LMFDB - Embedded newform 578.2.d.f.423.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [578,2,Mod(155,578)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(578, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([7]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("578.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 578 = 2 \cdot 17^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	578.d (of order $8$, degree $4$, 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:	$4.61535323683$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{8})$
Coefficient field:	$\Q(\zeta_{16})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 1 $ x^8 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	no (minimal twist has level 34)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			423.1
Root			$-0.382683 + 0.923880i$ of defining polynomial
Character	$\chi$	$=$	578.423
Dual form			578.2.d.f.399.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.30656 + 0.541196i) q^{5} +(-0.707107 + 0.707107i) q^{8} +(2.12132 - 2.12132i) q^{9} +O(q^{10})$	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.30656 + 0.541196i) q^{5} +(-0.707107 + 0.707107i) q^{8} +(2.12132 - 2.12132i) q^{9} +(-1.30656 - 0.541196i) q^{10} +(-2.16478 + 5.22625i) q^{11} +4.00000i q^{13} -1.00000 q^{16} +3.00000 q^{18} +(2.82843 + 2.82843i) q^{19} +(-0.541196 - 1.30656i) q^{20} +(-5.22625 + 2.16478i) q^{22} +(-2.16478 + 5.22625i) q^{23} +(-2.12132 + 2.12132i) q^{25} +(-2.82843 + 2.82843i) q^{26} +(3.91969 - 1.62359i) q^{29} +(-2.16478 - 5.22625i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.12132 + 2.12132i) q^{36} +(-1.62359 - 3.91969i) q^{37} +4.00000i q^{38} +(0.541196 - 1.30656i) q^{40} +(1.30656 + 0.541196i) q^{41} +(2.82843 - 2.82843i) q^{43} +(-5.22625 - 2.16478i) q^{44} +(-1.62359 + 3.91969i) q^{45} +(-5.22625 + 2.16478i) q^{46} +8.00000i q^{47} +(-4.94975 - 4.94975i) q^{49} -3.00000 q^{50} -4.00000 q^{52} +(-2.82843 - 2.82843i) q^{53} -8.00000i q^{55} +(3.91969 + 1.62359i) q^{58} +(2.82843 - 2.82843i) q^{59} +(11.7591 + 4.87076i) q^{61} +(2.16478 - 5.22625i) q^{62} -1.00000i q^{64} +(-2.16478 - 5.22625i) q^{65} +12.0000 q^{67} +(2.16478 + 5.22625i) q^{71} +3.00000i q^{72} +(6.53281 - 2.70598i) q^{73} +(1.62359 - 3.91969i) q^{74} +(-2.82843 + 2.82843i) q^{76} +(4.32957 - 10.4525i) q^{79} +(1.30656 - 0.541196i) q^{80} -9.00000i q^{81} +(0.541196 + 1.30656i) q^{82} +(2.82843 + 2.82843i) q^{83} +4.00000 q^{86} +(-2.16478 - 5.22625i) q^{88} +(-3.91969 + 1.62359i) q^{90} +(-5.22625 - 2.16478i) q^{92} +(-5.65685 + 5.65685i) q^{94} +(-5.22625 - 2.16478i) q^{95} +(-3.91969 + 1.62359i) q^{97} -7.00000i q^{98} +(6.49435 + 15.6788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 8 q^{16} + 24 q^{18} - 24 q^{50} - 32 q^{52} + 96 q^{67} + 32 q^{86}+O(q^{100}) $ 8 * q - 8 * q^16 + 24 * q^18 - 24 * q^50 - 32 * q^52 + 96 * q^67 + 32 * q^86

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/578\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{3}{8}\right)$

Coefficient data

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

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

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

$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$2$	0.707107	+	0.707107i	0.500000	+	0.500000i
$3$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$3$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$4$			1.00000i			0.500000i
$5$	−1.30656	+	0.541196i	−0.584313	+	0.242030i	−0.655202	−	0.755454i	$-0.727416\pi$
$5$	−1.30656	+	0.541196i	−0.584313	+	0.242030i	0.0708890	+	0.997484i	$0.477416\pi$
$6$		0			0
$7$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$7$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$8$	−0.707107	+	0.707107i	−0.250000	+	0.250000i
$9$	2.12132	−	2.12132i	0.707107	−	0.707107i
$10$	−1.30656	−	0.541196i	−0.413171	−	0.171141i
$11$	−2.16478	+	5.22625i	−0.652707	+	1.57577i	0.156127	+	0.987737i	$0.450099\pi$
$11$	−2.16478	+	5.22625i	−0.652707	+	1.57577i	−0.808834	+	0.588037i	$0.799901\pi$
$12$		0			0
$13$			4.00000i			1.10940i	0.832050	+	0.554700i	$0.187167\pi$
$13$			4.00000i			1.10940i	−0.832050	+	0.554700i	$0.812833\pi$
$14$		0			0
$15$		0			0
$16$	−1.00000			−0.250000
$17$		0			0
$17$		0			0
$18$	3.00000			0.707107
$19$	2.82843	+	2.82843i	0.648886	+	0.648886i	0.952724	−	0.303838i	$-0.0982682\pi$
$19$	2.82843	+	2.82843i	0.648886	+	0.648886i	−0.303838	+	0.952724i	$0.598268\pi$
$20$	−0.541196	−	1.30656i	−0.121015	−	0.292156i
$21$		0			0
$22$	−5.22625	+	2.16478i	−1.11424	+	0.461534i
$23$	−2.16478	+	5.22625i	−0.451389	+	1.08975i	0.520406	+	0.853919i	$0.325781\pi$
$23$	−2.16478	+	5.22625i	−0.451389	+	1.08975i	−0.971794	+	0.235830i	$0.924219\pi$
$24$		0			0
$25$	−2.12132	+	2.12132i	−0.424264	+	0.424264i
$26$	−2.82843	+	2.82843i	−0.554700	+	0.554700i
$27$		0			0
$28$		0			0
$29$	3.91969	−	1.62359i	0.727868	−	0.301493i	0.0121924	−	0.999926i	$-0.496119\pi$
$29$	3.91969	−	1.62359i	0.727868	−	0.301493i	0.715676	+	0.698433i	$0.246119\pi$
$30$		0			0
$31$	−2.16478	−	5.22625i	−0.388807	−	0.938663i	−0.990193	−	0.139704i	$-0.955385\pi$
$31$	−2.16478	−	5.22625i	−0.388807	−	0.938663i	0.601387	−	0.798958i	$-0.294615\pi$
$32$	−0.707107	−	0.707107i	−0.125000	−	0.125000i
$33$		0			0
$34$		0			0
$35$		0			0
$36$	2.12132	+	2.12132i	0.353553	+	0.353553i
$37$	−1.62359	−	3.91969i	−0.266916	−	0.644393i	0.732419	−	0.680854i	$-0.238391\pi$
$37$	−1.62359	−	3.91969i	−0.266916	−	0.644393i	−0.999335	+	0.0364615i	$0.988391\pi$
$38$			4.00000i			0.648886i
$39$		0			0
$40$	0.541196	−	1.30656i	0.0855706	−	0.206586i
$41$	1.30656	+	0.541196i	0.204051	+	0.0845206i	0.482368	−	0.875969i	$-0.339777\pi$
$41$	1.30656	+	0.541196i	0.204051	+	0.0845206i	−0.278317	+	0.960489i	$0.589777\pi$
$42$		0			0
$43$	2.82843	−	2.82843i	0.431331	−	0.431331i	−0.457750	−	0.889081i	$-0.651344\pi$
$43$	2.82843	−	2.82843i	0.431331	−	0.431331i	0.889081	+	0.457750i	$0.151344\pi$
$44$	−5.22625	−	2.16478i	−0.787887	−	0.326354i
$45$	−1.62359	+	3.91969i	−0.242030	+	0.584313i
$46$	−5.22625	+	2.16478i	−0.770569	+	0.319180i
$47$			8.00000i			1.16692i	0.812142	+	0.583460i	$0.198301\pi$
$47$			8.00000i			1.16692i	−0.812142	+	0.583460i	$0.801699\pi$
$48$		0			0
$49$	−4.94975	−	4.94975i	−0.707107	−	0.707107i
$50$	−3.00000			−0.424264
$51$		0			0
$52$	−4.00000			−0.554700
$53$	−2.82843	−	2.82843i	−0.388514	−	0.388514i	0.485643	−	0.874157i	$-0.338586\pi$
$53$	−2.82843	−	2.82843i	−0.388514	−	0.388514i	−0.874157	+	0.485643i	$0.838586\pi$
$54$		0			0
$55$		−	8.00000i		−	1.07872i
$56$		0			0
$57$		0			0
$58$	3.91969	+	1.62359i	0.514680	+	0.213188i
$59$	2.82843	−	2.82843i	0.368230	−	0.368230i	−0.498601	−	0.866831i	$-0.666153\pi$
$59$	2.82843	−	2.82843i	0.368230	−	0.368230i	0.866831	+	0.498601i	$0.166153\pi$
$60$		0			0
$61$	11.7591	+	4.87076i	1.50559	+	0.623638i	0.974643	−	0.223765i	$-0.0718348\pi$
$61$	11.7591	+	4.87076i	1.50559	+	0.623638i	0.530951	+	0.847402i	$0.321835\pi$
$62$	2.16478	−	5.22625i	0.274928	−	0.663735i
$63$		0			0
$64$		−	1.00000i		−	0.125000i
$65$	−2.16478	−	5.22625i	−0.268508	−	0.648237i
$66$		0			0
$67$	12.0000			1.46603			0.733017	−	0.680211i	$-0.238112\pi$
$67$	12.0000			1.46603			0.733017	+	0.680211i	$0.238112\pi$
