LMFDB - Embedded newform 440.2.y.b.361.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [440,2,Mod(81,440)] 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("440.81"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(440, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 2])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 440 = 2^{3} \cdot 5 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	440.y (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,-1,0,3,0,-8] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(7)] == traces)

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

Self dual:	no
Analytic conductor:	$3.51341768894$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2 x^{11} + 15 x^{10} - 22 x^{9} + 89 x^{8} - 118 x^{7} + 205 x^{6} - 68 x^{5} + 1061 x^{4} + \cdots + 400 $ x^12 - 2x^11 + 15x^10 - 22x^9 + 89x^8 - 118x^7 + 205x^6 - 68x^5 + 1061x^4 - 1490x^3 + 2760x^2 - 1600*x + 400
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			361.2
Root			$0.359793 + 0.261405i$ of defining polynomial
Character	$\chi$	$=$	440.361
Dual form			440.2.y.b.401.2

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.582157 + 0.422962i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(-3.38507 - 2.45940i) q^{7} +(-0.767041 + 2.36071i) q^{9} +(2.41269 + 2.27573i) q^{11} +(-1.86973 + 5.75443i) q^{13} +(0.582157 + 0.422962i) q^{15} +(2.01535 + 6.20260i) q^{17} +(-0.598231 + 0.434640i) q^{19} +3.01088 q^{21} -5.13093 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-1.21904 - 3.75183i) q^{27} +(-1.68305 - 1.22281i) q^{29} +(-0.348255 + 1.07182i) q^{31} +(-2.36711 - 0.304357i) q^{33} +(-1.29298 + 3.97939i) q^{35} +(-5.75758 - 4.18313i) q^{37} +(-1.34543 - 4.14080i) q^{39} +(3.25363 - 2.36390i) q^{41} +6.29891 q^{43} +2.48220 q^{45} +(-7.47651 + 5.43200i) q^{47} +(3.24696 + 9.99312i) q^{49} +(-3.79671 - 2.75847i) q^{51} +(2.40111 - 7.38985i) q^{53} +(1.41879 - 2.99784i) q^{55} +(0.164428 - 0.506058i) q^{57} +(-4.98691 - 3.62320i) q^{59} +(4.53849 + 13.9680i) q^{61} +(8.40242 - 6.10472i) q^{63} +6.05056 q^{65} -5.53268 q^{67} +(2.98700 - 2.17019i) q^{69} +(2.74176 + 8.43827i) q^{71} +(6.54779 + 4.75724i) q^{73} +(0.222364 - 0.684366i) q^{75} +(-2.57020 - 13.6373i) q^{77} +(-0.176289 + 0.542560i) q^{79} +(-3.72786 - 2.70845i) q^{81} +(-4.70399 - 14.4774i) q^{83} +(5.27625 - 3.83342i) q^{85} +1.49700 q^{87} -1.33867 q^{89} +(20.4816 - 14.8808i) q^{91} +(-0.250599 - 0.771266i) q^{93} +(0.598231 + 0.434640i) q^{95} +(3.07980 - 9.47864i) q^{97} +(-7.22296 + 3.95008i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - q^{3} + 3 q^{5} - 8 q^{7} + 10 q^{9} - 4 q^{11} - 7 q^{13} + q^{15} + 7 q^{17} + 3 q^{19} + 4 q^{21} + 36 q^{23} - 3 q^{25} + 8 q^{27} + 13 q^{29} + 2 q^{31} - 19 q^{33} - 2 q^{35} - 22 q^{37}+ \cdots - 79 q^{99}+O(q^{100}) $ 12 * q - q^3 + 3 * q^5 - 8 * q^7 + 10 * q^9 - 4 * q^11 - 7 * q^13 + q^15 + 7 * q^17 + 3 * q^19 + 4 * q^21 + 36 * q^23 - 3 * q^25 + 8 * q^27 + 13 * q^29 + 2 * q^31 - 19 * q^33 - 2 * q^35 - 22 * q^37 - q^39 + 7 * q^41 + 6 * q^43 - 20 * q^45 - 2 * q^47 - 19 * q^49 - 33 * q^51 + 3 * q^53 + 4 * q^55 - 25 * q^57 + 19 * q^59 + 22 * q^61 - 2 * q^63 + 12 * q^65 + 22 * q^67 + 21 * q^69 + 44 * q^71 + 17 * q^73 - q^75 - 38 * q^77 - 43 * q^79 - 85 * q^81 - 15 * q^83 + 18 * q^85 + 50 * q^87 + 2 * q^89 + 59 * q^91 + 5 * q^93 - 3 * q^95 - 20 * q^97 - 79 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/440\mathbb{Z}\right)^\times$.

$n$	$111$	$177$	$221$	$321$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	−0.582157	+	0.422962i	−0.336108	+	0.244197i	−0.743018	−	0.669271i	$-0.766606\pi$
$3$	−0.582157	+	0.422962i	−0.336108	+	0.244197i	0.406910	+	0.913468i	$0.366606\pi$
$4$		0			0
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$5$	−0.309017	−	0.951057i	−0.138197	−	0.425325i
$6$		0			0
$7$	−3.38507	−	2.45940i	−1.27944	−	0.929566i	−0.279902	−	0.960029i	$-0.590302\pi$
$7$	−3.38507	−	2.45940i	−1.27944	−	0.929566i	−0.999536	+	0.0304624i	$0.990302\pi$
$8$		0			0
$9$	−0.767041	+	2.36071i	−0.255680	+	0.786903i
$10$		0			0
$11$	2.41269	+	2.27573i	0.727452	+	0.686158i
$11$	2.41269	+	2.27573i	0.727452	+	0.686158i
$12$		0			0
$13$	−1.86973	+	5.75443i	−0.518569	+	1.59599i	0.258124	+	0.966112i	$0.416896\pi$
$13$	−1.86973	+	5.75443i	−0.518569	+	1.59599i	−0.776693	+	0.629880i	$0.783104\pi$
$14$		0			0
$15$	0.582157	+	0.422962i	0.150312	+	0.109208i
$16$		0			0
$17$	2.01535	+	6.20260i	0.488794	+	1.50435i	0.826410	+	0.563068i	$0.190379\pi$
$17$	2.01535	+	6.20260i	0.488794	+	1.50435i	−0.337617	+	0.941284i	$0.609621\pi$
$18$		0			0
$19$	−0.598231	+	0.434640i	−0.137244	+	0.0997134i	−0.654289	−	0.756245i	$-0.727032\pi$
$19$	−0.598231	+	0.434640i	−0.137244	+	0.0997134i	0.517045	+	0.855958i	$0.327032\pi$
$20$		0			0
$21$	3.01088			0.657027
$22$		0			0
$23$	−5.13093			−1.06987			−0.534936	−	0.844893i	$-0.679664\pi$
$23$	−5.13093			−1.06987			−0.534936	+	0.844893i	$0.679664\pi$
$24$		0			0
$25$	−0.809017	+	0.587785i	−0.161803	+	0.117557i
$26$		0			0
$27$	−1.21904	−	3.75183i	−0.234605	−	0.722040i
$28$		0			0
$29$	−1.68305	−	1.22281i	−0.312534	−	0.227069i	0.420449	−	0.907316i	$-0.361873\pi$
$29$	−1.68305	−	1.22281i	−0.312534	−	0.227069i	−0.732983	+	0.680247i	$0.761873\pi$
$30$		0			0
$31$	−0.348255	+	1.07182i	−0.0625485	+	0.192504i	−0.977448	−	0.211178i	$-0.932270\pi$
$31$	−0.348255	+	1.07182i	−0.0625485	+	0.192504i	0.914899	+	0.403683i	$0.132270\pi$
$32$		0			0
$33$	−2.36711	−	0.304357i	−0.412061	−	0.0529818i
$34$		0			0
$35$	−1.29298	+	3.97939i	−0.218554	+	0.672640i
$36$		0			0
$37$	−5.75758	−	4.18313i	−0.946540	−	0.687702i	0.00344564	−	0.999994i	$-0.498903\pi$
$37$	−5.75758	−	4.18313i	−0.946540	−	0.687702i	−0.949986	+	0.312292i	$0.898903\pi$
$38$		0			0
$39$	−1.34543	−	4.14080i	−0.215441	−	0.663059i
$40$		0			0
$41$	3.25363	−	2.36390i	0.508131	−	0.369179i	−0.303983	−	0.952677i	$-0.598317\pi$
$41$	3.25363	−	2.36390i	0.508131	−	0.369179i	0.812114	+	0.583499i	$0.198317\pi$
$42$		0			0
$43$	6.29891			0.960575			0.480288	−	0.877111i	$-0.340532\pi$
$43$	6.29891			0.960575			0.480288	+	0.877111i	$0.340532\pi$
$44$		0			0
$45$	2.48220			0.370024
$46$		0			0
$47$	−7.47651	+	5.43200i	−1.09056	+	0.792339i	−0.979494	−	0.201474i	$-0.935427\pi$
$47$	−7.47651	+	5.43200i	−1.09056	+	0.792339i	−0.111067	+	0.993813i	$0.535427\pi$
$48$		0			0
$49$	3.24696	+	9.99312i	0.463852	+	1.42759i
$50$		0			0
$51$	−3.79671	−	2.75847i	−0.531646	−	0.386263i
$52$		0			0
$53$	2.40111	−	7.38985i	0.329818	−	1.01507i	−0.639401	−	0.768873i	$-0.720818\pi$
$53$	2.40111	−	7.38985i	0.329818	−	1.01507i	0.969219	−	0.246201i	$-0.0791823\pi$
$54$		0			0
$55$	1.41879	−	2.99784i	0.191309	−	0.404229i
$56$		0			0
$57$	0.164428	−	0.506058i	0.0217790	−	0.0670290i
$58$		0			0
$59$	−4.98691	−	3.62320i	−0.649240	−	0.471701i	0.213772	−	0.976884i	$-0.431425\pi$
