LMFDB - Embedded newform 525.2.bc.a.418.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [525,2,Mod(82,525)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(525, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 10]))

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

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

chi := DirichletCharacter("525.82");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 525 = 3 \cdot 5^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	525.bc (of order $12$, degree $4$, 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:	$4.19214610612$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
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:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			418.2
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	525.418
Dual form			525.2.bc.a.157.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.965926 + 0.258819i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.63896 + 0.189469i) q^{7} +(0.866025 + 0.500000i) q^{9} +O(q^{10})$	\(q+(0.965926 + 0.258819i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.63896 + 0.189469i) q^{7} +(0.866025 + 0.500000i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(1.93185 - 0.517638i) q^{12} +(1.41421 - 1.41421i) q^{13} +(2.00000 - 3.46410i) q^{16} +(-1.55291 + 5.79555i) q^{17} +(-1.73205 + 3.00000i) q^{19} +(2.50000 + 0.866025i) q^{21} +(0.707107 + 0.707107i) q^{27} +(4.76028 - 2.31079i) q^{28} +(-4.50000 + 2.59808i) q^{31} +(-1.55291 - 5.79555i) q^{33} +2.00000 q^{36} +(2.24144 + 8.36516i) q^{37} +(1.73205 - 1.00000i) q^{39} -10.3923i q^{41} +(-3.67423 - 3.67423i) q^{43} +(-10.3923 - 6.00000i) q^{44} +(5.79555 - 1.55291i) q^{47} +(2.82843 - 2.82843i) q^{48} +(6.92820 + 1.00000i) q^{49} +(-3.00000 + 5.19615i) q^{51} +(1.03528 - 3.86370i) q^{52} +(-2.68973 + 10.0382i) q^{53} +(-2.44949 + 2.44949i) q^{57} +(5.19615 + 9.00000i) q^{59} +(7.50000 + 4.33013i) q^{61} +(2.19067 + 1.48356i) q^{63} -8.00000i q^{64} +(-3.34607 - 0.896575i) q^{67} +(3.10583 + 11.5911i) q^{68} -6.00000 q^{71} +(-0.965926 - 0.258819i) q^{73} +6.92820i q^{76} +(-6.93237 - 14.2808i) q^{77} +(-4.33013 - 2.50000i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-4.24264 + 4.24264i) q^{83} +(5.19615 - 1.00000i) q^{84} +(-5.19615 + 9.00000i) q^{89} +(4.00000 - 3.46410i) q^{91} +(-5.01910 + 1.34486i) q^{93} +(-9.19239 - 9.19239i) q^{97} -6.00000i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q+O(q^{10}) $ 8 * q	$ 8 q - 24 q^{11} + 16 q^{16} + 20 q^{21} - 36 q^{31} + 16 q^{36} - 24 q^{51} + 60 q^{61} - 48 q^{71} + 4 q^{81} + 32 q^{91}+O(q^{100}) $ 8 * q - 24 * q^11 + 16 * q^16 + 20 * q^21 - 36 * q^31 + 16 * q^36 - 24 * q^51 + 60 * q^61 - 48 * q^71 + 4 * q^81 + 32 * q^91

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/525\mathbb{Z}\right)^\times$.

$n$	$127$	$176$	$451$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$2$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$3$	0.965926	+	0.258819i	0.557678	+	0.149429i
$4$	1.73205	−	1.00000i	0.866025	−	0.500000i
$5$		0			0
$5$		0			0
$6$		0			0
$7$	2.63896	+	0.189469i	0.997433	+	0.0716124i
$7$	2.63896	+	0.189469i	0.997433	+	0.0716124i
$8$		0			0
$9$	0.866025	+	0.500000i	0.288675	+	0.166667i
$10$		0			0
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.821541	−	0.570149i	$-0.806886\pi$
$11$	−3.00000	−	5.19615i	−0.904534	−	1.56670i	−0.0829925	−	0.996550i	$-0.526448\pi$
$12$	1.93185	−	0.517638i	0.557678	−	0.149429i
$13$	1.41421	−	1.41421i	0.392232	−	0.392232i	−0.483250	−	0.875482i	$-0.660544\pi$
$13$	1.41421	−	1.41421i	0.392232	−	0.392232i	0.875482	+	0.483250i	$0.160544\pi$
$14$		0			0
$15$		0			0
$16$	2.00000	−	3.46410i	0.500000	−	0.866025i
$17$	−1.55291	+	5.79555i	−0.376637	+	1.40563i	0.474301	+	0.880363i	$0.342701\pi$
$17$	−1.55291	+	5.79555i	−0.376637	+	1.40563i	−0.850938	+	0.525266i	$0.823966\pi$
$18$		0			0
$19$	−1.73205	+	3.00000i	−0.397360	+	0.688247i	−0.993399	−	0.114708i	$-0.963407\pi$
$19$	−1.73205	+	3.00000i	−0.397360	+	0.688247i	0.596040	+	0.802955i	$0.296740\pi$
$20$		0			0
$21$	2.50000	+	0.866025i	0.545545	+	0.188982i
$22$		0			0
$23$		0			0		−0.258819	−	0.965926i	$-0.583333\pi$
$23$		0			0		0.258819	+	0.965926i	$0.416667\pi$
$24$		0			0
$25$		0			0
$26$		0			0
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	4.76028	−	2.31079i	0.899608	−	0.436698i
$29$		0			0		1.00000			$0$
$29$		0			0		−1.00000			$\pi$
$30$		0			0
$31$	−4.50000	+	2.59808i	−0.808224	+	0.466628i	−0.846339	−	0.532645i	$-0.821198\pi$
$31$	−4.50000	+	2.59808i	−0.808224	+	0.466628i	0.0381148	+	0.999273i	$0.487865\pi$
$32$		0			0
$33$	−1.55291	−	5.79555i	−0.270328	−	1.00888i
$34$		0			0
$35$		0			0
$36$	2.00000			0.333333
$37$	2.24144	+	8.36516i	0.368490	+	1.37522i	0.862627	+	0.505840i	$0.168817\pi$
$37$	2.24144	+	8.36516i	0.368490	+	1.37522i	−0.494137	+	0.869384i	$0.664516\pi$
$38$		0			0
$39$	1.73205	−	1.00000i	0.277350	−	0.160128i
$40$		0			0
$41$		−	10.3923i		−	1.62301i	−0.584349	−	0.811503i	$-0.698650\pi$
$41$		−	10.3923i		−	1.62301i	0.584349	−	0.811503i	$-0.301350\pi$
$42$		0			0
$43$	−3.67423	−	3.67423i	−0.560316	−	0.560316i	0.369082	−	0.929397i	$-0.379672\pi$
$43$	−3.67423	−	3.67423i	−0.560316	−	0.560316i	−0.929397	+	0.369082i	$0.879672\pi$
$44$	−10.3923	−	6.00000i	−1.56670	−	0.904534i
$45$		0			0
$46$		0			0
$47$	5.79555	−	1.55291i	0.845369	−	0.226516i	0.189961	−	0.981792i	$-0.439164\pi$
$47$	5.79555	−	1.55291i	0.845369	−	0.226516i	0.655407	+	0.755276i	$0.272497\pi$
$48$	2.82843	−	2.82843i	0.408248	−	0.408248i
$49$	6.92820	+	1.00000i	0.989743	+	0.142857i
$50$		0			0
$51$	−3.00000	+	5.19615i	−0.420084	+	0.727607i
$52$	1.03528	−	3.86370i	0.143567	−	0.535799i
$53$	−2.68973	+	10.0382i	−0.369462	+	1.37885i	0.491807	+	0.870704i	$0.336336\pi$
$53$	−2.68973	+	10.0382i	−0.369462	+	1.37885i	−0.861270	+	0.508148i	$0.830330\pi$
$54$		0			0
$55$		0			0
$56$		0			0
$57$	−2.44949	+	2.44949i	−0.324443	+	0.324443i
$58$		0			0
$59$	5.19615	+	9.00000i	0.676481	+	1.17170i	0.976034	+	0.217620i	$0.0698294\pi$
$59$	5.19615	+	9.00000i	0.676481	+	1.17170i	−0.299552	+	0.954080i	$0.596837\pi$
$60$		0			0
$61$	7.50000	+	4.33013i	0.960277	+	0.554416i	0.896258	−	0.443533i	$-0.146275\pi$
$61$	7.50000	+	4.33013i	0.960277	+	0.554416i	0.0640184	+	0.997949i	$0.479608\pi$
$62$		0			0
$63$	2.19067	+	1.48356i	0.275999	+	0.186911i
$64$		−	8.00000i		−	1.00000i
$65$		0			0
$66$		0			0
$67$	−3.34607	−	0.896575i	−0.408787	−	0.109534i	0.0485648	−	0.998820i	$-0.484535\pi$
$67$	−3.34607	−	0.896575i	−0.408787	−	0.109534i	−0.457352	+	0.889286i	$0.651202\pi$
