LMFDB - Embedded newform 720.2.t.c.541.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [720,2,Mod(181,720)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(720, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

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

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

chi := DirichletCharacter("720.181");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 720 = 2^{4} \cdot 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	720.t (of order $4$, degree $2$, 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:	$5.74922894553$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
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} - 4 x^{15} + 4 x^{14} + 7 x^{12} - 8 x^{11} - 28 x^{10} + 28 x^{9} + 17 x^{8} + 56 x^{7} + \cdots + 256 $ x^16 - 4x^15 + 4x^14 + 7x^12 - 8x^11 - 28x^10 + 28x^9 + 17x^8 + 56x^7 - 112x^6 - 64x^5 + 112x^4 + 256x^2 - 512*x + 256
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{5} $
Twist minimal:	no (minimal twist has level 80)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			541.6
Root			$1.21331 + 0.726558i$ of defining polynomial
Character	$\chi$	$=$	720.541
Dual form			720.2.t.c.181.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.376912 - 1.36306i) q^{2} +(-1.71587 - 1.02751i) q^{4} +(0.707107 - 0.707107i) q^{5} -4.50961i q^{7} +(-2.04729 + 1.95156i) q^{8} +O(q^{10})$	\(q+(0.376912 - 1.36306i) q^{2} +(-1.71587 - 1.02751i) q^{4} +(0.707107 - 0.707107i) q^{5} -4.50961i q^{7} +(-2.04729 + 1.95156i) q^{8} +(-0.697313 - 1.23035i) q^{10} +(1.64080 - 1.64080i) q^{11} +(1.51857 + 1.51857i) q^{13} +(-6.14687 - 1.69972i) q^{14} +(1.88845 + 3.52615i) q^{16} -1.45616 q^{17} +(-2.67964 - 2.67964i) q^{19} +(-1.93986 + 0.486749i) q^{20} +(-1.61808 - 2.85495i) q^{22} +2.37423i q^{23} -1.00000i q^{25} +(2.64228 - 1.49754i) q^{26} +(-4.63366 + 7.73792i) q^{28} +(-0.924966 - 0.924966i) q^{29} -7.20435 q^{31} +(5.51814 - 1.24503i) q^{32} +(-0.548843 + 1.98483i) q^{34} +(-3.18877 - 3.18877i) q^{35} +(-5.21123 + 5.21123i) q^{37} +(-4.66251 + 2.64253i) q^{38} +(-0.0676894 + 2.82762i) q^{40} -6.41166i q^{41} +(7.65800 - 7.65800i) q^{43} +(-4.50135 + 1.12947i) q^{44} +(3.23622 + 0.894875i) q^{46} +2.51027 q^{47} -13.3366 q^{49} +(-1.36306 - 0.376912i) q^{50} +(-1.04534 - 4.16603i) q^{52} +(-1.50312 + 1.50312i) q^{53} -2.32045i q^{55} +(8.80078 + 9.23248i) q^{56} +(-1.60942 + 0.912155i) q^{58} +(5.31807 - 5.31807i) q^{59} +(-1.02169 - 1.02169i) q^{61} +(-2.71541 + 9.81998i) q^{62} +(0.382800 - 7.99084i) q^{64} +2.14759 q^{65} +(5.22745 + 5.22745i) q^{67} +(2.49859 + 1.49622i) q^{68} +(-5.54838 + 3.14461i) q^{70} -1.92097i q^{71} +1.39412i q^{73} +(5.13905 + 9.06740i) q^{74} +(1.84458 + 7.35129i) q^{76} +(-7.39938 - 7.39938i) q^{77} +5.06317 q^{79} +(3.82870 + 1.15803i) q^{80} +(-8.73949 - 2.41663i) q^{82} +(2.44974 + 2.44974i) q^{83} +(-1.02966 + 1.02966i) q^{85} +(-7.55194 - 13.3247i) q^{86} +(-0.157070 + 6.56133i) q^{88} +9.36007i q^{89} +(6.84817 - 6.84817i) q^{91} +(2.43954 - 4.07388i) q^{92} +(0.946152 - 3.42166i) q^{94} -3.78959 q^{95} +18.6313 q^{97} +(-5.02671 + 18.1785i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 4 q^{4}+O(q^{10}) $ 16 * q - 4 * q^4	$ 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47} - 16 q^{49} + 4 q^{50} + 56 q^{52} - 16 q^{53} - 16 q^{56} - 12 q^{58} + 8 q^{59} + 16 q^{61} + 8 q^{62} - 16 q^{64} + 40 q^{67} + 48 q^{68} - 8 q^{70} + 72 q^{74} - 16 q^{77} + 16 q^{79} - 16 q^{80} - 76 q^{82} - 40 q^{83} - 16 q^{85} - 28 q^{86} + 32 q^{91} + 52 q^{92} - 36 q^{94} - 32 q^{95} - 60 q^{98}+O(q^{100}) $ 16 * q - 4 * q^4 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 8 * q^20 - 20 * q^22 + 16 * q^26 - 4 * q^28 + 16 * q^29 + 16 * q^34 - 16 * q^37 - 20 * q^38 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 40 * q^47 - 16 * q^49 + 4 * q^50 + 56 * q^52 - 16 * q^53 - 16 * q^56 - 12 * q^58 + 8 * q^59 + 16 * q^61 + 8 * q^62 - 16 * q^64 + 40 * q^67 + 48 * q^68 - 8 * q^70 + 72 * q^74 - 16 * q^77 + 16 * q^79 - 16 * q^80 - 76 * q^82 - 40 * q^83 - 16 * q^85 - 28 * q^86 + 32 * q^91 + 52 * q^92 - 36 * q^94 - 32 * q^95 - 60 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/720\mathbb{Z}\right)^\times$.

$n$	$181$	$271$	$577$	$641$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$1$	$1$

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 $

$2$	0.376912	−	1.36306i	0.266517	−	0.963830i
$2$	0.376912	−	1.36306i	0.266517	−	0.963830i
$3$		0			0
$3$		0			0
$4$	−1.71587	−	1.02751i	−0.857937	−	0.513754i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$5$	0.707107	−	0.707107i	0.316228	−	0.316228i
$6$		0			0
$7$		−	4.50961i		−	1.70447i	−0.523158	−	0.852236i	$-0.675246\pi$
$7$		−	4.50961i		−	1.70447i	0.523158	−	0.852236i	$-0.324754\pi$
$8$	−2.04729	+	1.95156i	−0.723827	+	0.689982i
$9$		0			0
$10$	−0.697313	−	1.23035i	−0.220510	−	0.389070i
$11$	1.64080	−	1.64080i	0.494721	−	0.494721i	−0.415069	−	0.909790i	$-0.636243\pi$
$11$	1.64080	−	1.64080i	0.494721	−	0.494721i	0.909790	+	0.415069i	$0.136243\pi$
$12$		0			0
$13$	1.51857	+	1.51857i	0.421176	+	0.421176i	0.885609	−	0.464432i	$-0.153742\pi$
$13$	1.51857	+	1.51857i	0.421176	+	0.421176i	−0.464432	+	0.885609i	$0.653742\pi$
$14$	−6.14687	−	1.69972i	−1.64282	−	0.454270i
$15$		0			0
$16$	1.88845	+	3.52615i	0.472113	+	0.881538i
$17$	−1.45616			−0.353170			−0.176585	−	0.984285i	$-0.556505\pi$
$17$	−1.45616			−0.353170			−0.176585	+	0.984285i	$0.556505\pi$
$18$		0			0
$19$	−2.67964	−	2.67964i	−0.614752	−	0.614752i	0.329428	−	0.944181i	$-0.393144\pi$
$19$	−2.67964	−	2.67964i	−0.614752	−	0.614752i	−0.944181	+	0.329428i	$0.893144\pi$
$20$	−1.93986	+	0.486749i	−0.433767	+	0.108840i
$21$		0			0
$22$	−1.61808	−	2.85495i	−0.344975	−	0.608678i
$23$			2.37423i			0.495061i	0.968880	+	0.247530i	$0.0796190\pi$
$23$			2.37423i			0.495061i	−0.968880	+	0.247530i	$0.920381\pi$
$24$		0			0
$25$		−	1.00000i		−	0.200000i
$26$	2.64228	−	1.49754i	0.518193	−	0.293692i
$27$		0			0
$28$	−4.63366	+	7.73792i	−0.875679	+	1.46233i
$29$	−0.924966	−	0.924966i	−0.171762	−	0.171762i	0.615991	−	0.787753i	$-0.288756\pi$
$29$	−0.924966	−	0.924966i	−0.171762	−	0.171762i	−0.787753	+	0.615991i	$0.788756\pi$
$30$		0			0
$31$	−7.20435			−1.29394			−0.646970	−	0.762515i	$-0.723964\pi$
$31$	−7.20435			−1.29394			−0.646970	+	0.762515i	$0.723964\pi$
$32$	5.51814	−	1.24503i	0.975479	−	0.220092i
$33$		0			0
$34$	−0.548843	+	1.98483i	−0.0941259	+	0.340396i
$35$	−3.18877	−	3.18877i	−0.539001	−	0.539001i
$36$		0			0
$37$	−5.21123	+	5.21123i	−0.856720	+	0.856720i	−0.990950	−	0.134230i	$-0.957144\pi$
$37$	−5.21123	+	5.21123i	−0.856720	+	0.856720i	0.134230	+	0.990950i	$0.457144\pi$
$38$	−4.66251	+	2.64253i	−0.756359	+	0.428675i
$39$		0			0
$40$	−0.0676894	+	2.82762i	−0.0107026	+	0.447086i
$41$		−	6.41166i		−	1.00133i	−0.865640	−	0.500667i	$-0.833088\pi$
$41$		−	6.41166i		−	1.00133i	0.865640	−	0.500667i	$-0.166912\pi$
$42$		0			0
$43$	7.65800	−	7.65800i	1.16783	−	1.16783i	0.185118	−	0.982716i	$-0.440733\pi$
$43$	7.65800	−	7.65800i	1.16783	−	1.16783i	0.982716	−	0.185118i	$-0.0592669\pi$
$44$	−4.50135	+	1.12947i	−0.678604	+	0.170275i
$45$		0			0
$46$	3.23622	+	0.894875i	0.477155	+	0.131942i
$47$	2.51027			0.366161			0.183081	−	0.983098i	$-0.441393\pi$
$47$	2.51027			0.366161			0.183081	+	0.983098i	$0.441393\pi$
$48$		0			0
$49$	−13.3366			−1.90522
$50$	−1.36306	−	0.376912i	−0.192766	−	0.0533034i
$51$		0			0
$52$	−1.04534	−	4.16603i	−0.144962	−	0.577724i
$53$	−1.50312	+	1.50312i	−0.206470	+	0.206470i	−0.802765	−	0.596295i	$-0.796639\pi$
$53$	−1.50312	+	1.50312i	−0.206470	+	0.206470i	0.596295	+	0.802765i	$0.296639\pi$
