LMFDB - Embedded newform 567.2.o.e.377.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [567,2,Mod(188,567)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(567, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([1, 3]))

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

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

chi := DirichletCharacter("567.188");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 567 = 3^{4} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	567.o (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:	$4.52751779461$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	no (minimal twist has level 189)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			377.3
Root			$0.965926 + 0.258819i$ of defining polynomial
Character	$\chi$	$=$	567.377
Dual form			567.2.o.e.188.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{5} +(-2.62132 + 0.358719i) q^{7} +2.82843i q^{8} +O(q^{10})$	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{5} +(-2.62132 + 0.358719i) q^{7} +2.82843i q^{8} +2.44949i q^{10} +(1.22474 - 0.707107i) q^{11} +(2.12132 + 1.22474i) q^{13} +(-2.95680 + 2.29289i) q^{14} +(2.00000 + 3.46410i) q^{16} -5.19615 q^{17} +7.34847i q^{19} +(1.00000 - 1.73205i) q^{22} +(2.44949 + 1.41421i) q^{23} +(1.00000 + 1.73205i) q^{25} +3.46410 q^{26} +(-6.12372 + 3.53553i) q^{29} +(2.12132 + 1.22474i) q^{31} +(-6.36396 + 3.67423i) q^{34} +(1.73205 - 4.24264i) q^{35} +5.00000 q^{37} +(5.19615 + 9.00000i) q^{38} +(-4.24264 - 2.44949i) q^{40} +(4.33013 - 7.50000i) q^{41} +(-2.50000 - 4.33013i) q^{43} +4.00000 q^{46} +(-4.33013 - 7.50000i) q^{47} +(6.74264 - 1.88064i) q^{49} +(2.44949 + 1.41421i) q^{50} -11.3137i q^{53} +2.44949i q^{55} +(-1.01461 - 7.41421i) q^{56} +(-5.00000 + 8.66025i) q^{58} +(4.33013 - 7.50000i) q^{59} +(2.12132 - 1.22474i) q^{61} +3.46410 q^{62} -8.00000 q^{64} +(-3.67423 + 2.12132i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(-0.878680 - 6.42090i) q^{70} +14.1421i q^{71} +(6.12372 - 3.53553i) q^{74} +(-2.95680 + 2.29289i) q^{77} +(6.50000 + 11.2583i) q^{79} -6.92820 q^{80} -12.2474i q^{82} +(0.866025 + 1.50000i) q^{83} +(4.50000 - 7.79423i) q^{85} +(-6.12372 - 3.53553i) q^{86} +(2.00000 + 3.46410i) q^{88} +10.3923 q^{89} +(-6.00000 - 2.44949i) q^{91} +(-10.6066 - 6.12372i) q^{94} +(-11.0227 - 6.36396i) q^{95} +(14.8492 - 8.57321i) q^{97} +(6.92820 - 7.07107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{7}+O(q^{10}) $ 8 * q - 4 * q^7	$ 8 q - 4 q^{7} + 16 q^{16} + 8 q^{22} + 8 q^{25} + 40 q^{37} - 20 q^{43} + 32 q^{46} + 20 q^{49} - 40 q^{58} - 64 q^{64} - 8 q^{67} - 24 q^{70} + 52 q^{79} + 36 q^{85} + 16 q^{88} - 48 q^{91}+O(q^{100}) $ 8 * q - 4 * q^7 + 16 * q^16 + 8 * q^22 + 8 * q^25 + 40 * q^37 - 20 * q^43 + 32 * q^46 + 20 * q^49 - 40 * q^58 - 64 * q^64 - 8 * q^67 - 24 * q^70 + 52 * q^79 + 36 * q^85 + 16 * q^88 - 48 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

$n$	$325$	$407$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	1.22474	−	0.707107i	0.866025	−	0.500000i		−	1.00000i	$-0.5\pi$
$2$	1.22474	−	0.707107i	0.866025	−	0.500000i	0.866025	+	0.500000i	$0.166667\pi$
$3$		0			0
$3$		0			0
$4$		0			0
$5$	−0.866025	+	1.50000i	−0.387298	+	0.670820i	−0.992085	−	0.125567i	$-0.959925\pi$
$5$	−0.866025	+	1.50000i	−0.387298	+	0.670820i	0.604787	+	0.796387i	$0.293258\pi$
$6$		0			0
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$7$	−2.62132	+	0.358719i	−0.990766	+	0.135583i
$8$			2.82843i			1.00000i
$9$		0			0
$10$			2.44949i			0.774597i
$11$	1.22474	−	0.707107i	0.369274	−	0.213201i	−0.303867	−	0.952714i	$-0.598278\pi$
$11$	1.22474	−	0.707107i	0.369274	−	0.213201i	0.673141	+	0.739514i	$0.264945\pi$
$12$		0			0
$13$	2.12132	+	1.22474i	0.588348	+	0.339683i	0.764444	−	0.644690i	$-0.223014\pi$
$13$	2.12132	+	1.22474i	0.588348	+	0.339683i	−0.176096	+	0.984373i	$0.556347\pi$
$14$	−2.95680	+	2.29289i	−0.790237	+	0.612801i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−5.19615			−1.26025			−0.630126	−	0.776493i	$-0.716997\pi$
$17$	−5.19615			−1.26025			−0.630126	+	0.776493i	$0.716997\pi$
$18$		0			0
$19$			7.34847i			1.68585i	0.538028	+	0.842927i	$0.319170\pi$
$19$			7.34847i			1.68585i	−0.538028	+	0.842927i	$0.680830\pi$
$20$		0			0
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	2.44949	+	1.41421i	0.510754	+	0.294884i	0.733144	−	0.680074i	$-0.238052\pi$
$23$	2.44949	+	1.41421i	0.510754	+	0.294884i	−0.222390	+	0.974958i	$0.571386\pi$
$24$		0			0
$25$	1.00000	+	1.73205i	0.200000	+	0.346410i
$26$	3.46410			0.679366
$27$		0			0
$28$		0			0
$29$	−6.12372	+	3.53553i	−1.13715	+	0.656532i	−0.945723	−	0.324975i	$-0.894644\pi$
$29$	−6.12372	+	3.53553i	−1.13715	+	0.656532i	−0.191425	+	0.981507i	$0.561311\pi$
$30$		0			0
$31$	2.12132	+	1.22474i	0.381000	+	0.219971i	0.678253	−	0.734828i	$-0.262737\pi$
$31$	2.12132	+	1.22474i	0.381000	+	0.219971i	−0.297253	+	0.954799i	$0.596070\pi$
$32$		0			0
$33$		0			0
$34$	−6.36396	+	3.67423i	−1.09141	+	0.630126i
$35$	1.73205	−	4.24264i	0.292770	−	0.717137i
$36$		0			0
$37$	5.00000			0.821995			0.410997	−	0.911636i	$-0.365181\pi$
$37$	5.00000			0.821995			0.410997	+	0.911636i	$0.365181\pi$
$38$	5.19615	+	9.00000i	0.842927	+	1.45999i
$39$		0			0
$40$	−4.24264	−	2.44949i	−0.670820	−	0.387298i
$41$	4.33013	−	7.50000i	0.676252	−	1.17130i	−0.299849	−	0.953987i	$-0.596936\pi$
$41$	4.33013	−	7.50000i	0.676252	−	1.17130i	0.976101	−	0.217317i	$-0.0697304\pi$
$42$		0			0
$43$	−2.50000	−	4.33013i	−0.381246	−	0.660338i	0.609994	−	0.792406i	$-0.291172\pi$
$43$	−2.50000	−	4.33013i	−0.381246	−	0.660338i	−0.991241	+	0.132068i	$0.957838\pi$
$44$		0			0
$45$		0			0
$46$	4.00000			0.589768
$47$	−4.33013	−	7.50000i	−0.631614	−	1.09399i	−0.987222	−	0.159352i	$-0.949059\pi$
$47$	−4.33013	−	7.50000i	−0.631614	−	1.09399i	0.355608	−	0.934635i	$-0.384274\pi$
$48$		0			0
$49$	6.74264	−	1.88064i	0.963234	−	0.268662i
$50$	2.44949	+	1.41421i	0.346410	+	0.200000i
$51$		0			0
$52$		0			0
$53$		−	11.3137i		−	1.55406i	−0.629465	−	0.777029i	$-0.716726\pi$
$53$		−	11.3137i		−	1.55406i	0.629465	−	0.777029i	$-0.283274\pi$
$54$		0			0
$55$			2.44949i			0.330289i
$56$	−1.01461	−	7.41421i	−0.135583	−	0.990766i
$57$		0			0
$58$	−5.00000	+	8.66025i	−0.656532	+	1.13715i
$59$	4.33013	−	7.50000i	0.563735	−	0.976417i	−0.433432	−	0.901186i	$-0.642697\pi$
$59$	4.33013	−	7.50000i	0.563735	−	0.976417i	0.997166	−	0.0752304i	$-0.0239692\pi$
$60$		0			0
$61$	2.12132	−	1.22474i	0.271607	−	0.156813i	−0.358011	−	0.933718i	$-0.616545\pi$
$61$	2.12132	−	1.22474i	0.271607	−	0.156813i	0.629618	+	0.776905i	$0.283211\pi$
$62$	3.46410			0.439941
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−3.67423	+	2.12132i	−0.455733	+	0.263117i
$66$		0			0
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	−0.920623	−	0.390453i	$-0.872318\pi$