$68$	3.10583	+	11.5911i	0.376637	+	1.40563i
$69$		0			0
$70$		0			0
$71$	−6.00000			−0.712069			−0.356034	−	0.934473i	$-0.615871\pi$
$71$	−6.00000			−0.712069			−0.356034	+	0.934473i	$0.615871\pi$
$72$		0			0
$73$	−0.965926	−	0.258819i	−0.113053	−	0.0302925i	0.201849	−	0.979417i	$-0.435305\pi$
$73$	−0.965926	−	0.258819i	−0.113053	−	0.0302925i	−0.314902	+	0.949124i	$0.601972\pi$
$74$		0			0
$75$		0			0
$76$			6.92820i			0.794719i
$77$	−6.93237	−	14.2808i	−0.790017	−	1.62745i
$78$		0			0
$79$	−4.33013	−	2.50000i	−0.487177	−	0.281272i	0.236225	−	0.971698i	$-0.424090\pi$
$79$	−4.33013	−	2.50000i	−0.487177	−	0.281272i	−0.723403	+	0.690426i	$0.757423\pi$
$80$		0			0
$81$	0.500000	+	0.866025i	0.0555556	+	0.0962250i
$82$		0			0
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	−0.900515	−	0.434825i	$-0.856810\pi$
$83$	−4.24264	+	4.24264i	−0.465690	+	0.465690i	0.434825	+	0.900515i	$0.356810\pi$
$84$	5.19615	−	1.00000i	0.566947	−	0.109109i
$85$		0			0
$86$		0			0
$87$		0			0
$88$		0			0
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	0.447427	+	0.894321i	$0.352341\pi$
$89$	−5.19615	+	9.00000i	−0.550791	+	0.953998i	−0.998218	+	0.0596775i	$0.980993\pi$
$90$		0			0
$91$	4.00000	−	3.46410i	0.419314	−	0.363137i
$92$		0			0
$93$	−5.01910	+	1.34486i	−0.520456	+	0.139456i
$94$		0			0
$95$		0			0
$96$		0			0
$97$	−9.19239	−	9.19239i	−0.933346	−	0.933346i	0.0645677	−	0.997913i	$-0.479433\pi$
$97$	−9.19239	−	9.19239i	−0.933346	−	0.933346i	−0.997913	+	0.0645677i	$0.979433\pi$
$98$		0			0
$99$		−	6.00000i		−	0.603023i
$100$		0			0
$101$		0			0		−0.500000	−	0.866025i	$-0.666667\pi$
$101$		0			0		0.500000	+	0.866025i	$0.333333\pi$
$102$		0			0
$103$	−1.81173	−	6.76148i	−0.178515	−	0.666228i	−0.995926	−	0.0901732i	$-0.971258\pi$
$103$	−1.81173	−	6.76148i	−0.178515	−	0.666228i	0.817411	−	0.576055i	$-0.195409\pi$
$104$		0			0
$105$		0			0
$106$		0			0
$107$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$107$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$108$	1.93185	+	0.517638i	0.185893	+	0.0498097i
$109$	8.66025	−	5.00000i	0.829502	−	0.478913i	−0.0241802	−	0.999708i	$-0.507698\pi$
$109$	8.66025	−	5.00000i	0.829502	−	0.478913i	0.853682	+	0.520794i	$0.174364\pi$
$110$		0			0
$111$			8.66025i			0.821995i
$112$	5.93426	−	8.76268i	0.560734	−	0.827996i
$113$	−7.34847	−	7.34847i	−0.691286	−	0.691286i	0.271229	−	0.962515i	$-0.412570\pi$
$113$	−7.34847	−	7.34847i	−0.691286	−	0.691286i	−0.962515	+	0.271229i	$0.912570\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	1.93185	−	0.517638i	0.178600	−	0.0478557i
$118$		0			0
$119$	−5.19615	+	15.0000i	−0.476331	+	1.37505i
$120$		0			0
$121$	−12.5000	+	21.6506i	−1.13636	+	1.96824i
$122$		0			0
$123$	2.68973	−	10.0382i	0.242524	−	0.905114i
$124$	−5.19615	+	9.00000i	−0.466628	+	0.808224i
$125$		0			0
$126$		0			0
$127$	−8.57321	+	8.57321i	−0.760750	+	0.760750i	−0.976458	−	0.215708i	$-0.930794\pi$
$127$	−8.57321	+	8.57321i	−0.760750	+	0.760750i	0.215708	+	0.976458i	$0.430794\pi$
$128$		0			0
$129$	−2.59808	−	4.50000i	−0.228748	−	0.396203i
$130$		0			0
$131$	9.00000	+	5.19615i	0.786334	+	0.453990i	0.838670	−	0.544640i	$-0.183334\pi$
$131$	9.00000	+	5.19615i	0.786334	+	0.453990i	−0.0523366	+	0.998630i	$0.516667\pi$
$132$	−8.48528	−	8.48528i	−0.738549	−	0.738549i
$133$	−5.13922	+	7.58871i	−0.445627	+	0.658024i
$134$		0			0
$135$		0			0
$136$		0			0
$137$	−20.0764	−	5.37945i	−1.71524	−	0.459598i	−0.738542	−	0.674207i	$-0.764485\pi$
$137$	−20.0764	−	5.37945i	−1.71524	−	0.459598i	−0.976700	+	0.214610i	$0.931152\pi$
$138$		0			0
$139$	−1.73205			−0.146911			−0.0734553	−	0.997299i	$-0.523403\pi$
$139$	−1.73205			−0.146911			−0.0734553	+	0.997299i	$0.523403\pi$
$140$		0			0
$141$	6.00000			0.505291
$142$		0			0
$143$	−11.5911	−	3.10583i	−0.969297	−	0.259722i
$144$	3.46410	−	2.00000i	0.288675	−	0.166667i
$145$		0			0
$146$		0			0
$147$	6.43331	+	2.75908i	0.530611	+	0.227565i
$148$	12.2474	+	12.2474i	1.00673	+	1.00673i
$149$	−10.3923	−	6.00000i	−0.851371	−	0.491539i	0.00974235	−	0.999953i	$-0.496899\pi$
$149$	−10.3923	−	6.00000i	−0.851371	−	0.491539i	−0.861113	+	0.508413i	$0.830232\pi$
$150$		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	$0.898548\pi$
$152$		0			0
$153$	−4.24264	+	4.24264i	−0.342997	+	0.342997i
$154$		0			0
$155$		0			0
$156$	2.00000	−	3.46410i	0.160128	−	0.277350i
$157$	−1.81173	+	6.76148i	−0.144592	+	0.539625i	0.855181	+	0.518329i	$0.173446\pi$
$157$	−1.81173	+	6.76148i	−0.144592	+	0.539625i	−0.999773	+	0.0212957i	$0.993221\pi$
$158$		0			0
$159$	−5.19615	+	9.00000i	−0.412082	+	0.713746i
$160$		0			0
$161$		0			0
$162$		0			0
$163$	−8.36516	+	2.24144i	−0.655210	+	0.175563i	−0.571083	−	0.820892i	$-0.693477\pi$
$163$	−8.36516	+	2.24144i	−0.655210	+	0.175563i	−0.0841267	+	0.996455i	$0.526810\pi$
$164$	−10.3923	−	18.0000i	−0.811503	−	1.40556i
$165$		0			0
$166$		0			0
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	0.954577	−	0.297966i	$-0.0963081\pi$
$167$	8.48528	+	8.48528i	0.656611	+	0.656611i	−0.297966	+	0.954577i	$0.596308\pi$
$168$		0			0
$169$			9.00000i			0.692308i
$170$		0			0
$171$	−3.00000	+	1.73205i	−0.229416	+	0.132453i
$172$	−10.0382	−	2.68973i	−0.765405	−	0.205090i
$173$	4.65874	+	17.3867i	0.354198	+	1.32188i	0.881491	+	0.472200i	$0.156540\pi$
$173$	4.65874	+	17.3867i	0.354198	+	1.32188i	−0.527294	+	0.849683i	$0.676793\pi$
$174$		0			0
$175$		0			0
$176$	−24.0000			−1.80907
$177$	2.68973	+	10.0382i	0.202172	+	0.754517i
$178$		0			0
$179$	20.7846	−	12.0000i	1.55351	−	0.896922i	0.555663	−	0.831408i	$-0.312464\pi$
$179$	20.7846	−	12.0000i	1.55351	−	0.896922i	0.997852	−	0.0655145i	$-0.0208689\pi$
$180$		0			0
$181$		−	5.19615i		−	0.386227i	−0.981176	−	0.193113i	$-0.938141\pi$
$181$		−	5.19615i		−	0.386227i	0.981176	−	0.193113i	$-0.0618586\pi$
$182$		0			0
$183$	6.12372	+	6.12372i	0.452679	+	0.452679i
$184$		0			0
$185$		0			0
$186$		0			0
$187$	34.7733	−	9.31749i	2.54288	−	0.681362i
$188$	8.48528	−	8.48528i	0.618853	−	0.618853i
$189$	1.73205	+	2.00000i	0.125988	+	0.145479i
$190$		0			0
$191$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$191$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$192$	2.07055	−	7.72741i	0.149429	−	0.557678i
$193$	4.03459	−	15.0573i	0.290416	−	1.08385i	−0.654374	−	0.756171i	$-0.727068\pi$
$193$	4.03459	−	15.0573i	0.290416	−	1.08385i	0.944790	−	0.327677i	$-0.106266\pi$
$194$		0			0
$195$		0			0
$196$	13.0000	−	5.19615i	0.928571	−	0.371154i
$197$	7.34847	−	7.34847i	0.523557	−	0.523557i	−0.395087	−	0.918644i	$-0.629286\pi$
$197$	7.34847	−	7.34847i	0.523557	−	0.523557i	0.918644	+	0.395087i	$0.129286\pi$
