833	−	0.989456i	$-0.453735\pi$
$313$	5.12472			0.289666			0.144833	+	0.989456i	$0.453735\pi$
$314$	−23.4326	−	5.66907i	−1.32238	−	0.319924i
$315$		0			0
$316$	−7.77351	+	15.1252i	−0.437294	+	0.850861i
$317$		−	28.6452i		−	1.60887i	−0.594038	−	0.804437i	$-0.702467\pi$
$317$		−	28.6452i		−	1.60887i	0.594038	−	0.804437i	$-0.297533\pi$
$318$		0			0
$319$			9.65685i			0.540680i
$320$	−13.8429	+	2.04372i	−0.773841	+	0.114247i
$321$		0			0
$322$	0.933971	−	3.86049i	0.0520482	−	0.215137i
$323$	6.32167			0.351747
$324$		0			0
$325$	−3.66352			−0.203215
$326$	4.17824	−	17.2704i	0.231411	−	0.956518i
$327$		0			0
$328$	13.2147	−	15.3089i	0.729660	−	0.845293i
$329$			26.1438i			1.44135i
$330$		0			0
$331$		−	18.4151i		−	1.01219i	−0.862479	−	0.506093i	$-0.831089\pi$
$331$		−	18.4151i		−	1.01219i	0.862479	−	0.506093i	$-0.168911\pi$
$332$	−0.892551	−	0.458720i	−0.0489851	−	0.0251755i
$333$		0			0
$334$	28.9339	+	7.00000i	1.58319	+	0.383023i
$335$	−14.3217			−0.782476
$336$		0			0
$337$	22.2158			1.21017			0.605085	−	0.796161i	$-0.293139\pi$
$337$	22.2158			1.21017			0.605085	+	0.796161i	$0.293139\pi$
$338$	−12.9704	−	3.13794i	−0.705498	−	0.170682i
$339$		0			0
$340$	7.00333	+	3.59931i	0.379809	+	0.195200i
$341$			1.08312i			0.0586542i
$342$		0			0
$343$			17.1662i			0.926887i
$344$	−1.44231	+	1.67088i	−0.0777639	+	0.0900876i
$345$		0			0
$346$	0.374897	−	1.54960i	0.0201546	−	0.0833072i
$347$	−33.4205			−1.79411			−0.897053	−	0.441924i	$-0.854296\pi$
$347$	−33.4205			−1.79411			−0.897053	+	0.441924i	$0.854296\pi$
$348$		0			0
$349$	−26.8414			−1.43678			−0.718392	−	0.695638i	$-0.755122\pi$
$349$	−26.8414			−1.43678			−0.718392	+	0.695638i	$0.755122\pi$
$350$	−1.81245	+	7.49162i	−0.0968797	+	0.400444i
$351$		0			0
$352$	−5.99334	−	14.8351i	−0.319446	−	0.790713i
$353$			6.37795i			0.339464i	0.985490	+	0.169732i	$0.0542902\pi$
$353$			6.37795i			0.339464i	−0.985490	+	0.169732i	$0.945710\pi$
$354$		0			0
$355$		−	7.29040i		−	0.386934i
$356$	1.81480	−	3.53113i	0.0961842	−	0.187150i
$357$		0			0
$358$	28.8087	+	6.96971i	1.52259	+	0.368361i
$359$	−12.4307			−0.656066			−0.328033	−	0.944666i	$-0.606386\pi$
$359$	−12.4307			−0.656066			−0.328033	+	0.944666i	$0.606386\pi$
$360$		0			0
$361$	11.1122			0.584851
$362$	−15.9457	−	3.85775i	−0.838086	−	0.202759i
$363$		0			0
$364$	4.84721	−	9.43142i	0.254063	−	0.494341i
$365$			22.0461i			1.15394i
$366$		0			0
$367$		−	29.2227i		−	1.52541i	−0.646744	−	0.762707i	$-0.723870\pi$
$367$		−	29.2227i		−	1.52541i	0.646744	−	0.762707i	$-0.276130\pi$
$368$	−2.32843	−	3.25245i	−0.121378	−	0.169546i
$369$		0			0
$370$	−2.99176	+	12.3662i	−0.155534	+	0.642887i
$371$	−14.8164			−0.769228
$372$		0			0
$373$	−28.2650			−1.46351			−0.731753	−	0.681570i	$-0.761298\pi$
$373$	−28.2650			−1.46351			−0.731753	+	0.681570i	$0.761298\pi$
$374$	−2.11715	+	8.75107i	−0.109475	+	0.452507i
$375$		0			0
$376$	19.9307	+	17.2042i	1.02785	+	0.887240i
$377$			6.44549i			0.331959i
$378$		0			0
$379$			7.91273i			0.406450i	0.979132	+	0.203225i	$0.0651422\pi$
$379$			7.91273i			0.406450i	−0.979132	+	0.203225i	$0.934858\pi$
$380$	−8.73838	−	4.49103i	−0.448269	−	0.230385i
$381$		0			0
$382$	2.43771	+	0.589756i	0.124724	+	0.0301746i
$383$	9.94595			0.508214			0.254107	−	0.967176i	$-0.418218\pi$
$383$	9.94595			0.508214			0.254107	+	0.967176i	$0.418218\pi$
$384$		0			0
$385$	13.8945			0.708129
$386$	−31.3367	−	7.58132i	−1.59500	−	0.385879i
$387$		0			0
$388$	−10.9050	−	5.60457i	−0.553620	−	0.284529i
$389$			13.3965i			0.679232i	0.940564	+	0.339616i	$0.110297\pi$
$389$			13.3965i			0.679232i	−0.940564	+	0.339616i	$0.889703\pi$
$390$		0			0
$391$			2.25088i			0.113832i
$392$	−1.90093	−	1.64089i	−0.0960116	−	0.0828775i
$393$		0			0
$394$	5.03579	−	20.8150i	0.253699	−	1.04864i
$395$	−14.8727			−0.748324
$396$		0			0
$397$	22.2047			1.11442			0.557211	−	0.830371i	$-0.311872\pi$
$397$	22.2047			1.11442			0.557211	+	0.830371i	$0.311872\pi$
$398$	6.00780	−	24.8327i	0.301144	−	1.24475i
$399$		0			0
$400$	4.51852	+	6.31166i	0.225926	+	0.315583i
$401$			1.24420i			0.0621322i	0.999517	+	0.0310661i	$0.00989024\pi$
$401$			1.24420i			0.0621322i	−0.999517	+	0.0310661i	$0.990110\pi$
$402$		0			0
$403$			0.722930i			0.0360117i
$404$	12.5621	−	24.4426i	0.624988	−	1.21606i
