LMFDB - Embedded newform 1024.2.g.h.385.4

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			385.4
Root			$1.66798 + 0.466730i$ of defining polynomial
Character	$\chi$	$=$	1024.385
Dual form			1024.2.g.h.641.4

$q$-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 $\left(\mathbb{Z}/1024\mathbb{Z}\right)^\times$.

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

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
$3$	2.90008	−	1.20125i	1.67436	−	0.693543i	0.675328	−	0.737517i	$-0.264002\pi$
$3$	2.90008	−	1.20125i	1.67436	−	0.693543i	0.999033	+	0.0439740i	$0.0140019\pi$
$4$		0			0
$5$	1.21229	−	2.92673i	0.542153	−	1.30887i	−0.381047	−	0.924556i	$-0.624437\pi$
$5$	1.21229	−	2.92673i	0.542153	−	1.30887i	0.923201	−	0.384318i	$-0.125563\pi$
$6$		0			0
$7$	−0.933460	−	0.933460i	−0.352815	−	0.352815i	0.508341	−	0.861156i	$-0.330259\pi$
$7$	−0.933460	−	0.933460i	−0.352815	−	0.352815i	−0.861156	+	0.508341i	$0.830259\pi$
$8$		0			0
$9$	4.84613	−	4.84613i	1.61538	−	1.61538i
$10$		0			0
$11$	1.05232	+	0.435885i	0.317286	+	0.131424i	0.535643	−	0.844445i	$-0.320069\pi$
$11$	1.05232	+	0.435885i	0.317286	+	0.131424i	−0.218356	+	0.975869i	$0.570069\pi$
$12$		0			0
$13$	1.09830	+	2.65154i	0.304615	+	0.735405i	0.999862	+	0.0166339i	$0.00529498\pi$
$13$	1.09830	+	2.65154i	0.304615	+	0.735405i	−0.695247	+	0.718771i	$0.744705\pi$
$14$		0			0
$15$		−	9.94402i		−	2.56753i
$16$		0			0
$17$			1.61082i			0.390681i	0.980735	+	0.195341i	$0.0625813\pi$
$17$			1.61082i			0.390681i	−0.980735	+	0.195341i	$0.937419\pi$
$18$		0			0
$19$	2.34533	+	5.66214i	0.538056	+	1.29898i	0.926078	+	0.377333i	$0.123159\pi$
$19$	2.34533	+	5.66214i	0.538056	+	1.29898i	−0.388021	+	0.921650i	$0.626841\pi$
$20$		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	$-0.829659\pi$
$23$	−1.67967	+	1.67967i	−0.350235	+	0.350235i	0.509962	+	0.860197i	$0.329659\pi$
$24$		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	$-0.876346\pi$
$29$	−7.06575	+	2.92673i	−1.31208	+	0.543480i	−0.386588	+	0.922253i	$0.626346\pi$
$30$		0			0
$31$	−1.53073			−0.274928			−0.137464	−	0.990507i	$-0.543895\pi$
$31$	−1.53073			−0.274928			−0.137464	+	0.990507i	$0.543895\pi$
$32$		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	−0.654128	−	0.756384i	$-0.726964\pi$
$37$	2.08793	−	5.04072i	0.343254	−	0.828689i	0.997383	−	0.0723054i	$-0.0230356\pi$
$38$		0			0
$39$	6.37033	+	6.37033i	1.02007	+	1.02007i
$40$		0			0
$41$	−1.03540	+	1.03540i	−0.161703	+	0.161703i	−0.783321	−	0.621618i	$-0.786476\pi$
$41$	−1.03540	+	1.03540i	−0.161703	+	0.161703i	0.621618	+	0.783321i	$0.286476\pi$
$42$		0			0
$43$	−3.98247	−	1.64959i	−0.607321	−	0.251561i	0.0577615	−	0.998330i	$-0.481604\pi$
$43$	−3.98247	−	1.64959i	−0.607321	−	0.251561i	−0.665083	+	0.746770i	$0.731604\pi$
$44$		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	$-0.647840\pi$
$53$	−10.1694	−	4.21229i	−1.39687	−	0.578603i	−0.948937	+	0.315464i	$0.897840\pi$
$54$		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	0.541415	+	0.840756i	$0.317889\pi$
$59$	−3.34842	+	8.08380i	−0.435927	+	1.05242i	−0.977342	+	0.211666i	$0.932111\pi$
$60$		0			0
$61$	12.6440	−	5.23733i	1.61890	−	0.670571i	0.624978	−	0.780643i	$-0.285108\pi$
$61$	12.6440	−	5.23733i	1.61890	−	0.670571i	0.993924	+	0.110072i	$0.0351081\pi$
$62$		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	−0.962180	−	0.272413i	$-0.912178\pi$
$67$	−11.8681	+	4.91593i	−1.44992	+	0.600577i	−0.487739	+	0.872989i	$0.662178\pi$
$68$		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	$-0.0854650\pi$
