LMFDB - Embedded newform 1040.2.dh.b.529.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1040,2,Mod(289,1040)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1040, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([0, 0, 3, 2])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("1040.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1040 = 2^{4} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1040.dh (of order $6$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,0,0,0,0,0,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(9)] == traces)

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

Self dual:	no
Analytic conductor:	$8.30444181021$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$6$ over $\Q(\zeta_{6})$
Coefficient field:	12.0.89539436150784.1
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 $ x^12 - 2x^11 + 2x^10 - 8x^9 + 4x^8 + 16x^7 - 8x^6 + 20x^5 + 20x^4 - 24x^3 + 8x^2 - 8*x + 4
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 130)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			529.4
Root			$-1.16746 + 0.312819i$ of defining polynomial
Character	$\chi$	$=$	1040.529
Dual form			1040.2.dh.b.289.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.466951 + 0.269594i) q^{3} +(-0.539189 - 2.17009i) q^{5} +(-0.614250 + 0.354638i) q^{7} +(-1.35464 - 2.34630i) q^{9} +(-2.25513 + 3.90600i) q^{11} +(-3.35963 + 1.30878i) q^{13} +(0.333268 - 1.15869i) q^{15} +(2.74538 - 1.58504i) q^{17} +(0.0603191 + 0.104476i) q^{19} -0.382433 q^{21} +(-4.30507 - 2.48554i) q^{23} +(-4.41855 + 2.34017i) q^{25} -3.07838i q^{27} +(-3.63090 + 6.28890i) q^{29} -9.66701 q^{31} +(-2.10607 + 1.21594i) q^{33} +(1.10079 + 1.14176i) q^{35} +(6.02558 + 3.47887i) q^{37} +(-1.92162 - 0.294598i) q^{39} +(-0.223740 + 0.387529i) q^{41} +(1.73205 - 1.00000i) q^{43} +(-4.36127 + 4.20478i) q^{45} +4.70928i q^{47} +(-3.24846 + 5.62651i) q^{49} +1.70928 q^{51} -9.58864i q^{53} +(9.69230 + 2.78776i) q^{55} +0.0650468i q^{57} +(2.87936 + 4.98720i) q^{59} +(-3.53139 - 6.11655i) q^{61} +(1.66417 + 0.960811i) q^{63} +(4.65165 + 6.58500i) q^{65} +(-2.53020 - 1.46081i) q^{67} +(-1.34017 - 2.32125i) q^{69} +(-4.09171 - 7.08705i) q^{71} -6.74539i q^{73} +(-2.69415 - 0.0984700i) q^{75} -3.19902i q^{77} -16.0072 q^{79} +(-3.23400 + 5.60145i) q^{81} -0.355771i q^{83} +(-4.91996 - 5.10306i) q^{85} +(-3.39090 + 1.95774i) q^{87} +(1.81545 - 3.14445i) q^{89} +(1.59951 - 1.99537i) q^{91} +(-4.51402 - 2.60617i) q^{93} +(0.194198 - 0.187230i) q^{95} +(-6.84878 + 3.95415i) q^{97} +12.2195 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 2 q^{9} + 6 q^{11} - 4 q^{15} + 26 q^{19} - 24 q^{21} + 4 q^{25} - 28 q^{29} - 24 q^{31} + 6 q^{35} - 36 q^{39} - 4 q^{41} + 12 q^{45} - 4 q^{49} - 8 q^{51} - 12 q^{55} - 16 q^{59} - 8 q^{61} - 10 q^{65}+ \cdots + 52 q^{99}+O(q^{100}) $ 12 * q - 2 * q^9 + 6 * q^11 - 4 * q^15 + 26 * q^19 - 24 * q^21 + 4 * q^25 - 28 * q^29 - 24 * q^31 + 6 * q^35 - 36 * q^39 - 4 * q^41 + 12 * q^45 - 4 * q^49 - 8 * q^51 - 12 * q^55 - 16 * q^59 - 8 * q^61 - 10 * q^65 + 28 * q^69 - 40 * q^71 + 8 * q^75 - 56 * q^79 + 26 * q^81 - 16 * q^85 + 14 * q^89 + 38 * q^91 + 8 * q^95 + 52 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times$.

$n$	$261$	$417$	$561$	$911$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.466951	+	0.269594i	0.269594	+	0.155650i	0.628703	−	0.777645i	$-0.283586\pi$
$3$	0.466951	+	0.269594i	0.269594	+	0.155650i	−0.359109	+	0.933296i	$0.616919\pi$
$4$		0			0
$5$	−0.539189	−	2.17009i	−0.241133	−	0.970492i
$5$	−0.539189	−	2.17009i	−0.241133	−	0.970492i
$6$		0			0
$7$	−0.614250	+	0.354638i	−0.232165	+	0.134040i	−0.611570	−	0.791190i	$-0.709462\pi$
$7$	−0.614250	+	0.354638i	−0.232165	+	0.134040i	0.379406	+	0.925230i	$0.376129\pi$
$8$		0			0
$9$	−1.35464	−	2.34630i	−0.451546	−	0.782100i
$10$		0			0
$11$	−2.25513	+	3.90600i	−0.679947	+	1.17770i	0.295049	+	0.955482i	$0.404664\pi$
$11$	−2.25513	+	3.90600i	−0.679947	+	1.17770i	−0.974996	+	0.222221i	$0.928669\pi$
$12$		0			0
$13$	−3.35963	+	1.30878i	−0.931793	+	0.362991i
$13$	−3.35963	+	1.30878i	−0.931793	+	0.362991i
$14$		0			0
$15$	0.333268	−	1.15869i	0.0860495	−	0.299172i
$16$		0			0
$17$	2.74538	−	1.58504i	0.665851	−	0.384429i	−0.128652	−	0.991690i	$-0.541065\pi$
$17$	2.74538	−	1.58504i	0.665851	−	0.384429i	0.794503	+	0.607260i	$0.207732\pi$
$18$		0			0
$19$	0.0603191	+	0.104476i	0.0138381	+	0.0239684i	0.872862	−	0.487968i	$-0.162262\pi$
$19$	0.0603191	+	0.104476i	0.0138381	+	0.0239684i	−0.859023	+	0.511936i	$0.828928\pi$
$20$		0			0
$21$	−0.382433			−0.0834538
$22$		0			0
$23$	−4.30507	−	2.48554i	−0.897670	−	0.518270i	−0.0212264	−	0.999775i	$-0.506757\pi$
$23$	−4.30507	−	2.48554i	−0.897670	−	0.518270i	−0.876443	+	0.481505i	$0.840090\pi$
$24$		0			0
$25$	−4.41855	+	2.34017i	−0.883710	+	0.468035i
$26$		0			0
$27$		−	3.07838i		−	0.592434i
$28$		0			0
$29$	−3.63090	+	6.28890i	−0.674241	+	1.16782i	0.302449	+	0.953165i	$0.402196\pi$
$29$	−3.63090	+	6.28890i	−0.674241	+	1.16782i	−0.976690	+	0.214654i	$0.931138\pi$
$30$		0			0
$31$	−9.66701			−1.73625			−0.868124	−	0.496348i	$-0.834674\pi$
$31$	−9.66701			−1.73625			−0.868124	+	0.496348i	$0.834674\pi$
$32$		0			0
$33$	−2.10607	+	1.21594i	−0.366620	+	0.211668i
$34$		0			0
$35$	1.10079	+	1.14176i	0.186068	+	0.192993i
$36$		0			0
$37$	6.02558	+	3.47887i	0.990599	+	0.571923i	0.905453	−	0.424446i	$-0.139531\pi$
$37$	6.02558	+	3.47887i	0.990599	+	0.571923i	0.0851458	+	0.996369i	$0.472864\pi$
$38$		0			0
$39$	−1.92162	−	0.294598i	−0.307706	−	0.0471735i
$40$		0			0
$41$	−0.223740	+	0.387529i	−0.0349423	+	0.0605219i	−0.882968	−	0.469434i	$-0.844458\pi$
$41$	−0.223740	+	0.387529i	−0.0349423	+	0.0605219i	0.848025	+	0.529956i	$0.177791\pi$
$42$		0			0
$43$	1.73205	−	1.00000i	0.264135	−	0.152499i	−0.362084	−	0.932145i	$-0.617935\pi$
$43$	1.73205	−	1.00000i	0.264135	−	0.152499i	0.626219	+	0.779647i	$0.284601\pi$
$44$		0			0
$45$	−4.36127	+	4.20478i	−0.650140	+	0.626812i
$46$		0			0
$47$			4.70928i			0.686918i	0.939168	+	0.343459i	$0.111599\pi$
$47$			4.70928i			0.686918i	−0.939168	+	0.343459i	$0.888401\pi$
$48$		0			0
$49$	−3.24846	+	5.62651i	−0.464066	+	0.803786i
$50$		0			0
$51$	1.70928			0.239346
$52$		0			0
$53$		−	9.58864i		−	1.31710i	−0.752537	−	0.658550i	$-0.771170\pi$
$53$		−	9.58864i		−	1.31710i	0.752537	−	0.658550i	$-0.228830\pi$
$54$		0			0
$55$	9.69230	+	2.78776i	1.30691	+	0.375901i
$56$		0			0
$57$			0.0650468i			0.00861565i
$58$		0			0
$59$	2.87936	+	4.98720i	0.374861	+	0.649278i	0.990306	−	0.138901i	$-0.0443571\pi$
$59$	2.87936	+	4.98720i	0.374861	+	0.649278i	−0.615445	+	0.788180i	$0.711024\pi$
$60$		0			0
$61$	−3.53139	−	6.11655i	−0.452148	−	0.783144i	0.546371	−	0.837543i	$-0.316009\pi$
$61$	−3.53139	−	6.11655i	−0.452148	−	0.783144i	−0.998519	+	0.0543997i	$0.982675\pi$
$62$		0			0
$63$	1.66417	+	0.960811i	0.209666	+	0.121051i