$59$	−4.98691	−	3.62320i	−0.649240	−	0.471701i	−0.863012	+	0.505183i	$0.831425\pi$
$60$		0			0
$61$	4.53849	+	13.9680i	0.581094	+	1.78842i	0.614420	+	0.788979i	$0.289390\pi$
$61$	4.53849	+	13.9680i	0.581094	+	1.78842i	−0.0333265	+	0.999445i	$0.510610\pi$
$62$		0			0
$63$	8.40242	−	6.10472i	1.05861	−	0.769122i
$64$		0			0
$65$	6.05056			0.750480
$66$		0			0
$67$	−5.53268			−0.675924			−0.337962	−	0.941160i	$-0.609738\pi$
$67$	−5.53268			−0.675924			−0.337962	+	0.941160i	$0.609738\pi$
$68$		0			0
$69$	2.98700	−	2.17019i	0.359593	−	0.261260i
$70$		0			0
$71$	2.74176	+	8.43827i	0.325387	+	1.00144i	0.971266	+	0.237998i	$0.0764911\pi$
$71$	2.74176	+	8.43827i	0.325387	+	1.00144i	−0.645879	+	0.763440i	$0.723509\pi$
$72$		0			0
$73$	6.54779	+	4.75724i	0.766360	+	0.556793i	0.900855	−	0.434121i	$-0.142941\pi$
$73$	6.54779	+	4.75724i	0.766360	+	0.556793i	−0.134494	+	0.990914i	$0.542941\pi$
$74$		0			0
$75$	0.222364	−	0.684366i	0.0256764	−	0.0790238i
$76$		0			0
$77$	−2.57020	−	13.6373i	−0.292901	−	1.55411i
$78$		0			0
$79$	−0.176289	+	0.542560i	−0.0198340	+	0.0610428i	−0.960484	−	0.278336i	$-0.910217\pi$
$79$	−0.176289	+	0.542560i	−0.0198340	+	0.0610428i	0.940650	+	0.339379i	$0.110217\pi$
$80$		0			0
$81$	−3.72786	−	2.70845i	−0.414207	−	0.300939i
$82$		0			0
$83$	−4.70399	−	14.4774i	−0.516329	−	1.58910i	−0.780850	−	0.624719i	$-0.785214\pi$
$83$	−4.70399	−	14.4774i	−0.516329	−	1.58910i	0.264520	−	0.964380i	$-0.414786\pi$
$84$		0			0
$85$	5.27625	−	3.83342i	0.572290	−	0.415793i
$86$		0			0
$87$	1.49700			0.160495
$88$		0			0
$89$	−1.33867			−0.141899			−0.0709495	−	0.997480i	$-0.522603\pi$
$89$	−1.33867			−0.141899			−0.0709495	+	0.997480i	$0.522603\pi$
$90$		0			0
$91$	20.4816	−	14.8808i	2.14706	−	1.55993i
$92$		0			0
$93$	−0.250599	−	0.771266i	−0.0259860	−	0.0799765i
$94$		0			0
$95$	0.598231	+	0.434640i	0.0613772	+	0.0445932i
$96$		0			0
$97$	3.07980	−	9.47864i	0.312706	−	0.962410i	−0.663982	−	0.747748i	$-0.731135\pi$
$97$	3.07980	−	9.47864i	0.312706	−	0.962410i	0.976688	−	0.214662i	$-0.0688650\pi$
$98$		0			0
$99$	−7.22296	+	3.95008i	−0.725935	+	0.396997i
$100$		0			0
$101$	3.66808	−	11.2892i	0.364987	−	1.12332i	−0.585002	−	0.811032i	$-0.698906\pi$
$101$	3.66808	−	11.2892i	0.364987	−	1.12332i	0.949989	−	0.312283i	$-0.101094\pi$
$102$		0			0
$103$	8.40851	+	6.10914i	0.828515	+	0.601951i	0.919139	−	0.393934i	$-0.128886\pi$
$103$	8.40851	+	6.10914i	0.828515	+	0.601951i	−0.0906238	+	0.995885i	$0.528886\pi$
$104$		0			0
$105$	−0.930412	−	2.86351i	−0.0907989	−	0.279450i
$106$		0			0
$107$	−6.75373	+	4.90687i	−0.652908	+	0.474365i	−0.864261	−	0.503044i	$-0.832213\pi$
$107$	−6.75373	+	4.90687i	−0.652908	+	0.474365i	0.211352	+	0.977410i	$0.432213\pi$
$108$		0			0
$109$	−6.25046			−0.598686			−0.299343	−	0.954146i	$-0.596767\pi$
$109$	−6.25046			−0.598686			−0.299343	+	0.954146i	$0.596767\pi$
$110$		0			0
$111$	5.12112			0.486075
$112$		0			0
$113$	−13.3437	+	9.69474i	−1.25527	+	0.912005i	−0.998515	−	0.0544726i	$-0.982652\pi$
$113$	−13.3437	+	9.69474i	−1.25527	+	0.912005i	−0.256752	+	0.966477i	$0.582652\pi$
$114$		0			0
$115$	1.58554	+	4.87980i	0.147853	+	0.455044i
$116$		0			0
$117$	−12.1504	−	8.82777i	−1.12330	−	0.816127i
$118$		0			0
$119$	8.43258	−	25.9528i	0.773014	−	2.37909i
$120$		0			0
$121$	0.642115	+	10.9812i	0.0583741	+	0.998295i
$122$		0			0
$123$	−0.894283	+	2.75232i	−0.0806347	+	0.248168i
$124$		0			0
$125$	0.809017	+	0.587785i	0.0723607	+	0.0525731i
$126$		0			0
$127$	5.10132	+	15.7003i	0.452669	+	1.39317i	0.873850	+	0.486196i	$0.161616\pi$
$127$	5.10132	+	15.7003i	0.452669	+	1.39317i	−0.421180	+	0.906977i	$0.638384\pi$
$128$		0			0
$129$	−3.66695	+	2.66420i	−0.322857	+	0.234570i
$130$		0			0
$131$	12.1354			1.06027			0.530137	−	0.847912i	$-0.322141\pi$
$131$	12.1354			1.06027			0.530137	+	0.847912i	$0.322141\pi$
$132$		0			0
$133$	3.09401			0.268285
$134$		0			0
$135$	−3.19150	+	2.31876i	−0.274680	+	0.199567i
$136$		0			0
$137$	1.91081	+	5.88088i	0.163252	+	0.502437i	0.998903	−	0.0468228i	$-0.0149096\pi$
$137$	1.91081	+	5.88088i	0.163252	+	0.502437i	−0.835651	+	0.549260i	$0.814910\pi$
$138$		0			0
$139$	4.20887	+	3.05792i	0.356992	+	0.259370i	0.751796	−	0.659395i	$-0.229188\pi$
$139$	4.20887	+	3.05792i	0.356992	+	0.259370i	−0.394804	+	0.918765i	$0.629188\pi$
$140$		0			0
$141$	2.05497	−	6.32455i	0.173060	−	0.532623i
$142$		0			0
$143$	−17.6066	+	9.62864i	−1.47234	+	0.805187i
$144$		0			0
$145$	−0.642867	+	1.97854i	−0.0533872	+	0.164309i
$146$		0			0
$147$	−6.11695	−	4.44422i	−0.504517	−	0.366553i
$148$		0			0
$149$	−3.48918	−	10.7386i	−0.285845	−	0.879739i	−0.986144	−	0.165890i	$-0.946950\pi$
$149$	−3.48918	−	10.7386i	−0.285845	−	0.879739i	0.700300	−	0.713849i	$-0.253050\pi$
$150$		0			0
$151$	0.126708	−	0.0920586i	0.0103113	−	0.00749162i	−0.582618	−	0.812746i	$-0.697971\pi$
$151$	0.126708	−	0.0920586i	0.0103113	−	0.00749162i	0.592929	+	0.805255i	$0.297971\pi$
$152$		0			0
$153$	−16.1884			−1.30875
$154$		0			0
$155$	1.12698			0.0905210
$156$		0			0
$157$	11.0827	−	8.05207i	0.884498	−	0.642625i	−0.0499396	−	0.998752i	$-0.515903\pi$
$157$	11.0827	−	8.05207i	0.884498	−	0.642625i	0.934438	+	0.356127i	$0.115903\pi$
$158$		0			0
$159$	1.72780	+	5.31763i	0.137024	+	0.421715i
$160$		0			0
$161$	17.3686	+	12.6190i	1.36884	+	0.994517i
$162$		0			0
$163$	1.80874	−	5.56673i	0.141671	−	0.436020i	−0.854897	−	0.518799i	$-0.826379\pi$
$163$	1.80874	−	5.56673i	0.141671	−	0.436020i	0.996568	+	0.0827788i	$0.0263795\pi$
$164$		0			0
$165$	0.442016	+	2.34531i	0.0344109	+	0.182582i
$166$		0			0
$167$	−3.79756	+	11.6877i	−0.293864	+	0.904422i	0.689736	+	0.724061i	$0.257727\pi$
$167$	−3.79756	+	11.6877i	−0.293864	+	0.904422i	−0.983601	+	0.180361i	$0.942273\pi$
$168$		0			0
$169$	−19.1003	−	13.8772i	−1.46926	−	1.06748i
$170$		0			0
$171$	−0.567192	−	1.74564i	−0.0433743	−	0.133492i
$172$		0			0
$173$	15.3840	−	11.1771i	1.16962	−	0.849782i	0.178660	−	0.983911i	$-0.442824\pi$
$173$	15.3840	−	11.1771i	1.16962	−	0.849782i	0.990964	+	0.134129i	$0.0428236\pi$
$174$		0			0
$175$	4.18418			0.316294
$176$		0			0
$177$	4.43564			0.333403
$178$		0			0
$179$	0.134643	−	0.0978237i	0.0100637	−	0.00731169i	−0.582742	−	0.812657i	$-0.698020\pi$
$179$	0.134643	−	0.0978237i	0.0100637	−	0.00731169i	0.592806	+	0.805346i	$0.298020\pi$
$180$		0			0
$181$	1.26224	+	3.88478i	0.0938216	+	0.288753i	0.986945	−	0.161059i	$-0.0514909\pi$
$181$	1.26224	+	3.88478i	0.0938216	+	0.288753i	−0.893123	+	0.449812i	$0.851491\pi$
$182$		0			0
$183$	−8.55006	−	6.21198i	−0.632038	−	0.459203i
$184$		0			0
$185$	−2.19920	+	6.76844i	−0.161688	+	0.497626i
$186$		0			0
$187$	−9.25304	+	19.5513i	−0.676649	+	1.42973i
$188$		0			0
$189$	−5.10070	+	15.6983i	−0.371022	+	1.14189i
$190$		0			0
$191$	−11.9198	−	8.66026i	−0.862488	−	0.626634i	0.0660726	−	0.997815i	$-0.478953\pi$
