LMFDB - Embedded newform 576.2.bb.e.529.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [576,2,Mod(49,576)]

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([0, 3, 4]))

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

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

chi := DirichletCharacter("576.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 576 = 2^{6} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	576.bb (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:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 144)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			529.7
Character	$\chi$	$=$	576.529
Dual form			576.2.bb.e.49.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.841300 - 1.51401i) q^{3} +(-0.0691269 - 0.0185225i) q^{5} +(-1.28192 - 0.740118i) q^{7} +(-1.58443 + 2.54747i) q^{9} +O(q^{10})$	\(q+(-0.841300 - 1.51401i) q^{3} +(-0.0691269 - 0.0185225i) q^{5} +(-1.28192 - 0.740118i) q^{7} +(-1.58443 + 2.54747i) q^{9} +(-0.587070 - 2.19098i) q^{11} +(0.104109 - 0.388539i) q^{13} +(0.0301133 + 0.120242i) q^{15} -0.851000 q^{17} +(-3.75230 - 3.75230i) q^{19} +(-0.0420615 + 2.56350i) q^{21} +(-7.44629 + 4.29912i) q^{23} +(-4.32569 - 2.49744i) q^{25} +(5.18986 + 0.255647i) q^{27} +(-4.77230 + 1.27873i) q^{29} +(4.50318 + 7.79974i) q^{31} +(-2.82325 + 2.73210i) q^{33} +(0.0749065 + 0.0749065i) q^{35} +(4.13315 - 4.13315i) q^{37} +(-0.675837 + 0.169257i) q^{39} +(-2.05305 + 1.18533i) q^{41} +(0.669562 + 2.49884i) q^{43} +(0.156712 - 0.146751i) q^{45} +(-3.42005 + 5.92370i) q^{47} +(-2.40445 - 4.16463i) q^{49} +(0.715947 + 1.28842i) q^{51} +(3.95421 - 3.95421i) q^{53} +0.162329i q^{55} +(-2.52419 + 8.83782i) q^{57} +(-13.7811 - 3.69264i) q^{59} +(-3.28936 + 0.881382i) q^{61} +(3.91654 - 2.09299i) q^{63} +(-0.0143934 + 0.0249301i) q^{65} +(1.73506 - 6.47532i) q^{67} +(12.7735 + 7.65687i) q^{69} -0.362864i q^{71} -15.8744i q^{73} +(-0.141931 + 8.65022i) q^{75} +(-0.869003 + 3.24316i) q^{77} +(5.45338 - 9.44553i) q^{79} +(-3.97918 - 8.07255i) q^{81} +(5.37105 - 1.43917i) q^{83} +(0.0588270 + 0.0157627i) q^{85} +(5.95094 + 6.14948i) q^{87} +13.1832i q^{89} +(-0.421024 + 0.421024i) q^{91} +(8.02033 - 13.3798i) q^{93} +(0.189883 + 0.328887i) q^{95} +(-0.627593 + 1.08702i) q^{97} +(6.51161 + 1.97590i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) $ 72 * q - 2 * q^3 + 4 * q^5	$ 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) $ 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$65$	$127$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$e\left(\frac{3}{4}\right)$

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
$3$	−0.841300	−	1.51401i	−0.485725	−	0.874112i
$3$	−0.841300	−	1.51401i	−0.485725	−	0.874112i
$4$		0			0
$5$	−0.0691269	−	0.0185225i	−0.0309145	−	0.00828352i	0.243329	−	0.969944i	$-0.421761\pi$
$5$	−0.0691269	−	0.0185225i	−0.0309145	−	0.00828352i	−0.274243	+	0.961660i	$0.588427\pi$
$6$		0			0
$7$	−1.28192	−	0.740118i	−0.484521	−	0.279738i	0.237778	−	0.971320i	$-0.423581\pi$
$7$	−1.28192	−	0.740118i	−0.484521	−	0.279738i	−0.722299	+	0.691581i	$0.756914\pi$
$8$		0			0
$9$	−1.58443	+	2.54747i	−0.528142	+	0.849156i
$10$		0			0
$11$	−0.587070	−	2.19098i	−0.177008	−	0.660604i	−0.996201	−	0.0870855i	$-0.972245\pi$
$11$	−0.587070	−	2.19098i	−0.177008	−	0.660604i	0.819192	−	0.573519i	$-0.194422\pi$
$12$		0			0
$13$	0.104109	−	0.388539i	0.0288745	−	0.107761i	−0.949985	−	0.312297i	$-0.898902\pi$
$13$	0.104109	−	0.388539i	0.0288745	−	0.107761i	0.978859	+	0.204535i	$0.0655684\pi$
$14$		0			0
$15$	0.0301133	+	0.120242i	0.00777523	+	0.0310462i
$16$		0			0
$17$	−0.851000			−0.206398			−0.103199	−	0.994661i	$-0.532908\pi$
$17$	−0.851000			−0.206398			−0.103199	+	0.994661i	$0.532908\pi$
$18$		0			0
$19$	−3.75230	−	3.75230i	−0.860837	−	0.860837i	0.130598	−	0.991435i	$-0.458310\pi$
$19$	−3.75230	−	3.75230i	−0.860837	−	0.860837i	−0.991435	+	0.130598i	$0.958310\pi$
$20$		0			0
$21$	−0.0420615	+	2.56350i	−0.00917857	+	0.559401i
$22$		0			0
$23$	−7.44629	+	4.29912i	−1.55266	+	0.896428i	−0.554734	+	0.832028i	$0.687180\pi$
$23$	−7.44629	+	4.29912i	−1.55266	+	0.896428i	−0.997924	+	0.0643999i	$0.979487\pi$
$24$		0			0
$25$	−4.32569	−	2.49744i	−0.865138	−	0.499488i
$26$		0			0
$27$	5.18986	+	0.255647i	0.998789	+	0.0491992i
$28$		0			0
$29$	−4.77230	+	1.27873i	−0.886193	+	0.237455i	−0.673077	−	0.739572i	$-0.735028\pi$
$29$	−4.77230	+	1.27873i	−0.886193	+	0.237455i	−0.213116	+	0.977027i	$0.568361\pi$
$30$		0			0
$31$	4.50318	+	7.79974i	0.808796	+	1.40088i	0.913698	+	0.406393i	$0.133214\pi$
$31$	4.50318	+	7.79974i	0.808796	+	1.40088i	−0.104902	+	0.994483i	$0.533453\pi$
$32$		0			0
$33$	−2.82325	+	2.73210i	−0.491464	+	0.475597i
$34$		0			0
$35$	0.0749065	+	0.0749065i	0.0126615	+	0.0126615i
$36$		0			0
$37$	4.13315	−	4.13315i	0.679485	−	0.679485i	−0.280399	−	0.959884i	$-0.590467\pi$
$37$	4.13315	−	4.13315i	0.679485	−	0.679485i	0.959884	+	0.280399i	$0.0904666\pi$
$38$		0			0
$39$	−0.675837	+	0.169257i	−0.108220	+	0.0271028i
$40$		0			0
$41$	−2.05305	+	1.18533i	−0.320633	+	0.185118i	−0.651675	−	0.758499i	$-0.725933\pi$
$41$	−2.05305	+	1.18533i	−0.320633	+	0.185118i	0.331042	+	0.943616i	$0.392600\pi$
$42$		0			0
$43$	0.669562	+	2.49884i	0.102107	+	0.381070i	0.998001	−	0.0631989i	$-0.0201303\pi$
$43$	0.669562	+	2.49884i	0.102107	+	0.381070i	−0.895894	+	0.444269i	$0.853464\pi$
$44$		0			0
$45$	0.156712	−	0.146751i	0.0233613	−	0.0218764i
$46$		0			0
$47$	−3.42005	+	5.92370i	−0.498865	+	0.864060i	−0.999999	−	0.00130966i	$-0.999583\pi$
$47$	−3.42005	+	5.92370i	−0.498865	+	0.864060i	0.501134	+	0.865370i	$0.332916\pi$
$48$		0			0
$49$	−2.40445	−	4.16463i	−0.343493	−	0.594947i
$50$		0			0
$51$	0.715947	+	1.28842i	0.100253	+	0.180415i
$52$		0			0
$53$	3.95421	−	3.95421i	0.543152	−	0.543152i	−0.381300	−	0.924452i	$-0.624523\pi$
$53$	3.95421	−	3.95421i	0.543152	−	0.543152i	0.924452	+	0.381300i	$0.124523\pi$
$54$		0			0
$55$			0.162329i			0.0218885i
$56$		0			0
$57$	−2.52419	+	8.83782i	−0.334338	+	1.17060i
$58$		0			0
$59$	−13.7811	−	3.69264i	−1.79415	−	0.480741i	−0.801109	−	0.598518i	$-0.795756\pi$
$59$	−13.7811	−	3.69264i	−1.79415	−	0.480741i	−0.993040	+	0.117777i	$0.962423\pi$
$60$		0			0
$61$	−3.28936	+	0.881382i	−0.421160	+	0.112849i	−0.463173	−	0.886268i	$-0.653289\pi$
$61$	−3.28936	+	0.881382i	−0.421160	+	0.112849i	0.0420139	+	0.999117i	$0.486623\pi$
$62$		0			0
$63$	3.91654	−	2.09299i	0.493438	−	0.263692i
$64$		0			0
$65$	−0.0143934	+	0.0249301i	−0.00178528	+	0.00309220i
$66$		0			0
$67$	1.73506	−	6.47532i	0.211971	−	0.791086i	−0.775240	−	0.631667i	$-0.782371\pi$
$67$	1.73506	−	6.47532i	0.211971	−	0.791086i	0.987211	−	0.159419i	$-0.0509622\pi$
$68$		0			0
$69$	12.7735	+	7.65687i	1.53774	+	0.921779i
$70$		0			0
$71$		−	0.362864i		−	0.0430640i	−0.999768	−	0.0215320i	$-0.993146\pi$
$71$		−	0.362864i		−	0.0430640i	0.999768	−	0.0215320i	$-0.00685439\pi$
$72$		0			0
$73$		−	15.8744i		−	1.85796i	−0.370128	−	0.928981i	$-0.620686\pi$
