LMFDB - Embedded newform 512.2.g.d.193.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [512,2,Mod(65,512)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(512, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([0, 7]))

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

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

chi := DirichletCharacter("512.65");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 512 = 2^{9} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	512.g (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:	$4.08834058349$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			193.1
Root			$-0.707107 - 0.707107i$ of defining polynomial
Character	$\chi$	$=$	512.193
Dual form			512.2.g.d.321.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.70711 - 0.707107i) q^{3} +(1.29289 - 3.12132i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(0.292893 - 0.292893i) q^{9} +O(q^{10})$	\(q+(1.70711 - 0.707107i) q^{3} +(1.29289 - 3.12132i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(0.292893 - 0.292893i) q^{9} +(0.292893 + 0.121320i) q^{11} +(-0.707107 - 1.70711i) q^{13} -6.24264i q^{15} -2.82843i q^{17} +(2.29289 + 5.53553i) q^{19} +(-2.41421 - 1.00000i) q^{21} +(-0.171573 + 0.171573i) q^{23} +(-4.53553 - 4.53553i) q^{25} +(-1.82843 + 4.41421i) q^{27} +(2.70711 - 1.12132i) q^{29} -4.00000 q^{31} +0.585786 q^{33} +(-4.41421 + 1.82843i) q^{35} +(-0.707107 + 1.70711i) q^{37} +(-2.41421 - 2.41421i) q^{39} +(5.82843 - 5.82843i) q^{41} +(7.94975 + 3.29289i) q^{43} +(-0.535534 - 1.29289i) q^{45} +11.6569i q^{47} -5.00000i q^{49} +(-2.00000 - 4.82843i) q^{51} +(7.53553 + 3.12132i) q^{53} +(0.757359 - 0.757359i) q^{55} +(7.82843 + 7.82843i) q^{57} +(2.53553 - 6.12132i) q^{59} +(0.707107 - 0.292893i) q^{61} -0.585786 q^{63} -6.24264 q^{65} +(3.70711 - 1.53553i) q^{67} +(-0.171573 + 0.414214i) q^{69} +(0.171573 + 0.171573i) q^{71} +(-7.00000 + 7.00000i) q^{73} +(-10.9497 - 4.53553i) q^{75} +(-0.171573 - 0.414214i) q^{77} -6.00000i q^{79} +10.0711i q^{81} +(-2.53553 - 6.12132i) q^{83} +(-8.82843 - 3.65685i) q^{85} +(3.82843 - 3.82843i) q^{87} +(2.65685 + 2.65685i) q^{89} +(-1.00000 + 2.41421i) q^{91} +(-6.82843 + 2.82843i) q^{93} +20.2426 q^{95} -1.51472 q^{97} +(0.121320 - 0.0502525i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} + 8 q^{5} - 4 q^{7} + 4 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 + 8 * q^5 - 4 * q^7 + 4 * q^9	$ 4 q + 4 q^{3} + 8 q^{5} - 4 q^{7} + 4 q^{9} + 4 q^{11} + 12 q^{19} - 4 q^{21} - 12 q^{23} - 4 q^{25} + 4 q^{27} + 8 q^{29} - 16 q^{31} + 8 q^{33} - 12 q^{35} - 4 q^{39} + 12 q^{41} + 12 q^{43} + 12 q^{45} - 8 q^{51} + 16 q^{53} + 20 q^{55} + 20 q^{57} - 4 q^{59} - 8 q^{63} - 8 q^{65} + 12 q^{67} - 12 q^{69} + 12 q^{71} - 28 q^{73} - 24 q^{75} - 12 q^{77} + 4 q^{83} - 24 q^{85} + 4 q^{87} - 12 q^{89} - 4 q^{91} - 16 q^{93} + 64 q^{95} - 40 q^{97} - 8 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 + 8 * q^5 - 4 * q^7 + 4 * q^9 + 4 * q^11 + 12 * q^19 - 4 * q^21 - 12 * q^23 - 4 * q^25 + 4 * q^27 + 8 * q^29 - 16 * q^31 + 8 * q^33 - 12 * q^35 - 4 * q^39 + 12 * q^41 + 12 * q^43 + 12 * q^45 - 8 * q^51 + 16 * q^53 + 20 * q^55 + 20 * q^57 - 4 * q^59 - 8 * q^63 - 8 * q^65 + 12 * q^67 - 12 * q^69 + 12 * q^71 - 28 * q^73 - 24 * q^75 - 12 * q^77 + 4 * q^83 - 24 * q^85 + 4 * q^87 - 12 * q^89 - 4 * q^91 - 16 * q^93 + 64 * q^95 - 40 * q^97 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/512\mathbb{Z}\right)^\times$.

$n$	$5$	$511$
$\chi(n)$	$e\left(\frac{5}{8}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.70711	−	0.707107i	0.985599	−	0.408248i	0.169102	−	0.985599i	$-0.445913\pi$
$3$	1.70711	−	0.707107i	0.985599	−	0.408248i	0.816497	+	0.577350i	$0.195913\pi$
$4$		0			0
$5$	1.29289	−	3.12132i	0.578199	−	1.39590i	−0.316228	−	0.948683i	$-0.602416\pi$
$5$	1.29289	−	3.12132i	0.578199	−	1.39590i	0.894427	−	0.447214i	$-0.147584\pi$
$6$		0			0
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	0.492403	−	0.870367i	$-0.336119\pi$
$7$	−1.00000	−	1.00000i	−0.377964	−	0.377964i	−0.870367	+	0.492403i	$0.836119\pi$
$8$		0			0
$9$	0.292893	−	0.292893i	0.0976311	−	0.0976311i
$10$		0			0
$11$	0.292893	+	0.121320i	0.0883106	+	0.0365795i	0.426401	−	0.904534i	$-0.359781\pi$
$11$	0.292893	+	0.121320i	0.0883106	+	0.0365795i	−0.338091	+	0.941113i	$0.609781\pi$
$12$		0			0
$13$	−0.707107	−	1.70711i	−0.196116	−	0.473466i	0.794977	−	0.606640i	$-0.207483\pi$
$13$	−0.707107	−	1.70711i	−0.196116	−	0.473466i	−0.991093	+	0.133174i	$0.957483\pi$
$14$		0			0
$15$		−	6.24264i		−	1.61184i
$16$		0			0
$17$		−	2.82843i		−	0.685994i	−0.939336	−	0.342997i	$-0.888558\pi$
$17$		−	2.82843i		−	0.685994i	0.939336	−	0.342997i	$-0.111442\pi$
$18$		0			0
$19$	2.29289	+	5.53553i	0.526026	+	1.26994i	0.934107	+	0.356993i	$0.116198\pi$
$19$	2.29289	+	5.53553i	0.526026	+	1.26994i	−0.408081	+	0.912946i	$0.633802\pi$
$20$		0			0
$21$	−2.41421	−	1.00000i	−0.526825	−	0.218218i
$22$		0			0
$23$	−0.171573	+	0.171573i	−0.0357754	+	0.0357754i	−0.724768	−	0.688993i	$-0.758053\pi$
$23$	−0.171573	+	0.171573i	−0.0357754	+	0.0357754i	0.688993	+	0.724768i	$0.258053\pi$
$24$		0			0
$25$	−4.53553	−	4.53553i	−0.907107	−	0.907107i
$26$		0			0
$27$	−1.82843	+	4.41421i	−0.351881	+	0.849516i
$28$		0			0
$29$	2.70711	−	1.12132i	0.502697	−	0.208224i	−0.116900	−	0.993144i	$-0.537296\pi$
$29$	2.70711	−	1.12132i	0.502697	−	0.208224i	0.619598	+	0.784920i	$0.287296\pi$
$30$		0			0
$31$	−4.00000			−0.718421			−0.359211	−	0.933257i	$-0.616954\pi$
$31$	−4.00000			−0.718421			−0.359211	+	0.933257i	$0.616954\pi$
$32$		0			0
$33$	0.585786			0.101972
$34$		0			0
$35$	−4.41421	+	1.82843i	−0.746138	+	0.309061i
$36$		0			0
$37$	−0.707107	+	1.70711i	−0.116248	+	0.280647i	−0.971285	−	0.237920i	$-0.923534\pi$
$37$	−0.707107	+	1.70711i	−0.116248	+	0.280647i	0.855037	+	0.518567i	$0.173534\pi$
$38$		0			0
$39$	−2.41421	−	2.41421i	−0.386584	−	0.386584i
$40$		0			0
$41$	5.82843	−	5.82843i	0.910247	−	0.910247i	−0.0860440	−	0.996291i	$-0.527423\pi$
$41$	5.82843	−	5.82843i	0.910247	−	0.910247i	0.996291	+	0.0860440i	$0.0274225\pi$
$42$		0			0
$43$	7.94975	+	3.29289i	1.21233	+	0.502162i	0.894962	−	0.446143i	$-0.147203\pi$
$43$	7.94975	+	3.29289i	1.21233	+	0.502162i	0.317363	+	0.948304i	$0.397203\pi$
$44$		0			0
$45$	−0.535534	−	1.29289i	−0.0798327	−	0.192733i
$46$		0			0
$47$			11.6569i			1.70033i	0.526519	+	0.850163i	$0.323497\pi$
$47$			11.6569i			1.70033i	−0.526519	+	0.850163i	$0.676503\pi$
$48$		0			0
$49$		−	5.00000i		−	0.714286i
$50$		0			0
$51$	−2.00000	−	4.82843i	−0.280056	−	0.676115i
$52$		0			0
$53$	7.53553	+	3.12132i	1.03509	+	0.428746i	0.834545	−	0.550939i	$-0.185730\pi$
$53$	7.53553	+	3.12132i	1.03509	+	0.428746i	0.200540	+	0.979686i	$0.435730\pi$
$54$		0			0
$55$	0.757359	−	0.757359i	0.102122	−	0.102122i
$56$		0			0
$57$	7.82843	+	7.82843i	1.03690	+	1.03690i
$58$		0			0
$59$	2.53553	−	6.12132i	0.330098	−	0.796928i	−0.668485	−	0.743725i	$-0.733057\pi$
