LMFDB - Embedded newform 810.2.i.b.109.1

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			109.1
Root			$-0.866025 + 0.500000i$ of defining polynomial
Character	$\chi$	$=$	810.109
Dual form			810.2.i.b.379.1

$q$ -expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.133975 + 2.23205i) q^{5} +(-1.73205 + 1.00000i) q^{7} +1.00000i q^{8} +(-1.00000 - 2.00000i) q^{10} +(1.00000 + 1.73205i) q^{11} +(-5.19615 - 3.00000i) q^{13} +(1.00000 - 1.73205i) q^{14} +(-0.500000 - 0.866025i) q^{16} +2.00000i q^{17} +(1.86603 + 1.23205i) q^{20} +(-1.73205 - 1.00000i) q^{22} +(-3.46410 - 2.00000i) q^{23} +(-4.96410 - 0.598076i) q^{25} +6.00000 q^{26} +2.00000i q^{28} +(4.00000 - 6.92820i) q^{31} +(0.866025 + 0.500000i) q^{32} +(-1.00000 - 1.73205i) q^{34} +(-2.00000 - 4.00000i) q^{35} -2.00000i q^{37} +(-2.23205 - 0.133975i) q^{40} +(1.00000 - 1.73205i) q^{41} +(-3.46410 + 2.00000i) q^{43} +2.00000 q^{44} +4.00000 q^{46} +(-6.92820 + 4.00000i) q^{47} +(-1.50000 + 2.59808i) q^{49} +(4.59808 - 1.96410i) q^{50} +(-5.19615 + 3.00000i) q^{52} -6.00000i q^{53} +(-4.00000 + 2.00000i) q^{55} +(-1.00000 - 1.73205i) q^{56} +(-5.00000 + 8.66025i) q^{59} +(-1.00000 - 1.73205i) q^{61} +8.00000i q^{62} -1.00000 q^{64} +(7.39230 - 11.1962i) q^{65} +(-6.92820 - 4.00000i) q^{67} +(1.73205 + 1.00000i) q^{68} +(3.73205 + 2.46410i) q^{70} -12.0000 q^{71} -4.00000i q^{73} +(1.00000 + 1.73205i) q^{74} +(-3.46410 - 2.00000i) q^{77} +(2.00000 - 1.00000i) q^{80} +2.00000i q^{82} +(3.46410 - 2.00000i) q^{83} +(-4.46410 - 0.267949i) q^{85} +(2.00000 - 3.46410i) q^{86} +(-1.73205 + 1.00000i) q^{88} -10.0000 q^{89} +12.0000 q^{91} +(-3.46410 + 2.00000i) q^{92} +(4.00000 - 6.92820i) q^{94} +(6.92820 - 4.00000i) q^{97} -3.00000i q^{98} +O(q^{100})$
$\operatorname{Tr}(f)(q)$	$=$	$4 q + 2 q^{4} - 4 q^{5} - 4 q^{10} + 4 q^{11} + 4 q^{14} - 2 q^{16} + 4 q^{20} - 6 q^{25} + 24 q^{26} + 16 q^{31} - 4 q^{34} - 8 q^{35} - 2 q^{40} + 4 q^{41} + 8 q^{44} + 16 q^{46} - 6 q^{49} + 8 q^{50}+ \cdots + 16 q^{94}+O(q^{100})$ 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

