LMFDB - Embedded newform 1170.2.bp.h.919.5

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [1170,2,Mod(289,1170)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(1170, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([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("1170.289"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1170.bp (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [12,0,0,6,0,0,0,0,0,-2,6] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(11)] == traces)

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

Self dual:	no
Analytic conductor:	$9.34249703649$
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:	$\Z[a_1, \ldots, a_{11}]$
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			919.5
Root			$-1.16746 - 0.312819i$ of defining polynomial
Character	$\chi$	$=$	1170.919
Dual form			1170.2.bp.h.289.5

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.539189 + 2.17009i) q^{5} +(0.614250 - 0.354638i) q^{7} +1.00000i q^{8} +(-0.618092 + 2.14894i) q^{10} +(-2.25513 + 3.90600i) q^{11} +(-3.35963 + 1.30878i) q^{13} +0.709275 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.74538 + 1.58504i) q^{17} +(-0.0603191 - 0.104476i) q^{19} +(-1.60976 + 1.55199i) q^{20} +(-3.90600 + 2.25513i) q^{22} +(-4.30507 - 2.48554i) q^{23} +(-4.41855 + 2.34017i) q^{25} +(-3.56391 - 0.546373i) q^{26} +(0.614250 + 0.354638i) q^{28} +(3.63090 - 6.28890i) q^{29} +9.66701 q^{31} +(-0.866025 + 0.500000i) q^{32} -3.17009 q^{34} +(1.10079 + 1.14176i) q^{35} +(6.02558 + 3.47887i) q^{37} -0.120638i q^{38} +(-2.17009 + 0.539189i) q^{40} +(0.223740 - 0.387529i) q^{41} +(-1.73205 + 1.00000i) q^{43} -4.51026 q^{44} +(-2.48554 - 4.30507i) q^{46} +4.70928i q^{47} +(-3.24846 + 5.62651i) q^{49} +(-4.99666 - 0.182626i) q^{50} +(-2.81325 - 2.25513i) q^{52} +9.58864i q^{53} +(-9.69230 - 2.78776i) q^{55} +(0.354638 + 0.614250i) q^{56} +(6.28890 - 3.63090i) q^{58} +(2.87936 + 4.98720i) q^{59} +(-3.53139 - 6.11655i) q^{61} +(8.37188 + 4.83351i) q^{62} -1.00000 q^{64} +(-4.65165 - 6.58500i) q^{65} +(2.53020 + 1.46081i) q^{67} +(-2.74538 - 1.58504i) q^{68} +(0.382433 + 1.53919i) q^{70} +(-4.09171 - 7.08705i) q^{71} -6.74539i q^{73} +(3.47887 + 6.02558i) q^{74} +(0.0603191 - 0.104476i) q^{76} +3.19902i q^{77} +16.0072 q^{79} +(-2.14894 - 0.618092i) q^{80} +(0.387529 - 0.223740i) q^{82} -0.355771i q^{83} +(-4.91996 - 5.10306i) q^{85} -2.00000 q^{86} +(-3.90600 - 2.25513i) q^{88} +(-1.81545 + 3.14445i) q^{89} +(-1.59951 + 1.99537i) q^{91} -4.97107i q^{92} +(-2.35464 + 4.07835i) q^{94} +(0.194198 - 0.187230i) q^{95} +(-6.84878 + 3.95415i) q^{97} +(-5.62651 + 3.24846i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 6 q^{4} - 2 q^{10} + 6 q^{11} - 20 q^{14} - 6 q^{16} - 26 q^{19} + 4 q^{25} + 28 q^{29} + 24 q^{31} - 16 q^{34} + 6 q^{35} - 4 q^{40} + 4 q^{41} + 12 q^{44} - 4 q^{49} + 8 q^{50} + 12 q^{55} - 10 q^{56}+ \cdots + 8 q^{95}+O(q^{100}) $ 12 * q + 6 * q^4 - 2 * q^10 + 6 * q^11 - 20 * q^14 - 6 * q^16 - 26 * q^19 + 4 * q^25 + 28 * q^29 + 24 * q^31 - 16 * q^34 + 6 * q^35 - 4 * q^40 + 4 * q^41 + 12 * q^44 - 4 * q^49 + 8 * q^50 + 12 * q^55 - 10 * q^56 - 16 * q^59 - 8 * q^61 - 12 * q^64 + 10 * q^65 + 24 * q^70 - 40 * q^71 + 10 * q^74 + 26 * q^76 + 56 * q^79 - 16 * q^85 - 24 * q^86 - 14 * q^89 - 38 * q^91 - 14 * q^94 + 8 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1170\mathbb{Z}\right)^\times$.

$n$	$911$	$937$	$1081$
$\chi(n)$	$1$	$-1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	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	$-0.623871\pi$
$7$	0.614250	−	0.354638i	0.232165	−	0.134040i	0.611570	+	0.791190i	$0.290538\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−0.618092	+	2.14894i	−0.195458	+	0.679556i
$11$	−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
$14$	0.709275			0.189562
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.74538	+	1.58504i	−0.665851	+	0.384429i	−0.794503	−	0.607260i	$-0.792268\pi$
$17$	−2.74538	+	1.58504i	−0.665851	+	0.384429i	0.128652	+	0.991690i	$0.458935\pi$
$18$		0			0
$19$	−0.0603191	−	0.104476i	−0.0138381	−	0.0239684i	0.859023	−	0.511936i	$-0.171072\pi$
$19$	−0.0603191	−	0.104476i	−0.0138381	−	0.0239684i	−0.872862	+	0.487968i	$0.837738\pi$
$20$	−1.60976	+	1.55199i	−0.359952	+	0.347037i
$21$		0			0
$22$	−3.90600	+	2.25513i	−0.832762	+	0.480795i
$23$	−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
$26$	−3.56391	−	0.546373i	−0.698941	−	0.107153i
$27$		0			0
$28$	0.614250	+	0.354638i	0.116082	+	0.0670202i
$29$	3.63090	−	6.28890i	0.674241	−	1.16782i	−0.302449	−	0.953165i	$-0.597804\pi$
$29$	3.63090	−	6.28890i	0.674241	−	1.16782i	0.976690	−	0.214654i	$-0.0688623\pi$
$30$		0			0
$31$	9.66701			1.73625			0.868124	−	0.496348i	$-0.165326\pi$
$31$	9.66701			1.73625			0.868124	+	0.496348i	$0.165326\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−3.17009			−0.543665
$35$	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	$0.472864\pi$
$38$		−	0.120638i		−	0.0195701i
$39$		0			0
$40$	−2.17009	+	0.539189i	−0.343121	+	0.0852532i
$41$	0.223740	−	0.387529i	0.0349423	−	0.0605219i	−0.848025	−	0.529956i	$-0.822209\pi$
$41$	0.223740	−	0.387529i	0.0349423	−	0.0605219i	0.882968	+	0.469434i	$0.155542\pi$
$42$		0			0
$43$	−1.73205	+	1.00000i	−0.264135	+	0.152499i	−0.626219	−	0.779647i	$-0.715399\pi$
$43$	−1.73205	+	1.00000i	−0.264135	+	0.152499i	0.362084	+	0.932145i	$0.382065\pi$
$44$	−4.51026			−0.679947
$45$		0			0
$46$	−2.48554	−	4.30507i	−0.366472	−	0.634748i
$47$			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
$50$	−4.99666	−	0.182626i	−0.706635	−	0.0258272i
$51$		0			0
$52$	−2.81325	−	2.25513i	−0.390128	−	0.312730i
$53$			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
$56$	0.354638	+	0.614250i	0.0473905	+	0.0820827i
$57$		0			0
$58$	6.28890	−	3.63090i	0.825773	−	0.476760i
$59$	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	$0.982675\pi$
$62$	8.37188	+	4.83351i	1.06323	+	0.613856i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−4.65165	−	6.58500i	−0.576966	−	0.816768i