$405$		0			0
$406$	13.1805	+	3.18878i	0.654139	+	0.158256i
$407$	−14.5478			−0.721109
$408$		0			0
$409$	−6.14805			−0.304002			−0.152001	−	0.988380i	$-0.548572\pi$
$409$	−6.14805			−0.304002			−0.152001	+	0.988380i	$0.548572\pi$
$410$	17.1907	+	4.15897i	0.848990	+	0.205397i
$411$		0			0
$412$	14.4234	−	28.0643i	0.710591	−	1.38263i
$413$		−	12.8793i		−	0.633750i
$414$		0			0
$415$		−	0.877646i		−	0.0430819i
$416$	−4.00026	−	9.90171i	−0.196129	−	0.485471i
$417$		0			0
$418$	2.64167	−	10.9191i	0.129208	−	0.534071i
$419$	−3.17784			−0.155248			−0.0776238	−	0.996983i	$-0.524733\pi$
$419$	−3.17784			−0.155248			−0.0776238	+	0.996983i	$0.524733\pi$
$420$		0			0
$421$	1.44275			0.0703153			0.0351576	−	0.999382i	$-0.488807\pi$
$421$	1.44275			0.0703153			0.0351576	+	0.999382i	$0.488807\pi$
$422$	−4.30245	+	17.7838i	−0.209440	+	0.865702i
$423$		0			0
$424$	−9.75008	+	11.2952i	−0.473506	+	0.548545i
$425$		−	4.36804i		−	0.211881i
$426$		0			0
$427$			36.2837i			1.75589i
$428$	−23.1017	−	11.8729i	−1.11666	−	0.573900i
$429$		0			0
$430$	−1.87627	−	0.453926i	−0.0904816	−	0.0218903i
$431$	3.85842			0.185854			0.0929269	−	0.995673i	$-0.470378\pi$
$431$	3.85842			0.185854			0.0929269	+	0.995673i	$0.470378\pi$
$432$		0			0
$433$	−24.4518			−1.17508			−0.587538	−	0.809196i	$-0.699903\pi$
$433$	−24.4518			−1.17508			−0.587538	+	0.809196i	$0.699903\pi$
$434$	1.47834	+	0.357655i	0.0709625	+	0.0171680i
$435$		0			0
$436$	25.5959	+	13.1548i	1.22582	+	0.630001i
$437$		−	2.80853i		−	0.134350i
$438$		0			0
$439$		−	22.7955i		−	1.08797i	−0.839096	−	0.543984i	$-0.816915\pi$
$439$		−	22.7955i		−	1.08797i	0.839096	−	0.543984i	$-0.183085\pi$
$440$	9.14343	−	10.5925i	0.435896	−	0.504975i
$441$		0			0
$442$	−1.41310	+	5.84092i	−0.0672142	+	0.277824i
$443$	2.21726			0.105345			0.0526726	−	0.998612i	$-0.483226\pi$
$443$	2.21726			0.105345			0.0526726	+	0.998612i	$0.483226\pi$
$444$		0			0
$445$	3.47216			0.164596
$446$	−1.58697	+	6.55960i	−0.0751451	+	0.310606i
$447$		0			0
$448$	−22.2273	+	3.28156i	−1.05014	+	0.155039i
$449$		−	7.15952i		−	0.337879i	−0.985626	−	0.168939i	$-0.945966\pi$
$449$		−	7.15952i		−	0.337879i	0.985626	−	0.168939i	$-0.0540342\pi$
$450$		0			0
$451$			20.2235i			0.952289i
$452$	15.5520	−	30.2602i	0.731506	−	1.42332i
$453$		0			0
$454$	13.0302	+	3.15240i	0.611536	+	0.147949i
$455$	9.27391			0.434768
$456$		0			0
$457$	0.601874			0.0281545			0.0140772	−	0.999901i	$-0.495519\pi$
$457$	0.601874			0.0281545			0.0140772	+	0.999901i	$0.495519\pi$
$458$	−13.7046	−	3.31557i	−0.640374	−	0.154926i
$459$		0			0
$460$	1.59907	−	3.11137i	0.0745569	−	0.145068i
$461$			4.18009i			0.194686i	0.995251	+	0.0973432i	$0.0310344\pi$
$461$			4.18009i			0.194686i	−0.995251	+	0.0973432i	$0.968966\pi$
$462$		0			0
$463$			33.5647i			1.55988i	0.625852	+	0.779942i	$0.284751\pi$
$463$			33.5647i			1.55988i	−0.625852	+	0.779942i	$0.715249\pi$
$464$	11.1046	−	7.94975i	0.515516	−	0.369058i
$465$		0			0
$466$	−7.91578	+	32.7192i	−0.366691	+	1.51569i
$467$	−1.96796			−0.0910662			−0.0455331	−	0.998963i	$-0.514499\pi$
$467$	−1.96796			−0.0910662			−0.0455331	+	0.998963i	$0.514499\pi$
$468$		0			0
$469$	−22.9961			−1.06186
$470$	−5.41456	+	22.3806i	−0.249755	+	1.03234i
$471$		0			0
$472$	−9.81853	−	8.47538i	−0.451934	−	0.390111i
$473$		−	2.20728i		−	0.101491i
$474$		0			0
$475$			5.45020i			0.250072i
$476$	11.2451	+	5.77936i	0.515420	+	0.264896i
$477$		0			0
$478$	−14.9476	−	3.61629i	−0.683688	−	0.165405i
$479$	36.4821			1.66691			0.833455	−	0.552587i	$-0.186359\pi$
$479$	36.4821			1.66691			0.833455	+	0.552587i	$0.186359\pi$
$480$		0			0
$481$	−9.70998			−0.442737
$482$	−15.9426	−	3.85701i	−0.726166	−	0.175682i
$483$		0			0
$484$	−5.33647	−	2.74264i	−0.242567	−	0.124665i
$485$		−	10.7229i		−	0.486903i
$486$		0			0
$487$		−	32.9269i		−	1.49206i	−0.665913	−	0.746029i	$-0.731958\pi$
$487$		−	32.9269i		−	1.49206i	0.665913	−	0.746029i	$-0.268042\pi$
$488$	27.6608	+	23.8769i	1.25215	+	1.08086i
$489$		0			0
$490$	0.516426	−	2.13460i	0.0233297	−	0.0964314i
$491$	−33.4205			−1.50825			−0.754123	−	0.656734i	$-0.771938\pi$
$491$	−33.4205			−1.50825			−0.754123	+	0.656734i	$0.771938\pi$
$492$		0			0
$493$	−7.68499			−0.346115
$494$	1.76319	−	7.28798i	0.0793295	−	0.327902i