Character values

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

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

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
$5$	−0.133975	+	2.23205i	−0.0599153	+	0.998203i
$5$	−0.133975	+	2.23205i	−0.0599153	+	0.998203i
$6$		0			0
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	−0.790237	−	0.612801i	$-0.790043\pi$
$7$	−1.73205	+	1.00000i	−0.654654	+	0.377964i	0.135583	+	0.990766i	$0.456709\pi$
$8$			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	0.976478	−	0.215615i	$-0.0691756\pi$
$11$	1.00000	+	1.73205i	0.301511	+	0.522233i	−0.674967	+	0.737848i	$0.735842\pi$
$12$		0			0
$13$	−5.19615	−	3.00000i	−1.44115	−	0.832050i	−0.443227	−	0.896410i	$-0.646166\pi$
$13$	−5.19615	−	3.00000i	−1.44115	−	0.832050i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$	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	$0.5\pi$
$20$	1.86603	+	1.23205i	0.417256	+	0.275495i
$21$		0			0
$22$	−1.73205	−	1.00000i	−0.369274	−	0.213201i
$23$	−3.46410	−	2.00000i	−0.722315	−	0.417029i	0.0932891	−	0.995639i	$-0.470262\pi$
$23$	−3.46410	−	2.00000i	−0.722315	−	0.417029i	−0.815604	+	0.578610i	$0.803595\pi$
$24$		0			0
$25$	−4.96410	−	0.598076i	−0.992820	−	0.119615i
$26$	6.00000			1.17670
$27$		0			0
$28$			2.00000i			0.377964i
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	−0.243204	−	0.969975i	$-0.578198\pi$
$31$	4.00000	−	6.92820i	0.718421	−	1.24434i	0.961625	−	0.274367i	$-0.0884683\pi$
$32$	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
$40$	−2.23205	−	0.133975i	−0.352918	−	0.0211832i
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	−0.777312	−	0.629115i	$-0.783417\pi$
$41$	1.00000	−	1.73205i	0.156174	−	0.270501i	0.933486	+	0.358614i	$0.116751\pi$
$42$		0			0
$43$	−3.46410	+	2.00000i	−0.528271	+	0.304997i	−0.740312	−	0.672264i	$-0.765322\pi$
$43$	−3.46410	+	2.00000i	−0.528271	+	0.304997i	0.212041	+	0.977261i	$0.431989\pi$
$44$	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	$-0.864968\pi$
$47$	−6.92820	+	4.00000i	−1.01058	+	0.583460i	−0.0992202	+	0.995066i	$0.531635\pi$
$48$		0			0
$49$	−1.50000	+	2.59808i	−0.214286	+	0.371154i
$50$	4.59808	−	1.96410i	0.650266	−	0.277766i
$51$		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	0.331949	+	0.943297i	$0.392294\pi$
$59$	−5.00000	+	8.66025i	−0.650945	+	1.12747i	−0.982894	+	0.184172i	$0.941040\pi$
$60$		0			0
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	0.794879	−	0.606768i	$-0.207534\pi$
$61$	−1.00000	−	1.73205i	−0.128037	−	0.221766i	−0.922916	+	0.385002i	$0.874201\pi$
$62$			8.00000i			1.01600i
$63$		0			0
$64$	−1.00000			−0.125000
$65$	7.39230	−	11.1962i	0.916903	−	1.38871i
$66$		0			0
$67$	−6.92820	−	4.00000i	−0.846415	−	0.488678i	0.0130248	−	0.999915i	$-0.495854\pi$
$67$	−6.92820	−	4.00000i	−0.846415	−	0.488678i	−0.859440	+	0.511237i	$0.829187\pi$
$68$	1.73205	+	1.00000i	0.210042	+	0.121268i
$69$		0			0
$70$	3.73205	+	2.46410i	0.446065	+	0.294516i
$71$	−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	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	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	$-0.596215\pi$
$83$	3.46410	−	2.00000i	0.380235	−	0.219529i	0.677920	+	0.735135i	$0.262881\pi$
$84$		0			0
$85$	−4.46410	−	0.267949i	−0.484200	−	0.0290632i
$86$	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	$-0.533542\pi$
$97$	6.92820	−	4.00000i	0.703452	−	0.406138i	0.808632	+	0.588315i	$0.200208\pi$
$98$		−	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	0.595466	−	0.803380i	$-0.296967\pi$
$101$	−4.00000	−	6.92820i	−0.398015	−	0.689382i	−0.993481	+	0.113998i	$0.963634\pi$
$102$		0			0
$103$	12.1244	+	7.00000i	1.19465	+	0.689730i	0.959357	−	0.282194i	$-0.0910623\pi$
$103$	12.1244	+	7.00000i	1.19465	+	0.689730i	0.235291	+	0.971925i	$0.424396\pi$
$104$	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	$0.658969\pi$
$110$	2.46410	−	3.73205i	0.234943	−	0.355837i
$111$		0			0
$112$	1.73205	+	1.00000i	0.163663	+	0.0944911i
$113$	5.19615	+	3.00000i	0.488813	+	0.282216i	0.724082	−	0.689714i	$-0.242264\pi$
$113$	5.19615	+	3.00000i	0.488813	+	0.282216i	−0.235269	+	0.971930i	$0.575597\pi$
$114$		0			0
$115$	4.92820	−	7.46410i	0.459557	−	0.696031i
$116$		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
$130$	−0.803848	+	13.3923i	−0.0705021	+	1.17458i
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	0.141865	+	0.989886i	$0.454690\pi$
$131$	−9.00000	+	15.5885i	−0.786334	+	1.36197i	−0.928199	+	0.372084i	$0.878643\pi$
$132$		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	$-0.945873\pi$