$54$		0			0
$55$		−	2.32045i		−	0.312889i
$56$	8.80078	+	9.23248i	1.17605	+	1.23374i
$57$		0			0
$58$	−1.60942	+	0.912155i	−0.211327	+	0.119772i
$59$	5.31807	−	5.31807i	0.692353	−	0.692353i	−0.270396	−	0.962749i	$-0.587155\pi$
$59$	5.31807	−	5.31807i	0.692353	−	0.692353i	0.962749	+	0.270396i	$0.0871546\pi$
$60$		0			0
$61$	−1.02169	−	1.02169i	−0.130815	−	0.130815i	0.638668	−	0.769483i	$-0.279486\pi$
$61$	−1.02169	−	1.02169i	−0.130815	−	0.130815i	−0.769483	+	0.638668i	$0.779486\pi$
$62$	−2.71541	+	9.81998i	−0.344857	+	1.24714i
$63$		0			0
$64$	0.382800	−	7.99084i	0.0478499	−	0.998855i
$65$	2.14759			0.266375
$66$		0			0
$67$	5.22745	+	5.22745i	0.638635	+	0.638635i	0.950219	−	0.311584i	$-0.100859\pi$
$67$	5.22745	+	5.22745i	0.638635	+	0.638635i	−0.311584	+	0.950219i	$0.600859\pi$
$68$	2.49859	+	1.49622i	0.302998	+	0.181443i
$69$		0			0
$70$	−5.54838	+	3.14461i	−0.663158	+	0.375853i
$71$		−	1.92097i		−	0.227978i	−0.993482	−	0.113989i	$-0.963637\pi$
$71$		−	1.92097i		−	0.227978i	0.993482	−	0.113989i	$-0.0363628\pi$
$72$		0			0
$73$			1.39412i			0.163169i	0.996666	+	0.0815847i	$0.0259981\pi$
$73$			1.39412i			0.163169i	−0.996666	+	0.0815847i	$0.974002\pi$
$74$	5.13905	+	9.06740i	0.597403	+	1.05406i
$75$		0			0
$76$	1.84458	+	7.35129i	0.211587	+	0.843250i
$77$	−7.39938	−	7.39938i	−0.843237	−	0.843237i
$78$		0			0
$79$	5.06317			0.569651			0.284825	−	0.958579i	$-0.408064\pi$
$79$	5.06317			0.569651			0.284825	+	0.958579i	$0.408064\pi$
$80$	3.82870	+	1.15803i	0.428062	+	0.129471i
$81$		0			0
$82$	−8.73949	−	2.41663i	−0.965115	−	0.266872i
$83$	2.44974	+	2.44974i	0.268894	+	0.268894i	0.828654	−	0.559761i	$-0.189107\pi$
$83$	2.44974	+	2.44974i	0.268894	+	0.268894i	−0.559761	+	0.828654i	$0.689107\pi$
$84$		0			0
$85$	−1.02966	+	1.02966i	−0.111682	+	0.111682i
$86$	−7.55194	−	13.3247i	−0.814347	−	1.43684i
$87$		0			0
$88$	−0.157070	+	6.56133i	−0.0167437	+	0.699440i
$89$			9.36007i			0.992165i	0.868275	+	0.496083i	$0.165229\pi$
$89$			9.36007i			0.992165i	−0.868275	+	0.496083i	$0.834771\pi$
$90$		0			0
$91$	6.84817	−	6.84817i	0.717883	−	0.717883i
$92$	2.43954	−	4.07388i	0.254340	−	0.424731i
$93$		0			0
$94$	0.946152	−	3.42166i	0.0975882	−	0.352917i
$95$	−3.78959			−0.388803
$96$		0			0
$97$	18.6313			1.89172			0.945859	−	0.324579i	$-0.105223\pi$
$97$	18.6313			1.89172			0.945859	+	0.324579i	$0.105223\pi$
$98$	−5.02671	+	18.1785i	−0.507774	+	1.83631i
$99$		0			0
$100$	−1.02751	+	1.71587i	−0.102751	+	0.171587i
$101$	4.84108	−	4.84108i	0.481705	−	0.481705i	−0.423971	−	0.905676i	$-0.639364\pi$
$101$	4.84108	−	4.84108i	0.481705	−	0.481705i	0.905676	+	0.423971i	$0.139364\pi$
$102$		0			0
$103$			9.12540i			0.899153i	0.893242	+	0.449576i	$0.148425\pi$
$103$			9.12540i			0.899153i	−0.893242	+	0.449576i	$0.851575\pi$
$104$	−6.07255	−	0.145369i	−0.595463	−	0.0142546i
$105$		0			0
$106$	1.48230	+	2.61539i	0.143974	+	0.254029i
$107$	10.1505	−	10.1505i	0.981290	−	0.981290i	−0.0185385	−	0.999828i	$-0.505901\pi$
$107$	10.1505	−	10.1505i	0.981290	−	0.981290i	0.999828	+	0.0185385i	$0.00590132\pi$
$108$		0			0
$109$	1.35489	+	1.35489i	0.129775	+	0.129775i	0.769011	−	0.639236i	$-0.220749\pi$
$109$	1.35489	+	1.35489i	0.129775	+	0.129775i	−0.639236	+	0.769011i	$0.720749\pi$
$110$	−3.16291	−	0.874603i	−0.301572	−	0.0833902i
$111$		0			0
$112$	15.9016	−	8.51618i	1.50256	−	0.804704i
$113$	2.56039			0.240861			0.120431	−	0.992722i	$-0.461572\pi$
$113$	2.56039			0.240861			0.120431	+	0.992722i	$0.461572\pi$
$114$		0			0
$115$	1.67883	+	1.67883i	0.156552	+	0.156552i
$116$	0.636716	+	2.53754i	0.0591176	+	0.235604i
$117$		0			0
$118$	−5.24441	−	9.25329i	−0.482787	−	0.851835i
$119$			6.56670i			0.601969i
$120$		0			0
$121$			5.61553i			0.510503i
$122$	−1.77772	+	1.00754i	−0.160947	+	0.0912188i
$123$		0			0
$124$	12.3618	+	7.40253i	1.11012	+	0.664767i
$125$	−0.707107	−	0.707107i	−0.0632456	−	0.0632456i
$126$		0			0
$127$	13.7354			1.21882			0.609409	−	0.792856i	$-0.291407\pi$
$127$	13.7354			1.21882			0.609409	+	0.792856i	$0.291407\pi$
$128$	−10.7477	−	3.53362i	−0.949973	−	0.312331i
$129$		0			0
$130$	0.809451	−	2.92729i	0.0709935	−	0.256741i
$131$	−5.20726	−	5.20726i	−0.454960	−	0.454960i	0.442037	−	0.896997i	$-0.354256\pi$
$131$	−5.20726	−	5.20726i	−0.454960	−	0.454960i	−0.896997	+	0.442037i	$0.854256\pi$
$132$		0			0
$133$	−12.0841	+	12.0841i	−1.04783	+	1.04783i
$134$	9.09563	−	5.15505i	0.785743	−	0.445329i
$135$		0			0
$136$	2.98118	−	2.84179i	0.255634	−	0.243681i
$137$			22.7563i			1.94420i	0.234559	+	0.972102i	$0.424635\pi$
$137$			22.7563i			1.94420i	−0.234559	+	0.972102i	$0.575365\pi$
$138$		0			0
$139$	6.28085	−	6.28085i	0.532734	−	0.532734i	−0.388651	−	0.921385i	$-0.627059\pi$
$139$	6.28085	−	6.28085i	0.532734	−	0.532734i	0.921385	+	0.388651i	$0.127059\pi$
$140$	2.19505	+	8.74803i	0.185515	+	0.739343i
$141$		0			0
$142$	−2.61841	−	0.724038i	−0.219732	−	0.0607599i
$143$	4.98336			0.416729
$144$		0			0
$145$	−1.30810			−0.108632
$146$	1.90027	+	0.525460i	0.157268	+	0.0434874i
$147$		0			0
$148$	14.2964	−	3.58723i	1.17516	−	0.294869i
$149$	12.9574	−	12.9574i	1.06151	−	1.06151i	0.0635329	−	0.997980i	$-0.479763\pi$
$149$	12.9574	−	12.9574i	1.06151	−	1.06151i	0.997980	−	0.0635329i	$-0.0202368\pi$
$150$		0			0
$151$		−	14.3417i		−	1.16711i	−0.812073	−	0.583555i	$-0.801661\pi$
$151$		−	14.3417i		−	1.16711i	0.812073	−	0.583555i	$-0.198339\pi$
$152$	10.7155	+	0.256515i	0.869142	+	0.0208061i
$153$		0			0
$154$	−12.8747	+	7.29689i	−1.03747	+	0.588001i
$155$	−5.09425	+	5.09425i	−0.409180	+	0.409180i
$156$		0			0
$157$	−2.10564	−	2.10564i	−0.168049	−	0.168049i	0.618073	−	0.786121i	$-0.287914\pi$
$157$	−2.10564	−	2.10564i	−0.168049	−	0.168049i	−0.786121	+	0.618073i	$0.787914\pi$
$158$	1.90837	−	6.90141i	0.151822	−	0.549047i
$159$		0			0
$160$	3.02155	−	4.78229i	0.238874	−	0.378073i
$161$	10.7068			0.843817
$162$		0			0
$163$	−5.34004	−	5.34004i	−0.418265	−	0.418265i	0.466341	−	0.884605i	$-0.345572\pi$
$163$	−5.34004	−	5.34004i	−0.418265	−	0.418265i	−0.884605	+	0.466341i	$0.845572\pi$
$164$	−6.58804	+	11.0016i	−0.514439	+	0.859081i
$165$		0			0
$166$	4.26248	−	2.41581i	0.330833	−	0.187503i
$167$		−	16.0686i		−	1.24343i	−0.783245	−	0.621714i	$-0.786437\pi$
$167$		−	16.0686i		−	1.24343i	0.783245	−	0.621714i	$-0.213563\pi$
$168$		0			0
$169$		−	8.38787i		−	0.645221i
$170$	1.01540	+	1.79158i	0.0778775	+	0.137408i
$171$		0			0
$172$	−21.0088	+	5.27151i	−1.60191	+	0.401949i
$173$	−17.1133	−	17.1133i	−1.30110	−	1.30110i	−0.927649	−	0.373453i	$-0.878174\pi$
$173$	−17.1133	−	17.1133i	−1.30110	−	1.30110i	−0.373453	−	0.927649i	$-0.621826\pi$
$174$		0			0
$175$	−4.50961			−0.340894
$176$	8.88430	+	2.68714i	0.669679	+	0.202551i
$177$		0			0
$178$	12.7584	+	3.52792i	0.956279	+	0.264429i
$179$	−1.04482	−	1.04482i	−0.0780933	−	0.0780933i	0.666981	−	0.745075i	$-0.267586\pi$
$179$	−1.04482	−	1.04482i	−0.0780933	−	0.0780933i	−0.745075	+	0.666981i	$0.767586\pi$
$180$		0			0
$181$	11.9886	−	11.9886i	0.891104	−	0.891104i	−0.103523	−	0.994627i	$-0.533012\pi$
$181$	11.9886	−	11.9886i	0.891104	−	0.891104i	0.994627	+	0.103523i	$0.0330115\pi$
$182$	−6.75332	−	11.9156i	−0.500589	−	0.883245i
$183$		0			0
$184$	−4.63346	−	4.86074i	−0.341583	−	0.358338i
$185$			7.36979i			0.541838i
$186$		0			0
$187$	−2.38927	+	2.38927i	−0.174721	+	0.174721i
$188$	−4.30732	−	2.57933i	−0.314143	−	0.188117i
$189$		0			0
$190$	−1.42834	+	5.16544i	−0.103623	+	0.374741i
$191$	−0.0667471			−0.00482965			−0.00241483	−	0.999997i	$-0.500769\pi$
$191$	−0.0667471			−0.00482965			−0.00241483	+	0.999997i	$0.500769\pi$
$192$		0			0
$193$	−1.09895			−0.0791039			−0.0395520	−	0.999218i	$-0.512593\pi$