$67$	−1.00000	+	1.73205i	−0.122169	+	0.211604i	0.798454	+	0.602056i	$0.205652\pi$
$68$		0			0
$69$		0			0
$70$	−0.878680	−	6.42090i	−0.105022	−	0.767444i
$71$			14.1421i			1.67836i	0.543852	+	0.839181i	$0.316965\pi$
$71$			14.1421i			1.67836i	−0.543852	+	0.839181i	$0.683035\pi$
$72$		0			0
$73$		0			0		1.00000			$0$
$73$		0			0		−1.00000			$\pi$
$74$	6.12372	−	3.53553i	0.711868	−	0.410997i
$75$		0			0
$76$		0			0
$77$	−2.95680	+	2.29289i	−0.336958	+	0.261299i
$78$		0			0
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	0.956325	+	0.292306i	$0.0944227\pi$
$79$	6.50000	+	11.2583i	0.731307	+	1.26666i	−0.225018	+	0.974355i	$0.572244\pi$
$80$	−6.92820			−0.774597
$81$		0			0
$82$		−	12.2474i		−	1.35250i
$83$	0.866025	+	1.50000i	0.0950586	+	0.164646i	0.909633	−	0.415413i	$-0.136363\pi$
$83$	0.866025	+	1.50000i	0.0950586	+	0.164646i	−0.814574	+	0.580059i	$0.803029\pi$
$84$		0			0
$85$	4.50000	−	7.79423i	0.488094	−	0.845403i
$86$	−6.12372	−	3.53553i	−0.660338	−	0.381246i
$87$		0			0
$88$	2.00000	+	3.46410i	0.213201	+	0.369274i
$89$	10.3923			1.10158			0.550791	−	0.834643i	$-0.314326\pi$
$89$	10.3923			1.10158			0.550791	+	0.834643i	$0.314326\pi$
$90$		0			0
$91$	−6.00000	−	2.44949i	−0.628971	−	0.256776i
$92$		0			0
$93$		0			0
$94$	−10.6066	−	6.12372i	−1.09399	−	0.631614i
$95$	−11.0227	−	6.36396i	−1.13091	−	0.652929i
$96$		0			0
$97$	14.8492	−	8.57321i	1.50771	−	0.870478i	0.507752	−	0.861503i	$-0.330476\pi$
$97$	14.8492	−	8.57321i	1.50771	−	0.870478i	0.999960	−	0.00897496i	$-0.00285686\pi$
$98$	6.92820	−	7.07107i	0.699854	−	0.714286i
$99$		0			0
$100$		0			0
$101$	−1.73205	−	3.00000i	−0.172345	−	0.298511i	0.766894	−	0.641774i	$-0.221801\pi$
$101$	−1.73205	−	3.00000i	−0.172345	−	0.298511i	−0.939239	+	0.343263i	$0.888468\pi$
$102$		0			0
$103$	8.48528	+	4.89898i	0.836080	+	0.482711i	0.855930	−	0.517092i	$-0.172986\pi$
$103$	8.48528	+	4.89898i	0.836080	+	0.482711i	−0.0198501	+	0.999803i	$0.506319\pi$
$104$	−3.46410	+	6.00000i	−0.339683	+	0.588348i
$105$		0			0
$106$	−8.00000	−	13.8564i	−0.777029	−	1.34585i
$107$			14.1421i			1.36717i	0.729870	+	0.683586i	$0.239581\pi$
$107$			14.1421i			1.36717i	−0.729870	+	0.683586i	$0.760419\pi$
$108$		0			0
$109$	−7.00000			−0.670478			−0.335239	−	0.942133i	$-0.608817\pi$
$109$	−7.00000			−0.670478			−0.335239	+	0.942133i	$0.608817\pi$
$110$	1.73205	+	3.00000i	0.165145	+	0.286039i
$111$		0			0
$112$	−6.48528	−	8.36308i	−0.612801	−	0.790237i
$113$	6.12372	+	3.53553i	0.576072	+	0.332595i	0.759571	−	0.650425i	$-0.225409\pi$
$113$	6.12372	+	3.53553i	0.576072	+	0.332595i	−0.183499	+	0.983020i	$0.558742\pi$
$114$		0			0
$115$	−4.24264	+	2.44949i	−0.395628	+	0.228416i
$116$		0			0
$117$		0			0
$118$		−	12.2474i		−	1.12747i
$119$	13.6208	−	1.86396i	1.24861	−	0.170869i
$120$		0			0
$121$	−4.50000	+	7.79423i	−0.409091	+	0.708566i
$122$	1.73205	−	3.00000i	0.156813	−	0.271607i
$123$		0			0
$124$		0			0
$125$	−12.1244			−1.08444
$126$		0			0
$127$	5.00000			0.443678			0.221839	−	0.975083i	$-0.428794\pi$
$127$	5.00000			0.443678			0.221839	+	0.975083i	$0.428794\pi$
$128$	−9.79796	+	5.65685i	−0.866025	+	0.500000i
$129$		0			0
$130$	−3.00000	+	5.19615i	−0.263117	+	0.455733i
$131$	−8.66025	+	15.0000i	−0.756650	+	1.31056i	0.187900	+	0.982188i	$0.439832\pi$
$131$	−8.66025	+	15.0000i	−0.756650	+	1.31056i	−0.944550	+	0.328368i	$0.893501\pi$
$132$		0			0
$133$	−2.63604	−	19.2627i	−0.228574	−	1.67029i
$134$			2.82843i			0.244339i
$135$		0			0
$136$		−	14.6969i		−	1.26025i
$137$	1.22474	−	0.707107i	0.104637	−	0.0604122i	−0.446768	−	0.894650i	$-0.647425\pi$
$137$	1.22474	−	0.707107i	0.104637	−	0.0604122i	0.551405	+	0.834238i	$0.314092\pi$
$138$		0			0
$139$	−10.6066	−	6.12372i	−0.899640	−	0.519408i	−0.0225568	−	0.999746i	$-0.507181\pi$
$139$	−10.6066	−	6.12372i	−0.899640	−	0.519408i	−0.877083	+	0.480338i	$0.840514\pi$
$140$		0			0
$141$		0			0
$142$	10.0000	+	17.3205i	0.839181	+	1.45350i
$143$	3.46410			0.289683
$144$		0			0
$145$		−	12.2474i		−	1.01710i
$146$		0			0
$147$		0			0
$148$		0			0
$149$	6.12372	+	3.53553i	0.501675	+	0.289642i	0.729405	−	0.684082i	$-0.239797\pi$
$149$	6.12372	+	3.53553i	0.501675	+	0.289642i	−0.227730	+	0.973724i	$0.573130\pi$
$150$		0			0
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	0.746190	−	0.665733i	$-0.231881\pi$
$151$	−2.50000	−	4.33013i	−0.203447	−	0.352381i	−0.949637	+	0.313353i	$0.898548\pi$
$152$	−20.7846			−1.68585
$153$		0			0
$154$	−2.00000	+	4.89898i	−0.161165	+	0.394771i
$155$	−3.67423	+	2.12132i	−0.295122	+	0.170389i
$156$		0			0
$157$	14.8492	+	8.57321i	1.18510	+	0.684217i	0.957189	−	0.289465i	$-0.0934775\pi$
$157$	14.8492	+	8.57321i	1.18510	+	0.684217i	0.227910	+	0.973682i	$0.426811\pi$
$158$	15.9217	+	9.19239i	1.26666	+	0.731307i
$159$		0			0
$160$		0			0
$161$	−6.92820	−	2.82843i	−0.546019	−	0.222911i
$162$		0			0
$163$	5.00000			0.391630			0.195815	−	0.980641i	$-0.437265\pi$
$163$	5.00000			0.391630			0.195815	+	0.980641i	$0.437265\pi$
$164$		0			0
$165$		0			0
$166$	2.12132	+	1.22474i	0.164646	+	0.0950586i
$167$	−6.06218	+	10.5000i	−0.469105	+	0.812514i	−0.999376	−	0.0353139i	$-0.988757\pi$
$167$	−6.06218	+	10.5000i	−0.469105	+	0.812514i	0.530271	+	0.847828i	$0.322090\pi$
$168$		0			0
$169$	−3.50000	−	6.06218i	−0.269231	−	0.466321i
$170$		−	12.7279i		−	0.976187i
$171$		0			0
$172$		0			0
$173$	3.46410	+	6.00000i	0.263371	+	0.456172i	0.967135	−	0.254262i	$-0.0818324\pi$
$173$	3.46410	+	6.00000i	0.263371	+	0.456172i	−0.703765	+	0.710433i	$0.748499\pi$
$174$		0			0
$175$	−3.24264	−	4.18154i	−0.245121	−	0.316095i
$176$	4.89898	+	2.82843i	0.369274	+	0.213201i
$177$		0			0
$178$	12.7279	−	7.34847i	0.953998	−	0.550791i
$179$		−	7.07107i		−	0.528516i	−0.964452	−	0.264258i	$-0.914873\pi$
$179$		−	7.07107i		−	0.528516i	0.964452	−	0.264258i	$-0.0851271\pi$
$180$		0			0
$181$			14.6969i			1.09241i	0.837650	+	0.546207i	$0.183929\pi$
$181$			14.6969i			1.09241i	−0.837650	+	0.546207i	$0.816071\pi$
$182$	−9.08052	+	1.24264i	−0.673093	+	0.0921107i
$183$		0			0
$184$	−4.00000	+	6.92820i	−0.294884	+	0.510754i
$185$	−4.33013	+	7.50000i	−0.318357	+	0.551411i
$186$		0			0
$187$	−6.36396	+	3.67423i	−0.465379	+	0.268687i
$188$		0			0
$189$		0			0
$190$	−18.0000			−1.30586
$191$	12.2474	−	7.07107i	0.886194	−	0.511645i	0.0134985	−	0.999909i	$-0.495703\pi$
$191$	12.2474	−	7.07107i	0.886194	−	0.511645i	0.872696	+	0.488264i	$0.162370\pi$
$192$		0			0
$193$	0.500000	−	0.866025i	0.0359908	−	0.0623379i	−0.847469	−	0.530845i	$-0.821875\pi$
$193$	0.500000	−	0.866025i	0.0359908	−	0.0623379i	0.883460	+	0.468507i	$0.155208\pi$
$194$	12.1244	−	21.0000i	0.870478	−	1.50771i
$195$		0			0
$196$		0			0
$197$			1.41421i			0.100759i	0.998730	+	0.0503793i	$0.0160430\pi$
$197$			1.41421i			0.100759i	−0.998730	+	0.0503793i	$0.983957\pi$
$198$		0			0