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.346235	+	0.938148i	$0.612540\pi$
$138$		0			0
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	0.0346338	+	0.999400i	$0.488974\pi$
$139$	−10.0000	+	17.3205i	−0.848189	+	1.46911i	−0.882823	+	0.469706i	$0.844360\pi$
$140$	−4.46410	−	0.267949i	−0.377285	−	0.0226458i
$141$		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	−0.0870170	−	0.996207i	$-0.527733\pi$
$149$	10.0000	−	17.3205i	0.819232	−	1.41895i	0.906249	−	0.422744i	$-0.138933\pi$
$150$		0			0
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	0.981617	−	0.190864i	$-0.0611289\pi$
$151$	4.00000	+	6.92820i	0.325515	+	0.563809i	−0.656101	+	0.754673i	$0.727796\pi$
$152$		0			0
$153$		0			0
$154$	4.00000			0.322329
$155$	14.9282	+	9.85641i	1.19906	+	0.791686i
$156$		0			0
$157$	19.0526	+	11.0000i	1.52056	+	0.877896i	0.999706	+	0.0242497i	$0.00771967\pi$
$157$	19.0526	+	11.0000i	1.52056	+	0.877896i	0.520854	+	0.853646i	$0.325614\pi$
$158$		0			0
$159$		0			0
$160$	−1.23205	+	1.86603i	−0.0974022	+	0.147522i
$161$	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	$-0.487025\pi$
$167$	−10.3923	−	6.00000i	−0.804181	−	0.464294i	−0.844931	+	0.534875i	$0.820359\pi$
$168$		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	$-0.488032\pi$
$173$	12.1244	−	7.00000i	0.921798	−	0.532200i	0.884208	+	0.467093i	$0.154699\pi$
$174$		0			0
$175$	9.19615	−	3.92820i	0.695164	−	0.296944i
$176$	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
$185$	4.46410	+	0.267949i	0.328207	+	0.0197000i
$186$		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	0.997225	−	0.0744412i	$-0.0237173\pi$
$191$	6.00000	+	10.3923i	0.434145	+	0.751961i	−0.563081	+	0.826402i	$0.690384\pi$
$192$		0			0
$193$	3.46410	+	2.00000i	0.249351	+	0.143963i	0.619467	−	0.785022i	$-0.287349\pi$
$193$	3.46410	+	2.00000i	0.249351	+	0.143963i	−0.370116	+	0.928986i	$0.620682\pi$
$194$	−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	$0.5\pi$
$200$	0.598076	−	4.96410i	0.0422904	−	0.351015i
$201$		0			0
$202$	6.92820	+	4.00000i	0.487467	+	0.281439i
$203$		0			0
$204$		0			0
$205$	3.73205	+	2.46410i	0.260658	+	0.172100i
$206$	−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	−0.995222	−	0.0976347i	$-0.968872\pi$
$211$	−6.00000	+	10.3923i	−0.413057	+	0.715436i	0.582165	+	0.813070i	$0.302206\pi$
$212$	−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
$220$	−0.267949	+	4.46410i	−0.0180651	+	0.300970i
$221$	6.00000	−	10.3923i	0.403604	−	0.699062i
$222$		0			0
$223$	22.5167	−	13.0000i	1.50783	−	0.870544i	0.507869	−	0.861435i	$-0.330434\pi$
$223$	22.5167	−	13.0000i	1.50783	−	0.870544i	0.999959	−	0.00910984i	$-0.00289979\pi$
$224$	−2.00000			−0.133631
$225$		0			0
$226$	−6.00000			−0.399114
$227$	−24.2487	+	14.0000i	−1.60944	+	0.929213i	−0.619949	+	0.784642i	$0.712847\pi$
$227$	−24.2487	+	14.0000i	−1.60944	+	0.929213i	−0.989494	+	0.144571i	$0.953820\pi$
$228$		0			0
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	−0.982592	−	0.185776i	$-0.940520\pi$
$229$	−5.00000	+	8.66025i	−0.330409	+	0.572286i	0.652183	+	0.758062i	$0.273853\pi$
$230$	−0.535898	+	8.92820i	−0.0353361	+	0.588708i
$231$		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	0.337026	+	0.941495i	$0.390579\pi$
$239$	−10.0000	+	17.3205i	−0.646846	+	1.12037i	−0.983872	+	0.178875i	$0.942754\pi$
$240$		0			0
$241$	−11.0000	−	19.0526i	−0.708572	−	1.22728i	−0.965387	−	0.260822i	$-0.916006\pi$
$241$	−11.0000	−	19.0526i	−0.708572	−	1.22728i	0.256814	−	0.966461i	$-0.417327\pi$
$242$			7.00000i			0.449977i
$243$		0			0
$244$	−2.00000			−0.128037
$245$	−5.59808	−	3.69615i	−0.357648	−	0.236139i
$246$		0			0
$247$		0			0
$248$	6.92820	+	4.00000i	0.439941	+	0.254000i
$249$		0			0
$250$	3.76795	+	10.5263i	0.238306	+	0.665740i
$251$	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	$-0.143595\pi$
$257$	15.5885	+	9.00000i	0.972381	+	0.561405i	0.0724199	+	0.997374i	$0.476928\pi$
$258$		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	$-0.627311\pi$
$263$	3.46410	−	2.00000i	0.213606	−	0.123325i	0.602986	+	0.797752i	$0.293977\pi$
$264$		0			0
$265$	13.3923	+	0.803848i	0.822683	+	0.0493800i
$266$		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
$275$	−3.92820	−	9.19615i	−0.236880	−	0.554549i
$276$		0			0
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	−0.551131	−	0.834419i	$-0.685804\pi$
$277$	−1.73205	+	1.00000i	−0.104069	+	0.0600842i	0.447062	+	0.894503i	$0.352470\pi$
$278$		−	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	−0.999069	−	0.0431402i	$-0.986264\pi$
$281$	−9.00000	−	15.5885i	−0.536895	−	0.929929i	0.462174	−	0.886789i	$-0.347070\pi$
