LMFDB - Embedded newform 512.2.g.c.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.c.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	$0.397584\pi$
$5$	−1.29289	+	3.12132i	−0.578199	+	1.39590i	−0.894427	+	0.447214i	$0.852416\pi$
$6$		0			0
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	0.870367	−	0.492403i	$-0.163881\pi$
$7$	1.00000	+	1.00000i	0.377964	+	0.377964i	−0.492403	+	0.870367i	$0.663881\pi$
$8$		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	0.991093	−	0.133174i	$-0.0425169\pi$
$13$	0.707107	+	1.70711i	0.196116	+	0.473466i	−0.794977	+	0.606640i	$0.792517\pi$
$14$		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	−0.688993	−	0.724768i	$-0.741947\pi$
$23$	0.171573	−	0.171573i	0.0357754	−	0.0357754i	0.724768	+	0.688993i	$0.241947\pi$
$24$		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	−0.619598	−	0.784920i	$-0.712704\pi$
$29$	−2.70711	+	1.12132i	−0.502697	+	0.208224i	0.116900	+	0.993144i	$0.462704\pi$
$30$		0			0
$31$	4.00000			0.718421			0.359211	−	0.933257i	$-0.383046\pi$
$31$	4.00000			0.718421			0.359211	+	0.933257i	$0.383046\pi$
$32$		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	−0.855037	−	0.518567i	$-0.826466\pi$
$37$	0.707107	−	1.70711i	0.116248	−	0.280647i	0.971285	+	0.237920i	$0.0764657\pi$
$38$		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	$-0.676503\pi$
$47$		−	11.6569i		−	1.70033i	0.526519	−	0.850163i	$-0.323497\pi$
$48$		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	−0.200540	−	0.979686i	$-0.564270\pi$
$53$	−7.53553	−	3.12132i	−1.03509	−	0.428746i	−0.834545	+	0.550939i	$0.814270\pi$
$54$		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	−0.427492	−	0.904019i	$-0.640603\pi$
$61$	−0.707107	+	0.292893i	−0.0905357	+	0.0375011i	0.336956	+	0.941520i	$0.390603\pi$
$62$		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	0.696853	−	0.717214i	$-0.254583\pi$
$71$	−0.171573	−	0.171573i	−0.0203620	−	0.0203620i	−0.717214	+	0.696853i	$0.754583\pi$
$72$		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	$0.109590\pi$
$79$			6.00000i			0.675053i	−0.941316	+	0.337526i	$0.890410\pi$
$80$		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	$-0.665381\pi$
$101$	4.70711	−	11.3640i	0.468375	−	1.13076i	0.964873	−	0.262718i	$-0.0846190\pi$
$102$		0			0
$103$	−7.48528	−	7.48528i	−0.737547	−	0.737547i	0.234556	−	0.972103i	$-0.424636\pi$
$103$	−7.48528	−	7.48528i	−0.737547	−	0.737547i	−0.972103	+	0.234556i	$0.924636\pi$
$104$		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	0.815555	−	0.578680i	$-0.196432\pi$
$109$	−1.77817	−	4.29289i	−0.170318	−	0.411185i	−0.985873	+	0.167496i	$0.946432\pi$
$110$		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	$-0.119444\pi$
$127$	20.9706			1.86084			0.930418	+	0.366499i	$0.119444\pi$
$128$		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	−0.248324	−	0.968677i	$-0.579880\pi$
$149$	−13.5355	−	5.60660i	−1.10887	−	0.459311i	−0.860550	+	0.509366i	$0.829880\pi$
$150$		0			0
$151$	15.4853	−	15.4853i	1.26017	−	1.26017i	0.309166	−	0.951008i	$-0.399950\pi$
$151$	15.4853	−	15.4853i	1.26017	−	1.26017i	0.951008	−	0.309166i	$-0.100050\pi$
$152$		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	−0.410722	−	0.911761i	$-0.634723\pi$
$157$	−0.707107	+	0.292893i	−0.0564333	+	0.0233754i	0.354288	+	0.935136i	$0.384723\pi$
$158$		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	0.824525	−	0.565825i	$-0.191442\pi$