$191$	−11.9198	−	8.66026i	−0.862488	−	0.626634i	−0.928561	+	0.371180i	$0.878953\pi$
$192$		0			0
$193$	0.0973330	+	0.299560i	0.00700618	+	0.0215628i	0.954498	−	0.298216i	$-0.0963915\pi$
$193$	0.0973330	+	0.299560i	0.00700618	+	0.0215628i	−0.947492	+	0.319779i	$0.896391\pi$
$194$		0			0
$195$	−3.52238	+	2.55916i	−0.252243	+	0.183265i
$196$		0			0
$197$	1.41533			0.100838			0.0504191	−	0.998728i	$-0.483944\pi$
$197$	1.41533			0.100838			0.0504191	+	0.998728i	$0.483944\pi$
$198$		0			0
$199$	22.3049			1.58115			0.790575	−	0.612365i	$-0.209782\pi$
$199$	22.3049			1.58115			0.790575	+	0.612365i	$0.209782\pi$
$200$		0			0
$201$	3.22089	−	2.34011i	0.227184	−	0.165059i
$202$		0			0
$203$	2.68987	+	8.27858i	0.188792	+	0.581042i
$204$		0			0
$205$	−3.25363	−	2.36390i	−0.227243	−	0.165102i
$206$		0			0
$207$	3.93563	−	12.1126i	0.273545	−	0.841886i
$208$		0			0
$209$	−2.43247	−	0.312761i	−0.168257	−	0.0216341i
$210$		0			0
$211$	−7.52419	+	23.1571i	−0.517986	+	1.59420i	0.259795	+	0.965664i	$0.416345\pi$
$211$	−7.52419	+	23.1571i	−0.517986	+	1.59420i	−0.777782	+	0.628535i	$0.783655\pi$
$212$		0			0
$213$	−5.16520	−	3.75274i	−0.353913	−	0.257133i
$214$		0			0
$215$	−1.94647	−	5.99062i	−0.132748	−	0.408557i
$216$		0			0
$217$	3.81490	−	2.77169i	0.258973	−	0.188155i
$218$		0			0
$219$	−5.82397			−0.393547
$220$		0			0
$221$	−39.4606			−2.65441
$222$		0			0
$223$	−5.03326	+	3.65688i	−0.337052	+	0.244883i	−0.743417	−	0.668828i	$-0.766796\pi$
$223$	−5.03326	+	3.65688i	−0.337052	+	0.244883i	0.406365	+	0.913711i	$0.366796\pi$
$224$		0			0
$225$	−0.767041	−	2.36071i	−0.0511361	−	0.157381i
$226$		0			0
$227$	12.9975	+	9.44323i	0.862674	+	0.626769i	0.928611	−	0.371054i	$-0.121004\pi$
$227$	12.9975	+	9.44323i	0.862674	+	0.626769i	−0.0659370	+	0.997824i	$0.521004\pi$
$228$		0			0
$229$	−4.84639	+	14.9157i	−0.320258	+	0.985654i	0.653277	+	0.757119i	$0.273394\pi$
$229$	−4.84639	+	14.9157i	−0.320258	+	0.985654i	−0.973536	+	0.228535i	$0.926606\pi$
$230$		0			0
$231$	7.26430	+	6.85194i	0.477956	+	0.450825i
$232$		0			0
$233$	−4.33354	+	13.3373i	−0.283899	+	0.873752i	0.702827	+	0.711361i	$0.251921\pi$
$233$	−4.33354	+	13.3373i	−0.283899	+	0.873752i	−0.986726	+	0.162392i	$0.948079\pi$
$234$		0			0
$235$	7.47651	+	5.43200i	0.487713	+	0.354345i
$236$		0			0
$237$	−0.126855	−	0.390419i	−0.00824010	−	0.0253604i
$238$		0			0
$239$	−8.74496	+	6.35359i	−0.565665	+	0.410979i	−0.833528	−	0.552478i	$-0.813683\pi$
$239$	−8.74496	+	6.35359i	−0.565665	+	0.410979i	0.267863	+	0.963457i	$0.413683\pi$
$240$		0			0
$241$	19.7912			1.27486			0.637431	−	0.770507i	$-0.279997\pi$
$241$	19.7912			1.27486			0.637431	+	0.770507i	$0.279997\pi$
$242$		0			0
$243$	15.1505			0.971905
$244$		0			0
$245$	8.50065	−	6.17609i	0.543087	−	0.394576i
$246$		0			0
$247$	−1.38258	−	4.25514i	−0.0879713	−	0.270748i
$248$		0			0
$249$	8.86183	+	6.43850i	0.561596	+	0.408023i
$250$		0			0
$251$	1.18337	−	3.64204i	0.0746937	−	0.229884i	−0.906738	−	0.421694i	$-0.861436\pi$
$251$	1.18337	−	3.64204i	0.0746937	−	0.229884i	0.981432	+	0.191810i	$0.0614358\pi$
$252$		0			0
$253$	−12.3793	−	11.6766i	−0.778281	−	0.734101i
$254$		0			0
$255$	−1.45021	+	4.46330i	−0.0908160	+	0.279503i
$256$		0			0
$257$	−15.3959	−	11.1858i	−0.960372	−	0.697751i	−0.00713517	−	0.999975i	$-0.502271\pi$
$257$	−15.3959	−	11.1858i	−0.960372	−	0.697751i	−0.953237	+	0.302223i	$0.902271\pi$
$258$		0			0
$259$	9.20186	+	28.3204i	0.571775	+	1.75974i
$260$		0			0
$261$	4.17766	−	3.03524i	0.258590	−	0.187877i
$262$		0			0
$263$	26.6567			1.64372			0.821862	−	0.569686i	$-0.192935\pi$
$263$	26.6567			1.64372			0.821862	+	0.569686i	$0.192935\pi$
$264$		0			0
$265$	−7.77015			−0.477317
$266$		0			0
$267$	0.779318	−	0.566208i	0.0476935	−	0.0346513i
$268$		0			0
$269$	0.140462	+	0.432297i	0.00856412	+	0.0263576i	0.955247	−	0.295809i	$-0.0955890\pi$
$269$	0.140462	+	0.432297i	0.00856412	+	0.0263576i	−0.946683	+	0.322166i	$0.895589\pi$
$270$		0			0
$271$	−13.1552	−	9.55784i	−0.799123	−	0.580597i	0.111533	−	0.993761i	$-0.464424\pi$
$271$	−13.1552	−	9.55784i	−0.799123	−	0.580597i	−0.910657	+	0.413164i	$0.864424\pi$
$272$		0			0
$273$	−5.62952	+	17.3259i	−0.340714	+	1.04861i
$274$		0			0
$275$	−3.28954	−	0.422962i	−0.198367	−	0.0255056i
$276$		0			0
$277$	−3.53323	+	10.8742i	−0.212291	+	0.653366i	0.787043	+	0.616898i	$0.211611\pi$
$277$	−3.53323	+	10.8742i	−0.212291	+	0.653366i	−0.999335	+	0.0364680i	$0.988389\pi$
$278$		0			0
$279$	−2.26313	−	1.64426i	−0.135490	−	0.0984392i
$280$		0			0
$281$	−1.75898	−	5.41357i	−0.104932	−	0.322947i	0.884783	−	0.466004i	$-0.154307\pi$
$281$	−1.75898	−	5.41357i	−0.104932	−	0.322947i	−0.989714	+	0.143057i	$0.954307\pi$
$282$		0			0
$283$	0.469970	−	0.341453i	0.0279368	−	0.0202973i	−0.573729	−	0.819045i	$-0.694504\pi$
$283$	0.469970	−	0.341453i	0.0279368	−	0.0202973i	0.601666	+	0.798748i	$0.294504\pi$
$284$		0			0
$285$	−0.532101			−0.0315189
$286$		0			0
$287$	−16.8275			−0.993298
$288$		0			0
$289$	−20.6574	+	15.0085i	−1.21514	+	0.882850i
$290$		0			0
$291$	2.21618	+	6.82069i	0.129915	+	0.399836i
$292$		0			0
$293$	0.952544	+	0.692064i	0.0556482	+	0.0404308i	0.615262	−	0.788323i	$-0.289050\pi$
$293$	0.952544	+	0.692064i	0.0556482	+	0.0404308i	−0.559613	+	0.828754i	$0.689050\pi$
$294$		0			0
$295$	−1.90483	+	5.86246i	−0.110903	+	0.341326i
$296$		0			0
$297$	5.59698	−	11.8262i	0.324770	−	0.686226i
$298$		0			0
$299$	9.59343	−	29.5255i	0.554803	−	1.70751i
$300$		0			0
$301$	−21.3223	−	15.4916i	−1.22900	−	0.892918i
$302$		0			0
$303$	2.63949	+	8.12353i	0.151635	+	0.466684i
$304$		0			0
$305$	11.8819	−	8.63272i	0.680357	−	0.494308i
$306$		0			0
$307$	−19.1615			−1.09360			−0.546802	−	0.837262i	$-0.684155\pi$
$307$	−19.1615			−1.09360			−0.546802	+	0.837262i	$0.684155\pi$
$308$		0			0
$309$	−7.47900			−0.425466
$310$		0			0
$311$	−15.1066	+	10.9756i	−0.856618	+	0.622369i	−0.926963	−	0.375154i	$-0.877590\pi$
$311$	−15.1066	+	10.9756i	−0.856618	+	0.622369i	0.0703451	+	0.997523i	$0.477590\pi$
$312$		0			0
$313$	−1.10929	−	3.41404i	−0.0627008	−	0.192973i	0.914799	−	0.403909i	$-0.132349\pi$
$313$	−1.10929	−	3.41404i	−0.0627008	−	0.192973i	−0.977500	+	0.210936i	$0.932349\pi$
$314$		0			0
$315$	−8.40242	−	6.10472i	−0.473423	−	0.343962i
$316$		0			0
$317$	0.772626	−	2.37790i	0.0433950	−	0.133556i	−0.927012	−	0.375032i	$-0.877632\pi$
$317$	0.772626	−	2.37790i	0.0433950	−	0.133556i	0.970407	+	0.241476i	$0.0776316\pi$
$318$		0			0
$319$	−1.27789	−	6.78041i	−0.0715483	−	0.379630i
$320$		0			0
$321$	1.85631	−	5.71314i	0.103609	−	0.318876i
$322$		0			0
$323$	−3.90155	−	2.83464i	−0.217088	−	0.157724i
$324$		0			0
$325$	−1.86973	−	5.75443i	−0.103714	−	0.319198i
$326$		0			0
$327$	3.63875	−	2.64371i	0.201223	−	0.146197i
$328$		0			0
$329$	38.6680			2.13184
$330$		0			0
$331$	−6.58629			−0.362015			−0.181008	−	0.983482i	$-0.557936\pi$
$331$	−6.58629			−0.362015			−0.181008	+	0.983482i	$0.557936\pi$
