LMFDB - Embedded newform 1040.2.dh.b.289.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1040,2,Mod(289,1040)]

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

lf = mfeigenbasis(mf)

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")

//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: f = N[0] # Warning: the index may be different

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			289.4
Root			$-1.16746 - 0.312819i$ of defining polynomial
Character	$\chi$	$=$	1040.289
Dual form			1040.2.dh.b.529.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

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

Display 100 coefficients 10 coefficients

Character values

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

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

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	−0.359109	−	0.933296i	$-0.616919\pi$
$3$	0.466951	−	0.269594i	0.269594	−	0.155650i	0.628703	+	0.777645i	$0.283586\pi$
$4$		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	0.379406	−	0.925230i	$-0.376129\pi$
$7$	−0.614250	−	0.354638i	−0.232165	−	0.134040i	−0.611570	+	0.791190i	$0.709462\pi$
$8$		0			0
$9$	−1.35464	+	2.34630i	−0.451546	+	0.782100i
$10$		0			0
$11$	−2.25513	−	3.90600i	−0.679947	−	1.17770i	−0.974996	−	0.222221i	$-0.928669\pi$
$11$	−2.25513	−	3.90600i	−0.679947	−	1.17770i	0.295049	−	0.955482i	$-0.404664\pi$
$12$		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	0.794503	−	0.607260i	$-0.207732\pi$
$17$	2.74538	+	1.58504i	0.665851	+	0.384429i	−0.128652	+	0.991690i	$0.541065\pi$
$18$		0			0
$19$	0.0603191	−	0.104476i	0.0138381	−	0.0239684i	−0.859023	−	0.511936i	$-0.828928\pi$
$19$	0.0603191	−	0.104476i	0.0138381	−	0.0239684i	0.872862	+	0.487968i	$0.162262\pi$
$20$		0			0
$21$	−0.382433			−0.0834538
$22$		0			0
$23$	−4.30507	+	2.48554i	−0.897670	+	0.518270i	−0.876443	−	0.481505i	$-0.840090\pi$
$23$	−4.30507	+	2.48554i	−0.897670	+	0.518270i	−0.0212264	+	0.999775i	$0.506757\pi$
$24$		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	−0.976690	−	0.214654i	$-0.931138\pi$
$29$	−3.63090	−	6.28890i	−0.674241	−	1.16782i	0.302449	−	0.953165i	$-0.402196\pi$
$30$		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	0.0851458	−	0.996369i	$-0.472864\pi$
$37$	6.02558	−	3.47887i	0.990599	−	0.571923i	0.905453	+	0.424446i	$0.139531\pi$
$38$		0			0
$39$	−1.92162	+	0.294598i	−0.307706	+	0.0471735i
$40$		0			0
$41$	−0.223740	−	0.387529i	−0.0349423	−	0.0605219i	0.848025	−	0.529956i	$-0.177791\pi$
$41$	−0.223740	−	0.387529i	−0.0349423	−	0.0605219i	−0.882968	+	0.469434i	$0.844458\pi$
$42$		0			0
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	0.626219	−	0.779647i	$-0.284601\pi$
$43$	1.73205	+	1.00000i	0.264135	+	0.152499i	−0.362084	+	0.932145i	$0.617935\pi$
$44$		0			0
$45$	−4.36127	−	4.20478i	−0.650140	−	0.626812i
$46$		0			0
$47$		−	4.70928i		−	0.686918i	−0.939168	−	0.343459i	$-0.888401\pi$
$47$		−	4.70928i		−	0.686918i	0.939168	−	0.343459i	$-0.111599\pi$
$48$		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	$0.228830\pi$
$53$			9.58864i			1.31710i	−0.752537	+	0.658550i	$0.771170\pi$
$54$		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	−0.615445	−	0.788180i	$-0.711024\pi$
$59$	2.87936	−	4.98720i	0.374861	−	0.649278i	0.990306	+	0.138901i	$0.0443571\pi$
$60$		0			0
$61$	−3.53139	+	6.11655i	−0.452148	+	0.783144i	−0.998519	−	0.0543997i	$-0.982675\pi$
$61$	−3.53139	+	6.11655i	−0.452148	+	0.783144i	0.546371	+	0.837543i	$0.316009\pi$
$62$		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	−0.646530	−	0.762889i	$-0.723780\pi$
$67$	−2.53020	+	1.46081i	−0.309113	+	0.178466i	0.337416	+	0.941355i	$0.390447\pi$
$68$		0			0