$66$		0			0
$67$	2.53020	+	1.46081i	0.309113	+	0.178466i	0.646530	−	0.762889i	$-0.276220\pi$
$67$	2.53020	+	1.46081i	0.309113	+	0.178466i	−0.337416	+	0.941355i	$0.609553\pi$
$68$	−2.74538	−	1.58504i	−0.332926	−	0.192215i
$69$		0			0
$70$	0.382433	+	1.53919i	0.0457095	+	0.183968i
$71$	−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	$-0.129167\pi$
$74$	3.47887	+	6.02558i	0.404410	+	0.700459i
$75$		0			0
$76$	0.0603191	−	0.104476i	0.00691907	−	0.0119842i
$77$			3.19902i			0.364562i
$78$		0			0
$79$	16.0072			1.80095			0.900475	−	0.434908i	$-0.143219\pi$
$79$	16.0072			1.80095			0.900475	+	0.434908i	$0.143219\pi$
$80$	−2.14894	−	0.618092i	−0.240259	−	0.0691048i
$81$		0			0
$82$	0.387529	−	0.223740i	0.0427954	−	0.0247080i
$83$		−	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
$86$	−2.00000			−0.215666
$87$		0			0
$88$	−3.90600	−	2.25513i	−0.416381	−	0.240398i
$89$	−1.81545	+	3.14445i	−0.192437	+	0.333311i	−0.946057	−	0.323999i	$-0.894973\pi$
$89$	−1.81545	+	3.14445i	−0.192437	+	0.333311i	0.753620	+	0.657310i	$0.228306\pi$
$90$		0			0
$91$	−1.59951	+	1.99537i	−0.167674	+	0.209172i
$92$		−	4.97107i		−	0.518270i
$93$		0			0
$94$	−2.35464	+	4.07835i	−0.242862	+	0.420650i
$95$	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	$0.464838\pi$
$98$	−5.62651	+	3.24846i	−0.568363	+	0.328144i
$99$		0			0
$100$	−4.23592	−	2.65649i	−0.423592	−	0.265649i
$101$	3.07058	−	5.31840i	0.305534	−	0.529200i	−0.671846	−	0.740691i	$-0.734498\pi$
$101$	3.07058	−	5.31840i	0.305534	−	0.529200i	0.977380	+	0.211490i	$0.0678317\pi$
$102$		0			0
$103$			17.6803i			1.74210i	0.491198	+	0.871048i	$0.336559\pi$
$103$			17.6803i			1.74210i	−0.491198	+	0.871048i	$0.663441\pi$
$104$	−1.30878	−	3.35963i	−0.128337	−	0.329438i
$105$		0			0
$106$	−4.79432	+	8.30400i	−0.465665	+	0.806556i
$107$	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	$0.323022\pi$
$110$	−6.99990	−	7.26042i	−0.667414	−	0.692253i
$111$		0			0
$112$			0.709275i			0.0670202i
$113$	−12.1244	+	7.00000i	−1.14056	+	0.658505i	−0.946570	−	0.322498i	$-0.895477\pi$
$113$	−12.1244	+	7.00000i	−1.14056	+	0.658505i	−0.193993	+	0.981003i	$0.562144\pi$
$114$		0			0
$115$	3.07258	−	10.6826i	0.286519	−	0.996153i
$116$	7.26180			0.674241
$117$		0			0
$118$			5.75872i			0.530133i
$119$	−1.12423	+	1.94723i	−0.103058	+	0.178502i
$120$		0			0
$121$	−4.67122	−	8.09079i	−0.424656	−	0.735526i
$122$		−	7.06278i		−	0.639434i
$123$		0			0
$124$	4.83351	+	8.37188i	0.434062	+	0.751817i
$125$	−7.46081	−	8.32684i	−0.667315	−	0.744775i
$126$		0			0
$127$	10.5458	+	6.08864i	0.935791	+	0.540279i	0.888638	−	0.458609i	$-0.151652\pi$
$127$	10.5458	+	6.08864i	0.935791	+	0.540279i	0.0471526	+	0.998888i	$0.484985\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−0.735945	−	8.02860i	−0.0645466	−	0.704155i
$131$	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
$134$	1.46081	+	2.53020i	0.126195	+	0.218576i
$135$		0			0
$136$	−1.58504	−	2.74538i	−0.135916	−	0.235414i
$137$	8.10037	−	4.67675i	0.692061	−	0.399562i	−0.112322	−	0.993672i	$-0.535829\pi$
$137$	8.10037	−	4.67675i	0.692061	−	0.399562i	0.804384	+	0.594110i	$0.202496\pi$
$138$		0			0
$139$	−1.32211	−	2.28997i	−0.112140	−	0.194233i	0.804493	−	0.593963i	$-0.202437\pi$
$139$	−1.32211	−	2.28997i	−0.112140	−	0.194233i	−0.916633	+	0.399730i	$0.869104\pi$
$140$	−0.438397	+	1.52419i	−0.0370513	+	0.128818i
$141$		0			0
$142$		−	8.18342i		−	0.686737i
$143$	2.46429	−	16.0742i	0.206074	−	1.34419i
$144$		0			0
$145$	15.6052	+	4.48846i	1.29594	+	0.372746i
$146$	3.37270	−	5.84168i	0.279126	−	0.483461i
$147$		0			0
$148$			6.95774i			0.571923i
$149$	4.61757	+	7.99786i	0.378286	+	0.655210i	0.990813	−	0.135239i	$-0.0431803\pi$
$149$	4.61757	+	7.99786i	0.378286	+	0.655210i	−0.612527	+	0.790450i	$0.709847\pi$
$150$		0			0
$151$	−9.42574			−0.767056			−0.383528	−	0.923529i	$-0.625291\pi$
$151$	−9.42574			−0.767056			−0.383528	+	0.923529i	$0.625291\pi$
$152$	0.104476	−	0.0603191i	0.00847410	−	0.00489252i
$153$		0			0
$154$	−1.59951	+	2.77043i	−0.128892	+	0.223248i
$155$	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	$-0.0739806\pi$
$158$	13.8626	+	8.00359i	1.10285	+	0.636732i
$159$		0			0
$160$	−1.55199	−	1.60976i	−0.122696	−	0.127262i
$161$	−3.52586			−0.277877
$162$		0			0
$163$	14.5678	−	8.41075i	1.14104	−	0.658781i	0.194354	−	0.980932i	$-0.437739\pi$
$163$	14.5678	−	8.41075i	1.14104	−	0.658781i	0.946688	+	0.322151i	$0.104406\pi$
$164$	0.447480			0.0349423
$165$		0			0
$166$	0.177886	−	0.308107i	0.0138066	−	0.0239137i
$167$	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
$170$	−1.70928	−	6.87936i	−0.131095	−	0.527623i
$171$		0			0
$172$	−1.73205	−	1.00000i	−0.132068	−	0.0762493i
$173$	8.92357	−	5.15203i	0.678447	−	0.391701i	−0.120823	−	0.992674i	$-0.538553\pi$
$173$	8.92357	−	5.15203i	0.678447	−	0.391701i	0.799270	+	0.600973i	$0.205220\pi$
$174$		0			0
$175$	−1.88418	+	3.00444i	−0.142431	+	0.227114i
$176$	−2.25513	−	3.90600i	−0.169987	−	0.294426i
$177$		0			0
$178$	−3.14445	+	1.81545i	−0.235686	+	0.136074i
$179$	−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	$0.471779\pi$
$182$	−2.38290	+	0.928288i	−0.176632	+	0.0688093i
$183$		0			0
$184$	2.48554	−	4.30507i	0.183236	−	0.317374i
$185$	−4.30052	+	14.9518i	−0.316181	+	1.09928i
$186$		0			0
$187$		−	14.2979i		−	1.04557i
$188$	−4.07835	+	2.35464i	−0.297444	+	0.171730i
$189$		0			0
$190$	0.261795	−	0.0650468i	0.0189926	−	0.00471899i
$191$	−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	$0.834758\pi$
$194$	−7.90829			−0.567782
$195$		0			0
$196$	−6.49693			−0.464066
$197$	−7.52895	−	4.34684i	−0.536415	−	0.309699i	0.207210	−	0.978297i	$-0.433562\pi$
$197$	−7.52895	−	4.34684i	−0.536415	−	0.309699i	−0.743625	+	0.668597i	$0.766895\pi$
$198$		0			0
$199$	10.7587	+	18.6347i	0.762666	+	1.32098i	0.941472	+	0.337091i	$0.109443\pi$
$199$	10.7587	+	18.6347i	0.762666	+	1.32098i	−0.178806	+	0.983884i	$0.557224\pi$
$200$	−2.34017	−	4.41855i	−0.165475	−	0.312439i
$201$		0			0
