LMFDB - Embedded newform 960.2.y.f.847.3

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [960,2,Mod(847,960)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("960.847"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(960, base_ring=CyclotomicField(4)) chi = DirichletCharacter(H, H._module([2, 1, 0, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 960 = 2^{6} \cdot 3 \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	960.y (of order $4$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [20,0,20,0,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(5)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$7.66563859404$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 2 x^{19} + 3 x^{18} - 6 x^{17} + 2 x^{16} + 4 x^{14} + 20 x^{13} - 24 x^{12} + 40 x^{11} + \cdots + 1024 $ x^20 - 2x^19 + 3x^18 - 6x^17 + 2x^16 + 4x^14 + 20x^13 - 24x^12 + 40x^11 - 124x^10 + 80x^9 - 96x^8 + 160x^7 + 64x^6 + 128x^4 - 768x^3 + 768x^2 - 1024*x + 1024
Coefficient ring:	$\Z[a_1, \ldots, a_{17}]$
Coefficient ring index:	$ 2^{17} $
Twist minimal:	no (minimal twist has level 240)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			847.3
Root			$1.40751 + 0.137540i$ of defining polynomial
Character	$\chi$	$=$	960.847
Dual form			960.2.y.f.943.3

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+1.00000 q^{3} +(-1.76195 - 1.37678i) q^{5} +(-0.159531 - 0.159531i) q^{7} +1.00000 q^{9} +(-1.60861 + 1.60861i) q^{11} -4.36332i q^{13} +(-1.76195 - 1.37678i) q^{15} +(-4.63479 - 4.63479i) q^{17} +(-3.97920 + 3.97920i) q^{19} +(-0.159531 - 0.159531i) q^{21} +(5.58779 - 5.58779i) q^{23} +(1.20897 + 4.85164i) q^{25} +1.00000 q^{27} +(-6.25463 - 6.25463i) q^{29} -1.69754i q^{31} +(-1.60861 + 1.60861i) q^{33} +(0.0614476 + 0.500725i) q^{35} +0.609145i q^{37} -4.36332i q^{39} +0.538520i q^{41} -0.592259i q^{43} +(-1.76195 - 1.37678i) q^{45} +(-4.85568 + 4.85568i) q^{47} -6.94910i q^{49} +(-4.63479 - 4.63479i) q^{51} -4.82837 q^{53} +(5.04901 - 0.619600i) q^{55} +(-3.97920 + 3.97920i) q^{57} +(-5.78762 - 5.78762i) q^{59} +(1.65469 - 1.65469i) q^{61} +(-0.159531 - 0.159531i) q^{63} +(-6.00733 + 7.68798i) q^{65} +0.485302i q^{67} +(5.58779 - 5.58779i) q^{69} -6.86042 q^{71} +(-0.160991 - 0.160991i) q^{73} +(1.20897 + 4.85164i) q^{75} +0.513248 q^{77} +7.13706 q^{79} +1.00000 q^{81} +6.88217 q^{83} +(1.78521 + 14.5474i) q^{85} +(-6.25463 - 6.25463i) q^{87} +17.0238 q^{89} +(-0.696085 + 0.696085i) q^{91} -1.69754i q^{93} +(12.4896 - 1.53269i) q^{95} +(9.64079 + 9.64079i) q^{97} +(-1.60861 + 1.60861i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 20 q^{3} + 4 q^{7} + 20 q^{9} - 8 q^{11} + 12 q^{17} - 16 q^{19} + 4 q^{21} + 16 q^{23} + 4 q^{25} + 20 q^{27} - 8 q^{33} + 28 q^{35} + 12 q^{51} + 8 q^{53} + 4 q^{55} - 16 q^{57} + 16 q^{59} - 12 q^{61}+ \cdots - 8 q^{99}+O(q^{100}) $ 20 * q + 20 * q^3 + 4 * q^7 + 20 * q^9 - 8 * q^11 + 12 * q^17 - 16 * q^19 + 4 * q^21 + 16 * q^23 + 4 * q^25 + 20 * q^27 - 8 * q^33 + 28 * q^35 + 12 * q^51 + 8 * q^53 + 4 * q^55 - 16 * q^57 + 16 * q^59 - 12 * q^61 + 4 * q^63 + 4 * q^65 + 16 * q^69 - 20 * q^73 + 4 * q^75 - 48 * q^79 + 20 * q^81 + 24 * q^83 + 4 * q^85 + 40 * q^89 + 24 * q^91 + 72 * q^95 - 28 * q^97 - 8 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/960\mathbb{Z}\right)^\times$.

$n$	$511$	$577$	$641$	$901$
$\chi(n)$	$-1$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{1}{4}\right)$

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
$2$		0			0
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		0			0
$5$	−1.76195	−	1.37678i	−0.787970	−	0.615714i
$5$	−1.76195	−	1.37678i	−0.787970	−	0.615714i
$6$		0			0
$7$	−0.159531	−	0.159531i	−0.0602971	−	0.0602971i	0.676315	−	0.736612i	$-0.263576\pi$
$7$	−0.159531	−	0.159531i	−0.0602971	−	0.0602971i	−0.736612	+	0.676315i	$0.763576\pi$
$8$		0			0
$9$	1.00000			0.333333
$10$		0			0
$11$	−1.60861	+	1.60861i	−0.485015	+	0.485015i	−0.906729	−	0.421714i	$-0.861429\pi$
$11$	−1.60861	+	1.60861i	−0.485015	+	0.485015i	0.421714	+	0.906729i	$0.361429\pi$
$12$		0			0
$13$		−	4.36332i		−	1.21017i	−0.796162	−	0.605084i	$-0.793139\pi$
$13$		−	4.36332i		−	1.21017i	0.796162	−	0.605084i	$-0.206861\pi$
$14$		0			0
$15$	−1.76195	−	1.37678i	−0.454935	−	0.355483i
$16$		0			0
$17$	−4.63479	−	4.63479i	−1.12410	−	1.12410i	−0.991118	−	0.132983i	$-0.957545\pi$
$17$	−4.63479	−	4.63479i	−1.12410	−	1.12410i	−0.132983	−	0.991118i	$-0.542455\pi$
$18$		0			0
$19$	−3.97920	+	3.97920i	−0.912891	+	0.912891i	−0.996499	−	0.0836074i	$-0.973356\pi$
$19$	−3.97920	+	3.97920i	−0.912891	+	0.912891i	0.0836074	+	0.996499i	$0.473356\pi$
$20$		0			0
$21$	−0.159531	−	0.159531i	−0.0348125	−	0.0348125i
$22$		0			0
$23$	5.58779	−	5.58779i	1.16513	−	1.16513i	0.181799	−	0.983336i	$-0.441808\pi$
$23$	5.58779	−	5.58779i	1.16513	−	1.16513i	0.983336	−	0.181799i	$-0.0581919\pi$
$24$		0			0
$25$	1.20897	+	4.85164i	0.241793	+	0.970328i
$26$		0			0
$27$	1.00000			0.192450
$28$		0			0
$29$	−6.25463	−	6.25463i	−1.16146	−	1.16146i	−0.984157	−	0.177299i	$-0.943264\pi$
$29$	−6.25463	−	6.25463i	−1.16146	−	1.16146i	−0.177299	−	0.984157i	$-0.556736\pi$
$30$		0			0
$31$		−	1.69754i		−	0.304886i	−0.988312	−	0.152443i	$-0.951286\pi$
$31$		−	1.69754i		−	0.304886i	0.988312	−	0.152443i	$-0.0487141\pi$
$32$		0			0
$33$	−1.60861	+	1.60861i	−0.280024	+	0.280024i
$34$		0			0
$35$	0.0614476	+	0.500725i	0.0103865	+	0.0846380i
$36$		0			0
$37$			0.609145i			0.100143i	0.998746	+	0.0500714i	$0.0159449\pi$
$37$			0.609145i			0.100143i	−0.998746	+	0.0500714i	$0.984055\pi$
$38$		0			0
$39$		−	4.36332i		−	0.698691i
$40$		0			0
$41$			0.538520i			0.0841026i	0.999115	+	0.0420513i	$0.0133893\pi$
$41$			0.538520i			0.0841026i	−0.999115	+	0.0420513i	$0.986611\pi$
$42$		0			0
$43$		−	0.592259i		−	0.0903186i	−0.998980	−	0.0451593i	$-0.985620\pi$
$43$		−	0.592259i		−	0.0903186i	0.998980	−	0.0451593i	$-0.0143795\pi$
$44$		0			0
$45$	−1.76195	−	1.37678i	−0.262657	−	0.205238i
$46$		0			0
$47$	−4.85568	+	4.85568i	−0.708274	+	0.708274i	−0.966172	−	0.257898i	$-0.916970\pi$
$47$	−4.85568	+	4.85568i	−0.708274	+	0.708274i	0.257898	+	0.966172i	$0.416970\pi$
$48$		0			0
$49$		−	6.94910i		−	0.992729i
$50$		0			0
$51$	−4.63479	−	4.63479i	−0.649000	−	0.649000i
$52$		0			0
$53$	−4.82837			−0.663227			−0.331613	−	0.943415i	$-0.607593\pi$
$53$	−4.82837			−0.663227			−0.331613	+	0.943415i	$0.607593\pi$
$54$		0			0
$55$	5.04901	−	0.619600i	0.680808	−	0.0835468i
$56$		0			0
$57$	−3.97920	+	3.97920i	−0.527058	+	0.527058i
$58$		0			0
$59$	−5.78762	−	5.78762i	−0.753483	−	0.753483i	0.221644	−	0.975128i	$-0.428858\pi$
