LMFDB - Embedded newform 576.2.y.a.335.13

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			335.13
Character	$\chi$	$=$	576.335
Dual form			576.2.y.a.239.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.501476 + 1.65787i) q^{3} +(3.72190 + 0.997280i) q^{5} +(0.481387 - 0.833787i) q^{7} +(-2.49704 + 1.66276i) q^{9} +O(q^{10})$	\(q+(0.501476 + 1.65787i) q^{3} +(3.72190 + 0.997280i) q^{5} +(0.481387 - 0.833787i) q^{7} +(-2.49704 + 1.66276i) q^{9} +(3.75758 - 1.00684i) q^{11} +(1.60802 + 0.430868i) q^{13} +(0.213084 + 6.67053i) q^{15} -2.58216i q^{17} +(-4.02190 - 4.02190i) q^{19} +(1.62371 + 0.379952i) q^{21} +(-0.600513 + 0.346706i) q^{23} +(8.52786 + 4.92356i) q^{25} +(-4.00884 - 3.30593i) q^{27} +(-5.75605 + 1.54233i) q^{29} +(-3.07839 + 1.77731i) q^{31} +(3.55354 + 5.72466i) q^{33} +(2.62320 - 2.62320i) q^{35} +(-2.11774 - 2.11774i) q^{37} +(0.0920616 + 2.88196i) q^{39} +(-4.97738 - 8.62108i) q^{41} +(1.78256 + 6.65259i) q^{43} +(-10.9520 + 3.69837i) q^{45} +(-2.88971 + 5.00512i) q^{47} +(3.03653 + 5.25943i) q^{49} +(4.28087 - 1.29489i) q^{51} +(-6.68090 + 6.68090i) q^{53} +14.9894 q^{55} +(4.65088 - 8.68465i) q^{57} +(2.34478 - 8.75083i) q^{59} +(0.570345 + 2.12855i) q^{61} +(0.184342 + 2.88243i) q^{63} +(5.55520 + 3.20730i) q^{65} +(1.12686 - 4.20548i) q^{67} +(-0.875935 - 0.821706i) q^{69} +9.40024i q^{71} +3.77840i q^{73} +(-3.88610 + 16.6071i) q^{75} +(0.969360 - 3.61770i) q^{77} +(9.52430 + 5.49886i) q^{79} +(3.47046 - 8.30397i) q^{81} +(-2.35550 - 8.79083i) q^{83} +(2.57514 - 9.61053i) q^{85} +(-5.44349 - 8.76932i) q^{87} -13.0545 q^{89} +(1.13333 - 1.13333i) q^{91} +(-4.49027 - 4.21228i) q^{93} +(-10.9581 - 18.9801i) q^{95} +(1.76559 - 3.05809i) q^{97} +(-7.70871 + 8.76208i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

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

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
$3$	0.501476	+	1.65787i	0.289527	+	0.957170i
$3$	0.501476	+	1.65787i	0.289527	+	0.957170i
$4$		0			0
$5$	3.72190	+	0.997280i	1.66448	+	0.445997i	0.963616	−	0.267292i	$-0.0861289\pi$
$5$	3.72190	+	0.997280i	1.66448	+	0.445997i	0.700869	+	0.713290i	$0.252796\pi$
$6$		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
$11$	3.75758	−	1.00684i	1.13295	−	0.303574i	0.356839	−	0.934166i	$-0.383855\pi$
$11$	3.75758	−	1.00684i	1.13295	−	0.303574i	0.776114	+	0.630592i	$0.217188\pi$
$12$		0			0
$13$	1.60802	+	0.430868i	0.445985	+	0.119501i	0.474820	−	0.880083i	$-0.342513\pi$
$13$	1.60802	+	0.430868i	0.445985	+	0.119501i	−0.0288351	+	0.999584i	$0.509180\pi$
$14$		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	0.0745325	−	0.997219i	$-0.476254\pi$
$19$	−4.02190	−	4.02190i	−0.922686	−	0.922686i	−0.997219	+	0.0745325i	$0.976254\pi$
$20$		0			0
$21$	1.62371	+	0.379952i	0.354323	+	0.0829123i
$22$		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
$27$	−4.00884	−	3.30593i	−0.771502	−	0.636227i
$28$		0			0
$29$	−5.75605	+	1.54233i	−1.06887	+	0.286403i	−0.750029	−	0.661405i	$-0.769961\pi$
$29$	−5.75605	+	1.54233i	−1.06887	+	0.286403i	−0.318842	+	0.947808i	$0.603294\pi$
$30$		0			0
$31$	−3.07839	+	1.77731i	−0.552894	+	0.319214i	−0.750289	−	0.661110i	$-0.770085\pi$
$31$	−3.07839	+	1.77731i	−0.552894	+	0.319214i	0.197394	+	0.980324i	$0.436752\pi$
$32$		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	0.511267	−	0.859422i	$-0.329176\pi$
$37$	−2.11774	−	2.11774i	−0.348154	−	0.348154i	−0.859422	+	0.511267i	$0.829176\pi$
$38$		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	$-0.883237\pi$
$41$	−4.97738	−	8.62108i	−0.777337	−	1.34639i	0.156135	−	0.987736i	$-0.450096\pi$
$42$		0			0
$43$	1.78256	+	6.65259i	0.271837	+	1.01451i	0.957931	+	0.286997i	$0.0926571\pi$
$43$	1.78256	+	6.65259i	0.271837	+	1.01451i	−0.686094	+	0.727513i	$0.740676\pi$
$44$		0			0
$45$	−10.9520	+	3.69837i	−1.63263	+	0.551321i
$46$		0			0
$47$	−2.88971	+	5.00512i	−0.421507	+	0.730072i	−0.996087	−	0.0883767i	$-0.971832\pi$
$47$	−2.88971	+	5.00512i	−0.421507	+	0.730072i	0.574580	+	0.818448i	$0.305165\pi$
$48$		0			0
$49$	3.03653	+	5.25943i	0.433790	+	0.751347i
$50$		0			0
$51$	4.28087	−	1.29489i	0.599442	−	0.181321i
$52$		0			0
$53$	−6.68090	+	6.68090i	−0.917692	+	0.917692i	−0.996861	−	0.0791696i	$-0.974773\pi$
$53$	−6.68090	+	6.68090i	−0.917692	+	0.917692i	0.0791696	+	0.996861i	$0.474773\pi$
$54$		0			0
$55$	14.9894			2.02118
$56$		0			0
$57$	4.65088	−	8.68465i	0.616025	−	1.15031i
$58$		0			0
$59$	2.34478	−	8.75083i	0.305264	−	1.13926i	−0.627454	−	0.778654i	$-0.715903\pi$
$59$	2.34478	−	8.75083i	0.305264	−	1.13926i	0.932718	−	0.360607i	$-0.117430\pi$
$60$		0			0
$61$	0.570345	+	2.12855i	0.0730251	+	0.272534i	0.992778	−	0.119964i	$-0.0382779\pi$
$61$	0.570345	+	2.12855i	0.0730251	+	0.272534i	−0.919753	+	0.392497i	$0.871611\pi$
$62$		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