$332$		0			0
$333$	14.2914	−	10.3833i	0.783167	−	0.569004i
$334$		0			0
$335$	1.70969	+	5.26189i	0.0934104	+	0.287488i
$336$		0			0
$337$	12.3093	+	8.94323i	0.670530	+	0.487169i	0.870203	−	0.492694i	$-0.163988\pi$
$337$	12.3093	+	8.94323i	0.670530	+	0.487169i	−0.199672	+	0.979863i	$0.563988\pi$
$338$		0			0
$339$	3.66760	−	11.2877i	0.199197	−	0.613065i
$340$		0			0
$341$	−3.27940	+	1.79343i	−0.177590	+	0.0971197i
$342$		0			0
$343$	4.53499	−	13.9573i	0.244867	−	0.753622i
$344$		0			0
$345$	−2.98700	−	2.17019i	−0.160815	−	0.116839i
$346$		0			0
$347$	2.36749	+	7.28638i	0.127093	+	0.391153i	0.994277	−	0.106836i	$-0.0340719\pi$
$347$	2.36749	+	7.28638i	0.127093	+	0.391153i	−0.867183	+	0.497989i	$0.834072\pi$
$348$		0			0
$349$	7.27630	−	5.28654i	0.389492	−	0.282982i	−0.375755	−	0.926719i	$-0.622617\pi$
$349$	7.27630	−	5.28654i	0.389492	−	0.282982i	0.765247	+	0.643737i	$0.222617\pi$
$350$		0			0
$351$	23.8689			1.27403
$352$		0			0
$353$	10.3310			0.549862			0.274931	−	0.961464i	$-0.411345\pi$
$353$	10.3310			0.549862			0.274931	+	0.961464i	$0.411345\pi$
$354$		0			0
$355$	7.17802	−	5.21514i	0.380970	−	0.276791i
$356$		0			0
$357$	6.06796	+	18.6753i	0.321151	+	0.988400i
$358$		0			0
$359$	−13.1568	−	9.55895i	−0.694387	−	0.504502i	0.183712	−	0.982980i	$-0.441189\pi$
$359$	−13.1568	−	9.55895i	−0.694387	−	0.504502i	−0.878099	+	0.478478i	$0.841189\pi$
$360$		0			0
$361$	−5.70235	+	17.5500i	−0.300124	+	0.923686i
$362$		0			0
$363$	−5.01846	−	6.12122i	−0.263401	−	0.321280i
$364$		0			0
$365$	2.50103	−	7.69738i	0.130910	−	0.402899i
$366$		0			0
$367$	27.9456	+	20.3037i	1.45875	+	1.05984i	0.983686	+	0.179893i	$0.0575751\pi$
$367$	27.9456	+	20.3037i	1.45875	+	1.05984i	0.475064	+	0.879951i	$0.342425\pi$
$368$		0			0
$369$	3.08481	+	9.49407i	0.160589	+	0.494242i
$370$		0			0
$371$	−26.3025	+	19.1099i	−1.36556	+	0.992137i
$372$		0			0
$373$	31.2168			1.61634			0.808172	−	0.588946i	$-0.200457\pi$
$373$	31.2168			1.61634			0.808172	+	0.588946i	$0.200457\pi$
$374$		0			0
$375$	−0.719585			−0.0371592
$376$		0			0
$377$	10.1834	−	7.39867i	0.524471	−	0.381051i
$378$		0			0
$379$	−10.3417	−	31.8284i	−0.531216	−	1.63491i	−0.751687	−	0.659520i	$-0.770759\pi$
$379$	−10.3417	−	31.8284i	−0.531216	−	1.63491i	0.220471	−	0.975394i	$-0.429241\pi$
$380$		0			0
$381$	−9.61038	−	6.98235i	−0.492355	−	0.357717i
$382$		0			0
$383$	−0.0414972	+	0.127715i	−0.00212041	+	0.00652594i	−0.952111	−	0.305752i	$-0.901092\pi$
$383$	−0.0414972	+	0.127715i	−0.00212041	+	0.00652594i	0.949991	+	0.312278i	$0.101092\pi$
$384$		0			0
$385$	−12.1756	+	6.65855i	−0.620525	+	0.339351i
$386$		0			0
$387$	−4.83152	+	14.8699i	−0.245600	+	0.755880i
$388$		0			0
$389$	6.90744	+	5.01855i	0.350221	+	0.254451i	0.748962	−	0.662613i	$-0.230553\pi$
$389$	6.90744	+	5.01855i	0.350221	+	0.254451i	−0.398741	+	0.917064i	$0.630553\pi$
$390$		0			0
$391$	−10.3406	−	31.8251i	−0.522947	−	1.60946i
$392$		0			0
$393$	−7.06470	+	5.13280i	−0.356367	+	0.258916i
$394$		0			0
$395$	0.570482			0.0287040
$396$		0			0
$397$	38.0250			1.90842			0.954211	−	0.299135i	$-0.0966982\pi$
$397$	38.0250			1.90842			0.954211	+	0.299135i	$0.0966982\pi$
$398$		0			0
$399$	−1.80120	+	1.30865i	−0.0901728	+	0.0655144i
$400$		0			0
$401$	−3.62609	−	11.1600i	−0.181078	−	0.557302i	0.818780	−	0.574107i	$-0.194651\pi$
$401$	−3.62609	−	11.1600i	−0.181078	−	0.557302i	−0.999859	+	0.0168049i	$0.994651\pi$
$402$		0			0
$403$	−5.51657	−	4.00802i	−0.274800	−	0.199654i
$404$		0			0
$405$	−1.42392	+	4.38236i	−0.0707550	+	0.217761i
$406$		0			0
$407$	−4.37158	−	23.1953i	−0.216691	−	1.14975i
$408$		0			0
$409$	−8.95644	+	27.5651i	−0.442868	+	1.36301i	0.441938	+	0.897046i	$0.354291\pi$
$409$	−8.95644	+	27.5651i	−0.442868	+	1.36301i	−0.884805	+	0.465961i	$0.845709\pi$
$410$		0			0
$411$	−3.59978	−	2.61539i	−0.177564	−	0.129008i
$412$		0			0
$413$	7.97016	+	24.5296i	0.392186	+	1.20702i
$414$		0			0
$415$	−12.3152	+	8.94751i	−0.604529	+	0.439216i
$416$		0			0
$417$	−3.74361			−0.183325
$418$		0			0
$419$	12.5318			0.612221			0.306110	−	0.951996i	$-0.400972\pi$
$419$	12.5318			0.612221			0.306110	+	0.951996i	$0.400972\pi$
$420$		0			0
$421$	9.24554	−	6.71728i	0.450600	−	0.327380i	−0.339232	−	0.940703i	$-0.610167\pi$
$421$	9.24554	−	6.71728i	0.450600	−	0.327380i	0.789833	+	0.613322i	$0.210167\pi$
$422$		0			0
$423$	−7.08859	−	21.8164i	−0.344659	−	1.06075i
$424$		0			0
$425$	−5.27625	−	3.83342i	−0.255936	−	0.185948i
$426$		0			0
$427$	18.9899	−	58.4448i	0.918984	−	2.82834i
$428$		0			0
$429$	6.17725	−	13.0523i	0.298240	−	0.630171i
$430$		0			0
$431$	1.17039	−	3.60210i	0.0563759	−	0.173507i	−0.918904	−	0.394482i	$-0.870924\pi$
$431$	1.17039	−	3.60210i	0.0563759	−	0.173507i	0.975279	+	0.220975i	$0.0709240\pi$
$432$		0			0
$433$	−20.7794	−	15.0971i	−0.998596	−	0.725522i	−0.0368093	−	0.999322i	$-0.511719\pi$
$433$	−20.7794	−	15.0971i	−0.998596	−	0.725522i	−0.961787	+	0.273800i	$0.911719\pi$
$434$		0			0
$435$	−0.462598	−	1.42373i	−0.0221799	−	0.0682626i
$436$		0			0
$437$	3.06948	−	2.23011i	0.146833	−	0.106681i
$438$		0			0
$439$	29.1218			1.38991			0.694955	−	0.719054i	$-0.255424\pi$
$439$	29.1218			1.38991			0.694955	+	0.719054i	$0.255424\pi$
$440$		0			0
$441$	−26.0814			−1.24197
$442$		0			0
$443$	−9.79844	+	7.11898i	−0.465538	+	0.338233i	−0.795700	−	0.605691i	$-0.792897\pi$
$443$	−9.79844	+	7.11898i	−0.465538	+	0.338233i	0.330162	+	0.943924i	$0.392897\pi$
$444$		0			0
$445$	0.413673	+	1.27315i	0.0196100	+	0.0603533i
$446$		0			0
$447$	6.57326	+	4.77575i	0.310905	+	0.225885i
$448$		0			0
$449$	9.17428	−	28.2355i	0.432961	−	1.33252i	−0.462200	−	0.886776i	$-0.652940\pi$
$449$	9.17428	−	28.2355i	0.432961	−	1.33252i	0.895161	−	0.445742i	$-0.147060\pi$
$450$		0			0
$451$	13.2296	+	1.70103i	0.622956	+	0.0800982i
$452$		0			0
$453$	−0.0348265	+	0.107185i	−0.00163629	+	0.00503599i
$454$		0			0
$455$	−20.4816	−	14.8808i	−0.960193	−	0.697621i
$456$		0			0
$457$	0.232225	+	0.714716i	0.0108630	+	0.0334330i	0.956341	−	0.292253i	$-0.0944049\pi$
$457$	0.232225	+	0.714716i	0.0108630	+	0.0334330i	−0.945478	+	0.325686i	$0.894405\pi$
$458$		0			0
$459$	20.8143	−	15.1225i	0.971529	−	0.705857i
$460$		0			0
$461$	−9.62920			−0.448477			−0.224238	−	0.974534i	$-0.571989\pi$
$461$	−9.62920			−0.448477			−0.224238	+	0.974534i	$0.571989\pi$
$462$		0			0
$463$	−3.33661			−0.155065			−0.0775327	−	0.996990i	$-0.524704\pi$
$463$	−3.33661			−0.155065			−0.0775327	+	0.996990i	$0.524704\pi$
$464$		0			0
$465$	−0.656078	+	0.476669i	−0.0304249	+	0.0221050i
$466$		0			0
$467$	0.524324	+	1.61370i	0.0242628	+	0.0746733i	0.962455	−	0.271442i	$-0.0875006\pi$
$467$	0.524324	+	1.61370i	0.0242628	+	0.0746733i	−0.938192	+	0.346115i	$0.887501\pi$
$468$		0			0
$469$	18.7285	+	13.6071i	0.864803	+	0.628316i
$470$		0			0
$471$	−3.04617	+	9.37514i	−0.140360	+	0.431984i
$472$		0			0