$199$		0			0		1.00000			$0$
$199$		0			0		−1.00000			$\pi$
$200$	−4.89898	+	2.82843i	−0.346410	+	0.200000i
$201$		0			0
$202$	−4.24264	−	2.44949i	−0.298511	−	0.172345i
$203$	14.7840	−	11.4645i	1.03763	−	0.804648i
$204$		0			0
$205$	7.50000	+	12.9904i	0.523823	+	0.907288i
$206$	13.8564			0.965422
$207$		0			0
$208$			9.79796i			0.679366i
$209$	5.19615	+	9.00000i	0.359425	+	0.622543i
$210$		0			0
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	−0.447478	−	0.894295i	$-0.647678\pi$
$211$	8.00000	−	13.8564i	0.550743	−	0.953914i	0.998221	−	0.0596196i	$-0.0189888\pi$
$212$		0			0
$213$		0			0
$214$	10.0000	+	17.3205i	0.683586	+	1.18401i
$215$	8.66025			0.590624
$216$		0			0
$217$	−6.00000	−	2.44949i	−0.407307	−	0.166282i
$218$	−8.57321	+	4.94975i	−0.580651	+	0.335239i
$219$		0			0
$220$		0			0
$221$	−11.0227	−	6.36396i	−0.741467	−	0.428086i
$222$		0			0
$223$	−10.6066	+	6.12372i	−0.710271	+	0.410075i	−0.811161	−	0.584823i	$-0.801164\pi$
$223$	−10.6066	+	6.12372i	−0.710271	+	0.410075i	0.100891	+	0.994898i	$0.467831\pi$
$224$		0			0
$225$		0			0
$226$	10.0000			0.665190
$227$	−6.92820	−	12.0000i	−0.459841	−	0.796468i	0.539111	−	0.842235i	$-0.318760\pi$
$227$	−6.92820	−	12.0000i	−0.459841	−	0.796468i	−0.998952	+	0.0457666i	$0.985427\pi$
$228$		0			0
$229$	−4.24264	−	2.44949i	−0.280362	−	0.161867i	0.353226	−	0.935538i	$-0.385085\pi$
$229$	−4.24264	−	2.44949i	−0.280362	−	0.161867i	−0.633587	+	0.773671i	$0.718418\pi$
$230$	−3.46410	+	6.00000i	−0.228416	+	0.395628i
$231$		0			0
$232$	−10.0000	−	17.3205i	−0.656532	−	1.13715i
$233$		−	7.07107i		−	0.463241i	−0.972806	−	0.231621i	$-0.925597\pi$
$233$		−	7.07107i		−	0.463241i	0.972806	−	0.231621i	$-0.0744028\pi$
$234$		0			0
$235$	15.0000			0.978492
$236$		0			0
$237$		0			0
$238$	15.3640	−	11.9142i	0.995898	−	0.772284i
$239$	−15.9217	−	9.19239i	−1.02989	−	0.594606i	−0.112935	−	0.993602i	$-0.536025\pi$
$239$	−15.9217	−	9.19239i	−1.02989	−	0.594606i	−0.916953	+	0.398996i	$0.869359\pi$
$240$		0			0
$241$	2.12132	−	1.22474i	0.136646	−	0.0788928i	−0.430118	−	0.902772i	$-0.641528\pi$
$241$	2.12132	−	1.22474i	0.136646	−	0.0788928i	0.566765	+	0.823880i	$0.308195\pi$
$242$			12.7279i			0.818182i
$243$		0			0
$244$		0			0
$245$	−3.01834	+	11.7426i	−0.192835	+	0.750210i
$246$		0			0
$247$	−9.00000	+	15.5885i	−0.572656	+	0.991870i
$248$	−3.46410	+	6.00000i	−0.219971	+	0.381000i
$249$		0			0
$250$	−14.8492	+	8.57321i	−0.939149	+	0.542218i
$251$	5.19615			0.327978			0.163989	−	0.986462i	$-0.447564\pi$
$251$	5.19615			0.327978			0.163989	+	0.986462i	$0.447564\pi$
$252$		0			0
$253$	4.00000			0.251478
$254$	6.12372	−	3.53553i	0.384237	−	0.221839i
$255$		0			0
$256$		0			0
$257$	1.73205	−	3.00000i	0.108042	−	0.187135i	−0.806935	−	0.590641i	$-0.798875\pi$
$257$	1.73205	−	3.00000i	0.108042	−	0.187135i	0.914977	+	0.403506i	$0.132208\pi$
$258$		0			0
$259$	−13.1066	+	1.79360i	−0.814405	+	0.111449i
$260$		0			0
$261$		0			0
$262$			24.4949i			1.51330i
$263$	1.22474	−	0.707107i	0.0755210	−	0.0436021i	−0.461764	−	0.887003i	$-0.652783\pi$
$263$	1.22474	−	0.707107i	0.0755210	−	0.0436021i	0.537285	+	0.843401i	$0.319450\pi$
$264$		0			0
$265$	16.9706	+	9.79796i	1.04249	+	0.601884i
$266$	−16.8493	−	21.7279i	−1.03309	−	1.33222i
$267$		0			0
$268$		0			0
$269$	25.9808			1.58408			0.792038	−	0.610472i	$-0.209020\pi$
$269$	25.9808			1.58408			0.792038	+	0.610472i	$0.209020\pi$
$270$		0			0
$271$			14.6969i			0.892775i	0.894840	+	0.446388i	$0.147290\pi$
$271$			14.6969i			0.892775i	−0.894840	+	0.446388i	$0.852710\pi$
$272$	−10.3923	−	18.0000i	−0.630126	−	1.09141i
$273$		0			0
$274$	1.00000	−	1.73205i	0.0604122	−	0.104637i
$275$	2.44949	+	1.41421i	0.147710	+	0.0852803i
$276$		0			0
$277$	−2.50000	−	4.33013i	−0.150210	−	0.260172i	0.781094	−	0.624413i	$-0.214662\pi$
$277$	−2.50000	−	4.33013i	−0.150210	−	0.260172i	−0.931305	+	0.364241i	$0.881328\pi$
$278$	−17.3205			−1.03882
$279$		0			0
$280$	12.0000	+	4.89898i	0.717137	+	0.292770i
$281$	12.2474	−	7.07107i	0.730622	−	0.421825i	−0.0880280	−	0.996118i	$-0.528056\pi$
$281$	12.2474	−	7.07107i	0.730622	−	0.421825i	0.818650	+	0.574293i	$0.194723\pi$
$282$		0			0
$283$	−10.6066	−	6.12372i	−0.630497	−	0.364018i	0.150448	−	0.988618i	$-0.451929\pi$
$283$	−10.6066	−	6.12372i	−0.630497	−	0.364018i	−0.780945	+	0.624600i	$0.785262\pi$
$284$		0			0
$285$		0			0
$286$	4.24264	−	2.44949i	0.250873	−	0.144841i
$287$	−8.66025	+	21.2132i	−0.511199	+	1.25218i
$288$		0			0
$289$	10.0000			0.588235
$290$	−8.66025	−	15.0000i	−0.508548	−	0.880830i
$291$		0			0
$292$		0			0
$293$	9.52628	−	16.5000i	0.556531	−	0.963940i	−0.441251	−	0.897384i	$-0.645465\pi$
$293$	9.52628	−	16.5000i	0.556531	−	0.963940i	0.997783	−	0.0665568i	$-0.0212014\pi$
$294$		0			0
$295$	7.50000	+	12.9904i	0.436667	+	0.756329i
$296$			14.1421i			0.821995i
$297$		0			0
$298$	10.0000			0.579284
$299$	3.46410	+	6.00000i	0.200334	+	0.346989i
$300$		0			0
$301$	8.10660	+	10.4539i	0.467257	+	0.602550i
$302$	−6.12372	−	3.53553i	−0.352381	−	0.203447i
$303$		0			0
$304$	−25.4558	+	14.6969i	−1.45999	+	0.842927i
$305$			4.24264i			0.242933i
$306$		0			0
$307$		0			0		1.00000			$0$
$307$		0			0		−1.00000			$\pi$
$308$		0			0
$309$		0			0
$310$	−3.00000	+	5.19615i	−0.170389	+	0.295122i
$311$	−6.06218	+	10.5000i	−0.343755	+	0.595400i	−0.985127	−	0.171830i	$-0.945032\pi$
$311$	−6.06218	+	10.5000i	−0.343755	+	0.595400i	0.641372	+	0.767230i	$0.278365\pi$
$312$		0			0
$313$	21.2132	−	12.2474i	1.19904	−	0.692267i	0.238700	−	0.971093i	$-0.423279\pi$
$313$	21.2132	−	12.2474i	1.19904	−	0.692267i	0.960341	+	0.278827i	$0.0899455\pi$
$314$	24.2487			1.36843
$315$		0			0
$316$		0			0
$317$	4.89898	−	2.82843i	0.275154	−	0.158860i	−0.356073	−	0.934458i	$-0.615885\pi$
$317$	4.89898	−	2.82843i	0.275154	−	0.158860i	0.631228	+	0.775598i	$0.282551\pi$
$318$		0			0
$319$	−5.00000	+	8.66025i	−0.279946	+	0.484881i
$320$	6.92820	−	12.0000i	0.387298	−	0.670820i
$321$		0			0
$322$	−10.4853	+	1.43488i	−0.584322	+	0.0799626i
$323$		−	38.1838i		−	2.12460i
$324$		0			0
$325$			4.89898i			0.271746i
$326$	6.12372	−	3.53553i	0.339162	−	0.195815i
$327$		0			0
$328$	21.2132	+	12.2474i	1.17130	+	0.676252i
$329$	14.0410	+	18.1066i	0.774108	+	0.998249i
$330$		0			0
$331$	12.5000	+	21.6506i	0.687062	+	1.19003i	0.972784	+	0.231714i	$0.0744333\pi$
$331$	12.5000	+	21.6506i	0.687062	+	1.19003i	−0.285722	+	0.958313i	$0.592233\pi$
$332$		0			0
$333$		0			0
$334$			17.1464i			0.938211i
$335$	−1.73205	−	3.00000i	−0.0946320	−	0.163908i
$336$		0			0
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	−0.754811	−	0.655942i	$-0.772271\pi$
$337$	3.50000	−	6.06218i	0.190657	−	0.330228i	0.945468	+	0.325714i	$0.105605\pi$
$338$	−8.57321	−	4.94975i	−0.466321	−	0.269231i
$339$		0			0
$340$		0			0
$341$	3.46410			0.187592
$342$		0			0
$343$	−17.0000	+	7.34847i	−0.917914	+	0.396780i
