LMFDB - Embedded newform 576.2.y.a.47.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(47,576)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(576, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 9, 2]))

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

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

chi := DirichletCharacter("576.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.y (of order $12$, degree $4$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.59938315643$
Analytic rank:	$0$
Dimension:	$88$
Relative dimension:	$22$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			47.20
Character	$\chi$	$=$	576.47
Dual form			576.2.y.a.527.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.65787 - 0.501476i) q^{3} +(0.997280 - 3.72190i) q^{5} +(0.481387 - 0.833787i) q^{7} +(2.49704 - 1.66276i) q^{9} +O(q^{10})$	\(q+(1.65787 - 0.501476i) q^{3} +(0.997280 - 3.72190i) q^{5} +(0.481387 - 0.833787i) q^{7} +(2.49704 - 1.66276i) q^{9} +(1.00684 + 3.75758i) q^{11} +(-0.430868 + 1.60802i) q^{13} +(-0.213084 - 6.67053i) q^{15} -2.58216i q^{17} +(-4.02190 + 4.02190i) q^{19} +(0.379952 - 1.62371i) q^{21} +(-0.600513 + 0.346706i) q^{23} +(-8.52786 - 4.92356i) q^{25} +(3.30593 - 4.00884i) q^{27} +(-1.54233 - 5.75605i) q^{29} +(3.07839 - 1.77731i) q^{31} +(3.55354 + 5.72466i) q^{33} +(-2.62320 - 2.62320i) q^{35} +(-2.11774 + 2.11774i) q^{37} +(0.0920616 + 2.88196i) q^{39} +(4.97738 + 8.62108i) q^{41} +(-6.65259 + 1.78256i) q^{43} +(-3.69837 - 10.9520i) q^{45} +(2.88971 - 5.00512i) q^{47} +(3.03653 + 5.25943i) q^{49} +(-1.29489 - 4.28087i) q^{51} +(6.68090 + 6.68090i) q^{53} +14.9894 q^{55} +(-4.65088 + 8.68465i) q^{57} +(8.75083 + 2.34478i) q^{59} +(-2.12855 + 0.570345i) q^{61} +(-0.184342 - 2.88243i) q^{63} +(5.55520 + 3.20730i) q^{65} +(-4.20548 - 1.12686i) q^{67} +(-0.821706 + 0.875935i) q^{69} +9.40024i q^{71} -3.77840i q^{73} +(-16.6071 - 3.88610i) q^{75} +(3.61770 + 0.969360i) q^{77} +(-9.52430 - 5.49886i) q^{79} +(3.47046 - 8.30397i) q^{81} +(-8.79083 + 2.35550i) q^{83} +(-9.61053 - 2.57514i) q^{85} +(-5.44349 - 8.76932i) q^{87} +13.0545 q^{89} +(1.13333 + 1.13333i) q^{91} +(4.21228 - 4.49027i) q^{93} +(10.9581 + 18.9801i) q^{95} +(1.76559 - 3.05809i) q^{97} +(8.76208 + 7.70871i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	$ 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) $ 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$-1$	$e\left(\frac{3}{4}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.65787	−	0.501476i	0.957170	−	0.289527i
$3$	1.65787	−	0.501476i	0.957170	−	0.289527i
$4$		0			0
$5$	0.997280	−	3.72190i	0.445997	−	1.66448i	−0.267292	−	0.963616i	$-0.586129\pi$
$5$	0.997280	−	3.72190i	0.445997	−	1.66448i	0.713290	−	0.700869i	$-0.247204\pi$
$6$		0			0
$7$	0.481387	−	0.833787i	0.181947	−	0.315142i	−0.760596	−	0.649225i	$-0.775093\pi$
$7$	0.481387	−	0.833787i	0.181947	−	0.315142i	0.942544	+	0.334083i	$0.108427\pi$
$8$		0			0
$9$	2.49704	−	1.66276i	0.832348	−	0.554253i
$10$		0			0
$11$	1.00684	+	3.75758i	0.303574	+	1.13295i	0.934166	+	0.356839i	$0.116145\pi$
$11$	1.00684	+	3.75758i	0.303574	+	1.13295i	−0.630592	+	0.776114i	$0.717188\pi$
$12$		0			0
$13$	−0.430868	+	1.60802i	−0.119501	+	0.445985i	−0.999584	−	0.0288351i	$-0.990820\pi$
$13$	−0.430868	+	1.60802i	−0.119501	+	0.445985i	0.880083	+	0.474820i	$0.157487\pi$
$14$		0			0
$15$	−0.213084	−	6.67053i	−0.0550181	−	1.72232i
$16$		0			0
$17$		−	2.58216i		−	0.626265i	−0.949709	−	0.313133i	$-0.898622\pi$
$17$		−	2.58216i		−	0.626265i	0.949709	−	0.313133i	$-0.101378\pi$
$18$		0			0
$19$	−4.02190	+	4.02190i	−0.922686	+	0.922686i	−0.997219	−	0.0745325i	$-0.976254\pi$
$19$	−4.02190	+	4.02190i	−0.922686	+	0.922686i	0.0745325	+	0.997219i	$0.476254\pi$
$20$		0			0
$21$	0.379952	−	1.62371i	0.0829123	−	0.354323i
$22$		0			0
$23$	−0.600513	+	0.346706i	−0.125216	+	0.0722933i	−0.561300	−	0.827613i	$-0.689698\pi$
$23$	−0.600513	+	0.346706i	−0.125216	+	0.0722933i	0.436084	+	0.899906i	$0.356365\pi$
$24$		0			0
$25$	−8.52786	−	4.92356i	−1.70557	−	0.984712i
$26$		0			0
$27$	3.30593	−	4.00884i	0.636227	−	0.771502i
$28$		0			0
$29$	−1.54233	−	5.75605i	−0.286403	−	1.06887i	−0.947808	−	0.318842i	$-0.896706\pi$
$29$	−1.54233	−	5.75605i	−0.286403	−	1.06887i	0.661405	−	0.750029i	$-0.269961\pi$
$30$		0			0
$31$	3.07839	−	1.77731i	0.552894	−	0.319214i	−0.197394	−	0.980324i	$-0.563248\pi$
$31$	3.07839	−	1.77731i	0.552894	−	0.319214i	0.750289	+	0.661110i	$0.229915\pi$
$32$		0			0
$33$	3.55354	+	5.72466i	0.618592	+	0.996536i
$34$		0			0
$35$	−2.62320	−	2.62320i	−0.443401	−	0.443401i
$36$		0			0
$37$	−2.11774	+	2.11774i	−0.348154	+	0.348154i	−0.859422	−	0.511267i	$-0.829176\pi$
$37$	−2.11774	+	2.11774i	−0.348154	+	0.348154i	0.511267	+	0.859422i	$0.329176\pi$
$38$		0			0
$39$	0.0920616	+	2.88196i	0.0147417	+	0.461482i
$40$		0			0
$41$	4.97738	+	8.62108i	0.777337	+	1.34639i	0.933472	+	0.358651i	$0.116763\pi$
$41$	4.97738	+	8.62108i	0.777337	+	1.34639i	−0.156135	+	0.987736i	$0.549904\pi$
$42$		0			0
$43$	−6.65259	+	1.78256i	−1.01451	+	0.271837i	−0.727513	−	0.686094i	$-0.759324\pi$
$43$	−6.65259	+	1.78256i	−1.01451	+	0.271837i	−0.286997	+	0.957931i	$0.592657\pi$
$44$		0			0
$45$	−3.69837	−	10.9520i	−0.551321	−	1.63263i
$46$		0			0
$47$	2.88971	−	5.00512i	0.421507	−	0.730072i	−0.574580	−	0.818448i	$-0.694835\pi$
$47$	2.88971	−	5.00512i	0.421507	−	0.730072i	0.996087	+	0.0883767i	$0.0281679\pi$
$48$		0			0
$49$	3.03653	+	5.25943i	0.433790	+	0.751347i
$50$		0			0
$51$	−1.29489	−	4.28087i	−0.181321	−	0.599442i
$52$		0			0
$53$	6.68090	+	6.68090i	0.917692	+	0.917692i	0.996861	−	0.0791696i	$-0.0252269\pi$
$53$	6.68090	+	6.68090i	0.917692	+	0.917692i	−0.0791696	+	0.996861i	$0.525227\pi$
$54$		0			0
$55$	14.9894			2.02118
$56$		0			0
$57$	−4.65088	+	8.68465i	−0.616025	+	1.15031i
$58$		0			0
$59$	8.75083	+	2.34478i	1.13926	+	0.305264i	0.778654	−	0.627454i	$-0.215903\pi$
$59$	8.75083	+	2.34478i	1.13926	+	0.305264i	0.360607	+	0.932718i	$0.382570\pi$
$60$		0			0
$61$	−2.12855	+	0.570345i	−0.272534	+	0.0730251i	−0.392497	−	0.919753i	$-0.628389\pi$
$61$	−2.12855	+	0.570345i	−0.272534	+	0.0730251i	0.119964	+	0.992778i	$0.461722\pi$
$62$		0			0
$63$	−0.184342	−	2.88243i	−0.0232249	−	0.363153i
$64$		0			0
$65$	5.55520	+	3.20730i	0.689038	+	0.397816i
$66$		0			0
$67$	−4.20548	−	1.12686i	−0.513782	−	0.137667i	−0.00739290	−	0.999973i	$-0.502353\pi$
$67$	−4.20548	−	1.12686i	−0.513782	−	0.137667i	−0.506389	+	0.862305i	$0.669020\pi$
$68$		0			0
$69$	−0.821706	+	0.875935i	−0.0989217	+	0.105450i
$70$		0			0
$71$			9.40024i			1.11560i	0.829974	+	0.557801i	$0.188355\pi$
$71$			9.40024i			1.11560i	−0.829974	+	0.557801i	$0.811645\pi$
$72$		0			0
$73$		−	3.77840i		−	0.442228i	−0.975248	−	0.221114i	$-0.929031\pi$
$73$		−	3.77840i		−	0.442228i	0.975248	−	0.221114i	$-0.0709693\pi$
$74$		0			0
$75$	−16.6071	−	3.88610i	−1.91762	−	0.448728i
$76$		0			0
