LMFDB - Embedded newform 810.2.i.b.379.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [810,2,Mod(109,810)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(810, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2, 3]))

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

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

chi := DirichletCharacter("810.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 810 = 2 \cdot 3^{4} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	810.i (of order $6$, degree $2$, 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:	$6.46788256372$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{12})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{2} + 1 $ x^4 - x^2 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 30)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			379.2
Root			$0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	810.379
Dual form			810.2.i.b.109.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +O(q^{10})$	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(-1.00000 - 2.00000i) q^{10} +(1.00000 - 1.73205i) q^{11} +(5.19615 - 3.00000i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.00000i q^{17} +(0.133975 - 2.23205i) q^{20} +(1.73205 - 1.00000i) q^{22} +(3.46410 - 2.00000i) q^{23} +(1.96410 + 4.59808i) q^{25} +6.00000 q^{26} +2.00000i q^{28} +(4.00000 + 6.92820i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.00000 + 1.73205i) q^{34} +(-2.00000 - 4.00000i) q^{35} -2.00000i q^{37} +(1.23205 - 1.86603i) q^{40} +(1.00000 + 1.73205i) q^{41} +(3.46410 + 2.00000i) q^{43} +2.00000 q^{44} +4.00000 q^{46} +(6.92820 + 4.00000i) q^{47} +(-1.50000 - 2.59808i) q^{49} +(-0.598076 + 4.96410i) q^{50} +(5.19615 + 3.00000i) q^{52} -6.00000i q^{53} +(-4.00000 + 2.00000i) q^{55} +(-1.00000 + 1.73205i) q^{56} +(-5.00000 - 8.66025i) q^{59} +(-1.00000 + 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(-13.3923 - 0.803848i) q^{65} +(6.92820 - 4.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +(0.267949 - 4.46410i) q^{70} -12.0000 q^{71} -4.00000i q^{73} +(1.00000 - 1.73205i) q^{74} +(3.46410 - 2.00000i) q^{77} +(2.00000 - 1.00000i) q^{80} +2.00000i q^{82} +(-3.46410 - 2.00000i) q^{83} +(2.46410 - 3.73205i) q^{85} +(2.00000 + 3.46410i) q^{86} +(1.73205 + 1.00000i) q^{88} -10.0000 q^{89} +12.0000 q^{91} +(3.46410 + 2.00000i) q^{92} +(4.00000 + 6.92820i) q^{94} +(-6.92820 - 4.00000i) q^{97} -3.00000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 2 q^{4} - 4 q^{5}+O(q^{10}) $ 4 * q + 2 * q^4 - 4 * q^5	$ 4 q + 2 q^{4} - 4 q^{5} - 4 q^{10} + 4 q^{11} + 4 q^{14} - 2 q^{16} + 4 q^{20} - 6 q^{25} + 24 q^{26} + 16 q^{31} - 4 q^{34} - 8 q^{35} - 2 q^{40} + 4 q^{41} + 8 q^{44} + 16 q^{46} - 6 q^{49} + 8 q^{50} - 16 q^{55} - 4 q^{56} - 20 q^{59} - 4 q^{61} - 4 q^{64} - 12 q^{65} + 8 q^{70} - 48 q^{71} + 4 q^{74} + 8 q^{80} - 4 q^{85} + 8 q^{86} - 40 q^{89} + 48 q^{91} + 16 q^{94}+O(q^{100}) $ 4 * q + 2 * q^4 - 4 * q^5 - 4 * q^10 + 4 * q^11 + 4 * q^14 - 2 * q^16 + 4 * q^20 - 6 * q^25 + 24 * q^26 + 16 * q^31 - 4 * q^34 - 8 * q^35 - 2 * q^40 + 4 * q^41 + 8 * q^44 + 16 * q^46 - 6 * q^49 + 8 * q^50 - 16 * q^55 - 4 * q^56 - 20 * q^59 - 4 * q^61 - 4 * q^64 - 12 * q^65 + 8 * q^70 - 48 * q^71 + 4 * q^74 + 8 * q^80 - 4 * q^85 + 8 * q^86 - 40 * q^89 + 48 * q^91 + 16 * q^94

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/810\mathbb{Z}\right)^\times$.

$n$	$487$	$731$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$2$	0.866025	+	0.500000i	0.612372	+	0.353553i
$3$		0			0
$3$		0			0
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$5$	−1.86603	−	1.23205i	−0.834512	−	0.550990i
$6$		0			0
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	0.790237	−	0.612801i	$-0.209957\pi$
$7$	1.73205	+	1.00000i	0.654654	+	0.377964i	−0.135583	+	0.990766i	$0.543291\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	−1.00000	−	2.00000i	−0.316228	−	0.632456i
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	−0.674967	−	0.737848i	$-0.735842\pi$
$11$	1.00000	−	1.73205i	0.301511	−	0.522233i	0.976478	+	0.215615i	$0.0691756\pi$
$12$		0			0
$13$	5.19615	−	3.00000i	1.44115	−	0.832050i	0.443227	−	0.896410i	$-0.353834\pi$
$13$	5.19615	−	3.00000i	1.44115	−	0.832050i	0.997927	+	0.0643593i	$0.0205004\pi$
$14$	1.00000	+	1.73205i	0.267261	+	0.462910i
$15$		0			0
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$			2.00000i			0.485071i	0.970143	+	0.242536i	$0.0779791\pi$
$17$			2.00000i			0.485071i	−0.970143	+	0.242536i	$0.922021\pi$
$18$		0			0
$19$		0			0			−	1.00000i	$-0.5\pi$
$19$		0			0				1.00000i	$0.5\pi$
$20$	0.133975	−	2.23205i	0.0299576	−	0.499102i
$21$		0			0
$22$	1.73205	−	1.00000i	0.369274	−	0.213201i
$23$	3.46410	−	2.00000i	0.722315	−	0.417029i	−0.0932891	−	0.995639i	$-0.529738\pi$
$23$	3.46410	−	2.00000i	0.722315	−	0.417029i	0.815604	+	0.578610i	$0.196405\pi$
$24$		0			0
$25$	1.96410	+	4.59808i	0.392820	+	0.919615i
$26$	6.00000			1.17670
$27$		0			0
$28$			2.00000i			0.377964i
$29$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$29$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$30$		0			0
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	0.961625	+	0.274367i	$0.0884683\pi$
$31$	4.00000	+	6.92820i	0.718421	+	1.24434i	−0.243204	+	0.969975i	$0.578198\pi$
$32$	−0.866025	+	0.500000i	−0.153093	+	0.0883883i
$33$		0			0
$34$	−1.00000	+	1.73205i	−0.171499	+	0.297044i
$35$	−2.00000	−	4.00000i	−0.338062	−	0.676123i
$36$		0			0
$37$		−	2.00000i		−	0.328798i	−0.986394	−	0.164399i	$-0.947432\pi$
$37$		−	2.00000i		−	0.328798i	0.986394	−	0.164399i	$-0.0525685\pi$
$38$		0			0
$39$		0			0
$40$	1.23205	−	1.86603i	0.194804	−	0.295045i
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	0.933486	−	0.358614i	$-0.116751\pi$
$41$	1.00000	+	1.73205i	0.156174	+	0.270501i	−0.777312	+	0.629115i	$0.783417\pi$
$42$		0			0
$43$	3.46410	+	2.00000i	0.528271	+	0.304997i	0.740312	−	0.672264i	$-0.234678\pi$
$43$	3.46410	+	2.00000i	0.528271	+	0.304997i	−0.212041	+	0.977261i	$0.568011\pi$
$44$	2.00000			0.301511
$45$		0			0
$46$	4.00000			0.589768
$47$	6.92820	+	4.00000i	1.01058	+	0.583460i	0.911362	−	0.411606i	$-0.135032\pi$
$47$	6.92820	+	4.00000i	1.01058	+	0.583460i	0.0992202	+	0.995066i	$0.468365\pi$
$48$		0			0
$49$	−1.50000	−	2.59808i	−0.214286	−	0.371154i
$50$	−0.598076	+	4.96410i	−0.0845807	+	0.702030i
$51$		0			0
$52$	5.19615	+	3.00000i	0.720577	+	0.416025i
$53$		−	6.00000i		−	0.824163i	−0.911147	−	0.412082i	$-0.864802\pi$
$53$		−	6.00000i		−	0.824163i	0.911147	−	0.412082i	$-0.135198\pi$
$54$		0			0
$55$	−4.00000	+	2.00000i	−0.539360	+	0.269680i
$56$	−1.00000	+	1.73205i	−0.133631	+	0.231455i
$57$		0			0
$58$		0			0
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	−0.982894	−	0.184172i	$-0.941040\pi$
$59$	−5.00000	−	8.66025i	−0.650945	−	1.12747i	0.331949	−	0.943297i	$-0.392294\pi$
$60$		0			0
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	−0.922916	−	0.385002i	$-0.874201\pi$
$61$	−1.00000	+	1.73205i	−0.128037	+	0.221766i	0.794879	+	0.606768i	$0.207534\pi$
$62$			8.00000i			1.01600i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	−13.3923	−	0.803848i	−1.66111	−	0.0997050i
$66$		0			0
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	−0.0130248	−	0.999915i	$-0.504146\pi$
$67$	6.92820	−	4.00000i	0.846415	−	0.488678i	0.859440	+	0.511237i	$0.170813\pi$