$68$		0			0
$69$		0			0
$70$		0			0
$71$	2.16478	+	5.22625i	0.256913	+	0.620242i	0.998731	−	0.0503587i	$-0.0160364\pi$
$71$	2.16478	+	5.22625i	0.256913	+	0.620242i	−0.741819	+	0.670601i	$0.766036\pi$
$72$			3.00000i			0.353553i
$73$	6.53281	−	2.70598i	0.764608	−	0.316711i	0.0339219	−	0.999424i	$-0.489200\pi$
$73$	6.53281	−	2.70598i	0.764608	−	0.316711i	0.730686	+	0.682713i	$0.239200\pi$
$74$	1.62359	−	3.91969i	0.188738	−	0.455655i
$75$		0			0
$76$	−2.82843	+	2.82843i	−0.324443	+	0.324443i
$77$		0			0
$78$		0			0
$79$	4.32957	−	10.4525i	0.487115	−	1.17600i	−0.469051	−	0.883171i	$-0.655404\pi$
$79$	4.32957	−	10.4525i	0.487115	−	1.17600i	0.956165	−	0.292827i	$-0.0945961\pi$
$80$	1.30656	−	0.541196i	0.146078	−	0.0605076i
$81$		−	9.00000i		−	1.00000i
$82$	0.541196	+	1.30656i	0.0597651	+	0.144286i
$83$	2.82843	+	2.82843i	0.310460	+	0.310460i	0.845088	−	0.534628i	$-0.179548\pi$
$83$	2.82843	+	2.82843i	0.310460	+	0.310460i	−0.534628	+	0.845088i	$0.679548\pi$
$84$		0			0
$85$		0			0
$86$	4.00000			0.431331
$87$		0			0
$88$	−2.16478	−	5.22625i	−0.230767	−	0.557120i
$89$		0			0		1.00000			$0$
$89$		0			0		−1.00000			$\pi$
$90$	−3.91969	+	1.62359i	−0.413171	+	0.171141i
$91$		0			0
$92$	−5.22625	−	2.16478i	−0.544874	−	0.225694i
$93$		0			0
$94$	−5.65685	+	5.65685i	−0.583460	+	0.583460i
$95$	−5.22625	−	2.16478i	−0.536202	−	0.222102i
$96$		0			0
$97$	−3.91969	+	1.62359i	−0.397984	+	0.164850i	−0.572693	−	0.819770i	$-0.694101\pi$
$97$	−3.91969	+	1.62359i	−0.397984	+	0.164850i	0.174709	+	0.984620i	$0.444101\pi$
$98$		−	7.00000i		−	0.707107i
$99$	6.49435	+	15.6788i	0.652707	+	1.57577i
$100$	−2.12132	−	2.12132i	−0.212132	−	0.212132i
$101$	−12.0000			−1.19404			−0.597022	−	0.802225i	$-0.703650\pi$
$101$	−12.0000			−1.19404			−0.597022	+	0.802225i	$0.703650\pi$
$102$		0			0
$103$	−16.0000			−1.57653			−0.788263	−	0.615338i	$-0.789020\pi$
$103$	−16.0000			−1.57653			−0.788263	+	0.615338i	$0.789020\pi$
$104$	−2.82843	−	2.82843i	−0.277350	−	0.277350i
$105$		0			0
$106$		−	4.00000i		−	0.388514i
$107$	10.4525	−	4.32957i	1.01048	−	0.418555i	0.184851	−	0.982767i	$-0.440820\pi$
$107$	10.4525	−	4.32957i	1.01048	−	0.418555i	0.825630	+	0.564211i	$0.190820\pi$
$108$		0			0
$109$	3.91969	+	1.62359i	0.375438	+	0.155512i	0.562420	−	0.826852i	$-0.309871\pi$
$109$	3.91969	+	1.62359i	0.375438	+	0.155512i	−0.186982	+	0.982363i	$0.559871\pi$
$110$	5.65685	−	5.65685i	0.539360	−	0.539360i
$111$		0			0
$112$		0			0
$113$	−0.541196	+	1.30656i	−0.0509114	+	0.122911i	−0.947289	−	0.320380i	$-0.896189\pi$
$113$	−0.541196	+	1.30656i	−0.0509114	+	0.122911i	0.896378	+	0.443291i	$0.146189\pi$
$114$		0			0
$115$		−	8.00000i		−	0.746004i
$116$	1.62359	+	3.91969i	0.150746	+	0.363934i
$117$	8.48528	+	8.48528i	0.784465	+	0.784465i
$118$	4.00000			0.368230
$119$		0			0
$120$		0			0
$121$	−14.8492	−	14.8492i	−1.34993	−	1.34993i
$122$	4.87076	+	11.7591i	0.440978	+	1.06462i
$123$		0			0
$124$	5.22625	−	2.16478i	0.469331	−	0.194403i
$125$	4.32957	−	10.4525i	0.387248	−	0.934900i
$126$		0			0
$127$	5.65685	−	5.65685i	0.501965	−	0.501965i	−0.410083	−	0.912048i	$-0.634500\pi$
$127$	5.65685	−	5.65685i	0.501965	−	0.501965i	0.912048	+	0.410083i	$0.134500\pi$
$128$	0.707107	−	0.707107i	0.0625000	−	0.0625000i
$129$		0			0
$130$	2.16478	−	5.22625i	0.189864	−	0.458373i
$131$	5.22625	−	2.16478i	0.456620	−	0.189138i	−0.142505	−	0.989794i	$-0.545516\pi$
$131$	5.22625	−	2.16478i	0.456620	−	0.189138i	0.599124	+	0.800656i	$0.295516\pi$
$132$		0			0
$133$		0			0
$134$	8.48528	+	8.48528i	0.733017	+	0.733017i
$135$		0			0
$136$		0			0
$137$	8.00000			0.683486			0.341743	−	0.939793i	$-0.388983\pi$
$137$	8.00000			0.683486			0.341743	+	0.939793i	$0.388983\pi$
$138$		0			0
$139$	4.32957	+	10.4525i	0.367229	+	0.886570i	0.994202	+	0.107529i	$0.0342937\pi$
$139$	4.32957	+	10.4525i	0.367229	+	0.886570i	−0.626973	+	0.779041i	$0.715706\pi$
$140$		0			0
$141$		0			0
$142$	−2.16478	+	5.22625i	−0.181665	+	0.438577i
$143$	−20.9050	−	8.65914i	−1.74816	−	0.724113i
$144$	−2.12132	+	2.12132i	−0.176777	+	0.176777i
$145$	−4.24264	+	4.24264i	−0.352332	+	0.352332i
$146$	6.53281	+	2.70598i	0.540660	+	0.223949i
$147$		0			0
$148$	3.91969	−	1.62359i	0.322196	−	0.133458i
$149$		−	10.0000i		−	0.819232i	−0.912258	−	0.409616i	$-0.865663\pi$
$149$		−	10.0000i		−	0.819232i	0.912258	−	0.409616i	$-0.134337\pi$
$150$		0			0
$151$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$151$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$152$	−4.00000			−0.324443
$153$		0			0
$154$		0			0
$155$	5.65685	+	5.65685i	0.454369	+	0.454369i
$156$		0			0
$157$			2.00000i			0.159617i	0.996810	+	0.0798087i	$0.0254309\pi$
$157$			2.00000i			0.159617i	−0.996810	+	0.0798087i	$0.974569\pi$
$158$	10.4525	−	4.32957i	0.831557	−	0.344442i
$159$		0			0
$160$	1.30656	+	0.541196i	0.103293	+	0.0427853i
$161$		0			0
$162$	6.36396	−	6.36396i	0.500000	−	0.500000i
$163$	−5.22625	−	2.16478i	−0.409352	−	0.169559i	0.168498	−	0.985702i	$-0.446108\pi$
$163$	−5.22625	−	2.16478i	−0.409352	−	0.169559i	−0.577850	+	0.816143i	$0.696108\pi$
$164$	−0.541196	+	1.30656i	−0.0422603	+	0.102025i
$165$		0			0
$166$			4.00000i			0.310460i
$167$	4.32957	+	10.4525i	0.335032	+	0.808839i	0.998177	+	0.0603483i	$0.0192211\pi$
$167$	4.32957	+	10.4525i	0.335032	+	0.808839i	−0.663145	+	0.748491i	$0.730779\pi$
$168$		0			0
$169$	−3.00000			−0.230769
$170$		0			0
$171$	12.0000			0.917663
$172$	2.82843	+	2.82843i	0.215666	+	0.215666i
$173$	−2.70598	−	6.53281i	−0.205732	−	0.496681i	0.787011	−	0.616939i	$-0.211628\pi$
$173$	−2.70598	−	6.53281i	−0.205732	−	0.496681i	−0.992743	+	0.120259i	$0.961628\pi$
$174$		0			0
$175$		0			0
$176$	2.16478	−	5.22625i	0.163177	−	0.393944i
$177$		0			0
$178$		0			0
$179$	−2.82843	+	2.82843i	−0.211407	+	0.211407i	−0.804865	−	0.593458i	$-0.797762\pi$
$179$	−2.82843	+	2.82843i	−0.211407	+	0.211407i	0.593458	+	0.804865i	$0.297762\pi$
$180$	−3.91969	−	1.62359i	−0.292156	−	0.121015i
$181$	5.95316	−	14.3722i	0.442495	−	1.06828i	−0.532576	−	0.846382i	$-0.678776\pi$
$181$	5.95316	−	14.3722i	0.442495	−	1.06828i	0.975071	−	0.221894i	$-0.0712241\pi$
$182$		0			0
$183$		0			0
$184$	−2.16478	−	5.22625i	−0.159590	−	0.385284i
$185$	4.24264	+	4.24264i	0.311925	+	0.311925i
$186$		0			0
$187$		0			0
$188$	−8.00000			−0.583460
$189$		0			0
$190$	−2.16478	−	5.22625i	−0.157050	−	0.379152i
$191$			8.00000i			0.578860i	0.957199	+	0.289430i	$0.0934657\pi$
$191$			8.00000i			0.578860i	−0.957199	+	0.289430i	$0.906534\pi$
$192$		0			0
$193$	5.95316	−	14.3722i	0.428518	−	1.03453i	−0.551240	−	0.834347i	$-0.685845\pi$
$193$	5.95316	−	14.3722i	0.428518	−	1.03453i	0.979758	−	0.200186i	$-0.0641548\pi$
$194$	−3.91969	−	1.62359i	−0.281417	−	0.116567i
$195$		0			0
$196$	4.94975	−	4.94975i	0.353553	−	0.353553i
$197$	−6.53281	−	2.70598i	−0.465444	−	0.192793i	0.137622	−	0.990485i	$-0.456054\pi$
$197$	−6.53281	−	2.70598i	−0.465444	−	0.192793i	−0.603065	+	0.797692i	$0.706054\pi$
$198$	−6.49435	+	15.6788i	−0.461534	+	1.11424i
$199$	−15.6788	+	6.49435i	−1.11144	+	0.460372i	−0.861433	−	0.507872i	$-0.830432\pi$
$199$	−15.6788	+	6.49435i	−1.11144	+	0.460372i	−0.250005	+	0.968245i	$0.580432\pi$
$200$		−	3.00000i		−	0.212132i
$201$		0			0
$202$	−8.48528	−	8.48528i	−0.597022	−	0.597022i
$203$		0			0