$77$	3.61770	+	0.969360i	0.412275	+	0.110469i
$78$		0			0
$79$	−9.52430	−	5.49886i	−1.07157	−	0.618670i	−0.142958	−	0.989729i	$-0.545661\pi$
$79$	−9.52430	−	5.49886i	−1.07157	−	0.618670i	−0.928609	+	0.371059i	$0.878995\pi$
$80$		0			0
$81$	3.47046	−	8.30397i	0.385607	−	0.922663i
$82$		0			0
$83$	−8.79083	+	2.35550i	−0.964919	+	0.258549i	−0.706681	−	0.707532i	$-0.749809\pi$
$83$	−8.79083	+	2.35550i	−0.964919	+	0.258549i	−0.258238	+	0.966081i	$0.583142\pi$
$84$		0			0
$85$	−9.61053	−	2.57514i	−1.04241	−	0.279313i
$86$		0			0
$87$	−5.44349	−	8.76932i	−0.583604	−	0.940170i
$88$		0			0
$89$	13.0545			1.38378			0.691889	−	0.722004i	$-0.256779\pi$
$89$	13.0545			1.38378			0.691889	+	0.722004i	$0.256779\pi$
$90$		0			0
$91$	1.13333	+	1.13333i	0.118806	+	0.118806i
$92$		0			0
$93$	4.21228	−	4.49027i	0.436793	−	0.465620i
$94$		0			0
$95$	10.9581	+	18.9801i	1.12428	+	1.94731i
$96$		0			0
$97$	1.76559	−	3.05809i	0.179268	−	0.310502i	−0.762362	−	0.647151i	$-0.775960\pi$
$97$	1.76559	−	3.05809i	0.179268	−	0.310502i	0.941630	+	0.336649i	$0.109294\pi$
$98$		0			0
$99$	8.76208	+	7.70871i	0.880622	+	0.774755i
$100$		0			0
$101$	−18.3403	+	4.91426i	−1.82492	+	0.488987i	−0.997375	−	0.0724058i	$-0.976932\pi$
$101$	−18.3403	+	4.91426i	−1.82492	+	0.488987i	−0.827549	+	0.561393i	$0.810266\pi$
$102$		0			0
$103$	−1.72391	−	2.98591i	−0.169862	−	0.294210i	0.768509	−	0.639839i	$-0.220999\pi$
$103$	−1.72391	−	2.98591i	−0.169862	−	0.294210i	−0.938371	+	0.345629i	$0.887666\pi$
$104$		0			0
$105$	−5.66438	−	3.03344i	−0.552787	−	0.296033i
$106$		0			0
$107$	6.09696	−	6.09696i	0.589415	−	0.589415i	−0.348058	−	0.937473i	$-0.613159\pi$
$107$	6.09696	−	6.09696i	0.589415	−	0.589415i	0.937473	+	0.348058i	$0.113159\pi$
$108$		0			0
$109$	3.96541	+	3.96541i	0.379817	+	0.379817i	0.871036	−	0.491219i	$-0.163448\pi$
$109$	3.96541	+	3.96541i	0.379817	+	0.379817i	−0.491219	+	0.871036i	$0.663448\pi$
$110$		0			0
$111$	−2.44894	+	4.57293i	−0.232443	+	0.434043i
$112$		0			0
$113$	5.53559	−	3.19597i	0.520744	−	0.300652i	−0.216495	−	0.976284i	$-0.569462\pi$
$113$	5.53559	−	3.19597i	0.520744	−	0.300652i	0.737239	+	0.675632i	$0.236129\pi$
$114$		0			0
$115$	0.691527	+	2.58081i	0.0644852	+	0.240662i
$116$		0			0
$117$	1.59786	+	4.73173i	0.147722	+	0.437449i
$118$		0			0
$119$	−2.15297	−	1.24302i	−0.197362	−	0.113947i
$120$		0			0
$121$	−3.57940	+	2.06657i	−0.325400	+	0.187870i
$122$		0			0
$123$	12.5751	+	11.7966i	1.13386	+	1.06366i
$124$		0			0
$125$	−13.2066	+	13.2066i	−1.18123	+	1.18123i
$126$		0			0
$127$			3.08724i			0.273948i	0.990575	+	0.136974i	$0.0437377\pi$
$127$			3.08724i			0.273948i	−0.990575	+	0.136974i	$0.956262\pi$
$128$		0			0
$129$	−10.1352	+	6.29135i	−0.892354	+	0.553922i
$130$		0			0
$131$	1.36018	−	5.07628i	0.118840	−	0.443516i	−0.880706	−	0.473664i	$-0.842931\pi$
$131$	1.36018	−	5.07628i	0.118840	−	0.443516i	0.999545	+	0.0301478i	$0.00959778\pi$
$132$		0			0
$133$	1.41732	+	5.28949i	0.122897	+	0.458657i
$134$		0			0
$135$	−11.6236	−	16.3023i	−1.00040	−	1.40308i
$136$		0			0
$137$	0.807507	−	1.39864i	0.0689899	−	0.119494i	−0.829467	−	0.558556i	$-0.811356\pi$
$137$	0.807507	−	1.39864i	0.0689899	−	0.119494i	0.898457	+	0.439062i	$0.144689\pi$
$138$		0			0
$139$	−1.02028	+	3.80774i	−0.0865390	+	0.322968i	−0.995601	−	0.0936925i	$-0.970133\pi$
$139$	−1.02028	+	3.80774i	−0.0865390	+	0.322968i	0.909062	+	0.416661i	$0.136800\pi$
$140$		0			0
$141$	2.28080	−	9.74694i	0.192078	−	0.820840i
$142$		0			0
$143$	−6.47609			−0.541558
$144$		0			0
$145$	−22.9616			−1.90685
$146$		0			0
$147$	7.67164	+	7.19669i	0.632746	+	0.593573i
$148$		0			0
$149$	1.15611	−	4.31466i	0.0947122	−	0.353471i	−0.902263	−	0.431185i	$-0.858096\pi$
$149$	1.15611	−	4.31466i	0.0947122	−	0.353471i	0.996976	+	0.0777144i	$0.0247622\pi$
$150$		0			0
$151$	−9.60303	+	16.6329i	−0.781483	+	1.35357i	0.149594	+	0.988747i	$0.452203\pi$
$151$	−9.60303	+	16.6329i	−0.781483	+	1.35357i	−0.931078	+	0.364821i	$0.881130\pi$
$152$		0			0
$153$	−4.29351	−	6.44776i	−0.347109	−	0.521271i
$154$		0			0
$155$	−3.54495	−	13.2299i	−0.284737	−	1.06265i
$156$		0			0
$157$	−4.88175	+	18.2189i	−0.389606	+	1.45403i	0.441170	+	0.897423i	$0.354564\pi$
$157$	−4.88175	+	18.2189i	−0.389606	+	1.45403i	−0.830776	+	0.556606i	$0.812103\pi$
$158$		0			0
$159$	14.4263	+	7.72573i	1.14408	+	0.612690i
$160$		0			0
$161$			0.667600i			0.0526142i
$162$		0			0
$163$	−10.2654	+	10.2654i	−0.804052	+	0.804052i	−0.983726	−	0.179675i	$-0.942496\pi$
$163$	−10.2654	+	10.2654i	−0.804052	+	0.804052i	0.179675	+	0.983726i	$0.442496\pi$
$164$		0			0
$165$	24.8505	−	7.51684i	1.93461	−	0.585185i
$166$		0			0
$167$	4.99449	−	2.88357i	0.386485	−	0.223137i	−0.294151	−	0.955759i	$-0.595037\pi$
$167$	4.99449	−	2.88357i	0.386485	−	0.223137i	0.680636	+	0.732622i	$0.261704\pi$
$168$		0			0
$169$	8.85824	+	5.11431i	0.681403	+	0.393408i
$170$		0			0
$171$	−3.35541	+	16.7303i	−0.256594	+	1.27940i
$172$		0			0
$173$	2.06432	+	7.70414i	0.156947	+	0.585735i	0.998931	+	0.0462316i	$0.0147212\pi$
$173$	2.06432	+	7.70414i	0.156947	+	0.585735i	−0.841984	+	0.539503i	$0.818612\pi$
$174$		0			0
$175$	−8.21040	+	4.74028i	−0.620648	+	0.358331i
$176$		0			0
$177$	15.6836	−	0.500998i	1.17885	−	0.0376573i
$178$		0			0
$179$	−1.48408	−	1.48408i	−0.110925	−	0.110925i	0.649466	−	0.760391i	$-0.274993\pi$
$179$	−1.48408	−	1.48408i	−0.110925	−	0.110925i	−0.760391	+	0.649466i	$0.774993\pi$
$180$		0			0
$181$	4.93884	−	4.93884i	0.367101	−	0.367101i	−0.499318	−	0.866419i	$-0.666416\pi$
$181$	4.93884	−	4.93884i	0.367101	−	0.367101i	0.866419	+	0.499318i	$0.166416\pi$
$182$		0			0
$183$	−3.24285	+	2.01297i	−0.239718	+	0.148803i
$184$		0			0
$185$	5.77004	+	9.99400i	0.424222	+	0.734774i
$186$		0			0
$187$	9.70266	−	2.59982i	0.709529	−	0.190118i
$188$		0			0
$189$	−1.75108	−	4.68625i	−0.127373	−	0.340875i
$190$		0			0
$191$	3.80239	−	6.58592i	0.275131	−	0.476541i	−0.695037	−	0.718974i	$-0.744612\pi$
$191$	3.80239	−	6.58592i	0.275131	−	0.476541i	0.970168	+	0.242433i	$0.0779455\pi$
$192$		0			0
$193$	0.964071	+	1.66982i	0.0693954	+	0.120196i	0.898635	−	0.438696i	$-0.144560\pi$
$193$	0.964071	+	1.66982i	0.0693954	+	0.120196i	−0.829240	+	0.558893i	$0.811226\pi$
$194$		0			0
$195$	10.8182	+	2.53147i	0.774705	+	0.181283i
$196$		0			0
$197$	−16.2088	−	16.2088i	−1.15483	−	1.15483i	−0.985573	−	0.169254i	$-0.945864\pi$
$197$	−16.2088	−	16.2088i	−1.15483	−	1.15483i	−0.169254	−	0.985573i	$-0.554136\pi$
$198$		0			0
$199$	6.55635			0.464768			0.232384	−	0.972624i	$-0.425347\pi$
$199$	6.55635			0.464768			0.232384	+	0.972624i	$0.425347\pi$
$200$		0			0
$201$	−7.53722	+	0.240770i	−0.531635	+	0.0169826i
$202$		0			0
$203$	−5.54178	−	1.48491i	−0.388956	−	0.104221i
$204$		0			0
$205$	37.0507	−	9.92769i	2.58773	−	0.693380i
$206$		0			0
$207$	−0.923018	+	1.86425i	−0.0641542	+	0.129574i
$208$		0			0
$209$	−19.1620	−	11.0632i	−1.32546	−	0.765257i
$210$		0			0
