LMFDB - Embedded newform 408.2.ba.b.145.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [408,2,Mod(25,408)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(408, base_ring=CyclotomicField(8)) chi = DirichletCharacter(H, H._module([0, 0, 0, 5])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("408.25"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 408 = 2^{3} \cdot 3 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	408.ba (of order $8$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,0,0,0,0,0,0,0,0,8] 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:	$3.25789640247$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 40 x^{14} - 112 x^{13} + 166 x^{12} - 328 x^{11} + 728 x^{10} - 368 x^{9} + \cdots + 12689 $ x^16 - 8x^15 + 40x^14 - 112x^13 + 166x^12 - 328x^11 + 728x^10 - 368x^9 + 210x^8 - 2712x^7 + 104x^6 + 11840x^5 - 6586x^4 - 32760x^3 + 63448x^2 - 46336*x + 12689
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			145.4
Root			$-1.52004 - 0.501266i$ of defining polynomial
Character	$\chi$	$=$	408.145
Dual form			408.2.ba.b.121.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.923880 + 0.382683i) q^{3} +(0.431802 - 1.04246i) q^{5} +(-1.16338 - 2.80866i) q^{7} +(0.707107 + 0.707107i) q^{9} +(3.84680 - 1.59340i) q^{11} +1.86212i q^{13} +(0.797866 - 0.797866i) q^{15} +(-1.96221 - 3.62626i) q^{17} +(5.77458 - 5.77458i) q^{19} -3.04007i q^{21} +(-6.03378 + 2.49927i) q^{23} +(2.63526 + 2.63526i) q^{25} +(0.382683 + 0.923880i) q^{27} +(-2.72602 + 6.58121i) q^{29} +(7.71819 + 3.19698i) q^{31} +4.16374 q^{33} -3.43027 q^{35} +(0.323617 + 0.134047i) q^{37} +(-0.712604 + 1.72038i) q^{39} +(1.40682 + 3.39636i) q^{41} +(-6.71026 - 6.71026i) q^{43} +(1.04246 - 0.431802i) q^{45} -4.96736i q^{47} +(-1.58535 + 1.58535i) q^{49} +(-0.425139 - 4.10113i) q^{51} +(-7.13683 + 7.13683i) q^{53} -4.69817i q^{55} +(7.54485 - 3.12518i) q^{57} +(0.0213015 + 0.0213015i) q^{59} +(1.66642 + 4.02310i) q^{61} +(1.16338 - 2.80866i) q^{63} +(1.94119 + 0.804069i) q^{65} +5.70338 q^{67} -6.53091 q^{69} +(-3.98661 - 1.65131i) q^{71} +(-3.25236 + 7.85188i) q^{73} +(1.42619 + 3.44313i) q^{75} +(-8.95061 - 8.95061i) q^{77} +(-8.15920 + 3.37965i) q^{79} +1.00000i q^{81} +(-10.1271 + 10.1271i) q^{83} +(-4.62752 + 0.479707i) q^{85} +(-5.03704 + 5.03704i) q^{87} -1.83702i q^{89} +(5.23007 - 2.16637i) q^{91} +(5.90725 + 5.90725i) q^{93} +(-3.52630 - 8.51325i) q^{95} +(-4.76740 + 11.5095i) q^{97} +(3.84680 + 1.59340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 8 q^{11} - 8 q^{15} - 16 q^{17} + 8 q^{19} + 8 q^{23} + 24 q^{25} + 8 q^{31} + 24 q^{33} + 16 q^{35} - 8 q^{37} + 24 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 40 q^{49} - 8 q^{51} - 24 q^{53} + 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) $ 16 * q + 8 * q^11 - 8 * q^15 - 16 * q^17 + 8 * q^19 + 8 * q^23 + 24 * q^25 + 8 * q^31 + 24 * q^33 + 16 * q^35 - 8 * q^37 + 24 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 40 * q^49 - 8 * q^51 - 24 * q^53 + 8 * q^57 - 32 * q^59 - 48 * q^61 + 48 * q^65 - 24 * q^69 - 32 * q^71 - 40 * q^73 + 16 * q^79 - 48 * q^83 + 32 * q^85 - 16 * q^87 + 16 * q^91 + 24 * q^93 - 56 * q^95 - 40 * q^97 + 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/408\mathbb{Z}\right)^\times$.

$n$	$103$	$137$	$205$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{8}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$3$	0.923880	+	0.382683i	0.533402	+	0.220942i
$4$		0			0
$5$	0.431802	−	1.04246i	0.193108	−	0.466203i	−0.797436	−	0.603404i	$-0.793811\pi$
$5$	0.431802	−	1.04246i	0.193108	−	0.466203i	0.990543	+	0.137201i	$0.0438106\pi$
$6$		0			0
$7$	−1.16338	−	2.80866i	−0.439718	−	1.06157i	−0.976046	−	0.217564i	$-0.930189\pi$
$7$	−1.16338	−	2.80866i	−0.439718	−	1.06157i	0.536328	−	0.844010i	$-0.319811\pi$
$8$		0			0
$9$	0.707107	+	0.707107i	0.235702	+	0.235702i
$10$		0			0
$11$	3.84680	−	1.59340i	1.15985	−	0.480427i	0.282027	−	0.959406i	$-0.408993\pi$
$11$	3.84680	−	1.59340i	1.15985	−	0.480427i	0.877826	+	0.478979i	$0.158993\pi$
$12$		0			0
$13$			1.86212i			0.516460i	0.966083	+	0.258230i	$0.0831393\pi$
$13$			1.86212i			0.516460i	−0.966083	+	0.258230i	$0.916861\pi$
$14$		0			0
$15$	0.797866	−	0.797866i	0.206008	−	0.206008i
$16$		0			0
$17$	−1.96221	−	3.62626i	−0.475906	−	0.879496i
$17$	−1.96221	−	3.62626i	−0.475906	−	0.879496i
$18$		0			0
$19$	5.77458	−	5.77458i	1.32478	−	1.32478i	0.414922	−	0.909857i	$-0.363809\pi$
$19$	5.77458	−	5.77458i	1.32478	−	1.32478i	0.909857	−	0.414922i	$-0.136191\pi$
$20$		0			0
$21$		−	3.04007i		−	0.663398i
$22$		0			0
$23$	−6.03378	+	2.49927i	−1.25813	+	0.521134i	−0.909335	−	0.416065i	$-0.863409\pi$
$23$	−6.03378	+	2.49927i	−1.25813	+	0.521134i	−0.348795	+	0.937199i	$0.613409\pi$
$24$		0			0
$25$	2.63526	+	2.63526i	0.527052	+	0.527052i
$26$		0			0
$27$	0.382683	+	0.923880i	0.0736475	+	0.177801i
$28$		0			0
$29$	−2.72602	+	6.58121i	−0.506210	+	1.22210i	0.439839	+	0.898077i	$0.355035\pi$
$29$	−2.72602	+	6.58121i	−0.506210	+	1.22210i	−0.946049	+	0.324023i	$0.894965\pi$
$30$		0			0
$31$	7.71819	+	3.19698i	1.38623	+	0.574194i	0.946139	−	0.323760i	$-0.104947\pi$
$31$	7.71819	+	3.19698i	1.38623	+	0.574194i	0.440089	+	0.897954i	$0.354947\pi$
$32$		0			0
$33$	4.16374			0.724815
$34$		0			0
$35$	−3.43027			−0.579822
$36$		0			0
$37$	0.323617	+	0.134047i	0.0532023	+	0.0220371i	0.409126	−	0.912478i	$-0.365834\pi$
$37$	0.323617	+	0.134047i	0.0532023	+	0.0220371i	−0.355924	+	0.934515i	$0.615834\pi$
$38$		0			0
$39$	−0.712604	+	1.72038i	−0.114108	+	0.275481i
$40$		0			0
$41$	1.40682	+	3.39636i	0.219708	+	0.530423i	0.994849	−	0.101366i	$-0.0323212\pi$
$41$	1.40682	+	3.39636i	0.219708	+	0.530423i	−0.775141	+	0.631788i	$0.782321\pi$
$42$		0			0
$43$	−6.71026	−	6.71026i	−1.02330	−	1.02330i	−0.999722	−	0.0235824i	$-0.992493\pi$
$43$	−6.71026	−	6.71026i	−1.02330	−	1.02330i	−0.0235824	−	0.999722i	$-0.507507\pi$
$44$		0			0
$45$	1.04246	−	0.431802i	0.155401	−	0.0643692i
$46$		0			0
$47$		−	4.96736i		−	0.724563i	−0.932069	−	0.362282i	$-0.881998\pi$
$47$		−	4.96736i		−	0.724563i	0.932069	−	0.362282i	$-0.118002\pi$
$48$		0			0
$49$	−1.58535	+	1.58535i	−0.226479	+	0.226479i
$50$		0			0
$51$	−0.425139	−	4.10113i	−0.0595314	−	0.574273i
$52$		0			0
$53$	−7.13683	+	7.13683i	−0.980319	+	0.980319i	−0.999810	−	0.0194913i	$-0.993795\pi$
$53$	−7.13683	+	7.13683i	−0.980319	+	0.980319i	0.0194913	+	0.999810i	$0.493795\pi$
$54$		0			0
$55$		−	4.69817i		−	0.633502i
$56$		0			0
$57$	7.54485	−	3.12518i	0.999340	−	0.413940i
$58$		0			0
$59$	0.0213015	+	0.0213015i	0.00277322	+	0.00277322i	0.708492	−	0.705719i	$-0.249376\pi$
$59$	0.0213015	+	0.0213015i	0.00277322	+	0.00277322i	−0.705719	+	0.708492i	$0.749376\pi$
$60$		0			0