$59$	−5.78762	−	5.78762i	−0.753483	−	0.753483i	−0.975128	+	0.221644i	$0.928858\pi$
$60$		0			0
$61$	1.65469	−	1.65469i	0.211861	−	0.211861i	−0.593197	−	0.805058i	$-0.702134\pi$
$61$	1.65469	−	1.65469i	0.211861	−	0.211861i	0.805058	+	0.593197i	$0.202134\pi$
$62$		0			0
$63$	−0.159531	−	0.159531i	−0.0200990	−	0.0200990i
$64$		0			0
$65$	−6.00733	+	7.68798i	−0.745117	+	0.953576i
$66$		0			0
$67$			0.485302i			0.0592891i	0.999561	+	0.0296446i	$0.00943754\pi$
$67$			0.485302i			0.0592891i	−0.999561	+	0.0296446i	$0.990562\pi$
$68$		0			0
$69$	5.58779	−	5.58779i	0.672691	−	0.672691i
$70$		0			0
$71$	−6.86042			−0.814182			−0.407091	−	0.913388i	$-0.633457\pi$
$71$	−6.86042			−0.814182			−0.407091	+	0.913388i	$0.633457\pi$
$72$		0			0
$73$	−0.160991	−	0.160991i	−0.0188426	−	0.0188426i	0.697623	−	0.716465i	$-0.254241\pi$
$73$	−0.160991	−	0.160991i	−0.0188426	−	0.0188426i	−0.716465	+	0.697623i	$0.754241\pi$
$74$		0			0
$75$	1.20897	+	4.85164i	0.139599	+	0.560219i
$76$		0			0
$77$	0.513248			0.0584900
$78$		0			0
$79$	7.13706			0.802982			0.401491	−	0.915863i	$-0.368492\pi$
$79$	7.13706			0.802982			0.401491	+	0.915863i	$0.368492\pi$
$80$		0			0
$81$	1.00000			0.111111
$82$		0			0
$83$	6.88217			0.755417			0.377708	−	0.925925i	$-0.376712\pi$
$83$	6.88217			0.755417			0.377708	+	0.925925i	$0.376712\pi$
$84$		0			0
$85$	1.78521	+	14.5474i	0.193633	+	1.57788i
$86$		0			0
$87$	−6.25463	−	6.25463i	−0.670567	−	0.670567i
$88$		0			0
$89$	17.0238			1.80451			0.902257	−	0.431198i	$-0.141909\pi$
$89$	17.0238			1.80451			0.902257	+	0.431198i	$0.141909\pi$
$90$		0			0
$91$	−0.696085	+	0.696085i	−0.0729696	+	0.0729696i
$92$		0			0
$93$		−	1.69754i		−	0.176026i
$94$		0			0
$95$	12.4896	−	1.53269i	1.28141	−	0.157251i
$96$		0			0
$97$	9.64079	+	9.64079i	0.978874	+	0.978874i	0.999781	−	0.0209077i	$-0.00665561\pi$
$97$	9.64079	+	9.64079i	0.978874	+	0.978874i	−0.0209077	+	0.999781i	$0.506656\pi$
$98$		0			0
$99$	−1.60861	+	1.60861i	−0.161672	+	0.161672i
$100$		0			0
$101$	−4.00201	−	4.00201i	−0.398214	−	0.398214i	0.479388	−	0.877603i	$-0.340859\pi$
$101$	−4.00201	−	4.00201i	−0.398214	−	0.398214i	−0.877603	+	0.479388i	$0.840859\pi$
$102$		0			0
$103$	8.06640	−	8.06640i	0.794806	−	0.794806i	−0.187465	−	0.982271i	$-0.560027\pi$
$103$	8.06640	−	8.06640i	0.794806	−	0.794806i	0.982271	+	0.187465i	$0.0600271\pi$
$104$		0			0
$105$	0.0614476	+	0.500725i	0.00599667	+	0.0488658i
$106$		0			0
$107$	−4.50489			−0.435504			−0.217752	−	0.976004i	$-0.569872\pi$
$107$	−4.50489			−0.435504			−0.217752	+	0.976004i	$0.569872\pi$
$108$		0			0
$109$	0.813992	+	0.813992i	0.0779663	+	0.0779663i	0.745015	−	0.667048i	$-0.232443\pi$
$109$	0.813992	+	0.813992i	0.0779663	+	0.0779663i	−0.667048	+	0.745015i	$0.732443\pi$
$110$		0			0
$111$			0.609145i			0.0578175i
$112$		0			0
$113$	7.69423	−	7.69423i	0.723813	−	0.723813i	−0.245567	−	0.969380i	$-0.578974\pi$
$113$	7.69423	−	7.69423i	0.723813	−	0.723813i	0.969380	+	0.245567i	$0.0789741\pi$
$114$		0			0
$115$	−17.5386	+	2.15228i	−1.63548	+	0.200702i
$116$		0			0
$117$		−	4.36332i		−	0.403389i
$118$		0			0
$119$			1.47878i			0.135560i
$120$		0			0
$121$			5.82472i			0.529520i
$122$		0			0
$123$			0.538520i			0.0485567i
$124$		0			0
$125$	4.54949	−	10.2128i	0.406919	−	0.913464i
$126$		0			0
$127$	−12.0279	+	12.0279i	−1.06731	+	1.06731i	−0.0697405	+	0.997565i	$0.522217\pi$
$127$	−12.0279	+	12.0279i	−1.06731	+	1.06731i	−0.997565	+	0.0697405i	$0.977783\pi$
$128$		0			0
$129$		−	0.592259i		−	0.0521455i
$130$		0			0
$131$	−13.2235	−	13.2235i	−1.15534	−	1.15534i	−0.985466	−	0.169874i	$-0.945664\pi$
$131$	−13.2235	−	13.2235i	−1.15534	−	1.15534i	−0.169874	−	0.985466i	$-0.554336\pi$
$132$		0			0
$133$	1.26961			0.110089
$134$		0			0
$135$	−1.76195	−	1.37678i	−0.151645	−	0.118494i
$136$		0			0
$137$	4.88182	−	4.88182i	0.417082	−	0.417082i	−0.467115	−	0.884197i	$-0.654706\pi$
$137$	4.88182	−	4.88182i	0.417082	−	0.417082i	0.884197	+	0.467115i	$0.154706\pi$
$138$		0			0
$139$	9.86643	+	9.86643i	0.836860	+	0.836860i	0.988444	−	0.151584i	$-0.0484375\pi$
$139$	9.86643	+	9.86643i	0.836860	+	0.836860i	−0.151584	+	0.988444i	$0.548438\pi$
$140$		0			0
$141$	−4.85568	+	4.85568i	−0.408922	+	0.408922i
$142$		0			0
$143$	7.01890	+	7.01890i	0.586950	+	0.586950i
$144$		0			0
$145$	2.40914	+	19.6316i	0.200068	+	1.63032i
$146$		0			0
$147$		−	6.94910i		−	0.573152i
$148$		0			0
$149$	−11.2851	+	11.2851i	−0.924515	+	0.924515i	−0.997344	−	0.0728290i	$-0.976797\pi$
$149$	−11.2851	+	11.2851i	−0.924515	+	0.924515i	0.0728290	+	0.997344i	$0.476797\pi$
$150$		0			0
$151$	−1.52546			−0.124140			−0.0620701	−	0.998072i	$-0.519770\pi$
$151$	−1.52546			−0.124140			−0.0620701	+	0.998072i	$0.519770\pi$
$152$		0			0
$153$	−4.63479	−	4.63479i	−0.374700	−	0.374700i
$154$		0			0
$155$	−2.33713	+	2.99098i	−0.187723	+	0.240241i
$156$		0			0
$157$	11.8705			0.947366			0.473683	−	0.880695i	$-0.342924\pi$
$157$	11.8705			0.947366			0.473683	+	0.880695i	$0.342924\pi$
$158$		0			0
$159$	−4.82837			−0.382914
$160$		0			0
$161$	−1.78285			−0.140508
$162$		0			0
$163$	6.57461			0.514963			0.257481	−	0.966283i	$-0.417107\pi$
$163$	6.57461			0.514963			0.257481	+	0.966283i	$0.417107\pi$
$164$		0			0
$165$	5.04901	−	0.619600i	0.393065	−	0.0482358i
$166$		0			0
$167$	18.2166	+	18.2166i	1.40964	+	1.40964i	0.761636	+	0.648005i	$0.224396\pi$
$167$	18.2166	+	18.2166i	1.40964	+	1.40964i	0.648005	+	0.761636i	$0.275604\pi$
$168$		0			0
$169$	−6.03860			−0.464507
$170$		0			0
$171$	−3.97920	+	3.97920i	−0.304297	+	0.304297i
$172$		0			0
$173$		−	4.84309i		−	0.368213i	−0.982906	−	0.184106i	$-0.941061\pi$
$173$		−	4.84309i		−	0.368213i	0.982906	−	0.184106i	$-0.0589391\pi$
$174$		0			0
$175$	0.581119	−	0.966854i	0.0439285	−	0.0730873i
$176$		0			0
$177$	−5.78762	−	5.78762i	−0.435024	−	0.435024i
$178$		0			0
$179$	−5.14531	+	5.14531i	−0.384579	+	0.384579i	−0.872749	−	0.488170i	$-0.837665\pi$
$179$	−5.14531	+	5.14531i	−0.384579	+	0.384579i	0.488170	+	0.872749i	$0.337665\pi$
$180$		0			0
$181$	−11.6902	−	11.6902i	−0.868925	−	0.868925i	0.123429	−	0.992353i	$-0.460611\pi$
$181$	−11.6902	−	11.6902i	−0.868925	−	0.868925i	−0.992353	+	0.123429i	$0.960611\pi$
$182$		0			0
$183$	1.65469	−	1.65469i	0.122318	−	0.122318i
$184$		0			0
$185$	0.838658	−	1.07329i	0.0616593	−	0.0789096i
$186$		0			0
$187$	14.9112			1.09041
$188$		0			0
$189$	−0.159531	−	0.159531i	−0.0116042	−	0.0116042i
$190$		0			0
$191$		−	15.8153i		−	1.14436i	−0.820129	−	0.572179i	$-0.806098\pi$
$191$		−	15.8153i		−	1.14436i	0.820129	−	0.572179i	$-0.193902\pi$
$192$		0			0
