LMFDB - Embedded newform 567.2.o.e.188.2

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			188.2
Root			$-0.258819 - 0.965926i$ of defining polynomial
Character	$\chi$	$=$	567.188
Dual form			567.2.o.e.377.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.22474 - 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{5} +(-2.62132 - 0.358719i) q^{7} +2.82843i q^{8} +O(q^{10})$	\(q+(-1.22474 - 0.707107i) q^{2} +(0.866025 + 1.50000i) q^{5} +(-2.62132 - 0.358719i) q^{7} +2.82843i q^{8} -2.44949i q^{10} +(-1.22474 - 0.707107i) q^{11} +(2.12132 - 1.22474i) q^{13} +(2.95680 + 2.29289i) q^{14} +(2.00000 - 3.46410i) q^{16} +5.19615 q^{17} -7.34847i q^{19} +(1.00000 + 1.73205i) q^{22} +(-2.44949 + 1.41421i) q^{23} +(1.00000 - 1.73205i) q^{25} -3.46410 q^{26} +(6.12372 + 3.53553i) q^{29} +(2.12132 - 1.22474i) q^{31} +(-6.36396 - 3.67423i) q^{34} +(-1.73205 - 4.24264i) q^{35} +5.00000 q^{37} +(-5.19615 + 9.00000i) q^{38} +(-4.24264 + 2.44949i) q^{40} +(-4.33013 - 7.50000i) q^{41} +(-2.50000 + 4.33013i) q^{43} +4.00000 q^{46} +(4.33013 - 7.50000i) q^{47} +(6.74264 + 1.88064i) q^{49} +(-2.44949 + 1.41421i) q^{50} -11.3137i q^{53} -2.44949i q^{55} +(1.01461 - 7.41421i) q^{56} +(-5.00000 - 8.66025i) q^{58} +(-4.33013 - 7.50000i) q^{59} +(2.12132 + 1.22474i) q^{61} -3.46410 q^{62} -8.00000 q^{64} +(3.67423 + 2.12132i) q^{65} +(-1.00000 - 1.73205i) q^{67} +(-0.878680 + 6.42090i) q^{70} +14.1421i q^{71} +(-6.12372 - 3.53553i) q^{74} +(2.95680 + 2.29289i) q^{77} +(6.50000 - 11.2583i) q^{79} +6.92820 q^{80} +12.2474i q^{82} +(-0.866025 + 1.50000i) q^{83} +(4.50000 + 7.79423i) q^{85} +(6.12372 - 3.53553i) q^{86} +(2.00000 - 3.46410i) q^{88} -10.3923 q^{89} +(-6.00000 + 2.44949i) q^{91} +(-10.6066 + 6.12372i) q^{94} +(11.0227 - 6.36396i) q^{95} +(14.8492 + 8.57321i) q^{97} +(-6.92820 - 7.07107i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/567\mathbb{Z}\right)^\times$.

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

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	$0.833333\pi$
$3$		0			0
$3$		0			0
$4$		0			0
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	0.992085	−	0.125567i	$-0.0400750\pi$
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	−0.604787	+	0.796387i	$0.706742\pi$
$6$		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	$-0.401722\pi$
$11$	−1.22474	−	0.707107i	−0.369274	−	0.213201i	−0.673141	+	0.739514i	$0.735055\pi$
$12$		0			0
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	−0.176096	−	0.984373i	$-0.556347\pi$
$13$	2.12132	−	1.22474i	0.588348	−	0.339683i	0.764444	+	0.644690i	$0.223014\pi$
$14$	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	$-0.283003\pi$
$17$	5.19615			1.26025			0.630126	+	0.776493i	$0.283003\pi$
$18$		0			0
$19$		−	7.34847i		−	1.68585i	−0.538028	−	0.842927i	$-0.680830\pi$
$19$		−	7.34847i		−	1.68585i	0.538028	−	0.842927i	$-0.319170\pi$
$20$		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	$-0.761948\pi$
$23$	−2.44949	+	1.41421i	−0.510754	+	0.294884i	0.222390	+	0.974958i	$0.428614\pi$
$24$		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	$-0.105356\pi$
$29$	6.12372	+	3.53553i	1.13715	+	0.656532i	0.191425	+	0.981507i	$0.438689\pi$
$30$		0			0
