LMFDB - Embedded newform 600.2.y.f.121.4

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [600,2,Mod(121,600)] 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("600.121"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(600, base_ring=CyclotomicField(10)) chi = DirichletCharacter(H, H._module([0, 0, 0, 6])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 600 = 2^{3} \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	600.y (of order $5$, degree $4$, minimal)

Newform invariants

comment:select newform

sage:traces = [16,0,4] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(3)] == traces)

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

Self dual:	no
Analytic conductor:	$4.79102412128$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 8 x^{15} + 29 x^{14} - 32 x^{13} - 144 x^{12} + 670 x^{11} - 790 x^{10} - 2180 x^{9} + \cdots + 390625 $ x^16 - 8x^15 + 29x^14 - 32x^13 - 144x^12 + 670x^11 - 790x^10 - 2180x^9 + 9705x^8 - 10900x^7 - 19750x^6 + 83750x^5 - 90000x^4 - 100000x^3 + 453125x^2 - 625000*x + 390625
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			121.4
Root			$1.95471 + 1.08587i$ of defining polynomial
Character	$\chi$	$=$	600.121
Dual form			600.2.y.f.481.4

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.809017 + 0.587785i) q^{3} +(2.21965 + 0.270458i) q^{5} +2.87749 q^{7} +(0.309017 + 0.951057i) q^{9} +(1.66222 - 5.11580i) q^{11} +(-1.94454 - 5.98468i) q^{13} +(1.63676 + 1.52348i) q^{15} +(0.476634 - 0.346295i) q^{17} +(-4.34238 + 3.15492i) q^{19} +(2.32794 + 1.69135i) q^{21} +(-2.68374 + 8.25969i) q^{23} +(4.85371 + 1.20064i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(1.81276 + 1.31705i) q^{29} +(-4.62337 + 3.35907i) q^{31} +(4.35176 - 3.16174i) q^{33} +(6.38702 + 0.778239i) q^{35} +(-2.07438 - 6.38428i) q^{37} +(1.94454 - 5.98468i) q^{39} +(-0.285900 - 0.879909i) q^{41} +1.68906 q^{43} +(0.428689 + 2.19459i) q^{45} +(-3.73299 - 2.71218i) q^{47} +1.27994 q^{49} +0.589152 q^{51} +(7.70817 + 5.60032i) q^{53} +(5.07316 - 10.9057i) q^{55} -5.36747 q^{57} +(4.05678 + 12.4855i) q^{59} +(0.274307 - 0.844229i) q^{61} +(0.889193 + 2.73665i) q^{63} +(-2.69760 - 13.8098i) q^{65} +(-7.75684 + 5.63568i) q^{67} +(-7.02612 + 5.10477i) q^{69} +(6.22696 + 4.52415i) q^{71} +(-3.28892 + 10.1222i) q^{73} +(3.22101 + 3.82428i) q^{75} +(4.78303 - 14.7206i) q^{77} +(2.79943 + 2.03390i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-9.75075 + 7.08434i) q^{83} +(1.15162 - 0.639744i) q^{85} +(0.692413 + 2.13103i) q^{87} +(-0.698279 + 2.14908i) q^{89} +(-5.59539 - 17.2209i) q^{91} -5.71480 q^{93} +(-10.4918 + 5.82840i) q^{95} +(-15.8693 - 11.5297i) q^{97} +5.37907 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{3} + 7 q^{5} - 10 q^{7} - 4 q^{9} + 9 q^{11} - 12 q^{13} - 2 q^{15} + 7 q^{17} - 9 q^{19} - 10 q^{21} + 7 q^{23} + 11 q^{25} + 4 q^{27} - 29 q^{29} - 2 q^{31} + 11 q^{33} + 30 q^{35} - 14 q^{37}+ \cdots + 4 q^{99}+O(q^{100}) $ 16 * q + 4 * q^3 + 7 * q^5 - 10 * q^7 - 4 * q^9 + 9 * q^11 - 12 * q^13 - 2 * q^15 + 7 * q^17 - 9 * q^19 - 10 * q^21 + 7 * q^23 + 11 * q^25 + 4 * q^27 - 29 * q^29 - 2 * q^31 + 11 * q^33 + 30 * q^35 - 14 * q^37 + 12 * q^39 + 4 * q^41 - 16 * q^43 + 2 * q^45 + 5 * q^47 + 78 * q^49 + 18 * q^51 + 8 * q^53 - 7 * q^55 + 14 * q^57 + 19 * q^59 - 22 * q^61 - 5 * q^63 - 54 * q^65 + 16 * q^67 - 2 * q^69 + 23 * q^71 - 30 * q^73 + 9 * q^75 + 40 * q^77 - 28 * q^79 - 4 * q^81 - 49 * q^83 + 9 * q^85 - 26 * q^87 + 9 * q^89 - 25 * q^91 - 28 * q^93 - 73 * q^95 - 53 * q^97 + 4 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/600\mathbb{Z}\right)^\times$.

$n$	$151$	$301$	$401$	$577$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{3}{5}\right)$

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
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$3$	0.809017	+	0.587785i	0.467086	+	0.339358i
$4$		0			0
$5$	2.21965	+	0.270458i	0.992658	+	0.120952i
$5$	2.21965	+	0.270458i	0.992658	+	0.120952i
$6$		0			0
$7$	2.87749			1.08759			0.543794	−	0.839219i	$-0.316987\pi$
$7$	2.87749			1.08759			0.543794	+	0.839219i	$0.316987\pi$
$8$		0			0
$9$	0.309017	+	0.951057i	0.103006	+	0.317019i
$10$		0			0
$11$	1.66222	−	5.11580i	0.501179	−	1.54247i	−0.305921	−	0.952057i	$-0.598964\pi$
$11$	1.66222	−	5.11580i	0.501179	−	1.54247i	0.807100	−	0.590414i	$-0.201036\pi$
$12$		0			0
$13$	−1.94454	−	5.98468i	−0.539319	−	1.65985i	−0.734128	−	0.679011i	$-0.762409\pi$
$13$	−1.94454	−	5.98468i	−0.539319	−	1.65985i	0.194810	−	0.980841i	$-0.437591\pi$
$14$		0			0
$15$	1.63676	+	1.52348i	0.422611	+	0.393362i
$16$		0			0
$17$	0.476634	−	0.346295i	0.115601	−	0.0839888i	−0.528483	−	0.848944i	$-0.677239\pi$
$17$	0.476634	−	0.346295i	0.115601	−	0.0839888i	0.644084	+	0.764955i	$0.277239\pi$
$18$		0			0
$19$	−4.34238	+	3.15492i	−0.996210	+	0.723789i	−0.961272	−	0.275601i	$-0.911123\pi$
$19$	−4.34238	+	3.15492i	−0.996210	+	0.723789i	−0.0349377	+	0.999389i	$0.511123\pi$
$20$		0			0
$21$	2.32794	+	1.69135i	0.507998	+	0.369082i
$22$		0			0
$23$	−2.68374	+	8.25969i	−0.559598	+	1.72227i	0.123883	+	0.992297i	$0.460465\pi$
$23$	−2.68374	+	8.25969i	−0.559598	+	1.72227i	−0.683481	+	0.729968i	$0.739535\pi$
$24$		0			0
$25$	4.85371	+	1.20064i	0.970741	+	0.240129i
$26$		0			0
$27$	−0.309017	+	0.951057i	−0.0594703	+	0.183031i
$28$		0			0
$29$	1.81276	+	1.31705i	0.336621	+	0.244570i	0.743235	−	0.669031i	$-0.233290\pi$
$29$	1.81276	+	1.31705i	0.336621	+	0.244570i	−0.406614	+	0.913600i	$0.633290\pi$
$30$		0			0
$31$	−4.62337	+	3.35907i	−0.830382	+	0.603308i	−0.919667	−	0.392698i	$-0.871542\pi$
$31$	−4.62337	+	3.35907i	−0.830382	+	0.603308i	0.0892855	+	0.996006i	$0.471542\pi$
$32$		0			0
$33$	4.35176	−	3.16174i	0.757544	−	0.550388i
$34$		0			0
$35$	6.38702	+	0.778239i	1.07960	+	0.131546i
$36$		0			0
$37$	−2.07438	−	6.38428i	−0.341026	−	1.04957i	−0.963677	−	0.267070i	$-0.913944\pi$
$37$	−2.07438	−	6.38428i	−0.341026	−	1.04957i	0.622651	−	0.782499i	$-0.286056\pi$
$38$		0			0
$39$	1.94454	−	5.98468i	0.311376	−	0.958316i
$40$		0			0
$41$	−0.285900	−	0.879909i	−0.0446501	−	0.137419i	0.926246	−	0.376919i	$-0.123016\pi$
$41$	−0.285900	−	0.879909i	−0.0446501	−	0.137419i	−0.970896	+	0.239500i	$0.923016\pi$
$42$		0			0
$43$	1.68906			0.257579			0.128790	−	0.991672i	$-0.458891\pi$
$43$	1.68906			0.257579			0.128790	+	0.991672i	$0.458891\pi$
$44$		0			0
$45$	0.428689	+	2.19459i	0.0639053	+	0.327150i
$46$		0			0
$47$	−3.73299	−	2.71218i	−0.544512	−	0.395611i	0.281246	−	0.959636i	$-0.409252\pi$
$47$	−3.73299	−	2.71218i	−0.544512	−	0.395611i	−0.825758	+	0.564024i	$0.809252\pi$
$48$		0			0
$49$	1.27994			0.182849
$50$		0			0
$51$	0.589152			0.0824977
$52$		0			0
$53$	7.70817	+	5.60032i	1.05880	+	0.769263i	0.973866	−	0.227124i	$-0.0729323\pi$
$53$	7.70817	+	5.60032i	1.05880	+	0.769263i	0.0849332	+	0.996387i	$0.472932\pi$