$193$	−1.54170	+	1.54170i	−0.110974	+	0.110974i	−0.760413	−	0.649439i	$-0.775004\pi$
$193$	−1.54170	+	1.54170i	−0.110974	+	0.110974i	0.649439	+	0.760413i	$0.275004\pi$
$194$		0			0
$195$	−6.00733	+	7.68798i	−0.430194	+	0.550547i
$196$		0			0
$197$			5.98026i			0.426076i	0.977044	+	0.213038i	$0.0683358\pi$
$197$			5.98026i			0.426076i	−0.977044	+	0.213038i	$0.931664\pi$
$198$		0			0
$199$		−	12.5564i		−	0.890102i	−0.895505	−	0.445051i	$-0.853185\pi$
$199$		−	12.5564i		−	0.890102i	0.895505	−	0.445051i	$-0.146815\pi$
$200$		0			0
$201$			0.485302i			0.0342306i
$202$		0			0
$203$			1.99561i			0.140065i
$204$		0			0
$205$	0.741422	−	0.948847i	0.0517832	−	0.0662704i
$206$		0			0
$207$	5.58779	−	5.58779i	0.388378	−	0.388378i
$208$		0			0
$209$		−	12.8020i		−	0.885533i
$210$		0			0
$211$	18.4049	+	18.4049i	1.26705	+	1.26705i	0.947605	+	0.319443i	$0.103496\pi$
$211$	18.4049	+	18.4049i	1.26705	+	1.26705i	0.319443	+	0.947605i	$0.396504\pi$
$212$		0			0
$213$	−6.86042			−0.470068
$214$		0			0
$215$	−0.815409	+	1.04353i	−0.0556104	+	0.0711684i
$216$		0			0
$217$	−0.270810	+	0.270810i	−0.0183838	+	0.0183838i
$218$		0			0
$219$	−0.160991	−	0.160991i	−0.0108788	−	0.0108788i
$220$		0			0
$221$	−20.2231	+	20.2231i	−1.36035	+	1.36035i
$222$		0			0
$223$	−11.6149	−	11.6149i	−0.777792	−	0.777792i	0.201663	−	0.979455i	$-0.435366\pi$
$223$	−11.6149	−	11.6149i	−0.777792	−	0.777792i	−0.979455	+	0.201663i	$0.935366\pi$
$224$		0			0
$225$	1.20897	+	4.85164i	0.0805977	+	0.323443i
$226$		0			0
$227$			0.411442i			0.0273084i	0.999907	+	0.0136542i	$0.00434640\pi$
$227$			0.411442i			0.0273084i	−0.999907	+	0.0136542i	$0.995654\pi$
$228$		0			0
$229$	11.2286	−	11.2286i	0.742009	−	0.742009i	−0.230955	−	0.972964i	$-0.574185\pi$
$229$	11.2286	−	11.2286i	0.742009	−	0.742009i	0.972964	+	0.230955i	$0.0741851\pi$
$230$		0			0
$231$	0.513248			0.0337692
$232$		0			0
$233$	18.9687	+	18.9687i	1.24268	+	1.24268i	0.958884	+	0.283799i	$0.0915947\pi$
$233$	18.9687	+	18.9687i	1.24268	+	1.24268i	0.283799	+	0.958884i	$0.408405\pi$
$234$		0			0
$235$	15.2407	−	1.87029i	0.994193	−	0.122005i
$236$		0			0
$237$	7.13706			0.463602
$238$		0			0
$239$	11.2094			0.725076			0.362538	−	0.931969i	$-0.381910\pi$
$239$	11.2094			0.725076			0.362538	+	0.931969i	$0.381910\pi$
$240$		0			0
$241$	0.0518990			0.00334311			0.00167156	−	0.999999i	$-0.499468\pi$
$241$	0.0518990			0.00334311			0.00167156	+	0.999999i	$0.499468\pi$
$242$		0			0
$243$	1.00000			0.0641500
$244$		0			0
$245$	−9.56737	+	12.2440i	−0.611237	+	0.782240i
$246$		0			0
$247$	17.3625	+	17.3625i	1.10475	+	1.10475i
$248$		0			0
$249$	6.88217			0.436140
$250$		0			0
$251$	2.45358	−	2.45358i	0.154869	−	0.154869i	−0.625420	−	0.780288i	$-0.715072\pi$
$251$	2.45358	−	2.45358i	0.154869	−	0.154869i	0.780288	+	0.625420i	$0.215072\pi$
$252$		0			0
$253$			17.9772i			1.13022i
$254$		0			0
$255$	1.78521	+	14.5474i	0.111794	+	0.910991i
$256$		0			0
$257$	−4.52073	−	4.52073i	−0.281995	−	0.281995i	0.551909	−	0.833904i	$-0.313900\pi$
$257$	−4.52073	−	4.52073i	−0.281995	−	0.281995i	−0.833904	+	0.551909i	$0.813900\pi$
$258$		0			0
$259$	0.0971776	−	0.0971776i	0.00603832	−	0.00603832i
$260$		0			0
$261$	−6.25463	−	6.25463i	−0.387152	−	0.387152i
$262$		0			0
$263$	−16.0925	+	16.0925i	−0.992304	+	0.992304i	−0.999971	−	0.00766695i	$-0.997560\pi$
$263$	−16.0925	+	16.0925i	−0.992304	+	0.992304i	0.00766695	+	0.999971i	$0.497560\pi$
$264$		0			0
$265$	8.50736	+	6.64759i	0.522603	+	0.408358i
$266$		0			0
$267$	17.0238			1.04184
$268$		0			0
$269$	8.32218	+	8.32218i	0.507412	+	0.507412i	0.913731	−	0.406319i	$-0.133188\pi$
$269$	8.32218	+	8.32218i	0.507412	+	0.507412i	−0.406319	+	0.913731i	$0.633188\pi$
$270$		0			0
$271$			2.91266i			0.176932i	0.996079	+	0.0884658i	$0.0281964\pi$
$271$			2.91266i			0.176932i	−0.996079	+	0.0884658i	$0.971804\pi$
$272$		0			0
$273$	−0.696085	+	0.696085i	−0.0421290	+	0.0421290i
$274$		0			0
$275$	−9.74917	−	5.85966i	−0.587897	−	0.353351i
$276$		0			0
$277$		−	0.339665i		−	0.0204085i	−0.999948	−	0.0102042i	$-0.996752\pi$
$277$		−	0.339665i		−	0.0204085i	0.999948	−	0.0102042i	$-0.00324817\pi$
$278$		0			0
$279$		−	1.69754i		−	0.101629i
$280$		0			0
$281$		−	20.9850i		−	1.25186i	−0.779878	−	0.625931i	$-0.784719\pi$
$281$		−	20.9850i		−	1.25186i	0.779878	−	0.625931i	$-0.215281\pi$
$282$		0			0
$283$			15.6290i			0.929047i	0.885561	+	0.464523i	$0.153774\pi$
$283$			15.6290i			0.929047i	−0.885561	+	0.464523i	$0.846226\pi$
$284$		0			0
$285$	12.4896	−	1.53269i	0.739823	−	0.0907890i
$286$		0			0
$287$	0.0859106	−	0.0859106i	0.00507114	−	0.00507114i
$288$		0			0
$289$			25.9625i			1.52721i
$290$		0			0
$291$	9.64079	+	9.64079i	0.565153	+	0.565153i
$292$		0			0
$293$	19.8819			1.16151			0.580756	−	0.814078i	$-0.302757\pi$
$293$	19.8819			1.16151			0.580756	+	0.814078i	$0.302757\pi$
$294$		0			0
$295$	2.22925	+	18.1658i	0.129792	+	1.05765i
$296$		0			0
$297$	−1.60861	+	1.60861i	−0.0933412	+	0.0933412i
$298$		0			0
$299$	−24.3813	−	24.3813i	−1.41001	−	1.41001i
$300$		0			0
$301$	−0.0944836	+	0.0944836i	−0.00544595	+	0.00544595i
$302$		0			0
$303$	−4.00201	−	4.00201i	−0.229909	−	0.229909i
$304$		0			0
$305$	−5.19362	+	0.637346i	−0.297386	+	0.0364943i
$306$		0			0
$307$		−	13.0401i		−	0.744239i	−0.928185	−	0.372119i	$-0.878631\pi$
$307$		−	13.0401i		−	0.744239i	0.928185	−	0.372119i	$-0.121369\pi$
$308$		0			0
$309$	8.06640	−	8.06640i	0.458882	−	0.458882i
$310$		0			0
$311$	−23.6036			−1.33843			−0.669217	−	0.743067i	$-0.733370\pi$
$311$	−23.6036			−1.33843			−0.669217	+	0.743067i	$0.733370\pi$
$312$		0			0
$313$	−23.0604	−	23.0604i	−1.30345	−	1.30345i	−0.926051	−	0.377399i	$-0.876818\pi$
$313$	−23.0604	−	23.0604i	−1.30345	−	1.30345i	−0.377399	−	0.926051i	$-0.623182\pi$
$314$		0			0
$315$	0.0614476	+	0.500725i	0.00346218	+	0.0282127i
$316$		0			0
$317$	10.0772			0.565991			0.282996	−	0.959121i	$-0.408672\pi$
$317$	10.0772			0.565991			0.282996	+	0.959121i	$0.408672\pi$
$318$		0			0
$319$	20.1226			1.12665
$320$		0			0
$321$	−4.50489			−0.251438
$322$		0			0
$323$	36.8855			2.05236
$324$		0			0
$325$	21.1693	−	5.27511i	1.17426	−	0.292610i
$326$		0			0
$327$	0.813992	+	0.813992i	0.0450138	+	0.0450138i
$328$		0			0
$329$	1.54926			0.0854137
$330$		0			0
$331$	−6.16029	+	6.16029i	−0.338600	+	0.338600i	−0.855840	−	0.517240i	$-0.826959\pi$
$331$	−6.16029	+	6.16029i	−0.338600	+	0.338600i	0.517240	+	0.855840i	$0.326959\pi$
$332$		0			0
$333$			0.609145i			0.0333810i
$334$		0			0
$335$	0.668153	−	0.855080i	0.0365051	−	0.0467180i
$336$		0			0