$67$	1.12686	−	4.20548i	0.137667	−	0.513782i	−0.862305	−	0.506389i	$-0.830980\pi$
$67$	1.12686	−	4.20548i	0.137667	−	0.513782i	0.999973	−	0.00739290i	$-0.00235325\pi$
$68$		0			0
$69$	−0.875935	−	0.821706i	−0.105450	−	0.0989217i
$70$		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	$0.0709693\pi$
$73$			3.77840i			0.442228i	−0.975248	+	0.221114i	$0.929031\pi$
$74$		0			0
$75$	−3.88610	+	16.6071i	−0.448728	+	1.91762i
$76$		0			0
$77$	0.969360	−	3.61770i	0.110469	−	0.412275i
$78$		0			0
$79$	9.52430	+	5.49886i	1.07157	+	0.618670i	0.928609	−	0.371059i	$-0.121005\pi$
$79$	9.52430	+	5.49886i	1.07157	+	0.618670i	0.142958	+	0.989729i	$0.454339\pi$
$80$		0			0
$81$	3.47046	−	8.30397i	0.385607	−	0.922663i
$82$		0			0
$83$	−2.35550	−	8.79083i	−0.258549	−	0.964919i	−0.966081	−	0.258238i	$-0.916858\pi$
$83$	−2.35550	−	8.79083i	−0.258549	−	0.964919i	0.707532	−	0.706681i	$-0.249809\pi$
$84$		0			0
$85$	2.57514	−	9.61053i	0.279313	−	1.04241i
$86$		0			0
$87$	−5.44349	−	8.76932i	−0.583604	−	0.940170i
$88$		0			0
$89$	−13.0545			−1.38378			−0.691889	−	0.722004i	$-0.743221\pi$
$89$	−13.0545			−1.38378			−0.691889	+	0.722004i	$0.743221\pi$
$90$		0			0
$91$	1.13333	−	1.13333i	0.118806	−	0.118806i
$92$		0			0
$93$	−4.49027	−	4.21228i	−0.465620	−	0.436793i
$94$		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
$99$	−7.70871	+	8.76208i	−0.774755	+	0.880622i
$100$		0			0
$101$	−4.91426	−	18.3403i	−0.488987	−	1.82492i	−0.561393	−	0.827549i	$-0.689734\pi$
$101$	−4.91426	−	18.3403i	−0.488987	−	1.82492i	0.0724058	−	0.997375i	$-0.476932\pi$
$102$		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	$-0.386841\pi$
$107$	−6.09696	−	6.09696i	−0.589415	−	0.589415i	−0.937473	+	0.348058i	$0.886841\pi$
$108$		0			0
$109$	3.96541	−	3.96541i	0.379817	−	0.379817i	−0.491219	−	0.871036i	$-0.663448\pi$
$109$	3.96541	−	3.96541i	0.379817	−	0.379817i	0.871036	+	0.491219i	$0.163448\pi$
$110$		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
$115$	−2.58081	+	0.691527i	−0.240662	+	0.0644852i
$116$		0			0
$117$	−4.73173	+	1.59786i	−0.437449	+	0.147722i
$118$		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
$123$	11.7966	−	12.5751i	1.06366	−	1.13386i
$124$		0			0
$125$	13.2066	+	13.2066i	1.18123	+	1.18123i
$126$		0			0
$127$		−	3.08724i		−	0.273948i	−0.990575	−	0.136974i	$-0.956262\pi$
$127$		−	3.08724i		−	0.273948i	0.990575	−	0.136974i	$-0.0437377\pi$
$128$		0			0
$129$	−10.1352	+	6.29135i	−0.892354	+	0.553922i
$130$		0			0
$131$	5.07628	+	1.36018i	0.443516	+	0.118840i	0.473664	−	0.880706i	$-0.342931\pi$
$131$	5.07628	+	1.36018i	0.443516	+	0.118840i	−0.0301478	+	0.999545i	$0.509598\pi$
$132$		0			0
$133$	−5.28949	+	1.41732i	−0.458657	+	0.122897i
$134$		0			0
$135$	−11.6236	−	16.3023i	−1.00040	−	1.40308i
$136$		0			0
$137$	−0.807507	+	1.39864i	−0.0689899	+	0.119494i	−0.898457	−	0.439062i	$-0.855311\pi$
$137$	−0.807507	+	1.39864i	−0.0689899	+	0.119494i	0.829467	+	0.558556i	$0.188644\pi$
$138$		0			0
$139$	3.80774	+	1.02028i	0.322968	+	0.0865390i	0.416661	−	0.909062i	$-0.363200\pi$
$139$	3.80774	+	1.02028i	0.322968	+	0.0865390i	−0.0936925	+	0.995601i	$0.529867\pi$
$140$		0			0
$141$	−9.74694	−	2.28080i	−0.820840	−	0.192078i
$142$		0			0
$143$	6.47609			0.541558
$144$		0			0
$145$	−22.9616			−1.90685
$146$		0			0
$147$	−7.19669	+	7.67164i	−0.593573	+	0.632746i
$148$		0			0
$149$	4.31466	+	1.15611i	0.353471	+	0.0947122i	0.431185	−	0.902263i	$-0.358096\pi$
$149$	4.31466	+	1.15611i	0.353471	+	0.0947122i	−0.0777144	+	0.996976i	$0.524762\pi$
$150$		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
$155$	−13.2299	+	3.54495i	−1.06265	+	0.284737i
$156$		0			0
$157$	18.2189	+	4.88175i	1.45403	+	0.389606i	0.897423	−	0.441170i	$-0.145436\pi$
$157$	18.2189	+	4.88175i	1.45403	+	0.389606i	0.556606	+	0.830776i	$0.312103\pi$
$158$		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	0.179675	−	0.983726i	$-0.442496\pi$
$163$	−10.2654	−	10.2654i	−0.804052	−	0.804052i	−0.983726	+	0.179675i	$0.942496\pi$
$164$		0			0
$165$	7.51684	+	24.8505i	0.585185	+	1.93461i
$166$		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
$171$	16.7303	+	3.35541i	1.27940	+	0.256594i
$172$		0			0
$173$	7.70414	−	2.06432i	0.585735	−	0.156947i	0.0462316	−	0.998931i	$-0.485279\pi$
$173$	7.70414	−	2.06432i	0.585735	−	0.156947i	0.539503	+	0.841984i	$0.318612\pi$
$174$		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	$-0.725007\pi$
$179$	1.48408	−	1.48408i	0.110925	−	0.110925i	0.760391	+	0.649466i	$0.225007\pi$
$180$		0			0
$181$	4.93884	+	4.93884i	0.367101	+	0.367101i	0.866419	−	0.499318i	$-0.166416\pi$
$181$	4.93884	+	4.93884i	0.367101	+	0.367101i	−0.499318	+	0.866419i	$0.666416\pi$
$182$		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
$187$	−2.59982	−	9.70266i	−0.190118	−	0.709529i
$188$		0			0
$189$	−4.68625	+	1.75108i	−0.340875	+	0.127373i
$190$		0			0
