LMFDB - Embedded newform 810.2.i.h.109.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.2702336256.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} + 9x^{6} + 56x^{4} + 225x^{2} + 625 $ x^8 + 9x^6 + 56x^4 + 225*x^2 + 625
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 270)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			109.2
Root			$-0.656712 + 2.13746i$ of defining polynomial
Character	$\chi$	$=$	810.109
Dual form			810.2.i.h.379.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.656712 - 2.13746i) q^{5} +(-3.77492 + 2.17945i) q^{7} +1.00000i q^{8} +(0.500000 + 2.17945i) q^{10} +(2.17945 + 3.77492i) q^{11} +(2.17945 - 3.77492i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.00000i q^{17} -6.00000 q^{19} +(-1.52274 - 1.63746i) q^{20} +(-3.77492 - 2.17945i) q^{22} +(1.73205 + 1.00000i) q^{23} +(-4.13746 - 2.80739i) q^{25} +4.35890i q^{28} +(-3.50000 + 6.06218i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.00000 + 3.46410i) q^{34} +(2.17945 + 9.50000i) q^{35} +8.71780i q^{37} +(5.19615 - 3.00000i) q^{38} +(2.13746 + 0.656712i) q^{40} +(-4.35890 + 7.54983i) q^{41} +(-7.54983 + 4.35890i) q^{43} +4.35890 q^{44} -2.00000 q^{46} +(-1.73205 + 1.00000i) q^{47} +(6.00000 - 10.3923i) q^{49} +(4.98684 + 0.362541i) q^{50} -3.00000i q^{53} +(9.50000 - 2.17945i) q^{55} +(-2.17945 - 3.77492i) q^{56} +(-4.35890 + 7.54983i) q^{59} +(2.00000 + 3.46410i) q^{61} -7.00000i q^{62} -1.00000 q^{64} +(7.54983 + 4.35890i) q^{67} +(-3.46410 - 2.00000i) q^{68} +(-6.63746 - 7.13752i) q^{70} +4.35890i q^{73} +(-4.35890 - 7.54983i) q^{74} +(-3.00000 + 5.19615i) q^{76} +(-16.4545 - 9.50000i) q^{77} +(-2.17945 + 0.500000i) q^{80} -8.71780i q^{82} +(-4.33013 + 2.50000i) q^{83} +(-8.54983 - 2.62685i) q^{85} +(4.35890 - 7.54983i) q^{86} +(-3.77492 + 2.17945i) q^{88} -8.71780 q^{89} +(1.73205 - 1.00000i) q^{92} +(1.00000 - 1.73205i) q^{94} +(-3.94027 + 12.8248i) q^{95} +(3.77492 - 2.17945i) q^{97} +12.0000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} + 4 q^{10} - 4 q^{16} - 48 q^{19} - 18 q^{25} - 28 q^{31} + 16 q^{34} + 2 q^{40} - 16 q^{46} + 48 q^{49} + 76 q^{55} + 16 q^{61} - 8 q^{64} - 38 q^{70} - 24 q^{76} - 8 q^{85} + 8 q^{94}+O(q^{100}) $ 8 * q + 4 * q^4 + 4 * q^10 - 4 * q^16 - 48 * q^19 - 18 * q^25 - 28 * q^31 + 16 * q^34 + 2 * q^40 - 16 * q^46 + 48 * q^49 + 76 * q^55 + 16 * q^61 - 8 * q^64 - 38 * q^70 - 24 * q^76 - 8 * q^85 + 8 * 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
$5$	0.656712	−	2.13746i	0.293691	−	0.955901i
$5$	0.656712	−	2.13746i	0.293691	−	0.955901i
$6$		0			0
$7$	−3.77492	+	2.17945i	−1.42678	+	0.823754i	−0.996866	−	0.0791130i	$-0.974791\pi$
$7$	−3.77492	+	2.17945i	−1.42678	+	0.823754i	−0.429919	+	0.902867i	$0.641458\pi$
$8$			1.00000i			0.353553i
$9$		0			0
$10$	0.500000	+	2.17945i	0.158114	+	0.689202i
$11$	2.17945	+	3.77492i	0.657129	+	1.13818i	0.981356	+	0.192201i	$0.0615626\pi$
$11$	2.17945	+	3.77492i	0.657129	+	1.13818i	−0.324227	+	0.945979i	$0.605104\pi$
$12$		0			0
$13$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$13$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$14$	2.17945	−	3.77492i	0.582482	−	1.00889i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		−	4.00000i		−	0.970143i	−0.874475	−	0.485071i	$-0.838794\pi$
$17$		−	4.00000i		−	0.970143i	0.874475	−	0.485071i	$-0.161206\pi$
$18$		0			0
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$	−1.52274	−	1.63746i	−0.340494	−	0.366147i
$21$		0			0
$22$	−3.77492	−	2.17945i	−0.804815	−	0.464660i
$23$	1.73205	+	1.00000i	0.361158	+	0.208514i	0.669588	−	0.742732i	$-0.266471\pi$
$23$	1.73205	+	1.00000i	0.361158	+	0.208514i	−0.308431	+	0.951247i	$0.599804\pi$
$24$		0			0
$25$	−4.13746	−	2.80739i	−0.827492	−	0.561478i
$26$		0			0
$27$		0			0
$28$			4.35890i			0.823754i
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	0.359211	+	0.933257i	$0.383046\pi$
$31$	−3.50000	+	6.06218i	−0.628619	+	1.08880i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	0.866025	+	0.500000i	0.153093	+	0.0883883i
$33$		0			0
$34$	2.00000	+	3.46410i	0.342997	+	0.594089i
$35$	2.17945	+	9.50000i	0.368394	+	1.60579i
$36$		0			0
$37$			8.71780i			1.43320i	0.697486	+	0.716599i	$0.254302\pi$
$37$			8.71780i			1.43320i	−0.697486	+	0.716599i	$0.745698\pi$
$38$	5.19615	−	3.00000i	0.842927	−	0.486664i
$39$		0			0
$40$	2.13746	+	0.656712i	0.337962	+	0.103835i
$41$	−4.35890	+	7.54983i	−0.680746	+	1.17909i	0.294008	+	0.955803i	$0.405011\pi$
$41$	−4.35890	+	7.54983i	−0.680746	+	1.17909i	−0.974754	+	0.223283i	$0.928323\pi$
$42$		0			0
$43$	−7.54983	+	4.35890i	−1.15134	+	0.664726i	−0.949213	−	0.314634i	$-0.898118\pi$
$43$	−7.54983	+	4.35890i	−1.15134	+	0.664726i	−0.202126	+	0.979360i	$0.564785\pi$
$44$	4.35890			0.657129
$45$		0			0
$46$	−2.00000			−0.294884
$47$	−1.73205	+	1.00000i	−0.252646	+	0.145865i	−0.620975	−	0.783830i	$-0.713263\pi$
$47$	−1.73205	+	1.00000i	−0.252646	+	0.145865i	0.368329	+	0.929695i	$0.379930\pi$
$48$		0			0
$49$	6.00000	−	10.3923i	0.857143	−	1.48461i
$50$	4.98684	+	0.362541i	0.705246	+	0.0512711i
$51$		0			0
$52$		0			0
$53$		−	3.00000i		−	0.412082i	−0.978543	−	0.206041i	$-0.933942\pi$
$53$		−	3.00000i		−	0.412082i	0.978543	−	0.206041i	$-0.0660580\pi$
$54$		0			0
$55$	9.50000	−	2.17945i	1.28098	−	0.293877i
$56$	−2.17945	−	3.77492i	−0.291241	−	0.504445i
$57$		0			0
$58$		0			0
$59$	−4.35890	+	7.54983i	−0.567480	+	0.982905i	0.429334	+	0.903146i	$0.358748\pi$
$59$	−4.35890	+	7.54983i	−0.567480	+	0.982905i	−0.996814	+	0.0797589i	$0.974585\pi$
$60$		0			0
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	0.965187	−	0.261562i	$-0.0842377\pi$
$61$	2.00000	+	3.46410i	0.256074	+	0.443533i	−0.709113	+	0.705095i	$0.750904\pi$
$62$		−	7.00000i		−	0.889001i
$63$		0			0
$64$	−1.00000			−0.125000
$65$		0			0
$66$		0			0
$67$	7.54983	+	4.35890i	0.922359	+	0.532524i	0.884387	−	0.466755i	$-0.154577\pi$
$67$	7.54983	+	4.35890i	0.922359	+	0.532524i	0.0379722	+	0.999279i	$0.487910\pi$
$68$	−3.46410	−	2.00000i	−0.420084	−	0.242536i
$69$		0			0
$70$	−6.63746	−	7.13752i	−0.793328	−	0.853096i
$71$		0			0			−	1.00000i	$-0.5\pi$
$71$		0			0				1.00000i	$0.5\pi$
$72$		0			0
$73$			4.35890i			0.510171i	0.966919	+	0.255085i	$0.0821035\pi$
$73$			4.35890i			0.510171i	−0.966919	+	0.255085i	$0.917896\pi$
$74$	−4.35890	−	7.54983i	−0.506712	−	0.877650i
$75$		0			0
$76$	−3.00000	+	5.19615i	−0.344124	+	0.596040i
$77$	−16.4545	−	9.50000i	−1.87516	−	1.08263i
$78$		0			0
$79$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$79$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$80$	−2.17945	+	0.500000i	−0.243670	+	0.0559017i
$81$		0			0
$82$		−	8.71780i		−	0.962720i
