LMFDB - Embedded newform 342.2.g.d.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,2,Mod(163,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("342.163");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	342.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.73088374913$
Analytic rank:	$0$
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:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	342.235
Dual form			342.2.g.d.163.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{5} -3.00000 q^{7} -1.00000 q^{8} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{5} -3.00000 q^{7} -1.00000 q^{8} +(2.00000 - 3.46410i) q^{10} -2.00000 q^{11} +(3.50000 - 6.06218i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.00000 - 1.73205i) q^{19} +4.00000 q^{20} +(-1.00000 - 1.73205i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-5.50000 + 9.52628i) q^{25} +7.00000 q^{26} +(1.50000 - 2.59808i) q^{28} +(2.00000 - 3.46410i) q^{29} +1.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(6.00000 + 10.3923i) q^{35} +7.00000 q^{37} +(-0.500000 - 4.33013i) q^{38} +(2.00000 + 3.46410i) q^{40} +(2.00000 + 3.46410i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(1.00000 - 1.73205i) q^{44} -4.00000 q^{46} +(1.00000 - 1.73205i) q^{47} +2.00000 q^{49} -11.0000 q^{50} +(3.50000 + 6.06218i) q^{52} +(-2.00000 + 3.46410i) q^{53} +(4.00000 + 6.92820i) q^{55} +3.00000 q^{56} +4.00000 q^{58} +(-3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(0.500000 + 0.866025i) q^{62} +1.00000 q^{64} -28.0000 q^{65} +(-1.50000 + 2.59808i) q^{67} +(-6.00000 + 10.3923i) q^{70} +(1.00000 + 1.73205i) q^{71} +(1.50000 + 2.59808i) q^{73} +(3.50000 + 6.06218i) q^{74} +(3.50000 - 2.59808i) q^{76} +6.00000 q^{77} +(-2.50000 - 4.33013i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-2.00000 + 3.46410i) q^{82} +12.0000 q^{83} +(3.50000 - 6.06218i) q^{86} +2.00000 q^{88} +(9.00000 - 15.5885i) q^{89} +(-10.5000 + 18.1865i) q^{91} +(-2.00000 - 3.46410i) q^{92} +2.00000 q^{94} +(2.00000 + 17.3205i) q^{95} +(-5.00000 - 8.66025i) q^{97} +(1.00000 + 1.73205i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + q^{2} - q^{4} - 4 q^{5} - 6 q^{7} - 2 q^{8}+O(q^{10}) $ 2 * q + q^2 - q^4 - 4 * q^5 - 6 * q^7 - 2 * q^8	$ 2 q + q^{2} - q^{4} - 4 q^{5} - 6 q^{7} - 2 q^{8} + 4 q^{10} - 4 q^{11} + 7 q^{13} - 3 q^{14} - q^{16} - 8 q^{19} + 8 q^{20} - 2 q^{22} - 4 q^{23} - 11 q^{25} + 14 q^{26} + 3 q^{28} + 4 q^{29} + 2 q^{31} + q^{32} + 12 q^{35} + 14 q^{37} - q^{38} + 4 q^{40} + 4 q^{41} - 7 q^{43} + 2 q^{44} - 8 q^{46} + 2 q^{47} + 4 q^{49} - 22 q^{50} + 7 q^{52} - 4 q^{53} + 8 q^{55} + 6 q^{56} + 8 q^{58} - 6 q^{59} + q^{61} + q^{62} + 2 q^{64} - 56 q^{65} - 3 q^{67} - 12 q^{70} + 2 q^{71} + 3 q^{73} + 7 q^{74} + 7 q^{76} + 12 q^{77} - 5 q^{79} - 4 q^{80} - 4 q^{82} + 24 q^{83} + 7 q^{86} + 4 q^{88} + 18 q^{89} - 21 q^{91} - 4 q^{92} + 4 q^{94} + 4 q^{95} - 10 q^{97} + 2 q^{98}+O(q^{100}) $ 2 * q + q^2 - q^4 - 4 * q^5 - 6 * q^7 - 2 * q^8 + 4 * q^10 - 4 * q^11 + 7 * q^13 - 3 * q^14 - q^16 - 8 * q^19 + 8 * q^20 - 2 * q^22 - 4 * q^23 - 11 * q^25 + 14 * q^26 + 3 * q^28 + 4 * q^29 + 2 * q^31 + q^32 + 12 * q^35 + 14 * q^37 - q^38 + 4 * q^40 + 4 * q^41 - 7 * q^43 + 2 * q^44 - 8 * q^46 + 2 * q^47 + 4 * q^49 - 22 * q^50 + 7 * q^52 - 4 * q^53 + 8 * q^55 + 6 * q^56 + 8 * q^58 - 6 * q^59 + q^61 + q^62 + 2 * q^64 - 56 * q^65 - 3 * q^67 - 12 * q^70 + 2 * q^71 + 3 * q^73 + 7 * q^74 + 7 * q^76 + 12 * q^77 - 5 * q^79 - 4 * q^80 - 4 * q^82 + 24 * q^83 + 7 * q^86 + 4 * q^88 + 18 * q^89 - 21 * q^91 - 4 * q^92 + 4 * q^94 + 4 * q^95 - 10 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$		0			0
$3$		0			0
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−2.00000	−	3.46410i	−0.894427	−	1.54919i	−0.834512	−	0.550990i	$-0.814250\pi$
$5$	−2.00000	−	3.46410i	−0.894427	−	1.54919i	−0.0599153	−	0.998203i	$-0.519083\pi$
$6$		0			0
$7$	−3.00000			−1.13389			−0.566947	−	0.823754i	$-0.691875\pi$
$7$	−3.00000			−1.13389			−0.566947	+	0.823754i	$0.691875\pi$
$8$	−1.00000			−0.353553
$9$		0			0
$10$	2.00000	−	3.46410i	0.632456	−	1.09545i
$11$	−2.00000			−0.603023			−0.301511	−	0.953463i	$-0.597491\pi$
$11$	−2.00000			−0.603023			−0.301511	+	0.953463i	$0.597491\pi$
$12$		0			0
$13$	3.50000	−	6.06218i	0.970725	−	1.68135i	0.277350	−	0.960769i	$-0.410544\pi$
$13$	3.50000	−	6.06218i	0.970725	−	1.68135i	0.693375	−	0.720577i	$-0.256123\pi$
$14$	−1.50000	−	2.59808i	−0.400892	−	0.694365i
$15$		0			0
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$17$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$18$		0			0
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$19$	−4.00000	−	1.73205i	−0.917663	−	0.397360i
$20$	4.00000			0.894427
$21$		0			0
$22$	−1.00000	−	1.73205i	−0.213201	−	0.369274i
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	−0.995639	−	0.0932891i	$-0.970262\pi$
$23$	−2.00000	+	3.46410i	−0.417029	+	0.722315i	0.578610	+	0.815604i	$0.303595\pi$
$24$		0			0
$25$	−5.50000	+	9.52628i	−1.10000	+	1.90526i
$26$	7.00000			1.37281
$27$		0			0
$28$	1.50000	−	2.59808i	0.283473	−	0.490990i
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	−0.618389	−	0.785872i	$-0.712214\pi$
$29$	2.00000	−	3.46410i	0.371391	−	0.643268i	0.989780	+	0.142605i	$0.0455477\pi$
$30$		0			0
$31$	1.00000			0.179605			0.0898027	−	0.995960i	$-0.471376\pi$
$31$	1.00000			0.179605			0.0898027	+	0.995960i	$0.471376\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$		0			0
$34$		0			0
$35$	6.00000	+	10.3923i	1.01419	+	1.75662i
$36$		0			0
$37$	7.00000			1.15079			0.575396	−	0.817875i	$-0.304848\pi$
$37$	7.00000			1.15079			0.575396	+	0.817875i	$0.304848\pi$
$38$	−0.500000	−	4.33013i	−0.0811107	−	0.702439i
$39$		0			0
$40$	2.00000	+	3.46410i	0.316228	+	0.547723i
$41$	2.00000	+	3.46410i	0.312348	+	0.541002i	0.978870	−	0.204483i	$-0.0655513\pi$
$41$	2.00000	+	3.46410i	0.312348	+	0.541002i	−0.666523	+	0.745485i	$0.732218\pi$
$42$		0			0
$43$	−3.50000	−	6.06218i	−0.533745	−	0.924473i	−0.999223	−	0.0394140i	$-0.987451\pi$
$43$	−3.50000	−	6.06218i	−0.533745	−	0.924473i	0.465478	−	0.885059i	$-0.345882\pi$
$44$	1.00000	−	1.73205i	0.150756	−	0.261116i
$45$		0			0
$46$	−4.00000			−0.589768
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	−0.783830	−	0.620975i	$-0.786737\pi$
$47$	1.00000	−	1.73205i	0.145865	−	0.252646i	0.929695	+	0.368329i	$0.120070\pi$
$48$		0			0
$49$	2.00000			0.285714
$50$	−11.0000			−1.55563
$51$		0			0
$52$	3.50000	+	6.06218i	0.485363	+	0.840673i
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	−0.970065	−	0.242846i	$-0.921919\pi$
$53$	−2.00000	+	3.46410i	−0.274721	+	0.475831i	0.695344	+	0.718677i	$0.255252\pi$
$54$		0			0
$55$	4.00000	+	6.92820i	0.539360	+	0.934199i
$56$	3.00000			0.400892
$57$		0			0
$58$	4.00000			0.525226
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	0.601958	−	0.798528i	$-0.294388\pi$
$59$	−3.00000	−	5.19615i	−0.390567	−	0.676481i	−0.992524	+	0.122047i	$0.961054\pi$
$60$		0			0
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	−0.832240	−	0.554416i	$-0.812942\pi$
$61$	0.500000	−	0.866025i	0.0640184	−	0.110883i	0.896258	+	0.443533i	$0.146275\pi$
