LMFDB - Embedded newform 576.2.bb.e.49.4

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			49.4
Character	$\chi$	$=$	576.49
Dual form			576.2.bb.e.529.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.31071 - 1.13227i) q^{3} +(-0.0112878 + 0.00302457i) q^{5} +(-1.05753 + 0.610563i) q^{7} +(0.435936 + 2.96816i) q^{9} +O(q^{10})$	\(q+(-1.31071 - 1.13227i) q^{3} +(-0.0112878 + 0.00302457i) q^{5} +(-1.05753 + 0.610563i) q^{7} +(0.435936 + 2.96816i) q^{9} +(0.490535 - 1.83070i) q^{11} +(-1.35786 - 5.06759i) q^{13} +(0.0182197 + 0.00881653i) q^{15} -1.54238 q^{17} +(-4.06823 + 4.06823i) q^{19} +(2.07744 + 0.397131i) q^{21} +(-5.20660 - 3.00603i) q^{23} +(-4.33001 + 2.49993i) q^{25} +(2.78937 - 4.38400i) q^{27} +(-2.98082 - 0.798708i) q^{29} +(-2.92831 + 5.07198i) q^{31} +(-2.71580 + 1.84411i) q^{33} +(0.0100905 - 0.0100905i) q^{35} +(0.923082 + 0.923082i) q^{37} +(-3.95811 + 8.17961i) q^{39} +(3.20829 + 1.85231i) q^{41} +(-1.29691 + 4.84015i) q^{43} +(-0.0138982 - 0.0321856i) q^{45} +(1.31218 + 2.27277i) q^{47} +(-2.75442 + 4.77080i) q^{49} +(2.02162 + 1.74639i) q^{51} +(-8.88508 - 8.88508i) q^{53} +0.0221483i q^{55} +(9.93862 - 0.725952i) q^{57} +(8.78724 - 2.35453i) q^{59} +(-12.1194 - 3.24737i) q^{61} +(-2.27326 - 2.87274i) q^{63} +(0.0306545 + 0.0530952i) q^{65} +(-3.18324 - 11.8800i) q^{67} +(3.42072 + 9.83532i) q^{69} -14.2363i q^{71} -4.32091i q^{73} +(8.50599 + 1.62604i) q^{75} +(0.599006 + 2.23552i) q^{77} +(0.261880 + 0.453589i) q^{79} +(-8.61992 + 2.58785i) q^{81} +(10.8824 + 2.91592i) q^{83} +(0.0174101 - 0.00466503i) q^{85} +(3.00264 + 4.42196i) q^{87} -10.7103i q^{89} +(4.53005 + 4.53005i) q^{91} +(9.58101 - 3.33227i) q^{93} +(0.0336169 - 0.0582262i) q^{95} +(8.78820 + 15.2216i) q^{97} +(5.64765 + 0.657918i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/576\mathbb{Z}\right)^\times$.

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

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
$3$	−1.31071	−	1.13227i	−0.756740	−	0.653716i
$3$	−1.31071	−	1.13227i	−0.756740	−	0.653716i
$4$		0			0
$5$	−0.0112878	+	0.00302457i	−0.00504807	+	0.00135263i	−0.261342	−	0.965246i	$-0.584165\pi$
$5$	−0.0112878	+	0.00302457i	−0.00504807	+	0.00135263i	0.256294	+	0.966599i	$0.417498\pi$
$6$		0			0
$7$	−1.05753	+	0.610563i	−0.399708	+	0.230771i	−0.686358	−	0.727264i	$-0.740792\pi$
$7$	−1.05753	+	0.610563i	−0.399708	+	0.230771i	0.286650	+	0.958035i	$0.407458\pi$
$8$		0			0
$9$	0.435936	+	2.96816i	0.145312	+	0.989386i
$10$		0			0
$11$	0.490535	−	1.83070i	0.147902	−	0.551977i	−0.851707	−	0.524018i	$-0.824432\pi$
$11$	0.490535	−	1.83070i	0.147902	−	0.551977i	0.999609	−	0.0279594i	$-0.00890090\pi$
$12$		0			0
$13$	−1.35786	−	5.06759i	−0.376602	−	1.40550i	−0.850991	−	0.525181i	$-0.823998\pi$
$13$	−1.35786	−	5.06759i	−0.376602	−	1.40550i	0.474389	−	0.880315i	$-0.342669\pi$
$14$		0			0
$15$	0.0182197	+	0.00881653i	0.00470432	+	0.00227642i
$16$		0			0
$17$	−1.54238			−0.374082			−0.187041	−	0.982352i	$-0.559890\pi$
$17$	−1.54238			−0.374082			−0.187041	+	0.982352i	$0.559890\pi$
$18$		0			0
$19$	−4.06823	+	4.06823i	−0.933317	+	0.933317i	−0.997912	−	0.0645950i	$-0.979424\pi$
$19$	−4.06823	+	4.06823i	−0.933317	+	0.933317i	0.0645950	+	0.997912i	$0.479424\pi$
$20$		0			0
$21$	2.07744	+	0.397131i	0.453334	+	0.0866611i
$22$		0			0
$23$	−5.20660	−	3.00603i	−1.08565	−	0.626801i	−0.153236	−	0.988190i	$-0.548970\pi$
$23$	−5.20660	−	3.00603i	−1.08565	−	0.626801i	−0.932415	+	0.361388i	$0.882303\pi$
$24$		0			0
$25$	−4.33001	+	2.49993i	−0.866002	+	0.499986i
$26$		0			0
$27$	2.78937	−	4.38400i	0.536814	−	0.843701i
$28$		0			0
$29$	−2.98082	−	0.798708i	−0.553524	−	0.148316i	−0.0287946	−	0.999585i	$-0.509167\pi$
$29$	−2.98082	−	0.798708i	−0.553524	−	0.148316i	−0.524730	+	0.851269i	$0.675834\pi$
$30$		0			0
$31$	−2.92831	+	5.07198i	−0.525939	+	0.910954i	0.473604	+	0.880738i	$0.342953\pi$
$31$	−2.92831	+	5.07198i	−0.525939	+	0.910954i	−0.999543	+	0.0302159i	$0.990381\pi$
$32$		0			0
$33$	−2.71580	+	1.84411i	−0.472760	+	0.321018i
$34$		0			0
$35$	0.0100905	−	0.0100905i	0.00170561	−	0.00170561i
$36$		0			0
$37$	0.923082	+	0.923082i	0.151754	+	0.151754i	0.778901	−	0.627147i	$-0.215777\pi$
$37$	0.923082	+	0.923082i	0.151754	+	0.151754i	−0.627147	+	0.778901i	$0.715777\pi$
$38$		0			0
$39$	−3.95811	+	8.17961i	−0.633805	+	1.30979i
$40$		0			0
$41$	3.20829	+	1.85231i	0.501051	+	0.289282i	0.729147	−	0.684357i	$-0.239917\pi$
$41$	3.20829	+	1.85231i	0.501051	+	0.289282i	−0.228096	+	0.973639i	$0.573250\pi$
$42$		0			0
$43$	−1.29691	+	4.84015i	−0.197777	+	0.738115i	0.793753	+	0.608240i	$0.208124\pi$
$43$	−1.29691	+	4.84015i	−0.197777	+	0.738115i	−0.991530	+	0.129875i	$0.958542\pi$
$44$		0			0
$45$	−0.0138982	−	0.0321856i	−0.00207182	−	0.00479794i
$46$		0			0
$47$	1.31218	+	2.27277i	0.191402	+	0.331517i	0.945715	−	0.324997i	$-0.105363\pi$
$47$	1.31218	+	2.27277i	0.191402	+	0.331517i	−0.754313	+	0.656515i	$0.772030\pi$
$48$		0			0
$49$	−2.75442	+	4.77080i	−0.393489	+	0.681543i
$50$		0			0
$51$	2.02162	+	1.74639i	0.283083	+	0.244543i
$52$		0			0
$53$	−8.88508	−	8.88508i	−1.22046	−	1.22046i	−0.967469	−	0.252991i	$-0.918586\pi$
$53$	−8.88508	−	8.88508i	−1.22046	−	1.22046i	−0.252991	−	0.967469i	$-0.581414\pi$
$54$		0			0
$55$			0.0221483i			0.00298648i
$56$		0			0
$57$	9.93862	−	0.725952i	1.31640	−	0.0961547i
$58$		0			0
$59$	8.78724	−	2.35453i	1.14400	−	0.306534i	0.363443	−	0.931617i	$-0.381601\pi$
$59$	8.78724	−	2.35453i	1.14400	−	0.306534i	0.780559	+	0.625082i	$0.214935\pi$
$60$		0			0
$61$	−12.1194	−	3.24737i	−1.55172	−	0.415783i	−0.621692	−	0.783262i	$-0.713555\pi$
$61$	−12.1194	−	3.24737i	−1.55172	−	0.415783i	−0.930032	+	0.367478i	$0.880221\pi$
$62$		0			0
$63$	−2.27326	−	2.87274i	−0.286404	−	0.361931i
$64$		0			0
$65$	0.0306545	+	0.0530952i	0.00380223	+	0.00658565i
$66$		0			0
$67$	−3.18324	−	11.8800i	−0.388895	−	1.45137i	−0.831935	−	0.554873i	$-0.812767\pi$
$67$	−3.18324	−	11.8800i	−0.388895	−	1.45137i	0.443041	−	0.896501i	$-0.353900\pi$
$68$		0			0
$69$	3.42072	+	9.83532i	0.411807	+	1.18403i
$70$		0			0
$71$		−	14.2363i		−	1.68954i	−0.535129	−	0.844771i	$-0.679737\pi$
$71$		−	14.2363i		−	1.68954i	0.535129	−	0.844771i	$-0.320263\pi$
$72$		0			0
$73$		−	4.32091i		−	0.505724i	−0.967502	−	0.252862i	$-0.918628\pi$
$73$		−	4.32091i		−	0.505724i	0.967502	−	0.252862i	$-0.0813718\pi$
$74$		0			0
$75$	8.50599	+	1.62604i	0.982187	+	0.187759i
$76$		0			0
$77$	0.599006	+	2.23552i	0.0682630	+	0.254761i
$78$		0			0
$79$	0.261880	+	0.453589i	0.0294638	+	0.0510328i	0.880381	−	0.474267i	$-0.157287\pi$
$79$	0.261880	+	0.453589i	0.0294638	+	0.0510328i	−0.850918	+	0.525299i	$0.823953\pi$
$80$		0			0
$81$	−8.61992	+	2.58785i	−0.957769	+	0.287539i
$82$		0			0
$83$	10.8824	+	2.91592i	1.19450	+	0.320064i	0.800661	−	0.599117i	$-0.204482\pi$