$83$	−4.33013	+	2.50000i	−0.475293	+	0.274411i	−0.718453	−	0.695576i	$-0.755149\pi$
$83$	−4.33013	+	2.50000i	−0.475293	+	0.274411i	0.243160	+	0.969986i	$0.421816\pi$
$84$		0			0
$85$	−8.54983	−	2.62685i	−0.927360	−	0.284922i
$86$	4.35890	−	7.54983i	0.470032	−	0.814120i
$87$		0			0
$88$	−3.77492	+	2.17945i	−0.402408	+	0.232330i
$89$	−8.71780			−0.924085			−0.462042	−	0.886858i	$-0.652883\pi$
$89$	−8.71780			−0.924085			−0.462042	+	0.886858i	$0.652883\pi$
$90$		0			0
$91$		0			0
$92$	1.73205	−	1.00000i	0.180579	−	0.104257i
$93$		0			0
$94$	1.00000	−	1.73205i	0.103142	−	0.178647i
$95$	−3.94027	+	12.8248i	−0.404263	+	1.31579i
$96$		0			0
$97$	3.77492	−	2.17945i	0.383285	−	0.221290i	−0.295962	−	0.955200i	$-0.595640\pi$
$97$	3.77492	−	2.17945i	0.383285	−	0.221290i	0.679246	+	0.733910i	$0.262307\pi$
$98$			12.0000i			1.21218i
$99$		0			0
$100$	−4.50000	+	2.17945i	−0.450000	+	0.217945i
$101$	−2.17945	−	3.77492i	−0.216863	−	0.375618i	0.736984	−	0.675910i	$-0.236249\pi$
$101$	−2.17945	−	3.77492i	−0.216863	−	0.375618i	−0.953847	+	0.300292i	$0.902916\pi$
$102$		0			0
$103$	−7.54983	−	4.35890i	−0.743907	−	0.429495i	0.0795810	−	0.996828i	$-0.474642\pi$
$103$	−7.54983	−	4.35890i	−0.743907	−	0.429495i	−0.823488	+	0.567333i	$0.807975\pi$
$104$		0			0
$105$		0			0
$106$	1.50000	+	2.59808i	0.145693	+	0.252347i
$107$		−	15.0000i		−	1.45010i	−0.688694	−	0.725052i	$-0.741816\pi$
$107$		−	15.0000i		−	1.45010i	0.688694	−	0.725052i	$-0.258184\pi$
$108$		0			0
$109$	−10.0000			−0.957826			−0.478913	−	0.877862i	$-0.658969\pi$
$109$	−10.0000			−0.957826			−0.478913	+	0.877862i	$0.658969\pi$
$110$	−7.13752	+	6.63746i	−0.680536	+	0.632857i
$111$		0			0
$112$	3.77492	+	2.17945i	0.356696	+	0.205939i
$113$	15.5885	+	9.00000i	1.46644	+	0.846649i	0.999295	−	0.0375328i	$-0.0119499\pi$
$113$	15.5885	+	9.00000i	1.46644	+	0.846649i	0.467143	+	0.884182i	$0.345283\pi$
$114$		0			0
$115$	3.27492	−	3.04547i	0.305388	−	0.283992i
$116$		0			0
$117$		0			0
$118$		−	8.71780i		−	0.802538i
$119$	8.71780	+	15.0997i	0.799159	+	1.38418i
$120$		0			0
$121$	−4.00000	+	6.92820i	−0.363636	+	0.629837i
$122$	−3.46410	−	2.00000i	−0.313625	−	0.181071i
$123$		0			0
$124$	3.50000	+	6.06218i	0.314309	+	0.544400i
$125$	−8.71780	+	7.00000i	−0.779744	+	0.626099i
$126$		0			0
$127$		−	4.35890i		−	0.386790i	−0.981121	−	0.193395i	$-0.938050\pi$
$127$		−	4.35890i		−	0.386790i	0.981121	−	0.193395i	$-0.0619498\pi$
$128$	0.866025	−	0.500000i	0.0765466	−	0.0441942i
$129$		0			0
$130$		0			0
$131$	6.53835	−	11.3248i	0.571258	−	0.989448i	−0.425179	−	0.905109i	$-0.639789\pi$
$131$	6.53835	−	11.3248i	0.571258	−	0.989448i	0.996437	−	0.0843389i	$-0.0268778\pi$
$132$		0			0
$133$	22.6495	−	13.0767i	1.96396	−	1.13389i
$134$	−8.71780			−0.753103
$135$		0			0
$136$	4.00000			0.342997
$137$	15.5885	−	9.00000i	1.33181	−	0.768922i	0.346235	−	0.938148i	$-0.387460\pi$
$137$	15.5885	−	9.00000i	1.33181	−	0.768922i	0.985577	+	0.169226i	$0.0541268\pi$
$138$		0			0
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	−0.768655	−	0.639664i	$-0.779074\pi$
$139$	2.00000	−	3.46410i	0.169638	−	0.293821i	0.938293	+	0.345843i	$0.112407\pi$
$140$	9.31697	+	2.86254i	0.787427	+	0.241929i
$141$		0			0
$142$		0			0
$143$		0			0
$144$		0			0
$145$		0			0
$146$	−2.17945	−	3.77492i	−0.180373	−	0.312414i
$147$		0			0
$148$	7.54983	+	4.35890i	0.620593	+	0.358299i
$149$	2.17945	−	3.77492i	0.178547	−	0.309253i	−0.762836	−	0.646592i	$-0.776194\pi$
$149$	2.17945	−	3.77492i	0.178547	−	0.309253i	0.941383	+	0.337339i	$0.109527\pi$
$150$		0			0
$151$	5.50000	+	9.52628i	0.447584	+	0.775238i	0.998228	−	0.0595022i	$-0.0189513\pi$
$151$	5.50000	+	9.52628i	0.447584	+	0.775238i	−0.550645	+	0.834740i	$0.685618\pi$
$152$		−	6.00000i		−	0.486664i
$153$		0			0
$154$	19.0000			1.53106
$155$	10.6592	+	11.4622i	0.856165	+	0.920667i
$156$		0			0
$157$	−15.0997	−	8.71780i	−1.20508	−	0.695756i	−0.243403	−	0.969925i	$-0.578264\pi$
$157$	−15.0997	−	8.71780i	−1.20508	−	0.695756i	−0.961681	+	0.274169i	$0.911597\pi$
$158$		0			0
$159$		0			0
$160$	1.63746	−	1.52274i	0.129452	−	0.120383i
$161$	−8.71780			−0.687059
$162$		0			0
$163$		−	17.4356i		−	1.36566i	−0.730577	−	0.682831i	$-0.760749\pi$
$163$		−	17.4356i		−	1.36566i	0.730577	−	0.682831i	$-0.239251\pi$
$164$	4.35890	+	7.54983i	0.340373	+	0.589543i
$165$		0			0
$166$	2.50000	−	4.33013i	0.194038	−	0.336083i
$167$	−15.5885	−	9.00000i	−1.20627	−	0.696441i	−0.244328	−	0.969693i	$-0.578568\pi$
$167$	−15.5885	−	9.00000i	−1.20627	−	0.696441i	−0.961943	+	0.273252i	$0.911901\pi$
$168$		0			0
$169$	−6.50000	−	11.2583i	−0.500000	−	0.866025i
$170$	8.71780	−	2.00000i	0.668625	−	0.153393i
$171$		0			0
$172$			8.71780i			0.664726i
$173$	−16.4545	+	9.50000i	−1.25101	+	0.722272i	−0.971310	−	0.237816i	$-0.923569\pi$
$173$	−16.4545	+	9.50000i	−1.25101	+	0.722272i	−0.279701	+	0.960087i	$0.590235\pi$
$174$		0			0
$175$	21.7371	+	1.58028i	1.64317	+	0.119458i
$176$	2.17945	−	3.77492i	0.164282	−	0.284545i
$177$		0			0
$178$	7.54983	−	4.35890i	0.565884	−	0.326713i
$179$	21.7945			1.62900			0.814499	−	0.580166i	$-0.197012\pi$
$179$	21.7945			1.62900			0.814499	+	0.580166i	$0.197012\pi$
$180$		0			0
$181$	8.00000			0.594635			0.297318	−	0.954779i	$-0.403908\pi$
$181$	8.00000			0.594635			0.297318	+	0.954779i	$0.403908\pi$
$182$		0			0
$183$		0			0
$184$	−1.00000	+	1.73205i	−0.0737210	+	0.127688i
$185$	18.6339	+	5.72508i	1.36999	+	0.420916i
$186$		0			0
$187$	15.0997	−	8.71780i	1.10420	−	0.637509i
$188$			2.00000i			0.145865i
$189$		0			0
$190$	−3.00000	−	13.0767i	−0.217643	−	0.948683i
$191$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$191$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$192$		0			0
$193$	18.8746	+	10.8972i	1.35862	+	0.784401i	0.989438	−	0.144955i	$-0.0463038\pi$
$193$	18.8746	+	10.8972i	1.35862	+	0.784401i	0.369184	+	0.929356i	$0.379637\pi$
$194$	−2.17945	+	3.77492i	−0.156475	+	0.271023i
$195$		0			0
$196$	−6.00000	−	10.3923i	−0.428571	−	0.742307i
$197$		−	5.00000i		−	0.356235i	−0.984009	−	0.178118i	$-0.942999\pi$
$197$		−	5.00000i		−	0.356235i	0.984009	−	0.178118i	$-0.0570008\pi$
$198$		0			0
$199$	3.00000			0.212664			0.106332	−	0.994331i	$-0.466089\pi$
$199$	3.00000			0.212664			0.106332	+	0.994331i	$0.466089\pi$
$200$	2.80739	−	4.13746i	0.198512	−	0.292563i
$201$		0			0
$202$	3.77492	+	2.17945i	0.265602	+	0.153346i
$203$		0			0
$204$		0			0
$205$	13.2749	+	14.2750i	0.927160	+	0.997012i
$206$	8.71780			0.607398
$207$		0			0
$208$		0			0
$209$	−13.0767	−	22.6495i	−0.904534	−	1.56670i
$210$		0			0
$211$	−3.00000	+	5.19615i	−0.206529	+	0.357718i	−0.950619	−	0.310361i	$-0.899550\pi$
$211$	−3.00000	+	5.19615i	−0.206529	+	0.357718i	0.744090	+	0.668079i	$0.232883\pi$