$59$	2.53553	−	6.12132i	0.330098	−	0.796928i	0.998584	−	0.0532027i	$-0.0169429\pi$
$60$		0			0
$61$	0.707107	−	0.292893i	0.0905357	−	0.0375011i	−0.336956	−	0.941520i	$-0.609397\pi$
$61$	0.707107	−	0.292893i	0.0905357	−	0.0375011i	0.427492	+	0.904019i	$0.359397\pi$
$62$		0			0
$63$	−0.585786			−0.0738022
$64$		0			0
$65$	−6.24264			−0.774304
$66$		0			0
$67$	3.70711	−	1.53553i	0.452895	−	0.187595i	−0.144563	−	0.989496i	$-0.546178\pi$
$67$	3.70711	−	1.53553i	0.452895	−	0.187595i	0.597458	+	0.801900i	$0.296178\pi$
$68$		0			0
$69$	−0.171573	+	0.414214i	−0.0206549	+	0.0498655i
$70$		0			0
$71$	0.171573	+	0.171573i	0.0203620	+	0.0203620i	0.717214	−	0.696853i	$-0.245417\pi$
$71$	0.171573	+	0.171573i	0.0203620	+	0.0203620i	−0.696853	+	0.717214i	$0.745417\pi$
$72$		0			0
$73$	−7.00000	+	7.00000i	−0.819288	+	0.819288i	−0.986005	−	0.166717i	$-0.946683\pi$
$73$	−7.00000	+	7.00000i	−0.819288	+	0.819288i	0.166717	+	0.986005i	$0.446683\pi$
$74$		0			0
$75$	−10.9497	−	4.53553i	−1.26437	−	0.523718i
$76$		0			0
$77$	−0.171573	−	0.414214i	−0.0195525	−	0.0472040i
$78$		0			0
$79$		−	6.00000i		−	0.675053i	−0.941316	−	0.337526i	$-0.890410\pi$
$79$		−	6.00000i		−	0.675053i	0.941316	−	0.337526i	$-0.109590\pi$
$80$		0			0
$81$			10.0711i			1.11901i
$82$		0			0
$83$	−2.53553	−	6.12132i	−0.278311	−	0.671902i	0.721478	−	0.692437i	$-0.243463\pi$
$83$	−2.53553	−	6.12132i	−0.278311	−	0.671902i	−0.999789	+	0.0205350i	$0.993463\pi$
$84$		0			0
$85$	−8.82843	−	3.65685i	−0.957577	−	0.396642i
$86$		0			0
$87$	3.82843	−	3.82843i	0.410450	−	0.410450i
$88$		0			0
$89$	2.65685	+	2.65685i	0.281626	+	0.281626i	0.833757	−	0.552131i	$-0.186185\pi$
$89$	2.65685	+	2.65685i	0.281626	+	0.281626i	−0.552131	+	0.833757i	$0.686185\pi$
$90$		0			0
$91$	−1.00000	+	2.41421i	−0.104828	+	0.253078i
$92$		0			0
$93$	−6.82843	+	2.82843i	−0.708075	+	0.293294i
$94$		0			0
$95$	20.2426			2.07685
$96$		0			0
$97$	−1.51472			−0.153796			−0.0768982	−	0.997039i	$-0.524502\pi$
$97$	−1.51472			−0.153796			−0.0768982	+	0.997039i	$0.524502\pi$
$98$		0			0
$99$	0.121320	−	0.0502525i	0.0121932	−	0.00505057i
$100$		0			0
$101$	−4.70711	+	11.3640i	−0.468375	+	1.13076i	0.496498	+	0.868038i	$0.334619\pi$
$101$	−4.70711	+	11.3640i	−0.468375	+	1.13076i	−0.964873	+	0.262718i	$0.915381\pi$
$102$		0			0
$103$	7.48528	+	7.48528i	0.737547	+	0.737547i	0.972103	−	0.234556i	$-0.0753636\pi$
$103$	7.48528	+	7.48528i	0.737547	+	0.737547i	−0.234556	+	0.972103i	$0.575364\pi$
$104$		0			0
$105$	−6.24264	+	6.24264i	−0.609219	+	0.609219i
$106$		0			0
$107$	0.292893	+	0.121320i	0.0283151	+	0.0117285i	0.396796	−	0.917907i	$-0.370122\pi$
$107$	0.292893	+	0.121320i	0.0283151	+	0.0117285i	−0.368481	+	0.929635i	$0.620122\pi$
$108$		0			0
$109$	1.77817	+	4.29289i	0.170318	+	0.411185i	0.985873	−	0.167496i	$-0.0535680\pi$
$109$	1.77817	+	4.29289i	0.170318	+	0.411185i	−0.815555	+	0.578680i	$0.803568\pi$
$110$		0			0
$111$			3.41421i			0.324063i
$112$		0			0
$113$			17.6569i			1.66102i	0.557006	+	0.830509i	$0.311950\pi$
$113$			17.6569i			1.66102i	−0.557006	+	0.830509i	$0.688050\pi$
$114$		0			0
$115$	0.313708	+	0.757359i	0.0292535	+	0.0706241i
$116$		0			0
$117$	−0.707107	−	0.292893i	−0.0653720	−	0.0270780i
$118$		0			0
$119$	−2.82843	+	2.82843i	−0.259281	+	0.259281i
$120$		0			0
$121$	−7.70711	−	7.70711i	−0.700646	−	0.700646i
$122$		0			0
$123$	5.82843	−	14.0711i	0.525532	−	1.26875i
$124$		0			0
$125$	−4.41421	+	1.82843i	−0.394819	+	0.163539i
$126$		0			0
$127$	−20.9706			−1.86084			−0.930418	−	0.366499i	$-0.880556\pi$
$127$	−20.9706			−1.86084			−0.930418	+	0.366499i	$0.880556\pi$
$128$		0			0
$129$	15.8995			1.39987
$130$		0			0
$131$	−8.77817	+	3.63604i	−0.766953	+	0.317682i	−0.731637	−	0.681694i	$-0.761244\pi$
$131$	−8.77817	+	3.63604i	−0.766953	+	0.317682i	−0.0353153	+	0.999376i	$0.511244\pi$
$132$		0			0
$133$	3.24264	−	7.82843i	0.281173	−	0.678811i
$134$		0			0
$135$	11.4142	+	11.4142i	0.982379	+	0.982379i
$136$		0			0
$137$	−2.65685	+	2.65685i	−0.226990	+	0.226990i	−0.811434	−	0.584444i	$-0.801313\pi$
$137$	−2.65685	+	2.65685i	−0.226990	+	0.226990i	0.584444	+	0.811434i	$0.301313\pi$
$138$		0			0
$139$	−12.5355	−	5.19239i	−1.06325	−	0.440413i	−0.218646	−	0.975804i	$-0.570164\pi$
$139$	−12.5355	−	5.19239i	−1.06325	−	0.440413i	−0.844604	+	0.535392i	$0.820164\pi$
$140$		0			0
$141$	8.24264	+	19.8995i	0.694156	+	1.67584i
$142$		0			0
$143$		−	0.585786i		−	0.0489859i
$144$		0			0
$145$		−	9.89949i		−	0.822108i
$146$		0			0
$147$	−3.53553	−	8.53553i	−0.291606	−	0.703999i
$148$		0			0
$149$	13.5355	+	5.60660i	1.10887	+	0.459311i	0.860550	−	0.509366i	$-0.170120\pi$
$149$	13.5355	+	5.60660i	1.10887	+	0.459311i	0.248324	+	0.968677i	$0.420120\pi$
$150$		0			0
$151$	−15.4853	+	15.4853i	−1.26017	+	1.26017i	−0.309166	+	0.951008i	$0.600050\pi$
$151$	−15.4853	+	15.4853i	−1.26017	+	1.26017i	−0.951008	+	0.309166i	$0.899950\pi$
$152$		0			0
$153$	−0.828427	−	0.828427i	−0.0669744	−	0.0669744i
$154$		0			0
$155$	−5.17157	+	12.4853i	−0.415391	+	1.00284i
$156$		0			0
$157$	0.707107	−	0.292893i	0.0564333	−	0.0233754i	−0.354288	−	0.935136i	$-0.615277\pi$
$157$	0.707107	−	0.292893i	0.0564333	−	0.0233754i	0.410722	+	0.911761i	$0.365277\pi$
$158$		0			0
$159$	15.0711			1.19521
$160$		0			0
$161$	0.343146			0.0270437
$162$		0			0
$163$	18.1924	−	7.53553i	1.42494	−	0.590229i	0.468842	−	0.883282i	$-0.344671\pi$
$163$	18.1924	−	7.53553i	1.42494	−	0.590229i	0.956096	+	0.293054i	$0.0946714\pi$
$164$		0			0
$165$	0.757359	−	1.82843i	0.0589603	−	0.142343i
$166$		0			0
$167$	−3.34315	−	3.34315i	−0.258700	−	0.258700i	0.565825	−	0.824525i	$-0.308558\pi$
$167$	−3.34315	−	3.34315i	−0.258700	−	0.258700i	−0.824525	+	0.565825i	$0.808558\pi$
$168$		0			0
$169$	6.77817	−	6.77817i	0.521398	−	0.521398i
$170$		0			0
$171$	2.29289	+	0.949747i	0.175342	+	0.0726290i
$172$		0			0
$173$	0.464466	+	1.12132i	0.0353127	+	0.0852524i	0.940552	−	0.339650i	$-0.110309\pi$
$173$	0.464466	+	1.12132i	0.0353127	+	0.0852524i	−0.905239	+	0.424902i	$0.860309\pi$
$174$		0			0
$175$			9.07107i			0.685708i
$176$		0			0
$177$		−	12.2426i		−	0.920213i
$178$		0			0
$179$	5.94975	+	14.3640i	0.444705	+	1.07361i	0.974278	+	0.225349i	$0.0723521\pi$
$179$	5.94975	+	14.3640i	0.444705	+	1.07361i	−0.529573	+	0.848264i	$0.677648\pi$
$180$		0			0
$181$	−5.29289	−	2.19239i	−0.393418	−	0.162959i	0.177200	−	0.984175i	$-0.443296\pi$
$181$	−5.29289	−	2.19239i	−0.393418	−	0.162959i	−0.570618	+	0.821216i	$0.693296\pi$
$182$		0			0
$183$	1.00000	−	1.00000i	0.0739221	−	0.0739221i
$184$		0			0
$185$	4.41421	+	4.41421i	0.324539	+	0.324539i
$186$		0			0
$187$	0.343146	−	0.828427i	0.0250933	−	0.0605806i
$188$		0			0
$189$	6.24264	−	2.58579i	0.454085	−	0.188088i
$190$		0			0
$191$	−12.0000			−0.868290			−0.434145	−	0.900843i	$-0.642949\pi$
$191$	−12.0000			−0.868290			−0.434145	+	0.900843i	$0.642949\pi$
$192$		0			0
$193$	−18.4853			−1.33060			−0.665300	−	0.746576i	$-0.731696\pi$
$193$	−18.4853			−1.33060			−0.665300	+	0.746576i	$0.731696\pi$
$194$		0			0
$195$	−10.6569	+	4.41421i	−0.763153	+	0.316108i
$196$		0			0