$68$	−1.73205	+	1.00000i	−0.210042	+	0.121268i
$69$		0			0
$70$	0.267949	−	4.46410i	0.0320261	−	0.533562i
$71$	−12.0000			−1.42414			−0.712069	−	0.702109i	$-0.752242\pi$
$71$	−12.0000			−1.42414			−0.712069	+	0.702109i	$0.752242\pi$
$72$		0			0
$73$		−	4.00000i		−	0.468165i	−0.972217	−	0.234082i	$-0.924791\pi$
$73$		−	4.00000i		−	0.468165i	0.972217	−	0.234082i	$-0.0752085\pi$
$74$	1.00000	−	1.73205i	0.116248	−	0.201347i
$75$		0			0
$76$		0			0
$77$	3.46410	−	2.00000i	0.394771	−	0.227921i
$78$		0			0
$79$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$79$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$80$	2.00000	−	1.00000i	0.223607	−	0.111803i
$81$		0			0
$82$			2.00000i			0.220863i
$83$	−3.46410	−	2.00000i	−0.380235	−	0.219529i	0.297686	−	0.954664i	$-0.403785\pi$
$83$	−3.46410	−	2.00000i	−0.380235	−	0.219529i	−0.677920	+	0.735135i	$0.737119\pi$
$84$		0			0
$85$	2.46410	−	3.73205i	0.267269	−	0.404798i
$86$	2.00000	+	3.46410i	0.215666	+	0.373544i
$87$		0			0
$88$	1.73205	+	1.00000i	0.184637	+	0.106600i
$89$	−10.0000			−1.06000			−0.529999	−	0.847998i	$-0.677808\pi$
$89$	−10.0000			−1.06000			−0.529999	+	0.847998i	$0.677808\pi$
$90$		0			0
$91$	12.0000			1.25794
$92$	3.46410	+	2.00000i	0.361158	+	0.208514i
$93$		0			0
$94$	4.00000	+	6.92820i	0.412568	+	0.714590i
$95$		0			0
$96$		0			0
$97$	−6.92820	−	4.00000i	−0.703452	−	0.406138i	0.105180	−	0.994453i	$-0.466458\pi$
$97$	−6.92820	−	4.00000i	−0.703452	−	0.406138i	−0.808632	+	0.588315i	$0.799792\pi$
$98$		−	3.00000i		−	0.303046i
$99$		0			0
$100$	−3.00000	+	4.00000i	−0.300000	+	0.400000i
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	−0.993481	−	0.113998i	$-0.963634\pi$
$101$	−4.00000	+	6.92820i	−0.398015	+	0.689382i	0.595466	+	0.803380i	$0.296967\pi$
$102$		0			0
$103$	−12.1244	+	7.00000i	−1.19465	+	0.689730i	−0.959357	−	0.282194i	$-0.908938\pi$
$103$	−12.1244	+	7.00000i	−1.19465	+	0.689730i	−0.235291	+	0.971925i	$0.575604\pi$
$104$	3.00000	+	5.19615i	0.294174	+	0.509525i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$			12.0000i			1.16008i	0.814587	+	0.580042i	$0.196964\pi$
$107$			12.0000i			1.16008i	−0.814587	+	0.580042i	$0.803036\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−4.46410	−	0.267949i	−0.425635	−	0.0255480i
$111$		0			0
$112$	−1.73205	+	1.00000i	−0.163663	+	0.0944911i
$113$	−5.19615	+	3.00000i	−0.488813	+	0.282216i	−0.724082	−	0.689714i	$-0.757736\pi$
$113$	−5.19615	+	3.00000i	−0.488813	+	0.282216i	0.235269	+	0.971930i	$0.424403\pi$
$114$		0			0
$115$	−8.92820	−	0.535898i	−0.832559	−	0.0499728i
$116$		0			0
$117$		0			0
$118$		−	10.0000i		−	0.920575i
$119$	−2.00000	+	3.46410i	−0.183340	+	0.317554i
$120$		0			0
$121$	3.50000	+	6.06218i	0.318182	+	0.551107i
$122$	−1.73205	+	1.00000i	−0.156813	+	0.0905357i
$123$		0			0
$124$	−4.00000	+	6.92820i	−0.359211	+	0.622171i
$125$	2.00000	−	11.0000i	0.178885	−	0.983870i
$126$		0			0
$127$		−	2.00000i		−	0.177471i	−0.996055	−	0.0887357i	$-0.971717\pi$
$127$		−	2.00000i		−	0.177471i	0.996055	−	0.0887357i	$-0.0282826\pi$
$128$	−0.866025	−	0.500000i	−0.0765466	−	0.0441942i
$129$		0			0
$130$	−11.1962	−	7.39230i	−0.981968	−	0.648348i
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$		0			0
$133$		0			0
$134$	8.00000			0.691095
$135$		0			0
$136$	−2.00000			−0.171499
$137$	15.5885	+	9.00000i	1.33181	+	0.768922i	0.985577	−	0.169226i	$-0.0541268\pi$
$137$	15.5885	+	9.00000i	1.33181	+	0.768922i	0.346235	+	0.938148i	$0.387460\pi$
$138$		0			0
$139$	−10.0000	−	17.3205i	−0.848189	−	1.46911i	−0.882823	−	0.469706i	$-0.844360\pi$
$139$	−10.0000	−	17.3205i	−0.848189	−	1.46911i	0.0346338	−	0.999400i	$-0.488974\pi$
$140$	2.46410	−	3.73205i	0.208255	−	0.315416i
$141$		0			0
$142$	−10.3923	−	6.00000i	−0.872103	−	0.503509i
$143$		−	12.0000i		−	1.00349i
$144$		0			0
$145$		0			0
$146$	2.00000	−	3.46410i	0.165521	−	0.286691i
$147$		0			0
$148$	1.73205	−	1.00000i	0.142374	−	0.0821995i
$149$	10.0000	+	17.3205i	0.819232	+	1.41895i	0.906249	+	0.422744i	$0.138933\pi$
$149$	10.0000	+	17.3205i	0.819232	+	1.41895i	−0.0870170	+	0.996207i	$0.527733\pi$
$150$		0			0
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	−0.656101	−	0.754673i	$-0.727796\pi$
$151$	4.00000	−	6.92820i	0.325515	−	0.563809i	0.981617	+	0.190864i	$0.0611289\pi$
$152$		0			0
$153$		0			0
$154$	4.00000			0.322329
$155$	1.07180	−	17.8564i	0.0860888	−	1.43426i
$156$		0			0
$157$	−19.0526	+	11.0000i	−1.52056	+	0.877896i	−0.520854	+	0.853646i	$0.674386\pi$
$157$	−19.0526	+	11.0000i	−1.52056	+	0.877896i	−0.999706	+	0.0242497i	$0.992280\pi$
$158$		0			0
$159$		0			0
$160$	2.23205	+	0.133975i	0.176459	+	0.0105916i
$161$	8.00000			0.630488
$162$		0			0
$163$			16.0000i			1.25322i	0.779334	+	0.626608i	$0.215557\pi$
$163$			16.0000i			1.25322i	−0.779334	+	0.626608i	$0.784443\pi$
$164$	−1.00000	+	1.73205i	−0.0780869	+	0.135250i
$165$		0			0
$166$	−2.00000	−	3.46410i	−0.155230	−	0.268866i
$167$	10.3923	−	6.00000i	0.804181	−	0.464294i	−0.0407502	−	0.999169i	$-0.512975\pi$
$167$	10.3923	−	6.00000i	0.804181	−	0.464294i	0.844931	+	0.534875i	$0.179641\pi$
$168$		0			0
$169$	11.5000	−	19.9186i	0.884615	−	1.53220i
$170$	4.00000	−	2.00000i	0.306786	−	0.153393i
$171$		0			0
$172$			4.00000i			0.304997i
$173$	−12.1244	−	7.00000i	−0.921798	−	0.532200i	−0.0375896	−	0.999293i	$-0.511968\pi$
$173$	−12.1244	−	7.00000i	−0.921798	−	0.532200i	−0.884208	+	0.467093i	$0.845301\pi$
$174$		0			0
$175$	−1.19615	+	9.92820i	−0.0904206	+	0.750502i
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$		0			0
$178$	−8.66025	−	5.00000i	−0.649113	−	0.374766i
$179$	10.0000			0.747435			0.373718	−	0.927543i	$-0.378083\pi$
$179$	10.0000			0.747435			0.373718	+	0.927543i	$0.378083\pi$
$180$		0			0
$181$	2.00000			0.148659			0.0743294	−	0.997234i	$-0.476318\pi$
$181$	2.00000			0.148659			0.0743294	+	0.997234i	$0.476318\pi$
$182$	10.3923	+	6.00000i	0.770329	+	0.444750i
$183$		0			0
$184$	2.00000	+	3.46410i	0.147442	+	0.255377i
$185$	−2.46410	+	3.73205i	−0.181164	+	0.274386i
$186$		0			0
$187$	3.46410	+	2.00000i	0.253320	+	0.146254i
$188$			8.00000i			0.583460i
$189$		0			0
$190$		0			0
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	−0.563081	−	0.826402i	$-0.690384\pi$
$191$	6.00000	−	10.3923i	0.434145	−	0.751961i	0.997225	+	0.0744412i	$0.0237173\pi$
$192$		0			0
$193$	−3.46410	+	2.00000i	−0.249351	+	0.143963i	−0.619467	−	0.785022i	$-0.712651\pi$
$193$	−3.46410	+	2.00000i	−0.249351	+	0.143963i	0.370116	+	0.928986i	$0.379318\pi$
$194$	−4.00000	−	6.92820i	−0.287183	−	0.497416i
$195$		0			0
$196$	1.50000	−	2.59808i	0.107143	−	0.185577i
$197$			22.0000i			1.56744i	0.621117	+	0.783718i	$0.286679\pi$
$197$			22.0000i			1.56744i	−0.621117	+	0.783718i	$0.713321\pi$
$198$		0			0
$199$		0			0			−	1.00000i	$-0.5\pi$
$199$		0			0				1.00000i	$0.5\pi$
$200$	−4.59808	+	1.96410i	−0.325133	+	0.138883i
$201$		0			0
$202$	−6.92820	+	4.00000i	−0.487467	+	0.281439i
$203$		0			0
$204$		0			0
$205$	0.267949	−	4.46410i	0.0187144	−	0.311786i
$206$	−14.0000			−0.975426
$207$		0			0
$208$			6.00000i			0.416025i
$209$		0			0
$210$		0			0
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	0.582165	−	0.813070i	$-0.302206\pi$
$211$	−6.00000	−	10.3923i	−0.413057	−	0.715436i	−0.995222	+	0.0976347i	$0.968872\pi$
$212$	5.19615	−	3.00000i	0.356873	−	0.206041i
$213$		0			0
$214$	−6.00000	+	10.3923i	−0.410152	+	0.710403i