$69$	−1.34017	+	2.32125i	−0.161338	+	0.279445i
$70$		0			0
$71$	−4.09171	+	7.08705i	−0.485596	+	0.841078i	−0.999863	−	0.0165526i	$-0.994731\pi$
$71$	−4.09171	+	7.08705i	−0.485596	+	0.841078i	0.514267	+	0.857630i	$0.328064\pi$
$72$		0			0
$73$			6.74539i			0.789488i	0.918791	+	0.394744i	$0.129167\pi$
$73$			6.74539i			0.789488i	−0.918791	+	0.394744i	$0.870833\pi$
$74$		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	$0.00621555\pi$
$83$			0.355771i			0.0390510i	−0.999809	+	0.0195255i	$0.993784\pi$
$84$		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	0.946057	−	0.323999i	$-0.105027\pi$
$89$	1.81545	+	3.14445i	0.192437	+	0.333311i	−0.753620	+	0.657310i	$0.771694\pi$
$90$		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	0.110239	−	0.993905i	$-0.464838\pi$
$97$	−6.84878	−	3.95415i	−0.695388	−	0.401483i	−0.805627	+	0.592422i	$0.798172\pi$
$98$		0			0
$99$	12.2195			1.22811
$100$		0			0
$101$	−3.07058	−	5.31840i	−0.305534	−	0.529200i	0.671846	−	0.740691i	$-0.265502\pi$
$101$	−3.07058	−	5.31840i	−0.305534	−	0.529200i	−0.977380	+	0.211490i	$0.932168\pi$
$102$		0			0
$103$			17.6803i			1.74210i	0.491198	+	0.871048i	$0.336559\pi$
$103$			17.6803i			1.74210i	−0.491198	+	0.871048i	$0.663441\pi$
$104$		0			0
$105$	0.206204	−	0.829914i	0.0201234	−	0.0809913i
$106$		0			0
$107$	0.466951	−	0.269594i	0.0451419	−	0.0260627i	−0.477259	−	0.878763i	$-0.658370\pi$
$107$	0.466951	−	0.269594i	0.0451419	−	0.0260627i	0.522401	+	0.852700i	$0.325036\pi$
$108$		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	0.946570	−	0.322498i	$-0.104523\pi$
$113$	12.1244	+	7.00000i	1.14056	+	0.658505i	0.193993	+	0.981003i	$0.437856\pi$
$114$		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	−0.888638	−	0.458609i	$-0.848348\pi$
$127$	−10.5458	+	6.08864i	−0.935791	+	0.540279i	−0.0471526	+	0.998888i	$0.515015\pi$
$128$		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	0.112322	−	0.993672i	$-0.464171\pi$
$137$	−8.10037	−	4.67675i	−0.692061	−	0.399562i	−0.804384	+	0.594110i	$0.797504\pi$
$138$		0			0
$139$	1.32211	−	2.28997i	0.112140	−	0.194233i	−0.804493	−	0.593963i	$-0.797563\pi$
$139$	1.32211	−	2.28997i	0.112140	−	0.194233i	0.916633	+	0.399730i	$0.130896\pi$
$140$		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	−0.990813	−	0.135239i	$-0.956820\pi$
$149$	−4.61757	+	7.99786i	−0.378286	+	0.655210i	0.612527	+	0.790450i	$0.290153\pi$
$150$		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	$0.0739806\pi$
$157$			5.77205i			0.460660i	−0.973113	+	0.230330i	$0.926019\pi$
$158$		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	−0.194354	−	0.980932i	$-0.562261\pi$
$163$	−14.5678	−	8.41075i	−1.14104	−	0.658781i	−0.946688	+	0.322151i	$0.895594\pi$
$164$		0			0
$165$	3.77427	−	3.91474i	0.293826	−	0.304762i
$166$		0			0
$167$	15.6919	−	9.05971i	1.21427	−	0.701061i	0.250586	−	0.968094i	$-0.419377\pi$
$167$	15.6919	−	9.05971i	1.21427	−	0.701061i	0.963687	+	0.267033i	$0.0860433\pi$
$168$		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	0.120823	−	0.992674i	$-0.461447\pi$
$173$	−8.92357	−	5.15203i	−0.678447	−	0.391701i	−0.799270	+	0.600973i	$0.794780\pi$
$174$		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	0.841484	−	0.540282i	$-0.181682\pi$
$179$	−0.630898	−	1.09275i	−0.0471555	−	0.0816757i	−0.888640	+	0.458606i	$0.848349\pi$
$180$		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	−0.993854	−	0.110696i	$-0.964692\pi$
$191$	−5.54278	+	9.60038i	−0.401062	+	0.694659i	0.592793	+	0.805355i	$0.298025\pi$
$192$		0			0
$193$	−12.1244	+	7.00000i	−0.872730	+	0.503871i	−0.868255	−	0.496119i	$-0.834758\pi$
$193$	−12.1244	+	7.00000i	−0.872730	+	0.503871i	−0.00447566	+	0.999990i	$0.501425\pi$