$282$		0			0
$283$	−13.8564	−	8.00000i	−0.823678	−	0.475551i	0.0280052	−	0.999608i	$-0.491084\pi$
$283$	−13.8564	−	8.00000i	−0.823678	−	0.475551i	−0.851683	+	0.524057i	$0.824418\pi$
$284$	−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	$-0.277256\pi$
$293$	5.19615	+	3.00000i	0.303562	+	0.175262i	−0.340480	+	0.940252i	$0.610589\pi$
$294$		0			0
$295$	−18.6603	−	12.3205i	−1.08644	−	0.717328i
$296$	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
$310$	−17.8564	−	1.07180i	−1.01418	−	0.0608740i
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	−0.644246	−	0.764818i	$-0.722829\pi$
$311$	6.00000	−	10.3923i	0.340229	−	0.589294i	0.984475	+	0.175525i	$0.0561621\pi$
$312$		0			0
$313$	−3.46410	+	2.00000i	−0.195803	+	0.113047i	−0.594696	−	0.803951i	$-0.702728\pi$
$313$	−3.46410	+	2.00000i	−0.195803	+	0.113047i	0.398894	+	0.916997i	$0.369394\pi$
$314$	−22.0000			−1.24153
$315$		0			0
$316$		0			0
$317$	1.73205	−	1.00000i	0.0972817	−	0.0561656i	−0.450570	−	0.892741i	$-0.648779\pi$
$317$	1.73205	−	1.00000i	0.0972817	−	0.0561656i	0.547852	+	0.836576i	$0.315446\pi$
$318$		0			0
$319$		0			0
$320$	0.133975	−	2.23205i	0.00748941	−	0.124775i
$321$		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	0.954765	−	0.297361i	$-0.0961066\pi$
$331$	4.00000	+	6.92820i	0.219860	+	0.380808i	−0.734905	+	0.678170i	$0.762773\pi$
$332$		−	4.00000i		−	0.219529i
$333$		0			0
$334$	12.0000			0.656611
$335$	9.85641	−	14.9282i	0.538513	−	0.815615i
$336$		0			0
$337$	−24.2487	−	14.0000i	−1.32091	−	0.762629i	−0.337037	−	0.941491i	$-0.609425\pi$
$337$	−24.2487	−	14.0000i	−1.32091	−	0.762629i	−0.983874	+	0.178863i	$0.942758\pi$
$338$	−19.9186	−	11.5000i	−1.08343	−	0.625518i
$339$		0			0
$340$	−2.46410	+	3.73205i	−0.133635	+	0.202399i
$341$	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	$-0.437721\pi$
$347$	−10.3923	−	6.00000i	−0.557888	−	0.322097i	−0.752297	+	0.658824i	$0.771054\pi$
$348$		0			0
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$	−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	$-0.545142\pi$
$353$	12.1244	−	7.00000i	0.645314	−	0.372572i	0.786659	+	0.617388i	$0.211809\pi$
$354$		0			0
$355$	1.60770	−	26.7846i	0.0853276	−	1.42158i
$356$	−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
$365$	8.92820	+	0.535898i	0.467324	+	0.0280502i
$366$		0			0
$367$	−1.73205	+	1.00000i	−0.0904123	+	0.0521996i	−0.544524	−	0.838745i	$-0.683290\pi$
$367$	−1.73205	+	1.00000i	−0.0904123	+	0.0521996i	0.454112	+	0.890945i	$0.349957\pi$
$368$			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	$-0.382979\pi$
$373$	−5.19615	−	3.00000i	−0.269047	−	0.155334i	−0.628454	+	0.777847i	$0.716312\pi$
$374$	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	$-0.199287\pi$
$383$	13.8564	+	8.00000i	0.708029	+	0.408781i	−0.102302	+	0.994753i	$0.532621\pi$
$384$		0			0
$385$	4.92820	−	7.46410i	0.251164	−	0.380406i
$386$	−4.00000			−0.203595
$387$		0			0
$388$		−	8.00000i		−	0.406138i
$389$	−10.0000	−	17.3205i	−0.507020	−	0.878185i	−0.999967	−	0.00812520i	$-0.997414\pi$
$389$	−10.0000	−	17.3205i	−0.507020	−	0.878185i	0.492947	−	0.870059i	$-0.335920\pi$
$390$		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
$400$	1.96410	+	4.59808i	0.0982051	+	0.229904i
$401$	11.0000	−	19.0526i	0.549314	−	0.951439i	−0.449008	−	0.893528i	$-0.648223\pi$
$401$	11.0000	−	19.0526i	0.549314	−	0.951439i	0.998322	−	0.0579116i	$-0.0184442\pi$
$402$		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	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$	−4.46410	−	0.267949i	−0.220466	−	0.0132331i
$411$		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	−0.717659	−	0.696395i	$-0.754786\pi$
$419$	5.00000	−	8.66025i	0.244266	−	0.423081i	0.961925	+	0.273314i	$0.0881197\pi$
$420$		0			0
$421$	−11.0000	−	19.0526i	−0.536107	−	0.928565i	−0.999109	−	0.0422075i	$-0.986561\pi$
$421$	−11.0000	−	19.0526i	−0.536107	−	0.928565i	0.463002	−	0.886357i	$-0.346772\pi$
$422$		−	12.0000i		−	0.584151i
$423$		0			0
$424$	6.00000			0.291386
$425$	1.19615	−	9.92820i	0.0580219	−	0.481589i
$426$		0			0
$427$	3.46410	+	2.00000i	0.167640	+	0.0967868i
$428$	10.3923	+	6.00000i	0.502331	+	0.290021i
$429$		0			0
$430$	7.46410	+	4.92820i	0.359951	+	0.237659i
$431$	−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	$-0.166667\pi$
$439$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$440$	−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	$-0.993236\pi$
$443$	−31.1769	+	18.0000i	−1.48126	+	0.855206i	−0.481486	+	0.876454i	$0.659903\pi$
$444$		0			0
$445$	1.33975	−	22.3205i	0.0635100	−	1.05809i