$215$	−4.00000	−	8.00000i	−0.272798	−	0.545595i
$216$		0			0
$217$			16.0000i			1.08615i
$218$	−8.66025	−	5.00000i	−0.586546	−	0.338643i
$219$		0			0
$220$	−3.73205	−	2.46410i	−0.251615	−	0.166130i
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$	−22.5167	−	13.0000i	−1.50783	−	0.870544i	−0.999959	−	0.00910984i	$-0.997100\pi$
$223$	−22.5167	−	13.0000i	−1.50783	−	0.870544i	−0.507869	−	0.861435i	$-0.669566\pi$
$224$	−2.00000			−0.133631
$225$		0			0
$226$	−6.00000			−0.399114
$227$	24.2487	+	14.0000i	1.60944	+	0.929213i	0.989494	+	0.144571i	$0.0461801\pi$
$227$	24.2487	+	14.0000i	1.60944	+	0.929213i	0.619949	+	0.784642i	$0.287153\pi$
$228$		0			0
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	0.652183	−	0.758062i	$-0.273853\pi$
$229$	−5.00000	−	8.66025i	−0.330409	−	0.572286i	−0.982592	+	0.185776i	$0.940520\pi$
$230$	−7.46410	−	4.92820i	−0.492168	−	0.324956i
$231$		0			0
$232$		0			0
$233$			14.0000i			0.917170i	0.888650	+	0.458585i	$0.151644\pi$
$233$			14.0000i			0.917170i	−0.888650	+	0.458585i	$0.848356\pi$
$234$		0			0
$235$	−8.00000	−	16.0000i	−0.521862	−	1.04372i
$236$	5.00000	−	8.66025i	0.325472	−	0.563735i
$237$		0			0
$238$	−3.46410	+	2.00000i	−0.224544	+	0.129641i
$239$	−10.0000	−	17.3205i	−0.646846	−	1.12037i	−0.983872	−	0.178875i	$-0.942754\pi$
$239$	−10.0000	−	17.3205i	−0.646846	−	1.12037i	0.337026	−	0.941495i	$-0.390579\pi$
$240$		0			0
$241$	−11.0000	+	19.0526i	−0.708572	+	1.22728i	0.256814	+	0.966461i	$0.417327\pi$
$241$	−11.0000	+	19.0526i	−0.708572	+	1.22728i	−0.965387	+	0.260822i	$0.916006\pi$
$242$			7.00000i			0.449977i
$243$		0			0
$244$	−2.00000			−0.128037
$245$	−0.401924	+	6.69615i	−0.0256780	+	0.427801i
$246$		0			0
$247$		0			0
$248$	−6.92820	+	4.00000i	−0.439941	+	0.254000i
$249$		0			0
$250$	7.23205	−	8.52628i	0.457395	−	0.539249i
$251$	18.0000			1.13615			0.568075	−	0.822977i	$-0.307688\pi$
$251$	18.0000			1.13615			0.568075	+	0.822977i	$0.307688\pi$
$252$		0			0
$253$		−	8.00000i		−	0.502956i
$254$	1.00000	−	1.73205i	0.0627456	−	0.108679i
$255$		0			0
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.899961	−	0.435970i	$-0.856405\pi$
$257$	−15.5885	+	9.00000i	−0.972381	+	0.561405i	−0.0724199	+	0.997374i	$0.523072\pi$
$258$		0			0
$259$	2.00000	−	3.46410i	0.124274	−	0.215249i
$260$	−6.00000	−	12.0000i	−0.372104	−	0.744208i
$261$		0			0
$262$		−	18.0000i		−	1.11204i
$263$	−3.46410	−	2.00000i	−0.213606	−	0.123325i	0.389380	−	0.921077i	$-0.372689\pi$
$263$	−3.46410	−	2.00000i	−0.213606	−	0.123325i	−0.602986	+	0.797752i	$0.706023\pi$
$264$		0			0
$265$	−7.39230	+	11.1962i	−0.454106	+	0.687774i
$266$		0			0
$267$		0			0
$268$	6.92820	+	4.00000i	0.423207	+	0.244339i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$	−8.00000			−0.485965			−0.242983	−	0.970031i	$-0.578126\pi$
$271$	−8.00000			−0.485965			−0.242983	+	0.970031i	$0.578126\pi$
$272$	−1.73205	−	1.00000i	−0.105021	−	0.0606339i
$273$		0			0
$274$	9.00000	+	15.5885i	0.543710	+	0.941733i
$275$	9.92820	+	1.19615i	0.598693	+	0.0721307i
$276$		0			0
$277$	1.73205	+	1.00000i	0.104069	+	0.0600842i	0.551131	−	0.834419i	$-0.314196\pi$
$277$	1.73205	+	1.00000i	0.104069	+	0.0600842i	−0.447062	+	0.894503i	$0.647530\pi$
$278$		−	20.0000i		−	1.19952i
$279$		0			0
$280$	4.00000	−	2.00000i	0.239046	−	0.119523i
$281$	−9.00000	+	15.5885i	−0.536895	+	0.929929i	0.462174	+	0.886789i	$0.347070\pi$
$281$	−9.00000	+	15.5885i	−0.536895	+	0.929929i	−0.999069	+	0.0431402i	$0.986264\pi$
$282$		0			0
$283$	13.8564	−	8.00000i	0.823678	−	0.475551i	−0.0280052	−	0.999608i	$-0.508916\pi$
$283$	13.8564	−	8.00000i	0.823678	−	0.475551i	0.851683	+	0.524057i	$0.175582\pi$
$284$	−6.00000	−	10.3923i	−0.356034	−	0.616670i
$285$		0			0
$286$	6.00000	−	10.3923i	0.354787	−	0.614510i
$287$			4.00000i			0.236113i
$288$		0			0
$289$	13.0000			0.764706
$290$		0			0
$291$		0			0
$292$	3.46410	−	2.00000i	0.202721	−	0.117041i
$293$	−5.19615	+	3.00000i	−0.303562	+	0.175262i	−0.644042	−	0.764990i	$-0.722744\pi$
$293$	−5.19615	+	3.00000i	−0.303562	+	0.175262i	0.340480	+	0.940252i	$0.389411\pi$
$294$		0			0
$295$	−1.33975	+	22.3205i	−0.0780030	+	1.29955i
$296$	2.00000			0.116248
$297$		0			0
$298$			20.0000i			1.15857i
$299$	12.0000	−	20.7846i	0.693978	−	1.20201i
$300$		0			0
$301$	4.00000	+	6.92820i	0.230556	+	0.399335i
$302$	6.92820	−	4.00000i	0.398673	−	0.230174i
$303$		0			0
$304$		0			0
$305$	4.00000	−	2.00000i	0.229039	−	0.114520i
$306$		0			0
$307$		−	12.0000i		−	0.684876i	−0.939540	−	0.342438i	$-0.888747\pi$
$307$		−	12.0000i		−	0.684876i	0.939540	−	0.342438i	$-0.111253\pi$
$308$	3.46410	+	2.00000i	0.197386	+	0.113961i
$309$		0			0
$310$	9.85641	−	14.9282i	0.559806	−	0.847865i
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	0.984475	−	0.175525i	$-0.0561621\pi$
$311$	6.00000	+	10.3923i	0.340229	+	0.589294i	−0.644246	+	0.764818i	$0.722829\pi$
$312$		0			0
$313$	3.46410	+	2.00000i	0.195803	+	0.113047i	0.594696	−	0.803951i	$-0.297272\pi$
$313$	3.46410	+	2.00000i	0.195803	+	0.113047i	−0.398894	+	0.916997i	$0.630606\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$		0			0
$317$	−1.73205	−	1.00000i	−0.0972817	−	0.0561656i	0.450570	−	0.892741i	$-0.351221\pi$
$317$	−1.73205	−	1.00000i	−0.0972817	−	0.0561656i	−0.547852	+	0.836576i	$0.684554\pi$
$318$		0			0
$319$		0			0
$320$	1.86603	+	1.23205i	0.104314	+	0.0688737i
$321$		0			0
$322$	6.92820	+	4.00000i	0.386094	+	0.222911i
$323$		0			0
$324$		0			0
$325$	24.0000	+	18.0000i	1.33128	+	0.998460i
$326$	−8.00000	+	13.8564i	−0.443079	+	0.767435i
$327$		0			0
$328$	−1.73205	+	1.00000i	−0.0956365	+	0.0552158i
$329$	8.00000	+	13.8564i	0.441054	+	0.763928i
$330$		0			0
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	−0.734905	−	0.678170i	$-0.762773\pi$
$331$	4.00000	−	6.92820i	0.219860	−	0.380808i	0.954765	+	0.297361i	$0.0961066\pi$
$332$		−	4.00000i		−	0.219529i
$333$		0			0
$334$	12.0000			0.656611
$335$	−17.8564	−	1.07180i	−0.975600	−	0.0585585i
$336$		0			0
$337$	24.2487	−	14.0000i	1.32091	−	0.762629i	0.337037	−	0.941491i	$-0.390575\pi$
$337$	24.2487	−	14.0000i	1.32091	−	0.762629i	0.983874	+	0.178863i	$0.0572418\pi$
$338$	19.9186	−	11.5000i	1.08343	−	0.625518i
$339$		0			0
$340$	4.46410	+	0.267949i	0.242100	+	0.0145316i
$341$	16.0000			0.866449
$342$		0			0
$343$		−	20.0000i		−	1.07990i
$344$	−2.00000	+	3.46410i	−0.107833	+	0.186772i
$345$		0			0
$346$	−7.00000	−	12.1244i	−0.376322	−	0.651809i
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	−0.194409	−	0.980921i	$-0.562279\pi$
$347$	10.3923	−	6.00000i	0.557888	−	0.322097i	0.752297	+	0.658824i	$0.228946\pi$
$348$		0			0
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	−0.700609	−	0.713545i	$-0.747088\pi$
$349$	5.00000	−	8.66025i	0.267644	−	0.463573i	0.968253	+	0.249973i	$0.0804216\pi$
$350$	−6.00000	+	8.00000i	−0.320713	+	0.427618i
$351$		0			0
$352$			2.00000i			0.106600i
$353$	−12.1244	−	7.00000i	−0.645314	−	0.372572i	0.141344	−	0.989960i	$-0.454858\pi$
$353$	−12.1244	−	7.00000i	−0.645314	−	0.372572i	−0.786659	+	0.617388i	$0.788191\pi$
$354$		0			0
$355$	22.3923	+	14.7846i	1.18846	+	0.784686i
$356$	−5.00000	−	8.66025i	−0.264999	−	0.458993i
$357$		0			0
$358$	8.66025	+	5.00000i	0.457709	+	0.264258i
$359$		0			0			−	1.00000i	$-0.5\pi$
$359$		0			0				1.00000i	$0.5\pi$
$360$		0			0
$361$	−19.0000			−1.00000
$362$	1.73205	+	1.00000i	0.0910346	+	0.0525588i