$31$	2.12132	−	1.22474i	0.381000	−	0.219971i	−0.297253	−	0.954799i	$-0.596070\pi$
$31$	2.12132	−	1.22474i	0.381000	−	0.219971i	0.678253	+	0.734828i	$0.262737\pi$
$32$		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	−0.976101	−	0.217317i	$-0.930270\pi$
$41$	−4.33013	−	7.50000i	−0.676252	−	1.17130i	0.299849	−	0.953987i	$-0.403064\pi$
$42$		0			0
$43$	−2.50000	+	4.33013i	−0.381246	+	0.660338i	−0.991241	−	0.132068i	$-0.957838\pi$
$43$	−2.50000	+	4.33013i	−0.381246	+	0.660338i	0.609994	+	0.792406i	$0.291172\pi$
$44$		0			0
$45$		0			0
$46$	4.00000			0.589768
$47$	4.33013	−	7.50000i	0.631614	−	1.09399i	−0.355608	−	0.934635i	$-0.615726\pi$
$47$	4.33013	−	7.50000i	0.631614	−	1.09399i	0.987222	−	0.159352i	$-0.0509405\pi$
$48$		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	−0.997166	−	0.0752304i	$-0.976031\pi$
$59$	−4.33013	−	7.50000i	−0.563735	−	0.976417i	0.433432	−	0.901186i	$-0.357303\pi$
$60$		0			0
$61$	2.12132	+	1.22474i	0.271607	+	0.156813i	0.629618	−	0.776905i	$-0.283211\pi$
$61$	2.12132	+	1.22474i	0.271607	+	0.156813i	−0.358011	+	0.933718i	$0.616545\pi$
$62$	−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	0.798454	−	0.602056i	$-0.205652\pi$
$67$	−1.00000	−	1.73205i	−0.122169	−	0.211604i	−0.920623	+	0.390453i	$0.872318\pi$
$68$		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	−0.225018	−	0.974355i	$-0.572244\pi$
$79$	6.50000	−	11.2583i	0.731307	−	1.26666i	0.956325	−	0.292306i	$-0.0944227\pi$
$80$	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	$-0.863637\pi$
$83$	−0.866025	+	1.50000i	−0.0950586	+	0.164646i	0.814574	+	0.580059i	$0.196971\pi$
$84$		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	$-0.685674\pi$
$89$	−10.3923			−1.10158			−0.550791	+	0.834643i	$0.685674\pi$
$90$		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	0.999960	+	0.00897496i	$0.00285686\pi$
$97$	14.8492	+	8.57321i	1.50771	+	0.870478i	0.507752	+	0.861503i	$0.330476\pi$
$98$	−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	$-0.778199\pi$
$101$	1.73205	−	3.00000i	0.172345	−	0.298511i	0.939239	+	0.343263i	$0.111532\pi$
$102$		0			0
$103$	8.48528	−	4.89898i	0.836080	−	0.482711i	−0.0198501	−	0.999803i	$-0.506319\pi$
$103$	8.48528	−	4.89898i	0.836080	−	0.482711i	0.855930	+	0.517092i	$0.172986\pi$
$104$	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	$-0.774591\pi$
$113$	−6.12372	+	3.53553i	−0.576072	+	0.332595i	0.183499	+	0.983020i	$0.441258\pi$
$114$		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	0.944550	+	0.328368i	$0.106499\pi$
$131$	8.66025	+	15.0000i	0.756650	+	1.31056i	−0.187900	+	0.982188i	$0.560168\pi$
$132$		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	$-0.352575\pi$
$137$	−1.22474	−	0.707107i	−0.104637	−	0.0604122i	−0.551405	+	0.834238i	$0.685908\pi$
$138$		0			0
$139$	−10.6066	+	6.12372i	−0.899640	+	0.519408i	−0.877083	−	0.480338i	$-0.840514\pi$
$139$	−10.6066	+	6.12372i	−0.899640	+	0.519408i	−0.0225568	+	0.999746i	$0.507181\pi$
$140$		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	$-0.760203\pi$
$149$	−6.12372	+	3.53553i	−0.501675	+	0.289642i	0.227730	+	0.973724i	$0.426870\pi$
$150$		0			0
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	−0.949637	−	0.313353i	$-0.898548\pi$
$151$	−2.50000	+	4.33013i	−0.203447	+	0.352381i	0.746190	+	0.665733i	$0.231881\pi$