$167$	3.34315	+	3.34315i	0.258700	+	0.258700i	−0.565825	+	0.824525i	$0.691442\pi$
$168$		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	0.905239	−	0.424902i	$-0.139691\pi$
$173$	−0.464466	−	1.12132i	−0.0353127	−	0.0852524i	−0.940552	+	0.339650i	$0.889691\pi$
$174$		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	0.570618	−	0.821216i	$-0.306704\pi$
$181$	5.29289	+	2.19239i	0.393418	+	0.162959i	−0.177200	+	0.984175i	$0.556704\pi$
$182$		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	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$		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	$-0.641495\pi$
$197$	7.19239	−	17.3640i	0.512436	−	1.23713i	0.942462	−	0.334314i	$-0.108505\pi$
$198$		0			0
$199$	17.9706	+	17.9706i	1.27390	+	1.27390i	0.944025	+	0.329875i	$0.107006\pi$
$199$	17.9706	+	17.9706i	1.27390	+	1.27390i	0.329875	+	0.944025i	$0.392994\pi$
$200$		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	$-0.642999\pi$
$223$	−12.9706			−0.868573			−0.434287	+	0.900775i	$0.642999\pi$
$224$		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	$0.471628\pi$
$229$	−10.2635	+	24.7782i	−0.678228	+	1.63739i	−0.767242	+	0.641357i	$0.778372\pi$
$230$		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	$0.189186\pi$
$239$			17.3137i			1.11993i	−0.828516	+	0.559965i	$0.810814\pi$
$240$		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	0.701797	−	0.712377i	$-0.252381\pi$
$263$	−0.171573	−	0.171573i	−0.0105796	−	0.0105796i	−0.712377	+	0.701797i	$0.752381\pi$
$264$		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	0.973435	−	0.228963i	$-0.0735335\pi$
$269$	2.02082	+	4.87868i	0.123211	+	0.297458i	−0.850224	+	0.526421i	$0.823533\pi$
$270$		0			0
$271$			18.0000i			1.09342i	0.837321	+	0.546711i	$0.184120\pi$
$271$			18.0000i			1.09342i	−0.837321	+	0.546711i	$0.815880\pi$
$272$		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	0.361339	−	0.932434i	$-0.382320\pi$
$277$	−0.707107	−	0.292893i	−0.0424859	−	0.0175982i	−0.403825	+	0.914836i	$0.632320\pi$
$278$		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	−0.999856	−	0.0169528i	$-0.994603\pi$
$293$	−4.80761	+	11.6066i	−0.280864	+	0.678065i	0.718993	+	0.695018i	$0.244603\pi$
$294$		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	−0.417700	−	0.908585i	$-0.637164\pi$
$311$	8.65685	−	8.65685i	0.490885	−	0.490885i	0.908585	+	0.417700i	$0.137164\pi$
$312$		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	−0.674170	−	0.738577i	$-0.735498\pi$
$317$	−11.1924	+	4.63604i	−0.628627	+	0.260386i	0.0455425	+	0.998962i	$0.485498\pi$
$318$		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	0.435426	−	0.900224i	$-0.356598\pi$
$349$	25.7782	−	10.6777i	1.37987	−	0.571563i	0.944448	+	0.328662i	$0.106598\pi$
$350$		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	0.308752	−	0.951143i	$-0.400089\pi$
$359$	−12.1716	−	12.1716i	−0.642391	−	0.642391i	−0.951143	+	0.308752i	$0.900089\pi$
$360$		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	$-0.949947\pi$
$367$		−	6.00000i		−	0.313197i	0.987662	−	0.156599i	$-0.0500529\pi$
$368$		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	0.965349	−	0.260962i	$-0.0840396\pi$
$373$	28.2635	+	11.7071i	1.46343	+	0.606171i	0.498077	+	0.867133i	$0.334040\pi$
$374$		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	$-0.642749\pi$