$54$		0			0
$55$	5.07316	−	10.9057i	0.684065	−	1.47053i
$56$		0			0
$57$	−5.36747			−0.710939
$58$		0			0
$59$	4.05678	+	12.4855i	0.528148	+	1.62547i	0.758006	+	0.652247i	$0.226174\pi$
$59$	4.05678	+	12.4855i	0.528148	+	1.62547i	−0.229859	+	0.973224i	$0.573826\pi$
$60$		0			0
$61$	0.274307	−	0.844229i	0.0351214	−	0.108093i	−0.931959	−	0.362564i	$-0.881901\pi$
$61$	0.274307	−	0.844229i	0.0351214	−	0.108093i	0.967080	+	0.254471i	$0.0819015\pi$
$62$		0			0
$63$	0.889193	+	2.73665i	0.112028	+	0.344786i
$64$		0			0
$65$	−2.69760	−	13.8098i	−0.334596	−	1.71290i
$66$		0			0
$67$	−7.75684	+	5.63568i	−0.947649	+	0.688507i	−0.950250	−	0.311489i	$-0.899172\pi$
$67$	−7.75684	+	5.63568i	−0.947649	+	0.688507i	0.00260062	+	0.999997i	$0.499172\pi$
$68$		0			0
$69$	−7.02612	+	5.10477i	−0.845845	+	0.614542i
$70$		0			0
$71$	6.22696	+	4.52415i	0.739005	+	0.536918i	0.892399	−	0.451247i	$-0.149021\pi$
$71$	6.22696	+	4.52415i	0.739005	+	0.536918i	−0.153395	+	0.988165i	$0.549021\pi$
$72$		0			0
$73$	−3.28892	+	10.1222i	−0.384939	+	1.18472i	0.551586	+	0.834118i	$0.314023\pi$
$73$	−3.28892	+	10.1222i	−0.384939	+	1.18472i	−0.936525	+	0.350601i	$0.885977\pi$
$74$		0			0
$75$	3.22101	+	3.82428i	0.371930	+	0.441590i
$76$		0			0
$77$	4.78303	−	14.7206i	0.545077	−	1.67757i
$78$		0			0
$79$	2.79943	+	2.03390i	0.314960	+	0.228832i	0.734022	−	0.679126i	$-0.237641\pi$
$79$	2.79943	+	2.03390i	0.314960	+	0.228832i	−0.419062	+	0.907958i	$0.637641\pi$
$80$		0			0
$81$	−0.809017	+	0.587785i	−0.0898908	+	0.0653095i
$82$		0			0
$83$	−9.75075	+	7.08434i	−1.07028	+	0.777607i	−0.975963	−	0.217935i	$-0.930068\pi$
$83$	−9.75075	+	7.08434i	−1.07028	+	0.777607i	−0.0943207	+	0.995542i	$0.530068\pi$
$84$		0			0
$85$	1.15162	−	0.639744i	0.124911	−	0.0693900i
$86$		0			0
$87$	0.692413	+	2.13103i	0.0742345	+	0.228470i
$88$		0			0
$89$	−0.698279	+	2.14908i	−0.0740174	+	0.227802i	−0.981220	−	0.192892i	$-0.938213\pi$
$89$	−0.698279	+	2.14908i	−0.0740174	+	0.227802i	0.907203	+	0.420694i	$0.138213\pi$
$90$		0			0
$91$	−5.59539	−	17.2209i	−0.586557	−	1.80524i
$92$		0			0
$93$	−5.71480			−0.592597
$94$		0			0
$95$	−10.4918	+	5.82840i	−1.07644	+	0.597981i
$96$		0			0
$97$	−15.8693	−	11.5297i	−1.61128	−	1.17066i	−0.859288	−	0.511492i	$-0.829093\pi$
$97$	−15.8693	−	11.5297i	−1.61128	−	1.17066i	−0.751992	−	0.659172i	$-0.770907\pi$
$98$		0			0
$99$	5.37907			0.540617
$100$		0			0
$101$	12.4683			1.24065			0.620323	−	0.784347i	$-0.287002\pi$
$101$	12.4683			1.24065			0.620323	+	0.784347i	$0.287002\pi$
$102$		0			0
$103$	−12.3919	−	9.00324i	−1.22101	−	0.887115i	−0.224826	−	0.974399i	$-0.572181\pi$
$103$	−12.3919	−	9.00324i	−1.22101	−	0.887115i	−0.996184	+	0.0872836i	$0.972181\pi$
$104$		0			0
$105$	4.70977	+	4.38381i	0.459627	+	0.427816i
$106$		0			0
$107$	2.48976			0.240695			0.120347	−	0.992732i	$-0.461599\pi$
$107$	2.48976			0.240695			0.120347	+	0.992732i	$0.461599\pi$
$108$		0			0
$109$	−1.32894	−	4.09007i	−0.127290	−	0.391758i	0.867022	−	0.498271i	$-0.166031\pi$
$109$	−1.32894	−	4.09007i	−0.127290	−	0.391758i	−0.994311	+	0.106513i	$0.966031\pi$
$110$		0			0
$111$	2.07438	−	6.38428i	0.196891	−	0.605969i
$112$		0			0
$113$	−0.863930	−	2.65890i	−0.0812717	−	0.250129i	0.902162	−	0.431398i	$-0.141979\pi$
$113$	−0.863930	−	2.65890i	−0.0812717	−	0.250129i	−0.983434	+	0.181269i	$0.941979\pi$
$114$		0			0
$115$	−8.19086	+	17.6078i	−0.763802	+	1.64194i
$116$		0			0
$117$	5.09087	−	3.69874i	0.470651	−	0.341948i
$118$		0			0
$119$	1.37151	−	0.996459i	0.125726	−	0.0913452i
$120$		0			0
$121$	−14.5092	−	10.5416i	−1.31902	−	0.958323i
$122$		0			0
$123$	0.285900	−	0.879909i	0.0257787	−	0.0793388i
$124$		0			0
$125$	10.4488	+	3.97773i	0.934570	+	0.355779i
$126$		0			0
$127$	0.931344	−	2.86638i	0.0826434	−	0.254350i	−0.901194	−	0.433417i	$-0.857308\pi$
$127$	0.931344	−	2.86638i	0.0826434	−	0.254350i	0.983837	+	0.179067i	$0.0573078\pi$
$128$		0			0
$129$	1.36648	+	0.992805i	0.120312	+	0.0874116i
$130$		0			0
$131$	1.44394	−	1.04908i	0.126157	−	0.0916587i	−0.522917	−	0.852384i	$-0.675156\pi$
$131$	1.44394	−	1.04908i	0.126157	−	0.0916587i	0.649075	+	0.760725i	$0.275156\pi$
$132$		0			0
$133$	−12.4951	+	9.07825i	−1.08347	+	0.787184i
$134$		0			0
$135$	−0.943131	+	2.02744i	−0.0811718	+	0.174494i
$136$		0			0
$137$	1.62532	+	5.00223i	0.138861	+	0.427369i	0.996171	−	0.0874315i	$-0.0278659\pi$
$137$	1.62532	+	5.00223i	0.138861	+	0.427369i	−0.857310	+	0.514801i	$0.827866\pi$
$138$		0			0
$139$	1.18893	−	3.65914i	0.100843	−	0.310364i	−0.887889	−	0.460058i	$-0.847829\pi$
$139$	1.18893	−	3.65914i	0.100843	−	0.310364i	0.988732	+	0.149694i	$0.0478287\pi$
$140$		0			0
$141$	−1.42587	−	4.38839i	−0.120080	−	0.369569i
$142$		0			0
$143$	−33.8487			−2.83057
$144$		0			0
$145$	3.66749	+	3.41366i	0.304569	+	0.283489i
$146$		0			0
$147$	1.03549	+	0.752330i	0.0854060	+	0.0620511i
$148$		0			0
$149$	2.18629			0.179108			0.0895538	−	0.995982i	$-0.471456\pi$
$149$	2.18629			0.179108			0.0895538	+	0.995982i	$0.471456\pi$
$150$		0			0
$151$	20.5957			1.67606			0.838028	−	0.545627i	$-0.183709\pi$
$151$	20.5957			1.67606			0.838028	+	0.545627i	$0.183709\pi$
$152$		0			0
$153$	0.476634	+	0.346295i	0.0385336	+	0.0279963i
$154$		0			0
$155$	−11.1708	+	6.20555i	−0.897257	+	0.498442i
$156$		0			0
$157$	−14.4299			−1.15163			−0.575814	−	0.817580i	$-0.695315\pi$
$157$	−14.4299			−1.15163			−0.575814	+	0.817580i	$0.695315\pi$
$158$		0			0
$159$	2.94426	+	9.06150i	0.233495	+	0.718624i
$160$		0			0
$161$	−7.72242	+	23.7672i	−0.608612	+	1.87312i
$162$		0			0
$163$	−0.0521767	−	0.160583i	−0.00408679	−	0.0125779i	0.948992	−	0.315299i	$-0.102105\pi$
$163$	−0.0521767	−	0.160583i	−0.00408679	−	0.0125779i	−0.953079	+	0.302721i	$0.902105\pi$
$164$		0			0
$165$	10.5145	−	5.84099i	0.818553	−	0.454720i
$166$		0			0
$167$	5.58870	−	4.06043i	0.432467	−	0.314205i	−0.350168	−	0.936687i	$-0.613875\pi$
$167$	5.58870	−	4.06043i	0.432467	−	0.314205i	0.782634	+	0.622482i	$0.213875\pi$
$168$		0			0
$169$	−21.5179	+	15.6337i	−1.65523	+	1.20259i
$170$		0			0
$171$	−4.34238	−	3.15492i	−0.332070	−	0.241263i
$172$		0			0
$173$	6.07796	−	18.7060i	0.462098	−	1.42219i	−0.400497	−	0.916298i	$-0.631163\pi$
$173$	6.07796	−	18.7060i	0.462098	−	1.42219i	0.862595	−	0.505894i	$-0.168837\pi$
$174$		0			0
$175$	13.9665	+	3.45484i	1.05577	+	0.261161i
$176$		0			0
$177$	−4.05678	+	12.4855i	−0.304926	+	0.938466i
$178$		0			0
$179$	−0.872817	−	0.634138i	−0.0652374	−	0.0473977i	0.554689	−	0.832058i	$-0.312837\pi$
$179$	−0.872817	−	0.634138i	−0.0652374	−	0.0473977i	−0.619926	+	0.784660i	$0.712837\pi$
$180$		0			0
$181$	16.9107	−	12.2863i	1.25696	−	0.913237i	0.258358	−	0.966049i	$-0.416819\pi$
$181$	16.9107	−	12.2863i	1.25696	−	0.913237i	0.998604	+	0.0528126i	$0.0168186\pi$
$182$		0			0
$183$	0.718144	−	0.521763i	0.0530868	−	0.0385698i
$184$		0			0
$185$	−2.87772	−	14.7319i	−0.211574	−	1.08311i
