LMFDB - Embedded newform 504.2.q.d.25.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(25,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 4, 4]))

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

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

chi := DirichletCharacter("504.25");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.q (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$22$
Relative dimension:	$11$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.3
Character	$\chi$	$=$	504.25
Dual form			504.2.q.d.121.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.47982 - 0.900079i) q^{3} +(1.26145 - 2.18490i) q^{5} +(2.63136 - 0.275550i) q^{7} +(1.37972 + 2.66390i) q^{9} +O(q^{10})$	\(q+(-1.47982 - 0.900079i) q^{3} +(1.26145 - 2.18490i) q^{5} +(2.63136 - 0.275550i) q^{7} +(1.37972 + 2.66390i) q^{9} +(2.85648 + 4.94757i) q^{11} +(-2.45245 - 4.24777i) q^{13} +(-3.83330 + 2.09784i) q^{15} +(2.49483 - 4.32118i) q^{17} +(-0.00383929 - 0.00664984i) q^{19} +(-4.14195 - 1.96067i) q^{21} +(-0.333877 + 0.578292i) q^{23} +(-0.682524 - 1.18217i) q^{25} +(0.355997 - 5.18394i) q^{27} +(3.85082 - 6.66981i) q^{29} -7.76605 q^{31} +(0.226135 - 9.89256i) q^{33} +(2.71729 - 6.09686i) q^{35} +(-3.19562 - 5.53498i) q^{37} +(-0.194150 + 8.49333i) q^{39} +(5.21159 + 9.02673i) q^{41} +(4.42935 - 7.67185i) q^{43} +(7.56081 + 0.345848i) q^{45} +2.16104 q^{47} +(6.84814 - 1.45015i) q^{49} +(-7.58129 + 4.14900i) q^{51} +(-3.69858 + 6.40613i) q^{53} +14.4133 q^{55} +(-0.000303939 + 0.0132962i) q^{57} -0.523594 q^{59} -8.99082 q^{61} +(4.36457 + 6.62952i) q^{63} -12.3746 q^{65} -5.09582 q^{67} +(1.01458 - 0.555250i) q^{69} -5.68471 q^{71} +(-1.52062 + 2.63379i) q^{73} +(-0.0540325 + 2.36372i) q^{75} +(8.87975 + 12.2318i) q^{77} +6.16230 q^{79} +(-5.19277 + 7.35086i) q^{81} +(-0.258726 + 0.448126i) q^{83} +(-6.29422 - 10.9019i) q^{85} +(-11.7019 + 6.40406i) q^{87} +(1.19093 + 2.06274i) q^{89} +(-7.62377 - 10.5017i) q^{91} +(11.4923 + 6.99006i) q^{93} -0.0193723 q^{95} +(4.32994 - 7.49968i) q^{97} +(-9.23873 + 14.4356i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9	$ 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) $ 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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
$3$	−1.47982	−	0.900079i	−0.854373	−	0.519661i
$3$	−1.47982	−	0.900079i	−0.854373	−	0.519661i
$4$		0			0
$5$	1.26145	−	2.18490i	0.564139	−	0.977117i	−0.432991	−	0.901398i	$-0.642542\pi$
$5$	1.26145	−	2.18490i	0.564139	−	0.977117i	0.997129	−	0.0757184i	$-0.0241250\pi$
$6$		0			0
$7$	2.63136	−	0.275550i	0.994562	−	0.104148i
$7$	2.63136	−	0.275550i	0.994562	−	0.104148i
$8$		0			0
$9$	1.37972	+	2.66390i	0.459905	+	0.887968i
$10$		0			0
$11$	2.85648	+	4.94757i	0.861262	+	1.49175i	0.870712	+	0.491794i	$0.163659\pi$
$11$	2.85648	+	4.94757i	0.861262	+	1.49175i	−0.00944971	+	0.999955i	$0.503008\pi$
$12$		0			0
$13$	−2.45245	−	4.24777i	−0.680188	−	1.17812i	−0.974923	−	0.222541i	$-0.928565\pi$
$13$	−2.45245	−	4.24777i	−0.680188	−	1.17812i	0.294735	−	0.955579i	$-0.404769\pi$
$14$		0			0
$15$	−3.83330	+	2.09784i	−0.989754	+	0.541661i
$16$		0			0
$17$	2.49483	−	4.32118i	0.605086	−	1.04804i	−0.386952	−	0.922100i	$-0.626472\pi$
$17$	2.49483	−	4.32118i	0.605086	−	1.04804i	0.992038	−	0.125939i	$-0.0401945\pi$
$18$		0			0
$19$	−0.00383929	−	0.00664984i	−0.000880793	−	0.00152558i	0.865585	−	0.500763i	$-0.166947\pi$
$19$	−0.00383929	−	0.00664984i	−0.000880793	−	0.00152558i	−0.866465	+	0.499237i	$0.833614\pi$
$20$		0			0
$21$	−4.14195	−	1.96067i	−0.903848	−	0.427853i
$22$		0			0
$23$	−0.333877	+	0.578292i	−0.0696181	+	0.120582i	−0.898733	−	0.438496i	$-0.855511\pi$
$23$	−0.333877	+	0.578292i	−0.0696181	+	0.120582i	0.829115	+	0.559078i	$0.188845\pi$
$24$		0			0
$25$	−0.682524	−	1.18217i	−0.136505	−	0.236433i
$26$		0			0
$27$	0.355997	−	5.18394i	0.0685117	−	0.997650i
$28$		0			0
$29$	3.85082	−	6.66981i	0.715079	−	1.23855i	−0.247851	−	0.968798i	$-0.579724\pi$
$29$	3.85082	−	6.66981i	0.715079	−	1.23855i	0.962929	−	0.269754i	$-0.0869424\pi$
$30$		0			0
$31$	−7.76605			−1.39482			−0.697412	−	0.716671i	$-0.745665\pi$
$31$	−7.76605			−1.39482			−0.697412	+	0.716671i	$0.745665\pi$
$32$		0			0
$33$	0.226135	−	9.89256i	0.0393651	−	1.72207i
$34$		0			0
$35$	2.71729	−	6.09686i	0.459306	−	1.03056i
$36$		0			0
$37$	−3.19562	−	5.53498i	−0.525357	−	0.909946i	−0.999564	−	0.0295319i	$-0.990598\pi$
$37$	−3.19562	−	5.53498i	−0.525357	−	0.909946i	0.474207	−	0.880414i	$-0.342735\pi$
$38$		0			0
$39$	−0.194150	+	8.49333i	−0.0310889	+	1.36002i
$40$		0			0
$41$	5.21159	+	9.02673i	0.813913	+	1.40974i	0.910106	+	0.414376i	$0.136000\pi$
$41$	5.21159	+	9.02673i	0.813913	+	1.40974i	−0.0961931	+	0.995363i	$0.530667\pi$
$42$		0			0
$43$	4.42935	−	7.67185i	0.675469	−	1.16995i	−0.300863	−	0.953668i	$-0.597275\pi$
$43$	4.42935	−	7.67185i	0.675469	−	1.16995i	0.976332	−	0.216279i	$-0.0693921\pi$
$44$		0			0
$45$	7.56081	+	0.345848i	1.12710	+	0.0515559i
$46$		0			0
$47$	2.16104			0.315220			0.157610	−	0.987501i	$-0.449621\pi$
$47$	2.16104			0.315220			0.157610	+	0.987501i	$0.449621\pi$
$48$		0			0
$49$	6.84814	−	1.45015i	0.978306	−	0.207164i
$50$		0			0
$51$	−7.58129	+	4.14900i	−1.06159	+	0.580977i
$52$		0			0
$53$	−3.69858	+	6.40613i	−0.508039	+	0.879950i	0.491917	+	0.870642i	$0.336296\pi$
$53$	−3.69858	+	6.40613i	−0.508039	+	0.879950i	−0.999957	+	0.00930815i	$0.997037\pi$
$54$		0			0
$55$	14.4133			1.94348
$56$		0			0
$57$	−0.000303939		0.0132962i	−4.02578e−5		0.00176112i
$58$		0			0
$59$	−0.523594			−0.0681661			−0.0340831	−	0.999419i	$-0.510851\pi$
$59$	−0.523594			−0.0681661			−0.0340831	+	0.999419i	$0.510851\pi$
$60$		0			0
$61$	−8.99082			−1.15116			−0.575578	−	0.817747i	$-0.695223\pi$
$61$	−8.99082			−1.15116			−0.575578	+	0.817747i	$0.695223\pi$
$62$		0			0
$63$	4.36457	+	6.62952i	0.549885	+	0.835241i
$64$		0			0
$65$	−12.3746			−1.53488
$66$		0			0
$67$	−5.09582			−0.622554			−0.311277	−	0.950319i	$-0.600757\pi$
$67$	−5.09582			−0.622554			−0.311277	+	0.950319i	$0.600757\pi$
$68$		0			0
$69$	1.01458	−	0.555250i	0.122142	−	0.0668443i
$70$		0			0
$71$	−5.68471			−0.674651			−0.337325	−	0.941388i	$-0.609522\pi$
$71$	−5.68471			−0.674651			−0.337325	+	0.941388i	$0.609522\pi$
$72$		0			0
$73$	−1.52062	+	2.63379i	−0.177975	+	0.308262i	−0.941187	−	0.337887i	$-0.890288\pi$
$73$	−1.52062	+	2.63379i	−0.177975	+	0.308262i	0.763212	+	0.646148i	$0.223621\pi$
$74$		0			0
$75$	−0.0540325	+	2.36372i	−0.00623913	+	0.272938i
$76$		0			0
$77$	8.87975	+	12.2318i	1.01194	+	1.39394i
$78$		0			0
$79$	6.16230			0.693313			0.346657	−	0.937992i	$-0.387317\pi$
$79$	6.16230			0.693313			0.346657	+	0.937992i	$0.387317\pi$
$80$		0			0
$81$	−5.19277	+	7.35086i	−0.576974	+	0.816762i