$197$	−7.19239	+	17.3640i	−0.512436	+	1.23713i	0.430025	+	0.902817i	$0.358505\pi$
$197$	−7.19239	+	17.3640i	−0.512436	+	1.23713i	−0.942462	+	0.334314i	$0.891495\pi$
$198$		0			0
$199$	−17.9706	−	17.9706i	−1.27390	−	1.27390i	−0.944025	−	0.329875i	$-0.892994\pi$
$199$	−17.9706	−	17.9706i	−1.27390	−	1.27390i	−0.329875	−	0.944025i	$-0.607006\pi$
$200$		0			0
$201$	5.24264	−	5.24264i	0.369787	−	0.369787i
$202$		0			0
$203$	−3.82843	−	1.58579i	−0.268703	−	0.111300i
$204$		0			0
$205$	−10.6569	−	25.7279i	−0.744307	−	1.79692i
$206$		0			0
$207$			0.100505i			0.00698558i
$208$		0			0
$209$			1.89949i			0.131391i
$210$		0			0
$211$	−0.192388	−	0.464466i	−0.0132445	−	0.0319752i	0.917119	−	0.398614i	$-0.130509\pi$
$211$	−0.192388	−	0.464466i	−0.0132445	−	0.0319752i	−0.930363	+	0.366639i	$0.880509\pi$
$212$		0			0
$213$	0.414214	+	0.171573i	0.0283814	+	0.0117560i
$214$		0			0
$215$	20.5563	−	20.5563i	1.40193	−	1.40193i
$216$		0			0
$217$	4.00000	+	4.00000i	0.271538	+	0.271538i
$218$		0			0
$219$	−7.00000	+	16.8995i	−0.473016	+	1.14196i
$220$		0			0
$221$	−4.82843	+	2.00000i	−0.324795	+	0.134535i
$222$		0			0
$223$	12.9706			0.868573			0.434287	−	0.900775i	$-0.357001\pi$
$223$	12.9706			0.868573			0.434287	+	0.900775i	$0.357001\pi$
$224$		0			0
$225$	−2.65685			−0.177124
$226$		0			0
$227$	−6.29289	+	2.60660i	−0.417674	+	0.173006i	−0.581616	−	0.813464i	$-0.697579\pi$
$227$	−6.29289	+	2.60660i	−0.417674	+	0.173006i	0.163942	+	0.986470i	$0.447579\pi$
$228$		0			0
$229$	10.2635	−	24.7782i	0.678228	−	1.63739i	−0.0890139	−	0.996030i	$-0.528372\pi$
$229$	10.2635	−	24.7782i	0.678228	−	1.63739i	0.767242	−	0.641357i	$-0.221628\pi$
$230$		0			0
$231$	−0.585786	−	0.585786i	−0.0385419	−	0.0385419i
$232$		0			0
$233$	−8.65685	+	8.65685i	−0.567129	+	0.567129i	−0.931323	−	0.364194i	$-0.881345\pi$
$233$	−8.65685	+	8.65685i	−0.567129	+	0.567129i	0.364194	+	0.931323i	$0.381345\pi$
$234$		0			0
$235$	36.3848	+	15.0711i	2.37348	+	0.983128i
$236$		0			0
$237$	−4.24264	−	10.2426i	−0.275589	−	0.665331i
$238$		0			0
$239$		−	17.3137i		−	1.11993i	−0.828516	−	0.559965i	$-0.810814\pi$
$239$		−	17.3137i		−	1.11993i	0.828516	−	0.559965i	$-0.189186\pi$
$240$		0			0
$241$		−	8.48528i		−	0.546585i	−0.961931	−	0.273293i	$-0.911887\pi$
$241$		−	8.48528i		−	0.546585i	0.961931	−	0.273293i	$-0.0881127\pi$
$242$		0			0
$243$	1.63604	+	3.94975i	0.104952	+	0.253376i
$244$		0			0
$245$	−15.6066	−	6.46447i	−0.997069	−	0.413000i
$246$		0			0
$247$	7.82843	−	7.82843i	0.498111	−	0.498111i
$248$		0			0
$249$	−8.65685	−	8.65685i	−0.548606	−	0.548606i
$250$		0			0
$251$	6.05025	−	14.6066i	0.381889	−	0.921961i	−0.609712	−	0.792623i	$-0.708715\pi$
$251$	6.05025	−	14.6066i	0.381889	−	0.921961i	0.991601	−	0.129338i	$-0.0412851\pi$
$252$		0			0
$253$	−0.0710678	+	0.0294373i	−0.00446800	+	0.00185070i
$254$		0			0
$255$	−17.6569			−1.10572
$256$		0			0
$257$	6.00000			0.374270			0.187135	−	0.982334i	$-0.440080\pi$
$257$	6.00000			0.374270			0.187135	+	0.982334i	$0.440080\pi$
$258$		0			0
$259$	2.41421	−	1.00000i	0.150012	−	0.0621370i
$260$		0			0
$261$	0.464466	−	1.12132i	0.0287497	−	0.0694080i
$262$		0			0
$263$	0.171573	+	0.171573i	0.0105796	+	0.0105796i	0.712377	−	0.701797i	$-0.247619\pi$
$263$	0.171573	+	0.171573i	0.0105796	+	0.0105796i	−0.701797	+	0.712377i	$0.747619\pi$
$264$		0			0
$265$	19.4853	−	19.4853i	1.19697	−	1.19697i
$266$		0			0
$267$	6.41421	+	2.65685i	0.392543	+	0.162597i
$268$		0			0
$269$	−2.02082	−	4.87868i	−0.123211	−	0.297458i	0.850224	−	0.526421i	$-0.176467\pi$
$269$	−2.02082	−	4.87868i	−0.123211	−	0.297458i	−0.973435	+	0.228963i	$0.926467\pi$
$270$		0			0
$271$		−	18.0000i		−	1.09342i	−0.837321	−	0.546711i	$-0.815880\pi$
$271$		−	18.0000i		−	1.09342i	0.837321	−	0.546711i	$-0.184120\pi$
$272$		0			0
$273$			4.82843i			0.292230i
$274$		0			0
$275$	−0.778175	−	1.87868i	−0.0469257	−	0.113289i
$276$		0			0
$277$	0.707107	+	0.292893i	0.0424859	+	0.0175982i	0.403825	−	0.914836i	$-0.367680\pi$
$277$	0.707107	+	0.292893i	0.0424859	+	0.0175982i	−0.361339	+	0.932434i	$0.617680\pi$
$278$		0			0
$279$	−1.17157	+	1.17157i	−0.0701402	+	0.0701402i
$280$		0			0
$281$	6.17157	+	6.17157i	0.368165	+	0.368165i	0.866808	−	0.498643i	$-0.166168\pi$
$281$	6.17157	+	6.17157i	0.368165	+	0.368165i	−0.498643	+	0.866808i	$0.666168\pi$
$282$		0			0
$283$	4.05025	−	9.77817i	0.240763	−	0.581252i	−0.756596	−	0.653882i	$-0.773139\pi$
$283$	4.05025	−	9.77817i	0.240763	−	0.581252i	0.997359	+	0.0726300i	$0.0231392\pi$
$284$		0			0
$285$	34.5563	−	14.3137i	2.04694	−	0.847871i
$286$		0			0
$287$	−11.6569			−0.688082
$288$		0			0
$289$	9.00000			0.529412
$290$		0			0
$291$	−2.58579	+	1.07107i	−0.151581	+	0.0627871i
$292$		0			0
$293$	4.80761	−	11.6066i	0.280864	−	0.678065i	−0.718993	−	0.695018i	$-0.755397\pi$
$293$	4.80761	−	11.6066i	0.280864	−	0.678065i	0.999856	+	0.0169528i	$0.00539650\pi$
$294$		0			0
$295$	−15.8284	−	15.8284i	−0.921567	−	0.921567i
$296$		0			0
$297$	−1.07107	+	1.07107i	−0.0621497	+	0.0621497i
$298$		0			0
$299$	0.414214	+	0.171573i	0.0239546	+	0.00992232i
$300$		0			0
$301$	−4.65685	−	11.2426i	−0.268417	−	0.648015i
$302$		0			0
$303$			22.7279i			1.30569i
$304$		0			0
$305$		−	2.58579i		−	0.148062i
$306$		0			0
$307$	−1.22183	−	2.94975i	−0.0697333	−	0.168351i	0.885170	−	0.465267i	$-0.154042\pi$
$307$	−1.22183	−	2.94975i	−0.0697333	−	0.168351i	−0.954904	+	0.296916i	$0.904042\pi$
$308$		0			0
$309$	18.0711	+	7.48528i	1.02803	+	0.425823i
$310$		0			0
$311$	−8.65685	+	8.65685i	−0.490885	+	0.490885i	−0.908585	−	0.417700i	$-0.862836\pi$
$311$	−8.65685	+	8.65685i	−0.490885	+	0.490885i	0.417700	+	0.908585i	$0.362836\pi$
$312$		0			0
$313$	−9.48528	−	9.48528i	−0.536140	−	0.536140i	0.386253	−	0.922393i	$-0.373769\pi$
$313$	−9.48528	−	9.48528i	−0.536140	−	0.536140i	−0.922393	+	0.386253i	$0.873769\pi$
$314$		0			0
$315$	−0.757359	+	1.82843i	−0.0426724	+	0.103020i
$316$		0			0
$317$	11.1924	−	4.63604i	0.628627	−	0.260386i	−0.0455425	−	0.998962i	$-0.514502\pi$
$317$	11.1924	−	4.63604i	0.628627	−	0.260386i	0.674170	+	0.738577i	$0.264502\pi$
$318$		0			0
$319$	0.928932			0.0520102
$320$		0			0
$321$	0.585786			0.0326954
$322$		0			0
$323$	15.6569	−	6.48528i	0.871171	−	0.360851i
$324$		0			0
$325$	−4.53553	+	10.9497i	−0.251586	+	0.607383i
$326$		0			0
$327$	6.07107	+	6.07107i	0.335731	+	0.335731i
$328$		0			0
$329$	11.6569	−	11.6569i	0.642663	−	0.642663i
$330$		0			0
$331$	−6.53553	−	2.70711i	−0.359225	−	0.148796i	0.195769	−	0.980650i	$-0.437280\pi$
$331$	−6.53553	−	2.70711i	−0.359225	−	0.148796i	−0.554995	+	0.831854i	$0.687280\pi$
$332$		0			0
$333$	0.292893	+	0.707107i	0.0160504	+	0.0387492i
$334$		0			0
$335$		−	13.5563i		−	0.740662i
$336$		0			0
$337$		−	16.9706i		−	0.924445i	−0.886764	−	0.462223i	$-0.847052\pi$
$337$		−	16.9706i		−	0.924445i	0.886764	−	0.462223i	$-0.152948\pi$
$338$		0			0
$339$	12.4853	+	30.1421i	0.678107	+	1.63710i
$340$		0			0
$341$	−1.17157	−	0.485281i	−0.0634442	−	0.0262795i
$342$		0			0
$343$	−12.0000	+	12.0000i	−0.647939	+	0.647939i