$61$	1.66642	+	4.02310i	0.213364	+	0.515106i	0.993936	−	0.109960i	$-0.0350722\pi$
$61$	1.66642	+	4.02310i	0.213364	+	0.515106i	−0.780572	+	0.625066i	$0.785072\pi$
$62$		0			0
$63$	1.16338	−	2.80866i	0.146573	−	0.353858i
$64$		0			0
$65$	1.94119	+	0.804069i	0.240776	+	0.0997325i
$66$		0			0
$67$	5.70338			0.696779			0.348390	−	0.937350i	$-0.386729\pi$
$67$	5.70338			0.696779			0.348390	+	0.937350i	$0.386729\pi$
$68$		0			0
$69$	−6.53091			−0.786230
$70$		0			0
$71$	−3.98661	−	1.65131i	−0.473123	−	0.195974i	0.133364	−	0.991067i	$-0.457422\pi$
$71$	−3.98661	−	1.65131i	−0.473123	−	0.195974i	−0.606488	+	0.795093i	$0.707422\pi$
$72$		0			0
$73$	−3.25236	+	7.85188i	−0.380659	+	0.918993i	0.611179	+	0.791492i	$0.290696\pi$
$73$	−3.25236	+	7.85188i	−0.380659	+	0.918993i	−0.991838	+	0.127501i	$0.959304\pi$
$74$		0			0
$75$	1.42619	+	3.44313i	0.164682	+	0.397579i
$76$		0			0
$77$	−8.95061	−	8.95061i	−1.02002	−	1.02002i
$78$		0			0
$79$	−8.15920	+	3.37965i	−0.917981	+	0.380240i	−0.791106	−	0.611678i	$-0.790495\pi$
$79$	−8.15920	+	3.37965i	−0.917981	+	0.380240i	−0.126875	+	0.991919i	$0.540495\pi$
$80$		0			0
$81$			1.00000i			0.111111i
$82$		0			0
$83$	−10.1271	+	10.1271i	−1.11160	+	1.11160i	−0.118664	+	0.992934i	$0.537861\pi$
$83$	−10.1271	+	10.1271i	−1.11160	+	1.11160i	−0.992934	+	0.118664i	$0.962139\pi$
$84$		0			0
$85$	−4.62752	+	0.479707i	−0.501925	+	0.0520316i
$86$		0			0
$87$	−5.03704	+	5.03704i	−0.540027	+	0.540027i
$88$		0			0
$89$		−	1.83702i		−	0.194723i	−0.995249	−	0.0973617i	$-0.968960\pi$
$89$		−	1.83702i		−	0.194723i	0.995249	−	0.0973617i	$-0.0310404\pi$
$90$		0			0
$91$	5.23007	−	2.16637i	0.548261	−	0.227097i
$92$		0			0
$93$	5.90725	+	5.90725i	0.612553	+	0.612553i
$94$		0			0
$95$	−3.52630	−	8.51325i	−0.361791	−	0.873441i
$96$		0			0
$97$	−4.76740	+	11.5095i	−0.484057	+	1.16862i	0.473610	+	0.880735i	$0.342951\pi$
$97$	−4.76740	+	11.5095i	−0.484057	+	1.16862i	−0.957666	+	0.287881i	$0.907049\pi$
$98$		0			0
$99$	3.84680	+	1.59340i	0.386618	+	0.160142i
$100$		0			0
$101$	−3.79369			−0.377486			−0.188743	−	0.982026i	$-0.560441\pi$
$101$	−3.79369			−0.377486			−0.188743	+	0.982026i	$0.560441\pi$
$102$		0			0
$103$	16.4743			1.62326			0.811632	−	0.584170i	$-0.198580\pi$
$103$	16.4743			1.62326			0.811632	+	0.584170i	$0.198580\pi$
$104$		0			0
$105$	−3.16916	−	1.31271i	−0.309278	−	0.128107i
$106$		0			0
$107$	−3.54644	+	8.56187i	−0.342847	+	0.827707i	0.654578	+	0.755995i	$0.272846\pi$
$107$	−3.54644	+	8.56187i	−0.342847	+	0.827707i	−0.997425	+	0.0717124i	$0.977154\pi$
$108$		0			0
$109$	−3.98225	−	9.61399i	−0.381430	−	0.920854i	−0.991690	−	0.128652i	$-0.958935\pi$
$109$	−3.98225	−	9.61399i	−0.381430	−	0.920854i	0.610260	−	0.792201i	$-0.291065\pi$
$110$		0			0
$111$	0.247686	+	0.247686i	0.0235093	+	0.0235093i
$112$		0			0
$113$	6.03063	−	2.49797i	0.567314	−	0.234989i	−0.0805429	−	0.996751i	$-0.525665\pi$
$113$	6.03063	−	2.49797i	0.567314	−	0.234989i	0.647857	+	0.761762i	$0.275665\pi$
$114$		0			0
$115$			7.36918i			0.687179i
$116$		0			0
$117$	−1.31672	+	1.31672i	−0.121731	+	0.121731i
$118$		0			0
$119$	−7.90211	+	9.72991i	−0.724385	+	0.891940i
$120$		0			0
$121$	4.48077	−	4.48077i	0.407343	−	0.407343i
$122$		0			0
$123$			3.67620i			0.331471i
$124$		0			0
$125$	9.09738	−	3.76826i	0.813694	−	0.337043i
$126$		0			0
$127$	2.55206	+	2.55206i	0.226459	+	0.226459i	0.811212	−	0.584753i	$-0.198808\pi$
$127$	2.55206	+	2.55206i	0.226459	+	0.226459i	−0.584753	+	0.811212i	$0.698808\pi$
$128$		0			0
$129$	−3.63156	−	8.76737i	−0.319741	−	0.771924i
$130$		0			0
$131$	−4.79230	+	11.5696i	−0.418705	+	1.01084i	0.564018	+	0.825763i	$0.309255\pi$
$131$	−4.79230	+	11.5696i	−0.418705	+	1.01084i	−0.982723	+	0.185081i	$0.940745\pi$
$132$		0			0
$133$	−22.9369	−	9.50076i	−1.98888	−	0.823821i
$134$		0			0
$135$	1.12835			0.0971132
$136$		0			0
$137$	6.95813			0.594473			0.297236	−	0.954804i	$-0.403935\pi$
$137$	6.95813			0.594473			0.297236	+	0.954804i	$0.403935\pi$
$138$		0			0
$139$	−15.3524	−	6.35918i	−1.30217	−	0.539378i	−0.379584	−	0.925157i	$-0.623933\pi$
$139$	−15.3524	−	6.35918i	−1.30217	−	0.539378i	−0.922591	+	0.385779i	$0.873933\pi$
$140$		0			0
$141$	1.90092	−	4.58924i	0.160087	−	0.386484i
$142$		0			0
$143$	2.96710	+	7.16322i	0.248121	+	0.599018i
$144$		0			0
$145$	5.68356	+	5.68356i	0.471994	+	0.471994i
$146$		0			0
$147$	−2.07137	+	0.857988i	−0.170843	+	0.0707656i
$148$		0			0
$149$		−	13.2038i		−	1.08169i	−0.841121	−	0.540847i	$-0.818104\pi$
$149$		−	13.2038i		−	1.08169i	0.841121	−	0.540847i	$-0.181896\pi$
$150$		0			0
$151$	2.65333	−	2.65333i	0.215925	−	0.215925i	−0.590854	−	0.806779i	$-0.701209\pi$
$151$	2.65333	−	2.65333i	0.215925	−	0.215925i	0.806779	+	0.590854i	$0.201209\pi$
$152$		0			0
$153$	1.17666	−	3.95164i	0.0951270	−	0.319471i
$154$		0			0
$155$	6.66546	−	6.66546i	0.535383	−	0.535383i
$156$		0			0
$157$			9.68851i			0.773227i	0.922242	+	0.386614i	$0.126355\pi$
$157$			9.68851i			0.773227i	−0.922242	+	0.386614i	$0.873645\pi$
$158$		0			0
$159$	−9.32472	+	3.86242i	−0.739498	+	0.306310i
$160$		0			0
$161$	14.0392	+	14.0392i	1.10644	+	1.10644i
$162$		0			0
$163$	−1.30464	−	3.14969i	−0.102188	−	0.246703i	0.864514	−	0.502608i	$-0.167626\pi$
$163$	−1.30464	−	3.14969i	−0.102188	−	0.246703i	−0.966702	+	0.255906i	$0.917626\pi$
$164$		0			0
$165$	1.79791	−	4.34055i	0.139967	−	0.337911i
$166$		0			0
$167$	14.0077	+	5.80220i	1.08395	+	0.448988i	0.851894	−	0.523714i	$-0.175454\pi$
$167$	14.0077	+	5.80220i	1.08395	+	0.448988i	0.232058	+	0.972702i	$0.425454\pi$
$168$		0			0
$169$	9.53249			0.733269
$170$		0			0
$171$	8.16649			0.624507
$172$		0			0
$173$	−13.4060	−	5.55293i	−1.01924	−	0.422182i	−0.190420	−	0.981703i	$-0.560985\pi$
$173$	−13.4060	−	5.55293i	−1.01924	−	0.422182i	−0.828816	+	0.559521i	$0.810985\pi$
$174$		0			0
$175$	4.33572	−	10.4674i	0.327750	−	0.791258i
$176$		0			0
$177$	0.0115283	+	0.0278318i	0.000866521	+	0.00209197i
$178$		0			0
$179$	3.61732	+	3.61732i	0.270371	+	0.270371i	0.829250	−	0.558878i	$-0.188768\pi$
$179$	3.61732	+	3.61732i	0.270371	+	0.270371i	−0.558878	+	0.829250i	$0.688768\pi$
$180$		0			0
$181$	3.99796	−	1.65601i	0.297166	−	0.123090i	−0.229119	−	0.973398i	$-0.573584\pi$
$181$	3.99796	−	1.65601i	0.297166	−	0.123090i	0.526285	+	0.850308i	$0.323584\pi$
$182$		0			0
$183$			4.35458i			0.321900i
$184$		0			0
$185$	0.279477	−	0.279477i	0.0205476	−	0.0205476i
$186$		0			0
$187$	−13.3263	−	10.8229i	−0.974515	−	0.791448i
$188$		0			0
$189$	2.14965	−	2.14965i	0.156364	−	0.156364i
$190$		0			0
$191$		−	13.6906i		−	0.990619i	−0.868716	−	0.495310i	$-0.835055\pi$
$191$		−	13.6906i		−	0.990619i	0.868716	−	0.495310i	$-0.164945\pi$
$192$		0			0
$193$	15.9828	−	6.62031i	1.15047	−	0.476541i	0.275779	−	0.961221i	$-0.411064\pi$
