LMFDB - Embedded newform 1024.2.g.c.641.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1024,2,Mod(129,1024)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1024, 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("1024.129");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1024 = 2^{10} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1024.g (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.17668116698$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{8})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8x^{14} + 32x^{12} - 64x^{10} + 127x^{8} - 576x^{6} + 2592x^{4} - 5832x^{2} + 6561 $ x^16 - 8x^14 + 32x^12 - 64x^10 + 127x^8 - 576x^6 + 2592x^4 - 5832*x^2 + 6561
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			641.4
Root			$1.66798 - 0.466730i$ of defining polynomial
Character	$\chi$	$=$	1024.641
Dual form			1024.2.g.c.385.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.90008 + 1.20125i) q^{3} +(-1.21229 - 2.92673i) q^{5} +(0.933460 - 0.933460i) q^{7} +(4.84613 + 4.84613i) q^{9} +O(q^{10})$	\(q+(2.90008 + 1.20125i) q^{3} +(-1.21229 - 2.92673i) q^{5} +(0.933460 - 0.933460i) q^{7} +(4.84613 + 4.84613i) q^{9} +(1.05232 - 0.435885i) q^{11} +(-1.09830 + 2.65154i) q^{13} -9.94402i q^{15} -1.61082i q^{17} +(2.34533 - 5.66214i) q^{19} +(3.82843 - 1.58579i) q^{21} +(1.67967 + 1.67967i) q^{23} +(-3.56057 + 3.56057i) q^{25} +(4.62898 + 11.1753i) q^{27} +(7.06575 + 2.92673i) q^{29} +1.53073 q^{31} +3.57542 q^{33} +(-3.86361 - 1.60036i) q^{35} +(-2.08793 - 5.04072i) q^{37} +(-6.37033 + 6.37033i) q^{39} +(-1.03540 - 1.03540i) q^{41} +(-3.98247 + 1.64959i) q^{43} +(8.30839 - 20.0582i) q^{45} +2.97641i q^{47} +5.25731i q^{49} +(1.93500 - 4.67151i) q^{51} +(10.1694 - 4.21229i) q^{53} +(-2.55144 - 2.55144i) q^{55} +(13.6033 - 13.6033i) q^{57} +(-3.34842 - 8.08380i) q^{59} +(-12.6440 - 5.23733i) q^{61} +9.04733 q^{63} +9.09181 q^{65} +(-11.8681 - 4.91593i) q^{67} +(2.85346 + 6.88887i) q^{69} +(-5.88894 + 5.88894i) q^{71} +(3.71444 + 3.71444i) q^{73} +(-14.6031 + 6.04879i) q^{75} +(0.575417 - 1.38918i) q^{77} +10.4058i q^{79} +17.4096i q^{81} +(-1.13163 + 2.73199i) q^{83} +(-4.71444 + 1.95278i) q^{85} +(16.9755 + 16.9755i) q^{87} +(-6.56361 + 6.56361i) q^{89} +(1.44988 + 3.50033i) q^{91} +(4.43925 + 1.83880i) q^{93} -19.4148 q^{95} +1.01037 q^{97} +(7.21203 + 2.98732i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{5} + 16 q^{9}+O(q^{10}) $ 16 * q - 8 * q^5 + 16 * q^9	$ 16 q - 8 q^{5} + 16 q^{9} - 24 q^{13} + 16 q^{21} + 32 q^{25} + 24 q^{29} + 80 q^{33} - 40 q^{37} + 16 q^{41} - 24 q^{45} + 56 q^{53} + 80 q^{57} - 8 q^{61} + 32 q^{65} - 32 q^{69} + 32 q^{73} + 32 q^{77} - 48 q^{85} - 32 q^{89} + 16 q^{93} + 16 q^{97}+O(q^{100}) $ 16 * q - 8 * q^5 + 16 * q^9 - 24 * q^13 + 16 * q^21 + 32 * q^25 + 24 * q^29 + 80 * q^33 - 40 * q^37 + 16 * q^41 - 24 * q^45 + 56 * q^53 + 80 * q^57 - 8 * q^61 + 32 * q^65 - 32 * q^69 + 32 * q^73 + 32 * q^77 - 48 * q^85 - 32 * q^89 + 16 * q^93 + 16 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

$n$	$5$	$1023$
$\chi(n)$	$e\left(\frac{3}{8}\right)$	$1$

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
$3$	2.90008	+	1.20125i	1.67436	+	0.693543i	0.999033	−	0.0439740i	$-0.0140019\pi$
$3$	2.90008	+	1.20125i	1.67436	+	0.693543i	0.675328	+	0.737517i	$0.264002\pi$
$4$		0			0
$5$	−1.21229	−	2.92673i	−0.542153	−	1.30887i	−0.923201	−	0.384318i	$-0.874437\pi$
$5$	−1.21229	−	2.92673i	−0.542153	−	1.30887i	0.381047	−	0.924556i	$-0.375563\pi$
$6$		0			0
$7$	0.933460	−	0.933460i	0.352815	−	0.352815i	−0.508341	−	0.861156i	$-0.669741\pi$
$7$	0.933460	−	0.933460i	0.352815	−	0.352815i	0.861156	+	0.508341i	$0.169741\pi$
$8$		0			0
$9$	4.84613	+	4.84613i	1.61538	+	1.61538i
$10$		0			0
$11$	1.05232	−	0.435885i	0.317286	−	0.131424i	−0.218356	−	0.975869i	$-0.570069\pi$
$11$	1.05232	−	0.435885i	0.317286	−	0.131424i	0.535643	+	0.844445i	$0.320069\pi$
$12$		0			0
$13$	−1.09830	+	2.65154i	−0.304615	+	0.735405i	0.695247	+	0.718771i	$0.255295\pi$
$13$	−1.09830	+	2.65154i	−0.304615	+	0.735405i	−0.999862	+	0.0166339i	$0.994705\pi$
$14$		0			0
$15$		−	9.94402i		−	2.56753i
$16$		0			0
$17$		−	1.61082i		−	0.390681i	−0.980735	−	0.195341i	$-0.937419\pi$
$17$		−	1.61082i		−	0.390681i	0.980735	−	0.195341i	$-0.0625813\pi$
$18$		0			0
$19$	2.34533	−	5.66214i	0.538056	−	1.29898i	−0.388021	−	0.921650i	$-0.626841\pi$
$19$	2.34533	−	5.66214i	0.538056	−	1.29898i	0.926078	−	0.377333i	$-0.123159\pi$
$20$		0			0
$21$	3.82843	−	1.58579i	0.835431	−	0.346047i
$22$		0			0
$23$	1.67967	+	1.67967i	0.350235	+	0.350235i	0.860197	−	0.509962i	$-0.170341\pi$
$23$	1.67967	+	1.67967i	0.350235	+	0.350235i	−0.509962	+	0.860197i	$0.670341\pi$
$24$		0			0
$25$	−3.56057	+	3.56057i	−0.712114	+	0.712114i
$26$		0			0
$27$	4.62898	+	11.1753i	0.890847	+	2.15070i
$28$		0			0
$29$	7.06575	+	2.92673i	1.31208	+	0.543480i	0.925490	−	0.378772i	$-0.123654\pi$
$29$	7.06575	+	2.92673i	1.31208	+	0.543480i	0.386588	+	0.922253i	$0.373654\pi$
$30$		0			0
$31$	1.53073			0.274928			0.137464	−	0.990507i	$-0.456105\pi$
$31$	1.53073			0.274928			0.137464	+	0.990507i	$0.456105\pi$
$32$		0			0
$33$	3.57542			0.622400
$34$		0			0
$35$	−3.86361	−	1.60036i	−0.653069	−	0.270510i
$36$		0			0
$37$	−2.08793	−	5.04072i	−0.343254	−	0.828689i	−0.997383	−	0.0723054i	$-0.976964\pi$
$37$	−2.08793	−	5.04072i	−0.343254	−	0.828689i	0.654128	−	0.756384i	$-0.273036\pi$
$38$		0			0
$39$	−6.37033	+	6.37033i	−1.02007	+	1.02007i
$40$		0			0
$41$	−1.03540	−	1.03540i	−0.161703	−	0.161703i	0.621618	−	0.783321i	$-0.286476\pi$
$41$	−1.03540	−	1.03540i	−0.161703	−	0.161703i	−0.783321	+	0.621618i	$0.786476\pi$
$42$		0			0
$43$	−3.98247	+	1.64959i	−0.607321	+	0.251561i	−0.665083	−	0.746770i	$-0.731604\pi$
$43$	−3.98247	+	1.64959i	−0.607321	+	0.251561i	0.0577615	+	0.998330i	$0.481604\pi$
$44$		0			0
$45$	8.30839	−	20.0582i	1.23854	−	2.99011i
$46$		0			0
$47$			2.97641i			0.434154i	0.976154	+	0.217077i	$0.0696523\pi$
$47$			2.97641i			0.434154i	−0.976154	+	0.217077i	$0.930348\pi$
$48$		0			0
$49$			5.25731i			0.751044i
$50$		0			0
$51$	1.93500	−	4.67151i	0.270954	−	0.654142i
$52$		0			0
$53$	10.1694	−	4.21229i	1.39687	−	0.578603i	0.447933	−	0.894067i	$-0.352160\pi$
$53$	10.1694	−	4.21229i	1.39687	−	0.578603i	0.948937	+	0.315464i	$0.102160\pi$
$54$		0			0
$55$	−2.55144	−	2.55144i	−0.344036	−	0.344036i
$56$		0			0
$57$	13.6033	−	13.6033i	1.80180	−	1.80180i
$58$		0			0
$59$	−3.34842	−	8.08380i	−0.435927	−	1.05242i	−0.977342	−	0.211666i	$-0.932111\pi$
$59$	−3.34842	−	8.08380i	−0.435927	−	1.05242i	0.541415	−	0.840756i	$-0.317889\pi$
$60$		0			0
$61$	−12.6440	−	5.23733i	−1.61890	−	0.670571i	−0.624978	−	0.780643i	$-0.714892\pi$
$61$	−12.6440	−	5.23733i	−1.61890	−	0.670571i	−0.993924	+	0.110072i	$0.964892\pi$
$62$		0			0
$63$	9.04733			1.13986