$152$	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	0.227910	−	0.973682i	$-0.426811\pi$
$157$	14.8492	−	8.57321i	1.18510	−	0.684217i	0.957189	+	0.289465i	$0.0934775\pi$
$158$	−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	$-0.0112431\pi$
$167$	6.06218	+	10.5000i	0.469105	+	0.812514i	−0.530271	+	0.847828i	$0.677910\pi$
$168$		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	$-0.918168\pi$
$173$	−3.46410	+	6.00000i	−0.263371	+	0.456172i	0.703765	+	0.710433i	$0.251501\pi$
$174$		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	$-0.816071\pi$
$181$		−	14.6969i		−	1.09241i	0.837650	−	0.546207i	$-0.183929\pi$
$182$	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	$-0.504297\pi$
$191$	−12.2474	−	7.07107i	−0.886194	−	0.511645i	−0.872696	+	0.488264i	$0.837630\pi$
$192$		0			0
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	0.883460	−	0.468507i	$-0.155208\pi$
$193$	0.500000	+	0.866025i	0.0359908	+	0.0623379i	−0.847469	+	0.530845i	$0.821875\pi$
$194$	−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	0.998221	+	0.0596196i	$0.0189888\pi$
$211$	8.00000	+	13.8564i	0.550743	+	0.953914i	−0.447478	+	0.894295i	$0.647678\pi$
$212$		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	0.100891	−	0.994898i	$-0.467831\pi$
$223$	−10.6066	−	6.12372i	−0.710271	−	0.410075i	−0.811161	+	0.584823i	$0.801164\pi$
$224$		0			0
$225$		0			0
$226$	10.0000			0.665190
$227$	6.92820	−	12.0000i	0.459841	−	0.796468i	−0.539111	−	0.842235i	$-0.681240\pi$
$227$	6.92820	−	12.0000i	0.459841	−	0.796468i	0.998952	+	0.0457666i	$0.0145731\pi$
$228$		0			0
$229$	−4.24264	+	2.44949i	−0.280362	+	0.161867i	−0.633587	−	0.773671i	$-0.718418\pi$
$229$	−4.24264	+	2.44949i	−0.280362	+	0.161867i	0.353226	+	0.935538i	$0.385085\pi$
$230$	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	$-0.463975\pi$
$239$	15.9217	−	9.19239i	1.02989	−	0.594606i	0.916953	+	0.398996i	$0.130641\pi$
$240$		0			0
$241$	2.12132	+	1.22474i	0.136646	+	0.0788928i	0.566765	−	0.823880i	$-0.308195\pi$
$241$	2.12132	+	1.22474i	0.136646	+	0.0788928i	−0.430118	+	0.902772i	$0.641528\pi$
$242$			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	$-0.552436\pi$
$251$	−5.19615			−0.327978			−0.163989	+	0.986462i	$0.552436\pi$
$252$		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	$-0.201125\pi$
$257$	−1.73205	−	3.00000i	−0.108042	−	0.187135i	−0.914977	+	0.403506i	$0.867792\pi$
$258$		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	$-0.347217\pi$
$263$	−1.22474	−	0.707107i	−0.0755210	−	0.0436021i	−0.537285	+	0.843401i	$0.680550\pi$
$264$		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	$-0.790980\pi$
$269$	−25.9808			−1.58408			−0.792038	+	0.610472i	$0.790980\pi$
$270$		0			0
$271$		−	14.6969i		−	0.892775i	−0.894840	−	0.446388i	$-0.852710\pi$
$271$		−	14.6969i		−	0.892775i	0.894840	−	0.446388i	$-0.147290\pi$
$272$	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	−0.931305	−	0.364241i	$-0.881328\pi$
$277$	−2.50000	+	4.33013i	−0.150210	+	0.260172i	0.781094	+	0.624413i	$0.214662\pi$
$278$	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	$-0.471944\pi$
$281$	−12.2474	−	7.07107i	−0.730622	−	0.421825i	−0.818650	+	0.574293i	$0.805277\pi$
$282$		0			0