$194$		0			0
$195$	0.396813	−	4.32893i	0.0284164	−	0.310001i
$196$		0			0
$197$	7.52895	−	4.34684i	0.536415	−	0.309699i	−0.207210	−	0.978297i	$-0.566438\pi$
$197$	7.52895	−	4.34684i	0.536415	−	0.309699i	0.743625	+	0.668597i	$0.233105\pi$
$198$		0			0
$199$	−10.7587	+	18.6347i	−0.762666	+	1.32098i	0.178806	+	0.983884i	$0.442776\pi$
$199$	−10.7587	+	18.6347i	−0.762666	+	1.32098i	−0.941472	+	0.337091i	$0.890557\pi$
$200$		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	0.753666	−	0.657258i	$-0.228284\pi$
$211$	−2.79432	−	4.83990i	−0.192369	−	0.333193i	−0.946035	+	0.324065i	$0.894950\pi$
$212$		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	0.435627	−	0.900127i	$-0.356527\pi$
$223$	21.3989	−	12.3546i	1.43297	−	0.827328i	0.997347	+	0.0727995i	$0.0231933\pi$
$224$		0			0
$225$	11.4763	−	7.19716i	0.765086	−	0.479811i
$226$		0			0
$227$	24.8504	+	14.3474i	1.64938	+	0.952268i	0.977320	+	0.211768i	$0.0679220\pi$
$227$	24.8504	+	14.3474i	1.64938	+	0.952268i	0.672056	+	0.740500i	$0.265411\pi$
$228$		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	$-0.740091\pi$
$233$		−	22.2485i		−	1.45755i	0.684756	−	0.728773i	$-0.259909\pi$
$234$		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	−0.814591	−	0.580036i	$-0.803038\pi$
$241$	1.47528	−	2.55525i	0.0950309	−	0.164598i	0.909621	+	0.415438i	$0.136372\pi$
$242$		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	−0.477034	−	0.878885i	$-0.658288\pi$
$251$	8.27985	−	14.3411i	0.522620	−	0.905204i	0.999654	−	0.0263190i	$-0.00837857\pi$
$252$		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	−0.514076	−	0.857745i	$-0.671865\pi$
$257$	−0.453443	+	0.261795i	−0.0282850	+	0.0163303i	0.485791	+	0.874075i	$0.338532\pi$
$258$		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	−0.537960	+	0.842971i	$0.680805\pi$
$263$	−24.9255	+	14.3908i	−1.53697	+	0.887372i	−0.999014	+	0.0444013i	$0.985862\pi$
$264$		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	−0.671030	−	0.741430i	$-0.734148\pi$
$269$	5.02832	−	8.70930i	0.306582	−	0.531016i	0.977612	+	0.210414i	$0.0674813\pi$
$270$		0			0
$271$	9.06278	+	15.6972i	0.550525	+	0.953537i	0.998237	+	0.0593589i	$0.0189056\pi$
$271$	9.06278	+	15.6972i	0.550525	+	0.953537i	−0.447712	+	0.894178i	$0.647761\pi$
$272$		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	−0.308149	−	0.951338i	$-0.599710\pi$
$277$	−21.4051	−	12.3582i	−1.28611	−	0.742534i	−0.977958	+	0.208804i	$0.933043\pi$
$278$		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	−0.887358	−	0.461081i	$-0.847462\pi$
$283$	−15.6741	+	9.04945i	−0.931729	+	0.537934i	−0.0443709	+	0.999015i	$0.514128\pi$
$284$		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	−0.0246988	−	0.999695i	$-0.507863\pi$
$293$	−15.4536	−	8.92214i	−0.902809	−	0.521237i	−0.878111	+	0.478458i	$0.841196\pi$
$294$		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	$0.0313451\pi$
$307$			3.44521i			0.196629i	−0.995155	+	0.0983143i	$0.968655\pi$
$308$		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	$0.364470\pi$
$313$			32.2245i			1.82143i	−0.413031	+	0.910717i	$0.635530\pi$
$314$		0			0
$315$	1.18774	+	4.12946i	0.0669215	+	0.232669i
$316$		0			0
$317$		−	1.90602i		−	0.107053i	−0.998566	−	0.0535265i	$-0.982954\pi$
$317$		−	1.90602i		−	0.107053i	0.998566	−	0.0535265i	$-0.0170462\pi$
$318$		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	−0.875637	−	0.482969i	$-0.839558\pi$
$331$	−0.355771	+	0.616214i	−0.0195550	+	0.0338702i	0.856082	+	0.516839i	$0.172892\pi$
$332$		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	$-0.913540\pi$
$337$		−	9.85043i		−	0.536587i	0.963337	−	0.268294i	$-0.0864597\pi$