$82$		0			0
$83$	−0.258726	+	0.448126i	−0.0283988	+	0.0491882i	−0.879876	−	0.475204i	$-0.842374\pi$
$83$	−0.258726	+	0.448126i	−0.0283988	+	0.0491882i	0.851477	+	0.524392i	$0.175708\pi$
$84$		0			0
$85$	−6.29422	−	10.9019i	−0.682704	−	1.18248i
$86$		0			0
$87$	−11.7019	+	6.40406i	−1.25457	+	0.686587i
$88$		0			0
$89$	1.19093	+	2.06274i	0.126238	+	0.218650i	0.922216	−	0.386675i	$-0.126376\pi$
$89$	1.19093	+	2.06274i	0.126238	+	0.218650i	−0.795978	+	0.605325i	$0.793043\pi$
$90$		0			0
$91$	−7.62377	−	10.5017i	−0.799188	−	1.10087i
$92$		0			0
$93$	11.4923	+	6.99006i	1.19170	+	0.724835i
$94$		0			0
$95$	−0.0193723			−0.00198756
$96$		0			0
$97$	4.32994	−	7.49968i	0.439639	−	0.761477i	−0.558022	−	0.829826i	$-0.688440\pi$
$97$	4.32994	−	7.49968i	0.439639	−	0.761477i	0.997662	+	0.0683485i	$0.0217730\pi$
$98$		0			0
$99$	−9.23873	+	14.4356i	−0.928527	+	1.45084i
$100$		0			0
$101$	4.66783	+	8.08492i	0.464466	+	0.804479i	0.999177	−	0.0405558i	$-0.0129128\pi$
$101$	4.66783	+	8.08492i	0.464466	+	0.804479i	−0.534711	+	0.845035i	$0.679580\pi$
$102$		0			0
$103$	−8.10926	+	14.0456i	−0.799029	+	1.38396i	0.121220	+	0.992626i	$0.461319\pi$
$103$	−8.10926	+	14.0456i	−0.799029	+	1.38396i	−0.920249	+	0.391333i	$0.872014\pi$
$104$		0			0
$105$	−9.50874	+	6.57646i	−0.927958	+	0.641797i
$106$		0			0
$107$	4.50171	+	7.79718i	0.435196	+	0.753782i	0.997312	−	0.0732767i	$-0.0233456\pi$
$107$	4.50171	+	7.79718i	0.435196	+	0.753782i	−0.562115	+	0.827059i	$0.690012\pi$
$108$		0			0
$109$	3.71563	−	6.43566i	0.355893	−	0.616424i	−0.631378	−	0.775476i	$-0.717510\pi$
$109$	3.71563	−	6.43566i	0.355893	−	0.616424i	0.987270	+	0.159051i	$0.0508435\pi$
$110$		0			0
$111$	−0.252984	+	11.0671i	−0.0240121	+	1.05044i
$112$		0			0
$113$	7.14642	+	12.3780i	0.672278	+	1.16442i	0.977256	+	0.212061i	$0.0680175\pi$
$113$	7.14642	+	12.3780i	0.672278	+	1.16442i	−0.304978	+	0.952359i	$0.598649\pi$
$114$		0			0
$115$	0.842339	+	1.45897i	0.0785486	+	0.136050i
$116$		0			0
$117$	7.93197	−	12.3938i	0.733311	−	1.14581i
$118$		0			0
$119$	5.37411	−	12.0580i	0.492644	−	1.10536i
$120$		0			0
$121$	−10.8190	+	18.7390i	−0.983544	+	1.70355i
$122$		0			0
$123$	0.412578	−	18.0487i	0.0372009	−	1.62740i
$124$		0			0
$125$	9.17064			0.820247
$126$		0			0
$127$	−1.96011			−0.173932			−0.0869660	−	0.996211i	$-0.527717\pi$
$127$	−1.96011			−0.173932			−0.0869660	+	0.996211i	$0.527717\pi$
$128$		0			0
$129$	−13.4599	+	7.36618i	−1.18508	+	0.648556i
$130$		0			0
$131$	1.99412	−	3.45392i	0.174227	−	0.301771i	−0.765666	−	0.643238i	$-0.777591\pi$
$131$	1.99412	−	3.45392i	0.174227	−	0.301771i	0.939894	+	0.341467i	$0.110924\pi$
$132$		0			0
$133$	−0.0119349	−	0.0164402i	−0.00103489	−	0.00142555i
$134$		0			0
$135$	−10.8773	−	7.31712i	−0.936171	−	0.629757i
$136$		0			0
$137$	3.70422	+	6.41589i	0.316473	+	0.548147i	0.979749	−	0.200227i	$-0.0641681\pi$
$137$	3.70422	+	6.41589i	0.316473	+	0.548147i	−0.663277	+	0.748374i	$0.730835\pi$
$138$		0			0
$139$	6.92660	+	11.9972i	0.587507	+	1.01759i	0.994558	+	0.104186i	$0.0332238\pi$
$139$	6.92660	+	11.9972i	0.587507	+	1.01759i	−0.407051	+	0.913405i	$0.633443\pi$
$140$		0			0
$141$	−3.19795	−	1.94511i	−0.269316	−	0.163808i
$142$		0			0
$143$	14.0108	−	24.2674i	1.17164	−	2.02934i
$144$		0			0
$145$	−9.71524	−	16.8273i	−0.806807	−	1.39743i
$146$		0			0
$147$	−11.4392	−	4.01792i	−0.943493	−	0.331392i
$148$		0			0
$149$	7.05202	−	12.2144i	0.577724	−	1.00065i	−0.418016	−	0.908440i	$-0.637274\pi$
$149$	7.05202	−	12.2144i	0.577724	−	1.00065i	0.995740	−	0.0922071i	$-0.0293922\pi$
$150$		0			0
$151$	5.30027	+	9.18034i	0.431330	+	0.747086i	0.996988	−	0.0775543i	$-0.0247111\pi$
$151$	5.30027	+	9.18034i	0.431330	+	0.747086i	−0.565658	+	0.824640i	$0.691378\pi$
$152$		0			0
$153$	14.9534	+	0.683999i	1.20891	+	0.0552980i
$154$		0			0
$155$	−9.79650	+	16.9680i	−0.786874	+	1.36291i
$156$		0			0
$157$	−0.259558			−0.0207150			−0.0103575	−	0.999946i	$-0.503297\pi$
$157$	−0.259558			−0.0207150			−0.0103575	+	0.999946i	$0.503297\pi$
$158$		0			0
$159$	11.2393	−	6.15089i	0.891331	−	0.487797i
$160$		0			0
$161$	−0.719203	+	1.61370i	−0.0566811	+	0.127177i
$162$		0			0
$163$	6.31882	+	10.9445i	0.494928	+	0.857241i	0.999983	−	0.00584647i	$-0.00186100\pi$
$163$	6.31882	+	10.9445i	0.494928	+	0.857241i	−0.505055	+	0.863087i	$0.668528\pi$
$164$		0			0
$165$	−21.3290	−	12.9731i	−1.66046	−	1.00995i
$166$		0			0
$167$	−5.74959	−	9.95859i	−0.444917	−	0.770619i	0.553129	−	0.833095i	$-0.313433\pi$
$167$	−5.74959	−	9.95859i	−0.444917	−	0.770619i	−0.998046	+	0.0624765i	$0.980100\pi$
$168$		0			0
$169$	−5.52905	+	9.57659i	−0.425311	+	0.736661i
$170$		0			0
$171$	0.0124174	−	0.0194024i	0.000949583	−	0.00148374i
$172$		0			0
$173$	−15.8094			−1.20197			−0.600984	−	0.799261i	$-0.705225\pi$
$173$	−15.8094			−1.20197			−0.600984	+	0.799261i	$0.705225\pi$
$174$		0			0
$175$	−2.12171	−	2.92264i	−0.160387	−	0.220931i
$176$		0			0
$177$	0.774823	+	0.471276i	0.0582393	+	0.0354233i
$178$		0			0
$179$	−8.49849	+	14.7198i	−0.635207	+	1.10021i	0.351265	+	0.936276i	$0.385752\pi$
$179$	−8.49849	+	14.7198i	−0.635207	+	1.10021i	−0.986471	+	0.163934i	$0.947582\pi$
$180$		0			0
$181$	6.35841			0.472617			0.236308	−	0.971678i	$-0.424062\pi$
$181$	6.35841			0.472617			0.236308	+	0.971678i	$0.424062\pi$
$182$		0			0
$183$	13.3048	+	8.09245i	0.983516	+	0.598211i
$184$		0			0
$185$	−16.1245			−1.18550
$186$		0			0
$187$	28.5058			2.08455
$188$		0			0
$189$	−0.491679	−	13.7389i	−0.0357644	−	0.999360i
$190$		0			0
$191$	−4.14094			−0.299628			−0.149814	−	0.988714i	$-0.547867\pi$
$191$	−4.14094			−0.299628			−0.149814	+	0.988714i	$0.547867\pi$
$192$		0			0
$193$	−7.69586			−0.553960			−0.276980	−	0.960876i	$-0.589334\pi$
$193$	−7.69586			−0.553960			−0.276980	+	0.960876i	$0.589334\pi$
$194$		0			0
$195$	18.3122	+	11.1381i	1.31136	+	0.797618i
$196$		0			0
$197$	3.29508			0.234765			0.117383	−	0.993087i	$-0.462550\pi$
$197$	3.29508			0.234765			0.117383	+	0.993087i	$0.462550\pi$
$198$		0			0
$199$	8.08840	−	14.0095i	0.573371	−	0.993108i	−0.422845	−	0.906202i	$-0.638969\pi$
$199$	8.08840	−	14.0095i	0.573371	−	0.993108i	0.996216	−	0.0869063i	$-0.0276981\pi$
$200$		0			0
$201$	7.54088	+	4.58664i	0.531893	+	0.323517i
$202$		0			0
$203$	8.29503	−	18.6118i	0.582197	−	1.30629i
$204$		0			0
$205$	26.2967			1.83664
$206$		0			0
$207$	−2.00117	−	0.0915377i	−0.139091	−	0.00636231i
$208$		0			0
$209$	0.0219337	−	0.0379903i	0.00151719	−	0.00262784i
$210$		0			0
$211$	−13.9633	−	24.1851i	−0.961273	−	1.66497i	−0.719312	−	0.694687i	$-0.755543\pi$
$211$	−13.9633	−	24.1851i	−0.961273	−	1.66497i	−0.241961	−	0.970286i	$-0.577791\pi$
$212$		0			0
$213$	8.41232	+	5.11668i	0.576403	+	0.350589i
$214$		0			0
$215$	−11.1748	−	19.3554i	−0.762116	−	1.32002i
$216$		0			0