$344$		0			0
$345$	1.07107	+	1.07107i	0.0576644	+	0.0576644i
$346$		0			0
$347$	−5.94975	+	14.3640i	−0.319399	+	0.771098i	0.679887	+	0.733317i	$0.262029\pi$
$347$	−5.94975	+	14.3640i	−0.319399	+	0.771098i	−0.999286	+	0.0377808i	$0.987971\pi$
$348$		0			0
$349$	−25.7782	+	10.6777i	−1.37987	+	0.571563i	−0.944448	−	0.328662i	$-0.893402\pi$
$349$	−25.7782	+	10.6777i	−1.37987	+	0.571563i	−0.435426	+	0.900224i	$0.643402\pi$
$350$		0			0
$351$	8.82843			0.471227
$352$		0			0
$353$	6.00000			0.319348			0.159674	−	0.987170i	$-0.448956\pi$
$353$	6.00000			0.319348			0.159674	+	0.987170i	$0.448956\pi$
$354$		0			0
$355$	0.757359	−	0.313708i	0.0401965	−	0.0166499i
$356$		0			0
$357$	−2.82843	+	6.82843i	−0.149696	+	0.361399i
$358$		0			0
$359$	12.1716	+	12.1716i	0.642391	+	0.642391i	0.951143	−	0.308752i	$-0.0999112\pi$
$359$	12.1716	+	12.1716i	0.642391	+	0.642391i	−0.308752	+	0.951143i	$0.599911\pi$
$360$		0			0
$361$	−11.9497	+	11.9497i	−0.628934	+	0.628934i
$362$		0			0
$363$	−18.6066	−	7.70711i	−0.976593	−	0.404518i
$364$		0			0
$365$	12.7990	+	30.8995i	0.669930	+	1.61735i
$366$		0			0
$367$			6.00000i			0.313197i	0.987662	+	0.156599i	$0.0500529\pi$
$367$			6.00000i			0.313197i	−0.987662	+	0.156599i	$0.949947\pi$
$368$		0			0
$369$		−	3.41421i		−	0.177737i
$370$		0			0
$371$	−4.41421	−	10.6569i	−0.229175	−	0.553276i
$372$		0			0
$373$	−28.2635	−	11.7071i	−1.46343	−	0.606171i	−0.498077	−	0.867133i	$-0.665960\pi$
$373$	−28.2635	−	11.7071i	−1.46343	−	0.606171i	−0.965349	+	0.260962i	$0.915960\pi$
$374$		0			0
$375$	−6.24264	+	6.24264i	−0.322369	+	0.322369i
$376$		0			0
$377$	−3.82843	−	3.82843i	−0.197174	−	0.197174i
$378$		0			0
$379$	−8.97918	+	21.6777i	−0.461230	+	1.11351i	0.506663	+	0.862144i	$0.330879\pi$
$379$	−8.97918	+	21.6777i	−0.461230	+	1.11351i	−0.967893	+	0.251363i	$0.919121\pi$
$380$		0			0
$381$	−35.7990	+	14.8284i	−1.83404	+	0.759683i
$382$		0			0
$383$	16.9706			0.867155			0.433578	−	0.901116i	$-0.357251\pi$
$383$	16.9706			0.867155			0.433578	+	0.901116i	$0.357251\pi$
$384$		0			0
$385$	−1.51472			−0.0771972
$386$		0			0
$387$	3.29289	−	1.36396i	0.167387	−	0.0693340i
$388$		0			0
$389$	12.2635	−	29.6066i	0.621782	−	1.50111i	−0.227827	−	0.973702i	$-0.573162\pi$
$389$	12.2635	−	29.6066i	0.621782	−	1.50111i	0.849609	−	0.527413i	$-0.176838\pi$
$390$		0			0
$391$	0.485281	+	0.485281i	0.0245417	+	0.0245417i
$392$		0			0
$393$	−12.4142	+	12.4142i	−0.626214	+	0.626214i
$394$		0			0
$395$	−18.7279	−	7.75736i	−0.942304	−	0.390315i
$396$		0			0
$397$	10.2635	+	24.7782i	0.515108	+	1.24358i	0.940877	+	0.338749i	$0.110004\pi$
$397$	10.2635	+	24.7782i	0.515108	+	1.24358i	−0.425769	+	0.904832i	$0.639996\pi$
$398$		0			0
$399$		−	15.6569i		−	0.783823i
$400$		0			0
$401$		−	2.82843i		−	0.141245i	−0.997503	−	0.0706225i	$-0.977501\pi$
$401$		−	2.82843i		−	0.141245i	0.997503	−	0.0706225i	$-0.0224986\pi$
$402$		0			0
$403$	2.82843	+	6.82843i	0.140894	+	0.340148i
$404$		0			0
$405$	31.4350	+	13.0208i	1.56202	+	0.647010i
$406$		0			0
$407$	−0.414214	+	0.414214i	−0.0205318	+	0.0205318i
$408$		0			0
$409$	−4.51472	−	4.51472i	−0.223238	−	0.223238i	0.586622	−	0.809861i	$-0.300457\pi$
$409$	−4.51472	−	4.51472i	−0.223238	−	0.223238i	−0.809861	+	0.586622i	$0.800457\pi$
$410$		0			0
$411$	−2.65685	+	6.41421i	−0.131053	+	0.316390i
$412$		0			0
$413$	−8.65685	+	3.58579i	−0.425976	+	0.176445i
$414$		0			0
$415$	−22.3848			−1.09883
$416$		0			0
$417$	−25.0711			−1.22774
$418$		0			0
$419$	−20.7782	+	8.60660i	−1.01508	+	0.420460i	−0.827306	−	0.561752i	$-0.810127\pi$
$419$	−20.7782	+	8.60660i	−1.01508	+	0.420460i	−0.187775	+	0.982212i	$0.560127\pi$
$420$		0			0
$421$	−3.19239	+	7.70711i	−0.155587	+	0.375621i	−0.982382	−	0.186882i	$-0.940162\pi$
$421$	−3.19239	+	7.70711i	−0.155587	+	0.375621i	0.826795	+	0.562504i	$0.190162\pi$
$422$		0			0
$423$	3.41421	+	3.41421i	0.166005	+	0.166005i
$424$		0			0
$425$	−12.8284	+	12.8284i	−0.622270	+	0.622270i
$426$		0			0
$427$	−1.00000	−	0.414214i	−0.0483934	−	0.0200452i
$428$		0			0
$429$	−0.414214	−	1.00000i	−0.0199984	−	0.0482805i
$430$		0			0
$431$			23.6569i			1.13951i	0.821814	+	0.569755i	$0.192962\pi$
$431$			23.6569i			1.13951i	−0.821814	+	0.569755i	$0.807038\pi$
$432$		0			0
$433$			32.4853i			1.56114i	0.625067	+	0.780571i	$0.285072\pi$
$433$			32.4853i			1.56114i	−0.625067	+	0.780571i	$0.714928\pi$
$434$		0			0
$435$	−7.00000	−	16.8995i	−0.335624	−	0.810269i
$436$		0			0
$437$	−1.34315	−	0.556349i	−0.0642514	−	0.0266138i
$438$		0			0
$439$	17.0000	−	17.0000i	0.811366	−	0.811366i	−0.173473	−	0.984839i	$-0.555499\pi$
$439$	17.0000	−	17.0000i	0.811366	−	0.811366i	0.984839	+	0.173473i	$0.0554989\pi$
$440$		0			0
$441$	−1.46447	−	1.46447i	−0.0697365	−	0.0697365i
$442$		0			0
$443$	8.53553	−	20.6066i	0.405535	−	0.979049i	−0.580762	−	0.814073i	$-0.697245\pi$
$443$	8.53553	−	20.6066i	0.405535	−	0.979049i	0.986298	−	0.164976i	$-0.0527546\pi$
$444$		0			0
$445$	11.7279	−	4.85786i	0.555957	−	0.230285i
$446$		0			0
$447$	27.0711			1.28042
$448$		0			0
$449$	31.4558			1.48449			0.742247	−	0.670127i	$-0.233760\pi$
$449$	31.4558			1.48449			0.742247	+	0.670127i	$0.233760\pi$
$450$		0			0
$451$	2.41421	−	1.00000i	0.113681	−	0.0470882i
$452$		0			0
$453$	−15.4853	+	37.3848i	−0.727562	+	1.75649i
$454$		0			0
$455$	6.24264	+	6.24264i	0.292660	+	0.292660i
$456$		0			0
$457$	−9.48528	+	9.48528i	−0.443703	+	0.443703i	−0.893254	−	0.449552i	$-0.851584\pi$
$457$	−9.48528	+	9.48528i	−0.443703	+	0.443703i	0.449552	+	0.893254i	$0.351584\pi$
$458$		0			0
$459$	12.4853	+	5.17157i	0.582763	+	0.241388i
$460$		0			0
$461$	−5.53553	−	13.3640i	−0.257816	−	0.622422i	0.740978	−	0.671529i	$-0.234362\pi$
$461$	−5.53553	−	13.3640i	−0.257816	−	0.622422i	−0.998793	+	0.0491076i	$0.984362\pi$
$462$		0			0
$463$			10.9706i			0.509845i	0.966961	+	0.254923i	$0.0820500\pi$
$463$			10.9706i			0.509845i	−0.966961	+	0.254923i	$0.917950\pi$
$464$		0			0
$465$			24.9706i			1.15798i
$466$		0			0
$467$	−12.0503	−	29.0919i	−0.557619	−	1.34621i	−0.911646	−	0.410977i	$-0.865188\pi$
$467$	−12.0503	−	29.0919i	−0.557619	−	1.34621i	0.354027	−	0.935235i	$-0.384812\pi$
$468$		0			0
$469$	−5.24264	−	2.17157i	−0.242083	−	0.100274i
$470$		0			0
$471$	1.00000	−	1.00000i	0.0460776	−	0.0460776i
$472$		0			0
$473$	1.92893	+	1.92893i	0.0886924	+	0.0886924i
$474$		0			0
$475$	14.7071	−	35.5061i	0.674808	−	1.62913i
$476$		0			0
$477$	3.12132	−	1.29289i	0.142915	−	0.0591975i
$478$		0			0
$479$	−4.97056			−0.227111			−0.113555	−	0.993532i	$-0.536224\pi$
$479$	−4.97056			−0.227111			−0.113555	+	0.993532i	$0.536224\pi$
$480$		0			0
$481$	3.41421			0.155675
$482$		0			0
$483$	0.585786	−	0.242641i	0.0266542	−	0.0110405i
$484$		0			0
$485$	−1.95837	+	4.72792i	−0.0889250	+	0.214684i
$486$		0			0
$487$	11.0000	+	11.0000i	0.498458	+	0.498458i	0.910958	−	0.412500i	$-0.135344\pi$
$487$	11.0000	+	11.0000i	0.498458	+	0.498458i	−0.412500	+	0.910958i	$0.635344\pi$
$488$		0			0
$489$	25.7279	−	25.7279i	1.16346	−	1.16346i
$490$		0			0