$344$	12.2474	−	7.07107i	0.660338	−	0.381246i
$345$		0			0
$346$	8.48528	+	4.89898i	0.456172	+	0.263371i
$347$	6.12372	+	3.53553i	0.328739	+	0.189797i	0.655281	−	0.755385i	$-0.272550\pi$
$347$	6.12372	+	3.53553i	0.328739	+	0.189797i	−0.326542	+	0.945183i	$0.605884\pi$
$348$		0			0
$349$	−16.9706	+	9.79796i	−0.908413	+	0.524473i	−0.879920	−	0.475121i	$-0.842404\pi$
$349$	−16.9706	+	9.79796i	−0.908413	+	0.524473i	−0.0284931	+	0.999594i	$0.509071\pi$
$350$	−6.92820	−	2.82843i	−0.370328	−	0.151186i
$351$		0			0
$352$		0			0
$353$	−4.33013	−	7.50000i	−0.230469	−	0.399185i	0.727477	−	0.686132i	$-0.240693\pi$
$353$	−4.33013	−	7.50000i	−0.230469	−	0.399185i	−0.957946	+	0.286947i	$0.907359\pi$
$354$		0			0
$355$	−21.2132	−	12.2474i	−1.12588	−	0.650027i
$356$		0			0
$357$		0			0
$358$	−5.00000	−	8.66025i	−0.264258	−	0.457709i
$359$		−	11.3137i		−	0.597115i	−0.954392	−	0.298557i	$-0.903495\pi$
$359$		−	11.3137i		−	0.597115i	0.954392	−	0.298557i	$-0.0965054\pi$
$360$		0			0
$361$	−35.0000			−1.84211
$362$	10.3923	+	18.0000i	0.546207	+	0.946059i
$363$		0			0
$364$		0			0
$365$		0			0
$366$		0			0
$367$	−4.24264	+	2.44949i	−0.221464	+	0.127862i	−0.606628	−	0.794986i	$-0.707478\pi$
$367$	−4.24264	+	2.44949i	−0.221464	+	0.127862i	0.385164	+	0.922848i	$0.374145\pi$
$368$			11.3137i			0.589768i
$369$		0			0
$370$			12.2474i			0.636715i
$371$	4.05845	+	29.6569i	0.210704	+	1.53971i
$372$		0			0
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	−0.336557	−	0.941663i	$-0.609263\pi$
$373$	12.5000	−	21.6506i	0.647225	−	1.12103i	0.983783	−	0.179364i	$-0.0574041\pi$
$374$	−5.19615	+	9.00000i	−0.268687	+	0.465379i
$375$		0			0
$376$	21.2132	−	12.2474i	1.09399	−	0.631614i
$377$	−17.3205			−0.892052
$378$		0			0
$379$	23.0000			1.18143			0.590715	−	0.806880i	$-0.298846\pi$
$379$	23.0000			1.18143			0.590715	+	0.806880i	$0.298846\pi$
$380$		0			0
$381$		0			0
$382$	10.0000	−	17.3205i	0.511645	−	0.886194i
$383$	−0.866025	+	1.50000i	−0.0442518	+	0.0766464i	−0.887303	−	0.461187i	$-0.847424\pi$
$383$	−0.866025	+	1.50000i	−0.0442518	+	0.0766464i	0.843051	+	0.537833i	$0.180757\pi$
$384$		0			0
$385$	−0.878680	−	6.42090i	−0.0447817	−	0.327239i
$386$		−	1.41421i		−	0.0719816i
$387$		0			0
$388$		0			0
$389$	−28.1691	+	16.2635i	−1.42823	+	0.824590i	−0.996981	−	0.0776423i	$-0.975261\pi$
$389$	−28.1691	+	16.2635i	−1.42823	+	0.824590i	−0.431250	+	0.902232i	$0.641927\pi$
$390$		0			0
$391$	−12.7279	−	7.34847i	−0.643679	−	0.371628i
$392$	5.31925	+	19.0711i	0.268662	+	0.963234i
$393$		0			0
$394$	1.00000	+	1.73205i	0.0503793	+	0.0872595i
$395$	−22.5167			−1.13294
$396$		0			0
$397$		0			0		1.00000			$0$
$397$		0			0		−1.00000			$\pi$
$398$		0			0
$399$		0			0
$400$	−4.00000	+	6.92820i	−0.200000	+	0.346410i
$401$	17.1464	+	9.89949i	0.856252	+	0.494357i	0.862755	−	0.505622i	$-0.168737\pi$
$401$	17.1464	+	9.89949i	0.856252	+	0.494357i	−0.00650355	+	0.999979i	$0.502070\pi$
$402$		0			0
$403$	3.00000	+	5.19615i	0.149441	+	0.258839i
$404$		0			0
$405$		0			0
$406$	10.0000	−	24.4949i	0.496292	−	1.21566i
$407$	6.12372	−	3.53553i	0.303542	−	0.175250i
$408$		0			0
$409$	−16.9706	−	9.79796i	−0.839140	−	0.484478i	0.0178316	−	0.999841i	$-0.494324\pi$
$409$	−16.9706	−	9.79796i	−0.839140	−	0.484478i	−0.856972	+	0.515363i	$0.827657\pi$
$410$	18.3712	+	10.6066i	0.907288	+	0.523823i
$411$		0			0
$412$		0			0
$413$	−8.66025	+	21.2132i	−0.426143	+	1.04383i
$414$		0			0
$415$	−3.00000			−0.147264
$416$		0			0
$417$		0			0
$418$	12.7279	+	7.34847i	0.622543	+	0.359425i
$419$	−0.866025	+	1.50000i	−0.0423081	+	0.0732798i	−0.886404	−	0.462912i	$-0.846804\pi$
$419$	−0.866025	+	1.50000i	−0.0423081	+	0.0732798i	0.844096	+	0.536192i	$0.180138\pi$
$420$		0			0
$421$	2.00000	+	3.46410i	0.0974740	+	0.168830i	0.910638	−	0.413204i	$-0.135590\pi$
$421$	2.00000	+	3.46410i	0.0974740	+	0.168830i	−0.813164	+	0.582034i	$0.802257\pi$
$422$		−	22.6274i		−	1.10149i
$423$		0			0
$424$	32.0000			1.55406
$425$	−5.19615	−	9.00000i	−0.252050	−	0.436564i
$426$		0			0
$427$	−5.12132	+	3.97141i	−0.247838	+	0.192190i
$428$		0			0
$429$		0			0
$430$	10.6066	−	6.12372i	0.511496	−	0.295312i
$431$			5.65685i			0.272481i	0.990676	+	0.136241i	$0.0435020\pi$
$431$			5.65685i			0.272481i	−0.990676	+	0.136241i	$0.956498\pi$
$432$		0			0
$433$		−	36.7423i		−	1.76572i	−0.469632	−	0.882862i	$-0.655613\pi$
$433$		−	36.7423i		−	1.76572i	0.469632	−	0.882862i	$-0.344387\pi$
$434$	−9.08052	+	1.24264i	−0.435879	+	0.0596487i
$435$		0			0
$436$		0			0
$437$	−10.3923	+	18.0000i	−0.497131	+	0.861057i
$438$		0			0
$439$	−16.9706	+	9.79796i	−0.809961	+	0.467631i	−0.846942	−	0.531685i	$-0.821559\pi$
$439$	−16.9706	+	9.79796i	−0.809961	+	0.467631i	0.0369815	+	0.999316i	$0.488226\pi$
$440$	−6.92820			−0.330289
$441$		0			0
$442$	−18.0000			−0.856173
$443$	−28.1691	+	16.2635i	−1.33836	+	0.772700i	−0.986564	−	0.163378i	$-0.947761\pi$
$443$	−28.1691	+	16.2635i	−1.33836	+	0.772700i	−0.351792	+	0.936078i	$0.614428\pi$
$444$		0			0
$445$	−9.00000	+	15.5885i	−0.426641	+	0.738964i
$446$	−8.66025	+	15.0000i	−0.410075	+	0.710271i
$447$		0			0
$448$	20.9706	−	2.86976i	0.990766	−	0.135583i
$449$		−	24.0416i		−	1.13459i	−0.823513	−	0.567297i	$-0.807989\pi$
$449$		−	24.0416i		−	1.13459i	0.823513	−	0.567297i	$-0.192011\pi$
$450$		0			0
$451$		−	12.2474i		−	0.576710i
$452$		0			0
$453$		0			0
$454$	−16.9706	−	9.79796i	−0.796468	−	0.459841i
$455$	8.87039	−	6.87868i	0.415850	−	0.322477i
$456$		0			0
$457$	−16.0000	−	27.7128i	−0.748448	−	1.29635i	−0.948566	−	0.316579i	$-0.897466\pi$
$457$	−16.0000	−	27.7128i	−0.748448	−	1.29635i	0.200118	−	0.979772i	$-0.435868\pi$
$458$	−6.92820			−0.323734
$459$		0			0
$460$		0			0
$461$	6.06218	+	10.5000i	0.282344	+	0.489034i	0.971962	−	0.235140i	$-0.0755548\pi$
$461$	6.06218	+	10.5000i	0.282344	+	0.489034i	−0.689618	+	0.724174i	$0.742221\pi$
$462$		0			0
$463$	−5.50000	+	9.52628i	−0.255607	+	0.442724i	−0.965060	−	0.262029i	$-0.915609\pi$
$463$	−5.50000	+	9.52628i	−0.255607	+	0.442724i	0.709453	+	0.704752i	$0.248942\pi$
$464$	−24.4949	−	14.1421i	−1.13715	−	0.656532i
$465$		0			0
$466$	−5.00000	−	8.66025i	−0.231621	−	0.401179i
$467$	−20.7846			−0.961797			−0.480899	−	0.876776i	$-0.659689\pi$
$467$	−20.7846			−0.961797			−0.480899	+	0.876776i	$0.659689\pi$
$468$		0			0
$469$	2.00000	−	4.89898i	0.0923514	−	0.226214i
$470$	18.3712	−	10.6066i	0.847399	−	0.489246i
$471$		0			0
$472$	21.2132	+	12.2474i	0.976417	+	0.563735i
$473$	−6.12372	−	3.53553i	−0.281569	−	0.162564i
$474$		0			0
$475$	−12.7279	+	7.34847i	−0.583997	+	0.337171i
$476$		0			0
$477$		0			0
$478$	−26.0000			−1.18921
$479$	16.4545	+	28.5000i	0.751825	+	1.30220i	0.946938	+	0.321417i	$0.104159\pi$
$479$	16.4545	+	28.5000i	0.751825	+	1.30220i	−0.195113	+	0.980781i	$0.562507\pi$
$480$		0			0
$481$	10.6066	+	6.12372i	0.483619	+	0.279218i