$64$		0			0
$65$	9.09181			1.12770
$66$		0			0
$67$	−11.8681	−	4.91593i	−1.44992	−	0.600577i	−0.487739	−	0.872989i	$-0.662178\pi$
$67$	−11.8681	−	4.91593i	−1.44992	−	0.600577i	−0.962180	+	0.272413i	$0.912178\pi$
$68$		0			0
$69$	2.85346	+	6.88887i	0.343516	+	0.829322i
$70$		0			0
$71$	−5.88894	+	5.88894i	−0.698889	+	0.698889i	−0.964171	−	0.265282i	$-0.914535\pi$
$71$	−5.88894	+	5.88894i	−0.698889	+	0.698889i	0.265282	+	0.964171i	$0.414535\pi$
$72$		0			0
$73$	3.71444	+	3.71444i	0.434742	+	0.434742i	0.890238	−	0.455496i	$-0.150538\pi$
$73$	3.71444	+	3.71444i	0.434742	+	0.434742i	−0.455496	+	0.890238i	$0.650538\pi$
$74$		0			0
$75$	−14.6031	+	6.04879i	−1.68622	+	0.698454i
$76$		0			0
$77$	0.575417	−	1.38918i	0.0655748	−	0.158312i
$78$		0			0
$79$			10.4058i			1.17074i	0.810766	+	0.585370i	$0.199051\pi$
$79$			10.4058i			1.17074i	−0.810766	+	0.585370i	$0.800949\pi$
$80$		0			0
$81$			17.4096i			1.93439i
$82$		0			0
$83$	−1.13163	+	2.73199i	−0.124212	+	0.299874i	−0.973738	−	0.227673i	$-0.926888\pi$
$83$	−1.13163	+	2.73199i	−0.124212	+	0.299874i	0.849526	+	0.527547i	$0.176888\pi$
$84$		0			0
$85$	−4.71444	+	1.95278i	−0.511353	+	0.211809i
$86$		0			0
$87$	16.9755	+	16.9755i	1.81996	+	1.81996i
$88$		0			0
$89$	−6.56361	+	6.56361i	−0.695741	+	0.695741i	−0.963489	−	0.267748i	$-0.913720\pi$
$89$	−6.56361	+	6.56361i	−0.695741	+	0.695741i	0.267748	+	0.963489i	$0.413720\pi$
$90$		0			0
$91$	1.44988	+	3.50033i	0.151989	+	0.366934i
$92$		0			0
$93$	4.43925	+	1.83880i	0.460329	+	0.190674i
$94$		0			0
$95$	−19.4148			−1.99191
$96$		0			0
$97$	1.01037			0.102587			0.0512937	−	0.998684i	$-0.483666\pi$
$97$	1.01037			0.102587			0.0512937	+	0.998684i	$0.483666\pi$
$98$		0			0
$99$	7.21203	+	2.98732i	0.724836	+	0.300237i
$100$		0			0
$101$	4.16937	+	10.0658i	0.414868	+	1.00158i	0.983812	+	0.179204i	$0.0573521\pi$
$101$	4.16937	+	10.0658i	0.414868	+	1.00158i	−0.568944	+	0.822376i	$0.692648\pi$
$102$		0			0
$103$	−10.1802	+	10.1802i	−1.00308	+	1.00308i	−0.00308887	+	0.999995i	$0.500983\pi$
$103$	−10.1802	+	10.1802i	−1.00308	+	1.00308i	−0.999995	+	0.00308887i	$0.999017\pi$
$104$		0			0
$105$	−9.28234	−	9.28234i	−0.905864	−	0.905864i
$106$		0			0
$107$	9.16246	−	3.79522i	0.885769	−	0.366897i	0.107038	−	0.994255i	$-0.465864\pi$
$107$	9.16246	−	3.79522i	0.885769	−	0.366897i	0.778731	+	0.627357i	$0.215864\pi$
$108$		0			0
$109$	−4.04072	+	9.75516i	−0.387031	+	0.934375i	0.603535	+	0.797336i	$0.293758\pi$
$109$	−4.04072	+	9.75516i	−0.387031	+	0.934375i	−0.990566	+	0.137038i	$0.956242\pi$
$110$		0			0
$111$		−	17.1266i		−	1.62559i
$112$		0			0
$113$			2.57112i			0.241871i	0.992660	+	0.120935i	$0.0385894\pi$
$113$			2.57112i			0.241871i	−0.992660	+	0.120935i	$0.961411\pi$
$114$		0			0
$115$	2.87969	−	6.95218i	0.268532	−	0.648294i
$116$		0			0
$117$	−18.1722	+	7.52718i	−1.68002	+	0.695888i
$118$		0			0
$119$	−1.50364	−	1.50364i	−0.137838	−	0.137838i
$120$		0			0
$121$	−6.86079	+	6.86079i	−0.623709	+	0.623709i
$122$		0			0
$123$	−1.75897	−	4.24653i	−0.158601	−	0.382897i
$124$		0			0
$125$	0.103618	+	0.0429201i	0.00926790	+	0.00383889i
$126$		0			0
$127$	−6.16126			−0.546723			−0.273362	−	0.961911i	$-0.588136\pi$
$127$	−6.16126			−0.546723			−0.273362	+	0.961911i	$0.588136\pi$
$128$		0			0
$129$	−13.5311			−1.19134
$130$		0			0
$131$	1.92409	+	0.796984i	0.168108	+	0.0696328i	0.465151	−	0.885232i	$-0.346000\pi$
$131$	1.92409	+	0.796984i	0.168108	+	0.0696328i	−0.297042	+	0.954864i	$0.596000\pi$
$132$		0			0
$133$	−3.09610	−	7.47465i	−0.268466	−	0.648135i
$134$		0			0
$135$	27.0955	−	27.0955i	2.33201	−	2.33201i
$136$		0			0
$137$	11.1315	+	11.1315i	0.951029	+	0.951029i	0.998856	−	0.0478269i	$-0.0152296\pi$
$137$	11.1315	+	11.1315i	0.951029	+	0.951029i	−0.0478269	+	0.998856i	$0.515230\pi$
$138$		0			0
$139$	−9.95493	+	4.12347i	−0.844366	+	0.349748i	−0.762574	−	0.646902i	$-0.776064\pi$
$139$	−9.95493	+	4.12347i	−0.844366	+	0.349748i	−0.0817925	+	0.996649i	$0.526064\pi$
$140$		0			0
$141$	−3.57542	+	8.63182i	−0.301104	+	0.726930i
$142$		0			0
$143$			3.26900i			0.273368i
$144$		0			0
$145$		−	24.2276i		−	2.01199i
$146$		0			0
$147$	−6.31535	+	15.2466i	−0.520881	+	1.25752i
$148$		0			0
$149$	13.0658	−	5.41201i	1.07039	−	0.443369i	0.223261	−	0.974759i	$-0.428330\pi$
$149$	13.0658	−	5.41201i	1.07039	−	0.443369i	0.847128	+	0.531389i	$0.178330\pi$
$150$		0			0
$151$	−14.0916	−	14.0916i	−1.14676	−	1.14676i	−0.987186	−	0.159572i	$-0.948988\pi$
$151$	−14.0916	−	14.0916i	−1.14676	−	1.14676i	−0.159572	−	0.987186i	$-0.551012\pi$
$152$		0			0
$153$	7.80625	−	7.80625i	0.631098	−	0.631098i
$154$		0			0
$155$	−1.85570	−	4.48005i	−0.149053	−	0.359846i
$156$		0			0
$157$	−2.86629	−	1.18726i	−0.228755	−	0.0947534i	0.265362	−	0.964149i	$-0.414509\pi$
$157$	−2.86629	−	1.18726i	−0.228755	−	0.0947534i	−0.494117	+	0.869395i	$0.664509\pi$
$158$		0			0
$159$	34.5520			2.74015
$160$		0			0
$161$	3.13580			0.247136
$162$		0			0
$163$	9.20872	+	3.81438i	0.721283	+	0.298765i	0.712964	−	0.701200i	$-0.247352\pi$
$163$	9.20872	+	3.81438i	0.721283	+	0.298765i	0.00831846	+	0.999965i	$0.497352\pi$
$164$		0			0
$165$	−4.33445	−	10.4643i	−0.337436	−	0.814643i
$166$		0			0
$167$	6.15971	−	6.15971i	0.476653	−	0.476653i	−0.427407	−	0.904059i	$-0.640573\pi$
$167$	6.15971	−	6.15971i	0.476653	−	0.476653i	0.904059	+	0.427407i	$0.140573\pi$
$168$		0			0
$169$	3.36800	+	3.36800i	0.259077	+	0.259077i
$170$		0			0
$171$	38.8052	−	16.0737i	2.96751	−	1.22918i
$172$		0			0
$173$	−4.02283	+	9.71198i	−0.305850	+	0.738388i	0.693980	+	0.719994i	$0.255855\pi$
$173$	−4.02283	+	9.71198i	−0.305850	+	0.738388i	−0.999831	+	0.0183942i	$0.994145\pi$
$174$		0			0
$175$			6.64730i			0.502488i
$176$		0			0
$177$		−	27.4660i		−	2.06447i
$178$		0			0
$179$	−6.34665	+	15.3222i	−0.474371	+	1.14523i	0.487841	+	0.872932i	$0.337785\pi$
$179$	−6.34665	+	15.3222i	−0.474371	+	1.14523i	−0.962212	+	0.272301i	$0.912215\pi$
$180$		0			0
$181$	4.12619	−	1.70912i	0.306697	−	0.127038i	−0.224026	−	0.974583i	$-0.571920\pi$
$181$	4.12619	−	1.70912i	0.306697	−	0.127038i	0.530724	+	0.847545i	$0.321920\pi$
$182$		0			0
$183$	−30.3773	−	30.3773i	−2.24556	−	2.24556i
$184$		0			0
$185$	−12.2216	+	12.2216i	−0.898553	+	0.898553i
$186$		0			0
$187$	−0.702133	−	1.69510i	−0.0513450	−	0.123958i
$188$		0			0
$189$	14.7527	+	6.11077i	1.07310	+	0.444493i
$190$		0			0
$191$	−14.7979			−1.07074			−0.535371	−	0.844617i	$-0.679828\pi$
$191$	−14.7979			−1.07074			−0.535371	+	0.844617i	$0.679828\pi$
$192$		0			0
$193$	−6.66722			−0.479917			−0.239959	−	0.970783i	$-0.577134\pi$
$193$	−6.66722			−0.479917			−0.239959	+	0.970783i	$0.577134\pi$
$194$		0			0
$195$	26.3670	+	10.9216i	1.88818	+	0.782108i
$196$		0			0
$197$	−6.25199	−	15.0936i	−0.445436	−	1.07538i	−0.974013	−	0.226492i	$-0.927274\pi$