$217$	−20.4353	+	2.13994i	−1.38724	+	0.145268i
$218$		0			0
$219$	4.62086	−	2.52885i	0.312249	−	0.170884i
$220$		0			0
$221$	−24.4738			−1.64629
$222$		0			0
$223$	−10.1652	+	17.6066i	−0.680711	+	1.17903i	0.294054	+	0.955789i	$0.404996\pi$
$223$	−10.1652	+	17.6066i	−0.680711	+	1.17903i	−0.974764	+	0.223237i	$0.928338\pi$
$224$		0			0
$225$	2.20749	−	3.44923i	0.147166	−	0.229949i
$226$		0			0
$227$	2.84470	+	4.92716i	0.188809	+	0.327027i	0.944853	−	0.327493i	$-0.106204\pi$
$227$	2.84470	+	4.92716i	0.188809	+	0.327027i	−0.756044	+	0.654520i	$0.772871\pi$
$228$		0			0
$229$	−7.42708	+	12.8641i	−0.490795	+	0.850082i	−0.999944	−	0.0105964i	$-0.996627\pi$
$229$	−7.42708	+	12.8641i	−0.490795	+	0.850082i	0.509149	+	0.860679i	$0.329960\pi$
$230$		0			0
$231$	−2.13085	−	26.0932i	−0.140200	−	1.71681i
$232$		0			0
$233$	6.70652	+	11.6160i	0.439358	+	0.760991i	0.997640	−	0.0686603i	$-0.0218725\pi$
$233$	6.70652	+	11.6160i	0.439358	+	0.760991i	−0.558282	+	0.829652i	$0.688539\pi$
$234$		0			0
$235$	2.72605	−	4.72166i	0.177828	−	0.308007i
$236$		0			0
$237$	−9.11908	−	5.54656i	−0.592348	−	0.360288i
$238$		0			0
$239$	−9.33123	−	16.1622i	−0.603587	−	1.04544i	−0.992273	−	0.124073i	$-0.960404\pi$
$239$	−9.33123	−	16.1622i	−0.603587	−	1.04544i	0.388686	−	0.921370i	$-0.372929\pi$
$240$		0			0
$241$	10.7080	+	18.5468i	0.689762	+	1.19470i	0.971915	+	0.235333i	$0.0756181\pi$
$241$	10.7080	+	18.5468i	0.689762	+	1.19470i	−0.282153	+	0.959369i	$0.591049\pi$
$242$		0			0
$243$	14.3007	−	6.20403i	0.917390	−	0.397988i
$244$		0			0
$245$	5.47018	−	16.7918i	0.349477	−	1.07279i
$246$		0			0
$247$	−0.0188313	+	0.0326168i	−0.00119821	+	0.00207536i
$248$		0			0
$249$	0.786216	−	0.430271i	0.0498244	−	0.0272673i
$250$		0			0
$251$	−0.462898			−0.0292179			−0.0146089	−	0.999893i	$-0.504650\pi$
$251$	−0.462898			−0.0292179			−0.0146089	+	0.999893i	$0.504650\pi$
$252$		0			0
$253$	−3.81485			−0.239838
$254$		0			0
$255$	−0.498286	+	21.7981i	−0.0312039	+	1.36505i
$256$		0			0
$257$	−0.401256	+	0.694996i	−0.0250297	+	0.0433527i	−0.878269	−	0.478167i	$-0.841301\pi$
$257$	−0.401256	+	0.694996i	−0.0250297	+	0.0433527i	0.853239	+	0.521520i	$0.174635\pi$
$258$		0			0
$259$	−9.93401	−	13.6840i	−0.617270	−	0.850282i
$260$		0			0
$261$	23.0808	+	1.05576i	1.42866	+	0.0653501i
$262$		0			0
$263$	−0.100693	−	0.174406i	−0.00620902	−	0.0107543i	0.862904	−	0.505368i	$-0.168643\pi$
$263$	−0.100693	−	0.174406i	−0.00620902	−	0.0107543i	−0.869113	+	0.494613i	$0.835310\pi$
$264$		0			0
$265$	9.33117	+	16.1621i	0.573209	+	0.992828i
$266$		0			0
$267$	0.0942803	−	4.12441i	0.00576986	−	0.252410i
$268$		0			0
$269$	−11.1773	+	19.3596i	−0.681490	+	1.18038i	0.293036	+	0.956101i	$0.405334\pi$
$269$	−11.1773	+	19.3596i	−0.681490	+	1.18038i	−0.974526	+	0.224274i	$0.927999\pi$
$270$		0			0
$271$	−1.78925	−	3.09907i	−0.108689	−	0.188255i	0.806550	−	0.591166i	$-0.201332\pi$
$271$	−1.78925	−	3.09907i	−0.108689	−	0.188255i	−0.915240	+	0.402910i	$0.867999\pi$
$272$		0			0
$273$	1.82946	+	22.4025i	0.110724	+	1.35586i
$274$		0			0
$275$	3.89924	−	6.75367i	0.235133	−	0.407262i
$276$		0			0
$277$	5.05336	+	8.75267i	0.303627	+	0.525897i	0.976955	−	0.213447i	$-0.0684690\pi$
$277$	5.05336	+	8.75267i	0.303627	+	0.525897i	−0.673328	+	0.739344i	$0.735136\pi$
$278$		0			0
$279$	−10.7149	−	20.6880i	−0.641487	−	1.23856i
$280$		0			0
$281$	12.7114	−	22.0167i	0.758296	−	1.31341i	−0.185422	−	0.982659i	$-0.559365\pi$
$281$	12.7114	−	22.0167i	0.758296	−	1.31341i	0.943719	−	0.330749i	$-0.107301\pi$
$282$		0			0
$283$	3.87666			0.230443			0.115222	−	0.993340i	$-0.463242\pi$
$283$	3.87666			0.230443			0.115222	+	0.993340i	$0.463242\pi$
$284$		0			0
$285$	0.0286675	+	0.0174366i	0.00169811	+	0.00103286i
$286$		0			0
$287$	16.2009	+	22.3166i	0.956308	+	1.31730i
$288$		0			0
$289$	−3.94838	−	6.83879i	−0.232257	−	0.402282i
$290$		0			0
$291$	−13.1578	+	7.20087i	−0.771326	+	0.422122i
$292$		0			0
$293$	0.428834	+	0.742762i	0.0250527	+	0.0433926i	0.878280	−	0.478147i	$-0.158691\pi$
$293$	0.428834	+	0.742762i	0.0250527	+	0.0433926i	−0.853227	+	0.521539i	$0.825358\pi$
$294$		0			0
$295$	−0.660489	+	1.14400i	−0.0384551	+	0.0666063i
$296$		0			0
$297$	26.6648	−	13.0465i	1.54725	−	0.757036i
$298$		0			0
$299$	3.27527			0.189414
$300$		0			0
$301$	9.54124	−	21.4079i	0.549948	−	1.23393i
$302$		0			0
$303$	0.369532	−	16.1656i	0.0212290	−	0.928690i
$304$		0			0
$305$	−11.3415	+	19.6440i	−0.649412	+	1.12481i
$306$		0			0
$307$	−0.717950			−0.0409756			−0.0204878	−	0.999790i	$-0.506522\pi$
$307$	−0.717950			−0.0409756			−0.0204878	+	0.999790i	$0.506522\pi$
$308$		0			0
$309$	24.6424	−	13.4860i	1.40186	−	0.767192i
$310$		0			0
$311$	−9.45213			−0.535981			−0.267990	−	0.963422i	$-0.586360\pi$
$311$	−9.45213			−0.535981			−0.267990	+	0.963422i	$0.586360\pi$
$312$		0			0
$313$	−23.2635			−1.31493			−0.657464	−	0.753486i	$-0.728371\pi$
$313$	−23.2635			−1.31493			−0.657464	+	0.753486i	$0.728371\pi$
$314$		0			0
$315$	19.9905	−	1.17333i	1.12634	−	0.0661098i
$316$		0			0
$317$	13.2354			0.743375			0.371687	−	0.928358i	$-0.378779\pi$
$317$	13.2354			0.743375			0.371687	+	0.928358i	$0.378779\pi$
$318$		0			0
$319$	43.9992			2.46348
$320$		0			0
$321$	0.356380	−	15.5903i	0.0198912	−	0.870165i
$322$		0			0
$323$	−0.0383135			−0.00213182
$324$		0			0
$325$	−3.34772	+	5.79841i	−0.185698	+	0.321638i
$326$		0			0
$327$	−11.2911	+	6.17924i	−0.624397	+	0.341713i
$328$		0			0
$329$	5.68649	−	0.595476i	0.313506	−	0.0328297i
$330$		0			0
$331$	−30.4330			−1.67275			−0.836375	−	0.548158i	$-0.815329\pi$
$331$	−30.4330			−1.67275			−0.836375	+	0.548158i	$0.815329\pi$
$332$		0			0
$333$	10.3356	−	16.1495i	0.566388	−	0.884989i
$334$		0			0
$335$	−6.42813	+	11.1339i	−0.351206	+	0.608307i
$336$		0			0
$337$	−0.767420	−	1.32921i	−0.0418041	−	0.0724067i	0.844366	−	0.535766i	$-0.179977\pi$
$337$	−0.767420	−	1.32921i	−0.0418041	−	0.0724067i	−0.886170	+	0.463360i	$0.846644\pi$
$338$		0			0
$339$	0.565751	−	24.7494i	0.0307274	−	1.34421i
$340$		0			0
$341$	−22.1836	−	38.4231i	−1.20131	−	2.08073i
$342$		0			0
$343$	17.6204	−	5.70287i	0.951410	−	0.307926i
$344$		0			0
$345$	0.0666843	−	2.91719i	0.00359016	−	0.157056i
$346$		0			0
$347$	−28.6072			−1.53571			−0.767856	−	0.640622i	$-0.778677\pi$
$347$	−28.6072			−1.53571			−0.767856	+	0.640622i	$0.778677\pi$
$348$		0			0
$349$	−9.05123	+	15.6772i	−0.484501	+	0.839181i	−0.999841	−	0.0178047i	$-0.994332\pi$
$349$	−9.05123	+	15.6772i	−0.484501	+	0.839181i	0.515340	+	0.856986i	$0.327666\pi$
$350$		0			0
$351$	−22.8933	+	11.2012i	−1.22195	+	0.597875i
$352$		0			0
$353$	−7.29541	−	12.6360i	−0.388295	−	0.672547i	0.603925	−	0.797041i	$-0.293603\pi$
$353$	−7.29541	−	12.6360i	−0.388295	−	0.672547i	−0.992220	+	0.124494i	$0.960269\pi$
$354$		0			0