$64$		0			0
$65$	4.65165	+	6.58500i	0.576966	+	0.816768i
$66$		0			0
$67$	−2.53020	−	1.46081i	−0.309113	−	0.178466i	0.337416	−	0.941355i	$-0.390447\pi$
$67$	−2.53020	−	1.46081i	−0.309113	−	0.178466i	−0.646530	+	0.762889i	$0.723780\pi$
$68$		0			0
$69$	−1.34017	−	2.32125i	−0.161338	−	0.279445i
$70$		0			0
$71$	−4.09171	−	7.08705i	−0.485596	−	0.841078i	0.514267	−	0.857630i	$-0.328064\pi$
$71$	−4.09171	−	7.08705i	−0.485596	−	0.841078i	−0.999863	+	0.0165526i	$0.994731\pi$
$72$		0			0
$73$		−	6.74539i		−	0.789488i	−0.918791	−	0.394744i	$-0.870833\pi$
$73$		−	6.74539i		−	0.789488i	0.918791	−	0.394744i	$-0.129167\pi$
$74$		0			0
$75$	−2.69415	−	0.0984700i	−0.311093	−	0.0113703i
$76$		0			0
$77$		−	3.19902i		−	0.364562i
$78$		0			0
$79$	−16.0072			−1.80095			−0.900475	−	0.434908i	$-0.856781\pi$
$79$	−16.0072			−1.80095			−0.900475	+	0.434908i	$0.856781\pi$
$80$		0			0
$81$	−3.23400	+	5.60145i	−0.359333	+	0.622383i
$82$		0			0
$83$		−	0.355771i		−	0.0390510i	−0.999809	−	0.0195255i	$-0.993784\pi$
$83$		−	0.355771i		−	0.0390510i	0.999809	−	0.0195255i	$-0.00621555\pi$
$84$		0			0
$85$	−4.91996	−	5.10306i	−0.533644	−	0.553505i
$86$		0			0
$87$	−3.39090	+	1.95774i	−0.363543	+	0.209892i
$88$		0			0
$89$	1.81545	−	3.14445i	0.192437	−	0.333311i	−0.753620	−	0.657310i	$-0.771694\pi$
$89$	1.81545	−	3.14445i	0.192437	−	0.333311i	0.946057	+	0.323999i	$0.105027\pi$
$90$		0			0
$91$	1.59951	−	1.99537i	0.167674	−	0.209172i
$92$		0			0
$93$	−4.51402	−	2.60617i	−0.468083	−	0.270248i
$94$		0			0
$95$	0.194198	−	0.187230i	0.0199243	−	0.0192094i
$96$		0			0
$97$	−6.84878	+	3.95415i	−0.695388	+	0.401483i	−0.805627	−	0.592422i	$-0.798172\pi$
$97$	−6.84878	+	3.95415i	−0.695388	+	0.401483i	0.110239	+	0.993905i	$0.464838\pi$
$98$		0			0
$99$	12.2195			1.22811
$100$		0			0
$101$	−3.07058	+	5.31840i	−0.305534	+	0.529200i	−0.977380	−	0.211490i	$-0.932168\pi$
$101$	−3.07058	+	5.31840i	−0.305534	+	0.529200i	0.671846	+	0.740691i	$0.265502\pi$
$102$		0			0
$103$		−	17.6803i		−	1.74210i	−0.491198	−	0.871048i	$-0.663441\pi$
$103$		−	17.6803i		−	1.74210i	0.491198	−	0.871048i	$-0.336559\pi$
$104$		0			0
$105$	0.206204	+	0.829914i	0.0201234	+	0.0809913i
$106$		0			0
$107$	0.466951	+	0.269594i	0.0451419	+	0.0260627i	0.522401	−	0.852700i	$-0.325036\pi$
$107$	0.466951	+	0.269594i	0.0451419	+	0.0260627i	−0.477259	+	0.878763i	$0.658370\pi$
$108$		0			0
$109$	11.0205			1.05557			0.527787	−	0.849377i	$-0.323022\pi$
$109$	11.0205			1.05557			0.527787	+	0.849377i	$0.323022\pi$
$110$		0			0
$111$	1.87577	+	3.24893i	0.178040	+	0.308374i
$112$		0			0
$113$	12.1244	−	7.00000i	1.14056	−	0.658505i	0.193993	−	0.981003i	$-0.437856\pi$
$113$	12.1244	−	7.00000i	1.14056	−	0.658505i	0.946570	+	0.322498i	$0.104523\pi$
$114$		0			0
$115$	−3.07258	+	10.6826i	−0.286519	+	0.996153i
$116$		0			0
$117$	7.62188	+	6.10977i	0.704643	+	0.564848i
$118$		0			0
$119$	−1.12423	+	1.94723i	−0.103058	+	0.178502i
$120$		0			0
$121$	−4.67122	−	8.09079i	−0.424656	−	0.735526i
$122$		0			0
$123$	−0.208951	+	0.120638i	−0.0188405	+	0.0108776i
$124$		0			0
$125$	7.46081	+	8.32684i	0.667315	+	0.744775i
$126$		0			0
$127$	−10.5458	−	6.08864i	−0.935791	−	0.540279i	−0.0471526	−	0.998888i	$-0.515015\pi$
$127$	−10.5458	−	6.08864i	−0.935791	−	0.540279i	−0.888638	+	0.458609i	$0.848348\pi$
$128$		0			0
$129$	1.07838			0.0949459
$130$		0			0
$131$	17.4547			1.52502			0.762511	−	0.646976i	$-0.223966\pi$
$131$	17.4547			1.52502			0.762511	+	0.646976i	$0.223966\pi$
$132$		0			0
$133$	−0.0741020	−	0.0427828i	−0.00642546	−	0.00370974i
$134$		0			0
$135$	−6.68035	+	1.65983i	−0.574953	+	0.142855i
$136$		0			0
$137$	−8.10037	+	4.67675i	−0.692061	+	0.399562i	−0.804384	−	0.594110i	$-0.797504\pi$
$137$	−8.10037	+	4.67675i	−0.692061	+	0.399562i	0.112322	+	0.993672i	$0.464171\pi$
$138$		0			0
$139$	1.32211	+	2.28997i	0.112140	+	0.194233i	0.916633	−	0.399730i	$-0.130896\pi$
$139$	1.32211	+	2.28997i	0.112140	+	0.194233i	−0.804493	+	0.593963i	$0.797563\pi$
$140$		0			0
$141$	−1.26959	+	2.19900i	−0.106919	+	0.185189i
$142$		0			0
$143$	2.46429	−	16.0742i	0.206074	−	1.34419i
$144$		0			0
$145$	15.6052	+	4.48846i	1.29594	+	0.372746i
$146$		0			0
$147$	−3.03375	+	1.75154i	−0.250219	+	0.144464i
$148$		0			0
$149$	−4.61757	−	7.99786i	−0.378286	−	0.655210i	0.612527	−	0.790450i	$-0.290153\pi$
$149$	−4.61757	−	7.99786i	−0.378286	−	0.655210i	−0.990813	+	0.135239i	$0.956820\pi$
$150$		0			0
$151$	9.42574			0.767056			0.383528	−	0.923529i	$-0.374709\pi$
$151$	9.42574			0.767056			0.383528	+	0.923529i	$0.374709\pi$
$152$		0			0
$153$	−7.43798	−	4.29432i	−0.601325	−	0.347175i
$154$		0			0
$155$	5.21235	+	20.9783i	0.418666	+	1.68501i
$156$		0			0
$157$		−	5.77205i		−	0.460660i	−0.973113	−	0.230330i	$-0.926019\pi$
$157$		−	5.77205i		−	0.460660i	0.973113	−	0.230330i	$-0.0739806\pi$
$158$		0			0
$159$	2.58504	−	4.47743i	0.205007	−	0.355083i
$160$		0			0
$161$	3.52586			0.277877
$162$		0			0
$163$	−14.5678	+	8.41075i	−1.14104	+	0.658781i	−0.946688	−	0.322151i	$-0.895594\pi$
$163$	−14.5678	+	8.41075i	−1.14104	+	0.658781i	−0.194354	+	0.980932i	$0.562261\pi$
$164$		0			0
$165$	3.77427	+	3.91474i	0.293826	+	0.304762i
$166$		0			0
$167$	15.6919	+	9.05971i	1.21427	+	0.701061i	0.963687	−	0.267033i	$-0.0860433\pi$
$167$	15.6919	+	9.05971i	1.21427	+	0.701061i	0.250586	+	0.968094i	$0.419377\pi$
$168$		0			0
$169$	9.57417	−	8.79404i	0.736475	−	0.676465i
$170$		0			0
$171$	0.163421	−	0.283053i	0.0124971	−	0.0216456i
$172$		0			0
$173$	−8.92357	+	5.15203i	−0.678447	+	0.391701i	−0.799270	−	0.600973i	$-0.794780\pi$
$173$	−8.92357	+	5.15203i	−0.678447	+	0.391701i	0.120823	+	0.992674i	$0.461447\pi$
$174$		0			0
$175$	1.88418	−	3.00444i	0.142431	−	0.227114i
$176$		0			0
$177$			3.10504i			0.233389i
$178$		0			0
$179$	−0.630898	+	1.09275i	−0.0471555	+	0.0816757i	−0.888640	−	0.458606i	$-0.848349\pi$
$179$	−0.630898	+	1.09275i	−0.0471555	+	0.0816757i	0.841484	+	0.540282i	$0.181682\pi$
$180$		0			0
$181$	2.38243			0.177085			0.0885424	−	0.996072i	$-0.471779\pi$
$181$	2.38243			0.177085			0.0885424	+	0.996072i	$0.471779\pi$
$182$		0			0
$183$		−	3.80817i		−	0.281508i
$184$		0			0
$185$	4.30052	−	14.9518i	0.316181	−	1.09928i
$186$		0			0
$187$			14.2979i			1.04557i
$188$		0			0
$189$	1.09171	+	1.89090i	0.0794101	+	0.137542i
$190$		0			0
$191$	−5.54278	−	9.60038i	−0.401062	−	0.694659i	0.592793	−	0.805355i	$-0.298025\pi$
$191$	−5.54278	−	9.60038i	−0.401062	−	0.694659i	−0.993854	+	0.110696i	$0.964692\pi$
$192$		0			0
$193$	−12.1244	−	7.00000i	−0.872730	−	0.503871i	−0.00447566	−	0.999990i	$-0.501425\pi$
$193$	−12.1244	−	7.00000i	−0.872730	−	0.503871i	−0.868255	+	0.496119i	$0.834758\pi$
$194$		0			0
$195$	0.396813	+	4.32893i	0.0284164	+	0.310001i
$196$		0			0
$197$	7.52895	+	4.34684i	0.536415	+	0.309699i	0.743625	−	0.668597i	$-0.233105\pi$
$197$	7.52895	+	4.34684i	0.536415	+	0.309699i	−0.207210	+	0.978297i	$0.566438\pi$