$193$	−1.09895			−0.0791039			−0.0395520	+	0.999218i	$0.512593\pi$
$194$	7.02234	−	25.3956i	0.504175	−	1.82329i
$195$		0			0
$196$	22.8839	+	13.7034i	1.63456	+	0.978816i
$197$	−11.9289	+	11.9289i	−0.849899	+	0.849899i	−0.990120	−	0.140222i	$-0.955218\pi$
$197$	−11.9289	+	11.9289i	−0.849899	+	0.849899i	0.140222	+	0.990120i	$0.455218\pi$
$198$		0			0
$199$			11.0397i			0.782584i	0.920267	+	0.391292i	$0.127972\pi$
$199$			11.0397i			0.782584i	−0.920267	+	0.391292i	$0.872028\pi$
$200$	1.95156	+	2.04729i	0.137996	+	0.144765i
$201$		0			0
$202$	−4.77403	−	8.42334i	−0.335899	−	0.592664i
$203$	−4.17123	+	4.17123i	−0.292763	+	0.292763i
$204$		0			0
$205$	−4.53373	−	4.53373i	−0.316649	−	0.316649i
$206$	12.4385	+	3.43947i	0.866631	+	0.239639i
$207$		0			0
$208$	−2.48696	+	8.22247i	−0.172440	+	0.570126i
$209$	−8.79353			−0.608261
$210$		0			0
$211$	−8.59737	−	8.59737i	−0.591868	−	0.591868i	0.346268	−	0.938136i	$-0.387449\pi$
$211$	−8.59737	−	8.59737i	−0.591868	−	0.591868i	−0.938136	+	0.346268i	$0.887449\pi$
$212$	4.12364	−	1.03470i	0.283213	−	0.0710634i
$213$		0			0
$214$	−10.0100	−	17.6617i	−0.684266	−	1.20733i
$215$		−	10.8301i		−	0.738603i
$216$		0			0
$217$			32.4888i			2.20548i
$218$	2.35748	−	1.33613i	0.159669	−	0.0904941i
$219$		0			0
$220$	−2.38428	+	3.98159i	−0.160748	+	0.268439i
$221$	−2.21128	−	2.21128i	−0.148747	−	0.148747i
$222$		0			0
$223$	−21.4238			−1.43465			−0.717323	−	0.696741i	$-0.754633\pi$
$223$	−21.4238			−1.43465			−0.717323	+	0.696741i	$0.754633\pi$
$224$	−5.61460	−	24.8847i	−0.375141	−	1.66268i
$225$		0			0
$226$	0.965041	−	3.48997i	0.0641936	−	0.232149i
$227$	8.06331	+	8.06331i	0.535181	+	0.535181i	0.922110	−	0.386929i	$-0.126464\pi$
$227$	8.06331	+	8.06331i	0.535181	+	0.535181i	−0.386929	+	0.922110i	$0.626464\pi$
$228$		0			0
$229$	4.63169	−	4.63169i	0.306071	−	0.306071i	−0.537313	−	0.843383i	$-0.680560\pi$
$229$	4.63169	−	4.63169i	0.306071	−	0.306071i	0.843383	+	0.537313i	$0.180560\pi$
$230$	2.92112	−	1.65558i	0.192613	−	0.109166i
$231$		0			0
$232$	3.69880	+	0.0885445i	0.242838	+	0.00581323i
$233$			26.0672i			1.70772i	0.520502	+	0.853860i	$0.325745\pi$
$233$			26.0672i			1.70772i	−0.520502	+	0.853860i	$0.674255\pi$
$234$		0			0
$235$	1.77503	−	1.77503i	0.115790	−	0.115790i
$236$	−14.5895	+	3.66078i	−0.949695	+	0.238296i
$237$		0			0
$238$	8.95082	+	2.47507i	0.580196	+	0.160435i
$239$	−5.12209			−0.331320			−0.165660	−	0.986183i	$-0.552975\pi$
$239$	−5.12209			−0.331320			−0.165660	+	0.986183i	$0.552975\pi$
$240$		0			0
$241$	11.4987			0.740695			0.370347	−	0.928893i	$-0.379239\pi$
$241$	11.4987			0.740695			0.370347	+	0.928893i	$0.379239\pi$
$242$	7.65432	+	2.11656i	0.492038	+	0.136058i
$243$		0			0
$244$	0.703301	+	2.80290i	0.0450242	+	0.179437i
$245$	−9.43037	+	9.43037i	−0.602484	+	0.602484i
$246$		0			0
$247$		−	8.13847i		−	0.517838i
$248$	14.7494	−	14.0598i	0.936588	−	0.892795i
$249$		0			0
$250$	−1.23035	+	0.697313i	−0.0778140	+	0.0441020i
$251$	19.8270	−	19.8270i	1.25147	−	1.25147i	0.296408	−	0.955061i	$-0.404211\pi$
$251$	19.8270	−	19.8270i	1.25147	−	1.25147i	0.955061	−	0.296408i	$-0.0957889\pi$
$252$		0			0
$253$	3.89564	+	3.89564i	0.244917	+	0.244917i
$254$	5.17703	−	18.7222i	0.324836	−	1.17473i
$255$		0			0
$256$	−8.86749	+	13.3179i	−0.554218	+	0.832372i
$257$	24.2494			1.51264			0.756319	−	0.654203i	$-0.226996\pi$
$257$	24.2494			1.51264			0.756319	+	0.654203i	$0.226996\pi$
$258$		0			0
$259$	23.5006	+	23.5006i	1.46026	+	1.46026i
$260$	−3.68499	−	2.20666i	−0.228533	−	0.136851i
$261$		0			0
$262$	−9.06049	+	5.13514i	−0.559759	+	0.317250i
$263$			22.5680i			1.39160i	0.718234	+	0.695802i	$0.244951\pi$
$263$			22.5680i			1.39160i	−0.718234	+	0.695802i	$0.755049\pi$
$264$		0			0
$265$			2.12574i			0.130583i
$266$	11.9168	+	21.0261i	0.730664	+	1.28919i
$267$		0			0
$268$	−3.59840	−	14.3409i	−0.219807	−	0.876010i
$269$	5.10558	+	5.10558i	0.311293	+	0.311293i	0.845410	−	0.534117i	$-0.179356\pi$
$269$	5.10558	+	5.10558i	0.311293	+	0.311293i	−0.534117	+	0.845410i	$0.679356\pi$
$270$		0			0
$271$	6.67920			0.405733			0.202866	−	0.979206i	$-0.434974\pi$
$271$	6.67920			0.405733			0.202866	+	0.979206i	$0.434974\pi$
$272$	−2.74989	−	5.13464i	−0.166736	−	0.311333i
$273$		0			0
$274$	31.0183	+	8.57713i	1.87388	+	0.518163i
$275$	−1.64080	−	1.64080i	−0.0989441	−	0.0989441i
$276$		0			0
$277$	−11.8524	+	11.8524i	−0.712141	+	0.712141i	−0.966983	−	0.254842i	$-0.917977\pi$
$277$	−11.8524	+	11.8524i	−0.712141	+	0.712141i	0.254842	+	0.966983i	$0.417977\pi$
$278$	−6.19386	−	10.9285i	−0.371483	−	0.655448i
$279$		0			0
$280$	12.7514	+	0.305253i	0.762044	+	0.0182423i
$281$			0.477460i			0.0284829i	0.999899	+	0.0142414i	$0.00453334\pi$
$281$			0.477460i			0.0284829i	−0.999899	+	0.0142414i	$0.995467\pi$
$282$		0			0
$283$	−0.482914	+	0.482914i	−0.0287063	+	0.0287063i	−0.721314	−	0.692608i	$-0.756462\pi$
$283$	−0.482914	+	0.482914i	−0.0287063	+	0.0287063i	0.692608	+	0.721314i	$0.256462\pi$
$284$	−1.97382	+	3.29615i	−0.117124	+	0.195591i
$285$		0			0
$286$	1.87829	−	6.79263i	0.111065	−	0.401656i
$287$	−28.9141			−1.70674
$288$		0			0
$289$	−14.8796			−0.875271
$290$	−0.493038	+	1.78302i	−0.0289522	+	0.104703i
$291$		0			0
$292$	1.43247	−	2.39214i	0.0838290	−	0.139989i
$293$	−7.46638	+	7.46638i	−0.436190	+	0.436190i	−0.890728	−	0.454537i	$-0.849805\pi$
$293$	−7.46638	+	7.46638i	−0.436190	+	0.436190i	0.454537	+	0.890728i	$0.349805\pi$
$294$		0			0
$295$		−	7.52088i		−	0.437883i
$296$	0.498857	−	20.8389i	0.0289955	−	1.21124i
$297$		0			0
$298$	−12.7780	−	22.5456i	−0.740207	−	1.30603i
$299$	−3.60544	+	3.60544i	−0.208508	+	0.208508i
$300$		0			0
$301$	−34.5346	−	34.5346i	−1.99054	−	1.99054i
$302$	−19.5486	−	5.40556i	−1.12490	−	0.311055i
$303$		0			0
$304$	4.38845	−	14.5092i	0.251695	−	0.832160i
$305$	−1.44489			−0.0827344
$306$		0			0
$307$	2.39349	+	2.39349i	0.136604	+	0.136604i	0.772102	−	0.635498i	$-0.219205\pi$
$307$	2.39349	+	2.39349i	0.136604	+	0.136604i	−0.635498	+	0.772102i	$0.719205\pi$
$308$	5.09348	+	20.2993i	0.290228	+	1.15666i
$309$		0			0
$310$	5.02369	+	8.86386i	0.285327	+	0.503433i
$311$			20.4404i			1.15907i	0.814948	+	0.579534i	$0.196765\pi$
$311$			20.4404i			1.15907i	−0.814948	+	0.579534i	$0.803235\pi$
$312$		0			0
$313$			2.46975i			0.139598i	0.997561	+	0.0697992i	$0.0222359\pi$
$313$			2.46975i			0.139598i	−0.997561	+	0.0697992i	$0.977764\pi$
$314$	−3.66376	+	2.07648i	−0.206758	+	0.117182i
$315$		0			0
$316$	−8.68776	−	5.20245i	−0.488725	−	0.292660i
$317$	16.2241	+	16.2241i	0.911234	+	0.911234i	0.996369	−	0.0851350i	$-0.0271322\pi$
$317$	16.2241	+	16.2241i	0.911234	+	0.911234i	−0.0851350	+	0.996369i	$0.527132\pi$
$318$		0			0
$319$	−3.03537			−0.169948
$320$	−5.37969	−	5.92105i	−0.300734	−	0.330997i
$321$		0			0
$322$	4.03553	−	14.5941i	0.224891	−	0.813296i
$323$	3.90198	+	3.90198i	0.217112	+	0.217112i
$324$		0			0
$325$	1.51857	−	1.51857i	0.0842353	−	0.0842353i
$326$	−9.29154	+	5.26608i	−0.514611	+	0.291661i
$327$		0			0
$328$	12.5128	+	13.1265i	0.690902	+	0.724792i
$329$		−	11.3204i		−	0.624111i
$330$		0			0
$331$	3.42340	−	3.42340i	0.188167	−	0.188167i	−0.606736	−	0.794903i	$-0.707521\pi$
$331$	3.42340	−	3.42340i	0.188167	−	0.188167i	0.794903	+	0.606736i	$0.207521\pi$
$332$	−1.68632	−	6.72057i	−0.0925487	−	0.368839i
$333$		0			0
$334$	−21.9025	−	6.05645i	−1.19845	−	0.331394i
$335$	7.39273			0.403908
$336$		0			0
$337$	−5.40017			−0.294166			−0.147083	−	0.989124i	$-0.546988\pi$
$337$	−5.40017			−0.294166			−0.147083	+	0.989124i	$0.546988\pi$
$338$	−11.4332	−	3.16149i	−0.621883	−	0.171962i
$339$		0			0
$340$	2.82475	−	0.708783i	0.153194	−	0.0384392i
$341$	−11.8209	+	11.8209i	−0.640139	+	0.640139i