$186$		0			0
$187$	−0.979302	−	3.01398i	−0.0716136	−	0.220404i
$188$		0			0
$189$	−0.889193	+	2.73665i	−0.0646793	+	0.199062i
$190$		0			0
$191$	−2.68535	−	8.26466i	−0.194305	−	0.598010i	−0.999984	−	0.00565714i	$-0.998199\pi$
$191$	−2.68535	−	8.26466i	−0.194305	−	0.598010i	0.805679	−	0.592353i	$-0.201801\pi$
$192$		0			0
$193$	8.56569			0.616572			0.308286	−	0.951294i	$-0.400245\pi$
$193$	8.56569			0.616572			0.308286	+	0.951294i	$0.400245\pi$
$194$		0			0
$195$	5.93481	−	12.7580i	0.425000	−	0.913619i
$196$		0			0
$197$	−17.9324	−	13.0287i	−1.27763	−	0.928255i	−0.278155	−	0.960536i	$-0.589723\pi$
$197$	−17.9324	−	13.0287i	−1.27763	−	0.928255i	−0.999479	+	0.0322807i	$0.989723\pi$
$198$		0			0
$199$	−4.59972			−0.326066			−0.163033	−	0.986621i	$-0.552128\pi$
$199$	−4.59972			−0.326066			−0.163033	+	0.986621i	$0.552128\pi$
$200$		0			0
$201$	−9.58798			−0.676284
$202$		0			0
$203$	5.21620	+	3.78979i	0.366105	+	0.265991i
$204$		0			0
$205$	−0.396620	−	2.03042i	−0.0277011	−	0.141810i
$206$		0			0
$207$	−8.68476			−0.603632
$208$		0			0
$209$	8.92194	+	27.4589i	0.617144	+	1.89937i
$210$		0			0
$211$	4.83703	−	14.8869i	0.332995	−	1.02485i	−0.634706	−	0.772754i	$-0.718879\pi$
$211$	4.83703	−	14.8869i	0.332995	−	1.02485i	0.967701	−	0.252100i	$-0.0811211\pi$
$212$		0			0
$213$	2.37849	+	7.32023i	0.162971	+	0.501574i
$214$		0			0
$215$	3.74913	+	0.456820i	0.255688	+	0.0311548i
$216$		0			0
$217$	−13.3037	+	9.66570i	−0.903114	+	0.656150i
$218$		0			0
$219$	−8.61050	+	6.25589i	−0.581843	+	0.422734i
$220$		0			0
$221$	−2.99930	−	2.17912i	−0.201755	−	0.146583i
$222$		0			0
$223$	5.72828	−	17.6298i	0.383594	−	1.18058i	−0.553901	−	0.832583i	$-0.686861\pi$
$223$	5.72828	−	17.6298i	0.383594	−	1.18058i	0.937495	−	0.347999i	$-0.113139\pi$
$224$		0			0
$225$	0.357997	+	4.98717i	0.0238665	+	0.332478i
$226$		0			0
$227$	1.88832	−	5.81164i	0.125332	−	0.385732i	−0.868629	−	0.495462i	$-0.834999\pi$
$227$	1.88832	−	5.81164i	0.125332	−	0.385732i	0.993961	+	0.109730i	$0.0349987\pi$
$228$		0			0
$229$	13.6039	+	9.88379i	0.898969	+	0.653139i	0.938201	−	0.346091i	$-0.112491\pi$
$229$	13.6039	+	9.88379i	0.898969	+	0.653139i	−0.0392321	+	0.999230i	$0.512491\pi$
$230$		0			0
$231$	12.5221	−	9.09786i	0.823896	−	0.598595i
$232$		0			0
$233$	−21.3638	+	15.5217i	−1.39959	+	1.01686i	−0.404852	+	0.914382i	$0.632677\pi$
$233$	−21.3638	+	15.5217i	−1.39959	+	1.01686i	−0.994735	+	0.102478i	$0.967323\pi$
$234$		0			0
$235$	−7.55241	−	7.02970i	−0.492665	−	0.458567i
$236$		0			0
$237$	1.06929	+	3.29092i	0.0694576	+	0.213768i
$238$		0			0
$239$	2.90739	−	8.94803i	0.188064	−	0.578800i	−0.811924	−	0.583763i	$-0.801580\pi$
$239$	2.90739	−	8.94803i	0.188064	−	0.578800i	0.999988	+	0.00496283i	$0.00157972\pi$
$240$		0			0
$241$	3.86568	+	11.8974i	0.249011	+	0.766376i	0.994951	+	0.100363i	$0.0320004\pi$
$241$	3.86568	+	11.8974i	0.249011	+	0.766376i	−0.745940	+	0.666013i	$0.768000\pi$
$242$		0			0
$243$	−1.00000			−0.0641500
$244$		0			0
$245$	2.84102	+	0.346170i	0.181506	+	0.0221160i
$246$		0			0
$247$	27.3251	+	19.8529i	1.73866	+	1.26321i
$248$		0			0
$249$	−12.0526			−0.763802
$250$		0			0
$251$	−20.1583			−1.27238			−0.636189	−	0.771533i	$-0.719490\pi$
$251$	−20.1583			−1.27238			−0.636189	+	0.771533i	$0.719490\pi$
$252$		0			0
$253$	37.7940	+	27.4589i	2.37609	+	1.72633i
$254$		0			0
$255$	1.30771	+	0.159341i	0.0818921	+	0.00997830i
$256$		0			0
$257$	10.0235			0.625252			0.312626	−	0.949876i	$-0.398791\pi$
$257$	10.0235			0.625252			0.312626	+	0.949876i	$0.398791\pi$
$258$		0			0
$259$	−5.96900	−	18.3707i	−0.370896	−	1.14150i
$260$		0			0
$261$	−0.692413	+	2.13103i	−0.0428593	+	0.131907i
$262$		0			0
$263$	−1.36296	−	4.19477i	−0.0840439	−	0.258661i	0.900200	−	0.435477i	$-0.143420\pi$
$263$	−1.36296	−	4.19477i	−0.0840439	−	0.258661i	−0.984244	+	0.176816i	$0.943420\pi$
$264$		0			0
$265$	15.5948	+	14.5155i	0.957982	+	0.891679i
$266$		0			0
$267$	−1.82812	+	1.32820i	−0.111879	+	0.0812848i
$268$		0			0
$269$	22.9554	−	16.6781i	1.39962	−	1.01688i	0.404884	−	0.914368i	$-0.367312\pi$
$269$	22.9554	−	16.6781i	1.39962	−	1.01688i	0.994732	−	0.102512i	$-0.0326880\pi$
$270$		0			0
$271$	−9.64643	−	7.00854i	−0.585979	−	0.425739i	0.254896	−	0.966969i	$-0.417959\pi$
$271$	−9.64643	−	7.00854i	−0.585979	−	0.425739i	−0.840875	+	0.541230i	$0.817959\pi$
$272$		0			0
$273$	5.59539	−	17.2209i	0.338649	−	1.04225i
$274$		0			0
$275$	14.2102	−	22.8348i	0.856907	−	1.37699i
$276$		0			0
$277$	−4.82281	+	14.8431i	−0.289774	+	0.891834i	0.695152	+	0.718862i	$0.255337\pi$
$277$	−4.82281	+	14.8431i	−0.289774	+	0.891834i	−0.984927	+	0.172972i	$0.944663\pi$
$278$		0			0
$279$	−4.62337	−	3.35907i	−0.276794	−	0.201103i
$280$		0			0
$281$	7.33799	−	5.33136i	0.437748	−	0.318043i	−0.346991	−	0.937868i	$-0.612797\pi$
$281$	7.33799	−	5.33136i	0.437748	−	0.318043i	0.784739	+	0.619826i	$0.212797\pi$
$282$		0			0
$283$	−1.84338	+	1.33929i	−0.109578	+	0.0796128i	−0.641225	−	0.767353i	$-0.721573\pi$
$283$	−1.84338	+	1.33929i	−0.109578	+	0.0796128i	0.531647	+	0.846966i	$0.321573\pi$
$284$		0			0
$285$	−11.9139	−	1.45167i	−0.705720	−	0.0859898i
$286$		0			0
$287$	−0.822674	−	2.53193i	−0.0485609	−	0.149455i
$288$		0			0
$289$	−5.14603	+	15.8378i	−0.302708	+	0.931638i
$290$		0			0
$291$	−6.06152	−	18.6554i	−0.355333	−	1.09360i
$292$		0			0
$293$	−11.6071			−0.678093			−0.339047	−	0.940770i	$-0.610104\pi$
$293$	−11.6071			−0.678093			−0.339047	+	0.940770i	$0.610104\pi$
$294$		0			0
$295$	5.62784	+	28.8106i	0.327665	+	1.67742i
$296$		0			0
$297$	4.35176	+	3.16174i	0.252515	+	0.183463i
$298$		0			0
$299$	54.6503			3.16051
$300$		0			0
$301$	4.86025			0.280140
$302$		0			0
$303$	10.0871	+	7.32870i	0.579488	+	0.421023i
$304$		0			0
$305$	0.837194	−	1.79971i	0.0479376	−	0.103051i
$306$		0			0
$307$	21.2703			1.21396			0.606979	−	0.794718i	$-0.292381\pi$
$307$	21.2703			1.21396			0.606979	+	0.794718i	$0.292381\pi$
$308$		0			0
$309$	−4.73328	−	14.5675i	−0.269267	−	0.828719i
$310$		0			0
$311$	0.929092	−	2.85945i	0.0526840	−	0.162145i	−0.921253	−	0.388965i	$-0.872833\pi$
$311$	0.929092	−	2.85945i	0.0526840	−	0.162145i	0.973937	+	0.226820i	$0.0728329\pi$
$312$		0			0
$313$	−3.74673	−	11.5312i	−0.211778	−	0.651784i	−0.999367	−	0.0355836i	$-0.988671\pi$
$313$	−3.74673	−	11.5312i	−0.211778	−	0.651784i	0.787589	−	0.616201i	$-0.211329\pi$
$314$		0			0
$315$	1.23355	+	6.31491i	0.0695026	+	0.355805i
$316$		0			0
$317$	6.59727	−	4.79320i	0.370540	−	0.269213i	−0.386895	−	0.922124i	$-0.626452\pi$
$317$	6.59727	−	4.79320i	0.370540	−	0.269213i	0.757435	+	0.652911i	$0.226452\pi$
$318$		0			0
$319$	9.75097	−	7.08449i	0.545949	−	0.396655i
$320$		0			0
$321$	2.01426	+	1.46345i	0.112425	+	0.0816816i
$322$		0			0
$323$	−0.977191	+	3.00749i	−0.0543724	+	0.167341i
$324$		0			0
$325$	−2.25276	−	31.3826i	−0.124961	−	1.74079i
$326$		0			0
