LMFDB - Embedded newform 297.2.e.a.199.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [297,2,Mod(100,297)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(297, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([4, 0])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("297.100"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 297 = 3^{3} \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	297.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment:select newform

sage:traces = [2,-2] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(2)] == traces)

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

Self dual:	no
Analytic conductor:	$2.37155694003$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment:defining polynomial gp:f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 99)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			199.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	297.199
Dual form			297.2.e.a.100.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-2.00000 - 3.46410i) q^{7} +4.00000 q^{10} +(0.500000 + 0.866025i) q^{11} +(-2.00000 + 3.46410i) q^{13} +(-4.00000 + 6.92820i) q^{14} +(2.00000 + 3.46410i) q^{16} -4.00000 q^{17} -6.00000 q^{19} +(-2.00000 - 3.46410i) q^{20} +(1.00000 - 1.73205i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{25} +8.00000 q^{26} +8.00000 q^{28} +(-0.500000 + 0.866025i) q^{31} +(4.00000 - 6.92820i) q^{32} +(4.00000 + 6.92820i) q^{34} +8.00000 q^{35} +3.00000 q^{37} +(6.00000 + 10.3923i) q^{38} +(-1.00000 + 1.73205i) q^{41} +(-6.00000 - 10.3923i) q^{43} -2.00000 q^{44} +2.00000 q^{46} +(-3.50000 - 6.06218i) q^{47} +(-4.50000 + 7.79423i) q^{49} +(1.00000 - 1.73205i) q^{50} +(-4.00000 - 6.92820i) q^{52} -3.00000 q^{53} -2.00000 q^{55} +(5.50000 - 9.52628i) q^{59} +2.00000 q^{62} -8.00000 q^{64} +(-4.00000 - 6.92820i) q^{65} +(2.00000 - 3.46410i) q^{67} +(4.00000 - 6.92820i) q^{68} +(-8.00000 - 13.8564i) q^{70} -15.0000 q^{71} -8.00000 q^{73} +(-3.00000 - 5.19615i) q^{74} +(6.00000 - 10.3923i) q^{76} +(2.00000 - 3.46410i) q^{77} +(5.00000 + 8.66025i) q^{79} -8.00000 q^{80} +4.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(4.00000 - 6.92820i) q^{85} +(-12.0000 + 20.7846i) q^{86} -3.00000 q^{89} +16.0000 q^{91} +(-1.00000 - 1.73205i) q^{92} +(-7.00000 + 12.1244i) q^{94} +(6.00000 - 10.3923i) q^{95} +(-8.50000 - 14.7224i) q^{97} +18.0000 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} + 8 q^{10} + q^{11} - 4 q^{13} - 8 q^{14} + 4 q^{16} - 8 q^{17} - 12 q^{19} - 4 q^{20} + 2 q^{22} - q^{23} + q^{25} + 16 q^{26} + 16 q^{28} - q^{31} + 8 q^{32}+ \cdots + 36 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 + 8 * q^10 + q^11 - 4 * q^13 - 8 * q^14 + 4 * q^16 - 8 * q^17 - 12 * q^19 - 4 * q^20 + 2 * q^22 - q^23 + q^25 + 16 * q^26 + 16 * q^28 - q^31 + 8 * q^32 + 8 * q^34 + 16 * q^35 + 6 * q^37 + 12 * q^38 - 2 * q^41 - 12 * q^43 - 4 * q^44 + 4 * q^46 - 7 * q^47 - 9 * q^49 + 2 * q^50 - 8 * q^52 - 6 * q^53 - 4 * q^55 + 11 * q^59 + 4 * q^62 - 16 * q^64 - 8 * q^65 + 4 * q^67 + 8 * q^68 - 16 * q^70 - 30 * q^71 - 16 * q^73 - 6 * q^74 + 12 * q^76 + 4 * q^77 + 10 * q^79 - 16 * q^80 + 8 * q^82 + 12 * q^83 + 8 * q^85 - 24 * q^86 - 6 * q^89 + 32 * q^91 - 2 * q^92 - 14 * q^94 + 12 * q^95 - 17 * q^97 + 36 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/297\mathbb{Z}\right)^\times$.

$n$	$56$	$244$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	−0.965926	−	0.258819i	$-0.916667\pi$
$2$	−1.00000	−	1.73205i	−0.707107	−	1.22474i	0.258819	−	0.965926i	$-0.416667\pi$
$3$		0			0
$3$		0			0
$4$	−1.00000	+	1.73205i	−0.500000	+	0.866025i
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	−0.998203	−	0.0599153i	$-0.980917\pi$
$5$	−1.00000	+	1.73205i	−0.447214	+	0.774597i	0.550990	+	0.834512i	$0.314250\pi$
$6$		0			0
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	−0.944911	−	0.327327i	$-0.893852\pi$
$7$	−2.00000	−	3.46410i	−0.755929	−	1.30931i	0.188982	−	0.981981i	$-0.439481\pi$
$8$		0			0
$9$		0			0
$10$	4.00000			1.26491
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$11$	0.500000	+	0.866025i	0.150756	+	0.261116i
$12$		0			0
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	0.443227	+	0.896410i	$0.353834\pi$
$13$	−2.00000	+	3.46410i	−0.554700	+	0.960769i	−0.997927	+	0.0643593i	$0.979500\pi$
$14$	−4.00000	+	6.92820i	−1.06904	+	1.85164i
$15$		0			0
$16$	2.00000	+	3.46410i	0.500000	+	0.866025i
$17$	−4.00000			−0.970143			−0.485071	−	0.874475i	$-0.661206\pi$
$17$	−4.00000			−0.970143			−0.485071	+	0.874475i	$0.661206\pi$
$18$		0			0
$19$	−6.00000			−1.37649			−0.688247	−	0.725476i	$-0.741620\pi$
$19$	−6.00000			−1.37649			−0.688247	+	0.725476i	$0.741620\pi$
$20$	−2.00000	−	3.46410i	−0.447214	−	0.774597i
$21$		0			0
$22$	1.00000	−	1.73205i	0.213201	−	0.369274i
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	−0.913434	−	0.406986i	$-0.866580\pi$
$23$	−0.500000	+	0.866025i	−0.104257	+	0.180579i	0.809177	+	0.587565i	$0.199913\pi$
$24$		0			0
$25$	0.500000	+	0.866025i	0.100000	+	0.173205i
$26$	8.00000			1.56893
$27$		0			0
$28$	8.00000			1.51186
$29$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$29$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$30$		0			0
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	−0.907428	−	0.420208i	$-0.861957\pi$
$31$	−0.500000	+	0.866025i	−0.0898027	+	0.155543i	0.817625	+	0.575751i	$0.195290\pi$
$32$	4.00000	−	6.92820i	0.707107	−	1.22474i
$33$		0			0
$34$	4.00000	+	6.92820i	0.685994	+	1.18818i
$35$	8.00000			1.35225
$36$		0			0
$37$	3.00000			0.493197			0.246598	−	0.969118i	$-0.420687\pi$
$37$	3.00000			0.493197			0.246598	+	0.969118i	$0.420687\pi$
$38$	6.00000	+	10.3923i	0.973329	+	1.68585i
$39$		0			0
$40$		0			0
$41$	−1.00000	+	1.73205i	−0.156174	+	0.270501i	−0.933486	−	0.358614i	$-0.883249\pi$
$41$	−1.00000	+	1.73205i	−0.156174	+	0.270501i	0.777312	+	0.629115i	$0.216583\pi$
$42$		0			0
$43$	−6.00000	−	10.3923i	−0.914991	−	1.58481i	−0.806914	−	0.590669i	$-0.798864\pi$
$43$	−6.00000	−	10.3923i	−0.914991	−	1.58481i	−0.108078	−	0.994142i	$-0.534469\pi$
$44$	−2.00000			−0.301511
$45$		0			0
$46$	2.00000			0.294884
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	−0.999926	−	0.0121990i	$-0.996117\pi$
$47$	−3.50000	−	6.06218i	−0.510527	−	0.884260i	0.489398	−	0.872060i	$-0.337217\pi$
$48$		0			0
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	1.00000	−	1.73205i	0.141421	−	0.244949i
$51$		0			0
$52$	−4.00000	−	6.92820i	−0.554700	−	0.960769i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$		0			0
$55$	−2.00000			−0.269680
$56$		0			0
$57$		0			0
$58$		0			0
$59$	5.50000	−	9.52628i	0.716039	−	1.24022i	−0.246518	−	0.969138i	$-0.579287\pi$
$59$	5.50000	−	9.52628i	0.716039	−	1.24022i	0.962557	−	0.271078i	$-0.0873801\pi$
$60$		0			0
$61$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$61$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$62$	2.00000			0.254000