$83$	10.8824	+	2.91592i	1.19450	+	0.320064i	0.393834	+	0.919181i	$0.371148\pi$
$84$		0			0
$85$	0.0174101	−	0.00466503i	0.00188839	−	0.000505994i
$86$		0			0
$87$	3.00264	+	4.42196i	0.321917	+	0.474084i
$88$		0			0
$89$		−	10.7103i		−	1.13529i	−0.823274	−	0.567644i	$-0.807855\pi$
$89$		−	10.7103i		−	1.13529i	0.823274	−	0.567644i	$-0.192145\pi$
$90$		0			0
$91$	4.53005	+	4.53005i	0.474879	+	0.474879i
$92$		0			0
$93$	9.58101	−	3.33227i	0.993504	−	0.345541i
$94$		0			0
$95$	0.0336169	−	0.0582262i	0.00344902	−	0.00597388i
$96$		0			0
$97$	8.78820	+	15.2216i	0.892306	+	1.54552i	0.837104	+	0.547044i	$0.184247\pi$
$97$	8.78820	+	15.2216i	0.892306	+	1.54552i	0.0552025	+	0.998475i	$0.482420\pi$
$98$		0			0
$99$	5.64765	+	0.657918i	0.567611	+	0.0661232i
$100$		0			0
$101$	−1.80361	+	6.73117i	−0.179466	+	0.669776i	0.816282	+	0.577654i	$0.196032\pi$
$101$	−1.80361	+	6.73117i	−0.179466	+	0.669776i	−0.995748	+	0.0921222i	$0.970635\pi$
$102$		0			0
$103$	−2.20609	−	1.27369i	−0.217373	−	0.125500i	0.387360	−	0.921928i	$-0.373387\pi$
$103$	−2.20609	−	1.27369i	−0.217373	−	0.125500i	−0.604733	+	0.796428i	$0.706720\pi$
$104$		0			0
$105$	−0.0246509	+	0.00180059i	−0.00240568	+	0.000175720i
$106$		0			0
$107$	−3.52175	−	3.52175i	−0.340460	−	0.340460i	0.516080	−	0.856540i	$-0.327391\pi$
$107$	−3.52175	−	3.52175i	−0.340460	−	0.340460i	−0.856540	+	0.516080i	$0.827391\pi$
$108$		0			0
$109$	3.14334	−	3.14334i	0.301077	−	0.301077i	−0.540358	−	0.841435i	$-0.681711\pi$
$109$	3.14334	−	3.14334i	0.301077	−	0.301077i	0.841435	+	0.540358i	$0.181711\pi$
$110$		0			0
$111$	−0.164719	−	2.25507i	−0.0156344	−	0.214042i
$112$		0			0
$113$	7.90904	−	13.6989i	0.744020	−	1.28868i	−0.206631	−	0.978419i	$-0.566250\pi$
$113$	7.90904	−	13.6989i	0.744020	−	1.28868i	0.950651	−	0.310262i	$-0.100417\pi$
$114$		0			0
$115$	0.0678632	+	0.0181839i	0.00632828	+	0.00169566i
$116$		0			0
$117$	14.4495	−	6.23947i	1.33585	−	0.576839i
$118$		0			0
$119$	1.63111	−	0.941721i	0.149523	−	0.0863274i
$120$		0			0
$121$	6.41543	+	3.70395i	0.583221	+	0.336723i
$122$		0			0
$123$	−2.10784	−	6.06049i	−0.190057	−	0.546456i
$124$		0			0
$125$	0.0826316	−	0.0826316i	0.00739079	−	0.00739079i
$126$		0			0
$127$	5.72603			0.508103			0.254052	−	0.967191i	$-0.418237\pi$
$127$	5.72603			0.508103			0.254052	+	0.967191i	$0.418237\pi$
$128$		0			0
$129$	7.18023	−	4.87559i	0.632184	−	0.429271i
$130$		0			0
$131$	1.75835	+	6.56224i	0.153628	+	0.573346i	0.999219	+	0.0395151i	$0.0125813\pi$
$131$	1.75835	+	6.56224i	0.153628	+	0.573346i	−0.845591	+	0.533831i	$0.820752\pi$
$132$		0			0
$133$	1.81835	−	6.78618i	0.157671	−	0.588436i
$134$		0			0
$135$	−0.0182262	+	0.0579225i	−0.00156866	+	0.00498517i
$136$		0			0
$137$	3.64923	−	2.10688i	0.311775	−	0.180003i	−0.335946	−	0.941881i	$-0.609056\pi$
$137$	3.64923	−	2.10688i	0.311775	−	0.180003i	0.647720	+	0.761878i	$0.275722\pi$
$138$		0			0
$139$	−15.6519	+	4.19392i	−1.32758	+	0.355724i	−0.851812	−	0.523847i	$-0.824496\pi$
$139$	−15.6519	+	4.19392i	−1.32758	+	0.355724i	−0.475767	+	0.879571i	$0.657830\pi$
$140$		0			0
$141$	0.853489	−	4.46469i	0.0718768	−	0.375995i
$142$		0			0
$143$	−9.94332			−0.831502
$144$		0			0
$145$	0.0360627			0.00299485
$146$		0			0
$147$	9.01209	−	3.13440i	0.743305	−	0.258521i
$148$		0			0
$149$	−3.76477	+	1.00877i	−0.308422	+	0.0826415i	−0.409710	−	0.912216i	$-0.634370\pi$
$149$	−3.76477	+	1.00877i	−0.308422	+	0.0826415i	0.101288	+	0.994857i	$0.467704\pi$
$150$		0			0
$151$	13.0073	−	7.50979i	1.05852	−	0.611138i	0.133499	−	0.991049i	$-0.457379\pi$
$151$	13.0073	−	7.50979i	1.05852	−	0.611138i	0.925023	+	0.379911i	$0.124045\pi$
$152$		0			0
$153$	−0.672378	−	4.57803i	−0.0543586	−	0.370112i
$154$		0			0
$155$	0.0177137	−	0.0661085i	0.00142280	−	0.00530996i
$156$		0			0
$157$	2.53825	+	9.47288i	0.202574	+	0.756018i	0.990175	+	0.139832i	$0.0446564\pi$
$157$	2.53825	+	9.47288i	0.202574	+	0.756018i	−0.787601	+	0.616186i	$0.788677\pi$
$158$		0			0
$159$	1.58549	+	21.7061i	0.125738	+	1.72140i
$160$		0			0
$161$	7.34150			0.578591
$162$		0			0
$163$	−5.22606	+	5.22606i	−0.409336	+	0.409336i	−0.881507	−	0.472171i	$-0.843471\pi$
$163$	−5.22606	+	5.22606i	−0.409336	+	0.409336i	0.472171	+	0.881507i	$0.343471\pi$
$164$		0			0
$165$	0.0250779	−	0.0290301i	0.00195231	−	0.00225999i
$166$		0			0
$167$	−6.31476	−	3.64583i	−0.488651	−	0.282123i	0.235364	−	0.971907i	$-0.424372\pi$
$167$	−6.31476	−	3.64583i	−0.488651	−	0.282123i	−0.724015	+	0.689785i	$0.757705\pi$
$168$		0			0
$169$	−12.5783	+	7.26211i	−0.967565	+	0.558624i
$170$		0			0
$171$	−13.8486	−	10.3017i	−1.05903	−	0.787788i
$172$		0			0
$173$	22.9394	+	6.14659i	1.74405	+	0.467317i	0.983340	−	0.181775i	$-0.0581842\pi$
$173$	22.9394	+	6.14659i	1.74405	+	0.467317i	0.760710	+	0.649092i	$0.224851\pi$
$174$		0			0
$175$	3.05273	−	5.28749i	0.230765	−	0.399697i
$176$		0			0
$177$	−14.1835	−	6.86340i	−1.06610	−	0.515885i
$178$		0			0
$179$	−11.4489	+	11.4489i	−0.855732	+	0.855732i	−0.990832	−	0.135100i	$-0.956864\pi$
$179$	−11.4489	+	11.4489i	−0.855732	+	0.855732i	0.135100	+	0.990832i	$0.456864\pi$
$180$		0			0
$181$	−3.01327	−	3.01327i	−0.223974	−	0.223974i	0.586195	−	0.810170i	$-0.300625\pi$
$181$	−3.01327	−	3.01327i	−0.223974	−	0.223974i	−0.810170	+	0.586195i	$0.800625\pi$
$182$		0			0
$183$	12.2081	+	17.9787i	0.902448	+	1.32903i
$184$		0			0
$185$	−0.0132115	−	0.00762768i	−0.000971331	−	0.000560798i
$186$		0			0
$187$	−0.756592	+	2.82364i	−0.0553275	+	0.206485i
$188$		0			0
$189$	−0.273120	+	6.33928i	−0.0198666	+	0.461115i
$190$		0			0
$191$	2.25702	+	3.90928i	0.163313	+	0.282866i	0.936055	−	0.351854i	$-0.114449\pi$
$191$	2.25702	+	3.90928i	0.163313	+	0.282866i	−0.772742	+	0.634720i	$0.781115\pi$
$192$		0			0
$193$	−1.75793	+	3.04482i	−0.126539	+	0.219171i	−0.922333	−	0.386395i	$-0.873720\pi$
$193$	−1.75793	+	3.04482i	−0.126539	+	0.219171i	0.795795	+	0.605566i	$0.207053\pi$
$194$		0			0
$195$	0.0199387	−	0.104302i	0.00142784	−	0.00746920i
$196$		0			0
$197$	−4.81922	−	4.81922i	−0.343355	−	0.343355i	0.514272	−	0.857627i	$-0.328062\pi$
$197$	−4.81922	−	4.81922i	−0.343355	−	0.343355i	−0.857627	+	0.514272i	$0.828062\pi$
$198$		0			0
$199$		−	4.66322i		−	0.330567i	−0.986246	−	0.165284i	$-0.947146\pi$
$199$		−	4.66322i		−	0.330567i	0.986246	−	0.165284i	$-0.0528539\pi$
$200$		0			0
$201$	−9.27905	+	19.1756i	−0.654494	+	1.35254i
$202$		0			0
$203$	3.63996	−	0.975324i	0.255475	−	0.0684543i
$204$		0			0
$205$	−0.0418171	−	0.0112049i	−0.00292063	−	0.000782581i
$206$		0			0
$207$	6.65264	−	16.7645i	0.462390	−	1.16521i
$208$		0			0
$209$	5.45211	+	9.44333i	0.377130	+	0.653209i
$210$		0			0
$211$	−4.67442	−	17.4452i	−0.321800	−	1.20097i	−0.917490	−	0.397760i	$-0.869788\pi$
$211$	−4.67442	−	17.4452i	−0.321800	−	1.20097i	0.595689	−	0.803215i	$-0.296879\pi$
$212$		0			0
$213$	−16.1193	+	18.6597i	−1.10448	+	1.27854i
$214$		0			0
$215$		−	0.0585574i		−	0.00399358i