$342$		0			0
$343$			28.5754i			1.54292i
$344$	−0.733080	+	30.6232i	−0.0395250	+	1.65109i
$345$		0			0
$346$	−29.7767	+	16.8763i	−1.60081	+	0.907276i
$347$	4.07531	−	4.07531i	0.218774	−	0.218774i	−0.589208	−	0.807982i	$-0.700560\pi$
$347$	4.07531	−	4.07531i	0.218774	−	0.218774i	0.807982	+	0.589208i	$0.200560\pi$
$348$		0			0
$349$	1.55681	+	1.55681i	0.0833339	+	0.0833339i	0.747545	−	0.664211i	$-0.231232\pi$
$349$	1.55681	+	1.55681i	0.0833339	+	0.0833339i	−0.664211	+	0.747545i	$0.731232\pi$
$350$	−1.69972	+	6.14687i	−0.0908541	+	0.328564i
$351$		0			0
$352$	7.01133	−	11.0970i	0.373705	−	0.591474i
$353$	−1.34919			−0.0718103			−0.0359052	−	0.999355i	$-0.511431\pi$
$353$	−1.34919			−0.0718103			−0.0359052	+	0.999355i	$0.511431\pi$
$354$		0			0
$355$	−1.35833	−	1.35833i	−0.0720929	−	0.0720929i
$356$	9.61755	−	16.0607i	0.509729	−	0.851216i
$357$		0			0
$358$	−1.81795	+	1.03035i	−0.0960819	+	0.0544555i
$359$			23.2192i			1.22546i	0.790291	+	0.612732i	$0.209929\pi$
$359$			23.2192i			1.22546i	−0.790291	+	0.612732i	$0.790071\pi$
$360$		0			0
$361$		−	4.63903i		−	0.244159i
$362$	−11.8225	−	20.8598i	−0.621379	−	1.09637i
$363$		0			0
$364$	−18.7871	+	4.71405i	−0.984714	+	0.247083i
$365$	0.985792	+	0.985792i	0.0515987	+	0.0515987i
$366$		0			0
$367$	−5.16452			−0.269586			−0.134793	−	0.990874i	$-0.543037\pi$
$367$	−5.16452			−0.269586			−0.134793	+	0.990874i	$0.543037\pi$
$368$	−8.37189	+	4.48362i	−0.436415	+	0.233725i
$369$		0			0
$370$	10.0455	+	2.77776i	0.522239	+	0.144409i
$371$	6.77849	+	6.77849i	0.351922	+	0.351922i
$372$		0			0
$373$	18.5056	−	18.5056i	0.958185	−	0.958185i	−0.0409750	−	0.999160i	$-0.513046\pi$
$373$	18.5056	−	18.5056i	0.958185	−	0.958185i	0.999160	+	0.0409750i	$0.0130464\pi$
$374$	2.35618	+	4.15727i	0.121835	+	0.214967i
$375$		0			0
$376$	−5.13926	+	4.89896i	−0.265037	+	0.252645i
$377$		−	2.80926i		−	0.144684i
$378$		0			0
$379$	−13.5254	+	13.5254i	−0.694754	+	0.694754i	−0.963274	−	0.268520i	$-0.913465\pi$
$379$	−13.5254	+	13.5254i	−0.694754	+	0.694754i	0.268520	+	0.963274i	$0.413465\pi$
$380$	6.50246	+	3.89383i	0.333569	+	0.199749i
$381$		0			0
$382$	−0.0251578	+	0.0909805i	−0.00128718	+	0.00465497i
$383$	−21.9051			−1.11930			−0.559650	−	0.828729i	$-0.689064\pi$
$383$	−21.9051			−1.11930			−0.559650	+	0.828729i	$0.689064\pi$
$384$		0			0
$385$	−10.4643			−0.533310
$386$	−0.414206	+	1.49793i	−0.0210825	+	0.0762427i
$387$		0			0
$388$	−31.9689	−	19.1438i	−1.62298	−	0.971878i
$389$	−4.48844	+	4.48844i	−0.227573	+	0.227573i	−0.811678	−	0.584105i	$-0.801446\pi$
$389$	−4.48844	+	4.48844i	−0.227573	+	0.227573i	0.584105	+	0.811678i	$0.301446\pi$
$390$		0			0
$391$		−	3.45725i		−	0.174841i
$392$	27.3038	−	26.0271i	1.37905	−	1.31457i
$393$		0			0
$394$	11.7637	+	20.7560i	0.592646	+	1.04567i
$395$	3.58020	−	3.58020i	0.180139	−	0.180139i
$396$		0			0
$397$	11.7892	+	11.7892i	0.591682	+	0.591682i	0.938086	−	0.346404i	$-0.112597\pi$
$397$	11.7892	+	11.7892i	0.591682	+	0.591682i	−0.346404	+	0.938086i	$0.612597\pi$
$398$	15.0478	+	4.16100i	0.754278	+	0.208572i
$399$		0			0
$400$	3.52615	−	1.88845i	0.176308	−	0.0944227i
$401$	−24.9259			−1.24474			−0.622371	−	0.782722i	$-0.713830\pi$
$401$	−24.9259			−1.24474			−0.622371	+	0.782722i	$0.713830\pi$
$402$		0			0
$403$	−10.9403	−	10.9403i	−0.544977	−	0.544977i
$404$	−13.2809	+	3.33244i	−0.660751	+	0.165795i
$405$		0			0
$406$	4.11346	+	7.25784i	0.204148	+	0.360200i
$407$			17.1012i			0.847675i
$408$		0			0
$409$			21.5355i			1.06486i	0.846474	+	0.532430i	$0.178721\pi$
$409$			21.5355i			1.06486i	−0.846474	+	0.532430i	$0.821279\pi$
$410$	−7.88857	+	4.47094i	−0.389589	+	0.220804i
$411$		0			0
$412$	9.37643	−	15.6581i	0.461943	−	0.771417i
$413$	−23.9824	−	23.9824i	−1.18010	−	1.18010i
$414$		0			0
$415$	3.46445			0.170063
$416$	10.2704	+	6.48903i	0.503546	+	0.318151i
$417$		0			0
$418$	−3.31439	+	11.9861i	−0.162112	+	0.586261i
$419$	17.2979	+	17.2979i	0.845060	+	0.845060i	0.989512	−	0.144452i	$-0.0461419\pi$
$419$	17.2979	+	17.2979i	0.845060	+	0.845060i	−0.144452	+	0.989512i	$0.546142\pi$
$420$		0			0
$421$	−19.4330	+	19.4330i	−0.947105	+	0.947105i	−0.998670	−	0.0515648i	$-0.983579\pi$
$421$	−19.4330	+	19.4330i	−0.947105	+	0.947105i	0.0515648	+	0.998670i	$0.483579\pi$
$422$	−14.9592	+	8.47830i	−0.728203	+	0.412717i
$423$		0			0
$424$	0.143890	−	6.01077i	0.00698791	−	0.291909i
$425$			1.45616i			0.0706341i
$426$		0			0
$427$	−4.60744	+	4.60744i	−0.222970	+	0.222970i
$428$	−27.8468	+	6.98729i	−1.34603	+	0.337744i
$429$		0			0
$430$	−14.7620	−	4.08198i	−0.711888	−	0.196850i
$431$	−28.3769			−1.36687			−0.683433	−	0.730013i	$-0.739514\pi$
$431$	−28.3769			−1.36687			−0.683433	+	0.730013i	$0.739514\pi$
$432$		0			0
$433$	9.04007			0.434438			0.217219	−	0.976123i	$-0.430301\pi$
$433$	9.04007			0.434438			0.217219	+	0.976123i	$0.430301\pi$
$434$	44.2842	+	12.2454i	2.12571	+	0.587799i
$435$		0			0
$436$	−0.932664	−	3.71699i	−0.0446665	−	0.178012i
$437$	6.36208	−	6.36208i	0.304340	−	0.304340i
$438$		0			0
$439$			28.2949i			1.35044i	0.737615	+	0.675221i	$0.235952\pi$
$439$			28.2949i			1.35044i	−0.737615	+	0.675221i	$0.764048\pi$
$440$	4.52850	+	4.75063i	0.215888	+	0.226477i
$441$		0			0
$442$	−3.84757	+	2.18066i	−0.183010	+	0.103723i
$443$	13.1232	−	13.1232i	0.623504	−	0.623504i	−0.322922	−	0.946426i	$-0.604665\pi$
$443$	13.1232	−	13.1232i	0.623504	−	0.623504i	0.946426	+	0.322922i	$0.104665\pi$
$444$		0			0
$445$	6.61857	+	6.61857i	0.313750	+	0.313750i
$446$	−8.07489	+	29.2020i	−0.382357	+	1.38275i
$447$		0			0
$448$	−36.0355	−	1.72628i	−1.70252	−	0.0815588i
$449$	14.3902			0.679116			0.339558	−	0.940585i	$-0.389723\pi$
$449$	14.3902			0.679116			0.339558	+	0.940585i	$0.389723\pi$
$450$		0			0
$451$	−10.5203	−	10.5203i	−0.495380	−	0.495380i
$452$	−4.39331	−	2.63082i	−0.206644	−	0.123743i
$453$		0			0
$454$	14.0299	−	7.95163i	0.658458	−	0.373189i
$455$		−	9.68477i		−	0.454029i
$456$		0			0
$457$		−	4.54538i		−	0.212624i	−0.994333	−	0.106312i	$-0.966096\pi$
$457$		−	4.54538i		−	0.212624i	0.994333	−	0.106312i	$-0.0339042\pi$
$458$	−4.56754	−	8.05902i	−0.213427	−	0.376573i
$459$		0			0
$460$	−1.15565	−	4.60568i	−0.0538826	−	0.214741i
$461$	−19.8046	−	19.8046i	−0.922393	−	0.922393i	0.0748050	−	0.997198i	$-0.476167\pi$
$461$	−19.8046	−	19.8046i	−0.922393	−	0.922393i	−0.997198	+	0.0748050i	$0.976167\pi$
$462$		0			0
$463$	−14.5997			−0.678506			−0.339253	−	0.940695i	$-0.610174\pi$
$463$	−14.5997			−0.678506			−0.339253	+	0.940695i	$0.610174\pi$
$464$	1.51481	−	5.00833i	0.0703235	−	0.232506i
$465$		0			0
$466$	35.5312	+	9.82505i	1.64595	+	0.455137i
$467$	−19.8105	−	19.8105i	−0.916722	−	0.916722i	0.0800671	−	0.996789i	$-0.474487\pi$
$467$	−19.8105	−	19.8105i	−0.916722	−	0.916722i	−0.996789	+	0.0800671i	$0.974487\pi$
$468$		0			0
$469$	23.5738	−	23.5738i	1.08853	−	1.08853i
$470$	−1.75045	−	3.08851i	−0.0807421	−	0.142462i
$471$		0			0
$472$	−0.509084	+	21.2662i	−0.0234325	+	0.978855i
$473$		−	25.1306i		−	1.15550i
$474$		0			0
$475$	−2.67964	+	2.67964i	−0.122950	+	0.122950i
$476$	6.74734	−	11.2676i	0.309264	−	0.516451i
$477$		0			0
$478$	−1.93058	+	6.98172i	−0.0883025	+	0.319337i
$479$	−21.0378			−0.961243			−0.480621	−	0.876928i	$-0.659589\pi$
$479$	−21.0378			−0.961243			−0.480621	+	0.876928i	$0.659589\pi$
$480$		0			0
$481$	−15.8273			−0.721661
$482$	4.33399	−	15.6734i	0.197408	−	0.713904i
$483$		0			0
$484$	5.77000	−	9.63555i	0.262273	−	0.437980i
$485$	13.1743	−	13.1743i	0.598214	−	0.598214i
$486$		0			0
$487$			10.2724i			0.465485i	0.972538	+	0.232743i	$0.0747699\pi$
$487$			10.2724i			0.465485i	−0.972538	+	0.232743i	$0.925230\pi$
$488$	4.08561	+	0.0978041i	0.184947	+	0.00442738i