$193$	15.9828	−	6.62031i	1.15047	−	0.476541i	0.874691	+	0.484680i	$0.161064\pi$
$194$		0			0
$195$	1.48573	+	1.48573i	0.106395	+	0.106395i
$196$		0			0
$197$	−1.97711	−	4.77317i	−0.140863	−	0.340074i	0.837666	−	0.546183i	$-0.183920\pi$
$197$	−1.97711	−	4.77317i	−0.140863	−	0.340074i	−0.978529	+	0.206109i	$0.933920\pi$
$198$		0			0
$199$	−9.76587	+	23.5769i	−0.692284	+	1.67132i	0.0478426	+	0.998855i	$0.484765\pi$
$199$	−9.76587	+	23.5769i	−0.692284	+	1.67132i	−0.740127	+	0.672467i	$0.765235\pi$
$200$		0			0
$201$	5.26924	+	2.18259i	0.371663	+	0.153948i
$202$		0			0
$203$	21.6558			1.51994
$204$		0			0
$205$	4.14805			0.289712
$206$		0			0
$207$	−6.03378	−	2.49927i	−0.419377	−	0.173711i
$208$		0			0
$209$	13.0124	−	31.4148i	0.900090	−	2.17301i
$210$		0			0
$211$	3.78592	+	9.14001i	0.260633	+	0.629225i	0.998978	−	0.0451990i	$-0.0143922\pi$
$211$	3.78592	+	9.14001i	0.260633	+	0.629225i	−0.738345	+	0.674424i	$0.764392\pi$
$212$		0			0
$213$	−3.05122	−	3.05122i	−0.209066	−	0.209066i
$214$		0			0
$215$	−9.89269	+	4.09769i	−0.674676	+	0.279460i
$216$		0			0
$217$		−	25.3971i		−	1.72407i
$218$		0			0
$219$	−6.00957	+	6.00957i	−0.406089	+	0.406089i
$220$		0			0
$221$	6.75254	−	3.65388i	0.454225	−	0.245787i
$222$		0			0
$223$	15.0502	−	15.0502i	1.00783	−	1.00783i	0.00786422	−	0.999969i	$-0.497497\pi$
$223$	15.0502	−	15.0502i	1.00783	−	1.00783i	0.999969	−	0.00786422i	$-0.00250328\pi$
$224$		0			0
$225$			3.72682i			0.248455i
$226$		0			0
$227$	16.3314	−	6.76468i	1.08395	−	0.448988i	0.232058	−	0.972702i	$-0.425454\pi$
$227$	16.3314	−	6.76468i	1.08395	−	0.448988i	0.851894	+	0.523714i	$0.175454\pi$
$228$		0			0
$229$	7.16062	+	7.16062i	0.473187	+	0.473187i	0.902944	−	0.429757i	$-0.141401\pi$
$229$	7.16062	+	7.16062i	0.473187	+	0.473187i	−0.429757	+	0.902944i	$0.641401\pi$
$230$		0			0
$231$	−4.84404	−	11.6945i	−0.318714	−	0.769444i
$232$		0			0
$233$	5.73036	−	13.8343i	0.375408	−	0.906316i	−0.617405	−	0.786645i	$-0.711816\pi$
$233$	5.73036	−	13.8343i	0.375408	−	0.906316i	0.992814	−	0.119671i	$-0.0381839\pi$
$234$		0			0
$235$	−5.17828	−	2.14491i	−0.337794	−	0.139919i
$236$		0			0
$237$	−8.83145			−0.573664
$238$		0			0
$239$	9.90412			0.640644			0.320322	−	0.947309i	$-0.396209\pi$
$239$	9.90412			0.640644			0.320322	+	0.947309i	$0.396209\pi$
$240$		0			0
$241$	−8.84148	−	3.66226i	−0.569530	−	0.235907i	0.0792868	−	0.996852i	$-0.474736\pi$
$241$	−8.84148	−	3.66226i	−0.569530	−	0.235907i	−0.648816	+	0.760945i	$0.724736\pi$
$242$		0			0
$243$	−0.382683	+	0.923880i	−0.0245492	+	0.0592669i
$244$		0			0
$245$	0.968113	+	2.33723i	0.0618505	+	0.149320i
$246$		0			0
$247$	10.7530	+	10.7530i	0.684196	+	0.684196i
$248$		0			0
$249$	−13.2317	+	5.48077i	−0.838528	+	0.347330i
$250$		0			0
$251$		−	12.0900i		−	0.763116i	−0.924345	−	0.381558i	$-0.875388\pi$
$251$		−	12.0900i		−	0.763116i	0.924345	−	0.381558i	$-0.124612\pi$
$252$		0			0
$253$	−19.2284	+	19.2284i	−1.20888	+	1.20888i
$254$		0			0
$255$	−4.45885	−	1.32768i	−0.279224	−	0.0831428i
$256$		0			0
$257$	−16.4018	+	16.4018i	−1.02312	+	1.02312i	−0.0233904	+	0.999726i	$0.507446\pi$
$257$	−16.4018	+	16.4018i	−1.02312	+	1.02312i	−0.999726	+	0.0233904i	$0.992554\pi$
$258$		0			0
$259$		−	1.06488i		−	0.0661683i
$260$		0			0
$261$	−6.58121	+	2.72602i	−0.407366	+	0.168737i
$262$		0			0
$263$	0.538629	+	0.538629i	0.0332133	+	0.0332133i	0.723518	−	0.690305i	$-0.242524\pi$
$263$	0.538629	+	0.538629i	0.0332133	+	0.0332133i	−0.690305	+	0.723518i	$0.742524\pi$
$264$		0			0
$265$	4.35818	+	10.5216i	0.267721	+	0.646335i
$266$		0			0
$267$	0.702996	−	1.69718i	0.0430226	−	0.103866i
$268$		0			0
$269$	20.5129	+	8.49673i	1.25069	+	0.518054i	0.907041	−	0.421042i	$-0.138336\pi$
$269$	20.5129	+	8.49673i	1.25069	+	0.518054i	0.343653	+	0.939097i	$0.388336\pi$
$270$		0			0
$271$	11.8379			0.719098			0.359549	−	0.933126i	$-0.382930\pi$
$271$	11.8379			0.719098			0.359549	+	0.933126i	$0.382930\pi$
$272$		0			0
$273$	5.66099			0.342619
$274$		0			0
$275$	14.3363	+	5.93830i	0.864513	+	0.358093i
$276$		0			0
$277$	7.20492	−	17.3942i	0.432902	−	1.04512i	−0.545445	−	0.838146i	$-0.683640\pi$
$277$	7.20492	−	17.3942i	0.432902	−	1.04512i	0.978347	−	0.206971i	$-0.0663605\pi$
$278$		0			0
$279$	3.19698	+	7.71819i	0.191398	+	0.462076i
$280$		0			0
$281$	16.6652	+	16.6652i	0.994164	+	0.994164i	0.999983	−	0.00581906i	$-0.00185228\pi$
$281$	16.6652	+	16.6652i	0.994164	+	0.994164i	−0.00581906	+	0.999983i	$0.501852\pi$
$282$		0			0
$283$	2.63035	−	1.08953i	0.156358	−	0.0647657i	−0.303132	−	0.952949i	$-0.598032\pi$
$283$	2.63035	−	1.08953i	0.156358	−	0.0647657i	0.459490	+	0.888183i	$0.348032\pi$
$284$		0			0
$285$		−	9.21468i		−	0.545830i
$286$		0			0
$287$	7.90255	−	7.90255i	0.466473	−	0.466473i
$288$		0			0
$289$	−9.29945	+	14.2310i	−0.547027	+	0.837115i
$290$		0			0
$291$	−8.80901	+	8.80901i	−0.516394	+	0.516394i
$292$		0			0
$293$		−	25.7688i		−	1.50543i	−0.658347	−	0.752715i	$-0.728744\pi$
$293$		−	25.7688i		−	1.50543i	0.658347	−	0.752715i	$-0.271256\pi$
$294$		0			0
$295$	0.0314041	−	0.0130080i	0.00182842	−	0.000757355i
$296$		0			0
$297$	2.94421	+	2.94421i	0.170841	+	0.170841i
$298$		0			0
$299$	−4.65396	−	11.2356i	−0.269145	−	0.649774i
$300$		0			0
$301$	−11.0402	+	26.6534i	−0.636347	+	1.53628i
$302$		0			0
$303$	−3.50491	−	1.45178i	−0.201352	−	0.0834027i
$304$		0			0
$305$	4.91350			0.281346
$306$		0			0
$307$	−34.5396			−1.97128			−0.985640	−	0.168859i	$-0.945992\pi$
$307$	−34.5396			−1.97128			−0.985640	+	0.168859i	$0.945992\pi$
$308$		0			0
$309$	15.2203	+	6.30445i	0.865852	+	0.358648i
$310$		0			0
$311$	−3.72089	+	8.98301i	−0.210992	+	0.509380i	−0.993576	−	0.113165i	$-0.963901\pi$
$311$	−3.72089	+	8.98301i	−0.210992	+	0.509380i	0.782584	+	0.622545i	$0.213901\pi$
$312$		0			0
$313$	−3.26511	−	7.88267i	−0.184555	−	0.445555i	0.804340	−	0.594169i	$-0.202519\pi$
$313$	−3.26511	−	7.88267i	−0.184555	−	0.445555i	−0.988895	+	0.148614i	$0.952519\pi$
$314$		0			0
$315$	−2.42557	−	2.42557i	−0.136665	−	0.136665i
$316$		0			0
$317$	−25.8225	+	10.6960i	−1.45034	+	0.600749i	−0.962280	−	0.272063i	$-0.912294\pi$
$317$	−25.8225	+	10.6960i	−1.45034	+	0.600749i	−0.488057	+	0.872812i	$0.662294\pi$
$318$		0			0
$319$			29.6602i			1.66065i
$320$		0			0
$321$	−6.55297	+	6.55297i	−0.365751	+	0.365751i
$322$		0			0
$323$	−32.2710	−	9.60915i	−1.79561	−	0.534667i
$324$		0			0
$325$	−4.90718	+	4.90718i	−0.272201	+	0.272201i
$326$		0			0
$327$		−	10.4061i		−	0.575459i
$328$		0			0
$329$	−13.9516	+	5.77895i	−0.769177	+	0.318604i
$330$		0			0
$331$	−19.0787	−	19.0787i	−1.04866	−	1.04866i	−0.998754	−	0.0499053i	$-0.984108\pi$
$331$	−19.0787	−	19.0787i	−1.04866	−	1.04866i	−0.0499053	−	0.998754i	$-0.515892\pi$
$332$		0			0