$446$	−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
$455$	−1.60770	+	26.7846i	−0.0753699	+	1.25568i
$456$		0			0
$457$	−27.7128	+	16.0000i	−1.29635	+	0.748448i	−0.979772	−	0.200118i	$-0.935868\pi$
$457$	−27.7128	+	16.0000i	−1.29635	+	0.748448i	−0.316579	+	0.948566i	$0.602534\pi$
$458$		−	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	0.971248	−	0.238071i	$-0.0765153\pi$
$461$	6.00000	+	10.3923i	0.279448	+	0.484018i	−0.691800	+	0.722089i	$0.743182\pi$
$462$		0			0
$463$	−5.19615	−	3.00000i	−0.241486	−	0.139422i	0.374374	−	0.927278i	$-0.377858\pi$
$463$	−5.19615	−	3.00000i	−0.241486	−	0.139422i	−0.615859	+	0.787856i	$0.711191\pi$
$464$		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
$470$	14.9282	+	9.85641i	0.688587	+	0.454642i
$471$		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	0.541884	−	0.840453i	$-0.317711\pi$
$479$	−10.0000	−	17.3205i	−0.456912	−	0.791394i	−0.998796	+	0.0490589i	$0.984378\pi$
$480$		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
$490$	6.69615	+	0.401924i	0.302501	+	0.0181571i
$491$	−9.00000	+	15.5885i	−0.406164	+	0.703497i	−0.994456	−	0.105151i	$-0.966467\pi$
$491$	−9.00000	+	15.5885i	−0.406164	+	0.703497i	0.588292	+	0.808649i	$0.299801\pi$
$492$		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	$-0.833333\pi$
$499$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$500$	−8.52628	−	7.23205i	−0.381307	−	0.323427i
$501$		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	$-0.833333\pi$
$509$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$510$		0			0
$511$	4.00000	+	6.92820i	0.176950	+	0.306486i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	−18.0000			−0.793946
$515$	−17.2487	+	26.1244i	−0.760069	+	1.15118i
$516$		0			0
$517$	−13.8564	−	8.00000i	−0.609404	−	0.351840i
$518$	−3.46410	−	2.00000i	−0.152204	−	0.0878750i
$519$		0			0
$520$	11.1962	+	7.39230i	0.490984	+	0.324174i
$521$	−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
$535$	−26.7846	−	1.60770i	−1.15800	−	0.0695067i
$536$	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
$545$	1.33975	−	22.3205i	0.0573884	−	0.956106i
$546$		0			0
$547$	24.2487	−	14.0000i	1.03680	−	0.598597i	0.117875	−	0.993028i	$-0.462392\pi$
$547$	24.2487	−	14.0000i	1.03680	−	0.598597i	0.918925	+	0.394432i	$0.129059\pi$
$548$			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
$560$	−2.46410	+	3.73205i	−0.104127	+	0.157708i
$561$		0			0
$562$	15.5885	+	9.00000i	0.657559	+	0.379642i
$563$	−38.1051	−	22.0000i	−1.60594	−	0.927189i	−0.990266	−	0.139188i	$-0.955551\pi$
$563$	−38.1051	−	22.0000i	−1.60594	−	0.927189i	−0.615673	−	0.788002i	$-0.711116\pi$
$564$		0			0
$565$	−7.39230	+	11.1962i	−0.310997	+	0.471026i
$566$	16.0000			0.672530
$567$		0			0
$568$		−	12.0000i		−	0.503509i
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	0.951592	−	0.307364i	$-0.0994469\pi$
$569$	5.00000	+	8.66025i	0.209611	+	0.363057i	−0.741981	+	0.670421i	$0.766114\pi$
$570$		0			0
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	−0.770108	−	0.637913i	$-0.779798\pi$
$571$	4.00000	−	6.92820i	0.167395	−	0.289936i	0.937503	+	0.347977i	$0.113131\pi$
$572$	−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	$-0.587010\pi$
$587$	10.3923	−	6.00000i	0.428936	−	0.247647i	0.698893	+	0.715226i	$0.253676\pi$
$588$		0			0
$589$		0			0
$590$	22.3205	+	1.33975i	0.918921	+	0.0551565i
$591$		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	$-0.833333\pi$
$599$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$600$		0			0
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	0.844909	−	0.534910i	$-0.179654\pi$
$601$	−1.00000	−	1.73205i	−0.0407909	−	0.0706518i	−0.885700	+	0.464258i	$0.846321\pi$
$602$			8.00000i			0.326056i
$603$		0			0
$604$	8.00000			0.325515
$605$	13.0622	+	8.62436i	0.531053	+	0.350630i
$606$		0			0
$607$	19.0526	+	11.0000i	0.773320	+	0.446476i	0.834058	−	0.551678i	$-0.186012\pi$
$607$	19.0526	+	11.0000i	0.773320	+	0.446476i	−0.0607380	+	0.998154i	$0.519345\pi$
$608$		0			0
$609$		0			0
$610$	−2.46410	+	3.73205i	−0.0997686	+	0.151106i
$611$	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	$-0.346151\pi$
$617$	−1.73205	−	1.00000i	−0.0697297	−	0.0402585i	−0.534460	+	0.845194i	$0.679485\pi$
$618$		0			0
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	0.993959	−	0.109749i	$-0.0350048\pi$
$619$	10.0000	+	17.3205i	0.401934	+	0.696170i	−0.592025	+	0.805919i	$0.701671\pi$
$620$	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
$625$	24.2846	+	5.93782i	0.971384	+	0.237513i
$626$	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
$635$	4.46410	+	0.267949i	0.177152	+	0.0106332i