$482$	1.73205	−	3.00000i	0.0788928	−	0.136646i
$483$		0			0
$484$		0			0
$485$			29.6985i			1.34854i
$486$		0			0
$487$	−22.0000			−0.996915			−0.498458	−	0.866914i	$-0.666100\pi$
$487$	−22.0000			−0.996915			−0.498458	+	0.866914i	$0.666100\pi$
$488$	3.46410	+	6.00000i	0.156813	+	0.271607i
$489$		0			0
$490$	4.60660	+	16.5160i	0.208105	+	0.746118i
$491$	13.4722	+	7.77817i	0.607992	+	0.351024i	0.772179	−	0.635405i	$-0.219167\pi$
$491$	13.4722	+	7.77817i	0.607992	+	0.351024i	−0.164187	+	0.986429i	$0.552500\pi$
$492$		0			0
$493$	31.8198	−	18.3712i	1.43309	−	0.827396i
$494$			25.4558i			1.14531i
$495$		0			0
$496$			9.79796i			0.439941i
$497$	−5.07306	−	37.0711i	−0.227558	−	1.66286i
$498$		0			0
$499$	−8.50000	+	14.7224i	−0.380512	+	0.659067i	−0.991136	−	0.132855i	$-0.957586\pi$
$499$	−8.50000	+	14.7224i	−0.380512	+	0.659067i	0.610623	+	0.791921i	$0.290919\pi$
$500$		0			0
$501$		0			0
$502$	6.36396	−	3.67423i	0.284037	−	0.163989i
$503$	36.3731			1.62179			0.810897	−	0.585188i	$-0.198979\pi$
$503$	36.3731			1.62179			0.810897	+	0.585188i	$0.198979\pi$
$504$		0			0
$505$	6.00000			0.266996
$506$	4.89898	−	2.82843i	0.217786	−	0.125739i
$507$		0			0
$508$		0			0
$509$	4.33013	−	7.50000i	0.191930	−	0.332432i	−0.753960	−	0.656920i	$-0.771859\pi$
$509$	4.33013	−	7.50000i	0.191930	−	0.332432i	0.945890	+	0.324489i	$0.105192\pi$
$510$		0			0
$511$		0			0
$512$		−	22.6274i		−	1.00000i
$513$		0			0
$514$		−	4.89898i		−	0.216085i
$515$	−14.6969	+	8.48528i	−0.647624	+	0.373906i
$516$		0			0
$517$	−10.6066	−	6.12372i	−0.466478	−	0.269321i
$518$	−14.7840	+	11.4645i	−0.649571	+	0.503720i
$519$		0			0
$520$	−6.00000	−	10.3923i	−0.263117	−	0.455733i
$521$	5.19615			0.227648			0.113824	−	0.993501i	$-0.463690\pi$
$521$	5.19615			0.227648			0.113824	+	0.993501i	$0.463690\pi$
$522$		0			0
$523$		−	36.7423i		−	1.60663i	−0.595554	−	0.803315i	$-0.703067\pi$
$523$		−	36.7423i		−	1.60663i	0.595554	−	0.803315i	$-0.296933\pi$
$524$		0			0
$525$		0			0
$526$	1.00000	−	1.73205i	0.0436021	−	0.0755210i
$527$	−11.0227	−	6.36396i	−0.480157	−	0.277218i
$528$		0			0
$529$	−7.50000	−	12.9904i	−0.326087	−	0.564799i
$530$	27.7128			1.20377
$531$		0			0
$532$		0			0
$533$	18.3712	−	10.6066i	0.795744	−	0.459423i
$534$		0			0
$535$	−21.2132	−	12.2474i	−0.917127	−	0.529503i
$536$	−4.89898	−	2.82843i	−0.211604	−	0.122169i
$537$		0			0
$538$	31.8198	−	18.3712i	1.37185	−	0.792038i
$539$	6.92820	−	7.07107i	0.298419	−	0.304572i
$540$		0			0
$541$	5.00000			0.214967			0.107483	−	0.994207i	$-0.465721\pi$
$541$	5.00000			0.214967			0.107483	+	0.994207i	$0.465721\pi$
$542$	10.3923	+	18.0000i	0.446388	+	0.773166i
$543$		0			0
$544$		0			0
$545$	6.06218	−	10.5000i	0.259675	−	0.449771i
$546$		0			0
$547$	6.50000	+	11.2583i	0.277920	+	0.481371i	0.970868	−	0.239616i	$-0.0770217\pi$
$547$	6.50000	+	11.2583i	0.277920	+	0.481371i	−0.692948	+	0.720988i	$0.743688\pi$
$548$		0			0
$549$		0			0
$550$	4.00000			0.170561
$551$	−25.9808	−	45.0000i	−1.10682	−	1.91706i
$552$		0			0
$553$	−21.0772	−	27.1800i	−0.896292	−	1.15581i
$554$	−6.12372	−	3.53553i	−0.260172	−	0.150210i
$555$		0			0
$556$		0			0
$557$			14.1421i			0.599222i	0.954062	+	0.299611i	$0.0968568\pi$
$557$			14.1421i			0.599222i	−0.954062	+	0.299611i	$0.903143\pi$
$558$		0			0
$559$		−	12.2474i		−	0.518012i
$560$	18.1610	−	2.48528i	0.767444	−	0.105022i
$561$		0			0
$562$	10.0000	−	17.3205i	0.421825	−	0.730622i
$563$	17.3205	−	30.0000i	0.729972	−	1.26435i	−0.226922	−	0.973913i	$-0.572866\pi$
$563$	17.3205	−	30.0000i	0.729972	−	1.26435i	0.956894	−	0.290436i	$-0.0938004\pi$
$564$		0			0
$565$	−10.6066	+	6.12372i	−0.446223	+	0.257627i
$566$	−17.3205			−0.728035
$567$		0			0
$568$	−40.0000			−1.67836
$569$	34.2929	−	19.7990i	1.43763	−	0.830017i	0.439946	−	0.898024i	$-0.354997\pi$
$569$	34.2929	−	19.7990i	1.43763	−	0.830017i	0.997685	+	0.0680072i	$0.0216641\pi$
$570$		0			0
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	−0.595862	−	0.803087i	$-0.703189\pi$
$571$	9.50000	−	16.4545i	0.397563	−	0.688599i	0.993425	+	0.114488i	$0.0365228\pi$
$572$		0			0
$573$		0			0
$574$	4.39340	+	32.1045i	0.183377	+	1.34002i
$575$			5.65685i			0.235907i
$576$		0			0
$577$		−	29.3939i		−	1.22368i	−0.790980	−	0.611842i	$-0.790429\pi$
$577$		−	29.3939i		−	1.22368i	0.790980	−	0.611842i	$-0.209571\pi$
$578$	12.2474	−	7.07107i	0.509427	−	0.294118i
$579$		0			0
$580$		0			0
$581$	−2.80821	−	3.62132i	−0.116504	−	0.150238i
$582$		0			0
$583$	−8.00000	−	13.8564i	−0.331326	−	0.573874i
$584$		0			0
$585$		0			0
$586$		−	26.9444i		−	1.11306i
$587$	−6.92820	−	12.0000i	−0.285958	−	0.495293i	0.686883	−	0.726768i	$-0.258978\pi$
$587$	−6.92820	−	12.0000i	−0.285958	−	0.495293i	−0.972841	+	0.231475i	$0.925645\pi$
$588$		0			0
$589$	−9.00000	+	15.5885i	−0.370839	+	0.642311i
$590$	18.3712	+	10.6066i	0.756329	+	0.436667i
$591$		0			0
$592$	10.0000	+	17.3205i	0.410997	+	0.711868i
$593$	15.5885			0.640141			0.320071	−	0.947394i	$-0.396293\pi$
$593$	15.5885			0.640141			0.320071	+	0.947394i	$0.396293\pi$
$594$		0			0
$595$	−9.00000	+	22.0454i	−0.368964	+	0.903774i
$596$		0			0
$597$		0			0
$598$	8.48528	+	4.89898i	0.346989	+	0.200334i
$599$	−15.9217	−	9.19239i	−0.650542	−	0.375591i	0.138122	−	0.990415i	$-0.455894\pi$
$599$	−15.9217	−	9.19239i	−0.650542	−	0.375591i	−0.788664	+	0.614824i	$0.789227\pi$
$600$		0			0
$601$	40.3051	−	23.2702i	1.64408	−	0.949209i	0.664717	−	0.747095i	$-0.268552\pi$
$601$	40.3051	−	23.2702i	1.64408	−	0.949209i	0.979362	−	0.202114i	$-0.0647811\pi$
$602$	17.3205	+	7.07107i	0.705931	+	0.288195i
$603$		0			0
$604$		0			0
$605$	−7.79423	−	13.5000i	−0.316880	−	0.548853i
$606$		0			0
$607$	−10.6066	−	6.12372i	−0.430509	−	0.248554i	0.269055	−	0.963125i	$-0.413289\pi$
$607$	−10.6066	−	6.12372i	−0.430509	−	0.248554i	−0.699563	+	0.714571i	$0.746622\pi$
$608$		0			0
$609$		0			0
$610$	3.00000	+	5.19615i	0.121466	+	0.210386i
$611$		−	21.2132i		−	0.858194i
$612$		0			0
$613$	−4.00000			−0.161558			−0.0807792	−	0.996732i	$-0.525741\pi$
$613$	−4.00000			−0.161558			−0.0807792	+	0.996732i	$0.525741\pi$
$614$		0			0
$615$		0			0
$616$	−6.48528	−	8.36308i	−0.261299	−	0.336958i
$617$	−41.6413	−	24.0416i	−1.67642	−	0.967880i	−0.963915	−	0.266209i	$-0.914229\pi$
$617$	−41.6413	−	24.0416i	−1.67642	−	0.967880i	−0.712501	−	0.701671i	$-0.752438\pi$
$618$		0			0
$619$	−23.3345	+	13.4722i	−0.937894	+	0.541493i	−0.889299	−	0.457325i	$-0.848807\pi$
$619$	−23.3345	+	13.4722i	−0.937894	+	0.541493i	−0.0485943	+	0.998819i	$0.515474\pi$
$620$		0			0
$621$		0			0
$622$			17.1464i			0.687509i
$623$	−27.2416	+	3.72792i	−1.09141	+	0.149356i
$624$		0			0
$625$	5.50000	−	9.52628i	0.220000	−	0.381051i
$626$	17.3205	−	30.0000i	0.692267	−	1.19904i
$627$		0			0
$628$		0			0
$629$	−25.9808			−1.03592
$630$		0			0
$631$	29.0000			1.15447			0.577236	−	0.816577i	$-0.304131\pi$
