LMFDB - Embedded newform 810.2.i.h.109.3

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			109.3
Root			$0.656712 - 2.13746i$ of defining polynomial
Character	$\chi$	$=$	810.109
Dual form			810.2.i.h.379.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.866025 - 0.500000i) q^{2} +(0.500000 - 0.866025i) q^{4} +(-0.656712 + 2.13746i) q^{5} +(-3.77492 + 2.17945i) q^{7} -1.00000i q^{8} +(0.500000 + 2.17945i) q^{10} +(-2.17945 - 3.77492i) q^{11} +(-2.17945 + 3.77492i) q^{14} +(-0.500000 - 0.866025i) q^{16} +4.00000i q^{17} -6.00000 q^{19} +(1.52274 + 1.63746i) q^{20} +(-3.77492 - 2.17945i) q^{22} +(-1.73205 - 1.00000i) q^{23} +(-4.13746 - 2.80739i) q^{25} +4.35890i q^{28} +(-3.50000 + 6.06218i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(2.00000 + 3.46410i) q^{34} +(-2.17945 - 9.50000i) q^{35} +8.71780i q^{37} +(-5.19615 + 3.00000i) q^{38} +(2.13746 + 0.656712i) q^{40} +(4.35890 - 7.54983i) q^{41} +(-7.54983 + 4.35890i) q^{43} -4.35890 q^{44} -2.00000 q^{46} +(1.73205 - 1.00000i) q^{47} +(6.00000 - 10.3923i) q^{49} +(-4.98684 - 0.362541i) q^{50} +3.00000i q^{53} +(9.50000 - 2.17945i) q^{55} +(2.17945 + 3.77492i) q^{56} +(4.35890 - 7.54983i) q^{59} +(2.00000 + 3.46410i) q^{61} +7.00000i q^{62} -1.00000 q^{64} +(7.54983 + 4.35890i) q^{67} +(3.46410 + 2.00000i) q^{68} +(-6.63746 - 7.13752i) q^{70} +4.35890i q^{73} +(4.35890 + 7.54983i) q^{74} +(-3.00000 + 5.19615i) q^{76} +(16.4545 + 9.50000i) q^{77} +(2.17945 - 0.500000i) q^{80} -8.71780i q^{82} +(4.33013 - 2.50000i) q^{83} +(-8.54983 - 2.62685i) q^{85} +(-4.35890 + 7.54983i) q^{86} +(-3.77492 + 2.17945i) q^{88} +8.71780 q^{89} +(-1.73205 + 1.00000i) q^{92} +(1.00000 - 1.73205i) q^{94} +(3.94027 - 12.8248i) q^{95} +(3.77492 - 2.17945i) q^{97} -12.0000i q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$-0.938437\pi$
$11$	−2.17945	−	3.77492i	−0.657129	−	1.13818i	0.324227	−	0.945979i	$-0.394896\pi$
$12$		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	$0.161206\pi$
$17$			4.00000i			0.970143i	−0.874475	+	0.485071i	$0.838794\pi$
$18$		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	0.308431	−	0.951247i	$-0.400196\pi$
$23$	−1.73205	−	1.00000i	−0.361158	−	0.208514i	−0.669588	+	0.742732i	$0.733529\pi$
$24$		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	$-0.594989\pi$
$41$	4.35890	−	7.54983i	0.680746	−	1.17909i	0.974754	−	0.223283i	$-0.0716774\pi$
$42$		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	−0.368329	−	0.929695i	$-0.620070\pi$
$47$	1.73205	−	1.00000i	0.252646	−	0.145865i	0.620975	+	0.783830i	$0.286737\pi$
$48$		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	$0.0660580\pi$
$53$			3.00000i			0.412082i	−0.978543	+	0.206041i	$0.933942\pi$
$54$		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	$-0.641252\pi$
$59$	4.35890	−	7.54983i	0.567480	−	0.982905i	0.996814	−	0.0797589i	$-0.0254150\pi$
$60$		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	−0.243160	−	0.969986i	$-0.578184\pi$
$83$	4.33013	−	2.50000i	0.475293	−	0.274411i	0.718453	+	0.695576i	$0.244851\pi$
$84$		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	$-0.347117\pi$
$89$	8.71780			0.924085			0.462042	+	0.886858i	$0.347117\pi$
$90$		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	0.953847	−	0.300292i	$-0.0970841\pi$
$101$	2.17945	+	3.77492i	0.216863	+	0.375618i	−0.736984	+	0.675910i	$0.763751\pi$
$102$		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	$0.258184\pi$
$107$			15.0000i			1.45010i	−0.688694	+	0.725052i	$0.741816\pi$
$108$		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	−0.467143	−	0.884182i	$-0.654717\pi$
$113$	−15.5885	−	9.00000i	−1.46644	−	0.846649i	−0.999295	+	0.0375328i	$0.988050\pi$
$114$		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	$0.360211\pi$
$131$	−6.53835	+	11.3248i	−0.571258	+	0.989448i	−0.996437	+	0.0843389i	$0.973122\pi$