$198$		0			0
$199$	−9.52628	−	16.5000i	−0.675300	−	1.16965i	−0.976381	−	0.216055i	$-0.930681\pi$
$199$	−9.52628	−	16.5000i	−0.675300	−	1.16965i	0.301081	−	0.953599i	$-0.402653\pi$
$200$		0			0
$201$	−3.00000	−	1.73205i	−0.211604	−	0.122169i
$202$		0			0
$203$		0			0
$204$			12.0000i			0.840168i
$205$		0			0
$206$		0			0
$207$		0			0
$208$	−2.07055	−	7.72741i	−0.143567	−	0.535799i
$209$	20.7846			1.43770
$210$		0			0
$211$	7.00000			0.481900			0.240950	−	0.970538i	$-0.422541\pi$
$211$	7.00000			0.481900			0.240950	+	0.970538i	$0.422541\pi$
$212$	5.37945	+	20.0764i	0.369462	+	1.37885i
$213$	−5.79555	−	1.55291i	−0.397105	−	0.106404i
$214$		0			0
$215$		0			0
$216$		0			0
$217$	−12.3676	+	6.00361i	−0.839565	+	0.407551i
$218$		0			0
$219$	−0.866025	−	0.500000i	−0.0585206	−	0.0337869i
$220$		0			0
$221$	6.00000	+	10.3923i	0.403604	+	0.699062i
$222$		0			0
$223$	−3.53553	+	3.53553i	−0.236757	+	0.236757i	−0.815506	−	0.578749i	$-0.803541\pi$
$223$	−3.53553	+	3.53553i	−0.236757	+	0.236757i	0.578749	+	0.815506i	$0.303541\pi$
$224$		0			0
$225$		0			0
$226$		0			0
$227$	−1.55291	+	5.79555i	−0.103071	+	0.384664i	−0.998119	−	0.0613041i	$-0.980474\pi$
$227$	−1.55291	+	5.79555i	−0.103071	+	0.384664i	0.895049	+	0.445969i	$0.147141\pi$
$228$	−1.79315	+	6.69213i	−0.118754	+	0.443197i
$229$	−3.46410	+	6.00000i	−0.228914	+	0.396491i	−0.957487	−	0.288478i	$-0.906851\pi$
$229$	−3.46410	+	6.00000i	−0.228914	+	0.396491i	0.728572	+	0.684969i	$0.240184\pi$
$230$		0			0
$231$	−3.00000	−	15.5885i	−0.197386	−	1.02565i
$232$		0			0
$233$	20.0764	−	5.37945i	1.31525	−	0.352420i	0.468052	−	0.883701i	$-0.344956\pi$
$233$	20.0764	−	5.37945i	1.31525	−	0.352420i	0.847196	+	0.531281i	$0.178289\pi$
$234$		0			0
$235$		0			0
$236$	18.0000	+	10.3923i	1.17170	+	0.676481i
$237$	−3.53553	−	3.53553i	−0.229658	−	0.229658i
$238$		0			0
$239$		−	18.0000i		−	1.16432i	−0.813073	−	0.582162i	$-0.802207\pi$
$239$		−	18.0000i		−	1.16432i	0.813073	−	0.582162i	$-0.197793\pi$
$240$		0			0
$241$	16.5000	−	9.52628i	1.06286	−	0.613642i	0.136637	−	0.990621i	$-0.456371\pi$
$241$	16.5000	−	9.52628i	1.06286	−	0.613642i	0.926222	+	0.376980i	$0.123037\pi$
$242$		0			0
$243$	0.258819	+	0.965926i	0.0166032	+	0.0619642i
$244$	17.3205			1.10883
$245$		0			0
$246$		0			0
$247$	1.79315	+	6.69213i	0.114095	+	0.425810i
$248$		0			0
$249$	−5.19615	+	3.00000i	−0.329293	+	0.190117i
$250$		0			0
$251$		−	20.7846i		−	1.31191i	−0.754799	−	0.655956i	$-0.772265\pi$
$251$		−	20.7846i		−	1.31191i	0.754799	−	0.655956i	$-0.227735\pi$
$252$	5.27792	+	0.378937i	0.332478	+	0.0238708i
$253$		0			0
$254$		0			0
$255$		0			0
$256$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$257$	−5.79555	+	1.55291i	−0.361517	+	0.0968681i	−0.435005	−	0.900428i	$-0.643253\pi$
$257$	−5.79555	+	1.55291i	−0.361517	+	0.0968681i	0.0734884	+	0.997296i	$0.476587\pi$
$258$		0			0
$259$	4.33013	+	22.5000i	0.269061	+	1.39808i
$260$		0			0
$261$		0			0
$262$		0			0
$263$	8.06918	−	30.1146i	0.497567	−	1.85694i	−0.0175838	−	0.999845i	$-0.505597\pi$
$263$	8.06918	−	30.1146i	0.497567	−	1.85694i	0.515151	−	0.857100i	$-0.327736\pi$
$264$		0			0
$265$		0			0
$266$		0			0
$267$	−7.34847	+	7.34847i	−0.449719	+	0.449719i
$268$	−6.69213	+	1.79315i	−0.408787	+	0.109534i
$269$	10.3923	+	18.0000i	0.633630	+	1.09748i	0.986804	+	0.161922i	$0.0517692\pi$
$269$	10.3923	+	18.0000i	0.633630	+	1.09748i	−0.353174	+	0.935558i	$0.614898\pi$
$270$		0			0
$271$	−27.0000	−	15.5885i	−1.64013	−	0.946931i	−0.980785	−	0.195094i	$-0.937499\pi$
$271$	−27.0000	−	15.5885i	−1.64013	−	0.946931i	−0.659349	−	0.751837i	$-0.729168\pi$
$272$	16.9706	+	16.9706i	1.02899	+	1.02899i
$273$	4.76028	−	2.31079i	0.288105	−	0.139855i
$274$		0			0
$275$		0			0
$276$		0			0
$277$	13.3843	+	3.58630i	0.804182	+	0.215480i	0.637419	−	0.770517i	$-0.280002\pi$
$277$	13.3843	+	3.58630i	0.804182	+	0.215480i	0.166763	+	0.985997i	$0.446669\pi$
$278$		0			0
$279$	−5.19615			−0.311086
$280$		0			0
$281$	−6.00000			−0.357930			−0.178965	−	0.983855i	$-0.557275\pi$
$281$	−6.00000			−0.357930			−0.178965	+	0.983855i	$0.557275\pi$
$282$		0			0
$283$	15.4548	+	4.14110i	0.918693	+	0.246163i	0.687027	−	0.726632i	$-0.258916\pi$
$283$	15.4548	+	4.14110i	0.918693	+	0.246163i	0.231667	+	0.972795i	$0.425582\pi$
$284$	−10.3923	+	6.00000i	−0.616670	+	0.356034i
$285$		0			0
$286$		0			0
$287$	1.96902	−	27.4249i	0.116227	−	1.61884i
$288$		0			0
$289$	−16.4545	−	9.50000i	−0.967911	−	0.558824i
$290$		0			0
$291$	−6.50000	−	11.2583i	−0.381037	−	0.659975i
$292$	−1.93185	+	0.517638i	−0.113053	+	0.0302925i
$293$	12.7279	−	12.7279i	0.743573	−	0.743573i	−0.229691	−	0.973264i	$-0.573771\pi$
$293$	12.7279	−	12.7279i	0.743573	−	0.743573i	0.973264	+	0.229691i	$0.0737714\pi$
$294$		0			0
$295$		0			0
$296$		0			0
$297$	1.55291	−	5.79555i	0.0901092	−	0.336292i
$298$		0			0
$299$		0			0
$300$		0			0
$301$	−9.00000	−	10.3923i	−0.518751	−	0.599002i
$302$		0			0
$303$		0			0
$304$	6.92820	+	12.0000i	0.397360	+	0.688247i
$305$		0			0
$306$		0			0
$307$	4.94975	+	4.94975i	0.282497	+	0.282497i	0.834104	−	0.551607i	$-0.185985\pi$
$307$	4.94975	+	4.94975i	0.282497	+	0.282497i	−0.551607	+	0.834104i	$0.685985\pi$
$308$	−26.2880	−	17.8028i	−1.49790	−	1.01441i
$309$		−	7.00000i		−	0.398216i
$310$		0			0
$311$	18.0000	−	10.3923i	1.02069	−	0.589294i	0.106384	−	0.994325i	$-0.466073\pi$
$311$	18.0000	−	10.3923i	1.02069	−	0.589294i	0.914303	+	0.405032i	$0.132739\pi$
$312$		0			0
$313$	4.91756	+	18.3526i	0.277957	+	1.03735i	0.953834	+	0.300335i	$0.0970985\pi$
$313$	4.91756	+	18.3526i	0.277957	+	1.03735i	−0.675877	+	0.737015i	$0.736235\pi$
$314$		0			0
$315$		0			0
$316$	−10.0000			−0.562544
$317$	2.68973	+	10.0382i	0.151070	+	0.563801i	0.999410	+	0.0343491i	$0.0109358\pi$
$317$	2.68973	+	10.0382i	0.151070	+	0.563801i	−0.848340	+	0.529452i	$0.822398\pi$
$318$		0			0
$319$		0			0
$320$		0			0
$321$		0			0
$322$		0			0
$323$	−14.6969	−	14.6969i	−0.817760	−	0.817760i
$324$	1.73205	+	1.00000i	0.0962250	+	0.0555556i
$325$		0			0
$326$		0			0
$327$	9.65926	−	2.58819i	0.534158	−	0.143127i
$328$		0			0
$329$	15.5885	−	3.00000i	0.859419	−	0.165395i
$330$		0			0
$331$	2.50000	−	4.33013i	0.137412	−	0.238005i	−0.789104	−	0.614260i	$-0.789455\pi$
$331$	2.50000	−	4.33013i	0.137412	−	0.238005i	0.926516	+	0.376254i	$0.122788\pi$
$332$	−3.10583	+	11.5911i	−0.170454	+	0.636145i
$333$	−2.24144	+	8.36516i	−0.122830	+	0.458408i
$334$		0			0
$335$		0			0
$336$	8.00000	−	6.92820i	0.436436	−	0.377964i
$337$	−18.3712	+	18.3712i	−1.00074	+	1.00074i	−0.000741840		1.00000i	$0.500236\pi$