$197$	−6.25199	−	15.0936i	−0.445436	−	1.07538i	0.528577	−	0.848885i	$-0.322726\pi$
$198$		0			0
$199$	0.682332	−	0.682332i	0.0483693	−	0.0483693i	−0.682508	−	0.730878i	$-0.739111\pi$
$199$	0.682332	−	0.682332i	0.0483693	−	0.0483693i	0.730878	+	0.682508i	$0.239111\pi$
$200$		0			0
$201$	−28.5132	−	28.5132i	−2.01116	−	2.01116i
$202$		0			0
$203$	9.32758	−	3.86361i	0.654668	−	0.271172i
$204$		0			0
$205$	−1.77514	+	4.28556i	−0.123981	+	0.299317i
$206$		0			0
$207$			16.2798i			1.13152i
$208$		0			0
$209$		−	6.98067i		−	0.482863i
$210$		0			0
$211$	6.43698	−	15.5403i	0.443140	−	1.06984i	−0.531700	−	0.846933i	$-0.678447\pi$
$211$	6.43698	−	15.5403i	0.443140	−	1.06984i	0.974841	−	0.222903i	$-0.0715533\pi$
$212$		0			0
$213$	−24.1525	+	10.0043i	−1.65490	+	0.685483i
$214$		0			0
$215$	9.65583	+	9.65583i	0.658522	+	0.658522i
$216$		0			0
$217$	1.42888	−	1.42888i	0.0969986	−	0.0969986i
$218$		0			0
$219$	6.31019	+	15.2341i	0.426403	+	1.02943i
$220$		0			0
$221$	4.27116	+	1.76917i	0.287309	+	0.119007i
$222$		0			0
$223$	1.47654			0.0988764			0.0494382	−	0.998777i	$-0.484257\pi$
$223$	1.47654			0.0988764			0.0494382	+	0.998777i	$0.484257\pi$
$224$		0			0
$225$	−34.5099			−2.30066
$226$		0			0
$227$	−26.1225	−	10.8203i	−1.73381	−	0.718169i	−0.999213	−	0.0396690i	$-0.987370\pi$
$227$	−26.1225	−	10.8203i	−1.73381	−	0.718169i	−0.734600	−	0.678500i	$-0.762630\pi$
$228$		0			0
$229$	3.61614	+	8.73012i	0.238961	+	0.576903i	0.997176	−	0.0751019i	$-0.0239282\pi$
$229$	3.61614	+	8.73012i	0.238961	+	0.576903i	−0.758215	+	0.652005i	$0.773928\pi$
$230$		0			0
$231$	3.33751	−	3.33751i	0.219592	−	0.219592i
$232$		0			0
$233$	9.99248	+	9.99248i	0.654629	+	0.654629i	0.954104	−	0.299475i	$-0.0968115\pi$
$233$	9.99248	+	9.99248i	0.654629	+	0.654629i	−0.299475	+	0.954104i	$0.596811\pi$
$234$		0			0
$235$	8.71115	−	3.60828i	0.568253	−	0.235378i
$236$		0			0
$237$	−12.4999	+	30.1775i	−0.811959	+	1.96024i
$238$		0			0
$239$			10.5759i			0.684097i	0.939682	+	0.342049i	$0.111121\pi$
$239$			10.5759i			0.684097i	−0.939682	+	0.342049i	$0.888879\pi$
$240$		0			0
$241$		−	0.690846i		−	0.0445013i	−0.999752	−	0.0222507i	$-0.992917\pi$
$241$		−	0.690846i		−	0.0445013i	0.999752	−	0.0222507i	$-0.00708319\pi$
$242$		0			0
$243$	−7.02632	+	16.9630i	−0.450739	+	1.08818i
$244$		0			0
$245$	15.3867	−	6.37339i	0.983021	−	0.407181i
$246$		0			0
$247$	12.4375	+	12.4375i	0.791379	+	0.791379i
$248$		0			0
$249$	−6.56361	+	6.56361i	−0.415952	+	0.415952i
$250$		0			0
$251$	−6.08493	−	14.6903i	−0.384077	−	0.927244i	−0.991168	−	0.132612i	$-0.957664\pi$
$251$	−6.08493	−	14.6903i	−0.384077	−	0.927244i	0.607091	−	0.794632i	$-0.292336\pi$
$252$		0			0
$253$	2.49969	+	1.03540i	0.157154	+	0.0650953i
$254$		0			0
$255$	−16.0180			−1.00309
$256$		0			0
$257$	−11.7928			−0.735612			−0.367806	−	0.929902i	$-0.619891\pi$
$257$	−11.7928			−0.735612			−0.367806	+	0.929902i	$0.619891\pi$
$258$		0			0
$259$	−6.65431	−	2.75631i	−0.413479	−	0.171269i
$260$		0			0
$261$	20.0582	+	48.4249i	1.24157	+	2.99742i
$262$		0			0
$263$	20.4934	−	20.4934i	1.26368	−	1.26368i	0.314384	−	0.949296i	$-0.398202\pi$
$263$	20.4934	−	20.4934i	1.26368	−	1.26368i	0.949296	−	0.314384i	$-0.101798\pi$
$264$		0			0
$265$	−24.6565	−	24.6565i	−1.51464	−	1.51464i
$266$		0			0
$267$	−26.9195	+	11.1504i	−1.64745	+	0.682395i
$268$		0			0
$269$	3.82741	−	9.24018i	0.233361	−	0.563384i	−0.763208	−	0.646153i	$-0.776377\pi$
$269$	3.82741	−	9.24018i	0.233361	−	0.563384i	0.996569	+	0.0827697i	$0.0263766\pi$
$270$		0			0
$271$		−	25.2037i		−	1.53102i	−0.643426	−	0.765508i	$-0.722488\pi$
$271$		−	25.2037i		−	1.53102i	0.643426	−	0.765508i	$-0.277512\pi$
$272$		0			0
$273$			11.8929i			0.719791i
$274$		0			0
$275$	−2.19486	+	5.29885i	−0.132355	+	0.319533i
$276$		0			0
$277$	−13.6544	+	5.65583i	−0.820413	+	0.339826i	−0.753100	−	0.657906i	$-0.771443\pi$
$277$	−13.6544	+	5.65583i	−0.820413	+	0.339826i	−0.0673127	+	0.997732i	$0.521443\pi$
$278$		0			0
$279$	7.41813	+	7.41813i	0.444112	+	0.444112i
$280$		0			0
$281$	4.45247	−	4.45247i	0.265612	−	0.265612i	−0.561717	−	0.827329i	$-0.689859\pi$
$281$	4.45247	−	4.45247i	0.265612	−	0.265612i	0.827329	+	0.561717i	$0.189859\pi$
$282$		0			0
$283$	−9.32635	−	22.5158i	−0.554394	−	1.33843i	−0.914149	−	0.405379i	$-0.867140\pi$
$283$	−9.32635	−	22.5158i	−0.554394	−	1.33843i	0.359755	−	0.933047i	$-0.382860\pi$
$284$		0			0
$285$	−56.3044	−	23.3220i	−3.33518	−	1.38148i
$286$		0			0
$287$	−1.93302			−0.114102
$288$		0			0
$289$	14.4053			0.847368
$290$		0			0
$291$	2.93015	+	1.21371i	0.171769	+	0.0711488i
$292$		0			0
$293$	2.76241	+	6.66906i	0.161382	+	0.389611i	0.983799	−	0.179274i	$-0.0573750\pi$
$293$	2.76241	+	6.66906i	0.161382	+	0.389611i	−0.822417	+	0.568885i	$0.807375\pi$
$294$		0			0
$295$	−19.5998	+	19.5998i	−1.14115	+	1.14115i
$296$		0			0
$297$	9.74233	+	9.74233i	0.565307	+	0.565307i
$298$		0			0
$299$	−6.29848	+	2.60892i	−0.364251	+	0.150878i
$300$		0			0
$301$	−2.17765	+	5.25731i	−0.125518	+	0.303026i
$302$		0			0
$303$			34.1999i			1.96474i
$304$		0			0
$305$			43.3548i			2.48249i
$306$		0			0
$307$	−6.76523	+	16.3327i	−0.386112	+	0.932158i	0.604643	+	0.796497i	$0.293316\pi$
$307$	−6.76523	+	16.3327i	−0.386112	+	0.932158i	−0.990755	+	0.135661i	$0.956684\pi$
$308$		0			0
$309$	−41.7523	+	17.2944i	−2.37521	+	0.983843i
$310$		0			0
$311$	−9.48818	−	9.48818i	−0.538025	−	0.538025i	0.384923	−	0.922949i	$-0.374228\pi$
$311$	−9.48818	−	9.48818i	−0.538025	−	0.538025i	−0.922949	+	0.384923i	$0.874228\pi$
$312$		0			0
$313$	8.39347	−	8.39347i	0.474427	−	0.474427i	−0.428917	−	0.903344i	$-0.641105\pi$
$313$	8.39347	−	8.39347i	0.474427	−	0.474427i	0.903344	+	0.428917i	$0.141105\pi$
$314$		0			0
$315$	−10.9680	−	26.4791i	−0.617977	−	1.49193i
$316$		0			0
$317$	26.5907	+	11.0142i	1.49348	+	0.618621i	0.972072	−	0.234683i	$-0.0754053\pi$
$317$	26.5907	+	11.0142i	1.49348	+	0.618621i	0.521413	+	0.853305i	$0.325405\pi$
$318$		0			0
$319$	8.71115			0.487731
$320$		0			0
$321$	31.1309			1.73756
$322$		0			0
$323$	−9.12069	−	3.77791i	−0.507489	−	0.210209i
$324$		0			0
$325$	−5.53040	−	13.3516i	−0.306772	−	0.740612i
$326$		0			0
$327$	−23.4368	+	23.4368i	−1.29606	+	1.29606i
$328$		0			0
$329$	2.77836	+	2.77836i	0.153176	+	0.153176i
$330$		0			0
$331$	−9.42728	+	3.90491i	−0.518170	+	0.214633i	−0.626413	−	0.779491i	$-0.715478\pi$
$331$	−9.42728	+	3.90491i	−0.518170	+	0.214633i	0.108243	+	0.994124i	$0.465478\pi$
$332$		0			0
$333$	14.3096	−	34.5464i	0.784160	−	1.89313i
$334$		0			0
$335$			40.6943i			2.22337i
$336$		0			0
$337$		−	2.82843i		−	0.154074i	−0.997028	−	0.0770371i	$-0.975454\pi$
$337$		−	2.82843i		−	0.154074i	0.997028	−	0.0770371i	$-0.0245460\pi$
$338$		0			0
$339$	−3.08856	+	7.45645i	−0.167748	+	0.404979i
$340$		0			0
$341$	1.61082	−	0.667224i	0.0872308	−	0.0361322i
$342$		0			0