$489$		0			0
$490$	9.29976	+	16.4086i	0.420120	+	0.741265i
$491$	5.95681	−	5.95681i	0.268827	−	0.268827i	−0.559801	−	0.828627i	$-0.689122\pi$
$491$	5.95681	−	5.95681i	0.268827	−	0.268827i	0.828627	+	0.559801i	$0.189122\pi$
$492$		0			0
$493$	1.34690	+	1.34690i	0.0606612	+	0.0606612i
$494$	−11.0932	−	3.06748i	−0.499108	−	0.138013i
$495$		0			0
$496$	−13.6051	−	25.4036i	−0.610886	−	1.14066i
$497$	−8.66284			−0.388581
$498$		0			0
$499$	−2.81466	−	2.81466i	−0.126002	−	0.126002i	0.641294	−	0.767295i	$-0.278398\pi$
$499$	−2.81466	−	2.81466i	−0.126002	−	0.126002i	−0.767295	+	0.641294i	$0.778398\pi$
$500$	0.486749	+	1.93986i	0.0217681	+	0.0867534i
$501$		0			0
$502$	−19.5524	−	34.4985i	−0.872666	−	1.53974i
$503$			5.49759i			0.245125i	0.992461	+	0.122563i	$0.0391113\pi$
$503$			5.49759i			0.245125i	−0.992461	+	0.122563i	$0.960889\pi$
$504$		0			0
$505$		−	6.84632i		−	0.304657i
$506$	6.77831	−	3.84169i	0.301333	−	0.170784i
$507$		0			0
$508$	−23.5682	−	14.1132i	−1.04567	−	0.626173i
$509$	4.37578	+	4.37578i	0.193953	+	0.193953i	0.797402	−	0.603449i	$-0.206207\pi$
$509$	4.37578	+	4.37578i	0.193953	+	0.193953i	−0.603449	+	0.797402i	$0.706207\pi$
$510$		0			0
$511$	6.28693			0.278118
$512$	14.8109	+	17.1066i	0.654556	+	0.756013i
$513$		0			0
$514$	9.13990	−	33.0535i	0.403144	−	1.45793i
$515$	6.45263	+	6.45263i	0.284337	+	0.284337i
$516$		0			0
$517$	4.11887	−	4.11887i	0.181148	−	0.181148i
$518$	40.8904	−	23.1751i	1.79662	−	1.01826i
$519$		0			0
$520$	−4.39673	+	4.19115i	−0.192810	+	0.183794i
$521$		−	33.8729i		−	1.48400i	−0.670401	−	0.741999i	$-0.733878\pi$
$521$		−	33.8729i		−	1.48400i	0.670401	−	0.741999i	$-0.266122\pi$
$522$		0			0
$523$	27.8060	−	27.8060i	1.21587	−	1.21587i	0.246804	−	0.969065i	$-0.420620\pi$
$523$	27.8060	−	27.8060i	1.21587	−	1.21587i	0.969065	−	0.246804i	$-0.0793803\pi$
$524$	3.58450	+	14.2855i	0.156590	+	0.624065i
$525$		0			0
$526$	30.7616	+	8.50615i	1.34127	+	0.370886i
$527$	10.4907			0.456981
$528$		0			0
$529$	17.3630			0.754915
$530$	2.89751	+	0.801215i	0.125860	+	0.0348025i
$531$		0			0
$532$	33.1514	−	8.31832i	1.43730	−	0.360645i
$533$	9.73658	−	9.73658i	0.421738	−	0.421738i
$534$		0			0
$535$		−	14.3550i		−	0.620622i
$536$	−20.9038	−	0.500410i	−0.902907	−	0.0216144i
$537$		0			0
$538$	8.88358	−	5.03487i	0.382998	−	0.217069i
$539$	−21.8827	+	21.8827i	−0.942553	+	0.942553i
$540$		0			0
$541$	3.03066	+	3.03066i	0.130298	+	0.130298i	0.769248	−	0.638950i	$-0.220631\pi$
$541$	3.03066	+	3.03066i	0.130298	+	0.130298i	−0.638950	+	0.769248i	$0.720631\pi$
$542$	2.51747	−	9.10416i	0.108135	−	0.391057i
$543$		0			0
$544$	−8.03529	+	1.81296i	−0.344510	+	0.0777301i
$545$	1.91611			0.0820771
$546$		0			0
$547$	−18.4783	−	18.4783i	−0.790074	−	0.790074i	0.191432	−	0.981506i	$-0.438687\pi$
$547$	−18.4783	−	18.4783i	−0.790074	−	0.790074i	−0.981506	+	0.191432i	$0.938687\pi$
$548$	23.3823	−	39.0470i	0.998843	−	1.66801i
$549$		0			0
$550$	−2.85495	+	1.61808i	−0.121736	+	0.0689951i
$551$			4.95716i			0.211182i
$552$		0			0
$553$		−	22.8329i		−	0.970953i
$554$	11.6882	+	20.6228i	0.496585	+	0.876181i
$555$		0			0
$556$	−17.2308	+	4.32353i	−0.730747	+	0.183358i
$557$	30.2060	+	30.2060i	1.27987	+	1.27987i	0.940741	+	0.339127i	$0.110132\pi$
$557$	30.2060	+	30.2060i	1.27987	+	1.27987i	0.339127	+	0.940741i	$0.389868\pi$
$558$		0			0
$559$	23.2585			0.983729
$560$	5.22225	−	17.2659i	0.220680	−	0.729620i
$561$		0			0
$562$	0.650807	+	0.179960i	0.0274526	+	0.00759117i
$563$	−2.86747	−	2.86747i	−0.120850	−	0.120850i	0.644095	−	0.764945i	$-0.277234\pi$
$563$	−2.86747	−	2.86747i	−0.120850	−	0.120850i	−0.764945	+	0.644095i	$0.777234\pi$
$564$		0			0
$565$	1.81047	−	1.81047i	0.0761670	−	0.0761670i
$566$	0.476226	+	0.840258i	0.0200173	+	0.0353187i
$567$		0			0
$568$	3.74890	+	3.93279i	0.157300	+	0.165016i
$569$		−	35.8628i		−	1.50345i	−0.659479	−	0.751723i	$-0.729223\pi$
$569$		−	35.8628i		−	1.50345i	0.659479	−	0.751723i	$-0.270777\pi$
$570$		0			0
$571$	−17.6509	+	17.6509i	−0.738667	+	0.738667i	−0.972320	−	0.233653i	$-0.924932\pi$
$571$	−17.6509	+	17.6509i	−0.738667	+	0.738667i	0.233653	+	0.972320i	$0.424932\pi$
$572$	−8.55082	−	5.12044i	−0.357528	−	0.214096i
$573$		0			0
$574$	−10.8981	+	39.4117i	−0.454876	+	1.64501i
$575$	2.37423			0.0990122
$576$		0			0
$577$	36.1387			1.50448			0.752238	−	0.658892i	$-0.228975\pi$
$577$	36.1387			1.50448			0.752238	+	0.658892i	$0.228975\pi$
$578$	−5.60830	+	20.2818i	−0.233274	+	0.843612i
$579$		0			0
$580$	2.24454	+	1.34408i	0.0931993	+	0.0558100i
$581$	11.0474	−	11.0474i	0.458322	−	0.458322i
$582$		0			0
$583$			4.93265i			0.204290i
$584$	−2.72071	−	2.85417i	−0.112584	−	0.118106i
$585$		0			0
$586$	7.36297	+	12.9913i	0.304161	+	0.536666i
$587$	11.4005	−	11.4005i	0.470550	−	0.470550i	−0.431542	−	0.902093i	$-0.642030\pi$
$587$	11.4005	−	11.4005i	0.470550	−	0.470550i	0.902093	+	0.431542i	$0.142030\pi$
$588$		0			0
$589$	19.3051	+	19.3051i	0.795453	+	0.795453i
$590$	−10.2514	−	2.83471i	−0.422045	−	0.116703i
$591$		0			0
$592$	−28.2167	−	8.53441i	−1.15970	−	0.350762i
$593$	35.0454			1.43914			0.719572	−	0.694418i	$-0.244338\pi$
$593$	35.0454			1.43914			0.719572	+	0.694418i	$0.244338\pi$
$594$		0			0
$595$	4.64336	+	4.64336i	0.190359	+	0.190359i
$596$	−35.5472	+	8.91945i	−1.45607	+	0.365355i
$597$		0			0
$598$	3.55550	+	6.27337i	0.145395	+	0.256537i
$599$		−	18.2753i		−	0.746707i	−0.927689	−	0.373354i	$-0.878208\pi$
$599$		−	18.2753i		−	0.746707i	0.927689	−	0.373354i	$-0.121792\pi$
$600$		0			0
$601$		−	0.480142i		−	0.0195854i	−0.999952	−	0.00979269i	$-0.996883\pi$
$601$		−	0.480142i		−	0.0195854i	0.999952	−	0.00979269i	$-0.00311716\pi$
$602$	−60.0893	+	34.0563i	−2.44906	+	1.38803i
$603$		0			0
$604$	−14.7362	+	24.6086i	−0.599608	+	1.00131i
$605$	3.97078	+	3.97078i	0.161435	+	0.161435i
$606$		0			0
$607$	−38.6107			−1.56716			−0.783581	−	0.621290i	$-0.786609\pi$
$607$	−38.6107			−1.56716			−0.783581	+	0.621290i	$0.786609\pi$
$608$	−18.1229	−	11.4504i	−0.734980	−	0.464376i
$609$		0			0
$610$	−0.544598	+	1.96948i	−0.0220501	+	0.0797419i
$611$	3.81204	+	3.81204i	0.154218	+	0.154218i
$612$		0			0
$613$	−5.53592	+	5.53592i	−0.223594	+	0.223594i	−0.810010	−	0.586416i	$-0.800538\pi$
$613$	−5.53592	+	5.53592i	−0.223594	+	0.223594i	0.586416	+	0.810010i	$0.300538\pi$
$614$	4.16461	−	2.36034i	0.168070	−	0.0952557i
$615$		0			0
$616$	29.5890	+	0.708322i	1.19218	+	0.0285391i
$617$			31.8836i			1.28358i	0.766879	+	0.641792i	$0.221809\pi$
$617$			31.8836i			1.28358i	−0.766879	+	0.641792i	$0.778191\pi$
$618$		0			0
$619$	−29.4054	+	29.4054i	−1.18190	+	1.18190i	−0.202650	+	0.979251i	$0.564955\pi$
$619$	−29.4054	+	29.4054i	−1.18190	+	1.18190i	−0.979251	+	0.202650i	$0.935045\pi$
$620$	13.9755	−	3.50671i	0.561269	−	0.140833i
$621$		0			0
$622$	27.8615	+	7.70422i	1.11714	+	0.308911i
$623$	42.2102			1.69112
$624$		0			0
$625$	−1.00000			−0.0400000
$626$	3.36642	+	0.930878i	0.134549	+	0.0372054i
$627$		0			0
$628$	1.44945	+	5.77658i	0.0578395	+	0.230511i
$629$	7.58837	−	7.58837i	0.302568	−	0.302568i
$630$		0			0
$631$			30.7381i			1.22367i	0.790987	+	0.611833i	$0.209568\pi$
$631$			30.7381i			1.22367i	−0.790987	+	0.611833i	$0.790432\pi$
$632$	−10.3658	+	9.88109i	−0.412328	+	0.393049i
$633$		0			0
$634$	28.2294	−	15.9994i	1.12113	−	0.635416i
$635$	9.71239	−	9.71239i	0.385424	−	0.385424i
$636$		0			0
$637$	−20.2525	−	20.2525i	−0.802435	−	0.802435i
$638$	−1.14407	+	4.13740i	−0.0452941	+	0.163801i
$639$		0			0
$640$	−10.0984	+	5.10114i	−0.399176	+	0.201640i
$641$	−13.6348			−0.538540			−0.269270	−	0.963065i	$-0.586782\pi$
$641$	−13.6348			−0.538540			−0.269270	+	0.963065i	$0.586782\pi$
$642$		0			0