$355$	−7.17099	+	12.4205i	−0.380596	+	0.659212i
$356$		0			0
$357$	−18.8059	+	13.0066i	−0.995313	+	0.688380i
$358$		0			0
$359$	−1.05831	−	1.83304i	−0.0558554	−	0.0967443i	0.836746	−	0.547592i	$-0.184455\pi$
$359$	−1.05831	−	1.83304i	−0.0558554	−	0.0967443i	−0.892601	+	0.450847i	$0.851122\pi$
$360$		0			0
$361$	9.49997	−	16.4544i	0.499998	−	0.866023i
$362$		0			0
$363$	32.8767	−	17.9924i	1.72558	−	0.944356i
$364$		0			0
$365$	3.83638	+	6.64480i	0.200805	+	0.347805i
$366$		0			0
$367$	−3.33104	−	5.76954i	−0.173879	−	0.301167i	0.765894	−	0.642967i	$-0.222297\pi$
$367$	−3.33104	−	5.76954i	−0.173879	−	0.301167i	−0.939773	+	0.341800i	$0.888964\pi$
$368$		0			0
$369$	−16.8558	+	26.3375i	−0.877480	+	1.37107i
$370$		0			0
$371$	−7.96710	+	17.8760i	−0.413631	+	0.928076i
$372$		0			0
$373$	6.24916	−	10.8239i	0.323569	−	0.560438i	−0.657653	−	0.753321i	$-0.728451\pi$
$373$	6.24916	−	10.8239i	0.323569	−	0.560438i	0.981222	+	0.192883i	$0.0617838\pi$
$374$		0			0
$375$	−13.5709	−	8.25430i	−0.700796	−	0.426250i
$376$		0			0
$377$	−37.7758			−1.94555
$378$		0			0
$379$	−19.5504			−1.00423			−0.502117	−	0.864800i	$-0.667445\pi$
$379$	−19.5504			−1.00423			−0.502117	+	0.864800i	$0.667445\pi$
$380$		0			0
$381$	2.90061	+	1.76426i	0.148603	+	0.0903856i
$382$		0			0
$383$	1.33740	−	2.31644i	0.0683379	−	0.118365i	−0.829832	−	0.558013i	$-0.811564\pi$
$383$	1.33740	−	2.31644i	0.0683379	−	0.118365i	0.898170	+	0.439649i	$0.144897\pi$
$384$		0			0
$385$	37.9265	−	3.97158i	1.93292	−	0.202411i
$386$		0			0
$387$	26.5483	+	1.21438i	1.34953	+	0.0617303i
$388$		0			0
$389$	1.98155	+	3.43214i	0.100469	+	0.174017i	0.911878	−	0.410462i	$-0.134632\pi$
$389$	1.98155	+	3.43214i	0.100469	+	0.174017i	−0.811409	+	0.584478i	$0.801299\pi$
$390$		0			0
$391$	1.66593	+	2.88548i	0.0842499	+	0.145925i
$392$		0			0
$393$	−6.05974	+	3.31631i	−0.305673	+	0.167285i
$394$		0			0
$395$	7.77345	−	13.4640i	0.391125	−	0.677448i
$396$		0			0
$397$	10.2978	+	17.8362i	0.516829	+	0.895175i	0.999809	+	0.0195431i	$0.00622114\pi$
$397$	10.2978	+	17.8362i	0.516829	+	0.895175i	−0.482980	+	0.875632i	$0.660446\pi$
$398$		0			0
$399$	0.00286400	+	0.0350709i	0.000143379	+	0.00175574i
$400$		0			0
$401$	1.91979	−	3.32517i	0.0958696	−	0.166051i	−0.814102	−	0.580722i	$-0.802770\pi$
$401$	1.91979	−	3.32517i	0.0958696	−	0.166051i	0.909971	+	0.414671i	$0.136103\pi$
$402$		0			0
$403$	19.0459	+	32.9884i	0.948742	+	1.64327i
$404$		0			0
$405$	9.51046	+	20.6184i	0.472579	+	1.02454i
$406$		0			0
$407$	18.2565	−	31.6212i	0.904940	−	1.56740i
$408$		0			0
$409$	−29.4227			−1.45486			−0.727428	−	0.686184i	$-0.759285\pi$
$409$	−29.4227			−1.45486			−0.727428	+	0.686184i	$0.759285\pi$
$410$		0			0
$411$	0.293247	−	12.8284i	0.0144648	−	0.632780i
$412$		0			0
$413$	−1.37777	+	0.144276i	−0.0677954	+	0.00709938i
$414$		0			0
$415$	0.652741	+	1.13058i	0.0320418	+	0.0554980i
$416$		0			0
$417$	0.548349	−	23.9882i	0.0268528	−	1.17471i
$418$		0			0
$419$	4.40821	+	7.63525i	0.215355	+	0.373006i	0.953382	−	0.301765i	$-0.0975757\pi$
$419$	4.40821	+	7.63525i	0.215355	+	0.373006i	−0.738027	+	0.674771i	$0.764242\pi$
$420$		0			0
$421$	−17.6437	+	30.5597i	−0.859899	+	1.48939i	0.0121255	+	0.999926i	$0.496140\pi$
$421$	−17.6437	+	30.5597i	−0.859899	+	1.48939i	−0.872024	+	0.489462i	$0.837193\pi$
$422$		0			0
$423$	2.98162	+	5.75681i	0.144972	+	0.279906i
$424$		0			0
$425$	−6.81113			−0.330388
$426$		0			0
$427$	−23.6581	+	2.47742i	−1.14490	+	0.119891i
$428$		0			0
$429$	−42.5759	+	23.3005i	−2.05559	+	1.12496i
$430$		0			0
$431$	−12.8099	+	22.1873i	−0.617030	+	1.06873i	0.372995	+	0.927833i	$0.378331\pi$
$431$	−12.8099	+	22.1873i	−0.617030	+	1.06873i	−0.990025	+	0.140893i	$0.955003\pi$
$432$		0			0
$433$	16.8556			0.810030			0.405015	−	0.914310i	$-0.367266\pi$
$433$	16.8556			0.810030			0.405015	+	0.914310i	$0.367266\pi$
$434$		0			0
$435$	−0.769113	+	33.6458i	−0.0368762	+	1.61319i
$436$		0			0
$437$	0.00512739			0.000245277
$438$		0			0
$439$	30.9192			1.47569			0.737846	−	0.674969i	$-0.235843\pi$
$439$	30.9192			1.47569			0.737846	+	0.674969i	$0.235843\pi$
$440$		0			0
$441$	13.3115	+	16.2420i	0.633883	+	0.773429i
$442$		0			0
$443$	−9.31087			−0.442373			−0.221186	−	0.975232i	$-0.570993\pi$
$443$	−9.31087			−0.442373			−0.221186	+	0.975232i	$0.570993\pi$
$444$		0			0
$445$	6.00918			0.284862
$446$		0			0
$447$	−21.4297	+	11.7278i	−1.01359	+	0.554705i
$448$		0			0
$449$	23.8055			1.12345			0.561724	−	0.827324i	$-0.310138\pi$
$449$	23.8055			1.12345			0.561724	+	0.827324i	$0.310138\pi$
$450$		0			0
$451$	−29.7736	+	51.5694i	−1.40198	+	2.42831i
$452$		0			0
$453$	0.419599	−	18.3559i	0.0197145	−	0.862435i
$454$		0			0
$455$	−32.5621	+	3.40983i	−1.52653	+	0.159855i
$456$		0			0
$457$	−13.8110			−0.646053			−0.323027	−	0.946390i	$-0.604700\pi$
$457$	−13.8110			−0.646053			−0.323027	+	0.946390i	$0.604700\pi$
$458$		0			0
$459$	−21.5126	−	14.4714i	−1.00412	−	0.675467i
$460$		0			0
$461$	−0.00256407	+	0.00444110i	−0.000119421	+	0.000206843i	−0.866085	−	0.499897i	$-0.833371\pi$
$461$	−0.00256407	+	0.00444110i	−0.000119421	+	0.000206843i	0.865966	+	0.500103i	$0.166705\pi$
$462$		0			0
$463$	12.9682	+	22.4616i	0.602685	+	1.04388i	0.992413	+	0.122951i	$0.0392358\pi$
$463$	12.9682	+	22.4616i	0.602685	+	1.04388i	−0.389728	+	0.920930i	$0.627431\pi$
$464$		0			0
$465$	29.7696	−	16.2920i	1.38053	−	0.755522i
$466$		0			0
$467$	−12.0484	−	20.8684i	−0.557532	−	0.965673i	−0.997702	−	0.0677588i	$-0.978415\pi$
$467$	−12.0484	−	20.8684i	−0.557532	−	0.965673i	0.440170	−	0.897914i	$-0.354918\pi$
$468$		0			0
$469$	−13.4090	+	1.40416i	−0.619168	+	0.0648379i
$470$		0			0
$471$	0.384098	+	0.233622i	0.0176983	+	0.0107648i
$472$		0			0
$473$	50.6094			2.32702
$474$		0			0
$475$	−0.00524081	+	0.00907735i	−0.000240465	+	0.000416497i
$476$		0			0
$477$	−22.1683	−	1.01403i	−1.01502	−	0.0464291i
$478$		0			0
$479$	−7.39114	−	12.8018i	−0.337710	−	0.584931i	0.646292	−	0.763091i	$-0.276319\pi$
$479$	−7.39114	−	12.8018i	−0.337710	−	0.584931i	−0.984002	+	0.178160i	$0.942986\pi$
$480$		0			0
$481$	−15.6742	+	27.1486i	−0.714683	+	1.23787i
$482$		0			0
$483$	2.51674	−	1.74063i	0.114516	−	0.0792016i
$484$		0			0
$485$	−10.9240	−	18.9210i	−0.496035	−	0.859158i
$486$		0			0
$487$	9.38360	−	16.2529i	0.425211	−	0.736488i	−0.571229	−	0.820791i	$-0.693533\pi$
$487$	9.38360	−	16.2529i	0.425211	−	0.736488i	0.996440	+	0.0843033i	$0.0268664\pi$
$488$		0			0
$489$	0.500234	−	21.8833i	0.0226213	−	0.989598i
$490$		0			0
$491$	18.2871	+	31.6741i	0.825284	+	1.42943i	0.901702	+	0.432358i	$0.142318\pi$
$491$	18.2871	+	31.6741i	0.825284	+	1.42943i	−0.0764182	+	0.997076i	$0.524348\pi$
$492$		0			0
$493$	−19.2143	−	33.2801i	−0.865368	−	1.49886i
$494$		0			0
$495$	19.8862	+	38.3956i	0.893819	+	1.72575i
$496$		0			0