$343$	11.4417	+	11.4417i	0.617794	+	0.617794i
$344$		0			0
$345$	16.7026	−	16.7026i	0.899239	−	0.899239i
$346$		0			0
$347$	−0.101243	−	0.244423i	−0.00543503	−	0.0131213i	0.921139	−	0.389234i	$-0.127260\pi$
$347$	−0.101243	−	0.244423i	−0.00543503	−	0.0131213i	−0.926574	+	0.376113i	$0.877260\pi$
$348$		0			0
$349$	1.72727	+	0.715459i	0.0924586	+	0.0382976i	0.428433	−	0.903573i	$-0.359066\pi$
$349$	1.72727	+	0.715459i	0.0924586	+	0.0382976i	−0.335975	+	0.941871i	$0.609066\pi$
$350$		0			0
$351$	−34.7159			−1.85300
$352$		0			0
$353$	22.0270			1.17238			0.586189	−	0.810175i	$-0.300628\pi$
$353$	22.0270			1.17238			0.586189	+	0.810175i	$0.300628\pi$
$354$		0			0
$355$	24.3745	+	10.0962i	1.29366	+	0.535853i
$356$		0			0
$357$	−2.55442	−	6.16691i	−0.135194	−	0.326388i
$358$		0			0
$359$	9.40689	−	9.40689i	0.496477	−	0.496477i	−0.413863	−	0.910339i	$-0.635821\pi$
$359$	9.40689	−	9.40689i	0.496477	−	0.496477i	0.910339	+	0.413863i	$0.135821\pi$
$360$		0			0
$361$	−13.1242	−	13.1242i	−0.690746	−	0.690746i
$362$		0			0
$363$	−28.1384	+	11.6553i	−1.47688	+	0.611745i
$364$		0			0
$365$	6.36818	−	15.3741i	0.333326	−	0.804720i
$366$		0			0
$367$		−	6.57941i		−	0.343442i	−0.985146	−	0.171721i	$-0.945067\pi$
$367$		−	6.57941i		−	0.343442i	0.985146	−	0.171721i	$-0.0549328\pi$
$368$		0			0
$369$		−	10.0354i		−	0.522422i
$370$		0			0
$371$	5.56069	−	13.4247i	0.288697	−	0.696976i
$372$		0			0
$373$	13.2298	−	5.47997i	0.685014	−	0.283742i	−0.0129074	−	0.999917i	$-0.504109\pi$
$373$	13.2298	−	5.47997i	0.685014	−	0.283742i	0.697921	+	0.716175i	$0.254109\pi$
$374$		0			0
$375$	0.248943	+	0.248943i	0.0128554	+	0.0128554i
$376$		0			0
$377$	−15.5207	+	15.5207i	−0.799356	+	0.799356i
$378$		0			0
$379$	−3.55000	−	8.57046i	−0.182351	−	0.440235i	0.806099	−	0.591781i	$-0.201575\pi$
$379$	−3.55000	−	8.57046i	−0.182351	−	0.440235i	−0.988450	+	0.151546i	$0.951575\pi$
$380$		0			0
$381$	−17.8681	−	7.40122i	−0.915412	−	0.379176i
$382$		0			0
$383$	21.6316			1.10532			0.552661	−	0.833406i	$-0.313612\pi$
$383$	21.6316			1.10532			0.552661	+	0.833406i	$0.313612\pi$
$384$		0			0
$385$	−4.76333			−0.242762
$386$		0			0
$387$	−27.2937	−	11.3054i	−1.38742	−	0.574687i
$388$		0			0
$389$	3.31161	+	7.99494i	0.167906	+	0.405360i	0.985326	−	0.170681i	$-0.0545968\pi$
$389$	3.31161	+	7.99494i	0.167906	+	0.405360i	−0.817421	+	0.576041i	$0.804597\pi$
$390$		0			0
$391$	2.70564	−	2.70564i	0.136830	−	0.136830i
$392$		0			0
$393$	4.62263	+	4.62263i	0.233181	+	0.233181i
$394$		0			0
$395$	30.4549	−	12.6148i	1.53235	−	0.634721i
$396$		0			0
$397$	−1.23136	+	2.97276i	−0.0618001	+	0.149199i	−0.951763	−	0.306834i	$-0.900730\pi$
$397$	−1.23136	+	2.97276i	−0.0618001	+	0.149199i	0.889963	+	0.456033i	$0.150730\pi$
$398$		0			0
$399$		−	25.3963i		−	1.27140i
$400$		0			0
$401$			22.2175i			1.10949i	0.832021	+	0.554744i	$0.187184\pi$
$401$			22.2175i			1.10949i	−0.832021	+	0.554744i	$0.812816\pi$
$402$		0			0
$403$	−1.68121	+	4.05880i	−0.0837471	+	0.202183i
$404$		0			0
$405$	50.9531	−	21.1055i	2.53188	−	1.04874i
$406$		0			0
$407$	−4.39435	−	4.39435i	−0.217820	−	0.217820i
$408$		0			0
$409$	17.8932	−	17.8932i	0.884760	−	0.884760i	−0.109254	−	0.994014i	$-0.534846\pi$
$409$	17.8932	−	17.8932i	0.884760	−	0.884760i	0.994014	+	0.109254i	$0.0348462\pi$
$410$		0			0
$411$	18.9105	+	45.6540i	0.932786	+	2.25195i
$412$		0			0
$413$	−10.6715	−	4.42029i	−0.525111	−	0.217508i
$414$		0			0
$415$	9.36765			0.459840
$416$		0			0
$417$	−33.8234			−1.65634
$418$		0			0
$419$	−23.2254	−	9.62029i	−1.13464	−	0.469982i	−0.265282	−	0.964171i	$-0.585465\pi$
$419$	−23.2254	−	9.62029i	−1.13464	−	0.469982i	−0.869354	+	0.494189i	$0.835465\pi$
$420$		0			0
$421$	8.42786	+	20.3467i	0.410749	+	0.991635i	0.984937	+	0.172912i	$0.0553176\pi$
$421$	8.42786	+	20.3467i	0.410749	+	0.991635i	−0.574189	+	0.818723i	$0.694682\pi$
$422$		0			0
$423$	−14.4241	+	14.4241i	−0.701322	+	0.701322i
$424$		0			0
$425$	5.73544	+	5.73544i	0.278210	+	0.278210i
$426$		0			0
$427$	−16.6915	+	6.91385i	−0.807759	+	0.334585i
$428$		0			0
$429$	−3.92689	+	9.48036i	−0.189592	+	0.457716i
$430$		0			0
$431$		−	32.2075i		−	1.55138i	−0.631115	−	0.775689i	$-0.717402\pi$
$431$		−	32.2075i		−	1.55138i	0.631115	−	0.775689i	$-0.282598\pi$
$432$		0			0
$433$		−	29.4806i		−	1.41675i	−0.705837	−	0.708374i	$-0.749429\pi$
$433$		−	29.4806i		−	1.41675i	0.705837	−	0.708374i	$-0.250571\pi$
$434$		0			0
$435$	29.1035	−	70.2620i	1.39540	−	3.36880i
$436$		0			0
$437$	13.4499	−	5.57112i	0.643395	−	0.266503i
$438$		0			0
$439$	13.2529	+	13.2529i	0.632526	+	0.632526i	0.948701	−	0.316175i	$-0.102399\pi$
$439$	13.2529	+	13.2529i	0.632526	+	0.632526i	−0.316175	+	0.948701i	$0.602399\pi$
$440$		0			0
$441$	−25.4776	+	25.4776i	−1.21322	+	1.21322i
$442$		0			0
$443$	13.1474	+	31.7407i	0.624653	+	1.50805i	0.846183	+	0.532893i	$0.178895\pi$
$443$	13.1474	+	31.7407i	0.624653	+	1.50805i	−0.221529	+	0.975154i	$0.571105\pi$
$444$		0			0
$445$	27.1669	+	11.2529i	1.28784	+	0.533439i
$446$		0			0
$447$	44.3929			2.09971
$448$		0			0
$449$	−34.2227			−1.61507			−0.807534	−	0.589821i	$-0.799198\pi$
$449$	−34.2227			−1.61507			−0.807534	+	0.589821i	$0.799198\pi$
$450$		0			0
$451$	−1.54089	−	0.638259i	−0.0725578	−	0.0300544i
$452$		0			0
$453$	−23.9392	−	57.7943i	−1.12476	−	2.71541i
$454$		0			0
$455$	8.48684	−	8.48684i	0.397869	−	0.397869i
$456$		0			0
$457$	9.79873	+	9.79873i	0.458365	+	0.458365i	0.898119	−	0.439753i	$-0.144934\pi$
$457$	9.79873	+	9.79873i	0.458365	+	0.458365i	−0.439753	+	0.898119i	$0.644934\pi$
$458$		0			0
$459$	18.0015	−	7.45645i	0.840237	−	0.348037i
$460$		0			0
$461$	1.83552	−	4.43134i	0.0854887	−	0.206388i	−0.875354	−	0.483483i	$-0.839372\pi$
$461$	1.83552	−	4.43134i	0.0854887	−	0.206388i	0.960843	+	0.277095i	$0.0893716\pi$
$462$		0			0
$463$		−	24.8164i		−	1.15332i	−0.816985	−	0.576658i	$-0.804356\pi$
$463$		−	24.8164i		−	1.15332i	0.816985	−	0.576658i	$-0.195644\pi$
$464$		0			0
$465$		−	15.2216i		−	0.705887i
$466$		0			0
$467$	−6.50725	+	15.7099i	−0.301120	+	0.726967i	0.698812	+	0.715305i	$0.253712\pi$
$467$	−6.50725	+	15.7099i	−0.301120	+	0.726967i	−0.999932	+	0.0116621i	$0.996288\pi$
$468$		0			0
$469$	−15.6672	+	6.48958i	−0.723445	+	0.299661i
$470$		0			0
$471$	−6.88628	−	6.88628i	−0.317303	−	0.317303i
$472$		0			0
$473$	−3.47180	+	3.47180i	−0.159633	+	0.159633i
$474$		0			0
$475$	11.8097	+	28.5111i	0.541866	+	1.30818i
$476$		0			0
$477$	69.6954	+	28.8688i	3.19113	+	1.32181i
$478$		0			0
$479$	−35.7254			−1.63234			−0.816168	−	0.577815i	$-0.803905\pi$
$479$	−35.7254			−1.63234			−0.816168	+	0.577815i	$0.803905\pi$
$480$		0			0
$481$	15.6589			0.713982
$482$		0			0
$483$	9.09407	+	3.76689i	0.413795	+	0.171399i
$484$		0			0
$485$	−1.22486	−	2.95708i	−0.0556181	−	0.134274i
$486$		0			0
$487$	−5.34809	+	5.34809i	−0.242345	+	0.242345i	−0.817820	−	0.575475i	$-0.804817\pi$