$204$		0			0
$205$	−2.00000			−0.139686
$206$	−11.3137	−	11.3137i	−0.788263	−	0.788263i
$207$	6.49435	+	15.6788i	0.451389	+	1.08975i
$208$		−	4.00000i		−	0.277350i
$209$	−20.9050	+	8.65914i	−1.44603	+	0.598965i
$210$		0			0
$211$	20.9050	+	8.65914i	1.43916	+	0.596120i	0.959595	−	0.281386i	$-0.0907943\pi$
$211$	20.9050	+	8.65914i	1.43916	+	0.596120i	0.479566	+	0.877506i	$0.340794\pi$
$212$	2.82843	−	2.82843i	0.194257	−	0.194257i
$213$		0			0
$214$	10.4525	+	4.32957i	0.714518	+	0.295963i
$215$	−2.16478	+	5.22625i	−0.147637	+	0.356427i
$216$		0			0
$217$		0			0
$218$	1.62359	+	3.91969i	0.109963	+	0.265475i
$219$		0			0
$220$	8.00000			0.539360
$221$		0			0
$222$		0			0
$223$	11.3137	+	11.3137i	0.757622	+	0.757622i	0.975889	−	0.218267i	$-0.0700404\pi$
$223$	11.3137	+	11.3137i	0.757622	+	0.757622i	−0.218267	+	0.975889i	$0.570040\pi$
$224$		0			0
$225$			9.00000i			0.600000i
$226$	−1.30656	+	0.541196i	−0.0869113	+	0.0359998i
$227$	−10.8239	+	26.1313i	−0.718409	+	1.73439i	−0.0405762	+	0.999176i	$0.512919\pi$
$227$	−10.8239	+	26.1313i	−0.718409	+	1.73439i	−0.677833	+	0.735216i	$0.737081\pi$
$228$		0			0
$229$	−4.24264	+	4.24264i	−0.280362	+	0.280362i	−0.833253	−	0.552892i	$-0.813524\pi$
$229$	−4.24264	+	4.24264i	−0.280362	+	0.280362i	0.552892	+	0.833253i	$0.313524\pi$
$230$	5.65685	−	5.65685i	0.373002	−	0.373002i
$231$		0			0
$232$	−1.62359	+	3.91969i	−0.106594	+	0.257340i
$233$	6.53281	−	2.70598i	0.427979	−	0.177275i	−0.158287	−	0.987393i	$-0.550597\pi$
$233$	6.53281	−	2.70598i	0.427979	−	0.177275i	0.586266	+	0.810118i	$0.300597\pi$
$234$			12.0000i			0.784465i
$235$	−4.32957	−	10.4525i	−0.282430	−	0.681846i
$236$	2.82843	+	2.82843i	0.184115	+	0.184115i
$237$		0			0
$238$		0			0
$239$		0			0			−	1.00000i	$-0.5\pi$
$239$		0			0				1.00000i	$0.5\pi$
$240$		0			0
$241$	−11.3651	−	27.4378i	−0.732092	−	1.76743i	−0.635499	−	0.772101i	$-0.719206\pi$
$241$	−11.3651	−	27.4378i	−0.732092	−	1.76743i	−0.0965924	−	0.995324i	$-0.530794\pi$
$242$		−	21.0000i		−	1.34993i
$243$		0			0
$244$	−4.87076	+	11.7591i	−0.311819	+	0.752797i
$245$	9.14594	+	3.78837i	0.584313	+	0.242030i
$246$		0			0
$247$	−11.3137	+	11.3137i	−0.719874	+	0.719874i
$248$	5.22625	+	2.16478i	0.331867	+	0.137464i
$249$		0			0
$250$	10.4525	−	4.32957i	0.661074	−	0.273826i
$251$			12.0000i			0.757433i	0.925513	+	0.378717i	$0.123635\pi$
$251$			12.0000i			0.757433i	−0.925513	+	0.378717i	$0.876365\pi$
$252$		0			0
$253$	−22.6274	−	22.6274i	−1.42257	−	1.42257i
$254$	8.00000			0.501965
$255$		0			0
$256$	1.00000			0.0625000
$257$	12.7279	+	12.7279i	0.793946	+	0.793946i	0.982133	−	0.188187i	$-0.0602612\pi$
$257$	12.7279	+	12.7279i	0.793946	+	0.793946i	−0.188187	+	0.982133i	$0.560261\pi$
$258$		0			0
$259$		0			0
$260$	5.22625	−	2.16478i	0.324118	−	0.134254i
$261$	4.87076	−	11.7591i	0.301493	−	0.727868i
$262$	5.22625	+	2.16478i	0.322879	+	0.133741i
$263$	−16.9706	+	16.9706i	−1.04645	+	1.04645i	−0.0475824	+	0.998867i	$0.515152\pi$
$263$	−16.9706	+	16.9706i	−1.04645	+	1.04645i	−0.998867	+	0.0475824i	$0.984848\pi$
$264$		0			0
$265$	5.22625	+	2.16478i	0.321046	+	0.132982i
$266$		0			0
$267$		0			0
$268$			12.0000i			0.733017i
$269$	−7.03555	−	16.9853i	−0.428965	−	1.03561i	−0.979616	−	0.200878i	$-0.935621\pi$
$269$	−7.03555	−	16.9853i	−0.428965	−	1.03561i	0.550651	−	0.834735i	$-0.314379\pi$
$270$		0			0
$271$	8.00000			0.485965			0.242983	−	0.970031i	$-0.421874\pi$
$271$	8.00000			0.485965			0.242983	+	0.970031i	$0.421874\pi$
$272$		0			0
$273$		0			0
$274$	5.65685	+	5.65685i	0.341743	+	0.341743i
$275$	−6.49435	−	15.6788i	−0.391624	−	0.945465i
$276$		0			0
$277$	−9.14594	+	3.78837i	−0.549526	+	0.227621i	−0.640131	−	0.768266i	$-0.721120\pi$
$277$	−9.14594	+	3.78837i	−0.549526	+	0.227621i	0.0906048	+	0.995887i	$0.471120\pi$
$278$	−4.32957	+	10.4525i	−0.259670	+	0.626900i
$279$	−15.6788	−	6.49435i	−0.938663	−	0.388807i
$280$		0			0
$281$		0			0		−0.707107	−	0.707107i	$-0.750000\pi$
$281$		0			0		0.707107	+	0.707107i	$0.250000\pi$
$282$		0			0
$283$	2.16478	−	5.22625i	0.128683	−	0.310668i	−0.846386	−	0.532570i	$-0.821226\pi$
$283$	2.16478	−	5.22625i	0.128683	−	0.310668i	0.975069	+	0.221901i	$0.0712263\pi$
$284$	−5.22625	+	2.16478i	−0.310121	+	0.128456i
$285$		0			0
$286$	−8.65914	−	20.9050i	−0.512026	−	1.23614i
$287$		0			0
$288$	−3.00000			−0.176777
$289$		0			0
$290$	−6.00000			−0.352332
$291$		0			0
$292$	2.70598	+	6.53281i	0.158356	+	0.382304i
$293$			6.00000i			0.350524i	0.984522	+	0.175262i	$0.0560772\pi$
$293$			6.00000i			0.350524i	−0.984522	+	0.175262i	$0.943923\pi$
$294$		0			0
$295$	−2.16478	+	5.22625i	−0.126039	+	0.304284i
$296$	3.91969	+	1.62359i	0.227827	+	0.0943692i
$297$		0			0
$298$	7.07107	−	7.07107i	0.409616	−	0.409616i
$299$	−20.9050	−	8.65914i	−1.20897	−	0.500771i
$300$		0			0
$301$		0			0
$302$		0			0
$303$		0			0
$304$	−2.82843	−	2.82843i	−0.162221	−	0.162221i
$305$	−18.0000			−1.03068
$306$		0			0
$307$	−12.0000			−0.684876			−0.342438	−	0.939540i	$-0.611253\pi$
$307$	−12.0000			−0.684876			−0.342438	+	0.939540i	$0.611253\pi$
$308$		0			0
$309$		0			0
$310$			8.00000i			0.454369i
$311$	−31.3575	+	12.9887i	−1.77812	+	0.736522i	−0.784991	+	0.619507i	$0.787333\pi$
$311$	−31.3575	+	12.9887i	−1.77812	+	0.736522i	−0.993130	+	0.117015i	$0.962667\pi$
$312$		0			0
$313$	11.7591	+	4.87076i	0.664662	+	0.275312i	0.689399	−	0.724382i	$-0.257875\pi$
$313$	11.7591	+	4.87076i	0.664662	+	0.275312i	−0.0247370	+	0.999694i	$0.507875\pi$
$314$	−1.41421	+	1.41421i	−0.0798087	+	0.0798087i
$315$		0			0
$316$	10.4525	+	4.32957i	0.587999	+	0.243557i
$317$	−8.11794	+	19.5984i	−0.455949	+	1.10076i	0.514074	+	0.857746i	$0.328136\pi$
$317$	−8.11794	+	19.5984i	−0.455949	+	1.10076i	−0.970023	+	0.243013i	$0.921864\pi$
$318$		0			0
$319$			24.0000i			1.34374i
$320$	0.541196	+	1.30656i	0.0302538	+	0.0730391i
$321$		0			0
$322$		0			0
$323$		0			0
$324$	9.00000			0.500000
$325$	−8.48528	−	8.48528i	−0.470679	−	0.470679i
$326$	−2.16478	−	5.22625i	−0.119896	−	0.289455i
$327$		0			0
$328$	−1.30656	+	0.541196i	−0.0721429	+	0.0298826i
$329$		0			0
$330$		0			0
$331$	14.1421	−	14.1421i	0.777322	−	0.777322i	−0.202053	−	0.979375i	$-0.564761\pi$
$331$	14.1421	−	14.1421i	0.777322	−	0.777322i	0.979375	+	0.202053i	$0.0647612\pi$
$332$	−2.82843	+	2.82843i	−0.155230	+	0.155230i
$333$	−11.7591	−	4.87076i	−0.644393	−	0.266916i
$334$	−4.32957	+	10.4525i	−0.236903	+	0.571936i
$335$	−15.6788	+	6.49435i	−0.856622	+	0.354824i
$336$		0			0
$337$	−3.78837	−	9.14594i	−0.206366	−	0.498211i	0.786480	−	0.617616i	$-0.211901\pi$
$337$	−3.78837	−	9.14594i	−0.206366	−	0.498211i	−0.992846	+	0.119405i	$0.961901\pi$
$338$	−2.12132	−	2.12132i	−0.115385	−	0.115385i
$339$		0			0
$340$		0			0
$341$	32.0000			1.73290
$342$	8.48528	+	8.48528i	0.458831	+	0.458831i
$343$		0			0
$344$			4.00000i			0.215666i
$345$		0			0
$346$	2.70598	−	6.53281i	0.145474	−	0.351206i
$347$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$347$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$348$		0			0
$349$	−2.82843	+	2.82843i	−0.151402	+	0.151402i	−0.778744	−	0.627342i	$-0.784143\pi$
$349$	−2.82843	+	2.82843i	−0.151402	+	0.151402i	0.627342	+	0.778744i	$0.284143\pi$
$350$		0			0
$351$		0			0
$352$	5.22625	−	2.16478i	0.278560	−	0.115383i