$71$	5.88894	+	5.88894i	0.698889	+	0.698889i	−0.265282	+	0.964171i	$0.585465\pi$
$72$		0			0
$73$	3.71444	−	3.71444i	0.434742	−	0.434742i	−0.455496	−	0.890238i	$-0.650538\pi$
$73$	3.71444	−	3.71444i	0.434742	−	0.434742i	0.890238	+	0.455496i	$0.150538\pi$
$74$		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	0.849526	−	0.527547i	$-0.176888\pi$
$83$	−1.13163	−	2.73199i	−0.124212	−	0.299874i	−0.973738	+	0.227673i	$0.926888\pi$
$84$		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	0.267748	−	0.963489i	$-0.413720\pi$
$89$	−6.56361	−	6.56361i	−0.695741	−	0.695741i	−0.963489	+	0.267748i	$0.913720\pi$
$90$		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	0.568944	+	0.822376i	$0.307352\pi$
$101$	−4.16937	+	10.0658i	−0.414868	+	1.00158i	−0.983812	+	0.179204i	$0.942648\pi$
$102$		0			0
$103$	10.1802	+	10.1802i	1.00308	+	1.00308i	0.999995	+	0.00308887i	$0.000983218\pi$
$103$	10.1802	+	10.1802i	1.00308	+	1.00308i	0.00308887	+	0.999995i	$0.499017\pi$
$104$		0			0
$105$	−9.28234	+	9.28234i	−0.905864	+	0.905864i
$106$		0			0
$107$	9.16246	+	3.79522i	0.885769	+	0.366897i	0.778731	−	0.627357i	$-0.215864\pi$
$107$	9.16246	+	3.79522i	0.885769	+	0.366897i	0.107038	+	0.994255i	$0.465864\pi$
$108$		0			0
$109$	4.04072	+	9.75516i	0.387031	+	0.934375i	0.990566	+	0.137038i	$0.0437583\pi$
$109$	4.04072	+	9.75516i	0.387031	+	0.934375i	−0.603535	+	0.797336i	$0.706242\pi$
$110$		0			0
$111$		−	17.1266i		−	1.62559i
$112$		0			0
$113$		−	2.57112i		−	0.241871i	−0.992660	−	0.120935i	$-0.961411\pi$
$113$		−	2.57112i		−	0.241871i	0.992660	−	0.120935i	$-0.0385894\pi$
$114$		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	$-0.411864\pi$
$127$	6.16126			0.546723			0.273362	+	0.961911i	$0.411864\pi$
$128$		0			0
$129$	−13.5311			−1.19134
$130$		0			0
$131$	1.92409	−	0.796984i	0.168108	−	0.0696328i	−0.297042	−	0.954864i	$-0.596000\pi$
$131$	1.92409	−	0.796984i	0.168108	−	0.0696328i	0.465151	+	0.885232i	$0.346000\pi$
$132$		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	−0.0478269	−	0.998856i	$-0.515230\pi$
$137$	11.1315	−	11.1315i	0.951029	−	0.951029i	0.998856	+	0.0478269i	$0.0152296\pi$
$138$		0			0
$139$	−9.95493	−	4.12347i	−0.844366	−	0.349748i	−0.0817925	−	0.996649i	$-0.526064\pi$
$139$	−9.95493	−	4.12347i	−0.844366	−	0.349748i	−0.762574	+	0.646902i	$0.776064\pi$
$140$		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	$-0.571670\pi$
$149$	−13.0658	−	5.41201i	−1.07039	−	0.443369i	−0.847128	+	0.531389i	$0.821670\pi$
$150$		0			0
$151$	14.0916	−	14.0916i	1.14676	−	1.14676i	0.159572	−	0.987186i	$-0.448988\pi$
$151$	14.0916	−	14.0916i	1.14676	−	1.14676i	0.987186	−	0.159572i	$-0.0510115\pi$
$152$		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	$-0.585491\pi$
$157$	2.86629	−	1.18726i	0.228755	−	0.0947534i	0.494117	+	0.869395i	$0.335491\pi$
$158$		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	0.00831846	−	0.999965i	$-0.497352\pi$
$163$	9.20872	−	3.81438i	0.721283	−	0.298765i	0.712964	+	0.701200i	$0.247352\pi$
$164$		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	$-0.359427\pi$
$167$	−6.15971	−	6.15971i	−0.476653	−	0.476653i	−0.904059	+	0.427407i	$0.859427\pi$
$168$		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	0.999831	+	0.0183942i	$0.00585539\pi$
$173$	4.02283	+	9.71198i	0.305850	+	0.738388i	−0.693980	+	0.719994i	$0.744145\pi$
$174$		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	−0.962212	−	0.272301i	$-0.912215\pi$
$179$	−6.34665	−	15.3222i	−0.474371	−	1.14523i	0.487841	−	0.872932i	$-0.337785\pi$
$180$		0			0