$636$		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	0.885098	−	0.465404i	$-0.154091\pi$
$641$	1.00000	+	1.73205i	0.0394976	+	0.0684119i	−0.845601	+	0.533816i	$0.820758\pi$
$642$		0			0
$643$	20.7846	+	12.0000i	0.819665	+	0.473234i	0.850301	−	0.526297i	$-0.176420\pi$
$643$	20.7846	+	12.0000i	0.819665	+	0.473234i	−0.0306359	+	0.999531i	$0.509753\pi$
$644$	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
$650$	−29.7846	−	3.58846i	−1.16825	−	0.140751i
$651$		0			0
$652$	13.8564	+	8.00000i	0.542659	+	0.313304i
$653$	22.5167	+	13.0000i	0.881145	+	0.508729i	0.871036	−	0.491220i	$-0.163449\pi$
$653$	22.5167	+	13.0000i	0.881145	+	0.508729i	0.0101092	+	0.999949i	$0.496782\pi$
$654$		0			0
$655$	−33.5885	−	22.1769i	−1.31241	−	0.866524i
$656$	−2.00000			−0.0780869
$657$		0			0
$658$			16.0000i			0.623745i
$659$	25.0000	+	43.3013i	0.973862	+	1.68678i	0.683641	+	0.729818i	$0.260395\pi$
$659$	25.0000	+	43.3013i	0.973862	+	1.68678i	0.290220	+	0.956960i	$0.406271\pi$
$660$		0			0
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	−0.884818	−	0.465937i	$-0.845717\pi$
$661$	−1.00000	+	1.73205i	−0.0388955	+	0.0673690i	0.845922	+	0.533306i	$0.179051\pi$
$662$	−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
$670$	−1.07180	+	17.8564i	−0.0414071	+	0.689853i
$671$	2.00000	−	3.46410i	0.0772091	−	0.133730i
$672$		0			0
$673$	31.1769	−	18.0000i	1.20178	−	0.693849i	0.240831	−	0.970567i	$-0.422580\pi$
$673$	31.1769	−	18.0000i	1.20178	−	0.693849i	0.960951	+	0.276718i	$0.0892468\pi$
$674$	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	$-0.654430\pi$
$677$	1.73205	−	1.00000i	0.0665681	−	0.0384331i	0.532915	+	0.846169i	$0.321097\pi$
$678$		0			0
$679$	−8.00000	+	13.8564i	−0.307012	+	0.531760i
$680$	0.267949	−	4.46410i	0.0102754	−	0.171190i
$681$		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	0.932024	−	0.362397i	$-0.118041\pi$
$691$	4.00000	+	6.92820i	0.152167	+	0.263561i	−0.779857	+	0.625958i	$0.784708\pi$
$692$		−	14.0000i		−	0.532200i
$693$		0			0
$694$	12.0000			0.455514
$695$	−37.3205	−	24.6410i	−1.41565	−	0.934687i
$696$		0			0
$697$	3.46410	+	2.00000i	0.131212	+	0.0757554i
$698$	−8.66025	−	5.00000i	−0.327795	−	0.189253i
$699$		0			0
$700$	1.19615	−	9.92820i	0.0452103	−	0.375251i
$701$	−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	0.997202	+	0.0747503i	$0.0238160\pi$
$709$	15.0000	+	25.9808i	0.563337	+	0.975728i	−0.433865	+	0.900978i	$0.642851\pi$
$710$	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
$715$	26.7846	+	1.60770i	1.00169	+	0.0601244i
$716$	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	$-0.558339\pi$
$727$	15.5885	−	9.00000i	0.578144	−	0.333792i	0.760395	+	0.649460i	$0.225005\pi$
$728$			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	$-0.250088\pi$
$733$	12.1244	+	7.00000i	0.447823	+	0.258551i	−0.259087	+	0.965854i	$0.583422\pi$
$734$	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	$0.763152\pi$
$740$	2.46410	−	3.73205i	0.0905822	−	0.137193i
$741$		0			0
$742$	−10.3923	−	6.00000i	−0.381514	−	0.220267i
$743$	−20.7846	−	12.0000i	−0.762513	−	0.440237i	0.0676840	−	0.997707i	$-0.478439\pi$
$743$	−20.7846	−	12.0000i	−0.762513	−	0.440237i	−0.830197	+	0.557470i	$0.811772\pi$
$744$		0			0
$745$	37.3205	+	24.6410i	1.36732	+	0.902777i
$746$	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	0.411170	+	0.911559i	$0.365120\pi$
$751$	−16.0000	+	27.7128i	−0.583848	+	1.01125i	−0.995018	+	0.0996961i	$0.968213\pi$
$752$	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	−0.981764	−	0.190101i	$-0.939118\pi$
$761$	−9.00000	+	15.5885i	−0.326250	+	0.565081i	0.655515	+	0.755182i	$0.272452\pi$
$762$		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	0.457938	+	0.888984i	$0.348588\pi$
$769$	−15.0000	+	25.9808i	−0.540914	+	0.936890i	−0.998852	+	0.0479061i	$0.984745\pi$
$770$	−0.535898	+	8.92820i	−0.0193124	+	0.321750i
$771$		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
$785$	−27.1051	+	41.0526i	−0.967423	+	1.46523i
$786$		0			0
$787$	27.7128	+	16.0000i	0.987855	+	0.570338i	0.904632	−	0.426193i	$-0.140145\pi$
$787$	27.7128	+	16.0000i	0.987855	+	0.570338i	0.0832226	+	0.996531i	$0.473479\pi$
$788$	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	$-0.344611\pi$
$797$	−1.73205	−	1.00000i	−0.0613524	−	0.0354218i	−0.530362	+	0.847771i	$0.677944\pi$
$798$		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
$805$	−1.07180	+	17.8564i	−0.0377759	+	0.629356i
$806$	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
$815$	−35.7128	−	2.14359i	−1.25097	−	0.0750868i
$816$		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	0.787745	−	0.616002i	$-0.211249\pi$