$333$	0.134047	+	0.323617i	0.00734571	+	0.0177341i
$334$		0			0
$335$	2.46273	−	5.94556i	0.134553	−	0.324841i
$336$		0			0
$337$	1.14872	+	0.475815i	0.0625747	+	0.0259193i	0.413751	−	0.910390i	$-0.364218\pi$
$337$	1.14872	+	0.475815i	0.0625747	+	0.0259193i	−0.351177	+	0.936309i	$0.614218\pi$
$338$		0			0
$339$	6.52751			0.354526
$340$		0			0
$341$	34.7844			1.88368
$342$		0			0
$343$	−13.3635	−	5.53535i	−0.721562	−	0.298881i
$344$		0			0
$345$	−2.82006	+	6.80823i	−0.151827	+	0.366543i
$346$		0			0
$347$	3.21081	+	7.75158i	0.172365	+	0.416127i	0.986329	−	0.164789i	$-0.0526944\pi$
$347$	3.21081	+	7.75158i	0.172365	+	0.416127i	−0.813963	+	0.580916i	$0.802694\pi$
$348$		0			0
$349$	−21.0987	−	21.0987i	−1.12939	−	1.12939i	−0.990277	−	0.139109i	$-0.955576\pi$
$349$	−21.0987	−	21.0987i	−1.12939	−	1.12939i	−0.139109	−	0.990277i	$-0.544424\pi$
$350$		0			0
$351$	−1.72038	+	0.712604i	−0.0918270	+	0.0380360i
$352$		0			0
$353$			28.4992i			1.51686i	0.651756	+	0.758429i	$0.274033\pi$
$353$			28.4992i			1.51686i	−0.651756	+	0.758429i	$0.725967\pi$
$354$		0			0
$355$	−3.44285	+	3.44285i	−0.182728	+	0.182728i
$356$		0			0
$357$	−11.0241	+	5.96526i	−0.583456	+	0.315715i
$358$		0			0
$359$	0.256594	−	0.256594i	0.0135425	−	0.0135425i	−0.700303	−	0.713846i	$-0.746952\pi$
$359$	0.256594	−	0.256594i	0.0135425	−	0.0135425i	0.713846	+	0.700303i	$0.246952\pi$
$360$		0			0
$361$		−	47.6915i		−	2.51008i
$362$		0			0
$363$	5.85441	−	2.42498i	0.307277	−	0.127278i
$364$		0			0
$365$	6.78092	+	6.78092i	0.354929	+	0.354929i
$366$		0			0
$367$	−1.52402	−	3.67930i	−0.0795530	−	0.192058i	0.879099	−	0.476640i	$-0.158145\pi$
$367$	−1.52402	−	3.67930i	−0.0795530	−	0.192058i	−0.958652	+	0.284582i	$0.908145\pi$
$368$		0			0
$369$	−1.40682	+	3.39636i	−0.0732361	+	0.176808i
$370$		0			0
$371$	28.3478	+	11.7420i	1.47174	+	0.609616i
$372$		0			0
$373$	28.5676			1.47918			0.739588	−	0.673060i	$-0.235020\pi$
$373$	28.5676			1.47918			0.739588	+	0.673060i	$0.235020\pi$
$374$		0			0
$375$	9.84693			0.508493
$376$		0			0
$377$	−12.2550	−	5.07620i	−0.631166	−	0.261437i
$378$		0			0
$379$	0.807955	−	1.95058i	0.0415018	−	0.100194i	−0.901769	−	0.432218i	$-0.857731\pi$
$379$	0.807955	−	1.95058i	0.0415018	−	0.100194i	0.943271	+	0.332023i	$0.107731\pi$
$380$		0			0
$381$	1.38117	+	3.33443i	0.0707593	+	0.170828i
$382$		0			0
$383$	−18.4619	−	18.4619i	−0.943358	−	0.943358i	0.0551214	−	0.998480i	$-0.482445\pi$
$383$	−18.4619	−	18.4619i	−0.943358	−	0.943358i	−0.998480	+	0.0551214i	$0.982445\pi$
$384$		0			0
$385$	−13.1956	+	5.46578i	−0.672508	+	0.278562i
$386$		0			0
$387$		−	9.48973i		−	0.482390i
$388$		0			0
$389$	−10.8944	+	10.8944i	−0.552366	+	0.552366i	−0.927123	−	0.374757i	$-0.877726\pi$
$389$	−10.8944	+	10.8944i	−0.552366	+	0.552366i	0.374757	+	0.927123i	$0.377726\pi$
$390$		0			0
$391$	20.9025	+	16.9759i	1.05709	+	0.858509i
$392$		0			0
$393$	−8.85502	+	8.85502i	−0.446677	+	0.446677i
$394$		0			0
$395$			9.96499i			0.501393i
$396$		0			0
$397$	−10.9520	+	4.53647i	−0.549666	+	0.227679i	−0.640192	−	0.768215i	$-0.721145\pi$
$397$	−10.9520	+	4.53647i	−0.549666	+	0.227679i	0.0905259	+	0.995894i	$0.471145\pi$
$398$		0			0
$399$	−17.5551	−	17.5551i	−0.878855	−	0.878855i
$400$		0			0
$401$	6.13786	+	14.8181i	0.306510	+	0.739980i	0.999813	+	0.0193343i	$0.00615469\pi$
$401$	6.13786	+	14.8181i	0.306510	+	0.739980i	−0.693303	+	0.720646i	$0.743845\pi$
$402$		0			0
$403$	−5.95317	+	14.3722i	−0.296549	+	0.715932i
$404$		0			0
$405$	1.04246	+	0.431802i	0.0518004	+	0.0214564i
$406$		0			0
$407$	1.45848			0.0722941
$408$		0			0
$409$	12.9679			0.641222			0.320611	−	0.947211i	$-0.396112\pi$
$409$	12.9679			0.641222			0.320611	+	0.947211i	$0.396112\pi$
$410$		0			0
$411$	6.42847	+	2.66276i	0.317093	+	0.131344i
$412$		0			0
$413$	0.0350469	−	0.0846107i	0.00172454	−	0.00416342i
$414$		0			0
$415$	6.18424	+	14.9301i	0.303573	+	0.732889i
$416$		0			0
$417$	−11.7502	−	11.7502i	−0.575411	−	0.575411i
$418$		0			0
$419$	−5.31947	+	2.20340i	−0.259873	+	0.107643i	−0.508816	−	0.860875i	$-0.669917\pi$
$419$	−5.31947	+	2.20340i	−0.259873	+	0.107643i	0.248943	+	0.968518i	$0.419917\pi$
$420$		0			0
$421$			7.37021i			0.359202i	0.983740	+	0.179601i	$0.0574807\pi$
$421$			7.37021i			0.359202i	−0.983740	+	0.179601i	$0.942519\pi$
$422$		0			0
$423$	3.51245	−	3.51245i	0.170781	−	0.170781i
$424$		0			0
$425$	4.38519	−	14.7271i	0.212713	−	0.714367i
$426$		0			0
$427$	9.36084	−	9.36084i	0.453003	−	0.453003i
$428$		0			0
$429$			7.75341i			0.374338i
$430$		0			0
$431$	−5.61283	+	2.32491i	−0.270361	+	0.111987i	−0.513745	−	0.857943i	$-0.671742\pi$
$431$	−5.61283	+	2.32491i	−0.270361	+	0.111987i	0.243385	+	0.969930i	$0.421742\pi$
$432$		0			0
$433$	24.3577	+	24.3577i	1.17056	+	1.17056i	0.982077	+	0.188478i	$0.0603554\pi$
$433$	24.3577	+	24.3577i	1.17056	+	1.17056i	0.188478	+	0.982077i	$0.439645\pi$
$434$		0			0
$435$	3.07592	+	7.42592i	0.147479	+	0.356046i
$436$		0			0
$437$	−20.4103	+	49.2748i	−0.976356	+	2.35713i
$438$		0			0
$439$	−37.1481	−	15.3872i	−1.77298	−	0.734392i	−0.994256	−	0.107026i	$-0.965867\pi$
$439$	−37.1481	−	15.3872i	−1.77298	−	0.734392i	−0.778724	−	0.627367i	$-0.784133\pi$
$440$		0			0
$441$	−2.24203			−0.106763
$442$		0			0
$443$	−12.5677			−0.597111			−0.298556	−	0.954392i	$-0.596505\pi$
$443$	−12.5677			−0.597111			−0.298556	+	0.954392i	$0.596505\pi$
$444$		0			0
$445$	−1.91502	−	0.793227i	−0.0907807	−	0.0376026i
$446$		0			0
$447$	5.05286	−	12.1987i	0.238992	−	0.576978i
$448$		0			0
$449$	−11.6152	−	28.0416i	−0.548156	−	1.32337i	−0.918848	−	0.394611i	$-0.870879\pi$
$449$	−11.6152	−	28.0416i	−0.548156	−	1.32337i	0.370692	−	0.928756i	$-0.379121\pi$
$450$		0			0
$451$	10.8235	+	10.8235i	0.509659	+	0.509659i
$452$		0			0
$453$	3.46674	−	1.43597i	0.162882	−	0.0674677i
$454$		0			0
$455$		−	6.38759i		−	0.299455i
$456$		0			0
$457$	−25.4059	+	25.4059i	−1.18844	+	1.18844i	−0.210939	+	0.977499i	$0.567652\pi$
$457$	−25.4059	+	25.4059i	−1.18844	+	1.18844i	−0.977499	+	0.210939i	$0.932348\pi$
$458$		0			0
$459$	2.59932	−	3.20055i	0.121326	−	0.149389i
$460$		0			0
$461$	6.83520	−	6.83520i	0.318347	−	0.318347i	−0.529785	−	0.848132i	$-0.677727\pi$
$461$	6.83520	−	6.83520i	0.318347	−	0.318347i	0.848132	+	0.529785i	$0.177727\pi$
$462$		0			0
$463$		−	19.7693i		−	0.918758i	−0.888240	−	0.459379i	$-0.848072\pi$
$463$		−	19.7693i		−	0.918758i	0.888240	−	0.459379i	$-0.151928\pi$
$464$		0			0
$465$	8.70884	−	3.60732i	0.403863	−	0.167286i
$466$		0			0
$467$	7.85421	+	7.85421i	0.363450	+	0.363450i	0.865081	−	0.501632i	$-0.167267\pi$
$467$	7.85421	+	7.85421i	0.363450	+	0.363450i	−0.501632	+	0.865081i	$0.667267\pi$
$468$		0			0
$469$	−6.63523	−	16.0189i	−0.306386	−	0.739682i
$470$		0			0
$471$	−3.70763	+	8.95102i	−0.170839	+	0.412441i