$353$			14.0000i			0.745145i	0.928003	+	0.372572i	$0.121524\pi$
$353$			14.0000i			0.745145i	−0.928003	+	0.372572i	$0.878476\pi$
$354$		0			0
$355$	−5.65685	−	5.65685i	−0.300235	−	0.300235i
$356$		0			0
$357$		0			0
$358$	−4.00000			−0.211407
$359$	16.9706	+	16.9706i	0.895672	+	0.895672i	0.995050	−	0.0993777i	$-0.0316852\pi$
$359$	16.9706	+	16.9706i	0.895672	+	0.895672i	−0.0993777	+	0.995050i	$0.531685\pi$
$360$	−1.62359	−	3.91969i	−0.0855706	−	0.206586i
$361$		−	3.00000i		−	0.157895i
$362$	14.3722	−	5.95316i	0.755386	−	0.312891i
$363$		0			0
$364$		0			0
$365$	−7.07107	+	7.07107i	−0.370117	+	0.370117i
$366$		0			0
$367$		0			0		0.382683	−	0.923880i	$-0.375000\pi$
$367$		0			0		−0.382683	+	0.923880i	$0.625000\pi$
$368$	2.16478	−	5.22625i	0.112847	−	0.272437i
$369$	3.91969	−	1.62359i	0.204051	−	0.0845206i
$370$			6.00000i			0.311925i
$371$		0			0
$372$		0			0
$373$	−4.00000			−0.207112			−0.103556	−	0.994624i	$-0.533022\pi$
$373$	−4.00000			−0.207112			−0.103556	+	0.994624i	$0.533022\pi$
$374$		0			0
$375$		0			0
$376$	−5.65685	−	5.65685i	−0.291730	−	0.291730i
$377$	6.49435	+	15.6788i	0.334476	+	0.807497i
$378$		0			0
$379$	15.6788	−	6.49435i	0.805364	−	0.333593i	0.0582611	−	0.998301i	$-0.481444\pi$
$379$	15.6788	−	6.49435i	0.805364	−	0.333593i	0.747102	+	0.664709i	$0.231444\pi$
$380$	2.16478	−	5.22625i	0.111051	−	0.268101i
$381$		0			0
$382$	−5.65685	+	5.65685i	−0.289430	+	0.289430i
$383$	16.9706	−	16.9706i	0.867155	−	0.867155i	−0.125001	−	0.992157i	$-0.539894\pi$
$383$	16.9706	−	16.9706i	0.867155	−	0.867155i	0.992157	+	0.125001i	$0.0398935\pi$
$384$		0			0
$385$		0			0
$386$	14.3722	−	5.95316i	0.731525	−	0.303008i
$387$		−	12.0000i		−	0.609994i
$388$	−1.62359	−	3.91969i	−0.0824252	−	0.198992i
$389$	4.24264	+	4.24264i	0.215110	+	0.215110i	0.806434	−	0.591324i	$-0.201394\pi$
$389$	4.24264	+	4.24264i	0.215110	+	0.215110i	−0.591324	+	0.806434i	$0.701394\pi$
$390$		0			0
$391$		0			0
$392$	7.00000			0.353553
$393$		0			0
$394$	−2.70598	−	6.53281i	−0.136325	−	0.329118i
$395$			16.0000i			0.805047i
$396$	−15.6788	+	6.49435i	−0.787887	+	0.326354i
$397$	−8.11794	+	19.5984i	−0.407428	+	0.983618i	0.578384	+	0.815765i	$0.303683\pi$
$397$	−8.11794	+	19.5984i	−0.407428	+	0.983618i	−0.985812	+	0.167853i	$0.946317\pi$
$398$	−15.6788	−	6.49435i	−0.785905	−	0.325533i
$399$		0			0
$400$	2.12132	−	2.12132i	0.106066	−	0.106066i
$401$	24.8247	+	10.2827i	1.23969	+	0.513495i	0.903617	−	0.428342i	$-0.140902\pi$
$401$	24.8247	+	10.2827i	1.23969	+	0.513495i	0.336070	+	0.941837i	$0.390902\pi$
$402$		0			0
$403$	20.9050	−	8.65914i	1.04135	−	0.431342i
$404$		−	12.0000i		−	0.597022i
$405$	4.87076	+	11.7591i	0.242030	+	0.584313i
$406$		0			0
$407$	24.0000			1.18964
$408$		0			0
$409$	−10.0000			−0.494468			−0.247234	−	0.968956i	$-0.579522\pi$
$409$	−10.0000			−0.494468			−0.247234	+	0.968956i	$0.579522\pi$
$410$	−1.41421	−	1.41421i	−0.0698430	−	0.0698430i
$411$		0			0
$412$		−	16.0000i		−	0.788263i
$413$		0			0
$414$	−6.49435	+	15.6788i	−0.319180	+	0.770569i
$415$	−5.22625	−	2.16478i	−0.256547	−	0.106265i
$416$	2.82843	−	2.82843i	0.138675	−	0.138675i
$417$		0			0
$418$	−20.9050	−	8.65914i	−1.02250	−	0.423532i
$419$	−6.49435	+	15.6788i	−0.317270	+	0.765957i	0.682127	+	0.731234i	$0.261055\pi$
$419$	−6.49435	+	15.6788i	−0.317270	+	0.765957i	−0.999397	+	0.0347236i	$0.988945\pi$
$420$		0			0
$421$		−	28.0000i		−	1.36464i	−0.731055	−	0.682318i	$-0.760972\pi$
$421$		−	28.0000i		−	1.36464i	0.731055	−	0.682318i	$-0.239028\pi$
$422$	8.65914	+	20.9050i	0.421520	+	1.01764i
$423$	16.9706	+	16.9706i	0.825137	+	0.825137i
$424$	4.00000			0.194257
$425$		0			0
$426$		0			0
$427$		0			0
$428$	4.32957	+	10.4525i	0.209278	+	0.505241i
$429$		0			0
$430$	−5.22625	+	2.16478i	−0.252032	+	0.104395i
$431$	12.9887	−	31.3575i	0.625644	−	1.51044i	−0.219341	−	0.975648i	$-0.570391\pi$
$431$	12.9887	−	31.3575i	0.625644	−	1.51044i	0.844985	−	0.534790i	$-0.179609\pi$
$432$		0			0
$433$	−9.89949	+	9.89949i	−0.475739	+	0.475739i	−0.903766	−	0.428027i	$-0.859209\pi$
$433$	−9.89949	+	9.89949i	−0.475739	+	0.475739i	0.428027	+	0.903766i	$0.359209\pi$
$434$		0			0
$435$		0			0
$436$	−1.62359	+	3.91969i	−0.0777558	+	0.187719i
$437$	−20.9050	+	8.65914i	−1.00002	+	0.414223i
$438$		0			0
$439$	6.49435	+	15.6788i	0.309959	+	0.748306i	0.999706	+	0.0242559i	$0.00772166\pi$
$439$	6.49435	+	15.6788i	0.309959	+	0.748306i	−0.689747	+	0.724050i	$0.742278\pi$
$440$	5.65685	+	5.65685i	0.269680	+	0.269680i
$441$	−21.0000			−1.00000
$442$		0			0
$443$	4.00000			0.190046			0.0950229	−	0.995475i	$-0.469708\pi$
$443$	4.00000			0.190046			0.0950229	+	0.995475i	$0.469708\pi$
$444$		0			0
$445$		0			0
$446$			16.0000i			0.757622i
$447$		0			0
$448$		0			0
$449$	3.91969	+	1.62359i	0.184982	+	0.0766219i	0.473252	−	0.880927i	$-0.343080\pi$
$449$	3.91969	+	1.62359i	0.184982	+	0.0766219i	−0.288270	+	0.957549i	$0.593080\pi$
$450$	−6.36396	+	6.36396i	−0.300000	+	0.300000i
$451$	−5.65685	+	5.65685i	−0.266371	+	0.266371i
$452$	−1.30656	−	0.541196i	−0.0614556	−	0.0254557i
$453$		0			0
$454$	−26.1313	+	10.8239i	−1.22640	+	0.507992i
$455$		0			0
$456$		0			0
$457$	15.5563	+	15.5563i	0.727695	+	0.727695i	0.970160	−	0.242465i	$-0.0779559\pi$
$457$	15.5563	+	15.5563i	0.727695	+	0.727695i	−0.242465	+	0.970160i	$0.577956\pi$
$458$	−6.00000			−0.280362
$459$		0			0
$460$	8.00000			0.373002
$461$	−14.1421	−	14.1421i	−0.658665	−	0.658665i	0.296399	−	0.955064i	$-0.404214\pi$
$461$	−14.1421	−	14.1421i	−0.658665	−	0.658665i	−0.955064	+	0.296399i	$0.904214\pi$
$462$		0			0
$463$		−	24.0000i		−	1.11537i	−0.830051	−	0.557687i	$-0.811689\pi$
$463$		−	24.0000i		−	1.11537i	0.830051	−	0.557687i	$-0.188311\pi$
$464$	−3.91969	+	1.62359i	−0.181967	+	0.0753732i
$465$		0			0
$466$	6.53281	+	2.70598i	0.302627	+	0.125352i
$467$	19.7990	−	19.7990i	0.916188	−	0.916188i	−0.0805616	−	0.996750i	$-0.525671\pi$
$467$	19.7990	−	19.7990i	0.916188	−	0.916188i	0.996750	+	0.0805616i	$0.0256714\pi$
$468$	−8.48528	+	8.48528i	−0.392232	+	0.392232i
$469$		0			0
$470$	4.32957	−	10.4525i	0.199708	−	0.482138i
$471$		0			0
$472$			4.00000i			0.184115i
$473$	8.65914	+	20.9050i	0.398148	+	0.961213i
$474$		0			0
$475$	−12.0000			−0.550598
$476$		0			0
$477$	−12.0000			−0.549442
$478$		0			0
$479$	4.32957	+	10.4525i	0.197823	+	0.477587i	0.991397	−	0.130886i	$-0.0417823\pi$
$479$	4.32957	+	10.4525i	0.197823	+	0.477587i	−0.793574	+	0.608473i	$0.791782\pi$
$480$		0			0
$481$	15.6788	−	6.49435i	0.714890	−	0.296117i
$482$	11.3651	−	27.4378i	0.517667	−	1.24976i
$483$		0			0
$484$	14.8492	−	14.8492i	0.674966	−	0.674966i
$485$	4.24264	−	4.24264i	0.192648	−	0.192648i
$486$		0			0
$487$	10.8239	−	26.1313i	0.490479	−	1.18412i	−0.463998	−	0.885836i	$-0.653586\pi$
$487$	10.8239	−	26.1313i	0.490479	−	1.18412i	0.954477	−	0.298284i	$-0.0964144\pi$
$488$	−11.7591	+	4.87076i	−0.532308	+	0.220489i
$489$		0			0
$490$	3.78837	+	9.14594i	0.171141	+	0.413171i
$491$	−14.1421	−	14.1421i	−0.638226	−	0.638226i	0.311892	−	0.950118i	$-0.399037\pi$
$491$	−14.1421	−	14.1421i	−0.638226	−	0.638226i	−0.950118	+	0.311892i	$0.899037\pi$
$492$		0			0
$493$		0			0
$494$	−16.0000			−0.719874
$495$	−16.9706	−	16.9706i	−0.762770	−	0.762770i
$496$	2.16478	+	5.22625i	0.0972017	+	0.234666i
$497$		0			0
$498$		0			0