$631$	29.0000			1.15447			0.577236	+	0.816577i	$0.304131\pi$
$632$	−31.8434	+	18.3848i	−1.26666	+	0.731307i
$633$		0			0
$634$	4.00000	−	6.92820i	0.158860	−	0.275154i
$635$	−4.33013	+	7.50000i	−0.171836	+	0.297628i
$636$		0			0
$637$	16.6066	+	4.26858i	0.657978	+	0.169127i
$638$			14.1421i			0.559893i
$639$		0			0
$640$		−	19.5959i		−	0.774597i
$641$	1.22474	−	0.707107i	0.0483745	−	0.0279290i	−0.475618	−	0.879652i	$-0.657775\pi$
$641$	1.22474	−	0.707107i	0.0483745	−	0.0279290i	0.523992	+	0.851723i	$0.324442\pi$
$642$		0			0
$643$	21.2132	+	12.2474i	0.836567	+	0.482992i	0.856096	−	0.516817i	$-0.172883\pi$
$643$	21.2132	+	12.2474i	0.836567	+	0.482992i	−0.0195288	+	0.999809i	$0.506217\pi$
$644$		0			0
$645$		0			0
$646$	−27.0000	−	46.7654i	−1.06230	−	1.83996i
$647$	−20.7846			−0.817127			−0.408564	−	0.912730i	$-0.633970\pi$
$647$	−20.7846			−0.817127			−0.408564	+	0.912730i	$0.633970\pi$
$648$		0			0
$649$		−	12.2474i		−	0.480754i
$650$	3.46410	+	6.00000i	0.135873	+	0.235339i
$651$		0			0
$652$		0			0
$653$	−15.9217	−	9.19239i	−0.623064	−	0.359726i	0.154997	−	0.987915i	$-0.450463\pi$
$653$	−15.9217	−	9.19239i	−0.623064	−	0.359726i	−0.778061	+	0.628189i	$0.783796\pi$
$654$		0			0
$655$	−15.0000	−	25.9808i	−0.586098	−	1.01515i
$656$	34.6410			1.35250
$657$		0			0
$658$	30.0000	+	12.2474i	1.16952	+	0.477455i
$659$	−9.79796	+	5.65685i	−0.381674	+	0.220360i	−0.678546	−	0.734557i	$-0.737390\pi$
$659$	−9.79796	+	5.65685i	−0.381674	+	0.220360i	0.296872	+	0.954917i	$0.404056\pi$
$660$		0			0
$661$	14.8492	+	8.57321i	0.577569	+	0.333459i	0.760167	−	0.649728i	$-0.225117\pi$
$661$	14.8492	+	8.57321i	0.577569	+	0.333459i	−0.182598	+	0.983188i	$0.558451\pi$
$662$	30.6186	+	17.6777i	1.19003	+	0.687062i
$663$		0			0
$664$	−4.24264	+	2.44949i	−0.164646	+	0.0950586i
$665$	31.1769	+	12.7279i	1.20899	+	0.493568i
$666$		0			0
$667$	−20.0000			−0.774403
$668$		0			0
$669$		0			0
$670$	−4.24264	−	2.44949i	−0.163908	−	0.0946320i
$671$	1.73205	−	3.00000i	0.0668651	−	0.115814i
$672$		0			0
$673$	20.0000	+	34.6410i	0.770943	+	1.33531i	0.937046	+	0.349205i	$0.113548\pi$
$673$	20.0000	+	34.6410i	0.770943	+	1.33531i	−0.166103	+	0.986108i	$0.553118\pi$
$674$		−	9.89949i		−	0.381314i
$675$		0			0
$676$		0			0
$677$	8.66025	+	15.0000i	0.332841	+	0.576497i	0.983068	−	0.183243i	$-0.0586596\pi$
$677$	8.66025	+	15.0000i	0.332841	+	0.576497i	−0.650227	+	0.759740i	$0.725326\pi$
$678$		0			0
$679$	−35.8492	+	27.7999i	−1.37577	+	1.06686i
$680$	22.0454	+	12.7279i	0.845403	+	0.488094i
$681$		0			0
$682$	4.24264	−	2.44949i	0.162459	−	0.0937958i
$683$		−	24.0416i		−	0.919927i	−0.887938	−	0.459964i	$-0.847862\pi$
$683$		−	24.0416i		−	0.919927i	0.887938	−	0.459964i	$-0.152138\pi$
$684$		0			0
$685$			2.44949i			0.0935902i
$686$	−15.6245	+	21.0208i	−0.596547	+	0.802578i
$687$		0			0
$688$	10.0000	−	17.3205i	0.381246	−	0.660338i
$689$	13.8564	−	24.0000i	0.527887	−	0.914327i
$690$		0			0
$691$	−23.3345	+	13.4722i	−0.887687	+	0.512506i	−0.873185	−	0.487388i	$-0.837950\pi$
$691$	−23.3345	+	13.4722i	−0.887687	+	0.512506i	−0.0145019	+	0.999895i	$0.504616\pi$
$692$		0			0
$693$		0			0
$694$	10.0000			0.379595
$695$	18.3712	−	10.6066i	0.696858	−	0.402331i
$696$		0			0
$697$	−22.5000	+	38.9711i	−0.852248	+	1.47614i
$698$	−13.8564	+	24.0000i	−0.524473	+	0.908413i
$699$		0			0
$700$		0			0
$701$			1.41421i			0.0534141i	0.999643	+	0.0267071i	$0.00850213\pi$
$701$			1.41421i			0.0534141i	−0.999643	+	0.0267071i	$0.991498\pi$
$702$		0			0
$703$			36.7423i			1.38576i
$704$	−9.79796	+	5.65685i	−0.369274	+	0.213201i
$705$		0			0
$706$	−10.6066	−	6.12372i	−0.399185	−	0.230469i
$707$	5.61642	+	7.24264i	0.211227	+	0.272388i
$708$		0			0
$709$	−2.50000	−	4.33013i	−0.0938895	−	0.162621i	0.815255	−	0.579102i	$-0.196597\pi$
$709$	−2.50000	−	4.33013i	−0.0938895	−	0.162621i	−0.909145	+	0.416481i	$0.863263\pi$
$710$	−34.6410			−1.30005
$711$		0			0
$712$			29.3939i			1.10158i
$713$	3.46410	+	6.00000i	0.129732	+	0.224702i
$714$		0			0
$715$	−3.00000	+	5.19615i	−0.112194	+	0.194325i
$716$		0			0
$717$		0			0
$718$	−8.00000	−	13.8564i	−0.298557	−	0.517116i
$719$	−15.5885			−0.581351			−0.290676	−	0.956822i	$-0.593880\pi$
$719$	−15.5885			−0.581351			−0.290676	+	0.956822i	$0.593880\pi$
$720$		0			0
$721$	−24.0000	−	9.79796i	−0.893807	−	0.364895i
$722$	−42.8661	+	24.7487i	−1.59531	+	0.921053i
$723$		0			0
$724$		0			0
$725$	−12.2474	−	7.07107i	−0.454859	−	0.262613i
$726$		0			0
$727$	−10.6066	+	6.12372i	−0.393377	+	0.227116i	−0.683622	−	0.729836i	$-0.739596\pi$
$727$	−10.6066	+	6.12372i	−0.393377	+	0.227116i	0.290245	+	0.956952i	$0.406263\pi$
$728$	6.92820	−	16.9706i	0.256776	−	0.628971i
$729$		0			0
$730$		0			0
$731$	12.9904	+	22.5000i	0.480467	+	0.832193i
$732$		0			0
$733$	33.9411	+	19.5959i	1.25364	+	0.723792i	0.971831	−	0.235678i	$-0.0757310\pi$
$733$	33.9411	+	19.5959i	1.25364	+	0.723792i	0.281813	+	0.959469i	$0.409064\pi$
$734$	−3.46410	+	6.00000i	−0.127862	+	0.221464i
$735$		0			0
$736$		0			0
$737$			2.82843i			0.104186i
$738$		0			0
$739$	−22.0000			−0.809283			−0.404642	−	0.914475i	$-0.632604\pi$
$739$	−22.0000			−0.809283			−0.404642	+	0.914475i	$0.632604\pi$
$740$		0			0
$741$		0			0
$742$	25.9411	+	33.4523i	0.952329	+	1.22807i
$743$	6.12372	+	3.53553i	0.224658	+	0.129706i	0.608105	−	0.793857i	$-0.291930\pi$
$743$	6.12372	+	3.53553i	0.224658	+	0.129706i	−0.383447	+	0.923563i	$0.625263\pi$
$744$		0			0
$745$	−10.6066	+	6.12372i	−0.388596	+	0.224356i
$746$		−	35.3553i		−	1.29445i
$747$		0			0
$748$		0			0
$749$	−5.07306	−	37.0711i	−0.185366	−	1.35455i
$750$		0			0
$751$	17.0000	−	29.4449i	0.620339	−	1.07446i	−0.369084	−	0.929396i	$-0.620328\pi$
$751$	17.0000	−	29.4449i	0.620339	−	1.07446i	0.989423	−	0.145062i	$-0.0463382\pi$
$752$	17.3205	−	30.0000i	0.631614	−	1.09399i
$753$		0			0
$754$	−21.2132	+	12.2474i	−0.772539	+	0.446026i
$755$	8.66025			0.315179
$756$		0			0
$757$	47.0000			1.70824			0.854122	−	0.520073i	$-0.174095\pi$
$757$	47.0000			1.70824			0.854122	+	0.520073i	$0.174095\pi$
$758$	28.1691	−	16.2635i	1.02315	−	0.590715i
$759$		0			0
$760$	18.0000	−	31.1769i	0.652929	−	1.13091i
$761$	−6.06218	+	10.5000i	−0.219754	+	0.380625i	−0.954733	−	0.297465i	$-0.903859\pi$
$761$	−6.06218	+	10.5000i	−0.219754	+	0.380625i	0.734979	+	0.678090i	$0.237192\pi$
$762$		0			0
$763$	18.3492	−	2.51104i	0.664287	−	0.0909056i
$764$		0			0
$765$		0			0
$766$			2.44949i			0.0885037i
$767$	18.3712	−	10.6066i	0.663345	−	0.382982i
$768$		0			0
$769$	−4.24264	−	2.44949i	−0.152994	−	0.0883309i	0.421549	−	0.906806i	$-0.361487\pi$
$769$	−4.24264	−	2.44949i	−0.152994	−	0.0883309i	−0.574542	+	0.818475i	$0.694820\pi$
$770$	−5.61642	−	7.24264i	−0.202402	−	0.261007i
$771$		0			0
$772$		0			0
$773$	15.5885			0.560678			0.280339	−	0.959901i	$-0.409553\pi$