$62$	0.500000	+	0.866025i	0.0635001	+	0.109985i
$63$		0			0
$64$	1.00000			0.125000
$65$	−28.0000			−3.47297
$66$		0			0
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	−0.942987	−	0.332830i	$-0.891996\pi$
$67$	−1.50000	+	2.59808i	−0.183254	+	0.317406i	0.759733	+	0.650236i	$0.225330\pi$
$68$		0			0
$69$		0			0
$70$	−6.00000	+	10.3923i	−0.717137	+	1.24212i
$71$	1.00000	+	1.73205i	0.118678	+	0.205557i	0.919244	−	0.393688i	$-0.128801\pi$
$71$	1.00000	+	1.73205i	0.118678	+	0.205557i	−0.800566	+	0.599245i	$0.795468\pi$
$72$		0			0
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	0.940356	−	0.340193i	$-0.110493\pi$
$73$	1.50000	+	2.59808i	0.175562	+	0.304082i	−0.764794	+	0.644275i	$0.777159\pi$
$74$	3.50000	+	6.06218i	0.406867	+	0.704714i
$75$		0			0
$76$	3.50000	−	2.59808i	0.401478	−	0.298020i
$77$	6.00000			0.683763
$78$		0			0
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	0.690426	−	0.723403i	$-0.257423\pi$
$79$	−2.50000	−	4.33013i	−0.281272	−	0.487177i	−0.971698	+	0.236225i	$0.924090\pi$
$80$	−2.00000	+	3.46410i	−0.223607	+	0.387298i
$81$		0			0
$82$	−2.00000	+	3.46410i	−0.220863	+	0.382546i
$83$	12.0000			1.31717			0.658586	−	0.752506i	$-0.271155\pi$
$83$	12.0000			1.31717			0.658586	+	0.752506i	$0.271155\pi$
$84$		0			0
$85$		0			0
$86$	3.50000	−	6.06218i	0.377415	−	0.653701i
$87$		0			0
$88$	2.00000			0.213201
$89$	9.00000	−	15.5885i	0.953998	−	1.65237i	0.217354	−	0.976093i	$-0.430258\pi$
$89$	9.00000	−	15.5885i	0.953998	−	1.65237i	0.736644	−	0.676280i	$-0.236409\pi$
$90$		0			0
$91$	−10.5000	+	18.1865i	−1.10070	+	1.90647i
$92$	−2.00000	−	3.46410i	−0.208514	−	0.361158i
$93$		0			0
$94$	2.00000			0.206284
$95$	2.00000	+	17.3205i	0.205196	+	1.77705i
$96$		0			0
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	−0.999961	−	0.00888289i	$-0.997172\pi$
$97$	−5.00000	−	8.66025i	−0.507673	−	0.879316i	0.492287	−	0.870433i	$-0.336161\pi$
$98$	1.00000	+	1.73205i	0.101015	+	0.174964i
$99$		0			0
$100$	−5.50000	−	9.52628i	−0.550000	−	0.952628i
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	−0.811976	−	0.583691i	$-0.801608\pi$
$101$	1.00000	−	1.73205i	0.0995037	−	0.172345i	0.911479	+	0.411346i	$0.134941\pi$
$102$		0			0
$103$	9.00000			0.886796			0.443398	−	0.896325i	$-0.353773\pi$
$103$	9.00000			0.886796			0.443398	+	0.896325i	$0.353773\pi$
$104$	−3.50000	+	6.06218i	−0.343203	+	0.594445i
$105$		0			0
$106$	−4.00000			−0.388514
$107$	−2.00000			−0.193347			−0.0966736	−	0.995316i	$-0.530820\pi$
$107$	−2.00000			−0.193347			−0.0966736	+	0.995316i	$0.530820\pi$
$108$		0			0
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	0.685828	−	0.727764i	$-0.259440\pi$
$109$	−3.00000	−	5.19615i	−0.287348	−	0.497701i	−0.973176	+	0.230063i	$0.926107\pi$
$110$	−4.00000	+	6.92820i	−0.381385	+	0.660578i
$111$		0			0
$112$	1.50000	+	2.59808i	0.141737	+	0.245495i
$113$	−2.00000			−0.188144			−0.0940721	−	0.995565i	$-0.529988\pi$
$113$	−2.00000			−0.188144			−0.0940721	+	0.995565i	$0.529988\pi$
$114$		0			0
$115$	16.0000			1.49201
$116$	2.00000	+	3.46410i	0.185695	+	0.321634i
$117$		0			0
$118$	3.00000	−	5.19615i	0.276172	−	0.478345i
$119$		0			0
$120$		0			0
$121$	−7.00000			−0.636364
$122$	1.00000			0.0905357
$123$		0			0
$124$	−0.500000	+	0.866025i	−0.0449013	+	0.0777714i
$125$	24.0000			2.14663
$126$		0			0
$127$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$127$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$		0			0
$130$	−14.0000	−	24.2487i	−1.22788	−	2.12675i
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	−0.928199	−	0.372084i	$-0.878643\pi$
$131$	−9.00000	−	15.5885i	−0.786334	−	1.36197i	0.141865	−	0.989886i	$-0.454690\pi$
$132$		0			0
$133$	12.0000	+	5.19615i	1.04053	+	0.450564i
$134$	−3.00000			−0.259161
$135$		0			0
$136$		0			0
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	−0.905577	−	0.424182i	$-0.860562\pi$
$137$	−1.00000	+	1.73205i	−0.0854358	+	0.147979i	0.820141	+	0.572161i	$0.193895\pi$
$138$		0			0
$139$	−10.5000	+	18.1865i	−0.890598	+	1.54256i	−0.0514389	+	0.998676i	$0.516381\pi$
$139$	−10.5000	+	18.1865i	−0.890598	+	1.54256i	−0.839159	+	0.543885i	$0.816953\pi$
$140$	−12.0000			−1.01419
$141$		0			0
$142$	−1.00000	+	1.73205i	−0.0839181	+	0.145350i
$143$	−7.00000	+	12.1244i	−0.585369	+	1.01389i
$144$		0			0
$145$	−16.0000			−1.32873
$146$	−1.50000	+	2.59808i	−0.124141	+	0.215018i
$147$		0			0
$148$	−3.50000	+	6.06218i	−0.287698	+	0.498308i
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	−0.953703	−	0.300750i	$-0.902763\pi$
$149$	−9.00000	−	15.5885i	−0.737309	−	1.27706i	0.216394	−	0.976306i	$-0.430570\pi$
$150$		0			0
$151$	20.0000			1.62758			0.813788	−	0.581161i	$-0.197401\pi$
$151$	20.0000			1.62758			0.813788	+	0.581161i	$0.197401\pi$
$152$	4.00000	+	1.73205i	0.324443	+	0.140488i
$153$		0			0
$154$	3.00000	+	5.19615i	0.241747	+	0.418718i
$155$	−2.00000	−	3.46410i	−0.160644	−	0.278243i
$156$		0			0
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	0.691888	−	0.722005i	$-0.256779\pi$
$157$	−3.50000	−	6.06218i	−0.279330	−	0.483814i	−0.971219	+	0.238190i	$0.923446\pi$
$158$	2.50000	−	4.33013i	0.198889	−	0.344486i
$159$		0			0
$160$	−4.00000			−0.316228
$161$	6.00000	−	10.3923i	0.472866	−	0.819028i
$162$		0			0
$163$	11.0000			0.861586			0.430793	−	0.902451i	$-0.358234\pi$
$163$	11.0000			0.861586			0.430793	+	0.902451i	$0.358234\pi$
$164$	−4.00000			−0.312348
$165$		0			0
$166$	6.00000	+	10.3923i	0.465690	+	0.806599i
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	−0.726293	−	0.687386i	$-0.758758\pi$
$167$	3.00000	−	5.19615i	0.232147	−	0.402090i	0.958440	+	0.285295i	$0.0920916\pi$
$168$		0			0
$169$	−18.0000	−	31.1769i	−1.38462	−	2.39822i
$170$		0			0
$171$		0			0
$172$	7.00000			0.533745
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	0.998755	−	0.0498898i	$-0.0158870\pi$
$173$	6.00000	+	10.3923i	0.456172	+	0.790112i	−0.542583	+	0.840002i	$0.682554\pi$
$174$		0			0
$175$	16.5000	−	28.5788i	1.24728	−	2.16036i
$176$	1.00000	+	1.73205i	0.0753778	+	0.130558i
$177$		0			0
$178$	18.0000			1.34916
$179$	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
$181$	1.00000	−	1.73205i	0.0743294	−	0.128742i	−0.826465	−	0.562988i	$-0.809652\pi$
$181$	1.00000	−	1.73205i	0.0743294	−	0.128742i	0.900794	+	0.434246i	$0.142985\pi$
$182$	−21.0000			−1.55662
$183$		0			0
$184$	2.00000	−	3.46410i	0.147442	−	0.255377i
$185$	−14.0000	−	24.2487i	−1.02930	−	1.78280i
$186$		0			0
$187$		0			0
$188$	1.00000	+	1.73205i	0.0729325	+	0.126323i
$189$		0			0
$190$	−14.0000	+	10.3923i	−1.01567	+	0.753937i
$191$	20.0000			1.44715			0.723575	−	0.690246i	$-0.242498\pi$
$191$	20.0000			1.44715			0.723575	+	0.690246i	$0.242498\pi$
$192$		0			0
$193$	10.5000	+	18.1865i	0.755807	+	1.30910i	0.944972	+	0.327150i	$0.106088\pi$
$193$	10.5000	+	18.1865i	0.755807	+	1.30910i	−0.189166	+	0.981945i	$0.560578\pi$
$194$	5.00000	−	8.66025i	0.358979	−	0.621770i
$195$		0			0
$196$	−1.00000	+	1.73205i	−0.0714286	+	0.123718i
$197$	10.0000			0.712470			0.356235	−	0.934396i	$-0.384060\pi$
$197$	10.0000			0.712470			0.356235	+	0.934396i	$0.384060\pi$