$191$	−3.80239	+	6.58592i	−0.275131	+	0.476541i	−0.970168	−	0.242433i	$-0.922055\pi$
$191$	−3.80239	+	6.58592i	−0.275131	+	0.476541i	0.695037	+	0.718974i	$0.255388\pi$
$192$		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
$195$	−2.53147	+	10.8182i	−0.181283	+	0.774705i
$196$		0			0
$197$	16.2088	−	16.2088i	1.15483	−	1.15483i	0.169254	−	0.985573i	$-0.445864\pi$
$197$	16.2088	−	16.2088i	1.15483	−	1.15483i	0.985573	−	0.169254i	$-0.0541357\pi$
$198$		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
$203$	−1.48491	+	5.54178i	−0.104221	+	0.388956i
$204$		0			0
$205$	−9.92769	−	37.0507i	−0.693380	−	2.58773i
$206$		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
$211$	1.56388	−	5.83649i	0.107662	−	0.401800i	−0.890971	−	0.454059i	$-0.849975\pi$
$211$	1.56388	−	5.83649i	0.107662	−	0.401800i	0.998634	+	0.0522589i	$0.0166421\pi$
$212$		0			0
$213$	−15.5843	+	4.71399i	−1.06782	+	0.322997i
$214$		0			0
$215$			26.5380i			1.80988i
$216$		0			0
$217$			3.42229i			0.232320i
$218$		0			0
$219$	−6.26408	+	1.89477i	−0.423287	+	0.128037i
$220$		0			0
$221$	1.11257	−	4.15217i	0.0748395	−	0.279305i
$222$		0			0
$223$	4.51028	+	2.60401i	0.302031	+	0.174377i	0.643355	−	0.765568i	$-0.277542\pi$
$223$	4.51028	+	2.60401i	0.302031	+	0.174377i	−0.341324	+	0.939946i	$0.610875\pi$
$224$		0			0
$225$	−29.4811	+	1.88542i	−1.96541	+	0.125695i
$226$		0			0
$227$	1.68430	+	6.28589i	0.111791	+	0.417209i	0.999027	−	0.0441067i	$-0.0140442\pi$
$227$	1.68430	+	6.28589i	0.111791	+	0.417209i	−0.887236	+	0.461316i	$0.847377\pi$
$228$		0			0
$229$	−1.07052	+	3.99522i	−0.0707418	+	0.264012i	−0.992234	−	0.124385i	$-0.960304\pi$
$229$	−1.07052	+	3.99522i	−0.0707418	+	0.264012i	0.921492	+	0.388397i	$0.126971\pi$
$230$		0			0
$231$	6.48378	−	0.207119i	0.426601	−	0.0136274i
$232$		0			0
$233$	17.2178			1.12797			0.563987	−	0.825783i	$-0.309267\pi$
$233$	17.2178			1.12797			0.563987	+	0.825783i	$0.309267\pi$
$234$		0			0
$235$	−15.7467	+	15.7467i	−1.02720	+	1.02720i
$236$		0			0
$237$	−4.34017	+	18.5476i	−0.281924	+	1.20479i
$238$		0			0
$239$	4.49270	+	7.78159i	0.290609	+	0.503349i	0.973954	−	0.226747i	$-0.0728089\pi$
$239$	4.49270	+	7.78159i	0.290609	+	0.503349i	−0.683345	+	0.730095i	$0.739476\pi$
$240$		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
$243$	15.5072	+	1.58933i	0.994789	+	0.101956i
$244$		0			0
$245$	6.05655	+	22.6034i	0.386939	+	1.44408i
$246$		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	$-0.240064\pi$
$251$	0.699267	+	0.699267i	0.0441373	+	0.0441373i	−0.684694	+	0.728831i	$0.740064\pi$
$252$		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
$259$	−2.78520	+	0.746291i	−0.173064	+	0.0463723i
$260$		0			0
$261$	11.8086	−	13.4222i	0.730933	−	0.830812i
$262$		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
$267$	−6.54653	−	21.6427i	−0.400641	−	1.32451i
$268$		0			0
$269$	13.2566	+	13.2566i	0.808267	+	0.808267i	0.984371	−	0.176105i	$-0.0563498\pi$
$269$	13.2566	+	13.2566i	0.808267	+	0.808267i	−0.176105	+	0.984371i	$0.556350\pi$
$270$		0			0
$271$			10.4494i			0.634755i	0.948299	+	0.317377i	$0.102802\pi$
$271$			10.4494i			0.634755i	−0.948299	+	0.317377i	$0.897198\pi$
$272$		0			0
$273$	2.44726	+	1.31058i	0.148115	+	0.0793197i
$274$		0			0
$275$	37.0013	+	9.91448i	2.23126	+	0.597866i
$276$		0			0
$277$	−15.6398	+	4.19068i	−0.939707	+	0.251794i	−0.695989	−	0.718052i	$-0.745034\pi$
$277$	−15.6398	+	4.19068i	−0.939707	+	0.251794i	−0.243718	+	0.969846i	$0.578367\pi$
$278$		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	$0.425431\pi$
$281$	−12.1751	+	21.0879i	−0.726306	+	1.25800i	−0.958434	+	0.285313i	$0.907902\pi$
$282$		0			0
$283$	8.50029	+	2.27765i	0.505290	+	0.135392i	0.502454	−	0.864604i	$-0.332431\pi$
$283$	8.50029	+	2.27765i	0.505290	+	0.135392i	0.00283598	+	0.999996i	$0.499097\pi$
$284$		0			0
$285$	25.9712	−	27.6852i	1.53840	−	1.63993i
$286$		0			0
$287$	−9.58419			−0.565737
$288$		0			0
$289$	10.3325			0.607792
$290$		0			0
$291$	5.95531	+	1.39355i	0.349106	+	0.0816916i
$292$		0			0
$293$	−0.808690	−	0.216688i	−0.0472442	−	0.0126590i	0.235120	−	0.971966i	$-0.424452\pi$
$293$	−0.808690	−	0.216688i	−0.0472442	−	0.0126590i	−0.282364	+	0.959307i	$0.591118\pi$
$294$		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
$299$	−1.11502	+	0.298769i	−0.0644834	+	0.0172783i
$300$		0			0
$301$	6.40494	+	1.71620i	0.369175	+	0.0989201i
$302$		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	0.971794	+	0.235831i	$0.0757813\pi$
$307$	21.1593	+	21.1593i	1.20763	+	1.20763i	0.235831	+	0.971794i	$0.424219\pi$
$308$		0			0
$309$	4.08574	−	4.35538i	0.232429	−	0.247769i
$310$		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	$0.0380425\pi$
$313$	28.1752	+	16.2670i	1.59256	+	0.919463i	0.599689	+	0.800233i	$0.295291\pi$
$314$		0			0
$315$	−2.18849	+	10.9120i	−0.123308	+	0.614820i
$316$		0			0
$317$	−13.4383	+	3.60078i	−0.754770	+	0.202240i	−0.615633	−	0.788033i	$-0.711100\pi$