$337$	−18.3712	+	18.3712i	−1.00074	+	1.00074i	−1.00000		0.000741840i	$0.999764\pi$
$338$		0			0
$339$	−5.19615	−	9.00000i	−0.282216	−	0.488813i
$340$		0			0
$341$	27.0000	+	15.5885i	1.46213	+	0.844162i
$342$		0			0
$343$	18.0938	+	3.95164i	0.976972	+	0.213368i
$344$		0			0
$345$		0			0
$346$		0			0
$347$	10.0382	+	2.68973i	0.538879	+	0.144392i	0.517985	−	0.855390i	$-0.326682\pi$
$347$	10.0382	+	2.68973i	0.538879	+	0.144392i	0.0208935	+	0.999782i	$0.493349\pi$
$348$		0			0
$349$	−20.7846			−1.11257			−0.556287	−	0.830990i	$-0.687775\pi$
$349$	−20.7846			−1.11257			−0.556287	+	0.830990i	$0.687775\pi$
$350$		0			0
$351$	2.00000			0.106752
$352$		0			0
$353$	34.7733	+	9.31749i	1.85080	+	0.495920i	0.999582	−	0.0288971i	$-0.00919951\pi$
$353$	34.7733	+	9.31749i	1.85080	+	0.495920i	0.851215	+	0.524817i	$0.175866\pi$
$354$		0			0
$355$		0			0
$356$			20.7846i			1.10158i
$357$	−8.90138	+	13.1440i	−0.471111	+	0.695656i
$358$		0			0
$359$	15.5885	+	9.00000i	0.822727	+	0.475002i	0.851356	−	0.524588i	$-0.175781\pi$
$359$	15.5885	+	9.00000i	0.822727	+	0.475002i	−0.0286287	+	0.999590i	$0.509114\pi$
$360$		0			0
$361$	3.50000	+	6.06218i	0.184211	+	0.319062i
$362$		0			0
$363$	−17.6777	+	17.6777i	−0.927837	+	0.927837i
$364$	3.46410	−	10.0000i	0.181568	−	0.524142i
$365$		0			0
$366$		0			0
$367$	4.39992	−	16.4207i	0.229674	−	0.857156i	−0.750804	−	0.660526i	$-0.770334\pi$
$367$	4.39992	−	16.4207i	0.229674	−	0.857156i	0.980478	−	0.196630i	$-0.0629998\pi$
$368$		0			0
$369$	5.19615	−	9.00000i	0.270501	−	0.468521i
$370$		0			0
$371$	−9.00000	+	25.9808i	−0.467257	+	1.34885i
$372$	−7.34847	+	7.34847i	−0.381000	+	0.381000i
$373$	−6.69213	+	1.79315i	−0.346505	+	0.0928458i	−0.427874	−	0.903838i	$-0.640737\pi$
$373$	−6.69213	+	1.79315i	−0.346505	+	0.0928458i	0.0813690	+	0.996684i	$0.474071\pi$
$374$		0			0
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$		−	28.0000i		−	1.43826i	−0.694874	−	0.719132i	$-0.744540\pi$
$379$		−	28.0000i		−	1.43826i	0.694874	−	0.719132i	$-0.255460\pi$
$380$		0			0
$381$	−10.5000	+	6.06218i	−0.537931	+	0.310575i
$382$		0			0
$383$	−6.21166	−	23.1822i	−0.317401	−	1.18456i	−0.921733	−	0.387824i	$-0.873227\pi$
$383$	−6.21166	−	23.1822i	−0.317401	−	1.18456i	0.604333	−	0.796732i	$-0.293440\pi$
$384$		0			0
$385$		0			0
$386$		0			0
$387$	−1.34486	−	5.01910i	−0.0683632	−	0.255135i
$388$	−25.1141	−	6.72930i	−1.27497	−	0.341628i
$389$	−5.19615	+	3.00000i	−0.263455	+	0.152106i	−0.625910	−	0.779895i	$-0.715272\pi$
$389$	−5.19615	+	3.00000i	−0.263455	+	0.152106i	0.362454	+	0.932002i	$0.381939\pi$
$390$		0			0
$391$		0			0
$392$		0			0
$393$	7.34847	+	7.34847i	0.370681	+	0.370681i
$394$		0			0
$395$		0			0
$396$	−6.00000	−	10.3923i	−0.301511	−	0.522233i
$397$	−6.76148	+	1.81173i	−0.339349	+	0.0909283i	−0.424469	−	0.905442i	$-0.639539\pi$
$397$	−6.76148	+	1.81173i	−0.339349	+	0.0909283i	0.0851201	+	0.996371i	$0.472873\pi$
$398$		0			0
$399$	−6.92820	+	6.00000i	−0.346844	+	0.300376i
$400$		0			0
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	−0.998350	−	0.0574304i	$-0.981709\pi$
$401$	−9.00000	+	15.5885i	−0.449439	+	0.778450i	0.548911	+	0.835881i	$0.315043\pi$
$402$		0			0
$403$	−2.68973	+	10.0382i	−0.133985	+	0.500038i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	36.7423	−	36.7423i	1.82125	−	1.82125i
$408$		0			0
$409$	−3.46410	−	6.00000i	−0.171289	−	0.296681i	0.767582	−	0.640951i	$-0.221460\pi$
$409$	−3.46410	−	6.00000i	−0.171289	−	0.296681i	−0.938871	+	0.344270i	$0.888126\pi$
$410$		0			0
$411$	−18.0000	−	10.3923i	−0.887875	−	0.512615i
$412$	−9.89949	−	9.89949i	−0.487713	−	0.487713i
$413$	12.0072	+	24.7351i	0.590836	+	1.21714i
$414$		0			0
$415$		0			0
$416$		0			0
$417$	−1.67303	−	0.448288i	−0.0819288	−	0.0219527i
$418$		0			0
$419$		0			0			−	1.00000i	$-0.5\pi$
$419$		0			0				1.00000i	$0.5\pi$
$420$		0			0
$421$	31.0000			1.51085			0.755424	−	0.655237i	$-0.227431\pi$
$421$	31.0000			1.51085			0.755424	+	0.655237i	$0.227431\pi$
$422$		0			0
$423$	5.79555	+	1.55291i	0.281790	+	0.0755053i
$424$		0			0
$425$		0			0
$426$		0			0
$427$	18.9718	+	12.8480i	0.918108	+	0.621760i
$428$		0			0
$429$	−10.3923	−	6.00000i	−0.501745	−	0.289683i
$430$		0			0
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	0.973574	−	0.228373i	$-0.0733406\pi$
$431$	6.00000	+	10.3923i	0.289010	+	0.500580i	−0.684564	+	0.728953i	$0.740007\pi$
$432$	3.86370	−	1.03528i	0.185893	−	0.0498097i
$433$	−20.5061	+	20.5061i	−0.985460	+	0.985460i	−0.999896	−	0.0144357i	$-0.995405\pi$
$433$	−20.5061	+	20.5061i	−0.985460	+	0.985460i	0.0144357	+	0.999896i	$0.495405\pi$
$434$		0			0
$435$		0			0
$436$	10.0000	−	17.3205i	0.478913	−	0.829502i
$437$		0			0
$438$		0			0
$439$	4.33013	−	7.50000i	0.206666	−	0.357955i	−0.743996	−	0.668184i	$-0.767072\pi$
$439$	4.33013	−	7.50000i	0.206666	−	0.357955i	0.950662	+	0.310228i	$0.100405\pi$
$440$		0			0
$441$	5.50000	+	4.33013i	0.261905	+	0.206197i
$442$		0			0
$443$	−10.0382	+	2.68973i	−0.476929	+	0.127793i	−0.489272	−	0.872131i	$-0.662738\pi$
$443$	−10.0382	+	2.68973i	−0.476929	+	0.127793i	0.0123433	+	0.999924i	$0.496071\pi$
$444$	8.66025	+	15.0000i	0.410997	+	0.711868i
$445$		0			0
$446$		0			0
$447$	−8.48528	−	8.48528i	−0.401340	−	0.401340i
$448$	1.51575	−	21.1117i	0.0716124	−	0.997433i
$449$		0			0		1.00000			$0$
$449$		0			0		−1.00000			$\pi$
$450$		0			0
$451$	−54.0000	+	31.1769i	−2.54276	+	1.46806i
$452$	−20.0764	−	5.37945i	−0.944314	−	0.253028i
$453$	−1.29410	−	4.82963i	−0.0608019	−	0.226916i
$454$		0			0
$455$		0			0
$456$		0			0
$457$	−4.93117	−	18.4034i	−0.230670	−	0.860873i	−0.980053	−	0.198736i	$-0.936316\pi$
$457$	−4.93117	−	18.4034i	−0.230670	−	0.860873i	0.749383	−	0.662137i	$-0.230350\pi$
$458$		0			0
$459$	−5.19615	+	3.00000i	−0.242536	+	0.140028i
$460$		0			0
$461$		−	31.1769i		−	1.45205i	−0.687666	−	0.726027i	$-0.741365\pi$
$461$		−	31.1769i		−	1.45205i	0.687666	−	0.726027i	$-0.258635\pi$
$462$		0			0
$463$	−1.22474	−	1.22474i	−0.0569187	−	0.0569187i	0.678074	−	0.734993i	$-0.262815\pi$
$463$	−1.22474	−	1.22474i	−0.0569187	−	0.0569187i	−0.734993	+	0.678074i	$0.762815\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	−28.9778	+	7.76457i	−1.34093	+	0.359302i	−0.856780	−	0.515683i	$-0.827538\pi$
$467$	−28.9778	+	7.76457i	−1.34093	+	0.359302i	−0.484152	+	0.874984i	$0.660872\pi$
$468$	2.82843	−	2.82843i	0.130744	−	0.130744i
$469$	−8.66025	−	3.00000i	−0.399893	−	0.138527i
$470$		0			0
$471$	−3.50000	+	6.06218i	−0.161271	+	0.279330i
$472$		0			0
$473$	−8.06918	+	30.1146i	−0.371021	+	1.38467i
$474$		0			0
$475$		0			0
$476$	6.00000	+	31.1769i	0.275010	+	1.42899i
$477$	−7.34847	+	7.34847i	−0.336463	+	0.336463i