$181$	−4.12619	−	1.70912i	−0.306697	−	0.127038i	0.224026	−	0.974583i	$-0.428080\pi$
$181$	−4.12619	−	1.70912i	−0.306697	−	0.127038i	−0.530724	+	0.847545i	$0.678080\pi$
$182$		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	$-0.320172\pi$
$191$	14.7979			1.07074			0.535371	+	0.844617i	$0.320172\pi$
$192$		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	−0.528577	−	0.848885i	$-0.677274\pi$
$197$	6.25199	−	15.0936i	0.445436	−	1.07538i	0.974013	−	0.226492i	$-0.0727258\pi$
$198$		0			0
$199$	−0.682332	−	0.682332i	−0.0483693	−	0.0483693i	0.682508	−	0.730878i	$-0.260889\pi$
$199$	−0.682332	−	0.682332i	−0.0483693	−	0.0483693i	−0.730878	+	0.682508i	$0.760889\pi$
$200$		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	0.974841	+	0.222903i	$0.0715533\pi$
$211$	6.43698	+	15.5403i	0.443140	+	1.06984i	−0.531700	+	0.846933i	$0.678447\pi$
$212$		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	$-0.515743\pi$
$223$	−1.47654			−0.0988764			−0.0494382	+	0.998777i	$0.515743\pi$
$224$		0			0
$225$	−34.5099			−2.30066
$226$		0			0
$227$	−26.1225	+	10.8203i	−1.73381	+	0.718169i	−0.734600	+	0.678500i	$0.762630\pi$
$227$	−26.1225	+	10.8203i	−1.73381	+	0.718169i	−0.999213	+	0.0396690i	$0.987370\pi$
$228$		0			0
$229$	−3.61614	+	8.73012i	−0.238961	+	0.576903i	−0.997176	−	0.0751019i	$-0.976072\pi$
$229$	−3.61614	+	8.73012i	−0.238961	+	0.576903i	0.758215	+	0.652005i	$0.226072\pi$
$230$		0			0
$231$	−3.33751	−	3.33751i	−0.219592	−	0.219592i
$232$		0			0
$233$	9.99248	−	9.99248i	0.654629	−	0.654629i	−0.299475	−	0.954104i	$-0.596811\pi$
$233$	9.99248	−	9.99248i	0.654629	−	0.654629i	0.954104	+	0.299475i	$0.0968115\pi$
$234$		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	$0.00708319\pi$
$241$			0.690846i			0.0445013i	−0.999752	+	0.0222507i	$0.992917\pi$
$242$		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	0.607091	+	0.794632i	$0.292336\pi$
$251$	−6.08493	+	14.6903i	−0.384077	+	0.927244i	−0.991168	+	0.132612i	$0.957664\pi$
$252$		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	−0.949296	−	0.314384i	$-0.898202\pi$
$263$	−20.4934	−	20.4934i	−1.26368	−	1.26368i	−0.314384	−	0.949296i	$-0.601798\pi$
$264$		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	$-0.223623\pi$
$269$	−3.82741	−	9.24018i	−0.233361	−	0.563384i	−0.996569	+	0.0827697i	$0.973623\pi$
$270$		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	$-0.228557\pi$
$277$	13.6544	+	5.65583i	0.820413	+	0.339826i	0.0673127	+	0.997732i	$0.478557\pi$
$278$		0			0
$279$	−7.41813	+	7.41813i	−0.444112	+	0.444112i
$280$		0			0
$281$	4.45247	+	4.45247i	0.265612	+	0.265612i	0.827329	−	0.561717i	$-0.189859\pi$
$281$	4.45247	+	4.45247i	0.265612	+	0.265612i	−0.561717	+	0.827329i	$0.689859\pi$
$282$		0			0
$283$	−9.32635	+	22.5158i	−0.554394	+	1.33843i	0.359755	+	0.933047i	$0.382860\pi$
$283$	−9.32635	+	22.5158i	−0.554394	+	1.33843i	−0.914149	+	0.405379i	$0.867140\pi$
$284$		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	$-0.942625\pi$
$293$	−2.76241	+	6.66906i	−0.161382	+	0.389611i	0.822417	+	0.568885i	$0.192625\pi$
$294$		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	−0.990755	−	0.135661i	$-0.956684\pi$
$307$	−6.76523	−	16.3327i	−0.386112	−	0.932158i	0.604643	−	0.796497i	$-0.293316\pi$
$308$		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	$-0.625772\pi$
$311$	9.48818	−	9.48818i	0.538025	−	0.538025i	0.922949	+	0.384923i	$0.125772\pi$
$312$		0			0
$313$	8.39347	+	8.39347i	0.474427	+	0.474427i	0.903344	−	0.428917i	$-0.141105\pi$
$313$	8.39347	+	8.39347i	0.474427	+	0.474427i	−0.428917	+	0.903344i	$0.641105\pi$