$198$		0			0
$199$	−10.7587	−	18.6347i	−0.762666	−	1.32098i	−0.941472	−	0.337091i	$-0.890557\pi$
$199$	−10.7587	−	18.6347i	−0.762666	−	1.32098i	0.178806	−	0.983884i	$-0.442776\pi$
$200$		0			0
$201$	−0.787653	−	1.36426i	−0.0555568	−	0.0962271i
$202$		0			0
$203$		−	5.15061i		−	0.361502i
$204$		0			0
$205$	0.961610	+	0.276584i	0.0671618	+	0.0193175i
$206$		0			0
$207$			13.4680i			0.936091i
$208$		0			0
$209$	−0.544109			−0.0376368
$210$		0			0
$211$	−2.79432	+	4.83990i	−0.192369	+	0.333193i	−0.946035	−	0.324065i	$-0.894950\pi$
$211$	−2.79432	+	4.83990i	−0.192369	+	0.333193i	0.753666	+	0.657258i	$0.228284\pi$
$212$		0			0
$213$		−	4.41241i		−	0.302333i
$214$		0			0
$215$	−3.10399	−	3.21951i	−0.211690	−	0.219569i
$216$		0			0
$217$	5.93797	−	3.42829i	0.403096	−	0.232727i
$218$		0			0
$219$	1.81852	−	3.14977i	0.122884	−	0.212842i
$220$		0			0
$221$	−7.14896	+	8.91825i	−0.480891	+	0.599907i
$222$		0			0
$223$	21.3989	+	12.3546i	1.43297	+	0.827328i	0.997347	−	0.0727995i	$-0.0231933\pi$
$223$	21.3989	+	12.3546i	1.43297	+	0.827328i	0.435627	+	0.900127i	$0.356527\pi$
$224$		0			0
$225$	11.4763	+	7.19716i	0.765086	+	0.479811i
$226$		0			0
$227$	24.8504	−	14.3474i	1.64938	−	0.952268i	0.672056	−	0.740500i	$-0.265411\pi$
$227$	24.8504	−	14.3474i	1.64938	−	0.952268i	0.977320	−	0.211768i	$-0.0679220\pi$
$228$		0			0
$229$	1.89988			0.125548			0.0627738	−	0.998028i	$-0.480005\pi$
$229$	1.89988			0.125548			0.0627738	+	0.998028i	$0.480005\pi$
$230$		0			0
$231$	0.862437	−	1.49378i	0.0567442	−	0.0982838i
$232$		0			0
$233$			22.2485i			1.45755i	0.684756	+	0.728773i	$0.259909\pi$
$233$			22.2485i			1.45755i	−0.684756	+	0.728773i	$0.740091\pi$
$234$		0			0
$235$	10.2195	−	2.53919i	0.666649	−	0.165638i
$236$		0			0
$237$	−7.47458	−	4.31545i	−0.485526	−	0.280319i
$238$		0			0
$239$	24.8710			1.60877			0.804384	−	0.594110i	$-0.202495\pi$
$239$	24.8710			1.60877			0.804384	+	0.594110i	$0.202495\pi$
$240$		0			0
$241$	1.47528	+	2.55525i	0.0950309	+	0.164598i	0.909621	−	0.415438i	$-0.136372\pi$
$241$	1.47528	+	2.55525i	0.0950309	+	0.164598i	−0.814591	+	0.580036i	$0.803038\pi$
$242$		0			0
$243$	−11.0181	+	6.36130i	−0.706811	+	0.408078i
$244$		0			0
$245$	13.9615	+	4.01570i	0.891970	+	0.256554i
$246$		0			0
$247$	−0.339386	−	0.272055i	−0.0215946	−	0.0173104i
$248$		0			0
$249$	0.0959140	−	0.166128i	0.00607830	−	0.0105279i
$250$		0			0
$251$	8.27985	+	14.3411i	0.522620	+	0.905204i	0.999654	+	0.0263190i	$0.00837857\pi$
$251$	8.27985	+	14.3411i	0.522620	+	0.905204i	−0.477034	+	0.878885i	$0.658288\pi$
$252$		0			0
$253$	19.4170	−	11.2104i	1.22074	−	0.704792i
$254$		0			0
$255$	−0.921622	−	3.70928i	−0.0577142	−	0.232284i
$256$		0			0
$257$	−0.453443	−	0.261795i	−0.0282850	−	0.0163303i	0.485791	−	0.874075i	$-0.338532\pi$
$257$	−0.453443	−	0.261795i	−0.0282850	−	0.0163303i	−0.514076	+	0.857745i	$0.671865\pi$
$258$		0			0
$259$	−4.93495			−0.306643
$260$		0			0
$261$	19.6742			1.21780
$262$		0			0
$263$	−24.9255	−	14.3908i	−1.53697	−	0.887372i	−0.999014	−	0.0444013i	$-0.985862\pi$
$263$	−24.9255	−	14.3908i	−1.53697	−	0.887372i	−0.537960	−	0.842971i	$-0.680805\pi$
$264$		0			0
$265$	−20.8082	+	5.17009i	−1.27824	+	0.317596i
$266$		0			0
$267$	1.69545	−	0.978870i	0.103760	−	0.0599059i
$268$		0			0
$269$	5.02832	+	8.70930i	0.306582	+	0.531016i	0.977612	−	0.210414i	$-0.0674813\pi$
$269$	5.02832	+	8.70930i	0.306582	+	0.531016i	−0.671030	+	0.741430i	$0.734148\pi$
$270$		0			0
$271$	9.06278	−	15.6972i	0.550525	−	0.953537i	−0.447712	−	0.894178i	$-0.647761\pi$
$271$	9.06278	−	15.6972i	0.550525	−	0.953537i	0.998237	−	0.0593589i	$-0.0189056\pi$
$272$		0			0
$273$	1.28483	−	0.500522i	0.0777616	−	0.0302930i
$274$		0			0
$275$	0.823691	−	22.5362i	0.0496704	−	1.35899i
$276$		0			0
$277$	−21.4051	+	12.3582i	−1.28611	+	0.742534i	−0.977958	−	0.208804i	$-0.933043\pi$
$277$	−21.4051	+	12.3582i	−1.28611	+	0.742534i	−0.308149	+	0.951338i	$0.599710\pi$
$278$		0			0
$279$	13.0953	+	22.6817i	0.783995	+	1.35792i
$280$		0			0
$281$	22.9854			1.37120			0.685598	−	0.727980i	$-0.259541\pi$
$281$	22.9854			1.37120			0.685598	+	0.727980i	$0.259541\pi$
$282$		0			0
$283$	−15.6741	−	9.04945i	−0.931729	−	0.537934i	−0.0443709	−	0.999015i	$-0.514128\pi$
$283$	−15.6741	−	9.04945i	−0.931729	−	0.537934i	−0.887358	+	0.461081i	$0.847462\pi$
$284$		0			0
$285$	0.141157	−	0.0350725i	0.00836142	−	0.00207751i
$286$		0			0
$287$		−	0.317387i		−	0.0187347i
$288$		0			0
$289$	−3.47528	+	6.01935i	−0.204428	+	0.354080i
$290$		0			0
$291$	−4.26406			−0.249964
$292$		0			0
$293$	−15.4536	+	8.92214i	−0.902809	+	0.521237i	−0.878111	−	0.478458i	$-0.841196\pi$
$293$	−15.4536	+	8.92214i	−0.902809	+	0.521237i	−0.0246988	+	0.999695i	$0.507863\pi$
$294$		0			0
$295$	9.27014	−	8.93751i	0.539728	−	0.520362i
$296$		0			0
$297$	12.0241	+	6.94214i	0.697711	+	0.402824i
$298$		0			0
$299$	17.7165	+	2.71606i	1.02457	+	0.157074i
$300$		0			0
$301$	−0.709275	+	1.22850i	−0.0408820	+	0.0708096i
$302$		0			0
$303$	−2.86762	+	1.65562i	−0.164741	+	0.0951130i
$304$		0			0
$305$	−11.3693	+	10.9614i	−0.651007	+	0.627648i
$306$		0			0
$307$		−	3.44521i		−	0.196629i	−0.995155	−	0.0983143i	$-0.968655\pi$
$307$		−	3.44521i		−	0.196629i	0.995155	−	0.0983143i	$-0.0313451\pi$
$308$		0			0
$309$	4.76652	−	8.25586i	0.271158	−	0.469659i
$310$		0			0
$311$	−17.8238			−1.01069			−0.505347	−	0.862916i	$-0.668635\pi$
$311$	−17.8238			−1.01069			−0.505347	+	0.862916i	$0.668635\pi$
$312$		0			0
$313$		−	32.2245i		−	1.82143i	−0.413031	−	0.910717i	$-0.635530\pi$
$313$		−	32.2245i		−	1.82143i	0.413031	−	0.910717i	$-0.364470\pi$
$314$		0			0
$315$	1.18774	−	4.12946i	0.0669215	−	0.232669i
$316$		0			0
$317$			1.90602i			0.107053i	0.998566	+	0.0535265i	$0.0170462\pi$
$317$			1.90602i			0.107053i	−0.998566	+	0.0535265i	$0.982954\pi$
$318$		0			0
$319$	−16.3763	−	28.3646i	−0.916896	−	1.58811i
$320$		0			0
$321$	0.145362	+	0.251775i	0.00811333	+	0.0140527i
$322$		0			0
$323$	0.331197	+	0.191217i	0.0184283	+	0.0106396i
$324$		0			0
$325$	11.7819	−	13.6450i	0.653542	−	0.756890i
$326$		0			0
$327$	5.14605	+	2.97107i	0.284577	+	0.164301i
$328$		0			0
$329$	−1.67009	−	2.89267i	−0.0920748	−	0.159478i
$330$		0			0
$331$	−0.355771	−	0.616214i	−0.0195550	−	0.0338702i	0.856082	−	0.516839i	$-0.172892\pi$
$331$	−0.355771	−	0.616214i	−0.0195550	−	0.0338702i	−0.875637	+	0.482969i	$0.839558\pi$
$332$		0			0
$333$		−	18.8504i		−	1.03300i
$334$		0			0
$335$	−1.80583	+	6.27840i	−0.0986631	+	0.343026i
$336$		0			0
$337$			9.85043i			0.536587i	0.963337	+	0.268294i	$0.0864597\pi$
$337$			9.85043i			0.536587i	−0.963337	+	0.268294i	$0.913540\pi$
$338$		0			0
$339$	7.54864			0.409986
$340$		0			0
$341$	21.8004	−	37.7594i	1.18056	−	2.04478i
$342$		0			0
$343$		−	9.57304i		−	0.516896i
$344$		0			0
$345$	−4.31470	+	4.15988i	−0.232296	+	0.223961i
$346$		0			0
$347$	22.1123	−	12.7665i	1.18705	−	0.685343i	0.229414	−	0.973329i	$-0.426319\pi$