$212$	−2.59808	−	1.50000i	−0.178437	−	0.103020i
$213$		0			0
$214$	7.50000	+	12.9904i	0.512689	+	0.888004i
$215$	4.35890	+	19.0000i	0.297274	+	1.29579i
$216$		0			0
$217$		−	30.5123i		−	2.07131i
$218$	8.66025	−	5.00000i	0.586546	−	0.338643i
$219$		0			0
$220$	2.86254	−	9.31697i	0.192993	−	0.628150i
$221$		0			0
$222$		0			0
$223$	−7.54983	+	4.35890i	−0.505574	+	0.291893i	−0.731013	−	0.682364i	$-0.760952\pi$
$223$	−7.54983	+	4.35890i	−0.505574	+	0.291893i	0.225438	+	0.974257i	$0.427619\pi$
$224$	−4.35890			−0.291241
$225$		0			0
$226$	−18.0000			−1.19734
$227$	−3.46410	+	2.00000i	−0.229920	+	0.132745i	−0.610535	−	0.791989i	$-0.709046\pi$
$227$	−3.46410	+	2.00000i	−0.229920	+	0.132745i	0.380615	+	0.924734i	$0.375712\pi$
$228$		0			0
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	0.231287	+	0.972886i	$0.425707\pi$
$229$	−11.0000	+	19.0526i	−0.726900	+	1.25903i	−0.958187	+	0.286143i	$0.907627\pi$
$230$	−1.31342	+	4.27492i	−0.0866046	+	0.281880i
$231$		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
$235$	1.00000	+	4.35890i	0.0652328	+	0.284343i
$236$	4.35890	+	7.54983i	0.283740	+	0.491452i
$237$		0			0
$238$	−15.0997	−	8.71780i	−0.978766	−	0.565091i
$239$	4.35890	−	7.54983i	0.281954	−	0.488358i	−0.689912	−	0.723893i	$-0.742351\pi$
$239$	4.35890	−	7.54983i	0.281954	−	0.488358i	0.971866	+	0.235535i	$0.0756842\pi$
$240$		0			0
$241$	7.00000	+	12.1244i	0.450910	+	0.780998i	0.998443	−	0.0557856i	$-0.0177663\pi$
$241$	7.00000	+	12.1244i	0.450910	+	0.780998i	−0.547533	+	0.836784i	$0.684433\pi$
$242$		−	8.00000i		−	0.514259i
$243$		0			0
$244$	4.00000			0.256074
$245$	−18.2728	−	19.6495i	−1.16741	−	1.25536i
$246$		0			0
$247$		0			0
$248$	−6.06218	−	3.50000i	−0.384949	−	0.222250i
$249$		0			0
$250$	4.04983	−	10.4211i	0.256134	−	0.659087i
$251$	26.1534			1.65079			0.825394	−	0.564557i	$-0.190953\pi$
$251$	26.1534			1.65079			0.825394	+	0.564557i	$0.190953\pi$
$252$		0			0
$253$			8.71780i			0.548083i
$254$	2.17945	+	3.77492i	0.136751	+	0.236859i
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	0.139533	−	0.990217i	$-0.455440\pi$
$257$	−10.3923	−	6.00000i	−0.648254	−	0.374270i	−0.787787	+	0.615948i	$0.788773\pi$
$258$		0			0
$259$	−19.0000	−	32.9090i	−1.18060	−	2.04486i
$260$		0			0
$261$		0			0
$262$			13.0767i			0.807881i
$263$	−1.73205	+	1.00000i	−0.106803	+	0.0616626i	−0.552450	−	0.833546i	$-0.686307\pi$
$263$	−1.73205	+	1.00000i	−0.106803	+	0.0616626i	0.445647	+	0.895209i	$0.352974\pi$
$264$		0			0
$265$	−6.41238	−	1.97014i	−0.393909	−	0.121024i
$266$	−13.0767	+	22.6495i	−0.801784	+	1.38873i
$267$		0			0
$268$	7.54983	−	4.35890i	0.461180	−	0.266262i
$269$		0			0			−	1.00000i	$-0.5\pi$
$269$		0			0				1.00000i	$0.5\pi$
$270$		0			0
$271$	−5.00000			−0.303728			−0.151864	−	0.988401i	$-0.548528\pi$
$271$	−5.00000			−0.303728			−0.151864	+	0.988401i	$0.548528\pi$
$272$	−3.46410	+	2.00000i	−0.210042	+	0.121268i
$273$		0			0
$274$	−9.00000	+	15.5885i	−0.543710	+	0.941733i
$275$	1.58028	−	21.7371i	0.0952945	−	1.31080i
$276$		0			0
$277$	−15.0997	+	8.71780i	−0.907251	+	0.523802i	−0.879546	−	0.475814i	$-0.842153\pi$
$277$	−15.0997	+	8.71780i	−0.907251	+	0.523802i	−0.0277055	+	0.999616i	$0.508820\pi$
$278$			4.00000i			0.239904i
$279$		0			0
$280$	−9.50000	+	2.17945i	−0.567734	+	0.130247i
$281$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$281$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$282$		0			0
$283$	−7.54983	−	4.35890i	−0.448791	−	0.259110i	0.258528	−	0.966004i	$-0.416762\pi$
$283$	−7.54983	−	4.35890i	−0.448791	−	0.259110i	−0.707319	+	0.706894i	$0.750096\pi$
$284$		0			0
$285$		0			0
$286$		0			0
$287$		−	38.0000i		−	2.24307i
$288$		0			0
$289$	1.00000			0.0588235
$290$		0			0
$291$		0			0
$292$	3.77492	+	2.17945i	0.220910	+	0.127543i
$293$	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
$295$	13.2749	+	14.2750i	0.772896	+	0.831125i
$296$	−8.71780			−0.506712
$297$		0			0
$298$			4.35890i			0.252504i
$299$		0			0
$300$		0			0
$301$	19.0000	−	32.9090i	1.09514	−	1.89684i
$302$	−9.52628	−	5.50000i	−0.548176	−	0.316489i
$303$		0			0
$304$	3.00000	+	5.19615i	0.172062	+	0.298020i
$305$	8.71780	−	2.00000i	0.499180	−	0.114520i
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$	−16.4545	+	9.50000i	−0.937581	+	0.541313i
$309$		0			0
$310$	−14.9622	−	4.59698i	−0.849796	−	0.261091i
$311$	−13.0767	+	22.6495i	−0.741511	+	1.28434i	0.210296	+	0.977638i	$0.432557\pi$
$311$	−13.0767	+	22.6495i	−0.741511	+	1.28434i	−0.951807	+	0.306698i	$0.900776\pi$
$312$		0			0
$313$	−18.8746	+	10.8972i	−1.06685	+	0.615949i	−0.927320	−	0.374268i	$-0.877894\pi$
$313$	−18.8746	+	10.8972i	−1.06685	+	0.615949i	−0.139534	+	0.990217i	$0.544561\pi$
$314$	17.4356			0.983948
$315$		0			0
$316$		0			0
$317$	14.7224	−	8.50000i	0.826894	−	0.477408i	−0.0258939	−	0.999665i	$-0.508243\pi$
$317$	14.7224	−	8.50000i	0.826894	−	0.477408i	0.852788	+	0.522257i	$0.174910\pi$
$318$		0			0
$319$		0			0
$320$	−0.656712	+	2.13746i	−0.0367113	+	0.119488i
$321$		0			0
$322$	7.54983	−	4.35890i	0.420736	−	0.242912i
$323$			24.0000i			1.33540i
$324$		0			0
$325$		0			0
$326$	8.71780	+	15.0997i	0.482834	+	0.836293i
$327$		0			0
$328$	−7.54983	−	4.35890i	−0.416870	−	0.240680i
$329$	4.35890	−	7.54983i	0.240314	−	0.416236i
$330$		0			0
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	0.695266	−	0.718752i	$-0.255287\pi$
$331$	−5.00000	−	8.66025i	−0.274825	−	0.476011i	−0.970091	+	0.242742i	$0.921953\pi$
$332$			5.00000i			0.274411i
$333$		0			0
$334$	18.0000			0.984916
$335$	14.2750	−	13.2749i	0.779928	−	0.725286i
$336$		0			0
$337$	15.0997	+	8.71780i	0.822531	+	0.474889i	0.851289	−	0.524698i	$-0.175822\pi$
$337$	15.0997	+	8.71780i	0.822531	+	0.474889i	−0.0287572	+	0.999586i	$0.509155\pi$
$338$	11.2583	+	6.50000i	0.612372	+	0.353553i
$339$		0			0
$340$	−6.54983	+	6.09095i	−0.355215	+	0.330328i
$341$	−30.5123			−1.65233
$342$		0			0
$343$			21.7945i			1.17679i
$344$	−4.35890	−	7.54983i	−0.235016	−	0.407060i
$345$		0			0
$346$	9.50000	−	16.4545i	0.510723	−	0.884598i
$347$	23.3827	+	13.5000i	1.25525	+	0.724718i	0.972147	−	0.234372i	$-0.0753034\pi$
$347$	23.3827	+	13.5000i	1.25525	+	0.724718i	0.283101	+	0.959090i	$0.408637\pi$
$348$		0			0
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	0.615581	−	0.788074i	$-0.288921\pi$
$349$	−7.00000	−	12.1244i	−0.374701	−	0.649002i	−0.990282	+	0.139072i	$0.955588\pi$
$350$	−19.6150	+	9.50000i	−1.04847	+	0.507796i
$351$		0			0
$352$			4.35890i			0.232330i
$353$	22.5167	−	13.0000i	1.19844	−	0.691920i	0.238233	−	0.971208i	$-0.423432\pi$
$353$	22.5167	−	13.0000i	1.19844	−	0.691920i	0.960207	+	0.279288i	$0.0900983\pi$
$354$		0			0
$355$		0			0