$473$	15.1973	+	14.3346i	0.698773	+	0.659106i
$474$		0			0
$475$	0.228504	−	0.703263i	0.0104845	−	0.0322679i
$476$		0			0
$477$	15.6035	+	11.3366i	0.714437	+	0.519069i
$478$		0			0
$479$	6.83901	+	21.0483i	0.312482	+	0.961721i	0.976778	+	0.214252i	$0.0687313\pi$
$479$	6.83901	+	21.0483i	0.312482	+	0.961721i	−0.664296	+	0.747469i	$0.731269\pi$
$480$		0			0
$481$	34.8366	−	25.3103i	1.58841	−	1.15405i
$482$		0			0
$483$	−15.4486			−0.702935
$484$		0			0
$485$	−9.96643			−0.452552
$486$		0			0
$487$	16.1329	−	11.7213i	0.731053	−	0.531141i	−0.158844	−	0.987304i	$-0.550777\pi$
$487$	16.1329	−	11.7213i	0.731053	−	0.531141i	0.889896	+	0.456163i	$0.150777\pi$
$488$		0			0
$489$	1.30154	+	4.00574i	0.0588578	+	0.181146i
$490$		0			0
$491$	−21.2327	−	15.4265i	−0.958220	−	0.696188i	−0.00548370	−	0.999985i	$-0.501746\pi$
$491$	−21.2327	−	15.4265i	−0.958220	−	0.696188i	−0.952737	+	0.303797i	$0.901746\pi$
$492$		0			0
$493$	4.19265	−	12.9037i	0.188828	−	0.581151i
$494$		0			0
$495$	5.98876	+	5.64881i	0.269175	+	0.253895i
$496$		0			0
$497$	11.4720	−	35.3072i	0.514590	−	1.58375i
$498$		0			0
$499$	6.75109	+	4.90495i	0.302220	+	0.219576i	0.728551	−	0.684991i	$-0.240194\pi$
$499$	6.75109	+	4.90495i	0.302220	+	0.219576i	−0.426331	+	0.904567i	$0.640194\pi$
$500$		0			0
$501$	−2.73267	−	8.41030i	−0.122087	−	0.375745i
$502$		0			0
$503$	−24.5799	+	17.8583i	−1.09596	+	0.796264i	−0.980396	−	0.197035i	$-0.936869\pi$
$503$	−24.5799	+	17.8583i	−1.09596	+	0.796264i	−0.115567	+	0.993300i	$0.536869\pi$
$504$		0			0
$505$	−11.8701			−0.528214
$506$		0			0
$507$	16.9889			0.754505
$508$		0			0
$509$	−13.9310	+	10.1215i	−0.617480	+	0.448626i	−0.852040	−	0.523476i	$-0.824635\pi$
$509$	−13.9310	+	10.1215i	−0.617480	+	0.448626i	0.234560	+	0.972102i	$0.424635\pi$
$510$		0			0
$511$	−10.4648	−	32.2073i	−0.462934	−	1.42477i
$512$		0			0
$513$	2.35997	+	1.71462i	0.104195	+	0.0757022i
$514$		0			0
$515$	3.21176	−	9.88480i	0.141527	−	0.435576i
$516$		0			0
$517$	−30.4002	−	3.90879i	−1.33700	−	0.171908i
$518$		0			0
$519$	−4.22840	+	13.0137i	−0.185606	+	0.571238i
$520$		0			0
$521$	17.3918	+	12.6359i	0.761950	+	0.553589i	0.899508	−	0.436905i	$-0.143925\pi$
$521$	17.3918	+	12.6359i	0.761950	+	0.553589i	−0.137558	+	0.990494i	$0.543925\pi$
$522$		0			0
$523$	−0.00430372	−	0.0132455i	−0.000188189	−	0.000579185i	0.950962	−	0.309307i	$-0.100097\pi$
$523$	−0.00430372	−	0.0132455i	−0.000188189	−	0.000579185i	−0.951151	+	0.308727i	$0.900097\pi$
$524$		0			0
$525$	−2.43585	+	1.76975i	−0.106309	+	0.0772382i
$526$		0			0
$527$	−7.34993			−0.320168
$528$		0			0
$529$	3.32640			0.144626
$530$		0			0
$531$	12.3785	−	8.99350i	0.537181	−	0.390285i
$532$		0			0
$533$	7.51949	+	23.1426i	0.325705	+	1.00242i
$534$		0			0
$535$	6.75373	+	4.90687i	0.291989	+	0.212143i
$536$		0			0
$537$	−0.0370075	+	0.113898i	−0.00159699	+	0.00491504i
$538$		0			0
$539$	−14.9077	+	31.4995i	−0.642121	+	1.35678i
$540$		0			0
$541$	−13.2033	+	40.6356i	−0.567654	+	1.74706i	0.0922772	+	0.995733i	$0.470585\pi$
$541$	−13.2033	+	40.6356i	−0.567654	+	1.74706i	−0.659931	+	0.751326i	$0.729415\pi$
$542$		0			0
$543$	−2.37793	−	1.72767i	−0.102047	−	0.0741414i
$544$		0			0
$545$	1.93150	+	5.94454i	0.0827363	+	0.254636i
$546$		0			0
$547$	−14.4263	+	10.4813i	−0.616825	+	0.448150i	−0.851811	−	0.523849i	$-0.824496\pi$
$547$	−14.4263	+	10.4813i	−0.616825	+	0.448150i	0.234986	+	0.971999i	$0.424496\pi$
$548$		0			0
$549$	−36.4557			−1.55589
$550$		0			0
$551$	1.53833			0.0655352
$552$		0			0
$553$	1.93112	−	1.40304i	0.0821197	−	0.0596635i
$554$		0			0
$555$	−1.58251	−	4.87047i	−0.0671739	−	0.206740i
$556$		0			0
$557$	14.4641	+	10.5088i	0.612864	+	0.445272i	0.850422	−	0.526102i	$-0.176347\pi$
$557$	14.4641	+	10.5088i	0.612864	+	0.445272i	−0.237558	+	0.971373i	$0.576347\pi$
$558$		0			0
$559$	−11.7772	+	36.2466i	−0.498125	+	1.53307i
$560$		0			0
$561$	−2.88274	−	15.2956i	−0.121709	−	0.645781i
$562$		0			0
$563$	−3.27590	+	10.0822i	−0.138063	+	0.424914i	−0.996054	−	0.0887508i	$-0.971713\pi$
$563$	−3.27590	+	10.0822i	−0.138063	+	0.424914i	0.857991	+	0.513665i	$0.171713\pi$
$564$		0			0
$565$	13.3437	+	9.69474i	0.561372	+	0.407861i
$566$		0			0
$567$	5.95793	+	18.3366i	0.250209	+	0.770065i
$568$		0			0
$569$	18.5037	−	13.4437i	0.775715	−	0.563590i	−0.127975	−	0.991777i	$-0.540848\pi$
$569$	18.5037	−	13.4437i	0.775715	−	0.563590i	0.903690	+	0.428187i	$0.140848\pi$
$570$		0			0
$571$	−20.5139			−0.858480			−0.429240	−	0.903191i	$-0.641218\pi$
$571$	−20.5139			−0.858480			−0.429240	+	0.903191i	$0.641218\pi$
$572$		0			0
$573$	10.6022			0.442912
$574$		0			0
$575$	4.15101	−	3.01588i	0.173109	−	0.125771i
$576$		0			0
$577$	7.48360	+	23.0322i	0.311546	+	0.958841i	0.977153	+	0.212538i	$0.0681730\pi$
$577$	7.48360	+	23.0322i	0.311546	+	0.958841i	−0.665606	+	0.746303i	$0.731827\pi$
$578$		0			0
$579$	−0.183366	−	0.133223i	−0.00762042	−	0.00553656i
$580$		0			0
$581$	−19.6823	+	60.5760i	−0.816561	+	2.51312i
$582$		0			0
$583$	22.6104	−	12.3651i	0.936428	−	0.512111i
$584$		0			0
$585$	−4.64103	+	14.2836i	−0.191883	+	0.590555i
$586$		0			0
$587$	25.8808	+	18.8035i	1.06822	+	0.776104i	0.975591	−	0.219597i	$-0.0704742\pi$
$587$	25.8808	+	18.8035i	1.06822	+	0.776104i	0.0926250	+	0.995701i	$0.470474\pi$
$588$		0			0
$589$	−0.257519	−	0.792562i	−0.0106109	−	0.0326569i
$590$		0			0
$591$	−0.823944	+	0.598631i	−0.0338925	+	0.0246244i
$592$		0			0
$593$	−42.5206			−1.74611			−0.873056	−	0.487620i	$-0.837865\pi$
$593$	−42.5206			−1.74611			−0.873056	+	0.487620i	$0.837865\pi$
$594$		0			0
$595$	−27.2884			−1.11872
$596$		0			0
$597$	−12.9849	+	9.43411i	−0.531438	+	0.386112i
$598$		0			0
$599$	−1.32580	−	4.08040i	−0.0541708	−	0.166721i	0.920311	−	0.391188i	$-0.127936\pi$
$599$	−1.32580	−	4.08040i	−0.0541708	−	0.166721i	−0.974482	+	0.224467i	$0.927936\pi$
$600$		0			0
$601$	−16.1781	−	11.7541i	−0.659919	−	0.479459i	0.206717	−	0.978401i	$-0.433722\pi$
$601$	−16.1781	−	11.7541i	−0.659919	−	0.479459i	−0.866635	+	0.498942i	$0.833722\pi$
$602$		0			0
$603$	4.24379	−	13.0610i	0.172821	−	0.531887i
$604$		0			0
$605$	10.2454	−	4.00408i	0.416533	−	0.162789i
$606$		0			0
$607$	−7.17271	+	22.0753i	−0.291131	+	0.896010i	0.693362	+	0.720589i	$0.256129\pi$
$607$	−7.17271	+	22.0753i	−0.291131	+	0.896010i	−0.984494	+	0.175421i	$0.943871\pi$
$608$		0			0
$609$	−5.06745	−	3.68172i	−0.205343	−	0.149191i
$610$		0			0
$611$	−17.2790	−	53.1794i	−0.699035	−	2.15141i
$612$		0			0
$613$	4.81297	−	3.49683i	0.194394	−	0.141236i	−0.486331	−	0.873775i	$-0.661665\pi$
$613$	4.81297	−	3.49683i	0.194394	−	0.141236i	0.680725	+	0.732539i	$0.261665\pi$
$614$		0			0
$615$	2.89396			0.116696
$616$		0			0
$617$	39.7576			1.60058			0.800291	−	0.599612i	$-0.204678\pi$
$617$	39.7576			1.60058			0.800291	+	0.599612i	$0.204678\pi$
$618$		0			0
$619$	9.56962	−	6.95274i	0.384636	−	0.279454i	−0.378618	−	0.925553i	$-0.623601\pi$