$317$	−13.4383	+	3.60078i	−0.754770	+	0.202240i	−0.139137	+	0.990273i	$0.544433\pi$
$318$		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
$331$	−1.41860	−	5.29427i	−0.0779731	−	0.291000i	0.915918	−	0.401366i	$-0.131464\pi$
$331$	−1.41860	−	5.29427i	−0.0779731	−	0.291000i	−0.993891	+	0.110366i	$0.964798\pi$
$332$		0			0
$333$	8.80938	+	1.76680i	0.482751	+	0.0968200i
$334$		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
$339$	8.07446	+	7.57456i	0.438544	+	0.411394i
$340$		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
$347$	3.55779	−	13.2779i	0.190992	−	0.712793i	−0.802276	−	0.596954i	$-0.796378\pi$
$347$	3.55779	−	13.2779i	0.190992	−	0.712793i	0.993268	−	0.115839i	$-0.0369557\pi$
$348$		0			0
$349$	4.16907	+	15.5592i	0.223165	+	0.832863i	0.983131	+	0.182901i	$0.0585487\pi$
$349$	4.16907	+	15.5592i	0.223165	+	0.832863i	−0.759966	+	0.649962i	$0.774785\pi$
$350$		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
$355$	−9.37467	+	34.9868i	−0.497556	+	1.85690i
$356$		0			0
$357$	0.981096	−	4.19268i	0.0519251	−	0.221900i
$358$		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
$363$	5.22108	+	4.89784i	0.274036	+	0.257070i
$364$		0			0
$365$	−3.76812	+	14.0628i	−0.197233	+	0.736082i
$366$		0			0
$367$	−20.8621	−	12.0447i	−1.08899	−	0.628729i	−0.155683	−	0.987807i	$-0.549758\pi$
$367$	−20.8621	−	12.0447i	−1.08899	−	0.628729i	−0.933308	+	0.359078i	$0.883091\pi$
$368$		0			0
$369$	26.7635	+	13.2510i	1.39325	+	0.689821i
$370$		0			0
$371$	2.35435	+	8.78654i	0.122232	+	0.456175i
$372$		0			0
$373$	7.05873	−	26.3435i	0.365487	−	1.36402i	−0.501272	−	0.865290i	$-0.667134\pi$
$373$	7.05873	−	26.3435i	0.365487	−	1.36402i	0.866759	−	0.498727i	$-0.166199\pi$
$374$		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	−0.482971	+	0.875636i	$0.660442\pi$
$379$	−26.4493	+	26.4493i	−1.35861	+	1.35861i	−0.875636	+	0.482971i	$0.839558\pi$
$380$		0			0
$381$	5.11823	−	1.54817i	0.262215	−	0.0793153i
$382$		0			0
$383$	14.2366	+	24.6585i	0.727455	+	1.25999i	0.957955	+	0.286917i	$0.0926305\pi$
$383$	14.2366	+	24.6585i	0.727455	+	1.25999i	−0.230500	+	0.973072i	$0.574036\pi$
$384$		0			0
$385$	7.21573	−	12.4980i	0.367748	−	0.636957i
$386$		0			0
$387$	−15.5128	−	13.6478i	−0.788559	−	0.693759i
$388$		0			0
$389$	5.20211	+	19.4146i	0.263758	+	0.984357i	0.963006	+	0.269479i	$0.0868513\pi$
$389$	5.20211	+	19.4146i	0.263758	+	0.984357i	−0.699249	+	0.714878i	$0.746482\pi$
$390$		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	−0.541823	−	0.840492i	$-0.682266\pi$
$397$	5.95094	−	5.95094i	0.298669	−	0.298669i	0.840492	+	0.541823i	$0.182266\pi$
$398$		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
$403$	−5.71590	+	1.53157i	−0.284729	+	0.0762929i
$404$		0			0
$405$	21.1981	−	27.4455i	1.05334	−	1.36378i
$406$		0			0
$407$	−10.0898	−	5.82535i	−0.500133	−	0.288752i
$408$		0			0
$409$	−7.24880	+	4.18510i	−0.358430	+	0.206940i	−0.668392	−	0.743809i	$-0.733017\pi$
$409$	−7.24880	+	4.18510i	−0.358430	+	0.206940i	0.309962	+	0.950749i	$0.399684\pi$
$410$		0			0
$411$	−2.72371	−	0.637353i	−0.134351	−	0.0314383i
$412$		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
$419$	−30.9427	−	8.29108i	−1.51165	−	0.405046i	−0.594668	−	0.803971i	$-0.702716\pi$
$419$	−30.9427	−	8.29108i	−1.51165	−	0.405046i	−0.916983	+	0.398926i	$0.869383\pi$
$420$		0			0
$421$	−28.9049	+	7.74504i	−1.40874	+	0.377470i	−0.881475	−	0.472232i	$-0.843449\pi$
$421$	−28.9049	+	7.74504i	−1.40874	+	0.377470i	−0.527264	+	0.849702i	$0.676782\pi$
$422$		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
$427$	2.04932	+	0.549113i	0.0991735	+	0.0265734i
$428$		0			0
$429$	3.24760	+	10.7365i	0.156796	+	0.518363i
$430$		0			0
$431$	10.3884			0.500389			0.250195	−	0.968196i	$-0.419505\pi$
$431$	10.3884			0.500389			0.250195	+	0.968196i	$0.419505\pi$
$432$		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
$435$	−11.5147	−	38.0672i	−0.552086	−	1.82518i
$436$		0			0
$437$	3.80962	+	1.02078i	0.182239	+	0.0488307i
$438$		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
$443$	−12.8638	+	3.44686i	−0.611180	+	0.163765i	−0.551115	−	0.834429i	$-0.685797\pi$
$443$	−12.8638	+	3.44686i	−0.611180	+	0.163765i	−0.0600649	+	0.998194i	$0.519131\pi$
$444$		0			0
$445$	−48.5877	−	13.0190i	−2.30328	−	0.617161i
$446$		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
$453$	−32.3909	−	7.57953i	−1.52186	−	0.356118i
$454$		0			0
$455$	5.34841	−	3.08790i	0.250737	−	0.144763i
$456$		0			0
$457$	10.0451	+	5.79955i	0.469890	+	0.271291i	0.716194	−	0.697901i	$-0.245883\pi$
$457$	10.0451	+	5.79955i	0.469890	+	0.271291i	−0.246303	+	0.969193i	$0.579216\pi$
$458$		0			0
$459$	−8.53644	+	10.3515i	−0.398447	+	0.483165i
$460$		0			0
$461$	−13.3098	+	3.56634i	−0.619898	+	0.166101i	−0.555081	−	0.831796i	$-0.687313\pi$