$132$		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	−0.985577	−	0.169226i	$-0.945873\pi$
$137$	−15.5885	+	9.00000i	−1.33181	+	0.768922i	−0.346235	+	0.938148i	$0.612540\pi$
$138$		0			0
$139$	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	−0.941383	−	0.337339i	$-0.890473\pi$
$149$	−2.17945	+	3.77492i	−0.178547	+	0.309253i	0.762836	+	0.646592i	$0.223806\pi$
$150$		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	0.961943	−	0.273252i	$-0.0880992\pi$
$167$	15.5885	+	9.00000i	1.20627	+	0.696441i	0.244328	+	0.969693i	$0.421432\pi$
$168$		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	0.279701	−	0.960087i	$-0.409765\pi$
$173$	16.4545	−	9.50000i	1.25101	−	0.722272i	0.971310	+	0.237816i	$0.0764314\pi$
$174$		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	$-0.802988\pi$
$179$	−21.7945			−1.62900			−0.814499	+	0.580166i	$0.802988\pi$
$180$		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	$0.0570008\pi$
$197$			5.00000i			0.356235i	−0.984009	+	0.178118i	$0.942999\pi$
$198$		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	−0.380615	−	0.924734i	$-0.624288\pi$
$227$	3.46410	−	2.00000i	0.229920	−	0.132745i	0.610535	+	0.791989i	$0.290954\pi$
$228$		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	$-0.848356\pi$
$233$		−	14.0000i		−	0.917170i	0.888650	−	0.458585i	$-0.151644\pi$
$234$		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	−0.971866	−	0.235535i	$-0.924316\pi$
$239$	−4.35890	+	7.54983i	−0.281954	+	0.488358i	0.689912	+	0.723893i	$0.257649\pi$
$240$		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	$-0.809047\pi$
$251$	−26.1534			−1.65079			−0.825394	+	0.564557i	$0.809047\pi$
$252$		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	0.787787	−	0.615948i	$-0.211227\pi$
$257$	10.3923	+	6.00000i	0.648254	+	0.374270i	−0.139533	+	0.990217i	$0.544560\pi$
$258$		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	−0.445647	−	0.895209i	$-0.647026\pi$
$263$	1.73205	−	1.00000i	0.106803	−	0.0616626i	0.552450	+	0.833546i	$0.313693\pi$
$264$		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	0.340480	−	0.940252i	$-0.389411\pi$
$293$	−5.19615	−	3.00000i	−0.303562	−	0.175262i	−0.644042	+	0.764990i	$0.722744\pi$
$294$		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	$-0.567443\pi$
$311$	13.0767	−	22.6495i	0.741511	−	1.28434i	0.951807	−	0.306698i	$-0.0992240\pi$
$312$		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	−0.852788	−	0.522257i	$-0.825090\pi$
$317$	−14.7224	+	8.50000i	−0.826894	+	0.477408i	0.0258939	+	0.999665i	$0.491757\pi$
$318$		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	−0.283101	−	0.959090i	$-0.591363\pi$
$347$	−23.3827	−	13.5000i	−1.25525	−	0.724718i	−0.972147	+	0.234372i	$0.924697\pi$
$348$		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	−0.960207	−	0.279288i	$-0.909902\pi$
$353$	−22.5167	+	13.0000i	−1.19844	+	0.691920i	−0.238233	+	0.971208i	$0.576568\pi$
$354$		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	$-0.257539\pi$
$359$	26.1534			1.38032			0.690162	+	0.723655i	$0.257539\pi$
$360$		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	0.408879	−	0.912589i	$-0.365920\pi$
$383$	−3.46410	−	2.00000i	−0.177007	−	0.102195i	−0.585886	+	0.810394i	$0.699253\pi$
$384$		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	0.915973	−	0.401240i	$-0.131421\pi$
$389$	2.17945	+	3.77492i	0.110502	+	0.191396i	−0.805470	+	0.592636i	$0.798087\pi$
$390$		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	$0.502995\pi$
$401$	−17.4356	+	30.1993i	−0.870692	+	1.50808i	−0.861282	+	0.508127i	$0.830338\pi$
$402$		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	−0.952635	−	0.304115i	$-0.901639\pi$
$419$	−4.35890	+	7.54983i	−0.212946	+	0.368834i	0.739689	+	0.672949i	$0.234973\pi$
$420$		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	$-0.567334\pi$
$431$	−8.71780			−0.419922			−0.209961	+	0.977710i	$0.567334\pi$