$363$		0			0
$364$	6.00000	+	10.3923i	0.314485	+	0.544705i
$365$	−4.92820	+	7.46410i	−0.257954	+	0.390689i
$366$		0			0
$367$	1.73205	+	1.00000i	0.0904123	+	0.0521996i	0.544524	−	0.838745i	$-0.316710\pi$
$367$	1.73205	+	1.00000i	0.0904123	+	0.0521996i	−0.454112	+	0.890945i	$0.650043\pi$
$368$			4.00000i			0.208514i
$369$		0			0
$370$	−4.00000	+	2.00000i	−0.207950	+	0.103975i
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$		0			0
$373$	5.19615	−	3.00000i	0.269047	−	0.155334i	−0.359408	−	0.933181i	$-0.617021\pi$
$373$	5.19615	−	3.00000i	0.269047	−	0.155334i	0.628454	+	0.777847i	$0.283688\pi$
$374$	2.00000	+	3.46410i	0.103418	+	0.179124i
$375$		0			0
$376$	−4.00000	+	6.92820i	−0.206284	+	0.357295i
$377$		0			0
$378$		0			0
$379$	−20.0000			−1.02733			−0.513665	−	0.857991i	$-0.671713\pi$
$379$	−20.0000			−1.02733			−0.513665	+	0.857991i	$0.671713\pi$
$380$		0			0
$381$		0			0
$382$	10.3923	−	6.00000i	0.531717	−	0.306987i
$383$	−13.8564	+	8.00000i	−0.708029	+	0.408781i	−0.810331	−	0.585973i	$-0.800713\pi$
$383$	−13.8564	+	8.00000i	−0.708029	+	0.408781i	0.102302	+	0.994753i	$0.467379\pi$
$384$		0			0
$385$	−8.92820	−	0.535898i	−0.455023	−	0.0273119i
$386$	−4.00000			−0.203595
$387$		0			0
$388$		−	8.00000i		−	0.406138i
$389$	−10.0000	+	17.3205i	−0.507020	+	0.878185i	0.492947	+	0.870059i	$0.335920\pi$
$389$	−10.0000	+	17.3205i	−0.507020	+	0.878185i	−0.999967	+	0.00812520i	$0.997414\pi$
$390$		0			0
$391$	4.00000	+	6.92820i	0.202289	+	0.350374i
$392$	2.59808	−	1.50000i	0.131223	−	0.0757614i
$393$		0			0
$394$	−11.0000	+	19.0526i	−0.554172	+	0.959854i
$395$		0			0
$396$		0			0
$397$		−	2.00000i		−	0.100377i	−0.998740	−	0.0501886i	$-0.984018\pi$
$397$		−	2.00000i		−	0.100377i	0.998740	−	0.0501886i	$-0.0159822\pi$
$398$		0			0
$399$		0			0
$400$	−4.96410	−	0.598076i	−0.248205	−	0.0299038i
$401$	11.0000	+	19.0526i	0.549314	+	0.951439i	0.998322	+	0.0579116i	$0.0184442\pi$
$401$	11.0000	+	19.0526i	0.549314	+	0.951439i	−0.449008	+	0.893528i	$0.648223\pi$
$402$		0			0
$403$	41.5692	+	24.0000i	2.07071	+	1.19553i
$404$	−8.00000			−0.398015
$405$		0			0
$406$		0			0
$407$	−3.46410	−	2.00000i	−0.171709	−	0.0991363i
$408$		0			0
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	0.715523	−	0.698589i	$-0.246188\pi$
$409$	−5.00000	−	8.66025i	−0.247234	−	0.428222i	−0.962757	+	0.270367i	$0.912855\pi$
$410$	2.46410	−	3.73205i	0.121693	−	0.184313i
$411$		0			0
$412$	−12.1244	−	7.00000i	−0.597324	−	0.344865i
$413$		−	20.0000i		−	0.984136i
$414$		0			0
$415$	4.00000	+	8.00000i	0.196352	+	0.392705i
$416$	−3.00000	+	5.19615i	−0.147087	+	0.254762i
$417$		0			0
$418$		0			0
$419$	5.00000	+	8.66025i	0.244266	+	0.423081i	0.961925	−	0.273314i	$-0.0881197\pi$
$419$	5.00000	+	8.66025i	0.244266	+	0.423081i	−0.717659	+	0.696395i	$0.754786\pi$
$420$		0			0
$421$	−11.0000	+	19.0526i	−0.536107	+	0.928565i	0.463002	+	0.886357i	$0.346772\pi$
$421$	−11.0000	+	19.0526i	−0.536107	+	0.928565i	−0.999109	+	0.0422075i	$0.986561\pi$
$422$		−	12.0000i		−	0.584151i
$423$		0			0
$424$	6.00000			0.291386
$425$	−9.19615	+	3.92820i	−0.446079	+	0.190546i
$426$		0			0
$427$	−3.46410	+	2.00000i	−0.167640	+	0.0967868i
$428$	−10.3923	+	6.00000i	−0.502331	+	0.290021i
$429$		0			0
$430$	0.535898	−	8.92820i	0.0258433	−	0.430556i
$431$	−32.0000			−1.54139			−0.770693	−	0.637207i	$-0.780090\pi$
$431$	−32.0000			−1.54139			−0.770693	+	0.637207i	$0.780090\pi$
$432$		0			0
$433$		−	4.00000i		−	0.192228i	−0.995370	−	0.0961139i	$-0.969359\pi$
$433$		−	4.00000i		−	0.192228i	0.995370	−	0.0961139i	$-0.0306413\pi$
$434$	−8.00000	+	13.8564i	−0.384012	+	0.665129i
$435$		0			0
$436$	−5.00000	−	8.66025i	−0.239457	−	0.414751i
$437$		0			0
$438$		0			0
$439$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$439$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$440$	−2.00000	−	4.00000i	−0.0953463	−	0.190693i
$441$		0			0
$442$			12.0000i			0.570782i
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.999774	−	0.0212481i	$-0.00676401\pi$
$443$	31.1769	+	18.0000i	1.48126	+	0.855206i	0.481486	+	0.876454i	$0.340097\pi$
$444$		0			0
$445$	18.6603	+	12.3205i	0.884581	+	0.584048i
$446$	−13.0000	−	22.5167i	−0.615568	−	1.06619i
$447$		0			0
$448$	−1.73205	−	1.00000i	−0.0818317	−	0.0472456i
$449$	30.0000			1.41579			0.707894	−	0.706319i	$-0.249646\pi$
$449$	30.0000			1.41579			0.707894	+	0.706319i	$0.249646\pi$
$450$		0			0
$451$	4.00000			0.188353
$452$	−5.19615	−	3.00000i	−0.244406	−	0.141108i
$453$		0			0
$454$	14.0000	+	24.2487i	0.657053	+	1.13805i
$455$	−22.3923	−	14.7846i	−1.04977	−	0.693113i
$456$		0			0
$457$	27.7128	+	16.0000i	1.29635	+	0.748448i	0.979772	−	0.200118i	$-0.0641325\pi$
$457$	27.7128	+	16.0000i	1.29635	+	0.748448i	0.316579	+	0.948566i	$0.397466\pi$
$458$		−	10.0000i		−	0.467269i
$459$		0			0
$460$	−4.00000	−	8.00000i	−0.186501	−	0.373002i
$461$	6.00000	−	10.3923i	0.279448	−	0.484018i	−0.691800	−	0.722089i	$-0.743182\pi$
$461$	6.00000	−	10.3923i	0.279448	−	0.484018i	0.971248	+	0.238071i	$0.0765153\pi$
$462$		0			0
$463$	5.19615	−	3.00000i	0.241486	−	0.139422i	−0.374374	−	0.927278i	$-0.622142\pi$
$463$	5.19615	−	3.00000i	0.241486	−	0.139422i	0.615859	+	0.787856i	$0.288809\pi$
$464$		0			0
$465$		0			0
$466$	−7.00000	+	12.1244i	−0.324269	+	0.561650i
$467$			12.0000i			0.555294i	0.960683	+	0.277647i	$0.0895545\pi$
$467$			12.0000i			0.555294i	−0.960683	+	0.277647i	$0.910445\pi$
$468$		0			0
$469$	16.0000			0.738811
$470$	1.07180	−	17.8564i	0.0494383	−	0.823655i
$471$		0			0
$472$	8.66025	−	5.00000i	0.398621	−	0.230144i
$473$	6.92820	−	4.00000i	0.318559	−	0.183920i
$474$		0			0
$475$		0			0
$476$	−4.00000			−0.183340
$477$		0			0
$478$		−	20.0000i		−	0.914779i
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	−0.998796	−	0.0490589i	$-0.984378\pi$
$479$	−10.0000	+	17.3205i	−0.456912	+	0.791394i	0.541884	+	0.840453i	$0.317711\pi$
$480$		0			0
$481$	−6.00000	−	10.3923i	−0.273576	−	0.473848i
$482$	−19.0526	+	11.0000i	−0.867820	+	0.501036i
$483$		0			0
$484$	−3.50000	+	6.06218i	−0.159091	+	0.275554i
$485$	8.00000	+	16.0000i	0.363261	+	0.726523i
$486$		0			0
$487$			18.0000i			0.815658i	0.913058	+	0.407829i	$0.133714\pi$
$487$			18.0000i			0.815658i	−0.913058	+	0.407829i	$0.866286\pi$
$488$	−1.73205	−	1.00000i	−0.0784063	−	0.0452679i
$489$		0			0
$490$	−3.69615	+	5.59808i	−0.166975	+	0.252895i
$491$	−9.00000	−	15.5885i	−0.406164	−	0.703497i	0.588292	−	0.808649i	$-0.299801\pi$
$491$	−9.00000	−	15.5885i	−0.406164	−	0.703497i	−0.994456	+	0.105151i	$0.966467\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−8.00000			−0.359211
$497$	−20.7846	−	12.0000i	−0.932317	−	0.538274i
$498$		0			0
$499$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$499$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$500$	10.5263	−	3.76795i	0.470750	−	0.168508i
$501$		0			0
$502$	15.5885	+	9.00000i	0.695747	+	0.401690i
$503$			24.0000i			1.07011i	0.844818	+	0.535054i	$0.179709\pi$
$503$			24.0000i			1.07011i	−0.844818	+	0.535054i	$0.820291\pi$
$504$		0			0
$505$	16.0000	−	8.00000i	0.711991	−	0.355995i
$506$	4.00000	−	6.92820i	0.177822	−	0.307996i
$507$		0			0
$508$	1.73205	−	1.00000i	0.0768473	−	0.0443678i
$509$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$509$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$510$		0			0