$327$	1.32894	−	4.09007i	0.0734908	−	0.226181i
$328$		0			0
$329$	−10.7416	−	7.80425i	−0.592205	−	0.430262i
$330$		0			0
$331$	−7.02884	+	5.10675i	−0.386340	+	0.280692i	−0.763954	−	0.645271i	$-0.776745\pi$
$331$	−7.02884	+	5.10675i	−0.386340	+	0.280692i	0.377614	+	0.925963i	$0.376745\pi$
$332$		0			0
$333$	5.43080	−	3.94570i	0.297606	−	0.216223i
$334$		0			0
$335$	−18.7417	+	10.4113i	−1.02397	+	0.568832i
$336$		0			0
$337$	−3.19097	−	9.82079i	−0.173823	−	0.534972i	0.825755	−	0.564029i	$-0.190750\pi$
$337$	−3.19097	−	9.82079i	−0.173823	−	0.534972i	−0.999578	+	0.0290570i	$0.990750\pi$
$338$		0			0
$339$	0.863930	−	2.65890i	0.0469223	−	0.144412i
$340$		0			0
$341$	9.49927	+	29.2358i	0.514414	+	1.58321i
$342$		0			0
$343$	−16.4594			−0.888724
$344$		0			0
$345$	−16.9762	+	9.43055i	−0.913965	+	0.507724i
$346$		0			0
$347$	0.304862	+	0.221495i	0.0163659	+	0.0118905i	0.595938	−	0.803030i	$-0.296780\pi$
$347$	0.304862	+	0.221495i	0.0163659	+	0.0118905i	−0.579572	+	0.814921i	$0.696780\pi$
$348$		0			0
$349$	9.22828			0.493979			0.246989	−	0.969018i	$-0.420559\pi$
$349$	9.22828			0.493979			0.246989	+	0.969018i	$0.420559\pi$
$350$		0			0
$351$	6.29267			0.335878
$352$		0			0
$353$	−10.2282	−	7.43125i	−0.544394	−	0.395525i	0.281320	−	0.959614i	$-0.409228\pi$
$353$	−10.2282	−	7.43125i	−0.544394	−	0.395525i	−0.825714	+	0.564089i	$0.809228\pi$
$354$		0			0
$355$	12.5981	+	11.7262i	0.668637	+	0.622361i
$356$		0			0
$357$	1.69528			0.0897236
$358$		0			0
$359$	6.19546	+	19.0677i	0.326984	+	1.00635i	0.970537	+	0.240952i	$0.0774595\pi$
$359$	6.19546	+	19.0677i	0.326984	+	1.00635i	−0.643553	+	0.765401i	$0.722540\pi$
$360$		0			0
$361$	3.03139	−	9.32966i	0.159547	−	0.491035i
$362$		0			0
$363$	−5.54203	−	17.0566i	−0.290881	−	0.895239i
$364$		0			0
$365$	−10.0379	+	21.5783i	−0.525407	+	1.12946i
$366$		0			0
$367$	4.89190	−	3.55417i	0.255355	−	0.185526i	−0.452742	−	0.891642i	$-0.649554\pi$
$367$	4.89190	−	3.55417i	0.255355	−	0.185526i	0.708097	+	0.706115i	$0.249554\pi$
$368$		0			0
$369$	0.748496	−	0.543814i	0.0389651	−	0.0283098i
$370$		0			0
$371$	22.1802	+	16.1148i	1.15154	+	0.836641i
$372$		0			0
$373$	6.41032	−	19.7289i	0.331914	−	1.02153i	−0.636309	−	0.771435i	$-0.719540\pi$
$373$	6.41032	−	19.7289i	0.331914	−	1.02153i	0.968222	−	0.250091i	$-0.0804605\pi$
$374$		0			0
$375$	6.11521	+	9.35971i	0.315788	+	0.483333i
$376$		0			0
$377$	4.35713	−	13.4099i	0.224403	−	0.690643i
$378$		0			0
$379$	1.17451	+	0.853329i	0.0603304	+	0.0438326i	0.617542	−	0.786538i	$-0.288129\pi$
$379$	1.17451	+	0.853329i	0.0603304	+	0.0438326i	−0.557211	+	0.830371i	$0.688129\pi$
$380$		0			0
$381$	2.43829	−	1.77152i	0.124917	−	0.0907578i
$382$		0			0
$383$	3.87359	−	2.81433i	0.197931	−	0.143806i	−0.484405	−	0.874844i	$-0.660964\pi$
$383$	3.87359	−	2.81433i	0.197931	−	0.143806i	0.682337	+	0.731038i	$0.260964\pi$
$384$		0			0
$385$	14.5980	−	31.3811i	0.743981	−	1.59933i
$386$		0			0
$387$	0.521949	+	1.60639i	0.0265321	+	0.0816575i
$388$		0			0
$389$	0.493063	−	1.51749i	0.0249993	−	0.0769399i	−0.937779	−	0.347234i	$-0.887121\pi$
$389$	0.493063	−	1.51749i	0.0249993	−	0.0769399i	0.962778	+	0.270294i	$0.0871210\pi$
$390$		0			0
$391$	1.58113	+	4.86621i	0.0799611	+	0.246095i
$392$		0			0
$393$	1.78481			0.0900315
$394$		0			0
$395$	5.66367	+	5.27168i	0.284970	+	0.265247i
$396$		0			0
$397$	9.09074	+	6.60481i	0.456251	+	0.331486i	0.792059	−	0.610445i	$-0.209009\pi$
$397$	9.09074	+	6.60481i	0.456251	+	0.331486i	−0.335808	+	0.941931i	$0.609009\pi$
$398$		0			0
$399$	−15.4448			−0.773209
$400$		0			0
$401$	23.9765			1.19733			0.598666	−	0.800999i	$-0.295698\pi$
$401$	23.9765			1.19733			0.598666	+	0.800999i	$0.295698\pi$
$402$		0			0
$403$	29.0933	+	21.1375i	1.44924	+	1.05294i
$404$		0			0
$405$	−1.95471	+	1.08587i	−0.0971302	+	0.0539575i
$406$		0			0
$407$	−36.1088			−1.78985
$408$		0			0
$409$	4.54034	+	13.9737i	0.224505	+	0.690956i	0.998341	+	0.0575702i	$0.0183353\pi$
$409$	4.54034	+	13.9737i	0.224505	+	0.690956i	−0.773836	+	0.633386i	$0.781665\pi$
$410$		0			0
$411$	−1.62532	+	5.00223i	−0.0801713	+	0.246742i
$412$		0			0
$413$	11.6733	+	35.9268i	0.574407	+	1.76784i
$414$		0			0
$415$	−23.5593	+	13.0876i	−1.15648	+	0.642444i
$416$		0			0
$417$	3.11265	−	2.26147i	0.152427	−	0.110745i
$418$		0			0
$419$	13.6045	−	9.88421i	0.664621	−	0.482875i	−0.203599	−	0.979054i	$-0.565264\pi$
$419$	13.6045	−	9.88421i	0.664621	−	0.482875i	0.868220	+	0.496179i	$0.165264\pi$
$420$		0			0
$421$	10.3144	+	7.49383i	0.502692	+	0.365227i	0.810044	−	0.586369i	$-0.199443\pi$
$421$	10.3144	+	7.49383i	0.502692	+	0.365227i	−0.307352	+	0.951596i	$0.599443\pi$
$422$		0			0
$423$	1.42587	−	4.38839i	0.0693284	−	0.213371i
$424$		0			0
$425$	2.72922	−	1.10855i	0.132386	−	0.0537723i
$426$		0			0
$427$	0.789315	−	2.42926i	0.0381976	−	0.117560i
$428$		0			0
$429$	−27.3842	−	19.8958i	−1.32212	−	0.960576i
$430$		0			0
$431$	−17.2659	+	12.5444i	−0.831670	+	0.604243i	−0.920031	−	0.391845i	$-0.871837\pi$
$431$	−17.2659	+	12.5444i	−0.831670	+	0.604243i	0.0883615	+	0.996088i	$0.471837\pi$
$432$		0			0
$433$	−7.07277	+	5.13867i	−0.339896	+	0.246949i	−0.744618	−	0.667491i	$-0.767368\pi$
$433$	−7.07277	+	5.13867i	−0.339896	+	0.246949i	0.404722	+	0.914440i	$0.367368\pi$
$434$		0			0
$435$	0.960563	+	4.91741i	0.0460555	+	0.235772i
$436$		0			0
$437$	−14.4049	−	44.3337i	−0.689079	−	2.12077i
$438$		0			0
$439$	1.82671	−	5.62203i	0.0871840	−	0.268325i	−0.897954	−	0.440089i	$-0.854947\pi$
$439$	1.82671	−	5.62203i	0.0871840	−	0.268325i	0.985138	+	0.171764i	$0.0549468\pi$
$440$		0			0
$441$	0.395523	+	1.21730i	0.0188344	+	0.0579664i
$442$		0			0
$443$	−22.8304			−1.08470			−0.542352	−	0.840152i	$-0.682466\pi$
$443$	−22.8304			−1.08470			−0.542352	+	0.840152i	$0.682466\pi$
$444$		0			0
$445$	−2.13117	+	4.58135i	−0.101027	+	0.217177i
$446$		0			0
$447$	1.76874	+	1.28507i	0.0836587	+	0.0607816i
$448$		0			0
$449$	−34.8068			−1.64263			−0.821317	−	0.570473i	$-0.806760\pi$
$449$	−34.8068			−1.64263			−0.821317	+	0.570473i	$0.806760\pi$
$450$		0			0
$451$	−4.97667			−0.234342
$452$		0			0
$453$	16.6623	+	12.1059i	0.782863	+	0.568783i
$454$		0			0
$455$	−7.76231	−	39.7376i	−0.363903	−	1.86293i
$456$		0			0
$457$	37.7912			1.76780			0.883898	−	0.467679i	$-0.154910\pi$
$457$	37.7912			1.76780			0.883898	+	0.467679i	$0.154910\pi$
$458$		0			0
$459$	0.182058	+	0.560317i	0.00849774	+	0.0261533i
$460$		0			0
$461$	−6.41364	+	19.7392i	−0.298713	+	0.919344i	0.683236	+	0.730198i	$0.260572\pi$
$461$	−6.41364	+	19.7392i	−0.298713	+	0.919344i	−0.981949	+	0.189146i	$0.939428\pi$
$462$		0			0
$463$	−4.27223	−	13.1486i	−0.198547	−	0.611066i	−0.999917	−	0.0128960i	$-0.995895\pi$
$463$	−4.27223	−	13.1486i	−0.198547	−	0.611066i	0.801370	−	0.598169i	$-0.204105\pi$
$464$		0			0
$465$	−12.6849	−	1.54561i	−0.588246	−	0.0716760i
$466$		0			0