$499$	−4.32957	+	10.4525i	−0.193818	+	0.467918i	−0.990674	−	0.136251i	$-0.956495\pi$
$499$	−4.32957	+	10.4525i	−0.193818	+	0.467918i	0.796856	+	0.604169i	$0.206495\pi$
$500$	10.4525	+	4.32957i	0.467450	+	0.193624i
$501$		0			0
$502$	−8.48528	+	8.48528i	−0.378717	+	0.378717i
$503$	−5.22625	−	2.16478i	−0.233027	−	0.0965230i	0.263115	−	0.964765i	$-0.415250\pi$
$503$	−5.22625	−	2.16478i	−0.233027	−	0.0965230i	−0.496142	+	0.868242i	$0.665250\pi$
$504$		0			0
$505$	15.6788	−	6.49435i	0.697695	−	0.288995i
$506$		−	32.0000i		−	1.42257i
$507$		0			0
$508$	5.65685	+	5.65685i	0.250982	+	0.250982i
$509$	30.0000			1.32973			0.664863	−	0.746965i	$-0.268490\pi$
$509$	30.0000			1.32973			0.664863	+	0.746965i	$0.268490\pi$
$510$		0			0
$511$		0			0
$512$	0.707107	+	0.707107i	0.0312500	+	0.0312500i
$513$		0			0
$514$			18.0000i			0.793946i
$515$	20.9050	−	8.65914i	0.921185	−	0.381567i
$516$		0			0
$517$	−41.8100	−	17.3183i	−1.83880	−	0.761657i
$518$		0			0
$519$		0			0
$520$	5.22625	+	2.16478i	0.229186	+	0.0949321i
$521$	0.541196	−	1.30656i	0.0237102	−	0.0572416i	−0.911581	−	0.411121i	$-0.865138\pi$
$521$	0.541196	−	1.30656i	0.0237102	−	0.0572416i	0.935291	+	0.353879i	$0.115138\pi$
$522$	11.7591	−	4.87076i	0.514680	−	0.213188i
$523$		−	36.0000i		−	1.57417i	−0.616844	−	0.787085i	$-0.711589\pi$
$523$		−	36.0000i		−	1.57417i	0.616844	−	0.787085i	$-0.288411\pi$
$524$	2.16478	+	5.22625i	0.0945690	+	0.228310i
$525$		0			0
$526$	−24.0000			−1.04645
$527$		0			0
$528$		0			0
$529$	−6.36396	−	6.36396i	−0.276694	−	0.276694i
$530$	2.16478	+	5.22625i	0.0940322	+	0.227014i
$531$		−	12.0000i		−	0.520756i
$532$		0			0
$533$	−2.16478	+	5.22625i	−0.0937672	+	0.226374i
$534$		0			0
$535$	−11.3137	+	11.3137i	−0.489134	+	0.489134i
$536$	−8.48528	+	8.48528i	−0.366508	+	0.366508i
$537$		0			0
$538$	7.03555	−	16.9853i	0.303324	−	0.732289i
$539$	36.5838	−	15.1535i	1.57577	−	0.652707i
$540$		0			0
$541$	−4.87076	−	11.7591i	−0.209411	−	0.505562i	0.783920	−	0.620862i	$-0.213217\pi$
$541$	−4.87076	−	11.7591i	−0.209411	−	0.505562i	−0.993331	+	0.115300i	$0.963217\pi$
$542$	5.65685	+	5.65685i	0.242983	+	0.242983i
$543$		0			0
$544$		0			0
$545$	−6.00000			−0.257012
$546$		0			0
$547$	6.49435	+	15.6788i	0.277678	+	0.670375i	0.999771	−	0.0214218i	$-0.00681930\pi$
$547$	6.49435	+	15.6788i	0.277678	+	0.670375i	−0.722092	+	0.691797i	$0.756819\pi$
$548$			8.00000i			0.341743i
$549$	35.2772	−	14.6123i	1.50559	−	0.623638i
$550$	6.49435	−	15.6788i	0.276920	−	0.668544i
$551$	15.6788	+	6.49435i	0.667937	+	0.276669i
$552$		0			0
$553$		0			0
$554$	−9.14594	−	3.78837i	−0.388574	−	0.160953i
$555$		0			0
$556$	−10.4525	+	4.32957i	−0.443285	+	0.183615i
$557$			28.0000i			1.18640i	0.805056	+	0.593199i	$0.202135\pi$
$557$			28.0000i			1.18640i	−0.805056	+	0.593199i	$0.797865\pi$
$558$	−6.49435	−	15.6788i	−0.274928	−	0.663735i
$559$	11.3137	+	11.3137i	0.478519	+	0.478519i
$560$		0			0
$561$		0			0
$562$		0			0
$563$	−2.82843	−	2.82843i	−0.119204	−	0.119204i	0.644988	−	0.764192i	$-0.276862\pi$
$563$	−2.82843	−	2.82843i	−0.119204	−	0.119204i	−0.764192	+	0.644988i	$0.776862\pi$
$564$		0			0
$565$		−	2.00000i		−	0.0841406i
$566$	5.22625	−	2.16478i	0.219676	−	0.0909927i
$567$		0			0
$568$	−5.22625	−	2.16478i	−0.219289	−	0.0908323i
$569$	16.9706	−	16.9706i	0.711443	−	0.711443i	−0.255394	−	0.966837i	$-0.582205\pi$
$569$	16.9706	−	16.9706i	0.711443	−	0.711443i	0.966837	+	0.255394i	$0.0822052\pi$
$570$		0			0
$571$	31.3575	+	12.9887i	1.31227	+	0.543560i	0.925546	−	0.378635i	$-0.123606\pi$
$571$	31.3575	+	12.9887i	1.31227	+	0.543560i	0.386725	+	0.922195i	$0.373606\pi$
$572$	8.65914	−	20.9050i	0.362057	−	0.874082i
$573$		0			0
$574$		0			0
$575$	−6.49435	−	15.6788i	−0.270833	−	0.653849i
$576$	−2.12132	−	2.12132i	−0.0883883	−	0.0883883i
$577$	32.0000			1.33218			0.666089	−	0.745873i	$-0.267967\pi$
$577$	32.0000			1.33218			0.666089	+	0.745873i	$0.267967\pi$
$578$		0			0
$579$		0			0
$580$	−4.24264	−	4.24264i	−0.176166	−	0.176166i
$581$		0			0
$582$		0			0
$583$	20.9050	−	8.65914i	0.865797	−	0.358625i
$584$	−2.70598	+	6.53281i	−0.111974	+	0.270330i
$585$	−15.6788	−	6.49435i	−0.648237	−	0.268508i
$586$	−4.24264	+	4.24264i	−0.175262	+	0.175262i
$587$	8.48528	−	8.48528i	0.350225	−	0.350225i	−0.509968	−	0.860193i	$-0.670343\pi$
$587$	8.48528	−	8.48528i	0.350225	−	0.350225i	0.860193	+	0.509968i	$0.170343\pi$
$588$		0			0
$589$	8.65914	−	20.9050i	0.356794	−	0.861376i
$590$	−5.22625	+	2.16478i	−0.215161	+	0.0891228i
$591$		0			0
$592$	1.62359	+	3.91969i	0.0667291	+	0.161098i
$593$	−11.3137	−	11.3137i	−0.464598	−	0.464598i	0.435561	−	0.900159i	$-0.356550\pi$
$593$	−11.3137	−	11.3137i	−0.464598	−	0.464598i	−0.900159	+	0.435561i	$0.856550\pi$
$594$		0			0
$595$		0			0
$596$	10.0000			0.409616
$597$		0			0
$598$	−8.65914	−	20.9050i	−0.354098	−	0.854869i
$599$		−	40.0000i		−	1.63436i	−0.576386	−	0.817178i	$-0.695537\pi$
$599$		−	40.0000i		−	1.63436i	0.576386	−	0.817178i	$-0.304463\pi$
$600$		0			0
$601$	10.2827	−	24.8247i	0.419441	−	1.01262i	−0.563069	−	0.826410i	$-0.690379\pi$
$601$	10.2827	−	24.8247i	0.419441	−	1.01262i	0.982510	−	0.186210i	$-0.0596206\pi$
$602$		0			0
$603$	25.4558	−	25.4558i	1.03664	−	1.03664i
$604$		0			0
$605$	27.4378	+	11.3651i	1.11551	+	0.462058i
$606$		0			0
$607$	−36.5838	+	15.1535i	−1.48489	+	0.615061i	−0.970198	−	0.242314i	$-0.922093\pi$
$607$	−36.5838	+	15.1535i	−1.48489	+	0.615061i	−0.514691	+	0.857376i	$0.672093\pi$
$608$		−	4.00000i		−	0.162221i
$609$		0			0
$610$	−12.7279	−	12.7279i	−0.515339	−	0.515339i
$611$	−32.0000			−1.29458
$612$		0			0
$613$	−26.0000			−1.05013			−0.525065	−	0.851062i	$-0.675959\pi$
$613$	−26.0000			−1.05013			−0.525065	+	0.851062i	$0.675959\pi$
$614$	−8.48528	−	8.48528i	−0.342438	−	0.342438i
$615$		0			0
$616$		0			0
$617$	3.91969	−	1.62359i	0.157801	−	0.0653632i	−0.302385	−	0.953186i	$-0.597783\pi$
$617$	3.91969	−	1.62359i	0.157801	−	0.0653632i	0.460186	+	0.887823i	$0.347783\pi$
$618$		0			0
$619$	10.4525	+	4.32957i	0.420122	+	0.174020i	0.582721	−	0.812672i	$-0.301988\pi$
$619$	10.4525	+	4.32957i	0.420122	+	0.174020i	−0.162600	+	0.986692i	$0.551988\pi$
$620$	−5.65685	+	5.65685i	−0.227185	+	0.227185i
$621$		0			0
$622$	−31.3575	−	12.9887i	−1.25732	−	0.520800i
$623$		0			0
$624$		0			0
$625$			1.00000i			0.0400000i
$626$	4.87076	+	11.7591i	0.194675	+	0.469987i
$627$		0			0
$628$	−2.00000			−0.0798087
$629$		0			0
$630$		0			0
$631$	−28.2843	−	28.2843i	−1.12598	−	1.12598i	−0.990825	−	0.135155i	$-0.956847\pi$
$631$	−28.2843	−	28.2843i	−1.12598	−	1.12598i	−0.135155	−	0.990825i	$-0.543153\pi$
$632$	4.32957	+	10.4525i	0.172221	+	0.415778i
$633$		0			0
$634$	−19.5984	+	8.11794i	−0.778354	+	0.322405i
$635$	−4.32957	+	10.4525i	−0.171814	+	0.414795i
$636$		0			0
$637$	19.7990	−	19.7990i	0.784465	−	0.784465i
$638$	−16.9706	+	16.9706i	−0.671871	+	0.671871i
$639$	15.6788	+	6.49435i	0.620242	+	0.256913i
$640$	−0.541196	+	1.30656i	−0.0213927	+	0.0516464i
$641$	−14.3722	+	5.95316i	−0.567667	+	0.235136i	−0.648010	−	0.761632i	$-0.724399\pi$
$641$	−14.3722	+	5.95316i	−0.567667	+	0.235136i	0.0803426	+	0.996767i	$0.474399\pi$
$642$		0			0
$643$		0			0		0.923880	−	0.382683i	$-0.125000\pi$
$643$		0			0		−0.923880	+	0.382683i	$0.875000\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−32.0000			−1.25805			−0.629025	−	0.777385i	$-0.716546\pi$