$202$	5.31840	−	3.07058i	0.374201	−	0.216045i
$203$		−	5.15061i		−	0.361502i
$204$		0			0
$205$	0.961610	+	0.276584i	0.0671618	+	0.0193175i
$206$	−8.84017	+	15.3116i	−0.615924	+	1.06681i
$207$		0			0
$208$	0.546373	−	3.56391i	0.0378842	−	0.247113i
$209$	0.544109			0.0376368
$210$		0			0
$211$	2.79432	−	4.83990i	0.192369	−	0.333193i	−0.753666	−	0.657258i	$-0.771716\pi$
$211$	2.79432	−	4.83990i	0.192369	−	0.333193i	0.946035	+	0.324065i	$0.105050\pi$
$212$	−8.30400	+	4.79432i	−0.570321	+	0.329275i
$213$		0			0
$214$	0.269594	+	0.466951i	0.0184291	+	0.0319201i
$215$	−3.10399	−	3.21951i	−0.211690	−	0.219569i
$216$		0			0
$217$	5.93797	−	3.42829i	0.403096	−	0.232727i
$218$	9.54405	+	5.51026i	0.646405	+	0.373202i
$219$		0			0
$220$	−2.43188	−	9.78765i	−0.163957	−	0.659883i
$221$	7.14896	−	8.91825i	0.480891	−	0.599907i
$222$		0			0
$223$	−21.3989	−	12.3546i	−1.43297	−	0.827328i	−0.435627	−	0.900127i	$-0.643473\pi$
$223$	−21.3989	−	12.3546i	−1.43297	−	0.827328i	−0.997347	+	0.0727995i	$0.976807\pi$
$224$	−0.354638	+	0.614250i	−0.0236952	+	0.0410413i
$225$		0			0
$226$	−14.0000			−0.931266
$227$	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	$0.480005\pi$
$230$	8.00221	−	7.71507i	0.527650	−	0.508717i
$231$		0			0
$232$	6.28890	+	3.63090i	0.412886	+	0.238380i
$233$		−	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
$236$	−2.87936	+	4.98720i	−0.187430	+	0.324639i
$237$		0			0
$238$	−1.94723	+	1.12423i	−0.126220	+	0.0728731i
$239$	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	$0.803038\pi$
$242$		−	9.34244i		−	0.600555i
$243$		0			0
$244$	3.53139	−	6.11655i	0.226074	−	0.391572i
$245$	−13.9615	−	4.01570i	−0.891970	−	0.256554i
$246$		0			0
$247$	0.339386	+	0.272055i	0.0215946	+	0.0173104i
$248$			9.66701i			0.613856i
$249$		0			0
$250$	−2.29783	−	10.9417i	−0.145328	−	0.692011i
$251$	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
$254$	6.08864	+	10.5458i	0.382035	+	0.661704i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	0.453443	+	0.261795i	0.0282850	+	0.0163303i	0.514076	−	0.857745i	$-0.328135\pi$
$257$	0.453443	+	0.261795i	0.0282850	+	0.0163303i	−0.485791	+	0.874075i	$0.661468\pi$
$258$		0			0
$259$	4.93495			0.306643
$260$	3.37695	−	7.32094i	0.209430	−	0.454026i
$261$		0			0
$262$	15.1162	+	8.72733i	0.933881	+	0.539176i
$263$	−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
$266$	−0.0427828	−	0.0741020i	−0.00262318	−	0.00454349i
$267$		0			0
$268$			2.92162i			0.178466i
$269$	−5.02832	−	8.70930i	−0.306582	−	0.531016i	0.671030	−	0.741430i	$-0.265852\pi$
$269$	−5.02832	−	8.70930i	−0.306582	−	0.531016i	−0.977612	+	0.210414i	$0.932519\pi$
$270$		0			0
$271$	−9.06278	+	15.6972i	−0.550525	+	0.953537i	0.447712	+	0.894178i	$0.352239\pi$
$271$	−9.06278	+	15.6972i	−0.550525	+	0.953537i	−0.998237	+	0.0593589i	$0.981094\pi$
$272$		−	3.17009i		−	0.192215i
$273$		0			0
$274$	9.35350			0.565066
$275$	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	$0.599710\pi$
$278$		−	2.64423i		−	0.158590i
$279$		0			0
$280$	−1.14176	+	1.10079i	−0.0682332	+	0.0657849i
$281$	−22.9854			−1.37120			−0.685598	−	0.727980i	$-0.740459\pi$
$281$	−22.9854			−1.37120			−0.685598	+	0.727980i	$0.740459\pi$
$282$		0			0
$283$	15.6741	+	9.04945i	0.931729	+	0.537934i	0.887358	−	0.461081i	$-0.152538\pi$
$283$	15.6741	+	9.04945i	0.931729	+	0.537934i	0.0443709	+	0.999015i	$0.485872\pi$
$284$	4.09171	−	7.08705i	0.242798	−	0.420539i
$285$		0			0
$286$	10.1712	−	12.6885i	0.601437	−	0.750287i
$287$		−	0.317387i		−	0.0187347i
$288$		0			0
$289$	−3.47528	+	6.01935i	−0.204428	+	0.354080i
$290$	11.2703	+	11.6897i	0.661813	+	0.686444i
$291$		0			0
$292$	5.84168	−	3.37270i	0.341859	−	0.197372i
$293$	15.4536	−	8.92214i	0.902809	−	0.521237i	0.0246988	−	0.999695i	$-0.492137\pi$
$293$	15.4536	−	8.92214i	0.902809	−	0.521237i	0.878111	+	0.478458i	$0.158804\pi$
$294$		0			0
$295$	−9.27014	+	8.93751i	−0.539728	+	0.520362i
$296$	−3.47887	+	6.02558i	−0.202205	+	0.350230i
$297$		0			0
$298$			9.23513i			0.534977i
$299$	17.7165	+	2.71606i	1.02457	+	0.157074i
$300$		0			0
$301$	−0.709275	+	1.22850i	−0.0408820	+	0.0708096i
$302$	−8.16293	−	4.71287i	−0.469724	−	0.271195i
$303$		0			0
$304$	0.120638			0.00691907
$305$	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	$0.968655\pi$
$308$	−2.77043	+	1.59951i	−0.157860	+	0.0911404i
$309$		0			0
$310$	−5.97510	+	20.7739i	−0.339363	+	1.17988i
$311$	−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	$-0.364470\pi$
$314$	2.88603	−	4.99875i	0.162868	−	0.282096i
$315$		0			0
$316$	8.00359	+	13.8626i	0.450237	+	0.779834i
$317$		−	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
$320$	−0.539189	−	2.17009i	−0.0301416	−	0.121312i
$321$		0			0
$322$	−3.05348	−	1.76293i	−0.170164	−	0.0982442i
$323$	0.331197	+	0.191217i	0.0184283	+	0.0106396i
$324$		0			0
$325$	11.7819	−	13.6450i	0.653542	−	0.756890i
$326$	16.8215			0.931657
$327$		0			0
$328$	0.387529	+	0.223740i	0.0213977	+	0.0123540i
$329$	1.67009	+	2.89267i	0.0920748	+	0.159478i
$330$		0			0
$331$	0.355771	+	0.616214i	0.0195550	+	0.0338702i	0.875637	−	0.482969i	$-0.160442\pi$
$331$	0.355771	+	0.616214i	0.0195550	+	0.0338702i	−0.856082	+	0.516839i	$0.827108\pi$
$332$	0.308107	−	0.177886i	0.0169096	−	0.00976275i
$333$		0			0
$334$	9.05971	+	15.6919i	0.495725	+	0.858621i
$335$	−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	$0.913540\pi$
$338$	12.6885	−	2.82878i	0.690163	−	0.153865i
$339$		0			0
$340$	1.95941	−	6.81234i	0.106264	−	0.369451i
$341$	−21.8004	+	37.7594i	−1.18056	+	2.04478i
$342$		0			0
$343$			9.57304i			0.516896i
$344$	−1.00000	−	1.73205i	−0.0539164	−	0.0933859i
$345$		0			0
$346$	10.3041			0.553949
$347$	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	$0.327219\pi$
$350$	−3.13397	+	1.65983i	−0.167518	+	0.0887215i
$351$		0			0
$352$		−	4.51026i		−	0.240398i
$353$	12.6842	+	7.32325i	0.675114	+	0.389777i	0.798012	−	0.602642i	$-0.205885\pi$
$353$	12.6842	+	7.32325i	0.675114	+	0.389777i	−0.122898	+	0.992419i	$0.539219\pi$
$354$		0			0