$63$		0			0
$64$	−8.00000			−1.00000
$65$	−4.00000	−	6.92820i	−0.496139	−	0.859338i
$66$		0			0
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	−0.717607	−	0.696449i	$-0.754762\pi$
$67$	2.00000	−	3.46410i	0.244339	−	0.423207i	0.961946	+	0.273241i	$0.0880957\pi$
$68$	4.00000	−	6.92820i	0.485071	−	0.840168i
$69$		0			0
$70$	−8.00000	−	13.8564i	−0.956183	−	1.65616i
$71$	−15.0000			−1.78017			−0.890086	−	0.455792i	$-0.849356\pi$
$71$	−15.0000			−1.78017			−0.890086	+	0.455792i	$0.849356\pi$
$72$		0			0
$73$	−8.00000			−0.936329			−0.468165	−	0.883641i	$-0.655085\pi$
$73$	−8.00000			−0.936329			−0.468165	+	0.883641i	$0.655085\pi$
$74$	−3.00000	−	5.19615i	−0.348743	−	0.604040i
$75$		0			0
$76$	6.00000	−	10.3923i	0.688247	−	1.19208i
$77$	2.00000	−	3.46410i	0.227921	−	0.394771i
$78$		0			0
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	0.997274	+	0.0737937i	$0.0235106\pi$
$79$	5.00000	+	8.66025i	0.562544	+	0.974355i	−0.434730	+	0.900561i	$0.643156\pi$
$80$	−8.00000			−0.894427
$81$		0			0
$82$	4.00000			0.441726
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	0.980982	+	0.194099i	$0.0621783\pi$
$83$	6.00000	+	10.3923i	0.658586	+	1.14070i	−0.322396	+	0.946605i	$0.604488\pi$
$84$		0			0
$85$	4.00000	−	6.92820i	0.433861	−	0.751469i
$86$	−12.0000	+	20.7846i	−1.29399	+	2.24126i
$87$		0			0
$88$		0			0
$89$	−3.00000			−0.317999			−0.159000	−	0.987279i	$-0.550827\pi$
$89$	−3.00000			−0.317999			−0.159000	+	0.987279i	$0.550827\pi$
$90$		0			0
$91$	16.0000			1.67726
$92$	−1.00000	−	1.73205i	−0.104257	−	0.180579i
$93$		0			0
$94$	−7.00000	+	12.1244i	−0.721995	+	1.25053i
$95$	6.00000	−	10.3923i	0.615587	−	1.06623i
$96$		0			0
$97$	−8.50000	−	14.7224i	−0.863044	−	1.49484i	−0.868976	−	0.494854i	$-0.835222\pi$
$97$	−8.50000	−	14.7224i	−0.863044	−	1.49484i	0.00593185	−	0.999982i	$-0.498112\pi$
$98$	18.0000			1.81827
$99$		0			0
$100$	−2.00000			−0.200000
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	0.911479	−	0.411346i	$-0.134941\pi$
$101$	1.00000	+	1.73205i	0.0995037	+	0.172345i	−0.811976	+	0.583691i	$0.801608\pi$
$102$		0			0
$103$	0.500000	−	0.866025i	0.0492665	−	0.0853320i	−0.840341	−	0.542059i	$-0.817645\pi$
$103$	0.500000	−	0.866025i	0.0492665	−	0.0853320i	0.889607	+	0.456727i	$0.150978\pi$
$104$		0			0
$105$		0			0
$106$	3.00000	+	5.19615i	0.291386	+	0.504695i
$107$	6.00000			0.580042			0.290021	−	0.957020i	$-0.406338\pi$
$107$	6.00000			0.580042			0.290021	+	0.957020i	$0.406338\pi$
$108$		0			0
$109$	10.0000			0.957826			0.478913	−	0.877862i	$-0.341031\pi$
$109$	10.0000			0.957826			0.478913	+	0.877862i	$0.341031\pi$
$110$	2.00000	+	3.46410i	0.190693	+	0.330289i
$111$		0			0
$112$	8.00000	−	13.8564i	0.755929	−	1.30931i
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	−0.927914	−	0.372794i	$-0.878400\pi$
$113$	−1.50000	+	2.59808i	−0.141108	+	0.244406i	0.786806	+	0.617200i	$0.211733\pi$
$114$		0			0
$115$	−1.00000	−	1.73205i	−0.0932505	−	0.161515i
$116$		0			0
$117$		0			0
$118$	−22.0000			−2.02526
$119$	8.00000	+	13.8564i	0.733359	+	1.27021i
$120$		0			0
$121$	−0.500000	+	0.866025i	−0.0454545	+	0.0787296i
$122$		0			0
$123$		0			0
$124$	−1.00000	−	1.73205i	−0.0898027	−	0.155543i
$125$	−12.0000			−1.07331
$126$		0			0
$127$	2.00000			0.177471			0.0887357	−	0.996055i	$-0.471717\pi$
$127$	2.00000			0.177471			0.0887357	+	0.996055i	$0.471717\pi$
$128$		0			0
$129$		0			0
$130$	−8.00000	+	13.8564i	−0.701646	+	1.21529i
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	−0.141865	−	0.989886i	$-0.545310\pi$
$131$	9.00000	−	15.5885i	0.786334	−	1.36197i	0.928199	−	0.372084i	$-0.121357\pi$
$132$		0			0
$133$	12.0000	+	20.7846i	1.04053	+	1.80225i
$134$	−8.00000			−0.691095
$135$		0			0
$136$		0			0
$137$	−3.50000	−	6.06218i	−0.299025	−	0.517927i	0.676888	−	0.736086i	$-0.263328\pi$
$137$	−3.50000	−	6.06218i	−0.299025	−	0.517927i	−0.975913	+	0.218159i	$0.929995\pi$
$138$		0			0
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	0.296866	+	0.954919i	$0.404058\pi$
$139$	−8.00000	+	13.8564i	−0.678551	+	1.17529i	−0.975417	+	0.220366i	$0.929275\pi$
$140$	−8.00000	+	13.8564i	−0.676123	+	1.17108i
$141$		0			0
$142$	15.0000	+	25.9808i	1.25877	+	2.18026i
$143$	−4.00000			−0.334497
$144$		0			0
$145$		0			0
$146$	8.00000	+	13.8564i	0.662085	+	1.14676i
$147$		0			0
$148$	−3.00000	+	5.19615i	−0.246598	+	0.427121i
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	−0.822153	−	0.569267i	$-0.807227\pi$
$149$	1.00000	−	1.73205i	0.0819232	−	0.141895i	0.904076	+	0.427372i	$0.140560\pi$
$150$		0			0
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	0.994540	−	0.104357i	$-0.0332784\pi$
$151$	5.00000	+	8.66025i	0.406894	+	0.704761i	−0.587646	+	0.809118i	$0.699945\pi$
$152$		0			0
$153$		0			0
$154$	−8.00000			−0.644658
$155$	−1.00000	−	1.73205i	−0.0803219	−	0.139122i
$156$		0			0
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	0.438948	+	0.898513i	$0.355351\pi$
$157$	−7.00000	+	12.1244i	−0.558661	+	0.967629i	−0.997609	+	0.0691164i	$0.977982\pi$
$158$	10.0000	−	17.3205i	0.795557	−	1.37795i
$159$		0			0
$160$	8.00000	+	13.8564i	0.632456	+	1.09545i
$161$	4.00000			0.315244
$162$		0			0
$163$	13.0000			1.01824			0.509119	−	0.860696i	$-0.329971\pi$
$163$	13.0000			1.01824			0.509119	+	0.860696i	$0.329971\pi$
$164$	−2.00000	−	3.46410i	−0.156174	−	0.270501i
$165$		0			0
$166$	12.0000	−	20.7846i	0.931381	−	1.61320i
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	0.273252	+	0.961943i	$0.411901\pi$
$167$	−9.00000	+	15.5885i	−0.696441	+	1.20627i	−0.969693	+	0.244328i	$0.921432\pi$
$168$		0			0
$169$	−1.50000	−	2.59808i	−0.115385	−	0.199852i
$170$	−16.0000			−1.22714
$171$		0			0
$172$	24.0000			1.82998
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	0.957241	−	0.289292i	$-0.0934200\pi$
$173$	3.00000	+	5.19615i	0.228086	+	0.395056i	−0.729155	+	0.684349i	$0.760087\pi$
$174$		0			0
$175$	2.00000	−	3.46410i	0.151186	−	0.261861i
$176$	−2.00000	+	3.46410i	−0.150756	+	0.261116i
$177$		0			0
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	12.0000			0.896922			0.448461	−	0.893802i	$-0.351972\pi$
$179$	12.0000			0.896922			0.448461	+	0.893802i	$0.351972\pi$
$180$		0			0
$181$	−14.0000			−1.04061			−0.520306	−	0.853980i	$-0.674182\pi$
$181$	−14.0000			−1.04061			−0.520306	+	0.853980i	$0.674182\pi$
$182$	−16.0000	−	27.7128i	−1.18600	−	2.05421i
$183$		0			0
$184$		0			0
$185$	−3.00000	+	5.19615i	−0.220564	+	0.382029i
$186$		0			0
$187$	−2.00000	−	3.46410i	−0.146254	−	0.253320i
$188$	14.0000			1.02105
$189$		0			0
$190$	−24.0000			−1.74114
$191$	10.0000	+	17.3205i	0.723575	+	1.25327i	0.959558	+	0.281511i	$0.0908356\pi$
$191$	10.0000	+	17.3205i	0.723575	+	1.25327i	−0.235983	+	0.971757i	$0.575831\pi$
$192$		0			0
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	−0.496119	−	0.868255i	$-0.665242\pi$