$73$		−	15.8744i		−	1.85796i	0.370128	−	0.928981i	$-0.379314\pi$
$74$		0			0
$75$	−0.141931	+	8.65022i	−0.0163888	+	0.998841i
$76$		0			0
$77$	−0.869003	+	3.24316i	−0.0990321	+	0.369593i
$78$		0			0
$79$	5.45338	−	9.44553i	0.613553	−	1.06271i	−0.377083	−	0.926179i	$-0.623073\pi$
$79$	5.45338	−	9.44553i	0.613553	−	1.06271i	0.990637	−	0.136526i	$-0.0435937\pi$
$80$		0			0
$81$	−3.97918	−	8.07255i	−0.442131	−	0.896950i
$82$		0			0
$83$	5.37105	−	1.43917i	0.589549	−	0.157969i	0.0483022	−	0.998833i	$-0.484619\pi$
$83$	5.37105	−	1.43917i	0.589549	−	0.157969i	0.541247	+	0.840863i	$0.317952\pi$
$84$		0			0
$85$	0.0588270	+	0.0157627i	0.00638069	+	0.00170970i
$86$		0			0
$87$	5.95094	+	6.14948i	0.638008	+	0.659294i
$88$		0			0
$89$			13.1832i			1.39741i	0.715408	+	0.698707i	$0.246241\pi$
$89$			13.1832i			1.39741i	−0.715408	+	0.698707i	$0.753759\pi$
$90$		0			0
$91$	−0.421024	+	0.421024i	−0.0441353	+	0.0441353i
$92$		0			0
$93$	8.02033	−	13.3798i	0.831669	−	1.38742i
$94$		0			0
$95$	0.189883	+	0.328887i	0.0194816	+	0.0337431i
$96$		0			0
$97$	−0.627593	+	1.08702i	−0.0637224	+	0.110370i	−0.896127	−	0.443799i	$-0.853631\pi$
$97$	−0.627593	+	1.08702i	−0.0637224	+	0.110370i	0.832404	+	0.554169i	$0.186964\pi$
$98$		0			0
$99$	6.51161	+	1.97590i	0.654442	+	0.198585i
$100$		0			0
$101$	−1.43047	−	5.33858i	−0.142337	−	0.531209i	−0.999860	−	0.0167625i	$-0.994664\pi$
$101$	−1.43047	−	5.33858i	−0.142337	−	0.531209i	0.857522	−	0.514446i	$-0.172003\pi$
$102$		0			0
$103$	9.59933	−	5.54217i	0.945850	−	0.546087i	0.0540605	−	0.998538i	$-0.482784\pi$
$103$	9.59933	−	5.54217i	0.945850	−	0.546087i	0.891789	+	0.452451i	$0.149450\pi$
$104$		0			0
$105$	0.0503900	−	0.176428i	0.00491756	−	0.0172176i
$106$		0			0
$107$	6.90288	−	6.90288i	0.667327	−	0.667327i	−0.289770	−	0.957096i	$-0.593579\pi$
$107$	6.90288	−	6.90288i	0.667327	−	0.667327i	0.957096	+	0.289770i	$0.0935787\pi$
$108$		0			0
$109$	9.39169	+	9.39169i	0.899560	+	0.899560i	0.995397	−	0.0958367i	$-0.0305527\pi$
$109$	9.39169	+	9.39169i	0.899560	+	0.899560i	−0.0958367	+	0.995397i	$0.530553\pi$
$110$		0			0
$111$	−9.73483	−	2.78039i	−0.923989	−	0.263903i
$112$		0			0
$113$	−5.81166	−	10.0661i	−0.546715	−	0.946938i	−0.998497	−	0.0548097i	$-0.982545\pi$
$113$	−5.81166	−	10.0661i	−0.546715	−	0.946938i	0.451782	−	0.892128i	$-0.350789\pi$
$114$		0			0
$115$	0.594369	−	0.159261i	0.0554252	−	0.0148511i
$116$		0			0
$117$	0.824837	+	0.880825i	0.0762562	+	0.0814323i
$118$		0			0
$119$	1.09092	+	0.629841i	0.100004	+	0.0577374i
$120$		0			0
$121$	5.07055	−	2.92749i	0.460959	−	0.266135i
$122$		0			0
$123$	3.52183	+	2.11111i	0.317553	+	0.190353i
$124$		0			0
$125$	0.505785	+	0.505785i	0.0452388	+	0.0452388i
$126$		0			0
$127$	10.1965			0.904796			0.452398	−	0.891816i	$-0.350569\pi$
$127$	10.1965			0.904796			0.452398	+	0.891816i	$0.350569\pi$
$128$		0			0
$129$	3.21996	−	3.11600i	0.283501	−	0.274348i
$130$		0			0
$131$	1.82077	−	6.79522i	0.159082	−	0.593701i	−0.839639	−	0.543144i	$-0.817234\pi$
$131$	1.82077	−	6.79522i	0.159082	−	0.593701i	0.998721	−	0.0505571i	$-0.0160997\pi$
$132$		0			0
$133$	2.03301	+	7.58731i	0.176285	+	0.657903i
$134$		0			0
$135$	−0.354024	−	0.113801i	−0.0304695	−	0.00979445i
$136$		0			0
$137$	12.5671	+	7.25564i	1.07368	+	0.619891i	0.929185	−	0.369614i	$-0.120510\pi$
$137$	12.5671	+	7.25564i	1.07368	+	0.619891i	0.144497	+	0.989505i	$0.453843\pi$
$138$		0			0
$139$	−5.09570	−	1.36539i	−0.432212	−	0.115811i	0.0361523	−	0.999346i	$-0.488490\pi$
$139$	−5.09570	−	1.36539i	−0.432212	−	0.115811i	−0.468364	+	0.883535i	$0.655157\pi$
$140$		0			0
$141$	11.8458	+	0.194364i	0.997596	+	0.0163684i
$142$		0			0
$143$	−0.912398			−0.0762986
$144$		0			0
$145$	0.353579			0.0293632
$146$		0			0
$147$	−4.28241	+	7.14406i	−0.353207	+	0.589232i
$148$		0			0
$149$	−19.3330	−	5.18027i	−1.58382	−	0.424384i	−0.643717	−	0.765264i	$-0.722609\pi$
$149$	−19.3330	−	5.18027i	−1.58382	−	0.424384i	−0.940107	+	0.340879i	$0.889275\pi$
$150$		0			0
$151$	−11.0910	−	6.40336i	−0.902569	−	0.521098i	−0.0245362	−	0.999699i	$-0.507811\pi$
$151$	−11.0910	−	6.40336i	−0.902569	−	0.521098i	−0.878033	+	0.478601i	$0.841144\pi$
$152$		0			0
$153$	1.34835	−	2.16790i	0.109007	−	0.175264i
$154$		0			0
$155$	−0.166821	−	0.622583i	−0.0133993	−	0.0500070i
$156$		0			0
$157$	1.98067	−	7.39195i	0.158074	−	0.589942i	−0.840748	−	0.541427i	$-0.817884\pi$
$157$	1.98067	−	7.39195i	0.158074	−	0.589942i	0.998822	−	0.0485153i	$-0.0154490\pi$
$158$		0			0
$159$	−9.31337	−	2.66002i	−0.738598	−	0.210953i
$160$		0			0
$161$	12.7274			1.00306
$162$		0			0
$163$	−10.3989	−	10.3989i	−0.814504	−	0.814504i	0.170802	−	0.985305i	$-0.445364\pi$
$163$	−10.3989	−	10.3989i	−0.814504	−	0.814504i	−0.985305	+	0.170802i	$0.945364\pi$
$164$		0			0
$165$	0.245768	−	0.136568i	0.0191330	−	0.0106318i
$166$		0			0
$167$	5.44443	−	3.14334i	0.421302	−	0.243239i	−0.274332	−	0.961635i	$-0.588457\pi$
$167$	5.44443	−	3.14334i	0.421302	−	0.243239i	0.695634	+	0.718396i	$0.255123\pi$
$168$		0			0
$169$	11.1182	+	6.41910i	0.855247	+	0.493777i
$170$		0			0
$171$	15.5041	−	3.61362i	1.18563	−	0.276340i
$172$		0			0
$173$	−11.3578	+	3.04333i	−0.863521	+	0.231380i	−0.663284	−	0.748368i	$-0.730838\pi$
$173$	−11.3578	+	3.04333i	−0.863521	+	0.231380i	−0.200237	+	0.979748i	$0.564171\pi$
$174$		0			0
$175$	3.69680	+	6.40305i	0.279452	+	0.484025i
$176$		0			0
$177$	6.00338	+	23.9713i	0.451242	+	1.80179i
$178$		0			0
$179$	9.21801	+	9.21801i	0.688986	+	0.688986i	0.962008	−	0.273021i	$-0.0880230\pi$
$179$	9.21801	+	9.21801i	0.688986	+	0.688986i	−0.273021	+	0.962008i	$0.588023\pi$
$180$		0			0
$181$	−11.5919	+	11.5919i	−0.861621	+	0.861621i	−0.991526	−	0.129905i	$-0.958533\pi$
$181$	−11.5919	+	11.5919i	−0.861621	+	0.861621i	0.129905	+	0.991526i	$0.458533\pi$
$182$		0			0
$183$	4.10176	+	4.23861i	0.303211	+	0.313327i
$184$		0			0
$185$	−0.362268	+	0.209155i	−0.0266345	+	0.0153774i
$186$		0			0
$187$	0.499597	+	1.86452i	0.0365341	+	0.136347i
$188$		0			0
$189$	−6.46379	−	4.16883i	−0.470171	−	0.303238i
$190$		0			0
$191$	−11.1864	+	19.3755i	−0.809423	+	1.40196i	0.103842	+	0.994594i	$0.466887\pi$
$191$	−11.1864	+	19.3755i	−0.809423	+	1.40196i	−0.913264	+	0.407368i	$0.866447\pi$
$192$		0			0
$193$	7.17911	+	12.4346i	0.516764	+	0.895061i	0.999811	+	0.0194663i	$0.00619671\pi$
$193$	7.17911	+	12.4346i	0.516764	+	0.895061i	−0.483047	+	0.875594i	$0.660470\pi$
$194$		0			0
$195$	0.0498536		0.000817989i	0.00357009		5.85774e-5i
$196$		0			0
$197$	1.57538	−	1.57538i	0.112241	−	0.112241i	−0.648756	−	0.760997i	$-0.724710\pi$
$197$	1.57538	−	1.57538i	0.112241	−	0.112241i	0.760997	+	0.648756i	$0.224710\pi$
$198$		0			0
$199$			1.72755i			0.122463i	0.998124	+	0.0612313i	$0.0195027\pi$
$199$			1.72755i			0.122463i	−0.998124	+	0.0612313i	$0.980497\pi$
$200$		0			0
$201$	−11.2634	+	2.82080i	−0.794457	+	0.198964i
$202$		0			0
$203$	7.06413	+	1.89283i	0.495804	+	0.132850i
$204$		0			0
$205$	0.163877	−	0.0439106i	0.0114456	−	0.00306685i
$206$		0			0
$207$	0.846243	−	25.7808i	0.0588179	−	1.79189i
$208$		0			0