$283$	−10.6066	+	6.12372i	−0.630497	+	0.364018i	−0.780945	−	0.624600i	$-0.785262\pi$
$283$	−10.6066	+	6.12372i	−0.630497	+	0.364018i	0.150448	+	0.988618i	$0.451929\pi$
$284$		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	−0.997783	−	0.0665568i	$-0.978799\pi$
$293$	−9.52628	−	16.5000i	−0.556531	−	0.963940i	0.441251	−	0.897384i	$-0.354535\pi$
$294$		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	$-0.0549678\pi$
$311$	6.06218	+	10.5000i	0.343755	+	0.595400i	−0.641372	+	0.767230i	$0.721635\pi$
$312$		0			0
$313$	21.2132	+	12.2474i	1.19904	+	0.692267i	0.960341	−	0.278827i	$-0.0899455\pi$
$313$	21.2132	+	12.2474i	1.19904	+	0.692267i	0.238700	+	0.971093i	$0.423279\pi$
$314$	−24.2487			−1.36843
$315$		0			0
$316$		0			0
$317$	−4.89898	−	2.82843i	−0.275154	−	0.158860i	0.356073	−	0.934458i	$-0.384115\pi$
$317$	−4.89898	−	2.82843i	−0.275154	−	0.158860i	−0.631228	+	0.775598i	$0.717449\pi$
$318$		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	−0.285722	−	0.958313i	$-0.592233\pi$
$331$	12.5000	−	21.6506i	0.687062	−	1.19003i	0.972784	−	0.231714i	$-0.0744333\pi$
$332$		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	0.945468	−	0.325714i	$-0.105605\pi$
$337$	3.50000	+	6.06218i	0.190657	+	0.330228i	−0.754811	+	0.655942i	$0.772271\pi$
$338$	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	$-0.727450\pi$
$347$	−6.12372	+	3.53553i	−0.328739	+	0.189797i	0.326542	+	0.945183i	$0.394116\pi$
$348$		0			0
$349$	−16.9706	−	9.79796i	−0.908413	−	0.524473i	−0.0284931	−	0.999594i	$-0.509071\pi$
$349$	−16.9706	−	9.79796i	−0.908413	−	0.524473i	−0.879920	+	0.475121i	$0.842404\pi$
$350$	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	$-0.759307\pi$
$353$	4.33013	−	7.50000i	0.230469	−	0.399185i	0.957946	+	0.286947i	$0.0926405\pi$
$354$		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	0.385164	−	0.922848i	$-0.374145\pi$
$367$	−4.24264	−	2.44949i	−0.221464	−	0.127862i	−0.606628	+	0.794986i	$0.707478\pi$
$368$			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	0.983783	+	0.179364i	$0.0574041\pi$
$373$	12.5000	+	21.6506i	0.647225	+	1.12103i	−0.336557	+	0.941663i	$0.609263\pi$
$374$	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	$-0.152576\pi$
$383$	0.866025	+	1.50000i	0.0442518	+	0.0766464i	−0.843051	+	0.537833i	$0.819243\pi$
$384$		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	$-0.0247392\pi$
$389$	28.1691	+	16.2635i	1.42823	+	0.824590i	0.431250	+	0.902232i	$0.358073\pi$
$390$		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	$-0.831263\pi$
$401$	−17.1464	+	9.89949i	−0.856252	+	0.494357i	0.00650355	+	0.999979i	$0.497930\pi$
$402$		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	−0.856972	−	0.515363i	$-0.827657\pi$
$409$	−16.9706	+	9.79796i	−0.839140	+	0.484478i	0.0178316	+	0.999841i	$0.494324\pi$
$410$	−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	$-0.153196\pi$
$419$	0.866025	+	1.50000i	0.0423081	+	0.0732798i	−0.844096	+	0.536192i	$0.819862\pi$
$420$		0			0
$421$	2.00000	−	3.46410i	0.0974740	−	0.168830i	−0.813164	−	0.582034i	$-0.802257\pi$
$421$	2.00000	−	3.46410i	0.0974740	−	0.168830i	0.910638	+	0.413204i	$0.135590\pi$
$422$		−	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	$0.344387\pi$