$356$	−4.35890	+	7.54983i	−0.231021	+	0.400140i
$357$		0			0
$358$	−18.8746	+	10.8972i	−0.997553	+	0.575937i
$359$	−26.1534			−1.38032			−0.690162	−	0.723655i	$-0.742461\pi$
$359$	−26.1534			−1.38032			−0.690162	+	0.723655i	$0.742461\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	−6.92820	+	4.00000i	−0.364138	+	0.210235i
$363$		0			0
$364$		0			0
$365$	9.31697	+	2.86254i	0.487672	+	0.149832i
$366$		0			0
$367$	−3.77492	+	2.17945i	−0.197049	+	0.113766i	−0.595278	−	0.803520i	$-0.702958\pi$
$367$	−3.77492	+	2.17945i	−0.197049	+	0.113766i	0.398229	+	0.917286i	$0.369625\pi$
$368$		−	2.00000i		−	0.104257i
$369$		0			0
$370$	−19.0000	+	4.35890i	−0.987763	+	0.226608i
$371$	6.53835	+	11.3248i	0.339454	+	0.587952i
$372$		0			0
$373$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$373$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$374$	−8.71780	+	15.0997i	−0.450787	+	0.780785i
$375$		0			0
$376$	−1.00000	−	1.73205i	−0.0515711	−	0.0893237i
$377$		0			0
$378$		0			0
$379$	4.00000			0.205466			0.102733	−	0.994709i	$-0.467241\pi$
$379$	4.00000			0.205466			0.102733	+	0.994709i	$0.467241\pi$
$380$	9.13642	+	9.82475i	0.468689	+	0.503999i
$381$		0			0
$382$		0			0
$383$	3.46410	+	2.00000i	0.177007	+	0.102195i	0.585886	−	0.810394i	$-0.300747\pi$
$383$	3.46410	+	2.00000i	0.177007	+	0.102195i	−0.408879	+	0.912589i	$0.634080\pi$
$384$		0			0
$385$	−31.1117	+	28.9320i	−1.58560	+	1.47451i
$386$	−21.7945			−1.10931
$387$		0			0
$388$		−	4.35890i		−	0.221290i
$389$	−2.17945	−	3.77492i	−0.110502	−	0.191396i	0.805470	−	0.592636i	$-0.201913\pi$
$389$	−2.17945	−	3.77492i	−0.110502	−	0.191396i	−0.915973	+	0.401240i	$0.868579\pi$
$390$		0			0
$391$	4.00000	−	6.92820i	0.202289	−	0.350374i
$392$	10.3923	+	6.00000i	0.524891	+	0.303046i
$393$		0			0
$394$	2.50000	+	4.33013i	0.125948	+	0.218149i
$395$		0			0
$396$		0			0
$397$			34.8712i			1.75013i	0.484001	+	0.875067i	$0.339183\pi$
$397$			34.8712i			1.75013i	−0.484001	+	0.875067i	$0.660817\pi$
$398$	−2.59808	+	1.50000i	−0.130230	+	0.0751882i
$399$		0			0
$400$	−0.362541	+	4.98684i	−0.0181271	+	0.249342i
$401$	17.4356	−	30.1993i	0.870692	−	1.50808i	0.00941009	−	0.999956i	$-0.497005\pi$
$401$	17.4356	−	30.1993i	0.870692	−	1.50808i	0.861282	−	0.508127i	$-0.169662\pi$
$402$		0			0
$403$		0			0
$404$	−4.35890			−0.216863
$405$		0			0
$406$		0			0
$407$	−32.9090	+	19.0000i	−1.63124	+	0.941795i
$408$		0			0
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	0.173064	+	0.984911i	$0.444633\pi$
$409$	−15.5000	+	26.8468i	−0.766426	+	1.32749i	−0.939490	+	0.342578i	$0.888700\pi$
$410$	−18.6339	−	5.72508i	−0.920264	−	0.282742i
$411$		0			0
$412$	−7.54983	+	4.35890i	−0.371954	+	0.214748i
$413$		−	38.0000i		−	1.86986i
$414$		0			0
$415$	2.50000	+	10.8972i	0.122720	+	0.534925i
$416$		0			0
$417$		0			0
$418$	22.6495	+	13.0767i	1.10782	+	0.639602i
$419$	4.35890	−	7.54983i	0.212946	−	0.368834i	−0.739689	−	0.672949i	$-0.765027\pi$
$419$	4.35890	−	7.54983i	0.212946	−	0.368834i	0.952635	+	0.304115i	$0.0983608\pi$
$420$		0			0
$421$	−8.00000	−	13.8564i	−0.389896	−	0.675320i	0.602539	−	0.798089i	$-0.294156\pi$
$421$	−8.00000	−	13.8564i	−0.389896	−	0.675320i	−0.992435	+	0.122769i	$0.960822\pi$
$422$		−	6.00000i		−	0.292075i
$423$		0			0
$424$	3.00000			0.145693
$425$	−11.2296	+	16.5498i	−0.544714	+	0.802785i
$426$		0			0
$427$	−15.0997	−	8.71780i	−0.730724	−	0.421884i
$428$	−12.9904	−	7.50000i	−0.627914	−	0.362526i
$429$		0			0
$430$	−13.2749	−	14.2750i	−0.640173	−	0.688403i
$431$	8.71780			0.419922			0.209961	−	0.977710i	$-0.432666\pi$
$431$	8.71780			0.419922			0.209961	+	0.977710i	$0.432666\pi$
$432$		0			0
$433$		−	21.7945i		−	1.04738i	−0.851910	−	0.523688i	$-0.824556\pi$
$433$		−	21.7945i		−	1.04738i	0.851910	−	0.523688i	$-0.175444\pi$
$434$	15.2561	+	26.4244i	0.732318	+	1.26841i
$435$		0			0
$436$	−5.00000	+	8.66025i	−0.239457	+	0.414751i
$437$	−10.3923	−	6.00000i	−0.497131	−	0.287019i
$438$		0			0
$439$	4.50000	+	7.79423i	0.214773	+	0.371998i	0.953202	−	0.302333i	$-0.0977654\pi$
$439$	4.50000	+	7.79423i	0.214773	+	0.371998i	−0.738429	+	0.674331i	$0.764432\pi$
$440$	2.17945	+	9.50000i	0.103901	+	0.452895i
$441$		0			0
$442$		0			0
$443$	10.3923	−	6.00000i	0.493753	−	0.285069i	−0.232377	−	0.972626i	$-0.574650\pi$
$443$	10.3923	−	6.00000i	0.493753	−	0.285069i	0.726130	+	0.687557i	$0.241317\pi$
$444$		0			0
$445$	−5.72508	+	18.6339i	−0.271395	+	0.883333i
$446$	4.35890	−	7.54983i	0.206400	−	0.357495i
$447$		0			0
$448$	3.77492	−	2.17945i	0.178348	−	0.102969i
$449$	−26.1534			−1.23425			−0.617127	−	0.786863i	$-0.711704\pi$
$449$	−26.1534			−1.23425			−0.617127	+	0.786863i	$0.711704\pi$
$450$		0			0
$451$	−38.0000			−1.78935
$452$	15.5885	−	9.00000i	0.733219	−	0.423324i
$453$		0			0
$454$	2.00000	−	3.46410i	0.0938647	−	0.162578i
$455$		0			0
$456$		0			0
$457$	−3.77492	+	2.17945i	−0.176583	+	0.101950i	−0.585686	−	0.810538i	$-0.699175\pi$
$457$	−3.77492	+	2.17945i	−0.176583	+	0.101950i	0.409103	+	0.912488i	$0.365842\pi$
$458$		−	22.0000i		−	1.02799i
$459$		0			0
$460$	−1.00000	−	4.35890i	−0.0466252	−	0.203235i
$461$	−19.6150	−	33.9743i	−0.913564	−	1.58234i	−0.808991	−	0.587822i	$-0.799986\pi$
$461$	−19.6150	−	33.9743i	−0.913564	−	1.58234i	−0.104573	−	0.994517i	$-0.533348\pi$
$462$		0			0
$463$	−11.3248	−	6.53835i	−0.526306	−	0.303863i	0.213205	−	0.977007i	$-0.431610\pi$
$463$	−11.3248	−	6.53835i	−0.526306	−	0.303863i	−0.739511	+	0.673145i	$0.764943\pi$
$464$		0			0
$465$		0			0
$466$	−7.00000	−	12.1244i	−0.324269	−	0.561650i
$467$			21.0000i			0.971764i	0.874024	+	0.485882i	$0.161502\pi$
$467$			21.0000i			0.971764i	−0.874024	+	0.485882i	$0.838498\pi$
$468$		0			0
$469$	−38.0000			−1.75468
$470$	−3.04547	−	3.27492i	−0.140477	−	0.151061i
$471$		0			0
$472$	−7.54983	−	4.35890i	−0.347509	−	0.200635i
$473$	−32.9090	−	19.0000i	−1.51316	−	0.873621i
$474$		0			0
$475$	24.8248	+	16.8443i	1.13904	+	0.772871i
$476$	17.4356			0.799159
$477$		0			0
$478$			8.71780i			0.398743i
$479$	4.35890	+	7.54983i	0.199163	+	0.344961i	0.948257	−	0.317503i	$-0.102844\pi$
$479$	4.35890	+	7.54983i	0.199163	+	0.344961i	−0.749094	+	0.662464i	$0.769511\pi$
$480$		0			0
$481$		0			0
$482$	−12.1244	−	7.00000i	−0.552249	−	0.318841i
$483$		0			0
$484$	4.00000	+	6.92820i	0.181818	+	0.314918i
$485$	−2.17945	−	9.50000i	−0.0989637	−	0.431373i
$486$		0			0
$487$			26.1534i			1.18512i	0.805525	+	0.592562i	$0.201883\pi$
$487$			26.1534i			1.18512i	−0.805525	+	0.592562i	$0.798117\pi$
$488$	−3.46410	+	2.00000i	−0.156813	+	0.0905357i
$489$		0			0
$490$	25.6495	+	7.88054i	1.15873	+	0.356007i
$491$	6.53835	−	11.3248i	0.295072	−	0.511079i	−0.679930	−	0.733277i	$-0.737990\pi$