$198$		0			0
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	−0.714893	−	0.699234i	$-0.753524\pi$
$199$	3.50000	−	6.06218i	0.248108	−	0.429736i	0.963001	+	0.269498i	$0.0868577\pi$
$200$	5.50000	−	9.52628i	0.388909	−	0.673610i
$201$		0			0
$202$	2.00000			0.140720
$203$	−6.00000	+	10.3923i	−0.421117	+	0.729397i
$204$		0			0
$205$	8.00000	−	13.8564i	0.558744	−	0.967773i
$206$	4.50000	+	7.79423i	0.313530	+	0.543050i
$207$		0			0
$208$	−7.00000			−0.485363
$209$	8.00000	+	3.46410i	0.553372	+	0.239617i
$210$		0			0
$211$	−4.50000	−	7.79423i	−0.309793	−	0.536577i	0.668524	−	0.743690i	$-0.266926\pi$
$211$	−4.50000	−	7.79423i	−0.309793	−	0.536577i	−0.978317	+	0.207114i	$0.933593\pi$
$212$	−2.00000	−	3.46410i	−0.137361	−	0.237915i
$213$		0			0
$214$	−1.00000	−	1.73205i	−0.0683586	−	0.118401i
$215$	−14.0000	+	24.2487i	−0.954792	+	1.65375i
$216$		0			0
$217$	−3.00000			−0.203653
$218$	3.00000	−	5.19615i	0.203186	−	0.351928i
$219$		0			0
$220$	−8.00000			−0.539360
$221$		0			0
$222$		0			0
$223$	−2.50000	−	4.33013i	−0.167412	−	0.289967i	0.770097	−	0.637927i	$-0.220208\pi$
$223$	−2.50000	−	4.33013i	−0.167412	−	0.289967i	−0.937509	+	0.347960i	$0.886874\pi$
$224$	−1.50000	+	2.59808i	−0.100223	+	0.173591i
$225$		0			0
$226$	−1.00000	−	1.73205i	−0.0665190	−	0.115214i
$227$	−4.00000			−0.265489			−0.132745	−	0.991150i	$-0.542379\pi$
$227$	−4.00000			−0.265489			−0.132745	+	0.991150i	$0.542379\pi$
$228$		0			0
$229$	−7.00000			−0.462573			−0.231287	−	0.972886i	$-0.574293\pi$
$229$	−7.00000			−0.462573			−0.231287	+	0.972886i	$0.574293\pi$
$230$	8.00000	+	13.8564i	0.527504	+	0.913664i
$231$		0			0
$232$	−2.00000	+	3.46410i	−0.131306	+	0.227429i
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	0.947403	−	0.320043i	$-0.103697\pi$
$233$	3.00000	+	5.19615i	0.196537	+	0.340411i	−0.750867	+	0.660454i	$0.770364\pi$
$234$		0			0
$235$	−8.00000			−0.521862
$236$	6.00000			0.390567
$237$		0			0
$238$		0			0
$239$	−24.0000			−1.55243			−0.776215	−	0.630468i	$-0.782863\pi$
$239$	−24.0000			−1.55243			−0.776215	+	0.630468i	$0.782863\pi$
$240$		0			0
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	−0.881680	−	0.471848i	$-0.843587\pi$
$241$	−0.500000	+	0.866025i	−0.0322078	+	0.0557856i	0.849472	+	0.527633i	$0.176921\pi$
$242$	−3.50000	−	6.06218i	−0.224989	−	0.389692i
$243$		0			0
$244$	0.500000	+	0.866025i	0.0320092	+	0.0554416i
$245$	−4.00000	−	6.92820i	−0.255551	−	0.442627i
$246$		0			0
$247$	−24.5000	+	18.1865i	−1.55890	+	1.15718i
$248$	−1.00000			−0.0635001
$249$		0			0
$250$	12.0000	+	20.7846i	0.758947	+	1.31453i
$251$	7.00000	−	12.1244i	0.441836	−	0.765283i	−0.555990	−	0.831189i	$-0.687661\pi$
$251$	7.00000	−	12.1244i	0.441836	−	0.765283i	0.997826	+	0.0659066i	$0.0209939\pi$
$252$		0			0
$253$	4.00000	−	6.92820i	0.251478	−	0.435572i
$254$		0			0
$255$		0			0
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−14.0000	+	24.2487i	−0.873296	+	1.51259i	−0.0147291	+	0.999892i	$0.504689\pi$
$257$	−14.0000	+	24.2487i	−0.873296	+	1.51259i	−0.858567	+	0.512702i	$0.828645\pi$
$258$		0			0
$259$	−21.0000			−1.30488
$260$	14.0000	−	24.2487i	0.868243	−	1.50384i
$261$		0			0
$262$	9.00000	−	15.5885i	0.556022	−	0.963058i
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	−0.997906	−	0.0646755i	$-0.979399\pi$
$263$	−9.00000	−	15.5885i	−0.554964	−	0.961225i	0.442943	−	0.896550i	$-0.353935\pi$
$264$		0			0
$265$	16.0000			0.982872
$266$	1.50000	+	12.9904i	0.0919709	+	0.796491i
$267$		0			0
$268$	−1.50000	−	2.59808i	−0.0916271	−	0.158703i
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	0.998361	+	0.0572259i	$0.0182255\pi$
$269$	9.00000	+	15.5885i	0.548740	+	0.950445i	−0.449622	+	0.893219i	$0.648441\pi$
$270$		0			0
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	0.961563	−	0.274586i	$-0.0885408\pi$
$271$	4.00000	+	6.92820i	0.242983	+	0.420858i	−0.718580	+	0.695444i	$0.755208\pi$
$272$		0			0
$273$		0			0
$274$	−2.00000			−0.120824
$275$	11.0000	−	19.0526i	0.663325	−	1.14891i
$276$		0			0
$277$	−26.0000			−1.56219			−0.781094	−	0.624413i	$-0.785338\pi$
$277$	−26.0000			−1.56219			−0.781094	+	0.624413i	$0.785338\pi$
$278$	−21.0000			−1.25950
$279$		0			0
$280$	−6.00000	−	10.3923i	−0.358569	−	0.621059i
$281$	2.00000	−	3.46410i	0.119310	−	0.206651i	−0.800184	−	0.599754i	$-0.795265\pi$
$281$	2.00000	−	3.46410i	0.119310	−	0.206651i	0.919494	+	0.393103i	$0.128598\pi$
$282$		0			0
$283$	6.00000	+	10.3923i	0.356663	+	0.617758i	0.987401	−	0.158237i	$-0.0505811\pi$
$283$	6.00000	+	10.3923i	0.356663	+	0.617758i	−0.630738	+	0.775996i	$0.717248\pi$
$284$	−2.00000			−0.118678
$285$		0			0
$286$	−14.0000			−0.827837
$287$	−6.00000	−	10.3923i	−0.354169	−	0.613438i
$288$		0			0
$289$	8.50000	−	14.7224i	0.500000	−	0.866025i
$290$	−8.00000	−	13.8564i	−0.469776	−	0.813676i
$291$		0			0
$292$	−3.00000			−0.175562
$293$	18.0000			1.05157			0.525786	−	0.850617i	$-0.323771\pi$
$293$	18.0000			1.05157			0.525786	+	0.850617i	$0.323771\pi$
$294$		0			0
$295$	−12.0000	+	20.7846i	−0.698667	+	1.21013i
$296$	−7.00000			−0.406867
$297$		0			0
$298$	9.00000	−	15.5885i	0.521356	−	0.903015i
$299$	14.0000	+	24.2487i	0.809641	+	1.40234i
$300$		0			0
$301$	10.5000	+	18.1865i	0.605210	+	1.04825i
$302$	10.0000	+	17.3205i	0.575435	+	0.996683i
$303$		0			0
$304$	0.500000	+	4.33013i	0.0286770	+	0.248350i
$305$	−4.00000			−0.229039
$306$		0			0
$307$	−6.00000	−	10.3923i	−0.342438	−	0.593120i	0.642447	−	0.766330i	$-0.277919\pi$
$307$	−6.00000	−	10.3923i	−0.342438	−	0.593120i	−0.984885	+	0.173210i	$0.944586\pi$
$308$	−3.00000	+	5.19615i	−0.170941	+	0.296078i
$309$		0			0
$310$	2.00000	−	3.46410i	0.113592	−	0.196748i
$311$	−34.0000			−1.92796			−0.963982	−	0.265969i	$-0.914308\pi$
$311$	−34.0000			−1.92796			−0.963982	+	0.265969i	$0.914308\pi$
$312$		0			0
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	−0.993186	−	0.116543i	$-0.962819\pi$
$313$	−7.00000	+	12.1244i	−0.395663	+	0.685309i	0.597522	+	0.801852i	$0.296152\pi$
$314$	3.50000	−	6.06218i	0.197516	−	0.342108i
$315$		0			0
$316$	5.00000			0.281272
$317$	−12.0000	+	20.7846i	−0.673987	+	1.16738i	0.302777	+	0.953062i	$0.402086\pi$
$317$	−12.0000	+	20.7846i	−0.673987	+	1.16738i	−0.976764	+	0.214318i	$0.931247\pi$
$318$		0			0
$319$	−4.00000	+	6.92820i	−0.223957	+	0.387905i
$320$	−2.00000	−	3.46410i	−0.111803	−	0.193649i
$321$		0			0
$322$	12.0000			0.668734
$323$		0			0
$324$		0			0
$325$	38.5000	+	66.6840i	2.13560	+	3.69896i
$326$	5.50000	+	9.52628i	0.304617	+	0.527612i
$327$		0			0
$328$	−2.00000	−	3.46410i	−0.110432	−	0.191273i
$329$	−3.00000	+	5.19615i	−0.165395	+	0.286473i
$330$		0			0
$331$	23.0000			1.26419			0.632097	−	0.774889i	$-0.282194\pi$
$331$	23.0000			1.26419			0.632097	+	0.774889i	$0.282194\pi$
$332$	−6.00000	+	10.3923i	−0.329293	+	0.570352i
$333$		0			0
$334$	6.00000			0.328305
$335$	12.0000			0.655630
$336$		0			0
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	0.632882	−	0.774248i	$-0.281872\pi$
$337$	−6.50000	−	11.2583i	−0.354078	−	0.613280i	−0.986960	+	0.160968i	$0.948538\pi$
$338$	18.0000	−	31.1769i	0.979071	−	1.69580i
$339$		0			0
$340$		0			0