$211$	−5.83649	−	1.56388i	−0.401800	−	0.107662i	0.0522589	−	0.998634i	$-0.483358\pi$
$211$	−5.83649	−	1.56388i	−0.401800	−	0.107662i	−0.454059	+	0.890971i	$0.650025\pi$
$212$		0			0
$213$	4.71399	+	15.5843i	0.322997	+	1.06782i
$214$		0			0
$215$			26.5380i			1.80988i
$216$		0			0
$217$		−	3.42229i		−	0.232320i
$218$		0			0
$219$	−1.89477	−	6.26408i	−0.128037	−	0.423287i
$220$		0			0
$221$	4.15217	+	1.11257i	0.279305	+	0.0748395i
$222$		0			0
$223$	−4.51028	−	2.60401i	−0.302031	−	0.174377i	0.341324	−	0.939946i	$-0.389125\pi$
$223$	−4.51028	−	2.60401i	−0.302031	−	0.174377i	−0.643355	+	0.765568i	$0.722458\pi$
$224$		0			0
$225$	−29.4811	+	1.88542i	−1.96541	+	0.125695i
$226$		0			0
$227$	6.28589	−	1.68430i	0.417209	−	0.111791i	−0.0441067	−	0.999027i	$-0.514044\pi$
$227$	6.28589	−	1.68430i	0.417209	−	0.111791i	0.461316	+	0.887236i	$0.347377\pi$
$228$		0			0
$229$	3.99522	+	1.07052i	0.264012	+	0.0707418i	0.388397	−	0.921492i	$-0.373029\pi$
$229$	3.99522	+	1.07052i	0.264012	+	0.0707418i	−0.124385	+	0.992234i	$0.539696\pi$
$230$		0			0
$231$	6.48378	−	0.207119i	0.426601	−	0.0136274i
$232$		0			0
$233$	−17.2178			−1.12797			−0.563987	−	0.825783i	$-0.690733\pi$
$233$	−17.2178			−1.12797			−0.563987	+	0.825783i	$0.690733\pi$
$234$		0			0
$235$	−15.7467	−	15.7467i	−1.02720	−	1.02720i
$236$		0			0
$237$	−18.5476	−	4.34017i	−1.20479	−	0.281924i
$238$		0			0
$239$	−4.49270	−	7.78159i	−0.290609	−	0.503349i	0.683345	−	0.730095i	$-0.260524\pi$
$239$	−4.49270	−	7.78159i	−0.290609	−	0.503349i	−0.973954	+	0.226747i	$0.927191\pi$
$240$		0			0
$241$	0.560812	−	0.971356i	0.0361251	−	0.0625705i	−0.847398	−	0.530959i	$-0.821832\pi$
$241$	0.560812	−	0.971356i	0.0361251	−	0.0625705i	0.883523	+	0.468388i	$0.155165\pi$
$242$		0			0
$243$	1.58933	−	15.5072i	0.101956	−	0.994789i
$244$		0			0
$245$	22.6034	−	6.05655i	1.44408	−	0.386939i
$246$		0			0
$247$	−4.73439	−	8.20020i	−0.301242	−	0.521766i
$248$		0			0
$249$	−13.3928	+	8.31349i	−0.848735	+	0.526846i
$250$		0			0
$251$	−0.699267	+	0.699267i	−0.0441373	+	0.0441373i	−0.728831	−	0.684694i	$-0.759936\pi$
$251$	−0.699267	+	0.699267i	−0.0441373	+	0.0441373i	0.684694	+	0.728831i	$0.259936\pi$
$252$		0			0
$253$	−1.90740	−	1.90740i	−0.119917	−	0.119917i
$254$		0			0
$255$	−17.2244	+	0.550217i	−1.07863	+	0.0344559i
$256$		0			0
$257$	5.79978	−	3.34851i	0.361781	−	0.208874i	−0.308081	−	0.951360i	$-0.599687\pi$
$257$	5.79978	−	3.34851i	0.361781	−	0.208874i	0.669862	+	0.742486i	$0.266353\pi$
$258$		0			0
$259$	0.746291	+	2.78520i	0.0463723	+	0.173064i
$260$		0			0
$261$	−13.4222	−	11.8086i	−0.830812	−	0.730933i
$262$		0			0
$263$	−12.2113	−	7.05022i	−0.752984	−	0.434735i	0.0737874	−	0.997274i	$-0.476491\pi$
$263$	−12.2113	−	7.05022i	−0.752984	−	0.434735i	−0.826771	+	0.562539i	$0.809825\pi$
$264$		0			0
$265$	31.5284	−	18.2029i	1.93677	−	1.11820i
$266$		0			0
$267$	21.6427	−	6.54653i	1.32451	−	0.400641i
$268$		0			0
$269$	−13.2566	+	13.2566i	−0.808267	+	0.808267i	−0.984371	−	0.176105i	$-0.943650\pi$
$269$	−13.2566	+	13.2566i	−0.808267	+	0.808267i	0.176105	+	0.984371i	$0.443650\pi$
$270$		0			0
$271$		−	10.4494i		−	0.634755i	−0.948299	−	0.317377i	$-0.897198\pi$
$271$		−	10.4494i		−	0.634755i	0.948299	−	0.317377i	$-0.102802\pi$
$272$		0			0
$273$	2.44726	+	1.31058i	0.148115	+	0.0793197i
$274$		0			0
$275$	9.91448	−	37.0013i	0.597866	−	2.23126i
$276$		0			0
$277$	4.19068	+	15.6398i	0.251794	+	0.939707i	0.969846	+	0.243718i	$0.0783672\pi$
$277$	4.19068	+	15.6398i	0.251794	+	0.939707i	−0.718052	+	0.695989i	$0.754966\pi$
$278$		0			0
$279$	4.73163	−	9.55663i	0.283275	−	0.572140i
$280$		0			0
$281$	12.1751	−	21.0879i	0.726306	−	1.25800i	−0.232129	−	0.972685i	$-0.574569\pi$
$281$	12.1751	−	21.0879i	0.726306	−	1.25800i	0.958434	−	0.285313i	$-0.0920977\pi$
$282$		0			0
$283$	−2.27765	+	8.50029i	−0.135392	+	0.505290i	0.864604	+	0.502454i	$0.167569\pi$
$283$	−2.27765	+	8.50029i	−0.135392	+	0.505290i	−0.999996	+	0.00283598i	$0.999097\pi$
$284$		0			0
$285$	27.6852	+	25.9712i	1.63993	+	1.53840i
$286$		0			0
$287$	9.58419			0.565737
$288$		0			0
$289$	10.3325			0.607792
$290$		0			0
$291$	1.39355	−	5.95531i	0.0816916	−	0.349106i
$292$		0			0
$293$	−0.216688	+	0.808690i	−0.0126590	+	0.0472442i	−0.971966	−	0.235120i	$-0.924452\pi$
$293$	−0.216688	+	0.808690i	−0.0126590	+	0.0472442i	0.959307	+	0.282364i	$0.0911185\pi$
$294$		0			0
$295$	17.4541	−	30.2313i	1.01621	−	1.76014i
$296$		0			0
$297$	18.3921	+	8.38605i	1.06722	+	0.486608i
$298$		0			0
$299$	−0.298769	−	1.11502i	−0.0172783	−	0.0644834i
$300$		0			0
$301$	−1.71620	+	6.40494i	−0.0989201	+	0.369175i
$302$		0			0
$303$	−27.9413	+	17.3444i	−1.60519	+	0.996409i
$304$		0			0
$305$			8.49106i			0.486197i
$306$		0			0
$307$	21.1593	−	21.1593i	1.20763	−	1.20763i	0.235831	−	0.971794i	$-0.424219\pi$
$307$	21.1593	−	21.1593i	1.20763	−	1.20763i	0.971794	−	0.235831i	$-0.0757813\pi$
$308$		0			0
$309$	−4.35538	−	4.08574i	−0.247769	−	0.232429i
$310$		0			0
$311$	−10.8454	+	6.26157i	−0.614984	+	0.355061i	−0.774914	−	0.632067i	$-0.782207\pi$
$311$	−10.8454	+	6.26157i	−0.614984	+	0.355061i	0.159929	+	0.987128i	$0.448873\pi$
$312$		0			0
$313$	−28.1752	−	16.2670i	−1.59256	−	0.919463i	−0.992867	−	0.119230i	$-0.961958\pi$
$313$	−28.1752	−	16.2670i	−1.59256	−	0.919463i	−0.599689	−	0.800233i	$-0.704709\pi$
$314$		0			0
$315$	−10.9120	−	2.18849i	−0.614820	−	0.123308i
$316$		0			0
$317$	−3.60078	−	13.4383i	−0.202240	−	0.754770i	−0.990273	−	0.139137i	$-0.955567\pi$
$317$	−3.60078	−	13.4383i	−0.202240	−	0.754770i	0.788033	−	0.615633i	$-0.211100\pi$
$318$		0			0
$319$	20.0759	−	11.5908i	1.12404	−	0.648963i
$320$		0			0
$321$	7.05047	−	13.1654i	0.393519	−	0.734822i
$322$		0			0
$323$	10.3852	+	10.3852i	0.577846	+	0.577846i
$324$		0			0
$325$	11.5916	−	11.5916i	0.642985	−	0.642985i
$326$		0			0
$327$	8.56268	+	4.58557i	0.473517	+	0.253582i
$328$		0			0
$329$	−2.78214	−	4.81880i	−0.153384	−	0.265669i
$330$		0			0
$331$	5.29427	−	1.41860i	0.291000	−	0.0779731i	−0.110366	−	0.993891i	$-0.535202\pi$
$331$	5.29427	−	1.41860i	0.291000	−	0.0779731i	0.401366	+	0.915918i	$0.368536\pi$
$332$		0			0
$333$	−1.76680	+	8.80938i	−0.0968200	+	0.482751i
$334$		0			0
$335$	−8.38809	+	14.5286i	−0.458291	+	0.793783i
$336$		0			0
$337$	−4.44303	−	7.69556i	−0.242027	−	0.419204i	0.719264	−	0.694737i	$-0.244479\pi$
$337$	−4.44303	−	7.69556i	−0.242027	−	0.419204i	−0.961292	+	0.275533i	$0.911146\pi$
$338$		0			0
$339$	7.57456	−	8.07446i	0.411394	−	0.438544i
$340$		0			0
$341$	9.77782	+	9.77782i	0.529498	+	0.529498i
$342$		0			0
$343$	12.5864			0.679602
$344$		0			0
$345$	2.44067	+	3.93186i	0.131401	+	0.211684i
$346$		0			0
$347$	13.2779	+	3.55779i	0.712793	+	0.190992i	0.596954	−	0.802276i	$-0.296378\pi$
$347$	13.2779	+	3.55779i	0.712793	+	0.190992i	0.115839	+	0.993268i	$0.463044\pi$
$348$		0			0
$349$	−15.5592	+	4.16907i	−0.832863	+	0.223165i	−0.649962	−	0.759966i	$-0.725215\pi$
$349$	−15.5592	+	4.16907i	−0.832863	+	0.223165i	−0.182901	+	0.983131i	$0.558549\pi$