$467$	9.10217	−	6.61311i	0.421198	−	0.306018i	−0.356922	−	0.934134i	$-0.616174\pi$
$467$	9.10217	−	6.61311i	0.421198	−	0.306018i	0.778120	+	0.628116i	$0.216174\pi$
$468$		0			0
$469$	−22.3202	+	16.2166i	−1.03065	+	0.748813i
$470$		0			0
$471$	−11.6740	−	8.48166i	−0.537910	−	0.390814i
$472$		0			0
$473$	2.80760	−	8.64089i	0.129093	−	0.397309i
$474$		0			0
$475$	−24.8646	+	10.0994i	−1.14086	+	0.463393i
$476$		0			0
$477$	−2.94426	+	9.06150i	−0.134808	+	0.414898i
$478$		0			0
$479$	−22.2090	−	16.1358i	−1.01476	−	0.737263i	−0.0495541	−	0.998771i	$-0.515780\pi$
$479$	−22.2090	−	16.1358i	−1.01476	−	0.737263i	−0.965201	+	0.261509i	$0.915780\pi$
$480$		0			0
$481$	−34.1742	+	24.8290i	−1.55821	+	1.13210i
$482$		0			0
$483$	−20.2176	+	14.6889i	−0.919931	+	0.668369i
$484$		0			0
$485$	−32.1060	−	29.8839i	−1.45786	−	1.35696i
$486$		0			0
$487$	9.71002	+	29.8844i	0.440003	+	1.35419i	0.887872	+	0.460090i	$0.152183\pi$
$487$	9.71002	+	29.8844i	0.440003	+	1.35419i	−0.447869	+	0.894099i	$0.647817\pi$
$488$		0			0
$489$	0.0521767	−	0.160583i	0.00235951	−	0.00726183i
$490$		0			0
$491$	−3.33800	−	10.2733i	−0.150642	−	0.463627i	0.847052	−	0.531511i	$-0.178375\pi$
$491$	−3.33800	−	10.2733i	−0.150642	−	0.463627i	−0.997693	+	0.0678833i	$0.978375\pi$
$492$		0			0
$493$	1.32011			0.0594548
$494$		0			0
$495$	11.9397	+	1.45481i	0.536648	+	0.0653889i
$496$		0			0
$497$	17.9180	+	13.0182i	0.803733	+	0.583946i
$498$		0			0
$499$	10.2053			0.456854			0.228427	−	0.973561i	$-0.426642\pi$
$499$	10.2053			0.456854			0.228427	+	0.973561i	$0.426642\pi$
$500$		0			0
$501$	6.90802			0.308627
$502$		0			0
$503$	21.1033	+	15.3324i	0.940950	+	0.683640i	0.948649	−	0.316330i	$-0.102451\pi$
$503$	21.1033	+	15.3324i	0.940950	+	0.683640i	−0.00769920	+	0.999970i	$0.502451\pi$
$504$		0			0
$505$	27.6753	+	3.37216i	1.23154	+	0.150059i
$506$		0			0
$507$	−26.5976			−1.18124
$508$		0			0
$509$	−4.67753	−	14.3960i	−0.207328	−	0.638090i	−0.999610	−	0.0279347i	$-0.991107\pi$
$509$	−4.67753	−	14.3960i	−0.207328	−	0.638090i	0.792282	−	0.610156i	$-0.208893\pi$
$510$		0			0
$511$	−9.46382	+	29.1266i	−0.418655	+	1.28849i
$512$		0			0
$513$	−1.65864	−	5.10477i	−0.0732308	−	0.225381i
$514$		0			0
$515$	−25.0707	−	23.3355i	−1.10475	−	1.02829i
$516$		0			0
$517$	−20.0800	+	14.5890i	−0.883117	+	0.641622i
$518$		0			0
$519$	15.9123	−	11.5610i	0.698472	−	0.507470i
$520$		0			0
$521$	−7.56416	−	5.49569i	−0.331392	−	0.240770i	0.409629	−	0.912252i	$-0.365658\pi$
$521$	−7.56416	−	5.49569i	−0.331392	−	0.240770i	−0.741021	+	0.671482i	$0.765658\pi$
$522$		0			0
$523$	3.88012	−	11.9418i	0.169666	−	0.522177i	−0.829684	−	0.558233i	$-0.811479\pi$
$523$	3.88012	−	11.9418i	0.169666	−	0.522177i	0.999350	+	0.0360560i	$0.0114795\pi$
$524$		0			0
$525$	9.26842	+	11.0043i	0.404507	+	0.480268i
$526$		0			0
$527$	−1.04042	+	3.20210i	−0.0453216	+	0.139486i
$528$		0			0
$529$	−42.4127	−	30.8146i	−1.84403	−	1.33977i
$530$		0			0
$531$	−10.6208	+	7.71645i	−0.460903	+	0.334865i
$532$		0			0
$533$	−4.71003	+	3.42204i	−0.204014	+	0.148225i
$534$		0			0
$535$	5.52641	+	0.673376i	0.238927	+	0.0291126i
$536$		0			0
$537$	−0.333386	−	1.02606i	−0.0143867	−	0.0442776i
$538$		0			0
$539$	2.12755	−	6.54791i	0.0916399	−	0.282039i
$540$		0			0
$541$	−0.241815	−	0.744229i	−0.0103964	−	0.0319969i	0.945724	−	0.324972i	$-0.105355\pi$
$541$	−0.241815	−	0.744229i	−0.0103964	−	0.0319969i	−0.956120	+	0.292975i	$0.905355\pi$
$542$		0			0
$543$	20.9028			0.897024
$544$		0			0
$545$	−1.84360	−	9.43795i	−0.0789713	−	0.404278i
$546$		0			0
$547$	−10.3829	−	7.54361i	−0.443940	−	0.322542i	0.343258	−	0.939241i	$-0.388469\pi$
$547$	−10.3829	−	7.54361i	−0.443940	−	0.322542i	−0.787199	+	0.616699i	$0.788469\pi$
$548$		0			0
$549$	0.887675			0.0378851
$550$		0			0
$551$	−12.0269			−0.512362
$552$		0			0
$553$	8.05532	+	5.85253i	0.342547	+	0.248875i
$554$		0			0
$555$	6.33108	−	13.6099i	0.268739	−	0.577706i
$556$		0			0
$557$	15.9970			0.677815			0.338907	−	0.940820i	$-0.389943\pi$
$557$	15.9970			0.677815			0.338907	+	0.940820i	$0.389943\pi$
$558$		0			0
$559$	−3.28445	−	10.1085i	−0.138917	−	0.427544i
$560$		0			0
$561$	0.979302	−	3.01398i	0.0413462	−	0.127250i
$562$		0			0
$563$	−6.55191	−	20.1647i	−0.276130	−	0.849841i	−0.988918	−	0.148461i	$-0.952568\pi$
$563$	−6.55191	−	20.1647i	−0.276130	−	0.849841i	0.712788	−	0.701379i	$-0.247432\pi$
$564$		0			0
$565$	−1.19850	−	6.13550i	−0.0504214	−	0.258122i
$566$		0			0
$567$	−2.32794	+	1.69135i	−0.0977642	+	0.0710298i
$568$		0			0
$569$	−17.7031	+	12.8620i	−0.742151	+	0.539204i	−0.893384	−	0.449294i	$-0.851676\pi$
$569$	−17.7031	+	12.8620i	−0.742151	+	0.539204i	0.151233	+	0.988498i	$0.451676\pi$
$570$		0			0
$571$	27.0956	+	19.6861i	1.13392	+	0.823838i	0.986260	−	0.165200i	$-0.0528271\pi$
$571$	27.0956	+	19.6861i	1.13392	+	0.823838i	0.147656	+	0.989039i	$0.452827\pi$
$572$		0			0
$573$	2.68535	−	8.26466i	0.112182	−	0.345261i
$574$		0			0
$575$	−22.9430	+	36.8679i	−0.956790	+	1.53750i
$576$		0			0
$577$	−4.65228	+	14.3182i	−0.193677	+	0.596076i	0.806313	+	0.591490i	$0.201460\pi$
$577$	−4.65228	+	14.3182i	−0.193677	+	0.596076i	−0.999989	+	0.00458657i	$0.998540\pi$
$578$		0			0
$579$	6.92979	+	5.03479i	0.287992	+	0.209239i
$580$		0			0
$581$	−28.0577	+	20.3851i	−1.16403	+	0.845716i
$582$		0			0
$583$	41.4628	−	30.1245i	1.71721	−	1.24763i
$584$		0			0
$585$	12.3003	−	6.83304i	0.508556	−	0.282511i
$586$		0			0
$587$	2.82659	+	8.69935i	0.116666	+	0.359061i	0.992291	−	0.123931i	$-0.0395501\pi$
$587$	2.82659	+	8.69935i	0.116666	+	0.359061i	−0.875625	+	0.482992i	$0.839550\pi$
$588$		0			0
$589$	9.47880	−	29.1727i	0.390567	−	1.20204i
$590$		0			0
$591$	−6.84959	−	21.0809i	−0.281754	−	0.867151i
$592$		0			0
$593$	38.5604			1.58349			0.791743	−	0.610855i	$-0.209174\pi$
$593$	38.5604			1.58349			0.791743	+	0.610855i	$0.209174\pi$
$594$		0			0
$595$	3.31377	−	1.84086i	0.135851	−	0.0754678i
$596$		0			0
$597$	−3.72125	−	2.70365i	−0.152301	−	0.110653i
$598$		0			0
$599$	26.8773			1.09818			0.549088	−	0.835765i	$-0.314975\pi$
$599$	26.8773			1.09818			0.549088	+	0.835765i	$0.314975\pi$
$600$		0			0
$601$	−27.8735			−1.13698			−0.568491	−	0.822689i	$-0.692473\pi$
$601$	−27.8735			−1.13698			−0.568491	+	0.822689i	$0.692473\pi$
$602$		0			0
$603$	−7.75684	−	5.63568i	−0.315883	−	0.229502i
$604$		0			0
$605$	−29.3543	−	27.3227i	−1.19342	−	1.11083i
$606$		0			0
$607$	−4.53467			−0.184057			−0.0920284	−	0.995756i	$-0.529335\pi$
$607$	−4.53467			−0.184057			−0.0920284	+	0.995756i	$0.529335\pi$
$608$		0			0
$609$	1.99241	+	6.13201i	0.0807366	+	0.248482i
$610$		0			0
$611$	−8.97255	+	27.6147i	−0.362991	+	1.11717i
$612$		0			0
$613$	5.32695	+	16.3947i	0.215154	+	0.662175i	0.999143	+	0.0414001i	$0.0131818\pi$
$613$	5.32695	+	16.3947i	0.215154	+	0.662175i	−0.783989	+	0.620775i	$0.786818\pi$
$614$		0			0
$615$	0.872576	−	1.87577i	0.0351857	−	0.0756383i