$193$	7.00000	−	12.1244i	0.503871	−	0.872730i	0.999990	−	0.00447566i	$-0.00142465\pi$
$194$	−17.0000	+	29.4449i	−1.22053	+	2.11402i
$195$		0			0
$196$	−9.00000	−	15.5885i	−0.642857	−	1.11346i
$197$	2.00000			0.142494			0.0712470	−	0.997459i	$-0.477302\pi$
$197$	2.00000			0.142494			0.0712470	+	0.997459i	$0.477302\pi$
$198$		0			0
$199$	−15.0000			−1.06332			−0.531661	−	0.846957i	$-0.678432\pi$
$199$	−15.0000			−1.06332			−0.531661	+	0.846957i	$0.678432\pi$
$200$		0			0
$201$		0			0
$202$	2.00000	−	3.46410i	0.140720	−	0.243733i
$203$		0			0
$204$		0			0
$205$	−2.00000	−	3.46410i	−0.139686	−	0.241943i
$206$	−2.00000			−0.139347
$207$		0			0
$208$	−16.0000			−1.10940
$209$	−3.00000	−	5.19615i	−0.207514	−	0.359425i
$210$		0			0
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	−0.582165	−	0.813070i	$-0.697794\pi$
$211$	6.00000	−	10.3923i	0.413057	−	0.715436i	0.995222	+	0.0976347i	$0.0311277\pi$
$212$	3.00000	−	5.19615i	0.206041	−	0.356873i
$213$		0			0
$214$	−6.00000	−	10.3923i	−0.410152	−	0.710403i
$215$	24.0000			1.63679
$216$		0			0
$217$	4.00000			0.271538
$218$	−10.0000	−	17.3205i	−0.677285	−	1.17309i
$219$		0			0
$220$	2.00000	−	3.46410i	0.134840	−	0.233550i
$221$	8.00000	−	13.8564i	0.538138	−	0.932083i
$222$		0			0
$223$	−3.50000	−	6.06218i	−0.234377	−	0.405953i	0.724714	−	0.689050i	$-0.241972\pi$
$223$	−3.50000	−	6.06218i	−0.234377	−	0.405953i	−0.959092	+	0.283096i	$0.908638\pi$
$224$	−32.0000			−2.13809
$225$		0			0
$226$	6.00000			0.399114
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	0.595274	−	0.803523i	$-0.297043\pi$
$227$	−6.00000	−	10.3923i	−0.398234	−	0.689761i	−0.993508	+	0.113761i	$0.963710\pi$
$228$		0			0
$229$	−1.50000	+	2.59808i	−0.0991228	+	0.171686i	−0.911322	−	0.411695i	$-0.864937\pi$
$229$	−1.50000	+	2.59808i	−0.0991228	+	0.171686i	0.812199	+	0.583380i	$0.198270\pi$
$230$	−2.00000	+	3.46410i	−0.131876	+	0.228416i
$231$		0			0
$232$		0			0
$233$		0			0			−	1.00000i	$-0.5\pi$
$233$		0			0				1.00000i	$0.5\pi$
$234$		0			0
$235$	14.0000			0.913259
$236$	11.0000	+	19.0526i	0.716039	+	1.24022i
$237$		0			0
$238$	16.0000	−	27.7128i	1.03713	−	1.79635i
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	0.157893	+	0.987456i	$0.449530\pi$
$239$	−12.0000	+	20.7846i	−0.776215	+	1.34444i	−0.934109	+	0.356988i	$0.883804\pi$
$240$		0			0
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	0.658838	−	0.752285i	$-0.271048\pi$
$241$	−5.00000	−	8.66025i	−0.322078	−	0.557856i	−0.980917	+	0.194429i	$0.937715\pi$
$242$	2.00000			0.128565
$243$		0			0
$244$		0			0
$245$	−9.00000	−	15.5885i	−0.574989	−	0.995910i
$246$		0			0
$247$	12.0000	−	20.7846i	0.763542	−	1.32249i
$248$		0			0
$249$		0			0
$250$	12.0000	+	20.7846i	0.758947	+	1.31453i
$251$	−13.0000			−0.820553			−0.410276	−	0.911961i	$-0.634568\pi$
$251$	−13.0000			−0.820553			−0.410276	+	0.911961i	$0.634568\pi$
$252$		0			0
$253$	−1.00000			−0.0628695
$254$	−2.00000	−	3.46410i	−0.125491	−	0.217357i
$255$		0			0
$256$	−8.00000	+	13.8564i	−0.500000	+	0.866025i
$257$	−13.0000	+	22.5167i	−0.810918	+	1.40455i	0.101305	+	0.994855i	$0.467698\pi$
$257$	−13.0000	+	22.5167i	−0.810918	+	1.40455i	−0.912222	+	0.409695i	$0.865635\pi$
$258$		0			0
$259$	−6.00000	−	10.3923i	−0.372822	−	0.645746i
$260$	16.0000			0.992278
$261$		0			0
$262$	−36.0000			−2.22409
$263$	1.00000	+	1.73205i	0.0616626	+	0.106803i	0.895209	−	0.445647i	$-0.147026\pi$
$263$	1.00000	+	1.73205i	0.0616626	+	0.106803i	−0.833546	+	0.552450i	$0.813693\pi$
$264$		0			0
$265$	3.00000	−	5.19615i	0.184289	−	0.319197i
$266$	24.0000	−	41.5692i	1.47153	−	2.54877i
$267$		0			0
$268$	4.00000	+	6.92820i	0.244339	+	0.423207i
$269$	5.00000			0.304855			0.152428	−	0.988315i	$-0.451291\pi$
$269$	5.00000			0.304855			0.152428	+	0.988315i	$0.451291\pi$
$270$		0			0
$271$	2.00000			0.121491			0.0607457	−	0.998153i	$-0.480652\pi$
$271$	2.00000			0.121491			0.0607457	+	0.998153i	$0.480652\pi$
$272$	−8.00000	−	13.8564i	−0.485071	−	0.840168i
$273$		0			0
$274$	−7.00000	+	12.1244i	−0.422885	+	0.732459i
$275$	−0.500000	+	0.866025i	−0.0301511	+	0.0522233i
$276$		0			0
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	0.894503	−	0.447062i	$-0.147530\pi$
$277$	1.00000	+	1.73205i	0.0600842	+	0.104069i	−0.834419	+	0.551131i	$0.814196\pi$
$278$	32.0000			1.91923
$279$		0			0
$280$		0			0
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	0.762561	−	0.646916i	$-0.223942\pi$
$281$	−3.00000	−	5.19615i	−0.178965	−	0.309976i	−0.941526	+	0.336939i	$0.890608\pi$
$282$		0			0
$283$	1.00000	−	1.73205i	0.0594438	−	0.102960i	−0.834772	−	0.550596i	$-0.814401\pi$
$283$	1.00000	−	1.73205i	0.0594438	−	0.102960i	0.894216	+	0.447636i	$0.147734\pi$
$284$	15.0000	−	25.9808i	0.890086	−	1.54167i
$285$		0			0
$286$	4.00000	+	6.92820i	0.236525	+	0.409673i
$287$	8.00000			0.472225
$288$		0			0
$289$	−1.00000			−0.0588235
$290$		0			0
$291$		0			0
$292$	8.00000	−	13.8564i	0.468165	−	0.810885i
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	0.473763	+	0.880652i	$0.342895\pi$
$293$	−9.00000	+	15.5885i	−0.525786	+	0.910687i	−0.999549	+	0.0300351i	$0.990438\pi$
$294$		0			0
$295$	11.0000	+	19.0526i	0.640445	+	1.10928i
$296$		0			0
$297$		0			0
$298$	−4.00000			−0.231714
$299$	−2.00000	−	3.46410i	−0.115663	−	0.200334i
$300$		0			0
$301$	−24.0000	+	41.5692i	−1.38334	+	2.39601i
$302$	10.0000	−	17.3205i	0.575435	−	0.996683i
$303$		0			0
$304$	−12.0000	−	20.7846i	−0.688247	−	1.19208i
$305$		0			0
$306$		0			0
$307$	20.0000			1.14146			0.570730	−	0.821138i	$-0.306660\pi$
$307$	20.0000			1.14146			0.570730	+	0.821138i	$0.306660\pi$
$308$	4.00000	+	6.92820i	0.227921	+	0.394771i
$309$		0			0
$310$	−2.00000	+	3.46410i	−0.113592	+	0.196748i
$311$	1.50000	−	2.59808i	0.0850572	−	0.147323i	−0.820358	−	0.571850i	$-0.806226\pi$
$311$	1.50000	−	2.59808i	0.0850572	−	0.147323i	0.905416	+	0.424526i	$0.139559\pi$
$312$		0			0
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	0.667674	−	0.744453i	$-0.267290\pi$
$313$	−5.50000	−	9.52628i	−0.310878	−	0.538457i	−0.978553	+	0.205996i	$0.933957\pi$
$314$	28.0000			1.58013
$315$		0			0
$316$	−20.0000			−1.12509
$317$	6.50000	+	11.2583i	0.365076	+	0.632331i	0.988788	−	0.149323i	$-0.0477095\pi$
$317$	6.50000	+	11.2583i	0.365076	+	0.632331i	−0.623712	+	0.781654i	$0.714376\pi$
$318$		0			0
$319$		0			0
$320$	8.00000	−	13.8564i	0.447214	−	0.774597i
$321$		0			0
$322$	−4.00000	−	6.92820i	−0.222911	−	0.386094i
$323$	24.0000			1.33540
$324$		0			0
$325$	−4.00000			−0.221880
$326$	−13.0000	−	22.5167i	−0.720003	−	1.24708i
$327$		0			0
$328$		0			0
$329$	−14.0000	+	24.2487i	−0.771845	+	1.33687i
$330$		0			0
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	0.805812	−	0.592172i	$-0.201729\pi$
$331$	−2.00000	−	3.46410i	−0.109930	−	0.190404i	−0.915742	+	0.401768i	$0.868396\pi$
$332$	−24.0000			−1.31717
$333$		0			0
$334$	36.0000			1.96983
$335$	4.00000	+	6.92820i	0.218543	+	0.378528i