$432$		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	−0.726130	−	0.687557i	$-0.758683\pi$
$443$	−10.3923	+	6.00000i	−0.493753	+	0.285069i	0.232377	+	0.972626i	$0.425350\pi$
$444$		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	$-0.288296\pi$
$449$	26.1534			1.23425			0.617127	+	0.786863i	$0.288296\pi$
$450$		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	$0.200014\pi$
$461$	19.6150	+	33.9743i	0.913564	+	1.58234i	0.104573	+	0.994517i	$0.466652\pi$
$462$		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	$-0.838498\pi$
$467$		−	21.0000i		−	0.971764i	0.874024	−	0.485882i	$-0.161502\pi$
$468$		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	0.749094	−	0.662464i	$-0.230489\pi$
$479$	−4.35890	−	7.54983i	−0.199163	−	0.344961i	−0.948257	+	0.317503i	$0.897156\pi$
$480$		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	−0.975002	−	0.222198i	$-0.928677\pi$
$491$	−6.53835	+	11.3248i	−0.295072	+	0.511079i	0.679930	+	0.733277i	$0.262010\pi$
$492$		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	$-0.766801\pi$
$503$		−	30.0000i		−	1.33763i	0.743427	−	0.668817i	$-0.233199\pi$
$504$		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	−0.683956	−	0.729523i	$-0.739742\pi$
$509$	6.53835	−	11.3248i	0.289807	−	0.501961i	0.973764	+	0.227562i	$0.0730755\pi$
$510$		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	$-0.624742\pi$
$521$	−17.4356			−0.763867			−0.381934	+	0.924190i	$0.624742\pi$
$522$		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	$-0.753572\pi$
$557$		−	33.0000i		−	1.39825i	0.714997	−	0.699127i	$-0.246428\pi$
$558$		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	0.687124	−	0.726540i	$-0.258873\pi$
$563$	9.52628	+	5.50000i	0.401485	+	0.231797i	−0.285640	+	0.958337i	$0.592206\pi$
$564$		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	0.988851	−	0.148906i	$-0.0475753\pi$
$569$	8.71780	+	15.0997i	0.365469	+	0.633011i	−0.623382	+	0.781917i	$0.714242\pi$
$570$		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	−0.445424	−	0.895320i	$-0.646947\pi$
$587$	2.59808	−	1.50000i	0.107234	−	0.0619116i	0.552658	+	0.833408i	$0.313614\pi$
$588$		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	$0.0393141\pi$
$593$			6.00000i			0.246390i	−0.992382	+	0.123195i	$0.960686\pi$
$594$		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	$-0.653909\pi$
$599$	13.0767	−	22.6495i	0.534299	−	0.925434i	0.999197	−	0.0400691i	$-0.0127578\pi$
$600$		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	0.534460	−	0.845194i	$-0.320515\pi$
$617$	1.73205	+	1.00000i	0.0697297	+	0.0402585i	−0.464730	+	0.885453i	$0.653849\pi$
$618$		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	0.939177	−	0.343434i	$-0.111590\pi$
$641$	4.35890	+	7.54983i	0.172166	+	0.298201i	−0.767011	+	0.641634i	$0.778257\pi$
$642$		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	$-0.924201\pi$
$647$		−	12.0000i		−	0.471769i	0.971781	−	0.235884i	$-0.0757987\pi$
$648$		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	−0.228726	−	0.973491i	$-0.573456\pi$
$653$	−30.3109	−	17.5000i	−1.18616	−	0.684828i	−0.957431	+	0.288663i	$0.906789\pi$
$654$		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	0.820449	−	0.571720i	$-0.193724\pi$
$659$	−2.17945	−	3.77492i	−0.0848993	−	0.147050i	−0.905348	+	0.424670i	$0.860390\pi$
$660$		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	−0.865812	−	0.500369i	$-0.833198\pi$
$677$	−22.5167	+	13.0000i	−0.865386	+	0.499631i	0.000426509		1.00000i	$0.499864\pi$
$678$		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	$0.124985\pi$
$683$			20.0000i			0.765279i	−0.923898	+	0.382639i	$0.875015\pi$
$684$		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	$-0.635024\pi$
$701$	−21.7945			−0.823167			−0.411583	+	0.911372i	$0.635024\pi$
$702$		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	$-0.274669\pi$