$491$	6.53835	−	11.3248i	0.295072	−	0.511079i	0.975002	+	0.222198i	$0.0713232\pi$
$492$		0			0
$493$		0			0
$494$		0			0
$495$		0			0
$496$	7.00000			0.314309
$497$		0			0
$498$		0			0
$499$	15.0000	−	25.9808i	0.671492	−	1.16306i	−0.305989	−	0.952035i	$-0.598987\pi$
$499$	15.0000	−	25.9808i	0.671492	−	1.16306i	0.977481	−	0.211024i	$-0.0676797\pi$
$500$	1.70328	+	11.0498i	0.0761729	+	0.494164i
$501$		0			0
$502$	−22.6495	+	13.0767i	−1.01090	+	0.583642i
$503$			30.0000i			1.33763i	0.743427	+	0.668817i	$0.233199\pi$
$503$			30.0000i			1.33763i	−0.743427	+	0.668817i	$0.766801\pi$
$504$		0			0
$505$	−9.50000	+	2.17945i	−0.422744	+	0.0969842i
$506$	−4.35890	−	7.54983i	−0.193777	−	0.335631i
$507$		0			0
$508$	−3.77492	−	2.17945i	−0.167485	−	0.0966974i
$509$	−6.53835	+	11.3248i	−0.289807	+	0.501961i	−0.973764	−	0.227562i	$-0.926925\pi$
$509$	−6.53835	+	11.3248i	−0.289807	+	0.501961i	0.683956	+	0.729523i	$0.260258\pi$
$510$		0			0
$511$	−9.50000	−	16.4545i	−0.420255	−	0.727903i
$512$		−	1.00000i		−	0.0441942i
$513$		0			0
$514$	12.0000			0.529297
$515$	−14.2750	+	13.2749i	−0.629033	+	0.584963i
$516$		0			0
$517$	−7.54983	−	4.35890i	−0.332041	−	0.191704i
$518$	32.9090	+	19.0000i	1.44594	+	0.834812i
$519$		0			0
$520$		0			0
$521$	17.4356			0.763867			0.381934	−	0.924190i	$-0.375258\pi$
$521$	17.4356			0.763867			0.381934	+	0.924190i	$0.375258\pi$
$522$		0			0
$523$			34.8712i			1.52481i	0.647100	+	0.762405i	$0.275982\pi$
$523$			34.8712i			1.52481i	−0.647100	+	0.762405i	$0.724018\pi$
$524$	−6.53835	−	11.3248i	−0.285629	−	0.494724i
$525$		0			0
$526$	1.00000	−	1.73205i	0.0436021	−	0.0755210i
$527$	24.2487	+	14.0000i	1.05629	+	0.609850i
$528$		0			0
$529$	−9.50000	−	16.4545i	−0.413043	−	0.715412i
$530$	6.53835	−	1.50000i	0.284008	−	0.0651558i
$531$		0			0
$532$		−	26.1534i		−	1.13389i
$533$		0			0
$534$		0			0
$535$	−32.0619	−	9.85068i	−1.38616	−	0.425882i
$536$	−4.35890	+	7.54983i	−0.188276	+	0.326103i
$537$		0			0
$538$		0			0
$539$	52.3068			2.25301
$540$		0			0
$541$	40.0000			1.71973			0.859867	−	0.510518i	$-0.170546\pi$
$541$	40.0000			1.71973			0.859867	+	0.510518i	$0.170546\pi$
$542$	4.33013	−	2.50000i	0.185995	−	0.107384i
$543$		0			0
$544$	2.00000	−	3.46410i	0.0857493	−	0.148522i
$545$	−6.56712	+	21.3746i	−0.281305	+	0.915587i
$546$		0			0
$547$	−15.0997	+	8.71780i	−0.645615	+	0.372746i	−0.786774	−	0.617241i	$-0.788250\pi$
$547$	−15.0997	+	8.71780i	−0.645615	+	0.372746i	0.141159	+	0.989987i	$0.454917\pi$
$548$		−	18.0000i		−	0.768922i
$549$		0			0
$550$	9.50000	+	19.6150i	0.405081	+	0.836388i
$551$		0			0
$552$		0			0
$553$		0			0
$554$	8.71780	−	15.0997i	0.370384	−	0.641523i
$555$		0			0
$556$	−2.00000	−	3.46410i	−0.0848189	−	0.146911i
$557$			33.0000i			1.39825i	0.714997	+	0.699127i	$0.246428\pi$
$557$			33.0000i			1.39825i	−0.714997	+	0.699127i	$0.753572\pi$
$558$		0			0
$559$		0			0
$560$	7.13752	−	6.63746i	0.301615	−	0.280484i
$561$		0			0
$562$		0			0
$563$	−9.52628	−	5.50000i	−0.401485	−	0.231797i	0.285640	−	0.958337i	$-0.407794\pi$
$563$	−9.52628	−	5.50000i	−0.401485	−	0.231797i	−0.687124	+	0.726540i	$0.741127\pi$
$564$		0			0
$565$	29.4743	−	27.4093i	1.23999	−	1.15312i
$566$	8.71780			0.366436
$567$		0			0
$568$		0			0
$569$	−8.71780	−	15.0997i	−0.365469	−	0.633011i	0.623382	−	0.781917i	$-0.285758\pi$
$569$	−8.71780	−	15.0997i	−0.365469	−	0.633011i	−0.988851	+	0.148906i	$0.952425\pi$
$570$		0			0
$571$	−8.00000	+	13.8564i	−0.334790	+	0.579873i	−0.983444	−	0.181210i	$-0.941999\pi$
$571$	−8.00000	+	13.8564i	−0.334790	+	0.579873i	0.648655	+	0.761083i	$0.275332\pi$
$572$		0			0
$573$		0			0
$574$	19.0000	+	32.9090i	0.793045	+	1.37359i
$575$	−4.35890	−	9.00000i	−0.181779	−	0.375326i
$576$		0			0
$577$		−	17.4356i		−	0.725853i	−0.931818	−	0.362927i	$-0.881778\pi$
$577$		−	17.4356i		−	0.725853i	0.931818	−	0.362927i	$-0.118222\pi$
$578$	−0.866025	+	0.500000i	−0.0360219	+	0.0207973i
$579$		0			0
$580$		0			0
$581$	10.8972	−	18.8746i	0.452094	−	0.783050i
$582$		0			0
$583$	11.3248	−	6.53835i	0.469023	−	0.270791i
$584$	−4.35890			−0.180373
$585$		0			0
$586$	−6.00000			−0.247858
$587$	−2.59808	+	1.50000i	−0.107234	+	0.0619116i	−0.552658	−	0.833408i	$-0.686386\pi$
$587$	−2.59808	+	1.50000i	−0.107234	+	0.0619116i	0.445424	+	0.895320i	$0.353053\pi$
$588$		0			0
$589$	21.0000	−	36.3731i	0.865290	−	1.49873i
$590$	−18.6339	−	5.72508i	−0.767147	−	0.235698i
$591$		0			0
$592$	7.54983	−	4.35890i	0.310296	−	0.179150i
$593$		−	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
$595$	38.0000	−	8.71780i	1.55785	−	0.357395i
$596$	−2.17945	−	3.77492i	−0.0892737	−	0.154627i
$597$		0			0
$598$		0			0
$599$	−13.0767	+	22.6495i	−0.534299	+	0.925434i	0.464898	+	0.885364i	$0.346091\pi$
$599$	−13.0767	+	22.6495i	−0.534299	+	0.925434i	−0.999197	+	0.0400691i	$0.987242\pi$
$600$		0			0
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	0.967600	−	0.252486i	$-0.0812483\pi$
$601$	6.50000	+	11.2583i	0.265141	+	0.459237i	−0.702460	+	0.711723i	$0.747915\pi$
$602$			38.0000i			1.54876i
$603$		0			0
$604$	11.0000			0.447584
$605$	12.1819	+	13.0997i	0.495265	+	0.532577i
$606$		0			0
$607$	7.54983	+	4.35890i	0.306438	+	0.176922i	0.645332	−	0.763903i	$-0.276719\pi$
$607$	7.54983	+	4.35890i	0.306438	+	0.176922i	−0.338893	+	0.940825i	$0.610053\pi$
$608$	−5.19615	−	3.00000i	−0.210732	−	0.121666i
$609$		0			0
$610$	−6.54983	+	6.09095i	−0.265195	+	0.246615i
$611$		0			0
$612$		0			0
$613$		−	8.71780i		−	0.352109i	−0.984380	−	0.176054i	$-0.943667\pi$
$613$		−	8.71780i		−	0.352109i	0.984380	−	0.176054i	$-0.0563334\pi$
$614$		0			0
$615$		0			0
$616$	9.50000	−	16.4545i	0.382766	−	0.662970i
$617$	−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
$619$	16.0000	+	27.7128i	0.643094	+	1.11387i	0.984738	+	0.174042i	$0.0556830\pi$
$619$	16.0000	+	27.7128i	0.643094	+	1.11387i	−0.341644	+	0.939829i	$0.610984\pi$
$620$	15.2561	−	3.50000i	0.612702	−	0.140563i
$621$		0			0
$622$		−	26.1534i		−	1.04866i
$623$	32.9090	−	19.0000i	1.31847	−	0.761219i
$624$		0			0
$625$	9.23713	+	23.2309i	0.369485	+	0.929237i
$626$	10.8972	−	18.8746i	0.435542	−	0.754380i
$627$		0			0
$628$	−15.0997	+	8.71780i	−0.602542	+	0.347878i
$629$	34.8712			1.39041
$630$		0			0
$631$	5.00000			0.199047			0.0995234	−	0.995035i	$-0.468268\pi$
$631$	5.00000			0.199047			0.0995234	+	0.995035i	$0.468268\pi$
$632$		0			0
$633$		0			0
$634$	−8.50000	+	14.7224i	−0.337578	+	0.584702i
$635$	−9.31697	−	2.86254i	−0.369733	−	0.113596i
$636$		0			0
$637$		0			0
$638$		0			0
$639$		0			0
$640$	−0.500000	−	2.17945i	−0.0197642	−	0.0861503i
$641$	−4.35890	−	7.54983i	−0.172166	−	0.298201i	0.767011	−	0.641634i	$-0.221743\pi$
$641$	−4.35890	−	7.54983i	−0.172166	−	0.298201i	−0.939177	+	0.343434i	$0.888410\pi$