$209$	−6.01834	+	10.4241i	−0.416297	+	0.721048i
$210$		0			0
$211$	−3.19942	+	11.9404i	−0.220257	+	0.822011i	0.763992	+	0.645225i	$0.223236\pi$
$211$	−3.19942	+	11.9404i	−0.220257	+	0.822011i	−0.984249	+	0.176785i	$0.943430\pi$
$212$		0			0
$213$	−0.549378	+	0.305278i	−0.0376428	+	0.0209173i
$214$		0			0
$215$		−	0.185139i		−	0.0126264i
$216$		0			0
$217$		−	13.3316i		−	0.905005i
$218$		0			0
$219$	−24.0340	+	13.3552i	−1.62407	+	0.902458i
$220$		0			0
$221$	−0.0885965	+	0.330647i	−0.00595964	+	0.0222417i
$222$		0			0
$223$	7.22081	−	12.5068i	0.483541	−	0.837518i	−0.516280	−	0.856420i	$-0.672684\pi$
$223$	7.22081	−	12.5068i	0.483541	−	0.837518i	0.999821	+	0.0189019i	$0.00601703\pi$
$224$		0			0
$225$	13.2159	−	7.06255i	0.881059	−	0.470837i
$226$		0			0
$227$	1.61577	−	0.432945i	0.107243	−	0.0287356i	−0.204799	−	0.978804i	$-0.565654\pi$
$227$	1.61577	−	0.432945i	0.107243	−	0.0287356i	0.312041	+	0.950069i	$0.398987\pi$
$228$		0			0
$229$	−19.6207	−	5.25735i	−1.29657	−	0.347416i	−0.456420	−	0.889765i	$-0.650868\pi$
$229$	−19.6207	−	5.25735i	−1.29657	−	0.347416i	−0.840153	+	0.542349i	$0.817535\pi$
$230$		0			0
$231$	5.64126	−	1.41280i	0.371168	−	0.0929553i
$232$		0			0
$233$		−	23.5814i		−	1.54487i	−0.635094	−	0.772435i	$-0.719039\pi$
$233$		−	23.5814i		−	1.54487i	0.635094	−	0.772435i	$-0.280961\pi$
$234$		0			0
$235$	0.346139	−	0.346139i	0.0225796	−	0.0225796i
$236$		0			0
$237$	−18.8885	−	0.309920i	−1.22694	−	0.0201315i
$238$		0			0
$239$	−4.28400	−	7.42011i	−0.277109	−	0.479967i	0.693556	−	0.720403i	$-0.256043\pi$
$239$	−4.28400	−	7.42011i	−0.277109	−	0.479967i	−0.970665	+	0.240436i	$0.922710\pi$
$240$		0			0
$241$	3.69013	−	6.39149i	0.237702	−	0.411712i	−0.722352	−	0.691525i	$-0.756939\pi$
$241$	3.69013	−	6.39149i	0.237702	−	0.411712i	0.960055	+	0.279813i	$0.0902725\pi$
$242$		0			0
$243$	−8.87421	+	12.8159i	−0.569281	+	0.822143i
$244$		0			0
$245$	0.0890729	+	0.332424i	0.00569066	+	0.0212378i
$246$		0			0
$247$	−1.84856	+	1.06727i	−0.117621	+	0.0679086i
$248$		0			0
$249$	−6.69758	−	6.92103i	−0.424442	−	0.438602i
$250$		0			0
$251$	8.74661	−	8.74661i	0.552081	−	0.552081i	−0.374960	−	0.927041i	$-0.622343\pi$
$251$	8.74661	−	8.74661i	0.552081	−	0.552081i	0.927041	+	0.374960i	$0.122343\pi$
$252$		0			0
$253$	13.7908	+	13.7908i	0.867017	+	0.867017i
$254$		0			0
$255$	−0.0256265	−	0.102326i	−0.00160479	−	0.00640788i
$256$		0			0
$257$	2.21071	+	3.82905i	0.137900	+	0.238850i	0.926702	−	0.375798i	$-0.122631\pi$
$257$	2.21071	+	3.82905i	0.137900	+	0.238850i	−0.788802	+	0.614648i	$0.789298\pi$
$258$		0			0
$259$	−8.35739	+	2.23936i	−0.519303	+	0.139147i
$260$		0			0
$261$	4.30383	−	14.1833i	0.266400	−	0.877926i
$262$		0			0
$263$	9.48601	+	5.47675i	0.584932	+	0.337711i	0.763091	−	0.646291i	$-0.223681\pi$
$263$	9.48601	+	5.47675i	0.584932	+	0.337711i	−0.178159	+	0.984002i	$0.557014\pi$
$264$		0			0
$265$	−0.346584	+	0.200100i	−0.0212905	+	0.0122921i
$266$		0			0
$267$	19.9594	−	11.0910i	1.22150	−	0.678759i
$268$		0			0
$269$	−10.6376	−	10.6376i	−0.648586	−	0.648586i	0.304065	−	0.952651i	$-0.401656\pi$
$269$	−10.6376	−	10.6376i	−0.648586	−	0.648586i	−0.952651	+	0.304065i	$0.901656\pi$
$270$		0			0
$271$	−19.1209			−1.16151			−0.580757	−	0.814077i	$-0.697243\pi$
$271$	−19.1209			−1.16151			−0.580757	+	0.814077i	$0.697243\pi$
$272$		0			0
$273$	0.991640	+	0.283225i	0.0600168	+	0.0171416i
$274$		0			0
$275$	−2.93235	+	10.9437i	−0.176827	+	0.659928i
$276$		0			0
$277$	2.70176	+	10.0831i	0.162333	+	0.605835i	0.998365	+	0.0571550i	$0.0182029\pi$
$277$	2.70176	+	10.0831i	0.162333	+	0.605835i	−0.836032	+	0.548680i	$0.815130\pi$
$278$		0			0
$279$	−27.0046	−	0.886412i	−1.61672	−	0.0530681i
$280$		0			0
$281$	12.1779	+	7.03092i	0.726473	+	0.419429i	0.817130	−	0.576453i	$-0.195564\pi$
$281$	12.1779	+	7.03092i	0.726473	+	0.419429i	−0.0906576	+	0.995882i	$0.528897\pi$
$282$		0			0
$283$	−24.6641	−	6.60872i	−1.46613	−	0.392848i	−0.564526	−	0.825415i	$-0.690941\pi$
$283$	−24.6641	−	6.60872i	−1.46613	−	0.392848i	−0.901601	+	0.432568i	$0.857608\pi$
$284$		0			0
$285$	0.338188	−	0.564177i	0.0200325	−	0.0334190i
$286$		0			0
$287$	3.50914			0.207138
$288$		0			0
$289$	−16.2758			−0.957400
$290$		0			0
$291$	2.17375	+	0.0356666i	0.127428	+	0.00209081i
$292$		0			0
$293$	−13.2569	−	3.55218i	−0.774476	−	0.207520i	−0.150128	−	0.988667i	$-0.547969\pi$
$293$	−13.2569	−	3.55218i	−0.774476	−	0.207520i	−0.624348	+	0.781146i	$0.714635\pi$
$294$		0			0
$295$	0.884250	+	0.510522i	0.0514830	+	0.0297237i
$296$		0			0
$297$	−2.48670	−	11.5209i	−0.144293	−	0.668513i
$298$		0			0
$299$	0.895150	+	3.34075i	0.0517679	+	0.193200i
$300$		0			0
$301$	0.991111	−	3.69888i	0.0571267	−	0.213200i
$302$		0			0
$303$	−6.87919	+	6.65709i	−0.395199	+	0.382440i
$304$		0			0
$305$	0.243709			0.0139547
$306$		0			0
$307$	14.1122	+	14.1122i	0.805426	+	0.805426i	0.983938	−	0.178512i	$-0.0571283\pi$
$307$	14.1122	+	14.1122i	0.805426	+	0.805426i	−0.178512	+	0.983938i	$0.557128\pi$
$308$		0			0
$309$	−16.4668	−	9.87080i	−0.936763	−	0.561530i
$310$		0			0
$311$	11.2914	−	6.51907i	0.640274	−	0.369662i	−0.144446	−	0.989513i	$-0.546140\pi$
$311$	11.2914	−	6.51907i	0.640274	−	0.369662i	0.784720	+	0.619850i	$0.212807\pi$
$312$		0			0
$313$	−6.50512	−	3.75573i	−0.367691	−	0.212287i	0.304758	−	0.952430i	$-0.401424\pi$
$313$	−6.50512	−	3.75573i	−0.367691	−	0.212287i	−0.672449	+	0.740143i	$0.734758\pi$
$314$		0			0
$315$	−0.309506	+	0.0721380i	−0.0174387	+	0.00406451i
$316$		0			0
$317$	1.45660	−	0.390294i	0.0818107	−	0.0219211i	−0.217682	−	0.976020i	$-0.569849\pi$
$317$	1.45660	−	0.390294i	0.0818107	−	0.0219211i	0.299492	+	0.954099i	$0.403183\pi$
$318$		0			0
$319$	5.60335	+	9.70528i	0.313727	+	0.543391i
$320$		0			0
$321$	−16.2584	−	4.64361i	−0.907456	−	0.259181i
$322$		0			0
$323$	3.19321	+	3.19321i	0.177675	+	0.177675i
$324$		0			0
$325$	−1.42069	+	1.42069i	−0.0788059	+	0.0788059i
$326$		0			0
$327$	6.31784	−	22.1203i	0.349377	−	1.22326i
$328$		0			0
$329$	8.76847	−	5.06248i	0.483422	−	0.279104i
$330$		0			0
$331$	5.29948	+	19.7779i	0.291286	+	1.08709i	0.944122	+	0.329595i	$0.106912\pi$
$331$	5.29948	+	19.7779i	0.291286	+	1.08709i	−0.652837	+	0.757499i	$0.726421\pi$
$332$		0			0
$333$	3.98039	+	17.0777i	0.218124	+	0.935854i
$334$		0			0
$335$	−0.239878	+	0.415481i	−0.0131059	+	0.0227002i
$336$		0			0
$337$	4.81432	+	8.33864i	0.262253	+	0.454235i	0.966840	−	0.255382i	$-0.0822013\pi$
$337$	4.81432	+	8.33864i	0.262253	+	0.454235i	−0.704588	+	0.709617i	$0.748868\pi$
$338$		0			0
$339$	−10.3508	+	17.2675i	−0.562177	+	0.937842i
$340$		0			0
$341$	14.4454	−	14.4454i	0.782261	−	0.782261i
$342$		0			0
$343$			17.4800i			0.943829i
$344$		0			0
$345$	−0.741165	−	0.765892i	−0.0399030	−	0.0412343i
$346$		0			0
$347$	−8.72145	−	2.33691i	−0.468192	−	0.125452i	0.0170070	−	0.999855i	$-0.494586\pi$
$347$	−8.72145	−	2.33691i	−0.468192	−	0.125452i	−0.485199	+	0.874404i	$0.661253\pi$
$348$		0			0
$349$	−26.4971	+	7.09989i	−1.41836	+	0.380048i	−0.884902	−	0.465778i	$-0.845775\pi$