$773$	15.5885			0.560678			0.280339	+	0.959901i	$0.409553\pi$
$774$		0			0
$775$			4.89898i			0.175977i
$776$	24.2487	+	42.0000i	0.870478	+	1.50771i
$777$		0			0
$778$	−23.0000	+	39.8372i	−0.824590	+	1.42823i
$779$	55.1135	+	31.8198i	1.97465	+	1.14006i
$780$		0			0
$781$	10.0000	+	17.3205i	0.357828	+	0.619777i
$782$	−20.7846			−0.743256
$783$		0			0
$784$	20.0000	+	19.5959i	0.714286	+	0.699854i
$785$	−25.7196	+	14.8492i	−0.917973	+	0.529992i
$786$		0			0
$787$	−4.24264	−	2.44949i	−0.151234	−	0.0873149i	0.422473	−	0.906375i	$-0.361162\pi$
$787$	−4.24264	−	2.44949i	−0.151234	−	0.0873149i	−0.573707	+	0.819060i	$0.694495\pi$
$788$		0			0
$789$		0			0
$790$	−27.5772	+	15.9217i	−0.981151	+	0.566468i
$791$	−17.3205	−	7.07107i	−0.615846	−	0.251418i
$792$		0			0
$793$	6.00000			0.213066
$794$		0			0
$795$		0			0
$796$		0			0
$797$	−19.0526	+	33.0000i	−0.674876	+	1.16892i	0.301629	+	0.953425i	$0.402470\pi$
$797$	−19.0526	+	33.0000i	−0.674876	+	1.16892i	−0.976505	+	0.215495i	$0.930864\pi$
$798$		0			0
$799$	22.5000	+	38.9711i	0.795993	+	1.37870i
$800$		0			0
$801$		0			0
$802$	28.0000			0.988714
$803$		0			0
$804$		0			0
$805$	10.2426	−	7.94282i	0.361006	−	0.279947i
$806$	7.34847	+	4.24264i	0.258839	+	0.149441i
$807$		0			0
$808$	8.48528	−	4.89898i	0.298511	−	0.172345i
$809$			14.1421i			0.497211i	0.968605	+	0.248606i	$0.0799723\pi$
$809$			14.1421i			0.497211i	−0.968605	+	0.248606i	$0.920028\pi$
$810$		0			0
$811$			36.7423i			1.29020i	0.764099	+	0.645099i	$0.223184\pi$
$811$			36.7423i			1.29020i	−0.764099	+	0.645099i	$0.776816\pi$
$812$		0			0
$813$		0			0
$814$	5.00000	−	8.66025i	0.175250	−	0.303542i
$815$	−4.33013	+	7.50000i	−0.151678	+	0.262714i
$816$		0			0
$817$	31.8198	−	18.3712i	1.11323	−	0.642726i
$818$	−27.7128			−0.968956
$819$		0			0
$820$		0			0
$821$	−31.8434	+	18.3848i	−1.11134	+	0.641633i	−0.939176	−	0.343435i	$-0.888409\pi$
$821$	−31.8434	+	18.3848i	−1.11134	+	0.641633i	−0.172165	+	0.985068i	$0.555076\pi$
$822$		0			0
$823$	27.5000	−	47.6314i	0.958590	−	1.66033i	0.232659	−	0.972558i	$-0.425257\pi$
$823$	27.5000	−	47.6314i	0.958590	−	1.66033i	0.725931	−	0.687768i	$-0.241409\pi$
$824$	−13.8564	+	24.0000i	−0.482711	+	0.836080i
$825$		0			0
$826$	4.39340	+	32.1045i	0.152866	+	1.11706i
$827$			26.8701i			0.934363i	0.884161	+	0.467182i	$0.154731\pi$
$827$			26.8701i			0.934363i	−0.884161	+	0.467182i	$0.845269\pi$
$828$		0			0
$829$			36.7423i			1.27611i	0.769989	+	0.638057i	$0.220262\pi$
$829$			36.7423i			1.27611i	−0.769989	+	0.638057i	$0.779738\pi$
$830$	−3.67423	+	2.12132i	−0.127535	+	0.0736321i
$831$		0			0
$832$	−16.9706	−	9.79796i	−0.588348	−	0.339683i
$833$	−35.0358	+	9.77208i	−1.21392	+	0.338582i
$834$		0			0
$835$	−10.5000	−	18.1865i	−0.363367	−	0.629371i
$836$		0			0
$837$		0			0
$838$			2.44949i			0.0846162i
$839$	−9.52628	−	16.5000i	−0.328884	−	0.569643i	0.653407	−	0.757007i	$-0.273339\pi$
$839$	−9.52628	−	16.5000i	−0.328884	−	0.569643i	−0.982291	+	0.187364i	$0.940006\pi$
$840$		0			0
$841$	10.5000	−	18.1865i	0.362069	−	0.627122i
$842$	4.89898	+	2.82843i	0.168830	+	0.0974740i
$843$		0			0
$844$		0			0
$845$	12.1244			0.417091
$846$		0			0
$847$	9.00000	−	22.0454i	0.309244	−	0.757489i
$848$	39.1918	−	22.6274i	1.34585	−	0.777029i
$849$		0			0
$850$	−12.7279	−	7.34847i	−0.436564	−	0.252050i
$851$	12.2474	+	7.07107i	0.419837	+	0.242393i
$852$		0			0
$853$	−42.4264	+	24.4949i	−1.45265	+	0.838689i	−0.998631	−	0.0523016i	$-0.983344\pi$
$853$	−42.4264	+	24.4949i	−1.45265	+	0.838689i	−0.454021	+	0.890991i	$0.650011\pi$
$854$	−3.46410	+	8.48528i	−0.118539	+	0.290360i
$855$		0			0
$856$	−40.0000			−1.36717
$857$	11.2583	+	19.5000i	0.384577	+	0.666107i	0.991710	−	0.128493i	$-0.0410139\pi$
$857$	11.2583	+	19.5000i	0.384577	+	0.666107i	−0.607133	+	0.794600i	$0.707681\pi$
$858$		0			0
$859$	−16.9706	−	9.79796i	−0.579028	−	0.334302i	0.181719	−	0.983351i	$-0.441834\pi$
$859$	−16.9706	−	9.79796i	−0.579028	−	0.334302i	−0.760747	+	0.649048i	$0.775167\pi$
$860$		0			0
$861$		0			0
$862$	4.00000	+	6.92820i	0.136241	+	0.235976i
$863$			39.5980i			1.34793i	0.738763	+	0.673965i	$0.235410\pi$
$863$			39.5980i			1.34793i	−0.738763	+	0.673965i	$0.764590\pi$
$864$		0			0
$865$	−12.0000			−0.408012
$866$	−25.9808	−	45.0000i	−0.882862	−	1.52916i
$867$		0			0
$868$		0			0
$869$	15.9217	+	9.19239i	0.540106	+	0.311830i
$870$		0			0
$871$	−4.24264	+	2.44949i	−0.143756	+	0.0829978i
$872$		−	19.7990i		−	0.670478i
$873$		0			0
$874$			29.3939i			0.994263i
$875$	31.7818	−	4.34924i	1.07442	−	0.147031i
$876$		0			0
$877$	21.5000	−	37.2391i	0.726003	−	1.25747i	−0.232556	−	0.972583i	$-0.574709\pi$
$877$	21.5000	−	37.2391i	0.726003	−	1.25747i	0.958560	−	0.284892i	$-0.0919577\pi$
$878$	−13.8564	+	24.0000i	−0.467631	+	0.809961i
$879$		0			0
$880$	−8.48528	+	4.89898i	−0.286039	+	0.165145i
$881$	−51.9615			−1.75063			−0.875314	−	0.483555i	$-0.839345\pi$
$881$	−51.9615			−1.75063			−0.875314	+	0.483555i	$0.839345\pi$
$882$		0			0
$883$	5.00000			0.168263			0.0841317	−	0.996455i	$-0.473188\pi$
$883$	5.00000			0.168263			0.0841317	+	0.996455i	$0.473188\pi$
$884$		0			0
$885$		0			0
$886$	−23.0000	+	39.8372i	−0.772700	+	1.33836i
$887$	14.7224	−	25.5000i	0.494331	−	0.856206i	−0.505648	−	0.862740i	$-0.668746\pi$
$887$	14.7224	−	25.5000i	0.494331	−	0.856206i	0.999979	+	0.00653381i	$0.00207979\pi$
$888$		0			0
$889$	−13.1066	+	1.79360i	−0.439581	+	0.0601553i
$890$			25.4558i			0.853282i
$891$		0			0
$892$		0			0
$893$	55.1135	−	31.8198i	1.84430	−	1.06481i
$894$		0			0
$895$	10.6066	+	6.12372i	0.354540	+	0.204694i
$896$	23.6544	−	18.3431i	0.790237	−	0.612801i
$897$		0			0
$898$	−17.0000	−	29.4449i	−0.567297	−	0.982588i
$899$	−17.3205			−0.577671
$900$		0			0
$901$			58.7878i			1.95850i
$902$	−8.66025	−	15.0000i	−0.288355	−	0.499445i
$903$		0			0
$904$	−10.0000	+	17.3205i	−0.332595	+	0.576072i
$905$	−22.0454	−	12.7279i	−0.732814	−	0.423090i
$906$		0			0
$907$	−11.5000	−	19.9186i	−0.381851	−	0.661386i	0.609476	−	0.792805i	$-0.291380\pi$
$907$	−11.5000	−	19.9186i	−0.381851	−	0.661386i	−0.991327	+	0.131419i	$0.958047\pi$
$908$		0			0
$909$		0			0
$910$	6.00000	−	14.6969i	0.198898	−	0.487199i
$911$	−6.12372	+	3.53553i	−0.202888	+	0.117137i	−0.598002	−	0.801495i	$-0.704038\pi$
$911$	−6.12372	+	3.53553i	−0.202888	+	0.117137i	0.395114	+	0.918632i	$0.370705\pi$
$912$		0			0
$913$	2.12132	+	1.22474i	0.0702055	+	0.0405331i
$914$	−39.1918	−	22.6274i	−1.29635	−	0.748448i
$915$		0			0
$916$		0			0
$917$	17.3205	−	42.4264i	0.571974	−	1.40104i
$918$		0			0
$919$	5.00000			0.164935			0.0824674	−	0.996594i	$-0.473720\pi$
$919$	5.00000			0.164935			0.0824674	+	0.996594i	$0.473720\pi$
$920$	−6.92820	−	12.0000i	−0.228416	−	0.395628i
$921$		0			0
$922$	14.8492	+	8.57321i	0.489034	+	0.282344i
$923$	−17.3205	+	30.0000i	−0.570111	+	0.987462i
$924$		0			0