$383$	−16.9706			−0.867155			−0.433578	+	0.901116i	$0.642749\pi$
$384$		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	$0.426838\pi$
$389$	−12.2635	+	29.6066i	−0.621782	+	1.50111i	−0.849609	+	0.527413i	$0.823162\pi$
$390$		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	$-0.889996\pi$
$397$	−10.2635	−	24.7782i	−0.515108	−	1.24358i	0.425769	−	0.904832i	$-0.360004\pi$
$398$		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	−0.826795	−	0.562504i	$-0.809838\pi$
$421$	3.19239	−	7.70711i	0.155587	−	0.375621i	0.982382	+	0.186882i	$0.0598383\pi$
$422$		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	$-0.807038\pi$
$431$		−	23.6569i		−	1.13951i	0.821814	−	0.569755i	$-0.192962\pi$
$432$		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	−0.984839	−	0.173473i	$-0.944501\pi$
$439$	−17.0000	+	17.0000i	−0.811366	+	0.811366i	0.173473	+	0.984839i	$0.444501\pi$
$440$		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	0.998793	−	0.0491076i	$-0.0156377\pi$
$461$	5.53553	+	13.3640i	0.257816	+	0.622422i	−0.740978	+	0.671529i	$0.765638\pi$
$462$		0			0
$463$		−	10.9706i		−	0.509845i	−0.966961	−	0.254923i	$-0.917950\pi$
$463$		−	10.9706i		−	0.509845i	0.966961	−	0.254923i	$-0.0820500\pi$
$464$		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	$-0.463776\pi$
$479$	4.97056			0.227111			0.113555	+	0.993532i	$0.463776\pi$
$480$		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	0.412500	−	0.910958i	$-0.364656\pi$
$487$	−11.0000	−	11.0000i	−0.498458	−	0.498458i	−0.910958	+	0.412500i	$0.864656\pi$
$488$		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	−0.212772	−	0.977102i	$-0.568249\pi$
$503$	17.1421	−	17.1421i	0.764330	−	0.764330i	0.977102	+	0.212772i	$0.0682491\pi$
$504$		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	−0.920154	−	0.391556i	$-0.871937\pi$
$509$	−29.1924	+	12.0919i	−1.29393	+	0.535963i	−0.373776	+	0.927519i	$0.621937\pi$
$510$		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	−0.638735	−	0.769427i	$-0.720542\pi$
$541$	−12.7071	+	5.26346i	−0.546321	+	0.226294i	0.0924135	+	0.995721i	$0.470542\pi$
$542$		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	0.990136	−	0.140113i	$-0.0447464\pi$
$557$	4.50610	+	10.8787i	0.190929	+	0.460944i	−0.799206	+	0.601057i	$0.794746\pi$
$558$		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	−0.947288	−	0.320384i	$-0.896188\pi$
$599$	−15.3431	+	15.3431i	−0.626904	+	0.626904i	0.320384	+	0.947288i	$0.396188\pi$
$600$		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	$-0.506270\pi$
$607$	−0.970563			−0.0393939			−0.0196970	+	0.999806i	$0.506270\pi$
$608$		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	$-0.578915\pi$
$613$	15.1924	−	36.6777i	0.613615	−	1.48140i	0.859002	−	0.511972i	$-0.171085\pi$
$614$		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	−0.971550	−	0.236834i	$-0.923890\pi$
$631$	−18.4558	+	18.4558i	−0.734716	+	0.734716i	0.236834	+	0.971550i	$0.423890\pi$
$632$		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	0.900298	−	0.435274i	$-0.143349\pi$
$647$	11.8284	+	11.8284i	0.465023	+	0.465023i	−0.435274	+	0.900298i	$0.643349\pi$
$648$		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	$-0.848047\pi$
$653$	−14.9497	−	36.0919i	−0.585029	−	1.41238i	0.303175	−	0.952935i	$-0.401953\pi$
$654$		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	−0.0120477	−	0.999927i	$-0.503835\pi$