$314$		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	$-0.924595\pi$
$317$	−26.5907	+	11.0142i	−1.49348	+	0.618621i	−0.521413	+	0.853305i	$0.674595\pi$
$318$		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	0.108243	−	0.994124i	$-0.465478\pi$
$331$	−9.42728	−	3.90491i	−0.518170	−	0.214633i	−0.626413	+	0.779491i	$0.715478\pi$
$332$		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	$0.0245460\pi$
$337$			2.82843i			0.154074i	−0.997028	+	0.0770371i	$0.975454\pi$
$338$		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	−0.926574	−	0.376113i	$-0.877260\pi$
$347$	−0.101243	+	0.244423i	−0.00543503	+	0.0131213i	0.921139	+	0.389234i	$0.127260\pi$
$348$		0			0
$349$	−1.72727	+	0.715459i	−0.0924586	+	0.0382976i	−0.428433	−	0.903573i	$-0.640934\pi$
$349$	−1.72727	+	0.715459i	−0.0924586	+	0.0382976i	0.335975	+	0.941871i	$0.390934\pi$
$350$		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	$-0.364179\pi$
$359$	−9.40689	−	9.40689i	−0.496477	−	0.496477i	−0.910339	+	0.413863i	$0.864179\pi$
$360$		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	$-0.495891\pi$
$373$	−13.2298	−	5.47997i	−0.685014	−	0.283742i	−0.697921	+	0.716175i	$0.745891\pi$
$374$		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	−0.988450	−	0.151546i	$-0.951575\pi$
$379$	−3.55000	+	8.57046i	−0.182351	+	0.440235i	0.806099	+	0.591781i	$0.201575\pi$
$380$		0			0
$381$	17.8681	−	7.40122i	0.915412	−	0.379176i
$382$		0			0
$383$	−21.6316			−1.10532			−0.552661	−	0.833406i	$-0.686388\pi$
$383$	−21.6316			−1.10532			−0.552661	+	0.833406i	$0.686388\pi$
$384$		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	$-0.945403\pi$
$389$	−3.31161	+	7.99494i	−0.167906	+	0.405360i	0.817421	+	0.576041i	$0.195403\pi$
$390$		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	$-0.0992698\pi$
$397$	1.23136	+	2.97276i	0.0618001	+	0.149199i	−0.889963	+	0.456033i	$0.849270\pi$
$398$		0			0
$399$		−	25.3963i		−	1.27140i
$400$		0			0
$401$		−	22.2175i		−	1.10949i	−0.832021	−	0.554744i	$-0.812816\pi$
$401$		−	22.2175i		−	1.10949i	0.832021	−	0.554744i	$-0.187184\pi$
$402$		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	0.994014	−	0.109254i	$-0.0348462\pi$
$409$	17.8932	+	17.8932i	0.884760	+	0.884760i	−0.109254	+	0.994014i	$0.534846\pi$
$410$		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	−0.869354	−	0.494189i	$-0.835465\pi$
$419$	−23.2254	+	9.62029i	−1.13464	+	0.469982i	−0.265282	+	0.964171i	$0.585465\pi$
$420$		0			0
$421$	−8.42786	+	20.3467i	−0.410749	+	0.991635i	0.574189	+	0.818723i	$0.305318\pi$
$421$	−8.42786	+	20.3467i	−0.410749	+	0.991635i	−0.984937	+	0.172912i	$0.944682\pi$
$422$		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	$0.250571\pi$
$433$			29.4806i			1.41675i	−0.705837	+	0.708374i	$0.749429\pi$
$434$		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	$-0.897601\pi$
$439$	−13.2529	+	13.2529i	−0.632526	+	0.632526i	0.316175	+	0.948701i	$0.397601\pi$
$440$		0			0
$441$	−25.4776	−	25.4776i	−1.21322	−	1.21322i
$442$		0			0
$443$	13.1474	−	31.7407i	0.624653	−	1.50805i	−0.221529	−	0.975154i	$-0.571105\pi$
$443$	13.1474	−	31.7407i	0.624653	−	1.50805i	0.846183	−	0.532893i	$-0.178895\pi$
$444$		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	−0.439753	−	0.898119i	$-0.644934\pi$
$457$	9.79873	−	9.79873i	0.458365	−	0.458365i	0.898119	+	0.439753i	$0.144934\pi$
$458$		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	$-0.160628\pi$
$461$	−1.83552	−	4.43134i	−0.0854887	−	0.206388i	−0.960843	+	0.277095i	$0.910628\pi$