$642$		0			0
$643$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$643$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$644$	−4.35890	+	7.54983i	−0.171765	+	0.297505i
$645$		0			0
$646$	−12.0000	−	20.7846i	−0.472134	−	0.817760i
$647$			12.0000i			0.471769i	0.971781	+	0.235884i	$0.0757987\pi$
$647$			12.0000i			0.471769i	−0.971781	+	0.235884i	$0.924201\pi$
$648$		0			0
$649$	−38.0000			−1.49163
$650$		0			0
$651$		0			0
$652$	−15.0997	−	8.71780i	−0.591349	−	0.341415i
$653$	30.3109	+	17.5000i	1.18616	+	0.684828i	0.957431	−	0.288663i	$-0.0932107\pi$
$653$	30.3109	+	17.5000i	1.18616	+	0.684828i	0.228726	+	0.973491i	$0.426544\pi$
$654$		0			0
$655$	−19.9124	−	21.4125i	−0.778041	−	0.836658i
$656$	8.71780			0.340373
$657$		0			0
$658$			8.71780i			0.339855i
$659$	2.17945	+	3.77492i	0.0848993	+	0.147050i	0.905348	−	0.424670i	$-0.139610\pi$
$659$	2.17945	+	3.77492i	0.0848993	+	0.147050i	−0.820449	+	0.571720i	$0.806276\pi$
$660$		0			0
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	−0.568831	−	0.822454i	$-0.692604\pi$
$661$	11.0000	−	19.0526i	0.427850	−	0.741059i	0.996682	+	0.0813955i	$0.0259377\pi$
$662$	8.66025	+	5.00000i	0.336590	+	0.194331i
$663$		0			0
$664$	−2.50000	−	4.33013i	−0.0970188	−	0.168042i
$665$	−13.0767	−	57.0000i	−0.507093	−	2.21037i
$666$		0			0
$667$		0			0
$668$	−15.5885	+	9.00000i	−0.603136	+	0.348220i
$669$		0			0
$670$	−5.72508	+	18.6339i	−0.221179	+	0.719892i
$671$	−8.71780	+	15.0997i	−0.336547	+	0.582916i
$672$		0			0
$673$	−11.3248	+	6.53835i	−0.436537	+	0.252035i	−0.702128	−	0.712051i	$-0.747766\pi$
$673$	−11.3248	+	6.53835i	−0.436537	+	0.252035i	0.265591	+	0.964086i	$0.414433\pi$
$674$	−17.4356			−0.671594
$675$		0			0
$676$	−13.0000			−0.500000
$677$	22.5167	−	13.0000i	0.865386	−	0.499631i	−0.000426509	−	1.00000i	$-0.500136\pi$
$677$	22.5167	−	13.0000i	0.865386	−	0.499631i	0.865812	+	0.500369i	$0.166802\pi$
$678$		0			0
$679$	−9.50000	+	16.4545i	−0.364577	+	0.631465i
$680$	2.62685	−	8.54983i	0.100735	−	0.327871i
$681$		0			0
$682$	26.4244	−	15.2561i	1.01184	−	0.584188i
$683$		−	20.0000i		−	0.765279i	−0.923898	−	0.382639i	$-0.875015\pi$
$683$		−	20.0000i		−	0.765279i	0.923898	−	0.382639i	$-0.124985\pi$
$684$		0			0
$685$	−9.00000	−	39.2301i	−0.343872	−	1.49890i
$686$	−10.8972	−	18.8746i	−0.416059	−	0.720635i
$687$		0			0
$688$	7.54983	+	4.35890i	0.287835	+	0.166181i
$689$		0			0
$690$		0			0
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	0.991122	−	0.132956i	$-0.0424468\pi$
$691$	10.0000	+	17.3205i	0.380418	+	0.658903i	−0.610704	+	0.791859i	$0.709113\pi$
$692$			19.0000i			0.722272i
$693$		0			0
$694$	−27.0000			−1.02491
$695$	−6.09095	−	6.54983i	−0.231043	−	0.248449i
$696$		0			0
$697$	30.1993	+	17.4356i	1.14388	+	0.660420i
$698$	12.1244	+	7.00000i	0.458914	+	0.264954i
$699$		0			0
$700$	12.2371	−	18.0348i	0.462520	−	0.681650i
$701$	21.7945			0.823167			0.411583	−	0.911372i	$-0.364976\pi$
$701$	21.7945			0.823167			0.411583	+	0.911372i	$0.364976\pi$
$702$		0			0
$703$		−	52.3068i		−	1.97279i
$704$	−2.17945	−	3.77492i	−0.0821411	−	0.142273i
$705$		0			0
$706$	−13.0000	+	22.5167i	−0.489261	+	0.847426i
$707$	16.4545	+	9.50000i	0.618835	+	0.357284i
$708$		0			0
$709$	6.00000	+	10.3923i	0.225335	+	0.390291i	0.956420	−	0.291995i	$-0.0943191\pi$
$709$	6.00000	+	10.3923i	0.225335	+	0.390291i	−0.731085	+	0.682286i	$0.760986\pi$
$710$		0			0
$711$		0			0
$712$		−	8.71780i		−	0.326713i
$713$	−12.1244	+	7.00000i	−0.454061	+	0.262152i
$714$		0			0
$715$		0			0
$716$	10.8972	−	18.8746i	0.407249	−	0.705376i
$717$		0			0
$718$	22.6495	−	13.0767i	0.845272	−	0.488018i
$719$	−34.8712			−1.30048			−0.650238	−	0.759731i	$-0.725331\pi$
$719$	−34.8712			−1.30048			−0.650238	+	0.759731i	$0.725331\pi$
$720$		0			0
$721$	38.0000			1.41519
$722$	−14.7224	+	8.50000i	−0.547912	+	0.316337i
$723$		0			0
$724$	4.00000	−	6.92820i	0.148659	−	0.257485i
$725$		0			0
$726$		0			0
$727$	33.9743	−	19.6150i	1.26004	−	0.727482i	0.286954	−	0.957944i	$-0.407357\pi$
$727$	33.9743	−	19.6150i	1.26004	−	0.727482i	0.973081	+	0.230463i	$0.0740239\pi$
$728$		0			0
$729$		0			0
$730$	−9.50000	+	2.17945i	−0.351611	+	0.0806650i
$731$	17.4356	+	30.1993i	0.644879	+	1.11696i
$732$		0			0
$733$	−7.54983	−	4.35890i	−0.278859	−	0.161000i	0.354047	−	0.935227i	$-0.384805\pi$
$733$	−7.54983	−	4.35890i	−0.278859	−	0.161000i	−0.632907	+	0.774228i	$0.718138\pi$
$734$	2.17945	−	3.77492i	0.0804449	−	0.139335i
$735$		0			0
$736$	1.00000	+	1.73205i	0.0368605	+	0.0638442i
$737$			38.0000i			1.39975i
$738$		0			0
$739$	−16.0000			−0.588570			−0.294285	−	0.955718i	$-0.595081\pi$
$739$	−16.0000			−0.588570			−0.294285	+	0.955718i	$0.595081\pi$
$740$	14.2750	−	13.2749i	0.524761	−	0.487996i
$741$		0			0
$742$	−11.3248	−	6.53835i	−0.415745	−	0.240030i
$743$	−41.5692	−	24.0000i	−1.52503	−	0.880475i	−0.999560	−	0.0296605i	$-0.990557\pi$
$743$	−41.5692	−	24.0000i	−1.52503	−	0.880475i	−0.525467	−	0.850814i	$-0.676109\pi$
$744$		0			0
$745$	−6.63746	−	7.13752i	−0.243178	−	0.261498i
$746$		0			0
$747$		0			0
$748$		−	17.4356i		−	0.637509i
$749$	32.6917	+	56.6238i	1.19453	+	2.06899i
$750$		0			0
$751$	−17.5000	+	30.3109i	−0.638584	+	1.10606i	0.347160	+	0.937806i	$0.387146\pi$
$751$	−17.5000	+	30.3109i	−0.638584	+	1.10606i	−0.985744	+	0.168254i	$0.946187\pi$
$752$	1.73205	+	1.00000i	0.0631614	+	0.0364662i
$753$		0			0
$754$		0			0
$755$	23.9739	−	5.50000i	0.872501	−	0.200165i
$756$		0			0
$757$			8.71780i			0.316854i	0.987371	+	0.158427i	$0.0506422\pi$
$757$			8.71780i			0.316854i	−0.987371	+	0.158427i	$0.949358\pi$
$758$	−3.46410	+	2.00000i	−0.125822	+	0.0726433i
$759$		0			0
$760$	−12.8248	−	3.94027i	−0.465203	−	0.142929i
$761$	−26.1534	+	45.2990i	−0.948060	+	1.64209i	−0.198554	+	0.980090i	$0.563625\pi$
$761$	−26.1534	+	45.2990i	−0.948060	+	1.64209i	−0.749506	+	0.661998i	$0.769709\pi$
$762$		0			0
$763$	37.7492	−	21.7945i	1.36661	−	0.789014i
$764$		0			0
$765$		0			0
$766$	−4.00000			−0.144526
$767$		0			0
$768$		0			0
$769$	4.50000	−	7.79423i	0.162274	−	0.281067i	−0.773410	−	0.633906i	$-0.781450\pi$
$769$	4.50000	−	7.79423i	0.162274	−	0.281067i	0.935684	+	0.352839i	$0.114784\pi$
$770$	12.4775	−	40.6117i	0.449659	−	1.46354i
$771$		0			0
$772$	18.8746	−	10.8972i	0.679311	−	0.392201i
$773$			18.0000i			0.647415i	0.946157	+	0.323708i	$0.104929\pi$
$773$			18.0000i			0.647415i	−0.946157	+	0.323708i	$0.895071\pi$
$774$		0			0
$775$	31.5000	−	15.2561i	1.13151	−	0.548017i
$776$	2.17945	+	3.77492i	0.0782377	+	0.135512i
$777$		0			0
$778$	3.77492	+	2.17945i	0.135337	+	0.0781370i
$779$	26.1534	−	45.2990i	0.937043	−	1.62301i
$780$		0			0
$781$		0			0
$782$			8.00000i			0.286079i
$783$		0			0