$350$		0			0
$351$	5.02188	+	7.04330i	0.268048	+	0.375943i
$352$		0			0
$353$	−7.72178	−	4.45817i	−0.410989	−	0.237284i	0.280226	−	0.959934i	$-0.409591\pi$
$353$	−7.72178	−	4.45817i	−0.410989	−	0.237284i	−0.691214	+	0.722650i	$0.742924\pi$
$354$		0			0
$355$	34.9868	+	9.37467i	1.85690	+	0.497556i
$356$		0			0
$357$	−4.19268	−	0.981096i	−0.221900	−	0.0519251i
$358$		0			0
$359$		−	20.3164i		−	1.07226i	−0.844136	−	0.536129i	$-0.819886\pi$
$359$		−	20.3164i		−	1.07226i	0.844136	−	0.536129i	$-0.180114\pi$
$360$		0			0
$361$		−	13.3513i		−	0.702699i
$362$		0			0
$363$	−4.89784	+	5.22108i	−0.257070	+	0.274036i
$364$		0			0
$365$	−14.0628	−	3.76812i	−0.736082	−	0.197233i
$366$		0			0
$367$	20.8621	+	12.0447i	1.08899	+	0.628729i	0.933308	−	0.359078i	$-0.116909\pi$
$367$	20.8621	+	12.0447i	1.08899	+	0.628729i	0.155683	+	0.987807i	$0.450242\pi$
$368$		0			0
$369$	26.7635	+	13.2510i	1.39325	+	0.689821i
$370$		0			0
$371$	8.78654	−	2.35435i	0.456175	−	0.122232i
$372$		0			0
$373$	−26.3435	−	7.05873i	−1.36402	−	0.365487i	−0.498727	−	0.866759i	$-0.666199\pi$
$373$	−26.3435	−	7.05873i	−1.36402	−	0.365487i	−0.865290	+	0.501272i	$0.832866\pi$
$374$		0			0
$375$	−15.2720	+	28.5175i	−0.788640	+	1.47264i
$376$		0			0
$377$	9.92039			0.510926
$378$		0			0
$379$	−26.4493	−	26.4493i	−1.35861	−	1.35861i	−0.875636	−	0.482971i	$-0.839558\pi$
$379$	−26.4493	−	26.4493i	−1.35861	−	1.35861i	−0.482971	−	0.875636i	$-0.660442\pi$
$380$		0			0
$381$	1.54817	+	5.11823i	0.0793153	+	0.262215i
$382$		0			0
$383$	−14.2366	−	24.6585i	−0.727455	−	1.25999i	−0.957955	−	0.286917i	$-0.907369\pi$
$383$	−14.2366	−	24.6585i	−0.727455	−	1.25999i	0.230500	−	0.973072i	$-0.425964\pi$
$384$		0			0
$385$	7.21573	−	12.4980i	0.367748	−	0.636957i
$386$		0			0
$387$	−13.6478	+	15.5128i	−0.693759	+	0.788559i
$388$		0			0
$389$	19.4146	−	5.20211i	0.984357	−	0.263758i	0.269479	−	0.963006i	$-0.413149\pi$
$389$	19.4146	−	5.20211i	0.984357	−	0.263758i	0.714878	+	0.699249i	$0.246482\pi$
$390$		0			0
$391$	0.895250	+	1.55062i	0.0452747	+	0.0784182i
$392$		0			0
$393$	−0.290624	−	9.09789i	−0.0146600	−	0.458928i
$394$		0			0
$395$	−29.9646	+	29.9646i	−1.50768	+	1.50768i
$396$		0			0
$397$	5.95094	+	5.95094i	0.298669	+	0.298669i	0.840492	−	0.541823i	$-0.182266\pi$
$397$	5.95094	+	5.95094i	0.298669	+	0.298669i	−0.541823	+	0.840492i	$0.682266\pi$
$398$		0			0
$399$	5.00227	+	8.05853i	0.250427	+	0.403431i
$400$		0			0
$401$	−4.11912	+	2.37818i	−0.205699	+	0.118761i	−0.599311	−	0.800516i	$-0.704559\pi$
$401$	−4.11912	+	2.37818i	−0.205699	+	0.118761i	0.393612	+	0.919277i	$0.371225\pi$
$402$		0			0
$403$	1.53157	+	5.71590i	0.0762929	+	0.284729i
$404$		0			0
$405$	−27.4455	−	21.1981i	−1.36378	−	1.05334i
$406$		0			0
$407$	−10.0898	−	5.82535i	−0.500133	−	0.288752i
$408$		0			0
$409$	7.24880	−	4.18510i	0.358430	−	0.206940i	−0.309962	−	0.950749i	$-0.600316\pi$
$409$	7.24880	−	4.18510i	0.358430	−	0.206940i	0.668392	+	0.743809i	$0.266983\pi$
$410$		0			0
$411$	0.637353	−	2.72371i	0.0314383	−	0.134351i
$412$		0			0
$413$	6.16758	−	6.16758i	0.303487	−	0.303487i
$414$		0			0
$415$			35.0677i			1.72141i
$416$		0			0
$417$	0.217998	+	6.82437i	0.0106754	+	0.334191i
$418$		0			0
$419$	−8.29108	+	30.9427i	−0.405046	+	1.51165i	0.398926	+	0.916983i	$0.369383\pi$
$419$	−8.29108	+	30.9427i	−0.405046	+	1.51165i	−0.803971	+	0.594668i	$0.797284\pi$
$420$		0			0
$421$	7.74504	+	28.9049i	0.377470	+	1.40874i	0.849702	+	0.527264i	$0.176782\pi$
$421$	7.74504	+	28.9049i	0.377470	+	1.40874i	−0.472232	+	0.881475i	$0.656551\pi$
$422$		0			0
$423$	−1.10658	−	17.3029i	−0.0538038	−	0.841295i
$424$		0			0
$425$	−12.7134	+	22.0203i	−0.616691	+	1.06814i
$426$		0			0
$427$	−0.549113	+	2.04932i	−0.0265734	+	0.0991735i
$428$		0			0
$429$	−10.7365	+	3.24760i	−0.518363	+	0.156796i
$430$		0			0
$431$	−10.3884			−0.500389			−0.250195	−	0.968196i	$-0.580495\pi$
$431$	−10.3884			−0.500389			−0.250195	+	0.968196i	$0.580495\pi$
$432$		0			0
$433$	−3.31869			−0.159486			−0.0797429	−	0.996815i	$-0.525410\pi$
$433$	−3.31869			−0.159486			−0.0797429	+	0.996815i	$0.525410\pi$
$434$		0			0
$435$	−38.0672	+	11.5147i	−1.82518	+	0.552086i
$436$		0			0
$437$	1.02078	−	3.80962i	0.0488307	−	0.182239i
$438$		0			0
$439$	−15.8616	+	27.4732i	−0.757035	+	1.31122i	0.187322	+	0.982299i	$0.440019\pi$
$439$	−15.8616	+	27.4732i	−0.757035	+	1.31122i	−0.944356	+	0.328924i	$0.893314\pi$
$440$		0			0
$441$	16.3275	+	8.08401i	0.777501	+	0.384953i
$442$		0			0
$443$	−3.44686	−	12.8638i	−0.163765	−	0.611180i	−0.998194	−	0.0600649i	$-0.980869\pi$
$443$	−3.44686	−	12.8638i	−0.163765	−	0.611180i	0.834429	−	0.551115i	$-0.185797\pi$
$444$		0			0
$445$	13.0190	−	48.5877i	0.617161	−	2.30328i
$446$		0			0
$447$	−0.247021	−	7.73289i	−0.0116837	−	0.365753i
$448$		0			0
$449$			13.0580i			0.616243i	0.951347	+	0.308121i	$0.0997003\pi$
$449$			13.0580i			0.616243i	−0.951347	+	0.308121i	$0.900300\pi$
$450$		0			0
$451$	−27.3830	+	27.3830i	−1.28941	+	1.28941i
$452$		0			0
$453$	−7.57953	+	32.3909i	−0.356118	+	1.52186i
$454$		0			0
$455$	5.34841	−	3.08790i	0.250737	−	0.144763i
$456$		0			0
$457$	−10.0451	−	5.79955i	−0.469890	−	0.271291i	0.246303	−	0.969193i	$-0.420784\pi$
$457$	−10.0451	−	5.79955i	−0.469890	−	0.271291i	−0.716194	+	0.697901i	$0.754117\pi$
$458$		0			0
$459$	−10.3515	−	8.53644i	−0.483165	−	0.398447i
$460$		0			0
$461$	−3.56634	−	13.3098i	−0.166101	−	0.619898i	−0.997897	−	0.0648164i	$-0.979354\pi$
$461$	−3.56634	−	13.3098i	−0.166101	−	0.619898i	0.831796	−	0.555081i	$-0.187313\pi$
$462$		0			0
$463$	11.4905	−	6.63406i	0.534010	−	0.308311i	−0.208638	−	0.977993i	$-0.566903\pi$
$463$	11.4905	−	6.63406i	0.534010	−	0.308311i	0.742648	+	0.669682i	$0.233570\pi$
$464$		0			0
$465$	−12.5115	−	20.1557i	−0.580208	−	0.934700i
$466$		0			0
$467$	−28.1581	−	28.1581i	−1.30300	−	1.30300i	−0.926357	−	0.376647i	$-0.877077\pi$
$467$	−28.1581	−	28.1581i	−1.30300	−	1.30300i	−0.376647	−	0.926357i	$-0.622923\pi$
$468$		0			0
$469$	−2.96402	+	2.96402i	−0.136866	+	0.136866i
$470$		0			0
$471$	1.04306	+	32.6527i	0.0480617	+	1.50456i
$472$		0			0
$473$	−13.3962	−	23.2029i	−0.615958	−	1.06687i
$474$		0			0
$475$	54.1002	−	14.4961i	2.48229	−	0.665127i
$476$		0			0
$477$	27.7912	+	5.57377i	1.27247	+	0.255206i
$478$		0			0
$479$	−3.40138	+	5.89137i	−0.155413	+	0.269183i	−0.933209	−	0.359333i	$-0.883004\pi$
$479$	−3.40138	+	5.89137i	−0.155413	+	0.269183i	0.777796	+	0.628517i	$0.216338\pi$
$480$		0			0
$481$	−2.49291	−	4.31784i	−0.113667	−	0.196877i
$482$		0			0
$483$	0.334785	+	1.10679i	0.0152332	+	0.0503608i
$484$		0			0
$485$	−9.62112	−	9.62112i	−0.436873	−	0.436873i
$486$		0			0
$487$	10.9714			0.497160			0.248580	−	0.968611i	$-0.420036\pi$
$487$	10.9714			0.497160			0.248580	+	0.968611i	$0.420036\pi$
$488$		0			0
$489$	−11.8709	+	22.1666i	−0.536819	+	1.00241i
$490$		0			0
$491$	6.98135	+	1.87065i	0.315064	+	0.0844211i	0.412886	−	0.910783i	$-0.364521\pi$