$338$		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	0.957635	−	0.287986i	$-0.0929857\pi$
$347$	22.1123	+	12.7665i	1.18705	+	0.685343i	0.229414	+	0.973329i	$0.426319\pi$
$348$		0			0
$349$	−9.02832	−	15.6375i	−0.483275	−	0.837056i	0.516541	−	0.856263i	$-0.327219\pi$
$349$	−9.02832	−	15.6375i	−0.483275	−	0.837056i	−0.999816	+	0.0192061i	$0.993886\pi$
$350$		0			0
$351$	4.02893	−	10.3422i	0.215048	−	0.552026i
$352$		0			0
$353$	−12.6842	+	7.32325i	−0.675114	+	0.389777i	−0.798012	−	0.602642i	$-0.794115\pi$
$353$	−12.6842	+	7.32325i	−0.675114	+	0.389777i	0.122898	+	0.992419i	$0.460781\pi$
$354$		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	0.0734954	−	0.997296i	$-0.476585\pi$
$367$	18.6577	−	10.7721i	0.973926	−	0.562297i	0.900431	+	0.434999i	$0.143251\pi$
$368$		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	0.895138	−	0.445790i	$-0.147077\pi$
$373$	18.4758	+	10.6670i	0.956641	+	0.552317i	0.0615036	+	0.998107i	$0.480410\pi$
$374$		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	0.742846	−	0.669462i	$-0.233476\pi$
$379$	−4.05611	−	7.02540i	−0.208349	−	0.360870i	−0.951194	+	0.308592i	$0.900142\pi$
$380$		0			0
$381$	−3.28293	+	5.68619i	−0.168189	+	0.291313i
$382$		0			0
$383$	−21.5986	−	12.4699i	−1.10364	−	0.637184i	−0.166462	−	0.986048i	$-0.553234\pi$
$383$	−21.5986	−	12.4699i	−1.10364	−	0.637184i	−0.937173	+	0.348864i	$0.886568\pi$
$384$		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	0.596520	−	0.802598i	$-0.296550\pi$
$397$	3.97920	+	2.29739i	0.199710	+	0.115303i	−0.396810	+	0.917901i	$0.629883\pi$
$398$		0			0
$399$	−0.0230680	+	0.0399550i	−0.00115485	+	0.00200025i
$400$		0			0
$401$	−14.8516	−	25.7237i	−0.741652	−	1.28458i	−0.951743	−	0.306897i	$-0.900709\pi$
$401$	−14.8516	−	25.7237i	−0.741652	−	1.28458i	0.210091	−	0.977682i	$-0.432624\pi$
$402$		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	−0.964876	−	0.262705i	$-0.915385\pi$
$409$	−5.15562	+	8.92980i	−0.254929	+	0.441550i	0.709947	+	0.704255i	$0.248719\pi$
$410$		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	−0.782602	−	0.622522i	$-0.786108\pi$
$419$	−19.0452	−	32.9873i	−0.930421	−	1.61154i	−0.147819	−	0.989014i	$-0.547225\pi$
$420$		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	0.501006	−	0.865444i	$-0.332963\pi$
$431$	−10.3594	−	17.9429i	−0.498993	−	0.864281i	−0.999999	+	0.00116231i	$0.999630\pi$
$432$		0			0
$433$	−13.7331	−	7.92881i	−0.659971	−	0.381034i	0.132295	−	0.991210i	$-0.457765\pi$
$433$	−13.7331	−	7.92881i	−0.659971	−	0.381034i	−0.792266	+	0.610176i	$0.791099\pi$
$434$		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	0.958518	−	0.285032i	$-0.0920041\pi$
$439$	4.86962	+	8.43444i	0.232415	+	0.402554i	−0.726104	+	0.687585i	$0.758671\pi$
$440$		0			0
$441$	17.6020			0.838189
$442$		0			0
$443$			9.23060i			0.438559i	0.975662	+	0.219279i	$0.0703707\pi$
$443$			9.23060i			0.438559i	−0.975662	+	0.219279i	$0.929629\pi$
$444$		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	−0.898458	−	0.439058i	$-0.855312\pi$
$449$	−1.46194	+	2.53216i	−0.0689934	+	0.119500i	0.829465	+	0.558559i	$0.188645\pi$
$450$		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	−0.245042	−	0.969512i	$-0.578802\pi$
$457$	10.0915	−	5.82632i	0.472060	−	0.272544i	0.717101	+	0.696969i	$0.245468\pi$
$458$		0			0
$459$	−4.87936	+	8.45130i	−0.227749	+	0.394473i
$460$		0			0
$461$	15.1490	−	26.2388i	0.705557	−	1.22206i	−0.260933	−	0.965357i	$-0.584030\pi$
$461$	15.1490	−	26.2388i	0.705557	−	1.22206i	0.966490	−	0.256704i	$-0.0826366\pi$
$462$		0			0
$463$			7.04331i			0.327330i	0.986516	+	0.163665i	$0.0523316\pi$
$463$			7.04331i			0.327330i	−0.986516	+	0.163665i	$0.947668\pi$
$464$		0			0
$465$	−3.22171	−	11.2010i	−0.149403	−	0.519436i