$487$	−5.34809	+	5.34809i	−0.242345	+	0.242345i	0.575475	+	0.817820i	$0.304817\pi$
$488$		0			0
$489$	22.1240	+	22.1240i	1.00048	+	1.00048i
$490$		0			0
$491$	40.7647	−	16.8853i	1.83968	−	0.762022i	0.884104	−	0.467291i	$-0.154770\pi$
$491$	40.7647	−	16.8853i	1.83968	−	0.762022i	0.955580	−	0.294731i	$-0.0952302\pi$
$492$		0			0
$493$	4.71444	−	11.3817i	0.212328	−	0.512604i
$494$		0			0
$495$		−	24.7292i		−	1.11149i
$496$		0			0
$497$			10.9942i			0.493157i
$498$		0			0
$499$	−1.95447	+	4.71852i	−0.0874943	+	0.211230i	−0.961570	−	0.274560i	$-0.911468\pi$
$499$	−1.95447	+	4.71852i	−0.0874943	+	0.211230i	0.874076	+	0.485790i	$0.161468\pi$
$500$		0			0
$501$	25.2630	−	10.4643i	1.12867	−	0.467510i
$502$		0			0
$503$	−4.81469	−	4.81469i	−0.214676	−	0.214676i	0.591574	−	0.806251i	$-0.298507\pi$
$503$	−4.81469	−	4.81469i	−0.214676	−	0.214676i	−0.806251	+	0.591574i	$0.798507\pi$
$504$		0			0
$505$	24.4053	−	24.4053i	1.08602	−	1.08602i
$506$		0			0
$507$	5.72164	+	13.8133i	0.254107	+	0.613469i
$508$		0			0
$509$	−5.71949	−	2.36909i	−0.253512	−	0.105008i	0.252308	−	0.967647i	$-0.418810\pi$
$509$	−5.71949	−	2.36909i	−0.253512	−	0.105008i	−0.505821	+	0.862639i	$0.668810\pi$
$510$		0			0
$511$	6.93456			0.306767
$512$		0			0
$513$	74.1328			3.27304
$514$		0			0
$515$	42.1360	+	17.4533i	1.85674	+	0.769085i
$516$		0			0
$517$	1.29737	+	3.13213i	0.0570584	+	0.137751i
$518$		0			0
$519$	−23.3331	+	23.3331i	−1.02421	+	1.02421i
$520$		0			0
$521$	13.8240	+	13.8240i	0.605642	+	0.605642i	0.941804	−	0.336162i	$-0.109129\pi$
$521$	13.8240	+	13.8240i	0.605642	+	0.605642i	−0.336162	+	0.941804i	$0.609129\pi$
$522$		0			0
$523$	7.51144	−	3.11134i	0.328452	−	0.136049i	−0.212363	−	0.977191i	$-0.568116\pi$
$523$	7.51144	−	3.11134i	0.328452	−	0.136049i	0.540815	+	0.841141i	$0.318116\pi$
$524$		0			0
$525$	−7.98508	+	19.2777i	−0.348497	+	0.841347i
$526$		0			0
$527$		−	2.46574i		−	0.107409i
$528$		0			0
$529$		−	17.3574i		−	0.754671i
$530$		0			0
$531$	22.9483	−	55.4020i	0.995870	−	2.40424i
$532$		0			0
$533$	3.88260	−	1.60823i	0.168174	−	0.0696600i
$534$		0			0
$535$	−22.2152	−	22.2152i	−0.960445	−	0.960445i
$536$		0			0
$537$	−36.8116	+	36.8116i	−1.58854	+	1.58854i
$538$		0			0
$539$	2.29158	+	5.53237i	0.0987054	+	0.238296i
$540$		0			0
$541$	−21.9728	−	9.10142i	−0.944683	−	0.391300i	−0.143453	−	0.989657i	$-0.545821\pi$
$541$	−21.9728	−	9.10142i	−0.944683	−	0.391300i	−0.801230	+	0.598357i	$0.795821\pi$
$542$		0			0
$543$	14.0194			0.601629
$544$		0			0
$545$	33.4493			1.43281
$546$		0			0
$547$	39.2456	+	16.2561i	1.67802	+	0.695060i	0.999229	−	0.0392692i	$-0.0125030\pi$
$547$	39.2456	+	16.2561i	1.67802	+	0.695060i	0.678794	+	0.734329i	$0.262503\pi$
$548$		0			0
$549$	−35.8938	−	86.6553i	−1.53191	−	3.69836i
$550$		0			0
$551$	33.1431	−	33.1431i	1.41194	−	1.41194i
$552$		0			0
$553$	9.71336	+	9.71336i	0.413054	+	0.413054i
$554$		0			0
$555$	−50.1250	+	20.7625i	−2.12769	+	0.881317i
$556$		0			0
$557$	16.0835	−	38.8291i	0.681481	−	1.64524i	−0.0797936	−	0.996811i	$-0.525426\pi$
$557$	16.0835	−	38.8291i	0.681481	−	1.64524i	0.761275	−	0.648429i	$-0.224574\pi$
$558$		0			0
$559$		−	12.3714i		−	0.523256i
$560$		0			0
$561$		−	5.75936i		−	0.243160i
$562$		0			0
$563$	−15.3396	+	37.0331i	−0.646487	+	1.56076i	0.171289	+	0.985221i	$0.445207\pi$
$563$	−15.3396	+	37.0331i	−0.646487	+	1.56076i	−0.817776	+	0.575536i	$0.804793\pi$
$564$		0			0
$565$	7.52498	−	3.11695i	0.316578	−	0.131131i
$566$		0			0
$567$	16.2511	+	16.2511i	0.682483	+	0.682483i
$568$		0			0
$569$	18.5518	−	18.5518i	0.777732	−	0.777732i	−0.201713	−	0.979445i	$-0.564651\pi$
$569$	18.5518	−	18.5518i	0.777732	−	0.777732i	0.979445	+	0.201713i	$0.0646508\pi$
$570$		0			0
$571$	1.94591	+	4.69785i	0.0814340	+	0.196599i	0.959352	−	0.282212i	$-0.0910680\pi$
$571$	1.94591	+	4.69785i	0.0814340	+	0.196599i	−0.877918	+	0.478811i	$0.841068\pi$
$572$		0			0
$573$	−42.9152	−	17.7761i	−1.79281	−	0.742606i
$574$		0			0
$575$	−11.9611			−0.498814
$576$		0			0
$577$	−36.3839			−1.51468			−0.757341	−	0.653020i	$-0.773502\pi$
$577$	−36.3839			−1.51468			−0.757341	+	0.653020i	$0.773502\pi$
$578$		0			0
$579$	−19.3355	−	8.00902i	−0.803555	−	0.332843i
$580$		0			0
$581$	1.49387	+	3.60653i	0.0619762	+	0.149624i
$582$		0			0
$583$	8.86535	−	8.86535i	0.367165	−	0.367165i
$584$		0			0
$585$	44.0601	+	44.0601i	1.82166	+	1.82166i
$586$		0			0
$587$	−26.2613	+	10.8778i	−1.08392	+	0.448974i	−0.851883	−	0.523733i	$-0.824539\pi$
$587$	−26.2613	+	10.8778i	−1.08392	+	0.448974i	−0.232037	+	0.972707i	$0.574539\pi$
$588$		0			0
$589$	3.59008	−	8.66722i	0.147927	−	0.357127i
$590$		0			0
$591$		−	51.2830i		−	2.10950i
$592$		0			0
$593$			8.36388i			0.343464i	0.985144	+	0.171732i	$0.0549362\pi$
$593$			8.36388i			0.343464i	−0.985144	+	0.171732i	$0.945064\pi$
$594$		0			0
$595$	−2.57789	+	6.22359i	−0.105683	+	0.255142i
$596$		0			0
$597$	2.79847	−	1.15916i	0.114534	−	0.0474414i
$598$		0			0
$599$	10.8797	+	10.8797i	0.444531	+	0.444531i	0.893531	−	0.449001i	$-0.148220\pi$
$599$	10.8797	+	10.8797i	0.444531	+	0.444531i	−0.449001	+	0.893531i	$0.648220\pi$
$600$		0			0
$601$	−13.9066	+	13.9066i	−0.567264	+	0.567264i	−0.931361	−	0.364097i	$-0.881378\pi$
$601$	−13.9066	+	13.9066i	−0.567264	+	0.567264i	0.364097	+	0.931361i	$0.381378\pi$
$602$		0			0
$603$	−33.6911	−	81.3376i	−1.37201	−	3.31232i
$604$		0			0
$605$	28.3970	+	11.7624i	1.15450	+	0.478210i
$606$		0			0
$607$	42.3665			1.71960			0.859801	−	0.510629i	$-0.170588\pi$
$607$	42.3665			1.71960			0.859801	+	0.510629i	$0.170588\pi$
$608$		0			0
$609$	31.6919			1.28422
$610$		0			0
$611$	−7.89207	−	3.26900i	−0.319279	−	0.132250i
$612$		0			0
$613$	5.50500	+	13.2902i	0.222345	+	0.536788i	0.995208	−	0.0977853i	$-0.0311758\pi$
$613$	5.50500	+	13.2902i	0.222345	+	0.536788i	−0.772863	+	0.634573i	$0.781176\pi$
$614$		0			0
$615$	−10.2961	+	10.2961i	−0.415178	+	0.415178i
$616$		0			0
$617$	17.8105	+	17.8105i	0.717025	+	0.717025i	0.967995	−	0.250970i	$-0.0807494\pi$
$617$	17.8105	+	17.8105i	0.717025	+	0.717025i	−0.250970	+	0.967995i	$0.580749\pi$
$618$		0			0
$619$	−11.6033	+	4.80624i	−0.466376	+	0.193179i	−0.603481	−	0.797377i	$-0.706220\pi$
$619$	−11.6033	+	4.80624i	−0.466376	+	0.193179i	0.137105	+	0.990556i	$0.456220\pi$
$620$		0			0
$621$	−10.9957	+	26.5460i	−0.441242	+	1.06525i
$622$		0			0
$623$			12.2537i			0.490935i
$624$		0			0
$625$			24.8217i			0.992869i
$626$		0			0
$627$	8.38555	−	20.2445i	0.334886	−	0.808487i
$628$		0			0
$629$	−8.11970	+	3.36329i	−0.323753	+	0.134103i
$630$		0			0
$631$	12.8865	+	12.8865i	0.513004	+	0.513004i	0.915446	−	0.402442i	$-0.131838\pi$
$631$	12.8865	+	12.8865i	0.513004	+	0.513004i	−0.402442	+	0.915446i	$0.631838\pi$
$632$		0			0
$633$	37.3355	−	37.3355i	1.48395	−	1.48395i
$634$		0			0