$511$	4.00000	−	6.92820i	0.176950	−	0.306486i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−18.0000			−0.793946
$515$	31.2487	+	1.87564i	1.37698	+	0.0826508i
$516$		0			0
$517$	13.8564	−	8.00000i	0.609404	−	0.351840i
$518$	3.46410	−	2.00000i	0.152204	−	0.0878750i
$519$		0			0
$520$	0.803848	−	13.3923i	0.0352510	−	0.587291i
$521$	−22.0000			−0.963837			−0.481919	−	0.876216i	$-0.660060\pi$
$521$	−22.0000			−0.963837			−0.481919	+	0.876216i	$0.660060\pi$
$522$		0			0
$523$			16.0000i			0.699631i	0.936819	+	0.349816i	$0.113756\pi$
$523$			16.0000i			0.699631i	−0.936819	+	0.349816i	$0.886244\pi$
$524$	9.00000	−	15.5885i	0.393167	−	0.680985i
$525$		0			0
$526$	−2.00000	−	3.46410i	−0.0872041	−	0.151042i
$527$	−13.8564	+	8.00000i	−0.603595	+	0.348485i
$528$		0			0
$529$	−3.50000	+	6.06218i	−0.152174	+	0.263573i
$530$	−12.0000	+	6.00000i	−0.521247	+	0.260623i
$531$		0			0
$532$		0			0
$533$	10.3923	+	6.00000i	0.450141	+	0.259889i
$534$		0			0
$535$	14.7846	−	22.3923i	0.639194	−	0.968104i
$536$	4.00000	+	6.92820i	0.172774	+	0.299253i
$537$		0			0
$538$		0			0
$539$	−6.00000			−0.258438
$540$		0			0
$541$	−38.0000			−1.63375			−0.816874	−	0.576816i	$-0.804295\pi$
$541$	−38.0000			−1.63375			−0.816874	+	0.576816i	$0.804295\pi$
$542$	−6.92820	−	4.00000i	−0.297592	−	0.171815i
$543$		0			0
$544$	−1.00000	−	1.73205i	−0.0428746	−	0.0742611i
$545$	18.6603	+	12.3205i	0.799317	+	0.527753i
$546$		0			0
$547$	−24.2487	−	14.0000i	−1.03680	−	0.598597i	−0.117875	−	0.993028i	$-0.537608\pi$
$547$	−24.2487	−	14.0000i	−1.03680	−	0.598597i	−0.918925	+	0.394432i	$0.870941\pi$
$548$			18.0000i			0.768922i
$549$		0			0
$550$	8.00000	+	6.00000i	0.341121	+	0.255841i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	1.00000	+	1.73205i	0.0424859	+	0.0735878i
$555$		0			0
$556$	10.0000	−	17.3205i	0.424094	−	0.734553i
$557$		−	18.0000i		−	0.762684i	−0.924434	−	0.381342i	$-0.875462\pi$
$557$		−	18.0000i		−	0.762684i	0.924434	−	0.381342i	$-0.124538\pi$
$558$		0			0
$559$	24.0000			1.01509
$560$	4.46410	+	0.267949i	0.188643	+	0.0113229i
$561$		0			0
$562$	−15.5885	+	9.00000i	−0.657559	+	0.379642i
$563$	38.1051	−	22.0000i	1.60594	−	0.927189i	0.615673	−	0.788002i	$-0.288884\pi$
$563$	38.1051	−	22.0000i	1.60594	−	0.927189i	0.990266	−	0.139188i	$-0.0444492\pi$
$564$		0			0
$565$	13.3923	+	0.803848i	0.563418	+	0.0338181i
$566$	16.0000			0.672530
$567$		0			0
$568$		−	12.0000i		−	0.503509i
$569$	5.00000	−	8.66025i	0.209611	−	0.363057i	−0.741981	−	0.670421i	$-0.766114\pi$
$569$	5.00000	−	8.66025i	0.209611	−	0.363057i	0.951592	+	0.307364i	$0.0994469\pi$
$570$		0			0
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	0.937503	−	0.347977i	$-0.113131\pi$
$571$	4.00000	+	6.92820i	0.167395	+	0.289936i	−0.770108	+	0.637913i	$0.779798\pi$
$572$	10.3923	−	6.00000i	0.434524	−	0.250873i
$573$		0			0
$574$	−2.00000	+	3.46410i	−0.0834784	+	0.144589i
$575$	16.0000	+	12.0000i	0.667246	+	0.500435i
$576$		0			0
$577$		−	32.0000i		−	1.33218i	−0.745873	−	0.666089i	$-0.767967\pi$
$577$		−	32.0000i		−	1.33218i	0.745873	−	0.666089i	$-0.232033\pi$
$578$	11.2583	+	6.50000i	0.468285	+	0.270364i
$579$		0			0
$580$		0			0
$581$	−4.00000	−	6.92820i	−0.165948	−	0.287430i
$582$		0			0
$583$	−10.3923	−	6.00000i	−0.430405	−	0.248495i
$584$	4.00000			0.165521
$585$		0			0
$586$	−6.00000			−0.247858
$587$	−10.3923	−	6.00000i	−0.428936	−	0.247647i	0.269957	−	0.962872i	$-0.412990\pi$
$587$	−10.3923	−	6.00000i	−0.428936	−	0.247647i	−0.698893	+	0.715226i	$0.746324\pi$
$588$		0			0
$589$		0			0
$590$	−12.3205	+	18.6603i	−0.507227	+	0.768231i
$591$		0			0
$592$	1.73205	+	1.00000i	0.0711868	+	0.0410997i
$593$		−	6.00000i		−	0.246390i	−0.992382	−	0.123195i	$-0.960686\pi$
$593$		−	6.00000i		−	0.246390i	0.992382	−	0.123195i	$-0.0393141\pi$
$594$		0			0
$595$	8.00000	−	4.00000i	0.327968	−	0.163984i
$596$	−10.0000	+	17.3205i	−0.409616	+	0.709476i
$597$		0			0
$598$	20.7846	−	12.0000i	0.849946	−	0.490716i
$599$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$599$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$600$		0			0
$601$	−1.00000	+	1.73205i	−0.0407909	+	0.0706518i	−0.885700	−	0.464258i	$-0.846321\pi$
$601$	−1.00000	+	1.73205i	−0.0407909	+	0.0706518i	0.844909	+	0.534910i	$0.179654\pi$
$602$			8.00000i			0.326056i
$603$		0			0
$604$	8.00000			0.325515
$605$	0.937822	−	15.6244i	0.0381279	−	0.635220i
$606$		0			0
$607$	−19.0526	+	11.0000i	−0.773320	+	0.446476i	−0.834058	−	0.551678i	$-0.813988\pi$
$607$	−19.0526	+	11.0000i	−0.773320	+	0.446476i	0.0607380	+	0.998154i	$0.480655\pi$
$608$		0			0
$609$		0			0
$610$	4.46410	+	0.267949i	0.180746	+	0.0108489i
$611$	48.0000			1.94187
$612$		0			0
$613$			26.0000i			1.05013i	0.851062	+	0.525065i	$0.175959\pi$
$613$			26.0000i			1.05013i	−0.851062	+	0.525065i	$0.824041\pi$
$614$	6.00000	−	10.3923i	0.242140	−	0.419399i
$615$		0			0
$616$	2.00000	+	3.46410i	0.0805823	+	0.139573i
$617$	1.73205	−	1.00000i	0.0697297	−	0.0402585i	−0.464730	−	0.885453i	$-0.653849\pi$
$617$	1.73205	−	1.00000i	0.0697297	−	0.0402585i	0.534460	+	0.845194i	$0.320515\pi$
$618$		0			0
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	−0.592025	−	0.805919i	$-0.701671\pi$
$619$	10.0000	−	17.3205i	0.401934	−	0.696170i	0.993959	+	0.109749i	$0.0350048\pi$
$620$	16.0000	−	8.00000i	0.642575	−	0.321288i
$621$		0			0
$622$			12.0000i			0.481156i
$623$	−17.3205	−	10.0000i	−0.693932	−	0.400642i
$624$		0			0
$625$	−17.2846	+	18.0622i	−0.691384	+	0.722487i
$626$	2.00000	+	3.46410i	0.0799361	+	0.138453i
$627$		0			0
$628$	−19.0526	−	11.0000i	−0.760280	−	0.438948i
$629$	4.00000			0.159490
$630$		0			0
$631$	32.0000			1.27390			0.636950	−	0.770905i	$-0.280196\pi$
$631$	32.0000			1.27390			0.636950	+	0.770905i	$0.280196\pi$
$632$		0			0
$633$		0			0
$634$	−1.00000	−	1.73205i	−0.0397151	−	0.0687885i
$635$	−2.46410	+	3.73205i	−0.0977849	+	0.148102i
$636$		0			0
$637$	−15.5885	−	9.00000i	−0.617637	−	0.356593i
$638$		0			0
$639$		0			0
$640$	1.00000	+	2.00000i	0.0395285	+	0.0790569i
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	−0.845601	−	0.533816i	$-0.820758\pi$
$641$	1.00000	−	1.73205i	0.0394976	−	0.0684119i	0.885098	+	0.465404i	$0.154091\pi$
$642$		0			0
$643$	−20.7846	+	12.0000i	−0.819665	+	0.473234i	−0.850301	−	0.526297i	$-0.823580\pi$
$643$	−20.7846	+	12.0000i	−0.819665	+	0.473234i	0.0306359	+	0.999531i	$0.490247\pi$
$644$	4.00000	+	6.92820i	0.157622	+	0.273009i
$645$		0			0
$646$		0			0
$647$		−	48.0000i		−	1.88707i	−0.331266	−	0.943537i	$-0.607476\pi$
$647$		−	48.0000i		−	1.88707i	0.331266	−	0.943537i	$-0.392524\pi$
$648$		0			0
$649$	−20.0000			−0.785069
$650$	11.7846	+	27.5885i	0.462230	+	1.08211i
$651$		0			0
$652$	−13.8564	+	8.00000i	−0.542659	+	0.313304i
$653$	−22.5167	+	13.0000i	−0.881145	+	0.508729i	−0.871036	−	0.491220i	$-0.836551\pi$
$653$	−22.5167	+	13.0000i	−0.881145	+	0.508729i	−0.0101092	+	0.999949i	$0.503218\pi$
$654$		0			0
$655$	−2.41154	+	40.1769i	−0.0942268	+	1.56984i
$656$	−2.00000			−0.0780869
$657$		0			0
$658$			16.0000i			0.623745i
$659$	25.0000	−	43.3013i	0.973862	−	1.68678i	0.290220	−	0.956960i	$-0.406271\pi$
$659$	25.0000	−	43.3013i	0.973862	−	1.68678i	0.683641	−	0.729818i	$-0.260395\pi$
$660$		0			0
$661$	−1.00000	−	1.73205i	−0.0388955	−	0.0673690i	0.845922	−	0.533306i	$-0.179051\pi$
$661$	−1.00000	−	1.73205i	−0.0388955	−	0.0673690i	−0.884818	+	0.465937i	$0.845717\pi$
$662$	6.92820	−	4.00000i	0.269272	−	0.155464i