$347$	22.1123	−	12.7665i	1.18705	−	0.685343i	0.957635	+	0.287986i	$0.0929857\pi$
$348$		0			0
$349$	−9.02832	+	15.6375i	−0.483275	+	0.837056i	−0.999816	−	0.0192061i	$-0.993886\pi$
$349$	−9.02832	+	15.6375i	−0.483275	+	0.837056i	0.516541	+	0.856263i	$0.327219\pi$
$350$		0			0
$351$	4.02893	+	10.3422i	0.215048	+	0.552026i
$352$		0			0
$353$	−12.6842	−	7.32325i	−0.675114	−	0.389777i	0.122898	−	0.992419i	$-0.460781\pi$
$353$	−12.6842	−	7.32325i	−0.675114	−	0.389777i	−0.798012	+	0.602642i	$0.794115\pi$
$354$		0			0
$355$	−13.1733	+	12.7006i	−0.699166	+	0.674079i
$356$		0			0
$357$	−1.04992	+	0.606173i	−0.0555678	+	0.0320821i
$358$		0			0
$359$	−13.4186			−0.708204			−0.354102	−	0.935207i	$-0.615213\pi$
$359$	−13.4186			−0.708204			−0.354102	+	0.935207i	$0.615213\pi$
$360$		0			0
$361$	9.49272	−	16.4419i	0.499617	−	0.865362i
$362$		0			0
$363$		−	5.03734i		−	0.264392i
$364$		0			0
$365$	−14.6381	+	3.63704i	−0.766192	+	0.190371i
$366$		0			0
$367$	18.6577	+	10.7721i	0.973926	+	0.562297i	0.900431	−	0.434999i	$-0.143251\pi$
$367$	18.6577	+	10.7721i	0.973926	+	0.562297i	0.0734954	+	0.997296i	$0.476585\pi$
$368$		0			0
$369$	1.21235			0.0631123
$370$		0			0
$371$	3.40049	+	5.88983i	0.176545	+	0.305784i
$372$		0			0
$373$	18.4758	−	10.6670i	0.956641	−	0.552317i	0.0615036	−	0.998107i	$-0.480410\pi$
$373$	18.4758	−	10.6670i	0.956641	−	0.552317i	0.895138	+	0.445790i	$0.147077\pi$
$374$		0			0
$375$	1.23896	+	5.89962i	0.0639799	+	0.304655i
$376$		0			0
$377$	3.96765	−	25.8804i	0.204344	−	1.33291i
$378$		0			0
$379$	−4.05611	+	7.02540i	−0.208349	+	0.360870i	−0.951194	−	0.308592i	$-0.900142\pi$
$379$	−4.05611	+	7.02540i	−0.208349	+	0.360870i	0.742846	+	0.669462i	$0.233476\pi$
$380$		0			0
$381$	−3.28293	−	5.68619i	−0.168189	−	0.291313i
$382$		0			0
$383$	−21.5986	+	12.4699i	−1.10364	+	0.637184i	−0.937173	−	0.348864i	$-0.886568\pi$
$383$	−21.5986	+	12.4699i	−1.10364	+	0.637184i	−0.166462	+	0.986048i	$0.553234\pi$
$384$		0			0
$385$	−6.94214	+	1.72487i	−0.353804	+	0.0879077i
$386$		0			0
$387$	−4.69260	−	2.70928i	−0.238538	−	0.137720i
$388$		0			0
$389$	−13.5330			−0.686153			−0.343076	−	0.939308i	$-0.611469\pi$
$389$	−13.5330			−0.686153			−0.343076	+	0.939308i	$0.611469\pi$
$390$		0			0
$391$	−15.7587			−0.796953
$392$		0			0
$393$	8.15048	+	4.70568i	0.411137	+	0.237370i
$394$		0			0
$395$	8.63090	+	34.7370i	0.434268	+	1.74781i
$396$		0			0
$397$	3.97920	−	2.29739i	0.199710	−	0.115303i	−0.396810	−	0.917901i	$-0.629883\pi$
$397$	3.97920	−	2.29739i	0.199710	−	0.115303i	0.596520	+	0.802598i	$0.296550\pi$
$398$		0			0
$399$	−0.0230680	−	0.0399550i	−0.00115485	−	0.00200025i
$400$		0			0
$401$	−14.8516	+	25.7237i	−0.741652	+	1.28458i	0.210091	+	0.977682i	$0.432624\pi$
$401$	−14.8516	+	25.7237i	−0.741652	+	1.28458i	−0.951743	+	0.306897i	$0.900709\pi$
$402$		0			0
$403$	32.4776	−	12.6520i	1.61782	−	0.630242i
$404$		0			0
$405$	13.8994	+	3.99782i	0.690665	+	0.198653i
$406$		0			0
$407$	−27.1769	+	15.6906i	−1.34711	+	0.777754i
$408$		0			0
$409$	−5.15562	−	8.92980i	−0.254929	−	0.441550i	0.709947	−	0.704255i	$-0.248719\pi$
$409$	−5.15562	−	8.92980i	−0.254929	−	0.441550i	−0.964876	+	0.262705i	$0.915385\pi$
$410$		0			0
$411$	−5.04331			−0.248768
$412$		0			0
$413$	−3.53730	−	2.04226i	−0.174059	−	0.100493i
$414$		0			0
$415$	−0.772055	+	0.191828i	−0.0378987	+	0.00941646i
$416$		0			0
$417$			1.42574i			0.0698187i
$418$		0			0
$419$	−19.0452	+	32.9873i	−0.930421	+	1.61154i	−0.147819	+	0.989014i	$0.547225\pi$
$419$	−19.0452	+	32.9873i	−0.930421	+	1.61154i	−0.782602	+	0.622522i	$0.786108\pi$
$420$		0			0
$421$	−26.7103			−1.30178			−0.650891	−	0.759171i	$-0.725604\pi$
$421$	−26.7103			−1.30178			−0.650891	+	0.759171i	$0.725604\pi$
$422$		0			0
$423$	11.0494	−	6.37936i	0.537239	−	0.310175i
$424$		0			0
$425$	−8.42131	+	13.4282i	−0.408493	+	0.651366i
$426$		0			0
$427$	4.33832	+	2.50473i	0.209946	+	0.121212i
$428$		0			0
$429$	5.48421	−	6.84150i	0.264780	−	0.330311i
$430$		0			0
$431$	−10.3594	+	17.9429i	−0.498993	+	0.864281i	−0.999999	−	0.00116231i	$-0.999630\pi$
$431$	−10.3594	+	17.9429i	−0.498993	+	0.864281i	0.501006	+	0.865444i	$0.332963\pi$
$432$		0			0
$433$	−13.7331	+	7.92881i	−0.659971	+	0.381034i	−0.792266	−	0.610176i	$-0.791099\pi$
$433$	−13.7331	+	7.92881i	−0.659971	+	0.381034i	0.132295	+	0.991210i	$0.457765\pi$
$434$		0			0
$435$	6.07680	+	6.30296i	0.291360	+	0.302204i
$436$		0			0
$437$		−	0.599701i		−	0.0286876i
$438$		0			0
$439$	4.86962	−	8.43444i	0.232415	−	0.402554i	−0.726104	−	0.687585i	$-0.758671\pi$
$439$	4.86962	−	8.43444i	0.232415	−	0.402554i	0.958518	+	0.285032i	$0.0920041\pi$
$440$		0			0
$441$	17.6020			0.838189
$442$		0			0
$443$		−	9.23060i		−	0.438559i	−0.975662	−	0.219279i	$-0.929629\pi$
$443$		−	9.23060i		−	0.438559i	0.975662	−	0.219279i	$-0.0703707\pi$
$444$		0			0
$445$	−7.80260	−	2.24423i	−0.369879	−	0.106387i
$446$		0			0
$447$		−	4.97948i		−	0.235521i
$448$		0			0
$449$	−1.46194	−	2.53216i	−0.0689934	−	0.119500i	0.829465	−	0.558559i	$-0.188645\pi$
$449$	−1.46194	−	2.53216i	−0.0689934	−	0.119500i	−0.898458	+	0.439058i	$0.855312\pi$
$450$		0			0
$451$	−1.00913	−	1.74786i	−0.0475179	−	0.0823034i
$452$		0			0
$453$	4.40136	+	2.54113i	0.206794	+	0.119393i
$454$		0			0
$455$	−5.19256	−	2.39519i	−0.243431	−	0.112288i
$456$		0			0
$457$	10.0915	+	5.82632i	0.472060	+	0.272544i	0.717101	−	0.696969i	$-0.245468\pi$
$457$	10.0915	+	5.82632i	0.472060	+	0.272544i	−0.245042	+	0.969512i	$0.578802\pi$
$458$		0			0
$459$	−4.87936	−	8.45130i	−0.227749	−	0.394473i
$460$		0			0
$461$	15.1490	+	26.2388i	0.705557	+	1.22206i	0.966490	+	0.256704i	$0.0826366\pi$
$461$	15.1490	+	26.2388i	0.705557	+	1.22206i	−0.260933	+	0.965357i	$0.584030\pi$
$462$		0			0
$463$		−	7.04331i		−	0.327330i	−0.986516	−	0.163665i	$-0.947668\pi$
$463$		−	7.04331i		−	0.327330i	0.986516	−	0.163665i	$-0.0523316\pi$
$464$		0			0
$465$	−3.22171	+	11.2010i	−0.149403	+	0.519436i
$466$		0			0
$467$			3.90110i			0.180522i	0.995918	+	0.0902608i	$0.0287700\pi$
$467$			3.90110i			0.180522i	−0.995918	+	0.0902608i	$0.971230\pi$
$468$		0			0
$469$	2.07223			0.0956869
$470$		0			0
$471$	1.55611	−	2.69527i	0.0717019	−	0.124191i
$472$		0			0
$473$			9.02052i			0.414764i
$474$		0			0
$475$	−0.511014	−	0.320474i	−0.0234469	−	0.0147044i
$476$		0			0
$477$	−22.4978	+	12.9891i	−1.03010	+	0.594731i
$478$		0			0
$479$	−8.75513	+	15.1643i	−0.400032	+	0.692876i	−0.993729	−	0.111813i	$-0.964334\pi$
$479$	−8.75513	+	15.1643i	−0.400032	+	0.692876i	0.593697	+	0.804689i	$0.297668\pi$
$480$		0			0
$481$	−24.7968	−	3.80152i	−1.13064	−	0.173335i
$482$		0			0
$483$	1.64640	+	0.950552i	0.0749140	+	0.0432516i
$484$		0			0
$485$	12.2736	+	12.7304i	0.557317	+	0.578058i
$486$		0			0
$487$	−33.3695	+	19.2659i	−1.51212	+	0.873022i	−0.512218	+	0.858855i	$0.671176\pi$
$487$	−33.3695	+	19.2659i	−1.51212	+	0.873022i	−0.999900	+	0.0141666i	$0.995490\pi$