$495$		0			0
$496$	1.24549	−	0.891649i	0.0559244	−	0.0400362i
$497$		−	11.7061i		−	0.525089i
$498$		0			0
$499$			40.5180i			1.81384i	0.421308	+	0.906918i	$0.361571\pi$
$499$			40.5180i			1.81384i	−0.421308	+	0.906918i	$0.638429\pi$
$500$	−11.0985	+	21.5947i	−0.496338	+	0.965746i
$501$		0			0
$502$	−19.4901	−	4.71524i	−0.869884	−	0.210452i
$503$	1.04648			0.0466603			0.0233301	−	0.999728i	$-0.492573\pi$
$503$	1.04648			0.0466603			0.0233301	+	0.999728i	$0.492573\pi$
$504$		0			0
$505$	24.0344			1.06952
$506$	3.88784	+	0.940588i	0.172836	+	0.0418142i
$507$		0			0
$508$	4.77649	−	9.29381i	0.211922	−	0.412346i
$509$			3.47440i			0.154000i	0.997031	+	0.0769999i	$0.0245341\pi$
$509$			3.47440i			0.154000i	−0.997031	+	0.0769999i	$0.975466\pi$
$510$		0			0
$511$			35.3990i			1.56596i
$512$	−12.1252	+	19.1044i	−0.535865	+	0.844304i
$513$		0			0
$514$	0.398830	−	1.64853i	0.0175916	−	0.0727136i
$515$	27.5956			1.21601
$516$		0			0
$517$	−26.3290			−1.15795
$518$	−4.80382	+	19.8562i	−0.211068	+	0.872430i
$519$		0			0
$520$	6.10280	−	7.06995i	0.267626	−	0.310038i
$521$		−	28.1892i		−	1.23499i	−0.786574	−	0.617496i	$-0.788147\pi$
$521$		−	28.1892i		−	1.23499i	0.786574	−	0.617496i	$-0.211853\pi$
$522$		0			0
$523$			22.1809i			0.969902i	0.874541	+	0.484951i	$0.161163\pi$
$523$			22.1809i			0.969902i	−0.874541	+	0.484951i	$0.838837\pi$
$524$	−22.9475	−	11.7937i	−1.00247	−	0.515211i
$525$		0			0
$526$	41.2431	+	9.97797i	1.79828	+	0.435060i
$527$	−0.861954			−0.0375473
$528$		0			0
$529$	1.00000			0.0434783
$530$	−12.6837	−	3.06857i	−0.550944	−	0.133290i
$531$		0			0
$532$	−14.0311	−	7.21117i	−0.608324	−	0.312644i
$533$			13.4982i			0.584673i
$534$		0			0
$535$		−	22.7159i		−	0.982093i
$536$	−15.1328	+	17.5310i	−0.653638	+	0.757225i
$537$		0			0
$538$	−2.89365	+	11.9607i	−0.124754	+	0.515661i
$539$	2.51119			0.108165
$540$		0			0
$541$	8.56707			0.368327			0.184164	−	0.982896i	$-0.441042\pi$
$541$	8.56707			0.368327			0.184164	+	0.982896i	$0.441042\pi$
$542$	7.88236	−	32.5811i	0.338576	−	1.39948i
$543$		0			0
$544$	11.8059	−	4.76954i	0.506173	−	0.204492i
$545$			25.1684i			1.07810i
$546$		0			0
$547$		−	32.8486i		−	1.40450i	−0.711928	−	0.702252i	$-0.752178\pi$
$547$		−	32.8486i		−	1.40450i	0.711928	−	0.702252i	$-0.247822\pi$
$548$	3.36743	−	6.55215i	0.143849	−	0.279894i
$549$		0			0
$550$	−7.54469	−	1.82529i	−0.321707	−	0.0778308i
$551$	9.58892			0.408502
$552$		0			0
$553$	−23.8808			−1.01551
$554$	16.6224	+	4.02148i	0.706219	+	0.170856i
$555$		0			0
$556$	12.2974	−	23.9276i	0.521527	−	1.01476i
$557$			18.7817i			0.795805i	0.917428	+	0.397902i	$0.130262\pi$
$557$			18.7817i			0.795805i	−0.917428	+	0.397902i	$0.869738\pi$
$558$		0			0
$559$		−	1.47325i		−	0.0623119i
$560$	−11.4383	−	15.9775i	−0.483355	−	0.675172i
$561$		0			0
$562$	−7.38520	+	30.5261i	−0.311526	+	1.28767i
$563$	18.9052			0.796760			0.398380	−	0.917220i	$-0.369572\pi$
$563$	18.9052			0.796760			0.398380	+	0.917220i	$0.369572\pi$
$564$		0			0
$565$	29.7549			1.25180
$566$	−6.00701	+	24.8295i	−0.252494	+	1.04366i
$567$		0			0
$568$	−8.92410	−	7.70331i	−0.374447	−	0.323224i
$569$			32.1916i			1.34954i	0.738028	+	0.674771i	$0.235757\pi$
$569$			32.1916i			1.34954i	−0.738028	+	0.674771i	$0.764243\pi$
$570$		0			0
$571$			40.0190i			1.67474i	0.546635	+	0.837371i	$0.315909\pi$
$571$			40.0190i			1.67474i	−0.546635	+	0.837371i	$0.684091\pi$
$572$	9.49824	+	4.88155i	0.397141	+	0.204108i
$573$		0			0
$574$	27.6029	+	6.67798i	1.15212	+	0.278734i
$575$	−1.94059			−0.0809281
$576$		0			0
$577$	12.4223			0.517149			0.258574	−	0.965991i	$-0.416747\pi$
$577$	12.4223			0.517149			0.258574	+	0.965991i	$0.416747\pi$
$578$	16.4033	+	3.96847i	0.682289	+	0.165067i
$579$		0			0
$580$	10.6229	+	5.45956i	0.441091	+	0.226696i
$581$		−	1.40922i		−	0.0584644i
$582$		0			0
$583$		−	14.9213i		−	0.617979i
$584$	26.9864	+	23.2947i	1.11670	+	0.963942i
$585$		0			0
$586$	−5.10894	+	21.1174i	−0.211048	+	0.872351i
$587$	14.7949			0.610651			0.305325	−	0.952248i	$-0.401235\pi$
$587$	14.7949			0.610651			0.305325	+	0.952248i	$0.401235\pi$
$588$		0			0
$589$	1.07550			0.0443152
$590$	2.66739	−	11.0254i	0.109815	−	0.453910i
$591$		0			0
$592$	11.9761	+	16.7288i	0.492215	+	0.687548i