$491$	−17.7071	−	7.33452i	−0.799111	−	0.331002i	−0.0545104	−	0.998513i	$-0.517360\pi$
$491$	−17.7071	−	7.33452i	−0.799111	−	0.331002i	−0.744600	+	0.667511i	$0.767360\pi$
$492$		0			0
$493$	−3.17157	−	7.65685i	−0.142840	−	0.344847i
$494$		0			0
$495$		−	0.443651i		−	0.0199406i
$496$		0			0
$497$		−	0.343146i		−	0.0153922i
$498$		0			0
$499$	−3.70711	−	8.94975i	−0.165953	−	0.400646i	0.818924	−	0.573902i	$-0.194571\pi$
$499$	−3.70711	−	8.94975i	−0.165953	−	0.400646i	−0.984877	+	0.173256i	$0.944571\pi$
$500$		0			0
$501$	−8.07107	−	3.34315i	−0.360589	−	0.149361i
$502$		0			0
$503$	−17.1421	+	17.1421i	−0.764330	+	0.764330i	−0.977102	−	0.212772i	$-0.931751\pi$
$503$	−17.1421	+	17.1421i	−0.764330	+	0.764330i	0.212772	+	0.977102i	$0.431751\pi$
$504$		0			0
$505$	29.3848	+	29.3848i	1.30761	+	1.30761i
$506$		0			0
$507$	6.77817	−	16.3640i	0.301029	−	0.726749i
$508$		0			0
$509$	29.1924	−	12.0919i	1.29393	−	0.535963i	0.373776	−	0.927519i	$-0.378063\pi$
$509$	29.1924	−	12.0919i	1.29393	−	0.535963i	0.920154	+	0.391556i	$0.128063\pi$
$510$		0			0
$511$	14.0000			0.619324
$512$		0			0
$513$	−28.6274			−1.26393
$514$		0			0
$515$	33.0416	−	13.6863i	1.45599	−	0.603090i
$516$		0			0
$517$	−1.41421	+	3.41421i	−0.0621970	+	0.150157i
$518$		0			0
$519$	1.58579	+	1.58579i	0.0696083	+	0.0696083i
$520$		0			0
$521$	−14.6569	+	14.6569i	−0.642128	+	0.642128i	−0.951078	−	0.308950i	$-0.900022\pi$
$521$	−14.6569	+	14.6569i	−0.642128	+	0.642128i	0.308950	+	0.951078i	$0.400022\pi$
$522$		0			0
$523$	1.94975	+	0.807612i	0.0852565	+	0.0353144i	0.424904	−	0.905238i	$-0.360308\pi$
$523$	1.94975	+	0.807612i	0.0852565	+	0.0353144i	−0.339648	+	0.940553i	$0.610308\pi$
$524$		0			0
$525$	6.41421	+	15.4853i	0.279939	+	0.675833i
$526$		0			0
$527$			11.3137i			0.492833i
$528$		0			0
$529$			22.9411i			0.997440i
$530$		0			0
$531$	−1.05025	−	2.53553i	−0.0455771	−	0.110033i
$532$		0			0
$533$	−14.0711	−	5.82843i	−0.609486	−	0.252457i
$534$		0			0
$535$	0.757359	−	0.757359i	0.0327435	−	0.0327435i
$536$		0			0
$537$	20.3137	+	20.3137i	0.876601	+	0.876601i
$538$		0			0
$539$	0.606602	−	1.46447i	0.0261282	−	0.0630790i
$540$		0			0
$541$	12.7071	−	5.26346i	0.546321	−	0.226294i	−0.0924135	−	0.995721i	$-0.529458\pi$
$541$	12.7071	−	5.26346i	0.546321	−	0.226294i	0.638735	+	0.769427i	$0.279458\pi$
$542$		0			0
$543$	−10.5858			−0.454280
$544$		0			0
$545$	15.6985			0.672449
$546$		0			0
$547$	−25.2635	+	10.4645i	−1.08019	+	0.447428i	−0.850575	−	0.525854i	$-0.823746\pi$
$547$	−25.2635	+	10.4645i	−1.08019	+	0.447428i	−0.229612	+	0.973282i	$0.573746\pi$
$548$		0			0
$549$	0.121320	−	0.292893i	0.00517783	−	0.0125004i
$550$		0			0
$551$	12.4142	+	12.4142i	0.528863	+	0.528863i
$552$		0			0
$553$	−6.00000	+	6.00000i	−0.255146	+	0.255146i
$554$		0			0
$555$	10.6569	+	4.41421i	0.452358	+	0.187373i
$556$		0			0
$557$	−4.50610	−	10.8787i	−0.190929	−	0.460944i	0.799206	−	0.601057i	$-0.205254\pi$
$557$	−4.50610	−	10.8787i	−0.190929	−	0.460944i	−0.990136	+	0.140113i	$0.955254\pi$
$558$		0			0
$559$		−	15.8995i		−	0.672477i
$560$		0			0
$561$		−	1.65685i		−	0.0699524i
$562$		0			0
$563$	−5.02082	−	12.1213i	−0.211602	−	0.510853i	0.782068	−	0.623194i	$-0.214165\pi$
$563$	−5.02082	−	12.1213i	−0.211602	−	0.510853i	−0.993670	+	0.112341i	$0.964165\pi$
$564$		0			0
$565$	55.1127	+	22.8284i	2.31861	+	0.960399i
$566$		0			0
$567$	10.0711	−	10.0711i	0.422945	−	0.422945i
$568$		0			0
$569$	−3.34315	−	3.34315i	−0.140152	−	0.140152i	0.633550	−	0.773702i	$-0.281597\pi$
$569$	−3.34315	−	3.34315i	−0.140152	−	0.140152i	−0.773702	+	0.633550i	$0.781597\pi$
$570$		0			0
$571$	0.535534	−	1.29289i	0.0224114	−	0.0541059i	−0.912278	−	0.409572i	$-0.865678\pi$
$571$	0.535534	−	1.29289i	0.0224114	−	0.0541059i	0.934689	+	0.355466i	$0.115678\pi$
$572$		0			0
$573$	−20.4853	+	8.48528i	−0.855785	+	0.354478i
$574$		0			0
$575$	1.55635			0.0649042
$576$		0			0
$577$	−14.9706			−0.623233			−0.311616	−	0.950208i	$-0.600870\pi$
$577$	−14.9706			−0.623233			−0.311616	+	0.950208i	$0.600870\pi$
$578$		0			0
$579$	−31.5563	+	13.0711i	−1.31144	+	0.543215i
$580$		0			0
$581$	−3.58579	+	8.65685i	−0.148763	+	0.359147i
$582$		0			0
$583$	1.82843	+	1.82843i	0.0757257	+	0.0757257i
$584$		0			0
$585$	−1.82843	+	1.82843i	−0.0755962	+	0.0755962i
$586$		0			0
$587$	20.7782	+	8.60660i	0.857607	+	0.355232i	0.767771	−	0.640724i	$-0.221366\pi$
$587$	20.7782	+	8.60660i	0.857607	+	0.355232i	0.0898359	+	0.995957i	$0.471366\pi$
$588$		0			0
$589$	−9.17157	−	22.1421i	−0.377908	−	0.912351i
$590$		0			0
$591$			34.7279i			1.42852i
$592$		0			0
$593$		−	28.2843i		−	1.16150i	−0.814083	−	0.580748i	$-0.802760\pi$
$593$		−	28.2843i		−	1.16150i	0.814083	−	0.580748i	$-0.197240\pi$
$594$		0			0
$595$	5.17157	+	12.4853i	0.212014	+	0.511847i
$596$		0			0
$597$	−43.3848	−	17.9706i	−1.77562	−	0.735486i
$598$		0			0
$599$	15.3431	−	15.3431i	0.626904	−	0.626904i	−0.320384	−	0.947288i	$-0.603812\pi$
$599$	15.3431	−	15.3431i	0.626904	−	0.626904i	0.947288	+	0.320384i	$0.103812\pi$
$600$		0			0
$601$	−11.9706	−	11.9706i	−0.488289	−	0.488289i	0.419477	−	0.907766i	$-0.362214\pi$
$601$	−11.9706	−	11.9706i	−0.488289	−	0.488289i	−0.907766	+	0.419477i	$0.862214\pi$
$602$		0			0
$603$	0.636039	−	1.53553i	0.0259015	−	0.0625318i
$604$		0			0
$605$	−34.0208	+	14.0919i	−1.38314	+	0.572917i
$606$		0			0
$607$	0.970563			0.0393939			0.0196970	−	0.999806i	$-0.493730\pi$
$607$	0.970563			0.0393939			0.0196970	+	0.999806i	$0.493730\pi$
$608$		0			0
$609$	−7.65685			−0.310271
$610$		0			0
$611$	19.8995	−	8.24264i	0.805047	−	0.333462i
$612$		0			0
$613$	−15.1924	+	36.6777i	−0.613615	+	1.48140i	0.245387	+	0.969425i	$0.421085\pi$
$613$	−15.1924	+	36.6777i	−0.613615	+	1.48140i	−0.859002	+	0.511972i	$0.828915\pi$
$614$		0			0
$615$	−36.3848	−	36.3848i	−1.46718	−	1.46718i
$616$		0			0
$617$	16.7990	−	16.7990i	0.676302	−	0.676302i	−0.282859	−	0.959161i	$-0.591283\pi$
$617$	16.7990	−	16.7990i	0.676302	−	0.676302i	0.959161	+	0.282859i	$0.0912830\pi$
$618$		0			0
$619$	−15.0208	−	6.22183i	−0.603738	−	0.250076i	0.0598107	−	0.998210i	$-0.480950\pi$
$619$	−15.0208	−	6.22183i	−0.603738	−	0.250076i	−0.663548	+	0.748133i	$0.730950\pi$
$620$		0			0
$621$	−0.443651	−	1.07107i	−0.0178031	−	0.0429805i
$622$		0			0
$623$		−	5.31371i		−	0.212889i
$624$		0			0
$625$		−	15.9289i		−	0.637157i
$626$		0			0
$627$	1.34315	+	3.24264i	0.0536401	+	0.129499i
$628$		0			0
$629$	4.82843	+	2.00000i	0.192522	+	0.0797452i
$630$		0			0
$631$	18.4558	−	18.4558i	0.734716	−	0.734716i	−0.236834	−	0.971550i	$-0.576110\pi$
$631$	18.4558	−	18.4558i	0.734716	−	0.734716i	0.971550	+	0.236834i	$0.0761099\pi$
$632$		0			0
$633$	−0.656854	−	0.656854i	−0.0261076	−	0.0261076i
$634$		0			0
$635$	−27.1127	+	65.4558i	−1.07593	+	2.59754i
$636$		0			0
$637$	−8.53553	+	3.53553i	−0.338190	+	0.140083i
$638$		0			0
$639$	0.100505			0.00397592
$640$		0			0
$641$	−43.4558			−1.71640			−0.858201	−	0.513313i	$-0.828418\pi$
$641$	−43.4558			−1.71640			−0.858201	+	0.513313i	$0.828418\pi$
$642$		0			0