$616$		0			0
$617$	16.8240	−	12.2233i	0.677307	−	0.492093i	−0.195156	−	0.980772i	$-0.562521\pi$
$617$	16.8240	−	12.2233i	0.677307	−	0.492093i	0.872463	+	0.488680i	$0.162521\pi$
$618$		0			0
$619$	−34.8069	+	25.2887i	−1.39901	+	1.01644i	−0.404199	+	0.914671i	$0.632450\pi$
$619$	−34.8069	+	25.2887i	−1.39901	+	1.01644i	−0.994808	+	0.101767i	$0.967550\pi$
$620$		0			0
$621$	−7.02612	−	5.10477i	−0.281948	−	0.204847i
$622$		0			0
$623$	−2.00929	+	6.18395i	−0.0805004	+	0.247755i
$624$		0			0
$625$	22.1169	+	11.6551i	0.884676	+	0.466206i
$626$		0			0
$627$	−8.92194	+	27.4589i	−0.356308	+	1.09660i
$628$		0			0
$629$	−3.19956	−	2.32462i	−0.127575	−	0.0926886i
$630$		0			0
$631$	−4.97867	+	3.61722i	−0.198198	+	0.143999i	−0.682458	−	0.730925i	$-0.739089\pi$
$631$	−4.97867	+	3.61722i	−0.198198	+	0.143999i	0.484260	+	0.874924i	$0.339089\pi$
$632$		0			0
$633$	12.6635	−	9.20058i	0.503330	−	0.365690i
$634$		0			0
$635$	2.84249	−	6.11048i	0.112801	−	0.242487i
$636$		0			0
$637$	−2.48890	−	7.66003i	−0.0986136	−	0.303502i
$638$		0			0
$639$	−2.37849	+	7.32023i	−0.0940915	+	0.289584i
$640$		0			0
$641$	5.03939	+	15.5096i	0.199044	+	0.612594i	0.999906	+	0.0137447i	$0.00437521\pi$
$641$	5.03939	+	15.5096i	0.199044	+	0.612594i	−0.800862	+	0.598849i	$0.795625\pi$
$642$		0			0
$643$	−12.6429			−0.498586			−0.249293	−	0.968428i	$-0.580198\pi$
$643$	−12.6429			−0.498586			−0.249293	+	0.968428i	$0.580198\pi$
$644$		0			0
$645$	2.76460	+	2.57326i	0.108856	+	0.101322i
$646$		0			0
$647$	33.8242	+	24.5748i	1.32977	+	0.966133i	0.999754	+	0.0221573i	$0.00705346\pi$
$647$	33.8242	+	24.5748i	1.32977	+	0.966133i	0.330014	+	0.943976i	$0.392947\pi$
$648$		0			0
$649$	70.6165			2.77194
$650$		0			0
$651$	−16.4443			−0.644502
$652$		0			0
$653$	−6.98041	−	5.07156i	−0.273164	−	0.198466i	0.442766	−	0.896637i	$-0.353997\pi$
$653$	−6.98041	−	5.07156i	−0.273164	−	0.198466i	−0.715930	+	0.698172i	$0.753997\pi$
$654$		0			0
$655$	3.48877	−	1.93807i	0.136318	−	0.0757268i
$656$		0			0
$657$	−10.6432			−0.415229
$658$		0			0
$659$	−1.64045	−	5.04878i	−0.0639028	−	0.196673i	0.914008	−	0.405697i	$-0.132971\pi$
$659$	−1.64045	−	5.04878i	−0.0639028	−	0.196673i	−0.977910	+	0.209024i	$0.932971\pi$
$660$		0			0
$661$	13.8367	−	42.5850i	0.538186	−	1.65637i	−0.198477	−	0.980105i	$-0.563600\pi$
$661$	13.8367	−	42.5850i	0.538186	−	1.65637i	0.736663	−	0.676260i	$-0.236400\pi$
$662$		0			0
$663$	−1.14563	−	3.52589i	−0.0444926	−	0.136934i
$664$		0			0
$665$	−30.1901	+	16.7711i	−1.17072	+	0.650357i
$666$		0			0
$667$	−15.7434	+	11.4382i	−0.609587	+	0.442891i
$668$		0			0
$669$	14.9968	−	10.8958i	0.579811	−	0.421257i
$670$		0			0
$671$	−3.86295	−	2.80660i	−0.149127	−	0.108347i
$672$		0			0
$673$	14.2348	−	43.8103i	0.548713	−	1.68876i	−0.163281	−	0.986580i	$-0.552208\pi$
$673$	14.2348	−	43.8103i	0.548713	−	1.68876i	0.711994	−	0.702185i	$-0.247792\pi$
$674$		0			0
$675$	−2.64176	+	4.24513i	−0.101681	+	0.163395i
$676$		0			0
$677$	−8.36841	+	25.7553i	−0.321624	+	0.989857i	0.651317	+	0.758805i	$0.274217\pi$
$677$	−8.36841	+	25.7553i	−0.321624	+	0.989857i	−0.972941	+	0.231052i	$0.925783\pi$
$678$		0			0
$679$	−45.6636	−	33.1766i	−1.75241	−	1.27320i
$680$		0			0
$681$	4.94368	−	3.59179i	0.189442	−	0.137638i
$682$		0			0
$683$	−22.7277	+	16.5126i	−0.869649	+	0.631837i	−0.930493	−	0.366310i	$-0.880621\pi$
$683$	−22.7277	+	16.5126i	−0.869649	+	0.631837i	0.0608434	+	0.998147i	$0.480621\pi$
$684$		0			0
$685$	2.25476	+	11.5428i	0.0861499	+	0.441027i
$686$		0			0
$687$	5.19621	+	15.9923i	0.198248	+	0.610145i
$688$		0			0
$689$	18.5272	−	57.0210i	0.705832	−	2.17233i
$690$		0			0
$691$	0.0930221	+	0.286293i	0.00353873	+	0.0108911i	0.952810	−	0.303566i	$-0.0981774\pi$
$691$	0.0930221	+	0.286293i	0.00353873	+	0.0108911i	−0.949272	+	0.314457i	$0.898177\pi$
$692$		0			0
$693$	15.4782			0.587968
$694$		0			0
$695$	3.62864	−	7.80046i	0.137642	−	0.295888i
$696$		0			0
$697$	−0.440978	−	0.320389i	−0.0167032	−	0.0121356i
$698$		0			0
$699$	−26.4071			−0.998808
$700$		0			0
$701$	−4.88956			−0.184676			−0.0923380	−	0.995728i	$-0.529434\pi$
$701$	−4.88956			−0.184676			−0.0923380	+	0.995728i	$0.529434\pi$
$702$		0			0
$703$	29.1497	+	21.1785i	1.09940	+	0.798761i
$704$		0			0
$705$	−1.97807	−	10.1263i	−0.0744985	−	0.381380i
$706$		0			0
$707$	35.8775			1.34931
$708$		0			0
$709$	−0.103426	−	0.318313i	−0.00388425	−	0.0119545i	0.949096	−	0.314988i	$-0.102001\pi$
$709$	−0.103426	−	0.318313i	−0.00388425	−	0.0119545i	−0.952980	+	0.303034i	$0.902001\pi$
$710$		0			0
$711$	−1.06929	+	3.29092i	−0.0401014	+	0.123419i
$712$		0			0
$713$	−15.3370	−	47.2025i	−0.574376	−	1.76775i
$714$		0			0
$715$	−75.1323	−	9.15464i	−2.80979	−	0.342364i
$716$		0			0
$717$	7.61165	−	5.53019i	0.284262	−	0.206529i
$718$		0			0
$719$	−38.0358	+	27.6347i	−1.41850	+	1.03060i	−0.426480	+	0.904497i	$0.640247\pi$
$719$	−38.0358	+	27.6347i	−1.41850	+	1.03060i	−0.992017	+	0.126102i	$0.959753\pi$
$720$		0			0
$721$	−35.6575	−	25.9067i	−1.32796	−	0.964816i
$722$		0			0
$723$	−3.86568	+	11.8974i	−0.143766	+	0.442467i
$724$		0			0
$725$	7.21730	+	8.56904i	0.268044	+	0.318246i
$726$		0			0
$727$	4.85292	−	14.9358i	0.179985	−	0.553936i	−0.819841	−	0.572591i	$-0.805938\pi$
$727$	4.85292	−	14.9358i	0.179985	−	0.553936i	0.999826	+	0.0186547i	$0.00593831\pi$
$728$		0			0
$729$	−0.809017	−	0.587785i	−0.0299636	−	0.0217698i
$730$		0			0
$731$	0.805063	−	0.584913i	0.0297763	−	0.0216338i
$732$		0			0
$733$	−26.4802	+	19.2390i	−0.978070	+	0.710610i	−0.957276	−	0.289174i	$-0.906619\pi$
$733$	−26.4802	+	19.2390i	−0.978070	+	0.710610i	−0.0207937	+	0.999784i	$0.506619\pi$
$734$		0			0
$735$	2.09496	+	1.94997i	0.0772738	+	0.0719256i
$736$		0			0
$737$	15.9374	+	49.0502i	0.587061	+	1.80679i
$738$		0			0
$739$	5.04654	−	15.5317i	0.185640	−	0.571341i	−0.814319	−	0.580418i	$-0.802889\pi$
$739$	5.04654	−	15.5317i	0.185640	−	0.571341i	0.999959	+	0.00907671i	$0.00288925\pi$
$740$		0			0
$741$	10.4373	+	32.1226i	0.383423	+	1.18005i
$742$		0			0
$743$	−7.09814			−0.260405			−0.130203	−	0.991487i	$-0.541563\pi$
$743$	−7.09814			−0.260405			−0.130203	+	0.991487i	$0.541563\pi$
$744$		0			0
$745$	4.85280	+	0.591298i	0.177793	+	0.0216635i
$746$		0			0
$747$	−9.75075	−	7.08434i	−0.356761	−	0.259202i
$748$		0			0
$749$	7.16427			0.261777
$750$		0			0
$751$	−17.6433			−0.643814			−0.321907	−	0.946771i	$-0.604324\pi$
$751$	−17.6433			−0.643814			−0.321907	+	0.946771i	$0.604324\pi$
$752$		0			0
$753$	−16.3084	−	11.8487i	−0.594310	−	0.431792i
$754$		0			0
$755$	45.7153	+	5.57027i	1.66375	+	0.202723i
$756$		0			0
$757$	−36.7515			−1.33576			−0.667878	−	0.744270i	$-0.732797\pi$
$757$	−36.7515			−1.33576			−0.667878	+	0.744270i	$0.732797\pi$
$758$		0			0
$759$	14.4360	+	44.4295i	0.523994	+	1.61269i
$760$		0			0
$761$	−5.40767	+	16.6431i	−0.196028	+	0.603312i	0.803935	+	0.594717i	$0.202736\pi$