$462$		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	−0.999932	−	0.0116621i	$-0.996288\pi$
$467$	−6.50725	−	15.7099i	−0.301120	−	0.726967i	0.698812	−	0.715305i	$-0.253712\pi$
$468$		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	$-0.196095\pi$
$479$	35.7254			1.63234			0.816168	+	0.577815i	$0.196095\pi$
$480$		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	$-0.195183\pi$
$487$	5.34809	+	5.34809i	0.242345	+	0.242345i	−0.575475	+	0.817820i	$0.695183\pi$
$488$		0			0
$489$	22.1240	−	22.1240i	1.00048	−	1.00048i
$490$		0			0
$491$	40.7647	+	16.8853i	1.83968	+	0.762022i	0.955580	+	0.294731i	$0.0952302\pi$
$491$	40.7647	+	16.8853i	1.83968	+	0.762022i	0.884104	+	0.467291i	$0.154770\pi$
$492$		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	0.874076	−	0.485790i	$-0.161468\pi$
$499$	−1.95447	−	4.71852i	−0.0874943	−	0.211230i	−0.961570	+	0.274560i	$0.911468\pi$
$500$		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	$-0.701493\pi$
$503$	4.81469	−	4.81469i	0.214676	−	0.214676i	0.806251	+	0.591574i	$0.201493\pi$
$504$		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	$-0.581190\pi$
$509$	5.71949	−	2.36909i	0.253512	−	0.105008i	0.505821	+	0.862639i	$0.331190\pi$
$510$		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	−0.336162	−	0.941804i	$-0.609129\pi$
$521$	13.8240	−	13.8240i	0.605642	−	0.605642i	0.941804	+	0.336162i	$0.109129\pi$
$522$		0			0
$523$	7.51144	+	3.11134i	0.328452	+	0.136049i	0.540815	−	0.841141i	$-0.318116\pi$
$523$	7.51144	+	3.11134i	0.328452	+	0.136049i	−0.212363	+	0.977191i	$0.568116\pi$
$524$		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	$-0.454179\pi$
$541$	21.9728	−	9.10142i	0.944683	−	0.391300i	0.801230	+	0.598357i	$0.204179\pi$
$542$		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	0.678794	−	0.734329i	$-0.262503\pi$
$547$	39.2456	−	16.2561i	1.67802	−	0.695060i	0.999229	+	0.0392692i	$0.0125030\pi$
$548$		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	−0.761275	−	0.648429i	$-0.775426\pi$
$557$	−16.0835	−	38.8291i	−0.681481	−	1.64524i	0.0797936	−	0.996811i	$-0.474574\pi$
$558$		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	−0.817776	−	0.575536i	$-0.804793\pi$
$563$	−15.3396	−	37.0331i	−0.646487	−	1.56076i	0.171289	−	0.985221i	$-0.445207\pi$
$564$		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	0.979445	−	0.201713i	$-0.0646508\pi$
$569$	18.5518	+	18.5518i	0.777732	+	0.777732i	−0.201713	+	0.979445i	$0.564651\pi$
$570$		0			0
$571$	1.94591	−	4.69785i	0.0814340	−	0.196599i	−0.877918	−	0.478811i	$-0.841068\pi$
$571$	1.94591	−	4.69785i	0.0814340	−	0.196599i	0.959352	+	0.282212i	$0.0910680\pi$
$572$		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	−0.232037	−	0.972707i	$-0.574539\pi$
$587$	−26.2613	−	10.8778i	−1.08392	−	0.448974i	−0.851883	+	0.523733i	$0.824539\pi$
$588$		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	$-0.945064\pi$
$593$		−	8.36388i		−	0.343464i	0.985144	−	0.171732i	$-0.0549362\pi$
$594$		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	$-0.851780\pi$
$599$	−10.8797	+	10.8797i	−0.444531	+	0.444531i	0.449001	+	0.893531i	$0.351780\pi$
$600$		0			0
$601$	−13.9066	−	13.9066i	−0.567264	−	0.567264i	0.364097	−	0.931361i	$-0.381378\pi$
$601$	−13.9066	−	13.9066i	−0.567264	−	0.567264i	−0.931361	+	0.364097i	$0.881378\pi$
$602$		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	$-0.829412\pi$
$607$	−42.3665			−1.71960			−0.859801	+	0.510629i	$0.829412\pi$
$608$		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	$-0.968824\pi$