$472$		0			0
$473$	−36.5051	−	15.1209i	−1.67851	−	0.695260i
$474$		0			0
$475$	30.4350			1.39645
$476$		0			0
$477$	−10.0930			−0.462127
$478$		0			0
$479$	−12.3588	−	5.11917i	−0.564686	−	0.233901i	0.0820320	−	0.996630i	$-0.473859\pi$
$479$	−12.3588	−	5.11917i	−0.564686	−	0.233901i	−0.646718	+	0.762729i	$0.723859\pi$
$480$		0			0
$481$	−0.249612	+	0.602616i	−0.0113813	+	0.0274769i
$482$		0			0
$483$	7.59797	+	18.3431i	0.345719	+	0.834640i
$484$		0			0
$485$	9.93968	+	9.93968i	0.451338	+	0.451338i
$486$		0			0
$487$	7.07504	−	2.93058i	0.320601	−	0.132797i	−0.216579	−	0.976265i	$-0.569490\pi$
$487$	7.07504	−	2.93058i	0.320601	−	0.132797i	0.537179	+	0.843468i	$0.319490\pi$
$488$		0			0
$489$		−	3.40920i		−	0.154169i
$490$		0			0
$491$	29.4129	−	29.4129i	1.32739	−	1.32739i	0.419743	−	0.907643i	$-0.362120\pi$
$491$	29.4129	−	29.4129i	1.32739	−	1.32739i	0.907643	−	0.419743i	$-0.137880\pi$
$492$		0			0
$493$	29.2142	−	3.02846i	1.31574	−	0.136395i
$494$		0			0
$495$	3.32211	−	3.32211i	0.149318	−	0.149318i
$496$		0			0
$497$			13.1181i			0.588429i
$498$		0			0
$499$	−39.9562	+	16.5504i	−1.78869	+	0.740898i	−0.798352	+	0.602190i	$0.794295\pi$
$499$	−39.9562	+	16.5504i	−1.78869	+	0.740898i	−0.990333	+	0.138707i	$0.955705\pi$
$500$		0			0
$501$	10.7211	+	10.7211i	0.478982	+	0.478982i
$502$		0			0
$503$	−6.36358	−	15.3630i	−0.283738	−	0.685004i	0.716179	−	0.697917i	$-0.245890\pi$
$503$	−6.36358	−	15.3630i	−0.283738	−	0.685004i	−0.999917	+	0.0129131i	$0.995890\pi$
$504$		0			0
$505$	−1.63812	+	3.95478i	−0.0728955	+	0.175985i
$506$		0			0
$507$	8.80688	+	3.64793i	0.391127	+	0.162010i
$508$		0			0
$509$	−6.81530			−0.302083			−0.151041	−	0.988527i	$-0.548263\pi$
$509$	−6.81530			−0.302083			−0.151041	+	0.988527i	$0.548263\pi$
$510$		0			0
$511$	25.8370			1.14296
$512$		0			0
$513$	7.54485	+	3.12518i	0.333113	+	0.137980i
$514$		0			0
$515$	7.11364	−	17.1739i	0.313465	−	0.756771i
$516$		0			0
$517$	−7.91496	−	19.1084i	−0.348100	−	0.840387i
$518$		0			0
$519$	−10.2605	−	10.2605i	−0.450385	−	0.450385i
$520$		0			0
$521$	−28.0793	+	11.6308i	−1.23017	+	0.509555i	−0.900631	−	0.434585i	$-0.856895\pi$
$521$	−28.0793	+	11.6308i	−1.23017	+	0.509555i	−0.329544	+	0.944140i	$0.606895\pi$
$522$		0			0
$523$		−	3.84347i		−	0.168063i	−0.996463	−	0.0840316i	$-0.973220\pi$
$523$		−	3.84347i		−	0.168063i	0.996463	−	0.0840316i	$-0.0267797\pi$
$524$		0			0
$525$	8.01137	−	8.01137i	0.349645	−	0.349645i
$526$		0			0
$527$	−3.55166	−	34.2613i	−0.154713	−	1.49244i
$528$		0			0
$529$	13.8967	−	13.8967i	0.604202	−	0.604202i
$530$		0			0
$531$			0.0301249i			0.00130731i
$532$		0			0
$533$	−6.32445	+	2.61967i	−0.273942	+	0.113471i
$534$		0			0
$535$	7.39406	+	7.39406i	0.319673	+	0.319673i
$536$		0			0
$537$	1.95768	+	4.72625i	0.0844801	+	0.203953i
$538$		0			0
$539$	−3.57244	+	8.62464i	−0.153876	+	0.371489i
$540$		0			0
$541$	11.0504	+	4.57722i	0.475093	+	0.196790i	0.607364	−	0.794424i	$-0.292227\pi$
$541$	11.0504	+	4.57722i	0.475093	+	0.196790i	−0.132271	+	0.991214i	$0.542227\pi$
$542$		0			0
$543$	4.32737			0.185705
$544$		0			0
$545$	−11.7418			−0.502962
$546$		0			0
$547$	−30.7478	−	12.7362i	−1.31468	−	0.544559i	−0.388435	−	0.921476i	$-0.626984\pi$
$547$	−30.7478	−	12.7362i	−1.31468	−	0.544559i	−0.926247	+	0.376917i	$0.876984\pi$
$548$		0			0
$549$	−1.66642	+	4.02310i	−0.0711213	+	0.171702i
$550$		0			0
$551$	22.2620	+	53.7453i	0.948395	+	2.28963i
$552$		0			0
$553$	18.9846	+	18.9846i	0.807306	+	0.807306i
$554$		0			0
$555$	0.365154	−	0.151252i	0.0154999	−	0.00642029i
$556$		0			0
$557$		−	13.0840i		−	0.554389i	−0.960814	−	0.277194i	$-0.910595\pi$
$557$		−	13.0840i		−	0.554389i	0.960814	−	0.277194i	$-0.0894046\pi$
$558$		0			0
$559$	12.4953	−	12.4953i	0.528496	−	0.528496i
$560$		0			0
$561$	−8.17015	−	15.0988i	−0.344944	−	0.637472i
$562$		0			0
$563$	−4.54370	+	4.54370i	−0.191494	+	0.191494i	−0.796341	−	0.604847i	$-0.793234\pi$
$563$	−4.54370	+	4.54370i	−0.191494	+	0.191494i	0.604847	+	0.796341i	$0.293234\pi$
$564$		0			0
$565$		−	7.36533i		−	0.309862i
$566$		0			0
$567$	2.80866	−	1.16338i	0.117953	−	0.0488576i
$568$		0			0
$569$	8.58835	+	8.58835i	0.360043	+	0.360043i	0.863828	−	0.503786i	$-0.168060\pi$
$569$	8.58835	+	8.58835i	0.360043	+	0.360043i	−0.503786	+	0.863828i	$0.668060\pi$
$570$		0			0
$571$	−3.61810	−	8.73487i	−0.151413	−	0.365543i	0.829914	−	0.557892i	$-0.188390\pi$
$571$	−3.61810	−	8.73487i	−0.151413	−	0.365543i	−0.981327	+	0.192349i	$0.938390\pi$
$572$		0			0
$573$	5.23918	−	12.6485i	0.218870	−	0.528398i
$574$		0			0
$575$	−22.4868	−	9.31434i	−0.937764	−	0.388435i
$576$		0			0
$577$	−27.5966			−1.14886			−0.574432	−	0.818552i	$-0.694777\pi$
$577$	−27.5966			−1.14886			−0.574432	+	0.818552i	$0.694777\pi$
$578$		0			0
$579$	17.2997			0.718951
$580$		0			0
$581$	40.2255	+	16.6619i	1.66883	+	0.691253i
$582$		0			0
$583$	−16.0821	+	38.8257i	−0.666054	+	1.60800i
$584$		0			0
$585$	0.804069	+	1.94119i	0.0332442	+	0.0802585i
$586$		0			0
$587$	−25.8311	−	25.8311i	−1.06616	−	1.06616i	−0.997650	−	0.0685130i	$-0.978175\pi$
$587$	−25.8311	−	25.8311i	−1.06616	−	1.06616i	−0.0685130	−	0.997650i	$-0.521825\pi$
$588$		0			0
$589$	63.0305	−	26.1081i	2.59713	−	1.07576i
$590$		0			0
$591$		−	5.16644i		−	0.212519i
$592$		0			0
$593$	14.0302	−	14.0302i	0.576153	−	0.576153i	−0.357688	−	0.933841i	$-0.616435\pi$
$593$	14.0302	−	14.0302i	0.576153	−	0.576153i	0.933841	+	0.357688i	$0.116435\pi$
$594$		0			0
$595$	6.73092	+	12.4390i	0.275941	+	0.509951i
$596$		0			0
$597$	−18.0450	+	18.0450i	−0.738532	+	0.738532i
$598$		0			0
$599$		−	3.58892i		−	0.146639i	−0.997308	−	0.0733197i	$-0.976641\pi$
$599$		−	3.58892i		−	0.146639i	0.997308	−	0.0733197i	$-0.0233593\pi$
$600$		0			0
$601$	16.7615	−	6.94283i	0.683715	−	0.283204i	−0.0136638	−	0.999907i	$-0.504349\pi$
$601$	16.7615	−	6.94283i	0.683715	−	0.283204i	0.697379	+	0.716703i	$0.254349\pi$
$602$		0			0
$603$	4.03290	+	4.03290i	0.164232	+	0.164232i
$604$		0			0
$605$	−2.73623	−	6.60584i	−0.111244	−	0.268566i
$606$		0			0
$607$	−2.35548	+	5.68663i	−0.0956060	+	0.230813i	−0.964446	−	0.264279i	$-0.914866\pi$
$607$	−2.35548	+	5.68663i	−0.0956060	+	0.230813i	0.868840	+	0.495093i	$0.164866\pi$
$608$		0			0
$609$	20.0073	+	8.28731i	0.810738	+	0.335819i
$610$		0			0
$611$	9.24983			0.374208
$612$		0			0
$613$	29.6968			1.19944			0.599721	−	0.800209i	$-0.295278\pi$
$613$	29.6968			1.19944			0.599721	+	0.800209i	$0.295278\pi$
$614$		0			0
$615$	3.83229	+	1.58739i	0.154533	+	0.0640097i
$616$		0			0
$617$	−2.30270	+	5.55921i	−0.0927033	+	0.223806i	−0.963429	−	0.267963i	$-0.913649\pi$
$617$	−2.30270	+	5.55921i	−0.0927033	+	0.223806i	0.870726	+	0.491769i	$0.163649\pi$
$618$		0			0
$619$	−5.36614	−	12.9550i	−0.215683	−	0.520706i	0.778595	−	0.627527i	$-0.215933\pi$