$821$	−4.00000	−	6.92820i	−0.139601	−	0.241796i	−0.927346	+	0.374206i	$0.877915\pi$
$822$		0			0
$823$	−5.19615	−	3.00000i	−0.181126	−	0.104573i	0.406695	−	0.913564i	$-0.366681\pi$
$823$	−5.19615	−	3.00000i	−0.181126	−	0.104573i	−0.587822	+	0.808990i	$0.700014\pi$
$824$	−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	$0.325570\pi$
$830$	−7.46410	−	4.92820i	−0.259083	−	0.171060i
$831$		0			0
$832$	5.19615	+	3.00000i	0.180144	+	0.104006i
$833$	−5.19615	−	3.00000i	−0.180036	−	0.103944i
$834$		0			0
$835$	14.7846	−	22.3923i	0.511643	−	0.774918i
$836$		0			0
$837$		0			0
$838$			10.0000i			0.345444i
$839$	−20.0000	−	34.6410i	−0.690477	−	1.19594i	−0.971682	−	0.236293i	$-0.924067\pi$
$839$	−20.0000	−	34.6410i	−0.690477	−	1.19594i	0.281205	−	0.959648i	$-0.409266\pi$
$840$		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
$850$	3.92820	+	9.19615i	0.134736	+	0.315425i
$851$	−4.00000	+	6.92820i	−0.137118	+	0.237496i
$852$		0			0
$853$	−12.1244	+	7.00000i	−0.415130	+	0.239675i	−0.692992	−	0.720946i	$-0.743708\pi$
$853$	−12.1244	+	7.00000i	−0.415130	+	0.239675i	0.277862	+	0.960621i	$0.410374\pi$
$854$	−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	$-0.412023\pi$
$857$	36.3731	−	21.0000i	1.24248	−	0.717346i	0.969599	+	0.244701i	$0.0786899\pi$
$858$		0			0
$859$	10.0000	−	17.3205i	0.341196	−	0.590968i	−0.643459	−	0.765480i	$-0.722501\pi$
$859$	10.0000	−	17.3205i	0.341196	−	0.590968i	0.984655	+	0.174512i	$0.0558348\pi$
$860$	−8.92820	−	0.535898i	−0.304449	−	0.0182740i
$861$		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
$875$	7.53590	+	21.0526i	0.254760	+	0.711706i
$876$		0			0
$877$	19.0526	+	11.0000i	0.643359	+	0.371444i	0.785907	−	0.618344i	$-0.212196\pi$
$877$	19.0526	+	11.0000i	0.643359	+	0.371444i	−0.142548	+	0.989788i	$0.545530\pi$
$878$		0			0
$879$		0			0
$880$	3.73205	+	2.46410i	0.125807	+	0.0830648i
$881$	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	$-0.397902\pi$
$887$	−10.3923	−	6.00000i	−0.348939	−	0.201460i	−0.664218	+	0.747539i	$0.731235\pi$
$888$		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
$895$	−1.33975	+	22.3205i	−0.0447828	+	0.746092i
$896$	−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
$905$	−0.267949	+	4.46410i	−0.00890693	+	0.148392i
$906$		0			0
$907$	−10.3923	+	6.00000i	−0.345071	+	0.199227i	−0.662512	−	0.749051i	$-0.730510\pi$
$907$	−10.3923	+	6.00000i	−0.345071	+	0.199227i	0.317441	+	0.948278i	$0.397176\pi$
$908$			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	−0.922740	−	0.385422i	$-0.874056\pi$
$911$	−24.0000	−	41.5692i	−0.795155	−	1.37725i	0.127585	−	0.991828i	$-0.459277\pi$
$912$		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	$0.5\pi$
$920$	7.46410	+	4.92820i	0.246084	+	0.162478i
$921$		0			0
$922$	−10.3923	−	6.00000i	−0.342252	−	0.197599i
$923$	62.3538	+	36.0000i	2.05240	+	1.18495i
$924$		0			0
$925$	−1.19615	+	9.92820i	−0.0393292	+	0.326437i
$926$	6.00000			0.197172
$927$		0			0
$928$		0			0
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	0.507825	−	0.861460i	$-0.330450\pi$
$929$	−15.0000	−	25.9808i	−0.492134	−	0.852401i	−0.999959	+	0.00905914i	$0.997116\pi$
$930$		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
$940$	−17.8564	−	1.07180i	−0.582412	−	0.0349582i
$941$	−14.0000	+	24.2487i	−0.456387	+	0.790485i	−0.998767	−	0.0496480i	$-0.984190\pi$
$941$	−14.0000	+	24.2487i	−0.456387	+	0.790485i	0.542380	+	0.840133i	$0.317523\pi$
$942$		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	$-0.604204\pi$
$947$	10.3923	−	6.00000i	0.337705	−	0.194974i	0.659256	+	0.751918i	$0.270871\pi$
$948$		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
$965$	−4.92820	+	7.46410i	−0.158644	+	0.240278i
$966$		0			0
$967$	−32.9090	−	19.0000i	−1.05828	−	0.610999i	−0.133325	−	0.991072i	$-0.542565\pi$
$967$	−32.9090	−	19.0000i	−1.05828	−	0.610999i	−0.924956	+	0.380074i	$0.875899\pi$
$968$	6.06218	+	3.50000i	0.194846	+	0.112494i
$969$		0			0
$970$	−14.9282	−	9.85641i	−0.479316	−	0.316470i
$971$	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	$-0.567833\pi$
$977$	−36.3731	−	21.0000i	−1.16368	−	0.671850i	−0.952183	+	0.305530i	$0.901167\pi$
$978$		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	$-0.748795\pi$
$983$	−13.8564	+	8.00000i	−0.441951	+	0.255160i	0.262474	+	0.964939i	$0.415462\pi$
$984$		0			0
$985$	−49.1051	−	2.94744i	−1.56462	−	0.0939133i
$986$		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	$-0.574662\pi$
$997$	15.5885	−	9.00000i	0.493691	−	0.285033i	0.726105	+	0.687584i	$0.241329\pi$
$998$		0			0
$999$		0			0