$216$		0			0
$217$		−	7.15167i		−	0.485487i
$218$		0			0
$219$	−4.89243	+	5.66347i	−0.330599	+	0.382702i
$220$		0			0
$221$	2.09433	+	7.81615i	0.140880	+	0.525771i
$222$		0			0
$223$	−2.85769	−	4.94966i	−0.191365	−	0.331454i	0.754338	−	0.656486i	$-0.227958\pi$
$223$	−2.85769	−	4.94966i	−0.191365	−	0.331454i	−0.945703	+	0.325032i	$0.894625\pi$
$224$		0			0
$225$	−9.30780	−	11.7623i	−0.620520	−	0.784156i
$226$		0			0
$227$	−19.6766	−	5.27233i	−1.30598	−	0.349937i	−0.462272	−	0.886738i	$-0.652966\pi$
$227$	−19.6766	−	5.27233i	−1.30598	−	0.349937i	−0.843709	+	0.536802i	$0.819632\pi$
$228$		0			0
$229$	3.70525	−	0.992819i	0.244850	−	0.0656073i	−0.134307	−	0.990940i	$-0.542881\pi$
$229$	3.70525	−	0.992819i	0.244850	−	0.0656073i	0.379157	+	0.925332i	$0.376214\pi$
$230$		0			0
$231$	1.74608	−	3.60836i	0.114884	−	0.237413i
$232$		0			0
$233$			5.33043i			0.349208i	0.984639	+	0.174604i	$0.0558645\pi$
$233$			5.33043i			0.349208i	−0.984639	+	0.174604i	$0.944136\pi$
$234$		0			0
$235$	−0.0216859	−	0.0216859i	−0.00141463	−	0.00141463i
$236$		0			0
$237$	0.170336	−	0.891043i	0.0110645	−	0.0578795i
$238$		0			0
$239$	13.8380	−	23.9681i	0.895104	−	1.55037i	0.0614282	−	0.998112i	$-0.480434\pi$
$239$	13.8380	−	23.9681i	0.895104	−	1.55037i	0.833676	−	0.552254i	$-0.186232\pi$
$240$		0			0
$241$	0.847203	+	1.46740i	0.0545731	+	0.0945234i	0.892021	−	0.451993i	$-0.149287\pi$
$241$	0.847203	+	1.46740i	0.0545731	+	0.0945234i	−0.837448	+	0.546517i	$0.815954\pi$
$242$		0			0
$243$	14.2284	+	6.36814i	0.912751	+	0.408516i
$244$		0			0
$245$	0.0166619	−	0.0621830i	0.00106449	−	0.00397273i
$246$		0			0
$247$	26.1402	+	15.0921i	1.66326	+	0.960284i
$248$		0			0
$249$	−10.9621	−	16.1437i	−0.694692	−	1.02307i
$250$		0			0
$251$	−0.987980	−	0.987980i	−0.0623607	−	0.0623607i	0.675239	−	0.737599i	$-0.264041\pi$
$251$	−0.987980	−	0.987980i	−0.0623607	−	0.0623607i	−0.737599	+	0.675239i	$0.764041\pi$
$252$		0			0
$253$	−8.05717	+	8.05717i	−0.506550	+	0.506550i
$254$		0			0
$255$	−0.0281018	−	0.0135984i	−0.00175980	−	0.000851567i
$256$		0			0
$257$	11.8214	−	20.4753i	0.737401	−	1.27722i	−0.216260	−	0.976336i	$-0.569386\pi$
$257$	11.8214	−	20.4753i	0.737401	−	1.27722i	0.953662	−	0.300881i	$-0.0972806\pi$
$258$		0			0
$259$	−1.53978	−	0.412584i	−0.0956776	−	0.0256367i
$260$		0			0
$261$	1.07125	−	9.19572i	0.0663085	−	0.569201i
$262$		0			0
$263$	−22.2619	+	12.8529i	−1.37273	+	0.792545i	−0.991271	−	0.131841i	$-0.957911\pi$
$263$	−22.2619	+	12.8529i	−1.37273	+	0.792545i	−0.381458	+	0.924386i	$0.624578\pi$
$264$		0			0
$265$	0.127167	+	0.0734198i	0.00781180	+	0.00451015i
$266$		0			0
$267$	−12.1269	+	14.0381i	−0.742156	+	0.859119i
$268$		0			0
$269$	−13.6891	+	13.6891i	−0.834637	+	0.834637i	−0.988147	−	0.153510i	$-0.950942\pi$
$269$	−13.6891	+	13.6891i	−0.834637	+	0.834637i	0.153510	+	0.988147i	$0.450942\pi$
$270$		0			0
$271$	7.11000			0.431902			0.215951	−	0.976404i	$-0.430715\pi$
$271$	7.11000			0.431902			0.215951	+	0.976404i	$0.430715\pi$
$272$		0			0
$273$	−0.808361	−	11.0668i	−0.0489242	−	0.669795i
$274$		0			0
$275$	2.45261	+	9.15326i	0.147898	+	0.551962i
$276$		0			0
$277$	5.81917	−	21.7174i	0.349640	−	1.30487i	−0.537457	−	0.843291i	$-0.680615\pi$
$277$	5.81917	−	21.7174i	0.349640	−	1.30487i	0.887097	−	0.461583i	$-0.152718\pi$
$278$		0			0
$279$	−16.3310	−	6.48062i	−0.977710	−	0.387985i
$280$		0			0
$281$	−19.7952	+	11.4288i	−1.18088	+	0.681783i	−0.956218	−	0.292654i	$-0.905462\pi$
$281$	−19.7952	+	11.4288i	−1.18088	+	0.681783i	−0.224664	+	0.974436i	$0.572128\pi$
$282$		0			0
$283$	5.96971	−	1.59958i	0.354862	−	0.0950851i	−0.0769838	−	0.997032i	$-0.524529\pi$
$283$	5.96971	−	1.59958i	0.354862	−	0.0950851i	0.431846	+	0.901947i	$0.357862\pi$
$284$		0			0
$285$	−0.109990	+	0.0382544i	−0.00651523	+	0.00226600i
$286$		0			0
$287$	−4.52381			−0.267032
$288$		0			0
$289$	−14.6211			−0.860063
$290$		0			0
$291$	5.71614	−	29.9017i	0.335086	−	1.75287i
$292$		0			0
$293$	−3.76752	+	1.00950i	−0.220101	+	0.0589758i	−0.367184	−	0.930148i	$-0.619678\pi$
$293$	−3.76752	+	1.00950i	−0.220101	+	0.0589758i	0.147083	+	0.989124i	$0.453011\pi$
$294$		0			0
$295$	−0.0920675	+	0.0531552i	−0.00536038	+	0.00309482i
$296$		0			0
$297$	−6.65751	−	7.25700i	−0.386308	−	0.421094i
$298$		0			0
$299$	−8.16352	+	30.4667i	−0.472109	+	1.76193i
$300$		0			0
$301$	−1.58370	−	5.91043i	−0.0912827	−	0.340672i
$302$		0			0
$303$	9.98550	−	6.78045i	0.573652	−	0.389527i
$304$		0			0
$305$	0.146623			0.00839562
$306$		0			0
$307$	−10.8111	+	10.8111i	−0.617023	+	0.617023i	−0.944767	−	0.327743i	$-0.893712\pi$
$307$	−10.8111	+	10.8111i	−0.617023	+	0.617023i	0.327743	+	0.944767i	$0.393712\pi$
$308$		0			0
$309$	1.44940	+	4.16733i	0.0824532	+	0.237071i
$310$		0			0
$311$	19.5372	+	11.2798i	1.10785	+	0.639619i	0.938273	−	0.345897i	$-0.112425\pi$
$311$	19.5372	+	11.2798i	1.10785	+	0.639619i	0.169581	+	0.985516i	$0.445759\pi$
$312$		0			0
$313$	5.17232	−	2.98624i	0.292357	−	0.168792i	−0.346647	−	0.937996i	$-0.612680\pi$
$313$	5.17232	−	2.98624i	0.292357	−	0.168792i	0.639004	+	0.769203i	$0.279347\pi$
$314$		0			0
$315$	0.0343490	+	0.0255514i	0.00193535	+	0.00143966i
$316$		0			0
$317$	−17.9792	−	4.81751i	−1.00981	−	0.270579i	−0.284262	−	0.958747i	$-0.591748\pi$
$317$	−17.9792	−	4.81751i	−1.00981	−	0.270579i	−0.725551	+	0.688168i	$0.758415\pi$
$318$		0			0
$319$	−2.92439	+	5.06520i	−0.163735	+	0.283597i
$320$		0			0
$321$	0.628435	+	8.60356i	0.0350758	+	0.480204i
$322$		0			0
$323$	6.27476	−	6.27476i	0.349137	−	0.349137i
$324$		0			0
$325$	18.5482	+	18.5482i	1.02887	+	1.02887i
$326$		0			0
$327$	−7.67912	+	0.560910i	−0.424656	+	0.0310184i
$328$		0			0
$329$	−2.77534	−	1.60234i	−0.153009	−	0.0883400i
$330$		0			0
$331$	−2.72957	+	10.1869i	−0.150031	+	0.559923i	0.849449	+	0.527671i	$0.176935\pi$
$331$	−2.72957	+	10.1869i	−0.150031	+	0.559923i	−0.999480	+	0.0322521i	$0.989732\pi$
$332$		0			0
$333$	−2.33745	+	3.14226i	−0.128091	+	0.172195i
$334$		0			0
$335$	0.0718638	+	0.124472i	0.00392634	+	0.00680062i
$336$		0			0
$337$	12.1222	−	20.9962i	0.660336	−	1.14374i	−0.320192	−	0.947353i	$-0.603747\pi$
$337$	12.1222	−	20.9962i	0.660336	−	1.14374i	0.980527	−	0.196382i	$-0.0629194\pi$
$338$		0			0
$339$	−25.8773	+	9.00011i	−1.40546	+	0.488819i
$340$		0			0
$341$	7.84884	+	7.84884i	0.425038	+	0.425038i
$342$		0			0
$343$		−	15.2749i		−	0.824767i
$344$		0			0
$345$	−0.0683602	−	0.100673i	−0.00368039	−	0.00542007i
$346$		0			0
$347$	18.5696	−	4.97570i	0.996867	−	0.267110i	0.276735	−	0.960946i	$-0.410748\pi$
$347$	18.5696	−	4.97570i	0.996867	−	0.267110i	0.720132	+	0.693837i	$0.244081\pi$
$348$		0			0
$349$	15.6423	+	4.19134i	0.837313	+	0.224357i	0.651901	−	0.758304i	$-0.273972\pi$
$349$	15.6423	+	4.19134i	0.837313	+	0.224357i	0.185411	+	0.982661i	$0.440638\pi$
$350$		0			0
$351$	−26.0039	−	8.18252i	−1.38798	−	0.436750i
$352$		0			0