$719$	34.8712			1.30048			0.650238	+	0.759731i	$0.274669\pi$
$720$		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	$0.00944260\pi$
$743$	41.5692	+	24.0000i	1.52503	+	0.880475i	0.525467	+	0.850814i	$0.323891\pi$
$744$		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	$-0.436375\pi$
$761$	26.1534	−	45.2990i	0.948060	−	1.64209i	0.749506	−	0.661998i	$-0.230291\pi$
$762$		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	$-0.895071\pi$
$773$		−	18.0000i		−	0.647415i	0.946157	−	0.323708i	$-0.104929\pi$
$774$		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	−0.189827	−	0.981818i	$-0.560793\pi$
$797$	−32.0429	−	18.5000i	−1.13502	−	0.655304i	−0.945192	+	0.326514i	$0.894126\pi$
$798$		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	$-0.347938\pi$
$809$	26.1534			0.919504			0.459752	+	0.888047i	$0.347938\pi$
$810$		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	$-0.958436\pi$
$821$	−17.4356	−	30.1993i	−0.608506	−	1.05396i	0.382980	−	0.923757i	$-0.374898\pi$
$822$		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	$0.0897336\pi$
$827$			16.0000i			0.556375i	−0.960527	+	0.278187i	$0.910266\pi$
$828$		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	$0.0389401\pi$
$839$	17.4356	+	30.1993i	0.601944	+	1.04260i	−0.390583	+	0.920568i	$0.627727\pi$
$840$		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	0.423681	−	0.905811i	$-0.360738\pi$
$857$	41.5692	−	24.0000i	1.41998	−	0.819824i	0.996296	+	0.0859870i	$0.0274043\pi$
$858$		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	$0.304348\pi$
$863$			48.0000i			1.63394i	−0.576681	+	0.816970i	$0.695652\pi$
$864$		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	0.108678	−	0.994077i	$-0.465338\pi$
$887$	−20.7846	−	12.0000i	−0.697879	−	0.402921i	−0.806557	+	0.591156i	$0.798672\pi$
$888$		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	0.563901	−	0.825843i	$-0.309300\pi$
$911$	−13.0767	−	22.6495i	−0.433250	−	0.750412i	−0.997151	+	0.0754311i	$0.975967\pi$
$912$		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	$-0.547774\pi$
$941$	23.9739	−	41.5241i	0.781528	−	1.35365i	0.931051	−	0.364888i	$-0.118893\pi$
$942$		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	−0.0694014	−	0.997589i	$-0.522109\pi$
$947$	23.3827	−	13.5000i	0.759835	−	0.438691i	0.829237	+	0.558898i	$0.188776\pi$
$948$		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	$-0.826568\pi$
$953$		−	32.0000i		−	1.03658i	0.855204	−	0.518291i	$-0.173432\pi$
$954$		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	$-0.716731\pi$
$971$	−39.2301			−1.25895			−0.629477	+	0.777019i	$0.716731\pi$
$972$		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	0.229465	−	0.973317i	$-0.426302\pi$
$977$	−15.5885	−	9.00000i	−0.498719	−	0.287936i	−0.728184	+	0.685381i	$0.759636\pi$
$978$		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	0.0494530	−	0.998776i	$-0.484252\pi$
$983$	29.4449	−	17.0000i	0.939145	−	0.542216i	0.889692	+	0.456561i	$0.150919\pi$
$984$		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.109.3		8
3.2	odd	2	inner	810.2.i.h.109.2		8
5.4	even	2	inner	810.2.i.h.109.1		8
9.2	odd	6	inner	810.2.i.h.379.4		8
9.4	even	3		270.2.c.c.109.4	yes	4
9.5	odd	6		270.2.c.c.109.1	✓	4
9.7	even	3	inner	810.2.i.h.379.1		8
15.14	odd	2	inner	810.2.i.h.109.4		8
36.23	even	6		2160.2.f.m.1729.2		4
36.31	odd	6		2160.2.f.m.1729.3		4
45.4	even	6		270.2.c.c.109.2	yes	4
45.13	odd	12		1350.2.a.x.1.1		2
45.14	odd	6		270.2.c.c.109.3	yes	4
45.22	odd	12		1350.2.a.w.1.2		2
45.23	even	12		1350.2.a.w.1.1		2
45.29	odd	6	inner	810.2.i.h.379.2		8
45.32	even	12		1350.2.a.x.1.2		2
45.34	even	6	inner	810.2.i.h.379.3		8
180.59	even	6		2160.2.f.m.1729.1		4
180.139	odd	6		2160.2.f.m.1729.4		4

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 810 = 2 \cdot 3^{4} \cdot 5 \)
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

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