$349$	−26.4971	+	7.09989i	−1.41836	+	0.380048i	−0.533458	+	0.845826i	$0.679108\pi$
$350$		0			0
$351$	0.639638	−	1.98985i	0.0341413	−	0.106210i
$352$		0			0
$353$	−2.21080	+	3.82922i	−0.117669	+	0.203809i	−0.918844	−	0.394622i	$-0.870876\pi$
$353$	−2.21080	+	3.82922i	−0.117669	+	0.203809i	0.801174	+	0.598431i	$0.204209\pi$
$354$		0			0
$355$	−0.00672115	+	0.0250837i	−0.000356722	+	0.00133130i
$356$		0			0
$357$	0.0357943	−	2.18154i	0.00189444	−	0.115459i
$358$		0			0
$359$		−	21.7288i		−	1.14680i	−0.819275	−	0.573400i	$-0.805624\pi$
$359$		−	21.7288i		−	1.14680i	0.819275	−	0.573400i	$-0.194376\pi$
$360$		0			0
$361$			9.15954i			0.482081i
$362$		0			0
$363$	−8.69809	−	5.21395i	−0.456531	−	0.273662i
$364$		0			0
$365$	−0.294034	+	1.09735i	−0.0153905	+	0.0574380i
$366$		0			0
$367$	−1.28705	+	2.22924i	−0.0671835	+	0.116365i	−0.897660	−	0.440688i	$-0.854735\pi$
$367$	−1.28705	+	2.22924i	−0.0671835	+	0.116365i	0.830477	+	0.557053i	$0.188068\pi$
$368$		0			0
$369$	0.233322	−	7.10816i	0.0121462	−	0.370036i
$370$		0			0
$371$	−7.99556	+	2.14241i	−0.415109	+	0.111228i
$372$		0			0
$373$	1.42780	+	0.382578i	0.0739287	+	0.0198091i	0.295594	−	0.955314i	$-0.404483\pi$
$373$	1.42780	+	0.382578i	0.0739287	+	0.0198091i	−0.221665	+	0.975123i	$0.571149\pi$
$374$		0			0
$375$	0.340244	−	1.19128i	0.0175701	−	0.0615174i
$376$		0			0
$377$			1.98735i			0.102354i
$378$		0			0
$379$	−4.66662	+	4.66662i	−0.239708	+	0.239708i	−0.816729	−	0.577021i	$-0.804215\pi$
$379$	−4.66662	+	4.66662i	−0.239708	+	0.239708i	0.577021	+	0.816729i	$0.304215\pi$
$380$		0			0
$381$	−8.57835	−	15.4376i	−0.439482	−	0.790893i
$382$		0			0
$383$	1.48376	+	2.56995i	0.0758165	+	0.131318i	0.901441	−	0.432902i	$-0.142510\pi$
$383$	1.48376	+	2.56995i	0.0758165	+	0.131318i	−0.825625	+	0.564220i	$0.809177\pi$
$384$		0			0
$385$	0.120143	−	0.208094i	0.00612305	−	0.0106054i
$386$		0			0
$387$	−7.42659	−	2.25354i	−0.377515	−	0.114554i
$388$		0			0
$389$	7.85632	+	29.3202i	0.398331	+	1.48659i	0.816031	+	0.578008i	$0.196170\pi$
$389$	7.85632	+	29.3202i	0.398331	+	1.48659i	−0.417700	+	0.908585i	$0.637164\pi$
$390$		0			0
$391$	6.33679	−	3.65855i	0.320465	−	0.185021i
$392$		0			0
$393$	−11.8198	+	2.96016i	−0.596231	+	0.149320i
$394$		0			0
$395$	−0.551930	+	0.551930i	−0.0277706	+	0.0277706i
$396$		0			0
$397$	11.6823	+	11.6823i	0.586319	+	0.586319i	0.936632	−	0.350314i	$-0.113925\pi$
$397$	11.6823	+	11.6823i	0.586319	+	0.586319i	−0.350314	+	0.936632i	$0.613925\pi$
$398$		0			0
$399$	9.77685	−	9.46120i	0.489455	−	0.473652i
$400$		0			0
$401$	0.390756	+	0.676809i	0.0195134	+	0.0337982i	0.875617	−	0.483006i	$-0.160455\pi$
$401$	0.390756	+	0.676809i	0.0195134	+	0.0337982i	−0.856104	+	0.516804i	$0.827122\pi$
$402$		0			0
$403$	3.49932	−	0.937641i	0.174314	−	0.0467072i
$404$		0			0
$405$	0.125545	+	0.631735i	0.00623836	+	0.0313912i
$406$		0			0
$407$	−11.4821	−	6.62918i	−0.569145	−	0.328596i
$408$		0			0
$409$	−26.9864	+	15.5806i	−1.33439	+	0.770412i	−0.985969	−	0.166926i	$-0.946616\pi$
$409$	−26.9864	+	15.5806i	−1.33439	+	0.770412i	−0.348423	+	0.937338i	$0.613283\pi$
$410$		0			0
$411$	0.412344	−	25.1309i	0.0203394	−	1.23962i
$412$		0			0
$413$	14.9333	+	14.9333i	0.734822	+	0.734822i
$414$		0			0
$415$	−0.397941			−0.0195342
$416$		0			0
$417$	2.21981	+	8.86363i	0.108705	+	0.434054i
$418$		0			0
$419$	5.93759	−	22.1594i	0.290070	−	1.08256i	−0.654984	−	0.755643i	$-0.727325\pi$
$419$	5.93759	−	22.1594i	0.290070	−	1.08256i	0.945054	−	0.326914i	$-0.106009\pi$
$420$		0			0
$421$	−6.71096	−	25.0456i	−0.327072	−	1.22065i	−0.912212	−	0.409718i	$-0.865627\pi$
$421$	−6.71096	−	25.0456i	−0.327072	−	1.22065i	0.585140	−	0.810932i	$-0.301039\pi$
$422$		0			0
$423$	−9.67161	−	18.0981i	−0.470250	−	0.879961i
$424$		0			0
$425$	3.68116	+	2.12532i	0.178563	+	0.103093i
$426$		0			0
$427$	4.86903	+	1.30465i	0.235629	+	0.0631366i
$428$		0			0
$429$	0.767601	+	1.38138i	0.0370601	+	0.0666935i
$430$		0			0
$431$	−8.53959			−0.411338			−0.205669	−	0.978622i	$-0.565937\pi$
$431$	−8.53959			−0.411338			−0.205669	+	0.978622i	$0.565937\pi$
$432$		0			0
$433$	−9.28283			−0.446104			−0.223052	−	0.974807i	$-0.571602\pi$
$433$	−9.28283			−0.446104			−0.223052	+	0.974807i	$0.571602\pi$
$434$		0			0
$435$	−0.297467	−	0.535321i	−0.0142624	−	0.0256667i
$436$		0			0
$437$	44.0723	+	11.8091i	2.10826	+	0.564908i
$438$		0			0
$439$	12.0947	+	6.98286i	0.577247	+	0.333274i	0.760038	−	0.649878i	$-0.225180\pi$
$439$	12.0947	+	6.98286i	0.577247	+	0.333274i	−0.182792	+	0.983152i	$0.558513\pi$
$440$		0			0
$441$	14.4189	+	0.473295i	0.686616	+	0.0225378i
$442$		0			0
$443$	3.19925	+	11.9398i	0.152001	+	0.567276i	0.999344	+	0.0362287i	$0.0115345\pi$
$443$	3.19925	+	11.9398i	0.152001	+	0.567276i	−0.847343	+	0.531047i	$0.821799\pi$
$444$		0			0
$445$	0.244185	−	0.911312i	0.0115755	−	0.0432004i
$446$		0			0
$447$	8.42193	+	33.6285i	0.398344	+	1.59057i
$448$		0			0
$449$	15.5226			0.732554			0.366277	−	0.930506i	$-0.380632\pi$
$449$	15.5226			0.732554			0.366277	+	0.930506i	$0.380632\pi$
$450$		0			0
$451$	3.80232	+	3.80232i	0.179044	+	0.179044i
$452$		0			0
$453$	−0.363908	+	22.1789i	−0.0170979	+	1.04206i
$454$		0			0
$455$	0.0369025	−	0.0213057i	0.00173002	−	0.000998825i
$456$		0			0
$457$	23.3712	+	13.4934i	1.09326	+	0.631194i	0.934442	−	0.356114i	$-0.115899\pi$
$457$	23.3712	+	13.4934i	1.09326	+	0.631194i	0.158817	+	0.987308i	$0.449232\pi$
$458$		0			0
$459$	−4.41657	−	0.217555i	−0.206148	−	0.0101546i
$460$		0			0
$461$	22.8014	−	6.10962i	1.06197	−	0.284554i	0.314779	−	0.949165i	$-0.398070\pi$
$461$	22.8014	−	6.10962i	1.06197	−	0.284554i	0.747189	+	0.664611i	$0.231403\pi$
$462$		0			0
$463$	−11.7055	−	20.2745i	−0.544001	−	0.942238i	−0.998669	−	0.0515769i	$-0.983575\pi$
$463$	−11.7055	−	20.2745i	−0.544001	−	0.942238i	0.454668	−	0.890661i	$-0.349758\pi$
$464$		0			0
$465$	−0.802248	+	0.776346i	−0.0372033	+	0.0360022i
$466$		0			0
$467$	−17.4581	−	17.4581i	−0.807865	−	0.807865i	0.176446	−	0.984310i	$-0.443540\pi$
$467$	−17.4581	−	17.4581i	−0.807865	−	0.807865i	−0.984310	+	0.176446i	$0.943540\pi$
$468$		0			0
$469$	−7.01671	+	7.01671i	−0.324001	+	0.324001i
$470$		0			0
$471$	−12.8578	+	3.22011i	−0.592456	+	0.148375i
$472$		0			0
$473$	5.08182	−	2.93399i	0.233662	−	0.134905i
$474$		0			0
$475$	6.86016	+	25.6024i	0.314766	+	1.17472i
$476$		0			0
$477$	3.80806	+	16.3384i	0.174359	+	0.748082i
$478$		0			0
$479$	9.62715	−	16.6747i	0.439876	−	0.761887i	−0.557804	−	0.829973i	$-0.688356\pi$
$479$	9.62715	−	16.6747i	0.439876	−	0.761887i	0.997679	+	0.0680859i	$0.0216892\pi$
$480$		0			0
$481$	−1.17559	−	2.03618i	−0.0536023	−	0.0928420i
$482$		0			0
$483$	−10.7076	−	19.2694i	−0.487212	−	0.876787i
$484$		0			0
$485$	0.0635180	−	0.0635180i	0.00288420	−	0.00288420i
$486$		0			0
$487$			15.8010i			0.716012i	0.933719	+	0.358006i	$0.116543\pi$
$487$			15.8010i			0.716012i	−0.933719	+	0.358006i	$0.883457\pi$
$488$		0			0
$489$	−6.99539	+	24.4926i	−0.316342	+	1.10759i
$490$		0			0