$353$	−7.69391	−	13.3262i	−0.409505	−	0.709284i	0.585329	−	0.810796i	$-0.300965\pi$
$353$	−7.69391	−	13.3262i	−0.409505	−	0.709284i	−0.994834	+	0.101512i	$0.967632\pi$
$354$		0			0
$355$	0.0430587	+	0.160697i	0.00228532	+	0.00852893i
$356$		0			0
$357$	−3.20420	−	0.612527i	−0.169584	−	0.0324184i
$358$		0			0
$359$			2.97883i			0.157217i	0.996906	+	0.0786083i	$0.0250476\pi$
$359$			2.97883i			0.157217i	−0.996906	+	0.0786083i	$0.974952\pi$
$360$		0			0
$361$		−	14.1010i		−	0.742159i
$362$		0			0
$363$	−4.21492	−	12.1188i	−0.221226	−	0.636073i
$364$		0			0
$365$	0.0130689	+	0.0487737i	0.000684056	+	0.00255293i
$366$		0			0
$367$	−12.5585	−	21.7519i	−0.655547	−	1.13544i	−0.981756	−	0.190143i	$-0.939105\pi$
$367$	−12.5585	−	21.7519i	−0.655547	−	1.13544i	0.326210	−	0.945297i	$-0.394228\pi$
$368$		0			0
$369$	−4.09933	+	10.3302i	−0.213403	+	0.537769i
$370$		0			0
$371$	14.8211	+	3.97131i	0.769474	+	0.206180i
$372$		0			0
$373$	−28.8046	+	7.71816i	−1.49144	+	0.399631i	−0.910224	−	0.414116i	$-0.864091\pi$
$373$	−28.8046	+	7.71816i	−1.49144	+	0.399631i	−0.581220	+	0.813747i	$0.697424\pi$
$374$		0			0
$375$	−0.201867	+	0.0147451i	−0.0104244	+	0.000761435i
$376$		0			0
$377$			16.1901i			0.833832i
$378$		0			0
$379$	−10.1985	−	10.1985i	−0.523864	−	0.523864i	0.394872	−	0.918736i	$-0.370789\pi$
$379$	−10.1985	−	10.1985i	−0.523864	−	0.523864i	−0.918736	+	0.394872i	$0.870789\pi$
$380$		0			0
$381$	−7.50518	−	6.48341i	−0.384502	−	0.332155i
$382$		0			0
$383$	−10.5750	+	18.3164i	−0.540356	+	0.935924i	0.458528	+	0.888680i	$0.348377\pi$
$383$	−10.5750	+	18.3164i	−0.540356	+	0.935924i	−0.998883	+	0.0472436i	$0.984956\pi$
$384$		0			0
$385$	−0.0135230	−	0.0234224i	−0.000689194	−	0.00119372i
$386$		0			0
$387$	−14.9317	−	1.73945i	−0.759020	−	0.0884213i
$388$		0			0
$389$	−8.13193	+	30.3488i	−0.412305	+	1.53874i	0.377867	+	0.925860i	$0.376658\pi$
$389$	−8.13193	+	30.3488i	−0.412305	+	1.53874i	−0.790173	+	0.612884i	$0.790009\pi$
$390$		0			0
$391$	8.03056	+	4.63645i	0.406123	+	0.234475i
$392$		0			0
$393$	5.12553	−	10.5921i	0.258549	−	0.534303i
$394$		0			0
$395$	−0.00432797	−	0.00432797i	−0.000217764	−	0.000217764i
$396$		0			0
$397$	−3.24113	+	3.24113i	−0.162668	+	0.162668i	−0.783747	−	0.621080i	$-0.786694\pi$
$397$	−3.24113	+	3.24113i	−0.162668	+	0.162668i	0.621080	+	0.783747i	$0.286694\pi$
$398$		0			0
$399$	−10.0671	+	6.83587i	−0.503986	+	0.342221i
$400$		0			0
$401$	−10.7429	+	18.6073i	−0.536476	+	0.929203i	0.462614	+	0.886560i	$0.346911\pi$
$401$	−10.7429	+	18.6073i	−0.536476	+	0.929203i	−0.999090	+	0.0426439i	$0.986422\pi$
$402$		0			0
$403$	29.6789	+	7.95244i	1.47841	+	0.396139i
$404$		0			0
$405$	0.0894731	−	0.0552828i	0.00444596	−	0.00274702i
$406$		0			0
$407$	2.14269	−	1.23708i	0.106209	−	0.0613200i
$408$		0			0
$409$	23.1426	+	13.3614i	1.14433	+	0.660678i	0.947499	−	0.319760i	$-0.103602\pi$
$409$	23.1426	+	13.3614i	1.14433	+	0.660678i	0.196829	+	0.980438i	$0.436936\pi$
$410$		0			0
$411$	−7.16865	−	1.37039i	−0.353604	−	0.0675963i
$412$		0			0
$413$	−7.85515	+	7.85515i	−0.386527	+	0.386527i
$414$		0			0
$415$	−0.131658			−0.00646283
$416$		0			0
$417$	25.2638	+	12.2252i	1.23718	+	0.598669i
$418$		0			0
$419$	−2.36864	−	8.83989i	−0.115716	−	0.431857i	0.883624	−	0.468198i	$-0.155097\pi$
$419$	−2.36864	−	8.83989i	−0.115716	−	0.431857i	−0.999339	+	0.0363407i	$0.988430\pi$
$420$		0			0
$421$	7.75295	−	28.9344i	0.377856	−	1.41018i	−0.471272	−	0.881988i	$-0.656205\pi$
$421$	7.75295	−	28.9344i	0.377856	−	1.41018i	0.849127	−	0.528188i	$-0.177128\pi$
$422$		0			0
$423$	−6.17391	+	4.88555i	−0.300186	+	0.237544i
$424$		0			0
$425$	6.67852	−	3.85585i	0.323956	−	0.187036i
$426$		0			0
$427$	14.7993	−	3.96545i	0.716187	−	0.191902i
$428$		0			0
$429$	13.0328	+	11.2585i	0.629231	+	0.543566i
$430$		0			0
$431$	7.05544			0.339849			0.169924	−	0.985457i	$-0.445648\pi$
$431$	7.05544			0.339849			0.169924	+	0.985457i	$0.445648\pi$
$432$		0			0
$433$	13.1552			0.632201			0.316100	−	0.948726i	$-0.397626\pi$
$433$	13.1552			0.632201			0.316100	+	0.948726i	$0.397626\pi$
$434$		0			0
$435$	−0.0472679	−	0.0408327i	−0.00226632	−	0.00195778i
$436$		0			0
$437$	33.4109	−	8.95243i	1.59826	−	0.428253i
$438$		0			0
$439$	−12.8757	+	7.43381i	−0.614525	+	0.354796i	−0.774734	−	0.632287i	$-0.782116\pi$
$439$	−12.8757	+	7.43381i	−0.614525	+	0.354796i	0.160209	+	0.987083i	$0.448783\pi$
$440$		0			0
$441$	−15.3612	−	6.09580i	−0.731488	−	0.290276i
$442$		0			0
$443$	−0.797625	+	2.97678i	−0.0378963	+	0.141431i	−0.982282	−	0.187409i	$-0.939991\pi$
$443$	−0.797625	+	2.97678i	−0.0378963	+	0.141431i	0.944386	+	0.328840i	$0.106658\pi$
$444$		0			0
$445$	0.0323940	+	0.120896i	0.00153562	+	0.00573102i
$446$		0			0
$447$	6.07673	+	2.94053i	0.287419	+	0.139082i
$448$		0			0
$449$	−21.8550			−1.03140			−0.515701	−	0.856769i	$-0.672468\pi$
$449$	−21.8550			−1.03140			−0.515701	+	0.856769i	$0.672468\pi$
$450$		0			0
$451$	4.96480	−	4.96480i	0.233783	−	0.233783i
$452$		0			0
$453$	−25.5520	−	4.88462i	−1.20054	−	0.229500i
$454$		0			0
$455$	−0.0648360	−	0.0374331i	−0.00303956	−	0.00175489i
$456$		0			0
$457$	2.32261	−	1.34096i	0.108647	−	0.0627275i	−0.444692	−	0.895684i	$-0.646687\pi$
$457$	2.32261	−	1.34096i	0.108647	−	0.0627275i	0.553339	+	0.832956i	$0.313353\pi$
$458$		0			0
$459$	−4.30226	+	6.76179i	−0.200812	+	0.315613i
$460$		0			0
$461$	−10.2573	−	2.74844i	−0.477732	−	0.128008i	0.0119146	−	0.999929i	$-0.496207\pi$
$461$	−10.2573	−	2.74844i	−0.477732	−	0.128008i	−0.489646	+	0.871921i	$0.662874\pi$
$462$		0			0
$463$	−11.8249	+	20.4814i	−0.549550	+	0.951849i	0.448755	+	0.893655i	$0.351868\pi$
$463$	−11.8249	+	20.4814i	−0.549550	+	0.951849i	−0.998305	+	0.0581943i	$0.981466\pi$
$464$		0			0
$465$	−0.0980702	+	0.0665926i	−0.00454790	+	0.00308816i
$466$		0			0
$467$	−2.22540	+	2.22540i	−0.102979	+	0.102979i	−0.756719	−	0.653740i	$-0.773199\pi$
$467$	−2.22540	+	2.22540i	−0.102979	+	0.102979i	0.653740	+	0.756719i	$0.273199\pi$
$468$		0			0
$469$	10.6199	+	10.6199i	0.490380	+	0.490380i
$470$		0			0
$471$	7.39893	−	15.2902i	0.340925	−	0.704536i
$472$		0			0
$473$	8.22468	+	4.74852i	0.378171	+	0.218337i
$474$		0			0
$475$	7.44518	−	27.7858i	0.341608	−	1.27490i
$476$		0			0
$477$	22.4990	−	30.2456i	1.03016	−	1.38485i
$478$		0			0
$479$	6.23896	+	10.8062i	0.285066	+	0.493748i	0.972625	−	0.232380i	$-0.0746513\pi$
$479$	6.23896	+	10.8062i	0.285066	+	0.493748i	−0.687559	+	0.726128i	$0.741318\pi$
$480$		0			0
$481$	3.42439	−	5.93121i	0.156139	−	0.270440i
$482$		0			0
$483$	−9.62259	−	8.31255i	−0.437843	−	0.378234i
$484$		0			0
$485$	−0.145238	−	0.145238i	−0.00659494	−	0.00659494i
$486$		0			0
$487$		−	12.5314i		−	0.567853i	−0.958846	−	0.283927i	$-0.908363\pi$
$487$		−	12.5314i		−	0.567853i	0.958846	−	0.283927i	$-0.0916372\pi$
$488$		0			0
$489$	12.7672	−	0.932559i	0.577351	−	0.0421718i
$490$		0			0