$466$		0			0
$467$		−	3.90110i		−	0.180522i	−0.995918	−	0.0902608i	$-0.971230\pi$
$467$		−	3.90110i		−	0.180522i	0.995918	−	0.0902608i	$-0.0287700\pi$
$468$		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	0.593697	−	0.804689i	$-0.297668\pi$
$479$	−8.75513	−	15.1643i	−0.400032	−	0.692876i	−0.993729	+	0.111813i	$0.964334\pi$
$480$		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	−0.999900	−	0.0141666i	$-0.995490\pi$
$487$	−33.3695	−	19.2659i	−1.51212	−	0.873022i	−0.512218	−	0.858855i	$-0.671176\pi$
$488$		0			0
$489$	−9.06997			−0.410158
$490$		0			0
$491$	3.41189	+	5.90956i	0.153976	+	0.266695i	0.932686	−	0.360690i	$-0.117459\pi$
$491$	3.41189	+	5.90956i	0.153976	+	0.266695i	−0.778710	+	0.627385i	$0.784125\pi$
$492$		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	0.786100	−	0.618099i	$-0.212097\pi$
$503$	14.4403	+	8.33710i	0.643860	+	0.371733i	−0.142240	+	0.989832i	$0.545430\pi$
$504$		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	−0.999598	−	0.0283510i	$-0.990974\pi$
$509$	−11.8299	−	20.4900i	−0.524352	−	0.908204i	0.475246	−	0.879853i	$-0.342359\pi$
$510$		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	−0.871853	−	0.489768i	$-0.837082\pi$
$523$	−20.2079	+	11.6670i	−0.883628	+	0.510163i	−0.0117752	+	0.999931i	$0.503748\pi$
$524$		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	$0.383428\pi$
$547$			43.6742i			1.86737i	−0.358090	+	0.933687i	$0.616572\pi$
$548$		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	−0.0291537	−	0.999575i	$-0.509281\pi$
$557$	19.3982	−	11.1995i	0.821927	−	0.474540i	0.851080	+	0.525035i	$0.175948\pi$
$558$		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	0.504397	−	0.863472i	$-0.331715\pi$
$563$	0.208951	+	0.120638i	0.00880625	+	0.00508429i	−0.495590	+	0.868556i	$0.665048\pi$
$564$		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	0.996612	+	0.0822501i	$0.0262106\pi$
$569$	13.5856	+	23.5309i	0.569537	+	0.986466i	−0.427075	+	0.904216i	$0.640456\pi$
$570$		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	$-0.947654\pi$
$577$		−	7.86481i		−	0.327416i	0.986509	−	0.163708i	$-0.0523455\pi$
$578$		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	−0.686692	−	0.726949i	$-0.740938\pi$
$587$	−9.70289	+	5.60197i	−0.400481	+	0.231218i	0.286210	+	0.958167i	$0.407604\pi$
$588$		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	$0.0888490\pi$
$593$			13.4186i			0.551034i	−0.961296	+	0.275517i	$0.911151\pi$
$594$		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	−0.999939	−	0.0110541i	$-0.996481\pi$
$601$	−12.4916	−	21.6361i	−0.509543	−	0.882554i	0.490396	−	0.871500i	$-0.336852\pi$
$602$		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	0.306112	−	0.951995i	$-0.400972\pi$
$607$	−8.99964	−	5.19594i	−0.365284	−	0.210897i	−0.671396	+	0.741099i	$0.734305\pi$
$608$		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	−0.927590	−	0.373599i	$-0.878124\pi$
$613$	−26.4385	+	15.2643i	−1.06784	+	0.616517i	−0.140249	+	0.990116i	$0.544790\pi$
$614$		0			0
$615$	0.374460	−	0.388396i	0.0150997	−	0.0156616i
$616$		0			0
$617$	6.32444	+	3.65142i	0.254612	+	0.147000i	0.621874	−	0.783117i	$-0.286371\pi$
$617$	6.32444	+	3.65142i	0.254612	+	0.147000i	−0.367262	+	0.930118i	$0.619705\pi$
$618$		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	−0.895035	−	0.445996i	$-0.852850\pi$
$631$	−1.53919	+	2.66595i	−0.0612741	+	0.106130i	0.833761	+	0.552125i	$0.186183\pi$
$632$		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	−0.840626	−	0.541616i	$-0.817813\pi$
$641$	1.23400	−	2.13735i	0.0487401	−	0.0844202i	0.889366	+	0.457196i	$0.151146\pi$
$642$		0			0
$643$	−16.2999	−	9.41075i	−0.642805	−	0.371124i	0.142889	−	0.989739i	$-0.454361\pi$