$433$			36.7423i			1.76572i	−0.469632	+	0.882862i	$0.655613\pi$
$434$	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	0.0369815	−	0.999316i	$-0.488226\pi$
$439$	−16.9706	−	9.79796i	−0.809961	−	0.467631i	−0.846942	+	0.531685i	$0.821559\pi$
$440$	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	$-0.0522390\pi$
$443$	28.1691	+	16.2635i	1.33836	+	0.772700i	0.351792	+	0.936078i	$0.385572\pi$
$444$		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	0.200118	+	0.979772i	$0.435868\pi$
$457$	−16.0000	+	27.7128i	−0.748448	+	1.29635i	−0.948566	+	0.316579i	$0.897466\pi$
$458$	6.92820			0.323734
$459$		0			0
$460$		0			0
$461$	−6.06218	+	10.5000i	−0.282344	+	0.489034i	−0.971962	−	0.235140i	$-0.924445\pi$
$461$	−6.06218	+	10.5000i	−0.282344	+	0.489034i	0.689618	+	0.724174i	$0.257779\pi$
$462$		0			0
$463$	−5.50000	−	9.52628i	−0.255607	−	0.442724i	0.709453	−	0.704752i	$-0.248942\pi$
$463$	−5.50000	−	9.52628i	−0.255607	−	0.442724i	−0.965060	+	0.262029i	$0.915609\pi$
$464$	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	$-0.340311\pi$
$467$	20.7846			0.961797			0.480899	+	0.876776i	$0.340311\pi$
$468$		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	0.195113	+	0.980781i	$0.437493\pi$
$479$	−16.4545	+	28.5000i	−0.751825	+	1.30220i	−0.946938	+	0.321417i	$0.895841\pi$
$480$		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	$-0.780833\pi$
$491$	−13.4722	+	7.77817i	−0.607992	+	0.351024i	0.164187	+	0.986429i	$0.447500\pi$
$492$		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	0.610623	−	0.791921i	$-0.290919\pi$
$499$	−8.50000	−	14.7224i	−0.380512	−	0.659067i	−0.991136	+	0.132855i	$0.957586\pi$
$500$		0			0
$501$		0			0
$502$	6.36396	+	3.67423i	0.284037	+	0.163989i
$503$	−36.3731			−1.62179			−0.810897	−	0.585188i	$-0.801021\pi$
$503$	−36.3731			−1.62179			−0.810897	+	0.585188i	$0.801021\pi$
$504$		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	$-0.228141\pi$
$509$	−4.33013	−	7.50000i	−0.191930	−	0.332432i	−0.945890	+	0.324489i	$0.894808\pi$
$510$		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	$-0.536310\pi$
$521$	−5.19615			−0.227648			−0.113824	+	0.993501i	$0.536310\pi$
$522$		0			0
$523$			36.7423i			1.60663i	0.595554	+	0.803315i	$0.296933\pi$
$523$			36.7423i			1.60663i	−0.595554	+	0.803315i	$0.703067\pi$
$524$		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	−0.692948	−	0.720988i	$-0.743688\pi$
$547$	6.50000	−	11.2583i	0.277920	−	0.481371i	0.970868	+	0.239616i	$0.0770217\pi$
$548$		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	−0.956894	−	0.290436i	$-0.906200\pi$
$563$	−17.3205	−	30.0000i	−0.729972	−	1.26435i	0.226922	−	0.973913i	$-0.427134\pi$
$564$		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	$-0.645003\pi$
$569$	−34.2929	−	19.7990i	−1.43763	−	0.830017i	−0.997685	+	0.0680072i	$0.978336\pi$
$570$		0			0
$571$	9.50000	+	16.4545i	0.397563	+	0.688599i	0.993425	−	0.114488i	$-0.0365228\pi$
$571$	9.50000	+	16.4545i	0.397563	+	0.688599i	−0.595862	+	0.803087i	$0.703189\pi$
$572$		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	$0.209571\pi$
$577$			29.3939i			1.22368i	−0.790980	+	0.611842i	$0.790429\pi$
$578$	−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	$-0.741022\pi$
$587$	6.92820	−	12.0000i	0.285958	−	0.495293i	0.972841	+	0.231475i	$0.0743550\pi$