$643$	14.9224	+	14.9224i	0.588480	+	0.588480i	0.937220	−	0.348740i	$-0.113390\pi$
$643$	14.9224	+	14.9224i	0.588480	+	0.588480i	−0.348740	+	0.937220i	$0.613390\pi$
$644$	−18.3716	−	11.0014i	−0.723942	−	0.433514i
$645$		0			0
$646$	6.78935	−	3.84794i	0.267123	−	0.151395i
$647$		−	4.87972i		−	0.191841i	−0.995389	−	0.0959207i	$-0.969420\pi$
$647$		−	4.87972i		−	0.191841i	0.995389	−	0.0959207i	$-0.0305795\pi$
$648$		0			0
$649$		−	17.4518i		−	0.685043i
$650$	−1.49754	−	2.64228i	−0.0587384	−	0.103639i
$651$		0			0
$652$	3.67591	+	14.6498i	0.143960	+	0.573730i
$653$	10.2913	+	10.2913i	0.402731	+	0.402731i	0.879194	−	0.476463i	$-0.158081\pi$
$653$	10.2913	+	10.2913i	0.402731	+	0.402731i	−0.476463	+	0.879194i	$0.658081\pi$
$654$		0			0
$655$	−7.36417			−0.287742
$656$	22.6085	−	12.1081i	0.882713	−	0.472743i
$657$		0			0
$658$	−15.4303	−	4.26677i	−0.601537	−	0.166336i
$659$	21.9025	+	21.9025i	0.853201	+	0.853201i	0.990526	−	0.137325i	$-0.0438505\pi$
$659$	21.9025	+	21.9025i	0.853201	+	0.853201i	−0.137325	+	0.990526i	$0.543851\pi$
$660$		0			0
$661$	5.40595	−	5.40595i	0.210267	−	0.210267i	−0.594114	−	0.804381i	$-0.702497\pi$
$661$	5.40595	−	5.40595i	0.210267	−	0.210267i	0.804381	+	0.594114i	$0.202497\pi$
$662$	−3.37599	−	5.95663i	−0.131212	−	0.231511i
$663$		0			0
$664$	−9.79615	−	0.234507i	−0.380164	−	0.00910063i
$665$			17.0895i			0.662704i
$666$		0			0
$667$	2.19608	−	2.19608i	0.0850326	−	0.0850326i
$668$	−16.5106	+	27.5717i	−0.638816	+	1.06678i
$669$		0			0
$670$	2.78641	−	10.0768i	0.107648	−	0.389299i
$671$	−3.35280			−0.129433
$672$		0			0
$673$	35.3820			1.36388			0.681938	−	0.731410i	$-0.261138\pi$
$673$	35.3820			1.36388			0.681938	+	0.731410i	$0.261138\pi$
$674$	−2.03539	+	7.36076i	−0.0784002	+	0.283526i
$675$		0			0
$676$	−8.61861	+	14.3925i	−0.331485	+	0.553559i
$677$	−5.17061	+	5.17061i	−0.198723	+	0.198723i	−0.799452	−	0.600730i	$-0.794877\pi$
$677$	−5.17061	+	5.17061i	−0.198723	+	0.198723i	0.600730	+	0.799452i	$0.294877\pi$
$678$		0			0
$679$		−	84.0196i		−	3.22438i
$680$	0.0985665	−	4.11746i	0.00377985	−	0.157897i
$681$		0			0
$682$	11.6572	+	20.5681i	0.446377	+	0.787593i
$683$	−26.5989	+	26.5989i	−1.01778	+	1.01778i	−0.0179409	+	0.999839i	$0.505711\pi$
$683$	−26.5989	+	26.5989i	−1.01778	+	1.01778i	−0.999839	+	0.0179409i	$0.994289\pi$
$684$		0			0
$685$	16.0912	+	16.0912i	0.614811	+	0.614811i
$686$	38.9500	+	10.7704i	1.48712	+	0.411216i
$687$		0			0
$688$	41.4651	+	12.5415i	1.58084	+	0.478140i
$689$	−4.56520			−0.173920
$690$		0			0
$691$	−21.7989	−	21.7989i	−0.829270	−	0.829270i	0.158146	−	0.987416i	$-0.449448\pi$
$691$	−21.7989	−	21.7989i	−0.829270	−	0.829270i	−0.987416	+	0.158146i	$0.949448\pi$
$692$	11.7802	+	46.9484i	0.447818	+	1.78471i
$693$		0			0
$694$	−4.01887	−	7.09093i	−0.152554	−	0.269168i
$695$		−	8.88246i		−	0.336931i
$696$		0			0
$697$			9.33640i			0.353641i
$698$	2.70880	−	1.53524i	0.102530	−	0.0581099i
$699$		0			0
$700$	7.73792	+	4.63366i	0.292466	+	0.175136i
$701$	15.2175	+	15.2175i	0.574756	+	0.574756i	0.933454	−	0.358698i	$-0.116779\pi$
$701$	15.2175	+	15.2175i	0.574756	+	0.574756i	−0.358698	+	0.933454i	$0.616779\pi$
$702$		0			0
$703$	27.9285			1.05334
$704$	−12.4833	−	13.7395i	−0.470482	−	0.517826i
$705$		0			0
$706$	−0.508527	+	1.83903i	−0.0191387	+	0.0692130i
$707$	−21.8313	−	21.8313i	−0.821052	−	0.821052i
$708$		0			0
$709$	4.87350	−	4.87350i	0.183028	−	0.183028i	−0.609646	−	0.792674i	$-0.708688\pi$
$709$	4.87350	−	4.87350i	0.183028	−	0.183028i	0.792674	+	0.609646i	$0.208688\pi$
$710$	−2.36346	+	1.33952i	−0.0886992	+	0.0502713i
$711$		0			0
$712$	−18.2668	−	19.1628i	−0.684576	−	0.718156i
$713$		−	17.1048i		−	0.640579i
$714$		0			0
$715$	3.52377	−	3.52377i	0.131781	−	0.131781i
$716$	0.719218	+	2.86633i	0.0268784	+	0.107120i
$717$		0			0
$718$	31.6492	+	8.75160i	1.18114	+	0.326607i
$719$	−9.27351			−0.345843			−0.172922	−	0.984936i	$-0.555321\pi$
$719$	−9.27351			−0.345843			−0.172922	+	0.984936i	$0.555321\pi$
$720$		0			0
$721$	41.1520			1.53258
$722$	−6.32328	−	1.74850i	−0.235328	−	0.0650726i
$723$		0			0
$724$	−32.8893	+	8.25254i	−1.22232	+	0.306703i
$725$	−0.924966	+	0.924966i	−0.0343524	+	0.0343524i
$726$		0			0
$727$			10.6056i			0.393341i	0.980470	+	0.196670i	$0.0630129\pi$
$727$			10.6056i			0.393341i	−0.980470	+	0.196670i	$0.936987\pi$
$728$	−0.655557	+	27.3848i	−0.0242965	+	1.01495i
$729$		0			0
$730$	1.71525	−	0.972138i	0.0634843	−	0.0359805i
$731$	−11.1513	+	11.1513i	−0.412445	+	0.412445i
$732$		0			0
$733$	−29.6530	−	29.6530i	−1.09526	−	1.09526i	−0.994957	−	0.100301i	$-0.968019\pi$
$733$	−29.6530	−	29.6530i	−1.09526	−	1.09526i	−0.100301	−	0.994957i	$-0.531981\pi$
$734$	−1.94657	+	7.03956i	−0.0718492	+	0.259835i
$735$		0			0
$736$	2.95599	+	13.1013i	0.108959	+	0.482921i
$737$	17.1544			0.631892
$738$		0			0
$739$	30.8751	+	30.8751i	1.13576	+	1.13576i	0.989202	+	0.146559i	$0.0468197\pi$
$739$	30.8751	+	30.8751i	1.13576	+	1.13576i	0.146559	+	0.989202i	$0.453180\pi$
$740$	7.57252	−	12.6456i	0.278371	−	0.464863i
$741$		0			0
$742$	11.7944	−	6.68461i	0.432986	−	0.245400i
$743$		−	22.3956i		−	0.821617i	−0.911722	−	0.410808i	$-0.865247\pi$
$743$		−	22.3956i		−	0.821617i	0.911722	−	0.410808i	$-0.134753\pi$
$744$		0			0
$745$		−	18.3245i		−	0.671360i
$746$	−18.2493	−	32.1993i	−0.668155	−	1.17890i
$747$		0			0
$748$	6.55468	−	1.64469i	0.239663	−	0.0601359i
$749$	−45.7749	−	45.7749i	−1.67258	−	1.67258i
$750$		0			0
$751$	20.6448			0.753341			0.376670	−	0.926347i	$-0.377069\pi$
$751$	20.6448			0.753341			0.376670	+	0.926347i	$0.377069\pi$
$752$	4.74054	+	8.85161i	0.172870	+	0.322785i
$753$		0			0
$754$	−3.82919	−	1.05884i	−0.139451	−	0.0385608i
$755$	−10.1411	−	10.1411i	−0.369073	−	0.369073i
$756$		0			0
$757$	24.1323	−	24.1323i	0.877104	−	0.877104i	−0.116130	−	0.993234i	$-0.537049\pi$
$757$	24.1323	−	24.1323i	0.877104	−	0.877104i	0.993234	+	0.116130i	$0.0370490\pi$
$758$	13.3381	+	23.5339i	0.484461	+	0.854788i
$759$		0			0
$760$	7.75839	−	7.39562i	0.281426	−	0.268267i
$761$			50.1874i			1.81929i	0.415383	+	0.909647i	$0.363648\pi$
$761$			50.1874i			1.81929i	−0.415383	+	0.909647i	$0.636352\pi$
$762$		0			0
$763$	6.11004	−	6.11004i	0.221198	−	0.221198i
$764$	0.114530	+	0.0685832i	0.00414354	+	0.00248125i
$765$		0			0
$766$	−8.25631	+	29.8581i	−0.298312	+	1.07882i
$767$	16.1517			0.583206
$768$		0			0
$769$	−28.6887			−1.03454			−0.517270	−	0.855822i	$-0.673052\pi$
$769$	−28.6887			−1.03454			−0.517270	+	0.855822i	$0.673052\pi$
$770$	−3.94412	+	14.2635i	−0.142136	+	0.514020i
$771$		0			0
$772$	1.88565	+	1.12918i	0.0678662	+	0.0406400i
$773$	37.5957	−	37.5957i	1.35222	−	1.35222i	0.469052	−	0.883171i	$-0.344596\pi$
$773$	37.5957	−	37.5957i	1.35222	−	1.35222i	0.883171	−	0.469052i	$-0.155404\pi$
$774$		0			0
$775$			7.20435i			0.258788i
$776$	−38.1436	+	36.3601i	−1.36928	+	1.30525i
$777$		0			0
$778$	4.42628	+	7.80977i	0.158690	+	0.279994i
$779$	−17.1810	+	17.1810i	−0.615572	+	0.615572i
$780$		0			0
$781$	−3.15194	−	3.15194i	−0.112785	−	0.112785i
$782$	−4.71245	−	1.30308i	−0.168517	−	0.0465980i
$783$		0			0
$784$	−25.1855	−	47.0267i	−0.899481	−	1.67953i
$785$	−2.97783			−0.106283
$786$		0			0
$787$	−3.13285	−	3.13285i	−0.111674	−	0.111674i	0.649062	−	0.760736i	$-0.275162\pi$
$787$	−3.13285	−	3.13285i	−0.111674	−	0.111674i	−0.760736	+	0.649062i	$0.775162\pi$
$788$	32.7255	−	8.21145i	1.16580	−	0.292521i
$789$		0			0
$790$	−3.53061	−	6.22945i	−0.125614	−	0.221634i
$791$		−	11.5463i		−	0.410541i
$792$		0			0
$793$		−	3.10304i		−	0.110192i
$794$	20.5129	−	11.6259i	0.727974	−	0.412588i
$795$		0			0
$796$	11.3434	−	18.9428i	0.402056	−	0.671408i
$797$	−0.0562195	−	0.0562195i	−0.00199140	−	0.00199140i	0.706110	−	0.708102i	$-0.250448\pi$