$355$	13.1733	−	12.7006i	0.699166	−	0.674079i
$356$	−3.63090			−0.192437
$357$		0			0
$358$	−1.09275	+	0.630898i	−0.0577535	+	0.0333440i
$359$	−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
$362$	2.06325	+	1.19122i	0.108442	+	0.0626090i
$363$		0			0
$364$	−2.52780	−	0.387529i	−0.132492	−	0.0203120i
$365$	14.6381	−	3.63704i	0.766192	−	0.190371i
$366$		0			0
$367$	−18.6577	−	10.7721i	−0.973926	−	0.562297i	−0.0734954	−	0.997296i	$-0.523415\pi$
$367$	−18.6577	−	10.7721i	−0.973926	−	0.562297i	−0.900431	+	0.434999i	$0.856749\pi$
$368$	4.30507	−	2.48554i	0.224417	−	0.129567i
$369$		0			0
$370$	−11.2003	+	10.7984i	−0.582274	+	0.561381i
$371$	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	$0.147077\pi$
$374$	7.14896	−	12.3824i	0.369664	−	0.640276i
$375$		0			0
$376$	−4.70928			−0.242862
$377$	−3.96765	+	25.8804i	−0.204344	+	1.33291i
$378$		0			0
$379$	4.05611	−	7.02540i	0.208349	−	0.360870i	−0.742846	−	0.669462i	$-0.766524\pi$
$379$	4.05611	−	7.02540i	0.208349	−	0.360870i	0.951194	+	0.308592i	$0.0998578\pi$
$380$	0.259245	+	0.0745655i	0.0132990	+	0.00382513i
$381$		0			0
$382$		−	11.0856i		−	0.567187i
$383$	−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
$386$	−7.00000	−	12.1244i	−0.356291	−	0.617113i
$387$		0			0
$388$	−6.84878	−	3.95415i	−0.347694	−	0.200741i
$389$	13.5330			0.686153			0.343076	−	0.939308i	$-0.388531\pi$
$389$	13.5330			0.686153			0.343076	+	0.939308i	$0.388531\pi$
$390$		0			0
$391$	15.7587			0.796953
$392$	−5.62651	−	3.24846i	−0.284181	−	0.164072i
$393$		0			0
$394$	−4.34684	−	7.52895i	−0.218991	−	0.379303i
$395$	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	$0.296550\pi$
$398$			21.5174i			1.07857i
$399$		0			0
$400$	0.182626	−	4.99666i	0.00913131	−	0.249833i
$401$	14.8516	−	25.7237i	0.741652	−	1.28458i	−0.210091	−	0.977682i	$-0.567376\pi$
$401$	14.8516	−	25.7237i	0.741652	−	1.28458i	0.951743	−	0.306897i	$-0.0992906\pi$
$402$		0			0
$403$	−32.4776	+	12.6520i	−1.61782	+	0.630242i
$404$	6.14116			0.305534
$405$		0			0
$406$	2.57531	−	4.46056i	0.127810	−	0.221374i
$407$	−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	$0.915385\pi$
$410$	0.694487	+	0.720334i	0.0342983	+	0.0355747i
$411$		0			0
$412$	−15.3116	+	8.84017i	−0.754350	+	0.435524i
$413$	3.53730	+	2.04226i	0.174059	+	0.100493i
$414$		0			0
$415$	0.772055	−	0.191828i	0.0378987	−	0.00941646i
$416$	2.25513	−	2.81325i	0.110567	−	0.137931i
$417$		0			0
$418$	0.471213	+	0.272055i	0.0230478	+	0.0133066i
$419$	−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	$0.725604\pi$
$422$	4.83990	−	2.79432i	0.235603	−	0.136025i
$423$		0			0
$424$	−9.58864			−0.465665
$425$	8.42131	−	13.4282i	0.408493	−	0.651366i
$426$		0			0
$427$	−4.33832	−	2.50473i	−0.209946	−	0.121212i
$428$			0.539189i			0.0260627i
$429$		0			0
$430$	−1.07838	−	4.34017i	−0.0520040	−	0.209302i
$431$	−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	$0.457765\pi$
$434$	6.85658			0.329126
$435$		0			0
$436$	5.51026	+	9.54405i	0.263894	+	0.457077i
$437$			0.599701i			0.0286876i
$438$		0			0
$439$	−4.86962	+	8.43444i	−0.232415	+	0.402554i	−0.958518	−	0.285032i	$-0.907996\pi$
$439$	−4.86962	+	8.43444i	−0.232415	+	0.402554i	0.726104	+	0.687585i	$0.241329\pi$
$440$	2.78776	−	9.69230i	0.132901	−	0.462062i
$441$		0			0
$442$	10.6503	−	4.14896i	0.506583	−	0.197346i
$443$		−	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
$446$	−12.3546	−	21.3989i	−0.585009	−	1.01327i
$447$		0			0
$448$	−0.614250	+	0.354638i	−0.0290206	+	0.0167551i
$449$	1.46194	+	2.53216i	0.0689934	+	0.119500i	0.898458	−	0.439058i	$-0.144688\pi$
$449$	1.46194	+	2.53216i	0.0689934	+	0.119500i	−0.829465	+	0.558559i	$0.811355\pi$
$450$		0			0
$451$	1.00913	+	1.74786i	0.0475179	+	0.0823034i
$452$	−12.1244	−	7.00000i	−0.570282	−	0.329252i
$453$		0			0
$454$	28.6947			1.34671
$455$	−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	$0.578802\pi$
$458$	1.64535	+	0.949940i	0.0768819	+	0.0443878i
$459$		0			0
$460$	10.7877	−	2.68035i	0.502977	−	0.124972i
$461$	−15.1490	−	26.2388i	−0.705557	−	1.22206i	−0.966490	−	0.256704i	$-0.917363\pi$
$461$	−15.1490	−	26.2388i	−0.705557	−	1.22206i	0.260933	−	0.965357i	$-0.415970\pi$
$462$		0			0
$463$			7.04331i			0.327330i	0.986516	+	0.163665i	$0.0523316\pi$
$463$			7.04331i			0.327330i	−0.986516	+	0.163665i	$0.947668\pi$
$464$	3.63090	+	6.28890i	0.168560	+	0.291955i
$465$		0			0
$466$	11.1242	−	19.2677i	0.515320	−	0.892561i
$467$			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
$470$	−10.1200	−	2.91077i	−0.466799	−	0.134264i
$471$		0			0
$472$	−4.98720	+	2.87936i	−0.229555	+	0.132533i
$473$		−	9.02052i		−	0.414764i
$474$		0			0
$475$	0.511014	+	0.320474i	0.0234469	+	0.0147044i
$476$	−2.24846			−0.103058
$477$		0			0
$478$	21.5389	+	12.4355i	0.985165	+	0.568785i
$479$	−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
$482$			2.95055i			0.134394i
$483$		0			0
$484$	4.67122	−	8.09079i	0.212328	−	0.367763i
$485$	−12.2736	−	12.7304i	−0.557317	−	0.578058i
$486$		0			0
$487$	33.3695	−	19.2659i	1.51212	−	0.873022i	0.512218	−	0.858855i	$-0.328824\pi$
$487$	33.3695	−	19.2659i	1.51212	−	0.873022i	0.999900	−	0.0141666i	$-0.00450951\pi$
$488$	6.11655	−	3.53139i	0.276883	−	0.159858i
$489$		0			0
$490$	−10.0832	−	10.4585i	−0.455512	−	0.472465i
$491$	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
$494$	0.157889	+	0.405299i	0.00710377	+	0.0182353i
$495$		0			0
$496$	−4.83351	+	8.37188i	−0.217031	+	0.375909i
$497$	−5.02667	−	2.90215i	−0.225477	−	0.130179i
$498$		0			0
$499$	−9.57918			−0.428823			−0.214412	−	0.976743i	$-0.568783\pi$
$499$	−9.57918			−0.428823			−0.214412	+	0.976743i	$0.568783\pi$
$500$	3.48085	−	10.6247i	0.155668	−	0.475150i
$501$		0			0
$502$			16.5597i			0.739096i
$503$	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
$506$	22.4208			0.996727
$507$		0			0
$508$			12.1773i			0.540279i
$509$	11.8299	−	20.4900i	0.524352	−	0.908204i	−0.475246	−	0.879853i	$-0.657641\pi$
$509$	11.8299	−	20.4900i	0.524352	−	0.908204i	0.999598	−	0.0283510i	$-0.00902561\pi$