$491$	−14.6898	+	3.93613i	−0.662942	+	0.177635i	−0.574574	−	0.818453i	$-0.694832\pi$
$491$	−14.6898	+	3.93613i	−0.662942	+	0.177635i	−0.0883688	+	0.996088i	$0.528165\pi$
$492$		0			0
$493$	4.59756	+	1.23191i	0.207064	+	0.0554825i
$494$		0			0
$495$	−0.0657397	+	0.00965524i	−0.00295478	+	0.000433971i
$496$		0			0
$497$	8.69218	+	15.0553i	0.389898	+	0.675322i
$498$		0			0
$499$	7.88570	+	29.4298i	0.353012	+	1.31746i	0.882967	+	0.469434i	$0.155542\pi$
$499$	7.88570	+	29.4298i	0.353012	+	1.31746i	−0.529955	+	0.848026i	$0.677791\pi$
$500$		0			0
$501$	4.14878	+	11.9286i	0.185354	+	0.532933i
$502$		0			0
$503$			1.90106i			0.0847639i	0.999101	+	0.0423820i	$0.0134946\pi$
$503$			1.90106i			0.0847639i	−0.999101	+	0.0423820i	$0.986505\pi$
$504$		0			0
$505$		−	0.0814355i		−	0.00362383i
$506$		0			0
$507$	24.7093	+	4.72352i	1.09738	+	0.209779i
$508$		0			0
$509$	−3.34659	−	12.4896i	−0.148335	−	0.553593i	−0.999584	−	0.0288320i	$-0.990821\pi$
$509$	−3.34659	−	12.4896i	−0.148335	−	0.553593i	0.851249	−	0.524761i	$-0.175845\pi$
$510$		0			0
$511$	2.63819	+	4.56947i	0.116706	+	0.202142i
$512$		0			0
$513$	6.48734	+	29.1829i	0.286423	+	1.28846i
$514$		0			0
$515$	0.0287544	+	0.00770471i	0.00126707	+	0.000339510i
$516$		0			0
$517$	4.80444	−	1.28734i	0.211299	−	0.0566174i
$518$		0			0
$519$	−23.1074	−	34.0300i	−1.01430	−	1.49375i
$520$		0			0
$521$		−	1.24885i		−	0.0547130i	−0.999626	−	0.0273565i	$-0.991291\pi$
$521$		−	1.24885i		−	0.0547130i	0.999626	−	0.0273565i	$-0.00870893\pi$
$522$		0			0
$523$	−9.58031	−	9.58031i	−0.418918	−	0.418918i	0.465913	−	0.884831i	$-0.345726\pi$
$523$	−9.58031	−	9.58031i	−0.418918	−	0.418918i	−0.884831	+	0.465913i	$0.845726\pi$
$524$		0			0
$525$	−9.98811	+	3.47387i	−0.435917	+	0.151612i
$526$		0			0
$527$	4.51656	−	7.82292i	0.196745	−	0.340772i
$528$		0			0
$529$	6.57248	+	11.3839i	0.285760	+	0.494951i
$530$		0			0
$531$	10.8193	+	25.0555i	0.469518	+	1.08732i
$532$		0			0
$533$	5.03034	−	18.7735i	0.217888	−	0.813169i
$534$		0			0
$535$	0.0504047	+	0.0291012i	0.00217918	+	0.00125815i
$536$		0			0
$537$	27.9695	−	2.04299i	1.20697	−	0.0881616i
$538$		0			0
$539$	7.38278	+	7.38278i	0.317999	+	0.317999i
$540$		0			0
$541$	13.0165	−	13.0165i	0.559622	−	0.559622i	−0.369578	−	0.929200i	$-0.620498\pi$
$541$	13.0165	−	13.0165i	0.559622	−	0.559622i	0.929200	+	0.369578i	$0.120498\pi$
$542$		0			0
$543$	0.537699	+	7.36135i	0.0230749	+	0.315906i
$544$		0			0
$545$	−0.0259743	+	0.0449887i	−0.00111262	+	0.00192711i
$546$		0			0
$547$	9.76080	+	2.61540i	0.417341	+	0.111826i	0.461378	−	0.887204i	$-0.347355\pi$
$547$	9.76080	+	2.61540i	0.417341	+	0.111826i	−0.0440366	+	0.999030i	$0.514022\pi$
$548$		0			0
$549$	4.35545	−	37.3878i	0.185886	−	1.59567i
$550$		0			0
$551$	15.3760	−	8.87733i	0.655039	−	0.378187i
$552$		0			0
$553$	−0.553890	−	0.319788i	−0.0235538	−	0.0135988i
$554$		0			0
$555$	0.00867994	+	0.0249567i	0.000368443	+	0.00105935i
$556$		0			0
$557$	26.6259	−	26.6259i	1.12818	−	1.12818i	0.137702	−	0.990474i	$-0.456029\pi$
$557$	26.6259	−	26.6259i	1.12818	−	1.12818i	0.990474	−	0.137702i	$-0.0439715\pi$
$558$		0			0
$559$	26.2889			1.11190
$560$		0			0
$561$	4.18879	−	2.84431i	0.176851	−	0.120087i
$562$		0			0
$563$	−5.67141	−	21.1660i	−0.239021	−	0.892039i	−0.976295	−	0.216445i	$-0.930554\pi$
$563$	−5.67141	−	21.1660i	−0.239021	−	0.892039i	0.737274	−	0.675594i	$-0.236113\pi$
$564$		0			0
$565$	−0.0478429	+	0.178552i	−0.00201276	+	0.00751174i
$566$		0			0
$567$	7.53575	−	7.99973i	0.316472	−	0.335957i
$568$		0			0
$569$	−8.15901	+	4.71061i	−0.342044	+	0.197479i	−0.661175	−	0.750231i	$-0.729942\pi$
$569$	−8.15901	+	4.71061i	−0.342044	+	0.197479i	0.319132	+	0.947710i	$0.396609\pi$
$570$		0			0
$571$	28.4258	−	7.61666i	1.18958	−	0.318747i	0.390861	−	0.920450i	$-0.372177\pi$
$571$	28.4258	−	7.61666i	1.18958	−	0.318747i	0.798720	+	0.601702i	$0.205511\pi$
$572$		0			0
$573$	1.46805	−	7.67950i	0.0613285	−	0.320816i
$574$		0			0
$575$	30.0595			1.25357
$576$		0			0
$577$	−42.9309			−1.78724			−0.893618	−	0.448828i	$-0.851842\pi$
$577$	−42.9309			−1.78724			−0.893618	+	0.448828i	$0.851842\pi$
$578$		0			0
$579$	5.75170	−	2.00044i	0.239033	−	0.0831355i
$580$		0			0
$581$	−13.2888	+	3.56071i	−0.551310	+	0.147723i
$582$		0			0
$583$	−20.6244	+	11.9075i	−0.854175	+	0.493158i
$584$		0			0
$585$	−0.144232	+	0.114134i	−0.00596324	+	0.00471884i
$586$		0			0
$587$	8.13523	−	30.3611i	0.335777	−	1.25314i	−0.567247	−	0.823548i	$-0.691992\pi$
$587$	8.13523	−	30.3611i	0.335777	−	1.25314i	0.903024	−	0.429589i	$-0.141342\pi$
$588$		0			0
$589$	−8.72095	−	32.5470i	−0.359340	−	1.34108i
$590$		0			0
$591$	0.859962	+	11.7733i	0.0353741	+	0.484288i
$592$		0			0
$593$	0.434128			0.0178275			0.00891374	−	0.999960i	$-0.497163\pi$
$593$	0.434128			0.0178275			0.00891374	+	0.999960i	$0.497163\pi$
$594$		0			0
$595$	−0.0155634	+	0.0155634i	−0.000638037	+	0.000638037i
$596$		0			0
$597$	−5.28002	+	6.11215i	−0.216097	+	0.250154i
$598$		0			0
$599$	3.46143	+	1.99846i	0.141430	+	0.0816547i	0.569045	−	0.822306i	$-0.307313\pi$
$599$	3.46143	+	1.99846i	0.141430	+	0.0816547i	−0.427615	+	0.903961i	$0.640646\pi$
$600$		0			0
$601$	3.54563	−	2.04707i	0.144629	−	0.0835019i	−0.425939	−	0.904752i	$-0.640056\pi$
$601$	3.54563	−	2.04707i	0.144629	−	0.0835019i	0.570569	+	0.821250i	$0.306723\pi$
$602$		0			0
$603$	33.8741	−	14.6273i	1.37946	−	0.595669i
$604$		0			0
$605$	−0.0836192	−	0.0224057i	−0.00339961	−	0.000910922i
$606$		0			0
$607$	−16.8996	+	29.2709i	−0.685932	+	1.18807i	0.287211	+	0.957867i	$0.407272\pi$
$607$	−16.8996	+	29.2709i	−0.685932	+	1.18807i	−0.973143	+	0.230202i	$0.926061\pi$
$608$		0			0
$609$	−5.87527	−	2.84304i	−0.238078	−	0.115206i
$610$		0			0
$611$	9.73570	−	9.73570i	0.393864	−	0.393864i
$612$		0			0
$613$	1.73094	+	1.73094i	0.0699119	+	0.0699119i	0.741198	−	0.671286i	$-0.234258\pi$
$613$	1.73094	+	1.73094i	0.0699119	+	0.0699119i	−0.671286	+	0.741198i	$0.734258\pi$
$614$		0			0
$615$	0.0421233	+	0.0620346i	0.00169858	+	0.00250147i
$616$		0			0
$617$	14.9093	+	8.60788i	0.600225	+	0.346540i	0.769130	−	0.639092i	$-0.220690\pi$
$617$	14.9093	+	8.60788i	0.600225	+	0.346540i	−0.168905	+	0.985632i	$0.554023\pi$
$618$		0			0
$619$	1.70053	−	6.34645i	0.0683499	−	0.255085i	−0.923293	−	0.384095i	$-0.874513\pi$
$619$	1.70053	−	6.34645i	0.0683499	−	0.255085i	0.991643	+	0.129010i	$0.0411800\pi$
$620$		0			0
$621$	−27.7016	+	14.4408i	−1.11163	+	0.579490i
$622$		0			0
$623$	6.53931	+	11.3264i	0.261992	+	0.453783i
$624$		0			0
$625$	12.4990	−	21.6489i	0.499959	−	0.865954i
$626$		0			0
$627$	3.54624	−	18.5507i	0.141623	−	0.740846i
$628$		0			0
$629$	−1.42374	−	1.42374i	−0.0567684	−	0.0567684i
$630$		0			0
$631$			13.3295i			0.530639i	0.964161	+	0.265319i	$0.0854774\pi$
$631$			13.3295i			0.530639i	−0.964161	+	0.265319i	$0.914523\pi$
$632$		0			0