$478$		0			0
$479$	−10.3923	−	18.0000i	−0.474837	−	0.822441i	0.524748	−	0.851258i	$-0.324159\pi$
$479$	−10.3923	−	18.0000i	−0.474837	−	0.822441i	−0.999585	+	0.0288165i	$0.990826\pi$
$480$		0			0
$481$	15.0000	+	8.66025i	0.683941	+	0.394874i
$482$		0			0
$483$		0			0
$484$			50.0000i			2.27273i
$485$		0			0
$486$		0			0
$487$	−35.1337	−	9.41404i	−1.59206	−	0.426591i	−0.649427	−	0.760424i	$-0.724991\pi$
$487$	−35.1337	−	9.41404i	−1.59206	−	0.426591i	−0.942632	+	0.333833i	$0.891658\pi$
$488$		0			0
$489$	−8.66025			−0.391630
$490$		0			0
$491$	12.0000			0.541552			0.270776	−	0.962642i	$-0.412720\pi$
$491$	12.0000			0.541552			0.270776	+	0.962642i	$0.412720\pi$
$492$	−5.37945	−	20.0764i	−0.242524	−	0.905114i
$493$		0			0
$494$		0			0
$495$		0			0
$496$			20.7846i			0.933257i
$497$	−15.8338	−	1.13681i	−0.710241	−	0.0509930i
$498$		0			0
$499$	17.3205	+	10.0000i	0.775372	+	0.447661i	0.834788	−	0.550572i	$-0.185590\pi$
$499$	17.3205	+	10.0000i	0.775372	+	0.447661i	−0.0594153	+	0.998233i	$0.518924\pi$
$500$		0			0
$501$	6.00000	+	10.3923i	0.268060	+	0.464294i
$502$		0			0
$503$	25.4558	−	25.4558i	1.13502	−	1.13502i	0.145690	−	0.989330i	$-0.453460\pi$
$503$	25.4558	−	25.4558i	1.13502	−	1.13502i	0.989330	−	0.145690i	$-0.0465401\pi$
$504$		0			0
$505$		0			0
$506$		0			0
$507$	−2.32937	+	8.69333i	−0.103451	+	0.386084i
$508$	−6.27603	+	23.4225i	−0.278454	+	1.03920i
$509$	−5.19615	+	9.00000i	−0.230315	+	0.398918i	−0.957901	−	0.287099i	$-0.907309\pi$
$509$	−5.19615	+	9.00000i	−0.230315	+	0.398918i	0.727586	+	0.686017i	$0.240642\pi$
$510$		0			0
$511$	−2.50000	−	0.866025i	−0.110593	−	0.0383107i
$512$		0			0
$513$	−3.34607	+	0.896575i	−0.147732	+	0.0395848i
$514$		0			0
$515$		0			0
$516$	−9.00000	−	5.19615i	−0.396203	−	0.228748i
$517$	−25.4558	−	25.4558i	−1.11955	−	1.11955i
$518$		0			0
$519$			18.0000i			0.790112i
$520$		0			0
$521$	−9.00000	+	5.19615i	−0.394297	+	0.227648i	−0.684020	−	0.729463i	$-0.739770\pi$
$521$	−9.00000	+	5.19615i	−0.394297	+	0.227648i	0.289723	+	0.957110i	$0.406437\pi$
$522$		0			0
$523$	−1.81173	−	6.76148i	−0.0792216	−	0.295659i	0.914936	−	0.403599i	$-0.132241\pi$
$523$	−1.81173	−	6.76148i	−0.0792216	−	0.295659i	−0.994157	+	0.107941i	$0.965574\pi$
$524$	20.7846			0.907980
$525$		0			0
$526$		0			0
$527$	−8.06918	−	30.1146i	−0.351499	−	1.31181i
$528$	−23.1822	−	6.21166i	−1.00888	−	0.270328i
$529$	−19.9186	+	11.5000i	−0.866025	+	0.500000i
$530$		0			0
$531$			10.3923i			0.450988i
$532$	−1.31268	+	18.2832i	−0.0569118	+	0.792679i
$533$	−14.6969	−	14.6969i	−0.636595	−	0.636595i
$534$		0			0
$535$		0			0
$536$		0			0
$537$	23.1822	−	6.21166i	1.00039	−	0.268053i
$538$		0			0
$539$	−15.5885	−	39.0000i	−0.671442	−	1.67985i
$540$		0			0
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	−0.738296	−	0.674477i	$-0.764369\pi$
$541$	5.00000	−	8.66025i	0.214967	−	0.372333i	0.953262	+	0.302144i	$0.0977023\pi$
$542$		0			0
$543$	1.34486	−	5.01910i	0.0577136	−	0.215390i
$544$		0			0
$545$		0			0
$546$		0			0
$547$	22.0454	−	22.0454i	0.942594	−	0.942594i	−0.0558458	−	0.998439i	$-0.517786\pi$
$547$	22.0454	−	22.0454i	0.942594	−	0.942594i	0.998439	+	0.0558458i	$0.0177855\pi$
$548$	−40.1528	+	10.7589i	−1.71524	+	0.459598i
$549$	4.33013	+	7.50000i	0.184805	+	0.320092i
$550$		0			0
$551$		0			0
$552$		0			0
$553$	−10.9534	−	7.41782i	−0.465784	−	0.315438i
$554$		0			0
$555$		0			0
$556$	−3.00000	+	1.73205i	−0.127228	+	0.0734553i
$557$	10.0382	+	2.68973i	0.425332	+	0.113967i	0.465134	−	0.885240i	$-0.346006\pi$
$557$	10.0382	+	2.68973i	0.425332	+	0.113967i	−0.0398021	+	0.999208i	$0.512673\pi$
$558$		0			0
$559$	−10.3923			−0.439548
$560$		0			0
$561$	36.0000			1.51992
$562$		0			0
$563$	5.79555	+	1.55291i	0.244254	+	0.0654475i	0.378869	−	0.925450i	$-0.376313\pi$
$563$	5.79555	+	1.55291i	0.244254	+	0.0654475i	−0.134615	+	0.990898i	$0.542980\pi$
$564$	10.3923	−	6.00000i	0.437595	−	0.252646i
$565$		0			0
$566$		0			0
$567$	1.15539	+	2.38014i	0.0485220	+	0.0999565i
$568$		0			0
$569$	20.7846	+	12.0000i	0.871336	+	0.503066i	0.867792	−	0.496928i	$-0.165539\pi$
$569$	20.7846	+	12.0000i	0.871336	+	0.503066i	0.00354413	+	0.999994i	$0.498872\pi$
$570$		0			0
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	0.577301	−	0.816532i	$-0.304106\pi$
$571$	−10.0000	−	17.3205i	−0.418487	−	0.724841i	−0.995788	+	0.0916910i	$0.970773\pi$
$572$	−23.1822	+	6.21166i	−0.969297	+	0.259722i
$573$		0			0
$574$		0			0
$575$		0			0
$576$	4.00000	−	6.92820i	0.166667	−	0.288675i
$577$	1.81173	−	6.76148i	0.0754234	−	0.281484i	−0.917906	−	0.396799i	$-0.870121\pi$
$577$	1.81173	−	6.76148i	0.0754234	−	0.281484i	0.993329	+	0.115315i	$0.0367877\pi$
$578$		0			0
$579$	7.79423	−	13.5000i	0.323917	−	0.561041i
$580$		0			0
$581$	−12.0000	+	10.3923i	−0.497844	+	0.431145i
$582$		0			0
$583$	60.2292	−	16.1384i	2.49444	−	0.668383i
$584$		0			0
$585$		0			0
$586$		0			0
$587$	12.7279	+	12.7279i	0.525338	+	0.525338i	0.919179	−	0.393841i	$-0.128854\pi$
$587$	12.7279	+	12.7279i	0.525338	+	0.525338i	−0.393841	+	0.919179i	$0.628854\pi$
$588$	13.9019	−	1.65445i	0.573305	−	0.0682284i
$589$		−	18.0000i		−	0.741677i
$590$		0			0
$591$	9.00000	−	5.19615i	0.370211	−	0.213741i
$592$	33.4607	+	8.96575i	1.37522	+	0.368490i
$593$		0			0		0.965926	−	0.258819i	$-0.0833333\pi$
$593$		0			0		−0.965926	+	0.258819i	$0.916667\pi$
$594$		0			0
$595$		0			0
$596$	−24.0000			−0.983078
$597$	−4.93117	−	18.4034i	−0.201819	−	0.753199i
$598$		0			0
$599$	10.3923	−	6.00000i	0.424618	−	0.245153i	−0.272433	−	0.962175i	$-0.587828\pi$
$599$	10.3923	−	6.00000i	0.424618	−	0.245153i	0.697051	+	0.717021i	$0.254495\pi$
$600$		0			0
$601$			34.6410i			1.41304i	0.707695	+	0.706518i	$0.249735\pi$
$601$			34.6410i			1.41304i	−0.707695	+	0.706518i	$0.750265\pi$
$602$		0			0
$603$	−2.44949	−	2.44949i	−0.0997509	−	0.0997509i
$604$	−8.66025	−	5.00000i	−0.352381	−	0.203447i
$605$		0			0
$606$		0			0
$607$	−24.1481	+	6.47048i	−0.980143	+	0.262629i	−0.713105	−	0.701057i	$-0.752712\pi$
$607$	−24.1481	+	6.47048i	−0.980143	+	0.262629i	−0.267038	+	0.963686i	$0.586045\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$	6.00000	−	10.3923i	0.242734	−	0.420428i
$612$	−3.10583	+	11.5911i	−0.125546	+	0.468543i
$613$		0			0		−0.965926	−	0.258819i	$-0.916667\pi$
$613$		0			0		0.965926	+	0.258819i	$0.0833333\pi$
$614$		0			0
$615$		0			0
$616$		0			0
$617$	7.34847	−	7.34847i	0.295838	−	0.295838i	−0.543543	−	0.839381i	$-0.682918\pi$
$617$	7.34847	−	7.34847i	0.295838	−	0.295838i	0.839381	+	0.543543i	$0.182918\pi$
$618$		0			0
$619$	23.3827	+	40.5000i	0.939829	+	1.62783i	0.765787	+	0.643094i	$0.222350\pi$