$635$	7.46924	+	18.0323i	0.296408	+	0.715592i
$636$		0			0
$637$	−13.9400	−	5.77412i	−0.552321	−	0.228779i
$638$		0			0
$639$	−57.0772			−2.25794
$640$		0			0
$641$	−12.6050			−0.497868			−0.248934	−	0.968520i	$-0.580080\pi$
$641$	−12.6050			−0.497868			−0.248934	+	0.968520i	$0.580080\pi$
$642$		0			0
$643$	14.2632	+	5.90799i	0.562484	+	0.232988i	0.645763	−	0.763538i	$-0.276539\pi$
$643$	14.2632	+	5.90799i	0.562484	+	0.232988i	−0.0832793	+	0.996526i	$0.526539\pi$
$644$		0			0
$645$	16.4036	+	39.6018i	0.645891	+	1.55932i
$646$		0			0
$647$	−19.4412	+	19.4412i	−0.764314	+	0.764314i	−0.977099	−	0.212785i	$-0.931747\pi$
$647$	−19.4412	+	19.4412i	−0.764314	+	0.764314i	0.212785	+	0.977099i	$0.431747\pi$
$648$		0			0
$649$	−7.04722	−	7.04722i	−0.276627	−	0.276627i
$650$		0			0
$651$	5.86030	−	2.42742i	0.229683	−	0.0951380i
$652$		0			0
$653$	−1.40282	+	3.38672i	−0.0548968	+	0.132533i	−0.948948	−	0.315432i	$-0.897851\pi$
$653$	−1.40282	+	3.38672i	−0.0548968	+	0.132533i	0.894052	+	0.447964i	$0.147851\pi$
$654$		0			0
$655$		−	6.59747i		−	0.257784i
$656$		0			0
$657$			36.0013i			1.40454i
$658$		0			0
$659$	6.44977	−	15.5711i	0.251247	−	0.606565i	−0.747058	−	0.664759i	$-0.768534\pi$
$659$	6.44977	−	15.5711i	0.251247	−	0.606565i	0.998305	+	0.0581942i	$0.0185343\pi$
$660$		0			0
$661$	−14.5801	+	6.03928i	−0.567100	+	0.234901i	−0.647764	−	0.761841i	$-0.724296\pi$
$661$	−14.5801	+	6.03928i	−0.567100	+	0.234901i	0.0806641	+	0.996741i	$0.474296\pi$
$662$		0			0
$663$	10.2615	+	10.2615i	0.398522	+	0.398522i
$664$		0			0
$665$	−18.1229	+	18.1229i	−0.702777	+	0.702777i
$666$		0			0
$667$	6.95218	+	16.7840i	0.269189	+	0.649880i
$668$		0			0
$669$	4.28208	+	1.77370i	0.165555	+	0.0685750i
$670$		0			0
$671$	−15.5884			−0.601784
$672$		0			0
$673$	−18.1812			−0.700834			−0.350417	−	0.936594i	$-0.613960\pi$
$673$	−18.1812			−0.700834			−0.350417	+	0.936594i	$0.613960\pi$
$674$		0			0
$675$	−56.2724	−	23.3088i	−2.16592	−	0.897155i
$676$		0			0
$677$	14.7255	+	35.5504i	0.565945	+	1.36631i	0.904946	+	0.425527i	$0.139911\pi$
$677$	14.7255	+	35.5504i	0.565945	+	1.36631i	−0.339000	+	0.940786i	$0.610089\pi$
$678$		0			0
$679$	0.943139	−	0.943139i	0.0361944	−	0.0361944i
$680$		0			0
$681$	−62.7595	−	62.7595i	−2.40495	−	2.40495i
$682$		0			0
$683$	5.69296	−	2.35810i	0.217835	−	0.0902303i	−0.271097	−	0.962552i	$-0.587386\pi$
$683$	5.69296	−	2.35810i	0.217835	−	0.0902303i	0.488932	+	0.872322i	$0.337386\pi$
$684$		0			0
$685$	19.0843	−	46.0736i	0.729173	−	1.76038i
$686$		0			0
$687$			29.6619i			1.13167i
$688$		0			0
$689$			31.5909i			1.20352i
$690$		0			0
$691$	2.68727	−	6.48765i	0.102229	−	0.246802i	−0.864487	−	0.502655i	$-0.832356\pi$
$691$	2.68727	−	6.48765i	0.102229	−	0.246802i	0.966716	+	0.255854i	$0.0823565\pi$
$692$		0			0
$693$	9.52069	−	3.94360i	0.361661	−	0.149805i
$694$		0			0
$695$	24.1366	+	24.1366i	0.915552	+	0.915552i
$696$		0			0
$697$	−1.66785	+	1.66785i	−0.0631743	+	0.0631743i
$698$		0			0
$699$	16.9755	+	40.9825i	0.642072	+	1.55010i
$700$		0			0
$701$	11.6300	+	4.81730i	0.439258	+	0.181947i	0.591342	−	0.806421i	$-0.298598\pi$
$701$	11.6300	+	4.81730i	0.439258	+	0.181947i	−0.152084	+	0.988368i	$0.548598\pi$
$702$		0			0
$703$	−33.4381			−1.26114
$704$		0			0
$705$	29.5975			1.11470
$706$		0			0
$707$	13.2879	+	5.50404i	0.499744	+	0.207001i
$708$		0			0
$709$	0.857335	+	2.06979i	0.0321979	+	0.0777326i	0.939161	−	0.343478i	$-0.111605\pi$
$709$	0.857335	+	2.06979i	0.0321979	+	0.0777326i	−0.906963	+	0.421211i	$0.861605\pi$
$710$		0			0
$711$	−50.4277	+	50.4277i	−1.89119	+	1.89119i
$712$		0			0
$713$	2.57112	+	2.57112i	0.0962893	+	0.0962893i
$714$		0			0
$715$	9.56749	−	3.96298i	0.357804	−	0.148207i
$716$		0			0
$717$	−12.7043	+	30.6709i	−0.474451	+	1.14543i
$718$		0			0
$719$			29.4245i			1.09735i	0.836036	+	0.548674i	$0.184867\pi$
$719$			29.4245i			1.09735i	−0.836036	+	0.548674i	$0.815133\pi$
$720$		0			0
$721$			19.0056i			0.707806i
$722$		0			0
$723$	0.829880	−	2.00351i	0.0308636	−	0.0745113i
$724$		0			0
$725$	−35.5789	+	14.7373i	−1.32137	+	0.547329i
$726$		0			0
$727$	−1.75350	−	1.75350i	−0.0650337	−	0.0650337i	0.673842	−	0.738876i	$-0.264643\pi$
$727$	−1.75350	−	1.75350i	−0.0650337	−	0.0650337i	−0.738876	+	0.673842i	$0.764643\pi$
$728$		0			0
$729$	−3.82254	+	3.82254i	−0.141575	+	0.141575i
$730$		0			0
$731$	2.65720	+	6.41505i	0.0982801	+	0.237269i
$732$		0			0
$733$	−1.08042	−	0.447524i	−0.0399062	−	0.0165297i	0.362641	−	0.931929i	$-0.381875\pi$
$733$	−1.08042	−	0.447524i	−0.0399062	−	0.0165297i	−0.402547	+	0.915399i	$0.631875\pi$
$734$		0			0
$735$	52.2787			1.92833
$736$		0			0
$737$	−14.6318			−0.538970
$738$		0			0
$739$	−36.3968	−	15.0760i	−1.33888	−	0.554581i	−0.405703	−	0.914005i	$-0.632973\pi$
$739$	−36.3968	−	15.0760i	−1.33888	−	0.554581i	−0.933174	+	0.359424i	$0.882973\pi$
$740$		0			0
$741$	21.1291	+	51.0103i	0.776198	+	1.87391i
$742$		0			0
$743$	1.45255	−	1.45255i	0.0532888	−	0.0532888i	−0.679960	−	0.733249i	$-0.738003\pi$
$743$	1.45255	−	1.45255i	0.0532888	−	0.0532888i	0.733249	+	0.679960i	$0.238003\pi$
$744$		0			0
$745$	−31.6790	−	31.6790i	−1.16063	−	1.16063i
$746$		0			0
$747$	−18.7236	+	7.75555i	−0.685059	+	0.283761i
$748$		0			0
$749$	5.01011	−	12.0955i	0.183065	−	0.441959i
$750$		0			0
$751$			17.4254i			0.635861i	0.948114	+	0.317931i	$0.102988\pi$
$751$			17.4254i			0.635861i	−0.948114	+	0.317931i	$0.897012\pi$
$752$		0			0
$753$		−	49.9126i		−	1.81892i
$754$		0			0
$755$	−24.1592	+	58.3255i	−0.879243	+	2.12268i
$756$		0			0
$757$	−26.2830	+	10.8868i	−0.955272	+	0.395686i	−0.805210	−	0.592990i	$-0.797947\pi$
$757$	−26.2830	+	10.8868i	−0.955272	+	0.395686i	−0.150062	+	0.988677i	$0.547947\pi$
$758$		0			0
$759$	6.00551	+	6.00551i	0.217986	+	0.217986i
$760$		0			0
$761$	13.6001	−	13.6001i	0.493003	−	0.493003i	−0.416248	−	0.909251i	$-0.636655\pi$
$761$	13.6001	−	13.6001i	0.493003	−	0.493003i	0.909251	+	0.416248i	$0.136655\pi$
$762$		0			0
$763$	5.33420	+	12.8779i	0.193111	+	0.466211i
$764$		0			0
$765$	−32.3102	−	13.3833i	−1.16818	−	0.483875i
$766$		0			0
$767$	25.1121			0.906745
$768$		0			0
$769$	−8.19053			−0.295358			−0.147679	−	0.989035i	$-0.547180\pi$
$769$	−8.19053			−0.295358			−0.147679	+	0.989035i	$0.547180\pi$
$770$		0			0
$771$	−34.1999	−	14.1661i	−1.23168	−	0.510179i
$772$		0			0
$773$	−12.3176	−	29.7373i	−0.443033	−	1.06958i	−0.974879	−	0.222735i	$-0.928502\pi$
$773$	−12.3176	−	29.7373i	−0.443033	−	1.06958i	0.531847	−	0.846841i	$-0.321498\pi$
$774$		0			0
$775$	−5.45028	+	5.45028i	−0.195780	+	0.195780i
$776$		0			0
$777$	−15.9870	−	15.9870i	−0.573531	−	0.573531i
$778$		0			0
$779$	−8.29097	+	3.43423i	−0.297055	+	0.123044i
$780$		0			0
$781$	−3.63015	+	8.76395i	−0.129897	+	0.313599i
$782$		0			0
$783$			92.5100i			3.30604i
$784$		0			0
$785$			9.82817i			0.350782i