$337$	−18.1642	−	18.1642i	−0.989467	−	0.989467i	0.0104777	−	0.999945i	$-0.496665\pi$
$337$	−18.1642	−	18.1642i	−0.989467	−	0.989467i	−0.999945	+	0.0104777i	$0.996665\pi$
$338$		0			0
$339$	7.69423	−	7.69423i	0.417893	−	0.417893i
$340$		0			0
$341$	2.73068	+	2.73068i	0.147875	+	0.147875i
$342$		0			0
$343$	−2.22531	+	2.22531i	−0.120156	+	0.120156i
$344$		0			0
$345$	−17.5386	+	2.15228i	−0.944245	+	0.115875i
$346$		0			0
$347$	2.80849			0.150767			0.0753837	−	0.997155i	$-0.475982\pi$
$347$	2.80849			0.150767			0.0753837	+	0.997155i	$0.475982\pi$
$348$		0			0
$349$	−13.8516	−	13.8516i	−0.741458	−	0.741458i	0.231401	−	0.972858i	$-0.425669\pi$
$349$	−13.8516	−	13.8516i	−0.741458	−	0.741458i	−0.972858	+	0.231401i	$0.925669\pi$
$350$		0			0
$351$		−	4.36332i		−	0.232897i
$352$		0			0
$353$	16.3758	−	16.3758i	0.871595	−	0.871595i	−0.121051	−	0.992646i	$-0.538626\pi$
$353$	16.3758	−	16.3758i	0.871595	−	0.871595i	0.992646	+	0.121051i	$0.0386265\pi$
$354$		0			0
$355$	12.0877	+	9.44528i	0.641551	+	0.501303i
$356$		0			0
$357$			1.47878i			0.0782656i
$358$		0			0
$359$			17.0587i			0.900325i	0.892947	+	0.450162i	$0.148634\pi$
$359$			17.0587i			0.900325i	−0.892947	+	0.450162i	$0.851366\pi$
$360$		0			0
$361$		−	12.6681i		−	0.666741i
$362$		0			0
$363$			5.82472i			0.305719i
$364$		0			0
$365$	0.0620100	+	0.505308i	0.00324575	+	0.0264490i
$366$		0			0
$367$	−13.9971	+	13.9971i	−0.730643	+	0.730643i	−0.970747	−	0.240104i	$-0.922818\pi$
$367$	−13.9971	+	13.9971i	−0.730643	+	0.730643i	0.240104	+	0.970747i	$0.422818\pi$
$368$		0			0
$369$			0.538520i			0.0280342i
$370$		0			0
$371$	0.770274	+	0.770274i	0.0399906	+	0.0399906i
$372$		0			0
$373$	16.4829			0.853450			0.426725	−	0.904381i	$-0.359667\pi$
$373$	16.4829			0.853450			0.426725	+	0.904381i	$0.359667\pi$
$374$		0			0
$375$	4.54949	−	10.2128i	0.234935	−	0.527389i
$376$		0			0
$377$	−27.2910	+	27.2910i	−1.40556	+	1.40556i
$378$		0			0
$379$	−9.73283	−	9.73283i	−0.499942	−	0.499942i	0.411478	−	0.911420i	$-0.365013\pi$
$379$	−9.73283	−	9.73283i	−0.499942	−	0.499942i	−0.911420	+	0.411478i	$0.865013\pi$
$380$		0			0
$381$	−12.0279	+	12.0279i	−0.616209	+	0.616209i
$382$		0			0
$383$	−5.51456	−	5.51456i	−0.281781	−	0.281781i	0.552038	−	0.833819i	$-0.313850\pi$
$383$	−5.51456	−	5.51456i	−0.281781	−	0.281781i	−0.833819	+	0.552038i	$0.813850\pi$
$384$		0			0
$385$	−0.904319	−	0.706628i	−0.0460883	−	0.0360131i
$386$		0			0
$387$		−	0.592259i		−	0.0301062i
$388$		0			0
$389$	−3.72303	+	3.72303i	−0.188765	+	0.188765i	−0.795162	−	0.606397i	$-0.792614\pi$
$389$	−3.72303	+	3.72303i	−0.188765	+	0.188765i	0.606397	+	0.795162i	$0.292614\pi$
$390$		0			0
$391$	−51.7964			−2.61946
$392$		0			0
$393$	−13.2235	−	13.2235i	−0.667036	−	0.667036i
$394$		0			0
$395$	−12.5752	−	9.82615i	−0.632726	−	0.494407i
$396$		0			0
$397$	30.9797			1.55483			0.777413	−	0.628991i	$-0.216532\pi$
$397$	30.9797			1.55483			0.777413	+	0.628991i	$0.216532\pi$
$398$		0			0
$399$	1.26961			0.0635601
$400$		0			0
$401$	0.563079			0.0281188			0.0140594	−	0.999901i	$-0.495525\pi$
$401$	0.563079			0.0281188			0.0140594	+	0.999901i	$0.495525\pi$
$402$		0			0
$403$	−7.40690			−0.368964
$404$		0			0
$405$	−1.76195	−	1.37678i	−0.0875522	−	0.0684126i
$406$		0			0
$407$	−0.979879	−	0.979879i	−0.0485708	−	0.0485708i
$408$		0			0
$409$	−33.9503			−1.67874			−0.839368	−	0.543563i	$-0.817075\pi$
$409$	−33.9503			−1.67874			−0.839368	+	0.543563i	$0.817075\pi$
$410$		0			0
$411$	4.88182	−	4.88182i	0.240803	−	0.240803i
$412$		0			0
$413$			1.84661i			0.0908657i
$414$		0			0
$415$	−12.1261	−	9.47522i	−0.595246	−	0.465120i
$416$		0			0
$417$	9.86643	+	9.86643i	0.483161	+	0.483161i
$418$		0			0
$419$	12.0118	−	12.0118i	0.586814	−	0.586814i	−0.349953	−	0.936767i	$-0.613803\pi$
$419$	12.0118	−	12.0118i	0.586814	−	0.586814i	0.936767	+	0.349953i	$0.113803\pi$
$420$		0			0
$421$	−5.06683	−	5.06683i	−0.246942	−	0.246942i	0.572772	−	0.819715i	$-0.305868\pi$
$421$	−5.06683	−	5.06683i	−0.246942	−	0.246942i	−0.819715	+	0.572772i	$0.805868\pi$
$422$		0			0
$423$	−4.85568	+	4.85568i	−0.236091	+	0.236091i
$424$		0			0
$425$	16.8830	−	28.0896i	0.818947	−	1.36255i
$426$		0			0
$427$	−0.527948			−0.0255492
$428$		0			0
$429$	7.01890	+	7.01890i	0.338876	+	0.338876i
$430$		0			0
$431$		−	17.0195i		−	0.819798i	−0.912131	−	0.409899i	$-0.865564\pi$
$431$		−	17.0195i		−	0.819798i	0.912131	−	0.409899i	$-0.134436\pi$
$432$		0			0
$433$	24.6355	−	24.6355i	1.18390	−	1.18390i	0.205180	−	0.978724i	$-0.434222\pi$
$433$	24.6355	−	24.6355i	1.18390	−	1.18390i	0.978724	−	0.205180i	$-0.0657780\pi$
$434$		0			0
$435$	2.40914	+	19.6316i	0.115509	+	0.941264i
$436$		0			0
$437$			44.4699i			2.12728i
$438$		0			0
$439$		−	27.5012i		−	1.31256i	−0.754516	−	0.656281i	$-0.772129\pi$
$439$		−	27.5012i		−	1.31256i	0.754516	−	0.656281i	$-0.227871\pi$
$440$		0			0
$441$		−	6.94910i		−	0.330910i
$442$		0			0
$443$		−	38.2663i		−	1.81809i	−0.416701	−	0.909044i	$-0.636814\pi$
$443$		−	38.2663i		−	1.81809i	0.416701	−	0.909044i	$-0.363186\pi$
$444$		0			0
$445$	−29.9951	−	23.4379i	−1.42190	−	1.11106i
$446$		0			0
$447$	−11.2851	+	11.2851i	−0.533769	+	0.533769i
$448$		0			0
$449$			19.7738i			0.933184i	0.884473	+	0.466592i	$0.154518\pi$
$449$			19.7738i			0.933184i	−0.884473	+	0.466592i	$0.845482\pi$
$450$		0			0
$451$	−0.866270	−	0.866270i	−0.0407911	−	0.0407911i
$452$		0			0
$453$	−1.52546			−0.0716723
$454$		0			0
$455$	2.18483	−	0.268116i	0.102426	−	0.0125695i
$456$		0			0
$457$	3.78901	−	3.78901i	0.177242	−	0.177242i	−0.612910	−	0.790153i	$-0.710001\pi$
$457$	3.78901	−	3.78901i	0.177242	−	0.177242i	0.790153	+	0.612910i	$0.210001\pi$
$458$		0			0
$459$	−4.63479	−	4.63479i	−0.216333	−	0.216333i
$460$		0			0
$461$	−3.32447	+	3.32447i	−0.154836	+	0.154836i	−0.780274	−	0.625438i	$-0.784920\pi$
$461$	−3.32447	+	3.32447i	−0.154836	+	0.154836i	0.625438	+	0.780274i	$0.284920\pi$
$462$		0			0
$463$	−8.53272	−	8.53272i	−0.396549	−	0.396549i	0.480465	−	0.877014i	$-0.340468\pi$
$463$	−8.53272	−	8.53272i	−0.396549	−	0.396549i	−0.877014	+	0.480465i	$0.840468\pi$
$464$		0			0
$465$	−2.33713	+	2.99098i	−0.108382	+	0.138703i
$466$		0			0
$467$		−	12.6255i		−	0.584240i	−0.956382	−	0.292120i	$-0.905639\pi$
$467$		−	12.6255i		−	0.584240i	0.956382	−	0.292120i	$-0.0943606\pi$
$468$		0			0
$469$	0.0774208	−	0.0774208i	0.00357496	−	0.00357496i
$470$		0			0
$471$	11.8705			0.546962
$472$		0			0
$473$	0.952716	+	0.952716i	0.0438059	+	0.0438059i
$474$		0			0
$475$	−24.1164	−	14.4949i	−1.10653	−	0.665073i
$476$		0			0
$477$	−4.82837			−0.221076
$478$		0			0
$479$	−24.0308			−1.09800			−0.548998	−	0.835824i	$-0.684991\pi$