$661$	−18.7071	−	7.74874i	−0.727622	−	0.301391i	−0.715574	+	0.698536i	$0.753835\pi$
$662$		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	−0.962203	−	0.272333i	$-0.912205\pi$
$677$	−2.32233	+	5.60660i	−0.0892544	+	0.215479i	0.872949	+	0.487812i	$0.162205\pi$
$678$		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	−0.682948	−	0.730467i	$-0.739303\pi$
$701$	−17.1924	+	7.12132i	−0.649348	+	0.268969i	0.0336007	+	0.999435i	$0.489303\pi$
$702$		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	−0.967791	−	0.251755i	$-0.918992\pi$
$709$	−2.80761	+	6.77817i	−0.105442	+	0.254560i	0.862349	+	0.506314i	$0.168992\pi$
$710$		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	$0.149976\pi$
$719$			24.3431i			0.907846i	−0.891041	+	0.453923i	$0.850024\pi$
$720$		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	−0.105410	−	0.994429i	$-0.533615\pi$
$727$	23.9706	−	23.9706i	0.889019	−	0.889019i	0.994429	+	0.105410i	$0.0336155\pi$
$728$		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	−0.349602	−	0.936898i	$-0.613683\pi$
$733$	1.77817	−	0.736544i	0.0656784	−	0.0272049i	0.415281	+	0.909693i	$0.363683\pi$
$734$		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	0.411478	−	0.911420i	$-0.365013\pi$
$743$	−13.6274	−	13.6274i	−0.499941	−	0.499941i	−0.911420	+	0.411478i	$0.865013\pi$
$744$		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	$0.137656\pi$
$751$			22.9706i			0.838208i	−0.907938	+	0.419104i	$0.862344\pi$
$752$		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	0.414764	−	0.909929i	$-0.363864\pi$
$757$	1.77817	+	0.736544i	0.0646289	+	0.0267701i	−0.350135	+	0.936699i	$0.613864\pi$
$758$		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	$0.294575\pi$
$773$	−10.8076	+	26.0919i	−0.388723	+	0.938460i	−0.990211	+	0.139578i	$0.955425\pi$
$774$		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	−0.834172	−	0.551505i	$-0.814054\pi$
$797$	−29.1924	+	12.0919i	−1.03405	+	0.428316i	−0.199876	+	0.979821i	$0.564054\pi$
$798$		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	0.399195	−	0.916866i	$-0.369290\pi$
$821$	0.949747	+	0.393398i	0.0331464	+	0.0137297i	−0.366049	+	0.930596i	$0.619290\pi$
$822$		0			0
$823$	2.02944	−	2.02944i	0.0707417	−	0.0707417i	−0.670851	−	0.741592i	$-0.734071\pi$
$823$	2.02944	−	2.02944i	0.0707417	−	0.0707417i	0.741592	+	0.670851i	$0.234071\pi$
$824$		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	−0.929355	−	0.369187i	$-0.879636\pi$
$829$	−38.1630	+	15.8076i	−1.32545	+	0.549021i	−0.396099	+	0.918208i	$0.629636\pi$
$830$		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	$0.0393198\pi$
$839$	32.3137	+	32.3137i	1.11559	+	1.11559i	0.123213	+	0.992380i	$0.460680\pi$
$840$		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	0.430231	−	0.902719i	$-0.358432\pi$
$853$	2.80761	+	1.16295i	0.0961308	+	0.0398187i	−0.334100	+	0.942538i	$0.608432\pi$
$854$		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	$-0.214237\pi$
$863$	45.9411			1.56385			0.781927	+	0.623370i	$0.214237\pi$
$864$		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	$-0.917018\pi$
$877$	−13.7782	−	33.2635i	−0.465256	−	1.12323i	0.500955	−	0.865473i	$-0.332982\pi$
$878$		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	−0.960466	−	0.278398i	$-0.910197\pi$
$887$	−20.3137	+	20.3137i	−0.682068	+	0.682068i	0.278398	+	0.960466i	$0.410197\pi$