$510$		0			0
$511$	−2.39217	−	4.14336i	−0.105823	−	0.183291i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	0.261795	+	0.453443i	0.0115473	+	0.0200005i
$515$	−38.3679	+	9.53305i	−1.69069	+	0.420076i
$516$		0			0
$517$	−18.3944	−	10.6200i	−0.808986	−	0.467068i
$518$	4.27379	+	2.46748i	0.187780	+	0.108415i
$519$		0			0
$520$	6.58500	−	4.65165i	0.288771	−	0.203988i
$521$	24.0472			1.05353			0.526763	−	0.850012i	$-0.323406\pi$
$521$	24.0472			1.05353			0.526763	+	0.850012i	$0.323406\pi$
$522$		0			0
$523$	20.2079	+	11.6670i	0.883628	+	0.510163i	0.871853	−	0.489768i	$-0.162918\pi$
$523$	20.2079	+	11.6670i	0.883628	+	0.510163i	0.0117752	+	0.999931i	$0.496252\pi$
$524$	8.72733	+	15.1162i	0.381255	+	0.660354i
$525$		0			0
$526$	−14.3908	−	24.9255i	−0.627467	−	1.08680i
$527$	−26.5396	+	15.3226i	−1.15608	+	0.667465i
$528$		0			0
$529$	0.855771	+	1.48224i	0.0372075	+	0.0644452i
$530$	−20.6054	−	5.92666i	−0.895044	−	0.257438i
$531$		0			0
$532$		−	0.0855657i		−	0.00370974i
$533$	−0.244491	+	1.59478i	−0.0105901	+	0.0690776i
$534$		0			0
$535$	−0.333268	+	1.15869i	−0.0144084	+	0.0500944i
$536$	−1.46081	+	2.53020i	−0.0630974	+	0.109288i
$537$		0			0
$538$		−	10.0566i		−	0.433572i
$539$	−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	$0.752483\pi$
$542$	−15.6972	+	9.06278i	−0.674252	+	0.389280i
$543$		0			0
$544$	1.58504	−	2.74538i	0.0679582	−	0.117707i
$545$	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	$0.616572\pi$
$548$	8.10037	+	4.67675i	0.346031	+	0.199781i
$549$		0			0
$550$	11.9815	−	19.1051i	0.510891	−	0.814645i
$551$	−0.876050			−0.0373210
$552$		0			0
$553$	9.83242	−	5.67675i	0.418117	−	0.241400i
$554$	−24.7165			−1.05010
$555$		0			0
$556$	1.32211	−	2.28997i	0.0560701	−	0.0971163i
$557$	−19.3982	−	11.1995i	−0.821927	−	0.474540i	0.0291537	−	0.999575i	$-0.490719\pi$
$557$	−19.3982	−	11.1995i	−0.821927	−	0.474540i	−0.851080	+	0.525035i	$0.824052\pi$
$558$		0			0
$559$	4.51026	−	5.62651i	0.190764	−	0.237976i
$560$	−1.53919	+	0.382433i	−0.0650426	+	0.0161608i
$561$		0			0
$562$	−19.9060	−	11.4927i	−0.839683	−	0.484791i
$563$	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
$566$	9.04945	+	15.6741i	0.380377	+	0.658832i
$567$		0			0
$568$	7.08705	−	4.09171i	0.297366	−	0.171684i
$569$	−13.5856	+	23.5309i	−0.569537	+	0.986466i	0.427075	+	0.904216i	$0.359544\pi$
$569$	−13.5856	+	23.5309i	−0.569537	+	0.986466i	−0.996612	+	0.0822501i	$0.973789\pi$
$570$		0			0
$571$	2.25461			0.0943524			0.0471762	−	0.998887i	$-0.484978\pi$
$571$	2.25461			0.0943524			0.0471762	+	0.998887i	$0.484978\pi$
$572$	15.1528	−	5.90295i	0.633570	−	0.246815i
$573$		0			0
$574$	0.158693	−	0.274865i	0.00662373	−	0.0114726i
$575$	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	$0.947654\pi$
$578$	−6.01935	+	3.47528i	−0.250372	+	0.144552i
$579$		0			0
$580$	3.91548	+	15.7587i	0.162581	+	0.654345i
$581$	−0.126170	−	0.218533i	−0.00523441	−	0.00906627i
$582$		0			0
$583$	−37.4532	−	21.6236i	−1.55115	−	0.895559i
$584$	6.74539			0.279126
$585$		0			0
$586$	17.8443			0.737141
$587$	−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
$590$	−12.4969	+	3.10504i	−0.514490	+	0.127832i
$591$		0			0
$592$	−6.02558	+	3.47887i	−0.247650	+	0.142981i
$593$			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
$596$	−4.61757	+	7.99786i	−0.189143	+	0.327605i
$597$		0			0
$598$	13.9849	+	11.2104i	0.571884	+	0.458428i
$599$	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	$0.996481\pi$
$602$	−1.22850	+	0.709275i	−0.0500700	+	0.0289079i
$603$		0			0
$604$	−4.71287	−	8.16293i	−0.191764	−	0.332145i
$605$	15.0390	−	14.4994i	0.611424	−	0.589485i
$606$		0			0
$607$	8.99964	−	5.19594i	0.365284	−	0.210897i	−0.306112	−	0.951995i	$-0.599028\pi$
$607$	8.99964	−	5.19594i	0.365284	−	0.210897i	0.671396	+	0.741099i	$0.265695\pi$
$608$	0.104476	+	0.0603191i	0.00423705	+	0.00244626i
$609$		0			0
$610$	15.3268	−	3.80817i	0.620566	−	0.154188i
$611$	−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	$0.878124\pi$
$614$	−1.72261	+	2.98364i	−0.0695187	+	0.120410i
$615$		0			0
$616$	−3.19902			−0.128892
$617$	−6.32444	+	3.65142i	−0.254612	+	0.147000i	−0.621874	−	0.783117i	$-0.713629\pi$
$617$	−6.32444	+	3.65142i	−0.254612	+	0.147000i	0.367262	+	0.930118i	$0.380295\pi$
$618$		0			0
$619$	24.5103			0.985151			0.492575	−	0.870270i	$-0.336056\pi$
$619$	24.5103			0.985151			0.492575	+	0.870270i	$0.336056\pi$
$620$	−15.5615	+	15.0032i	−0.624966	+	0.602541i
$621$		0			0
$622$	−15.4358	−	8.91189i	−0.618921	−	0.357334i
$623$			2.57531i			0.103177i
$624$		0			0
$625$	14.0472	−	20.6803i	0.561887	−	0.827214i
$626$	16.1122	−	27.9072i	0.643974	−	1.11540i
$627$		0			0
$628$	4.99875	−	2.88603i	0.199472	−	0.115165i
$629$	−22.0566			−0.879456
$630$		0			0
$631$	1.53919	+	2.66595i	0.0612741	+	0.106130i	0.895035	−	0.445996i	$-0.147150\pi$
$631$	1.53919	+	2.66595i	0.0612741	+	0.106130i	−0.833761	+	0.552125i	$0.813817\pi$
$632$			16.0072i			0.636732i
$633$		0			0
$634$	0.953012	−	1.65067i	0.0378489	−	0.0655563i
$635$	−7.52668	+	26.1683i	−0.298687	+	1.03846i
$636$		0			0
$637$	3.54975	−	23.1545i	0.140646	−	0.917414i
$638$			32.7526i			1.29669i
$639$		0			0
$640$	0.618092	−	2.14894i	0.0244322	−	0.0849445i
$641$	−1.23400	−	2.13735i	−0.0487401	−	0.0844202i	0.840626	−	0.541616i	$-0.182187\pi$
$641$	−1.23400	−	2.13735i	−0.0487401	−	0.0844202i	−0.889366	+	0.457196i	$0.848854\pi$
$642$		0			0
$643$	16.2999	−	9.41075i	0.642805	−	0.371124i	−0.142889	−	0.989739i	$-0.545639\pi$
$643$	16.2999	−	9.41075i	0.642805	−	0.371124i	0.785694	+	0.618615i	$0.212306\pi$
$644$	−1.76293	−	3.05348i	−0.0694691	−	0.120324i
$645$		0			0
$646$	0.191217	+	0.331197i	0.00752332	+	0.0130308i
$647$	−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
$650$	17.0259	−	5.92599i	0.667812	−	0.232437i
$651$		0			0
$652$	14.5678	+	8.41075i	0.570521	+	0.329390i
$653$	−12.7251	−	7.34684i	−0.497972	−	0.287504i	0.229904	−	0.973213i	$-0.426159\pi$
$653$	−12.7251	−	7.34684i	−0.497972	−	0.287504i	−0.727875	+	0.685709i	$0.759492\pi$
$654$		0			0