$479$	−24.0308			−1.09800			−0.548998	+	0.835824i	$0.684991\pi$
$480$		0			0
$481$	2.65790			0.121190
$482$		0			0
$483$	−1.78285			−0.0811225
$484$		0			0
$485$	−3.71340	−	30.2599i	−0.168617	−	1.37403i
$486$		0			0
$487$	−24.5449	−	24.5449i	−1.11223	−	1.11223i	−0.992848	−	0.119387i	$-0.961907\pi$
$487$	−24.5449	−	24.5449i	−1.11223	−	1.11223i	−0.119387	−	0.992848i	$-0.538093\pi$
$488$		0			0
$489$	6.57461			0.297314
$490$		0			0
$491$	−16.6457	+	16.6457i	−0.751211	+	0.751211i	−0.974705	−	0.223494i	$-0.928254\pi$
$491$	−16.6457	+	16.6457i	−0.751211	+	0.751211i	0.223494	+	0.974705i	$0.428254\pi$
$492$		0			0
$493$			57.9778i			2.61119i
$494$		0			0
$495$	5.04901	−	0.619600i	0.226936	−	0.0278489i
$496$		0			0
$497$	1.09445	+	1.09445i	0.0490928	+	0.0490928i
$498$		0			0
$499$	18.8910	−	18.8910i	0.845677	−	0.845677i	−0.143914	−	0.989590i	$-0.545969\pi$
$499$	18.8910	−	18.8910i	0.845677	−	0.845677i	0.989590	+	0.143914i	$0.0459687\pi$
$500$		0			0
$501$	18.2166	+	18.2166i	0.813857	+	0.813857i
$502$		0			0
$503$	−13.4812	+	13.4812i	−0.601095	+	0.601095i	−0.940603	−	0.339508i	$-0.889739\pi$
$503$	−13.4812	+	13.4812i	−0.601095	+	0.601095i	0.339508	+	0.940603i	$0.389739\pi$
$504$		0			0
$505$	1.54148	+	12.5612i	0.0685949	+	0.558967i
$506$		0			0
$507$	−6.03860			−0.268183
$508$		0			0
$509$	−24.1930	−	24.1930i	−1.07233	−	1.07233i	−0.997171	−	0.0751624i	$-0.976052\pi$
$509$	−24.1930	−	24.1930i	−1.07233	−	1.07233i	−0.0751624	−	0.997171i	$-0.523948\pi$
$510$		0			0
$511$			0.0513661i			0.00227230i
$512$		0			0
$513$	−3.97920	+	3.97920i	−0.175686	+	0.175686i
$514$		0			0
$515$	−25.3183	+	3.10699i	−1.11566	+	0.136910i
$516$		0			0
$517$		−	15.6218i		−	0.687048i
$518$		0			0
$519$		−	4.84309i		−	0.212588i
$520$		0			0
$521$			0.863518i			0.0378314i	0.999821	+	0.0189157i	$0.00602142\pi$
$521$			0.863518i			0.0378314i	−0.999821	+	0.0189157i	$0.993979\pi$
$522$		0			0
$523$		−	23.9267i		−	1.04624i	−0.852259	−	0.523121i	$-0.824768\pi$
$523$		−	23.9267i		−	1.04624i	0.852259	−	0.523121i	$-0.175232\pi$
$524$		0			0
$525$	0.581119	−	0.966854i	0.0253621	−	0.0421970i
$526$		0			0
$527$	−7.86772	+	7.86772i	−0.342723	+	0.342723i
$528$		0			0
$529$		−	39.4468i		−	1.71508i
$530$		0			0
$531$	−5.78762	−	5.78762i	−0.251161	−	0.251161i
$532$		0			0
$533$	2.34974			0.101778
$534$		0			0
$535$	7.93741	+	6.20223i	0.343164	+	0.268146i
$536$		0			0
$537$	−5.14531	+	5.14531i	−0.222037	+	0.222037i
$538$		0			0
$539$	11.1784	+	11.1784i	0.481489	+	0.481489i
$540$		0			0
$541$	−3.73413	+	3.73413i	−0.160543	+	0.160543i	−0.782807	−	0.622264i	$-0.786213\pi$
$541$	−3.73413	+	3.73413i	−0.160543	+	0.160543i	0.622264	+	0.782807i	$0.286213\pi$
$542$		0			0
$543$	−11.6902	−	11.6902i	−0.501674	−	0.501674i
$544$		0			0
$545$	−0.313530	−	2.55490i	−0.0134302	−	0.109440i
$546$		0			0
$547$		−	33.9579i		−	1.45193i	−0.687730	−	0.725967i	$-0.741393\pi$
$547$		−	33.9579i		−	1.45193i	0.687730	−	0.725967i	$-0.258607\pi$
$548$		0			0
$549$	1.65469	−	1.65469i	0.0706203	−	0.0706203i
$550$		0			0
$551$	49.7769			2.12057
$552$		0			0
$553$	−1.13858	−	1.13858i	−0.0484174	−	0.0484174i
$554$		0			0
$555$	0.838658	−	1.07329i	0.0355990	−	0.0455585i
$556$		0			0
$557$	17.7955			0.754018			0.377009	−	0.926210i	$-0.376953\pi$
$557$	17.7955			0.754018			0.377009	+	0.926210i	$0.376953\pi$
$558$		0			0
$559$	−2.58422			−0.109301
$560$		0			0
$561$	14.9112			0.629550
$562$		0			0
$563$	27.7570			1.16982			0.584909	−	0.811099i	$-0.301130\pi$
$563$	27.7570			1.16982			0.584909	+	0.811099i	$0.301130\pi$
$564$		0			0
$565$	−24.1501	+	2.96364i	−1.01600	+	0.124681i
$566$		0			0
$567$	−0.159531	−	0.159531i	−0.00669967	−	0.00669967i
$568$		0			0
$569$	−31.4665			−1.31915			−0.659573	−	0.751641i	$-0.729263\pi$
$569$	−31.4665			−1.31915			−0.659573	+	0.751641i	$0.729263\pi$
$570$		0			0
$571$	1.60655	−	1.60655i	0.0672319	−	0.0672319i	−0.672691	−	0.739923i	$-0.734862\pi$
$571$	1.60655	−	1.60655i	0.0672319	−	0.0672319i	0.739923	+	0.672691i	$0.234862\pi$
$572$		0			0
$573$		−	15.8153i		−	0.660696i
$574$		0			0
$575$	33.8654	+	20.3545i	1.41228	+	0.848841i
$576$		0			0
$577$	−21.8169	−	21.8169i	−0.908250	−	0.908250i	0.0878809	−	0.996131i	$-0.471990\pi$
$577$	−21.8169	−	21.8169i	−0.908250	−	0.908250i	−0.996131	+	0.0878809i	$0.971990\pi$
$578$		0			0
$579$	−1.54170	+	1.54170i	−0.0640710	+	0.0640710i
$580$		0			0
$581$	−1.09792	−	1.09792i	−0.0455494	−	0.0455494i
$582$		0			0
$583$	7.76697	−	7.76697i	0.321675	−	0.321675i
$584$		0			0
$585$	−6.00733	+	7.68798i	−0.248372	+	0.317859i
$586$		0			0
$587$	9.52161			0.392999			0.196499	−	0.980504i	$-0.437043\pi$
$587$	9.52161			0.392999			0.196499	+	0.980504i	$0.437043\pi$
$588$		0			0
$589$	6.75484	+	6.75484i	0.278328	+	0.278328i
$590$		0			0
$591$			5.98026i			0.245995i
$592$		0			0
$593$	14.3970	−	14.3970i	0.591215	−	0.591215i	−0.346745	−	0.937959i	$-0.612713\pi$
$593$	14.3970	−	14.3970i	0.591215	−	0.591215i	0.937959	+	0.346745i	$0.112713\pi$
$594$		0			0
$595$	2.03596	−	2.60555i	0.0834661	−	0.106817i
$596$		0			0
$597$		−	12.5564i		−	0.513901i
$598$		0			0
$599$			12.1649i			0.497045i	0.968626	+	0.248523i	$0.0799451\pi$
$599$			12.1649i			0.497045i	−0.968626	+	0.248523i	$0.920055\pi$
$600$		0			0
$601$			0.836112i			0.0341057i	0.999855	+	0.0170528i	$0.00542835\pi$
$601$			0.836112i			0.0341057i	−0.999855	+	0.0170528i	$0.994572\pi$
$602$		0			0
$603$			0.485302i			0.0197630i
$604$		0			0
$605$	8.01935	−	10.2629i	0.326033	−	0.417246i
$606$		0			0
$607$	20.7652	−	20.7652i	0.842835	−	0.842835i	−0.146392	−	0.989227i	$-0.546766\pi$
$607$	20.7652	−	20.7652i	0.842835	−	0.842835i	0.989227	+	0.146392i	$0.0467660\pi$
$608$		0			0
$609$			1.99561i			0.0808664i
$610$		0			0
$611$	21.1869	+	21.1869i	0.857131	+	0.857131i
$612$		0			0
$613$	−16.8630			−0.681089			−0.340545	−	0.940228i	$-0.610611\pi$
$613$	−16.8630			−0.681089			−0.340545	+	0.940228i	$0.610611\pi$
$614$		0			0
$615$	0.741422	−	0.948847i	0.0298970	−	0.0382612i
$616$		0			0
$617$	8.57198	−	8.57198i	0.345095	−	0.345095i	−0.513184	−	0.858279i	$-0.671534\pi$
$617$	8.57198	−	8.57198i	0.345095	−	0.345095i	0.858279	+	0.513184i	$0.171534\pi$
$618$		0			0
$619$	22.4414	+	22.4414i	0.901996	+	0.901996i	0.995609	−	0.0936130i	$-0.0298416\pi$
$619$	22.4414	+	22.4414i	0.901996	+	0.901996i	−0.0936130	+	0.995609i	$0.529842\pi$
$620$		0			0
$621$	5.58779	−	5.58779i	0.224230	−	0.224230i
$622$		0			0
$623$	−2.71582	−	2.71582i	−0.108807	−	0.108807i
$624$		0			0
$625$	−22.0768	+	11.7309i	−0.883072	+	0.469237i
$626$		0			0
$627$		−	12.8020i		−	0.511262i