$619$	23.3827	+	40.5000i	0.939829	+	1.62783i	0.174042	+	0.984738i	$0.444317\pi$
$620$		0			0
$621$		0			0
$622$		0			0
$623$	−15.4176	+	22.7661i	−0.617695	+	0.912105i
$624$		−	8.00000i		−	0.320256i
$625$		0			0
$626$		0			0
$627$	20.0764	+	5.37945i	0.801774	+	0.214835i
$628$	3.62347	+	13.5230i	0.144592	+	0.539625i
$629$	−51.9615			−2.07184
$630$		0			0
$631$	−1.00000			−0.0398094			−0.0199047	−	0.999802i	$-0.506336\pi$
$631$	−1.00000			−0.0398094			−0.0199047	+	0.999802i	$0.506336\pi$
$632$		0			0
$633$	6.76148	+	1.81173i	0.268745	+	0.0720099i
$634$		0			0
$635$		0			0
$636$			20.7846i			0.824163i
$637$	11.2122	−	8.38375i	0.444242	−	0.332176i
$638$		0			0
$639$	−5.19615	−	3.00000i	−0.205557	−	0.118678i
$640$		0			0
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$		0			0
$643$	−20.5061	+	20.5061i	−0.808682	+	0.808682i	−0.984434	−	0.175753i	$-0.943764\pi$
$643$	−20.5061	+	20.5061i	−0.808682	+	0.808682i	0.175753	+	0.984434i	$0.443764\pi$
$644$		0			0
$645$		0			0
$646$		0			0
$647$	−4.65874	+	17.3867i	−0.183154	+	0.683540i	0.811864	+	0.583846i	$0.198453\pi$
$647$	−4.65874	+	17.3867i	−0.183154	+	0.683540i	−0.995018	+	0.0996938i	$0.968214\pi$
$648$		0			0
$649$	31.1769	−	54.0000i	1.22380	−	2.11969i
$650$		0			0
$651$	−13.5000	+	2.59808i	−0.529107	+	0.101827i
$652$	−12.2474	+	12.2474i	−0.479647	+	0.479647i
$653$	10.0382	−	2.68973i	0.392825	−	0.105257i	−0.0569993	−	0.998374i	$-0.518153\pi$
$653$	10.0382	−	2.68973i	0.392825	−	0.105257i	0.449824	+	0.893117i	$0.351487\pi$
$654$		0			0
$655$		0			0
$656$	−36.0000	−	20.7846i	−1.40556	−	0.811503i
$657$	−0.707107	−	0.707107i	−0.0275869	−	0.0275869i
$658$		0			0
$659$		−	6.00000i		−	0.233727i	−0.993148	−	0.116863i	$-0.962716\pi$
$659$		−	6.00000i		−	0.233727i	0.993148	−	0.116863i	$-0.0372840\pi$
$660$		0			0
$661$	37.5000	−	21.6506i	1.45858	−	0.842112i	0.459639	−	0.888106i	$-0.347979\pi$
$661$	37.5000	−	21.6506i	1.45858	−	0.842112i	0.998942	+	0.0459936i	$0.0146454\pi$
$662$		0			0
$663$	3.10583	+	11.5911i	0.120620	+	0.450161i
$664$		0			0
$665$		0			0
$666$		0			0
$667$		0			0
$668$	23.1822	+	6.21166i	0.896947	+	0.240336i
$669$	−4.33013	+	2.50000i	−0.167412	+	0.0966556i
$670$		0			0
$671$		−	51.9615i		−	2.00595i
$672$		0			0
$673$	8.57321	+	8.57321i	0.330473	+	0.330473i	0.852766	−	0.522293i	$-0.174923\pi$
$673$	8.57321	+	8.57321i	0.330473	+	0.330473i	−0.522293	+	0.852766i	$0.674923\pi$
$674$		0			0
$675$		0			0
$676$	9.00000	+	15.5885i	0.346154	+	0.599556i
$677$	−46.3644	+	12.4233i	−1.78193	+	0.477467i	−0.990933	−	0.134354i	$-0.957104\pi$
$677$	−46.3644	+	12.4233i	−1.78193	+	0.477467i	−0.790997	+	0.611820i	$0.790438\pi$
$678$		0			0
$679$	−22.5167	−	26.0000i	−0.864110	−	0.997788i
$680$		0			0
$681$	−3.00000	+	5.19615i	−0.114960	+	0.199117i
$682$		0			0
$683$	−8.06918	+	30.1146i	−0.308759	+	1.15230i	0.620903	+	0.783888i	$0.286766\pi$
$683$	−8.06918	+	30.1146i	−0.308759	+	1.15230i	−0.929661	+	0.368415i	$0.879901\pi$
$684$	−3.46410	+	6.00000i	−0.132453	+	0.229416i
$685$		0			0
$686$		0			0
$687$	−4.89898	+	4.89898i	−0.186908	+	0.186908i
$688$	−20.0764	+	5.37945i	−0.765405	+	0.205090i
$689$	10.3923	+	18.0000i	0.395915	+	0.685745i
$690$		0			0
$691$	10.5000	+	6.06218i	0.399439	+	0.230616i	0.686242	−	0.727373i	$-0.259259\pi$
$691$	10.5000	+	6.06218i	0.399439	+	0.230616i	−0.286803	+	0.957990i	$0.592593\pi$
$692$	25.4558	+	25.4558i	0.967686	+	0.967686i
$693$	1.13681	−	15.8338i	0.0431839	−	0.601474i
$694$		0			0
$695$		0			0
$696$		0			0
$697$	60.2292	+	16.1384i	2.28134	+	0.611284i
$698$		0			0
$699$	20.7846			0.786146
$700$		0			0
$701$	−42.0000			−1.58632			−0.793159	−	0.609015i	$-0.791565\pi$
$701$	−42.0000			−1.58632			−0.793159	+	0.609015i	$0.791565\pi$
$702$		0			0
$703$	−28.9778	−	7.76457i	−1.09292	−	0.292846i
$704$	−41.5692	+	24.0000i	−1.56670	+	0.904534i
$705$		0			0
$706$		0			0
$707$		0			0
$708$	14.6969	+	14.6969i	0.552345	+	0.552345i
$709$	26.8468	+	15.5000i	1.00825	+	0.582115i	0.910679	−	0.413114i	$-0.135559\pi$
$709$	26.8468	+	15.5000i	1.00825	+	0.582115i	0.0975728	+	0.995228i	$0.468892\pi$
$710$		0			0
$711$	−2.50000	−	4.33013i	−0.0937573	−	0.162392i
$712$		0			0
$713$		0			0
$714$		0			0
$715$		0			0
$716$	24.0000	−	41.5692i	0.896922	−	1.55351i
$717$	4.65874	−	17.3867i	0.173984	−	0.649317i
$718$		0			0
$719$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$719$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$720$		0			0
$721$	−3.50000	−	18.1865i	−0.130347	−	0.677302i
$722$		0			0
$723$	18.4034	−	4.93117i	0.684428	−	0.183392i
$724$	−5.19615	−	9.00000i	−0.193113	−	0.334482i
$725$		0			0
$726$		0			0
$727$	28.2843	+	28.2843i	1.04901	+	1.04901i	0.998736	+	0.0502699i	$0.0160081\pi$
$727$	28.2843	+	28.2843i	1.04901	+	1.04901i	0.0502699	+	0.998736i	$0.483992\pi$
$728$		0			0
$729$			1.00000i			0.0370370i
$730$		0			0
$731$	27.0000	−	15.5885i	0.998631	−	0.576560i
$732$	16.7303	+	4.48288i	0.618371	+	0.165692i
$733$	−12.1645	−	45.3985i	−0.449306	−	1.67683i	−0.704310	−	0.709892i	$-0.748744\pi$
$733$	−12.1645	−	45.3985i	−0.449306	−	1.67683i	0.255004	−	0.966940i	$-0.417923\pi$
$734$		0			0
$735$		0			0
$736$		0			0
$737$	5.37945	+	20.0764i	0.198155	+	0.739523i
$738$		0			0
$739$	0.866025	−	0.500000i	0.0318573	−	0.0183928i	−0.483987	−	0.875075i	$-0.660812\pi$
$739$	0.866025	−	0.500000i	0.0318573	−	0.0183928i	0.515844	+	0.856683i	$0.327478\pi$
$740$		0			0
$741$			6.92820i			0.254514i
$742$		0			0
$743$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$743$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$744$		0			0
$745$		0			0
$746$		0			0
$747$	−5.79555	+	1.55291i	−0.212048	+	0.0568182i
$748$	50.9117	−	50.9117i	1.86152	−	1.86152i
$749$		0			0
$750$		0			0
$751$	−5.50000	+	9.52628i	−0.200698	+	0.347619i	−0.948753	−	0.316017i	$-0.897654\pi$
$751$	−5.50000	+	9.52628i	−0.200698	+	0.347619i	0.748056	+	0.663636i	$0.230988\pi$
$752$	6.21166	−	23.1822i	0.226516	−	0.845369i
$753$	5.37945	−	20.0764i	0.196038	−	0.731624i
$754$		0			0
$755$		0			0
$756$	5.00000	+	1.73205i	0.181848	+	0.0629941i
$757$	−20.8207	+	20.8207i	−0.756740	+	0.756740i	−0.975728	−	0.218988i	$-0.929725\pi$
$757$	−20.8207	+	20.8207i	−0.756740	+	0.756740i	0.218988	+	0.975728i	$0.429725\pi$
$758$		0			0
$759$		0			0
$760$		0			0
$761$	−18.0000	−	10.3923i	−0.652499	−	0.376721i	0.136914	−	0.990583i	$-0.456282\pi$
$761$	−18.0000	−	10.3923i	−0.652499	−	0.376721i	−0.789413	+	0.613862i	$0.789615\pi$
$762$		0			0
$763$	23.8014	−	11.5539i	0.861668	−	0.418281i
$764$		0			0
$765$		0			0
$766$		0			0
$767$	20.0764	+	5.37945i	0.724916	+	0.194241i