$633$	−13.6258	+	28.1583i	−0.541577	+	1.11919i
$634$		0			0
$635$	−0.0646345	+	0.0173188i	−0.00256494	+	0.000687274i
$636$		0			0
$637$	27.9166	+	7.48023i	1.10610	+	0.296377i
$638$		0			0
$639$	42.2557	−	6.20612i	1.67161	−	0.245510i
$640$		0			0
$641$	8.26044	+	14.3075i	0.326268	+	0.565113i	0.981768	−	0.190082i	$-0.0608755\pi$
$641$	8.26044	+	14.3075i	0.326268	+	0.565113i	−0.655500	+	0.755195i	$0.727542\pi$
$642$		0			0
$643$	−6.43213	−	24.0050i	−0.253659	−	0.946667i	−0.968832	−	0.247719i	$-0.920319\pi$
$643$	−6.43213	−	24.0050i	−0.253659	−	0.946667i	0.715173	−	0.698947i	$-0.246348\pi$
$644$		0			0
$645$	−0.0663027	+	0.0767519i	−0.00261067	+	0.00302210i
$646$		0			0
$647$			26.9660i			1.06014i	0.847954	+	0.530071i	$0.177835\pi$
$647$			26.9660i			1.06014i	−0.847954	+	0.530071i	$0.822165\pi$
$648$		0			0
$649$		−	17.2418i		−	0.676800i
$650$		0			0
$651$	−8.09761	+	9.37378i	−0.317370	+	0.367387i
$652$		0			0
$653$	−1.41419	−	5.27782i	−0.0553414	−	0.206537i	0.932719	−	0.360604i	$-0.117429\pi$
$653$	−1.41419	−	5.27782i	−0.0553414	−	0.206537i	−0.988060	+	0.154067i	$0.950763\pi$
$654$		0			0
$655$	−0.0396959	−	0.0687553i	−0.00155105	−	0.00268649i
$656$		0			0
$657$	12.8251	−	1.88364i	0.500356	−	0.0734876i
$658$		0			0
$659$	−0.689165	−	0.184661i	−0.0268460	−	0.00719337i	0.245371	−	0.969429i	$-0.421090\pi$
$659$	−0.689165	−	0.184661i	−0.0268460	−	0.00719337i	−0.272217	+	0.962236i	$0.587757\pi$
$660$		0			0
$661$	−36.9228	+	9.89344i	−1.43613	+	0.384810i	−0.891177	−	0.453656i	$-0.850120\pi$
$661$	−36.9228	+	9.89344i	−1.43613	+	0.384810i	−0.544954	+	0.838466i	$0.683453\pi$
$662$		0			0
$663$	6.10491	−	12.6161i	0.237095	−	0.489968i
$664$		0			0
$665$			0.0821010i			0.00318374i
$666$		0			0
$667$	13.1190	+	13.1190i	0.507970	+	0.507970i
$668$		0			0
$669$	−1.85874	+	9.72326i	−0.0718630	+	0.375923i
$670$		0			0
$671$	−11.8899	+	20.5940i	−0.459006	+	0.795022i
$672$		0			0
$673$	−6.39173	−	11.0708i	−0.246383	−	0.426748i	0.716137	−	0.697960i	$-0.245909\pi$
$673$	−6.39173	−	11.0708i	−0.246383	−	0.426748i	−0.962520	+	0.271212i	$0.912575\pi$
$674$		0			0
$675$	−1.11828	+	25.9560i	−0.0430427	+	0.999046i
$676$		0			0
$677$	6.82184	−	25.4595i	0.262185	−	0.978487i	−0.701766	−	0.712407i	$-0.747605\pi$
$677$	6.82184	−	25.4595i	0.262185	−	0.978487i	0.963951	−	0.266079i	$-0.0857284\pi$
$678$		0			0
$679$	−18.5875	−	10.7315i	−0.713323	−	0.411837i
$680$		0			0
$681$	19.8207	+	29.1897i	0.759529	+	1.11855i
$682$		0			0
$683$	−9.42670	−	9.42670i	−0.360703	−	0.360703i	0.503369	−	0.864072i	$-0.332094\pi$
$683$	−9.42670	−	9.42670i	−0.360703	−	0.360703i	−0.864072	+	0.503369i	$0.832094\pi$
$684$		0			0
$685$	−0.0348195	+	0.0348195i	−0.00133039	+	0.00133039i
$686$		0			0
$687$	−5.98065	−	2.89404i	−0.228176	−	0.110414i
$688$		0			0
$689$	−32.9613	+	57.0906i	−1.25572	+	2.17498i
$690$		0			0
$691$	15.1910	+	4.07041i	0.577891	+	0.154846i	0.535913	−	0.844273i	$-0.319967\pi$
$691$	15.1910	+	4.07041i	0.577891	+	0.154846i	0.0419780	+	0.999119i	$0.486634\pi$
$692$		0			0
$693$	−6.37425	+	2.75248i	−0.242138	+	0.104558i
$694$		0			0
$695$	0.163992	−	0.0946807i	0.00622056	−	0.00359144i
$696$		0			0
$697$	−4.94841	−	2.85696i	−0.187434	−	0.108215i
$698$		0			0
$699$	6.03547	−	6.98666i	0.228283	−	0.264260i
$700$		0			0
$701$	9.62303	−	9.62303i	0.363457	−	0.363457i	−0.501627	−	0.865084i	$-0.667265\pi$
$701$	9.62303	−	9.62303i	0.363457	−	0.363457i	0.865084	+	0.501627i	$0.167265\pi$
$702$		0			0
$703$	−7.51063			−0.283269
$704$		0			0
$705$	0.00386971	+	0.0529782i	0.000145742	+	0.00199527i
$706$		0			0
$707$	−2.20244	−	8.21961i	−0.0828312	−	0.309130i
$708$		0			0
$709$	−10.8223	+	40.3893i	−0.406439	+	1.51685i	0.394947	+	0.918704i	$0.370763\pi$
$709$	−10.8223	+	40.3893i	−0.406439	+	1.51685i	−0.801386	+	0.598148i	$0.795904\pi$
$710$		0			0
$711$	−1.23216	+	0.975036i	−0.0462097	+	0.0365667i
$712$		0			0
$713$	30.4931	−	17.6052i	1.14197	−	0.659319i
$714$		0			0
$715$	0.112239	−	0.0300742i	0.00419749	−	0.00112471i
$716$		0			0
$717$	−45.2759	+	15.7470i	−1.69086	+	0.588081i
$718$		0			0
$719$	−48.7757			−1.81903			−0.909514	−	0.415674i	$-0.863546\pi$
$719$	−48.7757			−1.81903			−0.909514	+	0.415674i	$0.863546\pi$
$720$		0			0
$721$	3.11067			0.115847
$722$		0			0
$723$	0.551050	−	2.88260i	0.0204938	−	0.107205i
$724$		0			0
$725$	14.9037	−	3.99343i	0.553509	−	0.148312i
$726$		0			0
$727$	−34.9918	+	20.2025i	−1.29777	+	0.749270i	−0.980019	−	0.198902i	$-0.936262\pi$
$727$	−34.9918	+	20.2025i	−1.29777	+	0.749270i	−0.317755	+	0.948173i	$0.602929\pi$
$728$		0			0
$729$	−11.4389	−	24.4571i	−0.423662	−	0.905820i
$730$		0			0
$731$	2.00033	−	7.46535i	0.0739850	−	0.276116i
$732$		0			0
$733$	7.60991	+	28.4006i	0.281078	+	1.04900i	0.951658	+	0.307161i	$0.0993789\pi$
$733$	7.60991	+	28.4006i	0.281078	+	1.04900i	−0.670579	+	0.741838i	$0.733954\pi$
$734$		0			0
$735$	−0.0922468	+	0.0626383i	−0.00340257	+	0.00231045i
$736$		0			0
$737$	−23.3102			−0.858644
$738$		0			0
$739$	−15.4222	+	15.4222i	−0.567316	+	0.567316i	−0.931376	−	0.364060i	$-0.881390\pi$
$739$	−15.4222	+	15.4222i	−0.567316	+	0.567316i	0.364060	+	0.931376i	$0.381390\pi$
$740$		0			0
$741$	−17.1740	−	49.3791i	−0.630904	−	1.81399i
$742$		0			0
$743$	−21.5896	−	12.4647i	−0.792045	−	0.457287i	0.0486373	−	0.998817i	$-0.484512\pi$
$743$	−21.5896	−	12.4647i	−0.792045	−	0.457287i	−0.840682	+	0.541529i	$0.817845\pi$
$744$		0			0
$745$	0.0394451	−	0.0227736i	0.00144515	−	0.000834361i
$746$		0			0
$747$	−3.91091	+	33.5718i	−0.143093	+	1.22833i
$748$		0			0
$749$	5.87459	+	1.57409i	0.214653	+	0.0575161i
$750$		0			0
$751$	21.2809	−	36.8596i	0.776551	−	1.34503i	−0.157368	−	0.987540i	$-0.550301\pi$
$751$	21.2809	−	36.8596i	0.776551	−	1.34503i	0.933919	−	0.357486i	$-0.116366\pi$
$752$		0			0
$753$	0.176299	+	2.41362i	0.00642470	+	0.0879571i
$754$		0			0
$755$	−0.124111	+	0.124111i	−0.00451686	+	0.00451686i
$756$		0			0
$757$	1.80855	+	1.80855i	0.0657328	+	0.0657328i	0.739209	−	0.673476i	$-0.235200\pi$
$757$	1.80855	+	1.80855i	0.0657328	+	0.0657328i	−0.673476	+	0.739209i	$0.735200\pi$
$758$		0			0
$759$	19.6835	−	1.43775i	0.714467	−	0.0521872i
$760$		0			0
$761$	−18.5805	−	10.7275i	−0.673543	−	0.388870i	0.123875	−	0.992298i	$-0.460468\pi$
$761$	−18.5805	−	10.7275i	−0.673543	−	0.388870i	−0.797418	+	0.603428i	$0.793801\pi$
$762$		0			0
$763$	−1.40496	+	5.24337i	−0.0508629	+	0.189823i
$764$		0			0
$765$	0.0214363	+	0.0496424i	0.000775029	+	0.00179482i
$766$		0			0
$767$	−23.8636	−	41.3330i	−0.861665	−	1.49245i
$768$		0			0
$769$	−9.98382	+	17.2925i	−0.360026	+	0.623583i	−0.987965	−	0.154680i	$-0.950565\pi$
$769$	−9.98382	+	17.2925i	−0.360026	+	0.623583i	0.627939	+	0.778263i	$0.283899\pi$
$770$		0			0
$771$	−38.6781	+	13.4522i	−1.39296	+	0.484471i
$772$		0			0
$773$	24.8049	+	24.8049i	0.892171	+	0.892171i	0.994727	−	0.102557i	$-0.0327022\pi$