$784$	−12.0000			−0.428571
$785$	−28.5501	+	26.5498i	−1.01900	+	0.947604i
$786$		0			0
$787$	15.0997	+	8.71780i	0.538245	+	0.310756i	0.744367	−	0.667770i	$-0.232751\pi$
$787$	15.0997	+	8.71780i	0.538245	+	0.310756i	−0.206122	+	0.978526i	$0.566084\pi$
$788$	−4.33013	−	2.50000i	−0.154254	−	0.0890588i
$789$		0			0
$790$		0			0
$791$	−78.4602			−2.78972
$792$		0			0
$793$		0			0
$794$	−17.4356	−	30.1993i	−0.618766	−	1.07173i
$795$		0			0
$796$	1.50000	−	2.59808i	0.0531661	−	0.0920864i
$797$	32.0429	+	18.5000i	1.13502	+	0.655304i	0.945192	−	0.326514i	$-0.105874\pi$
$797$	32.0429	+	18.5000i	1.13502	+	0.655304i	0.189827	+	0.981818i	$0.439207\pi$
$798$		0			0
$799$	4.00000	+	6.92820i	0.141510	+	0.245102i
$800$	−2.17945	−	4.50000i	−0.0770552	−	0.159099i
$801$		0			0
$802$			34.8712i			1.23134i
$803$	−16.4545	+	9.50000i	−0.580666	+	0.335248i
$804$		0			0
$805$	−5.72508	+	18.6339i	−0.201783	+	0.656760i
$806$		0			0
$807$		0			0
$808$	3.77492	−	2.17945i	0.132801	−	0.0766728i
$809$	−26.1534			−0.919504			−0.459752	−	0.888047i	$-0.652062\pi$
$809$	−26.1534			−0.919504			−0.459752	+	0.888047i	$0.652062\pi$
$810$		0			0
$811$	−14.0000			−0.491606			−0.245803	−	0.969320i	$-0.579052\pi$
$811$	−14.0000			−0.491606			−0.245803	+	0.969320i	$0.579052\pi$
$812$		0			0
$813$		0			0
$814$	19.0000	−	32.9090i	0.665950	−	1.15346i
$815$	−37.2679	−	11.4502i	−1.30544	−	0.401082i
$816$		0			0
$817$	45.2990	−	26.1534i	1.58481	−	0.914991i
$818$		−	31.0000i		−	1.08389i
$819$		0			0
$820$	19.0000	−	4.35890i	0.663509	−	0.152219i
$821$	17.4356	+	30.1993i	0.608506	+	1.05396i	0.991487	+	0.130208i	$0.0415644\pi$
$821$	17.4356	+	30.1993i	0.608506	+	1.05396i	−0.382980	+	0.923757i	$0.625102\pi$
$822$		0			0
$823$	33.9743	+	19.6150i	1.18427	+	0.683737i	0.956998	−	0.290094i	$-0.0936867\pi$
$823$	33.9743	+	19.6150i	1.18427	+	0.683737i	0.227270	+	0.973832i	$0.427020\pi$
$824$	4.35890	−	7.54983i	0.151849	−	0.263011i
$825$		0			0
$826$	19.0000	+	32.9090i	0.661095	+	1.14505i
$827$		−	16.0000i		−	0.556375i	−0.960527	−	0.278187i	$-0.910266\pi$
$827$		−	16.0000i		−	0.556375i	0.960527	−	0.278187i	$-0.0897336\pi$
$828$		0			0
$829$	42.0000			1.45872			0.729360	−	0.684130i	$-0.239818\pi$
$829$	42.0000			1.45872			0.729360	+	0.684130i	$0.239818\pi$
$830$	−7.61369	−	8.18729i	−0.264275	−	0.284185i
$831$		0			0
$832$		0			0
$833$	−41.5692	−	24.0000i	−1.44029	−	0.831551i
$834$		0			0
$835$	−29.4743	+	27.4093i	−1.02000	+	0.948537i
$836$	−26.1534			−0.904534
$837$		0			0
$838$			8.71780i			0.301151i
$839$	−17.4356	−	30.1993i	−0.601944	−	1.04260i	−0.992527	−	0.122029i	$-0.961060\pi$
$839$	−17.4356	−	30.1993i	−0.601944	−	1.04260i	0.390583	−	0.920568i	$-0.372273\pi$
$840$		0			0
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	13.8564	+	8.00000i	0.477523	+	0.275698i
$843$		0			0
$844$	3.00000	+	5.19615i	0.103264	+	0.178859i
$845$	−28.3328	+	6.50000i	−0.974679	+	0.223607i
$846$		0			0
$847$		−	34.8712i		−	1.19819i
$848$	−2.59808	+	1.50000i	−0.0892183	+	0.0515102i
$849$		0			0
$850$	1.45017	−	19.9474i	0.0497403	−	0.684189i
$851$	−8.71780	+	15.0997i	−0.298842	+	0.517610i
$852$		0			0
$853$	7.54983	−	4.35890i	0.258501	−	0.149246i	−0.365149	−	0.930949i	$-0.618982\pi$
$853$	7.54983	−	4.35890i	0.258501	−	0.149246i	0.623651	+	0.781703i	$0.285649\pi$
$854$	17.4356			0.596634
$855$		0			0
$856$	15.0000			0.512689
$857$	−41.5692	+	24.0000i	−1.41998	+	0.819824i	−0.996296	−	0.0859870i	$-0.972596\pi$
$857$	−41.5692	+	24.0000i	−1.41998	+	0.819824i	−0.423681	+	0.905811i	$0.639262\pi$
$858$		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	$0.0558348\pi$
$860$	18.6339	+	5.72508i	0.635412	+	0.195224i
$861$		0			0
$862$	−7.54983	+	4.35890i	−0.257148	+	0.148465i
$863$		−	48.0000i		−	1.63394i	−0.576681	−	0.816970i	$-0.695652\pi$
$863$		−	48.0000i		−	1.63394i	0.576681	−	0.816970i	$-0.304348\pi$
$864$		0			0
$865$	9.50000	+	41.4095i	0.323010	+	1.40797i
$866$	10.8972	+	18.8746i	0.370304	+	0.641385i
$867$		0			0
$868$	−26.4244	−	15.2561i	−0.896903	−	0.517827i
$869$		0			0
$870$		0			0
$871$		0			0
$872$		−	10.0000i		−	0.338643i
$873$		0			0
$874$	12.0000			0.405906
$875$	17.6528	−	45.4244i	0.596774	−	1.53563i
$876$		0			0
$877$	7.54983	+	4.35890i	0.254940	+	0.147190i	0.622024	−	0.782998i	$-0.286311\pi$
$877$	7.54983	+	4.35890i	0.254940	+	0.147190i	−0.367084	+	0.930188i	$0.619644\pi$
$878$	−7.79423	−	4.50000i	−0.263042	−	0.151868i
$879$		0			0
$880$	−6.63746	−	7.13752i	−0.223749	−	0.240606i
$881$		0			0			−	1.00000i	$-0.5\pi$
$881$		0			0				1.00000i	$0.5\pi$
$882$		0			0
$883$		−	26.1534i		−	0.880132i	−0.897965	−	0.440066i	$-0.854955\pi$
$883$		−	26.1534i		−	0.880132i	0.897965	−	0.440066i	$-0.145045\pi$
$884$		0			0
$885$		0			0
$886$	−6.00000	+	10.3923i	−0.201574	+	0.349136i
$887$	20.7846	+	12.0000i	0.697879	+	0.402921i	0.806557	−	0.591156i	$-0.201328\pi$
$887$	20.7846	+	12.0000i	0.697879	+	0.402921i	−0.108678	+	0.994077i	$0.534662\pi$
$888$		0			0
$889$	9.50000	+	16.4545i	0.318620	+	0.551866i
$890$	−4.35890	−	19.0000i	−0.146111	−	0.636881i
$891$		0			0
$892$			8.71780i			0.291893i
$893$	10.3923	−	6.00000i	0.347765	−	0.200782i
$894$		0			0
$895$	14.3127	−	46.5848i	0.478421	−	1.55716i
$896$	−2.17945	+	3.77492i	−0.0728103	+	0.126111i
$897$		0			0
$898$	22.6495	−	13.0767i	0.755824	−	0.436375i
$899$		0			0
$900$		0			0
$901$	−12.0000			−0.399778
$902$	32.9090	−	19.0000i	1.09575	−	0.632631i
$903$		0			0
$904$	−9.00000	+	15.5885i	−0.299336	+	0.518464i
$905$	5.25370	−	17.0997i	0.174639	−	0.568412i
$906$		0			0
$907$	−22.6495	+	13.0767i	−0.752064	+	0.434205i	−0.826439	−	0.563026i	$-0.809637\pi$
$907$	−22.6495	+	13.0767i	−0.752064	+	0.434205i	0.0743749	+	0.997230i	$0.476304\pi$
$908$			4.00000i			0.132745i
$909$		0			0
$910$		0			0
$911$	13.0767	+	22.6495i	0.433250	+	0.750412i	0.997151	−	0.0754311i	$-0.0240333\pi$
$911$	13.0767	+	22.6495i	0.433250	+	0.750412i	−0.563901	+	0.825843i	$0.690700\pi$
$912$		0			0
$913$	−18.8746	−	10.8972i	−0.624658	−	0.360646i
$914$	2.17945	−	3.77492i	0.0720898	−	0.124863i
$915$		0			0
$916$	11.0000	+	19.0526i	0.363450	+	0.629514i
$917$			57.0000i			1.88231i
$918$		0			0
$919$	−39.0000			−1.28649			−0.643246	−	0.765660i	$-0.722413\pi$
$919$	−39.0000			−1.28649			−0.643246	+	0.765660i	$0.722413\pi$
$920$	3.04547	+	3.27492i	0.100406	+	0.107971i
$921$		0			0
$922$	33.9743	+	19.6150i	1.11888	+	0.645987i
$923$		0			0
$924$		0			0
$925$	24.4743	−	36.0695i	0.804709	−	1.18596i
$926$	13.0767			0.429727
$927$		0			0
$928$		0			0
$929$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$929$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$930$		0			0
$931$	−36.0000	+	62.3538i	−1.17985	+	2.04356i
$932$	12.1244	+	7.00000i	0.397146	+	0.229293i
