LMFDB - Embedded newform 722.2.e.e.415.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [722,2,Mod(99,722)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(722, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([2]))

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

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

chi := DirichletCharacter("722.99");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 722 = 2 \cdot 19^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	722.e (of order $9$, degree $6$, not 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:	$5.76519902594$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 38)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			415.1
Root			$0.939693 - 0.342020i$ of defining polynomial
Character	$\chi$	$=$	722.415
Dual form			722.2.e.e.595.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.53209 + 1.28558i) q^{9} +O(q^{10})$	\(q+(0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.53209 + 1.28558i) q^{9} +(3.00000 - 5.19615i) q^{11} +(0.500000 + 0.866025i) q^{12} +(4.69846 + 1.71010i) q^{13} +(-0.173648 + 0.984808i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(2.29813 + 1.92836i) q^{17} -2.00000 q^{18} +(0.766044 + 0.642788i) q^{21} +(5.63816 - 2.05212i) q^{22} +(0.520945 + 2.95442i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(4.69846 + 1.71010i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-2.50000 + 4.33013i) q^{27} +(-0.766044 + 0.642788i) q^{28} +(-6.89440 + 5.78509i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(1.04189 - 5.90885i) q^{33} +(0.520945 + 2.95442i) q^{34} +(-1.53209 - 1.28558i) q^{36} -2.00000 q^{37} +5.00000 q^{39} +(0.173648 + 0.984808i) q^{42} +(1.38919 - 7.87846i) q^{43} +(5.63816 + 2.05212i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-0.766044 + 0.642788i) q^{48} +(3.00000 - 5.19615i) q^{49} +(2.50000 + 4.33013i) q^{50} +(2.81908 + 1.02606i) q^{51} +(-0.868241 + 4.92404i) q^{52} +(0.520945 + 2.95442i) q^{53} +(-4.69846 + 1.71010i) q^{54} -1.00000 q^{56} -9.00000 q^{58} +(-6.89440 - 5.78509i) q^{59} +(-1.73648 - 9.84808i) q^{61} +(0.694593 - 3.93923i) q^{62} +(-1.87939 - 0.684040i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(4.59627 - 3.85673i) q^{66} +(-3.83022 + 3.21394i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(1.50000 + 2.59808i) q^{69} +(1.04189 - 5.90885i) q^{71} +(-0.347296 - 1.96962i) q^{72} +(6.57785 - 2.39414i) q^{73} +(-1.53209 - 1.28558i) q^{74} +5.00000 q^{75} +6.00000 q^{77} +(3.83022 + 3.21394i) q^{78} +(-9.39693 + 3.42020i) q^{79} +(0.173648 - 0.984808i) q^{81} +(3.00000 + 5.19615i) q^{83} +(-0.500000 + 0.866025i) q^{84} +(6.12836 - 5.14230i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-11.2763 - 4.10424i) q^{89} +(0.868241 + 4.92404i) q^{91} +(-2.81908 + 1.02606i) q^{92} +(-3.06418 - 2.57115i) q^{93} -1.00000 q^{96} +(7.66044 + 6.42788i) q^{97} +(5.63816 - 2.05212i) q^{98} +(2.08378 + 11.8177i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{7} - 3 q^{8}+O(q^{10}) $ 6 * q + 3 * q^7 - 3 * q^8	$ 6 q + 3 q^{7} - 3 q^{8} + 18 q^{11} + 3 q^{12} - 12 q^{18} + 15 q^{26} - 15 q^{27} - 12 q^{31} - 12 q^{37} + 30 q^{39} - 9 q^{46} + 18 q^{49} + 15 q^{50} - 6 q^{56} - 54 q^{58} - 3 q^{64} - 9 q^{68} + 9 q^{69} + 30 q^{75} + 36 q^{77} + 18 q^{83} - 3 q^{84} - 27 q^{87} + 18 q^{88} - 6 q^{96}+O(q^{100}) $ 6 * q + 3 * q^7 - 3 * q^8 + 18 * q^11 + 3 * q^12 - 12 * q^18 + 15 * q^26 - 15 * q^27 - 12 * q^31 - 12 * q^37 + 30 * q^39 - 9 * q^46 + 18 * q^49 + 15 * q^50 - 6 * q^56 - 54 * q^58 - 3 * q^64 - 9 * q^68 + 9 * q^69 + 30 * q^75 + 36 * q^77 + 18 * q^83 - 3 * q^84 - 27 * q^87 + 18 * q^88 - 6 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/722\mathbb{Z}\right)^\times$.