$593$		−	24.7412i		−	1.01600i	−0.861357	−	0.508001i	$-0.830385\pi$
$593$		−	24.7412i		−	1.01600i	0.861357	−	0.508001i	$-0.169615\pi$
$594$		0			0
$595$			11.0573i			0.453307i
$596$	−9.49940	+	18.4834i	−0.389110	+	0.757109i
$597$		0			0
$598$	2.59495	+	0.627797i	0.106115	+	0.0256725i
$599$	1.11139			0.0454102			0.0227051	−	0.999742i	$-0.492772\pi$
$599$	1.11139			0.0454102			0.0227051	+	0.999742i	$0.492772\pi$
$600$		0			0
$601$	44.0533			1.79697			0.898486	−	0.439003i	$-0.144668\pi$
$601$	44.0533			1.79697			0.898486	+	0.439003i	$0.144668\pi$
$602$	−3.01269	−	0.728862i	−0.122788	−	0.0297062i
$603$		0			0
$604$	−4.02774	+	7.83695i	−0.163887	+	0.318881i
$605$		−	5.24735i		−	0.213335i
$606$		0			0
$607$		−	21.4647i		−	0.871226i	−0.900134	−	0.435613i	$-0.856532\pi$
$607$		−	21.4647i		−	0.871226i	0.900134	−	0.435613i	$-0.143468\pi$
$608$	−14.7307	+	5.95117i	−0.597410	+	0.241352i
$609$		0			0
$610$	−7.51460	+	31.0610i	−0.304257	+	1.25762i
$611$	−17.5734			−0.710942
$612$		0			0
$613$	−11.3926			−0.460143			−0.230072	−	0.973174i	$-0.573896\pi$
$613$	−11.3926			−0.460143			−0.230072	+	0.973174i	$0.573896\pi$
$614$	−3.25402	+	13.4502i	−0.131321	+	0.542806i
$615$		0			0
$616$	14.6815	−	17.0081i	0.591533	−	0.685277i
$617$		−	26.7776i		−	1.07803i	−0.842297	−	0.539013i	$-0.818797\pi$
$617$		−	26.7776i		−	1.07803i	0.842297	−	0.539013i	$-0.181203\pi$
$618$		0			0
$619$			0.761543i			0.0306090i	0.999883	+	0.0153045i	$0.00487176\pi$
$619$			0.761543i			0.0306090i	−0.999883	+	0.0153045i	$0.995128\pi$
$620$	1.19147	+	0.612348i	0.0478506	+	0.0245925i
$621$		0			0
$622$	−16.4965	−	3.99100i	−0.661448	−	0.160025i
$623$	5.57520			0.223366
$624$		0			0
$625$	−11.5312			−0.461247
$626$	7.04423	+	1.70421i	0.281544	+	0.0681141i
$627$		0			0
$628$	−30.3242	−	15.5849i	−1.21007	−	0.621906i
$629$		−	11.5773i		−	0.461616i
$630$		0			0
$631$		−	19.4828i		−	0.775598i	−0.921744	−	0.387799i	$-0.873235\pi$
$631$		−	19.4828i		−	0.775598i	0.921744	−	0.387799i	$-0.126765\pi$
$632$	−15.7150	+	18.2055i	−0.625110	+	0.724175i
$633$		0			0
$634$	9.52590	−	39.3745i	0.378322	−	1.56376i
$635$	9.13861			0.362655
$636$		0			0
$637$	1.67610			0.0664094
$638$	−3.21137	+	13.2739i	−0.127139	+	0.525519i
$639$		0			0
$640$	−19.7075	−	1.79422i	−0.779007	−	0.0709226i
$641$			45.4146i			1.79377i	0.442265	+	0.896885i	$0.354175\pi$
$641$			45.4146i			1.79377i	−0.442265	+	0.896885i	$0.645825\pi$
$642$		0			0
$643$		−	43.7604i		−	1.72574i	−0.505425	−	0.862870i	$-0.668664\pi$
$643$		−	43.7604i		−	1.72574i	0.505425	−	0.862870i	$-0.331336\pi$
$644$	2.56760	−	4.99588i	0.101177	−	0.196865i
$645$		0			0
$646$	8.68951	+	2.10226i	0.341884	+	0.0827123i
$647$	−20.6324			−0.811144			−0.405572	−	0.914063i	$-0.632928\pi$
$647$	−20.6324			−0.811144			−0.405572	+	0.914063i	$0.632928\pi$
$648$		0			0
$649$	12.9706			0.509139
$650$	−5.03572	−	1.21830i	−0.197517	−	0.0477855i
$651$		0			0
$652$	11.4865	−	22.3497i	0.449845	−	0.875282i
$653$			49.9638i			1.95524i	0.210387	+	0.977618i	$0.432528\pi$
$653$			49.9638i			1.95524i	−0.210387	+	0.977618i	$0.567472\pi$
$654$		0			0
$655$		−	22.5643i		−	0.881661i
$656$	23.2553	−	16.6485i	0.907968	−	0.650014i
$657$		0			0
$658$	−8.69407	+	35.9362i	−0.338930	+	1.40094i
$659$	−3.00130			−0.116914			−0.0584570	−	0.998290i	$-0.518618\pi$
$659$	−3.00130			−0.116914			−0.0584570	+	0.998290i	$0.518618\pi$
$660$		0			0
$661$	−34.1538			−1.32843			−0.664214	−	0.747542i	$-0.731234\pi$
$661$	−34.1538			−1.32843			−0.664214	+	0.747542i	$0.731234\pi$
$662$	6.12391	−	25.3127i	0.238013	−	0.983804i
$663$		0			0
$664$	−1.07432	−	0.927354i	−0.0416916	−	0.0359883i
$665$		−	13.7968i		−	0.535015i
$666$		0			0
$667$			3.41421i			0.132199i
$668$	37.4435	+	19.2438i	1.44873	+	0.744566i
$669$		0			0
$670$	−19.6860	−	4.76264i	−0.760536	−	0.183997i
$671$	−36.5408			−1.41064
$672$		0			0
$673$	−27.5117			−1.06050			−0.530250	−	0.847842i	$-0.677902\pi$
$673$	−27.5117			−1.06050			−0.530250	+	0.847842i	$0.677902\pi$
$674$	30.5369	+	7.38781i	1.17624	+	0.284568i
$675$		0			0
$676$	−16.7851	−	8.62658i	−0.645580	−	0.331791i
$677$		−	28.1804i		−	1.08306i	−0.840682	−	0.541529i	$-0.817845\pi$
$677$		−	28.1804i		−	1.08306i	0.840682	−	0.541529i	$-0.182155\pi$
$678$		0			0
$679$		−	17.2176i		−	0.660752i
$680$	8.42955	+	7.27641i	0.323258	+	0.279038i