$588$		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	$-0.603707\pi$
$593$	−15.5885			−0.640141			−0.320071	+	0.947394i	$0.603707\pi$
$594$		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	$-0.544106\pi$
$599$	15.9217	−	9.19239i	0.650542	−	0.375591i	0.788664	+	0.614824i	$0.210773\pi$
$600$		0			0
$601$	40.3051	+	23.2702i	1.64408	+	0.949209i	0.979362	+	0.202114i	$0.0647811\pi$
$601$	40.3051	+	23.2702i	1.64408	+	0.949209i	0.664717	+	0.747095i	$0.268552\pi$
$602$	−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	−0.699563	−	0.714571i	$-0.746622\pi$
$607$	−10.6066	+	6.12372i	−0.430509	+	0.248554i	0.269055	+	0.963125i	$0.413289\pi$
$608$		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	0.712501	−	0.701671i	$-0.247562\pi$
$617$	41.6413	−	24.0416i	1.67642	−	0.967880i	0.963915	−	0.266209i	$-0.0857711\pi$
$618$		0			0
$619$	−23.3345	−	13.4722i	−0.937894	−	0.541493i	−0.0485943	−	0.998819i	$-0.515474\pi$
$619$	−23.3345	−	13.4722i	−0.937894	−	0.541493i	−0.889299	+	0.457325i	$0.848807\pi$
$620$		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	$-0.342225\pi$
$641$	−1.22474	−	0.707107i	−0.0483745	−	0.0279290i	−0.523992	+	0.851723i	$0.675558\pi$
$642$		0			0
$643$	21.2132	−	12.2474i	0.836567	−	0.482992i	−0.0195288	−	0.999809i	$-0.506217\pi$
$643$	21.2132	−	12.2474i	0.836567	−	0.482992i	0.856096	+	0.516817i	$0.172883\pi$
$644$		0			0
$645$		0			0
$646$	−27.0000	+	46.7654i	−1.06230	+	1.83996i
$647$	20.7846			0.817127			0.408564	−	0.912730i	$-0.366030\pi$
$647$	20.7846			0.817127			0.408564	+	0.912730i	$0.366030\pi$
$648$		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	$-0.549537\pi$
$653$	15.9217	−	9.19239i	0.623064	−	0.359726i	0.778061	+	0.628189i	$0.216204\pi$
$654$		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	$-0.262610\pi$
$659$	9.79796	+	5.65685i	0.381674	+	0.220360i	−0.296872	+	0.954917i	$0.595944\pi$
$660$		0			0
$661$	14.8492	−	8.57321i	0.577569	−	0.333459i	−0.182598	−	0.983188i	$-0.558451\pi$
$661$	14.8492	−	8.57321i	0.577569	−	0.333459i	0.760167	+	0.649728i	$0.225117\pi$
$662$	−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	−0.166103	−	0.986108i	$-0.553118\pi$
$673$	20.0000	−	34.6410i	0.770943	−	1.33531i	0.937046	−	0.349205i	$-0.113548\pi$
$674$		−	9.89949i		−	0.381314i
$675$		0			0
$676$		0			0
$677$	−8.66025	+	15.0000i	−0.332841	+	0.576497i	−0.983068	−	0.183243i	$-0.941340\pi$
$677$	−8.66025	+	15.0000i	−0.332841	+	0.576497i	0.650227	+	0.759740i	$0.274674\pi$
$678$		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	−0.0145019	−	0.999895i	$-0.504616\pi$
$691$	−23.3345	−	13.4722i	−0.887687	−	0.512506i	−0.873185	+	0.487388i	$0.837950\pi$
$692$		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	−0.909145	−	0.416481i	$-0.863263\pi$
$709$	−2.50000	+	4.33013i	−0.0938895	+	0.162621i	0.815255	+	0.579102i	$0.196597\pi$
$710$	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	$-0.406120\pi$
$719$	15.5885			0.581351			0.290676	+	0.956822i	$0.406120\pi$
$720$		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	0.290245	−	0.956952i	$-0.406263\pi$
$727$	−10.6066	−	6.12372i	−0.393377	−	0.227116i	−0.683622	+	0.729836i	$0.739596\pi$