$643$	−37.2635	+	15.4350i	−1.46953	+	0.608698i	−0.966751	−	0.255719i	$-0.917688\pi$
$643$	−37.2635	+	15.4350i	−1.46953	+	0.608698i	−0.502776	+	0.864417i	$0.667688\pi$
$644$		0			0
$645$	20.5563	−	49.6274i	0.809405	−	1.95408i
$646$		0			0
$647$	−11.8284	−	11.8284i	−0.465023	−	0.465023i	0.435274	−	0.900298i	$-0.356651\pi$
$647$	−11.8284	−	11.8284i	−0.465023	−	0.465023i	−0.900298	+	0.435274i	$0.856651\pi$
$648$		0			0
$649$	1.48528	−	1.48528i	0.0583024	−	0.0583024i
$650$		0			0
$651$	9.65685	+	4.00000i	0.378482	+	0.156772i
$652$		0			0
$653$	14.9497	+	36.0919i	0.585029	+	1.41238i	0.888204	+	0.459450i	$0.151953\pi$
$653$	14.9497	+	36.0919i	0.585029	+	1.41238i	−0.303175	+	0.952935i	$0.598047\pi$
$654$		0			0
$655$			32.1005i			1.25427i
$656$		0			0
$657$			4.10051i			0.159976i
$658$		0			0
$659$	2.43503	+	5.87868i	0.0948553	+	0.229001i	0.964184	−	0.265233i	$-0.0854488\pi$
$659$	2.43503	+	5.87868i	0.0948553	+	0.229001i	−0.869329	+	0.494234i	$0.835449\pi$
$660$		0			0
$661$	18.7071	+	7.74874i	0.727622	+	0.301391i	0.715574	−	0.698536i	$-0.246165\pi$
$661$	18.7071	+	7.74874i	0.727622	+	0.301391i	0.0120477	+	0.999927i	$0.496165\pi$
$662$		0			0
$663$	−6.82843	+	6.82843i	−0.265194	+	0.265194i
$664$		0			0
$665$	−20.2426	−	20.2426i	−0.784976	−	0.784976i
$666$		0			0
$667$	−0.272078	+	0.656854i	−0.0105349	+	0.0254335i
$668$		0			0
$669$	22.1421	−	9.17157i	0.856064	−	0.354593i
$670$		0			0
$671$	0.242641			0.00936704
$672$		0			0
$673$	5.51472			0.212577			0.106288	−	0.994335i	$-0.466103\pi$
$673$	5.51472			0.212577			0.106288	+	0.994335i	$0.466103\pi$
$674$		0			0
$675$	28.3137	−	11.7279i	1.08980	−	0.451408i
$676$		0			0
$677$	2.32233	−	5.60660i	0.0892544	−	0.215479i	−0.872949	−	0.487812i	$-0.837795\pi$
$677$	2.32233	−	5.60660i	0.0892544	−	0.215479i	0.962203	+	0.272333i	$0.0877952\pi$
$678$		0			0
$679$	1.51472	+	1.51472i	0.0581296	+	0.0581296i
$680$		0			0
$681$	−8.89949	+	8.89949i	−0.341029	+	0.341029i
$682$		0			0
$683$	−14.1924	−	5.87868i	−0.543057	−	0.224941i	0.0942543	−	0.995548i	$-0.469953\pi$
$683$	−14.1924	−	5.87868i	−0.543057	−	0.224941i	−0.637311	+	0.770607i	$0.719953\pi$
$684$		0			0
$685$	4.85786	+	11.7279i	0.185609	+	0.448101i
$686$		0			0
$687$		−	49.5563i		−	1.89069i
$688$		0			0
$689$		−	15.0711i		−	0.574162i
$690$		0			0
$691$	11.8076	+	28.5061i	0.449183	+	1.08442i	0.972629	+	0.232364i	$0.0746461\pi$
$691$	11.8076	+	28.5061i	0.449183	+	1.08442i	−0.523446	+	0.852059i	$0.675354\pi$
$692$		0			0
$693$	−0.171573	−	0.0710678i	−0.00651751	−	0.00269964i
$694$		0			0
$695$	−32.4142	+	32.4142i	−1.22954	+	1.22954i
$696$		0			0
$697$	−16.4853	−	16.4853i	−0.624425	−	0.624425i
$698$		0			0
$699$	−8.65685	+	20.8995i	−0.327432	+	0.790491i
$700$		0			0
$701$	17.1924	−	7.12132i	0.649348	−	0.268969i	−0.0336007	−	0.999435i	$-0.510697\pi$
$701$	17.1924	−	7.12132i	0.649348	−	0.268969i	0.682948	+	0.730467i	$0.260697\pi$
$702$		0			0
$703$	−11.0711			−0.417553
$704$		0			0
$705$	72.7696			2.74066
$706$		0			0
$707$	16.0711	−	6.65685i	0.604415	−	0.250357i
$708$		0			0
$709$	2.80761	−	6.77817i	0.105442	−	0.254560i	−0.862349	−	0.506314i	$-0.831008\pi$
$709$	2.80761	−	6.77817i	0.105442	−	0.254560i	0.967791	+	0.251755i	$0.0810076\pi$
$710$		0			0
$711$	−1.75736	−	1.75736i	−0.0659061	−	0.0659061i
$712$		0			0
$713$	0.686292	−	0.686292i	0.0257018	−	0.0257018i
$714$		0			0
$715$	−1.82843	−	0.757359i	−0.0683793	−	0.0283236i
$716$		0			0
$717$	−12.2426	−	29.5563i	−0.457210	−	1.10380i
$718$		0			0
$719$		−	24.3431i		−	0.907846i	−0.891041	−	0.453923i	$-0.850024\pi$
$719$		−	24.3431i		−	0.907846i	0.891041	−	0.453923i	$-0.149976\pi$
$720$		0			0
$721$		−	14.9706i		−	0.557533i
$722$		0			0
$723$	−6.00000	−	14.4853i	−0.223142	−	0.538713i
$724$		0			0
$725$	−17.3640	−	7.19239i	−0.644881	−	0.267119i
$726$		0			0
$727$	−23.9706	+	23.9706i	−0.889019	+	0.889019i	−0.994429	−	0.105410i	$-0.966385\pi$
$727$	−23.9706	+	23.9706i	−0.889019	+	0.889019i	0.105410	+	0.994429i	$0.466385\pi$
$728$		0			0
$729$	−15.7782	−	15.7782i	−0.584377	−	0.584377i
$730$		0			0
$731$	9.31371	−	22.4853i	0.344480	−	0.831648i
$732$		0			0
$733$	−1.77817	+	0.736544i	−0.0656784	+	0.0272049i	−0.415281	−	0.909693i	$-0.636317\pi$
$733$	−1.77817	+	0.736544i	−0.0656784	+	0.0272049i	0.349602	+	0.936898i	$0.386317\pi$
$734$		0			0
$735$	−31.2132			−1.15132
$736$		0			0
$737$	1.27208			0.0468576
$738$		0			0
$739$	18.1924	−	7.53553i	0.669218	−	0.277199i	−0.0220937	−	0.999756i	$-0.507033\pi$
$739$	18.1924	−	7.53553i	0.669218	−	0.277199i	0.691312	+	0.722557i	$0.257033\pi$
$740$		0			0
$741$	7.82843	−	18.8995i	0.287584	−	0.694290i
$742$		0			0
$743$	13.6274	+	13.6274i	0.499941	+	0.499941i	0.911420	−	0.411478i	$-0.134987\pi$
$743$	13.6274	+	13.6274i	0.499941	+	0.499941i	−0.411478	+	0.911420i	$0.634987\pi$
$744$		0			0
$745$	35.0000	−	35.0000i	1.28230	−	1.28230i
$746$		0			0
$747$	−2.53553	−	1.05025i	−0.0927703	−	0.0384267i
$748$		0			0
$749$	−0.171573	−	0.414214i	−0.00626914	−	0.0151350i
$750$		0			0
$751$		−	22.9706i		−	0.838208i	−0.907938	−	0.419104i	$-0.862344\pi$
$751$		−	22.9706i		−	0.838208i	0.907938	−	0.419104i	$-0.137656\pi$
$752$		0			0
$753$		−	29.2132i		−	1.06459i
$754$		0			0
$755$	28.3137	+	68.3553i	1.03044	+	2.48771i
$756$		0			0
$757$	−1.77817	−	0.736544i	−0.0646289	−	0.0267701i	0.350135	−	0.936699i	$-0.386136\pi$
$757$	−1.77817	−	0.736544i	−0.0646289	−	0.0267701i	−0.414764	+	0.909929i	$0.636136\pi$
$758$		0			0
$759$	−0.100505	+	0.100505i	−0.00364810	+	0.00364810i
$760$		0			0
$761$	24.1716	+	24.1716i	0.876219	+	0.876219i	0.993141	−	0.116922i	$-0.0373028\pi$
$761$	24.1716	+	24.1716i	0.876219	+	0.876219i	−0.116922	+	0.993141i	$0.537303\pi$
$762$		0			0
$763$	2.51472	−	6.07107i	0.0910389	−	0.219787i
$764$		0			0
$765$	−3.65685	+	1.51472i	−0.132214	+	0.0547648i
$766$		0			0
$767$	−12.2426			−0.442056
$768$		0			0
$769$	22.4853			0.810840			0.405420	−	0.914131i	$-0.367125\pi$
$769$	22.4853			0.810840			0.405420	+	0.914131i	$0.367125\pi$
$770$		0			0
$771$	10.2426	−	4.24264i	0.368880	−	0.152795i
$772$		0			0
$773$	10.8076	−	26.0919i	0.388723	−	0.938460i	−0.601488	−	0.798882i	$-0.705425\pi$
$773$	10.8076	−	26.0919i	0.388723	−	0.938460i	0.990211	−	0.139578i	$-0.0445747\pi$
$774$		0			0
$775$	18.1421	+	18.1421i	0.651685	+	0.651685i
$776$		0			0
$777$	3.41421	−	3.41421i	0.122484	−	0.122484i
$778$		0			0
$779$	45.6274	+	18.8995i	1.63477	+	0.677145i
$780$		0			0
$781$	0.0294373	+	0.0710678i	0.00105335	+	0.00254301i
$782$		0			0
$783$			14.0000i			0.500319i
$784$		0			0
$785$		−	2.58579i		−	0.0922907i
$786$		0			0
$787$	−3.70711	−	8.94975i	−0.132144	−	0.319024i	0.843933	−	0.536448i	$-0.180234\pi$
$787$	−3.70711	−	8.94975i	−0.132144	−	0.319024i	−0.976077	+	0.217424i	$0.930234\pi$
$788$		0			0
$789$	0.414214	+	0.171573i	0.0147464	+	0.00610816i
$790$		0			0
$791$	17.6569	−	17.6569i	0.627805	−	0.627805i
$792$		0			0
$793$	−1.00000	−	1.00000i	−0.0355110	−	0.0355110i
$794$		0			0
$795$	19.4853	−	47.0416i	0.691072	−	1.66839i
$796$		0			0
$797$	29.1924	−	12.0919i	1.03405	−	0.428316i	0.199876	−	0.979821i	$-0.435946\pi$