$797$	−0.0562195	−	0.0562195i	−0.00199140	−	0.00199140i	−0.708102	+	0.706110i	$0.750448\pi$
$798$		0			0
$799$	−3.65536			−0.129317
$800$	−1.24503	−	5.51814i	−0.0440185	−	0.195096i
$801$		0			0
$802$	−9.39488	+	33.9756i	−0.331745	+	1.19972i
$803$	2.28748	+	2.28748i	0.0807233	+	0.0807233i
$804$		0			0
$805$	7.57088	−	7.57088i	0.266838	−	0.266838i
$806$	−19.0359	+	10.7888i	−0.670511	+	0.380020i
$807$		0			0
$808$	−0.463423	+	19.3588i	−0.0163032	+	0.681039i
$809$		−	3.59856i		−	0.126518i	−0.997997	−	0.0632592i	$-0.979851\pi$
$809$		−	3.59856i		−	0.126518i	0.997997	−	0.0632592i	$-0.0201495\pi$
$810$		0			0
$811$	−7.36274	+	7.36274i	−0.258541	+	0.258541i	−0.824460	−	0.565920i	$-0.808521\pi$
$811$	−7.36274	+	7.36274i	−0.258541	+	0.258541i	0.565920	+	0.824460i	$0.308521\pi$
$812$	11.4433	−	2.87134i	0.401581	−	0.100764i
$813$		0			0
$814$	23.3100	+	6.44564i	0.817014	+	0.225920i
$815$	−7.55196			−0.264534
$816$		0			0
$817$	−41.0414			−1.43586
$818$	29.3542	+	8.11697i	1.02634	+	0.283803i
$819$		0			0
$820$	3.12087	+	12.4378i	0.108985	+	0.434345i
$821$	−14.7799	+	14.7799i	−0.515824	+	0.515824i	−0.916305	−	0.400481i	$-0.868843\pi$
$821$	−14.7799	+	14.7799i	−0.515824	+	0.515824i	0.400481	+	0.916305i	$0.368843\pi$
$822$		0			0
$823$			52.7544i			1.83890i	0.393203	+	0.919452i	$0.371367\pi$
$823$			52.7544i			1.83890i	−0.393203	+	0.919452i	$0.628633\pi$
$824$	−17.8088	−	18.6824i	−0.620399	−	0.650831i
$825$		0			0
$826$	−41.7287	+	23.6502i	−1.45193	+	0.822897i
$827$	−16.8883	+	16.8883i	−0.587265	+	0.587265i	−0.936890	−	0.349625i	$-0.886309\pi$
$827$	−16.8883	+	16.8883i	−0.587265	+	0.587265i	0.349625	+	0.936890i	$0.386309\pi$
$828$		0			0
$829$	−8.55974	−	8.55974i	−0.297292	−	0.297292i	0.542660	−	0.839952i	$-0.317417\pi$
$829$	−8.55974	−	8.55974i	−0.297292	−	0.297292i	−0.839952	+	0.542660i	$0.817417\pi$
$830$	1.30579	−	4.72226i	0.0453247	−	0.163912i
$831$		0			0
$832$	12.7160	−	11.5534i	0.440847	−	0.400541i
$833$	19.4201			0.672868
$834$		0			0
$835$	−11.3622	−	11.3622i	−0.393206	−	0.393206i
$836$	15.0886	+	9.03543i	0.521850	+	0.312497i
$837$		0			0
$838$	30.0980	−	17.0584i	1.03972	−	0.589271i
$839$		−	17.5407i		−	0.605572i	−0.953059	−	0.302786i	$-0.902083\pi$
$839$		−	17.5407i		−	0.605572i	0.953059	−	0.302786i	$-0.0979168\pi$
$840$		0			0
$841$		−	27.2889i		−	0.940996i
$842$	19.1638	+	33.8129i	0.660429	+	1.16527i
$843$		0			0
$844$	5.91814	+	23.5859i	0.203711	+	0.811860i
$845$	−5.93112	−	5.93112i	−0.204037	−	0.204037i
$846$		0			0
$847$	25.3238			0.870137
$848$	−8.13881	−	2.46166i	−0.279488	−	0.0845337i
$849$		0			0
$850$	1.98483	+	0.548843i	0.0680793	+	0.0188252i
$851$	−12.3726	−	12.3726i	−0.424129	−	0.424129i
$852$		0			0
$853$	−15.3577	+	15.3577i	−0.525839	+	0.525839i	−0.919329	−	0.393490i	$-0.871268\pi$
$853$	−15.3577	+	15.3577i	−0.525839	+	0.525839i	0.393490	+	0.919329i	$0.371268\pi$
$854$	4.54363	+	8.01683i	0.155480	+	0.274330i
$855$		0			0
$856$	−0.971684	+	40.5905i	−0.0332115	+	1.38736i
$857$		−	17.9553i		−	0.613341i	−0.951816	−	0.306671i	$-0.900785\pi$
$857$		−	17.9553i		−	0.613341i	0.951816	−	0.306671i	$-0.0992150\pi$
$858$		0			0
$859$	−33.3048	+	33.3048i	−1.13634	+	1.13634i	−0.147245	+	0.989100i	$0.547040\pi$
$859$	−33.3048	+	33.3048i	−1.13634	+	1.13634i	−0.989100	+	0.147245i	$0.952960\pi$
$860$	−11.1280	+	18.5830i	−0.379461	+	0.633676i
$861$		0			0
$862$	−10.6956	+	38.6795i	−0.364293	+	1.31743i
$863$	32.3557			1.10140			0.550701	−	0.834703i	$-0.314361\pi$
$863$	32.3557			1.10140			0.550701	+	0.834703i	$0.314361\pi$
$864$		0			0
$865$	−24.2019			−0.822889
$866$	3.40731	−	12.3222i	0.115785	−	0.418724i
$867$		0			0
$868$	33.3825	−	55.7467i	1.13308	−	1.89217i
$869$	8.30766	−	8.30766i	0.281818	−	0.281818i
$870$		0			0
$871$			15.8765i			0.537956i
$872$	−5.41803	−	0.129700i	−0.183477	−	0.00439221i
$873$		0			0
$874$	−6.27397	−	11.0699i	−0.212220	−	0.374444i
$875$	−3.18877	+	3.18877i	−0.107800	+	0.107800i
$876$		0			0
$877$	26.2297	+	26.2297i	0.885714	+	0.885714i	0.994108	−	0.108394i	$-0.0345707\pi$
$877$	26.2297	+	26.2297i	0.885714	+	0.885714i	−0.108394	+	0.994108i	$0.534571\pi$
$878$	38.5677	+	10.6647i	1.30160	+	0.359916i
$879$		0			0
$880$	8.18224	−	4.38205i	0.275823	−	0.147719i
$881$	47.3359			1.59479			0.797394	−	0.603459i	$-0.206211\pi$
$881$	47.3359			1.59479			0.797394	+	0.603459i	$0.206211\pi$
$882$		0			0
$883$	8.08371	+	8.08371i	0.272039	+	0.272039i	0.829920	−	0.557882i	$-0.188386\pi$
$883$	8.08371	+	8.08371i	0.272039	+	0.272039i	−0.557882	+	0.829920i	$0.688386\pi$
$884$	1.52217	+	6.06640i	0.0511962	+	0.204035i
$885$		0			0
$886$	−12.9415	−	22.8341i	−0.434778	−	0.767127i
$887$		−	12.9255i		−	0.433994i	−0.976172	−	0.216997i	$-0.930374\pi$
$887$		−	12.9255i		−	0.433994i	0.976172	−	0.216997i	$-0.0696263\pi$
$888$		0			0
$889$		−	61.9412i		−	2.07744i
$890$	11.5161	−	6.52690i	0.386022	−	0.218782i
$891$		0			0
$892$	36.7606	+	22.0132i	1.23084	+	0.737055i
$893$	−6.72664	−	6.72664i	−0.225098	−	0.225098i
$894$		0			0
$895$	−1.47760			−0.0493906
$896$	−15.9352	+	48.4680i	−0.532359	+	1.61920i
$897$		0			0
$898$	5.42384	−	19.6147i	0.180996	−	0.654553i
$899$	6.66378	+	6.66378i	0.222250	+	0.222250i
$900$		0			0
$901$	2.18878	−	2.18878i	0.0729190	−	0.0729190i
$902$	−18.3050	+	10.3746i	−0.609490	+	0.345435i
$903$		0			0
$904$	−5.24186	+	4.99676i	−0.174342	+	0.166190i
$905$		−	16.9544i		−	0.563584i
$906$		0			0
$907$	16.4991	−	16.4991i	0.547844	−	0.547844i	−0.377973	−	0.925817i	$-0.623379\pi$
$907$	16.4991	−	16.4991i	0.547844	−	0.547844i	0.925817	+	0.377973i	$0.123379\pi$
$908$	−5.55051	−	22.1207i	−0.184200	−	0.734103i
$909$		0			0
$910$	−13.2009	−	3.65031i	−0.437607	−	0.121006i
$911$	26.6745			0.883765			0.441883	−	0.897073i	$-0.354311\pi$
$911$	26.6745			0.883765			0.441883	+	0.897073i	$0.354311\pi$
$912$		0			0
$913$	8.03908			0.266055
$914$	−6.19563	−	1.71321i	−0.204933	−	0.0566678i
$915$		0			0
$916$	−12.7065	+	3.18830i	−0.419834	+	0.105344i
$917$	−23.4827	+	23.4827i	−0.775467	+	0.775467i
$918$		0			0
$919$		−	57.7425i		−	1.90475i	−0.304932	−	0.952374i	$-0.598634\pi$
$919$		−	57.7425i		−	1.90475i	0.304932	−	0.952374i	$-0.401366\pi$
$920$	−6.71341	−	0.160710i	−0.221334	−	0.00529846i
$921$		0			0
$922$	−34.4595	+	19.5303i	−1.13486	+	0.643197i
$923$	2.91714	−	2.91714i	0.0960188	−	0.0960188i
$924$		0			0
$925$	5.21123	+	5.21123i	0.171344	+	0.171344i
$926$	−5.50280	+	19.9003i	−0.180833	+	0.653965i
$927$		0			0
$928$	−6.25571	−	3.95248i	−0.205354	−	0.129747i
$929$	−42.5386			−1.39565			−0.697823	−	0.716270i	$-0.745848\pi$
$929$	−42.5386			−1.39565			−0.697823	+	0.716270i	$0.745848\pi$
$930$		0			0
$931$	35.7372	+	35.7372i	1.17124	+	1.17124i
$932$	26.7843	−	44.7281i	0.877349	−	1.46512i
$933$		0			0
$934$	−34.4698	+	19.5362i	−1.12789	+	0.639243i
$935$			3.37894i			0.110503i
$936$		0			0
$937$			16.6795i			0.544894i	0.962171	+	0.272447i	$0.0878330\pi$
$937$			16.6795i			0.544894i	−0.962171	+	0.272447i	$0.912167\pi$
$938$	−23.2473	−	41.0177i	−0.759050	−	1.33928i
$939$		0			0
$940$	−4.86959	+	1.22187i	−0.158829	+	0.0398531i
$941$	−9.63152	−	9.63152i	−0.313979	−	0.313979i	0.532470	−	0.846449i	$-0.321264\pi$
$941$	−9.63152	−	9.63152i	−0.313979	−	0.313979i	−0.846449	+	0.532470i	$0.821264\pi$
$942$		0			0
$943$	15.2227			0.495721
$944$	28.7952	+	8.70938i	0.937205	+	0.283466i
$945$		0			0
$946$	−34.2545	−	9.47200i	−1.11371	−	0.307961i
$947$	3.44034	+	3.44034i	0.111796	+	0.111796i	0.760792	−	0.648996i	$-0.224811\pi$
$947$	3.44034	+	3.44034i	0.111796	+	0.111796i	−0.648996	+	0.760792i	$0.724811\pi$
$948$		0			0
$949$	−2.11707	+	2.11707i	−0.0687231	+	0.0687231i
$950$	2.64253	+	4.66251i	0.0857350	+	0.151272i