$761$	−5.40767	+	16.6431i	−0.196028	+	0.603312i	−0.999963	+	0.00859474i	$0.997264\pi$
$762$		0			0
$763$	−3.82402	−	11.7691i	−0.138439	−	0.426071i
$764$		0			0
$765$	0.964303	+	0.897563i	0.0348644	+	0.0324515i
$766$		0			0
$767$	66.8330	−	48.5570i	2.41320	−	1.75329i
$768$		0			0
$769$	−9.37830	+	6.81373i	−0.338190	+	0.245709i	−0.743898	−	0.668293i	$-0.767025\pi$
$769$	−9.37830	+	6.81373i	−0.338190	+	0.245709i	0.405708	+	0.914003i	$0.367025\pi$
$770$		0			0
$771$	8.10922	+	5.89169i	0.292046	+	0.212184i
$772$		0			0
$773$	−2.76949	+	8.52363i	−0.0996118	+	0.306574i	−0.988428	−	0.151690i	$-0.951528\pi$
$773$	−2.76949	+	8.52363i	−0.0996118	+	0.306574i	0.888816	+	0.458264i	$0.151528\pi$
$774$		0			0
$775$	−26.4735	+	10.7529i	−0.950957	+	0.386257i
$776$		0			0
$777$	5.96900	−	18.3707i	0.214137	−	0.659045i
$778$		0			0
$779$	4.01753	+	2.91891i	0.143943	+	0.104581i
$780$		0			0
$781$	33.4953	−	24.3357i	1.19855	−	0.870801i
$782$		0			0
$783$	−1.81276	+	1.31705i	−0.0647828	+	0.0470675i
$784$		0			0
$785$	−32.0293	−	3.90267i	−1.14317	−	0.139292i
$786$		0			0
$787$	12.4315	+	38.2601i	0.443134	+	1.36383i	0.884517	+	0.466508i	$0.154488\pi$
$787$	12.4315	+	38.2601i	0.443134	+	1.36383i	−0.441383	+	0.897319i	$0.645512\pi$
$788$		0			0
$789$	1.36296	−	4.19477i	0.0485228	−	0.149338i
$790$		0			0
$791$	−2.48595	−	7.65097i	−0.0883902	−	0.272037i
$792$		0			0
$793$	−5.58585			−0.198359
$794$		0			0
$795$	4.08448	+	20.9097i	0.144862	+	0.741590i
$796$		0			0
$797$	14.9568	+	10.8668i	0.529797	+	0.384920i	0.820282	−	0.571959i	$-0.193817\pi$
$797$	14.9568	+	10.8668i	0.529797	+	0.384920i	−0.290485	+	0.956880i	$0.593817\pi$
$798$		0			0
$799$	−2.71848			−0.0961729
$800$		0			0
$801$	−2.25968			−0.0798418
$802$		0			0
$803$	46.3164	+	33.6509i	1.63447	+	1.18751i
$804$		0			0
$805$	−23.5691	+	50.6663i	−0.830702	+	1.78575i
$806$		0			0
$807$	28.3744			0.998827
$808$		0			0
$809$	11.0538	+	34.0202i	0.388632	+	1.19609i	0.933811	+	0.357767i	$0.116462\pi$
$809$	11.0538	+	34.0202i	0.388632	+	1.19609i	−0.545179	+	0.838320i	$0.683538\pi$
$810$		0			0
$811$	−10.1203	+	31.1472i	−0.355373	+	1.09373i	0.600419	+	0.799685i	$0.295000\pi$
$811$	−10.1203	+	31.1472i	−0.355373	+	1.09373i	−0.955793	+	0.294041i	$0.905000\pi$
$812$		0			0
$813$	−3.68461	−	11.3401i	−0.129225	−	0.397713i
$814$		0			0
$815$	−0.0723830	−	0.370550i	−0.00253547	−	0.0129798i
$816$		0			0
$817$	−7.33454	+	5.32886i	−0.256603	+	0.186433i
$818$		0			0
$819$	14.6489	−	10.6431i	0.511875	−	0.371899i
$820$		0			0
$821$	24.6024	+	17.8747i	0.858629	+	0.623831i	0.927512	−	0.373794i	$-0.121943\pi$
$821$	24.6024	+	17.8747i	0.858629	+	0.623831i	−0.0688824	+	0.997625i	$0.521943\pi$
$822$		0			0
$823$	3.82918	−	11.7850i	0.133477	−	0.410799i	−0.861873	−	0.507124i	$-0.830709\pi$
$823$	3.82918	−	11.7850i	0.133477	−	0.410799i	0.995350	+	0.0963247i	$0.0307087\pi$
$824$		0			0
$825$	24.9183	−	10.1212i	0.867543	−	0.352376i
$826$		0			0
$827$	0.263018	−	0.809486i	0.00914603	−	0.0281486i	−0.946379	−	0.323057i	$-0.895289\pi$
$827$	0.263018	−	0.809486i	0.00914603	−	0.0281486i	0.955525	+	0.294909i	$0.0952893\pi$
$828$		0			0
$829$	−9.64116	−	7.00471i	−0.334851	−	0.243284i	0.407635	−	0.913145i	$-0.366354\pi$
$829$	−9.64116	−	7.00471i	−0.334851	−	0.243284i	−0.742486	+	0.669861i	$0.766354\pi$
$830$		0			0
$831$	−12.6263	+	9.17353i	−0.438001	+	0.318226i
$832$		0			0
$833$	0.610063	−	0.443236i	0.0211374	−	0.0153572i
$834$		0			0
$835$	13.5031	−	7.50123i	0.467296	−	0.259591i
$836$		0			0
$837$	−1.76597	−	5.43510i	−0.0610409	−	0.187864i
$838$		0			0
$839$	5.63458	−	17.3415i	0.194527	−	0.598694i	−0.805454	−	0.592658i	$-0.798079\pi$
$839$	5.63458	−	17.3415i	0.194527	−	0.598694i	0.999982	−	0.00603600i	$-0.00192133\pi$
$840$		0			0
$841$	−7.41000	−	22.8057i	−0.255517	−	0.786402i
$842$		0			0
$843$	9.07026			0.312396
$844$		0			0
$845$	−51.9906	+	28.8817i	−1.78853	+	0.993560i
$846$		0			0
$847$	−41.7501	−	30.3332i	−1.43455	−	1.04226i
$848$		0			0
$849$	−2.27854			−0.0781994
$850$		0			0
$851$	58.2993			1.99847
$852$		0			0
$853$	−24.5705	−	17.8515i	−0.841277	−	0.611223i	0.0814502	−	0.996677i	$-0.474045\pi$
$853$	−24.5705	−	17.8515i	−0.841277	−	0.611223i	−0.922727	+	0.385454i	$0.874045\pi$
$854$		0			0
$855$	−8.78529	−	8.17726i	−0.300451	−	0.279656i
$856$		0			0
$857$	−14.7279			−0.503096			−0.251548	−	0.967845i	$-0.580940\pi$
$857$	−14.7279			−0.503096			−0.251548	+	0.967845i	$0.580940\pi$
$858$		0			0
$859$	−13.0000	−	40.0098i	−0.443553	−	1.36512i	−0.884062	−	0.467369i	$-0.845202\pi$
$859$	−13.0000	−	40.0098i	−0.443553	−	1.36512i	0.440509	−	0.897748i	$-0.354798\pi$
$860$		0			0
$861$	0.822674	−	2.53193i	0.0280366	−	0.0862879i
$862$		0			0
$863$	−1.44503	−	4.44736i	−0.0491896	−	0.151390i	0.923445	−	0.383732i	$-0.125361\pi$
$863$	−1.44503	−	4.44736i	−0.0491896	−	0.151390i	−0.972634	+	0.232342i	$0.925361\pi$
$864$		0			0
$865$	18.5501	−	39.8770i	0.630723	−	1.35586i
$866$		0			0
$867$	−13.4725	+	9.78833i	−0.457549	+	0.332429i
$868$		0			0
$869$	15.0583	−	10.9405i	0.510818	−	0.371131i
$870$		0			0
$871$	48.8112	+	35.4634i	1.65390	+	1.20163i
$872$		0			0
$873$	6.06152	−	18.6554i	0.205151	−	0.631391i
$874$		0			0
$875$	30.0663	+	11.4459i	1.01643	+	0.386941i
$876$		0			0
$877$	12.1256	−	37.3188i	0.409453	−	1.26017i	−0.507666	−	0.861554i	$-0.669492\pi$
$877$	12.1256	−	37.3188i	0.409453	−	1.26017i	0.917119	−	0.398613i	$-0.130508\pi$
$878$		0			0
$879$	−9.39033	−	6.82247i	−0.316728	−	0.230116i
$880$		0			0
$881$	24.3184	−	17.6683i	0.819307	−	0.595262i	−0.0972066	−	0.995264i	$-0.530991\pi$
$881$	24.3184	−	17.6683i	0.819307	−	0.595262i	0.916514	+	0.400003i	$0.130991\pi$
$882$		0			0
$883$	18.1753	−	13.2051i	0.611647	−	0.444388i	−0.238347	−	0.971180i	$-0.576605\pi$
$883$	18.1753	−	13.2051i	0.611647	−	0.444388i	0.849994	+	0.526792i	$0.176605\pi$
$884$		0			0
$885$	−12.3814	+	26.6162i	−0.416197	+	0.894695i
$886$		0			0
$887$	−15.6805	−	48.2597i	−0.526500	−	1.62040i	−0.761330	−	0.648365i	$-0.775453\pi$
$887$	−15.6805	−	48.2597i	−0.526500	−	1.62040i	0.234830	−	0.972037i	$-0.424547\pi$
$888$		0			0
$889$	2.67993	−	8.24798i	0.0898820	−	0.276628i
$890$		0			0
$891$	1.66222	+	5.11580i	0.0556866	+	0.171386i
$892$		0			0
$893$	24.7668			0.828788
$894$		0			0
$895$	−1.76584	−	1.64363i	−0.0590256	−	0.0549404i
$896$		0			0
$897$	44.2130	+	32.1226i	1.47623	+	1.07254i
$898$		0			0
$899$	−12.8051			−0.427075
$900$		0			0
$901$	5.61334			0.187007
$902$		0			0
$903$	3.93203	+	2.85679i	0.130850	+	0.0950679i
$904$		0			0
$905$	40.8588	−	22.6978i	1.35819	−	0.754499i
$906$		0			0
$907$	43.8959			1.45754			0.728769	−	0.684760i	$-0.240093\pi$
$907$	43.8959			1.45754			0.728769	+	0.684760i	$0.240093\pi$
$908$		0			0
$909$	3.85293	+	11.8581i	0.127793	+	0.393308i
$910$		0			0
$911$	10.6485	−	32.7728i	0.352802	−	1.08581i	−0.604472	−	0.796627i	$-0.706616\pi$