$681$		0			0
$682$	−0.360189	+	1.48881i	−0.0137924	+	0.0570095i
$683$	−27.0800			−1.03619			−0.518093	−	0.855324i	$-0.673358\pi$
$683$	−27.0800			−1.03619			−0.518093	+	0.855324i	$0.673358\pi$
$684$		0			0
$685$	6.44273			0.246164
$686$	−5.70858	+	23.5959i	−0.217955	+	0.900897i
$687$		0			0
$688$	−2.53818	+	1.81708i	−0.0967672	+	0.0692756i
$689$		−	9.95928i		−	0.379418i
$690$		0			0
$691$			12.7057i			0.483348i	0.970358	+	0.241674i	$0.0776964\pi$
$691$			12.7057i			0.483348i	−0.970358	+	0.241674i	$0.922304\pi$
$692$	1.03064	−	2.00535i	0.0391789	−	0.0762320i
$693$		0			0
$694$	−45.9384	−	11.1139i	−1.74380	−	0.421878i
$695$	23.5280			0.892470
$696$		0			0
$697$	−16.0940			−0.609605
$698$	−36.8950	−	8.92604i	−1.39650	−	0.337856i
$699$		0			0
$700$	−4.98265	+	9.69494i	−0.188326	+	0.366434i
$701$			11.7156i			0.442492i	0.975218	+	0.221246i	$0.0710123\pi$
$701$			11.7156i			0.442492i	−0.975218	+	0.221246i	$0.928988\pi$
$702$		0			0
$703$			14.4455i			0.544822i
$704$	−3.30481	−	22.3848i	−0.124555	−	0.843658i
$705$		0			0
$706$	−2.12097	+	8.76687i	−0.0798239	+	0.329945i
$707$	38.5917			1.45139
$708$		0			0
$709$	12.2217			0.458997			0.229498	−	0.973309i	$-0.426291\pi$
$709$	12.2217			0.458997			0.229498	+	0.973309i	$0.426291\pi$
$710$	2.42441	−	10.0211i	0.0909864	−	0.376084i
$711$		0			0
$712$	3.66882	−	4.25024i	0.137495	−	0.159285i
$713$			0.382941i			0.0143412i
$714$		0			0
$715$			9.33962i			0.349282i
$716$	37.2815	+	19.1606i	1.39327	+	0.716064i
$717$		0			0
$718$	−17.0867	−	4.13380i	−0.637670	−	0.154272i
$719$	−12.4544			−0.464470			−0.232235	−	0.972660i	$-0.574604\pi$
$719$	−12.4544			−0.464470			−0.232235	+	0.972660i	$0.574604\pi$
$720$		0			0
$721$	44.3098			1.65018
$722$	15.2743	+	3.69533i	0.568451	+	0.137526i
$723$		0			0
$724$	−20.6354	−	10.6054i	−0.766908	−	0.394147i
$725$		−	6.62558i		−	0.246068i
$726$		0			0
$727$		−	25.5962i		−	0.949312i	−0.880171	−	0.474656i	$-0.842572\pi$
$727$		−	25.5962i		−	0.949312i	0.880171	−	0.474656i	$-0.157428\pi$
$728$	9.79917	−	11.3521i	0.363181	−	0.420737i
$729$		0			0
$730$	−7.33137	+	30.3036i	−0.271346	+	1.12159i
$731$	1.75657			0.0649690
$732$		0			0
$733$	16.1390			0.596107			0.298053	−	0.954549i	$-0.403663\pi$
$733$	16.1390			0.596107			0.298053	+	0.954549i	$0.403663\pi$
$734$	9.71796	−	40.1683i	0.358696	−	1.48264i
$735$		0			0
$736$	−2.11896	−	5.24500i	−0.0781061	−	0.193333i
$737$		−	23.1590i		−	0.853072i
$738$		0			0
$739$			16.0500i			0.590408i	0.955434	+	0.295204i	$0.0953875\pi$
$739$			16.0500i			0.590408i	−0.955434	+	0.295204i	$0.904612\pi$
$740$	−8.22470	+	16.0031i	−0.302346	+	0.588287i
$741$		0			0
$742$	−20.3660	−	4.92716i	−0.747659	−	0.180882i
$743$	−30.0368			−1.10194			−0.550971	−	0.834524i	$-0.685743\pi$
$743$	−30.0368			−1.10194			−0.550971	+	0.834524i	$0.685743\pi$
$744$		0			0
$745$	−18.1747			−0.665870
$746$	−38.8519	−	9.39947i	−1.42247	−	0.344139i
$747$		0			0
$748$	−5.82030	+	11.3248i	−0.212811	+	0.414076i
$749$		−	36.4745i		−	1.33275i
$750$		0			0
$751$		−	32.0167i		−	1.16831i	−0.811643	−	0.584154i	$-0.801427\pi$
$751$		−	32.0167i		−	1.16831i	0.811643	−	0.584154i	$-0.198573\pi$
$752$	21.6747	+	30.2761i	0.790394	+	1.10406i
$753$		0			0
$754$	−2.14343	+	8.85970i	−0.0780593	+	0.322651i
$755$	−7.70607			−0.280453
$756$		0			0
$757$	47.2504			1.71734			0.858672	−	0.512526i	$-0.171290\pi$
$757$	47.2504			1.71734			0.858672	+	0.512526i	$0.171290\pi$
$758$	−2.63136	+	10.8765i	−0.0955754	+	0.395053i
$759$		0			0
$760$	−10.5179	−	9.07911i	−0.381526	−	0.329334i
$761$		−	35.9215i		−	1.30215i	−0.759013	−	0.651076i	$-0.774318\pi$
$761$		−	35.9215i		−	1.30215i	0.759013	−	0.651076i	$-0.225682\pi$
$762$		0			0
$763$			40.4125i			1.46303i
$764$	3.15465	+	1.62131i	0.114131	+	0.0586569i
$765$		0			0
$766$	13.6713	+	3.30751i	0.493964	+	0.119505i
$767$	8.65723			0.312594
$768$		0			0
$769$	−6.18118			−0.222899			−0.111450	−	0.993770i	$-0.535549\pi$
$769$	−6.18118			−0.222899			−0.111450	+	0.993770i	$0.535549\pi$
$770$	19.0988	+	4.62059i	0.688273	+	0.166514i
$771$		0			0
$772$	−40.5530	−	20.8419i	−1.45954	−	0.750117i
$773$			22.6175i			0.813494i	0.913541	+	0.406747i	$0.133337\pi$
$773$			22.6175i			0.813494i	−0.913541	+	0.406747i	$0.866663\pi$
$774$		0			0
$775$		−	0.743130i		−	0.0266940i