$491$	6.98135	+	1.87065i	0.315064	+	0.0844211i	−0.0978219	+	0.995204i	$0.531188\pi$
$492$		0			0
$493$	−14.8630	+	3.98253i	−0.669397	+	0.179364i
$494$		0			0
$495$	37.4293	−	24.9238i	1.68232	−	1.12024i
$496$		0			0
$497$	7.83780	+	4.52515i	0.351573	+	0.202981i
$498$		0			0
$499$	−25.4020	−	6.80645i	−1.13715	−	0.304698i	−0.359346	−	0.933205i	$-0.617000\pi$
$499$	−25.4020	−	6.80645i	−1.13715	−	0.304698i	−0.777805	+	0.628506i	$0.783667\pi$
$500$		0			0
$501$	6.83415	−	7.28518i	0.305327	−	0.325478i
$502$		0			0
$503$			1.37571i			0.0613400i	0.999530	+	0.0306700i	$0.00976410\pi$
$503$			1.37571i			0.0613400i	−0.999530	+	0.0306700i	$0.990236\pi$
$504$		0			0
$505$			73.1616i			3.25565i
$506$		0			0
$507$	17.2505	+	4.03665i	0.766121	+	0.179274i
$508$		0			0
$509$	−14.7384	−	3.94915i	−0.653269	−	0.175043i	−0.0830623	−	0.996544i	$-0.526470\pi$
$509$	−14.7384	−	3.94915i	−0.653269	−	0.175043i	−0.570206	+	0.821502i	$0.693137\pi$
$510$		0			0
$511$	−3.15038	−	1.81887i	−0.139365	−	0.0804622i
$512$		0			0
$513$	2.82701	+	29.4193i	0.124816	+	1.29889i
$514$		0			0
$515$	−12.8325	+	3.43845i	−0.565467	+	0.151516i
$516$		0			0
$517$	21.7166	+	5.81895i	0.955096	+	0.255917i
$518$		0			0
$519$	7.28580	+	11.7372i	0.319811	+	0.515207i
$520$		0			0
$521$	−23.4677			−1.02814			−0.514070	−	0.857748i	$-0.671863\pi$
$521$	−23.4677			−1.02814			−0.514070	+	0.857748i	$0.671863\pi$
$522$		0			0
$523$	30.0762	+	30.0762i	1.31514	+	1.31514i	0.917573	+	0.397567i	$0.130145\pi$
$523$	30.0762	+	30.0762i	1.31514	+	1.31514i	0.397567	+	0.917573i	$0.369855\pi$
$524$		0			0
$525$	−11.2346	+	11.9761i	−0.490319	+	0.522678i
$526$		0			0
$527$	−4.58929	−	7.94888i	−0.199912	−	0.346259i
$528$		0			0
$529$	−11.2596	+	19.5022i	−0.489547	+	0.847921i
$530$		0			0
$531$	25.7500	−	8.69551i	1.11746	−	0.377353i
$532$		0			0
$533$	−16.0075	+	4.28919i	−0.693361	+	0.185786i
$534$		0			0
$535$	−16.6119	−	28.7727i	−0.718195	−	1.24395i
$536$		0			0
$537$	−3.20464	−	1.71618i	−0.138290	−	0.0740585i
$538$		0			0
$539$	−16.7054	+	16.7054i	−0.719553	+	0.719553i
$540$		0			0
$541$	−18.7809	−	18.7809i	−0.807453	−	0.807453i	0.176795	−	0.984248i	$-0.443427\pi$
$541$	−18.7809	−	18.7809i	−0.807453	−	0.807453i	−0.984248	+	0.176795i	$0.943427\pi$
$542$		0			0
$543$	5.71123	−	10.6646i	0.245092	−	0.457664i
$544$		0			0
$545$	18.7135	−	10.8042i	0.801598	−	0.462803i
$546$		0			0
$547$	−4.00793	−	14.9578i	−0.171366	−	0.639548i	−0.997142	−	0.0755496i	$-0.975929\pi$
$547$	−4.00793	−	14.9578i	−0.171366	−	0.639548i	0.825776	−	0.563999i	$-0.190738\pi$
$548$		0			0
$549$	−4.36675	+	4.96345i	−0.186368	+	0.211835i
$550$		0			0
$551$	29.3533	+	16.9471i	1.25049	+	0.721972i
$552$		0			0
$553$	−9.16975	+	5.29416i	−0.389937	+	0.225130i
$554$		0			0
$555$	14.5777	+	13.6752i	0.618789	+	0.580479i
$556$		0			0
$557$	31.8166	−	31.8166i	1.34811	−	1.34811i	0.460398	−	0.887712i	$-0.347707\pi$
$557$	31.8166	−	31.8166i	1.34811	−	1.34811i	0.887712	−	0.460398i	$-0.152293\pi$
$558$		0			0
$559$		−	11.4656i		−	0.484941i
$560$		0			0
$561$	14.7820	−	9.17580i	0.624096	−	0.387403i
$562$		0			0
$563$	−8.86755	+	33.0941i	−0.373723	+	1.39475i	0.481480	+	0.876457i	$0.340100\pi$
$563$	−8.86755	+	33.0941i	−0.373723	+	1.39475i	−0.855202	+	0.518294i	$0.826567\pi$
$564$		0			0
$565$	−6.37456	−	23.7902i	−0.268180	−	1.00086i
$566$		0			0
$567$	−5.25310	−	6.89105i	−0.220610	−	0.289397i
$568$		0			0
$569$	2.54964	−	4.41610i	0.106886	−	0.185133i	−0.807621	−	0.589702i	$-0.799245\pi$
$569$	2.54964	−	4.41610i	0.106886	−	0.185133i	0.914507	+	0.404569i	$0.132579\pi$
$570$		0			0
$571$	−1.79252	+	6.68977i	−0.0750146	+	0.279958i	−0.993237	−	0.116108i	$-0.962958\pi$
$571$	−1.79252	+	6.68977i	−0.0750146	+	0.279958i	0.918222	+	0.396066i	$0.129625\pi$
$572$		0			0
$573$	3.00117	−	12.8254i	0.125376	−	0.535788i
$574$		0			0
$575$	6.82812			0.284752
$576$		0			0
$577$	18.2939			0.761585			0.380793	−	0.924660i	$-0.375651\pi$
$577$	18.2939			0.761585			0.380793	+	0.924660i	$0.375651\pi$
$578$		0			0
$579$	2.43568	+	2.28488i	0.101223	+	0.0949564i
$580$		0			0
$581$	−2.26781	+	8.46359i	−0.0940847	+	0.351129i
$582$		0			0
$583$	−18.3774	+	31.8306i	−0.761114	+	1.31829i
$584$		0			0
$585$	19.2046	−	1.22820i	0.794011	−	0.0507798i
$586$		0			0
$587$	−3.71035	−	13.8472i	−0.153143	−	0.571536i	−0.999257	−	0.0385349i	$-0.987731\pi$
$587$	−3.71035	−	13.8472i	−0.153143	−	0.571536i	0.846115	−	0.533001i	$-0.178936\pi$
$588$		0			0
$589$	−5.23280	+	19.5291i	−0.215614	+	0.804682i
$590$		0			0
$591$	−35.0003	−	18.7437i	−1.43972	−	0.771011i
$592$		0			0
$593$			16.9058i			0.694238i	0.937821	+	0.347119i	$0.112840\pi$
$593$			16.9058i			0.694238i	−0.937821	+	0.347119i	$0.887160\pi$
$594$		0			0
$595$	−6.77350	+	6.77350i	−0.277687	+	0.277687i
$596$		0			0
$597$	10.8696	−	3.28785i	0.444861	−	0.134563i
$598$		0			0
$599$	18.4047	−	10.6260i	0.751997	−	0.434166i	−0.0744181	−	0.997227i	$-0.523710\pi$
$599$	18.4047	−	10.6260i	0.751997	−	0.434166i	0.826415	+	0.563062i	$0.190377\pi$
$600$		0			0
$601$	28.1475	+	16.2510i	1.14816	+	0.662891i	0.948438	−	0.316962i	$-0.102663\pi$
$601$	28.1475	+	16.2510i	1.14816	+	0.662891i	0.199722	+	0.979853i	$0.435996\pi$
$602$		0			0
$603$	−12.3750	+	4.17890i	−0.503948	+	0.170178i
$604$		0			0
$605$	4.12190	+	15.3831i	0.167579	+	0.625413i
$606$		0			0
$607$	9.86566	−	5.69594i	0.400435	−	0.231191i	−0.286237	−	0.958159i	$-0.592404\pi$
$607$	9.86566	−	5.69594i	0.400435	−	0.231191i	0.686672	+	0.726968i	$0.259071\pi$
$608$		0			0
$609$	−9.93217	+	0.317275i	−0.402472	+	0.0128566i
$610$		0			0
$611$	6.80326	+	6.80326i	0.275230	+	0.275230i
$612$		0			0
$613$	12.9149	−	12.9149i	0.521630	−	0.521630i	−0.396434	−	0.918063i	$-0.629752\pi$
$613$	12.9149	−	12.9149i	0.521630	−	0.521630i	0.918063	+	0.396434i	$0.129752\pi$
$614$		0			0
$615$	56.4466	−	35.0388i	2.27615	−	1.41290i
$616$		0			0
$617$	−5.36926	−	9.29983i	−0.216158	−	0.374397i	0.737472	−	0.675378i	$-0.236019\pi$
$617$	−5.36926	−	9.29983i	−0.216158	−	0.374397i	−0.953630	+	0.300981i	$0.902686\pi$
$618$		0			0
$619$	−15.0898	+	4.04330i	−0.606510	+	0.162514i	−0.548988	−	0.835830i	$-0.684987\pi$
$619$	−15.0898	+	4.04330i	−0.606510	+	0.162514i	−0.0575222	+	0.998344i	$0.518320\pi$
$620$		0			0
$621$	−0.595366	+	3.55355i	−0.0238912	+	0.142599i
$622$		0			0
$623$	6.28428	−	10.8847i	0.251774	−	0.436086i
$624$		0			0
$625$	11.3651	+	19.6849i	0.454603	+	0.787396i
$626$		0			0
$627$	−37.3160	−	8.73202i	−1.49026	−	0.348723i
$628$		0			0
$629$	5.46834	+	5.46834i	0.218037	+	0.218037i
$630$		0			0
$631$	−39.5399			−1.57406			−0.787029	−	0.616916i	$-0.788382\pi$
$631$	−39.5399			−1.57406			−0.787029	+	0.616916i	$0.788382\pi$
$632$		0			0
$633$	−10.4604	+	0.334147i	−0.415762	+	0.0132812i
$634$		0			0
$635$	11.4904	+	3.07884i	0.455982	+	0.122180i
$636$		0			0
$637$	−9.76562	+	2.61669i	−0.386928	+	0.103677i
$638$		0			0
$639$	15.6303	+	23.4728i	0.618326	+	0.928570i
$640$		0			0