$336$		0			0
$337$	−16.0000	+	27.7128i	−0.871576	+	1.50961i	−0.0112091	+	0.999937i	$0.503568\pi$
$337$	−16.0000	+	27.7128i	−0.871576	+	1.50961i	−0.860366	+	0.509676i	$0.829765\pi$
$338$	−3.00000	+	5.19615i	−0.163178	+	0.282633i
$339$		0			0
$340$	8.00000	+	13.8564i	0.433861	+	0.751469i
$341$	−1.00000			−0.0541530
$342$		0			0
$343$	8.00000			0.431959
$344$		0			0
$345$		0			0
$346$	6.00000	−	10.3923i	0.322562	−	0.558694i
$347$	−1.00000	+	1.73205i	−0.0536828	+	0.0929814i	−0.891618	−	0.452788i	$-0.850429\pi$
$347$	−1.00000	+	1.73205i	−0.0536828	+	0.0929814i	0.837935	+	0.545770i	$0.183763\pi$
$348$		0			0
$349$	−3.00000	−	5.19615i	−0.160586	−	0.278144i	0.774493	−	0.632583i	$-0.218005\pi$
$349$	−3.00000	−	5.19615i	−0.160586	−	0.278144i	−0.935079	+	0.354439i	$0.884672\pi$
$350$	−8.00000			−0.427618
$351$		0			0
$352$	8.00000			0.426401
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	0.903179	−	0.429263i	$-0.141227\pi$
$353$	1.50000	+	2.59808i	0.0798369	+	0.138282i	−0.823343	+	0.567545i	$0.807893\pi$
$354$		0			0
$355$	15.0000	−	25.9808i	0.796117	−	1.37892i
$356$	3.00000	−	5.19615i	0.159000	−	0.275396i
$357$		0			0
$358$	−12.0000	−	20.7846i	−0.634220	−	1.09850i
$359$	−10.0000			−0.527780			−0.263890	−	0.964553i	$-0.585006\pi$
$359$	−10.0000			−0.527780			−0.263890	+	0.964553i	$0.585006\pi$
$360$		0			0
$361$	17.0000			0.894737
$362$	14.0000	+	24.2487i	0.735824	+	1.27448i
$363$		0			0
$364$	−16.0000	+	27.7128i	−0.838628	+	1.45255i
$365$	8.00000	−	13.8564i	0.418739	−	0.725277i
$366$		0			0
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	0.951336	−	0.308155i	$-0.0997115\pi$
$367$	4.00000	+	6.92820i	0.208798	+	0.361649i	−0.742538	+	0.669804i	$0.766378\pi$
$368$	−4.00000			−0.208514
$369$		0			0
$370$	12.0000			0.623850
$371$	6.00000	+	10.3923i	0.311504	+	0.539542i
$372$		0			0
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	0.427051	+	0.904227i	$0.359552\pi$
$373$	−11.0000	+	19.0526i	−0.569558	+	0.986504i	−0.996610	+	0.0822766i	$0.973781\pi$
$374$	−4.00000	+	6.92820i	−0.206835	+	0.358249i
$375$		0			0
$376$		0			0
$377$		0			0
$378$		0			0
$379$	−29.0000			−1.48963			−0.744815	−	0.667271i	$-0.767462\pi$
$379$	−29.0000			−1.48963			−0.744815	+	0.667271i	$0.767462\pi$
$380$	12.0000	+	20.7846i	0.615587	+	1.06623i
$381$		0			0
$382$	20.0000	−	34.6410i	1.02329	−	1.77239i
$383$	4.00000	−	6.92820i	0.204390	−	0.354015i	−0.745548	−	0.666452i	$-0.767812\pi$
$383$	4.00000	−	6.92820i	0.204390	−	0.354015i	0.949938	+	0.312437i	$0.101145\pi$
$384$		0			0
$385$	4.00000	+	6.92820i	0.203859	+	0.353094i
$386$	−28.0000			−1.42516
$387$		0			0
$388$	34.0000			1.72609
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	0.957263	−	0.289220i	$-0.0933960\pi$
$389$	4.50000	+	7.79423i	0.228159	+	0.395183i	−0.729103	+	0.684403i	$0.760063\pi$
$390$		0			0
$391$	2.00000	−	3.46410i	0.101144	−	0.175187i
$392$		0			0
$393$		0			0
$394$	−2.00000	−	3.46410i	−0.100759	−	0.174519i
$395$	−20.0000			−1.00631
$396$		0			0
$397$	25.0000			1.25471			0.627357	−	0.778732i	$-0.284137\pi$
$397$	25.0000			1.25471			0.627357	+	0.778732i	$0.284137\pi$
$398$	15.0000	+	25.9808i	0.751882	+	1.30230i
$399$		0			0
$400$	−2.00000	+	3.46410i	−0.100000	+	0.173205i
$401$	14.5000	−	25.1147i	0.724095	−	1.25417i	−0.235250	−	0.971935i	$-0.575591\pi$
$401$	14.5000	−	25.1147i	0.724095	−	1.25417i	0.959345	−	0.282235i	$-0.0910758\pi$
$402$		0			0
$403$	−2.00000	−	3.46410i	−0.0996271	−	0.172559i
$404$	−4.00000			−0.199007
$405$		0			0
$406$		0			0
$407$	1.50000	+	2.59808i	0.0743522	+	0.128782i
$408$		0			0
$409$	−9.00000	+	15.5885i	−0.445021	+	0.770800i	−0.998054	−	0.0623602i	$-0.980137\pi$
$409$	−9.00000	+	15.5885i	−0.445021	+	0.770800i	0.553032	+	0.833160i	$0.313471\pi$
$410$	−4.00000	+	6.92820i	−0.197546	+	0.342160i
$411$		0			0
$412$	1.00000	+	1.73205i	0.0492665	+	0.0853320i
$413$	−44.0000			−2.16510
$414$		0			0
$415$	−24.0000			−1.17811
$416$	16.0000	+	27.7128i	0.784465	+	1.35873i
$417$		0			0
$418$	−6.00000	+	10.3923i	−0.293470	+	0.508304i
$419$	−3.50000	+	6.06218i	−0.170986	+	0.296157i	−0.938765	−	0.344558i	$-0.888029\pi$
$419$	−3.50000	+	6.06218i	−0.170986	+	0.296157i	0.767779	+	0.640715i	$0.221362\pi$
$420$		0			0
$421$	−18.5000	−	32.0429i	−0.901635	−	1.56168i	−0.825372	−	0.564590i	$-0.809034\pi$
$421$	−18.5000	−	32.0429i	−0.901635	−	1.56168i	−0.0762630	−	0.997088i	$-0.524299\pi$
$422$	−24.0000			−1.16830
$423$		0			0
$424$		0			0
$425$	−2.00000	−	3.46410i	−0.0970143	−	0.168034i
$426$		0			0
$427$		0			0
$428$	−6.00000	+	10.3923i	−0.290021	+	0.502331i
$429$		0			0
$430$	−24.0000	−	41.5692i	−1.15738	−	2.00465i
$431$	−12.0000			−0.578020			−0.289010	−	0.957326i	$-0.593326\pi$
$431$	−12.0000			−0.578020			−0.289010	+	0.957326i	$0.593326\pi$
$432$		0			0
$433$	13.0000			0.624740			0.312370	−	0.949960i	$-0.398877\pi$
$433$	13.0000			0.624740			0.312370	+	0.949960i	$0.398877\pi$
$434$	−4.00000	−	6.92820i	−0.192006	−	0.332564i
$435$		0			0
$436$	−10.0000	+	17.3205i	−0.478913	+	0.829502i
$437$	3.00000	−	5.19615i	0.143509	−	0.248566i
$438$		0			0
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	0.999661	−	0.0260459i	$-0.00829161\pi$
$439$	10.0000	+	17.3205i	0.477274	+	0.826663i	−0.522387	+	0.852709i	$0.674958\pi$
$440$		0			0
$441$		0			0
$442$	−32.0000			−1.52208
$443$	−20.5000	−	35.5070i	−0.973984	−	1.68699i	−0.683247	−	0.730188i	$-0.739433\pi$
$443$	−20.5000	−	35.5070i	−0.973984	−	1.68699i	−0.290738	−	0.956803i	$-0.593901\pi$
$444$		0			0
$445$	3.00000	−	5.19615i	0.142214	−	0.246321i
$446$	−7.00000	+	12.1244i	−0.331460	+	0.574105i
$447$		0			0
$448$	16.0000	+	27.7128i	0.755929	+	1.30931i
$449$	1.00000			0.0471929			0.0235965	−	0.999722i	$-0.492488\pi$
$449$	1.00000			0.0471929			0.0235965	+	0.999722i	$0.492488\pi$
$450$		0			0
$451$	−2.00000			−0.0941763
$452$	−3.00000	−	5.19615i	−0.141108	−	0.244406i
$453$		0			0
$454$	−12.0000	+	20.7846i	−0.563188	+	0.975470i
$455$	−16.0000	+	27.7128i	−0.750092	+	1.29920i
$456$		0			0
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	0.996038	−	0.0889312i	$-0.0283451\pi$
$457$	9.00000	+	15.5885i	0.421002	+	0.729197i	−0.575036	+	0.818128i	$0.695012\pi$
$458$	6.00000			0.280362
$459$		0			0
$460$	4.00000			0.186501
$461$	−15.0000	−	25.9808i	−0.698620	−	1.21004i	−0.968945	−	0.247276i	$-0.920465\pi$
$461$	−15.0000	−	25.9808i	−0.698620	−	1.21004i	0.270326	−	0.962769i	$-0.412869\pi$
$462$		0			0
$463$	17.5000	−	30.3109i	0.813294	−	1.40867i	−0.0972525	−	0.995260i	$-0.531005\pi$
$463$	17.5000	−	30.3109i	0.813294	−	1.40867i	0.910546	−	0.413407i	$-0.135661\pi$
$464$		0			0
$465$		0			0
$466$		0			0
$467$	36.0000			1.66588			0.832941	−	0.553362i	$-0.186655\pi$
$467$	36.0000			1.66588			0.832941	+	0.553362i	$0.186655\pi$
$468$		0			0
$469$	−16.0000			−0.738811
$470$	−14.0000	−	24.2487i	−0.645772	−	1.11851i
$471$		0			0
$472$		0			0
$473$	6.00000	−	10.3923i	0.275880	−	0.477839i