$951$		0			0
$952$	−12.8153	−	13.4440i	−0.415347	−	0.435721i
$953$			17.6965i			0.573247i	0.958043	+	0.286623i	$0.0925328\pi$
$953$			17.6965i			0.573247i	−0.958043	+	0.286623i	$0.907467\pi$
$954$		0			0
$955$	−0.0471973	+	0.0471973i	−0.00152727	+	0.00152727i
$956$	8.78886	+	5.26299i	0.284252	+	0.170217i
$957$		0			0
$958$	−7.92940	+	28.6759i	−0.256187	+	0.926475i
$959$	102.622			3.31384
$960$		0			0
$961$	20.9027			0.674281
$962$	−5.96548	+	21.5735i	−0.192335	+	0.695559i
$963$		0			0
$964$	−19.7303	−	11.8150i	−0.635470	−	0.380535i
$965$	−0.777073	+	0.777073i	−0.0250149	+	0.0250149i
$966$		0			0
$967$			15.0023i			0.482442i	0.970470	+	0.241221i	$0.0775479\pi$
$967$			15.0023i			0.482442i	−0.970470	+	0.241221i	$0.922452\pi$
$968$	−10.9591	−	11.4966i	−0.352238	−	0.369516i
$969$		0			0
$970$	−12.9918	−	22.9229i	−0.417142	−	0.736010i
$971$	14.3135	−	14.3135i	0.459340	−	0.459340i	−0.439098	−	0.898439i	$-0.644702\pi$
$971$	14.3135	−	14.3135i	0.459340	−	0.459340i	0.898439	+	0.439098i	$0.144702\pi$
$972$		0			0
$973$	−28.3241	−	28.3241i	−0.908030	−	0.908030i
$974$	14.0019	+	3.87177i	0.448649	+	0.124060i
$975$		0			0
$976$	1.67323	−	5.53207i	0.0535587	−	0.177077i
$977$	−48.1433			−1.54024			−0.770120	−	0.637900i	$-0.779804\pi$
$977$	−48.1433			−1.54024			−0.770120	+	0.637900i	$0.779804\pi$
$978$		0			0
$979$	15.3580	+	15.3580i	0.490845	+	0.490845i
$980$	25.8711	−	6.49155i	0.826422	−	0.207365i
$981$		0			0
$982$	−5.87430	−	10.3647i	−0.187457	−	0.330750i
$983$			0.791292i			0.0252383i	0.999920	+	0.0126191i	$0.00401690\pi$
$983$			0.791292i			0.0252383i	−0.999920	+	0.0126191i	$0.995983\pi$
$984$		0			0
$985$			16.8700i			0.537523i
$986$	2.34357	−	1.32824i	0.0746343	−	0.0422999i
$987$		0			0
$988$	−8.36234	+	13.9646i	−0.266042	+	0.444273i
$989$	18.1818	+	18.1818i	0.578149	+	0.578149i
$990$		0			0
$991$	−60.2424			−1.91366			−0.956832	−	0.290643i	$-0.906131\pi$
$991$	−60.2424			−1.91366			−0.956832	+	0.290643i	$0.906131\pi$
$992$	−39.7547	+	8.96964i	−1.26221	+	0.284786i
$993$		0			0
$994$	−3.26513	+	11.8080i	−0.103563	+	0.374526i
$995$	7.80625	+	7.80625i	0.247475	+	0.247475i
$996$		0			0
$997$	1.15773	−	1.15773i	0.0366655	−	0.0366655i	−0.688536	−	0.725202i	$-0.741746\pi$
$997$	1.15773	−	1.15773i	0.0366655	−	0.0366655i	0.725202	+	0.688536i	$0.241746\pi$
$998$	−4.89744	+	2.77568i	−0.155026	+	0.0878626i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	720.2.t.c.541.6		16
3.2	odd	2		80.2.l.a.61.3	yes	16
4.3	odd	2		2880.2.t.c.721.8		16
12.11	even	2		320.2.l.a.81.1		16
15.2	even	4		400.2.q.h.349.1		16
15.8	even	4		400.2.q.g.349.8		16
15.14	odd	2		400.2.l.h.301.6		16
16.5	even	4	inner	720.2.t.c.181.6		16
16.11	odd	4		2880.2.t.c.2161.5		16
24.5	odd	2		640.2.l.b.161.1		16
24.11	even	2		640.2.l.a.161.8		16
48.5	odd	4		80.2.l.a.21.3	✓	16
48.11	even	4		320.2.l.a.241.1		16
48.29	odd	4		640.2.l.b.481.1		16
48.35	even	4		640.2.l.a.481.8		16
60.23	odd	4		1600.2.q.h.849.8		16
60.47	odd	4		1600.2.q.g.849.1		16
60.59	even	2		1600.2.l.i.401.8		16
96.5	odd	8		5120.2.a.s.1.2		8
96.11	even	8		5120.2.a.t.1.2		8
96.53	odd	8		5120.2.a.v.1.7		8
96.59	even	8		5120.2.a.u.1.7		8
240.53	even	4		400.2.q.h.149.1		16
240.59	even	4		1600.2.l.i.1201.8		16
240.107	odd	4		1600.2.q.h.49.8		16
240.149	odd	4		400.2.l.h.101.6		16
240.197	even	4		400.2.q.g.149.8		16
240.203	odd	4		1600.2.q.g.49.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
80.2.l.a.21.3	✓	16	48.5	odd	4
80.2.l.a.61.3	yes	16	3.2	odd	2
320.2.l.a.81.1		16	12.11	even	2
320.2.l.a.241.1		16	48.11	even	4
400.2.l.h.101.6		16	240.149	odd	4
400.2.l.h.301.6		16	15.14	odd	2
400.2.q.g.149.8		16	240.197	even	4
400.2.q.g.349.8		16	15.8	even	4
400.2.q.h.149.1		16	240.53	even	4
400.2.q.h.349.1		16	15.2	even	4
640.2.l.a.161.8		16	24.11	even	2
640.2.l.a.481.8		16	48.35	even	4
640.2.l.b.161.1		16	24.5	odd	2
640.2.l.b.481.1		16	48.29	odd	4
720.2.t.c.181.6		16	16.5	even	4	inner
720.2.t.c.541.6		16	1.1	even	1	trivial
1600.2.l.i.401.8		16	60.59	even	2
1600.2.l.i.1201.8		16	240.59	even	4
1600.2.q.g.49.1		16	240.203	odd	4
1600.2.q.g.849.1		16	60.47	odd	4
1600.2.q.h.49.8		16	240.107	odd	4
1600.2.q.h.849.8		16	60.23	odd	4
2880.2.t.c.721.8		16	4.3	odd	2
2880.2.t.c.2161.5		16	16.11	odd	4
5120.2.a.s.1.2		8	96.5	odd	8
5120.2.a.t.1.2		8	96.11	even	8
5120.2.a.u.1.7		8	96.59	even	8
5120.2.a.v.1.7		8	96.53	odd	8

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:	\( N \)	\(=\)	\( 720 = 2^{4} \cdot 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	720.t (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.376912 - 1.36306i) q^{2} +(-1.71587 - 1.02751i) q^{4} +(0.707107 - 0.707107i) q^{5} -4.50961i q^{7} +(-2.04729 + 1.95156i) q^{8} +O(q^{10})\)	\(q+(0.376912 - 1.36306i) q^{2} +(-1.71587 - 1.02751i) q^{4} +(0.707107 - 0.707107i) q^{5} -4.50961i q^{7} +(-2.04729 + 1.95156i) q^{8} +(-0.697313 - 1.23035i) q^{10} +(1.64080 - 1.64080i) q^{11} +(1.51857 + 1.51857i) q^{13} +(-6.14687 - 1.69972i) q^{14} +(1.88845 + 3.52615i) q^{16} -1.45616 q^{17} +(-2.67964 - 2.67964i) q^{19} +(-1.93986 + 0.486749i) q^{20} +(-1.61808 - 2.85495i) q^{22} +2.37423i q^{23} -1.00000i q^{25} +(2.64228 - 1.49754i) q^{26} +(-4.63366 + 7.73792i) q^{28} +(-0.924966 - 0.924966i) q^{29} -7.20435 q^{31} +(5.51814 - 1.24503i) q^{32} +(-0.548843 + 1.98483i) q^{34} +(-3.18877 - 3.18877i) q^{35} +(-5.21123 + 5.21123i) q^{37} +(-4.66251 + 2.64253i) q^{38} +(-0.0676894 + 2.82762i) q^{40} -6.41166i q^{41} +(7.65800 - 7.65800i) q^{43} +(-4.50135 + 1.12947i) q^{44} +(3.23622 + 0.894875i) q^{46} +2.51027 q^{47} -13.3366 q^{49} +(-1.36306 - 0.376912i) q^{50} +(-1.04534 - 4.16603i) q^{52} +(-1.50312 + 1.50312i) q^{53} -2.32045i q^{55} +(8.80078 + 9.23248i) q^{56} +(-1.60942 + 0.912155i) q^{58} +(5.31807 - 5.31807i) q^{59} +(-1.02169 - 1.02169i) q^{61} +(-2.71541 + 9.81998i) q^{62} +(0.382800 - 7.99084i) q^{64} +2.14759 q^{65} +(5.22745 + 5.22745i) q^{67} +(2.49859 + 1.49622i) q^{68} +(-5.54838 + 3.14461i) q^{70} -1.92097i q^{71} +1.39412i q^{73} +(5.13905 + 9.06740i) q^{74} +(1.84458 + 7.35129i) q^{76} +(-7.39938 - 7.39938i) q^{77} +5.06317 q^{79} +(3.82870 + 1.15803i) q^{80} +(-8.73949 - 2.41663i) q^{82} +(2.44974 + 2.44974i) q^{83} +(-1.02966 + 1.02966i) q^{85} +(-7.55194 - 13.3247i) q^{86} +(-0.157070 + 6.56133i) q^{88} +9.36007i q^{89} +(6.84817 - 6.84817i) q^{91} +(2.43954 - 4.07388i) q^{92} +(0.946152 - 3.42166i) q^{94} -3.78959 q^{95} +18.6313 q^{97} +(-5.02671 + 18.1785i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 4 q^{4}+O(q^{10}) \) 16 * q - 4 * q^4	\( 16 q - 4 q^{4} + 4 q^{10} + 8 q^{11} - 4 q^{14} + 16 q^{16} - 8 q^{19} - 8 q^{20} - 20 q^{22} + 16 q^{26} - 4 q^{28} + 16 q^{29} + 16 q^{34} - 16 q^{37} - 20 q^{38} + 8 q^{43} - 40 q^{44} - 4 q^{46} + 40 q^{47} - 16 q^{49} + 4 q^{50} + 56 q^{52} - 16 q^{53} - 16 q^{56} - 12 q^{58} + 8 q^{59} + 16 q^{61} + 8 q^{62} - 16 q^{64} + 40 q^{67} + 48 q^{68} - 8 q^{70} + 72 q^{74} - 16 q^{77} + 16 q^{79} - 16 q^{80} - 76 q^{82} - 40 q^{83} - 16 q^{85} - 28 q^{86} + 32 q^{91} + 52 q^{92} - 36 q^{94} - 32 q^{95} - 60 q^{98}+O(q^{100}) \) 16 * q - 4 * q^4 + 4 * q^10 + 8 * q^11 - 4 * q^14 + 16 * q^16 - 8 * q^19 - 8 * q^20 - 20 * q^22 + 16 * q^26 - 4 * q^28 + 16 * q^29 + 16 * q^34 - 16 * q^37 - 20 * q^38 + 8 * q^43 - 40 * q^44 - 4 * q^46 + 40 * q^47 - 16 * q^49 + 4 * q^50 + 56 * q^52 - 16 * q^53 - 16 * q^56 - 12 * q^58 + 8 * q^59 + 16 * q^61 + 8 * q^62 - 16 * q^64 + 40 * q^67 + 48 * q^68 - 8 * q^70 + 72 * q^74 - 16 * q^77 + 16 * q^79 - 16 * q^80 - 76 * q^82 - 40 * q^83 - 16 * q^85 - 28 * q^86 + 32 * q^91 + 52 * q^92 - 36 * q^94 - 32 * q^95 - 60 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more