$641$	−18.9744	−	10.9549i	−0.749445	−	0.432692i	0.0760486	−	0.997104i	$-0.475770\pi$
$641$	−18.9744	−	10.9549i	−0.749445	−	0.432692i	−0.825493	+	0.564412i	$0.809103\pi$
$642$		0			0
$643$	41.5536	+	11.1343i	1.63871	+	0.439092i	0.956422	−	0.291988i	$-0.0943167\pi$
$643$	41.5536	+	11.1343i	1.63871	+	0.439092i	0.682292	+	0.731080i	$0.260983\pi$
$644$		0			0
$645$	13.3082	+	43.9964i	0.524008	+	1.73236i
$646$		0			0
$647$		−	31.4508i		−	1.23646i	−0.785998	−	0.618229i	$-0.787851\pi$
$647$		−	31.4508i		−	1.23646i	0.785998	−	0.618229i	$-0.212149\pi$
$648$		0			0
$649$			35.2428i			1.38340i
$650$		0			0
$651$	−1.71620	−	5.67370i	−0.0672630	−	0.222370i
$652$		0			0
$653$	38.0415	+	10.1932i	1.48868	+	0.398891i	0.909291	−	0.416160i	$-0.136624\pi$
$653$	38.0415	+	10.1932i	1.48868	+	0.398891i	0.579389	+	0.815051i	$0.303291\pi$
$654$		0			0
$655$	−17.5369	−	10.1249i	−0.685224	−	0.395614i
$656$		0			0
$657$	−6.28257	−	9.43483i	−0.245106	−	0.368088i
$658$		0			0
$659$	1.45690	−	0.390374i	0.0567526	−	0.0152068i	−0.230331	−	0.973112i	$-0.573981\pi$
$659$	1.45690	−	0.390374i	0.0567526	−	0.0152068i	0.287084	+	0.957906i	$0.407314\pi$
$660$		0			0
$661$	−35.7396	−	9.57641i	−1.39011	−	0.372479i	−0.515328	−	0.856993i	$-0.672330\pi$
$661$	−35.7396	−	9.57641i	−1.39011	−	0.372479i	−0.874783	+	0.484514i	$0.838996\pi$
$662$		0			0
$663$	7.44166	−	0.237717i	0.289010	−	0.00923218i
$664$		0			0
$665$	21.1004			0.818240
$666$		0			0
$667$	2.92185	+	2.92185i	0.113134	+	0.113134i
$668$		0			0
$669$	−8.78329	−	2.05531i	−0.339582	−	0.0794628i
$670$		0			0
$671$	−4.28623	−	7.42397i	−0.165468	−	0.286599i
$672$		0			0
$673$	1.54334	−	2.67314i	0.0594912	−	0.103042i	−0.834746	−	0.550635i	$-0.814386\pi$
$673$	1.54334	−	2.67314i	0.0594912	−	0.103042i	0.894237	+	0.447594i	$0.147719\pi$
$674$		0			0
$675$	−47.9303	+	17.9098i	−1.84484	+	0.689350i
$676$		0			0
$677$	−39.8275	+	10.6718i	−1.53070	+	0.410149i	−0.923246	−	0.384209i	$-0.874474\pi$
$677$	−39.8275	+	10.6718i	−1.53070	+	0.410149i	−0.607450	+	0.794358i	$0.707807\pi$
$678$		0			0
$679$	−1.69986	−	2.94425i	−0.0652348	−	0.112990i
$680$		0			0
$681$	9.57653	−	5.94456i	0.366974	−	0.227796i
$682$		0			0
$683$	15.0423	−	15.0423i	0.575578	−	0.575578i	−0.358104	−	0.933682i	$-0.616577\pi$
$683$	15.0423	−	15.0423i	0.575578	−	0.575578i	0.933682	+	0.358104i	$0.116577\pi$
$684$		0			0
$685$	−4.40030	−	4.40030i	−0.168127	−	0.168127i
$686$		0			0
$687$	7.16039	−	0.228732i	0.273186	−	0.00872668i
$688$		0			0
$689$	−13.6216	+	7.86444i	−0.518942	+	0.299611i
$690$		0			0
$691$	−11.3628	−	42.4064i	−0.432260	−	1.61321i	−0.747540	−	0.664216i	$-0.768765\pi$
$691$	−11.3628	−	42.4064i	−0.432260	−	1.61321i	0.315281	−	0.948998i	$-0.397901\pi$
$692$		0			0
$693$	10.6454	−	3.59483i	0.404384	−	0.136556i
$694$		0			0
$695$	13.1545	+	7.59476i	0.498979	+	0.288086i
$696$		0			0
$697$	22.2610	−	12.8524i	0.843195	−	0.486819i
$698$		0			0
$699$	−28.5448	+	8.63430i	−1.07966	+	0.326579i
$700$		0			0
$701$	−7.87056	+	7.87056i	−0.297267	+	0.297267i	−0.839942	−	0.542676i	$-0.817411\pi$
$701$	−7.87056	+	7.87056i	−0.297267	+	0.297267i	0.542676	+	0.839942i	$0.317411\pi$
$702$		0			0
$703$		−	17.0347i		−	0.642474i
$704$		0			0
$705$	−34.0025	−	18.2094i	−1.28061	−	0.685804i
$706$		0			0
$707$	−4.73132	+	17.6575i	−0.177940	+	0.664080i
$708$		0			0
$709$	−7.49458	−	27.9701i	−0.281465	−	1.05044i	−0.951384	−	0.308007i	$-0.900338\pi$
$709$	−7.49458	−	27.9701i	−0.281465	−	1.05044i	0.669919	−	0.742434i	$-0.266329\pi$
$710$		0			0
$711$	−32.9259	+	2.10573i	−1.23482	+	0.0789709i
$712$		0			0
$713$	−1.23241	+	2.13459i	−0.0461540	+	0.0799411i
$714$		0			0
$715$	−6.45848	+	24.1034i	−0.241533	+	0.901414i
$716$		0			0
$717$	−11.3506	−	10.6479i	−0.423895	−	0.397651i
$718$		0			0
$719$	−0.674555			−0.0251567			−0.0125783	−	0.999921i	$-0.504004\pi$
$719$	−0.674555			−0.0251567			−0.0125783	+	0.999921i	$0.504004\pi$
$720$		0			0
$721$	−3.31948			−0.123624
$722$		0			0
$723$	0.442641	−	1.89161i	0.0164620	−	0.0703498i
$724$		0			0
$725$	−15.1875	+	56.6805i	−0.564049	+	2.10506i
$726$		0			0
$727$	1.32251	−	2.29066i	0.0490493	−	0.0849559i	−0.840458	−	0.541876i	$-0.817714\pi$
$727$	1.32251	−	2.29066i	0.0490493	−	0.0849559i	0.889508	+	0.456920i	$0.151048\pi$
$728$		0			0
$729$	−5.14160	−	26.5059i	−0.190430	−	0.981701i
$730$		0			0
$731$	4.60284	+	17.1780i	0.170242	+	0.635352i
$732$		0			0
$733$	5.34335	−	19.9416i	0.197361	−	0.736562i	−0.794282	−	0.607549i	$-0.792153\pi$
$733$	5.34335	−	19.9416i	0.197361	−	0.736562i	0.991643	−	0.129012i	$-0.0411806\pi$
$734$		0			0
$735$	34.4361	−	21.3760i	1.27020	−	0.788465i
$736$		0			0
$737$		−	16.9370i		−	0.623883i
$738$		0			0
$739$	27.6094	−	27.6094i	1.01563	−	1.01563i	0.0157506	−	0.999876i	$-0.494986\pi$
$739$	27.6094	−	27.6094i	1.01563	−	1.01563i	0.999876	−	0.0157506i	$-0.00501379\pi$
$740$		0			0
$741$	−11.9612	−	11.2207i	−0.439405	−	0.412201i
$742$		0			0
$743$	−16.4755	+	9.51215i	−0.604429	+	0.348967i	−0.770782	−	0.637099i	$-0.780134\pi$
$743$	−16.4755	+	9.51215i	−0.604429	+	0.348967i	0.166353	+	0.986066i	$0.446801\pi$
$744$		0			0
$745$	−14.9058	−	8.60585i	−0.546105	−	0.315294i
$746$		0			0
$747$	−18.0345	+	20.4988i	−0.659847	+	0.750013i
$748$		0			0
$749$	−2.14857	−	8.01857i	−0.0785070	−	0.292992i
$750$		0			0
$751$	−30.5334	+	17.6285i	−1.11418	+	0.643273i	−0.939909	−	0.341425i	$-0.889091\pi$
$751$	−30.5334	+	17.6285i	−1.11418	+	0.643273i	−0.174272	+	0.984698i	$0.555757\pi$
$752$		0			0
$753$	−0.808626	+	1.50996i	−0.0294680	+	0.0550259i
$754$		0			0
$755$	52.3292	+	52.3292i	1.90446	+	1.90446i
$756$		0			0
$757$	24.8190	−	24.8190i	0.902061	−	0.902061i	−0.0935534	−	0.995614i	$-0.529823\pi$
$757$	24.8190	−	24.8190i	0.902061	−	0.902061i	0.995614	+	0.0935534i	$0.0298226\pi$
$758$		0			0
$759$	−4.11872	−	2.20570i	−0.149500	−	0.0800618i
$760$		0			0
$761$	2.73041	+	4.72921i	0.0989774	+	0.171434i	0.911262	−	0.411828i	$-0.135110\pi$
$761$	2.73041	+	4.72921i	0.0989774	+	0.171434i	−0.812284	+	0.583262i	$0.801776\pi$
$762$		0			0
$763$	5.21521	−	1.39741i	0.188803	−	0.0505897i
$764$		0			0
$765$	−28.2798	+	9.54978i	−1.02246	+	0.345273i
$766$		0			0
$767$	−7.54091	+	13.0612i	−0.272286	+	0.471614i
$768$		0			0
$769$	14.4745	+	25.0706i	0.521964	+	0.904068i	0.999674	+	0.0255501i	$0.00813372\pi$
$769$	14.4745	+	25.0706i	0.521964	+	0.904068i	−0.477710	+	0.878518i	$0.658533\pi$
$770$		0			0
$771$	7.93608	−	8.45983i	0.285811	−	0.304673i
$772$		0			0
$773$	11.3458	+	11.3458i	0.408079	+	0.408079i	0.881068	−	0.472989i	$-0.156825\pi$
$773$	11.3458	+	11.3458i	0.408079	+	0.408079i	−0.472989	+	0.881068i	$0.656825\pi$
$774$		0			0
$775$	−35.0027			−1.25733
$776$		0			0
$777$	2.63396	+	4.24324i	0.0944928	+	0.152225i
$778$		0			0
$779$	−54.6916	−	14.6546i	−1.95953	−	0.525054i
$780$		0			0
$781$	−35.3221	+	9.46454i	−1.26393	+	0.338668i
$782$		0			0
$783$	−28.1739	−	12.8462i	−1.00685	−	0.459085i
$784$		0			0
$785$	62.9406	+	36.3388i	2.24645	+	1.29699i