$488$		0			0
$489$	−9.06997			−0.410158
$490$		0			0
$491$	3.41189	−	5.90956i	0.153976	−	0.266695i	−0.778710	−	0.627385i	$-0.784125\pi$
$491$	3.41189	−	5.90956i	0.153976	−	0.266695i	0.932686	+	0.360690i	$0.117459\pi$
$492$		0			0
$493$			23.0205i			1.03679i
$494$		0			0
$495$	−6.58864	−	26.5174i	−0.296137	−	1.19187i
$496$		0			0
$497$	5.02667	+	2.90215i	0.225477	+	0.130179i
$498$		0			0
$499$	9.57918			0.428823			0.214412	−	0.976743i	$-0.431217\pi$
$499$	9.57918			0.428823			0.214412	+	0.976743i	$0.431217\pi$
$500$		0			0
$501$	4.88489	+	8.46088i	0.218241	+	0.378004i
$502$		0			0
$503$	14.4403	−	8.33710i	0.643860	−	0.371733i	−0.142240	−	0.989832i	$-0.545430\pi$
$503$	14.4403	−	8.33710i	0.643860	−	0.371733i	0.786100	+	0.618099i	$0.212097\pi$
$504$		0			0
$505$	13.1970	+	3.79580i	0.587259	+	0.168911i
$506$		0			0
$507$	6.84150	−	1.52525i	0.303842	−	0.0677386i
$508$		0			0
$509$	−11.8299	+	20.4900i	−0.524352	+	0.908204i	0.475246	+	0.879853i	$0.342359\pi$
$509$	−11.8299	+	20.4900i	−0.524352	+	0.908204i	−0.999598	+	0.0283510i	$0.990974\pi$
$510$		0			0
$511$	2.39217	+	4.14336i	0.105823	+	0.183291i
$512$		0			0
$513$	0.321616	−	0.185685i	0.0141997	−	0.00819819i
$514$		0			0
$515$	−38.3679	+	9.53305i	−1.69069	+	0.420076i
$516$		0			0
$517$	−18.3944	−	10.6200i	−0.808986	−	0.467068i
$518$		0			0
$519$	−5.55583			−0.243874
$520$		0			0
$521$	−24.0472			−1.05353			−0.526763	−	0.850012i	$-0.676594\pi$
$521$	−24.0472			−1.05353			−0.526763	+	0.850012i	$0.676594\pi$
$522$		0			0
$523$	−20.2079	−	11.6670i	−0.883628	−	0.510163i	−0.0117752	−	0.999931i	$-0.503748\pi$
$523$	−20.2079	−	11.6670i	−0.883628	−	0.510163i	−0.871853	+	0.489768i	$0.837082\pi$
$524$		0			0
$525$	1.68980	−	0.894960i	0.0737490	−	0.0390593i
$526$		0			0
$527$	−26.5396	+	15.3226i	−1.15608	+	0.667465i
$528$		0			0
$529$	0.855771	+	1.48224i	0.0372075	+	0.0644452i
$530$		0			0
$531$	7.80098	−	13.5117i	0.338534	−	0.586358i
$532$		0			0
$533$	0.244491	−	1.59478i	0.0105901	−	0.0690776i
$534$		0			0
$535$	0.333268	−	1.15869i	0.0144084	−	0.0500944i
$536$		0			0
$537$	−0.589197	+	0.340173i	−0.0254257	+	0.0146795i
$538$		0			0
$539$	−14.6514	−	25.3770i	−0.631081	−	1.09306i
$540$		0			0
$541$	−33.1494			−1.42520			−0.712602	−	0.701569i	$-0.752483\pi$
$541$	−33.1494			−1.42520			−0.712602	+	0.701569i	$0.752483\pi$
$542$		0			0
$543$	1.11248	+	0.642291i	0.0477411	+	0.0275633i
$544$		0			0
$545$	−5.94214	−	23.9155i	−0.254533	−	1.02443i
$546$		0			0
$547$		−	43.6742i		−	1.86737i	−0.358090	−	0.933687i	$-0.616572\pi$
$547$		−	43.6742i		−	1.86737i	0.358090	−	0.933687i	$-0.383428\pi$
$548$		0			0
$549$	−9.56751	+	16.5714i	−0.408331	+	0.707250i
$550$		0			0
$551$	−0.876050			−0.0373210
$552$		0			0
$553$	9.83242	−	5.67675i	0.418117	−	0.241400i
$554$		0			0
$555$	6.03906	−	5.82236i	0.256344	−	0.247146i
$556$		0			0
$557$	19.3982	+	11.1995i	0.821927	+	0.474540i	0.851080	−	0.525035i	$-0.175948\pi$
$557$	19.3982	+	11.1995i	0.821927	+	0.474540i	−0.0291537	+	0.999575i	$0.509281\pi$
$558$		0			0
$559$	−4.51026	+	5.62651i	−0.190764	+	0.237976i
$560$		0			0
$561$	−3.85464	+	6.67643i	−0.162743	+	0.281879i
$562$		0			0
$563$	0.208951	−	0.120638i	0.00880625	−	0.00508429i	−0.495590	−	0.868556i	$-0.665048\pi$
$563$	0.208951	−	0.120638i	0.00880625	−	0.00508429i	0.504397	+	0.863472i	$0.331715\pi$
$564$		0			0
$565$	−21.7279	−	22.5366i	−0.914101	−	0.948121i
$566$		0			0
$567$		−	4.58759i		−	0.192661i
$568$		0			0
$569$	13.5856	−	23.5309i	0.569537	−	0.986466i	−0.427075	−	0.904216i	$-0.640456\pi$
$569$	13.5856	−	23.5309i	0.569537	−	0.986466i	0.996612	−	0.0822501i	$-0.0262106\pi$
$570$		0			0
$571$	−2.25461			−0.0943524			−0.0471762	−	0.998887i	$-0.515022\pi$
$571$	−2.25461			−0.0943524			−0.0471762	+	0.998887i	$0.515022\pi$
$572$		0			0
$573$		−	5.97721i		−	0.249702i
$574$		0			0
$575$	24.8388	+	0.907847i	1.03585	+	0.0378598i
$576$		0			0
$577$			7.86481i			0.327416i	0.986509	+	0.163708i	$0.0523455\pi$
$577$			7.86481i			0.327416i	−0.986509	+	0.163708i	$0.947654\pi$
$578$		0			0
$579$	−3.77432	−	6.53732i	−0.156855	−	0.271682i
$580$		0			0
$581$	0.126170	+	0.218533i	0.00523441	+	0.00906627i
$582$		0			0
$583$	37.4532	+	21.6236i	1.55115	+	0.895559i
$584$		0			0
$585$	9.14909	−	19.8344i	0.378268	−	0.820054i
$586$		0			0
$587$	−9.70289	−	5.60197i	−0.400481	−	0.231218i	0.286210	−	0.958167i	$-0.407604\pi$
$587$	−9.70289	−	5.60197i	−0.400481	−	0.231218i	−0.686692	+	0.726949i	$0.740938\pi$
$588$		0			0
$589$	−0.583105	−	1.00997i	−0.0240264	−	0.0416150i
$590$		0			0
$591$	2.34377	+	4.05952i	0.0964097	+	0.166986i
$592$		0			0
$593$		−	13.4186i		−	0.551034i	−0.961296	−	0.275517i	$-0.911151\pi$
$593$		−	13.4186i		−	0.551034i	0.961296	−	0.275517i	$-0.0888490\pi$
$594$		0			0
$595$	4.83182	+	1.38976i	0.198086	+	0.0569745i
$596$		0			0
$597$		−	11.6020i		−	0.474837i
$598$		0			0
$599$	29.5753			1.20841			0.604207	−	0.796827i	$-0.293490\pi$
$599$	29.5753			1.20841			0.604207	+	0.796827i	$0.293490\pi$
$600$		0			0
$601$	−12.4916	+	21.6361i	−0.509543	+	0.882554i	0.490396	+	0.871500i	$0.336852\pi$
$601$	−12.4916	+	21.6361i	−0.509543	+	0.882554i	−0.999939	+	0.0110541i	$0.996481\pi$
$602$		0			0
$603$			7.91548i			0.322343i
$604$		0			0
$605$	−15.0390	+	14.4994i	−0.611424	+	0.589485i
$606$		0			0
$607$	−8.99964	+	5.19594i	−0.365284	+	0.210897i	−0.671396	−	0.741099i	$-0.734305\pi$
$607$	−8.99964	+	5.19594i	−0.365284	+	0.210897i	0.306112	+	0.951995i	$0.400972\pi$
$608$		0			0
$609$	1.38858	−	2.40508i	0.0562680	−	0.0974590i
$610$		0			0
$611$	−6.16342	−	15.8214i	−0.249345	−	0.640065i
$612$		0			0
$613$	−26.4385	−	15.2643i	−1.06784	−	0.616517i	−0.140249	−	0.990116i	$-0.544790\pi$
$613$	−26.4385	−	15.2643i	−1.06784	−	0.616517i	−0.927590	+	0.373599i	$0.878124\pi$
$614$		0			0
$615$	0.374460	+	0.388396i	0.0150997	+	0.0156616i
$616$		0			0
$617$	6.32444	−	3.65142i	0.254612	−	0.147000i	−0.367262	−	0.930118i	$-0.619705\pi$
$617$	6.32444	−	3.65142i	0.254612	−	0.147000i	0.621874	+	0.783117i	$0.286371\pi$
$618$		0			0
$619$	−24.5103			−0.985151			−0.492575	−	0.870270i	$-0.663944\pi$
$619$	−24.5103			−0.985151			−0.492575	+	0.870270i	$0.663944\pi$
$620$		0			0
$621$	−7.65142	+	13.2526i	−0.307041	+	0.531810i
$622$		0			0
$623$			2.57531i			0.103177i
$624$		0			0
$625$	14.0472	−	20.6803i	0.561887	−	0.827214i
$626$		0			0
$627$	−0.254073	−	0.146689i	−0.0101467	−	0.00585819i
$628$		0			0
$629$	22.0566			0.879456
$630$		0			0
$631$	−1.53919	−	2.66595i	−0.0612741	−	0.106130i	0.833761	−	0.552125i	$-0.186183\pi$
$631$	−1.53919	−	2.66595i	−0.0612741	−	0.106130i	−0.895035	+	0.445996i	$0.852850\pi$
$632$		0			0
$633$	−2.60962	+	1.50667i	−0.103723	+	0.0598846i
$634$		0			0
$635$	−7.52668	+	26.1683i	−0.298687	+	1.03846i
$636$		0			0
$637$	3.54975	−	23.1545i	0.140646	−	0.917414i
$638$		0			0
$639$	−11.0856	+	19.2008i	−0.438538	+	0.759570i