$776$	−13.1258	−	11.3303i	−0.471190	−	0.406733i
$777$		0			0
$778$	−4.45500	+	18.4143i	−0.159719	+	0.660186i
$779$	20.0813			0.719486
$780$		0			0
$781$	11.7890			0.421844
$782$	−0.748526	+	3.09397i	−0.0267673	+	0.110640i
$783$		0			0
$784$	−2.06727	−	2.88765i	−0.0738310	−	0.103130i
$785$		−	29.8178i		−	1.06424i
$786$		0			0
$787$		−	51.5449i		−	1.83738i	−0.394982	−	0.918689i	$-0.629249\pi$
$787$		−	51.5449i		−	1.83738i	0.394982	−	0.918689i	$-0.370751\pi$
$788$	13.8440	−	26.9368i	0.493171	−	0.959584i
$789$		0			0
$790$	−20.4433	−	4.94587i	−0.727341	−	0.175966i
$791$	47.7770			1.69875
$792$		0			0
$793$	−24.3892			−0.866086
$794$	30.5216	+	7.38412i	1.08317	+	0.262053i
$795$		0			0
$796$	16.5161	−	32.1362i	0.585399	−	1.13904i
$797$		−	32.7972i		−	1.16174i	−0.813997	−	0.580869i	$-0.802713\pi$
$797$		−	32.7972i		−	1.16174i	0.813997	−	0.580869i	$-0.197287\pi$
$798$		0			0
$799$		−	20.9528i		−	0.741258i
$800$	4.11204	+	10.1784i	0.145382	+	0.359860i
$801$		0			0
$802$	−0.413755	+	1.71022i	−0.0146102	+	0.0603900i
$803$	−35.6498			−1.25805
$804$		0			0
$805$	4.91245			0.173141
$806$	−0.240409	+	0.993710i	−0.00846805	+	0.0350019i
$807$		0			0
$808$	25.3957	−	29.4203i	0.893417	−	1.03500i
$809$		−	18.2052i		−	0.640061i	−0.947407	−	0.320031i	$-0.896307\pi$
$809$		−	18.2052i		−	0.640061i	0.947407	−	0.320031i	$-0.103693\pi$
$810$		0			0
$811$			5.20431i			0.182748i	0.995817	+	0.0913740i	$0.0291259\pi$
$811$			5.20431i			0.182748i	−0.995817	+	0.0913740i	$0.970874\pi$
$812$	17.0570	+	8.76632i	0.598583	+	0.307638i
$813$		0			0
$814$	−19.9968	−	4.83785i	−0.700889	−	0.169567i
$815$	21.9765			0.769802
$816$		0			0
$817$	−2.19175			−0.0766796
$818$	−8.45086	−	2.04452i	−0.295477	−	0.0714850i
$819$		0			0
$820$	22.2466	+	11.4335i	0.776885	+	0.399275i
$821$		−	7.95814i		−	0.277741i	−0.990311	−	0.138870i	$-0.955653\pi$
$821$		−	7.95814i		−	0.277741i	0.990311	−	0.138870i	$-0.0443472\pi$
$822$		0			0
$823$		−	39.9772i		−	1.39352i	−0.717305	−	0.696759i	$-0.754625\pi$
$823$		−	39.9772i		−	1.39352i	0.717305	−	0.696759i	$-0.245375\pi$
$824$	29.1586	−	33.7795i	1.01579	−	1.17676i
$825$		0			0
$826$	4.28299	−	17.7034i	0.149024	−	0.615979i
$827$	12.4938			0.434451			0.217226	−	0.976121i	$-0.430299\pi$
$827$	12.4938			0.434451			0.217226	+	0.976121i	$0.430299\pi$
$828$		0			0
$829$	−22.2373			−0.772332			−0.386166	−	0.922429i	$-0.626201\pi$
$829$	−22.2373			−0.772332			−0.386166	+	0.922429i	$0.626201\pi$
$830$	0.291859	−	1.20638i	0.0101306	−	0.0418739i
$831$		0			0
$832$	−2.20580	−	14.9408i	−0.0764725	−	0.517978i
$833$			1.99842i			0.0692412i
$834$		0			0
$835$			36.8182i			1.27415i
$836$	7.26226	−	14.1305i	0.251170	−	0.488713i
$837$		0			0
$838$	−4.36813	−	1.05678i	−0.150895	−	0.0365060i
$839$	29.4497			1.01672			0.508358	−	0.861146i	$-0.330253\pi$
$839$	29.4497			1.01672			0.508358	+	0.861146i	$0.330253\pi$
$840$		0			0
$841$	17.3431			0.598040
$842$	1.98314	+	0.479783i	0.0683436	+	0.0165344i
$843$		0			0
$844$	−11.8279	+	23.0141i	−0.407134	+	0.792178i
$845$		−	16.5048i		−	0.567782i
$846$		0			0
$847$		−	8.42559i		−	0.289507i
$848$	−17.1583	+	12.2836i	−0.589217	+	0.421820i
$849$		0			0
$850$	1.45258	−	6.00412i	0.0498231	−	0.205940i
$851$	−5.14343			−0.176315
$852$		0			0
$853$	42.5933			1.45837			0.729184	−	0.684318i	$-0.239900\pi$
$853$	42.5933			1.45837			0.729184	+	0.684318i	$0.239900\pi$
$854$	−12.0661	+	49.8741i	−0.412893	+	1.70666i
$855$		0			0
$856$	−27.8063	−	24.0025i	−0.950399	−	0.820387i
$857$		−	47.4210i		−	1.61987i	−0.586518	−	0.809936i	$-0.699502\pi$
$857$		−	47.4210i		−	1.61987i	0.586518	−	0.809936i	$-0.300498\pi$
$858$		0			0
$859$		−	29.9892i		−	1.02322i	−0.859218	−	0.511610i	$-0.829049\pi$
$859$		−	29.9892i		−	1.02322i	0.859218	−	0.511610i	$-0.170951\pi$
$860$	−2.42809	−	1.24790i	−0.0827970	−	0.0425529i
$861$		0			0
$862$	5.30363	+	1.28311i	0.180642	+	0.0437029i
$863$	42.0075			1.42995			0.714977	−	0.699148i	$-0.246437\pi$
$863$	42.0075			1.42995			0.714977	+	0.699148i	$0.246437\pi$
$864$		0			0
$865$	1.97186			0.0670453
$866$	−33.6104	−	8.13138i	−1.14213	−	0.276316i
$867$		0			0
$868$	1.91312	+	0.983237i	0.0649357	+	0.0333732i
$869$		−	24.0500i		−	0.815839i
$870$		0			0
$871$		−	15.4575i		−	0.523758i
$872$	30.8084	+	26.5939i	1.04330	+	0.900584i