$474$		0			0
$475$	−3.00000	−	5.19615i	−0.137649	−	0.238416i
$476$	−32.0000			−1.46672
$477$		0			0
$478$	48.0000			2.19547
$479$	−17.0000	−	29.4449i	−0.776750	−	1.34537i	−0.933806	−	0.357780i	$-0.883534\pi$
$479$	−17.0000	−	29.4449i	−0.776750	−	1.34537i	0.157056	−	0.987590i	$-0.449800\pi$
$480$		0			0
$481$	−6.00000	+	10.3923i	−0.273576	+	0.473848i
$482$	−10.0000	+	17.3205i	−0.455488	+	0.788928i
$483$		0			0
$484$	−1.00000	−	1.73205i	−0.0454545	−	0.0787296i
$485$	34.0000			1.54386
$486$		0			0
$487$	−19.0000			−0.860972			−0.430486	−	0.902597i	$-0.641658\pi$
$487$	−19.0000			−0.860972			−0.430486	+	0.902597i	$0.641658\pi$
$488$		0			0
$489$		0			0
$490$	−18.0000	+	31.1769i	−0.813157	+	1.40843i
$491$	5.00000	−	8.66025i	0.225647	−	0.390832i	−0.730866	−	0.682520i	$-0.760884\pi$
$491$	5.00000	−	8.66025i	0.225647	−	0.390832i	0.956513	+	0.291689i	$0.0942171\pi$
$492$		0			0
$493$		0			0
$494$	−48.0000			−2.15962
$495$		0			0
$496$	−4.00000			−0.179605
$497$	30.0000	+	51.9615i	1.34568	+	2.33079i
$498$		0			0
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	−0.437955	−	0.898997i	$-0.644297\pi$
$499$	12.5000	−	21.6506i	0.559577	−	0.969216i	0.997532	−	0.0702185i	$-0.0223697\pi$
$500$	12.0000	−	20.7846i	0.536656	−	0.929516i
$501$		0			0
$502$	13.0000	+	22.5167i	0.580218	+	1.00497i
$503$	−10.0000			−0.445878			−0.222939	−	0.974832i	$-0.571565\pi$
$503$	−10.0000			−0.445878			−0.222939	+	0.974832i	$0.571565\pi$
$504$		0			0
$505$	−4.00000			−0.177998
$506$	1.00000	+	1.73205i	0.0444554	+	0.0769991i
$507$		0			0
$508$	−2.00000	+	3.46410i	−0.0887357	+	0.153695i
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	−0.830866	−	0.556473i	$-0.812154\pi$
$509$	1.50000	−	2.59808i	0.0664863	−	0.115158i	0.897352	+	0.441315i	$0.145488\pi$
$510$		0			0
$511$	16.0000	+	27.7128i	0.707798	+	1.22594i
$512$	32.0000			1.41421
$513$		0			0
$514$	52.0000			2.29362
$515$	1.00000	+	1.73205i	0.0440653	+	0.0763233i
$516$		0			0
$517$	3.50000	−	6.06218i	0.153930	−	0.266614i
$518$	−12.0000	+	20.7846i	−0.527250	+	0.913223i
$519$		0			0
$520$		0			0
$521$	27.0000			1.18289			0.591446	−	0.806345i	$-0.298557\pi$
$521$	27.0000			1.18289			0.591446	+	0.806345i	$0.298557\pi$
$522$		0			0
$523$	−34.0000			−1.48672			−0.743358	−	0.668894i	$-0.766768\pi$
$523$	−34.0000			−1.48672			−0.743358	+	0.668894i	$0.766768\pi$
$524$	18.0000	+	31.1769i	0.786334	+	1.36197i
$525$		0			0
$526$	2.00000	−	3.46410i	0.0872041	−	0.151042i
$527$	2.00000	−	3.46410i	0.0871214	−	0.150899i
$528$		0			0
$529$	11.0000	+	19.0526i	0.478261	+	0.828372i
$530$	−12.0000			−0.521247
$531$		0			0
$532$	−48.0000			−2.08106
$533$	−4.00000	−	6.92820i	−0.173259	−	0.300094i
$534$		0			0
$535$	−6.00000	+	10.3923i	−0.259403	+	0.449299i
$536$		0			0
$537$		0			0
$538$	−5.00000	−	8.66025i	−0.215565	−	0.373370i
$539$	−9.00000			−0.387657
$540$		0			0
$541$	16.0000			0.687894			0.343947	−	0.938989i	$-0.388236\pi$
$541$	16.0000			0.687894			0.343947	+	0.938989i	$0.388236\pi$
$542$	−2.00000	−	3.46410i	−0.0859074	−	0.148796i
$543$		0			0
$544$	−16.0000	+	27.7128i	−0.685994	+	1.18818i
$545$	−10.0000	+	17.3205i	−0.428353	+	0.741929i
$546$		0			0
$547$	−1.00000	−	1.73205i	−0.0427569	−	0.0740571i	0.843855	−	0.536571i	$-0.180281\pi$
$547$	−1.00000	−	1.73205i	−0.0427569	−	0.0740571i	−0.886612	+	0.462514i	$0.846947\pi$
$548$	14.0000			0.598050
$549$		0			0
$550$	2.00000			0.0852803
$551$		0			0
$552$		0			0
$553$	20.0000	−	34.6410i	0.850487	−	1.47309i
$554$	2.00000	−	3.46410i	0.0849719	−	0.147176i
$555$		0			0
$556$	−16.0000	−	27.7128i	−0.678551	−	1.17529i
$557$	14.0000			0.593199			0.296600	−	0.955002i	$-0.404147\pi$
$557$	14.0000			0.593199			0.296600	+	0.955002i	$0.404147\pi$
$558$		0			0
$559$	48.0000			2.03018
$560$	16.0000	+	27.7128i	0.676123	+	1.17108i
$561$		0			0
$562$	−6.00000	+	10.3923i	−0.253095	+	0.438373i
$563$	−1.00000	+	1.73205i	−0.0421450	+	0.0729972i	−0.886328	−	0.463057i	$-0.846752\pi$
$563$	−1.00000	+	1.73205i	−0.0421450	+	0.0729972i	0.844183	+	0.536054i	$0.180086\pi$
$564$		0			0
$565$	−3.00000	−	5.19615i	−0.126211	−	0.218604i
$566$	−4.00000			−0.168133
$567$		0			0
$568$		0			0
$569$	−12.0000	−	20.7846i	−0.503066	−	0.871336i	−0.999994	−	0.00354413i	$-0.998872\pi$
$569$	−12.0000	−	20.7846i	−0.503066	−	0.871336i	0.496928	−	0.867792i	$-0.334461\pi$
$570$		0			0
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	−0.648655	−	0.761083i	$-0.724668\pi$
$571$	8.00000	−	13.8564i	0.334790	−	0.579873i	0.983444	+	0.181210i	$0.0580014\pi$
$572$	4.00000	−	6.92820i	0.167248	−	0.289683i
$573$		0			0
$574$	−8.00000	−	13.8564i	−0.333914	−	0.578355i
$575$	−1.00000			−0.0417029
$576$		0			0
$577$	−6.00000			−0.249783			−0.124892	−	0.992170i	$-0.539858\pi$
$577$	−6.00000			−0.249783			−0.124892	+	0.992170i	$0.539858\pi$
$578$	1.00000	+	1.73205i	0.0415945	+	0.0720438i
$579$		0			0
$580$		0			0
$581$	24.0000	−	41.5692i	0.995688	−	1.72458i
$582$		0			0
$583$	−1.50000	−	2.59808i	−0.0621237	−	0.107601i
$584$		0			0
$585$		0			0
$586$	36.0000			1.48715
$587$	−8.50000	−	14.7224i	−0.350833	−	0.607660i	0.635563	−	0.772049i	$-0.280768\pi$
$587$	−8.50000	−	14.7224i	−0.350833	−	0.607660i	−0.986396	+	0.164389i	$0.947435\pi$
$588$		0			0
$589$	3.00000	−	5.19615i	0.123613	−	0.214104i
$590$	22.0000	−	38.1051i	0.905726	−	1.56876i
$591$		0			0
$592$	6.00000	+	10.3923i	0.246598	+	0.427121i
$593$	22.0000			0.903432			0.451716	−	0.892162i	$-0.350812\pi$
$593$	22.0000			0.903432			0.451716	+	0.892162i	$0.350812\pi$
$594$		0			0
$595$	−32.0000			−1.31187
$596$	2.00000	+	3.46410i	0.0819232	+	0.141895i
$597$		0			0
$598$	−4.00000	+	6.92820i	−0.163572	+	0.283315i
$599$	8.00000	−	13.8564i	0.326871	−	0.566157i	−0.655018	−	0.755613i	$-0.727339\pi$
$599$	8.00000	−	13.8564i	0.326871	−	0.566157i	0.981889	+	0.189456i	$0.0606724\pi$
$600$		0			0
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	−0.999376	−	0.0353259i	$-0.988753\pi$
$601$	−13.0000	−	22.5167i	−0.530281	−	0.918474i	0.469095	−	0.883148i	$-0.344580\pi$
$602$	96.0000			3.91267
$603$		0			0
$604$	−20.0000			−0.813788
$605$	−1.00000	−	1.73205i	−0.0406558	−	0.0704179i
$606$		0			0
$607$	2.00000	−	3.46410i	0.0811775	−	0.140604i	−0.822578	−	0.568652i	$-0.807465\pi$
$607$	2.00000	−	3.46410i	0.0811775	−	0.140604i	0.903756	+	0.428048i	$0.140799\pi$
$608$	−24.0000	+	41.5692i	−0.973329	+	1.68585i
$609$		0			0
$610$		0			0
$611$	28.0000			1.13276
$612$		0			0
$613$	14.0000			0.565455			0.282727	−	0.959200i	$-0.408761\pi$
$613$	14.0000			0.565455			0.282727	+	0.959200i	$0.408761\pi$
$614$	−20.0000	−	34.6410i	−0.807134	−	1.39800i
$615$		0			0
$616$		0			0
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	0.455211	+	0.890384i	$0.349564\pi$
$617$	−13.5000	+	23.3827i	−0.543490	+	0.941351i	−0.998700	+	0.0509678i	$0.983769\pi$
$618$		0			0
$619$	15.5000	+	26.8468i	0.622998	+	1.07906i	0.988924	+	0.148420i	$0.0474187\pi$