$663$		0			0
$664$	2.00000	−	3.46410i	0.0776151	−	0.134433i
$665$		0			0
$666$		0			0
$667$		0			0
$668$	10.3923	+	6.00000i	0.402090	+	0.232147i
$669$		0			0
$670$	−14.9282	−	9.85641i	−0.576727	−	0.380786i
$671$	2.00000	+	3.46410i	0.0772091	+	0.133730i
$672$		0			0
$673$	−31.1769	−	18.0000i	−1.20178	−	0.693849i	−0.240831	−	0.970567i	$-0.577420\pi$
$673$	−31.1769	−	18.0000i	−1.20178	−	0.693849i	−0.960951	+	0.276718i	$0.910753\pi$
$674$	28.0000			1.07852
$675$		0			0
$676$	23.0000			0.884615
$677$	−1.73205	−	1.00000i	−0.0665681	−	0.0384331i	0.466347	−	0.884602i	$-0.345570\pi$
$677$	−1.73205	−	1.00000i	−0.0665681	−	0.0384331i	−0.532915	+	0.846169i	$0.678903\pi$
$678$		0			0
$679$	−8.00000	−	13.8564i	−0.307012	−	0.531760i
$680$	3.73205	+	2.46410i	0.143118	+	0.0944940i
$681$		0			0
$682$	13.8564	+	8.00000i	0.530589	+	0.306336i
$683$			4.00000i			0.153056i	0.997067	+	0.0765279i	$0.0243834\pi$
$683$			4.00000i			0.153056i	−0.997067	+	0.0765279i	$0.975617\pi$
$684$		0			0
$685$	−18.0000	−	36.0000i	−0.687745	−	1.37549i
$686$	10.0000	−	17.3205i	0.381802	−	0.661300i
$687$		0			0
$688$	−3.46410	+	2.00000i	−0.132068	+	0.0762493i
$689$	−18.0000	−	31.1769i	−0.685745	−	1.18775i
$690$		0			0
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	−0.779857	−	0.625958i	$-0.784708\pi$
$691$	4.00000	−	6.92820i	0.152167	−	0.263561i	0.932024	+	0.362397i	$0.118041\pi$
$692$		−	14.0000i		−	0.532200i
$693$		0			0
$694$	12.0000			0.455514
$695$	−2.67949	+	44.6410i	−0.101639	+	1.69333i
$696$		0			0
$697$	−3.46410	+	2.00000i	−0.131212	+	0.0757554i
$698$	8.66025	−	5.00000i	0.327795	−	0.189253i
$699$		0			0
$700$	−9.19615	+	3.92820i	−0.347582	+	0.148472i
$701$	−32.0000			−1.20862			−0.604312	−	0.796748i	$-0.706552\pi$
$701$	−32.0000			−1.20862			−0.604312	+	0.796748i	$0.706552\pi$
$702$		0			0
$703$		0			0
$704$	−1.00000	+	1.73205i	−0.0376889	+	0.0652791i
$705$		0			0
$706$	−7.00000	−	12.1244i	−0.263448	−	0.456306i
$707$	−13.8564	+	8.00000i	−0.521124	+	0.300871i
$708$		0			0
$709$	15.0000	−	25.9808i	0.563337	−	0.975728i	−0.433865	−	0.900978i	$-0.642851\pi$
$709$	15.0000	−	25.9808i	0.563337	−	0.975728i	0.997202	−	0.0747503i	$-0.0238160\pi$
$710$	12.0000	+	24.0000i	0.450352	+	0.900704i
$711$		0			0
$712$		−	10.0000i		−	0.374766i
$713$	27.7128	+	16.0000i	1.03785	+	0.599205i
$714$		0			0
$715$	−14.7846	+	22.3923i	−0.552913	+	0.837425i
$716$	5.00000	+	8.66025i	0.186859	+	0.323649i
$717$		0			0
$718$		0			0
$719$	−40.0000			−1.49175			−0.745874	−	0.666087i	$-0.767968\pi$
$719$	−40.0000			−1.49175			−0.745874	+	0.666087i	$0.767968\pi$
$720$		0			0
$721$	−28.0000			−1.04277
$722$	−16.4545	−	9.50000i	−0.612372	−	0.353553i
$723$		0			0
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$		0			0
$726$		0			0
$727$	−15.5885	−	9.00000i	−0.578144	−	0.333792i	0.182252	−	0.983252i	$-0.441661\pi$
$727$	−15.5885	−	9.00000i	−0.578144	−	0.333792i	−0.760395	+	0.649460i	$0.774995\pi$
$728$			12.0000i			0.444750i
$729$		0			0
$730$	−8.00000	+	4.00000i	−0.296093	+	0.148047i
$731$	−4.00000	+	6.92820i	−0.147945	+	0.256249i
$732$		0			0
$733$	−12.1244	+	7.00000i	−0.447823	+	0.258551i	−0.706910	−	0.707303i	$-0.749912\pi$
$733$	−12.1244	+	7.00000i	−0.447823	+	0.258551i	0.259087	+	0.965854i	$0.416578\pi$
$734$	1.00000	+	1.73205i	0.0369107	+	0.0639312i
$735$		0			0
$736$	−2.00000	+	3.46410i	−0.0737210	+	0.127688i
$737$		−	16.0000i		−	0.589368i
$738$		0			0
$739$	−40.0000			−1.47142			−0.735712	−	0.677295i	$-0.763152\pi$
$739$	−40.0000			−1.47142			−0.735712	+	0.677295i	$0.763152\pi$
$740$	−4.46410	−	0.267949i	−0.164104	−	0.00985001i
$741$		0			0
$742$	10.3923	−	6.00000i	0.381514	−	0.220267i
$743$	20.7846	−	12.0000i	0.762513	−	0.440237i	−0.0676840	−	0.997707i	$-0.521561\pi$
$743$	20.7846	−	12.0000i	0.762513	−	0.440237i	0.830197	+	0.557470i	$0.188228\pi$
$744$		0			0
$745$	2.67949	−	44.6410i	0.0981690	−	1.63552i
$746$	6.00000			0.219676
$747$		0			0
$748$			4.00000i			0.146254i
$749$	−12.0000	+	20.7846i	−0.438470	+	0.759453i
$750$		0			0
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	−0.995018	−	0.0996961i	$-0.968213\pi$
$751$	−16.0000	−	27.7128i	−0.583848	−	1.01125i	0.411170	−	0.911559i	$-0.365120\pi$
$752$	−6.92820	+	4.00000i	−0.252646	+	0.145865i
$753$		0			0
$754$		0			0
$755$	−16.0000	+	8.00000i	−0.582300	+	0.291150i
$756$		0			0
$757$		−	2.00000i		−	0.0726912i	−0.999339	−	0.0363456i	$-0.988428\pi$
$757$		−	2.00000i		−	0.0726912i	0.999339	−	0.0363456i	$-0.0115717\pi$
$758$	−17.3205	−	10.0000i	−0.629109	−	0.363216i
$759$		0			0
$760$		0			0
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	0.655515	−	0.755182i	$-0.272452\pi$
$761$	−9.00000	−	15.5885i	−0.326250	−	0.565081i	−0.981764	+	0.190101i	$0.939118\pi$
$762$		0			0
$763$	−17.3205	−	10.0000i	−0.627044	−	0.362024i
$764$	12.0000			0.434145
$765$		0			0
$766$	−16.0000			−0.578103
$767$	−51.9615	−	30.0000i	−1.87622	−	1.08324i
$768$		0			0
$769$	−15.0000	−	25.9808i	−0.540914	−	0.936890i	−0.998852	−	0.0479061i	$-0.984745\pi$
$769$	−15.0000	−	25.9808i	−0.540914	−	0.936890i	0.457938	−	0.888984i	$-0.348588\pi$
$770$	−7.46410	−	4.92820i	−0.268988	−	0.177600i
$771$		0			0
$772$	−3.46410	−	2.00000i	−0.124676	−	0.0719816i
$773$			54.0000i			1.94225i	0.238581	+	0.971123i	$0.423318\pi$
$773$			54.0000i			1.94225i	−0.238581	+	0.971123i	$0.576682\pi$
$774$		0			0
$775$	−24.0000	+	32.0000i	−0.862105	+	1.14947i
$776$	4.00000	−	6.92820i	0.143592	−	0.248708i
$777$		0			0
$778$	−17.3205	+	10.0000i	−0.620970	+	0.358517i
$779$		0			0
$780$		0			0
$781$	−12.0000	+	20.7846i	−0.429394	+	0.743732i
$782$			8.00000i			0.286079i
$783$		0			0
$784$	3.00000			0.107143
$785$	49.1051	+	2.94744i	1.75264	+	0.105199i
$786$		0			0
$787$	−27.7128	+	16.0000i	−0.987855	+	0.570338i	−0.904632	−	0.426193i	$-0.859855\pi$
$787$	−27.7128	+	16.0000i	−0.987855	+	0.570338i	−0.0832226	+	0.996531i	$0.526521\pi$
$788$	−19.0526	+	11.0000i	−0.678719	+	0.391859i
$789$		0			0
$790$		0			0
$791$	−12.0000			−0.426671
$792$		0			0
$793$			12.0000i			0.426132i
$794$	1.00000	−	1.73205i	0.0354887	−	0.0614682i
$795$		0			0
$796$		0			0
$797$	1.73205	−	1.00000i	0.0613524	−	0.0354218i	−0.469010	−	0.883193i	$-0.655389\pi$
$797$	1.73205	−	1.00000i	0.0613524	−	0.0354218i	0.530362	+	0.847771i	$0.322056\pi$
$798$		0			0
$799$	−8.00000	+	13.8564i	−0.283020	+	0.490204i
$800$	−4.00000	−	3.00000i	−0.141421	−	0.106066i
$801$		0			0
$802$			22.0000i			0.776847i
$803$	−6.92820	−	4.00000i	−0.244491	−	0.141157i
$804$		0			0
$805$	−14.9282	−	9.85641i	−0.526150	−	0.347393i
$806$	24.0000	+	41.5692i	0.845364	+	1.46421i
$807$		0			0
$808$	−6.92820	−	4.00000i	−0.243733	−	0.140720i
$809$	−30.0000			−1.05474			−0.527372	−	0.849635i	$-0.676823\pi$
$809$	−30.0000			−1.05474			−0.527372	+	0.849635i	$0.676823\pi$
$810$		0			0
$811$	52.0000			1.82597			0.912983	−	0.407997i	$-0.133772\pi$
$811$	52.0000			1.82597			0.912983	+	0.407997i	$0.133772\pi$
$812$		0			0
$813$		0			0
$814$	−2.00000	−	3.46410i	−0.0701000	−	0.121417i
$815$	19.7128	−	29.8564i	0.690510	−	1.04582i
$816$		0			0
$817$		0			0
$818$		−	10.0000i		−	0.349642i
$819$		0			0
$820$	4.00000	−	2.00000i	0.139686	−	0.0698430i
$821$	−4.00000	+	6.92820i	−0.139601	+	0.241796i	−0.927346	−	0.374206i	$-0.877915\pi$
$821$	−4.00000	+	6.92820i	−0.139601	+	0.241796i	0.787745	+	0.616002i	$0.211249\pi$
$822$		0			0