$873$		0			0
$874$	0.933971	−	3.86049i	0.0315920	−	0.130583i
$875$	−34.0953			−1.15263
$876$		0			0
$877$	−8.08293			−0.272941			−0.136471	−	0.990644i	$-0.543576\pi$
$877$	−8.08293			−0.272941			−0.136471	+	0.990644i	$0.543576\pi$
$878$	7.58058	−	31.3337i	0.255832	−	1.05746i
$879$		0			0
$880$	16.0907	−	11.5193i	0.542417	−	0.388316i
$881$		−	25.1701i		−	0.848003i	−0.905661	−	0.424002i	$-0.860625\pi$
$881$		−	25.1701i		−	0.848003i	0.905661	−	0.424002i	$-0.139375\pi$
$882$		0			0
$883$			2.56431i			0.0862959i	0.999069	+	0.0431480i	$0.0137387\pi$
$883$			2.56431i			0.0862959i	−0.999069	+	0.0431480i	$0.986261\pi$
$884$	−3.88477	+	7.55876i	−0.130659	+	0.254229i
$885$		0			0
$886$	3.04776	+	0.737346i	0.102391	+	0.0247716i
$887$	−34.5654			−1.16059			−0.580296	−	0.814405i	$-0.697063\pi$
$887$	−34.5654			−1.16059			−0.580296	+	0.814405i	$0.697063\pi$
$888$		0			0
$889$	14.6737			0.492140
$890$	4.77269	+	1.15466i	0.159981	+	0.0387043i
$891$		0			0
$892$	−4.36276	+	8.48881i	−0.146076	+	0.284226i
$893$			26.1438i			0.874869i
$894$		0			0
$895$			36.6589i			1.22537i
$896$	−31.6440	−	2.88094i	−1.05715	−	0.0962455i
$897$		0			0
$898$	2.38088	−	9.84118i	0.0794511	−	0.328405i
$899$	−1.30744			−0.0436056
$900$		0			0
$901$	11.8745			0.395597
$902$	−6.72529	+	27.7984i	−0.223928	+	0.925586i
$903$		0			0
$904$	31.4402	−	36.4227i	1.04568	−	1.21140i
$905$		−	20.2908i		−	0.674488i
$906$		0			0
$907$		−	35.1524i		−	1.16722i	−0.812035	−	0.583609i	$-0.801640\pi$
$907$		−	35.1524i		−	1.16722i	0.812035	−	0.583609i	$-0.198360\pi$
$908$	16.8624	+	8.66631i	0.559598	+	0.287601i
$909$		0			0
$910$	12.7475	+	3.08402i	0.422577	+	0.102234i
$911$	−28.1539			−0.932781			−0.466391	−	0.884579i	$-0.654446\pi$
$911$	−28.1539			−0.932781			−0.466391	+	0.884579i	$0.654446\pi$
$912$		0			0
$913$	1.41921			0.0469688
$914$	0.827311	+	0.200152i	0.0273650	+	0.00662044i
$915$		0			0
$916$	−17.7352	−	9.11488i	−0.585988	−	0.301164i
$917$		−	36.2311i		−	1.19646i
$918$		0			0
$919$		−	40.7332i		−	1.34366i	−0.740704	−	0.671832i	$-0.765508\pi$
$919$		−	40.7332i		−	1.34366i	0.740704	−	0.671832i	$-0.234492\pi$
$920$	3.23269	−	3.74500i	0.106579	−	0.123469i
$921$		0			0
$922$	−1.39008	+	5.74579i	−0.0457799	+	0.189227i
$923$	7.86860			0.258998
$924$		0			0
$925$	9.98128			0.328183
$926$	−11.1619	+	46.1366i	−0.366802	+	1.51614i
$927$		0			0
$928$	17.9075	−	7.23460i	0.587844	−	0.237487i
$929$			47.9152i			1.57205i	0.618197	+	0.786023i	$0.287863\pi$
$929$			47.9152i			1.57205i	−0.618197	+	0.786023i	$0.712137\pi$
$930$		0			0
$931$		−	2.49352i		−	0.0817219i
$932$	−21.7614	+	42.3421i	−0.712819	+	1.38696i
$933$		0			0
$934$	−2.70507	−	0.654440i	−0.0885127	−	0.0214139i
$935$	−11.1357			−0.364176
$936$		0			0
$937$	−39.5090			−1.29070			−0.645351	−	0.763886i	$-0.723289\pi$
$937$	−39.5090			−1.29070			−0.645351	+	0.763886i	$0.723289\pi$
$938$	−31.6095	−	7.64730i	−1.03209	−	0.249693i
$939$		0			0
$940$	−14.8853	+	28.9629i	−0.485504	+	0.944665i
$941$			15.7264i			0.512665i	0.966589	+	0.256332i	$0.0825142\pi$
$941$			15.7264i			0.512665i	−0.966589	+	0.256332i	$0.917486\pi$
$942$		0			0
$943$			7.15010i			0.232839i
$944$	−10.6777	−	14.9150i	−0.347529	−	0.485443i
$945$		0			0
$946$	0.734026	−	3.03403i	0.0238652	−	0.0986449i
$947$	5.61597			0.182495			0.0912473	−	0.995828i	$-0.470915\pi$
$947$	5.61597			0.182495			0.0912473	+	0.995828i	$0.470915\pi$
$948$		0			0
$949$	−23.7945			−0.772403
$950$	−1.81245	+	7.49162i	−0.0588037	+	0.243060i
$951$		0			0
$952$	13.5352	+	11.6836i	0.438678	+	0.378668i
$953$			13.7233i			0.444543i	0.974985	+	0.222271i	$0.0713471\pi$
$953$			13.7233i			0.444543i	−0.974985	+	0.222271i	$0.928653\pi$
$954$		0			0
$955$			3.10197i			0.100377i
$956$	−19.3438	−	9.94161i	−0.625623	−	0.321535i
$957$		0			0
$958$	50.1468	+	12.1321i	1.62017	+	0.391969i
$959$	10.3450			0.334057
$960$		0			0
$961$	30.8534			0.995270
$962$	−13.3469	−	3.22903i	−0.430322	−	0.104108i
$963$		0			0
$964$	−20.6314	−	10.6034i	−0.664493	−	0.341511i
$965$		−	39.8758i		−	1.28365i
$966$		0			0
$967$		−	26.4133i		−	0.849395i	−0.905335	−	0.424697i	$-0.860380\pi$
$967$		−	26.4133i		−	0.849395i	0.905335	−	0.424697i	$-0.139620\pi$
$968$	−6.42323	−	5.54455i	−0.206451	−	0.178209i
$969$		0			0