$461$	−13.3098	+	3.56634i	−0.619898	+	0.166101i	−0.0648164	+	0.997897i	$0.520646\pi$
$462$		0			0
$463$	−11.4905	+	6.63406i	−0.534010	+	0.308311i	−0.742648	−	0.669682i	$-0.766430\pi$
$463$	−11.4905	+	6.63406i	−0.534010	+	0.308311i	0.208638	+	0.977993i	$0.433097\pi$
$464$		0			0
$465$	−12.5115	−	20.1557i	−0.580208	−	0.934700i
$466$		0			0
$467$	28.1581	−	28.1581i	1.30300	−	1.30300i	0.376647	−	0.926357i	$-0.377077\pi$
$467$	28.1581	−	28.1581i	1.30300	−	1.30300i	0.926357	−	0.376647i	$-0.122923\pi$
$468$		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
$475$	−14.4961	−	54.1002i	−0.665127	−	2.48229i
$476$		0			0
$477$	5.57377	−	27.7912i	0.255206	−	1.27247i
$478$		0			0
$479$	3.40138	−	5.89137i	0.155413	−	0.269183i	−0.777796	−	0.628517i	$-0.783662\pi$
$479$	3.40138	−	5.89137i	0.155413	−	0.269183i	0.933209	+	0.359333i	$0.116996\pi$
$480$		0			0
$481$	−2.49291	−	4.31784i	−0.113667	−	0.196877i
$482$		0			0
$483$	−1.10679	+	0.334785i	−0.0503608	+	0.0152332i
$484$		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
$491$	1.87065	−	6.98135i	0.0844211	−	0.315064i	−0.910783	−	0.412886i	$-0.864521\pi$
$491$	1.87065	−	6.98135i	0.0844211	−	0.315064i	0.995204	+	0.0978219i	$0.0311876\pi$
$492$		0			0
$493$	3.98253	+	14.8630i	0.179364	+	0.669397i
$494$		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
$499$	6.80645	−	25.4020i	0.304698	−	1.13715i	−0.628506	−	0.777805i	$-0.716333\pi$
$499$	6.80645	−	25.4020i	0.304698	−	1.13715i	0.933205	−	0.359346i	$-0.117000\pi$
$500$		0			0
$501$	7.28518	+	6.83415i	0.325478	+	0.305327i
$502$		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
$507$	4.03665	−	17.2505i	0.179274	−	0.766121i
$508$		0			0
$509$	−3.94915	+	14.7384i	−0.175043	+	0.653269i	0.821502	+	0.570206i	$0.193137\pi$
$509$	−3.94915	+	14.7384i	−0.175043	+	0.653269i	−0.996544	+	0.0830623i	$0.973530\pi$
$510$		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
$515$	−3.43845	−	12.8325i	−0.151516	−	0.565467i
$516$		0			0
$517$	−5.81895	+	21.7166i	−0.255917	+	0.955096i
$518$		0			0
$519$	7.28580	+	11.7372i	0.319811	+	0.515207i
$520$		0			0
$521$	23.4677			1.02814			0.514070	−	0.857748i	$-0.328137\pi$
$521$	23.4677			1.02814			0.514070	+	0.857748i	$0.328137\pi$
$522$		0			0
$523$	30.0762	−	30.0762i	1.31514	−	1.31514i	0.397567	−	0.917573i	$-0.369855\pi$
$523$	30.0762	−	30.0762i	1.31514	−	1.31514i	0.917573	−	0.397567i	$-0.130145\pi$
$524$		0			0
$525$	11.9761	+	11.2346i	0.522678	+	0.490319i
$526$		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
$531$	8.69551	+	25.7500i	0.377353	+	1.11746i
$532$		0			0
$533$	−4.28919	−	16.0075i	−0.185786	−	0.693361i
$534$		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	−0.984248	−	0.176795i	$-0.943427\pi$
$541$	−18.7809	+	18.7809i	−0.807453	+	0.807453i	0.176795	+	0.984248i	$0.443427\pi$
$542$		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
$547$	14.9578	−	4.00793i	0.639548	−	0.171366i	0.0755496	−	0.997142i	$-0.475929\pi$
$547$	14.9578	−	4.00793i	0.639548	−	0.171366i	0.563999	+	0.825776i	$0.309262\pi$
$548$		0			0
$549$	−4.96345	−	4.36675i	−0.211835	−	0.186368i
$550$		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
$555$	13.6752	−	14.5777i	0.580479	−	0.618789i
$556$		0			0
$557$	−31.8166	−	31.8166i	−1.34811	−	1.34811i	−0.887712	−	0.460398i	$-0.847707\pi$
$557$	−31.8166	−	31.8166i	−1.34811	−	1.34811i	−0.460398	−	0.887712i	$-0.652293\pi$
$558$		0			0
$559$			11.4656i			0.484941i
$560$		0			0
$561$	14.7820	−	9.17580i	0.624096	−	0.387403i
$562$		0			0
$563$	−33.0941	−	8.86755i	−1.39475	−	0.373723i	−0.518294	−	0.855202i	$-0.673433\pi$
$563$	−33.0941	−	8.86755i	−1.39475	−	0.373723i	−0.876457	+	0.481480i	$0.840100\pi$
$564$		0			0
$565$	23.7902	−	6.37456i	1.00086	−	0.268180i
$566$		0			0
$567$	−5.25310	−	6.89105i	−0.220610	−	0.289397i
$568$		0			0
$569$	−2.54964	+	4.41610i	−0.106886	+	0.185133i	−0.914507	−	0.404569i	$-0.867421\pi$
$569$	−2.54964	+	4.41610i	−0.106886	+	0.185133i	0.807621	+	0.589702i	$0.200755\pi$
$570$		0			0
$571$	6.68977	+	1.79252i	0.279958	+	0.0750146i	0.396066	−	0.918222i	$-0.370375\pi$
$571$	6.68977	+	1.79252i	0.279958	+	0.0750146i	−0.116108	+	0.993237i	$0.537042\pi$
$572$		0			0
$573$	−12.8254	−	3.00117i	−0.535788	−	0.125376i
$574$		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
$579$	−2.28488	+	2.43568i	−0.0949564	+	0.101223i
$580$		0			0
$581$	−8.46359	−	2.26781i	−0.351129	−	0.0940847i
$582$		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
$587$	−13.8472	+	3.71035i	−0.571536	+	0.153143i	−0.533001	−	0.846115i	$-0.678936\pi$
$587$	−13.8472	+	3.71035i	−0.571536	+	0.153143i	−0.0385349	+	0.999257i	$0.512269\pi$
$588$		0			0
$589$	19.5291	+	5.23280i	0.804682	+	0.215614i
$590$		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
$597$	3.28785	+	10.8696i	0.134563	+	0.444861i
$598$		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	−0.199722	−	0.979853i	$-0.564004\pi$