$888$		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	$-0.727460\pi$
$911$		−	45.5980i		−	1.51073i	0.655305	−	0.755364i	$-0.272540\pi$
$912$		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	−0.988948	−	0.148266i	$-0.952631\pi$
$919$	−25.4853	+	25.4853i	−0.840682	+	0.840682i	0.148266	+	0.988948i	$0.452631\pi$
$920$		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	0.988060	−	0.154068i	$-0.0492376\pi$
$941$	5.53553	+	13.3640i	0.180453	+	0.435653i	−0.807607	+	0.589721i	$0.799238\pi$
$942$		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	$-0.886930\pi$
$967$	−39.9706	−	39.9706i	−1.28537	−	1.28537i	−0.347797	−	0.937570i	$-0.613070\pi$
$968$		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	−0.168341	−	0.985729i	$-0.553841\pi$
$983$	25.6274	−	25.6274i	0.817388	−	0.817388i	0.985729	+	0.168341i	$0.0538410\pi$
$984$		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	$-0.418211\pi$
$991$	16.0000			0.508257			0.254128	+	0.967170i	$0.418211\pi$
$992$		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	−0.935292	−	0.353876i	$-0.884864\pi$
$997$	−0.748737	+	1.80761i	−0.0237127	+	0.0572476i	0.911580	+	0.411124i	$0.134864\pi$
$998$		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.c.193.1		4
4.3	odd	2		512.2.g.a.193.1		4
8.3	odd	2		512.2.g.d.193.1		4
8.5	even	2		512.2.g.b.193.1		4
16.3	odd	4		256.2.g.b.225.1		4
16.5	even	4		128.2.g.a.113.1		4
16.11	odd	4		32.2.g.a.5.1	✓	4
16.13	even	4		256.2.g.a.225.1		4
32.3	odd	8		512.2.g.a.321.1		4
32.5	even	8		128.2.g.a.17.1		4
32.11	odd	8		256.2.g.b.33.1		4
32.13	even	8		512.2.g.b.321.1		4
32.19	odd	8		512.2.g.d.321.1		4
32.21	even	8		256.2.g.a.33.1		4
32.27	odd	8		32.2.g.a.13.1	yes	4
32.29	even	8	inner	512.2.g.c.321.1		4
48.5	odd	4		1152.2.v.a.1009.1		4
48.11	even	4		288.2.v.a.37.1		4
64.3	odd	16		4096.2.a.e.1.4		4
64.29	even	16		4096.2.a.f.1.4		4
64.35	odd	16		4096.2.a.e.1.1		4
64.61	even	16		4096.2.a.f.1.1		4
80.27	even	4		800.2.ba.b.549.1		4
80.43	even	4		800.2.ba.a.549.1		4
80.59	odd	4		800.2.y.a.101.1		4
96.5	odd	8		1152.2.v.a.145.1		4
96.59	even	8		288.2.v.a.109.1		4
160.27	even	8		800.2.ba.a.749.1		4
160.59	odd	8		800.2.y.a.301.1		4
160.123	even	8		800.2.ba.b.749.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.2.g.a.5.1	✓	4	16.11	odd	4
32.2.g.a.13.1	yes	4	32.27	odd	8
128.2.g.a.17.1		4	32.5	even	8
128.2.g.a.113.1		4	16.5	even	4
256.2.g.a.33.1		4	32.21	even	8
256.2.g.a.225.1		4	16.13	even	4
256.2.g.b.33.1		4	32.11	odd	8
256.2.g.b.225.1		4	16.3	odd	4
288.2.v.a.37.1		4	48.11	even	4
288.2.v.a.109.1		4	96.59	even	8
512.2.g.a.193.1		4	4.3	odd	2
512.2.g.a.321.1		4	32.3	odd	8
512.2.g.b.193.1		4	8.5	even	2
512.2.g.b.321.1		4	32.13	even	8
512.2.g.c.193.1		4	1.1	even	1	trivial
512.2.g.c.321.1		4	32.29	even	8	inner
512.2.g.d.193.1		4	8.3	odd	2
512.2.g.d.321.1		4	32.19	odd	8
800.2.y.a.101.1		4	80.59	odd	4
800.2.y.a.301.1		4	160.59	odd	8
800.2.ba.a.549.1		4	80.43	even	4
800.2.ba.a.749.1		4	160.27	even	8
800.2.ba.b.549.1		4	80.27	even	4
800.2.ba.b.749.1		4	160.123	even	8
1152.2.v.a.145.1		4	96.5	odd	8
1152.2.v.a.1009.1		4	48.5	odd	4
4096.2.a.e.1.1		4	64.35	odd	16
4096.2.a.e.1.4		4	64.3	odd	16
4096.2.a.f.1.1		4	64.61	even	16
4096.2.a.f.1.4		4	64.29	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:	\( N \)	\(=\)	\( 512 = 2^{9} \)
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

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