$647$	−32.0000			−1.25805			−0.629025	+	0.777385i	$0.716546\pi$
$648$	6.36396	+	6.36396i	0.250000	+	0.250000i
$649$	8.65914	+	20.9050i	0.339901	+	0.820593i
$650$		−	12.0000i		−	0.470679i
$651$		0			0
$652$	2.16478	−	5.22625i	0.0847795	−	0.204676i
$653$	37.8903	+	15.6947i	1.48276	+	0.614181i	0.969728	−	0.244187i	$-0.0785211\pi$
$653$	37.8903	+	15.6947i	1.48276	+	0.614181i	0.513035	+	0.858368i	$0.328521\pi$
$654$		0			0
$655$	−5.65685	+	5.65685i	−0.221032	+	0.221032i
$656$	−1.30656	−	0.541196i	−0.0510127	−	0.0211302i
$657$	8.11794	−	19.5984i	0.316711	−	0.764608i
$658$		0			0
$659$		−	20.0000i		−	0.779089i	−0.921008	−	0.389545i	$-0.872632\pi$
$659$		−	20.0000i		−	0.779089i	0.921008	−	0.389545i	$-0.127368\pi$
$660$		0			0
$661$	14.1421	+	14.1421i	0.550065	+	0.550065i	0.926460	−	0.376394i	$-0.122836\pi$
$661$	14.1421	+	14.1421i	0.550065	+	0.550065i	−0.376394	+	0.926460i	$0.622836\pi$
$662$	20.0000			0.777322
$663$		0			0
$664$	−4.00000			−0.155230
$665$		0			0
$666$	−4.87076	−	11.7591i	−0.188738	−	0.455655i
$667$			24.0000i			0.929284i
$668$	−10.4525	+	4.32957i	−0.404420	+	0.167516i
$669$		0			0
$670$	−15.6788	−	6.49435i	−0.605723	−	0.250899i
$671$	−50.9117	+	50.9117i	−1.96542	+	1.96542i
$672$		0			0
$673$	−24.8247	−	10.2827i	−0.956922	−	0.396370i	−0.151094	−	0.988519i	$-0.548279\pi$
$673$	−24.8247	−	10.2827i	−0.956922	−	0.396370i	−0.805828	+	0.592150i	$0.798279\pi$
$674$	3.78837	−	9.14594i	0.145923	−	0.352288i
$675$		0			0
$676$		−	3.00000i		−	0.115385i
$677$	7.03555	+	16.9853i	0.270398	+	0.652799i	0.999500	−	0.0316059i	$-0.0100622\pi$
$677$	7.03555	+	16.9853i	0.270398	+	0.652799i	−0.729102	+	0.684405i	$0.760062\pi$
$678$		0			0
$679$		0			0
$680$		0			0
$681$		0			0
$682$	22.6274	+	22.6274i	0.866449	+	0.866449i
$683$	−10.8239	−	26.1313i	−0.414166	−	0.999885i	−0.984007	−	0.178130i	$-0.942995\pi$
$683$	−10.8239	−	26.1313i	−0.414166	−	0.999885i	0.569841	−	0.821755i	$-0.307005\pi$
$684$			12.0000i			0.458831i
$685$	−10.4525	+	4.32957i	−0.399370	+	0.165424i
$686$		0			0
$687$		0			0
$688$	−2.82843	+	2.82843i	−0.107833	+	0.107833i
$689$	11.3137	−	11.3137i	0.431018	−	0.431018i
$690$		0			0
$691$	−12.9887	+	31.3575i	−0.494114	+	1.19290i	0.458495	+	0.888697i	$0.348389\pi$
$691$	−12.9887	+	31.3575i	−0.494114	+	1.19290i	−0.952609	+	0.304199i	$0.901611\pi$
$692$	6.53281	−	2.70598i	0.248340	−	0.102866i
$693$		0			0
$694$		0			0
$695$	−11.3137	−	11.3137i	−0.429153	−	0.429153i
$696$		0			0
$697$		0			0
$698$	−4.00000			−0.151402
$699$		0			0
$700$		0			0
$701$		−	12.0000i		−	0.453234i	−0.973984	−	0.226617i	$-0.927233\pi$
$701$		−	12.0000i		−	0.453234i	0.973984	−	0.226617i	$-0.0727665\pi$
$702$		0			0
$703$	6.49435	−	15.6788i	0.244939	−	0.591335i
$704$	5.22625	+	2.16478i	0.196972	+	0.0815884i
$705$		0			0
$706$	−9.89949	+	9.89949i	−0.372572	+	0.372572i
$707$		0			0
$708$		0			0
$709$	30.0509	−	12.4475i	1.12859	−	0.467476i	0.261287	−	0.965261i	$-0.415853\pi$
$709$	30.0509	−	12.4475i	1.12859	−	0.467476i	0.867300	+	0.497785i	$0.165853\pi$
$710$		−	8.00000i		−	0.300235i
$711$	−12.9887	−	31.3575i	−0.487115	−	1.17600i
$712$		0			0
$713$	32.0000			1.19841
$714$		0			0
$715$	32.0000			1.19673
$716$	−2.82843	−	2.82843i	−0.105703	−	0.105703i
$717$		0			0
$718$			24.0000i			0.895672i
$719$	−10.4525	+	4.32957i	−0.389813	+	0.161466i	−0.568977	−	0.822353i	$-0.692661\pi$
$719$	−10.4525	+	4.32957i	−0.389813	+	0.161466i	0.179164	+	0.983819i	$0.442661\pi$
$720$	1.62359	−	3.91969i	0.0605076	−	0.146078i
$721$		0			0
$722$	2.12132	−	2.12132i	0.0789474	−	0.0789474i
$723$		0			0
$724$	14.3722	+	5.95316i	0.534138	+	0.221247i
$725$	−4.87076	+	11.7591i	−0.180896	+	0.436721i
$726$		0			0
$727$			48.0000i			1.78022i	0.455744	+	0.890111i	$0.349373\pi$
$727$			48.0000i			1.78022i	−0.455744	+	0.890111i	$0.650627\pi$
$728$		0			0
$729$	−19.0919	−	19.0919i	−0.707107	−	0.707107i
$730$	−10.0000			−0.370117
$731$		0			0
$732$		0			0
$733$	25.4558	+	25.4558i	0.940233	+	0.940233i	0.998312	−	0.0580789i	$-0.0184975\pi$
$733$	25.4558	+	25.4558i	0.940233	+	0.940233i	−0.0580789	+	0.998312i	$0.518498\pi$
$734$		0			0
$735$		0			0
$736$	5.22625	−	2.16478i	0.192642	−	0.0797950i
$737$	−25.9774	+	62.7150i	−0.956890	+	2.31014i
$738$	3.91969	+	1.62359i	0.144286	+	0.0597651i
$739$	2.82843	−	2.82843i	0.104045	−	0.104045i	−0.653168	−	0.757213i	$-0.726560\pi$
$739$	2.82843	−	2.82843i	0.104045	−	0.104045i	0.757213	+	0.653168i	$0.226560\pi$
$740$	−4.24264	+	4.24264i	−0.155963	+	0.155963i
$741$		0			0
$742$		0			0
$743$		0			0		−0.382683	−	0.923880i	$-0.625000\pi$
$743$		0			0		0.382683	+	0.923880i	$0.375000\pi$
$744$		0			0
$745$	5.41196	+	13.0656i	0.198279	+	0.478688i
$746$	−2.82843	−	2.82843i	−0.103556	−	0.103556i
$747$	12.0000			0.439057
$748$		0			0
$749$		0			0
$750$		0			0
$751$	−8.65914	−	20.9050i	−0.315976	−	0.762835i	−0.999460	−	0.0328684i	$-0.989536\pi$
$751$	−8.65914	−	20.9050i	−0.315976	−	0.762835i	0.683483	−	0.729966i	$-0.260464\pi$
$752$		−	8.00000i		−	0.291730i
$753$		0			0
$754$	−6.49435	+	15.6788i	−0.236510	+	0.570987i
$755$		0			0
$756$		0			0
$757$	15.5563	−	15.5563i	0.565405	−	0.565405i	−0.365433	−	0.930838i	$-0.619079\pi$
$757$	15.5563	−	15.5563i	0.565405	−	0.565405i	0.930838	+	0.365433i	$0.119079\pi$
$758$	15.6788	+	6.49435i	0.569478	+	0.235886i
$759$		0			0
$760$	5.22625	−	2.16478i	0.189576	−	0.0785250i
$761$		−	8.00000i		−	0.290000i	−0.989432	−	0.145000i	$-0.953682\pi$
$761$		−	8.00000i		−	0.290000i	0.989432	−	0.145000i	$-0.0463182\pi$
$762$		0			0
$763$		0			0
$764$	−8.00000			−0.289430
$765$		0			0
$766$	24.0000			0.867155
$767$	11.3137	+	11.3137i	0.408514	+	0.408514i
$768$		0			0
$769$		−	40.0000i		−	1.44244i	−0.692708	−	0.721218i	$-0.743582\pi$
$769$		−	40.0000i		−	1.44244i	0.692708	−	0.721218i	$-0.256418\pi$
$770$		0			0
$771$		0			0
$772$	14.3722	+	5.95316i	0.517267	+	0.214259i
$773$	4.24264	−	4.24264i	0.152597	−	0.152597i	−0.626680	−	0.779277i	$-0.715587\pi$
$773$	4.24264	−	4.24264i	0.152597	−	0.152597i	0.779277	+	0.626680i	$0.215587\pi$
$774$	8.48528	−	8.48528i	0.304997	−	0.304997i
$775$	15.6788	+	6.49435i	0.563198	+	0.233284i
$776$	1.62359	−	3.91969i	0.0582834	−	0.140709i
$777$		0			0
$778$			6.00000i			0.215110i
$779$	2.16478	+	5.22625i	0.0775615	+	0.187250i
$780$		0			0
$781$	−32.0000			−1.14505
$782$		0			0
$783$		0			0
$784$	4.94975	+	4.94975i	0.176777	+	0.176777i
$785$	−1.08239	−	2.61313i	−0.0386322	−	0.0932665i
$786$		0			0
$787$	−15.6788	+	6.49435i	−0.558887	+	0.231499i	−0.644202	−	0.764855i	$-0.722810\pi$
$787$	−15.6788	+	6.49435i	−0.558887	+	0.231499i	0.0853148	+	0.996354i	$0.472810\pi$
$788$	2.70598	−	6.53281i	0.0963966	−	0.232722i
$789$		0			0
$790$	−11.3137	+	11.3137i	−0.402524	+	0.402524i
$791$		0			0
$792$	−15.6788	−	6.49435i	−0.557120	−	0.230767i
$793$	−19.4831	+	47.0363i	−0.691864	+	1.67031i
$794$	−19.5984	+	8.11794i	−0.695523	+	0.288095i
$795$		0			0
$796$	−6.49435	−	15.6788i	−0.230186	−	0.555719i
$797$	8.48528	+	8.48528i	0.300564	+	0.300564i	0.841235	−	0.540670i	$-0.181829\pi$
$797$	8.48528	+	8.48528i	0.300564	+	0.300564i	−0.540670	+	0.841235i	$0.681829\pi$
$798$		0			0
$799$		0			0
$800$	3.00000			0.106066
$801$		0			0
$802$	10.2827	+	24.8247i	0.363096	+	0.876591i