$n$	$363$
$\chi(n)$	$e\left(\frac{2}{9}\right)$

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 $

$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$2$	0.766044	+	0.642788i	0.541675	+	0.454519i
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i	−0.0561935	−	0.998420i	$-0.517896\pi$
$3$	0.939693	−	0.342020i	0.542532	−	0.197465i	0.598725	+	0.800954i	$0.295674\pi$
$4$	0.173648	+	0.984808i	0.0868241	+	0.492404i
$5$		0			0		−0.984808	−	0.173648i	$-0.944444\pi$
$5$		0			0		0.984808	+	0.173648i	$0.0555556\pi$
$6$	0.939693	+	0.342020i	0.383628	+	0.139629i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	0.944911	−	0.327327i	$-0.106148\pi$
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i	−0.755929	+	0.654654i	$0.772814\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−1.53209	+	1.28558i	−0.510696	+	0.428525i
$10$		0			0
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.0829925	−	0.996550i	$-0.473552\pi$
$11$	3.00000	−	5.19615i	0.904534	−	1.56670i	0.821541	−	0.570149i	$-0.193114\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	4.69846	+	1.71010i	1.30312	+	0.474297i	0.898011	−	0.439972i	$-0.145012\pi$
$13$	4.69846	+	1.71010i	1.30312	+	0.474297i	0.405108	+	0.914269i	$0.367234\pi$
$14$	−0.173648	+	0.984808i	−0.0464094	+	0.263201i
$15$		0			0
$16$	−0.939693	+	0.342020i	−0.234923	+	0.0855050i
$17$	2.29813	+	1.92836i	0.557379	+	0.467697i	0.877431	−	0.479703i	$-0.159256\pi$
$17$	2.29813	+	1.92836i	0.557379	+	0.467697i	−0.320051	+	0.947400i	$0.603700\pi$
$18$	−2.00000			−0.471405
$19$		0			0
$19$		0			0
$20$		0			0
$21$	0.766044	+	0.642788i	0.167165	+	0.140268i
$22$	5.63816	−	2.05212i	1.20206	−	0.437514i
$23$	0.520945	+	2.95442i	0.108624	+	0.616040i	0.989711	+	0.143084i	$0.0457019\pi$
$23$	0.520945	+	2.95442i	0.108624	+	0.616040i	−0.881086	+	0.472956i	$0.843187\pi$
$24$	−0.173648	+	0.984808i	−0.0354458	+	0.201023i
$25$	4.69846	+	1.71010i	0.939693	+	0.342020i
$26$	2.50000	+	4.33013i	0.490290	+	0.849208i
$27$	−2.50000	+	4.33013i	−0.481125	+	0.833333i
$28$	−0.766044	+	0.642788i	−0.144769	+	0.121475i
$29$	−6.89440	+	5.78509i	−1.28026	+	1.07426i	−0.287049	+	0.957916i	$0.592674\pi$
$29$	−6.89440	+	5.78509i	−1.28026	+	1.07426i	−0.993208	+	0.116348i	$0.962881\pi$
$30$		0			0
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	0.628619	−	0.777714i	$-0.283621\pi$
$31$	−2.00000	−	3.46410i	−0.359211	−	0.622171i	−0.987829	+	0.155543i	$0.950287\pi$
$32$	−0.939693	−	0.342020i	−0.166116	−	0.0604612i
$33$	1.04189	−	5.90885i	0.181370	−	1.02860i
$34$	0.520945	+	2.95442i	0.0893413	+	0.506679i
$35$		0			0
$36$	−1.53209	−	1.28558i	−0.255348	−	0.214263i
$37$	−2.00000			−0.328798			−0.164399	−	0.986394i	$-0.552568\pi$