$491$	10.9388	+	2.93103i	0.493659	+	0.132276i	0.497056	−	0.867719i	$-0.334414\pi$
$491$	10.9388	+	2.93103i	0.493659	+	0.132276i	−0.00339642	+	0.999994i	$0.501081\pi$
$492$		0			0
$493$	4.06122	−	1.08820i	0.182908	−	0.0490101i
$494$		0			0
$495$	−0.413529	−	0.257199i	−0.0185867	−	0.0115602i
$496$		0			0
$497$	−0.268562	+	0.465164i	−0.0120467	+	0.0208654i
$498$		0			0
$499$	1.04051	−	3.88323i	0.0465796	−	0.173837i	−0.938717	−	0.344688i	$-0.887985\pi$
$499$	1.04051	−	3.88323i	0.0465796	−	0.173837i	0.985297	+	0.170850i	$0.0546515\pi$
$500$		0			0
$501$	−9.33943	−	5.59840i	−0.417255	−	0.250118i
$502$		0			0
$503$			24.1846i			1.07834i	0.842198	+	0.539169i	$0.181261\pi$
$503$			24.1846i			1.07834i	−0.842198	+	0.539169i	$0.818739\pi$
$504$		0			0
$505$			0.395536i			0.0176011i
$506$		0			0
$507$	0.364802	−	22.2334i	0.0162014	−	0.987421i
$508$		0			0
$509$	3.36446	−	12.5563i	0.149127	−	0.556550i	−0.850410	−	0.526121i	$-0.823646\pi$
$509$	3.36446	−	12.5563i	0.149127	−	0.556550i	0.999537	−	0.0304290i	$-0.00968734\pi$
$510$		0			0
$511$	−11.7490	+	20.3498i	−0.519743	+	0.900222i
$512$		0			0
$513$	−18.5147	−	20.4332i	−0.817442	−	0.902147i
$514$		0			0
$515$	−0.766227	+	0.205310i	−0.0337640	+	0.00904703i
$516$		0			0
$517$	14.9865	+	4.01562i	0.659105	+	0.176607i
$518$		0			0
$519$	14.1630	+	14.6355i	0.621685	+	0.642427i
$520$		0			0
$521$		−	3.39592i		−	0.148778i	−0.997229	−	0.0743889i	$-0.976299\pi$
$521$		−	3.39592i		−	0.148778i	0.997229	−	0.0743889i	$-0.0237006\pi$
$522$		0			0
$523$	21.4956	−	21.4956i	0.939938	−	0.939938i	−0.0583574	−	0.998296i	$-0.518586\pi$
$523$	21.4956	−	21.4956i	0.939938	−	0.939938i	0.998296	+	0.0583574i	$0.0185863\pi$
$524$		0			0
$525$	6.58413	−	10.9839i	0.287355	−	0.479375i
$526$		0			0
$527$	−3.83221	−	6.63758i	−0.166934	−	0.289138i
$528$		0			0
$529$	25.4648	−	44.1063i	1.10716	−	1.91767i
$530$		0			0
$531$	31.2421	−	29.2562i	1.35579	−	1.26961i
$532$		0			0
$533$	0.246806	+	0.921094i	0.0106904	+	0.0398970i
$534$		0			0
$535$	−0.605034	+	0.349316i	−0.0261579	+	0.0151023i
$536$		0			0
$537$	6.20101	−	21.7112i	0.267593	−	0.936909i
$538$		0			0
$539$	−7.71302	+	7.71302i	−0.332223	+	0.332223i
$540$		0			0
$541$	−14.7438	−	14.7438i	−0.633886	−	0.633886i	0.315154	−	0.949041i	$-0.397944\pi$
$541$	−14.7438	−	14.7438i	−0.633886	−	0.633886i	−0.949041	+	0.315154i	$0.897944\pi$
$542$		0			0
$543$	27.3025	+	7.79795i	1.17166	+	0.334642i
$544$		0			0
$545$	−0.475261	−	0.823176i	−0.0203579	−	0.0352610i
$546$		0			0
$547$	30.6555	−	8.21413i	1.31074	−	0.351211i	0.465236	−	0.885186i	$-0.345969\pi$
$547$	30.6555	−	8.21413i	1.31074	−	0.351211i	0.845500	+	0.533976i	$0.179303\pi$
$548$		0			0
$549$	2.96646	−	9.77603i	0.126606	−	0.417231i
$550$		0			0
$551$	22.7053	+	13.1089i	0.967278	+	0.558458i
$552$		0			0
$553$	−13.9816	+	8.07229i	−0.594559	+	0.343269i
$554$		0			0
$555$	0.621439	+	0.372513i	0.0263786	+	0.0158123i
$556$		0			0
$557$	−16.6150	−	16.6150i	−0.704002	−	0.704002i	0.261265	−	0.965267i	$-0.415860\pi$
$557$	−16.6150	−	16.6150i	−0.704002	−	0.704002i	−0.965267	+	0.261265i	$0.915860\pi$
$558$		0			0
$559$	1.04060			0.0440129
$560$		0			0
$561$	2.40259	−	2.32502i	0.101437	−	0.0981622i
$562$		0			0
$563$	0.625738	−	2.33528i	0.0263717	−	0.0984205i	−0.951486	−	0.307693i	$-0.900443\pi$
$563$	0.625738	−	2.33528i	0.0263717	−	0.0984205i	0.977857	+	0.209273i	$0.0671096\pi$
$564$		0			0
$565$	0.215293	+	0.803484i	0.00905745	+	0.0338028i
$566$		0			0
$567$	−0.873644	+	13.2935i	−0.0366896	+	0.558272i
$568$		0			0
$569$	−8.83926	−	5.10335i	−0.370561	−	0.213943i	0.303143	−	0.952945i	$-0.401964\pi$
$569$	−8.83926	−	5.10335i	−0.370561	−	0.213943i	−0.673703	+	0.739002i	$0.735297\pi$
$570$		0			0
$571$	−20.9394	−	5.61069i	−0.876285	−	0.234800i	−0.207481	−	0.978239i	$-0.566527\pi$
$571$	−20.9394	−	5.61069i	−0.876285	−	0.234800i	−0.668804	+	0.743439i	$0.733193\pi$
$572$		0			0
$573$	38.7458	+	0.635734i	1.61863	+	0.0265582i
$574$		0			0
$575$	42.9471			1.79102
$576$		0			0
$577$	−17.0725			−0.710737			−0.355369	−	0.934726i	$-0.615645\pi$
$577$	−17.0725			−0.710737			−0.355369	+	0.934726i	$0.615645\pi$
$578$		0			0
$579$	12.7862	−	21.3304i	0.531378	−	0.886462i
$580$		0			0
$581$	−7.95043	−	2.13031i	−0.329839	−	0.0883802i
$582$		0			0
$583$	−10.9850	−	6.34217i	−0.454951	−	0.262666i
$584$		0			0
$585$	−0.0407034	−	0.0761668i	−0.00168288	−	0.00314911i
$586$		0			0
$587$	3.63287	+	13.5581i	0.149945	+	0.559602i	0.999485	+	0.0320783i	$0.0102126\pi$
$587$	3.63287	+	13.5581i	0.149945	+	0.559602i	−0.849541	+	0.527523i	$0.823121\pi$
$588$		0			0
$589$	12.3697	−	46.1643i	0.509684	−	1.90217i
$590$		0			0
$591$	−3.71049	−	1.05976i	−0.152629	−	0.0435928i
$592$		0			0
$593$	−27.5850			−1.13278			−0.566390	−	0.824137i	$-0.691660\pi$
$593$	−27.5850			−1.13278			−0.566390	+	0.824137i	$0.691660\pi$
$594$		0			0
$595$	−0.0637455	−	0.0637455i	−0.00261331	−	0.00261331i
$596$		0			0
$597$	2.61552	−	1.45339i	0.107046	−	0.0594832i
$598$		0			0
$599$	−34.8788	+	20.1373i	−1.42511	+	0.822788i	−0.996729	−	0.0808109i	$-0.974249\pi$
$599$	−34.8788	+	20.1373i	−1.42511	+	0.822788i	−0.428380	+	0.903598i	$0.640916\pi$
$600$		0			0
$601$	5.90297	+	3.40808i	0.240787	+	0.139018i	0.615538	−	0.788107i	$-0.288939\pi$
$601$	5.90297	+	3.40808i	0.240787	+	0.139018i	−0.374751	+	0.927125i	$0.622272\pi$
$602$		0			0
$603$	13.7466	+	14.6797i	0.559804	+	0.597802i
$604$		0			0
$605$	−0.404736	+	0.108449i	−0.0164549	+	0.00440907i
$606$		0			0
$607$	1.09235	+	1.89200i	0.0443370	+	0.0767939i	0.887342	−	0.461111i	$-0.152549\pi$
$607$	1.09235	+	1.89200i	0.0443370	+	0.0767939i	−0.843005	+	0.537905i	$0.819216\pi$
$608$		0			0
$609$	−3.07730	−	12.2876i	−0.124699	−	0.497917i
$610$		0			0
$611$	1.94553	+	1.94553i	0.0787077	+	0.0787077i
$612$		0			0
$613$	15.3068	−	15.3068i	0.618236	−	0.618236i	−0.326843	−	0.945079i	$-0.605985\pi$
$613$	15.3068	−	15.3068i	0.618236	−	0.618236i	0.945079	+	0.326843i	$0.105985\pi$
$614$		0			0
$615$	−0.204350	−	0.211168i	−0.00824020	−	0.00851512i
$616$		0			0
$617$	−10.1056	+	5.83447i	−0.406836	+	0.234887i	−0.689429	−	0.724353i	$-0.742139\pi$
$617$	−10.1056	+	5.83447i	−0.406836	+	0.234887i	0.282593	+	0.959240i	$0.408805\pi$
$618$		0			0
$619$	1.13744	+	4.24500i	0.0457178	+	0.170621i	0.985010	−	0.172497i	$-0.0551835\pi$
$619$	1.13744	+	4.24500i	0.0457178	+	0.170621i	−0.939292	+	0.343118i	$0.888517\pi$
$620$		0			0
$621$	−39.7442	+	20.4082i	−1.59488	+	0.818952i
$622$		0			0
$623$	9.75711	−	16.8998i	0.390910	−	0.677076i
$624$		0			0
$625$	12.4616	+	21.5841i	0.498464	+	0.863365i
$626$		0			0
$627$	20.8453	+	0.342027i	0.832483	+	0.0136592i
$628$		0			0
$629$	−3.51731	+	3.51731i	−0.140244	+	0.140244i
$630$		0			0
$631$			31.5374i			1.25548i	0.778422	+	0.627742i	$0.216021\pi$
$631$			31.5374i			1.25548i	−0.778422	+	0.627742i	$0.783979\pi$
$632$		0			0
$633$	20.7695	−	5.20152i	0.825513	−	0.206742i
$634$		0			0
$635$	−0.704855	−	0.188865i	−0.0279713	−	0.00749489i
$636$		0			0
$637$	−1.86844	+	0.500648i	−0.0740304	+	0.0198364i
$638$		0			0
$639$	0.924384	+	0.574932i	0.0365681	+	0.0227439i