$728$	−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	0.281813	−	0.959469i	$-0.409064\pi$
$733$	33.9411	−	19.5959i	1.25364	−	0.723792i	0.971831	+	0.235678i	$0.0757310\pi$
$734$	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	$-0.708070\pi$
$743$	−6.12372	+	3.53553i	−0.224658	+	0.129706i	0.383447	+	0.923563i	$0.374737\pi$
$744$		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	0.989423	+	0.145062i	$0.0463382\pi$
$751$	17.0000	+	29.4449i	0.620339	+	1.07446i	−0.369084	+	0.929396i	$0.620328\pi$
$752$	−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	$-0.0961413\pi$
$761$	6.06218	+	10.5000i	0.219754	+	0.380625i	−0.734979	+	0.678090i	$0.762808\pi$
$762$		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	−0.574542	−	0.818475i	$-0.694820\pi$
$769$	−4.24264	+	2.44949i	−0.152994	+	0.0883309i	0.421549	+	0.906806i	$0.361487\pi$
$770$	5.61642	−	7.24264i	0.202402	−	0.261007i
$771$		0			0
$772$		0			0
$773$	−15.5885			−0.560678			−0.280339	−	0.959901i	$-0.590447\pi$
$773$	−15.5885			−0.560678			−0.280339	+	0.959901i	$0.590447\pi$
$774$		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	−0.573707	−	0.819060i	$-0.694495\pi$
$787$	−4.24264	+	2.44949i	−0.151234	+	0.0873149i	0.422473	+	0.906375i	$0.361162\pi$
$788$		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	0.976505	+	0.215495i	$0.0691363\pi$
$797$	19.0526	+	33.0000i	0.674876	+	1.16892i	−0.301629	+	0.953425i	$0.597530\pi$
$798$		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	$-0.776816\pi$
$811$		−	36.7423i		−	1.29020i	0.764099	−	0.645099i	$-0.223184\pi$
$812$		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	$-0.111591\pi$
$821$	31.8434	+	18.3848i	1.11134	+	0.641633i	0.172165	+	0.985068i	$0.444924\pi$
$822$		0			0
$823$	27.5000	+	47.6314i	0.958590	+	1.66033i	0.725931	+	0.687768i	$0.241409\pi$
$823$	27.5000	+	47.6314i	0.958590	+	1.66033i	0.232659	+	0.972558i	$0.425257\pi$
$824$	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	$-0.779738\pi$
$829$		−	36.7423i		−	1.27611i	0.769989	−	0.638057i	$-0.220262\pi$
$830$	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	$-0.726661\pi$
$839$	9.52628	−	16.5000i	0.328884	−	0.569643i	0.982291	+	0.187364i	$0.0599943\pi$
$840$		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	−0.454021	−	0.890991i	$-0.650011\pi$
$853$	−42.4264	−	24.4949i	−1.45265	−	0.838689i	−0.998631	+	0.0523016i	$0.983344\pi$
$854$	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	$-0.958986\pi$
$857$	−11.2583	+	19.5000i	−0.384577	+	0.666107i	0.607133	+	0.794600i	$0.292319\pi$
$858$		0			0
$859$	−16.9706	+	9.79796i	−0.579028	+	0.334302i	−0.760747	−	0.649048i	$-0.775167\pi$
$859$	−16.9706	+	9.79796i	−0.579028	+	0.334302i	0.181719	+	0.983351i	$0.441834\pi$
$860$		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	0.958560	+	0.284892i	$0.0919577\pi$
$877$	21.5000	+	37.2391i	0.726003	+	1.25747i	−0.232556	+	0.972583i	$0.574709\pi$
$878$	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	$-0.160655\pi$
$881$	51.9615			1.75063			0.875314	+	0.483555i	$0.160655\pi$
$882$		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	$-0.331254\pi$
$887$	−14.7224	−	25.5000i	−0.494331	−	0.856206i	−0.999979	+	0.00653381i	$0.997920\pi$
$888$		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	−0.991327	−	0.131419i	$-0.958047\pi$