$619$	9.56962	−	6.95274i	0.384636	−	0.279454i	0.763254	+	0.646099i	$0.223601\pi$
$620$		0			0
$621$	6.25482	+	19.2504i	0.250997	+	0.772491i
$622$		0			0
$623$	4.53151	+	3.29233i	0.181551	+	0.131905i
$624$		0			0
$625$	0.309017	−	0.951057i	0.0123607	−	0.0380423i
$626$		0			0
$627$	1.54836	−	0.846765i	0.0618357	−	0.0338165i
$628$		0			0
$629$	14.3427	−	44.1424i	0.571883	−	1.76007i
$630$		0			0
$631$	−11.9825	−	8.70578i	−0.477015	−	0.346572i	0.323154	−	0.946346i	$-0.395257\pi$
$631$	−11.9825	−	8.70578i	−0.477015	−	0.346572i	−0.800169	+	0.599775i	$0.795257\pi$
$632$		0			0
$633$	−5.41430	−	16.6635i	−0.215199	−	0.662314i
$634$		0			0
$635$	13.3554	−	9.70330i	0.529995	−	0.385064i
$636$		0			0
$637$	−63.5756			−2.51896
$638$		0			0
$639$	−22.0233			−0.871230
$640$		0			0
$641$	6.88502	−	5.00226i	0.271942	−	0.197577i	−0.443453	−	0.896298i	$-0.646247\pi$
$641$	6.88502	−	5.00226i	0.271942	−	0.197577i	0.715395	+	0.698720i	$0.246247\pi$
$642$		0			0
$643$	10.6407	+	32.7486i	0.419627	+	1.29148i	0.908046	+	0.418871i	$0.137574\pi$
$643$	10.6407	+	32.7486i	0.419627	+	1.29148i	−0.488418	+	0.872610i	$0.662426\pi$
$644$		0			0
$645$	3.66695	+	2.66420i	0.144386	+	0.104903i
$646$		0			0
$647$	1.64549	−	5.06429i	0.0646908	−	0.199098i	−0.913487	−	0.406868i	$-0.866621\pi$
$647$	1.64549	−	5.06429i	0.0646908	−	0.199098i	0.978178	+	0.207771i	$0.0666208\pi$
$648$		0			0
$649$	−3.78642	−	20.0905i	−0.148630	−	0.788621i
$650$		0			0
$651$	−1.04855	+	3.22712i	−0.0410961	+	0.126481i
$652$		0			0
$653$	−22.8223	−	16.5814i	−0.893106	−	0.648880i	0.0435800	−	0.999050i	$-0.486124\pi$
$653$	−22.8223	−	16.5814i	−0.893106	−	0.648880i	−0.936686	+	0.350170i	$0.886124\pi$
$654$		0			0
$655$	−3.75004	−	11.5414i	−0.146526	−	0.450961i
$656$		0			0
$657$	−16.2529	+	11.8084i	−0.634086	+	0.460690i
$658$		0			0
$659$	−19.9228			−0.776082			−0.388041	−	0.921642i	$-0.626848\pi$
$659$	−19.9228			−0.776082			−0.388041	+	0.921642i	$0.626848\pi$
$660$		0			0
$661$	−16.6144			−0.646225			−0.323112	−	0.946361i	$-0.604729\pi$
$661$	−16.6144			−0.646225			−0.323112	+	0.946361i	$0.604729\pi$
$662$		0			0
$663$	22.9723	−	16.6903i	0.892168	−	0.648198i
$664$		0			0
$665$	−0.956103	−	2.94258i	−0.0370761	−	0.114108i
$666$		0			0
$667$	8.63559	+	6.27413i	0.334372	+	0.242935i
$668$		0			0
$669$	1.38343	−	4.25775i	0.0534864	−	0.164614i
$670$		0			0
$671$	−20.8375	+	44.0289i	−0.804423	+	1.69972i
$672$		0			0
$673$	10.1125	−	31.1229i	0.389807	−	1.19970i	−0.543126	−	0.839651i	$-0.682760\pi$
$673$	10.1125	−	31.1229i	0.389807	−	1.19970i	0.932933	−	0.360050i	$-0.117240\pi$
$674$		0			0
$675$	3.19150	+	2.31876i	0.122841	+	0.0892491i
$676$		0			0
$677$	12.6792	+	39.0227i	0.487302	+	1.49976i	0.828618	+	0.559814i	$0.189127\pi$
$677$	12.6792	+	39.0227i	0.487302	+	1.49976i	−0.341316	+	0.939949i	$0.610873\pi$
$678$		0			0
$679$	−33.7371	+	24.5115i	−1.29471	+	0.940663i
$680$		0			0
$681$	−11.5607			−0.443007
$682$		0			0
$683$	5.71534			0.218691			0.109346	−	0.994004i	$-0.465124\pi$
$683$	5.71534			0.218691			0.109346	+	0.994004i	$0.465124\pi$
$684$		0			0
$685$	5.00257	−	3.63458i	0.191139	−	0.138870i
$686$		0			0
$687$	−3.48739	−	10.7331i	−0.133052	−	0.409493i
$688$		0			0
$689$	38.0350	+	27.6340i	1.44902	+	1.05277i
$690$		0			0
$691$	−12.0118	+	36.9684i	−0.456949	+	1.40634i	0.411883	+	0.911237i	$0.364871\pi$
$691$	−12.0118	+	36.9684i	−0.456949	+	1.40634i	−0.868832	+	0.495107i	$0.835129\pi$
$692$		0			0
$693$	34.1651	+	4.39287i	1.29782	+	0.166871i
$694$		0			0
$695$	1.60765	−	4.94783i	0.0609815	−	0.187682i
$696$		0			0
$697$	21.2195	+	15.4169i	0.803746	+	0.583956i
$698$		0			0
$699$	−3.11835	−	9.59729i	−0.117947	−	0.363003i
$700$		0			0
$701$	−2.72643	+	1.98087i	−0.102976	+	0.0748163i	−0.638082	−	0.769969i	$-0.720272\pi$
$701$	−2.72643	+	1.98087i	−0.102976	+	0.0748163i	0.535106	+	0.844785i	$0.320272\pi$
$702$		0			0
$703$	5.26252			0.198480
$704$		0			0
$705$	−6.65003			−0.250455
$706$		0			0
$707$	−40.1813	+	29.1934i	−1.51117	+	1.09793i
$708$		0			0
$709$	−6.98822	−	21.5075i	−0.262448	−	0.807732i	−0.992270	−	0.124095i	$-0.960397\pi$
$709$	−6.98822	−	21.5075i	−0.262448	−	0.807732i	0.729822	−	0.683637i	$-0.239603\pi$
$710$		0			0
$711$	−1.14561	−	0.832332i	−0.0429636	−	0.0312149i
$712$		0			0
$713$	1.78687	−	5.49943i	0.0669189	−	0.205955i
$714$		0			0
$715$	14.5981	+	13.7694i	0.545939	+	0.514948i
$716$		0			0
$717$	2.40362	−	7.39757i	0.0897647	−	0.276267i
$718$		0			0
$719$	15.1343	+	10.9957i	0.564415	+	0.410072i	0.833072	−	0.553164i	$-0.186580\pi$
$719$	15.1343	+	10.9957i	0.564415	+	0.410072i	−0.268657	+	0.963236i	$0.586580\pi$
$720$		0			0
$721$	−13.4386	−	41.3598i	−0.500480	−	1.54032i
$722$		0			0
$723$	−11.5216	+	8.37092i	−0.428492	+	0.311318i
$724$		0			0
$725$	2.08036			0.0772627
$726$		0			0
$727$	−2.98028			−0.110532			−0.0552662	−	0.998472i	$-0.517601\pi$
$727$	−2.98028			−0.110532			−0.0552662	+	0.998472i	$0.517601\pi$
$728$		0			0
$729$	2.36362	−	1.71727i	0.0875415	−	0.0636026i
$730$		0			0
$731$	12.6945	+	39.0696i	0.469523	+	1.44504i
$732$		0			0
$733$	16.2972	+	11.8406i	0.601949	+	0.437342i	0.846570	−	0.532277i	$-0.178664\pi$
$733$	16.2972	+	11.8406i	0.601949	+	0.437342i	−0.244621	+	0.969619i	$0.578664\pi$
$734$		0			0
$735$	−2.33647	+	7.19090i	−0.0861818	+	0.265240i
$736$		0			0
$737$	−13.3486	−	12.5909i	−0.491703	−	0.463791i
$738$		0			0
$739$	7.17525	−	22.0831i	0.263946	−	0.812341i	−0.727989	−	0.685589i	$-0.759545\pi$
$739$	7.17525	−	22.0831i	0.263946	−	0.812341i	0.991934	−	0.126752i	$-0.0404553\pi$
$740$		0			0
$741$	2.60464	+	1.89238i	0.0956838	+	0.0695183i
$742$		0			0
$743$	9.71585	+	29.9023i	0.356440	+	1.09701i	0.955170	+	0.296058i	$0.0956723\pi$
$743$	9.71585	+	29.9023i	0.356440	+	1.09701i	−0.598730	+	0.800951i	$0.704328\pi$
$744$		0			0
$745$	−9.13479	+	6.63681i	−0.334673	+	0.243154i
$746$		0			0
$747$	37.7850			1.38248
$748$		0			0
$749$	34.9299			1.27631
$750$		0			0
$751$	−32.8274	+	23.8505i	−1.19789	+	0.870318i	−0.994076	−	0.108692i	$-0.965334\pi$
$751$	−32.8274	+	23.8505i	−1.19789	+	0.870318i	−0.203814	+	0.979010i	$0.565334\pi$
$752$		0			0
$753$	0.851536	+	2.62076i	0.0310317	+	0.0955058i
$754$		0			0
$755$	−0.126708	−	0.0920586i	−0.00461137	−	0.00335036i
$756$		0			0
$757$	−6.97501	+	21.4669i	−0.253511	+	0.780226i	0.740609	+	0.671937i	$0.234537\pi$
$757$	−6.97501	+	21.4669i	−0.253511	+	0.780226i	−0.994119	+	0.108289i	$0.965463\pi$
$758$		0			0
$759$	12.1455	+	1.56163i	0.440852	+	0.0566837i
$760$		0			0
$761$	6.79531	−	20.9138i	0.246330	−	0.758125i	−0.749085	−	0.662474i	$-0.769507\pi$
$761$	6.79531	−	20.9138i	0.246330	−	0.758125i	0.995415	−	0.0956511i	$-0.0304933\pi$
$762$		0			0
$763$	21.1583	+	15.3724i	0.765981	+	0.556518i
$764$		0			0
$765$	5.00249	+	15.3961i	0.180865	+	0.556646i
$766$		0			0
$767$	30.1736	−	21.9224i	1.08951	−	0.791572i
$768$		0			0