$601$	−28.1475	−	16.2510i	−1.14816	−	0.662891i	−0.948438	+	0.316962i	$0.897337\pi$
$602$		0			0
$603$	4.17890	+	12.3750i	0.170178	+	0.503948i
$604$		0			0
$605$	15.3831	−	4.12190i	0.625413	−	0.167579i
$606$		0			0
$607$	−9.86566	+	5.69594i	−0.400435	+	0.231191i	−0.686672	−	0.726968i	$-0.740929\pi$
$607$	−9.86566	+	5.69594i	−0.400435	+	0.231191i	0.286237	+	0.958159i	$0.407596\pi$
$608$		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	0.918063	−	0.396434i	$-0.129752\pi$
$613$	12.9149	+	12.9149i	0.521630	+	0.521630i	−0.396434	+	0.918063i	$0.629752\pi$
$614$		0			0
$615$	56.4466	−	35.0388i	2.27615	−	1.41290i
$616$		0			0
$617$	5.36926	+	9.29983i	0.216158	+	0.374397i	0.953630	−	0.300981i	$-0.0973139\pi$
$617$	5.36926	+	9.29983i	0.216158	+	0.374397i	−0.737472	+	0.675378i	$0.763981\pi$
$618$		0			0
$619$	4.04330	+	15.0898i	0.162514	+	0.606510i	0.998344	+	0.0575222i	$0.0183200\pi$
$619$	4.04330	+	15.0898i	0.162514	+	0.606510i	−0.835830	+	0.548988i	$0.815013\pi$
$620$		0			0
$621$	3.55355	+	0.595366i	0.142599	+	0.0238912i
$622$		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
$627$	8.73202	−	37.3160i	0.348723	−	1.49026i
$628$		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
$635$	3.07884	−	11.4904i	0.122180	−	0.455982i
$636$		0			0
$637$	2.61669	+	9.76562i	0.103677	+	0.386928i
$638$		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
$643$	−11.1343	+	41.5536i	−0.439092	+	1.63871i	0.291988	+	0.956422i	$0.405683\pi$
$643$	−11.1343	+	41.5536i	−0.439092	+	1.63871i	−0.731080	+	0.682292i	$0.760983\pi$
$644$		0			0
$645$	−43.9964	+	13.3082i	−1.73236	+	0.524008i
$646$		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
$651$	−5.67370	+	1.71620i	−0.222370	+	0.0672630i
$652$		0			0
$653$	10.1932	−	38.0415i	0.398891	−	1.48868i	−0.416160	−	0.909291i	$-0.636624\pi$
$653$	10.1932	−	38.0415i	0.398891	−	1.48868i	0.815051	−	0.579389i	$-0.196709\pi$
$654$		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
$659$	0.390374	+	1.45690i	0.0152068	+	0.0567526i	0.973112	−	0.230331i	$-0.0739809\pi$
$659$	0.390374	+	1.45690i	0.0152068	+	0.0567526i	−0.957906	+	0.287084i	$0.907314\pi$
$660$		0			0
$661$	9.57641	−	35.7396i	0.372479	−	1.39011i	−0.484514	−	0.874783i	$-0.661004\pi$
$661$	9.57641	−	35.7396i	0.372479	−	1.39011i	0.856993	−	0.515328i	$-0.172330\pi$
$662$		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
$669$	−2.05531	+	8.78329i	−0.0794628	+	0.339582i
$670$		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
$675$	−17.9098	−	47.9303i	−0.689350	−	1.84484i
$676$		0			0
$677$	−10.6718	−	39.8275i	−0.410149	−	1.53070i	−0.794358	−	0.607450i	$-0.792193\pi$
$677$	−10.6718	−	39.8275i	−0.410149	−	1.53070i	0.384209	−	0.923246i	$-0.374474\pi$
$678$		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	$-0.383423\pi$
$683$	−15.0423	−	15.0423i	−0.575578	−	0.575578i	−0.933682	+	0.358104i	$0.883423\pi$
$684$		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
$691$	42.4064	−	11.3628i	1.61321	−	0.432260i	0.664216	−	0.747540i	$-0.268765\pi$
$691$	42.4064	−	11.3628i	1.61321	−	0.432260i	0.948998	+	0.315281i	$0.102099\pi$
$692$		0			0
$693$	3.59483	+	10.6454i	0.136556	+	0.404384i
$694$		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
$699$	8.63430	+	28.5448i	0.326579	+	1.07966i
$700$		0			0
$701$	7.87056	+	7.87056i	0.297267	+	0.297267i	0.839942	−	0.542676i	$-0.182589\pi$
$701$	7.87056	+	7.87056i	0.297267	+	0.297267i	−0.542676	+	0.839942i	$0.682589\pi$
$702$		0			0
$703$			17.0347i			0.642474i
$704$		0			0
$705$	−34.0025	−	18.2094i	−1.28061	−	0.685804i
$706$		0			0
$707$	−17.6575	−	4.73132i	−0.664080	−	0.177940i
$708$		0			0
$709$	27.9701	−	7.49458i	1.05044	−	0.281465i	0.308007	−	0.951384i	$-0.400338\pi$
$709$	27.9701	−	7.49458i	1.05044	−	0.281465i	0.742434	+	0.669919i	$0.233671\pi$
$710$		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
$715$	24.1034	+	6.45848i	0.901414	+	0.241533i
$716$		0			0
$717$	−10.6479	+	11.3506i	−0.397651	+	0.423895i
$718$		0			0
$719$	0.674555			0.0251567			0.0125783	−	0.999921i	$-0.495996\pi$
$719$	0.674555			0.0251567			0.0125783	+	0.999921i	$0.495996\pi$
$720$		0			0
$721$	−3.31948			−0.123624
$722$		0			0
$723$	1.89161	+	0.442641i	0.0703498	+	0.0164620i
$724$		0			0
$725$	−56.6805	−	15.1875i	−2.10506	−	0.564049i
$726$		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
$731$	17.1780	−	4.60284i	0.635352	−	0.170242i
$732$		0			0
$733$	−19.9416	−	5.34335i	−0.736562	−	0.197361i	−0.129012	−	0.991643i	$-0.541181\pi$
$733$	−19.9416	−	5.34335i	−0.736562	−	0.197361i	−0.607549	+	0.794282i	$0.707847\pi$
$734$		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	0.999876	+	0.0157506i	$0.00501379\pi$
$739$	27.6094	+	27.6094i	1.01563	+	1.01563i	0.0157506	+	0.999876i	$0.494986\pi$
$740$		0			0
$741$	11.2207	−	11.9612i	0.412201	−	0.439405i
$742$		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