$970$	3.56589	−	14.7393i	0.114494	−	0.473250i
$971$	−20.6087			−0.661365			−0.330682	−	0.943742i	$-0.607279\pi$
$971$	−20.6087			−0.661365			−0.330682	+	0.943742i	$0.607279\pi$
$972$		0			0
$973$	37.7786			1.21113
$974$	10.9498	−	45.2599i	0.350853	−	1.45022i
$975$		0			0
$976$	30.0812	+	42.0188i	0.962876	+	1.34499i
$977$		−	12.7517i		−	0.407964i	−0.978975	−	0.203982i	$-0.934612\pi$
$977$		−	12.7517i		−	0.407964i	0.978975	−	0.203982i	$-0.0653884\pi$
$978$		0			0
$979$			5.61470i			0.179446i
$980$	1.41971	−	2.76240i	0.0453511	−	0.0882416i
$981$		0			0
$982$	−45.9384	−	11.1139i	−1.46595	−	0.354659i
$983$	36.7981			1.17368			0.586838	−	0.809704i	$-0.300373\pi$
$983$	36.7981			1.17368			0.586838	+	0.809704i	$0.300373\pi$
$984$		0			0
$985$	26.4870			0.843945
$986$	−10.5635	−	2.55563i	−0.336410	−	0.0813878i
$987$		0			0
$988$	4.84721	−	9.43142i	0.154210	−	0.300053i
$989$		−	0.780391i		−	0.0248150i
$990$		0			0
$991$			30.2463i			0.960805i	0.877048	+	0.480402i	$0.159509\pi$
$991$			30.2463i			0.960805i	−0.877048	+	0.480402i	$0.840491\pi$
$992$	2.00852	−	0.811437i	0.0637706	−	0.0257632i
$993$		0			0
$994$	3.89283	−	16.0907i	0.123473	−	0.510366i
$995$	31.5995			1.00177
$996$		0			0
$997$	12.2794			0.388893			0.194446	−	0.980913i	$-0.437709\pi$
$997$	12.2794			0.388893			0.194446	+	0.980913i	$0.437709\pi$
$998$	−13.4742	+	55.6944i	−0.426518	+	1.76298i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	828.2.c.d.323.8	yes	8
3.2	odd	2		828.2.c.c.323.1	✓	8
4.3	odd	2		828.2.c.c.323.2	yes	8
12.11	even	2	inner	828.2.c.d.323.7	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
828.2.c.c.323.1	✓	8	3.2	odd	2
828.2.c.c.323.2	yes	8	4.3	odd	2
828.2.c.d.323.7	yes	8	12.11	even	2	inner
828.2.c.d.323.8	yes	8	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 828 = 2^{2} \cdot 3^{2} \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	828.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(1.37456 + 0.332548i) q^{2} +(1.77882 + 0.914214i) q^{4} +1.74912i q^{5} +2.80853i q^{7} +(2.14108 + 1.84818i) q^{8} +(-0.581666 + 2.40426i) q^{10} -2.82843 q^{11} -1.88784 q^{13} +(-0.933971 + 3.86049i) q^{14} +(2.32843 + 3.25245i) q^{16} -2.25088i q^{17} +2.80853i q^{19} +(-1.59907 + 3.11137i) q^{20} +(-3.88784 - 0.940588i) q^{22} -1.00000 q^{23} +1.94059 q^{25} +(-2.59495 - 0.627797i) q^{26} +(-2.56760 + 4.99588i) q^{28} -3.41421i q^{29} -0.382941i q^{31} +(2.11896 + 5.24500i) q^{32} +(0.748526 - 3.09397i) q^{34} -4.91245 q^{35} +5.14343 q^{37} +(-0.933971 + 3.86049i) q^{38} +(-3.23269 + 3.74500i) q^{40} -7.15010i q^{41} +0.780391i q^{43} +(-5.03127 - 2.58579i) q^{44} +(-1.37456 - 0.332548i) q^{46} +9.30872 q^{47} -0.887839 q^{49} +(2.66745 + 0.645339i) q^{50} +(-3.35813 - 1.72589i) q^{52} +5.27549i q^{53} -4.94725i q^{55} +(-5.19068 + 6.01328i) q^{56} +(1.13539 - 4.69304i) q^{58} -4.58579 q^{59} +12.9191 q^{61} +(0.127346 - 0.526374i) q^{62} +(1.16843 + 7.91421i) q^{64} -3.30205i q^{65} +8.18794i q^{67} +(2.05779 - 4.00392i) q^{68} +(-6.75245 - 1.63363i) q^{70} -4.16804 q^{71} +12.6041 q^{73} +(7.06995 + 1.71044i) q^{74} +(-2.56760 + 4.99588i) q^{76} -7.94372i q^{77} +8.50295i q^{79} +(-5.68892 + 4.07269i) q^{80} +(2.37775 - 9.82823i) q^{82} -0.501765 q^{83} +3.93706 q^{85} +(-0.259517 + 1.07269i) q^{86} +(-6.05588 - 5.22746i) q^{88} -1.98509i q^{89} -5.30205i q^{91} +(-1.77882 - 0.914214i) q^{92} +(12.7954 + 3.09560i) q^{94} -4.91245 q^{95} -6.13048 q^{97} +(-1.22039 - 0.295249i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{2} + 4 q^{8} + 8 q^{10} + 8 q^{13} - 4 q^{16} - 8 q^{20} - 8 q^{22} - 8 q^{23} + 16 q^{25} + 8 q^{26} + 12 q^{28} + 4 q^{32} + 24 q^{34} + 24 q^{37} + 4 q^{40} - 4 q^{46} + 16 q^{47} + 16 q^{49}+ \cdots + 12 q^{98}+O(q^{100}) \) 8 * q + 4 * q^2 + 4 * q^8 + 8 * q^10 + 8 * q^13 - 4 * q^16 - 8 * q^20 - 8 * q^22 - 8 * q^23 + 16 * q^25 + 8 * q^26 + 12 * q^28 + 4 * q^32 + 24 * q^34 + 24 * q^37 + 4 * q^40 - 4 * q^46 + 16 * q^47 + 16 * q^49 + 20 * q^50 - 4 * q^52 - 20 * q^56 + 12 * q^58 - 48 * q^59 + 40 * q^61 + 24 * q^62 - 24 * q^68 - 28 * q^70 + 32 * q^73 + 20 * q^74 + 12 * q^76 + 4 * q^80 + 12 * q^82 - 32 * q^83 - 24 * q^85 + 36 * q^86 + 8 * q^88 - 20 * q^94 + 8 * q^97 + 12 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more