$640$		0			0
$641$	9.38996	−	16.2639i	0.370881	−	0.642385i	−0.618820	−	0.785533i	$-0.712389\pi$
$641$	9.38996	−	16.2639i	0.370881	−	0.642385i	0.989701	+	0.143148i	$0.0457225\pi$
$642$		0			0
$643$	6.94427	−	25.9164i	0.273855	−	1.02204i	−0.682749	−	0.730653i	$-0.739216\pi$
$643$	6.94427	−	25.9164i	0.273855	−	1.02204i	0.956605	−	0.291389i	$-0.0941175\pi$
$644$		0			0
$645$	−0.280302	+	0.155758i	−0.0110369	+	0.00613295i
$646$		0			0
$647$		−	16.5176i		−	0.649373i	−0.945822	−	0.324686i	$-0.894741\pi$
$647$		−	16.5176i		−	0.649373i	0.945822	−	0.324686i	$-0.105259\pi$
$648$		0			0
$649$			32.3620i			1.27032i
$650$		0			0
$651$	−20.1841	+	11.2158i	−0.791075	+	0.439584i
$652$		0			0
$653$	10.8252	−	40.4003i	0.423624	−	1.58099i	−0.343285	−	0.939231i	$-0.611540\pi$
$653$	10.8252	−	40.4003i	0.423624	−	1.58099i	0.766909	−	0.641756i	$-0.221794\pi$
$654$		0			0
$655$	−0.251729	+	0.436008i	−0.00983587	+	0.0170362i
$656$		0			0
$657$	40.4396	+	25.1519i	1.57770	+	0.981268i
$658$		0			0
$659$	11.3797	−	3.04918i	0.443290	−	0.118779i	−0.0302682	−	0.999542i	$-0.509636\pi$
$659$	11.3797	−	3.04918i	0.443290	−	0.118779i	0.473558	+	0.880763i	$0.342969\pi$
$660$		0			0
$661$	39.1808	+	10.4985i	1.52396	+	0.408343i	0.921042	−	0.389464i	$-0.127340\pi$
$661$	39.1808	+	10.4985i	1.52396	+	0.408343i	0.602913	+	0.797807i	$0.294006\pi$
$662$		0			0
$663$	0.575137	−	0.144037i	0.0223365	−	0.00559395i
$664$		0			0
$665$		−	0.562144i		−	0.0217990i
$666$		0			0
$667$	30.0385	−	30.0385i	1.16309	−	1.16309i
$668$		0			0
$669$	−25.0102	−	0.410364i	−0.966952	−	0.0158656i
$670$		0			0
$671$	3.86217	+	6.68948i	0.149098	+	0.258245i
$672$		0			0
$673$	−6.73175	+	11.6597i	−0.259490	+	0.449450i	−0.966105	−	0.258148i	$-0.916888\pi$
$673$	−6.73175	+	11.6597i	−0.259490	+	0.449450i	0.706615	+	0.707598i	$0.250221\pi$
$674$		0			0
$675$	−21.8113	−	14.0672i	−0.839516	−	0.541447i
$676$		0			0
$677$	2.56756	+	9.58227i	0.0986794	+	0.368277i	0.997552	−	0.0699343i	$-0.0222790\pi$
$677$	2.56756	+	9.58227i	0.0986794	+	0.368277i	−0.898872	+	0.438211i	$0.855612\pi$
$678$		0			0
$679$	1.60905	−	0.928986i	0.0617497	−	0.0356512i
$680$		0			0
$681$	−2.01483	−	2.08205i	−0.0772085	−	0.0797844i
$682$		0			0
$683$	−4.48800	+	4.48800i	−0.171728	+	0.171728i	−0.787738	−	0.616010i	$-0.788748\pi$
$683$	−4.48800	+	4.48800i	−0.171728	+	0.171728i	0.616010	+	0.787738i	$0.288748\pi$
$684$		0			0
$685$	−0.734335	−	0.734335i	−0.0280575	−	0.0280575i
$686$		0			0
$687$	8.54725	+	34.1289i	0.326098	+	1.30210i
$688$		0			0
$689$	−1.12470	−	1.94803i	−0.0428475	−	0.0742140i
$690$		0			0
$691$	−35.9149	+	9.62336i	−1.36627	+	0.366090i	−0.866114	−	0.499847i	$-0.833390\pi$
$691$	−35.9149	+	9.62336i	−1.36627	+	0.366090i	−0.500153	+	0.865937i	$0.666723\pi$
$692$		0			0
$693$	−6.88498	−	7.35231i	−0.261539	−	0.279291i
$694$		0			0
$695$	0.326960	+	0.188770i	0.0124023	+	0.00716047i
$696$		0			0
$697$	1.74715	−	1.00872i	0.0661780	−	0.0382079i
$698$		0			0
$699$	−35.7024	+	19.8391i	−1.35039	+	0.750382i
$700$		0			0
$701$	36.9558	+	36.9558i	1.39580	+	1.39580i	0.811628	+	0.584175i	$0.198582\pi$
$701$	36.9558	+	36.9558i	1.39580	+	1.39580i	0.584175	+	0.811628i	$0.301418\pi$
$702$		0			0
$703$	−31.0176			−1.16985
$704$		0			0
$705$	−0.815264	−	0.232850i	−0.0307046	−	0.00876963i
$706$		0			0
$707$	−2.11743	+	7.90237i	−0.0796343	+	0.297199i
$708$		0			0
$709$	−1.53529	−	5.72979i	−0.0576591	−	0.215187i	0.931085	−	0.364802i	$-0.118863\pi$
$709$	−1.53529	−	5.72979i	−0.0576591	−	0.215187i	−0.988744	+	0.149615i	$0.952197\pi$
$710$		0			0
$711$	15.4217	+	28.8581i	0.578359	+	1.08226i
$712$		0			0
$713$	−67.0640	−	38.7194i	−2.51157	−	1.45005i
$714$		0			0
$715$	0.0630713	+	0.0168999i	0.00235873	+	0.000632021i
$716$		0			0
$717$	−7.62996	+	12.7285i	−0.284946	+	0.475356i
$718$		0			0
$719$	−9.58462			−0.357446			−0.178723	−	0.983899i	$-0.557197\pi$
$719$	−9.58462			−0.357446			−0.178723	+	0.983899i	$0.557197\pi$
$720$		0			0
$721$	−16.4075			−0.611046
$722$		0			0
$723$	−12.7813	−	0.209713i	−0.475340	−	0.00779931i
$724$		0			0
$725$	23.8370	+	6.38711i	0.885285	+	0.237211i
$726$		0			0
$727$	−34.4374	−	19.8824i	−1.27721	−	0.737399i	−0.300877	−	0.953663i	$-0.597279\pi$
$727$	−34.4374	−	19.8824i	−1.27721	−	0.737399i	−0.976335	+	0.216264i	$0.930613\pi$
$728$		0			0
$729$	26.8693	+	2.65354i	0.995159	+	0.0982793i
$730$		0			0
$731$	−0.569798	−	2.12651i	−0.0210747	−	0.0786520i
$732$		0			0
$733$	−9.37557	+	34.9901i	−0.346295	+	1.29239i	0.544798	+	0.838567i	$0.316606\pi$
$733$	−9.37557	+	34.9901i	−0.346295	+	1.29239i	−0.891092	+	0.453822i	$0.850060\pi$
$734$		0			0
$735$	0.428356	−	0.414526i	0.0158001	−	0.0152900i
$736$		0			0
$737$	−15.2059			−0.560115
$738$		0			0
$739$	7.78860	+	7.78860i	0.286508	+	0.286508i	0.835698	−	0.549190i	$-0.185064\pi$
$739$	7.78860	+	7.78860i	0.286508	+	0.286508i	−0.549190	+	0.835698i	$0.685064\pi$
$740$		0			0
$741$	3.17105	+	1.90084i	0.116491	+	0.0698291i
$742$		0			0
$743$	3.75539	−	2.16817i	0.137772	−	0.0795426i	−0.429530	−	0.903053i	$-0.641321\pi$
$743$	3.75539	−	2.16817i	0.137772	−	0.0795426i	0.567302	+	0.823510i	$0.307987\pi$
$744$		0			0
$745$	1.24048	+	0.716193i	0.0454477	+	0.0262393i
$746$		0			0
$747$	−4.84380	+	15.9628i	−0.177226	+	0.584050i
$748$		0			0
$749$	−13.9579	+	3.74001i	−0.510011	+	0.136657i
$750$		0			0
$751$	6.74026	+	11.6745i	0.245956	+	0.426008i	0.962400	−	0.271637i	$-0.0875649\pi$
$751$	6.74026	+	11.6745i	0.245956	+	0.426008i	−0.716444	+	0.697644i	$0.754232\pi$
$752$		0			0
$753$	−20.6010	−	5.88389i	−0.750741	−	0.214421i
$754$		0			0
$755$	0.648077	+	0.648077i	0.0235859	+	0.0235859i
$756$		0			0
$757$	25.9901	−	25.9901i	0.944625	−	0.944625i	−0.0539205	−	0.998545i	$-0.517172\pi$
$757$	25.9901	−	25.9901i	0.944625	−	0.944625i	0.998545	+	0.0539205i	$0.0171718\pi$
$758$		0			0
$759$	9.27712	−	32.4815i	0.336738	−	1.17900i
$760$		0			0
$761$	−29.3955	+	16.9715i	−1.06558	+	0.615216i	−0.926972	−	0.375131i	$-0.877598\pi$
$761$	−29.3955	+	16.9715i	−1.06558	+	0.615216i	−0.138613	+	0.990347i	$0.544264\pi$
$762$		0			0
$763$	−5.08845	−	18.9904i	−0.184214	−	0.687498i
$764$		0			0
$765$	−0.133362	+	0.124885i	−0.00482171	+	0.00451523i
$766$		0			0
$767$	−2.86947	+	4.97006i	−0.103610	+	0.179459i
$768$		0			0
$769$	2.38011	+	4.12248i	0.0858291	+	0.148660i	0.905744	−	0.423825i	$-0.139313\pi$
$769$	2.38011	+	4.12248i	0.0858291	+	0.148660i	−0.819915	+	0.572485i	$0.805979\pi$
$770$		0			0
$771$	3.93734	−	6.56840i	0.141800	−	0.236555i
$772$		0			0
$773$	−38.1267	+	38.1267i	−1.37132	+	1.37132i	−0.512837	+	0.858486i	$0.671405\pi$
$773$	−38.1267	+	38.1267i	−1.37132	+	1.37132i	−0.858486	+	0.512837i	$0.828595\pi$
$774$		0			0
$775$		−	44.9857i		−	1.61593i
$776$		0			0
$777$	10.4215	+	10.7692i	0.373868	+	0.386342i
$778$		0			0
$779$	12.1514	+	3.25596i	0.435369	+	0.116657i
$780$		0			0
$781$	−0.795027	+	0.213027i	−0.0284483	+	0.00762270i
$782$		0			0
$783$	−25.0944	+	5.41642i	−0.896802	+	0.193567i
$784$		0			0
$785$	−0.273835	+	0.474296i	−0.00977359	+	0.0169284i