$823$	5.19615	−	3.00000i	0.181126	−	0.104573i	−0.406695	−	0.913564i	$-0.633319\pi$
$823$	5.19615	−	3.00000i	0.181126	−	0.104573i	0.587822	+	0.808990i	$0.299986\pi$
$824$	−7.00000	−	12.1244i	−0.243857	−	0.422372i
$825$		0			0
$826$	10.0000	−	17.3205i	0.347945	−	0.602658i
$827$		−	28.0000i		−	0.973655i	−0.873498	−	0.486828i	$-0.838154\pi$
$827$		−	28.0000i		−	0.973655i	0.873498	−	0.486828i	$-0.161846\pi$
$828$		0			0
$829$	30.0000			1.04194			0.520972	−	0.853574i	$-0.325570\pi$
$829$	30.0000			1.04194			0.520972	+	0.853574i	$0.325570\pi$
$830$	−0.535898	+	8.92820i	−0.0186013	+	0.309902i
$831$		0			0
$832$	−5.19615	+	3.00000i	−0.180144	+	0.104006i
$833$	5.19615	−	3.00000i	0.180036	−	0.103944i
$834$		0			0
$835$	−26.7846	−	1.60770i	−0.926920	−	0.0556366i
$836$		0			0
$837$		0			0
$838$			10.0000i			0.345444i
$839$	−20.0000	+	34.6410i	−0.690477	+	1.19594i	0.281205	+	0.959648i	$0.409266\pi$
$839$	−20.0000	+	34.6410i	−0.690477	+	1.19594i	−0.971682	+	0.236293i	$0.924067\pi$
$840$		0			0
$841$	14.5000	+	25.1147i	0.500000	+	0.866025i
$842$	−19.0526	+	11.0000i	−0.656595	+	0.379085i
$843$		0			0
$844$	6.00000	−	10.3923i	0.206529	−	0.357718i
$845$	−46.0000	+	23.0000i	−1.58245	+	0.791224i
$846$		0			0
$847$			14.0000i			0.481046i
$848$	5.19615	+	3.00000i	0.178437	+	0.103020i
$849$		0			0
$850$	−9.92820	−	1.19615i	−0.340535	−	0.0410277i
$851$	−4.00000	−	6.92820i	−0.137118	−	0.237496i
$852$		0			0
$853$	12.1244	+	7.00000i	0.415130	+	0.239675i	0.692992	−	0.720946i	$-0.256292\pi$
$853$	12.1244	+	7.00000i	0.415130	+	0.239675i	−0.277862	+	0.960621i	$0.589626\pi$
$854$	−4.00000			−0.136877
$855$		0			0
$856$	−12.0000			−0.410152
$857$	−36.3731	−	21.0000i	−1.24248	−	0.717346i	−0.272882	−	0.962048i	$-0.587977\pi$
$857$	−36.3731	−	21.0000i	−1.24248	−	0.717346i	−0.969599	+	0.244701i	$0.921310\pi$
$858$		0			0
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	0.984655	−	0.174512i	$-0.0558348\pi$
$859$	10.0000	+	17.3205i	0.341196	+	0.590968i	−0.643459	+	0.765480i	$0.722501\pi$
$860$	4.92820	−	7.46410i	0.168050	−	0.254524i
$861$		0			0
$862$	−27.7128	−	16.0000i	−0.943902	−	0.544962i
$863$		−	36.0000i		−	1.22545i	−0.790295	−	0.612727i	$-0.790072\pi$
$863$		−	36.0000i		−	1.22545i	0.790295	−	0.612727i	$-0.209928\pi$
$864$		0			0
$865$	14.0000	+	28.0000i	0.476014	+	0.952029i
$866$	2.00000	−	3.46410i	0.0679628	−	0.117715i
$867$		0			0
$868$	−13.8564	+	8.00000i	−0.470317	+	0.271538i
$869$		0			0
$870$		0			0
$871$	24.0000	−	41.5692i	0.813209	−	1.40852i
$872$		−	10.0000i		−	0.338643i
$873$		0			0
$874$		0			0
$875$	14.4641	−	17.0526i	0.488976	−	0.576482i
$876$		0			0
$877$	−19.0526	+	11.0000i	−0.643359	+	0.371444i	−0.785907	−	0.618344i	$-0.787804\pi$
$877$	−19.0526	+	11.0000i	−0.643359	+	0.371444i	0.142548	+	0.989788i	$0.454470\pi$
$878$		0			0
$879$		0			0
$880$	0.267949	−	4.46410i	0.00903257	−	0.150485i
$881$	18.0000			0.606435			0.303218	−	0.952921i	$-0.401939\pi$
$881$	18.0000			0.606435			0.303218	+	0.952921i	$0.401939\pi$
$882$		0			0
$883$		−	24.0000i		−	0.807664i	−0.914833	−	0.403832i	$-0.867678\pi$
$883$		−	24.0000i		−	0.807664i	0.914833	−	0.403832i	$-0.132322\pi$
$884$	−6.00000	+	10.3923i	−0.201802	+	0.349531i
$885$		0			0
$886$	18.0000	+	31.1769i	0.604722	+	1.04741i
$887$	10.3923	−	6.00000i	0.348939	−	0.201460i	−0.315279	−	0.948999i	$-0.602098\pi$
$887$	10.3923	−	6.00000i	0.348939	−	0.201460i	0.664218	+	0.747539i	$0.268765\pi$
$888$		0			0
$889$	2.00000	−	3.46410i	0.0670778	−	0.116182i
$890$	10.0000	+	20.0000i	0.335201	+	0.670402i
$891$		0			0
$892$		−	26.0000i		−	0.870544i
$893$		0			0
$894$		0			0
$895$	−18.6603	−	12.3205i	−0.623744	−	0.411829i
$896$	−1.00000	−	1.73205i	−0.0334077	−	0.0578638i
$897$		0			0
$898$	25.9808	+	15.0000i	0.866989	+	0.500556i
$899$		0			0
$900$		0			0
$901$	12.0000			0.399778
$902$	3.46410	+	2.00000i	0.115342	+	0.0665927i
$903$		0			0
$904$	−3.00000	−	5.19615i	−0.0997785	−	0.172821i
$905$	−3.73205	−	2.46410i	−0.124058	−	0.0819095i
$906$		0			0
$907$	10.3923	+	6.00000i	0.345071	+	0.199227i	0.662512	−	0.749051i	$-0.269490\pi$
$907$	10.3923	+	6.00000i	0.345071	+	0.199227i	−0.317441	+	0.948278i	$0.602824\pi$
$908$			28.0000i			0.929213i
$909$		0			0
$910$	−12.0000	−	24.0000i	−0.397796	−	0.795592i
$911$	−24.0000	+	41.5692i	−0.795155	+	1.37725i	0.127585	+	0.991828i	$0.459277\pi$
$911$	−24.0000	+	41.5692i	−0.795155	+	1.37725i	−0.922740	+	0.385422i	$0.874056\pi$
$912$		0			0
$913$	−6.92820	+	4.00000i	−0.229290	+	0.132381i
$914$	16.0000	+	27.7128i	0.529233	+	0.916658i
$915$		0			0
$916$	5.00000	−	8.66025i	0.165205	−	0.286143i
$917$		−	36.0000i		−	1.18882i
$918$		0			0
$919$		0			0			−	1.00000i	$-0.5\pi$
$919$		0			0				1.00000i	$0.5\pi$
$920$	0.535898	−	8.92820i	0.0176680	−	0.294354i
$921$		0			0
$922$	10.3923	−	6.00000i	0.342252	−	0.197599i
$923$	−62.3538	+	36.0000i	−2.05240	+	1.18495i
$924$		0			0
$925$	9.19615	−	3.92820i	0.302368	−	0.129159i
$926$	6.00000			0.197172
$927$		0			0
$928$		0			0
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	−0.999959	−	0.00905914i	$-0.997116\pi$
$929$	−15.0000	+	25.9808i	−0.492134	+	0.852401i	0.507825	+	0.861460i	$0.330450\pi$
$930$		0			0
$931$		0			0
$932$	−12.1244	+	7.00000i	−0.397146	+	0.229293i
$933$		0			0
$934$	−6.00000	+	10.3923i	−0.196326	+	0.340047i
$935$	−4.00000	−	8.00000i	−0.130814	−	0.261628i
$936$		0			0
$937$			8.00000i			0.261349i	0.991425	+	0.130674i	$0.0417142\pi$
$937$			8.00000i			0.261349i	−0.991425	+	0.130674i	$0.958286\pi$
$938$	13.8564	+	8.00000i	0.452428	+	0.261209i
$939$		0			0
$940$	9.85641	−	14.9282i	0.321481	−	0.486904i
$941$	−14.0000	−	24.2487i	−0.456387	−	0.790485i	0.542380	−	0.840133i	$-0.317523\pi$
$941$	−14.0000	−	24.2487i	−0.456387	−	0.790485i	−0.998767	+	0.0496480i	$0.984190\pi$
$942$		0			0
$943$	6.92820	+	4.00000i	0.225613	+	0.130258i
$944$	10.0000			0.325472
$945$		0			0
$946$	8.00000			0.260102
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	0.321552	−	0.946892i	$-0.395796\pi$
$947$	−10.3923	−	6.00000i	−0.337705	−	0.194974i	−0.659256	+	0.751918i	$0.729129\pi$
$948$		0			0
$949$	−12.0000	−	20.7846i	−0.389536	−	0.674697i
$950$		0			0
$951$		0			0
$952$	−3.46410	−	2.00000i	−0.112272	−	0.0648204i
$953$		−	46.0000i		−	1.49009i	−0.667016	−	0.745043i	$-0.732429\pi$
$953$		−	46.0000i		−	1.49009i	0.667016	−	0.745043i	$-0.267571\pi$
$954$		0			0
$955$	−24.0000	+	12.0000i	−0.776622	+	0.388311i
$956$	10.0000	−	17.3205i	0.323423	−	0.560185i
$957$		0			0
$958$	−17.3205	+	10.0000i	−0.559600	+	0.323085i
$959$	18.0000	+	31.1769i	0.581250	+	1.00676i
$960$		0			0
$961$	−16.5000	+	28.5788i	−0.532258	+	0.921898i
$962$		−	12.0000i		−	0.386896i
$963$		0			0
$964$	−22.0000			−0.708572
$965$	8.92820	+	0.535898i	0.287409	+	0.0172512i
$966$		0			0
$967$	32.9090	−	19.0000i	1.05828	−	0.610999i	0.133325	−	0.991072i	$-0.457435\pi$
$967$	32.9090	−	19.0000i	1.05828	−	0.610999i	0.924956	+	0.380074i	$0.124101\pi$
$968$	−6.06218	+	3.50000i	−0.194846	+	0.112494i
$969$		0			0
$970$	−1.07180	+	17.8564i	−0.0344133	+	0.573335i
$971$	18.0000			0.577647			0.288824	−	0.957382i	$-0.406736\pi$
$971$	18.0000			0.577647			0.288824	+	0.957382i	$0.406736\pi$
$972$		0			0
$973$		−	40.0000i		−	1.28234i
$974$	−9.00000	+	15.5885i	−0.288379	+	0.499486i
$975$		0			0
$976$	−1.00000	−	1.73205i	−0.0320092	−	0.0554416i
$977$	36.3731	−	21.0000i	1.16368	−	0.671850i	0.211495	−	0.977379i	$-0.432167\pi$