$786$		0			0
$787$	−25.6596	−	6.87546i	−0.914665	−	0.245084i	−0.229362	−	0.973341i	$-0.573664\pi$
$787$	−25.6596	−	6.87546i	−0.914665	−	0.245084i	−0.685304	+	0.728257i	$0.740331\pi$
$788$		0			0
$789$	−23.7803	−	5.56464i	−0.846601	−	0.198106i
$790$		0			0
$791$		−	6.15400i		−	0.218811i
$792$		0			0
$793$		−	3.66851i		−	0.130272i
$794$		0			0
$795$	43.1415	−	45.9887i	1.53007	−	1.63105i
$796$		0			0
$797$	20.8451	+	5.58542i	0.738371	+	0.197846i	0.608354	−	0.793666i	$-0.291830\pi$
$797$	20.8451	+	5.58542i	0.738371	+	0.197846i	0.130017	+	0.991512i	$0.458497\pi$
$798$		0			0
$799$	−12.9240	−	7.46168i	−0.457218	−	0.263975i
$800$		0			0
$801$	32.5977	−	21.7065i	1.15178	−	0.766963i
$802$		0			0
$803$	14.1976	−	3.80424i	0.501024	−	0.134249i
$804$		0			0
$805$	2.48474	+	0.665784i	0.0875756	+	0.0234658i
$806$		0			0
$807$	−15.3298	+	28.6254i	−0.539633	+	1.00766i
$808$		0			0
$809$	−36.1898			−1.27236			−0.636182	−	0.771539i	$-0.719487\pi$
$809$	−36.1898			−1.27236			−0.636182	+	0.771539i	$0.719487\pi$
$810$		0			0
$811$	−17.4150	−	17.4150i	−0.611523	−	0.611523i	0.331820	−	0.943343i	$-0.392337\pi$
$811$	−17.4150	−	17.4150i	−0.611523	−	0.611523i	−0.943343	+	0.331820i	$0.892337\pi$
$812$		0			0
$813$	−5.24011	−	17.3237i	−0.183779	−	0.607568i
$814$		0			0
$815$	27.9694	+	48.4445i	0.979727	+	1.69694i
$816$		0			0
$817$	19.5868	−	33.9253i	0.685254	−	1.18689i
$818$		0			0
$819$	4.71445	+	0.945524i	0.164736	+	0.0330393i
$820$		0			0
$821$	33.8975	−	9.08280i	1.18303	−	0.316992i	0.386902	−	0.922121i	$-0.373545\pi$
$821$	33.8975	−	9.08280i	1.18303	−	0.316992i	0.796127	+	0.605129i	$0.206878\pi$
$822$		0			0
$823$	19.3027	+	33.4332i	0.672849	+	1.16541i	0.977093	+	0.212815i	$0.0682630\pi$
$823$	19.3027	+	33.4332i	0.672849	+	1.16541i	−0.304244	+	0.952594i	$0.598404\pi$
$824$		0			0
$825$	−2.11838	−	66.3152i	−0.0737525	−	2.30880i
$826$		0			0
$827$	39.6335	−	39.6335i	1.37819	−	1.37819i	0.530517	−	0.847674i	$-0.321998\pi$
$827$	39.6335	−	39.6335i	1.37819	−	1.37819i	0.847674	−	0.530517i	$-0.178002\pi$
$828$		0			0
$829$	−20.5229	−	20.5229i	−0.712789	−	0.712789i	0.254329	−	0.967118i	$-0.418145\pi$
$829$	−20.5229	−	20.5229i	−0.712789	−	0.712789i	−0.967118	+	0.254329i	$0.918145\pi$
$830$		0			0
$831$	14.7906	+	23.8273i	0.513080	+	0.826558i
$832$		0			0
$833$	13.5807	−	7.84080i	0.470542	−	0.271668i
$834$		0			0
$835$	−5.75145	−	21.4647i	−0.199037	−	0.742817i
$836$		0			0
$837$	3.05200	−	18.2164i	0.105493	−	0.629651i
$838$		0			0
$839$	4.64087	+	2.67941i	0.160221	+	0.0925035i	0.577967	−	0.816060i	$-0.303846\pi$
$839$	4.64087	+	2.67941i	0.160221	+	0.0925035i	−0.417746	+	0.908564i	$0.637180\pi$
$840$		0			0
$841$	−5.63857	+	3.25543i	−0.194433	+	0.112256i
$842$		0			0
$843$	9.60963	−	41.0664i	0.330973	−	1.41440i
$844$		0			0
$845$	27.8691	−	27.8691i	0.958726	−	0.958726i
$846$		0			0
$847$			3.97928i			0.136730i
$848$		0			0
$849$	0.486654	+	15.2345i	0.0167019	+	0.522848i
$850$		0			0
$851$	0.537496	−	2.00596i	0.0184251	−	0.0687636i
$852$		0			0
$853$	14.2790	+	53.2899i	0.488903	+	1.82461i	0.561803	+	0.827271i	$0.310108\pi$
$853$	14.2790	+	53.2899i	0.488903	+	1.82461i	−0.0729001	+	0.997339i	$0.523225\pi$
$854$		0			0
$855$	58.9222	+	29.1733i	2.01510	+	0.997706i
$856$		0			0
$857$	−16.8544	+	29.1927i	−0.575737	+	0.997205i	0.420224	+	0.907420i	$0.361951\pi$
$857$	−16.8544	+	29.1927i	−0.575737	+	0.997205i	−0.995961	+	0.0897851i	$0.971382\pi$
$858$		0			0
$859$	−14.1550	+	52.8271i	−0.482962	+	1.80244i	0.106107	+	0.994355i	$0.466161\pi$
$859$	−14.1550	+	52.8271i	−0.482962	+	1.80244i	−0.589069	+	0.808083i	$0.700505\pi$
$860$		0			0
$861$	15.8893	−	4.80624i	0.541507	−	0.163796i
$862$		0			0
$863$	28.6860			0.976481			0.488241	−	0.872709i	$-0.337639\pi$
$863$	28.6860			0.976481			0.488241	+	0.872709i	$0.337639\pi$
$864$		0			0
$865$	30.7327			1.04494
$866$		0			0
$867$	17.1298	−	5.18148i	0.581760	−	0.175972i
$868$		0			0
$869$	11.0729	−	41.3248i	0.375624	−	1.40185i
$870$		0			0
$871$	3.62402	−	6.27698i	0.122795	−	0.212688i
$872$		0			0
$873$	−0.676113	−	10.5719i	−0.0228829	−	0.357806i
$874$		0			0
$875$	4.65399	+	17.3689i	0.157334	+	0.587177i
$876$		0			0
$877$	−1.37118	+	5.11731i	−0.0463014	+	0.172799i	−0.985205	−	0.171382i	$-0.945177\pi$
$877$	−1.37118	+	5.11731i	−0.0463014	+	0.172799i	0.938903	+	0.344181i	$0.111843\pi$
$878$		0			0
$879$	0.0462987	+	1.44936i	0.00156162	+	0.0488858i
$880$		0			0
$881$			33.4396i			1.12661i	0.826249	+	0.563305i	$0.190470\pi$
$881$			33.4396i			1.12661i	−0.826249	+	0.563305i	$0.809530\pi$
$882$		0			0
$883$	26.9753	−	26.9753i	0.907790	−	0.907790i	−0.0883036	−	0.996094i	$-0.528145\pi$
$883$	26.9753	−	26.9753i	0.907790	−	0.907790i	0.996094	+	0.0883036i	$0.0281446\pi$
$884$		0			0
$885$	13.7762	−	58.8723i	0.463083	−	1.97897i
$886$		0			0
$887$	49.0505	−	28.3193i	1.64695	−	0.950869i	0.668680	−	0.743550i	$-0.266860\pi$
$887$	49.0505	−	28.3193i	1.64695	−	0.950869i	0.978274	−	0.207318i	$-0.0664736\pi$
$888$		0			0
$889$	2.57410	+	1.48616i	0.0863325	+	0.0498441i
$890$		0			0
$891$	34.6970	+	4.67977i	1.16239	+	0.156778i
$892$		0			0
$893$	8.50797	+	31.7522i	0.284708	+	1.06255i
$894$		0			0
$895$	−7.00364	+	4.04356i	−0.234106	+	0.135161i
$896$		0			0
$897$	−1.05448	−	1.69873i	−0.0352079	−	0.0567191i
$898$		0			0
$899$	−14.9781	−	14.9781i	−0.499549	−	0.499549i
$900$		0			0
$901$	17.2511	−	17.2511i	0.574718	−	0.574718i
$902$		0			0
$903$	0.366692	+	11.4792i	0.0122028	+	0.382003i
$904$		0			0
$905$	−13.4565	−	23.3073i	−0.447308	−	0.774760i
$906$		0			0
$907$	−9.71055	+	2.60194i	−0.322434	+	0.0863958i	−0.416405	−	0.909179i	$-0.636710\pi$
$907$	−9.71055	+	2.60194i	−0.322434	+	0.0863958i	0.0939718	+	0.995575i	$0.470044\pi$
$908$		0			0
$909$	−37.6252	+	42.7666i	−1.24795	+	1.41848i
$910$		0			0
$911$	23.4920	−	40.6893i	0.778325	−	1.34810i	−0.154582	−	0.987980i	$-0.549403\pi$
$911$	23.4920	−	40.6893i	0.778325	−	1.34810i	0.932907	−	0.360118i	$-0.117263\pi$
$912$		0			0
$913$	−17.7019	−	30.6607i	−0.585849	−	1.01472i
$914$		0			0
$915$	4.25806	+	14.0771i	0.140767	+	0.465373i
$916$		0			0
$917$	−3.57776	−	3.57776i	−0.118148	−	0.118148i
$918$		0			0
$919$	49.8848			1.64555			0.822774	−	0.568369i	$-0.192425\pi$
$919$	49.8848			1.64555			0.822774	+	0.568369i	$0.192425\pi$
$920$		0			0
$921$	24.4684	−	45.6902i	0.806262	−	1.50554i
$922$		0			0
$923$	−15.1158	−	4.05026i	−0.497542	−	0.133316i
$924$		0			0
$925$	28.4866	−	7.63296i	0.936634	−	0.250970i
$926$		0			0
$927$	−9.26953	−	4.58949i	−0.304451	−	0.150739i
$928$		0			0
$929$	−29.2209	−	16.8707i	−0.958707	−	0.553510i	−0.0629322	−	0.998018i	$-0.520045\pi$
$929$	−29.2209	−	16.8707i	−0.958707	−	0.553510i	−0.895775	+	0.444508i	$0.853379\pi$
$930$		0			0
$931$	−33.3655	−	8.94026i	−1.09351	−	0.293005i
$932$		0			0
$933$	−14.8401	+	15.8195i	−0.485845	+	0.517909i
$934$		0			0
$935$		−	38.7051i		−	1.26579i
$936$		0			0
$937$		−	16.7455i		−	0.547052i	−0.961865	−	0.273526i	$-0.911810\pi$