$619$	15.5000	+	26.8468i	0.622998	+	1.07906i	−0.365927	+	0.930644i	$0.619248\pi$
$620$	4.00000			0.160644
$621$		0			0
$622$	−6.00000			−0.240578
$623$	6.00000	+	10.3923i	0.240385	+	0.416359i
$624$		0			0
$625$	9.50000	−	16.4545i	0.380000	−	0.658179i
$626$	−11.0000	+	19.0526i	−0.439648	+	0.761493i
$627$		0			0
$628$	−14.0000	−	24.2487i	−0.558661	−	0.967629i
$629$	−12.0000			−0.478471
$630$		0			0
$631$	−32.0000			−1.27390			−0.636950	−	0.770905i	$-0.719804\pi$
$631$	−32.0000			−1.27390			−0.636950	+	0.770905i	$0.719804\pi$
$632$		0			0
$633$		0			0
$634$	13.0000	−	22.5167i	0.516296	−	0.894251i
$635$	−2.00000	+	3.46410i	−0.0793676	+	0.137469i
$636$		0			0
$637$	−18.0000	−	31.1769i	−0.713186	−	1.23527i
$638$		0			0
$639$		0			0
$640$		0			0
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	0.937451	+	0.348117i	$0.113179\pi$
$641$	19.5000	+	33.7750i	0.770204	+	1.33403i	−0.167247	+	0.985915i	$0.553488\pi$
$642$		0			0
$643$	−8.50000	+	14.7224i	−0.335207	+	0.580596i	−0.983525	−	0.180774i	$-0.942140\pi$
$643$	−8.50000	+	14.7224i	−0.335207	+	0.580596i	0.648317	+	0.761370i	$0.275473\pi$
$644$	−4.00000	+	6.92820i	−0.157622	+	0.273009i
$645$		0			0
$646$	−24.0000	−	41.5692i	−0.944267	−	1.63552i
$647$	−17.0000			−0.668339			−0.334169	−	0.942513i	$-0.608456\pi$
$647$	−17.0000			−0.668339			−0.334169	+	0.942513i	$0.608456\pi$
$648$		0			0
$649$	11.0000			0.431788
$650$	4.00000	+	6.92820i	0.156893	+	0.271746i
$651$		0			0
$652$	−13.0000	+	22.5167i	−0.509119	+	0.881820i
$653$	9.50000	−	16.4545i	0.371764	−	0.643914i	−0.618073	−	0.786121i	$-0.712086\pi$
$653$	9.50000	−	16.4545i	0.371764	−	0.643914i	0.989837	+	0.142207i	$0.0454198\pi$
$654$		0			0
$655$	18.0000	+	31.1769i	0.703318	+	1.21818i
$656$	−8.00000			−0.312348
$657$		0			0
$658$	56.0000			2.18311
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	0.602844	−	0.797859i	$-0.294034\pi$
$659$	−10.0000	−	17.3205i	−0.389545	−	0.674711i	−0.992388	+	0.123148i	$0.960701\pi$
$660$		0			0
$661$	−18.5000	+	32.0429i	−0.719567	+	1.24633i	0.241605	+	0.970375i	$0.422326\pi$
$661$	−18.5000	+	32.0429i	−0.719567	+	1.24633i	−0.961172	+	0.275951i	$0.911007\pi$
$662$	−4.00000	+	6.92820i	−0.155464	+	0.269272i
$663$		0			0
$664$		0			0
$665$	−48.0000			−1.86136
$666$		0			0
$667$		0			0
$668$	−18.0000	−	31.1769i	−0.696441	−	1.20627i
$669$		0			0
$670$	8.00000	−	13.8564i	0.309067	−	0.535320i
$671$		0			0
$672$		0			0
$673$	−10.0000	−	17.3205i	−0.385472	−	0.667657i	0.606363	−	0.795188i	$-0.292628\pi$
$673$	−10.0000	−	17.3205i	−0.385472	−	0.667657i	−0.991835	+	0.127532i	$0.959295\pi$
$674$	64.0000			2.46519
$675$		0			0
$676$	6.00000			0.230769
$677$	−15.0000	−	25.9808i	−0.576497	−	0.998522i	−0.995877	−	0.0907112i	$-0.971086\pi$
$677$	−15.0000	−	25.9808i	−0.576497	−	0.998522i	0.419380	−	0.907811i	$-0.362247\pi$
$678$		0			0
$679$	−34.0000	+	58.8897i	−1.30480	+	2.25998i
$680$		0			0
$681$		0			0
$682$	1.00000	+	1.73205i	0.0382920	+	0.0663237i
$683$	−29.0000			−1.10965			−0.554827	−	0.831966i	$-0.687216\pi$
$683$	−29.0000			−1.10965			−0.554827	+	0.831966i	$0.687216\pi$
$684$		0			0
$685$	14.0000			0.534913
$686$	−8.00000	−	13.8564i	−0.305441	−	0.529040i
$687$		0			0
$688$	24.0000	−	41.5692i	0.914991	−	1.58481i
$689$	6.00000	−	10.3923i	0.228582	−	0.395915i
$690$		0			0
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	0.901557	−	0.432660i	$-0.142425\pi$
$691$	2.00000	+	3.46410i	0.0760836	+	0.131781i	−0.825473	+	0.564441i	$0.809092\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	4.00000			0.151838
$695$	−16.0000	−	27.7128i	−0.606915	−	1.05121i
$696$		0			0
$697$	4.00000	−	6.92820i	0.151511	−	0.262424i
$698$	−6.00000	+	10.3923i	−0.227103	+	0.393355i
$699$		0			0
$700$	4.00000	+	6.92820i	0.151186	+	0.261861i
$701$	28.0000			1.05755			0.528773	−	0.848763i	$-0.322652\pi$
$701$	28.0000			1.05755			0.528773	+	0.848763i	$0.322652\pi$
$702$		0			0
$703$	−18.0000			−0.678883
$704$	−4.00000	−	6.92820i	−0.150756	−	0.261116i
$705$		0			0
$706$	3.00000	−	5.19615i	0.112906	−	0.195560i
$707$	4.00000	−	6.92820i	0.150435	−	0.260562i
$708$		0			0
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	0.511683	−	0.859174i	$-0.329022\pi$
$709$	−13.0000	−	22.5167i	−0.488225	−	0.845631i	−0.999908	+	0.0135434i	$0.995689\pi$
$710$	−60.0000			−2.25176
$711$		0			0
$712$		0			0
$713$	−0.500000	−	0.866025i	−0.0187251	−	0.0324329i
$714$		0			0
$715$	4.00000	−	6.92820i	0.149592	−	0.259100i
$716$	−12.0000	+	20.7846i	−0.448461	+	0.776757i
$717$		0			0
$718$	10.0000	+	17.3205i	0.373197	+	0.646396i
$719$	12.0000			0.447524			0.223762	−	0.974644i	$-0.428166\pi$
$719$	12.0000			0.447524			0.223762	+	0.974644i	$0.428166\pi$
$720$		0			0
$721$	−4.00000			−0.148968
$722$	−17.0000	−	29.4449i	−0.632674	−	1.09582i
$723$		0			0
$724$	14.0000	−	24.2487i	0.520306	−	0.901196i
$725$		0			0
$726$		0			0
$727$	−10.5000	−	18.1865i	−0.389423	−	0.674501i	0.602949	−	0.797780i	$-0.293992\pi$
$727$	−10.5000	−	18.1865i	−0.389423	−	0.674501i	−0.992372	+	0.123279i	$0.960659\pi$
$728$		0			0
$729$		0			0
$730$	−32.0000			−1.18437
$731$	24.0000	+	41.5692i	0.887672	+	1.53749i
$732$		0			0
$733$	−3.00000	+	5.19615i	−0.110808	+	0.191924i	−0.916096	−	0.400959i	$-0.868677\pi$
$733$	−3.00000	+	5.19615i	−0.110808	+	0.191924i	0.805289	+	0.592883i	$0.202010\pi$
$734$	8.00000	−	13.8564i	0.295285	−	0.511449i
$735$		0			0
$736$	4.00000	+	6.92820i	0.147442	+	0.255377i
$737$	4.00000			0.147342
$738$		0			0
$739$	−40.0000			−1.47142			−0.735712	−	0.677295i	$-0.763152\pi$
$739$	−40.0000			−1.47142			−0.735712	+	0.677295i	$0.763152\pi$
$740$	−6.00000	−	10.3923i	−0.220564	−	0.382029i
$741$		0			0
$742$	12.0000	−	20.7846i	0.440534	−	0.763027i
$743$	5.00000	−	8.66025i	0.183432	−	0.317714i	−0.759615	−	0.650373i	$-0.774613\pi$
$743$	5.00000	−	8.66025i	0.183432	−	0.317714i	0.943047	+	0.332659i	$0.107946\pi$
$744$		0			0
$745$	2.00000	+	3.46410i	0.0732743	+	0.126915i
$746$	44.0000			1.61095
$747$		0			0
$748$	8.00000			0.292509
$749$	−12.0000	−	20.7846i	−0.438470	−	0.759453i
$750$		0			0
$751$	2.50000	−	4.33013i	0.0912263	−	0.158009i	−0.816801	−	0.576919i	$-0.804255\pi$
$751$	2.50000	−	4.33013i	0.0912263	−	0.158009i	0.908027	+	0.418911i	$0.137588\pi$
$752$	14.0000	−	24.2487i	0.510527	−	0.884260i
$753$		0			0
$754$		0			0
$755$	−20.0000			−0.727875
$756$		0			0
$757$	−43.0000			−1.56286			−0.781431	−	0.623992i	$-0.785510\pi$
$757$	−43.0000			−1.56286			−0.781431	+	0.623992i	$0.785510\pi$
$758$	29.0000	+	50.2295i	1.05333	+	1.82442i
$759$		0			0
$760$		0			0
$761$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$761$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$762$		0			0
$763$	−20.0000	−	34.6410i	−0.724049	−	1.25409i
$764$	−40.0000			−1.44715
$765$		0			0
$766$	−16.0000			−0.578103
$767$	22.0000	+	38.1051i	0.794374	+	1.37590i
$768$		0			0
$769$	17.0000	−	29.4449i	0.613036	−	1.06181i	−0.377690	−	0.925932i	$-0.623282\pi$