$640$		0			0
$641$	1.23400	+	2.13735i	0.0487401	+	0.0844202i	0.889366	−	0.457196i	$-0.151146\pi$
$641$	1.23400	+	2.13735i	0.0487401	+	0.0844202i	−0.840626	+	0.541616i	$0.817813\pi$
$642$		0			0
$643$	−16.2999	+	9.41075i	−0.642805	+	0.371124i	−0.785694	−	0.618615i	$-0.787694\pi$
$643$	−16.2999	+	9.41075i	−0.642805	+	0.371124i	0.142889	+	0.989739i	$0.454361\pi$
$644$		0			0
$645$	−0.581449	−	2.34017i	−0.0228945	−	0.0921442i
$646$		0			0
$647$	−10.1352	−	5.85157i	−0.398456	−	0.230049i	0.287361	−	0.957822i	$-0.407222\pi$
$647$	−10.1352	−	5.85157i	−0.398456	−	0.230049i	−0.685818	+	0.727773i	$0.740555\pi$
$648$		0			0
$649$	−25.9733			−1.01954
$650$		0			0
$651$	3.69699			0.144896
$652$		0			0
$653$	12.7251	+	7.34684i	0.497972	+	0.287504i	0.727875	−	0.685709i	$-0.240508\pi$
$653$	12.7251	+	7.34684i	0.497972	+	0.287504i	−0.229904	+	0.973213i	$0.573841\pi$
$654$		0			0
$655$	−9.41136	−	37.8781i	−0.367732	−	1.48002i
$656$		0			0
$657$	−15.8267	+	9.13756i	−0.617459	+	0.356490i
$658$		0			0
$659$	−9.39383	−	16.2706i	−0.365932	−	0.633812i	0.622994	−	0.782227i	$-0.285916\pi$
$659$	−9.39383	−	16.2706i	−0.365932	−	0.633812i	−0.988925	+	0.148415i	$0.952583\pi$
$660$		0			0
$661$	2.92101	−	5.05934i	0.113614	−	0.196785i	−0.803611	−	0.595155i	$-0.797091\pi$
$661$	2.92101	−	5.05934i	0.113614	−	0.196785i	0.917225	+	0.398370i	$0.130424\pi$
$662$		0			0
$663$	−5.74253	+	2.23707i	−0.223021	+	0.0868806i
$664$		0			0
$665$	−0.0528875	+	0.183876i	−0.00205089	+	0.00713040i
$666$		0			0
$667$	31.2626	−	18.0494i	1.21049	−	0.698877i
$668$		0			0
$669$	6.66148	+	11.5380i	0.257548	+	0.446086i
$670$		0			0
$671$	31.8550			1.22975
$672$		0			0
$673$	−35.4140	−	20.4463i	−1.36511	−	0.788145i	−0.374809	−	0.927102i	$-0.622292\pi$
$673$	−35.4140	−	20.4463i	−1.36511	−	0.788145i	−0.990298	+	0.138957i	$0.955625\pi$
$674$		0			0
$675$	7.20394	+	13.6020i	0.277280	+	0.523540i
$676$		0			0
$677$		−	28.2700i		−	1.08651i	−0.839569	−	0.543253i	$-0.817193\pi$
$677$		−	28.2700i		−	1.08651i	0.839569	−	0.543253i	$-0.182807\pi$
$678$		0			0
$679$	2.80458	−	4.85767i	0.107630	−	0.186420i
$680$		0			0
$681$	15.4719			0.592884
$682$		0			0
$683$	−35.9445	+	20.7526i	−1.37538	+	0.794075i	−0.991599	−	0.129349i	$-0.958711\pi$
$683$	−35.9445	+	20.7526i	−1.37538	+	0.794075i	−0.383780	+	0.923425i	$0.625378\pi$
$684$		0			0
$685$	14.5166	+	15.0569i	0.554650	+	0.575293i
$686$		0			0
$687$	0.887152	+	0.512197i	0.0338469	+	0.0195415i
$688$		0			0
$689$	12.5494	+	32.2142i	0.478096	+	1.22726i
$690$		0			0
$691$	−12.0542	+	20.8784i	−0.458562	+	0.794253i	−0.998885	−	0.0472043i	$-0.984969\pi$
$691$	−12.0542	+	20.8784i	−0.458562	+	0.794253i	0.540323	+	0.841458i	$0.318302\pi$
$692$		0			0
$693$	−7.50586	+	4.33351i	−0.285124	+	0.164616i
$694$		0			0
$695$	4.25656	−	4.10383i	0.161461	−	0.155667i
$696$		0			0
$697$			1.41855i			0.0537314i
$698$		0			0
$699$	−5.99806	+	10.3889i	−0.226868	+	0.392946i
$700$		0			0
$701$	−14.1822			−0.535654			−0.267827	−	0.963467i	$-0.586306\pi$
$701$	−14.1822			−0.535654			−0.267827	+	0.963467i	$0.586306\pi$
$702$		0			0
$703$			0.839369i			0.0316574i
$704$		0			0
$705$	5.45658	+	1.56945i	0.205507	+	0.0591090i
$706$		0			0
$707$		−	4.35577i		−	0.163816i
$708$		0			0
$709$	−23.2479	−	40.2665i	−0.873091	−	1.51224i	−0.858782	−	0.512341i	$-0.828778\pi$
$709$	−23.2479	−	40.2665i	−0.873091	−	1.51224i	−0.0143094	−	0.999898i	$-0.504555\pi$
$710$		0			0
$711$	21.6839	+	37.5577i	0.813211	+	1.40852i
$712$		0			0
$713$	41.6172	+	24.0277i	1.55858	+	0.899845i
$714$		0			0
$715$	−36.2111	+	3.31930i	−1.35422	+	0.124135i
$716$		0			0
$717$	11.6135	+	6.70507i	0.433715	+	0.250405i
$718$		0			0
$719$	6.36069	+	11.0170i	0.237214	+	0.410866i	0.959914	−	0.280296i	$-0.0904325\pi$
$719$	6.36069	+	11.0170i	0.237214	+	0.410866i	−0.722700	+	0.691162i	$0.757099\pi$
$720$		0			0
$721$	6.27012	+	10.8602i	0.233511	+	0.404454i
$722$		0			0
$723$			1.59090i			0.0591664i
$724$		0			0
$725$	1.32619	−	36.2847i	0.0492536	−	1.34758i
$726$		0			0
$727$			13.2595i			0.491769i	0.969299	+	0.245884i	$0.0790783\pi$
$727$			13.2595i			0.491769i	−0.969299	+	0.245884i	$0.920922\pi$
$728$		0			0
$729$	12.5441			0.464597
$730$		0			0
$731$	3.17009	−	5.49075i	0.117250	−	0.203083i
$732$		0			0
$733$			31.5848i			1.16661i	0.812253	+	0.583305i	$0.198241\pi$
$733$			31.5848i			1.16661i	−0.812253	+	0.583305i	$0.801759\pi$
$734$		0			0
$735$	5.43675	+	5.63909i	0.200537	+	0.208001i
$736$		0			0
$737$	11.4119	−	6.58864i	0.420361	−	0.242696i
$738$		0			0
$739$	−1.41609	+	2.45274i	−0.0520917	+	0.0902255i	−0.890895	−	0.454208i	$-0.849922\pi$
$739$	−1.41609	+	2.45274i	−0.0520917	+	0.0902255i	0.838804	+	0.544434i	$0.183255\pi$
$740$		0			0
$741$	−0.0851321	−	0.218533i	−0.00312741	−	0.00802800i
$742$		0			0
$743$	18.0151	+	10.4010i	0.660909	+	0.381576i	0.792623	−	0.609712i	$-0.208715\pi$
$743$	18.0151	+	10.4010i	0.660909	+	0.381576i	−0.131714	+	0.991288i	$0.542048\pi$
$744$		0			0
$745$	−14.8663	+	14.3329i	−0.544659	+	0.525116i
$746$		0			0
$747$	−0.834747	+	0.481941i	−0.0305418	+	0.0176333i
$748$		0			0
$749$	−0.382433			−0.0139738
$750$		0			0
$751$	18.1412	−	31.4214i	0.661980	−	1.14658i	−0.318114	−	0.948052i	$-0.603050\pi$
$751$	18.1412	−	31.4214i	0.661980	−	1.14658i	0.980095	−	0.198531i	$-0.0636171\pi$
$752$		0			0
$753$			8.92881i			0.325384i
$754$		0			0
$755$	−5.08225	−	20.4547i	−0.184962	−	0.744422i
$756$		0			0
$757$	35.3933	+	20.4343i	1.28639	+	0.742699i	0.978009	−	0.208563i	$-0.0668788\pi$
$757$	35.3933	+	20.4343i	1.28639	+	0.742699i	0.308383	+	0.951262i	$0.400212\pi$
$758$		0			0
$759$	12.0891			0.438805
$760$		0			0
$761$	−17.8112	−	30.8500i	−0.645657	−	1.11831i	−0.984149	−	0.177342i	$-0.943250\pi$
$761$	−17.8112	−	30.8500i	−0.645657	−	1.11831i	0.338492	−	0.940969i	$-0.390083\pi$
$762$		0			0
$763$	−6.76936	+	3.90829i	−0.245067	+	0.141490i
$764$		0			0
$765$	−5.30857	+	18.4565i	−0.191932	+	0.667296i
$766$		0			0
$767$	−16.2007	−	12.9867i	−0.584975	−	0.468921i
$768$		0			0
$769$	1.68455	−	2.91773i	0.0607465	−	0.105216i	−0.834053	−	0.551685i	$-0.813985\pi$
$769$	1.68455	−	2.91773i	0.0607465	−	0.105216i	0.894799	+	0.446469i	$0.147319\pi$
$770$		0			0
$771$	−0.141157	−	0.244491i	−0.00508365	−	0.00880514i
$772$		0			0
$773$	−9.59506	+	5.53971i	−0.345110	+	0.199250i	−0.662530	−	0.749036i	$-0.730517\pi$
$773$	−9.59506	+	5.53971i	−0.345110	+	0.199250i	0.317419	+	0.948285i	$0.397184\pi$
$774$		0			0
$775$	42.7142	−	22.6225i	1.53434	−	0.812624i
$776$		0			0
$777$	−2.30438	−	1.33044i	−0.0826693	−	0.0477291i
$778$		0			0
$779$	−0.0539832			−0.00193415
$780$		0			0
$781$	36.9093			1.32072
$782$		0			0
$783$	19.3596	+	11.1773i	0.691856	+	0.399443i
$784$		0			0
$785$	−12.5259	+	3.11223i	−0.447067	+	0.111080i
$786$		0			0
$787$	−4.91114	+	2.83545i	−0.175063	+	0.101073i	−0.584971	−	0.811054i	$-0.698894\pi$
$787$	−4.91114	+	2.83545i	−0.175063	+	0.101073i	0.409908	+	0.912127i	$0.365561\pi$