$497$	−14.9585	+	1.56642i	−0.670982	+	0.0702637i
$498$		0			0
$499$	−2.31591	+	4.01127i	−0.103674	+	0.179569i	−0.913196	−	0.407521i	$-0.866393\pi$
$499$	−2.31591	+	4.01127i	−0.103674	+	0.179569i	0.809521	+	0.587090i	$0.199727\pi$
$500$		0			0
$501$	−0.455170	+	19.9120i	−0.0203355	+	0.889602i
$502$		0			0
$503$	16.4143			0.731879			0.365940	−	0.930639i	$-0.380748\pi$
$503$	16.4143			0.731879			0.365940	+	0.930639i	$0.380748\pi$
$504$		0			0
$505$	23.5530			1.04809
$506$		0			0
$507$	16.8017	−	9.19502i	0.746188	−	0.408365i
$508$		0			0
$509$	−5.24169	+	9.07888i	−0.232334	+	0.402414i	−0.958495	−	0.285111i	$-0.907970\pi$
$509$	−5.24169	+	9.07888i	−0.232334	+	0.402414i	0.726161	+	0.687525i	$0.241303\pi$
$510$		0			0
$511$	−3.27556	+	7.34947i	−0.144902	+	0.325121i
$512$		0			0
$513$	−0.0358392	+	0.0175353i	−0.00158234	+	0.000774203i
$514$		0			0
$515$	20.4589	+	35.4358i	0.901526	+	1.56149i
$516$		0			0
$517$	6.17298	+	10.6919i	0.271487	+	0.470230i
$518$		0			0
$519$	23.3951	+	14.2297i	1.02693	+	0.624616i
$520$		0			0
$521$	−11.0087	+	19.0675i	−0.482298	+	0.835364i	−0.999793	−	0.0203215i	$-0.993531\pi$
$521$	−11.0087	+	19.0675i	−0.482298	+	0.835364i	0.517496	+	0.855686i	$0.326864\pi$
$522$		0			0
$523$	−1.18541	−	2.05320i	−0.0518346	−	0.0897801i	0.838944	−	0.544218i	$-0.183174\pi$
$523$	−1.18541	−	2.05320i	−0.0518346	−	0.0897801i	−0.890778	+	0.454438i	$0.849840\pi$
$524$		0			0
$525$	0.509144	+	6.23468i	0.0222208	+	0.272104i
$526$		0			0
$527$	−19.3750	+	33.5585i	−0.843988	+	1.46183i
$528$		0			0
$529$	11.2771	+	19.5324i	0.490307	+	0.849236i
$530$		0			0
$531$	−0.722411	−	1.39480i	−0.0313500	−	0.0605293i
$532$		0			0
$533$	25.5623	−	44.2753i	1.10723	−	1.91777i
$534$		0			0
$535$	22.7147			0.982044
$536$		0			0
$537$	25.8252	−	14.1333i	1.11444	−	0.609898i
$538$		0			0
$539$	26.7363	+	29.7394i	1.15161	+	1.28097i
$540$		0			0
$541$	6.65209	+	11.5218i	0.285996	+	0.495359i	0.972850	−	0.231436i	$-0.0743423\pi$
$541$	6.65209	+	11.5218i	0.285996	+	0.495359i	−0.686854	+	0.726795i	$0.741009\pi$
$542$		0			0
$543$	−9.40928	−	5.72307i	−0.403791	−	0.245600i
$544$		0			0
$545$	−9.37418	−	16.2366i	−0.401546	−	0.695498i
$546$		0			0
$547$	−2.43685	+	4.22074i	−0.104192	+	0.180466i	−0.913408	−	0.407046i	$-0.866559\pi$
$547$	−2.43685	+	4.22074i	−0.104192	+	0.180466i	0.809216	+	0.587512i	$0.199892\pi$
$548$		0			0
$549$	−12.4048	−	23.9507i	−0.529423	−	1.02219i
$550$		0			0
$551$	−0.0591375			−0.00251934
$552$		0			0
$553$	16.2153	−	1.69802i	0.689543	−	0.0722074i
$554$		0			0
$555$	23.8613	+	14.5133i	1.01286	+	0.616057i
$556$		0			0
$557$	7.09601	−	12.2907i	0.300668	−	0.520772i	−0.675620	−	0.737250i	$-0.736124\pi$
$557$	7.09601	−	12.2907i	0.300668	−	0.520772i	0.976287	+	0.216479i	$0.0694572\pi$
$558$		0			0
$559$	−43.4511			−1.83778
$560$		0			0
$561$	−42.1833	−	25.6575i	−1.78098	−	1.08326i
$562$		0			0
$563$	7.03971			0.296688			0.148344	−	0.988936i	$-0.452606\pi$
$563$	7.03971			0.296688			0.148344	+	0.988936i	$0.452606\pi$
$564$		0			0
$565$	36.0595			1.51703
$566$		0			0
$567$	−11.6385	+	20.7737i	−0.488772	+	0.872411i
$568$		0			0
$569$	−18.3016			−0.767244			−0.383622	−	0.923490i	$-0.625323\pi$
$569$	−18.3016			−0.767244			−0.383622	+	0.923490i	$0.625323\pi$
$570$		0			0
$571$	−30.4383			−1.27380			−0.636902	−	0.770944i	$-0.719785\pi$
$571$	−30.4383			−1.27380			−0.636902	+	0.770944i	$0.719785\pi$
$572$		0			0
$573$	6.12783	+	3.72717i	0.255994	+	0.155705i
$574$		0			0
$575$	0.911516			0.0380128
$576$		0			0
$577$	5.65385	−	9.79275i	0.235373	−	0.407678i	−0.724008	−	0.689791i	$-0.757702\pi$
$577$	5.65385	−	9.79275i	0.235373	−	0.407678i	0.959381	+	0.282114i	$0.0910356\pi$
$578$		0			0
$579$	11.3885	+	6.92688i	0.473288	+	0.287871i
$580$		0			0
$581$	−0.557320	+	1.25047i	−0.0231215	+	0.0518784i
$582$		0			0
$583$	−42.2597			−1.75022
$584$		0			0
$585$	−17.0734	−	32.9648i	−0.705900	−	1.36293i
$586$		0			0
$587$	−9.89755	+	17.1431i	−0.408516	+	0.707570i	−0.994724	−	0.102591i	$-0.967287\pi$
$587$	−9.89755	+	17.1431i	−0.408516	+	0.707570i	0.586208	+	0.810161i	$0.300620\pi$
$588$		0			0
$589$	0.0298161	+	0.0516430i	0.00122855	+	0.00212791i
$590$		0			0
$591$	−4.87612	−	2.96584i	−0.200577	−	0.121998i
$592$		0			0
$593$	2.69067	+	4.66038i	0.110493	+	0.191379i	0.915969	−	0.401249i	$-0.131424\pi$
$593$	2.69067	+	4.66038i	0.110493	+	0.191379i	−0.805476	+	0.592628i	$0.798090\pi$
$594$		0			0
$595$	−19.5664	−	26.9525i	−0.802145	−	1.10495i
$596$		0			0
$597$	−24.5790	+	13.4513i	−1.00595	+	0.550526i
$598$		0			0
$599$	2.25959			0.0923243			0.0461622	−	0.998934i	$-0.485301\pi$
$599$	2.25959			0.0923243			0.0461622	+	0.998934i	$0.485301\pi$
$600$		0			0
$601$	18.1873	−	31.5013i	0.741875	−	1.28496i	−0.209766	−	0.977752i	$-0.567270\pi$
$601$	18.1873	−	31.5013i	0.741875	−	1.28496i	0.951641	−	0.307213i	$-0.0993964\pi$
$602$		0			0
$603$	−7.03078	−	13.5748i	−0.286316	−	0.552808i
$604$		0			0
$605$	27.2953	+	47.2768i	1.10971	+	1.92207i
$606$		0			0
$607$	−8.10803	+	14.0435i	−0.329095	+	0.570009i	−0.982333	−	0.187144i	$-0.940077\pi$
$607$	−8.10803	+	14.0435i	−0.329095	+	0.570009i	0.653238	+	0.757153i	$0.273410\pi$
$608$		0			0
$609$	−29.0272	+	20.0759i	−1.17624	+	0.813515i
$610$		0			0
$611$	−5.29985	−	9.17961i	−0.214409	−	0.371367i
$612$		0			0
$613$	21.6357	−	37.4741i	0.873857	−	1.51357i	0.0158822	−	0.999874i	$-0.494944\pi$
$613$	21.6357	−	37.4741i	0.873857	−	1.51357i	0.857975	−	0.513691i	$-0.171722\pi$
$614$		0			0
$615$	−38.9142	−	23.6691i	−1.56917	−	0.954429i
$616$		0			0
$617$	−5.92248	−	10.2580i	−0.238430	−	0.412973i	0.721834	−	0.692066i	$-0.243299\pi$
$617$	−5.92248	−	10.2580i	−0.238430	−	0.412973i	−0.960264	+	0.279093i	$0.909966\pi$
$618$		0			0
$619$	−20.1644	−	34.9257i	−0.810475	−	1.40378i	−0.912532	−	0.409006i	$-0.865876\pi$
$619$	−20.1644	−	34.9257i	−0.810475	−	1.40378i	0.102057	−	0.994779i	$-0.467458\pi$
$620$		0			0
$621$	2.87897	+	1.93667i	0.115529	+	0.0777158i
$622$		0			0
$623$	3.70215	+	5.09967i	0.148323	+	0.204314i
$624$		0			0
$625$	14.9809	−	25.9478i	0.599238	−	1.03791i
$626$		0			0
$627$	−0.0666521	+	0.0364766i	−0.00266183	+	0.00145674i
$628$		0			0
$629$	−31.8902			−1.27154
$630$		0			0
$631$	13.9489			0.555298			0.277649	−	0.960683i	$-0.410445\pi$
$631$	13.9489			0.555298			0.277649	+	0.960683i	$0.410445\pi$
$632$		0			0
$633$	−1.10541	+	48.3576i	−0.0439362	+	1.92204i
$634$		0			0
$635$	−2.47259	+	4.28265i	−0.0981217	+	0.169952i
$636$		0			0
$637$	−22.9546	−	25.5329i	−0.909496	−	1.01165i
$638$		0			0
$639$	−7.84328	−	15.1435i	−0.310275	−	0.599068i
$640$		0			0
$641$	−8.76975	−	15.1896i	−0.346384	−	0.599955i	0.639220	−	0.769024i	$-0.279257\pi$
$641$	−8.76975	−	15.1896i	−0.346384	−	0.599955i	−0.985604	+	0.169069i	$0.945924\pi$
$642$		0			0