$628$		0			0
$629$	2.82326	−	2.82326i	0.112571	−	0.112571i
$630$		0			0
$631$	−0.149433			−0.00594882			−0.00297441	−	0.999996i	$-0.500947\pi$
$631$	−0.149433			−0.00594882			−0.00297441	+	0.999996i	$0.500947\pi$
$632$		0			0
$633$	18.4049	+	18.4049i	0.731531	+	0.731531i
$634$		0			0
$635$	37.7524	−	4.63287i	1.49816	−	0.183850i
$636$		0			0
$637$	−30.3212			−1.20137
$638$		0			0
$639$	−6.86042			−0.271394
$640$		0			0
$641$	20.6789			0.816766			0.408383	−	0.912811i	$-0.366093\pi$
$641$	20.6789			0.816766			0.408383	+	0.912811i	$0.366093\pi$
$642$		0			0
$643$	−42.0475			−1.65819			−0.829097	−	0.559105i	$-0.811145\pi$
$643$	−42.0475			−1.65819			−0.829097	+	0.559105i	$0.811145\pi$
$644$		0			0
$645$	−0.815409	+	1.04353i	−0.0321067	+	0.0410891i
$646$		0			0
$647$	−2.09704	−	2.09704i	−0.0824431	−	0.0824431i	0.664683	−	0.747126i	$-0.268567\pi$
$647$	−2.09704	−	2.09704i	−0.0824431	−	0.0824431i	−0.747126	+	0.664683i	$0.768567\pi$
$648$		0			0
$649$	18.6201			0.730902
$650$		0			0
$651$	−0.270810	+	0.270810i	−0.0106139	+	0.0106139i
$652$		0			0
$653$			33.4870i			1.31045i	0.755435	+	0.655223i	$0.227425\pi$
$653$			33.4870i			1.31045i	−0.755435	+	0.655223i	$0.772575\pi$
$654$		0			0
$655$	5.09337	+	41.5049i	0.199014	+	1.62173i
$656$		0			0
$657$	−0.160991	−	0.160991i	−0.00628086	−	0.00628086i
$658$		0			0
$659$	−32.5431	+	32.5431i	−1.26770	+	1.26770i	−0.320427	+	0.947273i	$0.603826\pi$
$659$	−32.5431	+	32.5431i	−1.26770	+	1.26770i	−0.947273	+	0.320427i	$0.896174\pi$
$660$		0			0
$661$	−8.31994	−	8.31994i	−0.323608	−	0.323608i	0.526541	−	0.850149i	$-0.323488\pi$
$661$	−8.31994	−	8.31994i	−0.323608	−	0.323608i	−0.850149	+	0.526541i	$0.823488\pi$
$662$		0			0
$663$	−20.2231	+	20.2231i	−0.785399	+	0.785399i
$664$		0			0
$665$	−2.23700	−	1.74797i	−0.0867471	−	0.0677835i
$666$		0			0
$667$	−69.8991			−2.70650
$668$		0			0
$669$	−11.6149	−	11.6149i	−0.449059	−	0.449059i
$670$		0			0
$671$			5.32350i			0.205512i
$672$		0			0
$673$	−9.07931	+	9.07931i	−0.349982	+	0.349982i	−0.860103	−	0.510121i	$-0.829601\pi$
$673$	−9.07931	+	9.07931i	−0.349982	+	0.349982i	0.510121	+	0.860103i	$0.329601\pi$
$674$		0			0
$675$	1.20897	+	4.85164i	0.0465331	+	0.186740i
$676$		0			0
$677$			10.6497i			0.409301i	0.978835	+	0.204650i	$0.0656058\pi$
$677$			10.6497i			0.409301i	−0.978835	+	0.204650i	$0.934394\pi$
$678$		0			0
$679$		−	3.07601i		−	0.118046i
$680$		0			0
$681$			0.411442i			0.0157665i
$682$		0			0
$683$			40.7197i			1.55809i	0.626965	+	0.779047i	$0.284297\pi$
$683$			40.7197i			1.55809i	−0.626965	+	0.779047i	$0.715703\pi$
$684$		0			0
$685$	−15.3227	+	1.88036i	−0.585452	+	0.0718450i
$686$		0			0
$687$	11.2286	−	11.2286i	0.428399	−	0.428399i
$688$		0			0
$689$			21.0677i			0.802616i
$690$		0			0
$691$	23.4396	+	23.4396i	0.891684	+	0.891684i	0.994682	−	0.102997i	$-0.0328433\pi$
$691$	23.4396	+	23.4396i	0.891684	+	0.891684i	−0.102997	+	0.994682i	$0.532843\pi$
$692$		0			0
$693$	0.513248			0.0194967
$694$		0			0
$695$	−3.80032	−	30.9681i	−0.144154	−	1.17469i
$696$		0			0
$697$	2.49592	−	2.49592i	0.0945399	−	0.0945399i
$698$		0			0
$699$	18.9687	+	18.9687i	0.717463	+	0.717463i
$700$		0			0
$701$	−8.98392	+	8.98392i	−0.339318	+	0.339318i	−0.856111	−	0.516793i	$-0.827126\pi$
$701$	−8.98392	+	8.98392i	−0.339318	+	0.339318i	0.516793	+	0.856111i	$0.327126\pi$
$702$		0			0
$703$	−2.42391	−	2.42391i	−0.0914195	−	0.0914195i
$704$		0			0
$705$	15.2407	−	1.87029i	0.573998	−	0.0704394i
$706$		0			0
$707$			1.27689i			0.0480223i
$708$		0			0
$709$	10.0094	−	10.0094i	0.375912	−	0.375912i	−0.493713	−	0.869625i	$-0.664361\pi$
$709$	10.0094	−	10.0094i	0.375912	−	0.375912i	0.869625	+	0.493713i	$0.164361\pi$
$710$		0			0
$711$	7.13706			0.267661
$712$		0			0
$713$	−9.48547	−	9.48547i	−0.355234	−	0.355234i
$714$		0			0
$715$	−2.70352	−	22.0305i	−0.101106	−	0.823892i
$716$		0			0
$717$	11.2094			0.418623
$718$		0			0
$719$	−11.6941			−0.436118			−0.218059	−	0.975936i	$-0.569973\pi$
$719$	−11.6941			−0.436118			−0.218059	+	0.975936i	$0.569973\pi$
$720$		0			0
$721$	−2.57368			−0.0958490
$722$		0			0
$723$	0.0518990			0.00193015
$724$		0			0
$725$	22.7836	−	37.9068i	0.846161	−	1.40782i
$726$		0			0
$727$	15.5108	+	15.5108i	0.575263	+	0.575263i	0.933594	−	0.358331i	$-0.116654\pi$
$727$	15.5108	+	15.5108i	0.575263	+	0.575263i	−0.358331	+	0.933594i	$0.616654\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$		0			0
$731$	−2.74499	+	2.74499i	−0.101527	+	0.101527i
$732$		0			0
$733$		−	39.4855i		−	1.45843i	−0.684285	−	0.729214i	$-0.739886\pi$
$733$		−	39.4855i		−	1.45843i	0.684285	−	0.729214i	$-0.260114\pi$
$734$		0			0
$735$	−9.56737	+	12.2440i	−0.352898	+	0.451627i
$736$		0			0
$737$	−0.780664	−	0.780664i	−0.0287561	−	0.0287561i
$738$		0			0
$739$	−8.55700	+	8.55700i	−0.314774	+	0.314774i	−0.846756	−	0.531982i	$-0.821448\pi$
$739$	−8.55700	+	8.55700i	−0.314774	+	0.314774i	0.531982	+	0.846756i	$0.321448\pi$
$740$		0			0
$741$	17.3625	+	17.3625i	0.637829	+	0.637829i
$742$		0			0
$743$	20.9783	−	20.9783i	0.769621	−	0.769621i	−0.208419	−	0.978040i	$-0.566832\pi$
$743$	20.9783	−	20.9783i	0.769621	−	0.769621i	0.978040	+	0.208419i	$0.0668317\pi$
$744$		0			0
$745$	35.4211	−	4.34677i	1.29773	−	0.159253i
$746$		0			0
$747$	6.88217			0.251806
$748$		0			0
$749$	0.718670	+	0.718670i	0.0262596	+	0.0262596i
$750$		0			0
$751$		−	28.3484i		−	1.03445i	−0.855850	−	0.517224i	$-0.826966\pi$
$751$		−	28.3484i		−	1.03445i	0.855850	−	0.517224i	$-0.173034\pi$
$752$		0			0
$753$	2.45358	−	2.45358i	0.0894134	−	0.0894134i
$754$		0			0
$755$	2.68779	+	2.10022i	0.0978187	+	0.0764348i
$756$		0			0
$757$			18.6273i			0.677022i	0.940962	+	0.338511i	$0.109923\pi$
$757$			18.6273i			0.677022i	−0.940962	+	0.338511i	$0.890077\pi$
$758$		0			0
$759$			17.9772i			0.652531i
$760$		0			0
$761$		−	33.8880i		−	1.22844i	−0.789135	−	0.614220i	$-0.789471\pi$
$761$		−	33.8880i		−	1.22844i	0.789135	−	0.614220i	$-0.210529\pi$
$762$		0			0
$763$		−	0.259714i		−	0.00940227i
$764$		0			0
$765$	1.78521	+	14.5474i	0.0645444	+	0.525961i
$766$		0			0
$767$	−25.2532	+	25.2532i	−0.911842	+	0.911842i
$768$		0			0
$769$			4.73758i			0.170841i	0.996345	+	0.0854207i	$0.0272234\pi$
$769$			4.73758i			0.170841i	−0.996345	+	0.0854207i	$0.972777\pi$
$770$		0			0
$771$	−4.52073	−	4.52073i	−0.162810	−	0.162810i
$772$		0			0
$773$	−1.05525			−0.0379546			−0.0189773	−	0.999820i	$-0.506041\pi$
$773$	−1.05525			−0.0379546			−0.0189773	+	0.999820i	$0.506041\pi$
$774$		0			0
$775$	8.23583	−	2.05226i	0.295840	−	0.0737194i
$776$		0			0
$777$	0.0971776	−	0.0971776i	0.00348623	−	0.00348623i