$747$	20.4988	+	18.0345i	0.750013	+	0.659847i
$748$		0			0
$749$	−8.01857	+	2.14857i	−0.292992	+	0.0785070i
$750$		0			0
$751$	30.5334	−	17.6285i	1.11418	−	0.643273i	0.174272	−	0.984698i	$-0.444243\pi$
$751$	30.5334	−	17.6285i	1.11418	−	0.643273i	0.939909	+	0.341425i	$0.110909\pi$
$752$		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	0.995614	−	0.0935534i	$-0.0298226\pi$
$757$	24.8190	+	24.8190i	0.902061	+	0.902061i	−0.0935534	+	0.995614i	$0.529823\pi$
$758$		0			0
$759$	−4.11872	−	2.20570i	−0.149500	−	0.0800618i
$760$		0			0
$761$	−2.73041	−	4.72921i	−0.0989774	−	0.171434i	0.812284	−	0.583262i	$-0.198224\pi$
$761$	−2.73041	−	4.72921i	−0.0989774	−	0.171434i	−0.911262	+	0.411828i	$0.864890\pi$
$762$		0			0
$763$	−1.39741	−	5.21521i	−0.0505897	−	0.188803i
$764$		0			0
$765$	9.54978	+	28.2798i	0.345273	+	1.02246i
$766$		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
$771$	8.45983	+	7.93608i	0.304673	+	0.285811i
$772$		0			0
$773$	−11.3458	+	11.3458i	−0.408079	+	0.408079i	−0.881068	−	0.472989i	$-0.843175\pi$
$773$	−11.3458	+	11.3458i	−0.408079	+	0.408079i	0.472989	+	0.881068i	$0.343175\pi$
$774$		0			0
$775$	−35.0027			−1.25733
$776$		0			0
$777$	−2.63396	−	4.24324i	−0.0944928	−	0.152225i
$778$		0			0
$779$	−14.6546	+	54.6916i	−0.525054	+	1.95953i
$780$		0			0
$781$	9.46454	+	35.3221i	0.338668	+	1.26393i
$782$		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
$787$	6.87546	−	25.6596i	0.245084	−	0.914665i	−0.728257	−	0.685304i	$-0.759669\pi$
$787$	6.87546	−	25.6596i	0.245084	−	0.914665i	0.973341	−	0.229362i	$-0.0736638\pi$
$788$		0			0
$789$	5.56464	−	23.7803i	0.198106	−	0.846601i
$790$		0			0
$791$		−	6.15400i		−	0.218811i
$792$		0			0
$793$			3.66851i			0.130272i
$794$		0			0
$795$	−45.9887	−	43.1415i	−1.63105	−	1.53007i
$796$		0			0
$797$	5.58542	−	20.8451i	0.197846	−	0.738371i	−0.793666	−	0.608354i	$-0.791830\pi$
$797$	5.58542	−	20.8451i	0.197846	−	0.738371i	0.991512	−	0.130017i	$-0.0415032\pi$
$798$		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
$803$	3.80424	+	14.1976i	0.134249	+	0.501024i
$804$		0			0
$805$	−0.665784	+	2.48474i	−0.0234658	+	0.0875756i
$806$		0			0
$807$	−15.3298	+	28.6254i	−0.539633	+	1.00766i
$808$		0			0
$809$	36.1898			1.27236			0.636182	−	0.771539i	$-0.280513\pi$
$809$	36.1898			1.27236			0.636182	+	0.771539i	$0.280513\pi$
$810$		0			0
$811$	−17.4150	+	17.4150i	−0.611523	+	0.611523i	−0.943343	−	0.331820i	$-0.892337\pi$
$811$	−17.4150	+	17.4150i	−0.611523	+	0.611523i	0.331820	+	0.943343i	$0.392337\pi$
$812$		0			0
$813$	−17.3237	+	5.24011i	−0.607568	+	0.183779i
$814$		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
$819$	−0.945524	+	4.71445i	−0.0330393	+	0.164736i
$820$		0			0
$821$	9.08280	+	33.8975i	0.316992	+	1.18303i	0.922121	+	0.386902i	$0.126455\pi$
$821$	9.08280	+	33.8975i	0.316992	+	1.18303i	−0.605129	+	0.796127i	$0.706878\pi$
$822$		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	−0.847674	−	0.530517i	$-0.821998\pi$
$827$	−39.6335	−	39.6335i	−1.37819	−	1.37819i	−0.530517	−	0.847674i	$-0.678002\pi$
$828$		0			0
$829$	−20.5229	+	20.5229i	−0.712789	+	0.712789i	−0.967118	−	0.254329i	$-0.918145\pi$
$829$	−20.5229	+	20.5229i	−0.712789	+	0.712789i	0.254329	+	0.967118i	$0.418145\pi$
$830$		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
$835$	21.4647	−	5.75145i	0.742817	−	0.199037i
$836$		0			0
$837$	18.2164	+	3.05200i	0.629651	+	0.105493i
$838$		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
$843$	−41.0664	−	9.60963i	−1.41440	−	0.330973i
$844$		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
$851$	2.00596	+	0.537496i	0.0687636	+	0.0184251i
$852$		0			0
$853$	−53.2899	+	14.2790i	−1.82461	+	0.488903i	−0.997339	−	0.0729001i	$-0.976775\pi$
$853$	−53.2899	+	14.2790i	−1.82461	+	0.488903i	−0.827271	+	0.561803i	$0.810108\pi$
$854$		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	$-0.638049\pi$
$857$	16.8544	−	29.1927i	0.575737	−	0.997205i	0.995961	−	0.0897851i	$-0.0286180\pi$
$858$		0			0
$859$	52.8271	+	14.1550i	1.80244	+	0.482962i	0.994355	−	0.106107i	$-0.0338386\pi$
$859$	52.8271	+	14.1550i	1.80244	+	0.482962i	0.808083	+	0.589069i	$0.200505\pi$
$860$		0			0
$861$	−4.80624	−	15.8893i	−0.163796	−	0.541507i
$862$		0			0
$863$	−28.6860			−0.976481			−0.488241	−	0.872709i	$-0.662361\pi$
$863$	−28.6860			−0.976481			−0.488241	+	0.872709i	$0.662361\pi$
$864$		0			0
$865$	30.7327			1.04494
$866$		0			0
$867$	5.18148	+	17.1298i	0.175972	+	0.581760i
$868$		0			0
$869$	41.3248	+	11.0729i	1.40185	+	0.375624i
$870$		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
$875$	17.3689	−	4.65399i	0.587177	−	0.157334i
$876$		0			0
$877$	5.11731	+	1.37118i	0.172799	+	0.0463014i	0.344181	−	0.938903i	$-0.388157\pi$
$877$	5.11731	+	1.37118i	0.172799	+	0.0463014i	−0.171382	+	0.985205i	$0.554823\pi$
$878$		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	0.996094	−	0.0883036i	$-0.0281446\pi$