$37$	−2.00000			−0.328798			−0.164399	+	0.986394i	$0.552568\pi$
$38$		0			0
$39$	5.00000			0.800641
$40$		0			0
$41$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$41$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$42$	0.173648	+	0.984808i	0.0267945	+	0.151959i
$43$	1.38919	−	7.87846i	0.211849	−	1.20145i	−0.674443	−	0.738327i	$-0.735616\pi$
$43$	1.38919	−	7.87846i	0.211849	−	1.20145i	0.886292	−	0.463127i	$-0.153273\pi$
$44$	5.63816	+	2.05212i	0.849984	+	0.309369i
$45$		0			0
$46$	−1.50000	+	2.59808i	−0.221163	+	0.383065i
$47$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$47$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$48$	−0.766044	+	0.642788i	−0.110569	+	0.0927784i
$49$	3.00000	−	5.19615i	0.428571	−	0.742307i
$50$	2.50000	+	4.33013i	0.353553	+	0.612372i
$51$	2.81908	+	1.02606i	0.394750	+	0.143677i
$52$	−0.868241	+	4.92404i	−0.120403	+	0.682841i
$53$	0.520945	+	2.95442i	0.0715572	+	0.405821i	0.999456	+	0.0329883i	$0.0105024\pi$
$53$	0.520945	+	2.95442i	0.0715572	+	0.405821i	−0.927899	+	0.372833i	$0.878386\pi$
$54$	−4.69846	+	1.71010i	−0.639380	+	0.232715i
$55$		0			0
$56$	−1.00000			−0.133631
$57$		0			0
$58$	−9.00000			−1.18176
$59$	−6.89440	−	5.78509i	−0.897574	−	0.753154i	0.0721404	−	0.997394i	$-0.477017\pi$
$59$	−6.89440	−	5.78509i	−0.897574	−	0.753154i	−0.969715	+	0.244240i	$0.921461\pi$
$60$		0			0
$61$	−1.73648	−	9.84808i	−0.222334	−	1.26092i	−0.867717	−	0.497058i	$-0.834413\pi$
$61$	−1.73648	−	9.84808i	−0.222334	−	1.26092i	0.645383	−	0.763859i	$-0.276698\pi$
$62$	0.694593	−	3.93923i	0.0882134	−	0.500283i
$63$	−1.87939	−	0.684040i	−0.236780	−	0.0861810i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	4.59627	−	3.85673i	0.565761	−	0.474730i
$67$	−3.83022	+	3.21394i	−0.467936	+	0.392645i	−0.846041	−	0.533118i	$-0.821020\pi$
$67$	−3.83022	+	3.21394i	−0.467936	+	0.392645i	0.378105	+	0.925763i	$0.376576\pi$
$68$	−1.50000	+	2.59808i	−0.181902	+	0.315063i
$69$	1.50000	+	2.59808i	0.180579	+	0.312772i
$70$		0			0
$71$	1.04189	−	5.90885i	0.123649	−	0.701251i	−0.858451	−	0.512895i	$-0.828573\pi$
$71$	1.04189	−	5.90885i	0.123649	−	0.701251i	0.982101	−	0.188356i	$-0.0603159\pi$
$72$	−0.347296	−	1.96962i	−0.0409293	−	0.232121i
$73$	6.57785	−	2.39414i	0.769879	−	0.280213i	0.0729331	−	0.997337i	$-0.476764\pi$
$73$	6.57785	−	2.39414i	0.769879	−	0.280213i	0.696946	+	0.717124i	$0.254542\pi$
$74$	−1.53209	−	1.28558i	−0.178102	−	0.149445i
$75$	5.00000			0.577350
$76$		0			0
$77$	6.00000			0.683763
$78$	3.83022	+	3.21394i	0.433687	+	0.363907i
$79$	−9.39693	+	3.42020i	−1.05724	+	0.384803i	−0.811389	−	0.584506i	$-0.801288\pi$