$643$	−16.2999	−	9.41075i	−0.642805	−	0.371124i	−0.785694	+	0.618615i	$0.787694\pi$
$644$		0			0
$645$	−0.581449	+	2.34017i	−0.0228945	+	0.0921442i
$646$		0			0
$647$	−10.1352	+	5.85157i	−0.398456	+	0.230049i	−0.685818	−	0.727773i	$-0.740555\pi$
$647$	−10.1352	+	5.85157i	−0.398456	+	0.230049i	0.287361	+	0.957822i	$0.407222\pi$
$648$		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	−0.229904	−	0.973213i	$-0.573841\pi$
$653$	12.7251	−	7.34684i	0.497972	−	0.287504i	0.727875	+	0.685709i	$0.240508\pi$
$654$		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	−0.988925	−	0.148415i	$-0.952583\pi$
$659$	−9.39383	+	16.2706i	−0.365932	+	0.633812i	0.622994	+	0.782227i	$0.285916\pi$
$660$		0			0
$661$	2.92101	+	5.05934i	0.113614	+	0.196785i	0.917225	−	0.398370i	$-0.130424\pi$
$661$	2.92101	+	5.05934i	0.113614	+	0.196785i	−0.803611	+	0.595155i	$0.797091\pi$
$662$		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	−0.990298	−	0.138957i	$-0.955625\pi$
$673$	−35.4140	+	20.4463i	−1.36511	+	0.788145i	−0.374809	+	0.927102i	$0.622292\pi$
$674$		0			0
$675$	7.20394	−	13.6020i	0.277280	−	0.523540i
$676$		0			0
$677$			28.2700i			1.08651i	0.839569	+	0.543253i	$0.182807\pi$
$677$			28.2700i			1.08651i	−0.839569	+	0.543253i	$0.817193\pi$
$678$		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	−0.383780	−	0.923425i	$-0.625378\pi$
$683$	−35.9445	−	20.7526i	−1.37538	−	0.794075i	−0.991599	+	0.129349i	$0.958711\pi$
$684$		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	0.540323	−	0.841458i	$-0.318302\pi$
$691$	−12.0542	−	20.8784i	−0.458562	−	0.794253i	−0.998885	+	0.0472043i	$0.984969\pi$
$692$		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	−0.0143094	+	0.999898i	$0.504555\pi$
$709$	−23.2479	+	40.2665i	−0.873091	+	1.51224i	−0.858782	+	0.512341i	$0.828778\pi$
$710$		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	−0.722700	−	0.691162i	$-0.757099\pi$
$719$	6.36069	−	11.0170i	0.237214	−	0.410866i	0.959914	+	0.280296i	$0.0904325\pi$
$720$		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	$-0.920922\pi$
$727$		−	13.2595i		−	0.491769i	0.969299	−	0.245884i	$-0.0790783\pi$
$728$		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	$-0.801759\pi$
$733$		−	31.5848i		−	1.16661i	0.812253	−	0.583305i	$-0.198241\pi$
$734$		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	0.838804	−	0.544434i	$-0.183255\pi$
$739$	−1.41609	−	2.45274i	−0.0520917	−	0.0902255i	−0.890895	+	0.454208i	$0.849922\pi$
$740$		0			0
$741$	−0.0851321	+	0.218533i	−0.00312741	+	0.00802800i
$742$		0			0
$743$	18.0151	−	10.4010i	0.660909	−	0.381576i	−0.131714	−	0.991288i	$-0.542048\pi$
$743$	18.0151	−	10.4010i	0.660909	−	0.381576i	0.792623	+	0.609712i	$0.208715\pi$
$744$		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	0.980095	+	0.198531i	$0.0636171\pi$
$751$	18.1412	+	31.4214i	0.661980	+	1.14658i	−0.318114	+	0.948052i	$0.603050\pi$
$752$		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	0.308383	−	0.951262i	$-0.400212\pi$
$757$	35.3933	−	20.4343i	1.28639	−	0.742699i	0.978009	+	0.208563i	$0.0668788\pi$
$758$		0			0
$759$	12.0891			0.438805
$760$		0			0
$761$	−17.8112	+	30.8500i	−0.645657	+	1.11831i	0.338492	+	0.940969i	$0.390083\pi$
$761$	−17.8112	+	30.8500i	−0.645657	+	1.11831i	−0.984149	+	0.177342i	$0.943250\pi$
$762$		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	0.894799	−	0.446469i	$-0.147319\pi$
$769$	1.68455	+	2.91773i	0.0607465	+	0.105216i	−0.834053	+	0.551685i	$0.813985\pi$
$770$		0			0
$771$	−0.141157	+	0.244491i	−0.00508365	+	0.00880514i
$772$		0			0
$773$	−9.59506	−	5.53971i	−0.345110	−	0.199250i	0.317419	−	0.948285i	$-0.397184\pi$