$778$		0			0
$779$	−2.14288	−	2.14288i	−0.0767766	−	0.0767766i
$780$		0			0
$781$	11.0358	−	11.0358i	0.394891	−	0.394891i
$782$		0			0
$783$	−6.25463	−	6.25463i	−0.223522	−	0.223522i
$784$		0			0
$785$	−20.9152	−	16.3430i	−0.746496	−	0.583307i
$786$		0			0
$787$		−	0.792266i		−	0.0282412i	−0.999900	−	0.0141206i	$-0.995505\pi$
$787$		−	0.792266i		−	0.0282412i	0.999900	−	0.0141206i	$-0.00449488\pi$
$788$		0			0
$789$	−16.0925	+	16.0925i	−0.572907	+	0.572907i
$790$		0			0
$791$	−2.45494			−0.0872875
$792$		0			0
$793$	−7.21994	−	7.21994i	−0.256387	−	0.256387i
$794$		0			0
$795$	8.50736	+	6.64759i	0.301725	+	0.235766i
$796$		0			0
$797$	5.92235			0.209780			0.104890	−	0.994484i	$-0.466551\pi$
$797$	5.92235			0.209780			0.104890	+	0.994484i	$0.466551\pi$
$798$		0			0
$799$	45.0101			1.59234
$800$		0			0
$801$	17.0238			0.601505
$802$		0			0
$803$	0.517945			0.0182779
$804$		0			0
$805$	3.14130	+	2.45459i	0.110716	+	0.0865129i
$806$		0			0
$807$	8.32218	+	8.32218i	0.292955	+	0.292955i
$808$		0			0
$809$	28.0382			0.985772			0.492886	−	0.870094i	$-0.335942\pi$
$809$	28.0382			0.985772			0.492886	+	0.870094i	$0.335942\pi$
$810$		0			0
$811$	14.8696	−	14.8696i	0.522141	−	0.522141i	−0.396077	−	0.918217i	$-0.629629\pi$
$811$	14.8696	−	14.8696i	0.522141	−	0.522141i	0.918217	+	0.396077i	$0.129629\pi$
$812$		0			0
$813$			2.91266i			0.102152i
$814$		0			0
$815$	−11.5842	−	9.05177i	−0.405775	−	0.317070i
$816$		0			0
$817$	2.35672	+	2.35672i	0.0824511	+	0.0824511i
$818$		0			0
$819$	−0.696085	+	0.696085i	−0.0243232	+	0.0243232i
$820$		0			0
$821$	−33.9440	−	33.9440i	−1.18466	−	1.18466i	−0.978524	−	0.206131i	$-0.933913\pi$
$821$	−33.9440	−	33.9440i	−1.18466	−	1.18466i	−0.206131	−	0.978524i	$-0.566087\pi$
$822$		0			0
$823$	−26.0121	+	26.0121i	−0.906724	+	0.906724i	−0.996006	−	0.0892823i	$-0.971543\pi$
$823$	−26.0121	+	26.0121i	−0.906724	+	0.906724i	0.0892823	+	0.996006i	$0.471543\pi$
$824$		0			0
$825$	−9.74917	−	5.85966i	−0.339423	−	0.204007i
$826$		0			0
$827$	14.1684			0.492682			0.246341	−	0.969183i	$-0.420772\pi$
$827$	14.1684			0.492682			0.246341	+	0.969183i	$0.420772\pi$
$828$		0			0
$829$	19.7985	+	19.7985i	0.687630	+	0.687630i	0.961708	−	0.274077i	$-0.0883724\pi$
$829$	19.7985	+	19.7985i	0.687630	+	0.687630i	−0.274077	+	0.961708i	$0.588372\pi$
$830$		0			0
$831$		−	0.339665i		−	0.0117829i
$832$		0			0
$833$	−32.2076	+	32.2076i	−1.11593	+	1.11593i
$834$		0			0
$835$	−7.01659	−	57.1770i	−0.242819	−	1.97869i
$836$		0			0
$837$		−	1.69754i		−	0.0586754i
$838$		0			0
$839$			21.1013i			0.728499i	0.931301	+	0.364250i	$0.118674\pi$
$839$			21.1013i			0.728499i	−0.931301	+	0.364250i	$0.881326\pi$
$840$		0			0
$841$			49.2408i			1.69796i
$842$		0			0
$843$		−	20.9850i		−	0.722763i
$844$		0			0
$845$	10.6397	+	8.31380i	0.366018	+	0.286004i
$846$		0			0
$847$	0.929224	−	0.929224i	0.0319285	−	0.0319285i
$848$		0			0
$849$			15.6290i			0.536385i
$850$		0			0
$851$	3.40377	+	3.40377i	0.116680	+	0.116680i
$852$		0			0
$853$	−0.282088			−0.00965852			−0.00482926	−	0.999988i	$-0.501537\pi$
$853$	−0.282088			−0.00965852			−0.00482926	+	0.999988i	$0.501537\pi$
$854$		0			0
$855$	12.4896	−	1.53269i	0.427137	−	0.0524170i
$856$		0			0
$857$	−31.6316	+	31.6316i	−1.08051	+	1.08051i	−0.0840520	+	0.996461i	$0.526786\pi$
$857$	−31.6316	+	31.6316i	−1.08051	+	1.08051i	−0.996461	+	0.0840520i	$0.973214\pi$
$858$		0			0
$859$	12.4550	+	12.4550i	0.424958	+	0.424958i	0.886907	−	0.461949i	$-0.152850\pi$
$859$	12.4550	+	12.4550i	0.424958	+	0.424958i	−0.461949	+	0.886907i	$0.652850\pi$
$860$		0			0
$861$	0.0859106	−	0.0859106i	0.00292783	−	0.00292783i
$862$		0			0
$863$	28.8568	+	28.8568i	0.982298	+	0.982298i	0.999846	−	0.0175484i	$-0.00558612\pi$
$863$	28.8568	+	28.8568i	0.982298	+	0.982298i	−0.0175484	+	0.999846i	$0.505586\pi$
$864$		0			0
$865$	−6.66785	+	8.53329i	−0.226714	+	0.290141i
$866$		0			0
$867$			25.9625i			0.881733i
$868$		0			0
$869$	−11.4808	+	11.4808i	−0.389459	+	0.389459i
$870$		0			0
$871$	2.11753			0.0717498
$872$		0			0
$873$	9.64079	+	9.64079i	0.326291	+	0.326291i
$874$		0			0
$875$	−2.35505	+	0.903481i	−0.0796152	+	0.0305432i
$876$		0			0
$877$	2.39445			0.0808547			0.0404273	−	0.999182i	$-0.487128\pi$
$877$	2.39445			0.0808547			0.0404273	+	0.999182i	$0.487128\pi$
$878$		0			0
$879$	19.8819			0.670599
$880$		0			0
$881$	−16.8589			−0.567991			−0.283996	−	0.958826i	$-0.591660\pi$
$881$	−16.8589			−0.567991			−0.283996	+	0.958826i	$0.591660\pi$
$882$		0			0
$883$	−32.1936			−1.08340			−0.541700	−	0.840572i	$-0.682219\pi$
$883$	−32.1936			−1.08340			−0.541700	+	0.840572i	$0.682219\pi$
$884$		0			0
$885$	2.22925	+	18.1658i	0.0749355	+	0.610636i
$886$		0			0
$887$	7.86611	+	7.86611i	0.264118	+	0.264118i	0.826725	−	0.562607i	$-0.190201\pi$
$887$	7.86611	+	7.86611i	0.264118	+	0.264118i	−0.562607	+	0.826725i	$0.690201\pi$
$888$		0			0
$889$	3.83765			0.128711
$890$		0			0
$891$	−1.60861	+	1.60861i	−0.0538906	+	0.0538906i
$892$		0			0
$893$		−	38.6435i		−	1.29315i
$894$		0			0
$895$	16.1497	−	1.98185i	0.539827	−	0.0662460i
$896$		0			0
$897$	−24.3813	−	24.3813i	−0.814069	−	0.814069i
$898$		0			0
$899$	−10.6175	+	10.6175i	−0.354112	+	0.354112i
$900$		0			0
$901$	22.3784	+	22.3784i	0.745534	+	0.745534i
$902$		0			0
$903$	−0.0944836	+	0.0944836i	−0.00314422	+	0.00314422i
$904$		0			0
$905$	4.50278	+	36.6924i	0.149678	+	1.21970i
$906$		0			0
$907$	50.7262			1.68433			0.842167	−	0.539217i	$-0.181280\pi$
$907$	50.7262			1.68433			0.842167	+	0.539217i	$0.181280\pi$
$908$		0			0
$909$	−4.00201	−	4.00201i	−0.132738	−	0.132738i
$910$		0			0
$911$		−	1.86790i		−	0.0618862i	−0.999521	−	0.0309431i	$-0.990149\pi$
$911$		−	1.86790i		−	0.0618862i	0.999521	−	0.0309431i	$-0.00985106\pi$
$912$		0			0
$913$	−11.0708	+	11.0708i	−0.366389	+	0.366389i
$914$		0			0
$915$	−5.19362	+	0.637346i	−0.171696	+	0.0210700i
$916$		0			0
$917$			4.21911i			0.139327i
$918$		0			0
$919$		−	14.5671i		−	0.480525i	−0.970708	−	0.240263i	$-0.922766\pi$
$919$		−	14.5671i		−	0.480525i	0.970708	−	0.240263i	$-0.0772336\pi$
$920$		0			0
$921$		−	13.0401i		−	0.429686i
$922$		0			0
$923$			29.9342i			0.985297i
$924$		0			0
$925$	−2.95535	+	0.736436i	−0.0971714	+	0.0242139i
$926$		0			0
$927$	8.06640	−	8.06640i	0.264935	−	0.264935i
$928$		0			0
$929$			53.6486i			1.76015i	0.474831	+	0.880077i	$0.342509\pi$
$929$			53.6486i			1.76015i	−0.474831	+	0.880077i	$0.657491\pi$
$930$		0			0
$931$	27.6519	+	27.6519i	0.906253	+	0.906253i
$932$		0			0
$933$	−23.6036			−0.772746
$934$		0			0
$935$	−26.2728	−	20.5294i	−0.859212	−	0.671382i