$613$	−5.50500	+	13.2902i	−0.222345	+	0.536788i	0.772863	+	0.634573i	$0.218824\pi$
$614$		0			0
$615$	10.2961	+	10.2961i	0.415178	+	0.415178i
$616$		0			0
$617$	17.8105	−	17.8105i	0.717025	−	0.717025i	−0.250970	−	0.967995i	$-0.580749\pi$
$617$	17.8105	−	17.8105i	0.717025	−	0.717025i	0.967995	+	0.250970i	$0.0807494\pi$
$618$		0			0
$619$	−11.6033	−	4.80624i	−0.466376	−	0.193179i	0.137105	−	0.990556i	$-0.456220\pi$
$619$	−11.6033	−	4.80624i	−0.466376	−	0.193179i	−0.603481	+	0.797377i	$0.706220\pi$
$620$		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	$-0.868162\pi$
$631$	−12.8865	+	12.8865i	−0.513004	+	0.513004i	0.402442	+	0.915446i	$0.368162\pi$
$632$		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	−0.0832793	−	0.996526i	$-0.526539\pi$
$643$	14.2632	−	5.90799i	0.562484	−	0.232988i	0.645763	+	0.763538i	$0.276539\pi$
$644$		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	$-0.0682534\pi$
$647$	19.4412	+	19.4412i	0.764314	+	0.764314i	−0.212785	+	0.977099i	$0.568253\pi$
$648$		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	$-0.102149\pi$
$653$	1.40282	+	3.38672i	0.0548968	+	0.132533i	−0.894052	+	0.447964i	$0.852149\pi$
$654$		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	0.998305	−	0.0581942i	$-0.0185343\pi$
$659$	6.44977	+	15.5711i	0.251247	+	0.606565i	−0.747058	+	0.664759i	$0.768534\pi$
$660$		0			0
$661$	14.5801	+	6.03928i	0.567100	+	0.234901i	0.647764	−	0.761841i	$-0.275704\pi$
$661$	14.5801	+	6.03928i	0.567100	+	0.234901i	−0.0806641	+	0.996741i	$0.525704\pi$
$662$		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	0.339000	+	0.940786i	$0.389911\pi$
$677$	−14.7255	+	35.5504i	−0.565945	+	1.36631i	−0.904946	+	0.425527i	$0.860089\pi$
$678$		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	0.488932	−	0.872322i	$-0.337386\pi$
$683$	5.69296	+	2.35810i	0.217835	+	0.0902303i	−0.271097	+	0.962552i	$0.587386\pi$
$684$		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	0.966716	−	0.255854i	$-0.0823565\pi$
$691$	2.68727	+	6.48765i	0.102229	+	0.246802i	−0.864487	+	0.502655i	$0.832356\pi$
$692$		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	$-0.701402\pi$
$701$	−11.6300	+	4.81730i	−0.439258	+	0.181947i	0.152084	+	0.988368i	$0.451402\pi$
$702$		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	$-0.888395\pi$
$709$	−0.857335	+	2.06979i	−0.0321979	+	0.0777326i	0.906963	+	0.421211i	$0.138395\pi$
$710$		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	$-0.735357\pi$
$727$	1.75350	−	1.75350i	0.0650337	−	0.0650337i	0.738876	+	0.673842i	$0.235357\pi$
$728$		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	$-0.618125\pi$
$733$	1.08042	−	0.447524i	0.0399062	−	0.0165297i	0.402547	+	0.915399i	$0.368125\pi$
$734$		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	−0.933174	−	0.359424i	$-0.882973\pi$
$739$	−36.3968	+	15.0760i	−1.33888	+	0.554581i	−0.405703	+	0.914005i	$0.632973\pi$
$740$		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	$-0.261997\pi$
$743$	−1.45255	−	1.45255i	−0.0532888	−	0.0532888i	−0.733249	+	0.679960i	$0.761997\pi$
$744$		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	$-0.202053\pi$
$757$	26.2830	+	10.8868i	0.955272	+	0.395686i	0.150062	+	0.988677i	$0.452053\pi$
$758$		0			0
$759$	−6.00551	+	6.00551i	−0.217986	+	0.217986i
$760$		0			0
$761$	13.6001	+	13.6001i	0.493003	+	0.493003i	0.909251	−	0.416248i	$-0.136655\pi$
$761$	13.6001	+	13.6001i	0.493003	+	0.493003i	−0.416248	+	0.909251i	$0.636655\pi$
$762$		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	−0.531847	−	0.846841i	$-0.678502\pi$