$769$	−41.1834			−1.48511			−0.742556	−	0.669784i	$-0.766387\pi$
$769$	−41.1834			−1.48511			−0.742556	+	0.669784i	$0.766387\pi$
$770$		0			0
$771$	13.6940			0.493178
$772$		0			0
$773$	8.76589	−	6.36879i	0.315287	−	0.229070i	−0.418875	−	0.908044i	$-0.637575\pi$
$773$	8.76589	−	6.36879i	0.315287	−	0.229070i	0.734162	+	0.678975i	$0.237575\pi$
$774$		0			0
$775$	−0.348255	−	1.07182i	−0.0125097	−	0.0385009i
$776$		0			0
$777$	−17.3354	−	12.5949i	−0.621903	−	0.451839i
$778$		0			0
$779$	−0.918975	+	2.82832i	−0.0329257	+	0.101335i
$780$		0			0
$781$	−12.5882	+	26.5984i	−0.450441	+	0.951765i
$782$		0			0
$783$	−2.53605	+	7.80517i	−0.0906311	+	0.278934i
$784$		0			0
$785$	−11.0827	−	8.05207i	−0.395560	−	0.287391i
$786$		0			0
$787$	−9.68298	−	29.8011i	−0.345161	−	1.06230i	−0.961498	−	0.274813i	$-0.911384\pi$
$787$	−9.68298	−	29.8011i	−0.345161	−	1.06230i	0.616337	−	0.787483i	$-0.288616\pi$
$788$		0			0
$789$	−15.5184	+	11.2748i	−0.552470	+	0.401393i
$790$		0			0
$791$	69.0126			2.45381
$792$		0			0
$793$	−88.8638			−3.15565
$794$		0			0
$795$	4.52345	−	3.28648i	0.160430	−	0.116559i
$796$		0			0
$797$	−2.94208	−	9.05479i	−0.104214	−	0.320737i	0.885331	−	0.464961i	$-0.153932\pi$
$797$	−2.94208	−	9.05479i	−0.104214	−	0.320737i	−0.989545	+	0.144224i	$0.953932\pi$
$798$		0			0
$799$	−48.7603	−	35.4264i	−1.72502	−	1.25330i
$800$		0			0
$801$	1.02682	−	3.16022i	0.0362808	−	0.111661i
$802$		0			0
$803$	4.97156	+	26.3787i	0.175442	+	0.930885i
$804$		0			0
$805$	6.63420	−	20.4180i	0.233825	−	0.719639i
$806$		0			0
$807$	−0.264616	−	0.192255i	−0.00931493	−	0.00676769i
$808$		0			0
$809$	−8.98937	−	27.6664i	−0.316049	−	0.972700i	−0.975320	−	0.220795i	$-0.929135\pi$
$809$	−8.98937	−	27.6664i	−0.316049	−	0.972700i	0.659271	−	0.751906i	$-0.270865\pi$
$810$		0			0
$811$	35.2897	−	25.6395i	1.23919	−	0.900324i	0.241646	−	0.970364i	$-0.422313\pi$
$811$	35.2897	−	25.6395i	1.23919	−	0.900324i	0.997544	+	0.0700400i	$0.0223127\pi$
$812$		0			0
$813$	11.7010			0.410372
$814$		0			0
$815$	−5.85320			−0.205029
$816$		0			0
$817$	−3.76821	+	2.73776i	−0.131833	+	0.0957822i
$818$		0			0
$819$	19.4189	+	59.7653i	0.678552	+	2.08837i
$820$		0			0
$821$	−21.5502	−	15.6571i	−0.752108	−	0.546438i	0.144372	−	0.989524i	$-0.453884\pi$
$821$	−21.5502	−	15.6571i	−0.752108	−	0.546438i	−0.896479	+	0.443085i	$0.853884\pi$
$822$		0			0
$823$	6.16748	−	18.9816i	0.214985	−	0.661656i	−0.784170	−	0.620546i	$-0.786911\pi$
$823$	6.16748	−	18.9816i	0.214985	−	0.661656i	0.999155	−	0.0411092i	$-0.0130892\pi$
$824$		0			0
$825$	2.09393	−	1.14512i	0.0729012	−	0.0398680i
$826$		0			0
$827$	8.24515	−	25.3760i	0.286712	−	0.882408i	−0.699168	−	0.714957i	$-0.746446\pi$
$827$	8.24515	−	25.3760i	0.286712	−	0.882408i	0.985880	−	0.167451i	$-0.0535537\pi$
$828$		0			0
$829$	41.0234	+	29.8052i	1.42480	+	1.03518i	0.990955	+	0.134192i	$0.0428439\pi$
$829$	41.0234	+	29.8052i	1.42480	+	1.03518i	0.433846	+	0.900987i	$0.357156\pi$
$830$		0			0
$831$	−2.54246	−	7.82489i	−0.0881970	−	0.271443i
$832$		0			0
$833$	−55.4396	+	40.2792i	−1.92087	+	1.39559i
$834$		0			0
$835$	12.2892			0.425285
$836$		0			0
$837$	4.44583			0.153670
$838$		0			0
$839$	2.18338	−	1.58632i	0.0753788	−	0.0547659i	−0.549458	−	0.835522i	$-0.685166\pi$
$839$	2.18338	−	1.58632i	0.0753788	−	0.0547659i	0.624836	+	0.780756i	$0.285166\pi$
$840$		0			0
$841$	−7.62410	−	23.4646i	−0.262900	−	0.809123i
$842$		0			0
$843$	3.31374	+	2.40757i	0.114131	+	0.0829211i
$844$		0			0
$845$	−7.29568	+	22.4538i	−0.250979	+	0.772434i
$846$		0			0
$847$	24.8337	−	38.7515i	0.853295	−	1.33152i
$848$		0			0
$849$	−0.129174	+	0.397558i	−0.00443326	+	0.0136442i
$850$		0			0
$851$	29.5417	+	21.4633i	1.01268	+	0.735753i
$852$		0			0
$853$	−5.45078	−	16.7758i	−0.186631	−	0.574392i	0.813341	−	0.581787i	$-0.197646\pi$
$853$	−5.45078	−	16.7758i	−0.186631	−	0.574392i	−0.999973	+	0.00739490i	$0.997646\pi$
$854$		0			0
$855$	−1.48493	+	1.07886i	−0.0507835	+	0.0368963i
$856$		0			0
$857$	−8.72254			−0.297956			−0.148978	−	0.988840i	$-0.547598\pi$
$857$	−8.72254			−0.297956			−0.148978	+	0.988840i	$0.547598\pi$
$858$		0			0
$859$	−34.2322			−1.16799			−0.583993	−	0.811759i	$-0.698510\pi$
$859$	−34.2322			−1.16799			−0.583993	+	0.811759i	$0.698510\pi$
$860$		0			0
$861$	9.79627	−	7.11741i	0.333856	−	0.242561i
$862$		0			0
$863$	−12.6167	−	38.8303i	−0.429478	−	1.32180i	−0.898640	−	0.438686i	$-0.855444\pi$
$863$	−12.6167	−	38.8303i	−0.429478	−	1.32180i	0.469162	−	0.883112i	$-0.344556\pi$
$864$		0			0
$865$	−15.3840	−	11.1771i	−0.523072	−	0.380034i
$866$		0			0
$867$	5.67782	−	17.4745i	0.192829	−	0.593467i
$868$		0			0
$869$	−1.66005	+	0.907843i	−0.0563133	+	0.0307965i
$870$		0			0
$871$	10.3446	−	31.8374i	0.350513	−	1.07877i
$872$		0			0
$873$	20.0140	+	14.5410i	0.677371	+	0.492139i
$874$		0			0
$875$	−1.29298	−	3.97939i	−0.0437108	−	0.134528i
$876$		0			0
$877$	3.24735	−	2.35934i	0.109655	−	0.0796692i	−0.531606	−	0.846992i	$-0.678411\pi$
$877$	3.24735	−	2.35934i	0.109655	−	0.0796692i	0.641262	+	0.767322i	$0.278411\pi$
$878$		0			0
$879$	−0.847247			−0.0285769
$880$		0			0
$881$	21.1713			0.713278			0.356639	−	0.934242i	$-0.383923\pi$
$881$	21.1713			0.713278			0.356639	+	0.934242i	$0.383923\pi$
$882$		0			0
$883$	−5.39607	+	3.92047i	−0.181592	+	0.131934i	−0.674868	−	0.737939i	$-0.735799\pi$
$883$	−5.39607	+	3.92047i	−0.181592	+	0.131934i	0.493276	+	0.869873i	$0.335799\pi$
$884$		0			0
$885$	−1.37069	−	4.21854i	−0.0460752	−	0.141805i
$886$		0			0
$887$	−2.05125	−	1.49032i	−0.0688742	−	0.0500400i	0.552815	−	0.833304i	$-0.313553\pi$
$887$	−2.05125	−	1.49032i	−0.0688742	−	0.0500400i	−0.621690	+	0.783264i	$0.713553\pi$
$888$		0			0
$889$	21.3449	−	65.6928i	0.715884	−	2.20326i
$890$		0			0
$891$	−2.83046	−	15.0182i	−0.0948241	−	0.503130i
$892$		0			0
$893$	2.11171	−	6.49918i	0.0706658	−	0.217487i
$894$		0			0
$895$	−0.134643	−	0.0978237i	−0.00450061	−	0.00326989i
$896$		0			0
$897$	6.90329	+	21.2462i	0.230494	+	0.709388i
$898$		0			0
$899$	1.89676	−	1.37808i	0.0632604	−	0.0459614i
$900$		0			0
$901$	50.6754			1.68824
$902$		0			0
$903$	18.9653			0.631124
$904$		0			0
$905$	3.30459	−	2.40092i	0.109848	−	0.0798094i
$906$		0			0
$907$	−11.2423	−	34.6002i	−0.373294	−	1.14888i	−0.944622	−	0.328160i	$-0.893572\pi$
$907$	−11.2423	−	34.6002i	−0.373294	−	1.14888i	0.571328	−	0.820722i	$-0.306428\pi$
$908$		0			0
$909$	23.8369	+	17.3185i	0.790620	+	0.574419i
$910$		0			0
$911$	−18.0238	+	55.4717i	−0.597157	+	1.83786i	−0.0534731	+	0.998569i	$0.517029\pi$
$911$	−18.0238	+	55.4717i	−0.597157	+	1.83786i	−0.543684	+	0.839290i	$0.682971\pi$
$912$		0			0
$913$	21.5973	−	45.6344i	0.714768	−	1.51028i
$914$		0			0
$915$	−3.26583	+	10.0512i	−0.107965	+	0.332282i
$916$		0			0
$917$	−41.0792	−	29.8458i	−1.35655	−	0.985594i
$918$		0			0
$919$	9.19511	+	28.2997i	0.303319	+	0.933519i	0.980299	+	0.197518i	$0.0632882\pi$