$936$		0			0
$937$	28.3937	−	28.3937i	0.927582	−	0.927582i	−0.0699675	−	0.997549i	$-0.522290\pi$
$937$	28.3937	−	28.3937i	0.927582	−	0.927582i	0.997549	+	0.0699675i	$0.0222896\pi$
$938$		0			0
$939$	−23.0604	−	23.0604i	−0.752547	−	0.752547i
$940$		0			0
$941$	37.0652	−	37.0652i	1.20829	−	1.20829i	0.236713	−	0.971580i	$-0.423930\pi$
$941$	37.0652	−	37.0652i	1.20829	−	1.20829i	0.971580	−	0.236713i	$-0.0760701\pi$
$942$		0			0
$943$	3.00913	+	3.00913i	0.0979909	+	0.0979909i
$944$		0			0
$945$	0.0614476	+	0.500725i	0.00199889	+	0.0162886i
$946$		0			0
$947$		−	9.52796i		−	0.309617i	−0.987944	−	0.154809i	$-0.950524\pi$
$947$		−	9.52796i		−	0.309617i	0.987944	−	0.154809i	$-0.0494761\pi$
$948$		0			0
$949$	−0.702456	+	0.702456i	−0.0228027	+	0.0228027i
$950$		0			0
$951$	10.0772			0.326775
$952$		0			0
$953$	26.6687	+	26.6687i	0.863883	+	0.863883i	0.991787	−	0.127903i	$-0.0408248\pi$
$953$	26.6687	+	26.6687i	0.863883	+	0.863883i	−0.127903	+	0.991787i	$0.540825\pi$
$954$		0			0
$955$	−21.7742	+	27.8659i	−0.704597	+	0.901720i
$956$		0			0
$957$	20.1226			0.650470
$958$		0			0
$959$	−1.55760			−0.0502977
$960$		0			0
$961$	28.1184			0.907044
$962$		0			0
$963$	−4.50489			−0.145168
$964$		0			0
$965$	4.83900	−	0.593828i	0.155773	−	0.0191160i
$966$		0			0
$967$	−6.91802	−	6.91802i	−0.222468	−	0.222468i	0.587069	−	0.809537i	$-0.300282\pi$
$967$	−6.91802	−	6.91802i	−0.222468	−	0.222468i	−0.809537	+	0.587069i	$0.800282\pi$
$968$		0			0
$969$	36.8855			1.18493
$970$		0			0
$971$	21.6040	−	21.6040i	0.693305	−	0.693305i	−0.269652	−	0.962958i	$-0.586909\pi$
$971$	21.6040	−	21.6040i	0.693305	−	0.693305i	0.962958	+	0.269652i	$0.0869088\pi$
$972$		0			0
$973$		−	3.14800i		−	0.100920i
$974$		0			0
$975$	21.1693	−	5.27511i	0.677959	−	0.168939i
$976$		0			0
$977$	1.13074	+	1.13074i	0.0361757	+	0.0361757i	0.724963	−	0.688788i	$-0.241857\pi$
$977$	1.13074	+	1.13074i	0.0361757	+	0.0361757i	−0.688788	+	0.724963i	$0.741857\pi$
$978$		0			0
$979$	−27.3846	+	27.3846i	−0.875217	+	0.875217i
$980$		0			0
$981$	0.813992	+	0.813992i	0.0259888	+	0.0259888i
$982$		0			0
$983$	24.3146	−	24.3146i	0.775517	−	0.775517i	−0.203548	−	0.979065i	$-0.565247\pi$
$983$	24.3146	−	24.3146i	0.775517	−	0.775517i	0.979065	+	0.203548i	$0.0652473\pi$
$984$		0			0
$985$	8.23349	−	10.5369i	0.262341	−	0.335735i
$986$		0			0
$987$	1.54926			0.0493136
$988$		0			0
$989$	−3.30942	−	3.30942i	−0.105233	−	0.105233i
$990$		0			0
$991$		−	21.3602i		−	0.678529i	−0.940691	−	0.339264i	$-0.889822\pi$
$991$		−	21.3602i		−	0.678529i	0.940691	−	0.339264i	$-0.110178\pi$
$992$		0			0
$993$	−6.16029	+	6.16029i	−0.195491	+	0.195491i
$994$		0			0
$995$	−17.2874	+	22.1239i	−0.548048	+	0.701374i
$996$		0			0
$997$		−	32.6767i		−	1.03488i	−0.855719	−	0.517442i	$-0.826885\pi$
$997$		−	32.6767i		−	1.03488i	0.855719	−	0.517442i	$-0.173115\pi$
$998$		0			0
$999$			0.609145i			0.0192725i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	960.2.y.f.847.3		20
4.3	odd	2		240.2.y.f.187.5	yes	20
5.3	odd	4		960.2.bc.f.463.2		20
8.3	odd	2		1920.2.y.l.1567.8		20
8.5	even	2		1920.2.y.k.1567.8		20
12.11	even	2		720.2.z.h.667.6		20
16.3	odd	4		960.2.bc.f.367.2		20
16.5	even	4		1920.2.bc.k.607.9		20
16.11	odd	4		1920.2.bc.l.607.9		20
16.13	even	4		240.2.bc.f.67.10	yes	20
20.3	even	4		240.2.bc.f.43.10	yes	20
40.3	even	4		1920.2.bc.k.1183.9		20
40.13	odd	4		1920.2.bc.l.1183.9		20
48.29	odd	4		720.2.bd.h.307.1		20
60.23	odd	4		720.2.bd.h.523.1		20
80.3	even	4	inner	960.2.y.f.943.3		20
80.13	odd	4		240.2.y.f.163.5	✓	20
80.43	even	4		1920.2.y.k.223.8		20
80.53	odd	4		1920.2.y.l.223.8		20
240.173	even	4		720.2.z.h.163.6		20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
240.2.y.f.163.5	✓	20	80.13	odd	4
240.2.y.f.187.5	yes	20	4.3	odd	2
240.2.bc.f.43.10	yes	20	20.3	even	4
240.2.bc.f.67.10	yes	20	16.13	even	4
720.2.z.h.163.6		20	240.173	even	4
720.2.z.h.667.6		20	12.11	even	2
720.2.bd.h.307.1		20	48.29	odd	4
720.2.bd.h.523.1		20	60.23	odd	4
960.2.y.f.847.3		20	1.1	even	1	trivial
960.2.y.f.943.3		20	80.3	even	4	inner
960.2.bc.f.367.2		20	16.3	odd	4
960.2.bc.f.463.2		20	5.3	odd	4
1920.2.y.k.223.8		20	80.43	even	4
1920.2.y.k.1567.8		20	8.5	even	2
1920.2.y.l.223.8		20	80.53	odd	4
1920.2.y.l.1567.8		20	8.3	odd	2
1920.2.bc.k.607.9		20	16.5	even	4
1920.2.bc.k.1183.9		20	40.3	even	4
1920.2.bc.l.607.9		20	16.11	odd	4
1920.2.bc.l.1183.9		20	40.13	odd	4

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 960 = 2^{6} \cdot 3 \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	960.y (of order \(4\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{3} +(-1.76195 - 1.37678i) q^{5} +(-0.159531 - 0.159531i) q^{7} +1.00000 q^{9} +(-1.60861 + 1.60861i) q^{11} -4.36332i q^{13} +(-1.76195 - 1.37678i) q^{15} +(-4.63479 - 4.63479i) q^{17} +(-3.97920 + 3.97920i) q^{19} +(-0.159531 - 0.159531i) q^{21} +(5.58779 - 5.58779i) q^{23} +(1.20897 + 4.85164i) q^{25} +1.00000 q^{27} +(-6.25463 - 6.25463i) q^{29} -1.69754i q^{31} +(-1.60861 + 1.60861i) q^{33} +(0.0614476 + 0.500725i) q^{35} +0.609145i q^{37} -4.36332i q^{39} +0.538520i q^{41} -0.592259i q^{43} +(-1.76195 - 1.37678i) q^{45} +(-4.85568 + 4.85568i) q^{47} -6.94910i q^{49} +(-4.63479 - 4.63479i) q^{51} -4.82837 q^{53} +(5.04901 - 0.619600i) q^{55} +(-3.97920 + 3.97920i) q^{57} +(-5.78762 - 5.78762i) q^{59} +(1.65469 - 1.65469i) q^{61} +(-0.159531 - 0.159531i) q^{63} +(-6.00733 + 7.68798i) q^{65} +0.485302i q^{67} +(5.58779 - 5.58779i) q^{69} -6.86042 q^{71} +(-0.160991 - 0.160991i) q^{73} +(1.20897 + 4.85164i) q^{75} +0.513248 q^{77} +7.13706 q^{79} +1.00000 q^{81} +6.88217 q^{83} +(1.78521 + 14.5474i) q^{85} +(-6.25463 - 6.25463i) q^{87} +17.0238 q^{89} +(-0.696085 + 0.696085i) q^{91} -1.69754i q^{93} +(12.4896 - 1.53269i) q^{95} +(9.64079 + 9.64079i) q^{97} +(-1.60861 + 1.60861i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 20 q^{3} + 4 q^{7} + 20 q^{9} - 8 q^{11} + 12 q^{17} - 16 q^{19} + 4 q^{21} + 16 q^{23} + 4 q^{25} + 20 q^{27} - 8 q^{33} + 28 q^{35} + 12 q^{51} + 8 q^{53} + 4 q^{55} - 16 q^{57} + 16 q^{59} - 12 q^{61}+ \cdots - 8 q^{99}+O(q^{100}) \) 20 * q + 20 * q^3 + 4 * q^7 + 20 * q^9 - 8 * q^11 + 12 * q^17 - 16 * q^19 + 4 * q^21 + 16 * q^23 + 4 * q^25 + 20 * q^27 - 8 * q^33 + 28 * q^35 + 12 * q^51 + 8 * q^53 + 4 * q^55 - 16 * q^57 + 16 * q^59 - 12 * q^61 + 4 * q^63 + 4 * q^65 + 16 * q^69 - 20 * q^73 + 4 * q^75 - 48 * q^79 + 20 * q^81 + 24 * q^83 + 4 * q^85 + 40 * q^89 + 24 * q^91 + 72 * q^95 - 28 * q^97 - 8 * q^99

Introduction

L-functions

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