$786$		0			0
$787$	3.89741	−	9.40919i	0.138928	−	0.335401i	−0.839068	−	0.544027i	$-0.816899\pi$
$787$	3.89741	−	9.40919i	0.138928	−	0.335401i	0.977996	+	0.208626i	$0.0668990\pi$
$788$		0			0
$789$	84.0504	−	34.8148i	2.99227	−	1.23944i
$790$		0			0
$791$	2.40004	+	2.40004i	0.0853356	+	0.0853356i
$792$		0			0
$793$	27.7740	−	27.7740i	0.986282	−	0.986282i
$794$		0			0
$795$	−41.8871	−	101.124i	−1.48558	−	3.58651i
$796$		0			0
$797$	17.2799	+	7.15756i	0.612085	+	0.253534i	0.667120	−	0.744951i	$-0.267527\pi$
$797$	17.2799	+	7.15756i	0.612085	+	0.253534i	−0.0550349	+	0.998484i	$0.517527\pi$
$798$		0			0
$799$	4.79446			0.169616
$800$		0			0
$801$	−63.6162			−2.24777
$802$		0			0
$803$	5.52785	+	2.28971i	0.195073	+	0.0808021i
$804$		0			0
$805$	−3.80151	−	9.17765i	−0.133985	−	0.323470i
$806$		0			0
$807$	22.1996	−	22.1996i	0.781462	−	0.781462i
$808$		0			0
$809$	−28.3548	−	28.3548i	−0.996902	−	0.996902i	0.00309284	−	0.999995i	$-0.499016\pi$
$809$	−28.3548	−	28.3548i	−0.996902	−	0.996902i	−0.999995	+	0.00309284i	$0.999016\pi$
$810$		0			0
$811$	−3.90316	+	1.61674i	−0.137059	+	0.0567716i	−0.450159	−	0.892949i	$-0.648633\pi$
$811$	−3.90316	+	1.61674i	−0.137059	+	0.0567716i	0.313100	+	0.949720i	$0.398633\pi$
$812$		0			0
$813$	30.2760	−	73.0927i	1.06183	−	2.56347i
$814$		0			0
$815$		−	31.5756i		−	1.10604i
$816$		0			0
$817$			26.4181i			0.924254i
$818$		0			0
$819$	−9.93672	+	23.9894i	−0.347217	+	0.838256i
$820$		0			0
$821$	27.8360	−	11.5300i	0.971482	−	0.402401i	0.160218	−	0.987082i	$-0.448780\pi$
$821$	27.8360	−	11.5300i	0.971482	−	0.402401i	0.811264	+	0.584681i	$0.198780\pi$
$822$		0			0
$823$	−30.7602	−	30.7602i	−1.07223	−	1.07223i	−0.997179	−	0.0750551i	$-0.976087\pi$
$823$	−30.7602	−	30.7602i	−1.07223	−	1.07223i	−0.0750551	−	0.997179i	$-0.523913\pi$
$824$		0			0
$825$	−12.7305	+	12.7305i	−0.443220	+	0.443220i
$826$		0			0
$827$	−9.60486	−	23.1882i	−0.333994	−	0.806332i	−0.998267	−	0.0588423i	$-0.981259\pi$
$827$	−9.60486	−	23.1882i	−0.333994	−	0.806332i	0.664274	−	0.747489i	$-0.268741\pi$
$828$		0			0
$829$	−41.5185	−	17.1975i	−1.44200	−	0.597295i	−0.481715	−	0.876328i	$-0.659986\pi$
$829$	−41.5185	−	17.1975i	−1.44200	−	0.597295i	−0.960281	+	0.279033i	$0.909986\pi$
$830$		0			0
$831$	−46.3929			−1.60935
$832$		0			0
$833$	8.46858			0.293419
$834$		0			0
$835$	−25.4952	−	10.5605i	−0.882297	−	0.365459i
$836$		0			0
$837$	7.08573	+	17.1065i	0.244919	+	0.591286i
$838$		0			0
$839$	31.1198	−	31.1198i	1.07437	−	1.07437i	0.0773708	−	0.997002i	$-0.475347\pi$
$839$	31.1198	−	31.1198i	1.07437	−	1.07437i	0.997002	−	0.0773708i	$-0.0246525\pi$
$840$		0			0
$841$	20.8530	+	20.8530i	0.719070	+	0.719070i
$842$		0			0
$843$	18.2611	−	7.56398i	0.628944	−	0.260517i
$844$		0			0
$845$	5.77423	−	13.9402i	0.198639	−	0.479558i
$846$		0			0
$847$			12.8086i			0.440107i
$848$		0			0
$849$		−	76.5009i		−	2.62550i
$850$		0			0
$851$	4.95969	−	11.9738i	0.170016	−	0.410455i
$852$		0			0
$853$	−23.6797	+	9.80845i	−0.810777	+	0.335835i	−0.749264	−	0.662271i	$-0.769593\pi$
$853$	−23.6797	+	9.80845i	−0.810777	+	0.335835i	−0.0615130	+	0.998106i	$0.519593\pi$
$854$		0			0
$855$	−94.0865	−	94.0865i	−3.21769	−	3.21769i
$856$		0			0
$857$	24.7590	−	24.7590i	0.845752	−	0.845752i	−0.143847	−	0.989600i	$-0.545947\pi$
$857$	24.7590	−	24.7590i	0.845752	−	0.845752i	0.989600	+	0.143847i	$0.0459475\pi$
$858$		0			0
$859$	−3.30545	−	7.98006i	−0.112780	−	0.272276i	0.857404	−	0.514644i	$-0.172076\pi$
$859$	−3.30545	−	7.98006i	−0.112780	−	0.272276i	−0.970184	+	0.242368i	$0.922076\pi$
$860$		0			0
$861$	−5.60590	−	2.32204i	−0.191049	−	0.0791349i
$862$		0			0
$863$	35.4394			1.20637			0.603185	−	0.797601i	$-0.293898\pi$
$863$	35.4394			1.20637			0.603185	+	0.797601i	$0.293898\pi$
$864$		0			0
$865$	33.3012			1.13227
$866$		0			0
$867$	41.7764	+	17.3043i	1.41880	+	0.587686i
$868$		0			0
$869$	4.53572	+	10.9502i	0.153864	+	0.371460i
$870$		0			0
$871$	26.0696	−	26.0696i	0.883334	−	0.883334i
$872$		0			0
$873$	4.89638	+	4.89638i	0.165717	+	0.165717i
$874$		0			0
$875$	0.136788	−	0.0566593i	0.00462427	−	0.00191543i
$876$		0			0
$877$	−17.9341	+	43.2968i	−0.605593	+	1.46203i	0.262155	+	0.965026i	$0.415567\pi$
$877$	−17.9341	+	43.2968i	−0.605593	+	1.46203i	−0.867748	+	0.497005i	$0.834433\pi$
$878$		0			0
$879$			22.6591i			0.764274i
$880$		0			0
$881$		−	4.84917i		−	0.163373i	−0.996658	−	0.0816863i	$-0.973969\pi$
$881$		−	4.84917i		−	0.163373i	0.996658	−	0.0816863i	$-0.0260306\pi$
$882$		0			0
$883$	16.9445	−	40.9077i	0.570228	−	1.37665i	−0.331133	−	0.943584i	$-0.607431\pi$
$883$	16.9445	−	40.9077i	0.570228	−	1.37665i	0.901361	−	0.433068i	$-0.142569\pi$
$884$		0			0
$885$	−80.3855	+	33.2967i	−2.70213	+	1.11926i
$886$		0			0
$887$	7.77550	+	7.77550i	0.261076	+	0.261076i	0.825491	−	0.564415i	$-0.190898\pi$
$887$	7.77550	+	7.77550i	0.261076	+	0.261076i	−0.564415	+	0.825491i	$0.690898\pi$
$888$		0			0
$889$	−5.75128	+	5.75128i	−0.192892	+	0.192892i
$890$		0			0
$891$	7.58856	+	18.3204i	0.254226	+	0.613757i
$892$		0			0
$893$	16.8528	+	6.98067i	0.563959	+	0.233599i
$894$		0			0
$895$	52.5379			1.75615
$896$		0			0
$897$	−21.4001			−0.714527
$898$		0			0
$899$	10.8158	+	4.48005i	0.360727	+	0.149418i
$900$		0			0
$901$	−6.78525	−	16.3810i	−0.226049	−	0.545731i
$902$		0			0
$903$	−12.6307	+	12.6307i	−0.420323	+	0.420323i
$904$		0			0
$905$	−10.0043	−	10.0043i	−0.332554	−	0.332554i
$906$		0			0
$907$	5.75906	−	2.38548i	0.191226	−	0.0792086i	−0.285015	−	0.958523i	$-0.591999\pi$
$907$	5.75906	−	2.38548i	0.191226	−	0.0792086i	0.476242	+	0.879314i	$0.341999\pi$
$908$		0			0
$909$	−28.5746	+	68.9853i	−0.947761	+	2.28810i
$910$		0			0
$911$			15.3924i			0.509973i	0.966945	+	0.254986i	$0.0820710\pi$
$911$			15.3924i			0.509973i	−0.966945	+	0.254986i	$0.917929\pi$
$912$		0			0
$913$			3.36818i			0.111470i
$914$		0			0
$915$	−52.0801	+	125.732i	−1.72171	+	4.15658i
$916$		0			0
$917$	2.54001	−	1.05211i	0.0838786	−	0.0347437i
$918$		0			0
$919$	13.0672	+	13.0672i	0.431046	+	0.431046i	0.888984	−	0.457938i	$-0.151412\pi$
$919$	13.0672	+	13.0672i	0.431046	+	0.431046i	−0.457938	+	0.888984i	$0.651412\pi$
$920$		0			0
$921$	−39.2394	+	39.2394i	−1.29298	+	1.29298i
$922$		0			0
$923$	−9.14692	−	22.0826i	−0.301075	−	0.726858i
$924$		0			0
$925$	25.3821	+	10.5136i	0.834557	+	0.345685i
$926$		0			0
$927$	−98.6690			−3.24072
$928$		0			0
$929$	14.4450			0.473924			0.236962	−	0.971519i	$-0.423848\pi$
$929$	14.4450			0.473924			0.236962	+	0.971519i	$0.423848\pi$
$930$		0			0
$931$	29.7676	+	12.3301i	0.975593	+	0.404104i
$932$		0			0
$933$	−16.1188	−	38.9142i	−0.527705	−	1.27399i
$934$		0			0
$935$	−4.10991	+	4.10991i	−0.134408	+	0.134408i
$936$		0			0
$937$	4.56931	+	4.56931i	0.149273	+	0.149273i	0.777793	−	0.628520i	$-0.216339\pi$