$619$	−5.36614	−	12.9550i	−0.215683	−	0.520706i	−0.994278	+	0.106821i	$0.965933\pi$
$620$		0			0
$621$	−4.61805	−	4.61805i	−0.185316	−	0.185316i
$622$		0			0
$623$	−5.15955	+	2.13716i	−0.206713	+	0.0856234i
$624$		0			0
$625$			7.52328i			0.300931i
$626$		0			0
$627$	24.0439	−	24.0439i	0.960219	−	0.960219i
$628$		0			0
$629$	−0.148918	−	1.43655i	−0.00593775	−	0.0572789i
$630$		0			0
$631$	−0.675270	+	0.675270i	−0.0268821	+	0.0268821i	−0.720420	−	0.693538i	$-0.756051\pi$
$631$	−0.675270	+	0.675270i	−0.0268821	+	0.0268821i	0.693538	+	0.720420i	$0.256051\pi$
$632$		0			0
$633$			9.89308i			0.393215i
$634$		0			0
$635$	3.76242	−	1.55844i	0.149307	−	0.0618450i
$636$		0			0
$637$	−2.95213	−	2.95213i	−0.116968	−	0.116968i
$638$		0			0
$639$	−1.65131	−	3.98661i	−0.0653247	−	0.157708i
$640$		0			0
$641$	9.44907	−	22.8121i	0.373216	−	0.901023i	−0.619986	−	0.784613i	$-0.712862\pi$
$641$	9.44907	−	22.8121i	0.373216	−	0.901023i	0.993201	−	0.116409i	$-0.0371384\pi$
$642$		0			0
$643$	22.5279	+	9.33134i	0.888412	+	0.367992i	0.779753	−	0.626087i	$-0.215344\pi$
$643$	22.5279	+	9.33134i	0.888412	+	0.367992i	0.108659	+	0.994079i	$0.465344\pi$
$644$		0			0
$645$	−10.7078			−0.421618
$646$		0			0
$647$	−14.0125			−0.550889			−0.275444	−	0.961317i	$-0.588825\pi$
$647$	−14.0125			−0.550889			−0.275444	+	0.961317i	$0.588825\pi$
$648$		0			0
$649$	0.115885	+	0.0480009i	0.00454887	+	0.00188420i
$650$		0			0
$651$	9.71904	−	23.4638i	0.380919	−	0.919621i
$652$		0			0
$653$	6.66788	+	16.0977i	0.260934	+	0.629952i	0.998997	−	0.0447809i	$-0.0142590\pi$
$653$	6.66788	+	16.0977i	0.260934	+	0.629952i	−0.738062	+	0.674733i	$0.764259\pi$
$654$		0			0
$655$	9.99159	+	9.99159i	0.390404	+	0.390404i
$656$		0			0
$657$	−7.85188	+	3.25236i	−0.306331	+	0.126886i
$658$		0			0
$659$			5.78554i			0.225373i	0.993631	+	0.112686i	$0.0359455\pi$
$659$			5.78554i			0.225373i	−0.993631	+	0.112686i	$0.964054\pi$
$660$		0			0
$661$	1.07951	−	1.07951i	0.0419881	−	0.0419881i	−0.685801	−	0.727789i	$-0.740548\pi$
$661$	1.07951	−	1.07951i	0.0419881	−	0.0419881i	0.727789	+	0.685801i	$0.240548\pi$
$662$		0			0
$663$	7.63681	−	0.791662i	0.296589	−	0.0307456i
$664$		0			0
$665$	−19.8084	+	19.8084i	−0.768136	+	0.768136i
$666$		0			0
$667$		−	46.5226i		−	1.80136i
$668$		0			0
$669$	19.6640	−	8.14509i	0.760253	−	0.314907i
$670$		0			0
$671$	12.8208	+	12.8208i	0.494941	+	0.494941i
$672$		0			0
$673$	−15.5659	−	37.5795i	−0.600023	−	1.44858i	−0.873557	−	0.486721i	$-0.838193\pi$
$673$	−15.5659	−	37.5795i	−0.600023	−	1.44858i	0.273535	−	0.961862i	$-0.411807\pi$
$674$		0			0
$675$	−1.42619	+	3.44313i	−0.0548942	+	0.132526i
$676$		0			0
$677$	−11.7647	−	4.87309i	−0.452153	−	0.187288i	0.144973	−	0.989436i	$-0.453691\pi$
$677$	−11.7647	−	4.87309i	−0.452153	−	0.187288i	−0.597126	+	0.802148i	$0.703691\pi$
$678$		0			0
$679$	37.8727			1.45342
$680$		0			0
$681$	17.6770			0.677383
$682$		0			0
$683$	−9.56229	−	3.96083i	−0.365891	−	0.151557i	0.192160	−	0.981364i	$-0.438451\pi$
$683$	−9.56229	−	3.96083i	−0.365891	−	0.151557i	−0.558051	+	0.829807i	$0.688451\pi$
$684$		0			0
$685$	3.00453	−	7.25359i	0.114797	−	0.277145i
$686$		0			0
$687$	3.87530	+	9.35580i	0.147852	+	0.356946i
$688$		0			0
$689$	−13.2897	−	13.2897i	−0.506296	−	0.506296i
$690$		0			0
$691$	3.77755	−	1.56471i	0.143705	−	0.0595245i	−0.309672	−	0.950843i	$-0.600219\pi$
$691$	3.77755	−	1.56471i	0.143705	−	0.0595245i	0.453377	+	0.891319i	$0.350219\pi$
$692$		0			0
$693$		−	12.6581i		−	0.480841i
$694$		0			0
$695$	−13.2584	+	13.2584i	−0.502920	+	0.502920i
$696$		0			0
$697$	9.55560	−	11.7659i	0.361944	−	0.445664i
$698$		0			0
$699$	10.5883	−	10.5883i	0.400487	−	0.400487i
$700$		0			0
$701$		−	34.7020i		−	1.31068i	−0.755336	−	0.655338i	$-0.772526\pi$
$701$		−	34.7020i		−	1.31068i	0.755336	−	0.655338i	$-0.227474\pi$
$702$		0			0
$703$	2.64282	−	1.09469i	0.0996757	−	0.0412870i
$704$		0			0
$705$	−3.96328	−	3.96328i	−0.149266	−	0.149266i
$706$		0			0
$707$	4.41352	+	10.6552i	0.165988	+	0.400729i
$708$		0			0
$709$	5.14435	−	12.4195i	0.193200	−	0.466426i	−0.797360	−	0.603503i	$-0.793771\pi$
$709$	5.14435	−	12.4195i	0.193200	−	0.466426i	0.990560	+	0.137078i	$0.0437709\pi$
$710$		0			0
$711$	−8.15920	−	3.37965i	−0.305994	−	0.126747i
$712$		0			0
$713$	−54.5600			−2.04329
$714$		0			0
$715$	8.74858			0.327178
$716$		0			0
$717$	9.15022	+	3.79014i	0.341721	+	0.141546i
$718$		0			0
$719$	−14.8983	+	35.9677i	−0.555613	+	1.34137i	0.357596	+	0.933876i	$0.383597\pi$
$719$	−14.8983	+	35.9677i	−0.555613	+	1.34137i	−0.913209	+	0.407492i	$0.866403\pi$
$720$		0			0
$721$	−19.1660	−	46.2707i	−0.713778	−	1.72321i
$722$		0			0
$723$	−6.76697	−	6.76697i	−0.251666	−	0.251666i
$724$		0			0
$725$	−24.5270	+	10.1594i	−0.910909	+	0.377311i
$726$		0			0
$727$			18.9158i			0.701549i	0.936460	+	0.350775i	$0.114082\pi$
$727$			18.9158i			0.701549i	−0.936460	+	0.350775i	$0.885918\pi$
$728$		0			0
$729$	−0.707107	+	0.707107i	−0.0261891	+	0.0261891i
$730$		0			0
$731$	−11.1662	+	37.5000i	−0.412995	+	1.38699i
$732$		0			0
$733$	11.8968	−	11.8968i	0.439419	−	0.439419i	−0.452397	−	0.891817i	$-0.649431\pi$
$733$	11.8968	−	11.8968i	0.439419	−	0.439419i	0.891817	+	0.452397i	$0.149431\pi$
$734$		0			0
$735$			2.52980i			0.0933131i
$736$		0			0
$737$	21.9398	−	9.08775i	0.808162	−	0.334751i
$738$		0			0
$739$	−2.89713	−	2.89713i	−0.106573	−	0.106573i	0.651810	−	0.758382i	$-0.274010\pi$
$739$	−2.89713	−	2.89713i	−0.106573	−	0.106573i	−0.758382	+	0.651810i	$0.774010\pi$
$740$		0			0
$741$	5.81947	+	14.0494i	0.213784	+	0.516119i
$742$		0			0
$743$	8.78506	−	21.2090i	0.322292	−	0.778083i	−0.676828	−	0.736142i	$-0.736646\pi$
$743$	8.78506	−	21.2090i	0.322292	−	0.778083i	0.999120	−	0.0419412i	$-0.0133542\pi$
$744$		0			0
$745$	−13.7644	−	5.70141i	−0.504289	−	0.208884i
$746$		0			0
$747$	−14.3219			−0.524012
$748$		0			0
$749$	28.1732			1.02943
$750$		0			0
$751$	−13.5006	−	5.59214i	−0.492644	−	0.204060i	0.122509	−	0.992467i	$-0.460906\pi$
$751$	−13.5006	−	5.59214i	−0.492644	−	0.204060i	−0.615153	+	0.788407i	$0.710906\pi$
$752$		0			0
$753$	4.62665	−	11.1697i	0.168605	−	0.407047i
$754$		0			0
$755$	−1.62028	−	3.91170i	−0.0589681	−	0.142361i
$756$		0			0
$757$	23.6323	+	23.6323i	0.858932	+	0.858932i	0.991212	−	0.132281i	$-0.0422301\pi$
$757$	23.6323	+	23.6323i	0.858932	+	0.858932i	−0.132281	+	0.991212i	$0.542230\pi$
$758$		0			0
$759$	−25.1231	+	10.4063i	−0.911911	+	0.377726i
$760$		0			0
$761$		−	1.19606i		−	0.0433573i	−0.999765	−	0.0216786i	$-0.993099\pi$
$761$		−	1.19606i		−	0.0433573i	0.999765	−	0.0216786i	$-0.00690106\pi$
$762$		0			0
$763$	−22.3695	+	22.3695i	−0.809832	+	0.809832i
$764$		0			0
$765$	−3.61136	−	2.93295i	−0.130569	−	0.106041i