$786$		0			0
$787$	−6.10176	+	22.7721i	−0.217504	+	0.811736i	0.767766	+	0.640730i	$0.221368\pi$
$787$	−6.10176	+	22.7721i	−0.217504	+	0.811736i	−0.985270	+	0.171006i	$0.945298\pi$
$788$		0			0
$789$	0.311248	−	18.9695i	0.0110807	−	0.675331i
$790$		0			0
$791$			17.2053i			0.611749i
$792$		0			0
$793$			1.36980i			0.0486432i
$794$		0			0
$795$	0.594534	+	0.356386i	0.0210860	+	0.0126397i
$796$		0			0
$797$	−11.8678	+	44.2911i	−0.420378	+	1.56887i	0.353436	+	0.935459i	$0.385013\pi$
$797$	−11.8678	+	44.2911i	−0.420378	+	1.56887i	−0.773814	+	0.633413i	$0.781654\pi$
$798$		0			0
$799$	2.91046	−	5.04107i	0.102965	−	0.178340i
$800$		0			0
$801$	−33.5837	−	20.8878i	−1.18662	−	0.738034i
$802$		0			0
$803$	−34.7805	+	9.31941i	−1.22738	+	0.328875i
$804$		0			0
$805$	−0.879807	−	0.235744i	−0.0310091	−	0.00830887i
$806$		0			0
$807$	−7.15597	+	25.0548i	−0.251902	+	0.881971i
$808$		0			0
$809$			8.89301i			0.312662i	0.987705	+	0.156331i	$0.0499666\pi$
$809$			8.89301i			0.312662i	−0.987705	+	0.156331i	$0.950033\pi$
$810$		0			0
$811$	31.7492	−	31.7492i	1.11487	−	1.11487i	0.122384	−	0.992483i	$-0.460946\pi$
$811$	31.7492	−	31.7492i	1.11487	−	1.11487i	0.992483	−	0.122384i	$-0.0390538\pi$
$812$		0			0
$813$	16.0865	+	28.9492i	0.564177	+	1.01529i
$814$		0			0
$815$	0.526230	+	0.911457i	0.0184330	+	0.0319269i
$816$		0			0
$817$	6.86401	−	11.8888i	0.240141	−	0.415937i
$818$		0			0
$819$	−0.405463	−	1.73963i	−0.0141680	−	0.0607875i
$820$		0			0
$821$	−12.5747	−	46.9294i	−0.438860	−	1.63785i	−0.731657	−	0.681673i	$-0.761253\pi$
$821$	−12.5747	−	46.9294i	−0.438860	−	1.63785i	0.292797	−	0.956175i	$-0.405414\pi$
$822$		0			0
$823$	9.69600	−	5.59799i	0.337981	−	0.195134i	−0.321398	−	0.946944i	$-0.604153\pi$
$823$	9.69600	−	5.59799i	0.337981	−	0.195134i	0.659379	+	0.751811i	$0.270819\pi$
$824$		0			0
$825$	19.0357	−	4.76732i	0.662740	−	0.165977i
$826$		0			0
$827$	−11.9898	+	11.9898i	−0.416927	+	0.416927i	−0.884143	−	0.467216i	$-0.845257\pi$
$827$	−11.9898	+	11.9898i	−0.416927	+	0.416927i	0.467216	+	0.884143i	$0.345257\pi$
$828$		0			0
$829$	−34.3253	−	34.3253i	−1.19217	−	1.19217i	−0.976458	−	0.215708i	$-0.930794\pi$
$829$	−34.3253	−	34.3253i	−1.19217	−	1.19217i	−0.215708	−	0.976458i	$-0.569206\pi$
$830$		0			0
$831$	12.9929	−	12.5734i	0.450718	−	0.436167i
$832$		0			0
$833$	2.04619	+	3.54410i	0.0708962	+	0.122796i
$834$		0			0
$835$	−0.434579	+	0.116445i	−0.0150392	+	0.00402975i
$836$		0			0
$837$	21.3769	+	41.6308i	0.738894	+	1.43897i
$838$		0			0
$839$	−43.4830	−	25.1049i	−1.50120	−	0.866719i	−0.999999	−	0.00138814i	$-0.999558\pi$
$839$	−43.4830	−	25.1049i	−1.50120	−	0.866719i	−0.501202	−	0.865331i	$-0.667109\pi$
$840$		0			0
$841$	−3.97509	+	2.29502i	−0.137072	+	0.0791386i
$842$		0			0
$843$	0.399572	−	24.3525i	0.0137620	−	0.838746i
$844$		0			0
$845$	−0.649670	−	0.649670i	−0.0223493	−	0.0223493i
$846$		0			0
$847$	−8.66674			−0.297793
$848$		0			0
$849$	10.7443	+	42.9015i	0.368742	+	1.47237i
$850$		0			0
$851$	−13.0077	+	48.5455i	−0.445899	+	1.66412i
$852$		0			0
$853$	6.97320	+	26.0243i	0.238758	+	0.891056i	0.976419	+	0.215885i	$0.0692635\pi$
$853$	6.97320	+	26.0243i	0.238758	+	0.891056i	−0.737661	+	0.675171i	$0.764070\pi$
$854$		0			0
$855$	−1.13869	−	0.0373768i	−0.0389422	−	0.00127826i
$856$		0			0
$857$	−12.5955	−	7.27203i	−0.430255	−	0.248408i	0.269200	−	0.963084i	$-0.413241\pi$
$857$	−12.5955	−	7.27203i	−0.430255	−	0.248408i	−0.699455	+	0.714676i	$0.746574\pi$
$858$		0			0
$859$	−4.49231	−	1.20371i	−0.153276	−	0.0410701i	0.181365	−	0.983416i	$-0.441948\pi$
$859$	−4.49231	−	1.20371i	−0.153276	−	0.0410701i	−0.334641	+	0.942346i	$0.608615\pi$
$860$		0			0
$861$	−2.95224	−	5.31286i	−0.100612	−	0.181062i
$862$		0			0
$863$	−6.06219			−0.206359			−0.103180	−	0.994663i	$-0.532902\pi$
$863$	−6.06219			−0.206359			−0.103180	+	0.994663i	$0.532902\pi$
$864$		0			0
$865$	0.841503			0.0286120
$866$		0			0
$867$	13.6928	+	24.6417i	0.465033	+	0.836874i
$868$		0			0
$869$	−23.8965	−	6.40303i	−0.810632	−	0.217208i
$870$		0			0
$871$	−2.33528	−	1.34827i	−0.0791278	−	0.0456845i
$872$		0			0
$873$	−1.77478	−	3.32108i	−0.0600672	−	0.112402i
$874$		0			0
$875$	−0.274036	−	1.02272i	−0.00926412	−	0.0345742i
$876$		0			0
$877$	5.44913	−	20.3364i	0.184004	−	0.686713i	−0.810837	−	0.585271i	$-0.800988\pi$
$877$	5.44913	−	20.3364i	0.184004	−	0.686713i	0.994842	−	0.101441i	$-0.0323454\pi$
$878$		0			0
$879$	5.77502	+	23.0595i	0.194787	+	0.777777i
$880$		0			0
$881$	3.07747			0.103682			0.0518412	−	0.998655i	$-0.483491\pi$
$881$	3.07747			0.103682			0.0518412	+	0.998655i	$0.483491\pi$
$882$		0			0
$883$	2.89268	+	2.89268i	0.0973465	+	0.0973465i	0.754103	−	0.656756i	$-0.228072\pi$
$883$	2.89268	+	2.89268i	0.0973465	+	0.0973465i	−0.656756	+	0.754103i	$0.728072\pi$
$884$		0			0
$885$	0.0290134	−	1.76826i	0.000975273	−	0.0594395i
$886$		0			0
$887$	43.0227	−	24.8392i	1.44456	−	0.834017i	0.446411	−	0.894828i	$-0.352702\pi$
$887$	43.0227	−	24.8392i	1.44456	−	0.834017i	0.998149	+	0.0608108i	$0.0193686\pi$
$888$		0			0
$889$	−13.0712	−	7.54664i	−0.438393	−	0.253106i
$890$		0			0
$891$	−15.3507	+	13.4574i	−0.514268	+	0.450841i
$892$		0			0
$893$	35.0606	−	9.39445i	1.17326	−	0.314373i
$894$		0			0
$895$	−0.466472	−	0.807953i	−0.0155924	−	0.0270069i
$896$		0			0
$897$	4.30482	−	4.16583i	0.143734	−	0.139093i
$898$		0			0
$899$	−31.4643	−	31.4643i	−1.04939	−	1.04939i
$900$		0			0
$901$	−3.36503	+	3.36503i	−0.112105	+	0.112105i
$902$		0			0
$903$	−6.43394	+	1.61132i	−0.214108	+	0.0536213i
$904$		0			0
$905$	1.01603	−	0.586603i	0.0337738	−	0.0194993i
$906$		0			0
$907$	−3.27515	−	12.2230i	−0.108750	−	0.405859i	0.889994	−	0.455973i	$-0.150708\pi$
$907$	−3.27515	−	12.2230i	−0.108750	−	0.405859i	−0.998744	+	0.0501131i	$0.984042\pi$
$908$		0			0
$909$	15.8663	+	4.81452i	0.526253	+	0.159688i
$910$		0			0
$911$	26.6903	−	46.2289i	0.884289	−	1.53163i	0.0377625	−	0.999287i	$-0.487977\pi$
$911$	26.6903	−	46.2289i	0.884289	−	1.53163i	0.846526	−	0.532347i	$-0.178690\pi$
$912$		0			0
$913$	−6.30637	−	10.9230i	−0.208710	−	0.361497i
$914$		0			0
$915$	−0.205032	−	0.368977i	−0.00677816	−	0.0121980i
$916$		0			0
$917$	−7.36336	+	7.36336i	−0.243160	+	0.243160i
$918$		0			0
$919$		−	38.5309i		−	1.27102i	−0.772094	−	0.635509i	$-0.780790\pi$
$919$		−	38.5309i		−	1.27102i	0.772094	−	0.635509i	$-0.219210\pi$
$920$		0			0
$921$	9.49335	−	33.2386i	0.312817	−	1.09525i
$922$		0			0
$923$	−0.140987	−	0.0377773i	−0.00464064	−	0.00124345i
$924$		0			0
$925$	−28.2010	+	7.55643i	−0.927243	+	0.248454i
$926$		0			0
$927$	−1.09093	+	33.2351i	−0.0358308	+	1.09159i
$928$		0			0
$929$	5.92500	−	10.2624i	0.194393	−	0.336699i	−0.752308	−	0.658811i	$-0.771060\pi$
$929$	5.92500	−	10.2624i	0.194393	−	0.336699i	0.946701	+	0.322113i	$0.104393\pi$
$930$		0			0
$931$	−6.60473	+	24.6492i	−0.216461	+	0.807844i
$932$		0			0
$933$	−19.3693	−	11.6107i	−0.634124	−	0.380117i
$934$		0			0
$935$		−	0.138142i		−	0.00451774i
$936$		0			0
$937$			0.288917i			0.00943850i	0.999989	+	0.00471925i	$0.00150219\pi$