$937$	4.56931	+	4.56931i	0.149273	+	0.149273i	−0.628520	+	0.777793i	$0.716339\pi$
$938$		0			0
$939$	34.4244	−	14.2591i	1.12340	−	0.465327i
$940$		0			0
$941$	−7.29813	+	17.6192i	−0.237912	+	0.574371i	−0.997067	−	0.0765397i	$-0.975613\pi$
$941$	−7.29813	+	17.6192i	−0.237912	+	0.574371i	0.759154	+	0.650911i	$0.225613\pi$
$942$		0			0
$943$		−	3.47827i		−	0.113268i
$944$		0			0
$945$		−	50.5852i		−	1.64554i
$946$		0			0
$947$	4.50198	−	10.8687i	0.146295	−	0.353187i	−0.833698	−	0.552221i	$-0.813780\pi$
$947$	4.50198	−	10.8687i	0.146295	−	0.353187i	0.979993	+	0.199034i	$0.0637805\pi$
$948$		0			0
$949$	−13.9286	+	5.76940i	−0.452140	+	0.187283i
$950$		0			0
$951$	63.8843	+	63.8843i	2.07159	+	2.07159i
$952$		0			0
$953$	−9.88290	+	9.88290i	−0.320138	+	0.320138i	−0.848820	−	0.528682i	$-0.822687\pi$
$953$	−9.88290	+	9.88290i	−0.320138	+	0.320138i	0.528682	+	0.848820i	$0.322687\pi$
$954$		0			0
$955$	17.9394	+	43.3096i	0.580506	+	1.40147i
$956$		0			0
$957$	25.2630	+	10.4643i	0.816637	+	0.338262i
$958$		0			0
$959$	20.7816			0.671074
$960$		0			0
$961$	−28.6569			−0.924415
$962$		0			0
$963$	62.7946	+	26.0104i	2.02353	+	0.838173i
$964$		0			0
$965$	8.08262	+	19.5132i	0.260189	+	0.628151i
$966$		0			0
$967$	27.4467	−	27.4467i	0.882626	−	0.882626i	−0.111175	−	0.993801i	$-0.535461\pi$
$967$	27.4467	−	27.4467i	0.882626	−	0.882626i	0.993801	+	0.111175i	$0.0354614\pi$
$968$		0			0
$969$	−21.9125	−	21.9125i	−0.703931	−	0.703931i
$970$		0			0
$971$	52.2342	−	21.6361i	1.67627	−	0.694335i	0.677136	−	0.735858i	$-0.263221\pi$
$971$	52.2342	−	21.6361i	1.67627	−	0.694335i	0.999138	+	0.0415225i	$0.0132208\pi$
$972$		0			0
$973$	−5.44344	+	13.1416i	−0.174509	+	0.421301i
$974$		0			0
$975$		−	45.3640i		−	1.45281i
$976$		0			0
$977$		−	23.1041i		−	0.739165i	−0.929198	−	0.369582i	$-0.879501\pi$
$977$		−	23.1041i		−	0.739165i	0.929198	−	0.369582i	$-0.120499\pi$
$978$		0			0
$979$	−4.04603	+	9.76799i	−0.129312	+	0.312186i
$980$		0			0
$981$	−66.8566	+	27.6929i	−2.13457	+	0.884167i
$982$		0			0
$983$	−17.7442	−	17.7442i	−0.565951	−	0.565951i	0.365041	−	0.930991i	$-0.381055\pi$
$983$	−17.7442	−	17.7442i	−0.565951	−	0.565951i	−0.930991	+	0.365041i	$0.881055\pi$
$984$		0			0
$985$	−36.5958	+	36.5958i	−1.16604	+	1.16604i
$986$		0			0
$987$	4.71995	+	11.3950i	0.150238	+	0.362706i
$988$		0			0
$989$	−9.45999	−	3.91846i	−0.300810	−	0.124600i
$990$		0			0
$991$	−6.68692			−0.212417			−0.106208	−	0.994344i	$-0.533871\pi$
$991$	−6.68692			−0.212417			−0.106208	+	0.994344i	$0.533871\pi$
$992$		0			0
$993$	−32.0306			−1.01646
$994$		0			0
$995$	−2.82419	−	1.16982i	−0.0895328	−	0.0370857i
$996$		0			0
$997$	1.39557	+	3.36920i	0.0441981	+	0.106704i	0.944437	−	0.328693i	$-0.106608\pi$
$997$	1.39557	+	3.36920i	0.0441981	+	0.106704i	−0.900239	+	0.435397i	$0.856608\pi$
$998$		0			0
$999$	46.6668	−	46.6668i	1.47647	−	1.47647i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1024.2.g.c.641.4	yes	16
4.3	odd	2	inner	1024.2.g.c.641.1	yes	16
8.3	odd	2		1024.2.g.h.641.4	yes	16
8.5	even	2		1024.2.g.h.641.1	yes	16
16.3	odd	4		1024.2.g.b.129.4	yes	16
16.5	even	4		1024.2.g.e.129.4	yes	16
16.11	odd	4		1024.2.g.e.129.1	yes	16
16.13	even	4		1024.2.g.b.129.1	✓	16
32.3	odd	8		1024.2.g.e.897.1	yes	16
32.5	even	8		1024.2.g.h.385.1	yes	16
32.11	odd	8	inner	1024.2.g.c.385.1	yes	16
32.13	even	8		1024.2.g.b.897.1	yes	16
32.19	odd	8		1024.2.g.b.897.4	yes	16
32.21	even	8	inner	1024.2.g.c.385.4	yes	16
32.27	odd	8		1024.2.g.h.385.4	yes	16
32.29	even	8		1024.2.g.e.897.4	yes	16
64.11	odd	16		4096.2.a.n.1.2		8
64.21	even	16		4096.2.a.n.1.1		8
64.43	odd	16		4096.2.a.o.1.7		8
64.53	even	16		4096.2.a.o.1.8		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.b.129.1	✓	16	16.13	even	4
1024.2.g.b.129.4	yes	16	16.3	odd	4
1024.2.g.b.897.1	yes	16	32.13	even	8
1024.2.g.b.897.4	yes	16	32.19	odd	8
1024.2.g.c.385.1	yes	16	32.11	odd	8	inner
1024.2.g.c.385.4	yes	16	32.21	even	8	inner
1024.2.g.c.641.1	yes	16	4.3	odd	2	inner
1024.2.g.c.641.4	yes	16	1.1	even	1	trivial
1024.2.g.e.129.1	yes	16	16.11	odd	4
1024.2.g.e.129.4	yes	16	16.5	even	4
1024.2.g.e.897.1	yes	16	32.3	odd	8
1024.2.g.e.897.4	yes	16	32.29	even	8
1024.2.g.h.385.1	yes	16	32.5	even	8
1024.2.g.h.385.4	yes	16	32.27	odd	8
1024.2.g.h.641.1	yes	16	8.5	even	2
1024.2.g.h.641.4	yes	16	8.3	odd	2
4096.2.a.n.1.1		8	64.21	even	16
4096.2.a.n.1.2		8	64.11	odd	16
4096.2.a.o.1.7		8	64.43	odd	16
4096.2.a.o.1.8		8	64.53	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:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1024.g (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(2.90008 + 1.20125i) q^{3} +(-1.21229 - 2.92673i) q^{5} +(0.933460 - 0.933460i) q^{7} +(4.84613 + 4.84613i) q^{9} +O(q^{10})\)	\(q+(2.90008 + 1.20125i) q^{3} +(-1.21229 - 2.92673i) q^{5} +(0.933460 - 0.933460i) q^{7} +(4.84613 + 4.84613i) q^{9} +(1.05232 - 0.435885i) q^{11} +(-1.09830 + 2.65154i) q^{13} -9.94402i q^{15} -1.61082i q^{17} +(2.34533 - 5.66214i) q^{19} +(3.82843 - 1.58579i) q^{21} +(1.67967 + 1.67967i) q^{23} +(-3.56057 + 3.56057i) q^{25} +(4.62898 + 11.1753i) q^{27} +(7.06575 + 2.92673i) q^{29} +1.53073 q^{31} +3.57542 q^{33} +(-3.86361 - 1.60036i) q^{35} +(-2.08793 - 5.04072i) q^{37} +(-6.37033 + 6.37033i) q^{39} +(-1.03540 - 1.03540i) q^{41} +(-3.98247 + 1.64959i) q^{43} +(8.30839 - 20.0582i) q^{45} +2.97641i q^{47} +5.25731i q^{49} +(1.93500 - 4.67151i) q^{51} +(10.1694 - 4.21229i) q^{53} +(-2.55144 - 2.55144i) q^{55} +(13.6033 - 13.6033i) q^{57} +(-3.34842 - 8.08380i) q^{59} +(-12.6440 - 5.23733i) q^{61} +9.04733 q^{63} +9.09181 q^{65} +(-11.8681 - 4.91593i) q^{67} +(2.85346 + 6.88887i) q^{69} +(-5.88894 + 5.88894i) q^{71} +(3.71444 + 3.71444i) q^{73} +(-14.6031 + 6.04879i) q^{75} +(0.575417 - 1.38918i) q^{77} +10.4058i q^{79} +17.4096i q^{81} +(-1.13163 + 2.73199i) q^{83} +(-4.71444 + 1.95278i) q^{85} +(16.9755 + 16.9755i) q^{87} +(-6.56361 + 6.56361i) q^{89} +(1.44988 + 3.50033i) q^{91} +(4.43925 + 1.83880i) q^{93} -19.4148 q^{95} +1.01037 q^{97} +(7.21203 + 2.98732i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{5} + 16 q^{9}+O(q^{10}) \) 16 * q - 8 * q^5 + 16 * q^9	\( 16 q - 8 q^{5} + 16 q^{9} - 24 q^{13} + 16 q^{21} + 32 q^{25} + 24 q^{29} + 80 q^{33} - 40 q^{37} + 16 q^{41} - 24 q^{45} + 56 q^{53} + 80 q^{57} - 8 q^{61} + 32 q^{65} - 32 q^{69} + 32 q^{73} + 32 q^{77} - 48 q^{85} - 32 q^{89} + 16 q^{93} + 16 q^{97}+O(q^{100}) \) 16 * q - 8 * q^5 + 16 * q^9 - 24 * q^13 + 16 * q^21 + 32 * q^25 + 24 * q^29 + 80 * q^33 - 40 * q^37 + 16 * q^41 - 24 * q^45 + 56 * q^53 + 80 * q^57 - 8 * q^61 + 32 * q^65 - 32 * q^69 + 32 * q^73 + 32 * q^77 - 48 * q^85 - 32 * q^89 + 16 * q^93 + 16 * q^97

Introduction

L-functions

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Representations

Groups

Database

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