$79$	−9.39693	+	3.42020i	−1.05724	+	0.384803i	−0.245847	+	0.969309i	$0.579066\pi$
$80$		0			0
$81$	0.173648	−	0.984808i	0.0192942	−	0.109423i
$82$		0			0
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	0.982372	−	0.186938i	$-0.0598564\pi$
$83$	3.00000	+	5.19615i	0.329293	+	0.570352i	−0.653079	+	0.757290i	$0.726523\pi$
$84$	−0.500000	+	0.866025i	−0.0545545	+	0.0944911i
$85$		0			0
$86$	6.12836	−	5.14230i	0.660838	−	0.554509i
$87$	−4.50000	+	7.79423i	−0.482451	+	0.835629i
$88$	3.00000	+	5.19615i	0.319801	+	0.553912i
$89$	−11.2763	−	4.10424i	−1.19529	−	0.435049i	−0.333710	−	0.942676i	$-0.608301\pi$
$89$	−11.2763	−	4.10424i	−1.19529	−	0.435049i	−0.861577	+	0.507627i	$0.830523\pi$
$90$		0			0
$91$	0.868241	+	4.92404i	0.0910164	+	0.516180i
$92$	−2.81908	+	1.02606i	−0.293909	+	0.106974i
$93$	−3.06418	−	2.57115i	−0.317740	−	0.266616i
$94$		0			0
$95$		0			0
$96$	−1.00000			−0.102062
$97$	7.66044	+	6.42788i	0.777800	+	0.652652i	0.942694	−	0.333659i	$-0.108284\pi$
$97$	7.66044	+	6.42788i	0.777800	+	0.652652i	−0.164893	+	0.986311i	$0.552728\pi$
$98$	5.63816	−	2.05212i	0.569540	−	0.207296i
$99$	2.08378	+	11.8177i	0.209428	+	1.18772i
$100$	−0.868241	+	4.92404i	−0.0868241	+	0.492404i
$101$	−16.9145	−	6.15636i	−1.68305	−	0.612581i	−0.689329	−	0.724448i	$-0.742095\pi$
$101$	−16.9145	−	6.15636i	−1.68305	−	0.612581i	−0.993723	+	0.111867i	$0.964317\pi$
$102$	1.50000	+	2.59808i	0.148522	+	0.257248i
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	−0.282194	−	0.959357i	$-0.591062\pi$
$103$	7.00000	−	12.1244i	0.689730	−	1.19465i	0.971925	−	0.235291i	$-0.0756043\pi$
$104$	−3.83022	+	3.21394i	−0.375584	+	0.315153i
$105$		0			0
$106$	−1.50000	+	2.59808i	−0.145693	+	0.252347i
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	0.562267	−	0.826956i	$-0.309929\pi$
$107$	−4.50000	−	7.79423i	−0.435031	−	0.753497i	−0.997298	+	0.0734594i	$0.976596\pi$
$108$	−4.69846	−	1.71010i	−0.452110	−	0.164555i
$109$	−1.91013	+	10.8329i	−0.182957	+	1.03760i	0.745595	+	0.666400i	$0.232166\pi$
$109$	−1.91013	+	10.8329i	−0.182957	+	1.03760i	−0.928552	+	0.371203i	$0.878946\pi$
$110$		0			0
$111$	−1.87939	+	0.684040i	−0.178383	+	0.0649262i
$112$	−0.766044	−	0.642788i	−0.0723844	−	0.0607377i
$113$	−6.00000			−0.564433			−0.282216	−	0.959351i	$-0.591070\pi$
$113$	−6.00000			−0.564433			−0.282216	+	0.959351i	$0.591070\pi$
$114$		0			0
$115$		0			0
$116$	−6.89440	−	5.78509i	−0.640129	−	0.537132i
$117$	−9.39693	+	3.42020i	−0.868746	+	0.316198i
$118$	−1.56283	−	8.86327i	−0.143870	−	0.815930i
$119$	−0.520945	+	2.95442i	−0.0477549	+	0.270832i
$120$		0			0
$121$	−12.5000	−	21.6506i	−1.13636	−	1.96824i
$122$	5.00000	−	8.66025i	0.452679	−	0.784063i
$123$		0			0