$643$	−13.5329	−	23.4397i	−0.533686	−	0.924371i	−0.999226	−	0.0393443i	$-0.987473\pi$
$643$	−13.5329	−	23.4397i	−0.533686	−	0.924371i	0.465540	−	0.885027i	$-0.345860\pi$
$644$		0			0
$645$	−0.884662	+	38.7006i	−0.0348335	+	1.52383i
$646$		0			0
$647$	11.3252	−	19.6159i	0.445240	−	0.771179i	−0.552828	−	0.833295i	$-0.686452\pi$
$647$	11.3252	−	19.6159i	0.445240	−	0.771179i	0.998069	+	0.0621160i	$0.0197849\pi$
$648$		0			0
$649$	−1.49564	−	2.59052i	−0.0587089	−	0.101687i
$650$		0			0
$651$	32.1666	+	15.2267i	1.26071	+	0.596780i
$652$		0			0
$653$	0.392054	−	0.679058i	0.0153423	−	0.0265736i	−0.858252	−	0.513228i	$-0.828450\pi$
$653$	0.392054	−	0.679058i	0.0153423	−	0.0265736i	0.873595	+	0.486654i	$0.161783\pi$
$654$		0			0
$655$	−5.03098	−	8.71392i	−0.196577	−	0.340481i
$656$		0			0
$657$	−9.11419	−	0.416903i	−0.355578	−	0.0162649i
$658$		0			0
$659$	−16.7219	+	28.9632i	−0.651392	+	1.12824i	0.331393	+	0.943493i	$0.392481\pi$
$659$	−16.7219	+	28.9632i	−0.651392	+	1.12824i	−0.982785	+	0.184752i	$0.940852\pi$
$660$		0			0
$661$	3.06516			0.119221			0.0596104	−	0.998222i	$-0.481014\pi$
$661$	3.06516			0.119221			0.0596104	+	0.998222i	$0.481014\pi$
$662$		0			0
$663$	36.2168	+	22.0284i	1.40654	+	0.855511i
$664$		0			0
$665$	−0.0509756	+	0.00533805i	−0.00197675	+	0.000207001i
$666$		0			0
$667$	2.57140	+	4.45379i	0.0995649	+	0.172451i
$668$		0			0
$669$	30.8899	−	16.9051i	1.19427	−	0.653588i
$670$		0			0
$671$	−25.6821	−	44.4827i	−0.991447	−	1.71724i
$672$		0			0
$673$	14.4618	−	25.0487i	0.557463	−	0.965555i	−0.440244	−	0.897878i	$-0.645108\pi$
$673$	14.4618	−	25.0487i	0.557463	−	0.965555i	0.997707	−	0.0676766i	$-0.0215586\pi$
$674$		0			0
$675$	−6.37126	+	3.11732i	−0.245230	+	0.119986i
$676$		0			0
$677$	−11.7164			−0.450296			−0.225148	−	0.974325i	$-0.572287\pi$
$677$	−11.7164			−0.450296			−0.225148	+	0.974325i	$0.572287\pi$
$678$		0			0
$679$	9.32711	−	20.9275i	0.357942	−	0.803124i
$680$		0			0
$681$	0.225202	−	9.85174i	0.00862977	−	0.377520i
$682$		0			0
$683$	20.7190	−	35.8864i	0.792791	−	1.37315i	−0.131441	−	0.991324i	$-0.541960\pi$
$683$	20.7190	−	35.8864i	0.792791	−	1.37315i	0.924232	−	0.381831i	$-0.124706\pi$
$684$		0			0
$685$	18.6908			0.714138
$686$		0			0
$687$	22.5694	−	12.3515i	0.861076	−	0.471240i
$688$		0			0
$689$	36.2824			1.38225
$690$		0			0
$691$	−6.91350			−0.263002			−0.131501	−	0.991316i	$-0.541980\pi$
$691$	−6.91350			−0.263002			−0.131501	+	0.991316i	$0.541980\pi$
$692$		0			0
$693$	−20.3327	+	40.5311i	−0.772375	+	1.53965i
$694$		0			0
$695$	34.9503			1.32574
$696$		0			0
$697$	52.0081			1.96995
$698$		0			0
$699$	0.530926	−	23.2260i	0.0200815	−	0.878487i
$700$		0			0
$701$	39.1954			1.48039			0.740195	−	0.672392i	$-0.234733\pi$
$701$	39.1954			1.48039			0.740195	+	0.672392i	$0.234733\pi$
$702$		0			0
$703$	−0.0245378	+	0.0425008i	−0.000925462	+	0.00160295i
$704$		0			0
$705$	−8.28392	+	4.53353i	−0.311991	+	0.170743i
$706$		0			0
$707$	14.5106	+	19.9881i	0.545726	+	0.751731i
$708$		0			0
$709$	20.4871			0.769409			0.384705	−	0.923040i	$-0.374303\pi$
$709$	20.4871			0.769409			0.384705	+	0.923040i	$0.374303\pi$
$710$		0			0
$711$	8.50223	+	16.4158i	0.318858	+	0.615640i
$712$		0			0
$713$	2.59290	−	4.49104i	0.0971050	−	0.168191i
$714$		0			0
$715$	−35.3479	−	61.2243i	−1.32193	−	2.28966i
$716$		0			0
$717$	−0.738713	+	32.3159i	−0.0275877	+	1.20686i
$718$		0			0
$719$	17.1300	+	29.6700i	0.638840	+	1.10650i	0.985688	+	0.168582i	$0.0539187\pi$
$719$	17.1300	+	29.6700i	0.638840	+	1.10650i	−0.346848	+	0.937921i	$0.612748\pi$
$720$		0			0
$721$	−17.4681	+	39.1937i	−0.650547	+	1.45965i
$722$		0			0
$723$	0.847704	−	37.0839i	0.0315265	−	1.37916i
$724$		0			0
$725$	−10.5131			−0.390447
$726$		0			0
$727$	7.18914	−	12.4520i	0.266631	−	0.461818i	−0.701359	−	0.712808i	$-0.747423\pi$
$727$	7.18914	−	12.4520i	0.266631	−	0.461818i	0.967990	+	0.250991i	$0.0807563\pi$
$728$		0			0
$729$	−26.7465	−	3.69094i	−0.990612	−	0.136701i
$730$		0			0
$731$	−22.1010	−	38.2800i	−0.817433	−	1.41584i
$732$		0			0
$733$	−19.7887	+	34.2750i	−0.730911	+	1.26597i	0.225584	+	0.974224i	$0.427571\pi$
$733$	−19.7887	+	34.2750i	−0.730911	+	1.26597i	−0.956494	+	0.291751i	$0.905762\pi$
$734$		0			0
$735$	−23.2088	+	19.9252i	−0.856070	+	0.734952i
$736$		0			0
$737$	−14.5561	−	25.2119i	−0.536182	−	0.928694i
$738$		0			0
$739$	10.8407	−	18.7767i	0.398783	−	0.690712i	−0.594793	−	0.803879i	$-0.702766\pi$
$739$	10.8407	−	18.7767i	0.398783	−	0.690712i	0.993576	+	0.113167i	$0.0360995\pi$
$740$		0			0
$741$	0.0572246	−	0.0313172i	0.00210220	−	0.00115047i
$742$		0			0
$743$	16.5692	+	28.6987i	0.607864	+	1.05285i	0.991592	+	0.129406i	$0.0413069\pi$
$743$	16.5692	+	28.6987i	0.607864	+	1.05285i	−0.383727	+	0.923446i	$0.625360\pi$
$744$		0			0
$745$	−17.7916	−	30.8159i	−0.651832	−	1.12901i
$746$		0			0
$747$	−1.55073	−	0.0709339i	−0.0567384	−	0.00259533i
$748$		0			0
$749$	13.9941	+	19.2768i	0.511335	+	0.704358i
$750$		0			0
$751$	12.9662	−	22.4581i	0.473144	−	0.819509i	−0.526384	−	0.850247i	$-0.676452\pi$
$751$	12.9662	−	22.4581i	0.473144	−	0.819509i	0.999527	+	0.0307381i	$0.00978577\pi$
$752$		0			0
$753$	0.685005	+	0.416645i	0.0249630	+	0.0151834i
$754$		0			0
$755$	26.7442			0.973320
$756$		0			0
$757$	−30.5846			−1.11162			−0.555808	−	0.831311i	$-0.687591\pi$
$757$	−30.5846			−1.11162			−0.555808	+	0.831311i	$0.687591\pi$
$758$		0			0
$759$	5.64528	+	3.43367i	0.204911	+	0.124634i
$760$		0			0
$761$	18.2648	−	31.6355i	0.662097	−	1.14679i	−0.317967	−	0.948102i	$-0.603000\pi$
$761$	18.2648	−	31.6355i	0.662097	−	1.14679i	0.980064	−	0.198684i	$-0.0636667\pi$
$762$		0			0
$763$	8.00382	−	17.9584i	0.289758	−	0.650138i
$764$		0			0
$765$	20.3574	−	31.8088i	0.736024	−	1.15005i
$766$		0			0
$767$	1.28409	+	2.22411i	0.0463658	+	0.0803079i
$768$		0			0
$769$	−21.3107	−	36.9113i	−0.768485	−	1.33105i	−0.938384	−	0.345593i	$-0.887678\pi$
$769$	−21.3107	−	36.9113i	−0.768485	−	1.33105i	0.169900	−	0.985461i	$-0.445656\pi$
$770$		0			0
$771$	1.21934	−	0.667305i	0.0439134	−	0.0240324i
$772$		0			0
$773$	16.1309	−	27.9395i	0.580187	−	1.00491i	−0.415270	−	0.909698i	$-0.636313\pi$
$773$	16.1309	−	27.9395i	0.580187	−	1.00491i	0.995457	−	0.0952148i	$-0.0303538\pi$
$774$		0			0
$775$	5.30051	+	9.18076i	0.190400	+	0.329783i
$776$		0			0
$777$	2.38384	+	29.1912i	0.0855200	+	1.04723i
$778$		0			0
$779$	0.0400175	−	0.0693124i	0.00143378	−	0.00248337i
$780$		0			0
$781$	−16.2383	−	28.1255i	−0.581051	−	1.00641i
$782$		0			0
$783$	−33.2050	−	22.3368i	−1.18665	−	0.798254i
$784$		0			0
$785$	−0.327420	+	0.567107i	−0.0116861	+	0.0202409i
$786$		0			0
$787$	30.7676			1.09675			0.548373	−	0.836234i	$-0.315247\pi$
$787$	30.7676			1.09675			0.548373	+	0.836234i	$0.315247\pi$
$788$		0			0
$789$	−0.00797146	+	0.348721i	−0.000283791	+	0.0124148i