$341$	−2.00000			−0.108306
$342$		0			0
$343$	15.0000			0.809924
$344$	3.50000	+	6.06218i	0.188707	+	0.326851i
$345$		0			0
$346$	−6.00000	+	10.3923i	−0.322562	+	0.558694i
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	0.947067	+	0.321037i	$0.104031\pi$
$347$	14.0000	+	24.2487i	0.751559	+	1.30174i	−0.195507	+	0.980702i	$0.562635\pi$
$348$		0			0
$349$	31.0000			1.65939			0.829696	−	0.558216i	$-0.188514\pi$
$349$	31.0000			1.65939			0.829696	+	0.558216i	$0.188514\pi$
$350$	33.0000			1.76392
$351$		0			0
$352$	−1.00000	+	1.73205i	−0.0533002	+	0.0923186i
$353$		0			0			−	1.00000i	$-0.5\pi$
$353$		0			0				1.00000i	$0.5\pi$
$354$		0			0
$355$	4.00000	−	6.92820i	0.212298	−	0.367711i
$356$	9.00000	+	15.5885i	0.476999	+	0.826187i
$357$		0			0
$358$	6.00000	+	10.3923i	0.317110	+	0.549250i
$359$	−6.00000	−	10.3923i	−0.316668	−	0.548485i	0.663123	−	0.748511i	$-0.269231\pi$
$359$	−6.00000	−	10.3923i	−0.316668	−	0.548485i	−0.979791	+	0.200026i	$0.935897\pi$
$360$		0			0
$361$	13.0000	+	13.8564i	0.684211	+	0.729285i
$362$	2.00000			0.105118
$363$		0			0
$364$	−10.5000	−	18.1865i	−0.550350	−	0.953233i
$365$	6.00000	−	10.3923i	0.314054	−	0.543958i
$366$		0			0
$367$	−9.50000	+	16.4545i	−0.495896	+	0.858917i	−0.999989	−	0.00473247i	$-0.998494\pi$
$367$	−9.50000	+	16.4545i	−0.495896	+	0.858917i	0.504093	+	0.863649i	$0.331827\pi$
$368$	4.00000			0.208514
$369$		0			0
$370$	14.0000	−	24.2487i	0.727825	−	1.26063i
$371$	6.00000	−	10.3923i	0.311504	−	0.539542i
$372$		0			0
$373$	−22.0000			−1.13912			−0.569558	−	0.821951i	$-0.692886\pi$
$373$	−22.0000			−1.13912			−0.569558	+	0.821951i	$0.692886\pi$
$374$		0			0
$375$		0			0
$376$	−1.00000	+	1.73205i	−0.0515711	+	0.0893237i
$377$	−14.0000	−	24.2487i	−0.721037	−	1.24887i
$378$		0			0
$379$	−21.0000			−1.07870			−0.539349	−	0.842082i	$-0.681330\pi$
$379$	−21.0000			−1.07870			−0.539349	+	0.842082i	$0.681330\pi$
$380$	−16.0000	−	6.92820i	−0.820783	−	0.355409i
$381$		0			0
$382$	10.0000	+	17.3205i	0.511645	+	0.886194i
$383$	−7.00000	−	12.1244i	−0.357683	−	0.619526i	0.629890	−	0.776684i	$-0.283100\pi$
$383$	−7.00000	−	12.1244i	−0.357683	−	0.619526i	−0.987573	+	0.157159i	$0.949767\pi$
$384$		0			0
$385$	−12.0000	−	20.7846i	−0.611577	−	1.05928i
$386$	−10.5000	+	18.1865i	−0.534436	+	0.925670i
$387$		0			0
$388$	10.0000			0.507673
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	0.383076	+	0.923717i	$0.374865\pi$
$389$	−12.0000	+	20.7846i	−0.608424	+	1.05382i	−0.991500	+	0.130105i	$0.958469\pi$
$390$		0			0
$391$		0			0
$392$	−2.00000			−0.101015
$393$		0			0
$394$	5.00000	+	8.66025i	0.251896	+	0.436297i
$395$	−10.0000	+	17.3205i	−0.503155	+	0.871489i
$396$		0			0
$397$	6.50000	+	11.2583i	0.326226	+	0.565039i	0.981760	−	0.190126i	$-0.0608897\pi$
$397$	6.50000	+	11.2583i	0.326226	+	0.565039i	−0.655534	+	0.755166i	$0.727556\pi$
$398$	7.00000			0.350878
$399$		0			0
$400$	11.0000			0.550000
$401$	5.00000	+	8.66025i	0.249688	+	0.432472i	0.963439	−	0.267927i	$-0.0863386\pi$
$401$	5.00000	+	8.66025i	0.249688	+	0.432472i	−0.713751	+	0.700399i	$0.753005\pi$
$402$		0			0
$403$	3.50000	−	6.06218i	0.174347	−	0.301979i
$404$	1.00000	+	1.73205i	0.0497519	+	0.0861727i
$405$		0			0
$406$	−12.0000			−0.595550
$407$	−14.0000			−0.693954
$408$		0			0
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	−0.962757	−	0.270367i	$-0.912855\pi$
$409$	−5.00000	+	8.66025i	−0.247234	+	0.428222i	0.715523	+	0.698589i	$0.246188\pi$
$410$	16.0000			0.790184
$411$		0			0
$412$	−4.50000	+	7.79423i	−0.221699	+	0.383994i
$413$	9.00000	+	15.5885i	0.442861	+	0.767058i
$414$		0			0
$415$	−24.0000	−	41.5692i	−1.17811	−	2.04055i
$416$	−3.50000	−	6.06218i	−0.171602	−	0.297223i
$417$		0			0
$418$	1.00000	+	8.66025i	0.0489116	+	0.423587i
$419$	−30.0000			−1.46560			−0.732798	−	0.680446i	$-0.761786\pi$
$419$	−30.0000			−1.46560			−0.732798	+	0.680446i	$0.761786\pi$
$420$		0			0
$421$	−13.0000	−	22.5167i	−0.633581	−	1.09739i	−0.986814	−	0.161859i	$-0.948251\pi$
$421$	−13.0000	−	22.5167i	−0.633581	−	1.09739i	0.353233	−	0.935536i	$-0.385082\pi$
$422$	4.50000	−	7.79423i	0.219057	−	0.379417i
$423$		0			0
$424$	2.00000	−	3.46410i	0.0971286	−	0.168232i
$425$		0			0
$426$		0			0
$427$	−1.50000	+	2.59808i	−0.0725901	+	0.125730i
$428$	1.00000	−	1.73205i	0.0483368	−	0.0837218i
$429$		0			0
$430$	−28.0000			−1.35028
$431$	3.00000	−	5.19615i	0.144505	−	0.250290i	−0.784683	−	0.619897i	$-0.787174\pi$
$431$	3.00000	−	5.19615i	0.144505	−	0.250290i	0.929188	+	0.369607i	$0.120508\pi$
$432$		0			0
$433$	−11.5000	+	19.9186i	−0.552655	+	0.957226i	0.445427	+	0.895318i	$0.353052\pi$
$433$	−11.5000	+	19.9186i	−0.552655	+	0.957226i	−0.998082	+	0.0619079i	$0.980282\pi$
$434$	−1.50000	−	2.59808i	−0.0720023	−	0.124712i
$435$		0			0
$436$	6.00000			0.287348
$437$	14.0000	−	10.3923i	0.669711	−	0.497131i
$438$		0			0
$439$	−11.5000	−	19.9186i	−0.548865	−	0.950662i	−0.998353	−	0.0573756i	$-0.981727\pi$
$439$	−11.5000	−	19.9186i	−0.548865	−	0.950662i	0.449488	−	0.893287i	$-0.351607\pi$
$440$	−4.00000	−	6.92820i	−0.190693	−	0.330289i
$441$		0			0
$442$		0			0
$443$	2.00000	−	3.46410i	0.0950229	−	0.164584i	−0.814595	−	0.580030i	$-0.803041\pi$
$443$	2.00000	−	3.46410i	0.0950229	−	0.164584i	0.909618	+	0.415445i	$0.136374\pi$
$444$		0			0
$445$	−72.0000			−3.41313
$446$	2.50000	−	4.33013i	0.118378	−	0.205037i
$447$		0			0
$448$	−3.00000			−0.141737
$449$	−16.0000			−0.755087			−0.377543	−	0.925992i	$-0.623231\pi$
$449$	−16.0000			−0.755087			−0.377543	+	0.925992i	$0.623231\pi$
$450$		0			0
$451$	−4.00000	−	6.92820i	−0.188353	−	0.326236i
$452$	1.00000	−	1.73205i	0.0470360	−	0.0814688i
$453$		0			0
$454$	−2.00000	−	3.46410i	−0.0938647	−	0.162578i
$455$	84.0000			3.93798
$456$		0			0
$457$	29.0000			1.35656			0.678281	−	0.734802i	$-0.262725\pi$
$457$	29.0000			1.35656			0.678281	+	0.734802i	$0.262725\pi$
$458$	−3.50000	−	6.06218i	−0.163544	−	0.283267i
$459$		0			0
$460$	−8.00000	+	13.8564i	−0.373002	+	0.646058i
$461$	−17.0000	−	29.4449i	−0.791769	−	1.37138i	−0.924871	−	0.380282i	$-0.875827\pi$
$461$	−17.0000	−	29.4449i	−0.791769	−	1.37138i	0.133102	−	0.991102i	$-0.457506\pi$
$462$		0			0
$463$	19.0000			0.883005			0.441502	−	0.897260i	$-0.354446\pi$
$463$	19.0000			0.883005			0.441502	+	0.897260i	$0.354446\pi$
$464$	−4.00000			−0.185695
$465$		0			0
$466$	−3.00000	+	5.19615i	−0.138972	+	0.240707i
$467$	8.00000			0.370196			0.185098	−	0.982720i	$-0.440740\pi$
$467$	8.00000			0.370196			0.185098	+	0.982720i	$0.440740\pi$
$468$		0			0
$469$	4.50000	−	7.79423i	0.207791	−	0.359904i
$470$	−4.00000	−	6.92820i	−0.184506	−	0.319574i
$471$		0			0
$472$	3.00000	+	5.19615i	0.138086	+	0.239172i
$473$	7.00000	+	12.1244i	0.321860	+	0.557478i
$474$		0			0
$475$	38.5000	−	28.5788i	1.76650	−	1.31129i
$476$		0			0
$477$		0			0
$478$	−12.0000	−	20.7846i	−0.548867	−	0.950666i
$479$	17.0000	−	29.4449i	0.776750	−	1.34537i	−0.157056	−	0.987590i	$-0.550200\pi$
$479$	17.0000	−	29.4449i	0.776750	−	1.34537i	0.933806	−	0.357780i	$-0.116466\pi$
$480$		0			0
$481$	24.5000	−	42.4352i	1.11710	−	1.93488i
$482$	−1.00000			−0.0455488
$483$		0			0
$484$	3.50000	−	6.06218i	0.159091	−	0.275554i