$773$	24.8049	+	24.8049i	0.892171	+	0.892171i	−0.102557	+	0.994727i	$0.532702\pi$
$774$		0			0
$775$		−	29.2823i		−	1.05185i
$776$		0			0
$777$	1.55106	+	2.28423i	0.0556439	+	0.0819463i
$778$		0			0
$779$	−20.5877	+	5.51646i	−0.737631	+	0.197648i
$780$		0			0
$781$	−26.0625	−	6.98342i	−0.932589	−	0.249886i
$782$		0			0
$783$	−11.8161	+	10.8400i	−0.422274	+	0.387391i
$784$		0			0
$785$	−0.0573027	−	0.0992512i	−0.00204522	−	0.00354243i
$786$		0			0
$787$	2.76911	+	10.3344i	0.0987080	+	0.368383i	0.997556	−	0.0698783i	$-0.0222611\pi$
$787$	2.76911	+	10.3344i	0.0987080	+	0.368383i	−0.898848	+	0.438261i	$0.855594\pi$
$788$		0			0
$789$	43.7319	+	8.35998i	1.55690	+	0.297623i
$790$		0			0
$791$			19.3159i			0.686794i
$792$		0			0
$793$			65.8254i			2.33753i
$794$		0			0
$795$	−0.0835483	−	0.240219i	−0.00296315	−	0.00851971i
$796$		0			0
$797$	−12.5408	−	46.8027i	−0.444216	−	1.65784i	−0.717997	−	0.696046i	$-0.754941\pi$
$797$	−12.5408	−	46.8027i	−0.444216	−	1.65784i	0.273781	−	0.961792i	$-0.411726\pi$
$798$		0			0
$799$	−2.02389	−	3.50547i	−0.0716000	−	0.124015i
$800$		0			0
$801$	31.7898	−	4.66900i	1.12324	−	0.164971i
$802$		0			0
$803$	−7.91029	−	2.11956i	−0.279148	−	0.0747975i
$804$		0			0
$805$	−0.0828696	+	0.0222048i	−0.00292077	+	0.000782618i
$806$		0			0
$807$	33.4421	−	2.44273i	1.17722	−	0.0859883i
$808$		0			0
$809$		−	51.3577i		−	1.80564i	−0.430019	−	0.902820i	$-0.641493\pi$
$809$		−	51.3577i		−	1.80564i	0.430019	−	0.902820i	$-0.358507\pi$
$810$		0			0
$811$	2.55652	+	2.55652i	0.0897715	+	0.0897715i	0.750566	−	0.660795i	$-0.229781\pi$
$811$	2.55652	+	2.55652i	0.0897715	+	0.0897715i	−0.660795	+	0.750566i	$0.729781\pi$
$812$		0			0
$813$	−9.31917	−	8.05043i	−0.326837	−	0.282341i
$814$		0			0
$815$	0.0431843	−	0.0747975i	0.00151268	−	0.00262004i
$816$		0			0
$817$	−14.4147	−	24.9670i	−0.504306	−	0.873484i
$818$		0			0
$819$	−11.4711	+	15.4207i	−0.400833	+	0.538844i
$820$		0			0
$821$	−0.0479933	+	0.179113i	−0.00167498	+	0.00625110i	−0.966758	−	0.255692i	$-0.917697\pi$
$821$	−0.0479933	+	0.179113i	−0.00167498	+	0.00625110i	0.965083	+	0.261943i	$0.0843633\pi$
$822$		0			0
$823$	−16.8590	−	9.73353i	−0.587667	−	0.339290i	0.176508	−	0.984299i	$-0.443520\pi$
$823$	−16.8590	−	9.73353i	−0.587667	−	0.339290i	−0.764174	+	0.645010i	$0.776853\pi$
$824$		0			0
$825$	7.14928	−	14.7743i	0.248906	−	0.514375i
$826$		0			0
$827$	−7.70731	−	7.70731i	−0.268009	−	0.268009i	0.560288	−	0.828298i	$-0.310690\pi$
$827$	−7.70731	−	7.70731i	−0.268009	−	0.268009i	−0.828298	+	0.560288i	$0.810690\pi$
$828$		0			0
$829$	−23.8166	+	23.8166i	−0.827184	+	0.827184i	−0.987126	−	0.159942i	$-0.948869\pi$
$829$	−23.8166	+	23.8166i	−0.827184	+	0.827184i	0.159942	+	0.987126i	$0.448869\pi$
$830$		0			0
$831$	−32.2172	+	21.8765i	−1.11760	+	0.758886i
$832$		0			0
$833$	4.24837	−	7.35839i	0.147197	−	0.254953i
$834$		0			0
$835$	0.0823071	+	0.0220541i	0.00284835	+	0.000763214i
$836$		0			0
$837$	14.0674	+	26.9853i	0.486241	+	0.932748i
$838$		0			0
$839$	18.6769	−	10.7831i	0.644799	−	0.372275i	−0.141662	−	0.989915i	$-0.545245\pi$
$839$	18.6769	−	10.7831i	0.644799	−	0.372275i	0.786461	+	0.617640i	$0.211911\pi$
$840$		0			0
$841$	−16.8674	−	9.73839i	−0.581634	−	0.335807i
$842$		0			0
$843$	38.8862	+	7.43366i	1.33931	+	0.256029i
$844$		0			0
$845$	0.120018	−	0.120018i	0.00412873	−	0.00412873i
$846$		0			0
$847$	−9.04599			−0.310824
$848$		0			0
$849$	−9.63573	−	4.66273i	−0.330697	−	0.160024i
$850$		0			0
$851$	−2.03131	−	7.58094i	−0.0696323	−	0.259871i
$852$		0			0
$853$	−10.3419	+	38.5967i	−0.354102	+	1.32153i	0.527510	+	0.849549i	$0.323126\pi$
$853$	−10.3419	+	38.5967i	−0.354102	+	1.32153i	−0.881611	+	0.471976i	$0.843541\pi$
$854$		0			0
$855$	0.187479	+	0.0743974i	0.00641166	+	0.00254434i
$856$		0			0
$857$	−14.5777	+	8.41643i	−0.497964	+	0.287500i	−0.727872	−	0.685713i	$-0.759491\pi$
$857$	−14.5777	+	8.41643i	−0.497964	+	0.287500i	0.229908	+	0.973212i	$0.426157\pi$
$858$		0			0
$859$	−20.7346	+	5.55582i	−0.707455	+	0.189562i	−0.594568	−	0.804046i	$-0.702677\pi$
$859$	−20.7346	+	5.55582i	−0.707455	+	0.189562i	−0.112888	+	0.993608i	$0.536010\pi$
$860$		0			0
$861$	5.92941	+	5.12216i	0.202074	+	0.174563i
$862$		0			0
$863$	−20.3421			−0.692455			−0.346227	−	0.938151i	$-0.612537\pi$
$863$	−20.3421			−0.692455			−0.346227	+	0.938151i	$0.612537\pi$
$864$		0			0
$865$	−0.277527			−0.00943620
$866$		0			0
$867$	19.1640	+	16.5550i	0.650844	+	0.562236i
$868$		0			0
$869$	0.958848	−	0.256922i	0.0325267	−	0.00871550i
$870$		0			0
$871$	−55.8806	+	32.2627i	−1.89344	+	1.09318i
$872$		0			0
$873$	−41.3490	+	32.7204i	−1.39945	+	1.10742i
$874$		0			0
$875$	−0.0369333	+	0.137837i	−0.00124857	+	0.00465974i
$876$		0			0
$877$	4.98805	+	18.6156i	0.168434	+	0.628606i	0.997577	+	0.0695688i	$0.0221624\pi$
$877$	4.98805	+	18.6156i	0.168434	+	0.628606i	−0.829143	+	0.559037i	$0.811171\pi$
$878$		0			0
$879$	6.08116	+	2.94267i	0.205113	+	0.0992539i
$880$		0			0
$881$	37.3378			1.25794			0.628972	−	0.777428i	$-0.283476\pi$
$881$	37.3378			1.25794			0.628972	+	0.777428i	$0.283476\pi$
$882$		0			0
$883$	16.7468	−	16.7468i	0.563576	−	0.563576i	−0.366745	−	0.930321i	$-0.619528\pi$
$883$	16.7468	−	16.7468i	0.563576	−	0.563576i	0.930321	+	0.366745i	$0.119528\pi$
$884$		0			0
$885$	0.180860	+	0.0345740i	0.00607954	+	0.00116219i
$886$		0			0
$887$	36.4841	+	21.0641i	1.22502	+	0.707263i	0.965983	−	0.258606i	$-0.0832630\pi$
$887$	36.4841	+	21.0641i	1.22502	+	0.707263i	0.259033	+	0.965869i	$0.416596\pi$
$888$		0			0
$889$	−6.05543	+	3.49611i	−0.203093	+	0.117256i
$890$		0			0
$891$	0.509210	+	17.0499i	0.0170592	+	0.571194i
$892$		0			0
$893$	−14.5844	−	3.90788i	−0.488049	−	0.130772i
$894$		0			0
$895$	0.0946055	−	0.163862i	0.00316231	−	0.00547729i
$896$		0			0
$897$	45.1965	−	30.6898i	1.50907	−	1.02470i
$898$		0			0
$899$	12.7798	−	12.7798i	0.426229	−	0.426229i
$900$		0			0
$901$	13.7042	+	13.7042i	0.456552	+	0.456552i
$902$		0			0
$903$	−4.61643	+	9.54004i	−0.153625	+	0.317473i
$904$		0			0
$905$	0.0431271	+	0.0248994i	0.00143359	+	0.000827685i
$906$		0			0
$907$	0.275009	−	1.02635i	0.00913154	−	0.0340794i	−0.961210	−	0.275818i	$-0.911051\pi$
$907$	0.275009	−	1.02635i	0.00913154	−	0.0340794i	0.970341	+	0.241739i	$0.0777178\pi$
$908$		0			0
$909$	−20.7654	−	2.41905i	−0.688746	−	0.0802347i
$910$		0			0
$911$	−1.91307	−	3.31354i	−0.0633829	−	0.109782i	0.832593	−	0.553886i	$-0.186856\pi$
$911$	−1.91307	−	3.31354i	−0.0633829	−	0.109782i	−0.895976	+	0.444103i	$0.853522\pi$
$912$		0			0
$913$	10.6764	−	18.4920i	0.353336	−	0.611996i
$914$		0			0
$915$	−0.192181	−	0.166017i	−0.00635330	−	0.00548835i
$916$		0			0
$917$	−5.86616	−	5.86616i	−0.193718	−	0.193718i
$918$		0			0
$919$		−	5.73779i		−	0.189272i	−0.995512	−	0.0946361i	$-0.969831\pi$
$919$		−	5.73779i		−	0.189272i	0.995512	−	0.0946361i	$-0.0301688\pi$
$920$		0			0
$921$	26.4114	−	1.92918i	0.870284	−	0.0635687i