$124$	3.06418	−	2.57115i	0.275171	−	0.230896i
$125$		0			0
$126$	−1.00000	−	1.73205i	−0.0890871	−	0.154303i
$127$	1.87939	+	0.684040i	0.166768	+	0.0606988i	0.424055	−	0.905636i	$-0.360606\pi$
$127$	1.87939	+	0.684040i	0.166768	+	0.0606988i	−0.257287	+	0.966335i	$0.582828\pi$
$128$	0.173648	−	0.984808i	0.0153485	−	0.0870455i
$129$	−1.38919	−	7.87846i	−0.122311	−	0.693660i
$130$		0			0
$131$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$131$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$132$	6.00000			0.522233
$133$		0			0
$134$	−5.00000			−0.431934
$135$		0			0
$136$	−2.81908	+	1.02606i	−0.241734	+	0.0879840i
$137$	−1.56283	−	8.86327i	−0.133522	−	0.757240i	−0.975878	−	0.218318i	$-0.929943\pi$
$137$	−1.56283	−	8.86327i	−0.133522	−	0.757240i	0.842356	−	0.538922i	$-0.181168\pi$
$138$	−0.520945	+	2.95442i	−0.0443457	+	0.251497i
$139$	3.75877	+	1.36808i	0.318815	+	0.116039i	0.496470	−	0.868054i	$-0.334629\pi$
$139$	3.75877	+	1.36808i	0.318815	+	0.116039i	−0.177656	+	0.984093i	$0.556851\pi$
$140$		0			0
$141$		0			0
$142$	4.59627	−	3.85673i	0.385710	−	0.323649i
$143$	22.9813	−	19.2836i	1.92180	−	1.61258i
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$		0			0
$146$	6.57785	+	2.39414i	0.544387	+	0.198141i
$147$	1.04189	−	5.90885i	0.0859336	−	0.487353i
$148$	−0.347296	−	1.96962i	−0.0285476	−	0.161901i
$149$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$149$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$150$	3.83022	+	3.21394i	0.312736	+	0.262417i
$151$	10.0000			0.813788			0.406894	−	0.913475i	$-0.366612\pi$
$151$	10.0000			0.813788			0.406894	+	0.913475i	$0.366612\pi$
$152$		0			0
$153$	−6.00000			−0.485071
$154$	4.59627	+	3.85673i	0.370378	+	0.310784i
$155$		0			0
$156$	0.868241	+	4.92404i	0.0695149	+	0.394239i
$157$	−3.82026	+	21.6658i	−0.304890	+	1.72912i	0.319132	+	0.947710i	$0.396609\pi$
$157$	−3.82026	+	21.6658i	−0.304890	+	1.72912i	−0.624022	+	0.781407i	$0.714503\pi$
$158$	−9.39693	−	3.42020i	−0.747579	−	0.272097i
$159$	1.50000	+	2.59808i	0.118958	+	0.206041i
$160$		0			0
$161$	−2.29813	+	1.92836i	−0.181118	+	0.151976i
$162$	0.766044	−	0.642788i	0.0601861	−	0.0505022i
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	0.146772	+	0.989170i	$0.453112\pi$
$163$	−10.0000	+	17.3205i	−0.783260	+	1.35665i	−0.930033	+	0.367477i	$0.880222\pi$
$164$		0			0
$165$		0			0
$166$	−1.04189	+	5.90885i	−0.0808663	+	0.458615i
$167$	−2.08378	−	11.8177i	−0.161248	−	0.914481i	−0.952849	−	0.303443i	$-0.901864\pi$
$167$	−2.08378	−	11.8177i	−0.161248	−	0.914481i	0.791602	−	0.611037i	$-0.209247\pi$
$168$	−0.939693	+	0.342020i	−0.0724989	+	0.0263874i
$169$	9.19253	+	7.71345i	0.707118	+	0.593342i