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

)

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.i.b.109.1		4
3.2	odd	2		810.2.i.e.109.2		4
5.4	even	2	inner	810.2.i.b.109.2		4
9.2	odd	6		810.2.i.e.379.1		4
9.4	even	3		90.2.c.a.19.1		2
9.5	odd	6		30.2.c.a.19.2	yes	2
9.7	even	3	inner	810.2.i.b.379.2		4
15.14	odd	2		810.2.i.e.109.1		4
36.23	even	6		240.2.f.a.49.2		2
36.31	odd	6		720.2.f.f.289.1		2
45.4	even	6		90.2.c.a.19.2		2
45.13	odd	12		450.2.a.b.1.1		1
45.14	odd	6		30.2.c.a.19.1	✓	2
45.22	odd	12		450.2.a.f.1.1		1
45.23	even	12		150.2.a.c.1.1		1
45.29	odd	6		810.2.i.e.379.2		4
45.32	even	12		150.2.a.a.1.1		1
45.34	even	6	inner	810.2.i.b.379.1		4
63.5	even	6		1470.2.n.a.949.2		4
63.23	odd	6		1470.2.n.h.949.2		4
63.32	odd	6		1470.2.n.h.79.1		4
63.41	even	6		1470.2.g.g.589.2		2
63.59	even	6		1470.2.n.a.79.1		4
72.5	odd	6		960.2.f.h.769.2		2
72.13	even	6		2880.2.f.e.1729.2		2
72.59	even	6		960.2.f.i.769.1		2
72.67	odd	6		2880.2.f.c.1729.2		2
144.5	odd	12		3840.2.d.g.2689.1		2
144.59	even	12		3840.2.d.x.2689.1		2
144.77	odd	12		3840.2.d.y.2689.2		2
144.131	even	12		3840.2.d.j.2689.2		2
180.23	odd	12		1200.2.a.g.1.1		1
180.59	even	6		240.2.f.a.49.1		2
180.67	even	12		3600.2.a.o.1.1		1
180.103	even	12		3600.2.a.bg.1.1		1
180.139	odd	6		720.2.f.f.289.2		2
180.167	odd	12		1200.2.a.m.1.1		1
315.59	even	6		1470.2.n.a.79.2		4
315.104	even	6		1470.2.g.g.589.1		2
315.149	odd	6		1470.2.n.h.949.1		4
315.167	odd	12		7350.2.a.bg.1.1		1
315.194	even	6		1470.2.n.a.949.1		4
315.284	odd	6		1470.2.n.h.79.2		4
315.293	odd	12		7350.2.a.cc.1.1		1
360.59	even	6		960.2.f.i.769.2		2
360.77	even	12		4800.2.a.cg.1.1		1
360.139	odd	6		2880.2.f.c.1729.1		2
360.149	odd	6		960.2.f.h.769.1		2
360.203	odd	12		4800.2.a.cj.1.1		1
360.229	even	6		2880.2.f.e.1729.1		2
360.293	even	12		4800.2.a.l.1.1		1
360.347	odd	12		4800.2.a.m.1.1		1
720.59	even	12		3840.2.d.j.2689.1		2
720.149	odd	12		3840.2.d.y.2689.1		2
720.419	even	12		3840.2.d.x.2689.2		2
720.509	odd	12		3840.2.d.g.2689.2		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
30.2.c.a.19.1	✓	2	45.14	odd	6
30.2.c.a.19.2	yes	2	9.5	odd	6
90.2.c.a.19.1		2	9.4	even	3
90.2.c.a.19.2		2	45.4	even	6
150.2.a.a.1.1		1	45.32	even	12
150.2.a.c.1.1		1	45.23	even	12
240.2.f.a.49.1		2	180.59	even	6
240.2.f.a.49.2		2	36.23	even	6
450.2.a.b.1.1		1	45.13	odd	12
450.2.a.f.1.1		1	45.22	odd	12
720.2.f.f.289.1		2	36.31	odd	6
720.2.f.f.289.2		2	180.139	odd	6
810.2.i.b.109.1		4	1.1	even	1	trivial
810.2.i.b.109.2		4	5.4	even	2	inner
810.2.i.b.379.1		4	45.34	even	6	inner
810.2.i.b.379.2		4	9.7	even	3	inner
810.2.i.e.109.1		4	15.14	odd	2
810.2.i.e.109.2		4	3.2	odd	2
810.2.i.e.379.1		4	9.2	odd	6
810.2.i.e.379.2		4	45.29	odd	6
960.2.f.h.769.1		2	360.149	odd	6
960.2.f.h.769.2		2	72.5	odd	6
960.2.f.i.769.1		2	72.59	even	6
960.2.f.i.769.2		2	360.59	even	6
1200.2.a.g.1.1		1	180.23	odd	12
1200.2.a.m.1.1		1	180.167	odd	12
1470.2.g.g.589.1		2	315.104	even	6
1470.2.g.g.589.2		2	63.41	even	6
1470.2.n.a.79.1		4	63.59	even	6
1470.2.n.a.79.2		4	315.59	even	6
1470.2.n.a.949.1		4	315.194	even	6
1470.2.n.a.949.2		4	63.5	even	6
1470.2.n.h.79.1		4	63.32	odd	6
1470.2.n.h.79.2		4	315.284	odd	6
1470.2.n.h.949.1		4	315.149	odd	6
1470.2.n.h.949.2		4	63.23	odd	6
2880.2.f.c.1729.1		2	360.139	odd	6
2880.2.f.c.1729.2		2	72.67	odd	6
2880.2.f.e.1729.1		2	360.229	even	6
2880.2.f.e.1729.2		2	72.13	even	6
3600.2.a.o.1.1		1	180.67	even	12
3600.2.a.bg.1.1		1	180.103	even	12
3840.2.d.g.2689.1		2	144.5	odd	12
3840.2.d.g.2689.2		2	720.509	odd	12
3840.2.d.j.2689.1		2	720.59	even	12
3840.2.d.j.2689.2		2	144.131	even	12
3840.2.d.x.2689.1		2	144.59	even	12
3840.2.d.x.2689.2		2	720.419	even	12
3840.2.d.y.2689.1		2	720.149	odd	12
3840.2.d.y.2689.2		2	144.77	odd	12
4800.2.a.l.1.1		1	360.293	even	12
4800.2.a.m.1.1		1	360.347	odd	12
4800.2.a.cg.1.1		1	360.77	even	12
4800.2.a.cj.1.1		1	360.203	odd	12
7350.2.a.bg.1.1		1	315.167	odd	12
7350.2.a.cc.1.1		1	315.293	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 $\F_{q}$

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

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Newspace parameters

Newform invariants

Embedding invariants

$q$ -expansion

Character values

Coefficient data

Twists

This project is supported by grants from the US National Science Foundation, the UK Engineering and Physical Sciences Research Council, and the Simons Foundation.

Label	810.2.i.b.109.1

Level	$810$
Weight	$2$
Character	810.109
Analytic conductor	$6.468$
Analytic rank	$0$
Dimension	$4$
Inner twists	$4$