$773$	−9.59506	−	5.53971i	−0.345110	−	0.199250i	−0.662530	+	0.749036i	$0.730517\pi$
$774$		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	0.409908	−	0.912127i	$-0.365561\pi$
$787$	−4.91114	−	2.83545i	−0.175063	−	0.101073i	−0.584971	+	0.811054i	$0.698894\pi$
$788$		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	0.856843	−	0.515577i	$-0.172422\pi$
$797$	23.6792	+	13.6712i	0.838762	+	0.484259i	−0.0180812	+	0.999837i	$0.505756\pi$
$798$		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	0.818433	−	0.574602i	$-0.194843\pi$
$809$	−2.51446	−	4.35518i	−0.0884039	−	0.153120i	−0.906837	+	0.421482i	$0.861510\pi$
$810$		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	0.988109	−	0.153758i	$-0.0491376\pi$
$821$	10.3408	+	17.9108i	0.360896	+	0.625090i	−0.627213	+	0.778848i	$0.715804\pi$
$822$		0			0
$823$	−17.1794	−	9.91855i	−0.598837	−	0.345739i	0.169747	−	0.985488i	$-0.445705\pi$
$823$	−17.1794	−	9.91855i	−0.598837	−	0.345739i	−0.768584	+	0.639749i	$0.779038\pi$
$824$		0			0
$825$	6.46027	+	10.3013i	0.224918	+	0.358644i
$826$		0			0
$827$			39.6730i			1.37956i	0.724017	+	0.689782i	$0.242294\pi$
$827$			39.6730i			1.37956i	−0.724017	+	0.689782i	$0.757706\pi$
$828$		0			0
$829$	−12.6937	−	21.9861i	−0.440870	−	0.763609i	0.556885	−	0.830590i	$-0.311997\pi$
$829$	−12.6937	−	21.9861i	−0.440870	−	0.763609i	−0.997754	+	0.0669813i	$0.978663\pi$
$830$		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	−0.595915	−	0.803048i	$-0.703210\pi$
$839$	11.5139	−	19.9426i	0.397502	−	0.688494i	0.993417	+	0.114553i	$0.0365437\pi$
$840$		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	$-0.924615\pi$
$853$		−	13.7047i		−	0.469241i	0.972087	−	0.234621i	$-0.0753848\pi$
$854$		0			0
$855$	−0.702365	+	0.202018i	−0.0240204	+	0.00690888i
$856$		0			0
$857$			17.8648i			0.610250i	0.952312	+	0.305125i	$0.0986983\pi$
$857$			17.8648i			0.610250i	−0.952312	+	0.305125i	$0.901302\pi$
$858$		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	$0.110208\pi$
$863$			19.9383i			0.678706i	−0.940659	+	0.339353i	$0.889792\pi$
$864$		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	0.149441	−	0.988771i	$-0.452253\pi$
$877$	−18.7203	−	10.8082i	−0.632140	−	0.364966i	−0.781580	+	0.623805i	$0.785586\pi$
$878$		0			0
$879$	−9.62144			−0.324523
$880$		0			0
$881$	3.99693	+	6.92288i	0.134660	+	0.233238i	0.925468	−	0.378827i	$-0.123672\pi$
$881$	3.99693	+	6.92288i	0.134660	+	0.233238i	−0.790808	+	0.612065i	$0.790339\pi$
$882$		0			0
$883$		−	26.2713i		−	0.884098i	−0.896991	−	0.442049i	$-0.854252\pi$
$883$		−	26.2713i		−	0.884098i	0.896991	−	0.442049i	$-0.145748\pi$
$884$		0			0
$885$	6.73820	+	1.67420i	0.226502	+	0.0562777i
$886$		0			0
$887$	14.8634	−	8.58136i	0.499063	−	0.288134i	−0.229264	−	0.973364i	$-0.573632\pi$
$887$	14.8634	−	8.58136i	0.499063	−	0.288134i	0.728326	+	0.685230i	$0.240299\pi$
$888$		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	−0.245083	−	0.969502i	$-0.578815\pi$
$907$	14.2146	−	8.20682i	0.471989	−	0.272503i	0.717072	+	0.696999i	$0.245482\pi$
$908$		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	−0.796087	−	0.605182i	$-0.793100\pi$
$919$	3.82150	−	6.61904i	0.126060	−	0.218342i	0.922147	+	0.386840i	$0.126434\pi$
$920$		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	0.287735	−	0.957710i	$-0.407098\pi$
$929$	29.6647	−	51.3808i	0.973269	−	1.68575i	0.685534	−	0.728041i	$-0.259569\pi$
$930$		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	$-0.990854\pi$
$937$		−	1.75872i		−	0.0574550i	0.999587	−	0.0287275i	$-0.00914551\pi$
$938$		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	−0.430372	−	0.902651i	$-0.641618\pi$
$947$	4.19011	−	2.41916i	0.136160	−	0.0786122i	0.566533	+	0.824039i	$0.308284\pi$