$925$	5.00000	+	8.66025i	0.164399	+	0.284747i
$926$			15.5563i			0.511213i
$927$		0			0
$928$		0			0
$929$	16.4545	+	28.5000i	0.539854	+	0.935055i	0.998911	+	0.0466480i	$0.0148539\pi$
$929$	16.4545	+	28.5000i	0.539854	+	0.935055i	−0.459057	+	0.888407i	$0.651813\pi$
$930$		0			0
$931$	13.8198	+	49.5481i	0.452926	+	1.62387i
$932$		0			0
$933$		0			0
$934$	−25.4558	+	14.6969i	−0.832941	+	0.480899i
$935$		−	12.7279i		−	0.416248i
$936$		0			0
$937$		−	36.7423i		−	1.20032i	−0.799880	−	0.600160i	$-0.795104\pi$
$937$		−	36.7423i		−	1.20032i	0.799880	−	0.600160i	$-0.204896\pi$
$938$	−1.01461	−	7.41421i	−0.0331283	−	0.242083i
$939$		0			0
$940$		0			0
$941$	−21.6506	+	37.5000i	−0.705791	+	1.22247i	0.260615	+	0.965443i	$0.416075\pi$
$941$	−21.6506	+	37.5000i	−0.705791	+	1.22247i	−0.966405	+	0.257022i	$0.917259\pi$
$942$		0			0
$943$	21.2132	−	12.2474i	0.690797	−	0.398832i
$944$	34.6410			1.12747
$945$		0			0
$946$	−10.0000			−0.325128
$947$	4.89898	−	2.82843i	0.159195	−	0.0919115i	−0.418286	−	0.908315i	$-0.637369\pi$
$947$	4.89898	−	2.82843i	0.159195	−	0.0919115i	0.577481	+	0.816404i	$0.304036\pi$
$948$		0			0
$949$		0			0
$950$	−10.3923	+	18.0000i	−0.337171	+	0.583997i
$951$		0			0
$952$	5.27208	+	38.5254i	0.170869	+	1.24861i
$953$			56.5685i			1.83243i	0.400681	+	0.916217i	$0.368773\pi$
$953$			56.5685i			1.83243i	−0.400681	+	0.916217i	$0.631227\pi$
$954$		0			0
$955$			24.4949i			0.792636i
$956$		0			0
$957$		0			0
$958$	40.3051	+	23.2702i	1.30220	+	0.751825i
$959$	−2.95680	+	2.29289i	−0.0954799	+	0.0740414i
$960$		0			0
$961$	−12.5000	−	21.6506i	−0.403226	−	0.698408i
$962$	17.3205			0.558436
$963$		0			0
$964$		0			0
$965$	0.866025	+	1.50000i	0.0278783	+	0.0482867i
$966$		0			0
$967$	5.00000	−	8.66025i	0.160789	−	0.278495i	−0.774363	−	0.632742i	$-0.781929\pi$
$967$	5.00000	−	8.66025i	0.160789	−	0.278495i	0.935152	+	0.354247i	$0.115263\pi$
$968$	−22.0454	−	12.7279i	−0.708566	−	0.409091i
$969$		0			0
$970$	21.0000	+	36.3731i	0.674269	+	1.16787i
$971$	5.19615			0.166752			0.0833762	−	0.996518i	$-0.473430\pi$
$971$	5.19615			0.166752			0.0833762	+	0.996518i	$0.473430\pi$
$972$		0			0
$973$	30.0000	+	12.2474i	0.961756	+	0.392635i
$974$	−26.9444	+	15.5563i	−0.863354	+	0.498458i
$975$		0			0
$976$	8.48528	+	4.89898i	0.271607	+	0.156813i
$977$	2.44949	+	1.41421i	0.0783661	+	0.0452447i	0.538671	−	0.842516i	$-0.318927\pi$
$977$	2.44949	+	1.41421i	0.0783661	+	0.0452447i	−0.460305	+	0.887761i	$0.652260\pi$
$978$		0			0
$979$	12.7279	−	7.34847i	0.406786	−	0.234858i
$980$		0			0
$981$		0			0
$982$	22.0000			0.702048
$983$	16.4545	+	28.5000i	0.524816	+	0.909009i	0.999582	+	0.0288967i	$0.00919939\pi$
$983$	16.4545	+	28.5000i	0.524816	+	0.909009i	−0.474766	+	0.880112i	$0.657467\pi$
$984$		0			0
$985$	−2.12132	−	1.22474i	−0.0675909	−	0.0390236i
$986$	25.9808	−	45.0000i	0.827396	−	1.43309i
$987$		0			0
$988$		0			0
$989$		−	14.1421i		−	0.449694i
$990$		0			0
$991$	41.0000			1.30241			0.651204	−	0.758903i	$-0.274264\pi$
$991$	41.0000			1.30241			0.651204	+	0.758903i	$0.274264\pi$
$992$		0			0
$993$		0			0
$994$	−32.4264	−	41.8154i	−1.02850	−	1.32630i
$995$		0			0
$996$		0			0
$997$	−10.6066	+	6.12372i	−0.335914	+	0.193940i	−0.658464	−	0.752612i	$-0.728793\pi$
$997$	−10.6066	+	6.12372i	−0.335914	+	0.193940i	0.322549	+	0.946553i	$0.395460\pi$
$998$			24.0416i			0.761025i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	567.2.o.e.377.3		8
3.2	odd	2	inner	567.2.o.e.377.2		8
7.6	odd	2	inner	567.2.o.e.377.4		8
9.2	odd	6	inner	567.2.o.e.188.4		8
9.4	even	3		189.2.c.c.188.4	yes	4
9.5	odd	6		189.2.c.c.188.1	✓	4
9.7	even	3	inner	567.2.o.e.188.1		8
21.20	even	2	inner	567.2.o.e.377.1		8
36.23	even	6		3024.2.k.g.1889.2		4
36.31	odd	6		3024.2.k.g.1889.4		4
63.13	odd	6		189.2.c.c.188.3	yes	4
63.20	even	6	inner	567.2.o.e.188.3		8
63.34	odd	6	inner	567.2.o.e.188.2		8
63.41	even	6		189.2.c.c.188.2	yes	4
252.139	even	6		3024.2.k.g.1889.1		4
252.167	odd	6		3024.2.k.g.1889.3		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.c.c.188.1	✓	4	9.5	odd	6
189.2.c.c.188.2	yes	4	63.41	even	6
189.2.c.c.188.3	yes	4	63.13	odd	6
189.2.c.c.188.4	yes	4	9.4	even	3
567.2.o.e.188.1		8	9.7	even	3	inner
567.2.o.e.188.2		8	63.34	odd	6	inner
567.2.o.e.188.3		8	63.20	even	6	inner
567.2.o.e.188.4		8	9.2	odd	6	inner
567.2.o.e.377.1		8	21.20	even	2	inner
567.2.o.e.377.2		8	3.2	odd	2	inner
567.2.o.e.377.3		8	1.1	even	1	trivial
567.2.o.e.377.4		8	7.6	odd	2	inner
3024.2.k.g.1889.1		4	252.139	even	6
3024.2.k.g.1889.2		4	36.23	even	6
3024.2.k.g.1889.3		4	252.167	odd	6
3024.2.k.g.1889.4		4	36.31	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:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	567.o (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{5} +(-2.62132 + 0.358719i) q^{7} +2.82843i q^{8} +O(q^{10})\)	\(q+(1.22474 - 0.707107i) q^{2} +(-0.866025 + 1.50000i) q^{5} +(-2.62132 + 0.358719i) q^{7} +2.82843i q^{8} +2.44949i q^{10} +(1.22474 - 0.707107i) q^{11} +(2.12132 + 1.22474i) q^{13} +(-2.95680 + 2.29289i) q^{14} +(2.00000 + 3.46410i) q^{16} -5.19615 q^{17} +7.34847i q^{19} +(1.00000 - 1.73205i) q^{22} +(2.44949 + 1.41421i) q^{23} +(1.00000 + 1.73205i) q^{25} +3.46410 q^{26} +(-6.12372 + 3.53553i) q^{29} +(2.12132 + 1.22474i) q^{31} +(-6.36396 + 3.67423i) q^{34} +(1.73205 - 4.24264i) q^{35} +5.00000 q^{37} +(5.19615 + 9.00000i) q^{38} +(-4.24264 - 2.44949i) q^{40} +(4.33013 - 7.50000i) q^{41} +(-2.50000 - 4.33013i) q^{43} +4.00000 q^{46} +(-4.33013 - 7.50000i) q^{47} +(6.74264 - 1.88064i) q^{49} +(2.44949 + 1.41421i) q^{50} -11.3137i q^{53} +2.44949i q^{55} +(-1.01461 - 7.41421i) q^{56} +(-5.00000 + 8.66025i) q^{58} +(4.33013 - 7.50000i) q^{59} +(2.12132 - 1.22474i) q^{61} +3.46410 q^{62} -8.00000 q^{64} +(-3.67423 + 2.12132i) q^{65} +(-1.00000 + 1.73205i) q^{67} +(-0.878680 - 6.42090i) q^{70} +14.1421i q^{71} +(6.12372 - 3.53553i) q^{74} +(-2.95680 + 2.29289i) q^{77} +(6.50000 + 11.2583i) q^{79} -6.92820 q^{80} -12.2474i q^{82} +(0.866025 + 1.50000i) q^{83} +(4.50000 - 7.79423i) q^{85} +(-6.12372 - 3.53553i) q^{86} +(2.00000 + 3.46410i) q^{88} +10.3923 q^{89} +(-6.00000 - 2.44949i) q^{91} +(-10.6066 - 6.12372i) q^{94} +(-11.0227 - 6.36396i) q^{95} +(14.8492 - 8.57321i) q^{97} +(6.92820 - 7.07107i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{7}+O(q^{10}) \) 8 * q - 4 * q^7	\( 8 q - 4 q^{7} + 16 q^{16} + 8 q^{22} + 8 q^{25} + 40 q^{37} - 20 q^{43} + 32 q^{46} + 20 q^{49} - 40 q^{58} - 64 q^{64} - 8 q^{67} - 24 q^{70} + 52 q^{79} + 36 q^{85} + 16 q^{88} - 48 q^{91}+O(q^{100}) \) 8 * q - 4 * q^7 + 16 * q^16 + 8 * q^22 + 8 * q^25 + 40 * q^37 - 20 * q^43 + 32 * q^46 + 20 * q^49 - 40 * q^58 - 64 * q^64 - 8 * q^67 - 24 * q^70 + 52 * q^79 + 36 * q^85 + 16 * q^88 - 48 * q^91

Introduction

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