$773$	12.3176	−	29.7373i	0.443033	−	1.06958i	0.974879	−	0.222735i	$-0.0714983\pi$
$774$		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	0.977996	−	0.208626i	$-0.0668990\pi$
$787$	3.89741	+	9.40919i	0.138928	+	0.335401i	−0.839068	+	0.544027i	$0.816899\pi$
$788$		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	$-0.732473\pi$
$797$	−17.2799	+	7.15756i	−0.612085	+	0.253534i	0.0550349	+	0.998484i	$0.482473\pi$
$798$		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	−0.999995	−	0.00309284i	$-0.999016\pi$
$809$	−28.3548	+	28.3548i	−0.996902	+	0.996902i	0.00309284	+	0.999995i	$0.499016\pi$
$810$		0			0
$811$	−3.90316	−	1.61674i	−0.137059	−	0.0567716i	0.313100	−	0.949720i	$-0.398633\pi$
$811$	−3.90316	−	1.61674i	−0.137059	−	0.0567716i	−0.450159	+	0.892949i	$0.648633\pi$
$812$		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	$-0.551220\pi$
$821$	−27.8360	−	11.5300i	−0.971482	−	0.402401i	−0.811264	+	0.584681i	$0.801220\pi$
$822$		0			0
$823$	30.7602	−	30.7602i	1.07223	−	1.07223i	0.0750551	−	0.997179i	$-0.476087\pi$
$823$	30.7602	−	30.7602i	1.07223	−	1.07223i	0.997179	−	0.0750551i	$-0.0239133\pi$
$824$		0			0
$825$	−12.7305	−	12.7305i	−0.443220	−	0.443220i
$826$		0			0
$827$	−9.60486	+	23.1882i	−0.333994	+	0.806332i	0.664274	+	0.747489i	$0.268741\pi$
$827$	−9.60486	+	23.1882i	−0.333994	+	0.806332i	−0.998267	+	0.0588423i	$0.981259\pi$
$828$		0			0
$829$	41.5185	−	17.1975i	1.44200	−	0.597295i	0.481715	−	0.876328i	$-0.340014\pi$
$829$	41.5185	−	17.1975i	1.44200	−	0.597295i	0.960281	+	0.279033i	$0.0900140\pi$
$830$		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	−0.997002	−	0.0773708i	$-0.975347\pi$
$839$	−31.1198	−	31.1198i	−1.07437	−	1.07437i	−0.0773708	−	0.997002i	$-0.524653\pi$
$840$		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	$-0.230407\pi$
$853$	23.6797	+	9.80845i	0.810777	+	0.335835i	0.0615130	+	0.998106i	$0.480407\pi$
$854$		0			0
$855$	94.0865	−	94.0865i	3.21769	−	3.21769i
$856$		0			0
$857$	24.7590	+	24.7590i	0.845752	+	0.845752i	0.989600	−	0.143847i	$-0.0459475\pi$
$857$	24.7590	+	24.7590i	0.845752	+	0.845752i	−0.143847	+	0.989600i	$0.545947\pi$
$858$		0			0
$859$	−3.30545	+	7.98006i	−0.112780	+	0.272276i	−0.970184	−	0.242368i	$-0.922076\pi$
$859$	−3.30545	+	7.98006i	−0.112780	+	0.272276i	0.857404	+	0.514644i	$0.172076\pi$
$860$		0			0
$861$	5.60590	−	2.32204i	0.191049	−	0.0791349i
$862$		0			0
$863$	−35.4394			−1.20637			−0.603185	−	0.797601i	$-0.706102\pi$
$863$	−35.4394			−1.20637			−0.603185	+	0.797601i	$0.706102\pi$
$864$		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	0.867748	+	0.497005i	$0.165567\pi$
$877$	17.9341	+	43.2968i	0.605593	+	1.46203i	−0.262155	+	0.965026i	$0.584433\pi$
$878$		0			0
$879$			22.6591i			0.764274i
$880$		0			0
$881$			4.84917i			0.163373i	0.996658	+	0.0816863i	$0.0260306\pi$
$881$			4.84917i			0.163373i	−0.996658	+	0.0816863i	$0.973969\pi$
$882$		0			0
$883$	16.9445	+	40.9077i	0.570228	+	1.37665i	0.901361	+	0.433068i	$0.142569\pi$
$883$	16.9445	+	40.9077i	0.570228	+	1.37665i	−0.331133	+	0.943584i	$0.607431\pi$
$884$		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	$-0.809102\pi$
$887$	−7.77550	+	7.77550i	−0.261076	+	0.261076i	0.564415	+	0.825491i	$0.309102\pi$
$888$		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	0.476242	−	0.879314i	$-0.341999\pi$
$907$	5.75906	+	2.38548i	0.191226	+	0.0792086i	−0.285015	+	0.958523i	$0.591999\pi$
$908$		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	$-0.848588\pi$
$919$	−13.0672	+	13.0672i	−0.431046	+	0.431046i	0.457938	+	0.888984i	$0.348588\pi$