$948$		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	0.0896318	−	0.995975i	$-0.471431\pi$
$953$	−22.4767	−	12.9769i	−0.728092	−	0.420364i	−0.817724	+	0.575611i	$0.804764\pi$
$954$		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	$-0.839813\pi$
$967$		−	29.9939i		−	0.964537i	0.876023	−	0.482269i	$-0.160187\pi$
$968$		0			0
$969$	0.103102	−	0.178578i	0.00331211	−	0.00573674i
$970$		0			0
$971$	7.86429	−	13.6213i	0.252377	−	0.437130i	−0.711803	−	0.702379i	$-0.752121\pi$
$971$	7.86429	−	13.6213i	0.252377	−	0.437130i	0.964180	+	0.265250i	$0.0854544\pi$
$972$		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	−0.830427	−	0.557128i	$-0.811903\pi$
$977$	−23.8539	+	13.7721i	−0.763154	+	0.440607i	0.0672731	+	0.997735i	$0.478570\pi$
$978$		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	$0.0928297\pi$
$983$			18.0289i			0.575034i	−0.957776	+	0.287517i	$0.907170\pi$
$984$		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	0.943499	−	0.331376i	$-0.107513\pi$
$991$	5.81658	+	10.0746i	0.184770	+	0.320031i	−0.758729	+	0.651406i	$0.774179\pi$
$992$		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	0.840555	−	0.541726i	$-0.182229\pi$
$997$	24.9977	+	14.4324i	0.791684	+	0.457079i	−0.0488712	+	0.998805i	$0.515562\pi$
$998$		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.289.4		12
4.3	odd	2		130.2.n.a.29.2	yes	12
5.4	even	2	inner	1040.2.dh.b.289.3		12
12.11	even	2		1170.2.bp.h.289.5		12
13.9	even	3	inner	1040.2.dh.b.529.3		12
20.3	even	4		650.2.e.k.601.2		6
20.7	even	4		650.2.e.j.601.2		6
20.19	odd	2		130.2.n.a.29.5	yes	12
52.3	odd	6		1690.2.b.c.339.2		6
52.11	even	12		1690.2.c.c.1689.3		6
52.15	even	12		1690.2.c.b.1689.3		6
52.23	odd	6		1690.2.b.b.339.5		6
52.35	odd	6		130.2.n.a.9.5	yes	12
60.59	even	2		1170.2.bp.h.289.2		12
65.9	even	6	inner	1040.2.dh.b.529.4		12
156.35	even	6		1170.2.bp.h.919.2		12
260.3	even	12		8450.2.a.bu.1.2		3
260.23	even	12		8450.2.a.ca.1.2		3
260.87	even	12		650.2.e.j.451.2		6
260.107	even	12		8450.2.a.cb.1.2		3
260.119	even	12		1690.2.c.c.1689.4		6
260.127	even	12		8450.2.a.bt.1.2		3
260.139	odd	6		130.2.n.a.9.2	✓	12
260.159	odd	6		1690.2.b.c.339.5		6
260.179	odd	6		1690.2.b.b.339.2		6
260.219	even	12		1690.2.c.b.1689.4		6
260.243	even	12		650.2.e.k.451.2		6
780.659	even	6		1170.2.bp.h.919.5		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.2	✓	12	260.139	odd	6
130.2.n.a.9.5	yes	12	52.35	odd	6
130.2.n.a.29.2	yes	12	4.3	odd	2
130.2.n.a.29.5	yes	12	20.19	odd	2
650.2.e.j.451.2		6	260.87	even	12
650.2.e.j.601.2		6	20.7	even	4
650.2.e.k.451.2		6	260.243	even	12
650.2.e.k.601.2		6	20.3	even	4
1040.2.dh.b.289.3		12	5.4	even	2	inner
1040.2.dh.b.289.4		12	1.1	even	1	trivial
1040.2.dh.b.529.3		12	13.9	even	3	inner
1040.2.dh.b.529.4		12	65.9	even	6	inner
1170.2.bp.h.289.2		12	60.59	even	2
1170.2.bp.h.289.5		12	12.11	even	2
1170.2.bp.h.919.2		12	156.35	even	6
1170.2.bp.h.919.5		12	780.659	even	6
1690.2.b.b.339.2		6	260.179	odd	6
1690.2.b.b.339.5		6	52.23	odd	6
1690.2.b.c.339.2		6	52.3	odd	6
1690.2.b.c.339.5		6	260.159	odd	6
1690.2.c.b.1689.3		6	52.15	even	12
1690.2.c.b.1689.4		6	260.219	even	12
1690.2.c.c.1689.3		6	52.11	even	12
1690.2.c.c.1689.4		6	260.119	even	12
8450.2.a.bt.1.2		3	260.127	even	12
8450.2.a.bu.1.2		3	260.3	even	12
8450.2.a.ca.1.2		3	260.23	even	12
8450.2.a.cb.1.2		3	260.107	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 $\F_{q}$

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

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

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Representations

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Database

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