$911$	10.6485	−	32.7728i	0.352802	−	1.08581i	0.957273	−	0.289185i	$-0.0933842\pi$
$912$		0			0
$913$	20.0341	+	61.6586i	0.663032	+	2.04060i
$914$		0			0
$915$	1.73515	−	0.963903i	0.0573621	−	0.0318657i
$916$		0			0
$917$	4.15491	−	3.01872i	0.137207	−	0.0996870i
$918$		0			0
$919$	−0.306244	+	0.222499i	−0.0101021	+	0.00733958i	−0.592825	−	0.805331i	$-0.701987\pi$
$919$	−0.306244	+	0.222499i	−0.0101021	+	0.00733958i	0.582723	+	0.812671i	$0.301987\pi$
$920$		0			0
$921$	17.2080	+	12.5023i	0.567023	+	0.411966i
$922$		0			0
$923$	14.9670	−	46.0638i	0.492646	−	1.51621i
$924$		0			0
$925$	−2.40318	−	33.4780i	−0.0790160	−	1.10075i
$926$		0			0
$927$	4.73328	−	14.5675i	0.155461	−	0.478461i
$928$		0			0
$929$	30.1601	+	21.9126i	0.989519	+	0.718928i	0.959816	−	0.280631i	$-0.0905437\pi$
$929$	30.1601	+	21.9126i	0.989519	+	0.718928i	0.0297036	+	0.999559i	$0.490544\pi$
$930$		0			0
$931$	−5.55798	+	4.03811i	−0.182156	+	0.132344i
$932$		0			0
$933$	2.43240	−	1.76724i	0.0796330	−	0.0578568i
$934$		0			0
$935$	−1.35855	−	6.95485i	−0.0444295	−	0.227448i
$936$		0			0
$937$	14.6002	+	44.9347i	0.476967	+	1.46795i	0.843287	+	0.537464i	$0.180618\pi$
$937$	14.6002	+	44.9347i	0.476967	+	1.46795i	−0.366320	+	0.930489i	$0.619382\pi$
$938$		0			0
$939$	3.74673	−	11.5312i	0.122270	−	0.376308i
$940$		0			0
$941$	16.1039	+	49.5628i	0.524973	+	1.61570i	0.764370	+	0.644778i	$0.223050\pi$
$941$	16.1039	+	49.5628i	0.524973	+	1.61570i	−0.239397	+	0.970922i	$0.576950\pi$
$942$		0			0
$943$	8.03506			0.261658
$944$		0			0
$945$	−2.71385	+	5.83393i	−0.0882815	+	0.189778i
$946$		0			0
$947$	−3.02205	−	2.19565i	−0.0982035	−	0.0713490i	0.537600	−	0.843200i	$-0.319331\pi$
$947$	−3.02205	−	2.19565i	−0.0982035	−	0.0713490i	−0.635803	+	0.771851i	$0.719331\pi$
$948$		0			0
$949$	66.9739			2.17406
$950$		0			0
$951$	8.15468			0.264434
$952$		0			0
$953$	12.0381	+	8.74616i	0.389951	+	0.283316i	0.765435	−	0.643513i	$-0.222524\pi$
$953$	12.0381	+	8.74616i	0.389951	+	0.283316i	−0.375485	+	0.926829i	$0.622524\pi$
$954$		0			0
$955$	−3.72530	−	19.0709i	−0.120548	−	0.617121i
$956$		0			0
$957$	12.0529			0.389614
$958$		0			0
$959$	4.67685	+	14.3939i	0.151023	+	0.464802i
$960$		0			0
$961$	0.512639	−	1.57774i	0.0165367	−	0.0508949i
$962$		0			0
$963$	0.769379	+	2.36791i	0.0247929	+	0.0763047i
$964$		0			0
$965$	19.0128	+	2.31666i	0.612045	+	0.0745758i
$966$		0			0
$967$	−21.2027	+	15.4046i	−0.681831	+	0.495380i	−0.873965	−	0.485989i	$-0.838459\pi$
$967$	−21.2027	+	15.4046i	−0.681831	+	0.495380i	0.192133	+	0.981369i	$0.438459\pi$
$968$		0			0
$969$	−2.55832	+	1.85873i	−0.0821851	+	0.0597109i
$970$		0			0
$971$	9.89863	+	7.19178i	0.317662	+	0.230795i	0.735177	−	0.677875i	$-0.237099\pi$
$971$	9.89863	+	7.19178i	0.317662	+	0.230795i	−0.417515	+	0.908670i	$0.637099\pi$
$972$		0			0
$973$	3.42112	−	10.5291i	0.109676	−	0.337548i
$974$		0			0
$975$	16.6237	−	26.7132i	0.532384	−	0.855506i
$976$		0			0
$977$	−10.7898	+	33.2077i	−0.345198	+	1.06241i	0.616280	+	0.787527i	$0.288639\pi$
$977$	−10.7898	+	33.2077i	−0.345198	+	1.06241i	−0.961478	+	0.274882i	$0.911361\pi$
$978$		0			0
$979$	9.83357	+	7.14450i	0.314282	+	0.228339i
$980$		0			0
$981$	3.47922	−	2.52780i	0.111083	−	0.0807065i
$982$		0			0
$983$	−26.6735	+	19.3795i	−0.850753	+	0.618109i	−0.925354	−	0.379105i	$-0.876232\pi$
$983$	−26.6735	+	19.3795i	−0.850753	+	0.618109i	0.0746002	+	0.997214i	$0.476232\pi$
$984$		0			0
$985$	−36.2801	−	33.7691i	−1.15598	−	1.07597i
$986$		0			0
$987$	−4.10294	−	12.6275i	−0.130598	−	0.401939i
$988$		0			0
$989$	−4.53300	+	13.9511i	−0.144141	+	0.443620i
$990$		0			0
$991$	16.1064	+	49.5704i	0.511637	+	1.57466i	0.789319	+	0.613983i	$0.210434\pi$
$991$	16.1064	+	49.5704i	0.511637	+	1.57466i	−0.277682	+	0.960673i	$0.589566\pi$
$992$		0			0
$993$	−8.68812			−0.275709
$994$		0			0
$995$	−10.2098	−	1.24403i	−0.323672	−	0.0394384i
$996$		0			0
$997$	−41.4842	−	30.1400i	−1.31382	−	0.954544i	−0.999987	−	0.00506549i	$-0.998388\pi$
$997$	−41.4842	−	30.1400i	−1.31382	−	0.954544i	−0.313831	−	0.949479i	$-0.601612\pi$
$998$		0			0
$999$	6.71283			0.212385

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	600.2.y.f.121.4	✓	16
25.6	even	5	inner	600.2.y.f.481.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
600.2.y.f.121.4	✓	16	1.1	even	1	trivial
600.2.y.f.481.4	yes	16	25.6	even	5	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 600 = 2^{3} \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	600.y (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.809017 + 0.587785i) q^{3} +(2.21965 + 0.270458i) q^{5} +2.87749 q^{7} +(0.309017 + 0.951057i) q^{9} +(1.66222 - 5.11580i) q^{11} +(-1.94454 - 5.98468i) q^{13} +(1.63676 + 1.52348i) q^{15} +(0.476634 - 0.346295i) q^{17} +(-4.34238 + 3.15492i) q^{19} +(2.32794 + 1.69135i) q^{21} +(-2.68374 + 8.25969i) q^{23} +(4.85371 + 1.20064i) q^{25} +(-0.309017 + 0.951057i) q^{27} +(1.81276 + 1.31705i) q^{29} +(-4.62337 + 3.35907i) q^{31} +(4.35176 - 3.16174i) q^{33} +(6.38702 + 0.778239i) q^{35} +(-2.07438 - 6.38428i) q^{37} +(1.94454 - 5.98468i) q^{39} +(-0.285900 - 0.879909i) q^{41} +1.68906 q^{43} +(0.428689 + 2.19459i) q^{45} +(-3.73299 - 2.71218i) q^{47} +1.27994 q^{49} +0.589152 q^{51} +(7.70817 + 5.60032i) q^{53} +(5.07316 - 10.9057i) q^{55} -5.36747 q^{57} +(4.05678 + 12.4855i) q^{59} +(0.274307 - 0.844229i) q^{61} +(0.889193 + 2.73665i) q^{63} +(-2.69760 - 13.8098i) q^{65} +(-7.75684 + 5.63568i) q^{67} +(-7.02612 + 5.10477i) q^{69} +(6.22696 + 4.52415i) q^{71} +(-3.28892 + 10.1222i) q^{73} +(3.22101 + 3.82428i) q^{75} +(4.78303 - 14.7206i) q^{77} +(2.79943 + 2.03390i) q^{79} +(-0.809017 + 0.587785i) q^{81} +(-9.75075 + 7.08434i) q^{83} +(1.15162 - 0.639744i) q^{85} +(0.692413 + 2.13103i) q^{87} +(-0.698279 + 2.14908i) q^{89} +(-5.59539 - 17.2209i) q^{91} -5.71480 q^{93} +(-10.4918 + 5.82840i) q^{95} +(-15.8693 - 11.5297i) q^{97} +5.37907 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{3} + 7 q^{5} - 10 q^{7} - 4 q^{9} + 9 q^{11} - 12 q^{13} - 2 q^{15} + 7 q^{17} - 9 q^{19} - 10 q^{21} + 7 q^{23} + 11 q^{25} + 4 q^{27} - 29 q^{29} - 2 q^{31} + 11 q^{33} + 30 q^{35} - 14 q^{37}+ \cdots + 4 q^{99}+O(q^{100}) \) 16 * q + 4 * q^3 + 7 * q^5 - 10 * q^7 - 4 * q^9 + 9 * q^11 - 12 * q^13 - 2 * q^15 + 7 * q^17 - 9 * q^19 - 10 * q^21 + 7 * q^23 + 11 * q^25 + 4 * q^27 - 29 * q^29 - 2 * q^31 + 11 * q^33 + 30 * q^35 - 14 * q^37 + 12 * q^39 + 4 * q^41 - 16 * q^43 + 2 * q^45 + 5 * q^47 + 78 * q^49 + 18 * q^51 + 8 * q^53 - 7 * q^55 + 14 * q^57 + 19 * q^59 - 22 * q^61 - 5 * q^63 - 54 * q^65 + 16 * q^67 - 2 * q^69 + 23 * q^71 - 30 * q^73 + 9 * q^75 + 40 * q^77 - 28 * q^79 - 4 * q^81 - 49 * q^83 + 9 * q^85 - 26 * q^87 + 9 * q^89 - 25 * q^91 - 28 * q^93 - 73 * q^95 - 53 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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