$788$		0			0
$789$	−7.75933	−	13.4396i	−0.276240	−	0.478461i
$790$		0			0
$791$	−4.96493	+	8.59951i	−0.176532	+	0.305763i
$792$		0			0
$793$	19.8694	+	15.9275i	0.705582	+	0.565602i
$794$		0			0
$795$	−11.1102	−	3.19559i	−0.394039	−	0.113336i
$796$		0			0
$797$	23.6792	−	13.6712i	0.838762	−	0.484259i	−0.0180812	−	0.999837i	$-0.505756\pi$
$797$	23.6792	−	13.6712i	0.838762	−	0.484259i	0.856843	+	0.515577i	$0.172422\pi$
$798$		0			0
$799$	7.46441	+	12.9287i	0.264072	+	0.457386i
$800$		0			0
$801$	−9.83710			−0.347577
$802$		0			0
$803$	26.3475	+	15.2117i	0.929783	+	0.536810i
$804$		0			0
$805$	−1.90110	−	7.65142i	−0.0670051	−	0.269677i
$806$		0			0
$807$			5.42243i			0.190878i
$808$		0			0
$809$	−2.51446	+	4.35518i	−0.0884039	+	0.153120i	−0.906837	−	0.421482i	$-0.861510\pi$
$809$	−2.51446	+	4.35518i	−0.0884039	+	0.153120i	0.818433	+	0.574602i	$0.194843\pi$
$810$		0			0
$811$	−47.3390			−1.66230			−0.831148	−	0.556052i	$-0.812316\pi$
$811$	−47.3390			−1.66230			−0.831148	+	0.556052i	$0.812316\pi$
$812$		0			0
$813$	8.46375	−	4.88655i	0.296837	−	0.171379i
$814$		0			0
$815$	26.1069	+	27.0785i	0.914484	+	0.948519i
$816$		0			0
$817$	0.208951	+	0.120638i	0.00731028	+	0.00422059i
$818$		0			0
$819$	−6.84849	−	1.04992i	−0.239306	−	0.0366873i
$820$		0			0
$821$	10.3408	−	17.9108i	0.360896	−	0.625090i	−0.627213	−	0.778848i	$-0.715804\pi$
$821$	10.3408	−	17.9108i	0.360896	−	0.625090i	0.988109	+	0.153758i	$0.0491376\pi$
$822$		0			0
$823$	−17.1794	+	9.91855i	−0.598837	+	0.345739i	−0.768584	−	0.639749i	$-0.779038\pi$
$823$	−17.1794	+	9.91855i	−0.598837	+	0.345739i	0.169747	+	0.985488i	$0.445705\pi$
$824$		0			0
$825$	6.46027	−	10.3013i	0.224918	−	0.358644i
$826$		0			0
$827$		−	39.6730i		−	1.37956i	−0.724017	−	0.689782i	$-0.757706\pi$
$827$		−	39.6730i		−	1.37956i	0.724017	−	0.689782i	$-0.242294\pi$
$828$		0			0
$829$	−12.6937	+	21.9861i	−0.440870	+	0.763609i	−0.997754	−	0.0669813i	$-0.978663\pi$
$829$	−12.6937	+	21.9861i	−0.440870	+	0.763609i	0.556885	+	0.830590i	$0.311997\pi$
$830$		0			0
$831$	−13.3268			−0.462303
$832$		0			0
$833$			20.5958i			0.713603i
$834$		0			0
$835$	11.1995	−	38.9376i	0.387573	−	1.34749i
$836$		0			0
$837$			29.7587i			1.02861i
$838$		0			0
$839$	11.5139	+	19.9426i	0.397502	+	0.688494i	0.993417	−	0.114553i	$-0.0365437\pi$
$839$	11.5139	+	19.9426i	0.397502	+	0.688494i	−0.595915	+	0.803048i	$0.703210\pi$
$840$		0			0
$841$	−11.8668	−	20.5540i	−0.409201	−	0.708757i
$842$		0			0
$843$	10.7331	+	6.19675i	0.369667	+	0.213427i
$844$		0			0
$845$	−24.2461	−	16.0351i	−0.834092	−	0.551625i
$846$		0			0
$847$	5.73860	+	3.31318i	0.197181	+	0.113842i
$848$		0			0
$849$	−4.87936	−	8.45130i	−0.167459	−	0.290048i
$850$		0			0
$851$	−17.2937	−	29.9536i	−0.592821	−	1.02680i
$852$		0			0
$853$			13.7047i			0.469241i	0.972087	+	0.234621i	$0.0753848\pi$
$853$			13.7047i			0.469241i	−0.972087	+	0.234621i	$0.924615\pi$
$854$		0			0
$855$	−0.702365	−	0.202018i	−0.0240204	−	0.00690888i
$856$		0			0
$857$		−	17.8648i		−	0.610250i	−0.952312	−	0.305125i	$-0.901302\pi$
$857$		−	17.8648i		−	0.610250i	0.952312	−	0.305125i	$-0.0986983\pi$
$858$		0			0
$859$	13.7187			0.468077			0.234039	−	0.972227i	$-0.424806\pi$
$859$	13.7187			0.468077			0.234039	+	0.972227i	$0.424806\pi$
$860$		0			0
$861$	0.0855657	−	0.148204i	0.00291607	−	0.00505078i
$862$		0			0
$863$		−	19.9383i		−	0.678706i	−0.940659	−	0.339353i	$-0.889792\pi$
$863$		−	19.9383i		−	0.678706i	0.940659	−	0.339353i	$-0.110208\pi$
$864$		0			0
$865$	15.9918	+	16.5870i	0.543739	+	0.563975i
$866$		0			0
$867$	−3.24557	+	1.87383i	−0.110225	+	0.0636386i
$868$		0			0
$869$	36.0983	−	62.5241i	1.22455	−	2.12098i
$870$		0			0
$871$	10.4124	+	1.59630i	0.352811	+	0.0540884i
$872$		0			0
$873$	18.5552	+	10.7129i	0.628000	+	0.362576i
$874$		0			0
$875$	−7.53582	−	2.46888i	−0.254757	−	0.0834634i
$876$		0			0
$877$	−18.7203	+	10.8082i	−0.632140	+	0.364966i	−0.781580	−	0.623805i	$-0.785586\pi$
$877$	−18.7203	+	10.8082i	−0.632140	+	0.364966i	0.149441	+	0.988771i	$0.452253\pi$
$878$		0			0
$879$	−9.62144			−0.324523
$880$		0			0
$881$	3.99693	−	6.92288i	0.134660	−	0.233238i	−0.790808	−	0.612065i	$-0.790339\pi$
$881$	3.99693	−	6.92288i	0.134660	−	0.233238i	0.925468	+	0.378827i	$0.123672\pi$
$882$		0			0
$883$			26.2713i			0.884098i	0.896991	+	0.442049i	$0.145748\pi$
$883$			26.2713i			0.884098i	−0.896991	+	0.442049i	$0.854252\pi$
$884$		0			0
$885$	6.73820	−	1.67420i	0.226502	−	0.0562777i
$886$		0			0
$887$	14.8634	+	8.58136i	0.499063	+	0.288134i	0.728326	−	0.685230i	$-0.240299\pi$
$887$	14.8634	+	8.58136i	0.499063	+	0.288134i	−0.229264	+	0.973364i	$0.573632\pi$
$888$		0			0
$889$	8.63704			0.289677
$890$		0			0
$891$	−14.5862	−	25.2640i	−0.488655	−	0.846376i
$892$		0			0
$893$	−0.492005	+	0.284059i	−0.0164643	+	0.00950568i
$894$		0			0
$895$	2.71153	+	0.779906i	0.0906364	+	0.0260694i
$896$		0			0
$897$	7.54049	+	6.04453i	0.251770	+	0.201821i
$898$		0			0
$899$	35.0999	−	60.7949i	1.17065	−	2.02762i
$900$		0			0
$901$	−15.1984	−	26.3244i	−0.506332	−	0.876993i
$902$		0			0
$903$	−0.662394	+	0.382433i	−0.0220431	+	0.0127266i
$904$		0			0
$905$	−1.28458	−	5.17009i	−0.0427009	−	0.171859i
$906$		0			0
$907$	14.2146	+	8.20682i	0.471989	+	0.272503i	0.717072	−	0.696999i	$-0.245482\pi$
$907$	14.2146	+	8.20682i	0.471989	+	0.272503i	−0.245083	+	0.969502i	$0.578815\pi$
$908$		0			0
$909$	16.6381			0.551850
$910$		0			0
$911$	4.52359			0.149873			0.0749366	−	0.997188i	$-0.476125\pi$
$911$	4.52359			0.149873			0.0749366	+	0.997188i	$0.476125\pi$
$912$		0			0
$913$	1.38964	+	0.802311i	0.0459905	+	0.0265526i
$914$		0			0
$915$	−8.26406	+	2.05332i	−0.273201	+	0.0678808i
$916$		0			0
$917$	−10.7215	+	6.19008i	−0.354056	+	0.204415i
$918$		0			0
$919$	3.82150	+	6.61904i	0.126060	+	0.218342i	0.922147	−	0.386840i	$-0.126434\pi$
$919$	3.82150	+	6.61904i	0.126060	+	0.218342i	−0.796087	+	0.605182i	$0.793100\pi$
$920$		0			0
$921$	0.928810	−	1.60875i	0.0306053	−	0.0530100i
$922$		0			0
$923$	23.0220	+	18.4547i	0.757779	+	0.607443i
$924$		0			0
$925$	−34.7655	−	1.27066i	−1.14308	−	0.0417792i
$926$		0			0
$927$	−41.4834	+	23.9505i	−1.36249	+	0.786636i
$928$		0			0
$929$	29.6647	+	51.3808i	0.973269	+	1.68575i	0.685534	+	0.728041i	$0.259569\pi$
$929$	29.6647	+	51.3808i	0.973269	+	1.68575i	0.287735	+	0.957710i	$0.407098\pi$
$930$		0			0
$931$	−0.783777			−0.0256873
$932$		0			0
$933$	−8.32283	−	4.80519i	−0.272477	−	0.157315i
$934$		0			0
$935$	31.0277	−	7.70928i	1.01471	−	0.252120i
$936$		0			0
$937$			1.75872i			0.0574550i	0.999587	+	0.0287275i	$0.00914551\pi$
$937$			1.75872i			0.0574550i	−0.999587	+	0.0287275i	$0.990854\pi$
$938$		0			0
$939$	8.68753	−	15.0473i	0.283507	−	0.491048i
$940$		0			0
$941$	42.2967			1.37883			0.689416	−	0.724365i	$-0.257867\pi$
$941$	42.2967			1.37883			0.689416	+	0.724365i	$0.257867\pi$
$942$		0			0