$768$	−4.14110	−	15.4548i	−0.149429	−	0.557678i
$769$	−5.19615			−0.187378			−0.0936890	−	0.995602i	$-0.529866\pi$
$769$	−5.19615			−0.187378			−0.0936890	+	0.995602i	$0.529866\pi$
$770$		0			0
$771$	−6.00000			−0.216085
$772$	−8.06918	−	30.1146i	−0.290416	−	1.08385i
$773$	−23.1822	−	6.21166i	−0.833806	−	0.223418i	−0.183433	−	0.983032i	$-0.558721\pi$
$773$	−23.1822	−	6.21166i	−0.833806	−	0.223418i	−0.650374	+	0.759614i	$0.725388\pi$
$774$		0			0
$775$		0			0
$776$		0			0
$777$	−1.64085	+	22.8541i	−0.0588651	+	0.819884i
$778$		0			0
$779$	31.1769	+	18.0000i	1.11703	+	0.644917i
$780$		0			0
$781$	18.0000	+	31.1769i	0.644091	+	1.11560i
$782$		0			0
$783$		0			0
$784$	17.3205	−	22.0000i	0.618590	−	0.785714i
$785$		0			0
$786$		0			0
$787$	−2.84701	+	10.6252i	−0.101485	+	0.378747i	−0.997923	−	0.0644227i	$-0.979479\pi$
$787$	−2.84701	+	10.6252i	−0.101485	+	0.378747i	0.896438	+	0.443170i	$0.146146\pi$
$788$	5.37945	−	20.0764i	0.191635	−	0.715192i
$789$	15.5885	−	27.0000i	0.554964	−	0.961225i
$790$		0			0
$791$	−18.0000	−	20.7846i	−0.640006	−	0.739016i
$792$		0			0
$793$	16.7303	−	4.48288i	0.594111	−	0.159192i
$794$		0			0
$795$		0			0
$796$	−33.0000	−	19.0526i	−1.16965	−	0.675300i
$797$	8.48528	+	8.48528i	0.300564	+	0.300564i	0.841235	−	0.540670i	$-0.181829\pi$
$797$	8.48528	+	8.48528i	0.300564	+	0.300564i	−0.540670	+	0.841235i	$0.681829\pi$
$798$		0			0
$799$			36.0000i			1.27359i
$800$		0			0
$801$	−9.00000	+	5.19615i	−0.317999	+	0.183597i
$802$		0			0
$803$	1.55291	+	5.79555i	0.0548012	+	0.204521i
$804$	−6.92820			−0.244339
$805$		0			0
$806$		0			0
$807$	5.37945	+	20.0764i	0.189366	+	0.706722i
$808$		0			0
$809$	−20.7846	+	12.0000i	−0.730748	+	0.421898i	−0.818696	−	0.574228i	$-0.805302\pi$
$809$	−20.7846	+	12.0000i	−0.730748	+	0.421898i	0.0879478	+	0.996125i	$0.471969\pi$
$810$		0			0
$811$		−	39.8372i		−	1.39887i	−0.714695	−	0.699436i	$-0.753435\pi$
$811$		−	39.8372i		−	1.39887i	0.714695	−	0.699436i	$-0.246565\pi$
$812$		0			0
$813$	−22.0454	−	22.0454i	−0.773166	−	0.773166i
$814$		0			0
$815$		0			0
$816$	12.0000	+	20.7846i	0.420084	+	0.727607i
$817$	17.3867	−	4.65874i	0.608282	−	0.162989i
$818$		0			0
$819$	5.19615	−	1.00000i	0.181568	−	0.0349428i
$820$		0			0
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	−0.577016	−	0.816733i	$-0.695783\pi$
$821$	12.0000	−	20.7846i	0.418803	−	0.725388i	0.995819	+	0.0913446i	$0.0291165\pi$
$822$		0			0
$823$	10.3106	−	38.4797i	0.359406	−	1.34132i	−0.515443	−	0.856924i	$-0.672373\pi$
$823$	10.3106	−	38.4797i	0.359406	−	1.34132i	0.874849	−	0.484396i	$-0.160961\pi$
$824$		0			0
$825$		0			0
$826$		0			0
$827$	22.0454	−	22.0454i	0.766594	−	0.766594i	−0.210911	−	0.977505i	$-0.567643\pi$
$827$	22.0454	−	22.0454i	0.766594	−	0.766594i	0.977505	+	0.210911i	$0.0676431\pi$
$828$		0			0
$829$	−4.33013	−	7.50000i	−0.150392	−	0.260486i	0.780980	−	0.624556i	$-0.214720\pi$
$829$	−4.33013	−	7.50000i	−0.150392	−	0.260486i	−0.931371	+	0.364070i	$0.881387\pi$
$830$		0			0
$831$	12.0000	+	6.92820i	0.416275	+	0.240337i
$832$	−11.3137	−	11.3137i	−0.392232	−	0.392232i
$833$	−16.5545	+	38.5999i	−0.573578	+	1.33741i
$834$		0			0
$835$		0			0
$836$	36.0000	−	20.7846i	1.24509	−	0.718851i
$837$	−5.01910	−	1.34486i	−0.173485	−	0.0464853i
$838$		0			0
$839$	−31.1769			−1.07635			−0.538173	−	0.842834i	$-0.680885\pi$
$839$	−31.1769			−1.07635			−0.538173	+	0.842834i	$0.680885\pi$
$840$		0			0
$841$	29.0000			1.00000
$842$		0			0
$843$	−5.79555	−	1.55291i	−0.199610	−	0.0534852i
$844$	12.1244	−	7.00000i	0.417338	−	0.240950i
$845$		0			0
$846$		0			0
$847$	−37.0891	+	54.7668i	−1.27440	+	1.88181i
$848$	29.3939	+	29.3939i	1.00939	+	1.00939i
$849$	13.8564	+	8.00000i	0.475551	+	0.274559i
$850$		0			0
$851$		0			0
$852$	−11.5911	+	3.10583i	−0.397105	+	0.106404i
$853$	−13.4350	+	13.4350i	−0.460007	+	0.460007i	−0.898658	−	0.438651i	$-0.855456\pi$
$853$	−13.4350	+	13.4350i	−0.460007	+	0.460007i	0.438651	+	0.898658i	$0.355456\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	6.21166	−	23.1822i	0.212186	−	0.791890i	−0.774952	−	0.632020i	$-0.782226\pi$
$857$	6.21166	−	23.1822i	0.212186	−	0.791890i	0.987138	−	0.159869i	$-0.0511073\pi$
$858$		0			0
$859$	−5.19615	+	9.00000i	−0.177290	+	0.307076i	−0.940952	−	0.338541i	$-0.890067\pi$
$859$	−5.19615	+	9.00000i	−0.177290	+	0.307076i	0.763661	+	0.645617i	$0.223400\pi$
$860$		0			0
$861$	9.00000	−	25.9808i	0.306719	−	0.885422i
$862$		0			0
$863$	30.1146	−	8.06918i	1.02511	−	0.274678i	0.293181	−	0.956057i	$-0.405286\pi$
$863$	30.1146	−	8.06918i	1.02511	−	0.274678i	0.731931	+	0.681379i	$0.238619\pi$
$864$		0			0
$865$		0			0
$866$		0			0
$867$	−13.4350	−	13.4350i	−0.456278	−	0.456278i
$868$	−15.4176	+	22.7661i	−0.523309	+	0.772732i
$869$			30.0000i			1.01768i
$870$		0			0
$871$	−6.00000	+	3.46410i	−0.203302	+	0.117377i
$872$		0			0
$873$	−3.36465	−	12.5570i	−0.113876	−	0.424991i
$874$		0			0
$875$		0			0
$876$	−2.00000			−0.0675737
$877$	−5.82774	−	21.7494i	−0.196789	−	0.734426i	−0.991797	−	0.127827i	$-0.959200\pi$
$877$	−5.82774	−	21.7494i	−0.196789	−	0.734426i	0.795008	−	0.606599i	$-0.207467\pi$
$878$		0			0
$879$	15.5885	−	9.00000i	0.525786	−	0.303562i
$880$		0			0
$881$		−	10.3923i		−	0.350126i	−0.984557	−	0.175063i	$-0.943987\pi$
$881$		−	10.3923i		−	0.350126i	0.984557	−	0.175063i	$-0.0560129\pi$
$882$		0			0
$883$	2.44949	+	2.44949i	0.0824319	+	0.0824319i	0.747121	−	0.664689i	$-0.231436\pi$
$883$	2.44949	+	2.44949i	0.0824319	+	0.0824319i	−0.664689	+	0.747121i	$0.731436\pi$
$884$	20.7846	+	12.0000i	0.699062	+	0.403604i
$885$		0			0
$886$		0			0
$887$	−17.3867	+	4.65874i	−0.583787	+	0.156425i	−0.538612	−	0.842554i	$-0.681051\pi$
$887$	−17.3867	+	4.65874i	−0.583787	+	0.156425i	−0.0451749	+	0.998979i	$0.514385\pi$
$888$		0			0
$889$	−24.2487	+	21.0000i	−0.813276	+	0.704317i
$890$		0			0
$891$	3.00000	−	5.19615i	0.100504	−	0.174078i
$892$	−2.58819	+	9.65926i	−0.0866590	+	0.323416i
$893$	−5.37945	+	20.0764i	−0.180017	+	0.671831i
$894$		0			0
$895$		0			0
$896$		0			0
$897$		0			0
$898$		0			0
$899$		0			0
$900$		0			0
$901$	−54.0000	−	31.1769i	−1.79900	−	1.03865i
$902$		0			0
$903$	−6.00361	−	12.3676i	−0.199787	−	0.411567i
$904$		0			0
$905$		0			0
$906$		0			0
$907$	1.67303	+	0.448288i	0.0555521	+	0.0148851i	0.286488	−	0.958084i	$-0.407512\pi$
$907$	1.67303	+	0.448288i	0.0555521	+	0.0148851i	−0.230936	+	0.972969i	$0.574179\pi$
$908$	3.10583	+	11.5911i	0.103071	+	0.384664i
$909$		0			0
$910$		0			0
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$	3.58630	+	13.3843i	0.118754	+	0.443197i
$913$	34.7733	+	9.31749i	1.15083	+	0.308364i
$914$		0			0
$915$		0			0