$797$	29.1924	−	12.0919i	1.03405	−	0.428316i	0.834172	+	0.551505i	$0.185946\pi$
$798$		0			0
$799$	32.9706			1.16641
$800$		0			0
$801$	1.55635			0.0549909
$802$		0			0
$803$	−2.89949	+	1.20101i	−0.102321	+	0.0423827i
$804$		0			0
$805$	0.443651	−	1.07107i	0.0156366	−	0.0377502i
$806$		0			0
$807$	−6.89949	−	6.89949i	−0.242874	−	0.242874i
$808$		0			0
$809$	0.857864	−	0.857864i	0.0301609	−	0.0301609i	−0.691865	−	0.722026i	$-0.743211\pi$
$809$	0.857864	−	0.857864i	0.0301609	−	0.0301609i	0.722026	+	0.691865i	$0.243211\pi$
$810$		0			0
$811$	−23.5061	−	9.73654i	−0.825411	−	0.341896i	−0.0703264	−	0.997524i	$-0.522404\pi$
$811$	−23.5061	−	9.73654i	−0.825411	−	0.341896i	−0.755084	+	0.655628i	$0.772404\pi$
$812$		0			0
$813$	−12.7279	−	30.7279i	−0.446388	−	1.07768i
$814$		0			0
$815$		−	66.5269i		−	2.33034i
$816$		0			0
$817$			51.5563i			1.80373i
$818$		0			0
$819$	0.414214	+	1.00000i	0.0144738	+	0.0349428i
$820$		0			0
$821$	−0.949747	−	0.393398i	−0.0331464	−	0.0137297i	0.366049	−	0.930596i	$-0.380710\pi$
$821$	−0.949747	−	0.393398i	−0.0331464	−	0.0137297i	−0.399195	+	0.916866i	$0.630710\pi$
$822$		0			0
$823$	−2.02944	+	2.02944i	−0.0707417	+	0.0707417i	−0.741592	−	0.670851i	$-0.765929\pi$
$823$	−2.02944	+	2.02944i	−0.0707417	+	0.0707417i	0.670851	+	0.741592i	$0.265929\pi$
$824$		0			0
$825$	−2.65685	−	2.65685i	−0.0924998	−	0.0924998i
$826$		0			0
$827$	−4.92031	+	11.8787i	−0.171096	+	0.413062i	−0.986047	−	0.166468i	$-0.946764\pi$
$827$	−4.92031	+	11.8787i	−0.171096	+	0.413062i	0.814951	+	0.579530i	$0.196764\pi$
$828$		0			0
$829$	38.1630	−	15.8076i	1.32545	−	0.549021i	0.396099	−	0.918208i	$-0.370364\pi$
$829$	38.1630	−	15.8076i	1.32545	−	0.549021i	0.929355	+	0.369187i	$0.120364\pi$
$830$		0			0
$831$	1.41421			0.0490585
$832$		0			0
$833$	−14.1421			−0.489996
$834$		0			0
$835$	−14.7574	+	6.11270i	−0.510699	+	0.211539i
$836$		0			0
$837$	7.31371	−	17.6569i	0.252799	−	0.610310i
$838$		0			0
$839$	−32.3137	−	32.3137i	−1.11559	−	1.11559i	−0.992380	−	0.123213i	$-0.960680\pi$
$839$	−32.3137	−	32.3137i	−1.11559	−	1.11559i	−0.123213	−	0.992380i	$-0.539320\pi$
$840$		0			0
$841$	−14.4350	+	14.4350i	−0.497760	+	0.497760i
$842$		0			0
$843$	14.8995	+	6.17157i	0.513166	+	0.212560i
$844$		0			0
$845$	−12.3934	−	29.9203i	−0.426346	−	1.02929i
$846$		0			0
$847$			15.4142i			0.529639i
$848$		0			0
$849$		−	19.5563i		−	0.671172i
$850$		0			0
$851$	−0.171573	−	0.414214i	−0.00588144	−	0.0141991i
$852$		0			0
$853$	−2.80761	−	1.16295i	−0.0961308	−	0.0398187i	0.334100	−	0.942538i	$-0.391568\pi$
$853$	−2.80761	−	1.16295i	−0.0961308	−	0.0398187i	−0.430231	+	0.902719i	$0.641568\pi$
$854$		0			0
$855$	5.92893	−	5.92893i	0.202765	−	0.202765i
$856$		0			0
$857$	−32.3137	−	32.3137i	−1.10382	−	1.10382i	−0.993946	−	0.109869i	$-0.964957\pi$
$857$	−32.3137	−	32.3137i	−1.10382	−	1.10382i	−0.109869	−	0.993946i	$-0.535043\pi$
$858$		0			0
$859$	−13.9497	+	33.6777i	−0.475959	+	1.14907i	0.485529	+	0.874221i	$0.338627\pi$
$859$	−13.9497	+	33.6777i	−0.475959	+	1.14907i	−0.961488	+	0.274847i	$0.911373\pi$
$860$		0			0
$861$	−19.8995	+	8.24264i	−0.678173	+	0.280908i
$862$		0			0
$863$	−45.9411			−1.56385			−0.781927	−	0.623370i	$-0.785763\pi$
$863$	−45.9411			−1.56385			−0.781927	+	0.623370i	$0.785763\pi$
$864$		0			0
$865$	4.10051			0.139421
$866$		0			0
$867$	15.3640	−	6.36396i	0.521787	−	0.216131i
$868$		0			0
$869$	0.727922	−	1.75736i	0.0246931	−	0.0596143i
$870$		0			0
$871$	−5.24264	−	5.24264i	−0.177640	−	0.177640i
$872$		0			0
$873$	−0.443651	+	0.443651i	−0.0150153	+	0.0150153i
$874$		0			0
$875$	6.24264	+	2.58579i	0.211040	+	0.0874155i
$876$		0			0
$877$	13.7782	+	33.2635i	0.465256	+	1.12323i	0.966211	+	0.257754i	$0.0829823\pi$
$877$	13.7782	+	33.2635i	0.465256	+	1.12323i	−0.500955	+	0.865473i	$0.667018\pi$
$878$		0			0
$879$		−	23.2132i		−	0.782962i
$880$		0			0
$881$			22.6274i			0.762337i	0.924506	+	0.381169i	$0.124478\pi$
$881$			22.6274i			0.762337i	−0.924506	+	0.381169i	$0.875522\pi$
$882$		0			0
$883$	−19.6482	−	47.4350i	−0.661216	−	1.59632i	−0.795901	−	0.605427i	$-0.793002\pi$
$883$	−19.6482	−	47.4350i	−0.661216	−	1.59632i	0.134685	−	0.990888i	$-0.456998\pi$
$884$		0			0
$885$	−38.2132	−	15.8284i	−1.28452	−	0.532067i
$886$		0			0
$887$	20.3137	−	20.3137i	0.682068	−	0.682068i	−0.278398	−	0.960466i	$-0.589803\pi$
$887$	20.3137	−	20.3137i	0.682068	−	0.682068i	0.960466	+	0.278398i	$0.0898035\pi$
$888$		0			0
$889$	20.9706	+	20.9706i	0.703330	+	0.703330i
$890$		0			0
$891$	−1.22183	+	2.94975i	−0.0409327	+	0.0988203i
$892$		0			0
$893$	−64.5269	+	26.7279i	−2.15931	+	0.894416i
$894$		0			0
$895$	52.5269			1.75578
$896$		0			0
$897$	0.828427			0.0276604
$898$		0			0
$899$	−10.8284	+	4.48528i	−0.361148	+	0.149593i
$900$		0			0
$901$	8.82843	−	21.3137i	0.294118	−	0.710063i
$902$		0			0
$903$	−15.8995	−	15.8995i	−0.529102	−	0.529102i
$904$		0			0
$905$	−13.6863	+	13.6863i	−0.454948	+	0.454948i
$906$		0			0
$907$	−0.535534	−	0.221825i	−0.0177821	−	0.00736559i	0.373775	−	0.927520i	$-0.378063\pi$
$907$	−0.535534	−	0.221825i	−0.0177821	−	0.00736559i	−0.391557	+	0.920154i	$0.628063\pi$
$908$		0			0
$909$	1.94975	+	4.70711i	0.0646690	+	0.156125i
$910$		0			0
$911$			45.5980i			1.51073i	0.655305	+	0.755364i	$0.272540\pi$
$911$			45.5980i			1.51073i	−0.655305	+	0.755364i	$0.727460\pi$
$912$		0			0
$913$		−	2.10051i		−	0.0695166i
$914$		0			0
$915$	−1.82843	−	4.41421i	−0.0604459	−	0.145929i
$916$		0			0
$917$	12.4142	+	5.14214i	0.409953	+	0.169808i
$918$		0			0
$919$	25.4853	−	25.4853i	0.840682	−	0.840682i	−0.148266	−	0.988948i	$-0.547369\pi$
$919$	25.4853	−	25.4853i	0.840682	−	0.840682i	0.988948	+	0.148266i	$0.0473691\pi$
$920$		0			0
$921$	−4.17157	−	4.17157i	−0.137458	−	0.137458i
$922$		0			0
$923$	0.171573	−	0.414214i	0.00564739	−	0.0136340i
$924$		0			0
$925$	10.9497	−	4.53553i	0.360025	−	0.149127i
$926$		0			0
$927$	4.38478			0.144015
$928$		0			0
$929$	−26.4853			−0.868954			−0.434477	−	0.900683i	$-0.643067\pi$
$929$	−26.4853			−0.868954			−0.434477	+	0.900683i	$0.643067\pi$
$930$		0			0
$931$	27.6777	−	11.4645i	0.907099	−	0.375733i
$932$		0			0
$933$	−8.65685	+	20.8995i	−0.283413	+	0.684219i
$934$		0			0
$935$	−2.14214	−	2.14214i	−0.0700553	−	0.0700553i
$936$		0			0
$937$	−19.0000	+	19.0000i	−0.620703	+	0.620703i	−0.945711	−	0.325008i	$-0.894633\pi$
$937$	−19.0000	+	19.0000i	−0.620703	+	0.620703i	0.325008	+	0.945711i	$0.394633\pi$
$938$		0			0
$939$	−22.8995	−	9.48528i	−0.747297	−	0.309540i
$940$		0			0
$941$	−5.53553	−	13.3640i	−0.180453	−	0.435653i	0.807607	−	0.589721i	$-0.200762\pi$
$941$	−5.53553	−	13.3640i	−0.180453	−	0.435653i	−0.988060	+	0.154068i	$0.950762\pi$
$942$		0			0
$943$			2.00000i			0.0651290i
$944$		0			0
$945$		−	22.8284i		−	0.742609i
$946$		0			0
$947$	15.4645	+	37.3345i	0.502528	+	1.21321i	0.948103	+	0.317964i	$0.102999\pi$
$947$	15.4645	+	37.3345i	0.502528	+	1.21321i	−0.445575	+	0.895245i	$0.647001\pi$
$948$		0			0
$949$	16.8995	+	7.00000i	0.548581	+	0.227230i
$950$		0			0