$790$		0			0
$791$	22.2156	+	30.6017i	0.789895	+	1.08807i
$792$		0			0
$793$	22.0496	+	38.1910i	0.783003	+	1.35620i
$794$		0			0
$795$	0.738708	−	32.3157i	0.0261993	−	1.14612i
$796$		0			0
$797$	−3.59378	−	6.22460i	−0.127298	−	0.220487i	0.795331	−	0.606176i	$-0.207297\pi$
$797$	−3.59378	−	6.22460i	−0.127298	−	0.220487i	−0.922629	+	0.385689i	$0.873964\pi$
$798$		0			0
$799$	5.39144	−	9.33824i	0.190735	−	0.330363i
$800$		0			0
$801$	−3.85181	+	6.01851i	−0.136097	+	0.212654i
$802$		0			0
$803$	−17.3745			−0.613133
$804$		0			0
$805$	2.61852	+	3.60699i	0.0922908	+	0.127130i
$806$		0			0
$807$	33.9655	−	18.5882i	1.19564	−	0.654337i
$808$		0			0
$809$	−23.3886	+	40.5103i	−0.822301	+	1.42427i	0.0816637	+	0.996660i	$0.473977\pi$
$809$	−23.3886	+	40.5103i	−0.822301	+	1.42427i	−0.903965	+	0.427607i	$0.859357\pi$
$810$		0			0
$811$	17.6946			0.621341			0.310671	−	0.950518i	$-0.399446\pi$
$811$	17.6946			0.621341			0.310671	+	0.950518i	$0.399446\pi$
$812$		0			0
$813$	−0.141647	+	6.19653i	−0.00496779	+	0.217322i
$814$		0			0
$815$	31.8836			1.11683
$816$		0			0
$817$	−0.0680221			−0.00237979
$818$		0			0
$819$	17.4568	−	34.7983i	0.609989	−	1.21595i
$820$		0			0
$821$	−17.2215			−0.601034			−0.300517	−	0.953776i	$-0.597159\pi$
$821$	−17.2215			−0.601034			−0.300517	+	0.953776i	$0.597159\pi$
$822$		0			0
$823$	11.5434			0.402378			0.201189	−	0.979552i	$-0.435520\pi$
$823$	11.5434			0.402378			0.201189	+	0.979552i	$0.435520\pi$
$824$		0			0
$825$	−11.8490	+	6.48458i	−0.412529	+	0.225764i
$826$		0			0
$827$	−20.1448			−0.700503			−0.350251	−	0.936656i	$-0.613904\pi$
$827$	−20.1448			−0.700503			−0.350251	+	0.936656i	$0.613904\pi$
$828$		0			0
$829$	−4.01358	+	6.95172i	−0.139397	+	0.241443i	−0.927269	−	0.374397i	$-0.877850\pi$
$829$	−4.01358	+	6.95172i	−0.139397	+	0.241443i	0.787871	+	0.615840i	$0.211183\pi$
$830$		0			0
$831$	0.400052	−	17.5008i	0.0138777	−	0.607095i
$832$		0			0
$833$	10.8186	−	33.2099i	0.374843	−	1.15066i
$834$		0			0
$835$	−29.0114			−1.00398
$836$		0			0
$837$	−2.76469	+	40.2588i	−0.0955617	+	1.39155i
$838$		0			0
$839$	−4.59341	+	7.95603i	−0.158582	+	0.274673i	−0.934358	−	0.356337i	$-0.884026\pi$
$839$	−4.59341	+	7.95603i	−0.158582	+	0.274673i	0.775775	+	0.631009i	$0.217359\pi$
$840$		0			0
$841$	−15.1576	−	26.2537i	−0.522675	−	0.905299i
$842$		0			0
$843$	−38.6273	+	21.1395i	−1.33039	+	0.728083i
$844$		0			0
$845$	13.9493	+	24.1608i	0.479869	+	0.831158i
$846$		0			0
$847$	−23.3051	+	52.2904i	−0.800774	+	1.79672i
$848$		0			0
$849$	−5.73674	−	3.48930i	−0.196884	−	0.119752i
$850$		0			0
$851$	4.26778			0.146298
$852$		0			0
$853$	−10.7925	+	18.6931i	−0.369527	+	0.640040i	−0.989492	−	0.144590i	$-0.953814\pi$
$853$	−10.7925	+	18.6931i	−0.369527	+	0.640040i	0.619964	+	0.784630i	$0.287147\pi$
$854$		0			0
$855$	−0.0267283	−	0.0516060i	−0.000914088	−	0.00176489i
$856$		0			0
$857$	−12.0326	−	20.8410i	−0.411024	−	0.711915i	0.583978	−	0.811770i	$-0.301496\pi$
$857$	−12.0326	−	20.8410i	−0.411024	−	0.711915i	−0.995002	+	0.0998547i	$0.968162\pi$
$858$		0			0
$859$	8.15861	−	14.1311i	0.278368	−	0.482148i	−0.692611	−	0.721311i	$-0.743540\pi$
$859$	8.15861	−	14.1311i	0.278368	−	0.482148i	0.970979	+	0.239163i	$0.0768731\pi$
$860$		0			0
$861$	−3.88769	−	47.6065i	−0.132492	−	1.62242i
$862$		0			0
$863$	−9.64675	−	16.7087i	−0.328379	−	0.568770i	0.653811	−	0.756658i	$-0.273169\pi$
$863$	−9.64675	−	16.7087i	−0.328379	−	0.568770i	−0.982190	+	0.187888i	$0.939836\pi$
$864$		0			0
$865$	−19.9428	+	34.5420i	−0.678077	+	1.17446i
$866$		0			0
$867$	−0.312576	+	13.6740i	−0.0106156	+	0.464393i
$868$		0			0
$869$	17.6025	+	30.4884i	0.597124	+	1.03425i
$870$		0			0
$871$	12.4973	+	21.6459i	0.423453	+	0.733443i
$872$		0			0
$873$	25.9525	+	1.18712i	0.878360	+	0.0401781i
$874$		0			0
$875$	24.1313	−	2.52697i	0.815786	−	0.0854273i
$876$		0			0
$877$	−15.1464	+	26.2343i	−0.511457	+	0.885870i	0.488454	+	0.872589i	$0.337561\pi$
$877$	−15.1464	+	26.2343i	−0.511457	+	0.885870i	−0.999912	+	0.0132808i	$0.995772\pi$
$878$		0			0
$879$	0.0339489	−	1.48514i	0.00114507	−	0.0500924i
$880$		0			0
$881$	19.4943			0.656779			0.328390	−	0.944542i	$-0.393494\pi$
$881$	19.4943			0.656779			0.328390	+	0.944542i	$0.393494\pi$
$882$		0			0
$883$	47.5302			1.59952			0.799759	−	0.600321i	$-0.204960\pi$
$883$	47.5302			1.59952			0.799759	+	0.600321i	$0.204960\pi$
$884$		0			0
$885$	2.00709	−	1.09842i	0.0674677	−	0.0369229i
$886$		0			0
$887$	2.05946	−	3.56709i	0.0691499	−	0.119771i	−0.829377	−	0.558689i	$-0.811305\pi$
$887$	2.05946	−	3.56709i	0.0691499	−	0.119771i	0.898527	+	0.438918i	$0.144638\pi$
$888$		0			0
$889$	−5.15777	+	0.540110i	−0.172986	+	0.0181147i
$890$		0			0
$891$	−51.2020	−	4.69400i	−1.71533	−	0.157255i
$892$		0			0
$893$	−0.00829686	−	0.0143706i	−0.000277644	−	0.000480893i
$894$		0			0
$895$	21.4409	+	37.1367i	0.716689	+	1.24134i
$896$		0			0
$897$	−4.84680	−	2.94800i	−0.161830	−	0.0984309i
$898$		0			0
$899$	−29.9056	+	51.7981i	−0.997408	+	1.72756i
$900$		0			0
$901$	18.4547	+	31.9645i	0.614815	+	1.06489i
$902$		0			0
$903$	−33.3881	+	23.0920i	−1.11109	+	0.768452i
$904$		0			0
$905$	8.02083	−	13.8925i	0.266621	−	0.461802i
$906$		0			0
$907$	−4.07084	−	7.05090i	−0.135170	−	0.234121i	0.790492	−	0.612472i	$-0.209825\pi$
$907$	−4.07084	−	7.05090i	−0.135170	−	0.234121i	−0.925662	+	0.378351i	$0.876491\pi$
$908$		0			0
$909$	−15.0972	+	23.5895i	−0.500741	+	0.782415i
$910$		0			0
$911$	−24.6454	+	42.6871i	−0.816540	+	1.41429i	0.0916774	+	0.995789i	$0.470777\pi$
$911$	−24.6454	+	42.6871i	−0.816540	+	1.41429i	−0.908217	+	0.418499i	$0.862556\pi$
$912$		0			0
$913$	−2.95618			−0.0978354
$914$		0			0
$915$	34.4645	−	18.8613i	1.13936	−	0.623537i
$916$		0			0
$917$	4.29553	−	9.63801i	0.141851	−	0.318275i
$918$		0			0
$919$	−4.71585	−	8.16809i	−0.155561	−	0.269440i	0.777702	−	0.628633i	$-0.216385\pi$
$919$	−4.71585	−	8.16809i	−0.155561	−	0.269440i	−0.933263	+	0.359193i	$0.883052\pi$
$920$		0			0
$921$	1.06243	+	0.646211i	0.0350084	+	0.0212934i
$922$		0			0
$923$	13.9415	+	24.1473i	0.458889	+	0.794819i
$924$		0			0
$925$	−4.36218	+	7.55552i	−0.143428	+	0.248424i
$926$		0			0
$927$	−48.6047	−	2.22328i	−1.59639	−	0.0730222i
$928$		0			0
$929$	29.4739			0.967006			0.483503	−	0.875343i	$-0.339364\pi$
$929$	29.4739			0.967006			0.483503	+	0.875343i	$0.339364\pi$
$930$		0			0
$931$	−0.0359352	−	0.0399715i	−0.00117773	−	0.00131001i
$932$		0			0
$933$	13.9874	+	8.50766i	0.457927	+	0.278528i
$934$		0			0
$935$	35.9587	−	62.2823i	1.17597	−	2.03685i
$936$		0			0
$937$	−54.3451			−1.77538			−0.887688	−	0.460445i	$-0.847690\pi$
$937$	−54.3451			−1.77538			−0.887688	+	0.460445i	$0.847690\pi$
$938$		0			0
$939$	34.4257	+	20.9390i	1.12344	+	0.683317i
$940$		0			0