$485$	−20.0000	+	34.6410i	−0.908153	+	1.57297i
$486$		0			0
$487$	16.0000			0.725029			0.362515	−	0.931978i	$-0.381918\pi$
$487$	16.0000			0.725029			0.362515	+	0.931978i	$0.381918\pi$
$488$	−0.500000	+	0.866025i	−0.0226339	+	0.0392031i
$489$		0			0
$490$	4.00000	−	6.92820i	0.180702	−	0.312984i
$491$	13.0000	+	22.5167i	0.586682	+	1.01616i	0.994663	+	0.103173i	$0.0328994\pi$
$491$	13.0000	+	22.5167i	0.586682	+	1.01616i	−0.407982	+	0.912990i	$0.633767\pi$
$492$		0			0
$493$		0			0
$494$	−28.0000	−	12.1244i	−1.25978	−	0.545501i
$495$		0			0
$496$	−0.500000	−	0.866025i	−0.0224507	−	0.0388857i
$497$	−3.00000	−	5.19615i	−0.134568	−	0.233079i
$498$		0			0
$499$	5.50000	+	9.52628i	0.246214	+	0.426455i	0.962472	−	0.271380i	$-0.0874801\pi$
$499$	5.50000	+	9.52628i	0.246214	+	0.426455i	−0.716258	+	0.697835i	$0.754147\pi$
$500$	−12.0000	+	20.7846i	−0.536656	+	0.929516i
$501$		0			0
$502$	14.0000			0.624851
$503$	−6.00000	+	10.3923i	−0.267527	+	0.463370i	−0.968223	−	0.250090i	$-0.919540\pi$
$503$	−6.00000	+	10.3923i	−0.267527	+	0.463370i	0.700696	+	0.713460i	$0.252873\pi$
$504$		0			0
$505$	−8.00000			−0.355995
$506$	8.00000			0.355643
$507$		0			0
$508$		0			0
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	−0.924821	−	0.380402i	$-0.875786\pi$
$509$	−3.00000	+	5.19615i	−0.132973	+	0.230315i	0.791849	+	0.610718i	$0.209119\pi$
$510$		0			0
$511$	−4.50000	−	7.79423i	−0.199068	−	0.344796i
$512$	−1.00000			−0.0441942
$513$		0			0
$514$	−28.0000			−1.23503
$515$	−18.0000	−	31.1769i	−0.793175	−	1.37382i
$516$		0			0
$517$	−2.00000	+	3.46410i	−0.0879599	+	0.152351i
$518$	−10.5000	−	18.1865i	−0.461344	−	0.799070i
$519$		0			0
$520$	28.0000			1.22788
$521$	−38.0000			−1.66481			−0.832405	−	0.554168i	$-0.813037\pi$
$521$	−38.0000			−1.66481			−0.832405	+	0.554168i	$0.813037\pi$
$522$		0			0
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	0.352677	+	0.935745i	$0.385272\pi$
$523$	−14.5000	+	25.1147i	−0.634041	+	1.09819i	−0.986718	+	0.162446i	$0.948062\pi$
$524$	18.0000			0.786334
$525$		0			0
$526$	9.00000	−	15.5885i	0.392419	−	0.679689i
$527$		0			0
$528$		0			0
$529$	3.50000	+	6.06218i	0.152174	+	0.263573i
$530$	8.00000	+	13.8564i	0.347498	+	0.601884i
$531$		0			0
$532$	−10.5000	+	7.79423i	−0.455233	+	0.337923i
$533$	28.0000			1.21281
$534$		0			0
$535$	4.00000	+	6.92820i	0.172935	+	0.299532i
$536$	1.50000	−	2.59808i	0.0647901	−	0.112220i
$537$		0			0
$538$	−9.00000	+	15.5885i	−0.388018	+	0.672066i
$539$	−4.00000			−0.172292
$540$		0			0
$541$	9.50000	−	16.4545i	0.408437	−	0.707433i	−0.586278	−	0.810110i	$-0.699407\pi$
$541$	9.50000	−	16.4545i	0.408437	−	0.707433i	0.994715	+	0.102677i	$0.0327407\pi$
$542$	−4.00000	+	6.92820i	−0.171815	+	0.297592i
$543$		0			0
$544$		0			0
$545$	−12.0000	+	20.7846i	−0.514024	+	0.890315i
$546$		0			0
$547$	14.5000	−	25.1147i	0.619975	−	1.07383i	−0.369514	−	0.929225i	$-0.620476\pi$
$547$	14.5000	−	25.1147i	0.619975	−	1.07383i	0.989490	−	0.144604i	$-0.0461907\pi$
$548$	−1.00000	−	1.73205i	−0.0427179	−	0.0739895i
$549$		0			0
$550$	22.0000			0.938083
$551$	−14.0000	+	10.3923i	−0.596420	+	0.442727i
$552$		0			0
$553$	7.50000	+	12.9904i	0.318932	+	0.552407i
$554$	−13.0000	−	22.5167i	−0.552317	−	0.956641i
$555$		0			0
$556$	−10.5000	−	18.1865i	−0.445299	−	0.771281i
$557$	11.0000	−	19.0526i	0.466085	−	0.807283i	−0.533165	−	0.846011i	$-0.678997\pi$
$557$	11.0000	−	19.0526i	0.466085	−	0.807283i	0.999250	+	0.0387286i	$0.0123308\pi$
$558$		0			0
$559$	−49.0000			−2.07248
$560$	6.00000	−	10.3923i	0.253546	−	0.439155i
$561$		0			0
$562$	4.00000			0.168730
$563$	42.0000			1.77009			0.885044	−	0.465506i	$-0.154128\pi$
$563$	42.0000			1.77009			0.885044	+	0.465506i	$0.154128\pi$
$564$		0			0
$565$	4.00000	+	6.92820i	0.168281	+	0.291472i
$566$	−6.00000	+	10.3923i	−0.252199	+	0.436821i
$567$		0			0
$568$	−1.00000	−	1.73205i	−0.0419591	−	0.0726752i
$569$	−16.0000			−0.670755			−0.335377	−	0.942084i	$-0.608864\pi$
$569$	−16.0000			−0.670755			−0.335377	+	0.942084i	$0.608864\pi$
$570$		0			0
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$	−7.00000	−	12.1244i	−0.292685	−	0.506945i
$573$		0			0
$574$	6.00000	−	10.3923i	0.250435	−	0.433766i
$575$	−22.0000	−	38.1051i	−0.917463	−	1.58909i
$576$		0			0
$577$	2.00000			0.0832611			0.0416305	−	0.999133i	$-0.486745\pi$
$577$	2.00000			0.0832611			0.0416305	+	0.999133i	$0.486745\pi$
$578$	17.0000			0.707107
$579$		0			0
$580$	8.00000	−	13.8564i	0.332182	−	0.575356i
$581$	−36.0000			−1.49353
$582$		0			0
$583$	4.00000	−	6.92820i	0.165663	−	0.286937i
$584$	−1.50000	−	2.59808i	−0.0620704	−	0.107509i
$585$		0			0
$586$	9.00000	+	15.5885i	0.371787	+	0.643953i
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	0.618322	−	0.785925i	$-0.287813\pi$
$587$	−9.00000	−	15.5885i	−0.371470	−	0.643404i	−0.989792	+	0.142520i	$0.954479\pi$
$588$		0			0
$589$	−4.00000	−	1.73205i	−0.164817	−	0.0713679i
$590$	−24.0000			−0.988064
$591$		0			0
$592$	−3.50000	−	6.06218i	−0.143849	−	0.249154i
$593$	17.0000	−	29.4449i	0.698106	−	1.20916i	−0.271016	−	0.962575i	$-0.587360\pi$
$593$	17.0000	−	29.4449i	0.698106	−	1.20916i	0.969122	−	0.246581i	$-0.0793071\pi$
$594$		0			0
$595$		0			0
$596$	18.0000			0.737309
$597$		0			0
$598$	−14.0000	+	24.2487i	−0.572503	+	0.991604i
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	−0.377869	−	0.925859i	$-0.623343\pi$
$599$	15.0000	−	25.9808i	0.612883	−	1.06155i	0.990752	−	0.135686i	$-0.0433238\pi$
$600$		0			0
$601$	19.0000			0.775026			0.387513	−	0.921864i	$-0.373334\pi$
$601$	19.0000			0.775026			0.387513	+	0.921864i	$0.373334\pi$
$602$	−10.5000	+	18.1865i	−0.427948	+	0.741228i
$603$		0			0
$604$	−10.0000	+	17.3205i	−0.406894	+	0.704761i
$605$	14.0000	+	24.2487i	0.569181	+	0.985850i
$606$		0			0
$607$	41.0000			1.66414			0.832069	−	0.554672i	$-0.187156\pi$
$607$	41.0000			1.66414			0.832069	+	0.554672i	$0.187156\pi$
$608$	−3.50000	+	2.59808i	−0.141944	+	0.105366i
$609$		0			0
$610$	−2.00000	−	3.46410i	−0.0809776	−	0.140257i
$611$	−7.00000	−	12.1244i	−0.283190	−	0.490499i
$612$		0			0
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	0.938967	+	0.344008i	$0.111785\pi$
$613$	19.0000	+	32.9090i	0.767403	+	1.32918i	−0.171564	+	0.985173i	$0.554882\pi$
$614$	6.00000	−	10.3923i	0.242140	−	0.419399i
$615$		0			0
$616$	−6.00000			−0.241747
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	−0.626017	−	0.779809i	$-0.715316\pi$
$617$	9.00000	−	15.5885i	0.362326	−	0.627568i	0.988343	+	0.152242i	$0.0486493\pi$
$618$		0			0
$619$	−23.0000			−0.924448			−0.462224	−	0.886763i	$-0.652948\pi$
$619$	−23.0000			−0.924448			−0.462224	+	0.886763i	$0.652948\pi$
$620$	4.00000			0.160644
$621$		0			0
$622$	−17.0000	−	29.4449i	−0.681638	−	1.18063i
$623$	−27.0000	+	46.7654i	−1.08173	+	1.87362i
$624$		0			0
$625$	−20.5000	−	35.5070i	−0.820000	−	1.42028i
$626$	−14.0000			−0.559553
$627$		0			0
$628$	7.00000			0.279330
$629$		0			0
$630$		0			0
$631$	9.50000	−	16.4545i	0.378189	−	0.655043i	−0.612610	−	0.790386i	$-0.709880\pi$
$631$	9.50000	−	16.4545i	0.378189	−	0.655043i	0.990799	+	0.135343i	$0.0432136\pi$
$632$	2.50000	+	4.33013i	0.0994447	+	0.172243i