$883$	26.9753	+	26.9753i	0.907790	+	0.907790i	−0.0883036	+	0.996094i	$0.528145\pi$
$884$		0			0
$885$	58.8723	+	13.7762i	1.97897	+	0.463083i
$886$		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
$891$	4.67977	−	34.6970i	0.156778	−	1.16239i
$892$		0			0
$893$	31.7522	−	8.50797i	1.06255	−	0.284708i
$894$		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
$907$	2.60194	+	9.71055i	0.0863958	+	0.322434i	0.995575	−	0.0939718i	$-0.0299564\pi$
$907$	2.60194	+	9.71055i	0.0863958	+	0.322434i	−0.909179	+	0.416405i	$0.863290\pi$
$908$		0			0
$909$	42.7666	+	37.6252i	1.41848	+	1.24795i
$910$		0			0
$911$	−23.4920	+	40.6893i	−0.778325	+	1.34810i	0.154582	+	0.987980i	$0.450597\pi$
$911$	−23.4920	+	40.6893i	−0.778325	+	1.34810i	−0.932907	+	0.360118i	$0.882737\pi$
$912$		0			0
$913$	−17.7019	−	30.6607i	−0.585849	−	1.01472i
$914$		0			0
$915$	−14.0771	+	4.25806i	−0.465373	+	0.140767i
$916$		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
$923$	−4.05026	+	15.1158i	−0.133316	+	0.497542i
$924$		0			0
$925$	−7.63296	−	28.4866i	−0.250970	−	0.936634i
$926$		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
$931$	8.94026	−	33.3655i	0.293005	−	1.09351i
$932$		0			0
$933$	−15.8195	−	14.8401i	−0.517909	−	0.485845i
$934$		0			0
$935$		−	38.7051i		−	1.26579i
$936$		0			0
$937$			16.7455i			0.547052i	0.961865	+	0.273526i	$0.0881899\pi$
$937$			16.7455i			0.547052i	−0.961865	+	0.273526i	$0.911810\pi$
$938$		0			0
$939$	−12.8393	+	54.8682i	−0.418994	+	1.79056i
$940$		0			0
$941$	−1.50628	+	5.62151i	−0.0491033	+	0.183256i	−0.986122	−	0.166024i	$-0.946907\pi$
$941$	−1.50628	+	5.62151i	−0.0491033	+	0.183256i	0.937018	+	0.349280i	$0.113574\pi$
$942$		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
$947$	−1.73267	−	6.46641i	−0.0563042	−	0.210130i	0.932043	−	0.362348i	$-0.118025\pi$
$947$	−1.73267	−	6.46641i	−0.0563042	−	0.210130i	−0.988347	+	0.152218i	$0.951358\pi$
$948$		0			0
$949$	−1.62799	+	6.07575i	−0.0528468	+	0.197227i
$950$		0			0
$951$	−12.7086	−	20.4732i	−0.412104	−	0.663889i
$952$		0			0
$953$	0.390160			0.0126385			0.00631925	−	0.999980i	$-0.497989\pi$
$953$	0.390160			0.0126385			0.00631925	+	0.999980i	$0.497989\pi$
$954$		0			0
$955$	−20.7201	+	20.7201i	−0.670487	+	0.670487i
$956$		0			0
$957$	−29.2837	−	27.4707i	−0.946606	−	0.888001i
$958$		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
$963$	25.3622	+	5.08661i	0.817284	+	0.163914i
$964$		0			0
$965$	1.92290	+	7.17636i	0.0619003	+	0.231015i
$966$		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	$-0.382543\pi$
$971$	−17.8241	−	17.8241i	−0.572003	−	0.572003i	−0.932688	+	0.360685i	$0.882543\pi$
$972$		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
$979$	−49.0534	+	13.1438i	−1.56775	+	0.420079i
$980$		0			0
$981$	−3.30828	+	16.4953i	−0.105625	+	0.526655i
$982$		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
$987$	−6.59376	+	7.02892i	−0.209882	+	0.223733i
$988$		0			0
$989$	−3.37694	−	3.37694i	−0.107381	−	0.107381i
$990$		0			0
$991$		−	45.9493i		−	1.45963i	−0.683646	−	0.729814i	$-0.739607\pi$
$991$		−	45.9493i		−	1.45963i	0.683646	−	0.729814i	$-0.260393\pi$
$992$		0			0
$993$	8.06581	−	5.00679i	0.255961	−	0.158886i
$994$		0			0
$995$	24.4021	+	6.53852i	0.773599	+	0.207285i
$996$		0			0
$997$	11.9748	−	3.20864i	0.379246	−	0.101619i	−0.0641600	−	0.997940i	$-0.520437\pi$
$997$	11.9748	−	3.20864i	0.379246	−	0.101619i	0.443406	+	0.896321i	$0.353770\pi$
$998$		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.335.13		88
3.2	odd	2		1728.2.z.a.143.2		88
4.3	odd	2		144.2.u.a.11.17	✓	88
9.4	even	3		1728.2.z.a.719.2		88
9.5	odd	6	inner	576.2.y.a.527.20		88
12.11	even	2		432.2.v.a.251.6		88
16.3	odd	4	inner	576.2.y.a.47.20		88
16.13	even	4		144.2.u.a.83.9	yes	88
36.23	even	6		144.2.u.a.59.9	yes	88
36.31	odd	6		432.2.v.a.395.14		88
48.29	odd	4		432.2.v.a.35.14		88
48.35	even	4		1728.2.z.a.1007.2		88
144.13	even	12		432.2.v.a.179.6		88
144.67	odd	12		1728.2.z.a.1583.2		88
144.77	odd	12		144.2.u.a.131.17	yes	88
144.131	even	12	inner	576.2.y.a.239.13		88

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.u.a.11.17	✓	88	4.3	odd	2
144.2.u.a.59.9	yes	88	36.23	even	6
144.2.u.a.83.9	yes	88	16.13	even	4
144.2.u.a.131.17	yes	88	144.77	odd	12
432.2.v.a.35.14		88	48.29	odd	4
432.2.v.a.179.6		88	144.13	even	12
432.2.v.a.251.6		88	12.11	even	2
432.2.v.a.395.14		88	36.31	odd	6
576.2.y.a.47.20		88	16.3	odd	4	inner
576.2.y.a.239.13		88	144.131	even	12	inner
576.2.y.a.335.13		88	1.1	even	1	trivial
576.2.y.a.527.20		88	9.5	odd	6	inner
1728.2.z.a.143.2		88	3.2	odd	2
1728.2.z.a.719.2		88	9.4	even	3
1728.2.z.a.1007.2		88	48.35	even	4
1728.2.z.a.1583.2		88	144.67	odd	12

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)

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

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