$655$	9.41136	+	37.8781i	0.367732	+	1.48002i
$656$	0.223740	+	0.387529i	0.00873558	+	0.0151305i
$657$		0			0
$658$			3.34017i			0.130213i
$659$	−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	$0.130424\pi$
$662$			0.711543i			0.0276549i
$663$		0			0
$664$	0.355771			0.0138066
$665$	0.0528875	−	0.183876i	0.00205089	−	0.00713040i
$666$		0			0
$667$	−31.2626	+	18.0494i	−1.21049	+	0.698877i
$668$			18.1194i			0.701061i
$669$		0			0
$670$	−4.70310	+	4.53434i	−0.181697	+	0.175177i
$671$	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	$0.955625\pi$
$674$	−4.92522	+	8.53072i	−0.189712	+	0.328591i
$675$		0			0
$676$	12.4030	+	3.89445i	0.477037	+	0.149787i
$677$			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
$680$	5.10306	−	4.91996i	0.195694	−	0.188672i
$681$		0			0
$682$	−37.7594	+	21.8004i	−1.44588	+	0.834779i
$683$	−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
$686$	−4.78652	+	8.29049i	−0.182750	+	0.316533i
$687$		0			0
$688$		−	2.00000i		−	0.0762493i
$689$	−12.5494	−	32.2142i	−0.478096	−	1.22726i
$690$		0			0
$691$	12.0542	−	20.8784i	0.458562	−	0.794253i	−0.540323	−	0.841458i	$-0.681698\pi$
$691$	12.0542	−	20.8784i	0.458562	−	0.794253i	0.998885	+	0.0472043i	$0.0150312\pi$
$692$	8.92357	+	5.15203i	0.339223	+	0.195851i
$693$		0			0
$694$	25.5330			0.969221
$695$	4.25656	−	4.10383i	0.161461	−	0.155667i
$696$		0			0
$697$			1.41855i			0.0537314i
$698$	−15.6375	+	9.02832i	−0.591888	+	0.341727i
$699$		0			0
$700$	−3.54401	−	0.129532i	−0.133951	−	0.00489586i
$701$	14.1822			0.535654			0.267827	−	0.963467i	$-0.413694\pi$
$701$	14.1822			0.535654			0.267827	+	0.963467i	$0.413694\pi$
$702$		0			0
$703$		−	0.839369i		−	0.0316574i
$704$	2.25513	−	3.90600i	0.0849934	−	0.147213i
$705$		0			0
$706$	7.32325	+	12.6842i	0.275614	+	0.477378i
$707$		−	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	$-0.504555\pi$
$710$	17.7587	−	4.41241i	0.666473	−	0.165595i
$711$		0			0
$712$	−3.14445	−	1.81545i	−0.117843	−	0.0680368i
$713$	−41.6172	−	24.0277i	−1.55858	−	0.899845i
$714$		0			0
$715$	36.2111	−	3.31930i	1.35422	−	0.124135i
$716$	−1.26180			−0.0471555
$717$		0			0
$718$	−11.6208	−	6.70928i	−0.433685	−	0.250388i
$719$	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
$722$	16.4419	−	9.49272i	0.611903	−	0.353283i
$723$		0			0
$724$	1.19122	+	2.06325i	0.0442712	+	0.0766800i
$725$	−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	$-0.0790783\pi$
$728$	−1.99537	−	1.59951i	−0.0739534	−	0.0592817i
$729$		0			0
$730$	14.4955	+	4.16927i	0.536502	+	0.154312i
$731$	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	$0.801759\pi$
$734$	−10.7721	−	18.6577i	−0.397604	−	0.688670i
$735$		0			0
$736$	4.97107			0.183236
$737$	−11.4119	+	6.58864i	−0.420361	+	0.242696i
$738$		0			0
$739$	1.41609	−	2.45274i	0.0520917	−	0.0902255i	−0.838804	−	0.544434i	$-0.816745\pi$
$739$	1.41609	−	2.45274i	0.0520917	−	0.0902255i	0.890895	+	0.454208i	$0.150078\pi$
$740$	−15.0989	+	3.75154i	−0.555046	+	0.137909i
$741$		0			0
$742$			6.80098i			0.249672i
$743$	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
$746$	21.3340			0.781094
$747$		0			0
$748$	12.3824	−	7.14896i	0.452744	−	0.261392i
$749$	0.382433			0.0139738
$750$		0			0
$751$	−18.1412	+	31.4214i	−0.661980	+	1.14658i	0.318114	+	0.948052i	$0.396950\pi$
$751$	−18.1412	+	31.4214i	−0.661980	+	1.14658i	−0.980095	+	0.198531i	$0.936383\pi$
$752$	−4.07835	−	2.35464i	−0.148722	−	0.0858648i
$753$		0			0
$754$	−16.3763	+	20.4293i	−0.596389	+	0.743990i
$755$	−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	$0.400212\pi$
$758$	7.02540	−	4.05611i	0.255174	−	0.147325i
$759$		0			0
$760$	0.187230	+	0.194198i	0.00679154	+	0.00704430i
$761$	17.8112	+	30.8500i	0.645657	+	1.11831i	0.984149	+	0.177342i	$0.0567498\pi$
$761$	17.8112	+	30.8500i	0.645657	+	1.11831i	−0.338492	+	0.940969i	$0.609917\pi$
$762$		0			0
$763$	6.76936	−	3.90829i	0.245067	−	0.141490i
$764$	5.54278	−	9.60038i	0.200531	−	0.347330i
$765$		0			0
$766$	−24.9399			−0.901114
$767$	−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	$0.147319\pi$
$770$	−6.87451	−	1.97729i	−0.247740	−	0.0712564i
$771$		0			0
$772$		−	14.0000i		−	0.503871i
$773$	9.59506	−	5.53971i	0.345110	−	0.199250i	−0.317419	−	0.948285i	$-0.602816\pi$
$773$	9.59506	−	5.53971i	0.345110	−	0.199250i	0.662530	+	0.749036i	$0.269483\pi$
$774$		0			0
$775$	−42.7142	+	22.6225i	−1.53434	+	0.812624i
$776$	−3.95415	−	6.84878i	−0.141946	−	0.245857i
$777$		0			0
$778$	11.7200	+	6.76652i	0.420181	+	0.242592i
$779$	−0.0539832			−0.00193415
$780$		0			0
$781$	36.9093			1.32072
$782$	13.6475	+	7.87936i	0.488032	+	0.281765i
$783$		0			0
$784$	−3.24846	−	5.62651i	−0.116017	−	0.200947i
$785$	12.5259	−	3.11223i	0.447067	−	0.111080i
$786$		0			0
$787$	4.91114	−	2.83545i	0.175063	−	0.101073i	−0.409908	−	0.912127i	$-0.634439\pi$
$787$	4.91114	−	2.83545i	0.175063	−	0.101073i	0.584971	+	0.811054i	$0.301106\pi$
$788$		−	8.69368i		−	0.309699i
$789$		0			0
$790$	−9.89391	+	34.3986i	−0.352010	+	1.22385i
$791$	−4.96493	+	8.59951i	−0.176532	+	0.305763i
$792$		0			0
$793$	19.8694	+	15.9275i	0.705582	+	0.565602i
$794$	4.59478			0.163063
$795$		0			0
$796$	−10.7587	+	18.6347i	−0.381333	+	0.660488i
$797$	−23.6792	+	13.6712i	−0.838762	+	0.484259i	−0.856843	−	0.515577i	$-0.827578\pi$
$797$	−23.6792	+	13.6712i	−0.838762	+	0.484259i	0.0180812	+	0.999837i	$0.494244\pi$
$798$		0			0
$799$	−7.46441	−	12.9287i	−0.264072	−	0.457386i
$800$	2.65649	−	4.23592i	0.0939211	−	0.149763i
$801$		0			0
$802$	25.7237	−	14.8516i	0.908334	−	0.524427i
$803$	26.3475	+	15.2117i	0.929783	+	0.536810i
$804$		0			0
$805$	−1.90110	−	7.65142i	−0.0670051	−	0.269677i
$806$	−34.4524	−	5.28180i	−1.21353	−	0.186043i
$807$		0			0
$808$	5.31840	+	3.07058i	0.187101	+	0.108023i
$809$	2.51446	−	4.35518i	0.0884039	−	0.153120i	−0.818433	−	0.574602i	$-0.805157\pi$
$809$	2.51446	−	4.35518i	0.0884039	−	0.153120i	0.906837	+	0.421482i	$0.138490\pi$
$810$		0			0
$811$	47.3390			1.66230			0.831148	−	0.556052i	$-0.187684\pi$