$633$		0			0
$634$	−24.0000			−0.953162
$635$		0			0
$636$		0			0
$637$	7.00000	−	12.1244i	0.277350	−	0.480384i
$638$	−8.00000			−0.316723
$639$		0			0
$640$	2.00000	−	3.46410i	0.0790569	−	0.136931i
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	0.987200	−	0.159489i	$-0.0509845\pi$
$641$	9.00000	+	15.5885i	0.355479	+	0.615707i	−0.631721	+	0.775196i	$0.717651\pi$
$642$		0			0
$643$	−6.50000	−	11.2583i	−0.256335	−	0.443985i	0.708922	−	0.705287i	$-0.249182\pi$
$643$	−6.50000	−	11.2583i	−0.256335	−	0.443985i	−0.965257	+	0.261301i	$0.915848\pi$
$644$	6.00000	+	10.3923i	0.236433	+	0.409514i
$645$		0			0
$646$		0			0
$647$	28.0000			1.10079			0.550397	−	0.834903i	$-0.314476\pi$
$647$	28.0000			1.10079			0.550397	+	0.834903i	$0.314476\pi$
$648$		0			0
$649$	6.00000	+	10.3923i	0.235521	+	0.407934i
$650$	−38.5000	+	66.6840i	−1.51009	+	2.61556i
$651$		0			0
$652$	−5.50000	+	9.52628i	−0.215397	+	0.373078i
$653$	30.0000			1.17399			0.586995	−	0.809590i	$-0.300311\pi$
$653$	30.0000			1.17399			0.586995	+	0.809590i	$0.300311\pi$
$654$		0			0
$655$	−36.0000	+	62.3538i	−1.40664	+	2.43637i
$656$	2.00000	−	3.46410i	0.0780869	−	0.135250i
$657$		0			0
$658$	−6.00000			−0.233904
$659$	−5.00000	+	8.66025i	−0.194772	+	0.337356i	−0.946826	−	0.321746i	$-0.895730\pi$
$659$	−5.00000	+	8.66025i	−0.194772	+	0.337356i	0.752054	+	0.659102i	$0.229063\pi$
$660$		0			0
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	−0.946729	−	0.322031i	$-0.895634\pi$
$661$	−5.00000	+	8.66025i	−0.194477	+	0.336845i	0.752252	+	0.658876i	$0.228968\pi$
$662$	11.5000	+	19.9186i	0.446960	+	0.774158i
$663$		0			0
$664$	−12.0000			−0.465690
$665$	−6.00000	−	51.9615i	−0.232670	−	2.01498i
$666$		0			0
$667$	8.00000	+	13.8564i	0.309761	+	0.536522i
$668$	3.00000	+	5.19615i	0.116073	+	0.201045i
$669$		0			0
$670$	6.00000	+	10.3923i	0.231800	+	0.401490i
$671$	−1.00000	+	1.73205i	−0.0386046	+	0.0668651i
$672$		0			0
$673$	−1.00000			−0.0385472			−0.0192736	−	0.999814i	$-0.506135\pi$
$673$	−1.00000			−0.0385472			−0.0192736	+	0.999814i	$0.506135\pi$
$674$	6.50000	−	11.2583i	0.250371	−	0.433655i
$675$		0			0
$676$	36.0000			1.38462
$677$	38.0000			1.46046			0.730229	−	0.683202i	$-0.239413\pi$
$677$	38.0000			1.46046			0.730229	+	0.683202i	$0.239413\pi$
$678$		0			0
$679$	15.0000	+	25.9808i	0.575647	+	0.997050i
$680$		0			0
$681$		0			0
$682$	−1.00000	−	1.73205i	−0.0382920	−	0.0663237i
$683$	−40.0000			−1.53056			−0.765279	−	0.643699i	$-0.777399\pi$
$683$	−40.0000			−1.53056			−0.765279	+	0.643699i	$0.777399\pi$
$684$		0			0
$685$	8.00000			0.305664
$686$	7.50000	+	12.9904i	0.286351	+	0.495975i
$687$		0			0
$688$	−3.50000	+	6.06218i	−0.133436	+	0.231118i
$689$	14.0000	+	24.2487i	0.533358	+	0.923802i
$690$		0			0
$691$	12.0000			0.456502			0.228251	−	0.973602i	$-0.426699\pi$
$691$	12.0000			0.456502			0.228251	+	0.973602i	$0.426699\pi$
$692$	−12.0000			−0.456172
$693$		0			0
$694$	−14.0000	+	24.2487i	−0.531433	+	0.920468i
$695$	84.0000			3.18630
$696$		0			0
$697$		0			0
$698$	15.5000	+	26.8468i	0.586684	+	1.01617i
$699$		0			0
$700$	16.5000	+	28.5788i	0.623641	+	1.08018i
$701$	4.00000	+	6.92820i	0.151078	+	0.261675i	0.931624	−	0.363424i	$-0.118392\pi$
$701$	4.00000	+	6.92820i	0.151078	+	0.261675i	−0.780546	+	0.625098i	$0.785059\pi$
$702$		0			0
$703$	−28.0000	−	12.1244i	−1.05604	−	0.457279i
$704$	−2.00000			−0.0753778
$705$		0			0
$706$		0			0
$707$	−3.00000	+	5.19615i	−0.112827	+	0.195421i
$708$		0			0
$709$	1.50000	−	2.59808i	0.0563337	−	0.0975728i	−0.836483	−	0.547992i	$-0.815392\pi$
$709$	1.50000	−	2.59808i	0.0563337	−	0.0975728i	0.892817	+	0.450420i	$0.148726\pi$
$710$	8.00000			0.300235
$711$		0			0
$712$	−9.00000	+	15.5885i	−0.337289	+	0.584202i
$713$	−2.00000	+	3.46410i	−0.0749006	+	0.129732i
$714$		0			0
$715$	56.0000			2.09428
$716$	−6.00000	+	10.3923i	−0.224231	+	0.388379i
$717$		0			0
$718$	6.00000	−	10.3923i	0.223918	−	0.387837i
$719$	8.00000	+	13.8564i	0.298350	+	0.516757i	0.975759	−	0.218850i	$-0.0702305\pi$
$719$	8.00000	+	13.8564i	0.298350	+	0.516757i	−0.677409	+	0.735607i	$0.736897\pi$
$720$		0			0
$721$	−27.0000			−1.00553
$722$	−5.50000	+	18.1865i	−0.204689	+	0.676833i
$723$		0			0
$724$	1.00000	+	1.73205i	0.0371647	+	0.0643712i
$725$	22.0000	+	38.1051i	0.817059	+	1.41519i
$726$		0			0
$727$	−18.5000	−	32.0429i	−0.686127	−	1.18841i	−0.973081	−	0.230463i	$-0.925976\pi$
$727$	−18.5000	−	32.0429i	−0.686127	−	1.18841i	0.286954	−	0.957944i	$-0.407357\pi$
$728$	10.5000	−	18.1865i	0.389156	−	0.674038i
$729$		0			0
$730$	12.0000			0.444140
$731$		0			0
$732$		0			0
$733$	30.0000			1.10808			0.554038	−	0.832492i	$-0.313086\pi$
$733$	30.0000			1.10808			0.554038	+	0.832492i	$0.313086\pi$
$734$	−19.0000			−0.701303
$735$		0			0
$736$	2.00000	+	3.46410i	0.0737210	+	0.127688i
$737$	3.00000	−	5.19615i	0.110506	−	0.191403i
$738$		0			0
$739$	−17.5000	−	30.3109i	−0.643748	−	1.11500i	−0.984589	−	0.174883i	$-0.944045\pi$
$739$	−17.5000	−	30.3109i	−0.643748	−	1.11500i	0.340841	−	0.940121i	$-0.389288\pi$
$740$	28.0000			1.02930
$741$		0			0
$742$	12.0000			0.440534
$743$	13.0000	+	22.5167i	0.476924	+	0.826056i	0.999650	−	0.0264443i	$-0.00841845\pi$
$743$	13.0000	+	22.5167i	0.476924	+	0.826056i	−0.522727	+	0.852500i	$0.675085\pi$
$744$		0			0
$745$	−36.0000	+	62.3538i	−1.31894	+	2.28447i
$746$	−11.0000	−	19.0526i	−0.402739	−	0.697564i
$747$		0			0
$748$		0			0
$749$	6.00000			0.219235
$750$		0			0
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	−0.431390	−	0.902165i	$-0.641977\pi$
$751$	15.5000	−	26.8468i	0.565603	−	0.979653i	0.996993	−	0.0774878i	$-0.0246899\pi$
$752$	−2.00000			−0.0729325
$753$		0			0
$754$	14.0000	−	24.2487i	0.509850	−	0.883086i
$755$	−40.0000	−	69.2820i	−1.45575	−	2.52143i
$756$		0			0
$757$	11.5000	+	19.9186i	0.417975	+	0.723953i	0.995736	−	0.0922527i	$-0.0294068\pi$
$757$	11.5000	+	19.9186i	0.417975	+	0.723953i	−0.577761	+	0.816206i	$0.696073\pi$
$758$	−10.5000	−	18.1865i	−0.381377	−	0.660565i
$759$		0			0
$760$	−2.00000	−	17.3205i	−0.0725476	−	0.628281i
$761$	42.0000			1.52250			0.761249	−	0.648459i	$-0.224586\pi$
$761$	42.0000			1.52250			0.761249	+	0.648459i	$0.224586\pi$
$762$		0			0
$763$	9.00000	+	15.5885i	0.325822	+	0.564340i
$764$	−10.0000	+	17.3205i	−0.361787	+	0.626634i
$765$		0			0
$766$	7.00000	−	12.1244i	0.252920	−	0.438071i
$767$	−42.0000			−1.51653
$768$		0			0
$769$	2.50000	−	4.33013i	0.0901523	−	0.156148i	−0.817423	−	0.576038i	$-0.804598\pi$
$769$	2.50000	−	4.33013i	0.0901523	−	0.156148i	0.907575	+	0.419890i	$0.137931\pi$
$770$	12.0000	−	20.7846i	0.432450	−	0.749025i
$771$		0			0
$772$	−21.0000			−0.755807
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	−0.807018	−	0.590527i	$-0.798920\pi$
$773$	3.00000	−	5.19615i	0.107903	−	0.186893i	0.914920	+	0.403634i	$0.132253\pi$
$774$		0			0
$775$	−5.50000	+	9.52628i	−0.197566	+	0.342194i
$776$	5.00000	+	8.66025i	0.179490	+	0.310885i
$777$		0			0
$778$	−24.0000			−0.860442
$779$	−2.00000	−	17.3205i	−0.0716574	−	0.620572i
$780$		0			0
$781$	−2.00000	−	3.46410i	−0.0715656	−	0.123955i
$782$		0			0
$783$		0			0
$784$	−1.00000	−	1.73205i	−0.0357143	−	0.0618590i