$803$			40.0000i			1.41157i
$804$		0			0
$805$		0			0
$806$	20.9050	+	8.65914i	0.736347	+	0.305005i
$807$		0			0
$808$	8.48528	−	8.48528i	0.298511	−	0.298511i
$809$	−30.0509	−	12.4475i	−1.05654	−	0.437631i	−0.214315	−	0.976765i	$-0.568752\pi$
$809$	−30.0509	−	12.4475i	−1.05654	−	0.437631i	−0.842220	+	0.539133i	$0.818752\pi$
$810$	−4.87076	+	11.7591i	−0.171141	+	0.413171i
$811$	5.22625	−	2.16478i	0.183519	−	0.0760159i	−0.289032	−	0.957319i	$-0.593333\pi$
$811$	5.22625	−	2.16478i	0.183519	−	0.0760159i	0.472551	+	0.881304i	$0.343333\pi$
$812$		0			0
$813$		0			0
$814$	16.9706	+	16.9706i	0.594818	+	0.594818i
$815$	8.00000			0.280228
$816$		0			0
$817$	16.0000			0.559769
$818$	−7.07107	−	7.07107i	−0.247234	−	0.247234i
$819$		0			0
$820$		−	2.00000i		−	0.0698430i
$821$	−24.8247	+	10.2827i	−0.866388	+	0.358870i	−0.771202	−	0.636590i	$-0.780344\pi$
$821$	−24.8247	+	10.2827i	−0.866388	+	0.358870i	−0.0951854	+	0.995460i	$0.530344\pi$
$822$		0			0
$823$	−47.0363	−	19.4831i	−1.63958	−	0.679137i	−0.643326	−	0.765593i	$-0.722446\pi$
$823$	−47.0363	−	19.4831i	−1.63958	−	0.679137i	−0.996256	+	0.0864560i	$0.972446\pi$
$824$	11.3137	−	11.3137i	0.394132	−	0.394132i
$825$		0			0
$826$		0			0
$827$	−10.8239	+	26.1313i	−0.376385	+	0.908673i	0.616253	+	0.787548i	$0.288650\pi$
$827$	−10.8239	+	26.1313i	−0.376385	+	0.908673i	−0.992637	+	0.121124i	$0.961350\pi$
$828$	−15.6788	+	6.49435i	−0.544874	+	0.225694i
$829$			30.0000i			1.04194i	0.853574	+	0.520972i	$0.174430\pi$
$829$			30.0000i			1.04194i	−0.853574	+	0.520972i	$0.825570\pi$
$830$	−2.16478	−	5.22625i	−0.0751408	−	0.181406i
$831$		0			0
$832$	4.00000			0.138675
$833$		0			0
$834$		0			0
$835$	−11.3137	−	11.3137i	−0.391527	−	0.391527i
$836$	−8.65914	−	20.9050i	−0.299483	−	0.723015i
$837$		0			0
$838$	−15.6788	+	6.49435i	−0.541614	+	0.224344i
$839$	17.3183	−	41.8100i	0.597893	−	1.44344i	−0.277831	−	0.960630i	$-0.589615\pi$
$839$	17.3183	−	41.8100i	0.597893	−	1.44344i	0.875724	−	0.482812i	$-0.160385\pi$
$840$		0			0
$841$	−7.77817	+	7.77817i	−0.268213	+	0.268213i
$842$	19.7990	−	19.7990i	0.682318	−	0.682318i
$843$		0			0
$844$	−8.65914	+	20.9050i	−0.298060	+	0.719580i
$845$	3.91969	−	1.62359i	0.134841	−	0.0558531i
$846$			24.0000i			0.825137i
$847$		0			0
$848$	2.82843	+	2.82843i	0.0971286	+	0.0971286i
$849$		0			0
$850$		0			0
$851$	24.0000			0.822709
$852$		0			0
$853$	13.5299	+	32.6641i	0.463255	+	1.11840i	0.967053	+	0.254575i	$0.0819356\pi$
$853$	13.5299	+	32.6641i	0.463255	+	1.11840i	−0.503798	+	0.863822i	$0.668064\pi$
$854$		0			0
$855$	−15.6788	+	6.49435i	−0.536202	+	0.222102i
$856$	−4.32957	+	10.4525i	−0.147982	+	0.357259i
$857$	−19.5984	−	8.11794i	−0.669470	−	0.277304i	0.0219473	−	0.999759i	$-0.493013\pi$
$857$	−19.5984	−	8.11794i	−0.669470	−	0.277304i	−0.691417	+	0.722456i	$0.743013\pi$
$858$		0			0
$859$	25.4558	−	25.4558i	0.868542	−	0.868542i	−0.123769	−	0.992311i	$-0.539498\pi$
$859$	25.4558	−	25.4558i	0.868542	−	0.868542i	0.992311	+	0.123769i	$0.0394981\pi$
$860$	−5.22625	−	2.16478i	−0.178214	−	0.0738185i
$861$		0			0
$862$	31.3575	−	12.9887i	1.06804	−	0.442397i
$863$			24.0000i			0.816970i	0.912765	+	0.408485i	$0.133943\pi$
$863$			24.0000i			0.816970i	−0.912765	+	0.408485i	$0.866057\pi$
$864$		0			0
$865$	7.07107	+	7.07107i	0.240424	+	0.240424i
$866$	−14.0000			−0.475739
$867$		0			0
$868$		0			0
$869$	45.2548	+	45.2548i	1.53517	+	1.53517i
$870$		0			0
$871$			48.0000i			1.62642i
$872$	−3.91969	+	1.62359i	−0.132737	+	0.0549816i
$873$	−4.87076	+	11.7591i	−0.164850	+	0.397984i
$874$	−20.9050	−	8.65914i	−0.707122	−	0.292900i
$875$		0			0
$876$		0			0
$877$	−45.7297	−	18.9419i	−1.54418	−	0.639621i	−0.561930	−	0.827185i	$-0.689941\pi$
$877$	−45.7297	−	18.9419i	−1.54418	−	0.639621i	−0.982252	+	0.187564i	$0.939941\pi$
$878$	−6.49435	+	15.6788i	−0.219174	+	0.529132i
$879$		0			0
$880$			8.00000i			0.269680i
$881$	−21.1066	−	50.9560i	−0.711101	−	1.71675i	−0.697232	−	0.716846i	$-0.745585\pi$
$881$	−21.1066	−	50.9560i	−0.711101	−	1.71675i	−0.0138695	−	0.999904i	$-0.504415\pi$
$882$	−14.8492	−	14.8492i	−0.500000	−	0.500000i
$883$	−44.0000			−1.48072			−0.740359	−	0.672212i	$-0.765344\pi$
$883$	−44.0000			−1.48072			−0.740359	+	0.672212i	$0.765344\pi$
$884$		0			0
$885$		0			0
$886$	2.82843	+	2.82843i	0.0950229	+	0.0950229i
$887$	−15.1535	−	36.5838i	−0.508804	−	1.22836i	−0.944572	−	0.328303i	$-0.893523\pi$
$887$	−15.1535	−	36.5838i	−0.508804	−	1.22836i	0.435768	−	0.900059i	$-0.356477\pi$
$888$		0			0
$889$		0			0
$890$		0			0
$891$	47.0363	+	19.4831i	1.57577	+	0.652707i
$892$	−11.3137	+	11.3137i	−0.378811	+	0.378811i
$893$	−22.6274	+	22.6274i	−0.757198	+	0.757198i
$894$		0			0
$895$	2.16478	−	5.22625i	0.0723608	−	0.174694i
$896$		0			0
$897$		0			0
$898$	1.62359	+	3.91969i	0.0541798	+	0.130802i
$899$	−16.9706	−	16.9706i	−0.566000	−	0.566000i
$900$	−9.00000			−0.300000
$901$		0			0
$902$	−8.00000			−0.266371
$903$		0			0
$904$	−0.541196	−	1.30656i	−0.0179999	−	0.0434556i
$905$			22.0000i			0.731305i
$906$		0			0
$907$	−10.8239	+	26.1313i	−0.359402	+	0.867674i	0.635982	+	0.771704i	$0.280595\pi$
$907$	−10.8239	+	26.1313i	−0.359402	+	0.867674i	−0.995384	+	0.0959702i	$0.969405\pi$
$908$	−26.1313	−	10.8239i	−0.867196	−	0.359204i
$909$	−25.4558	+	25.4558i	−0.844317	+	0.844317i
$910$		0			0
$911$	5.22625	+	2.16478i	0.173153	+	0.0717225i	0.467576	−	0.883953i	$-0.345127\pi$
$911$	5.22625	+	2.16478i	0.173153	+	0.0717225i	−0.294423	+	0.955675i	$0.595127\pi$
$912$		0			0
$913$	−20.9050	+	8.65914i	−0.691855	+	0.286576i
$914$			22.0000i			0.727695i
$915$		0			0
$916$	−4.24264	−	4.24264i	−0.140181	−	0.140181i
$917$		0			0
$918$		0			0
$919$	40.0000			1.31948			0.659739	−	0.751495i	$-0.270667\pi$
$919$	40.0000			1.31948			0.659739	+	0.751495i	$0.270667\pi$
$920$	5.65685	+	5.65685i	0.186501	+	0.186501i
$921$		0			0
$922$		−	20.0000i		−	0.658665i
$923$	−20.9050	+	8.65914i	−0.688097	+	0.285019i
$924$		0			0
$925$	11.7591	+	4.87076i	0.386636	+	0.160150i
$926$	16.9706	−	16.9706i	0.557687	−	0.557687i
$927$	−33.9411	+	33.9411i	−1.11477	+	1.11477i
$928$	−3.91969	−	1.62359i	−0.128670	−	0.0532969i
$929$	7.03555	−	16.9853i	0.230829	−	0.557270i	−0.765446	−	0.643500i	$-0.777482\pi$
$929$	7.03555	−	16.9853i	0.230829	−	0.557270i	0.996275	+	0.0862294i	$0.0274818\pi$
$930$		0			0
$931$		−	28.0000i		−	0.917663i
$932$	2.70598	+	6.53281i	0.0886373	+	0.213989i
$933$		0			0
$934$	28.0000			0.916188
$935$		0			0
$936$	−12.0000			−0.392232
$937$	33.9411	+	33.9411i	1.10881	+	1.10881i	0.993307	+	0.115501i	$0.0368473\pi$
$937$	33.9411	+	33.9411i	1.10881	+	1.10881i	0.115501	+	0.993307i	$0.463153\pi$
$938$		0			0
$939$		0			0
$940$	10.4525	−	4.32957i	0.340923	−	0.141215i
$941$	−0.541196	+	1.30656i	−0.0176425	+	0.0425927i	−0.932455	−	0.361285i	$-0.882338\pi$
$941$	−0.541196	+	1.30656i	−0.0176425	+	0.0425927i	0.914813	+	0.403878i	$0.132338\pi$
$942$		0			0
$943$	−5.65685	+	5.65685i	−0.184213	+	0.184213i
$944$	−2.82843	+	2.82843i	−0.0920575	+	0.0920575i
$945$		0			0
$946$	−8.65914	+	20.9050i	−0.281533	+	0.679680i
$947$	15.6788	−	6.49435i	0.509491	−	0.211038i	−0.113103	−	0.993583i	$-0.536079\pi$
$947$	15.6788	−	6.49435i	0.509491	−	0.211038i	0.622594	+	0.782545i	$0.286079\pi$
$948$		0			0
$949$	10.8239	+	26.1313i	0.351359	+	0.848257i