$951$	15.8284	−	15.8284i	0.513272	−	0.513272i
$952$		0			0
$953$	−3.34315	−	3.34315i	−0.108295	−	0.108295i	0.650883	−	0.759178i	$-0.274399\pi$
$953$	−3.34315	−	3.34315i	−0.108295	−	0.108295i	−0.759178	+	0.650883i	$0.774399\pi$
$954$		0			0
$955$	−15.5147	+	37.4558i	−0.502045	+	1.21204i
$956$		0			0
$957$	1.58579	−	0.656854i	0.0512612	−	0.0212331i
$958$		0			0
$959$	5.31371			0.171589
$960$		0			0
$961$	−15.0000			−0.483871
$962$		0			0
$963$	0.121320	−	0.0502525i	0.00390949	−	0.00161937i
$964$		0			0
$965$	−23.8995	+	57.6985i	−0.769352	+	1.85738i
$966$		0			0
$967$	39.9706	+	39.9706i	1.28537	+	1.28537i	0.937570	+	0.347797i	$0.113070\pi$
$967$	39.9706	+	39.9706i	1.28537	+	1.28537i	0.347797	+	0.937570i	$0.386930\pi$
$968$		0			0
$969$	22.1421	−	22.1421i	0.711308	−	0.711308i
$970$		0			0
$971$	23.2635	+	9.63604i	0.746560	+	0.309235i	0.723337	−	0.690495i	$-0.242607\pi$
$971$	23.2635	+	9.63604i	0.746560	+	0.309235i	0.0232228	+	0.999730i	$0.492607\pi$
$972$		0			0
$973$	7.34315	+	17.7279i	0.235410	+	0.568331i
$974$		0			0
$975$			21.8995i			0.701345i
$976$		0			0
$977$			14.1421i			0.452447i	0.974075	+	0.226224i	$0.0726380\pi$
$977$			14.1421i			0.452447i	−0.974075	+	0.226224i	$0.927362\pi$
$978$		0			0
$979$	0.455844	+	1.10051i	0.0145688	+	0.0351723i
$980$		0			0
$981$	1.77817	+	0.736544i	0.0567727	+	0.0235160i
$982$		0			0
$983$	−25.6274	+	25.6274i	−0.817388	+	0.817388i	−0.985729	−	0.168341i	$-0.946159\pi$
$983$	−25.6274	+	25.6274i	−0.817388	+	0.817388i	0.168341	+	0.985729i	$0.446159\pi$
$984$		0			0
$985$	44.8995	+	44.8995i	1.43062	+	1.43062i
$986$		0			0
$987$	11.6569	−	28.1421i	0.371042	−	0.895774i
$988$		0			0
$989$	−1.92893	+	0.798990i	−0.0613365	+	0.0254064i
$990$		0			0
$991$	−16.0000			−0.508257			−0.254128	−	0.967170i	$-0.581789\pi$
$991$	−16.0000			−0.508257			−0.254128	+	0.967170i	$0.581789\pi$
$992$		0			0
$993$	−13.0711			−0.414798
$994$		0			0
$995$	−79.3259	+	32.8579i	−2.51480	+	1.04166i
$996$		0			0
$997$	0.748737	−	1.80761i	0.0237127	−	0.0572476i	−0.911580	−	0.411124i	$-0.865136\pi$
$997$	0.748737	−	1.80761i	0.0237127	−	0.0572476i	0.935292	+	0.353876i	$0.115136\pi$
$998$		0			0
$999$	−6.24264	−	6.24264i	−0.197508	−	0.197508i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	512.2.g.d.193.1		4
4.3	odd	2		512.2.g.b.193.1		4
8.3	odd	2		512.2.g.c.193.1		4
8.5	even	2		512.2.g.a.193.1		4
16.3	odd	4		128.2.g.a.113.1		4
16.5	even	4		256.2.g.b.225.1		4
16.11	odd	4		256.2.g.a.225.1		4
16.13	even	4		32.2.g.a.5.1	✓	4
32.3	odd	8		512.2.g.b.321.1		4
32.5	even	8		256.2.g.b.33.1		4
32.11	odd	8		128.2.g.a.17.1		4
32.13	even	8		512.2.g.a.321.1		4
32.19	odd	8		512.2.g.c.321.1		4
32.21	even	8		32.2.g.a.13.1	yes	4
32.27	odd	8		256.2.g.a.33.1		4
32.29	even	8	inner	512.2.g.d.321.1		4
48.29	odd	4		288.2.v.a.37.1		4
48.35	even	4		1152.2.v.a.1009.1		4
64.3	odd	16		4096.2.a.f.1.4		4
64.29	even	16		4096.2.a.e.1.4		4
64.35	odd	16		4096.2.a.f.1.1		4
64.61	even	16		4096.2.a.e.1.1		4
80.13	odd	4		800.2.ba.a.549.1		4
80.29	even	4		800.2.y.a.101.1		4
80.77	odd	4		800.2.ba.b.549.1		4
96.11	even	8		1152.2.v.a.145.1		4
96.53	odd	8		288.2.v.a.109.1		4
160.53	odd	8		800.2.ba.b.749.1		4
160.117	odd	8		800.2.ba.a.749.1		4
160.149	even	8		800.2.y.a.301.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.a.5.1	✓	4	16.13	even	4
32.2.g.a.13.1	yes	4	32.21	even	8
128.2.g.a.17.1		4	32.11	odd	8
128.2.g.a.113.1		4	16.3	odd	4
256.2.g.a.33.1		4	32.27	odd	8
256.2.g.a.225.1		4	16.11	odd	4
256.2.g.b.33.1		4	32.5	even	8
256.2.g.b.225.1		4	16.5	even	4
288.2.v.a.37.1		4	48.29	odd	4
288.2.v.a.109.1		4	96.53	odd	8
512.2.g.a.193.1		4	8.5	even	2
512.2.g.a.321.1		4	32.13	even	8
512.2.g.b.193.1		4	4.3	odd	2
512.2.g.b.321.1		4	32.3	odd	8
512.2.g.c.193.1		4	8.3	odd	2
512.2.g.c.321.1		4	32.19	odd	8
512.2.g.d.193.1		4	1.1	even	1	trivial
512.2.g.d.321.1		4	32.29	even	8	inner
800.2.y.a.101.1		4	80.29	even	4
800.2.y.a.301.1		4	160.149	even	8
800.2.ba.a.549.1		4	80.13	odd	4
800.2.ba.a.749.1		4	160.117	odd	8
800.2.ba.b.549.1		4	80.77	odd	4
800.2.ba.b.749.1		4	160.53	odd	8
1152.2.v.a.145.1		4	96.11	even	8
1152.2.v.a.1009.1		4	48.35	even	4
4096.2.a.e.1.1		4	64.61	even	16
4096.2.a.e.1.4		4	64.29	even	16
4096.2.a.f.1.1		4	64.35	odd	16
4096.2.a.f.1.4		4	64.3	odd	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	512.g (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.70711 - 0.707107i) q^{3} +(1.29289 - 3.12132i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(0.292893 - 0.292893i) q^{9} +O(q^{10})\)	\(q+(1.70711 - 0.707107i) q^{3} +(1.29289 - 3.12132i) q^{5} +(-1.00000 - 1.00000i) q^{7} +(0.292893 - 0.292893i) q^{9} +(0.292893 + 0.121320i) q^{11} +(-0.707107 - 1.70711i) q^{13} -6.24264i q^{15} -2.82843i q^{17} +(2.29289 + 5.53553i) q^{19} +(-2.41421 - 1.00000i) q^{21} +(-0.171573 + 0.171573i) q^{23} +(-4.53553 - 4.53553i) q^{25} +(-1.82843 + 4.41421i) q^{27} +(2.70711 - 1.12132i) q^{29} -4.00000 q^{31} +0.585786 q^{33} +(-4.41421 + 1.82843i) q^{35} +(-0.707107 + 1.70711i) q^{37} +(-2.41421 - 2.41421i) q^{39} +(5.82843 - 5.82843i) q^{41} +(7.94975 + 3.29289i) q^{43} +(-0.535534 - 1.29289i) q^{45} +11.6569i q^{47} -5.00000i q^{49} +(-2.00000 - 4.82843i) q^{51} +(7.53553 + 3.12132i) q^{53} +(0.757359 - 0.757359i) q^{55} +(7.82843 + 7.82843i) q^{57} +(2.53553 - 6.12132i) q^{59} +(0.707107 - 0.292893i) q^{61} -0.585786 q^{63} -6.24264 q^{65} +(3.70711 - 1.53553i) q^{67} +(-0.171573 + 0.414214i) q^{69} +(0.171573 + 0.171573i) q^{71} +(-7.00000 + 7.00000i) q^{73} +(-10.9497 - 4.53553i) q^{75} +(-0.171573 - 0.414214i) q^{77} -6.00000i q^{79} +10.0711i q^{81} +(-2.53553 - 6.12132i) q^{83} +(-8.82843 - 3.65685i) q^{85} +(3.82843 - 3.82843i) q^{87} +(2.65685 + 2.65685i) q^{89} +(-1.00000 + 2.41421i) q^{91} +(-6.82843 + 2.82843i) q^{93} +20.2426 q^{95} -1.51472 q^{97} +(0.121320 - 0.0502525i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} + 8 q^{5} - 4 q^{7} + 4 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 + 8 * q^5 - 4 * q^7 + 4 * q^9	\( 4 q + 4 q^{3} + 8 q^{5} - 4 q^{7} + 4 q^{9} + 4 q^{11} + 12 q^{19} - 4 q^{21} - 12 q^{23} - 4 q^{25} + 4 q^{27} + 8 q^{29} - 16 q^{31} + 8 q^{33} - 12 q^{35} - 4 q^{39} + 12 q^{41} + 12 q^{43} + 12 q^{45} - 8 q^{51} + 16 q^{53} + 20 q^{55} + 20 q^{57} - 4 q^{59} - 8 q^{63} - 8 q^{65} + 12 q^{67} - 12 q^{69} + 12 q^{71} - 28 q^{73} - 24 q^{75} - 12 q^{77} + 4 q^{83} - 24 q^{85} + 4 q^{87} - 12 q^{89} - 4 q^{91} - 16 q^{93} + 64 q^{95} - 40 q^{97} - 8 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 + 8 * q^5 - 4 * q^7 + 4 * q^9 + 4 * q^11 + 12 * q^19 - 4 * q^21 - 12 * q^23 - 4 * q^25 + 4 * q^27 + 8 * q^29 - 16 * q^31 + 8 * q^33 - 12 * q^35 - 4 * q^39 + 12 * q^41 + 12 * q^43 + 12 * q^45 - 8 * q^51 + 16 * q^53 + 20 * q^55 + 20 * q^57 - 4 * q^59 - 8 * q^63 - 8 * q^65 + 12 * q^67 - 12 * q^69 + 12 * q^71 - 28 * q^73 - 24 * q^75 - 12 * q^77 + 4 * q^83 - 24 * q^85 + 4 * q^87 - 12 * q^89 - 4 * q^91 - 16 * q^93 + 64 * q^95 - 40 * q^97 - 8 * q^99

Introduction

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