$766$		0			0
$767$	−0.0396661	+	0.0396661i	−0.00143226	+	0.00143226i
$768$		0			0
$769$			4.75309i			0.171401i	0.996321	+	0.0857004i	$0.0273128\pi$
$769$			4.75309i			0.171401i	−0.996321	+	0.0857004i	$0.972687\pi$
$770$		0			0
$771$	−21.4300	+	8.87660i	−0.771783	+	0.319683i
$772$		0			0
$773$	−17.9671	−	17.9671i	−0.646232	−	0.646232i	0.305849	−	0.952080i	$-0.401060\pi$
$773$	−17.9671	−	17.9671i	−0.646232	−	0.646232i	−0.952080	+	0.305849i	$0.901060\pi$
$774$		0			0
$775$	11.9146	+	28.7643i	0.427984	+	1.03324i
$776$		0			0
$777$	0.407511	−	0.983819i	0.0146194	−	0.0352943i
$778$		0			0
$779$	27.7363	+	11.4888i	0.993757	+	0.411628i
$780$		0			0
$781$	−17.9669			−0.642905
$782$		0			0
$783$	−7.12345			−0.254571
$784$		0			0
$785$	10.0999	+	4.18352i	0.360481	+	0.149316i
$786$		0			0
$787$	−12.5428	+	30.2811i	−0.447103	+	1.07940i	0.526299	+	0.850300i	$0.323579\pi$
$787$	−12.5428	+	30.2811i	−0.447103	+	1.07940i	−0.973402	+	0.229103i	$0.926421\pi$
$788$		0			0
$789$	0.291504	+	0.703753i	0.0103778	+	0.0250543i
$790$		0			0
$791$	−14.0319	−	14.0319i	−0.498917	−	0.498917i
$792$		0			0
$793$	−7.49152	+	3.10309i	−0.266032	+	0.110194i
$794$		0			0
$795$			11.3885i			0.403907i
$796$		0			0
$797$	−24.6843	+	24.6843i	−0.874362	+	0.874362i	−0.992944	−	0.118583i	$-0.962165\pi$
$797$	−24.6843	+	24.6843i	−0.874362	+	0.874362i	0.118583	+	0.992944i	$0.462165\pi$
$798$		0			0
$799$	−18.0129	+	9.74700i	−0.637251	+	0.344824i
$800$		0			0
$801$	1.29897	−	1.29897i	0.0458967	−	0.0458967i
$802$		0			0
$803$			35.3869i			1.24878i
$804$		0			0
$805$	20.6975	−	8.57319i	0.729491	−	0.302165i
$806$		0			0
$807$	15.6999	+	15.6999i	0.552663	+	0.552663i
$808$		0			0
$809$	15.7969	+	38.1372i	0.555390	+	1.34083i	0.913381	+	0.407106i	$0.133462\pi$
$809$	15.7969	+	38.1372i	0.555390	+	1.34083i	−0.357990	+	0.933725i	$0.616538\pi$
$810$		0			0
$811$	−6.61194	+	15.9626i	−0.232176	+	0.560524i	−0.996433	−	0.0843889i	$-0.973106\pi$
$811$	−6.61194	+	15.9626i	−0.232176	+	0.560524i	0.764256	+	0.644913i	$0.223106\pi$
$812$		0			0
$813$	10.9367	+	4.53015i	0.383569	+	0.158879i
$814$		0			0
$815$	−3.84678			−0.134747
$816$		0			0
$817$	−77.4978			−2.71130
$818$		0			0
$819$	5.23007	+	2.16637i	0.182754	+	0.0756990i
$820$		0			0
$821$	14.0626	−	33.9501i	0.490788	−	1.18487i	−0.463532	−	0.886080i	$-0.653418\pi$
$821$	14.0626	−	33.9501i	0.490788	−	1.18487i	0.954320	−	0.298787i	$-0.0965821\pi$
$822$		0			0
$823$	7.79341	+	18.8150i	0.271661	+	0.655848i	0.999555	−	0.0298422i	$-0.00950048\pi$
$823$	7.79341	+	18.8150i	0.271661	+	0.655848i	−0.727893	+	0.685690i	$0.759500\pi$
$824$		0			0
$825$	10.9725	+	10.9725i	0.382015	+	0.382015i
$826$		0			0
$827$	29.0481	−	12.0321i	1.01010	−	0.418398i	0.184610	−	0.982812i	$-0.440898\pi$
$827$	29.0481	−	12.0321i	1.01010	−	0.418398i	0.825492	+	0.564414i	$0.190898\pi$
$828$		0			0
$829$		−	4.24281i		−	0.147359i	−0.997282	−	0.0736794i	$-0.976526\pi$
$829$		−	4.24281i		−	0.147359i	0.997282	−	0.0736794i	$-0.0234742\pi$
$830$		0			0
$831$	13.3130	−	13.3130i	0.461821	−	0.461821i
$832$		0			0
$833$	8.85970	+	2.63810i	0.306970	+	0.0914047i
$834$		0			0
$835$	12.0971	−	12.0971i	0.418639	−	0.418639i
$836$		0			0
$837$			8.35411i			0.288760i
$838$		0			0
$839$	9.78940	−	4.05490i	0.337967	−	0.139991i	−0.207244	−	0.978289i	$-0.566449\pi$
$839$	9.78940	−	4.05490i	0.337967	−	0.139991i	0.545211	+	0.838299i	$0.316449\pi$
$840$		0			0
$841$	−15.3750	−	15.3750i	−0.530171	−	0.530171i
$842$		0			0
$843$	9.01916	+	21.7742i	0.310636	+	0.749942i
$844$		0			0
$845$	4.11615	−	9.93726i	0.141600	−	0.341852i
$846$		0			0
$847$	−17.7978	−	7.37210i	−0.611540	−	0.253308i
$848$		0			0
$849$	2.84707			0.0977113
$850$		0			0
$851$	−2.28765			−0.0784198
$852$		0			0
$853$	−23.7180	−	9.82433i	−0.812090	−	0.336379i	−0.0623025	−	0.998057i	$-0.519844\pi$
$853$	−23.7180	−	9.82433i	−0.812090	−	0.336379i	−0.749788	+	0.661679i	$0.769844\pi$
$854$		0			0
$855$	3.52630	−	8.51325i	0.120597	−	0.291147i
$856$		0			0
$857$	1.45297	+	3.50777i	0.0496324	+	0.119823i	0.946751	−	0.321966i	$-0.104344\pi$
$857$	1.45297	+	3.50777i	0.0496324	+	0.119823i	−0.897119	+	0.441790i	$0.854344\pi$
$858$		0			0
$859$	24.7280	+	24.7280i	0.843709	+	0.843709i	0.989339	−	0.145631i	$-0.0465211\pi$
$859$	24.7280	+	24.7280i	0.843709	+	0.843709i	−0.145631	+	0.989339i	$0.546521\pi$
$860$		0			0
$861$	10.3252	−	4.27683i	0.351881	−	0.145754i
$862$		0			0
$863$		−	13.1041i		−	0.446069i	−0.974811	−	0.223035i	$-0.928404\pi$
$863$		−	13.1041i		−	0.446069i	0.974811	−	0.223035i	$-0.0715963\pi$
$864$		0			0
$865$	−11.5774	+	11.5774i	−0.393645	+	0.393645i
$866$		0			0
$867$	−14.0375	+	9.58895i	−0.476739	+	0.325658i
$868$		0			0
$869$	−26.0017	+	26.0017i	−0.882046	+	0.882046i
$870$		0			0
$871$			10.6204i			0.359859i
$872$		0			0
$873$	−11.5095	+	4.76740i	−0.389539	+	0.161352i
$874$		0			0
$875$	−21.1675	−	21.1675i	−0.715592	−	0.715592i
$876$		0			0
$877$	17.9543	+	43.3456i	0.606275	+	1.46368i	0.867022	+	0.498270i	$0.166031\pi$
$877$	17.9543	+	43.3456i	0.606275	+	1.46368i	−0.260747	+	0.965407i	$0.583969\pi$
$878$		0			0
$879$	9.86129	−	23.8073i	0.332613	−	0.802999i
$880$		0			0
$881$	−5.25764	−	2.17779i	−0.177134	−	0.0733715i	0.292354	−	0.956310i	$-0.405562\pi$
$881$	−5.25764	−	2.17779i	−0.177134	−	0.0733715i	−0.469488	+	0.882939i	$0.655562\pi$
$882$		0			0
$883$	−22.1929			−0.746851			−0.373426	−	0.927660i	$-0.621817\pi$
$883$	−22.1929			−0.746851			−0.373426	+	0.927660i	$0.621817\pi$
$884$		0			0
$885$	0.0339916			0.00114261
$886$		0			0
$887$	−29.9326	−	12.3985i	−1.00504	−	0.416301i	−0.181397	−	0.983410i	$-0.558062\pi$
$887$	−29.9326	−	12.3985i	−1.00504	−	0.416301i	−0.823643	+	0.567109i	$0.808062\pi$
$888$		0			0
$889$	4.19885	−	10.1369i	0.140825	−	0.339981i
$890$		0			0
$891$	1.59340	+	3.84680i	0.0533808	+	0.128873i
$892$		0			0
$893$	−28.6844	−	28.6844i	−0.959886	−	0.959886i
$894$		0			0
$895$	5.33288	−	2.20895i	0.178259	−	0.0738371i
$896$		0			0
$897$		−	12.1614i		−	0.406056i
$898$		0			0
$899$	−42.0800	+	42.0800i	−1.40345	+	1.40345i
$900$		0			0
$901$	39.8839	+	11.8760i	1.32873	+	0.395647i
$902$		0			0
$903$	−20.3996	+	20.3996i	−0.678858	+	0.678858i
$904$		0			0
$905$		−	4.88280i		−	0.162310i
$906$		0			0
$907$	−6.98093	+	2.89160i	−0.231798	+	0.0960139i	−0.495559	−	0.868574i	$-0.665037\pi$
$907$	−6.98093	+	2.89160i	−0.231798	+	0.0960139i	0.263761	+	0.964588i	$0.415037\pi$
$908$		0			0
$909$	−2.68254	−	2.68254i	−0.0889744	−	0.0889744i
$910$		0			0
$911$	−1.92896	−	4.65692i	−0.0639093	−	0.154291i	0.888698	−	0.458492i	$-0.151610\pi$
$911$	−1.92896	−	4.65692i	−0.0639093	−	0.154291i	−0.952608	+	0.304202i	$0.901610\pi$
$912$		0			0
$913$	−22.8205	+	55.0936i	−0.755249	+	1.82333i
$914$		0			0
$915$	4.53948	+	1.88031i	0.150071	+	0.0621613i