$937$		−	16.7455i		−	0.547052i	0.961865	−	0.273526i	$-0.0881899\pi$
$938$		0			0
$939$	−54.8682	−	12.8393i	−1.79056	−	0.418994i
$940$		0			0
$941$	−5.62151	−	1.50628i	−0.183256	−	0.0491033i	0.166024	−	0.986122i	$-0.446907\pi$
$941$	−5.62151	−	1.50628i	−0.183256	−	0.0491033i	−0.349280	+	0.937018i	$0.613574\pi$
$942$		0			0
$943$	−5.97797	−	3.45138i	−0.194669	−	0.112392i
$944$		0			0
$945$	−19.1881	+	1.84386i	−0.624188	+	0.0599807i
$946$		0			0
$947$	−6.46641	+	1.73267i	−0.210130	+	0.0563042i	−0.362348	−	0.932043i	$-0.618025\pi$
$947$	−6.46641	+	1.73267i	−0.210130	+	0.0563042i	0.152218	+	0.988347i	$0.451358\pi$
$948$		0			0
$949$	6.07575	+	1.62799i	0.197227	+	0.0528468i
$950$		0			0
$951$	−12.7086	−	20.4732i	−0.412104	−	0.663889i
$952$		0			0
$953$	−0.390160			−0.0126385			−0.00631925	−	0.999980i	$-0.502011\pi$
$953$	−0.390160			−0.0126385			−0.00631925	+	0.999980i	$0.502011\pi$
$954$		0			0
$955$	−20.7201	−	20.7201i	−0.670487	−	0.670487i
$956$		0			0
$957$	27.4707	−	29.2837i	0.888001	−	0.946606i
$958$		0			0
$959$	−0.777447	−	1.34658i	−0.0251051	−	0.0434832i
$960$		0			0
$961$	−9.18236	+	15.9043i	−0.296205	+	0.513042i
$962$		0			0
$963$	5.08661	−	25.3622i	0.163914	−	0.817284i
$964$		0			0
$965$	7.17636	−	1.92290i	0.231015	−	0.0619003i
$966$		0			0
$967$	0.0976589	+	0.169150i	0.00314050	+	0.00543950i	0.867591	−	0.497278i	$-0.165667\pi$
$967$	0.0976589	+	0.169150i	0.00314050	+	0.00543950i	−0.864451	+	0.502717i	$0.832334\pi$
$968$		0			0
$969$	22.4251	+	12.0093i	0.720399	+	0.385795i
$970$		0			0
$971$	17.8241	−	17.8241i	0.572003	−	0.572003i	−0.360685	−	0.932688i	$-0.617457\pi$
$971$	17.8241	−	17.8241i	0.572003	−	0.572003i	0.932688	+	0.360685i	$0.117457\pi$
$972$		0			0
$973$	2.68369	+	2.68369i	0.0860352	+	0.0860352i
$974$		0			0
$975$	13.4044	−	25.0302i	0.429284	−	0.801607i
$976$		0			0
$977$	−44.7934	+	25.8615i	−1.43307	+	0.827382i	−0.997354	−	0.0727039i	$-0.976837\pi$
$977$	−44.7934	+	25.8615i	−1.43307	+	0.827382i	−0.435713	+	0.900085i	$0.643504\pi$
$978$		0			0
$979$	13.1438	+	49.0534i	0.420079	+	1.56775i
$980$		0			0
$981$	16.4953	+	3.30828i	0.526655	+	0.105625i
$982$		0			0
$983$	−48.7340	−	28.1366i	−1.55437	−	0.897419i	−0.997777	−	0.0666364i	$-0.978773\pi$
$983$	−48.7340	−	28.1366i	−1.55437	−	0.897419i	−0.556597	−	0.830782i	$-0.687893\pi$
$984$		0			0
$985$	−76.4921	+	44.1627i	−2.43724	+	1.40714i
$986$		0			0
$987$	−7.02892	−	6.59376i	−0.223733	−	0.209882i
$988$		0			0
$989$	3.37694	−	3.37694i	0.107381	−	0.107381i
$990$		0			0
$991$			45.9493i			1.45963i	0.683646	+	0.729814i	$0.260393\pi$
$991$			45.9493i			1.45963i	−0.683646	+	0.729814i	$0.739607\pi$
$992$		0			0
$993$	8.06581	−	5.00679i	0.255961	−	0.158886i
$994$		0			0
$995$	6.53852	−	24.4021i	0.207285	−	0.773599i
$996$		0			0
$997$	−3.20864	−	11.9748i	−0.101619	−	0.379246i	0.896321	−	0.443406i	$-0.146230\pi$
$997$	−3.20864	−	11.9748i	−0.101619	−	0.379246i	−0.997940	+	0.0641600i	$0.979563\pi$
$998$		0			0
$999$	1.48857	+	15.4908i	0.0470963	+	0.490107i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.y.a.47.20		88
3.2	odd	2		1728.2.z.a.1007.2		88
4.3	odd	2		144.2.u.a.83.9	yes	88
9.4	even	3		1728.2.z.a.1583.2		88
9.5	odd	6	inner	576.2.y.a.239.13		88
12.11	even	2		432.2.v.a.35.14		88
16.5	even	4		144.2.u.a.11.17	✓	88
16.11	odd	4	inner	576.2.y.a.335.13		88
36.23	even	6		144.2.u.a.131.17	yes	88
36.31	odd	6		432.2.v.a.179.6		88
48.5	odd	4		432.2.v.a.251.6		88
48.11	even	4		1728.2.z.a.143.2		88
144.5	odd	12		144.2.u.a.59.9	yes	88
144.59	even	12	inner	576.2.y.a.527.20		88
144.85	even	12		432.2.v.a.395.14		88
144.139	odd	12		1728.2.z.a.719.2		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.17	✓	88	16.5	even	4
144.2.u.a.59.9	yes	88	144.5	odd	12
144.2.u.a.83.9	yes	88	4.3	odd	2
144.2.u.a.131.17	yes	88	36.23	even	6
432.2.v.a.35.14		88	12.11	even	2
432.2.v.a.179.6		88	36.31	odd	6
432.2.v.a.251.6		88	48.5	odd	4
432.2.v.a.395.14		88	144.85	even	12
576.2.y.a.47.20		88	1.1	even	1	trivial
576.2.y.a.239.13		88	9.5	odd	6	inner
576.2.y.a.335.13		88	16.11	odd	4	inner
576.2.y.a.527.20		88	144.59	even	12	inner
1728.2.z.a.143.2		88	48.11	even	4
1728.2.z.a.719.2		88	144.139	odd	12
1728.2.z.a.1007.2		88	3.2	odd	2
1728.2.z.a.1583.2		88	9.4	even	3

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:	\( N \)	\(=\)	\( 576 = 2^{6} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	576.y (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.65787 - 0.501476i) q^{3} +(0.997280 - 3.72190i) q^{5} +(0.481387 - 0.833787i) q^{7} +(2.49704 - 1.66276i) q^{9} +O(q^{10})\)	\(q+(1.65787 - 0.501476i) q^{3} +(0.997280 - 3.72190i) q^{5} +(0.481387 - 0.833787i) q^{7} +(2.49704 - 1.66276i) q^{9} +(1.00684 + 3.75758i) q^{11} +(-0.430868 + 1.60802i) q^{13} +(-0.213084 - 6.67053i) q^{15} -2.58216i q^{17} +(-4.02190 + 4.02190i) q^{19} +(0.379952 - 1.62371i) q^{21} +(-0.600513 + 0.346706i) q^{23} +(-8.52786 - 4.92356i) q^{25} +(3.30593 - 4.00884i) q^{27} +(-1.54233 - 5.75605i) q^{29} +(3.07839 - 1.77731i) q^{31} +(3.55354 + 5.72466i) q^{33} +(-2.62320 - 2.62320i) q^{35} +(-2.11774 + 2.11774i) q^{37} +(0.0920616 + 2.88196i) q^{39} +(4.97738 + 8.62108i) q^{41} +(-6.65259 + 1.78256i) q^{43} +(-3.69837 - 10.9520i) q^{45} +(2.88971 - 5.00512i) q^{47} +(3.03653 + 5.25943i) q^{49} +(-1.29489 - 4.28087i) q^{51} +(6.68090 + 6.68090i) q^{53} +14.9894 q^{55} +(-4.65088 + 8.68465i) q^{57} +(8.75083 + 2.34478i) q^{59} +(-2.12855 + 0.570345i) q^{61} +(-0.184342 - 2.88243i) q^{63} +(5.55520 + 3.20730i) q^{65} +(-4.20548 - 1.12686i) q^{67} +(-0.821706 + 0.875935i) q^{69} +9.40024i q^{71} -3.77840i q^{73} +(-16.6071 - 3.88610i) q^{75} +(3.61770 + 0.969360i) q^{77} +(-9.52430 - 5.49886i) q^{79} +(3.47046 - 8.30397i) q^{81} +(-8.79083 + 2.35550i) q^{83} +(-9.61053 - 2.57514i) q^{85} +(-5.44349 - 8.76932i) q^{87} +13.0545 q^{89} +(1.13333 + 1.13333i) q^{91} +(4.21228 - 4.49027i) q^{93} +(10.9581 + 18.9801i) q^{95} +(1.76559 - 3.05809i) q^{97} +(8.76208 + 7.70871i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7}+O(q^{10}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7	\( 88 q + 4 q^{3} - 6 q^{5} + 4 q^{7} + 6 q^{11} - 2 q^{13} + 8 q^{19} + 2 q^{21} + 12 q^{23} + 16 q^{27} - 6 q^{29} - 8 q^{33} - 8 q^{37} + 32 q^{39} + 2 q^{43} + 6 q^{45} - 24 q^{49} + 12 q^{51} + 16 q^{55} + 42 q^{59} - 2 q^{61} - 12 q^{65} + 2 q^{67} - 10 q^{69} + 56 q^{75} - 6 q^{77} - 8 q^{81} - 54 q^{83} + 8 q^{85} - 48 q^{87} - 20 q^{91} - 34 q^{93} - 4 q^{97} - 46 q^{99}+O(q^{100}) \) 88 * q + 4 * q^3 - 6 * q^5 + 4 * q^7 + 6 * q^11 - 2 * q^13 + 8 * q^19 + 2 * q^21 + 12 * q^23 + 16 * q^27 - 6 * q^29 - 8 * q^33 - 8 * q^37 + 32 * q^39 + 2 * q^43 + 6 * q^45 - 24 * q^49 + 12 * q^51 + 16 * q^55 + 42 * q^59 - 2 * q^61 - 12 * q^65 + 2 * q^67 - 10 * q^69 + 56 * q^75 - 6 * q^77 - 8 * q^81 - 54 * q^83 + 8 * q^85 - 48 * q^87 - 20 * q^91 - 34 * q^93 - 4 * q^97 - 46 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more