$916$			13.8564i			0.457829i
$917$	22.7661	+	15.4176i	0.751803	+	0.509136i
$918$		0			0
$919$	21.6506	+	12.5000i	0.714189	+	0.412337i	0.812610	−	0.582808i	$-0.198046\pi$
$919$	21.6506	+	12.5000i	0.714189	+	0.412337i	−0.0984214	+	0.995145i	$0.531379\pi$
$920$		0			0
$921$	3.50000	+	6.06218i	0.115329	+	0.199756i
$922$		0			0
$923$	−8.48528	+	8.48528i	−0.279296	+	0.279296i
$924$	−20.7846	−	24.0000i	−0.683763	−	0.789542i
$925$		0			0
$926$		0			0
$927$	1.81173	−	6.76148i	0.0595051	−	0.222076i
$928$		0			0
$929$	5.19615	−	9.00000i	0.170480	−	0.295280i	−0.768108	−	0.640321i	$-0.778801\pi$
$929$	5.19615	−	9.00000i	0.170480	−	0.295280i	0.938588	+	0.345040i	$0.112135\pi$
$930$		0			0
$931$	−15.0000	+	19.0526i	−0.491605	+	0.624422i
$932$	29.3939	−	29.3939i	0.962828	−	0.962828i
$933$	20.0764	−	5.37945i	0.657272	−	0.176115i
$934$		0			0
$935$		0			0
$936$		0			0
$937$	20.5061	+	20.5061i	0.669905	+	0.669905i	0.957694	−	0.287789i	$-0.0929201\pi$
$937$	20.5061	+	20.5061i	0.669905	+	0.669905i	−0.287789	+	0.957694i	$0.592920\pi$
$938$		0			0
$939$			19.0000i			0.620042i
$940$		0			0
$941$	−27.0000	+	15.5885i	−0.880175	+	0.508169i	−0.870716	−	0.491786i	$-0.836344\pi$
$941$	−27.0000	+	15.5885i	−0.880175	+	0.508169i	−0.00945879	+	0.999955i	$0.503011\pi$
$942$		0			0
$943$		0			0
$944$	41.5692			1.35296
$945$		0			0
$946$		0			0
$947$	−2.68973	−	10.0382i	−0.0874044	−	0.326198i	0.908354	−	0.418202i	$-0.137339\pi$
$947$	−2.68973	−	10.0382i	−0.0874044	−	0.326198i	−0.995759	+	0.0920040i	$0.970673\pi$
$948$	−9.65926	−	2.58819i	−0.313718	−	0.0840605i
$949$	−1.73205	+	1.00000i	−0.0562247	+	0.0324614i
$950$		0			0
$951$			10.3923i			0.336994i
$952$		0			0
$953$		0			0		0.707107	−	0.707107i	$-0.250000\pi$
$953$		0			0		−0.707107	+	0.707107i	$0.750000\pi$
$954$		0			0
$955$		0			0
$956$	−18.0000	−	31.1769i	−0.582162	−	1.00833i
$957$		0			0
$958$		0			0
$959$	−51.9615	−	18.0000i	−1.67793	−	0.581250i
$960$		0			0
$961$	−2.00000	+	3.46410i	−0.0645161	+	0.111745i
$962$		0			0
$963$		0			0
$964$	19.0526	−	33.0000i	0.613642	−	1.06286i
$965$		0			0
$966$		0			0
$967$	30.6186	−	30.6186i	0.984628	−	0.984628i	−0.0152551	−	0.999884i	$-0.504856\pi$
$967$	30.6186	−	30.6186i	0.984628	−	0.984628i	0.999884	+	0.0152551i	$0.00485605\pi$
$968$		0			0
$969$	−10.3923	−	18.0000i	−0.333849	−	0.578243i
$970$		0			0
$971$	18.0000	+	10.3923i	0.577647	+	0.333505i	0.760198	−	0.649692i	$-0.225102\pi$
$971$	18.0000	+	10.3923i	0.577647	+	0.333505i	−0.182550	+	0.983196i	$0.558435\pi$
$972$	1.41421	+	1.41421i	0.0453609	+	0.0453609i
$973$	−4.57081	−	0.328169i	−0.146533	−	0.0105206i
$974$		0			0
$975$		0			0
$976$	30.0000	−	17.3205i	0.960277	−	0.554416i
$977$		0			0		0.258819	−	0.965926i	$-0.416667\pi$
$977$		0			0		−0.258819	+	0.965926i	$0.583333\pi$
$978$		0			0
$979$	62.3538			1.99284
$980$		0			0
$981$	10.0000			0.319275
$982$		0			0
$983$	−40.5689	−	10.8704i	−1.29395	−	0.346712i	−0.454788	−	0.890600i	$-0.650285\pi$
$983$	−40.5689	−	10.8704i	−1.29395	−	0.346712i	−0.839158	+	0.543888i	$0.816952\pi$
$984$		0			0
$985$		0			0
$986$		0			0
$987$	15.8338	+	1.13681i	0.503994	+	0.0361851i
$988$	9.79796	+	9.79796i	0.311715	+	0.311715i
$989$		0			0
$990$		0			0
$991$	14.5000	+	25.1147i	0.460608	+	0.797796i	0.998991	−	0.0449040i	$-0.0142982\pi$
$991$	14.5000	+	25.1147i	0.460608	+	0.797796i	−0.538384	+	0.842700i	$0.680965\pi$
$992$		0			0
$993$	3.53553	−	3.53553i	0.112197	−	0.112197i
$994$		0			0
$995$		0			0
$996$	−6.00000	+	10.3923i	−0.190117	+	0.329293i
$997$	1.29410	−	4.82963i	0.0409844	−	0.152956i	−0.942401	−	0.334484i	$-0.891438\pi$
$997$	1.29410	−	4.82963i	0.0409844	−	0.152956i	0.983386	+	0.181529i	$0.0581045\pi$
$998$		0			0
$999$	−4.33013	+	7.50000i	−0.136999	+	0.237289i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	525.2.bc.a.418.2	yes	8
5.2	odd	4	inner	525.2.bc.a.82.2	yes	8
5.3	odd	4	inner	525.2.bc.a.82.1	✓	8
5.4	even	2	inner	525.2.bc.a.418.1	yes	8
7.3	odd	6	inner	525.2.bc.a.493.2	yes	8
35.3	even	12	inner	525.2.bc.a.157.1	yes	8
35.17	even	12	inner	525.2.bc.a.157.2	yes	8
35.24	odd	6	inner	525.2.bc.a.493.1	yes	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
525.2.bc.a.82.1	✓	8	5.3	odd	4	inner
525.2.bc.a.82.2	yes	8	5.2	odd	4	inner
525.2.bc.a.157.1	yes	8	35.3	even	12	inner
525.2.bc.a.157.2	yes	8	35.17	even	12	inner
525.2.bc.a.418.1	yes	8	5.4	even	2	inner
525.2.bc.a.418.2	yes	8	1.1	even	1	trivial
525.2.bc.a.493.1	yes	8	35.24	odd	6	inner
525.2.bc.a.493.2	yes	8	7.3	odd	6	inner

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:	\( N \)	\(=\)	\( 525 = 3 \cdot 5^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	525.bc (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.965926 + 0.258819i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.63896 + 0.189469i) q^{7} +(0.866025 + 0.500000i) q^{9} +O(q^{10})\)	\(q+(0.965926 + 0.258819i) q^{3} +(1.73205 - 1.00000i) q^{4} +(2.63896 + 0.189469i) q^{7} +(0.866025 + 0.500000i) q^{9} +(-3.00000 - 5.19615i) q^{11} +(1.93185 - 0.517638i) q^{12} +(1.41421 - 1.41421i) q^{13} +(2.00000 - 3.46410i) q^{16} +(-1.55291 + 5.79555i) q^{17} +(-1.73205 + 3.00000i) q^{19} +(2.50000 + 0.866025i) q^{21} +(0.707107 + 0.707107i) q^{27} +(4.76028 - 2.31079i) q^{28} +(-4.50000 + 2.59808i) q^{31} +(-1.55291 - 5.79555i) q^{33} +2.00000 q^{36} +(2.24144 + 8.36516i) q^{37} +(1.73205 - 1.00000i) q^{39} -10.3923i q^{41} +(-3.67423 - 3.67423i) q^{43} +(-10.3923 - 6.00000i) q^{44} +(5.79555 - 1.55291i) q^{47} +(2.82843 - 2.82843i) q^{48} +(6.92820 + 1.00000i) q^{49} +(-3.00000 + 5.19615i) q^{51} +(1.03528 - 3.86370i) q^{52} +(-2.68973 + 10.0382i) q^{53} +(-2.44949 + 2.44949i) q^{57} +(5.19615 + 9.00000i) q^{59} +(7.50000 + 4.33013i) q^{61} +(2.19067 + 1.48356i) q^{63} -8.00000i q^{64} +(-3.34607 - 0.896575i) q^{67} +(3.10583 + 11.5911i) q^{68} -6.00000 q^{71} +(-0.965926 - 0.258819i) q^{73} +6.92820i q^{76} +(-6.93237 - 14.2808i) q^{77} +(-4.33013 - 2.50000i) q^{79} +(0.500000 + 0.866025i) q^{81} +(-4.24264 + 4.24264i) q^{83} +(5.19615 - 1.00000i) q^{84} +(-5.19615 + 9.00000i) q^{89} +(4.00000 - 3.46410i) q^{91} +(-5.01910 + 1.34486i) q^{93} +(-9.19239 - 9.19239i) q^{97} -6.00000i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q+O(q^{10}) \) 8 * q	\( 8 q - 24 q^{11} + 16 q^{16} + 20 q^{21} - 36 q^{31} + 16 q^{36} - 24 q^{51} + 60 q^{61} - 48 q^{71} + 4 q^{81} + 32 q^{91}+O(q^{100}) \) 8 * q - 24 * q^11 + 16 * q^16 + 20 * q^21 - 36 * q^31 + 16 * q^36 - 24 * q^51 + 60 * q^61 - 48 * q^71 + 4 * q^81 + 32 * q^91

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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