$907$	−11.5000	+	19.9186i	−0.381851	+	0.661386i	0.609476	+	0.792805i	$0.291380\pi$
$908$		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	$-0.295962\pi$
$911$	6.12372	+	3.53553i	0.202888	+	0.117137i	−0.395114	+	0.918632i	$0.629295\pi$
$912$		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	0.459057	+	0.888407i	$0.348187\pi$
$929$	−16.4545	+	28.5000i	−0.539854	+	0.935055i	−0.998911	+	0.0466480i	$0.985146\pi$
$930$		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	$0.204896\pi$
$937$			36.7423i			1.20032i	−0.799880	+	0.600160i	$0.795104\pi$
$938$	1.01461	−	7.41421i	0.0331283	−	0.242083i
$939$		0			0
$940$		0			0
$941$	21.6506	+	37.5000i	0.705791	+	1.22247i	0.966405	+	0.257022i	$0.0827414\pi$
$941$	21.6506	+	37.5000i	0.705791	+	1.22247i	−0.260615	+	0.965443i	$0.583925\pi$
$942$		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	$-0.362631\pi$
$947$	−4.89898	−	2.82843i	−0.159195	−	0.0919115i	−0.577481	+	0.816404i	$0.695964\pi$
$948$		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	0.935152	−	0.354247i	$-0.115263\pi$
$967$	5.00000	+	8.66025i	0.160789	+	0.278495i	−0.774363	+	0.632742i	$0.781929\pi$
$968$	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	$-0.526570\pi$
$971$	−5.19615			−0.166752			−0.0833762	+	0.996518i	$0.526570\pi$
$972$		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	$-0.681073\pi$
$977$	−2.44949	+	1.41421i	−0.0783661	+	0.0452447i	0.460305	+	0.887761i	$0.347740\pi$
$978$		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	0.474766	+	0.880112i	$0.342533\pi$
$983$	−16.4545	+	28.5000i	−0.524816	+	0.909009i	−0.999582	+	0.0288967i	$0.990801\pi$
$984$		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	0.322549	−	0.946553i	$-0.395460\pi$
$997$	−10.6066	−	6.12372i	−0.335914	−	0.193940i	−0.658464	+	0.752612i	$0.728793\pi$
$998$			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.188.2		8
3.2	odd	2	inner	567.2.o.e.188.3		8
7.6	odd	2	inner	567.2.o.e.188.1		8
9.2	odd	6		189.2.c.c.188.2	yes	4
9.4	even	3	inner	567.2.o.e.377.4		8
9.5	odd	6	inner	567.2.o.e.377.1		8
9.7	even	3		189.2.c.c.188.3	yes	4
21.20	even	2	inner	567.2.o.e.188.4		8
36.7	odd	6		3024.2.k.g.1889.1		4
36.11	even	6		3024.2.k.g.1889.3		4
63.13	odd	6	inner	567.2.o.e.377.3		8
63.20	even	6		189.2.c.c.188.1	✓	4
63.34	odd	6		189.2.c.c.188.4	yes	4
63.41	even	6	inner	567.2.o.e.377.2		8
252.83	odd	6		3024.2.k.g.1889.2		4
252.223	even	6		3024.2.k.g.1889.4		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
189.2.c.c.188.1	✓	4	63.20	even	6
189.2.c.c.188.2	yes	4	9.2	odd	6
189.2.c.c.188.3	yes	4	9.7	even	3
189.2.c.c.188.4	yes	4	63.34	odd	6
567.2.o.e.188.1		8	7.6	odd	2	inner
567.2.o.e.188.2		8	1.1	even	1	trivial
567.2.o.e.188.3		8	3.2	odd	2	inner
567.2.o.e.188.4		8	21.20	even	2	inner
567.2.o.e.377.1		8	9.5	odd	6	inner
567.2.o.e.377.2		8	63.41	even	6	inner
567.2.o.e.377.3		8	63.13	odd	6	inner
567.2.o.e.377.4		8	9.4	even	3	inner
3024.2.k.g.1889.1		4	36.7	odd	6
3024.2.k.g.1889.2		4	252.83	odd	6
3024.2.k.g.1889.3		4	36.11	even	6
3024.2.k.g.1889.4		4	252.223	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 567 = 3^{4} \cdot 7 \)
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

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more