$785$	−14.0000	+	24.2487i	−0.499681	+	0.865474i
$786$		0			0
$787$	49.0000			1.74666			0.873331	−	0.487128i	$-0.161955\pi$
$787$	49.0000			1.74666			0.873331	+	0.487128i	$0.161955\pi$
$788$	−5.00000	+	8.66025i	−0.178118	+	0.308509i
$789$		0			0
$790$	−20.0000			−0.711568
$791$	6.00000			0.213335
$792$		0			0
$793$	−3.50000	−	6.06218i	−0.124289	−	0.215274i
$794$	−6.50000	+	11.2583i	−0.230676	+	0.399543i
$795$		0			0
$796$	3.50000	+	6.06218i	0.124054	+	0.214868i
$797$	−6.00000			−0.212531			−0.106265	−	0.994338i	$-0.533889\pi$
$797$	−6.00000			−0.212531			−0.106265	+	0.994338i	$0.533889\pi$
$798$		0			0
$799$		0			0
$800$	5.50000	+	9.52628i	0.194454	+	0.336805i
$801$		0			0
$802$	−5.00000	+	8.66025i	−0.176556	+	0.305804i
$803$	−3.00000	−	5.19615i	−0.105868	−	0.183368i
$804$		0			0
$805$	−48.0000			−1.69178
$806$	7.00000			0.246564
$807$		0			0
$808$	−1.00000	+	1.73205i	−0.0351799	+	0.0609333i
$809$	−36.0000			−1.26569			−0.632846	−	0.774277i	$-0.718114\pi$
$809$	−36.0000			−1.26569			−0.632846	+	0.774277i	$0.718114\pi$
$810$		0			0
$811$	−18.0000	+	31.1769i	−0.632065	+	1.09477i	0.355063	+	0.934842i	$0.384459\pi$
$811$	−18.0000	+	31.1769i	−0.632065	+	1.09477i	−0.987129	+	0.159927i	$0.948874\pi$
$812$	−6.00000	−	10.3923i	−0.210559	−	0.364698i
$813$		0			0
$814$	−7.00000	−	12.1244i	−0.245350	−	0.424958i
$815$	−22.0000	−	38.1051i	−0.770626	−	1.33476i
$816$		0			0
$817$	3.50000	+	30.3109i	0.122449	+	1.06044i
$818$	−10.0000			−0.349642
$819$		0			0
$820$	8.00000	+	13.8564i	0.279372	+	0.483887i
$821$	6.00000	−	10.3923i	0.209401	−	0.362694i	−0.742125	−	0.670262i	$-0.766182\pi$
$821$	6.00000	−	10.3923i	0.209401	−	0.362694i	0.951526	+	0.307568i	$0.0995151\pi$
$822$		0			0
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	0.172379	+	0.985031i	$0.444854\pi$
$823$	−22.0000	+	38.1051i	−0.766872	+	1.32826i	−0.939251	+	0.343230i	$0.888479\pi$
$824$	−9.00000			−0.313530
$825$		0			0
$826$	−9.00000	+	15.5885i	−0.313150	+	0.542392i
$827$	4.00000	−	6.92820i	0.139094	−	0.240917i	−0.788060	−	0.615598i	$-0.788914\pi$
$827$	4.00000	−	6.92820i	0.139094	−	0.240917i	0.927154	+	0.374681i	$0.122248\pi$
$828$		0			0
$829$	45.0000			1.56291			0.781457	−	0.623959i	$-0.214477\pi$
$829$	45.0000			1.56291			0.781457	+	0.623959i	$0.214477\pi$
$830$	24.0000	−	41.5692i	0.833052	−	1.44289i
$831$		0			0
$832$	3.50000	−	6.06218i	0.121341	−	0.210168i
$833$		0			0
$834$		0			0
$835$	−24.0000			−0.830554
$836$	−7.00000	+	5.19615i	−0.242100	+	0.179713i
$837$		0			0
$838$	−15.0000	−	25.9808i	−0.518166	−	0.897491i
$839$	−20.0000	−	34.6410i	−0.690477	−	1.19594i	−0.971682	−	0.236293i	$-0.924067\pi$
$839$	−20.0000	−	34.6410i	−0.690477	−	1.19594i	0.281205	−	0.959648i	$-0.409266\pi$
$840$		0			0
$841$	6.50000	+	11.2583i	0.224138	+	0.388218i
$842$	13.0000	−	22.5167i	0.448010	−	0.775975i
$843$		0			0
$844$	9.00000			0.309793
$845$	−72.0000	+	124.708i	−2.47688	+	4.29007i
$846$		0			0
$847$	21.0000			0.721569
$848$	4.00000			0.137361
$849$		0			0
$850$		0			0
$851$	−14.0000	+	24.2487i	−0.479914	+	0.831235i
$852$		0			0
$853$	4.50000	+	7.79423i	0.154077	+	0.266869i	0.932723	−	0.360595i	$-0.117426\pi$
$853$	4.50000	+	7.79423i	0.154077	+	0.266869i	−0.778646	+	0.627464i	$0.784093\pi$
$854$	−3.00000			−0.102658
$855$		0			0
$856$	2.00000			0.0683586
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	0.810227	−	0.586116i	$-0.199344\pi$
$857$	−3.00000	−	5.19615i	−0.102478	−	0.177497i	−0.912705	+	0.408619i	$0.866010\pi$
$858$		0			0
$859$	−3.50000	+	6.06218i	−0.119418	+	0.206839i	−0.919537	−	0.393003i	$-0.871436\pi$
$859$	−3.50000	+	6.06218i	−0.119418	+	0.206839i	0.800119	+	0.599841i	$0.204770\pi$
$860$	−14.0000	−	24.2487i	−0.477396	−	0.826874i
$861$		0			0
$862$	6.00000			0.204361
$863$	6.00000			0.204242			0.102121	−	0.994772i	$-0.467437\pi$
$863$	6.00000			0.204242			0.102121	+	0.994772i	$0.467437\pi$
$864$		0			0
$865$	24.0000	−	41.5692i	0.816024	−	1.41340i
$866$	−23.0000			−0.781572
$867$		0			0
$868$	1.50000	−	2.59808i	0.0509133	−	0.0881845i
$869$	5.00000	+	8.66025i	0.169613	+	0.293779i
$870$		0			0
$871$	10.5000	+	18.1865i	0.355779	+	0.616227i
$872$	3.00000	+	5.19615i	0.101593	+	0.175964i
$873$		0			0
$874$	16.0000	+	6.92820i	0.541208	+	0.234350i
$875$	−72.0000			−2.43404
$876$		0			0
$877$	−9.50000	−	16.4545i	−0.320792	−	0.555628i	0.659860	−	0.751389i	$-0.270616\pi$
$877$	−9.50000	−	16.4545i	−0.320792	−	0.555628i	−0.980652	+	0.195761i	$0.937282\pi$
$878$	11.5000	−	19.9186i	0.388106	−	0.672220i
$879$		0			0
$880$	4.00000	−	6.92820i	0.134840	−	0.233550i
$881$	24.0000			0.808581			0.404290	−	0.914631i	$-0.367519\pi$
$881$	24.0000			0.808581			0.404290	+	0.914631i	$0.367519\pi$
$882$		0			0
$883$	20.5000	−	35.5070i	0.689880	−	1.19491i	−0.281996	−	0.959415i	$-0.590997\pi$
$883$	20.5000	−	35.5070i	0.689880	−	1.19491i	0.971876	−	0.235492i	$-0.0756700\pi$
$884$		0			0
$885$		0			0
$886$	4.00000			0.134383
$887$	5.00000	−	8.66025i	0.167884	−	0.290783i	−0.769792	−	0.638295i	$-0.779640\pi$
$887$	5.00000	−	8.66025i	0.167884	−	0.290783i	0.937676	+	0.347512i	$0.112973\pi$
$888$		0			0
$889$		0			0
$890$	−36.0000	−	62.3538i	−1.20672	−	2.09011i
$891$		0			0
$892$	5.00000			0.167412
$893$	−7.00000	+	5.19615i	−0.234246	+	0.173883i
$894$		0			0
$895$	−24.0000	−	41.5692i	−0.802232	−	1.38951i
$896$	−1.50000	−	2.59808i	−0.0501115	−	0.0867956i
$897$		0			0
$898$	−8.00000	−	13.8564i	−0.266963	−	0.462394i
$899$	2.00000	−	3.46410i	0.0667037	−	0.115534i
$900$		0			0
$901$		0			0
$902$	4.00000	−	6.92820i	0.133185	−	0.230684i
$903$		0			0
$904$	2.00000			0.0665190
$905$	−8.00000			−0.265929
$906$		0			0
$907$	−10.0000	−	17.3205i	−0.332045	−	0.575118i	0.650868	−	0.759191i	$-0.274405\pi$
$907$	−10.0000	−	17.3205i	−0.332045	−	0.575118i	−0.982913	+	0.184073i	$0.941072\pi$
$908$	2.00000	−	3.46410i	0.0663723	−	0.114960i
$909$		0			0
$910$	42.0000	+	72.7461i	1.39229	+	2.41151i
$911$	12.0000			0.397578			0.198789	−	0.980042i	$-0.436299\pi$
$911$	12.0000			0.397578			0.198789	+	0.980042i	$0.436299\pi$
$912$		0			0
$913$	−24.0000			−0.794284
$914$	14.5000	+	25.1147i	0.479617	+	0.830722i
$915$		0			0
$916$	3.50000	−	6.06218i	0.115643	−	0.200300i
$917$	27.0000	+	46.7654i	0.891619	+	1.54433i
$918$		0			0
$919$	11.0000			0.362857			0.181428	−	0.983404i	$-0.441928\pi$
$919$	11.0000			0.362857			0.181428	+	0.983404i	$0.441928\pi$
$920$	−16.0000			−0.527504
$921$		0			0
$922$	17.0000	−	29.4449i	0.559865	−	0.969715i
$923$	14.0000			0.460816
$924$		0			0
$925$	−38.5000	+	66.6840i	−1.26587	+	2.19255i
$926$	9.50000	+	16.4545i	0.312189	+	0.540728i
$927$		0			0
$928$	−2.00000	−	3.46410i	−0.0656532	−	0.113715i
$929$	4.00000	+	6.92820i	0.131236	+	0.227307i	0.924153	−	0.382022i	$-0.124772\pi$
$929$	4.00000	+	6.92820i	0.131236	+	0.227307i	−0.792917	+	0.609329i	$0.791439\pi$
$930$		0			0
$931$	−8.00000	−	3.46410i	−0.262189	−	0.113531i
$932$	−6.00000			−0.196537
$933$		0			0
$934$	4.00000	+	6.92820i	0.130884	+	0.226698i
$935$		0			0
$936$		0			0
$937$	12.5000	−	21.6506i	0.408357	−	0.707295i	−0.586349	−	0.810059i	$-0.699435\pi$
$937$	12.5000	−	21.6506i	0.408357	−	0.707295i	0.994706	+	0.102763i	$0.0327685\pi$