$920$		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	−0.628520	−	0.777793i	$-0.716339\pi$
$937$	4.56931	−	4.56931i	0.149273	−	0.149273i	0.777793	+	0.628520i	$0.216339\pi$
$938$		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	$-0.0243872\pi$
$941$	7.29813	+	17.6192i	0.237912	+	0.574371i	−0.759154	+	0.650911i	$0.774387\pi$
$942$		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	0.979993	−	0.199034i	$-0.0637805\pi$
$947$	4.50198	+	10.8687i	0.146295	+	0.353187i	−0.833698	+	0.552221i	$0.813780\pi$
$948$		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	0.528682	−	0.848820i	$-0.322687\pi$
$953$	−9.88290	−	9.88290i	−0.320138	−	0.320138i	−0.848820	+	0.528682i	$0.822687\pi$
$954$		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	$-0.464539\pi$
$967$	−27.4467	−	27.4467i	−0.882626	−	0.882626i	−0.993801	+	0.111175i	$0.964539\pi$
$968$		0			0
$969$	−21.9125	+	21.9125i	−0.703931	+	0.703931i
$970$		0			0
$971$	52.2342	+	21.6361i	1.67627	+	0.694335i	0.999138	−	0.0415225i	$-0.0132208\pi$
$971$	52.2342	+	21.6361i	1.67627	+	0.694335i	0.677136	+	0.735858i	$0.263221\pi$
$972$		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	$0.120499\pi$
$977$			23.1041i			0.739165i	−0.929198	+	0.369582i	$0.879501\pi$
$978$		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	$-0.618945\pi$
$983$	17.7442	−	17.7442i	0.565951	−	0.565951i	0.930991	+	0.365041i	$0.118945\pi$
$984$		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	$-0.466129\pi$
$991$	6.68692			0.212417			0.106208	+	0.994344i	$0.466129\pi$
$992$		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	$-0.893392\pi$
$997$	−1.39557	+	3.36920i	−0.0441981	+	0.106704i	0.900239	+	0.435397i	$0.143392\pi$
$998$		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.h.385.4	yes	16
4.3	odd	2	inner	1024.2.g.h.385.1	yes	16
8.3	odd	2		1024.2.g.c.385.4	yes	16
8.5	even	2		1024.2.g.c.385.1	yes	16
16.3	odd	4		1024.2.g.b.897.1	yes	16
16.5	even	4		1024.2.g.e.897.1	yes	16
16.11	odd	4		1024.2.g.e.897.4	yes	16
16.13	even	4		1024.2.g.b.897.4	yes	16
32.3	odd	8	inner	1024.2.g.h.641.1	yes	16
32.5	even	8		1024.2.g.e.129.1	yes	16
32.11	odd	8		1024.2.g.b.129.1	✓	16
32.13	even	8		1024.2.g.c.641.1	yes	16
32.19	odd	8		1024.2.g.c.641.4	yes	16
32.21	even	8		1024.2.g.b.129.4	yes	16
32.27	odd	8		1024.2.g.e.129.4	yes	16
32.29	even	8	inner	1024.2.g.h.641.4	yes	16
64.3	odd	16		4096.2.a.o.1.8		8
64.29	even	16		4096.2.a.o.1.7		8
64.35	odd	16		4096.2.a.n.1.1		8
64.61	even	16		4096.2.a.n.1.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1024.2.g.b.129.1	✓	16	32.11	odd	8
1024.2.g.b.129.4	yes	16	32.21	even	8
1024.2.g.b.897.1	yes	16	16.3	odd	4
1024.2.g.b.897.4	yes	16	16.13	even	4
1024.2.g.c.385.1	yes	16	8.5	even	2
1024.2.g.c.385.4	yes	16	8.3	odd	2
1024.2.g.c.641.1	yes	16	32.13	even	8
1024.2.g.c.641.4	yes	16	32.19	odd	8
1024.2.g.e.129.1	yes	16	32.5	even	8
1024.2.g.e.129.4	yes	16	32.27	odd	8
1024.2.g.e.897.1	yes	16	16.5	even	4
1024.2.g.e.897.4	yes	16	16.11	odd	4
1024.2.g.h.385.1	yes	16	4.3	odd	2	inner
1024.2.g.h.385.4	yes	16	1.1	even	1	trivial
1024.2.g.h.641.1	yes	16	32.3	odd	8	inner
1024.2.g.h.641.4	yes	16	32.29	even	8	inner
4096.2.a.n.1.1		8	64.35	odd	16
4096.2.a.n.1.2		8	64.61	even	16
4096.2.a.o.1.7		8	64.29	even	16
4096.2.a.o.1.8		8	64.3	odd	16

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1024 = 2^{10} \)
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

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Database

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