$977$	36.3731	−	21.0000i	1.16368	−	0.671850i	0.952183	+	0.305530i	$0.0988335\pi$
$978$		0			0
$979$	−10.0000	+	17.3205i	−0.319601	+	0.553566i
$980$	−6.00000	+	3.00000i	−0.191663	+	0.0958315i
$981$		0			0
$982$		−	18.0000i		−	0.574403i
$983$	13.8564	+	8.00000i	0.441951	+	0.255160i	0.704425	−	0.709779i	$-0.251205\pi$
$983$	13.8564	+	8.00000i	0.441951	+	0.255160i	−0.262474	+	0.964939i	$0.584538\pi$
$984$		0			0
$985$	27.1051	−	41.0526i	0.863641	−	1.30804i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	16.0000			0.508770
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	−6.92820	−	4.00000i	−0.219971	−	0.127000i
$993$		0			0
$994$	−12.0000	−	20.7846i	−0.380617	−	0.659248i
$995$		0			0
$996$		0			0
$997$	−15.5885	−	9.00000i	−0.493691	−	0.285033i	0.232413	−	0.972617i	$-0.425338\pi$
$997$	−15.5885	−	9.00000i	−0.493691	−	0.285033i	−0.726105	+	0.687584i	$0.758671\pi$
$998$		0			0
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.i.b.379.2		4
3.2	odd	2		810.2.i.e.379.1		4
5.4	even	2	inner	810.2.i.b.379.1		4
9.2	odd	6		30.2.c.a.19.2	yes	2
9.4	even	3	inner	810.2.i.b.109.1		4
9.5	odd	6		810.2.i.e.109.2		4
9.7	even	3		90.2.c.a.19.1		2
15.14	odd	2		810.2.i.e.379.2		4
36.7	odd	6		720.2.f.f.289.1		2
36.11	even	6		240.2.f.a.49.2		2
45.2	even	12		150.2.a.a.1.1		1
45.4	even	6	inner	810.2.i.b.109.2		4
45.7	odd	12		450.2.a.f.1.1		1
45.14	odd	6		810.2.i.e.109.1		4
45.29	odd	6		30.2.c.a.19.1	✓	2
45.34	even	6		90.2.c.a.19.2		2
45.38	even	12		150.2.a.c.1.1		1
45.43	odd	12		450.2.a.b.1.1		1
63.2	odd	6		1470.2.n.h.949.2		4
63.11	odd	6		1470.2.n.h.79.1		4
63.20	even	6		1470.2.g.g.589.2		2
63.38	even	6		1470.2.n.a.79.1		4
63.47	even	6		1470.2.n.a.949.2		4
72.11	even	6		960.2.f.i.769.1		2
72.29	odd	6		960.2.f.h.769.2		2
72.43	odd	6		2880.2.f.c.1729.2		2
72.61	even	6		2880.2.f.e.1729.2		2
144.11	even	12		3840.2.d.x.2689.1		2
144.29	odd	12		3840.2.d.y.2689.2		2
144.83	even	12		3840.2.d.j.2689.2		2
144.101	odd	12		3840.2.d.g.2689.1		2
180.7	even	12		3600.2.a.o.1.1		1
180.43	even	12		3600.2.a.bg.1.1		1
180.47	odd	12		1200.2.a.m.1.1		1
180.79	odd	6		720.2.f.f.289.2		2
180.83	odd	12		1200.2.a.g.1.1		1
180.119	even	6		240.2.f.a.49.1		2
315.74	odd	6		1470.2.n.h.79.2		4
315.83	odd	12		7350.2.a.cc.1.1		1
315.164	even	6		1470.2.n.a.79.2		4
315.209	even	6		1470.2.g.g.589.1		2
315.254	odd	6		1470.2.n.h.949.1		4
315.272	odd	12		7350.2.a.bg.1.1		1
315.299	even	6		1470.2.n.a.949.1		4
360.29	odd	6		960.2.f.h.769.1		2
360.83	odd	12		4800.2.a.cj.1.1		1
360.173	even	12		4800.2.a.l.1.1		1
360.227	odd	12		4800.2.a.m.1.1		1
360.259	odd	6		2880.2.f.c.1729.1		2
360.299	even	6		960.2.f.i.769.2		2
360.317	even	12		4800.2.a.cg.1.1		1
360.349	even	6		2880.2.f.e.1729.1		2
720.29	odd	12		3840.2.d.g.2689.2		2
720.299	even	12		3840.2.d.j.2689.1		2
720.389	odd	12		3840.2.d.y.2689.1		2
720.659	even	12		3840.2.d.x.2689.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.2.c.a.19.1	✓	2	45.29	odd	6
30.2.c.a.19.2	yes	2	9.2	odd	6
90.2.c.a.19.1		2	9.7	even	3
90.2.c.a.19.2		2	45.34	even	6
150.2.a.a.1.1		1	45.2	even	12
150.2.a.c.1.1		1	45.38	even	12
240.2.f.a.49.1		2	180.119	even	6
240.2.f.a.49.2		2	36.11	even	6
450.2.a.b.1.1		1	45.43	odd	12
450.2.a.f.1.1		1	45.7	odd	12
720.2.f.f.289.1		2	36.7	odd	6
720.2.f.f.289.2		2	180.79	odd	6
810.2.i.b.109.1		4	9.4	even	3	inner
810.2.i.b.109.2		4	45.4	even	6	inner
810.2.i.b.379.1		4	5.4	even	2	inner
810.2.i.b.379.2		4	1.1	even	1	trivial
810.2.i.e.109.1		4	45.14	odd	6
810.2.i.e.109.2		4	9.5	odd	6
810.2.i.e.379.1		4	3.2	odd	2
810.2.i.e.379.2		4	15.14	odd	2
960.2.f.h.769.1		2	360.29	odd	6
960.2.f.h.769.2		2	72.29	odd	6
960.2.f.i.769.1		2	72.11	even	6
960.2.f.i.769.2		2	360.299	even	6
1200.2.a.g.1.1		1	180.83	odd	12
1200.2.a.m.1.1		1	180.47	odd	12
1470.2.g.g.589.1		2	315.209	even	6
1470.2.g.g.589.2		2	63.20	even	6
1470.2.n.a.79.1		4	63.38	even	6
1470.2.n.a.79.2		4	315.164	even	6
1470.2.n.a.949.1		4	315.299	even	6
1470.2.n.a.949.2		4	63.47	even	6
1470.2.n.h.79.1		4	63.11	odd	6
1470.2.n.h.79.2		4	315.74	odd	6
1470.2.n.h.949.1		4	315.254	odd	6
1470.2.n.h.949.2		4	63.2	odd	6
2880.2.f.c.1729.1		2	360.259	odd	6
2880.2.f.c.1729.2		2	72.43	odd	6
2880.2.f.e.1729.1		2	360.349	even	6
2880.2.f.e.1729.2		2	72.61	even	6
3600.2.a.o.1.1		1	180.7	even	12
3600.2.a.bg.1.1		1	180.43	even	12
3840.2.d.g.2689.1		2	144.101	odd	12
3840.2.d.g.2689.2		2	720.29	odd	12
3840.2.d.j.2689.1		2	720.299	even	12
3840.2.d.j.2689.2		2	144.83	even	12
3840.2.d.x.2689.1		2	144.11	even	12
3840.2.d.x.2689.2		2	720.659	even	12
3840.2.d.y.2689.1		2	720.389	odd	12
3840.2.d.y.2689.2		2	144.29	odd	12
4800.2.a.l.1.1		1	360.173	even	12
4800.2.a.m.1.1		1	360.227	odd	12
4800.2.a.cg.1.1		1	360.317	even	12
4800.2.a.cj.1.1		1	360.83	odd	12
7350.2.a.bg.1.1		1	315.272	odd	12
7350.2.a.cc.1.1		1	315.83	odd	12

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	810.i (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +O(q^{10})\)	\(q+(0.866025 + 0.500000i) q^{2} +(0.500000 + 0.866025i) q^{4} +(-1.86603 - 1.23205i) q^{5} +(1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(-1.00000 - 2.00000i) q^{10} +(1.00000 - 1.73205i) q^{11} +(5.19615 - 3.00000i) q^{13} +(1.00000 + 1.73205i) q^{14} +(-0.500000 + 0.866025i) q^{16} +2.00000i q^{17} +(0.133975 - 2.23205i) q^{20} +(1.73205 - 1.00000i) q^{22} +(3.46410 - 2.00000i) q^{23} +(1.96410 + 4.59808i) q^{25} +6.00000 q^{26} +2.00000i q^{28} +(4.00000 + 6.92820i) q^{31} +(-0.866025 + 0.500000i) q^{32} +(-1.00000 + 1.73205i) q^{34} +(-2.00000 - 4.00000i) q^{35} -2.00000i q^{37} +(1.23205 - 1.86603i) q^{40} +(1.00000 + 1.73205i) q^{41} +(3.46410 + 2.00000i) q^{43} +2.00000 q^{44} +4.00000 q^{46} +(6.92820 + 4.00000i) q^{47} +(-1.50000 - 2.59808i) q^{49} +(-0.598076 + 4.96410i) q^{50} +(5.19615 + 3.00000i) q^{52} -6.00000i q^{53} +(-4.00000 + 2.00000i) q^{55} +(-1.00000 + 1.73205i) q^{56} +(-5.00000 - 8.66025i) q^{59} +(-1.00000 + 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(-13.3923 - 0.803848i) q^{65} +(6.92820 - 4.00000i) q^{67} +(-1.73205 + 1.00000i) q^{68} +(0.267949 - 4.46410i) q^{70} -12.0000 q^{71} -4.00000i q^{73} +(1.00000 - 1.73205i) q^{74} +(3.46410 - 2.00000i) q^{77} +(2.00000 - 1.00000i) q^{80} +2.00000i q^{82} +(-3.46410 - 2.00000i) q^{83} +(2.46410 - 3.73205i) q^{85} +(2.00000 + 3.46410i) q^{86} +(1.73205 + 1.00000i) q^{88} -10.0000 q^{89} +12.0000 q^{91} +(3.46410 + 2.00000i) q^{92} +(4.00000 + 6.92820i) q^{94} +(-6.92820 - 4.00000i) q^{97} -3.00000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 2 q^{4} - 4 q^{5}+O(q^{10}) \) 4 * q + 2 * q^4 - 4 * q^5	\( 4 q + 2 q^{4} - 4 q^{5} - 4 q^{10} + 4 q^{11} + 4 q^{14} - 2 q^{16} + 4 q^{20} - 6 q^{25} + 24 q^{26} + 16 q^{31} - 4 q^{34} - 8 q^{35} - 2 q^{40} + 4 q^{41} + 8 q^{44} + 16 q^{46} - 6 q^{49} + 8 q^{50} - 16 q^{55} - 4 q^{56} - 20 q^{59} - 4 q^{61} - 4 q^{64} - 12 q^{65} + 8 q^{70} - 48 q^{71} + 4 q^{74} + 8 q^{80} - 4 q^{85} + 8 q^{86} - 40 q^{89} + 48 q^{91} + 16 q^{94}+O(q^{100}) \) 4 * q + 2 * q^4 - 4 * q^5 - 4 * q^10 + 4 * q^11 + 4 * q^14 - 2 * q^16 + 4 * q^20 - 6 * q^25 + 24 * q^26 + 16 * q^31 - 4 * q^34 - 8 * q^35 - 2 * q^40 + 4 * q^41 + 8 * q^44 + 16 * q^46 - 6 * q^49 + 8 * q^50 - 16 * q^55 - 4 * q^56 - 20 * q^59 - 4 * q^61 - 4 * q^64 - 12 * q^65 + 8 * q^70 - 48 * q^71 + 4 * q^74 + 8 * q^80 - 4 * q^85 + 8 * q^86 - 40 * q^89 + 48 * q^91 + 16 * q^94

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