$938$	9.00000			0.293860
$939$		0			0
$940$	4.00000	−	6.92820i	0.130466	−	0.225973i
$941$	8.00000	−	13.8564i	0.260793	−	0.451706i	−0.705660	−	0.708550i	$-0.749349\pi$
$941$	8.00000	−	13.8564i	0.260793	−	0.451706i	0.966453	+	0.256844i	$0.0826828\pi$
$942$		0			0
$943$	−16.0000			−0.521032
$944$	−3.00000	+	5.19615i	−0.0976417	+	0.169120i
$945$		0			0
$946$	−7.00000	+	12.1244i	−0.227590	+	0.394197i
$947$	27.0000	+	46.7654i	0.877382	+	1.51967i	0.854203	+	0.519939i	$0.174045\pi$
$947$	27.0000	+	46.7654i	0.877382	+	1.51967i	0.0231788	+	0.999731i	$0.492621\pi$
$948$		0			0
$949$	21.0000			0.681689
$950$	44.0000	+	19.0526i	1.42755	+	0.618147i
$951$		0			0
$952$		0			0
$953$	−5.00000	−	8.66025i	−0.161966	−	0.280533i	0.773608	−	0.633665i	$-0.218450\pi$
$953$	−5.00000	−	8.66025i	−0.161966	−	0.280533i	−0.935574	+	0.353132i	$0.885117\pi$
$954$		0			0
$955$	−40.0000	−	69.2820i	−1.29437	−	2.24191i
$956$	12.0000	−	20.7846i	0.388108	−	0.672222i
$957$		0			0
$958$	34.0000			1.09849
$959$	3.00000	−	5.19615i	0.0968751	−	0.167793i
$960$		0			0
$961$	−30.0000			−0.967742
$962$	49.0000			1.57982
$963$		0			0
$964$	−0.500000	−	0.866025i	−0.0161039	−	0.0278928i
$965$	42.0000	−	72.7461i	1.35203	−	2.34178i
$966$		0			0
$967$	4.50000	+	7.79423i	0.144710	+	0.250645i	0.929265	−	0.369414i	$-0.120442\pi$
$967$	4.50000	+	7.79423i	0.144710	+	0.250645i	−0.784555	+	0.620060i	$0.787108\pi$
$968$	7.00000			0.224989
$969$		0			0
$970$	−40.0000			−1.28432
$971$	7.00000	+	12.1244i	0.224641	+	0.389089i	0.956212	−	0.292676i	$-0.0945458\pi$
$971$	7.00000	+	12.1244i	0.224641	+	0.389089i	−0.731571	+	0.681765i	$0.761212\pi$
$972$		0			0
$973$	31.5000	−	54.5596i	1.00984	−	1.74910i
$974$	8.00000	+	13.8564i	0.256337	+	0.443988i
$975$		0			0
$976$	−1.00000			−0.0320092
$977$	−14.0000			−0.447900			−0.223950	−	0.974601i	$-0.571895\pi$
$977$	−14.0000			−0.447900			−0.223950	+	0.974601i	$0.571895\pi$
$978$		0			0
$979$	−18.0000	+	31.1769i	−0.575282	+	0.996419i
$980$	8.00000			0.255551
$981$		0			0
$982$	−13.0000	+	22.5167i	−0.414847	+	0.718536i
$983$	3.00000	+	5.19615i	0.0956851	+	0.165732i	0.909894	−	0.414840i	$-0.136162\pi$
$983$	3.00000	+	5.19615i	0.0956851	+	0.165732i	−0.814209	+	0.580572i	$0.802829\pi$
$984$		0			0
$985$	−20.0000	−	34.6410i	−0.637253	−	1.10375i
$986$		0			0
$987$		0			0
$988$	−3.50000	−	30.3109i	−0.111350	−	0.964318i
$989$	28.0000			0.890348
$990$		0			0
$991$	14.5000	+	25.1147i	0.460608	+	0.797796i	0.998991	−	0.0449040i	$-0.0142982\pi$
$991$	14.5000	+	25.1147i	0.460608	+	0.797796i	−0.538384	+	0.842700i	$0.680965\pi$
$992$	0.500000	−	0.866025i	0.0158750	−	0.0274963i
$993$		0			0
$994$	3.00000	−	5.19615i	0.0951542	−	0.164812i
$995$	−28.0000			−0.887660
$996$		0			0
$997$	26.5000	−	45.8993i	0.839263	−	1.45365i	−0.0512480	−	0.998686i	$-0.516320\pi$
$997$	26.5000	−	45.8993i	0.839263	−	1.45365i	0.890511	−	0.454961i	$-0.150347\pi$
$998$	−5.50000	+	9.52628i	−0.174099	+	0.301549i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.2.g.d.235.1		2
3.2	odd	2		114.2.e.a.7.1	✓	2
4.3	odd	2		2736.2.s.c.577.1		2
12.11	even	2		912.2.q.d.577.1		2
19.7	even	3		6498.2.a.l.1.1		1
19.11	even	3	inner	342.2.g.d.163.1		2
19.12	odd	6		6498.2.a.x.1.1		1
57.11	odd	6		114.2.e.a.49.1	yes	2
57.26	odd	6		2166.2.a.f.1.1		1
57.50	even	6		2166.2.a.c.1.1		1
76.11	odd	6		2736.2.s.c.1873.1		2
228.11	even	6		912.2.q.d.49.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.2.e.a.7.1	✓	2	3.2	odd	2
114.2.e.a.49.1	yes	2	57.11	odd	6
342.2.g.d.163.1		2	19.11	even	3	inner
342.2.g.d.235.1		2	1.1	even	1	trivial
912.2.q.d.49.1		2	228.11	even	6
912.2.q.d.577.1		2	12.11	even	2
2166.2.a.c.1.1		1	57.50	even	6
2166.2.a.f.1.1		1	57.26	odd	6
2736.2.s.c.577.1		2	4.3	odd	2
2736.2.s.c.1873.1		2	76.11	odd	6
6498.2.a.l.1.1		1	19.7	even	3
6498.2.a.x.1.1		1	19.12	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	342.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{5} -3.00000 q^{7} -1.00000 q^{8} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(-2.00000 - 3.46410i) q^{5} -3.00000 q^{7} -1.00000 q^{8} +(2.00000 - 3.46410i) q^{10} -2.00000 q^{11} +(3.50000 - 6.06218i) q^{13} +(-1.50000 - 2.59808i) q^{14} +(-0.500000 - 0.866025i) q^{16} +(-4.00000 - 1.73205i) q^{19} +4.00000 q^{20} +(-1.00000 - 1.73205i) q^{22} +(-2.00000 + 3.46410i) q^{23} +(-5.50000 + 9.52628i) q^{25} +7.00000 q^{26} +(1.50000 - 2.59808i) q^{28} +(2.00000 - 3.46410i) q^{29} +1.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(6.00000 + 10.3923i) q^{35} +7.00000 q^{37} +(-0.500000 - 4.33013i) q^{38} +(2.00000 + 3.46410i) q^{40} +(2.00000 + 3.46410i) q^{41} +(-3.50000 - 6.06218i) q^{43} +(1.00000 - 1.73205i) q^{44} -4.00000 q^{46} +(1.00000 - 1.73205i) q^{47} +2.00000 q^{49} -11.0000 q^{50} +(3.50000 + 6.06218i) q^{52} +(-2.00000 + 3.46410i) q^{53} +(4.00000 + 6.92820i) q^{55} +3.00000 q^{56} +4.00000 q^{58} +(-3.00000 - 5.19615i) q^{59} +(0.500000 - 0.866025i) q^{61} +(0.500000 + 0.866025i) q^{62} +1.00000 q^{64} -28.0000 q^{65} +(-1.50000 + 2.59808i) q^{67} +(-6.00000 + 10.3923i) q^{70} +(1.00000 + 1.73205i) q^{71} +(1.50000 + 2.59808i) q^{73} +(3.50000 + 6.06218i) q^{74} +(3.50000 - 2.59808i) q^{76} +6.00000 q^{77} +(-2.50000 - 4.33013i) q^{79} +(-2.00000 + 3.46410i) q^{80} +(-2.00000 + 3.46410i) q^{82} +12.0000 q^{83} +(3.50000 - 6.06218i) q^{86} +2.00000 q^{88} +(9.00000 - 15.5885i) q^{89} +(-10.5000 + 18.1865i) q^{91} +(-2.00000 - 3.46410i) q^{92} +2.00000 q^{94} +(2.00000 + 17.3205i) q^{95} +(-5.00000 - 8.66025i) q^{97} +(1.00000 + 1.73205i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + q^{2} - q^{4} - 4 q^{5} - 6 q^{7} - 2 q^{8}+O(q^{10}) \) 2 * q + q^2 - q^4 - 4 * q^5 - 6 * q^7 - 2 * q^8	\( 2 q + q^{2} - q^{4} - 4 q^{5} - 6 q^{7} - 2 q^{8} + 4 q^{10} - 4 q^{11} + 7 q^{13} - 3 q^{14} - q^{16} - 8 q^{19} + 8 q^{20} - 2 q^{22} - 4 q^{23} - 11 q^{25} + 14 q^{26} + 3 q^{28} + 4 q^{29} + 2 q^{31} + q^{32} + 12 q^{35} + 14 q^{37} - q^{38} + 4 q^{40} + 4 q^{41} - 7 q^{43} + 2 q^{44} - 8 q^{46} + 2 q^{47} + 4 q^{49} - 22 q^{50} + 7 q^{52} - 4 q^{53} + 8 q^{55} + 6 q^{56} + 8 q^{58} - 6 q^{59} + q^{61} + q^{62} + 2 q^{64} - 56 q^{65} - 3 q^{67} - 12 q^{70} + 2 q^{71} + 3 q^{73} + 7 q^{74} + 7 q^{76} + 12 q^{77} - 5 q^{79} - 4 q^{80} - 4 q^{82} + 24 q^{83} + 7 q^{86} + 4 q^{88} + 18 q^{89} - 21 q^{91} - 4 q^{92} + 4 q^{94} + 4 q^{95} - 10 q^{97} + 2 q^{98}+O(q^{100}) \) 2 * q + q^2 - q^4 - 4 * q^5 - 6 * q^7 - 2 * q^8 + 4 * q^10 - 4 * q^11 + 7 * q^13 - 3 * q^14 - q^16 - 8 * q^19 + 8 * q^20 - 2 * q^22 - 4 * q^23 - 11 * q^25 + 14 * q^26 + 3 * q^28 + 4 * q^29 + 2 * q^31 + q^32 + 12 * q^35 + 14 * q^37 - q^38 + 4 * q^40 + 4 * q^41 - 7 * q^43 + 2 * q^44 - 8 * q^46 + 2 * q^47 + 4 * q^49 - 22 * q^50 + 7 * q^52 - 4 * q^53 + 8 * q^55 + 6 * q^56 + 8 * q^58 - 6 * q^59 + q^61 + q^62 + 2 * q^64 - 56 * q^65 - 3 * q^67 - 12 * q^70 + 2 * q^71 + 3 * q^73 + 7 * q^74 + 7 * q^76 + 12 * q^77 - 5 * q^79 - 4 * q^80 - 4 * q^82 + 24 * q^83 + 7 * q^86 + 4 * q^88 + 18 * q^89 - 21 * q^91 - 4 * q^92 + 4 * q^94 + 4 * q^95 - 10 * q^97 + 2 * q^98

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