$922$		0			0
$923$	−72.1438	+	19.3309i	−2.37464	+	0.636284i
$924$		0			0
$925$	−6.30460	−	1.68931i	−0.207294	−	0.0555442i
$926$		0			0
$927$	2.81879	−	7.10327i	0.0925813	−	0.233302i
$928$		0			0
$929$	−20.2911	−	35.1451i	−0.665728	−	1.15307i	−0.979087	−	0.203440i	$-0.934788\pi$
$929$	−20.2911	−	35.1451i	−0.665728	−	1.15307i	0.313359	−	0.949635i	$-0.398546\pi$
$930$		0			0
$931$	−8.20310	−	30.6144i	−0.268846	−	1.00335i
$932$		0			0
$933$	−12.8359	−	36.9060i	−0.420228	−	1.20825i
$934$		0			0
$935$		−	0.0341611i		−	0.00111719i
$936$		0			0
$937$		−	27.9974i		−	0.914635i	−0.889304	−	0.457317i	$-0.848810\pi$
$937$		−	27.9974i		−	0.914635i	0.889304	−	0.457317i	$-0.151190\pi$
$938$		0			0
$939$	−10.1607	−	1.94235i	−0.331581	−	0.0633863i
$940$		0			0
$941$	9.68215	+	36.1343i	0.315629	+	1.17794i	0.923402	+	0.383833i	$0.125396\pi$
$941$	9.68215	+	36.1343i	0.315629	+	1.17794i	−0.607773	+	0.794111i	$0.707937\pi$
$942$		0			0
$943$	−11.1362	−	19.2885i	−0.362645	−	0.628119i
$944$		0			0
$945$	−0.0160906	−	0.0723828i	−0.000523429	−	0.00235461i
$946$		0			0
$947$	−18.3948	−	4.92887i	−0.597751	−	0.160167i	−0.0527575	−	0.998607i	$-0.516801\pi$
$947$	−18.3948	−	4.92887i	−0.597751	−	0.160167i	−0.544993	+	0.838441i	$0.683468\pi$
$948$		0			0
$949$	−21.8966	+	5.86717i	−0.710793	+	0.190456i
$950$		0			0
$951$	18.1109	+	26.6717i	0.587285	+	0.864888i
$952$		0			0
$953$			2.49861i			0.0809380i	0.999181	+	0.0404690i	$0.0128852\pi$
$953$			2.49861i			0.0809380i	−0.999181	+	0.0404690i	$0.987115\pi$
$954$		0			0
$955$	−0.0373008	−	0.0373008i	−0.00120703	−	0.00120703i
$956$		0			0
$957$	9.56820	−	3.32782i	0.309296	−	0.107573i
$958$		0			0
$959$	−2.57277	+	4.45617i	−0.0830792	+	0.143897i
$960$		0			0
$961$	−1.64996	−	2.85782i	−0.0532246	−	0.0921877i
$962$		0			0
$963$	8.91785	−	11.9884i	0.287374	−	0.386319i
$964$		0			0
$965$	0.0106340	−	0.0396865i	0.000342319	−	0.00127755i
$966$		0			0
$967$	−3.08638	−	1.78192i	−0.0992513	−	0.0573028i	0.449553	−	0.893254i	$-0.351583\pi$
$967$	−3.08638	−	1.78192i	−0.0992513	−	0.0573028i	−0.548804	+	0.835951i	$0.684917\pi$
$968$		0			0
$969$	−15.3291	+	1.11969i	−0.492442	+	0.0359698i
$970$		0			0
$971$	0.578866	+	0.578866i	0.0185767	+	0.0185767i	0.716334	−	0.697757i	$-0.245819\pi$
$971$	0.578866	+	0.578866i	0.0185767	+	0.0185767i	−0.697757	+	0.716334i	$0.745819\pi$
$972$		0			0
$973$	13.9917	−	13.9917i	0.448553	−	0.448553i
$974$		0			0
$975$	−3.30981	−	45.3128i	−0.105999	−	1.45117i
$976$		0			0
$977$	10.3841	−	17.9859i	0.332218	−	0.575418i	−0.650728	−	0.759310i	$-0.725536\pi$
$977$	10.3841	−	17.9859i	0.332218	−	0.575418i	0.982946	+	0.183892i	$0.0588697\pi$
$978$		0			0
$979$	−19.6074	−	5.25377i	−0.626654	−	0.167911i
$980$		0			0
$981$	10.7002	+	7.95963i	0.341632	+	0.254132i
$982$		0			0
$983$	9.13353	−	5.27325i	0.291314	−	0.168190i	−0.347220	−	0.937784i	$-0.612874\pi$
$983$	9.13353	−	5.27325i	0.291314	−	0.168190i	0.638534	+	0.769593i	$0.279541\pi$
$984$		0			0
$985$	0.0689747	+	0.0398225i	0.00219772	+	0.00126885i
$986$		0			0
$987$	1.82339	+	5.24264i	0.0580391	+	0.166875i
$988$		0			0
$989$	21.3022	−	21.3022i	0.677369	−	0.677369i
$990$		0			0
$991$	24.1374			0.766749			0.383374	−	0.923593i	$-0.374762\pi$
$991$	24.1374			0.766749			0.383374	+	0.923593i	$0.374762\pi$
$992$		0			0
$993$	15.1120	−	10.2615i	0.479565	−	0.325639i
$994$		0			0
$995$	0.0141042	+	0.0526377i	0.000447134	+	0.00166873i
$996$		0			0
$997$	6.02848	−	22.4986i	0.190924	−	0.712538i	−0.802361	−	0.596840i	$-0.796423\pi$
$997$	6.02848	−	22.4986i	0.190924	−	0.712538i	0.993284	−	0.115698i	$-0.0369105\pi$
$998$		0			0
$999$	6.62161	−	1.47198i	0.209498	−	0.0465713i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	576.2.bb.e.49.4		72
3.2	odd	2		1728.2.bc.e.1009.9		72
4.3	odd	2		144.2.x.e.85.12	yes	72
9.2	odd	6		1728.2.bc.e.1585.10		72
9.7	even	3	inner	576.2.bb.e.241.14		72
12.11	even	2		432.2.y.e.37.7		72
16.3	odd	4		144.2.x.e.13.13	✓	72
16.13	even	4	inner	576.2.bb.e.337.14		72
36.7	odd	6		144.2.x.e.133.13	yes	72
36.11	even	6		432.2.y.e.181.6		72
48.29	odd	4		1728.2.bc.e.145.10		72
48.35	even	4		432.2.y.e.253.6		72
144.29	odd	12		1728.2.bc.e.721.9		72
144.61	even	12	inner	576.2.bb.e.529.4		72
144.83	even	12		432.2.y.e.397.7		72
144.115	odd	12		144.2.x.e.61.12	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
144.2.x.e.13.13	✓	72	16.3	odd	4
144.2.x.e.61.12	yes	72	144.115	odd	12
144.2.x.e.85.12	yes	72	4.3	odd	2
144.2.x.e.133.13	yes	72	36.7	odd	6
432.2.y.e.37.7		72	12.11	even	2
432.2.y.e.181.6		72	36.11	even	6
432.2.y.e.253.6		72	48.35	even	4
432.2.y.e.397.7		72	144.83	even	12
576.2.bb.e.49.4		72	1.1	even	1	trivial
576.2.bb.e.241.14		72	9.7	even	3	inner
576.2.bb.e.337.14		72	16.13	even	4	inner
576.2.bb.e.529.4		72	144.61	even	12	inner
1728.2.bc.e.145.10		72	48.29	odd	4
1728.2.bc.e.721.9		72	144.29	odd	12
1728.2.bc.e.1009.9		72	3.2	odd	2
1728.2.bc.e.1585.10		72	9.2	odd	6

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)

\(f(q)\)	\(=\)	\(q+(-1.31071 - 1.13227i) q^{3} +(-0.0112878 + 0.00302457i) q^{5} +(-1.05753 + 0.610563i) q^{7} +(0.435936 + 2.96816i) q^{9} +O(q^{10})\)	\(q+(-1.31071 - 1.13227i) q^{3} +(-0.0112878 + 0.00302457i) q^{5} +(-1.05753 + 0.610563i) q^{7} +(0.435936 + 2.96816i) q^{9} +(0.490535 - 1.83070i) q^{11} +(-1.35786 - 5.06759i) q^{13} +(0.0182197 + 0.00881653i) q^{15} -1.54238 q^{17} +(-4.06823 + 4.06823i) q^{19} +(2.07744 + 0.397131i) q^{21} +(-5.20660 - 3.00603i) q^{23} +(-4.33001 + 2.49993i) q^{25} +(2.78937 - 4.38400i) q^{27} +(-2.98082 - 0.798708i) q^{29} +(-2.92831 + 5.07198i) q^{31} +(-2.71580 + 1.84411i) q^{33} +(0.0100905 - 0.0100905i) q^{35} +(0.923082 + 0.923082i) q^{37} +(-3.95811 + 8.17961i) q^{39} +(3.20829 + 1.85231i) q^{41} +(-1.29691 + 4.84015i) q^{43} +(-0.0138982 - 0.0321856i) q^{45} +(1.31218 + 2.27277i) q^{47} +(-2.75442 + 4.77080i) q^{49} +(2.02162 + 1.74639i) q^{51} +(-8.88508 - 8.88508i) q^{53} +0.0221483i q^{55} +(9.93862 - 0.725952i) q^{57} +(8.78724 - 2.35453i) q^{59} +(-12.1194 - 3.24737i) q^{61} +(-2.27326 - 2.87274i) q^{63} +(0.0306545 + 0.0530952i) q^{65} +(-3.18324 - 11.8800i) q^{67} +(3.42072 + 9.83532i) q^{69} -14.2363i q^{71} -4.32091i q^{73} +(8.50599 + 1.62604i) q^{75} +(0.599006 + 2.23552i) q^{77} +(0.261880 + 0.453589i) q^{79} +(-8.61992 + 2.58785i) q^{81} +(10.8824 + 2.91592i) q^{83} +(0.0174101 - 0.00466503i) q^{85} +(3.00264 + 4.42196i) q^{87} -10.7103i q^{89} +(4.53005 + 4.53005i) q^{91} +(9.58101 - 3.33227i) q^{93} +(0.0336169 - 0.0582262i) q^{95} +(8.78820 + 15.2216i) q^{97} +(5.64765 + 0.657918i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q - 2 q^{3} + 4 q^{5}+O(q^{10}) \) 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

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Representations

Groups

Database

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