$811$	47.3390			1.66230			0.831148	+	0.556052i	$0.187684\pi$
$812$	4.46056	−	2.57531i	0.156535	−	0.0903755i
$813$		0			0
$814$	−31.3812			−1.09991
$815$	26.1069	+	27.0785i	0.914484	+	0.948519i
$816$		0			0
$817$	0.208951	+	0.120638i	0.00731028	+	0.00422059i
$818$		−	10.3112i		−	0.360524i
$819$		0			0
$820$	0.241276	+	0.971071i	0.00842573	+	0.0339113i
$821$	−10.3408	+	17.9108i	−0.360896	+	0.625090i	−0.988109	−	0.153758i	$-0.950862\pi$
$821$	−10.3408	+	17.9108i	−0.360896	+	0.625090i	0.627213	+	0.778848i	$0.284196\pi$
$822$		0			0
$823$	17.1794	−	9.91855i	0.598837	−	0.345739i	−0.169747	−	0.985488i	$-0.554295\pi$
$823$	17.1794	−	9.91855i	0.598837	−	0.345739i	0.768584	+	0.639749i	$0.220962\pi$
$824$	−17.6803			−0.615924
$825$		0			0
$826$	2.04226	+	3.53730i	0.0710593	+	0.123078i
$827$		−	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	$0.311997\pi$
$830$	0.764533	+	0.219899i	0.0265373	+	0.00763282i
$831$		0			0
$832$	3.35963	−	1.30878i	0.116474	−	0.0453739i
$833$		−	20.5958i		−	0.713603i
$834$		0			0
$835$	−11.1995	+	38.9376i	−0.387573	+	1.34749i
$836$	0.272055	+	0.471213i	0.00940921	+	0.0162972i
$837$		0			0
$838$	−32.9873	+	19.0452i	−1.13953	+	0.657907i
$839$	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
$842$	−23.1318	−	13.3552i	−0.797175	−	0.460249i
$843$		0			0
$844$	5.58864			0.192369
$845$	24.2461	+	16.0351i	0.834092	+	0.551625i
$846$		0			0
$847$	−5.73860	−	3.31318i	−0.197181	−	0.113842i
$848$	−8.30400	−	4.79432i	−0.285161	−	0.164638i
$849$		0			0
$850$	14.0072	−	7.41855i	0.480443	−	0.254454i
$851$	−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	$0.924615\pi$
$854$	−2.50473	−	4.33832i	−0.0857100	−	0.148454i
$855$		0			0
$856$	−0.269594	+	0.466951i	−0.00921455	+	0.0159601i
$857$			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	$-0.575194\pi$
$859$	−13.7187			−0.468077			−0.234039	+	0.972227i	$0.575194\pi$
$860$	1.23618	−	4.29789i	0.0421535	−	0.146557i
$861$		0			0
$862$	−17.9429	+	10.3594i	−0.611139	+	0.352841i
$863$		−	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
$866$	−15.8576			−0.538864
$867$		0			0
$868$	5.93797	+	3.42829i	0.201548	+	0.116364i
$869$	−36.0983	+	62.5241i	−1.22455	+	2.12098i
$870$		0			0
$871$	−10.4124	−	1.59630i	−0.352811	−	0.0540884i
$872$			11.0205i			0.373202i
$873$		0			0
$874$	−0.299850	+	0.519356i	−0.0101426	+	0.0175675i
$875$	−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	$0.452253\pi$
$878$	−8.43444	+	4.86962i	−0.284648	+	0.164342i
$879$		0			0
$880$	7.26042	−	6.99990i	0.244749	−	0.235967i
$881$	−3.99693	+	6.92288i	−0.134660	+	0.233238i	−0.925468	−	0.378827i	$-0.876328\pi$
$881$	−3.99693	+	6.92288i	−0.134660	+	0.233238i	0.790808	+	0.612065i	$0.209661\pi$
$882$		0			0
$883$		−	26.2713i		−	0.884098i	−0.896991	−	0.442049i	$-0.854252\pi$
$883$		−	26.2713i		−	0.884098i	0.896991	−	0.442049i	$-0.145748\pi$
$884$	11.2979	+	1.73205i	0.379990	+	0.0582552i
$885$		0			0
$886$	4.61530	−	7.99393i	0.155054	−	0.268561i
$887$	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
$890$	−5.63513	−	5.84486i	−0.188890	−	0.195920i
$891$		0			0
$892$		−	24.7093i		−	0.827328i
$893$	0.492005	−	0.284059i	0.0164643	−	0.00950568i
$894$		0			0
$895$	−2.71153	−	0.779906i	−0.0906364	−	0.0260694i
$896$	−0.709275			−0.0236952
$897$		0			0
$898$			2.92389i			0.0975715i
$899$	35.0999	−	60.7949i	1.17065	−	2.02762i
$900$		0			0
$901$	−15.1984	−	26.3244i	−0.506332	−	0.876993i
$902$			2.01825i			0.0672004i
$903$		0			0
$904$	−7.00000	−	12.1244i	−0.232817	−	0.403250i
$905$	1.28458	+	5.17009i	0.0427009	+	0.171859i
$906$		0			0
$907$	−14.2146	−	8.20682i	−0.471989	−	0.272503i	0.245083	−	0.969502i	$-0.421185\pi$
$907$	−14.2146	−	8.20682i	−0.471989	−	0.272503i	−0.717072	+	0.696999i	$0.754518\pi$
$908$	24.8504	+	14.3474i	0.824688	+	0.476134i
$909$		0			0
$910$	−3.29930	−	4.67058i	−0.109371	−	0.154828i
$911$	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
$914$	5.82632	+	10.0915i	0.192718	+	0.333797i
$915$		0			0
$916$	0.949940	+	1.64535i	0.0313869	+	0.0543637i
$917$	10.7215	−	6.19008i	0.354056	−	0.204415i
$918$		0			0
$919$	−3.82150	−	6.61904i	−0.126060	−	0.218342i	0.796087	−	0.605182i	$-0.206900\pi$
$919$	−3.82150	−	6.61904i	−0.126060	−	0.218342i	−0.922147	+	0.386840i	$0.873566\pi$
$920$	10.6826	+	3.07258i	0.352193	+	0.101300i
$921$		0			0
$922$		−	30.2979i		−	0.997809i
$923$	23.0220	+	18.4547i	0.757779	+	0.607443i
$924$		0			0
$925$	−34.7655	−	1.27066i	−1.14308	−	0.0417792i
$926$	−3.52165	+	6.09968i	−0.115729	+	0.200448i
$927$		0			0
$928$			7.26180i			0.238380i
$929$	−29.6647	−	51.3808i	−0.973269	−	1.68575i	−0.685534	−	0.728041i	$-0.740431\pi$
$929$	−29.6647	−	51.3808i	−0.973269	−	1.68575i	−0.287735	−	0.957710i	$-0.592902\pi$
$930$		0			0
$931$	0.783777			0.0256873
$932$	19.2677	−	11.1242i	0.631136	−	0.364386i
$933$		0			0
$934$	−1.95055	+	3.37845i	−0.0638240	+	0.110546i
$935$	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	$0.990854\pi$
$938$	1.79461	+	1.03612i	0.0585960	+	0.0338304i
$939$		0			0
$940$	−7.30877	−	7.58078i	−0.238386	−	0.247258i
$941$	−42.2967			−1.37883			−0.689416	−	0.724365i	$-0.742133\pi$
$941$	−42.2967			−1.37883			−0.689416	+	0.724365i	$0.742133\pi$
$942$		0			0
$943$	−1.92643	+	1.11223i	−0.0627333	+	0.0362191i
$944$	−5.75872			−0.187430
$945$		0			0
$946$	4.51026	−	7.81200i	0.146641	−	0.253990i
$947$	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
$950$	0.282314	+	0.533046i	0.00915948	+	0.0172943i
$951$		0			0
$952$	−1.94723	−	1.12423i	−0.0631100	−	0.0364366i
$953$	22.4767	−	12.9769i	0.728092	−	0.420364i	−0.0896318	−	0.995975i	$-0.528569\pi$
$953$	22.4767	−	12.9769i	0.728092	−	0.420364i	0.817724	+	0.575611i	$0.195236\pi$
$954$		0			0
$955$	17.8451	−	17.2047i	0.577452	−	0.556732i
$956$	12.4355	+	21.5389i	0.402192	+	0.696617i
$957$		0			0
$958$	−15.1643	+	8.75513i	−0.489937	+	0.282865i
$959$	3.31710	−	5.74539i	0.107115	−	0.185528i
$960$		0			0
$961$	62.4512			2.01455
$962$	−19.5739	−	15.6906i	−0.631087	−	0.505885i
$963$		0			0
$964$	−1.47528	+	2.55525i	−0.0475154	+	0.0822991i