$916$		0			0
$917$	38.0705			1.25720
$918$		0			0
$919$	−38.3451			−1.26489			−0.632444	−	0.774606i	$-0.717948\pi$
$919$	−38.3451			−1.26489			−0.632444	+	0.774606i	$0.717948\pi$
$920$		0			0
$921$	−31.9105	−	13.2177i	−1.05149	−	0.435539i
$922$		0			0
$923$	3.07494	−	7.42356i	0.101213	−	0.244350i
$924$		0			0
$925$	0.499568	+	1.20606i	0.0164257	+	0.0396551i
$926$		0			0
$927$	11.6491	+	11.6491i	0.382607	+	0.382607i
$928$		0			0
$929$	−33.7519	+	13.9805i	−1.10736	+	0.458685i	−0.860029	−	0.510245i	$-0.829555\pi$
$929$	−33.7519	+	13.9805i	−1.10736	+	0.458685i	−0.247335	+	0.968930i	$0.579555\pi$
$930$		0			0
$931$			18.3095i			0.600070i
$932$		0			0
$933$	−6.87530	+	6.87530i	−0.225087	+	0.225087i
$934$		0			0
$935$	−17.0368	+	9.21881i	−0.557162	+	0.301487i
$936$		0			0
$937$	33.2508	−	33.2508i	1.08626	−	1.08626i	0.0903462	−	0.995910i	$-0.471203\pi$
$937$	33.2508	−	33.2508i	1.08626	−	1.08626i	0.995910	−	0.0903462i	$-0.0287974\pi$
$938$		0			0
$939$		−	8.53214i		−	0.278436i
$940$		0			0
$941$	−9.34074	+	3.86906i	−0.304500	+	0.126128i	−0.529701	−	0.848184i	$-0.677696\pi$
$941$	−9.34074	+	3.86906i	−0.304500	+	0.126128i	0.225202	+	0.974312i	$0.427696\pi$
$942$		0			0
$943$	−16.9769	−	16.9769i	−0.552843	−	0.552843i
$944$		0			0
$945$	−1.31271	−	3.16916i	−0.0427024	−	0.103093i
$946$		0			0
$947$	19.5154	−	47.1142i	0.634164	−	1.53101i	−0.200178	−	0.979760i	$-0.564152\pi$
$947$	19.5154	−	47.1142i	0.634164	−	1.53101i	0.834342	−	0.551248i	$-0.185848\pi$
$948$		0			0
$949$	−14.6212	−	6.05629i	−0.474624	−	0.196596i
$950$		0			0
$951$	−27.9501			−0.906344
$952$		0			0
$953$	32.3984			1.04949			0.524743	−	0.851261i	$-0.324161\pi$
$953$	32.3984			1.04949			0.524743	+	0.851261i	$0.324161\pi$
$954$		0			0
$955$	−14.2720	−	5.91164i	−0.461830	−	0.191296i
$956$		0			0
$957$	−11.3505	+	27.4025i	−0.366909	+	0.885796i
$958$		0			0
$959$	−8.09498	−	19.5430i	−0.261400	−	0.631077i
$960$		0			0
$961$	27.4295	+	27.4295i	0.884822	+	0.884822i
$962$		0			0
$963$	−8.56187	+	3.54644i	−0.275902	+	0.114282i
$964$		0			0
$965$		−	19.5202i		−	0.628377i
$966$		0			0
$967$	26.2196	−	26.2196i	0.843166	−	0.843166i	−0.146103	−	0.989269i	$-0.546673\pi$
$967$	26.2196	−	26.2196i	0.843166	−	0.843166i	0.989269	+	0.146103i	$0.0466732\pi$
$968$		0			0
$969$	−26.1373	−	21.2273i	−0.839651	−	0.681919i
$970$		0			0
$971$	9.14662	−	9.14662i	0.293529	−	0.293529i	−0.544944	−	0.838473i	$-0.683449\pi$
$971$	9.14662	−	9.14662i	0.293529	−	0.293529i	0.838473	+	0.544944i	$0.183449\pi$
$972$		0			0
$973$			50.5179i			1.61953i
$974$		0			0
$975$	−6.41154	+	2.65575i	−0.205334	+	0.0850520i
$976$		0			0
$977$	−25.9677	−	25.9677i	−0.830779	−	0.830779i	0.156844	−	0.987623i	$-0.449868\pi$
$977$	−25.9677	−	25.9677i	−0.830779	−	0.830779i	−0.987623	+	0.156844i	$0.949868\pi$
$978$		0			0
$979$	−2.92709	−	7.06663i	−0.0935504	−	0.225851i
$980$		0			0
$981$	3.98225	−	9.61399i	0.127143	−	0.306951i
$982$		0			0
$983$	45.3866	+	18.7997i	1.44761	+	0.599618i	0.961629	−	0.274353i	$-0.0884638\pi$
$983$	45.3866	+	18.7997i	1.44761	+	0.599618i	0.485977	+	0.873971i	$0.338464\pi$
$984$		0			0
$985$	−5.82956			−0.185745
$986$		0			0
$987$	−15.1011			−0.480674
$988$		0			0
$989$	57.2589	+	23.7174i	1.82073	+	0.754170i
$990$		0			0
$991$	15.6480	−	37.7777i	0.497076	−	1.20005i	−0.453975	−	0.891014i	$-0.649995\pi$
$991$	15.6480	−	37.7777i	0.497076	−	1.20005i	0.951051	−	0.309033i	$-0.100005\pi$
$992$		0			0
$993$	−10.3253	−	24.9275i	−0.327664	−	0.791050i
$994$		0			0
$995$	20.3611	+	20.3611i	0.645490	+	0.645490i
$996$		0			0
$997$	29.6933	−	12.2994i	0.940398	−	0.389525i	0.140784	−	0.990040i	$-0.455038\pi$
$997$	29.6933	−	12.2994i	0.940398	−	0.389525i	0.799614	+	0.600515i	$0.205038\pi$
$998$		0			0
$999$			0.350281i			0.0110824i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	408.2.ba.b.145.4	yes	16
3.2	odd	2		1224.2.bq.d.145.2		16
4.3	odd	2		816.2.bq.e.145.2		16
17.2	even	8	inner	408.2.ba.b.121.4	✓	16
17.6	odd	16		6936.2.a.bn.1.4		8
17.11	odd	16		6936.2.a.bm.1.5		8
51.2	odd	8		1224.2.bq.d.937.2		16
68.19	odd	8		816.2.bq.e.529.2		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
408.2.ba.b.121.4	✓	16	17.2	even	8	inner
408.2.ba.b.145.4	yes	16	1.1	even	1	trivial
816.2.bq.e.145.2		16	4.3	odd	2
816.2.bq.e.529.2		16	68.19	odd	8
1224.2.bq.d.145.2		16	3.2	odd	2
1224.2.bq.d.937.2		16	51.2	odd	8
6936.2.a.bm.1.5		8	17.11	odd	16
6936.2.a.bn.1.4		8	17.6	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 408 = 2^{3} \cdot 3 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	408.ba (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.923880 + 0.382683i) q^{3} +(0.431802 - 1.04246i) q^{5} +(-1.16338 - 2.80866i) q^{7} +(0.707107 + 0.707107i) q^{9} +(3.84680 - 1.59340i) q^{11} +1.86212i q^{13} +(0.797866 - 0.797866i) q^{15} +(-1.96221 - 3.62626i) q^{17} +(5.77458 - 5.77458i) q^{19} -3.04007i q^{21} +(-6.03378 + 2.49927i) q^{23} +(2.63526 + 2.63526i) q^{25} +(0.382683 + 0.923880i) q^{27} +(-2.72602 + 6.58121i) q^{29} +(7.71819 + 3.19698i) q^{31} +4.16374 q^{33} -3.43027 q^{35} +(0.323617 + 0.134047i) q^{37} +(-0.712604 + 1.72038i) q^{39} +(1.40682 + 3.39636i) q^{41} +(-6.71026 - 6.71026i) q^{43} +(1.04246 - 0.431802i) q^{45} -4.96736i q^{47} +(-1.58535 + 1.58535i) q^{49} +(-0.425139 - 4.10113i) q^{51} +(-7.13683 + 7.13683i) q^{53} -4.69817i q^{55} +(7.54485 - 3.12518i) q^{57} +(0.0213015 + 0.0213015i) q^{59} +(1.66642 + 4.02310i) q^{61} +(1.16338 - 2.80866i) q^{63} +(1.94119 + 0.804069i) q^{65} +5.70338 q^{67} -6.53091 q^{69} +(-3.98661 - 1.65131i) q^{71} +(-3.25236 + 7.85188i) q^{73} +(1.42619 + 3.44313i) q^{75} +(-8.95061 - 8.95061i) q^{77} +(-8.15920 + 3.37965i) q^{79} +1.00000i q^{81} +(-10.1271 + 10.1271i) q^{83} +(-4.62752 + 0.479707i) q^{85} +(-5.03704 + 5.03704i) q^{87} -1.83702i q^{89} +(5.23007 - 2.16637i) q^{91} +(5.90725 + 5.90725i) q^{93} +(-3.52630 - 8.51325i) q^{95} +(-4.76740 + 11.5095i) q^{97} +(3.84680 + 1.59340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 8 q^{11} - 8 q^{15} - 16 q^{17} + 8 q^{19} + 8 q^{23} + 24 q^{25} + 8 q^{31} + 24 q^{33} + 16 q^{35} - 8 q^{37} + 24 q^{39} - 8 q^{41} + 8 q^{43} + 8 q^{45} - 40 q^{49} - 8 q^{51} - 24 q^{53} + 8 q^{57}+ \cdots + 8 q^{99}+O(q^{100}) \) 16 * q + 8 * q^11 - 8 * q^15 - 16 * q^17 + 8 * q^19 + 8 * q^23 + 24 * q^25 + 8 * q^31 + 24 * q^33 + 16 * q^35 - 8 * q^37 + 24 * q^39 - 8 * q^41 + 8 * q^43 + 8 * q^45 - 40 * q^49 - 8 * q^51 - 24 * q^53 + 8 * q^57 - 32 * q^59 - 48 * q^61 + 48 * q^65 - 24 * q^69 - 32 * q^71 - 40 * q^73 + 16 * q^79 - 48 * q^83 + 32 * q^85 - 16 * q^87 + 16 * q^91 + 24 * q^93 - 56 * q^95 - 40 * q^97 + 8 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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