$943$	1.92643	−	1.11223i	0.0627333	−	0.0362191i
$944$		0			0
$945$	3.51477	−	3.38865i	0.114335	−	0.110233i
$946$		0			0
$947$	4.19011	+	2.41916i	0.136160	+	0.0786122i	0.566533	−	0.824039i	$-0.308284\pi$
$947$	4.19011	+	2.41916i	0.136160	+	0.0786122i	−0.430372	+	0.902651i	$0.641618\pi$
$948$		0			0
$949$	8.82826	+	22.6620i	0.286577	+	0.735640i
$950$		0			0
$951$	−0.513853	+	0.890020i	−0.0166628	+	0.0288609i
$952$		0			0
$953$	−22.4767	+	12.9769i	−0.728092	+	0.420364i	−0.817724	−	0.575611i	$-0.804764\pi$
$953$	−22.4767	+	12.9769i	−0.728092	+	0.420364i	0.0896318	+	0.995975i	$0.471431\pi$
$954$		0			0
$955$	−17.8451	+	17.2047i	−0.577452	+	0.556732i
$956$		0			0
$957$		−	17.6598i		−	0.570861i
$958$		0			0
$959$	3.31710	−	5.74539i	0.107115	−	0.185528i
$960$		0			0
$961$	62.4512			2.01455
$962$		0			0
$963$		−	1.46081i		−	0.0470740i
$964$		0			0
$965$	−8.65329	+	30.0852i	−0.278559	+	0.968478i
$966$		0			0
$967$			29.9939i			0.964537i	0.876023	+	0.482269i	$0.160187\pi$
$967$			29.9939i			0.964537i	−0.876023	+	0.482269i	$0.839813\pi$
$968$		0			0
$969$	0.103102	+	0.178578i	0.00331211	+	0.00573674i
$970$		0			0
$971$	7.86429	+	13.6213i	0.252377	+	0.437130i	0.964180	−	0.265250i	$-0.0854544\pi$
$971$	7.86429	+	13.6213i	0.252377	+	0.437130i	−0.711803	+	0.702379i	$0.752121\pi$
$972$		0			0
$973$	−1.62422	−	0.937743i	−0.0520701	−	0.0300627i
$974$		0			0
$975$	9.18020	−	3.19523i	0.294002	−	0.102329i
$976$		0			0
$977$	−23.8539	−	13.7721i	−0.763154	−	0.440607i	0.0672731	−	0.997735i	$-0.478570\pi$
$977$	−23.8539	−	13.7721i	−0.763154	−	0.440607i	−0.830427	+	0.557128i	$0.811903\pi$
$978$		0			0
$979$	8.18815	+	14.1823i	0.261694	+	0.453268i
$980$		0			0
$981$	−14.9288	−	25.8575i	−0.476640	−	0.825565i
$982$		0			0
$983$		−	18.0289i		−	0.575034i	−0.957776	−	0.287517i	$-0.907170\pi$
$983$		−	18.0289i		−	0.575034i	0.957776	−	0.287517i	$-0.0928297\pi$
$984$		0			0
$985$	5.37349	−	18.6822i	0.171214	−	0.595265i
$986$		0			0
$987$		−	1.80098i		−	0.0573260i
$988$		0			0
$989$	−9.94214			−0.316142
$990$		0			0
$991$	5.81658	−	10.0746i	0.184770	−	0.320031i	−0.758729	−	0.651406i	$-0.774179\pi$
$991$	5.81658	−	10.0746i	0.184770	−	0.320031i	0.943499	+	0.331376i	$0.107513\pi$
$992$		0			0
$993$		−	0.383656i		−	0.0121750i
$994$		0			0
$995$	−34.6378	+	33.3950i	−1.09809	+	1.05869i
$996$		0			0
$997$	24.9977	−	14.4324i	0.791684	−	0.457079i	−0.0488712	−	0.998805i	$-0.515562\pi$
$997$	24.9977	−	14.4324i	0.791684	−	0.457079i	0.840555	+	0.541726i	$0.182229\pi$
$998$		0			0
$999$	10.7093	−	18.5490i	0.338826	−	0.586865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1040.2.dh.b.529.4		12
4.3	odd	2		130.2.n.a.9.2	✓	12
5.4	even	2	inner	1040.2.dh.b.529.3		12
12.11	even	2		1170.2.bp.h.919.5		12
13.3	even	3	inner	1040.2.dh.b.289.3		12
20.3	even	4		650.2.e.j.451.2		6
20.7	even	4		650.2.e.k.451.2		6
20.19	odd	2		130.2.n.a.9.5	yes	12
52.3	odd	6		130.2.n.a.29.5	yes	12
52.7	even	12		1690.2.c.b.1689.4		6
52.19	even	12		1690.2.c.c.1689.4		6
52.35	odd	6		1690.2.b.c.339.5		6
52.43	odd	6		1690.2.b.b.339.2		6
60.59	even	2		1170.2.bp.h.919.2		12
65.29	even	6	inner	1040.2.dh.b.289.4		12
156.107	even	6		1170.2.bp.h.289.2		12
260.3	even	12		650.2.e.j.601.2		6
260.19	even	12		1690.2.c.b.1689.3		6
260.43	even	12		8450.2.a.bt.1.2		3
260.59	even	12		1690.2.c.c.1689.3		6
260.87	even	12		8450.2.a.bu.1.2		3
260.107	even	12		650.2.e.k.601.2		6
260.139	odd	6		1690.2.b.c.339.2		6
260.147	even	12		8450.2.a.ca.1.2		3
260.159	odd	6		130.2.n.a.29.2	yes	12
260.199	odd	6		1690.2.b.b.339.5		6
260.243	even	12		8450.2.a.cb.1.2		3
780.419	even	6		1170.2.bp.h.289.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.2	✓	12	4.3	odd	2
130.2.n.a.9.5	yes	12	20.19	odd	2
130.2.n.a.29.2	yes	12	260.159	odd	6
130.2.n.a.29.5	yes	12	52.3	odd	6
650.2.e.j.451.2		6	20.3	even	4
650.2.e.j.601.2		6	260.3	even	12
650.2.e.k.451.2		6	20.7	even	4
650.2.e.k.601.2		6	260.107	even	12
1040.2.dh.b.289.3		12	13.3	even	3	inner
1040.2.dh.b.289.4		12	65.29	even	6	inner
1040.2.dh.b.529.3		12	5.4	even	2	inner
1040.2.dh.b.529.4		12	1.1	even	1	trivial
1170.2.bp.h.289.2		12	156.107	even	6
1170.2.bp.h.289.5		12	780.419	even	6
1170.2.bp.h.919.2		12	60.59	even	2
1170.2.bp.h.919.5		12	12.11	even	2
1690.2.b.b.339.2		6	52.43	odd	6
1690.2.b.b.339.5		6	260.199	odd	6
1690.2.b.c.339.2		6	260.139	odd	6
1690.2.b.c.339.5		6	52.35	odd	6
1690.2.c.b.1689.3		6	260.19	even	12
1690.2.c.b.1689.4		6	52.7	even	12
1690.2.c.c.1689.3		6	260.59	even	12
1690.2.c.c.1689.4		6	52.19	even	12
8450.2.a.bt.1.2		3	260.43	even	12
8450.2.a.bu.1.2		3	260.87	even	12
8450.2.a.ca.1.2		3	260.147	even	12
8450.2.a.cb.1.2		3	260.243	even	12

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:	\( N \)	\(=\)	\( 1040 = 2^{4} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1040.dh (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.466951 + 0.269594i) q^{3} +(-0.539189 - 2.17009i) q^{5} +(-0.614250 + 0.354638i) q^{7} +(-1.35464 - 2.34630i) q^{9} +(-2.25513 + 3.90600i) q^{11} +(-3.35963 + 1.30878i) q^{13} +(0.333268 - 1.15869i) q^{15} +(2.74538 - 1.58504i) q^{17} +(0.0603191 + 0.104476i) q^{19} -0.382433 q^{21} +(-4.30507 - 2.48554i) q^{23} +(-4.41855 + 2.34017i) q^{25} -3.07838i q^{27} +(-3.63090 + 6.28890i) q^{29} -9.66701 q^{31} +(-2.10607 + 1.21594i) q^{33} +(1.10079 + 1.14176i) q^{35} +(6.02558 + 3.47887i) q^{37} +(-1.92162 - 0.294598i) q^{39} +(-0.223740 + 0.387529i) q^{41} +(1.73205 - 1.00000i) q^{43} +(-4.36127 + 4.20478i) q^{45} +4.70928i q^{47} +(-3.24846 + 5.62651i) q^{49} +1.70928 q^{51} -9.58864i q^{53} +(9.69230 + 2.78776i) q^{55} +0.0650468i q^{57} +(2.87936 + 4.98720i) q^{59} +(-3.53139 - 6.11655i) q^{61} +(1.66417 + 0.960811i) q^{63} +(4.65165 + 6.58500i) q^{65} +(-2.53020 - 1.46081i) q^{67} +(-1.34017 - 2.32125i) q^{69} +(-4.09171 - 7.08705i) q^{71} -6.74539i q^{73} +(-2.69415 - 0.0984700i) q^{75} -3.19902i q^{77} -16.0072 q^{79} +(-3.23400 + 5.60145i) q^{81} -0.355771i q^{83} +(-4.91996 - 5.10306i) q^{85} +(-3.39090 + 1.95774i) q^{87} +(1.81545 - 3.14445i) q^{89} +(1.59951 - 1.99537i) q^{91} +(-4.51402 - 2.60617i) q^{93} +(0.194198 - 0.187230i) q^{95} +(-6.84878 + 3.95415i) q^{97} +12.2195 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 2 q^{9} + 6 q^{11} - 4 q^{15} + 26 q^{19} - 24 q^{21} + 4 q^{25} - 28 q^{29} - 24 q^{31} + 6 q^{35} - 36 q^{39} - 4 q^{41} + 12 q^{45} - 4 q^{49} - 8 q^{51} - 12 q^{55} - 16 q^{59} - 8 q^{61} - 10 q^{65}+ \cdots + 52 q^{99}+O(q^{100}) \) 12 * q - 2 * q^9 + 6 * q^11 - 4 * q^15 + 26 * q^19 - 24 * q^21 + 4 * q^25 - 28 * q^29 - 24 * q^31 + 6 * q^35 - 36 * q^39 - 4 * q^41 + 12 * q^45 - 4 * q^49 - 8 * q^51 - 12 * q^55 - 16 * q^59 - 8 * q^61 - 10 * q^65 + 28 * q^69 - 40 * q^71 + 8 * q^75 - 56 * q^79 + 26 * q^81 - 16 * q^85 + 14 * q^89 + 38 * q^91 + 8 * q^95 + 52 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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