$941$	−2.98173			−0.0972017			−0.0486008	−	0.998818i	$-0.515476\pi$
$941$	−2.98173			−0.0972017			−0.0486008	+	0.998818i	$0.515476\pi$
$942$		0			0
$943$	−6.96011			−0.226652
$944$		0			0
$945$	−30.6384	−	16.2567i	−0.996668	−	0.528832i
$946$		0			0
$947$	30.3292			0.985567			0.492783	−	0.870152i	$-0.335979\pi$
$947$	30.3292			0.985567			0.492783	+	0.870152i	$0.335979\pi$
$948$		0			0
$949$	14.9170			0.484226
$950$		0			0
$951$	−19.5860	−	11.9129i	−0.635119	−	0.386303i
$952$		0			0
$953$	0.380127			0.0123135			0.00615676	−	0.999981i	$-0.498040\pi$
$953$	0.380127			0.0123135			0.00615676	+	0.999981i	$0.498040\pi$
$954$		0			0
$955$	−5.22360	+	9.04754i	−0.169032	+	0.292771i
$956$		0			0
$957$	−65.1107	−	39.6027i	−2.10473	−	1.28017i
$958$		0			0
$959$	11.5150	+	15.8618i	0.371840	+	0.512206i
$960$		0			0
$961$	29.3115			0.945533
$962$		0			0
$963$	−14.5599	+	22.7500i	−0.469185	+	0.733109i
$964$		0			0
$965$	−9.70796	+	16.8147i	−0.312510	+	0.541284i
$966$		0			0
$967$	−22.6744	−	39.2732i	−0.729160	−	1.26294i	−0.957239	−	0.289300i	$-0.906578\pi$
$967$	−22.6744	−	39.2732i	−0.729160	−	1.26294i	0.228078	−	0.973643i	$-0.426756\pi$
$968$		0			0
$969$	0.0566970	+	0.0344852i	0.00182137	+	0.00110782i
$970$		0			0
$971$	−27.3746	−	47.4141i	−0.878491	−	1.52159i	−0.852996	−	0.521917i	$-0.825217\pi$
$971$	−27.3746	−	47.4141i	−0.878491	−	1.52159i	−0.0254951	−	0.999675i	$-0.508116\pi$
$972$		0			0
$973$	21.5323	+	29.6604i	0.690292	+	0.950870i
$974$		0			0
$975$	10.1730	−	5.56738i	0.325798	−	0.178299i
$976$		0			0
$977$	2.71311			0.0868001			0.0434001	−	0.999058i	$-0.486181\pi$
$977$	2.71311			0.0868001			0.0434001	+	0.999058i	$0.486181\pi$
$978$		0			0
$979$	−6.80371	+	11.7844i	−0.217448	+	0.376630i
$980$		0			0
$981$	22.2705	+	1.01870i	0.711042	+	0.0325246i
$982$		0			0
$983$	−21.3828	−	37.0361i	−0.682006	−	1.18127i	−0.974368	−	0.224961i	$-0.927774\pi$
$983$	−21.3828	−	37.0361i	−0.682006	−	1.18127i	0.292362	−	0.956308i	$-0.405559\pi$
$984$		0			0
$985$	4.15659	−	7.19943i	0.132440	−	0.229393i
$986$		0			0
$987$	−8.95093	−	4.23709i	−0.284911	−	0.134868i
$988$		0			0
$989$	2.95771	+	5.12291i	0.0940498	+	0.162899i
$990$		0			0
$991$	29.6731	−	51.3954i	0.942598	−	1.63263i	0.182107	−	0.983279i	$-0.441708\pi$
$991$	29.6731	−	51.3954i	0.942598	−	1.63263i	0.760491	−	0.649349i	$-0.224958\pi$
$992$		0			0
$993$	45.0353	+	27.3921i	1.42915	+	0.869262i
$994$		0			0
$995$	−20.4063	−	35.3447i	−0.646922	−	1.12050i
$996$		0			0
$997$	−22.0320	−	38.1606i	−0.697762	−	1.20856i	−0.969241	−	0.246114i	$-0.920846\pi$
$997$	−22.0320	−	38.1606i	−0.697762	−	1.20856i	0.271479	−	0.962444i	$-0.412487\pi$
$998$		0			0
$999$	−29.8307	+	14.5955i	−0.943801	+	0.461781i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.q.d.25.3	✓	22
3.2	odd	2		1512.2.q.c.1369.3		22
4.3	odd	2		1008.2.q.k.529.9		22
7.2	even	3		504.2.t.d.457.10	yes	22
9.4	even	3		504.2.t.d.193.10	yes	22
9.5	odd	6		1512.2.t.d.361.9		22
12.11	even	2		3024.2.q.k.2881.3		22
21.2	odd	6		1512.2.t.d.289.9		22
28.23	odd	6		1008.2.t.k.961.2		22
36.23	even	6		3024.2.t.l.1873.9		22
36.31	odd	6		1008.2.t.k.193.2		22
63.23	odd	6		1512.2.q.c.793.3		22
63.58	even	3	inner	504.2.q.d.121.3	yes	22
84.23	even	6		3024.2.t.l.289.9		22
252.23	even	6		3024.2.q.k.2305.3		22
252.247	odd	6		1008.2.q.k.625.9		22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.q.d.25.3	✓	22	1.1	even	1	trivial
504.2.q.d.121.3	yes	22	63.58	even	3	inner
504.2.t.d.193.10	yes	22	9.4	even	3
504.2.t.d.457.10	yes	22	7.2	even	3
1008.2.q.k.529.9		22	4.3	odd	2
1008.2.q.k.625.9		22	252.247	odd	6
1008.2.t.k.193.2		22	36.31	odd	6
1008.2.t.k.961.2		22	28.23	odd	6
1512.2.q.c.793.3		22	63.23	odd	6
1512.2.q.c.1369.3		22	3.2	odd	2
1512.2.t.d.289.9		22	21.2	odd	6
1512.2.t.d.361.9		22	9.5	odd	6
3024.2.q.k.2305.3		22	252.23	even	6
3024.2.q.k.2881.3		22	12.11	even	2
3024.2.t.l.289.9		22	84.23	even	6
3024.2.t.l.1873.9		22	36.23	even	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:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.47982 - 0.900079i) q^{3} +(1.26145 - 2.18490i) q^{5} +(2.63136 - 0.275550i) q^{7} +(1.37972 + 2.66390i) q^{9} +O(q^{10})\)	\(q+(-1.47982 - 0.900079i) q^{3} +(1.26145 - 2.18490i) q^{5} +(2.63136 - 0.275550i) q^{7} +(1.37972 + 2.66390i) q^{9} +(2.85648 + 4.94757i) q^{11} +(-2.45245 - 4.24777i) q^{13} +(-3.83330 + 2.09784i) q^{15} +(2.49483 - 4.32118i) q^{17} +(-0.00383929 - 0.00664984i) q^{19} +(-4.14195 - 1.96067i) q^{21} +(-0.333877 + 0.578292i) q^{23} +(-0.682524 - 1.18217i) q^{25} +(0.355997 - 5.18394i) q^{27} +(3.85082 - 6.66981i) q^{29} -7.76605 q^{31} +(0.226135 - 9.89256i) q^{33} +(2.71729 - 6.09686i) q^{35} +(-3.19562 - 5.53498i) q^{37} +(-0.194150 + 8.49333i) q^{39} +(5.21159 + 9.02673i) q^{41} +(4.42935 - 7.67185i) q^{43} +(7.56081 + 0.345848i) q^{45} +2.16104 q^{47} +(6.84814 - 1.45015i) q^{49} +(-7.58129 + 4.14900i) q^{51} +(-3.69858 + 6.40613i) q^{53} +14.4133 q^{55} +(-0.000303939 + 0.0132962i) q^{57} -0.523594 q^{59} -8.99082 q^{61} +(4.36457 + 6.62952i) q^{63} -12.3746 q^{65} -5.09582 q^{67} +(1.01458 - 0.555250i) q^{69} -5.68471 q^{71} +(-1.52062 + 2.63379i) q^{73} +(-0.0540325 + 2.36372i) q^{75} +(8.87975 + 12.2318i) q^{77} +6.16230 q^{79} +(-5.19277 + 7.35086i) q^{81} +(-0.258726 + 0.448126i) q^{83} +(-6.29422 - 10.9019i) q^{85} +(-11.7019 + 6.40406i) q^{87} +(1.19093 + 2.06274i) q^{89} +(-7.62377 - 10.5017i) q^{91} +(11.4923 + 6.99006i) q^{93} -0.0193723 q^{95} +(4.32994 - 7.49968i) q^{97} +(-9.23873 + 14.4356i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9}+O(q^{10}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9	\( 22 q + 2 q^{3} + 3 q^{5} - 5 q^{7} + 10 q^{9} - 3 q^{11} - 3 q^{13} - q^{15} + 7 q^{17} - q^{19} + 2 q^{23} - 10 q^{25} - 4 q^{27} + 9 q^{29} + 8 q^{31} + 29 q^{33} + 14 q^{35} + 2 q^{37} - 16 q^{39} + 16 q^{41} + q^{45} - 10 q^{47} + 15 q^{49} + 7 q^{51} + 11 q^{53} + 22 q^{55} + 7 q^{57} + 38 q^{59} + 26 q^{61} + 48 q^{63} - 26 q^{65} - 52 q^{67} - 4 q^{69} - 48 q^{71} - 35 q^{73} - 23 q^{75} + 17 q^{77} - 20 q^{79} - 38 q^{81} - 28 q^{83} - 20 q^{85} - 33 q^{87} + 6 q^{89} - 37 q^{91} + 19 q^{93} - 24 q^{95} - 29 q^{97} - 56 q^{99}+O(q^{100}) \) 22 * q + 2 * q^3 + 3 * q^5 - 5 * q^7 + 10 * q^9 - 3 * q^11 - 3 * q^13 - q^15 + 7 * q^17 - q^19 + 2 * q^23 - 10 * q^25 - 4 * q^27 + 9 * q^29 + 8 * q^31 + 29 * q^33 + 14 * q^35 + 2 * q^37 - 16 * q^39 + 16 * q^41 + q^45 - 10 * q^47 + 15 * q^49 + 7 * q^51 + 11 * q^53 + 22 * q^55 + 7 * q^57 + 38 * q^59 + 26 * q^61 + 48 * q^63 - 26 * q^65 - 52 * q^67 - 4 * q^69 - 48 * q^71 - 35 * q^73 - 23 * q^75 + 17 * q^77 - 20 * q^79 - 38 * q^81 - 28 * q^83 - 20 * q^85 - 33 * q^87 + 6 * q^89 - 37 * q^91 + 19 * q^93 - 24 * q^95 - 29 * q^97 - 56 * q^99

Introduction

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