$933$		0			0
$934$	−10.5000	−	18.1865i	−0.343570	−	0.595082i
$935$	−8.71780	−	38.0000i	−0.285102	−	1.24273i
$936$		0			0
$937$		−	47.9479i		−	1.56639i	−0.621777	−	0.783195i	$-0.713589\pi$
$937$		−	47.9479i		−	1.56639i	0.621777	−	0.783195i	$-0.286411\pi$
$938$	32.9090	−	19.0000i	1.07452	−	0.620372i
$939$		0			0
$940$	4.27492	+	1.31342i	0.139432	+	0.0428392i
$941$	−23.9739	+	41.5241i	−0.781528	+	1.35365i	0.149523	+	0.988758i	$0.452226\pi$
$941$	−23.9739	+	41.5241i	−0.781528	+	1.35365i	−0.931051	+	0.364888i	$0.881107\pi$
$942$		0			0
$943$	−15.0997	+	8.71780i	−0.491713	+	0.283891i
$944$	8.71780			0.283740
$945$		0			0
$946$	38.0000			1.23549
$947$	−23.3827	+	13.5000i	−0.759835	+	0.438691i	−0.829237	−	0.558898i	$-0.811224\pi$
$947$	−23.3827	+	13.5000i	−0.759835	+	0.438691i	0.0694014	+	0.997589i	$0.477891\pi$
$948$		0			0
$949$		0			0
$950$	−29.9210	−	2.17525i	−0.970767	−	0.0705744i
$951$		0			0
$952$	−15.0997	+	8.71780i	−0.489383	+	0.282545i
$953$			32.0000i			1.03658i	0.855204	+	0.518291i	$0.173432\pi$
$953$			32.0000i			1.03658i	−0.855204	+	0.518291i	$0.826568\pi$
$954$		0			0
$955$		0			0
$956$	−4.35890	−	7.54983i	−0.140977	−	0.244179i
$957$		0			0
$958$	−7.54983	−	4.35890i	−0.243924	−	0.140830i
$959$	−39.2301	+	67.9485i	−1.26681	+	2.19417i
$960$		0			0
$961$	−9.00000	−	15.5885i	−0.290323	−	0.502853i
$962$		0			0
$963$		0			0
$964$	14.0000			0.450910
$965$	35.6876	−	33.1873i	1.14882	−	1.06834i
$966$		0			0
$967$	−26.4244	−	15.2561i	−0.849752	−	0.490605i	0.0108151	−	0.999942i	$-0.496557\pi$
$967$	−26.4244	−	15.2561i	−0.849752	−	0.490605i	−0.860567	+	0.509337i	$0.829891\pi$
$968$	−6.92820	−	4.00000i	−0.222681	−	0.128565i
$969$		0			0
$970$	6.63746	+	7.13752i	0.213116	+	0.229172i
$971$	39.2301			1.25895			0.629477	−	0.777019i	$-0.283269\pi$
$971$	39.2301			1.25895			0.629477	+	0.777019i	$0.283269\pi$
$972$		0			0
$973$			17.4356i			0.558960i
$974$	−13.0767	−	22.6495i	−0.419004	−	0.725737i
$975$		0			0
$976$	2.00000	−	3.46410i	0.0640184	−	0.110883i
$977$	15.5885	+	9.00000i	0.498719	+	0.287936i	0.728184	−	0.685381i	$-0.240364\pi$
$977$	15.5885	+	9.00000i	0.498719	+	0.287936i	−0.229465	+	0.973317i	$0.573698\pi$
$978$		0			0
$979$	−19.0000	−	32.9090i	−0.607243	−	1.05178i
$980$	−26.1534	+	6.00000i	−0.835440	+	0.191663i
$981$		0			0
$982$			13.0767i			0.417294i
$983$	−29.4449	+	17.0000i	−0.939145	+	0.542216i	−0.889692	−	0.456561i	$-0.849081\pi$
$983$	−29.4449	+	17.0000i	−0.939145	+	0.542216i	−0.0494530	+	0.998776i	$0.515748\pi$
$984$		0			0
$985$	−10.6873	−	3.28356i	−0.340525	−	0.104623i
$986$		0			0
$987$		0			0
$988$		0			0
$989$	−17.4356			−0.554420
$990$		0			0
$991$	−53.0000			−1.68360			−0.841800	−	0.539789i	$-0.818504\pi$
$991$	−53.0000			−1.68360			−0.841800	+	0.539789i	$0.818504\pi$
$992$	−6.06218	+	3.50000i	−0.192474	+	0.111125i
$993$		0			0
$994$		0			0
$995$	1.97014	−	6.41238i	0.0624575	−	0.203286i
$996$		0			0
$997$	−45.2990	+	26.1534i	−1.43463	+	0.828286i	−0.997470	−	0.0710953i	$-0.977351\pi$
$997$	−45.2990	+	26.1534i	−1.43463	+	0.828286i	−0.437164	+	0.899382i	$0.644017\pi$
$998$			30.0000i			0.949633i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	810.2.i.h.109.2		8
3.2	odd	2	inner	810.2.i.h.109.3		8
5.4	even	2	inner	810.2.i.h.109.4		8
9.2	odd	6	inner	810.2.i.h.379.1		8
9.4	even	3		270.2.c.c.109.1	✓	4
9.5	odd	6		270.2.c.c.109.4	yes	4
9.7	even	3	inner	810.2.i.h.379.4		8
15.14	odd	2	inner	810.2.i.h.109.1		8
36.23	even	6		2160.2.f.m.1729.3		4
36.31	odd	6		2160.2.f.m.1729.2		4
45.4	even	6		270.2.c.c.109.3	yes	4
45.13	odd	12		1350.2.a.w.1.1		2
45.14	odd	6		270.2.c.c.109.2	yes	4
45.22	odd	12		1350.2.a.x.1.2		2
45.23	even	12		1350.2.a.x.1.1		2
45.29	odd	6	inner	810.2.i.h.379.3		8
45.32	even	12		1350.2.a.w.1.2		2
45.34	even	6	inner	810.2.i.h.379.2		8
180.59	even	6		2160.2.f.m.1729.4		4
180.139	odd	6		2160.2.f.m.1729.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
270.2.c.c.109.1	✓	4	9.4	even	3
270.2.c.c.109.2	yes	4	45.14	odd	6
270.2.c.c.109.3	yes	4	45.4	even	6
270.2.c.c.109.4	yes	4	9.5	odd	6
810.2.i.h.109.1		8	15.14	odd	2	inner
810.2.i.h.109.2		8	1.1	even	1	trivial
810.2.i.h.109.3		8	3.2	odd	2	inner
810.2.i.h.109.4		8	5.4	even	2	inner
810.2.i.h.379.1		8	9.2	odd	6	inner
810.2.i.h.379.2		8	45.34	even	6	inner
810.2.i.h.379.3		8	45.29	odd	6	inner
810.2.i.h.379.4		8	9.7	even	3	inner
1350.2.a.w.1.1		2	45.13	odd	12
1350.2.a.w.1.2		2	45.32	even	12
1350.2.a.x.1.1		2	45.23	even	12
1350.2.a.x.1.2		2	45.22	odd	12
2160.2.f.m.1729.1		4	180.139	odd	6
2160.2.f.m.1729.2		4	36.31	odd	6
2160.2.f.m.1729.3		4	36.23	even	6
2160.2.f.m.1729.4		4	180.59	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(-0.866025 + 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(0.656712 - 2.13746i) q^{5} +(-3.77492 + 2.17945i) q^{7} +1.00000i q^{8} +(0.500000 + 2.17945i) q^{10} +(2.17945 + 3.77492i) q^{11} +(2.17945 - 3.77492i) q^{14} +(-0.500000 - 0.866025i) q^{16} -4.00000i q^{17} -6.00000 q^{19} +(-1.52274 - 1.63746i) q^{20} +(-3.77492 - 2.17945i) q^{22} +(1.73205 + 1.00000i) q^{23} +(-4.13746 - 2.80739i) q^{25} +4.35890i q^{28} +(-3.50000 + 6.06218i) q^{31} +(0.866025 + 0.500000i) q^{32} +(2.00000 + 3.46410i) q^{34} +(2.17945 + 9.50000i) q^{35} +8.71780i q^{37} +(5.19615 - 3.00000i) q^{38} +(2.13746 + 0.656712i) q^{40} +(-4.35890 + 7.54983i) q^{41} +(-7.54983 + 4.35890i) q^{43} +4.35890 q^{44} -2.00000 q^{46} +(-1.73205 + 1.00000i) q^{47} +(6.00000 - 10.3923i) q^{49} +(4.98684 + 0.362541i) q^{50} -3.00000i q^{53} +(9.50000 - 2.17945i) q^{55} +(-2.17945 - 3.77492i) q^{56} +(-4.35890 + 7.54983i) q^{59} +(2.00000 + 3.46410i) q^{61} -7.00000i q^{62} -1.00000 q^{64} +(7.54983 + 4.35890i) q^{67} +(-3.46410 - 2.00000i) q^{68} +(-6.63746 - 7.13752i) q^{70} +4.35890i q^{73} +(-4.35890 - 7.54983i) q^{74} +(-3.00000 + 5.19615i) q^{76} +(-16.4545 - 9.50000i) q^{77} +(-2.17945 + 0.500000i) q^{80} -8.71780i q^{82} +(-4.33013 + 2.50000i) q^{83} +(-8.54983 - 2.62685i) q^{85} +(4.35890 - 7.54983i) q^{86} +(-3.77492 + 2.17945i) q^{88} -8.71780 q^{89} +(1.73205 - 1.00000i) q^{92} +(1.00000 - 1.73205i) q^{94} +(-3.94027 + 12.8248i) q^{95} +(3.77492 - 2.17945i) q^{97} +12.0000i q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} + 4 q^{10} - 4 q^{16} - 48 q^{19} - 18 q^{25} - 28 q^{31} + 16 q^{34} + 2 q^{40} - 16 q^{46} + 48 q^{49} + 76 q^{55} + 16 q^{61} - 8 q^{64} - 38 q^{70} - 24 q^{76} - 8 q^{85} + 8 q^{94}+O(q^{100}) \) 8 * q + 4 * q^4 + 4 * q^10 - 4 * q^16 - 48 * q^19 - 18 * q^25 - 28 * q^31 + 16 * q^34 + 2 * q^40 - 16 * q^46 + 48 * q^49 + 76 * q^55 + 16 * q^61 - 8 * q^64 - 38 * q^70 - 24 * q^76 - 8 * q^85 + 8 * q^94

Introduction

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