$950$	−8.48528	−	8.48528i	−0.275299	−	0.275299i
$951$		0			0
$952$		0			0
$953$	24.0000			0.777436			0.388718	−	0.921357i	$-0.372918\pi$
$953$	24.0000			0.777436			0.388718	+	0.921357i	$0.372918\pi$
$954$	−8.48528	−	8.48528i	−0.274721	−	0.274721i
$955$	−4.32957	−	10.4525i	−0.140102	−	0.338235i
$956$		0			0
$957$		0			0
$958$	−4.32957	+	10.4525i	−0.139882	+	0.337705i
$959$		0			0
$960$		0			0
$961$	−0.707107	+	0.707107i	−0.0228099	+	0.0228099i
$962$	15.6788	+	6.49435i	0.505503	+	0.209386i
$963$	12.9887	−	31.3575i	0.418555	−	1.01048i
$964$	27.4378	−	11.3651i	0.883713	−	0.366046i
$965$			22.0000i			0.708205i
$966$		0			0
$967$	22.6274	+	22.6274i	0.727649	+	0.727649i	0.970151	−	0.242502i	$-0.0779682\pi$
$967$	22.6274	+	22.6274i	0.727649	+	0.727649i	−0.242502	+	0.970151i	$0.577968\pi$
$968$	21.0000			0.674966
$969$		0			0
$970$	6.00000			0.192648
$971$	−14.1421	−	14.1421i	−0.453843	−	0.453843i	0.442785	−	0.896628i	$-0.353990\pi$
$971$	−14.1421	−	14.1421i	−0.453843	−	0.453843i	−0.896628	+	0.442785i	$0.853990\pi$
$972$		0			0
$973$		0			0
$974$	26.1313	−	10.8239i	0.837300	−	0.346821i
$975$		0			0
$976$	−11.7591	−	4.87076i	−0.376399	−	0.155909i
$977$	5.65685	−	5.65685i	0.180979	−	0.180979i	−0.610803	−	0.791782i	$-0.709153\pi$
$977$	5.65685	−	5.65685i	0.180979	−	0.180979i	0.791782	+	0.610803i	$0.209153\pi$
$978$		0			0
$979$		0			0
$980$	−3.78837	+	9.14594i	−0.121015	+	0.292156i
$981$	11.7591	−	4.87076i	0.375438	−	0.155512i
$982$		−	20.0000i		−	0.638226i
$983$	−10.8239	−	26.1313i	−0.345229	−	0.833458i	−0.997169	−	0.0751871i	$-0.976045\pi$
$983$	−10.8239	−	26.1313i	−0.345229	−	0.833458i	0.651940	−	0.758271i	$-0.273955\pi$
$984$		0			0
$985$	10.0000			0.318626
$986$		0			0
$987$		0			0
$988$	−11.3137	−	11.3137i	−0.359937	−	0.359937i
$989$	8.65914	+	20.9050i	0.275345	+	0.664741i
$990$		−	24.0000i		−	0.762770i
$991$	−31.3575	+	12.9887i	−0.996104	+	0.412600i	−0.820367	−	0.571837i	$-0.806231\pi$
$991$	−31.3575	+	12.9887i	−0.996104	+	0.412600i	−0.175737	+	0.984437i	$0.556231\pi$
$992$	−2.16478	+	5.22625i	−0.0687320	+	0.165934i
$993$		0			0
$994$		0			0
$995$	16.9706	−	16.9706i	0.538003	−	0.538003i
$996$		0			0
$997$	−18.9419	+	45.7297i	−0.599895	+	1.44827i	0.273794	+	0.961788i	$0.411721\pi$
$997$	−18.9419	+	45.7297i	−0.599895	+	1.44827i	−0.873688	+	0.486486i	$0.838279\pi$
$998$	−10.4525	+	4.32957i	−0.330868	+	0.137050i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	578.2.d.f.423.1		8
17.2	even	8	inner	578.2.d.f.179.2		8
17.3	odd	16		578.2.b.c.577.1		2
17.4	even	4	inner	578.2.d.f.155.2		8
17.5	odd	16		578.2.a.b.1.2		2
17.6	odd	16		578.2.c.b.251.1		2
17.7	odd	16		578.2.c.b.327.1		2
17.8	even	8	inner	578.2.d.f.399.1		8
17.9	even	8	inner	578.2.d.f.399.2		8
17.10	odd	16		34.2.c.b.21.1	yes	2
17.11	odd	16		34.2.c.b.13.1	✓	2
17.12	odd	16		578.2.a.b.1.1		2
17.13	even	4	inner	578.2.d.f.155.1		8
17.14	odd	16		578.2.b.c.577.2		2
17.15	even	8	inner	578.2.d.f.179.1		8
17.16	even	2	inner	578.2.d.f.423.2		8
51.5	even	16		5202.2.a.bb.1.1		2
51.11	even	16		306.2.g.d.217.1		2
51.29	even	16		5202.2.a.bb.1.2		2
51.44	even	16		306.2.g.d.55.1		2
68.11	even	16		272.2.o.c.81.1		2
68.27	even	16		272.2.o.c.225.1		2
68.39	even	16		4624.2.a.l.1.2		2
68.63	even	16		4624.2.a.l.1.1		2
85.27	even	16		850.2.g.d.599.1		2
85.28	even	16		850.2.g.d.149.1		2
85.44	odd	16		850.2.h.c.701.1		2
85.62	even	16		850.2.g.a.149.1		2
85.78	even	16		850.2.g.a.599.1		2
85.79	odd	16		850.2.h.c.251.1		2
136.11	even	16		1088.2.o.i.897.1		2
136.27	even	16		1088.2.o.i.769.1		2
136.45	odd	16		1088.2.o.k.897.1		2
136.61	odd	16		1088.2.o.k.769.1		2
204.11	odd	16		2448.2.be.j.1441.1		2
204.95	odd	16		2448.2.be.j.1585.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
34.2.c.b.13.1	✓	2	17.11	odd	16
34.2.c.b.21.1	yes	2	17.10	odd	16
272.2.o.c.81.1		2	68.11	even	16
272.2.o.c.225.1		2	68.27	even	16
306.2.g.d.55.1		2	51.44	even	16
306.2.g.d.217.1		2	51.11	even	16
578.2.a.b.1.1		2	17.12	odd	16
578.2.a.b.1.2		2	17.5	odd	16
578.2.b.c.577.1		2	17.3	odd	16
578.2.b.c.577.2		2	17.14	odd	16
578.2.c.b.251.1		2	17.6	odd	16
578.2.c.b.327.1		2	17.7	odd	16
578.2.d.f.155.1		8	17.13	even	4	inner
578.2.d.f.155.2		8	17.4	even	4	inner
578.2.d.f.179.1		8	17.15	even	8	inner
578.2.d.f.179.2		8	17.2	even	8	inner
578.2.d.f.399.1		8	17.8	even	8	inner
578.2.d.f.399.2		8	17.9	even	8	inner
578.2.d.f.423.1		8	1.1	even	1	trivial
578.2.d.f.423.2		8	17.16	even	2	inner
850.2.g.a.149.1		2	85.62	even	16
850.2.g.a.599.1		2	85.78	even	16
850.2.g.d.149.1		2	85.28	even	16
850.2.g.d.599.1		2	85.27	even	16
850.2.h.c.251.1		2	85.79	odd	16
850.2.h.c.701.1		2	85.44	odd	16
1088.2.o.i.769.1		2	136.27	even	16
1088.2.o.i.897.1		2	136.11	even	16
1088.2.o.k.769.1		2	136.61	odd	16
1088.2.o.k.897.1		2	136.45	odd	16
2448.2.be.j.1441.1		2	204.11	odd	16
2448.2.be.j.1585.1		2	204.95	odd	16
4624.2.a.l.1.1		2	68.63	even	16
4624.2.a.l.1.2		2	68.39	even	16
5202.2.a.bb.1.1		2	51.5	even	16
5202.2.a.bb.1.2		2	51.29	even	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 578 = 2 \cdot 17^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	578.d (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.30656 + 0.541196i) q^{5} +(-0.707107 + 0.707107i) q^{8} +(2.12132 - 2.12132i) q^{9} +O(q^{10})\)	\(q+(0.707107 + 0.707107i) q^{2} +1.00000i q^{4} +(-1.30656 + 0.541196i) q^{5} +(-0.707107 + 0.707107i) q^{8} +(2.12132 - 2.12132i) q^{9} +(-1.30656 - 0.541196i) q^{10} +(-2.16478 + 5.22625i) q^{11} +4.00000i q^{13} -1.00000 q^{16} +3.00000 q^{18} +(2.82843 + 2.82843i) q^{19} +(-0.541196 - 1.30656i) q^{20} +(-5.22625 + 2.16478i) q^{22} +(-2.16478 + 5.22625i) q^{23} +(-2.12132 + 2.12132i) q^{25} +(-2.82843 + 2.82843i) q^{26} +(3.91969 - 1.62359i) q^{29} +(-2.16478 - 5.22625i) q^{31} +(-0.707107 - 0.707107i) q^{32} +(2.12132 + 2.12132i) q^{36} +(-1.62359 - 3.91969i) q^{37} +4.00000i q^{38} +(0.541196 - 1.30656i) q^{40} +(1.30656 + 0.541196i) q^{41} +(2.82843 - 2.82843i) q^{43} +(-5.22625 - 2.16478i) q^{44} +(-1.62359 + 3.91969i) q^{45} +(-5.22625 + 2.16478i) q^{46} +8.00000i q^{47} +(-4.94975 - 4.94975i) q^{49} -3.00000 q^{50} -4.00000 q^{52} +(-2.82843 - 2.82843i) q^{53} -8.00000i q^{55} +(3.91969 + 1.62359i) q^{58} +(2.82843 - 2.82843i) q^{59} +(11.7591 + 4.87076i) q^{61} +(2.16478 - 5.22625i) q^{62} -1.00000i q^{64} +(-2.16478 - 5.22625i) q^{65} +12.0000 q^{67} +(2.16478 + 5.22625i) q^{71} +3.00000i q^{72} +(6.53281 - 2.70598i) q^{73} +(1.62359 - 3.91969i) q^{74} +(-2.82843 + 2.82843i) q^{76} +(4.32957 - 10.4525i) q^{79} +(1.30656 - 0.541196i) q^{80} -9.00000i q^{81} +(0.541196 + 1.30656i) q^{82} +(2.82843 + 2.82843i) q^{83} +4.00000 q^{86} +(-2.16478 - 5.22625i) q^{88} +(-3.91969 + 1.62359i) q^{90} +(-5.22625 - 2.16478i) q^{92} +(-5.65685 + 5.65685i) q^{94} +(-5.22625 - 2.16478i) q^{95} +(-3.91969 + 1.62359i) q^{97} -7.00000i q^{98} +(6.49435 + 15.6788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 8 q^{16} + 24 q^{18} - 24 q^{50} - 32 q^{52} + 96 q^{67} + 32 q^{86}+O(q^{100}) \) 8 * q - 8 * q^16 + 24 * q^18 - 24 * q^50 - 32 * q^52 + 96 * q^67 + 32 * q^86

Introduction

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Modular forms

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Database

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