$937$			0.288917i			0.00943850i	−0.999989	+	0.00471925i	$0.998498\pi$
$938$		0			0
$939$	−0.213441	+	13.0085i	−0.00696539	+	0.424516i
$940$		0			0
$941$	−8.87473	+	33.1209i	−0.289308	+	1.07971i	0.656326	+	0.754478i	$0.272110\pi$
$941$	−8.87473	+	33.1209i	−0.289308	+	1.07971i	−0.945634	+	0.325234i	$0.894557\pi$
$942$		0			0
$943$	10.1917	−	17.6526i	0.331889	−	0.574849i
$944$		0			0
$945$	0.369605	+	0.407904i	0.0120232	+	0.0132691i
$946$		0			0
$947$	−22.3187	+	5.98027i	−0.725259	+	0.194333i	−0.602517	−	0.798106i	$-0.705835\pi$
$947$	−22.3187	+	5.98027i	−0.725259	+	0.194333i	−0.122742	+	0.992439i	$0.539169\pi$
$948$		0			0
$949$	−6.16783	−	1.65267i	−0.200216	−	0.0536478i
$950$		0			0
$951$	−1.81634	−	1.87694i	−0.0588990	−	0.0608640i
$952$		0			0
$953$			31.0900i			1.00710i	0.863965	+	0.503552i	$0.167974\pi$
$953$			31.0900i			1.00710i	−0.863965	+	0.503552i	$0.832026\pi$
$954$		0			0
$955$	1.13217	−	1.13217i	0.0366361	−	0.0366361i
$956$		0			0
$957$	9.97975	−	16.6486i	0.322600	−	0.538171i
$958$		0			0
$959$	−10.7401	−	18.6023i	−0.346815	−	0.600701i
$960$		0			0
$961$	−25.0573	+	43.4006i	−0.808302	+	1.40002i
$962$		0			0
$963$	6.64775	+	28.5220i	0.214221	+	0.919108i
$964$		0			0
$965$	−0.265950	−	0.992539i	−0.00856124	−	0.0319510i
$966$		0			0
$967$	24.9481	−	14.4038i	0.802277	−	0.463195i	−0.0419899	−	0.999118i	$-0.513370\pi$
$967$	24.9481	−	14.4038i	0.802277	−	0.463195i	0.844267	+	0.535923i	$0.180036\pi$
$968$		0			0
$969$	2.14809	−	7.52099i	0.0690066	−	0.241609i
$970$		0			0
$971$	−11.6466	+	11.6466i	−0.373757	+	0.373757i	−0.868844	−	0.495087i	$-0.835136\pi$
$971$	−11.6466	+	11.6466i	−0.373757	+	0.373757i	0.495087	+	0.868844i	$0.335136\pi$
$972$		0			0
$973$	5.52175	+	5.52175i	0.177019	+	0.177019i
$974$		0			0
$975$	3.34617	+	0.955708i	0.107163	+	0.0306072i
$976$		0			0
$977$	−12.0661	−	20.8990i	−0.386028	−	0.668619i	0.605884	−	0.795553i	$-0.292820\pi$
$977$	−12.0661	−	20.8990i	−0.386028	−	0.668619i	−0.991911	+	0.126934i	$0.959486\pi$
$978$		0			0
$979$	28.8840	−	7.73945i	0.923137	−	0.247354i
$980$		0			0
$981$	−38.8055	+	9.04457i	−1.23896	+	0.288771i
$982$		0			0
$983$	−18.5016	−	10.6819i	−0.590109	−	0.340700i	0.175031	−	0.984563i	$-0.443997\pi$
$983$	−18.5016	−	10.6819i	−0.590109	−	0.340700i	−0.765141	+	0.643863i	$0.777331\pi$
$984$		0			0
$985$	−0.138081	+	0.0797210i	−0.00439962	+	0.00254012i
$986$		0			0
$987$	−15.0415	−	9.01645i	−0.478778	−	0.286997i
$988$		0			0
$989$	−15.7286	−	15.7286i	−0.500139	−	0.500139i
$990$		0			0
$991$	−28.0624			−0.891433			−0.445717	−	0.895174i	$-0.647051\pi$
$991$	−28.0624			−0.891433			−0.445717	+	0.895174i	$0.647051\pi$
$992$		0			0
$993$	25.4855	−	24.6626i	0.808756	−	0.782645i
$994$		0			0
$995$	0.0319985	−	0.119420i	0.00101442	−	0.00378587i
$996$		0			0
$997$	−15.0100	−	56.0181i	−0.475372	−	1.77411i	−0.619975	−	0.784622i	$-0.712857\pi$
$997$	−15.0100	−	56.0181i	−0.475372	−	1.77411i	0.144603	−	0.989490i	$-0.453810\pi$
$998$		0			0
$999$	22.5071	−	20.3938i	0.712092	−	0.645232i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.529.7		72
3.2	odd	2		1728.2.bc.e.721.10		72
4.3	odd	2		144.2.x.e.61.2	yes	72
9.4	even	3	inner	576.2.bb.e.337.4		72
9.5	odd	6		1728.2.bc.e.145.9		72
12.11	even	2		432.2.y.e.397.17		72
16.5	even	4	inner	576.2.bb.e.241.4		72
16.11	odd	4		144.2.x.e.133.12	yes	72
36.23	even	6		432.2.y.e.253.7		72
36.31	odd	6		144.2.x.e.13.12	✓	72
48.5	odd	4		1728.2.bc.e.1585.9		72
48.11	even	4		432.2.y.e.181.7		72
144.5	odd	12		1728.2.bc.e.1009.10		72
144.59	even	12		432.2.y.e.37.17		72
144.85	even	12	inner	576.2.bb.e.49.7		72
144.139	odd	12		144.2.x.e.85.2	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.12	✓	72	36.31	odd	6
144.2.x.e.61.2	yes	72	4.3	odd	2
144.2.x.e.85.2	yes	72	144.139	odd	12
144.2.x.e.133.12	yes	72	16.11	odd	4
432.2.y.e.37.17		72	144.59	even	12
432.2.y.e.181.7		72	48.11	even	4
432.2.y.e.253.7		72	36.23	even	6
432.2.y.e.397.17		72	12.11	even	2
576.2.bb.e.49.7		72	144.85	even	12	inner
576.2.bb.e.241.4		72	16.5	even	4	inner
576.2.bb.e.337.4		72	9.4	even	3	inner
576.2.bb.e.529.7		72	1.1	even	1	trivial
1728.2.bc.e.145.9		72	9.5	odd	6
1728.2.bc.e.721.10		72	3.2	odd	2
1728.2.bc.e.1009.10		72	144.5	odd	12
1728.2.bc.e.1585.9		72	48.5	odd	4

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.bb (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.841300 - 1.51401i) q^{3} +(-0.0691269 - 0.0185225i) q^{5} +(-1.28192 - 0.740118i) q^{7} +(-1.58443 + 2.54747i) q^{9} +O(q^{10})\)	\(q+(-0.841300 - 1.51401i) q^{3} +(-0.0691269 - 0.0185225i) q^{5} +(-1.28192 - 0.740118i) q^{7} +(-1.58443 + 2.54747i) q^{9} +(-0.587070 - 2.19098i) q^{11} +(0.104109 - 0.388539i) q^{13} +(0.0301133 + 0.120242i) q^{15} -0.851000 q^{17} +(-3.75230 - 3.75230i) q^{19} +(-0.0420615 + 2.56350i) q^{21} +(-7.44629 + 4.29912i) q^{23} +(-4.32569 - 2.49744i) q^{25} +(5.18986 + 0.255647i) q^{27} +(-4.77230 + 1.27873i) q^{29} +(4.50318 + 7.79974i) q^{31} +(-2.82325 + 2.73210i) q^{33} +(0.0749065 + 0.0749065i) q^{35} +(4.13315 - 4.13315i) q^{37} +(-0.675837 + 0.169257i) q^{39} +(-2.05305 + 1.18533i) q^{41} +(0.669562 + 2.49884i) q^{43} +(0.156712 - 0.146751i) q^{45} +(-3.42005 + 5.92370i) q^{47} +(-2.40445 - 4.16463i) q^{49} +(0.715947 + 1.28842i) q^{51} +(3.95421 - 3.95421i) q^{53} +0.162329i q^{55} +(-2.52419 + 8.83782i) q^{57} +(-13.7811 - 3.69264i) q^{59} +(-3.28936 + 0.881382i) q^{61} +(3.91654 - 2.09299i) q^{63} +(-0.0143934 + 0.0249301i) q^{65} +(1.73506 - 6.47532i) q^{67} +(12.7735 + 7.65687i) q^{69} -0.362864i q^{71} -15.8744i q^{73} +(-0.141931 + 8.65022i) q^{75} +(-0.869003 + 3.24316i) q^{77} +(5.45338 - 9.44553i) q^{79} +(-3.97918 - 8.07255i) q^{81} +(5.37105 - 1.43917i) q^{83} +(0.0588270 + 0.0157627i) q^{85} +(5.95094 + 6.14948i) q^{87} +13.1832i q^{89} +(-0.421024 + 0.421024i) q^{91} +(8.02033 - 13.3798i) q^{93} +(0.189883 + 0.328887i) q^{95} +(-0.627593 + 1.08702i) q^{97} +(6.51161 + 1.97590i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 72 * q - 2 * q^3 + 4 * q^5	\( 72 q - 2 q^{3} + 4 q^{5} + 2 q^{11} - 16 q^{13} + 20 q^{15} - 16 q^{17} - 28 q^{19} - 16 q^{21} - 8 q^{27} + 4 q^{29} - 28 q^{31} - 32 q^{33} + 16 q^{35} + 16 q^{37} + 10 q^{43} + 40 q^{45} + 56 q^{47} + 4 q^{49} + 54 q^{51} - 8 q^{53} + 14 q^{59} - 32 q^{61} + 108 q^{63} - 64 q^{65} + 18 q^{67} + 32 q^{69} - 86 q^{75} - 36 q^{77} - 44 q^{79} - 44 q^{81} - 20 q^{83} - 8 q^{85} + 80 q^{91} - 4 q^{93} - 48 q^{95} + 40 q^{97} - 28 q^{99}+O(q^{100}) \) 72 * q - 2 * q^3 + 4 * q^5 + 2 * q^11 - 16 * q^13 + 20 * q^15 - 16 * q^17 - 28 * q^19 - 16 * q^21 - 8 * q^27 + 4 * q^29 - 28 * q^31 - 32 * q^33 + 16 * q^35 + 16 * q^37 + 10 * q^43 + 40 * q^45 + 56 * q^47 + 4 * q^49 + 54 * q^51 - 8 * q^53 + 14 * q^59 - 32 * q^61 + 108 * q^63 - 64 * q^65 + 18 * q^67 + 32 * q^69 - 86 * q^75 - 36 * q^77 - 44 * q^79 - 44 * q^81 - 20 * q^83 - 8 * q^85 + 80 * q^91 - 4 * q^93 - 48 * q^95 + 40 * q^97 - 28 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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