$769$	17.0000	−	29.4449i	0.613036	−	1.06181i	0.990726	−	0.135877i	$-0.0433852\pi$
$770$	8.00000	−	13.8564i	0.288300	−	0.499350i
$771$		0			0
$772$	14.0000	+	24.2487i	0.503871	+	0.872730i
$773$	−42.0000			−1.51064			−0.755318	−	0.655359i	$-0.772517\pi$
$773$	−42.0000			−1.51064			−0.755318	+	0.655359i	$0.772517\pi$
$774$		0			0
$775$	−1.00000			−0.0359211
$776$		0			0
$777$		0			0
$778$	9.00000	−	15.5885i	0.322666	−	0.558873i
$779$	6.00000	−	10.3923i	0.214972	−	0.372343i
$780$		0			0
$781$	−7.50000	−	12.9904i	−0.268371	−	0.464832i
$782$	−8.00000			−0.286079
$783$		0			0
$784$	−36.0000			−1.28571
$785$	−14.0000	−	24.2487i	−0.499681	−	0.865474i
$786$		0			0
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	−0.899468	−	0.436987i	$-0.856046\pi$
$787$	−2.00000	+	3.46410i	−0.0712923	+	0.123482i	0.828176	+	0.560469i	$0.189379\pi$
$788$	−2.00000	+	3.46410i	−0.0712470	+	0.123404i
$789$		0			0
$790$	20.0000	+	34.6410i	0.711568	+	1.23247i
$791$	12.0000			0.426671
$792$		0			0
$793$		0			0
$794$	−25.0000	−	43.3013i	−0.887217	−	1.53670i
$795$		0			0
$796$	15.0000	−	25.9808i	0.531661	−	0.920864i
$797$	−15.5000	+	26.8468i	−0.549038	+	0.950962i	0.449303	+	0.893380i	$0.351673\pi$
$797$	−15.5000	+	26.8468i	−0.549038	+	0.950962i	−0.998341	+	0.0575824i	$0.981661\pi$
$798$		0			0
$799$	14.0000	+	24.2487i	0.495284	+	0.857858i
$800$	8.00000			0.282843
$801$		0			0
$802$	−58.0000			−2.04805
$803$	−4.00000	−	6.92820i	−0.141157	−	0.244491i
$804$		0			0
$805$	−4.00000	+	6.92820i	−0.140981	+	0.244187i
$806$	−4.00000	+	6.92820i	−0.140894	+	0.244036i
$807$		0			0
$808$		0			0
$809$	6.00000			0.210949			0.105474	−	0.994422i	$-0.466364\pi$
$809$	6.00000			0.210949			0.105474	+	0.994422i	$0.466364\pi$
$810$		0			0
$811$	40.0000			1.40459			0.702295	−	0.711886i	$-0.252159\pi$
$811$	40.0000			1.40459			0.702295	+	0.711886i	$0.252159\pi$
$812$		0			0
$813$		0			0
$814$	3.00000	−	5.19615i	0.105150	−	0.182125i
$815$	−13.0000	+	22.5167i	−0.455370	+	0.788724i
$816$		0			0
$817$	36.0000	+	62.3538i	1.25948	+	2.18148i
$818$	36.0000			1.25871
$819$		0			0
$820$	8.00000			0.279372
$821$	26.0000	+	45.0333i	0.907406	+	1.57167i	0.817654	+	0.575710i	$0.195274\pi$
$821$	26.0000	+	45.0333i	0.907406	+	1.57167i	0.0897520	+	0.995964i	$0.471393\pi$
$822$		0			0
$823$	4.50000	−	7.79423i	0.156860	−	0.271690i	−0.776875	−	0.629655i	$-0.783196\pi$
$823$	4.50000	−	7.79423i	0.156860	−	0.271690i	0.933735	+	0.357966i	$0.116529\pi$
$824$		0			0
$825$		0			0
$826$	44.0000	+	76.2102i	1.53096	+	2.65169i
$827$	28.0000			0.973655			0.486828	−	0.873498i	$-0.338154\pi$
$827$	28.0000			0.973655			0.486828	+	0.873498i	$0.338154\pi$
$828$		0			0
$829$	34.0000			1.18087			0.590434	−	0.807086i	$-0.298956\pi$
$829$	34.0000			1.18087			0.590434	+	0.807086i	$0.298956\pi$
$830$	24.0000	+	41.5692i	0.833052	+	1.44289i
$831$		0			0
$832$	16.0000	−	27.7128i	0.554700	−	0.960769i
$833$	18.0000	−	31.1769i	0.623663	−	1.08022i
$834$		0			0
$835$	−18.0000	−	31.1769i	−0.622916	−	1.07892i
$836$	12.0000			0.415029
$837$		0			0
$838$	14.0000			0.483622
$839$	−2.50000	−	4.33013i	−0.0863096	−	0.149493i	0.819639	−	0.572880i	$-0.194174\pi$
$839$	−2.50000	−	4.33013i	−0.0863096	−	0.149493i	−0.905949	+	0.423388i	$0.860841\pi$
$840$		0			0
$841$	14.5000	−	25.1147i	0.500000	−	0.866025i
$842$	−37.0000	+	64.0859i	−1.27510	+	2.20855i
$843$		0			0
$844$	12.0000	+	20.7846i	0.413057	+	0.715436i
$845$	6.00000			0.206406
$846$		0			0
$847$	4.00000			0.137442
$848$	−6.00000	−	10.3923i	−0.206041	−	0.356873i
$849$		0			0
$850$	−4.00000	+	6.92820i	−0.137199	+	0.237635i
$851$	−1.50000	+	2.59808i	−0.0514193	+	0.0890609i
$852$		0			0
$853$	8.00000	+	13.8564i	0.273915	+	0.474434i	0.969861	−	0.243660i	$-0.0783480\pi$
$853$	8.00000	+	13.8564i	0.273915	+	0.474434i	−0.695946	+	0.718094i	$0.745015\pi$
$854$		0			0
$855$		0			0
$856$		0			0
$857$	−11.0000	−	19.0526i	−0.375753	−	0.650823i	0.614687	−	0.788771i	$-0.289283\pi$
$857$	−11.0000	−	19.0526i	−0.375753	−	0.650823i	−0.990439	+	0.137948i	$0.955949\pi$
$858$		0			0
$859$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$859$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$860$	−24.0000	+	41.5692i	−0.818393	+	1.41750i
$861$		0			0
$862$	12.0000	+	20.7846i	0.408722	+	0.707927i
$863$	−48.0000			−1.63394			−0.816970	−	0.576681i	$-0.804348\pi$
$863$	−48.0000			−1.63394			−0.816970	+	0.576681i	$0.804348\pi$
$864$		0			0
$865$	−12.0000			−0.408012
$866$	−13.0000	−	22.5167i	−0.441758	−	0.765147i
$867$		0			0
$868$	−4.00000	+	6.92820i	−0.135769	+	0.235159i
$869$	−5.00000	+	8.66025i	−0.169613	+	0.293779i
$870$		0			0
$871$	8.00000	+	13.8564i	0.271070	+	0.469506i
$872$		0			0
$873$		0			0
$874$	−12.0000			−0.405906
$875$	24.0000	+	41.5692i	0.811348	+	1.40530i
$876$		0			0
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	−0.673109	−	0.739543i	$-0.735042\pi$
$877$	9.00000	−	15.5885i	0.303908	−	0.526385i	0.977018	+	0.213158i	$0.0683750\pi$
$878$	20.0000	−	34.6410i	0.674967	−	1.16908i
$879$		0			0
$880$	−4.00000	−	6.92820i	−0.134840	−	0.233550i
$881$	−2.00000			−0.0673817			−0.0336909	−	0.999432i	$-0.510726\pi$
$881$	−2.00000			−0.0673817			−0.0336909	+	0.999432i	$0.510726\pi$
$882$		0			0
$883$	−41.0000			−1.37976			−0.689880	−	0.723924i	$-0.742337\pi$
$883$	−41.0000			−1.37976			−0.689880	+	0.723924i	$0.742337\pi$
$884$	16.0000	+	27.7128i	0.538138	+	0.932083i
$885$		0			0
$886$	−41.0000	+	71.0141i	−1.37742	+	2.38576i
$887$	−26.0000	+	45.0333i	−0.872995	+	1.51207i	−0.0141108	+	0.999900i	$0.504492\pi$
$887$	−26.0000	+	45.0333i	−0.872995	+	1.51207i	−0.858884	+	0.512170i	$0.828842\pi$
$888$		0			0
$889$	−4.00000	−	6.92820i	−0.134156	−	0.232364i
$890$	−12.0000			−0.402241
$891$		0			0
$892$	14.0000			0.468755
$893$	21.0000	+	36.3731i	0.702738	+	1.21718i
$894$		0			0
$895$	−12.0000	+	20.7846i	−0.401116	+	0.694753i
$896$		0			0
$897$		0			0
$898$	−1.00000	−	1.73205i	−0.0333704	−	0.0577993i
$899$		0			0
$900$		0			0
$901$	12.0000			0.399778
$902$	2.00000	+	3.46410i	0.0665927	+	0.115342i
$903$		0			0
$904$		0			0
$905$	14.0000	−	24.2487i	0.465376	−	0.806054i
$906$		0			0
$907$	30.0000	+	51.9615i	0.996134	+	1.72535i	0.574148	+	0.818752i	$0.305333\pi$
$907$	30.0000	+	51.9615i	0.996134	+	1.72535i	0.421986	+	0.906602i	$0.361333\pi$
$908$	24.0000			0.796468
$909$		0			0
$910$	64.0000			2.12158
$911$	−28.5000	−	49.3634i	−0.944247	−	1.63548i	−0.757252	−	0.653123i	$-0.773458\pi$
$911$	−28.5000	−	49.3634i	−0.944247	−	1.63548i	−0.186995	−	0.982361i	$-0.559875\pi$
$912$		0			0
$913$	−6.00000	+	10.3923i	−0.198571	+	0.343935i
$914$	18.0000	−	31.1769i	0.595387	−	1.03124i
$915$		0			0
$916$	−3.00000	−	5.19615i	−0.0991228	−	0.171686i
$917$	−72.0000			−2.37765
$918$		0			0
$919$	22.0000			0.725713			0.362857	−	0.931845i	$-0.381802\pi$
$919$	22.0000			0.725713			0.362857	+	0.931845i	$0.381802\pi$
$920$		0			0
$921$		0			0