$965$	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	$-0.160187\pi$
$968$	8.09079	−	4.67122i	0.260048	−	0.150139i
$969$		0			0
$970$	−4.26406	−	17.1617i	−0.136911	−	0.551028i
$971$	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
$974$	38.5318			1.23464
$975$		0			0
$976$	7.06278			0.226074
$977$	23.8539	+	13.7721i	0.763154	+	0.440607i	0.830427	−	0.557128i	$-0.188097\pi$
$977$	23.8539	+	13.7721i	0.763154	+	0.440607i	−0.0672731	+	0.997735i	$0.521430\pi$
$978$		0			0
$979$	−8.18815	−	14.1823i	−0.261694	−	0.453268i
$980$	−3.50307	−	14.0989i	−0.111902	−	0.450373i
$981$		0			0
$982$	5.90956	−	3.41189i	0.188582	−	0.108878i
$983$		−	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
$986$	−11.5103	+	19.9364i	−0.366561	+	0.634903i
$987$		0			0
$988$	−0.0659135	+	0.429944i	−0.00209699	+	0.0136783i
$989$	9.94214			0.316142
$990$		0			0
$991$	−5.81658	+	10.0746i	−0.184770	+	0.320031i	−0.943499	−	0.331376i	$-0.892487\pi$
$991$	−5.81658	+	10.0746i	−0.184770	+	0.320031i	0.758729	+	0.651406i	$0.225821\pi$
$992$	−8.37188	+	4.83351i	−0.265807	+	0.153464i
$993$		0			0
$994$	−2.90215	−	5.02667i	−0.0920506	−	0.159436i
$995$	−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	$0.182229\pi$
$998$	−8.29581	−	4.78959i	−0.262599	−	0.151612i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1170.2.bp.h.919.5		12
3.2	odd	2		130.2.n.a.9.2	✓	12
5.4	even	2	inner	1170.2.bp.h.919.2		12
12.11	even	2		1040.2.dh.b.529.4		12
13.3	even	3	inner	1170.2.bp.h.289.2		12
15.2	even	4		650.2.e.k.451.2		6
15.8	even	4		650.2.e.j.451.2		6
15.14	odd	2		130.2.n.a.9.5	yes	12
39.17	odd	6		1690.2.b.b.339.2		6
39.20	even	12		1690.2.c.b.1689.4		6
39.29	odd	6		130.2.n.a.29.5	yes	12
39.32	even	12		1690.2.c.c.1689.4		6
39.35	odd	6		1690.2.b.c.339.5		6
60.59	even	2		1040.2.dh.b.529.3		12
65.29	even	6	inner	1170.2.bp.h.289.5		12
156.107	even	6		1040.2.dh.b.289.3		12
195.17	even	12		8450.2.a.ca.1.2		3
195.29	odd	6		130.2.n.a.29.2	yes	12
195.59	even	12		1690.2.c.c.1689.3		6
195.68	even	12		650.2.e.j.601.2		6
195.74	odd	6		1690.2.b.c.339.2		6
195.107	even	12		650.2.e.k.601.2		6
195.113	even	12		8450.2.a.cb.1.2		3
195.134	odd	6		1690.2.b.b.339.5		6
195.149	even	12		1690.2.c.b.1689.3		6
195.152	even	12		8450.2.a.bu.1.2		3
195.173	even	12		8450.2.a.bt.1.2		3
780.419	even	6		1040.2.dh.b.289.4		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
130.2.n.a.9.2	✓	12	3.2	odd	2
130.2.n.a.9.5	yes	12	15.14	odd	2
130.2.n.a.29.2	yes	12	195.29	odd	6
130.2.n.a.29.5	yes	12	39.29	odd	6
650.2.e.j.451.2		6	15.8	even	4
650.2.e.j.601.2		6	195.68	even	12
650.2.e.k.451.2		6	15.2	even	4
650.2.e.k.601.2		6	195.107	even	12
1040.2.dh.b.289.3		12	156.107	even	6
1040.2.dh.b.289.4		12	780.419	even	6
1040.2.dh.b.529.3		12	60.59	even	2
1040.2.dh.b.529.4		12	12.11	even	2
1170.2.bp.h.289.2		12	13.3	even	3	inner
1170.2.bp.h.289.5		12	65.29	even	6	inner
1170.2.bp.h.919.2		12	5.4	even	2	inner
1170.2.bp.h.919.5		12	1.1	even	1	trivial
1690.2.b.b.339.2		6	39.17	odd	6
1690.2.b.b.339.5		6	195.134	odd	6
1690.2.b.c.339.2		6	195.74	odd	6
1690.2.b.c.339.5		6	39.35	odd	6
1690.2.c.b.1689.3		6	195.149	even	12
1690.2.c.b.1689.4		6	39.20	even	12
1690.2.c.c.1689.3		6	195.59	even	12
1690.2.c.c.1689.4		6	39.32	even	12
8450.2.a.bt.1.2		3	195.173	even	12
8450.2.a.bu.1.2		3	195.152	even	12
8450.2.a.ca.1.2		3	195.17	even	12
8450.2.a.cb.1.2		3	195.113	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:	\( N \)	\(=\)	\( 1170 = 2 \cdot 3^{2} \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1170.bp (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(0.539189 + 2.17009i) q^{5} +(0.614250 - 0.354638i) q^{7} +1.00000i q^{8} +(-0.618092 + 2.14894i) q^{10} +(-2.25513 + 3.90600i) q^{11} +(-3.35963 + 1.30878i) q^{13} +0.709275 q^{14} +(-0.500000 + 0.866025i) q^{16} +(-2.74538 + 1.58504i) q^{17} +(-0.0603191 - 0.104476i) q^{19} +(-1.60976 + 1.55199i) q^{20} +(-3.90600 + 2.25513i) q^{22} +(-4.30507 - 2.48554i) q^{23} +(-4.41855 + 2.34017i) q^{25} +(-3.56391 - 0.546373i) q^{26} +(0.614250 + 0.354638i) q^{28} +(3.63090 - 6.28890i) q^{29} +9.66701 q^{31} +(-0.866025 + 0.500000i) q^{32} -3.17009 q^{34} +(1.10079 + 1.14176i) q^{35} +(6.02558 + 3.47887i) q^{37} -0.120638i q^{38} +(-2.17009 + 0.539189i) q^{40} +(0.223740 - 0.387529i) q^{41} +(-1.73205 + 1.00000i) q^{43} -4.51026 q^{44} +(-2.48554 - 4.30507i) q^{46} +4.70928i q^{47} +(-3.24846 + 5.62651i) q^{49} +(-4.99666 - 0.182626i) q^{50} +(-2.81325 - 2.25513i) q^{52} +9.58864i q^{53} +(-9.69230 - 2.78776i) q^{55} +(0.354638 + 0.614250i) q^{56} +(6.28890 - 3.63090i) q^{58} +(2.87936 + 4.98720i) q^{59} +(-3.53139 - 6.11655i) q^{61} +(8.37188 + 4.83351i) q^{62} -1.00000 q^{64} +(-4.65165 - 6.58500i) q^{65} +(2.53020 + 1.46081i) q^{67} +(-2.74538 - 1.58504i) q^{68} +(0.382433 + 1.53919i) q^{70} +(-4.09171 - 7.08705i) q^{71} -6.74539i q^{73} +(3.47887 + 6.02558i) q^{74} +(0.0603191 - 0.104476i) q^{76} +3.19902i q^{77} +16.0072 q^{79} +(-2.14894 - 0.618092i) q^{80} +(0.387529 - 0.223740i) q^{82} -0.355771i q^{83} +(-4.91996 - 5.10306i) q^{85} -2.00000 q^{86} +(-3.90600 - 2.25513i) q^{88} +(-1.81545 + 3.14445i) q^{89} +(-1.59951 + 1.99537i) q^{91} -4.97107i q^{92} +(-2.35464 + 4.07835i) q^{94} +(0.194198 - 0.187230i) q^{95} +(-6.84878 + 3.95415i) q^{97} +(-5.62651 + 3.24846i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 6 q^{4} - 2 q^{10} + 6 q^{11} - 20 q^{14} - 6 q^{16} - 26 q^{19} + 4 q^{25} + 28 q^{29} + 24 q^{31} - 16 q^{34} + 6 q^{35} - 4 q^{40} + 4 q^{41} + 12 q^{44} - 4 q^{49} + 8 q^{50} + 12 q^{55} - 10 q^{56}+ \cdots + 8 q^{95}+O(q^{100}) \) 12 * q + 6 * q^4 - 2 * q^10 + 6 * q^11 - 20 * q^14 - 6 * q^16 - 26 * q^19 + 4 * q^25 + 28 * q^29 + 24 * q^31 - 16 * q^34 + 6 * q^35 - 4 * q^40 + 4 * q^41 + 12 * q^44 - 4 * q^49 + 8 * q^50 + 12 * q^55 - 10 * q^56 - 16 * q^59 - 8 * q^61 - 12 * q^64 + 10 * q^65 + 24 * q^70 - 40 * q^71 + 10 * q^74 + 26 * q^76 + 56 * q^79 - 16 * q^85 - 24 * q^86 - 14 * q^89 - 38 * q^91 - 14 * q^94 + 8 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more