$919$	9.19511	+	28.2997i	0.303319	+	0.933519i	−0.676980	+	0.736001i	$0.736712\pi$
$920$		0			0
$921$	11.1550	−	8.10458i	0.367570	−	0.267055i
$922$		0			0
$923$	−53.6837			−1.76702
$924$		0			0
$925$	7.11676			0.233998
$926$		0			0
$927$	−20.8716	+	15.1641i	−0.685512	+	0.498054i
$928$		0			0
$929$	−8.03546	−	24.7306i	−0.263635	−	0.811384i	−0.992005	−	0.126200i	$-0.959722\pi$
$929$	−8.03546	−	24.7306i	−0.263635	−	0.811384i	0.728370	−	0.685184i	$-0.240278\pi$
$930$		0			0
$931$	−6.28585	−	4.56693i	−0.206010	−	0.149675i
$932$		0			0
$933$	4.15216	−	12.7790i	0.135936	−	0.418367i
$934$		0			0
$935$	21.4538	+	2.75847i	0.701613	+	0.0902117i
$936$		0			0
$937$	−1.99643	+	6.14437i	−0.0652205	+	0.200728i	−0.978356	−	0.206928i	$-0.933654\pi$
$937$	−1.99643	+	6.14437i	−0.0652205	+	0.200728i	0.913136	+	0.407655i	$0.133654\pi$
$938$		0			0
$939$	2.08979	+	1.51832i	0.0681977	+	0.0495485i
$940$		0			0
$941$	−9.22366	−	28.3875i	−0.300683	−	0.925406i	−0.981253	−	0.192724i	$-0.938268\pi$
$941$	−9.22366	−	28.3875i	−0.300683	−	0.925406i	0.680570	−	0.732683i	$-0.261732\pi$
$942$		0			0
$943$	−16.6941	+	12.1290i	−0.543635	+	0.394974i
$944$		0			0
$945$	16.5062			0.536947
$946$		0			0
$947$	36.1069			1.17332			0.586658	−	0.809834i	$-0.300443\pi$
$947$	36.1069			1.17332			0.586658	+	0.809834i	$0.300443\pi$
$948$		0			0
$949$	−39.6178	+	28.7840i	−1.28605	+	0.934369i
$950$		0			0
$951$	0.555971	+	1.71110i	0.0180286	+	0.0554863i
$952$		0			0
$953$	27.9265	+	20.2898i	0.904628	+	0.657250i	0.939650	−	0.342136i	$-0.111150\pi$
$953$	27.9265	+	20.2898i	0.904628	+	0.657250i	−0.0350228	+	0.999387i	$0.511150\pi$
$954$		0			0
$955$	−4.55297	+	14.0126i	−0.147331	+	0.453437i
$956$		0			0
$957$	3.61179	+	3.40676i	0.116753	+	0.110125i
$958$		0			0
$959$	7.99519	−	24.6067i	0.258178	−	0.794591i
$960$		0			0
$961$	24.0520	+	17.4748i	0.775871	+	0.563704i
$962$		0			0
$963$	−6.40331	−	19.7074i	−0.206344	−	0.635061i
$964$		0			0
$965$	0.254821	−	0.185138i	0.00820298	−	0.00595982i
$966$		0			0
$967$	−28.4086			−0.913559			−0.456780	−	0.889580i	$-0.650997\pi$
$967$	−28.4086			−0.913559			−0.456780	+	0.889580i	$0.650997\pi$
$968$		0			0
$969$	3.47026			0.111481
$970$		0			0
$971$	25.0567	−	18.2048i	0.804108	−	0.584219i	−0.108008	−	0.994150i	$-0.534447\pi$
$971$	25.0567	−	18.2048i	0.804108	−	0.584219i	0.912116	+	0.409931i	$0.134447\pi$
$972$		0			0
$973$	−6.72668	−	20.7026i	−0.215648	−	0.663695i
$974$		0			0
$975$	3.52238	+	2.55916i	0.112806	+	0.0819586i
$976$		0			0
$977$	−11.9662	+	36.8282i	−0.382833	+	1.17824i	0.555207	+	0.831712i	$0.312639\pi$
$977$	−11.9662	+	36.8282i	−0.382833	+	1.17824i	−0.938040	+	0.346527i	$0.887361\pi$
$978$		0			0
$979$	−3.22980	−	3.04646i	−0.103225	−	0.0973652i
$980$		0			0
$981$	4.79436	−	14.7555i	0.153072	−	0.471108i
$982$		0			0
$983$	−8.99601	−	6.53598i	−0.286928	−	0.208465i	0.435006	−	0.900428i	$-0.356746\pi$
$983$	−8.99601	−	6.53598i	−0.286928	−	0.208465i	−0.721934	+	0.691962i	$0.756746\pi$
$984$		0			0
$985$	−0.437361	−	1.34606i	−0.0139355	−	0.0428890i
$986$		0			0
$987$	−22.5108	+	16.3551i	−0.716528	+	0.520588i
$988$		0			0
$989$	−32.3193			−1.02769
$990$		0			0
$991$	−11.5682			−0.367475			−0.183737	−	0.982975i	$-0.558820\pi$
$991$	−11.5682			−0.367475			−0.183737	+	0.982975i	$0.558820\pi$
$992$		0			0
$993$	3.83426	−	2.78575i	0.121676	−	0.0884031i
$994$		0			0
$995$	−6.89259	−	21.2132i	−0.218510	−	0.672504i
$996$		0			0
$997$	−22.7886	−	16.5569i	−0.721722	−	0.524362i	0.165212	−	0.986258i	$-0.447169\pi$
$997$	−22.7886	−	16.5569i	−0.721722	−	0.524362i	−0.886934	+	0.461896i	$0.847169\pi$
$998$		0			0
$999$	−8.67564	+	26.7009i	−0.274485	+	0.844779i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	440.2.y.b.361.2	✓	12
4.3	odd	2		880.2.bo.j.801.2		12
11.4	even	5		4840.2.a.bf.1.3		6
11.5	even	5	inner	440.2.y.b.401.2	yes	12
11.7	odd	10		4840.2.a.be.1.3		6
44.7	even	10		9680.2.a.cy.1.4		6
44.15	odd	10		9680.2.a.cx.1.4		6
44.27	odd	10		880.2.bo.j.401.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
440.2.y.b.361.2	✓	12	1.1	even	1	trivial
440.2.y.b.401.2	yes	12	11.5	even	5	inner
880.2.bo.j.401.2		12	44.27	odd	10
880.2.bo.j.801.2		12	4.3	odd	2
4840.2.a.be.1.3		6	11.7	odd	10
4840.2.a.bf.1.3		6	11.4	even	5
9680.2.a.cx.1.4		6	44.15	odd	10
9680.2.a.cy.1.4		6	44.7	even	10

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:	\( N \)	\(=\)	\( 440 = 2^{3} \cdot 5 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	440.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.582157 + 0.422962i) q^{3} +(-0.309017 - 0.951057i) q^{5} +(-3.38507 - 2.45940i) q^{7} +(-0.767041 + 2.36071i) q^{9} +(2.41269 + 2.27573i) q^{11} +(-1.86973 + 5.75443i) q^{13} +(0.582157 + 0.422962i) q^{15} +(2.01535 + 6.20260i) q^{17} +(-0.598231 + 0.434640i) q^{19} +3.01088 q^{21} -5.13093 q^{23} +(-0.809017 + 0.587785i) q^{25} +(-1.21904 - 3.75183i) q^{27} +(-1.68305 - 1.22281i) q^{29} +(-0.348255 + 1.07182i) q^{31} +(-2.36711 - 0.304357i) q^{33} +(-1.29298 + 3.97939i) q^{35} +(-5.75758 - 4.18313i) q^{37} +(-1.34543 - 4.14080i) q^{39} +(3.25363 - 2.36390i) q^{41} +6.29891 q^{43} +2.48220 q^{45} +(-7.47651 + 5.43200i) q^{47} +(3.24696 + 9.99312i) q^{49} +(-3.79671 - 2.75847i) q^{51} +(2.40111 - 7.38985i) q^{53} +(1.41879 - 2.99784i) q^{55} +(0.164428 - 0.506058i) q^{57} +(-4.98691 - 3.62320i) q^{59} +(4.53849 + 13.9680i) q^{61} +(8.40242 - 6.10472i) q^{63} +6.05056 q^{65} -5.53268 q^{67} +(2.98700 - 2.17019i) q^{69} +(2.74176 + 8.43827i) q^{71} +(6.54779 + 4.75724i) q^{73} +(0.222364 - 0.684366i) q^{75} +(-2.57020 - 13.6373i) q^{77} +(-0.176289 + 0.542560i) q^{79} +(-3.72786 - 2.70845i) q^{81} +(-4.70399 - 14.4774i) q^{83} +(5.27625 - 3.83342i) q^{85} +1.49700 q^{87} -1.33867 q^{89} +(20.4816 - 14.8808i) q^{91} +(-0.250599 - 0.771266i) q^{93} +(0.598231 + 0.434640i) q^{95} +(3.07980 - 9.47864i) q^{97} +(-7.22296 + 3.95008i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - q^{3} + 3 q^{5} - 8 q^{7} + 10 q^{9} - 4 q^{11} - 7 q^{13} + q^{15} + 7 q^{17} + 3 q^{19} + 4 q^{21} + 36 q^{23} - 3 q^{25} + 8 q^{27} + 13 q^{29} + 2 q^{31} - 19 q^{33} - 2 q^{35} - 22 q^{37}+ \cdots - 79 q^{99}+O(q^{100}) \) 12 * q - q^3 + 3 * q^5 - 8 * q^7 + 10 * q^9 - 4 * q^11 - 7 * q^13 + q^15 + 7 * q^17 + 3 * q^19 + 4 * q^21 + 36 * q^23 - 3 * q^25 + 8 * q^27 + 13 * q^29 + 2 * q^31 - 19 * q^33 - 2 * q^35 - 22 * q^37 - q^39 + 7 * q^41 + 6 * q^43 - 20 * q^45 - 2 * q^47 - 19 * q^49 - 33 * q^51 + 3 * q^53 + 4 * q^55 - 25 * q^57 + 19 * q^59 + 22 * q^61 - 2 * q^63 + 12 * q^65 + 22 * q^67 + 21 * q^69 + 44 * q^71 + 17 * q^73 - q^75 - 38 * q^77 - 43 * q^79 - 85 * q^81 - 15 * q^83 + 18 * q^85 + 50 * q^87 + 2 * q^89 + 59 * q^91 + 5 * q^93 - 3 * q^95 - 20 * q^97 - 79 * q^99

Introduction

L-functions

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Database

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