$922$	−30.0000	+	51.9615i	−0.987997	+	1.71126i
$923$	30.0000	−	51.9615i	0.987462	−	1.71033i
$924$		0			0
$925$	1.50000	+	2.59808i	0.0493197	+	0.0854242i
$926$	−70.0000			−2.30034
$927$		0			0
$928$		0			0
$929$	−1.50000	−	2.59808i	−0.0492134	−	0.0852401i	0.840369	−	0.542014i	$-0.182338\pi$
$929$	−1.50000	−	2.59808i	−0.0492134	−	0.0852401i	−0.889583	+	0.456774i	$0.849005\pi$
$930$		0			0
$931$	27.0000	−	46.7654i	0.884889	−	1.53267i
$932$		0			0
$933$		0			0
$934$	−36.0000	−	62.3538i	−1.17796	−	2.04028i
$935$	8.00000			0.261628
$936$		0			0
$937$	−16.0000			−0.522697			−0.261349	−	0.965244i	$-0.584167\pi$
$937$	−16.0000			−0.522697			−0.261349	+	0.965244i	$0.584167\pi$
$938$	16.0000	+	27.7128i	0.522419	+	0.904855i
$939$		0			0
$940$	−14.0000	+	24.2487i	−0.456630	+	0.790906i
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	−0.992607	−	0.121376i	$-0.961269\pi$
$941$	−12.0000	+	20.7846i	−0.391189	+	0.677559i	0.601418	+	0.798935i	$0.294603\pi$
$942$		0			0
$943$	−1.00000	−	1.73205i	−0.0325645	−	0.0564033i
$944$	44.0000			1.43208
$945$		0			0
$946$	−24.0000			−0.780307
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	0.946892	−	0.321552i	$-0.104204\pi$
$947$	6.00000	+	10.3923i	0.194974	+	0.337705i	−0.751918	+	0.659256i	$0.770871\pi$
$948$		0			0
$949$	16.0000	−	27.7128i	0.519382	−	0.899596i
$950$	−6.00000	+	10.3923i	−0.194666	+	0.337171i
$951$		0			0
$952$		0			0
$953$	20.0000			0.647864			0.323932	−	0.946080i	$-0.394995\pi$
$953$	20.0000			0.647864			0.323932	+	0.946080i	$0.394995\pi$
$954$		0			0
$955$	−40.0000			−1.29437
$956$	−24.0000	−	41.5692i	−0.776215	−	1.34444i
$957$		0			0
$958$	−34.0000	+	58.8897i	−1.09849	+	1.90264i
$959$	−14.0000	+	24.2487i	−0.452084	+	0.783032i
$960$		0			0
$961$	15.0000	+	25.9808i	0.483871	+	0.838089i
$962$	24.0000			0.773791
$963$		0			0
$964$	20.0000			0.644157
$965$	14.0000	+	24.2487i	0.450676	+	0.780594i
$966$		0			0
$967$	−29.0000	+	50.2295i	−0.932577	+	1.61527i	−0.153679	+	0.988121i	$0.549112\pi$
$967$	−29.0000	+	50.2295i	−0.932577	+	1.61527i	−0.778898	+	0.627150i	$0.784221\pi$
$968$		0			0
$969$		0			0
$970$	−34.0000	−	58.8897i	−1.09167	−	1.89084i
$971$	−35.0000			−1.12320			−0.561602	−	0.827408i	$-0.689815\pi$
$971$	−35.0000			−1.12320			−0.561602	+	0.827408i	$0.689815\pi$
$972$		0			0
$973$	64.0000			2.05175
$974$	19.0000	+	32.9090i	0.608799	+	1.05447i
$975$		0			0
$976$		0			0
$977$	−13.5000	+	23.3827i	−0.431903	+	0.748078i	−0.997037	−	0.0769208i	$-0.975491\pi$
$977$	−13.5000	+	23.3827i	−0.431903	+	0.748078i	0.565134	+	0.824999i	$0.308824\pi$
$978$		0			0
$979$	−1.50000	−	2.59808i	−0.0479402	−	0.0830349i
$980$	36.0000			1.14998
$981$		0			0
$982$	−20.0000			−0.638226
$983$	16.5000	+	28.5788i	0.526268	+	0.911523i	0.999532	+	0.0306024i	$0.00974257\pi$
$983$	16.5000	+	28.5788i	0.526268	+	0.911523i	−0.473263	+	0.880921i	$0.656924\pi$
$984$		0			0
$985$	−2.00000	+	3.46410i	−0.0637253	+	0.110375i
$986$		0			0
$987$		0			0
$988$	24.0000	+	41.5692i	0.763542	+	1.32249i
$989$	12.0000			0.381578
$990$		0			0
$991$	−8.00000			−0.254128			−0.127064	−	0.991894i	$-0.540555\pi$
$991$	−8.00000			−0.254128			−0.127064	+	0.991894i	$0.540555\pi$
$992$	4.00000	+	6.92820i	0.127000	+	0.219971i
$993$		0			0
$994$	60.0000	−	103.923i	1.90308	−	3.29624i
$995$	15.0000	−	25.9808i	0.475532	−	0.823646i
$996$		0			0
$997$	26.0000	+	45.0333i	0.823428	+	1.42622i	0.903115	+	0.429400i	$0.141275\pi$
$997$	26.0000	+	45.0333i	0.823428	+	1.42622i	−0.0796863	+	0.996820i	$0.525392\pi$
$998$	−50.0000			−1.58272
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	297.2.e.a.199.1		2
3.2	odd	2		99.2.e.c.67.1	yes	2
9.2	odd	6		99.2.e.c.34.1	✓	2
9.4	even	3		891.2.a.h.1.1		1
9.5	odd	6		891.2.a.a.1.1		1
9.7	even	3	inner	297.2.e.a.100.1		2
33.32	even	2		1089.2.e.a.364.1		2
99.32	even	6		9801.2.a.l.1.1		1
99.65	even	6		1089.2.e.a.727.1		2
99.76	odd	6		9801.2.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
99.2.e.c.34.1	✓	2	9.2	odd	6
99.2.e.c.67.1	yes	2	3.2	odd	2
297.2.e.a.100.1		2	9.7	even	3	inner
297.2.e.a.199.1		2	1.1	even	1	trivial
891.2.a.a.1.1		1	9.5	odd	6
891.2.a.h.1.1		1	9.4	even	3
1089.2.e.a.364.1		2	33.32	even	2
1089.2.e.a.727.1		2	99.65	even	6
9801.2.a.a.1.1		1	99.76	odd	6
9801.2.a.l.1.1		1	99.32	even	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 297 = 3^{3} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	297.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-1.00000 + 1.73205i) q^{4} +(-1.00000 + 1.73205i) q^{5} +(-2.00000 - 3.46410i) q^{7} +4.00000 q^{10} +(0.500000 + 0.866025i) q^{11} +(-2.00000 + 3.46410i) q^{13} +(-4.00000 + 6.92820i) q^{14} +(2.00000 + 3.46410i) q^{16} -4.00000 q^{17} -6.00000 q^{19} +(-2.00000 - 3.46410i) q^{20} +(1.00000 - 1.73205i) q^{22} +(-0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{25} +8.00000 q^{26} +8.00000 q^{28} +(-0.500000 + 0.866025i) q^{31} +(4.00000 - 6.92820i) q^{32} +(4.00000 + 6.92820i) q^{34} +8.00000 q^{35} +3.00000 q^{37} +(6.00000 + 10.3923i) q^{38} +(-1.00000 + 1.73205i) q^{41} +(-6.00000 - 10.3923i) q^{43} -2.00000 q^{44} +2.00000 q^{46} +(-3.50000 - 6.06218i) q^{47} +(-4.50000 + 7.79423i) q^{49} +(1.00000 - 1.73205i) q^{50} +(-4.00000 - 6.92820i) q^{52} -3.00000 q^{53} -2.00000 q^{55} +(5.50000 - 9.52628i) q^{59} +2.00000 q^{62} -8.00000 q^{64} +(-4.00000 - 6.92820i) q^{65} +(2.00000 - 3.46410i) q^{67} +(4.00000 - 6.92820i) q^{68} +(-8.00000 - 13.8564i) q^{70} -15.0000 q^{71} -8.00000 q^{73} +(-3.00000 - 5.19615i) q^{74} +(6.00000 - 10.3923i) q^{76} +(2.00000 - 3.46410i) q^{77} +(5.00000 + 8.66025i) q^{79} -8.00000 q^{80} +4.00000 q^{82} +(6.00000 + 10.3923i) q^{83} +(4.00000 - 6.92820i) q^{85} +(-12.0000 + 20.7846i) q^{86} -3.00000 q^{89} +16.0000 q^{91} +(-1.00000 - 1.73205i) q^{92} +(-7.00000 + 12.1244i) q^{94} +(6.00000 - 10.3923i) q^{95} +(-8.50000 - 14.7224i) q^{97} +18.0000 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 2 q^{4} - 2 q^{5} - 4 q^{7} + 8 q^{10} + q^{11} - 4 q^{13} - 8 q^{14} + 4 q^{16} - 8 q^{17} - 12 q^{19} - 4 q^{20} + 2 q^{22} - q^{23} + q^{25} + 16 q^{26} + 16 q^{28} - q^{31} + 8 q^{32}+ \cdots + 36 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 2 * q^4 - 2 * q^5 - 4 * q^7 + 8 * q^10 + q^11 - 4 * q^13 - 8 * q^14 + 4 * q^16 - 8 * q^17 - 12 * q^19 - 4 * q^20 + 2 * q^22 - q^23 + q^25 + 16 * q^26 + 16 * q^28 - q^31 + 8 * q^32 + 8 * q^34 + 16 * q^35 + 6 * q^37 + 12 * q^38 - 2 * q^41 - 12 * q^43 - 4 * q^44 + 4 * q^46 - 7 * q^47 - 9 * q^49 + 2 * q^50 - 8 * q^52 - 6 * q^53 - 4 * q^55 + 11 * q^59 + 4 * q^62 - 16 * q^64 - 8 * q^65 + 4 * q^67 + 8 * q^68 - 16 * q^70 - 30 * q^71 - 16 * q^73 - 6 * q^74 + 12 * q^76 + 4 * q^77 + 10 * q^79 - 16 * q^80 + 8 * q^82 + 12 * q^83 + 8 * q^85 - 24 * q^86 - 6 * q^89 + 32 * q^91 - 2 * q^92 - 14 * q^94 + 12 * q^95 - 17 * q^97 + 36 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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