$170$		0			0
$171$		0			0
$172$	8.00000			0.609994
$173$	−4.59627	−	3.85673i	−0.349448	−	0.293221i	0.451121	−	0.892463i	$-0.351024\pi$
$173$	−4.59627	−	3.85673i	−0.349448	−	0.293221i	−0.800568	+	0.599242i	$0.795469\pi$
$174$	−8.45723	+	3.07818i	−0.641141	+	0.233356i
$175$	0.868241	+	4.92404i	0.0656328	+	0.372222i
$176$	−1.04189	+	5.90885i	−0.0785353	+	0.445396i
$177$	−8.45723	−	3.07818i	−0.635685	−	0.231370i
$178$	−6.00000	−	10.3923i	−0.449719	−	0.778936i
$179$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$179$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$180$		0			0
$181$	−1.53209	+	1.28558i	−0.113879	+	0.0955561i	−0.697949	−	0.716147i	$-0.745904\pi$
$181$	−1.53209	+	1.28558i	−0.113879	+	0.0955561i	0.584070	+	0.811703i	$0.301459\pi$
$182$	−2.50000	+	4.33013i	−0.185312	+	0.320970i
$183$	−5.00000	−	8.66025i	−0.369611	−	0.640184i
$184$	−2.81908	−	1.02606i	−0.207825	−	0.0756422i
$185$		0			0
$186$	−0.694593	−	3.93923i	−0.0509300	−	0.288838i
$187$	16.9145	−	6.15636i	1.23691	−	0.450198i
$188$		0			0
$189$	−5.00000			−0.363696
$190$		0			0
$191$	3.00000			0.217072			0.108536	−	0.994092i	$-0.465384\pi$
$191$	3.00000			0.217072			0.108536	+	0.994092i	$0.465384\pi$
$192$	−0.766044	−	0.642788i	−0.0552845	−	0.0463892i
$193$	13.1557	−	4.78828i	0.946968	−	0.344668i	0.178054	−	0.984021i	$-0.443020\pi$
$193$	13.1557	−	4.78828i	0.946968	−	0.344668i	0.768914	+	0.639353i	$0.220798\pi$
$194$	1.73648	+	9.84808i	0.124672	+	0.707051i
$195$		0			0
$196$	5.63816	+	2.05212i	0.402725	+	0.146580i
$197$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$197$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$198$	−6.00000	+	10.3923i	−0.426401	+	0.738549i
$199$	8.42649	−	7.07066i	0.597338	−	0.501226i	−0.293251	−	0.956036i	$-0.594737\pi$
$199$	8.42649	−	7.07066i	0.597338	−	0.501226i	0.890589	+	0.454809i	$0.150293\pi$
$200$	−3.83022	+	3.21394i	−0.270838	+	0.227260i
$201$	−2.50000	+	4.33013i	−0.176336	+	0.305424i
$202$	−9.00000	−	15.5885i	−0.633238	−	1.09680i
$203$	−8.45723	−	3.07818i	−0.593581	−	0.216046i
$204$	−0.520945	+	2.95442i	−0.0364734	+	0.206851i
$205$		0			0
$206$	13.1557	−	4.78828i	0.916601	−	0.333615i
$207$	−4.59627	−	3.85673i	−0.319463	−	0.268061i
$208$	−5.00000			−0.346688
$209$		0			0
$210$		0			0
$211$	−3.83022	−	3.21394i	−0.263683	−	0.221257i	0.501354	−	0.865242i	$-0.332835\pi$
$211$	−3.83022	−	3.21394i	−0.263683	−	0.221257i	−0.765038	+	0.643985i	$0.777280\pi$
$212$	−2.81908	+	1.02606i	−0.193615	+	0.0704701i
$213$	−1.04189	−	5.90885i	−0.0713891	−	0.404867i
$214$	1.56283	−	8.86327i	0.106833	−	0.605881i
$215$		0			0
$216$	−2.50000	−	4.33013i	−0.170103	−	0.294628i
$217$	2.00000	−	3.46410i	0.135769	−	0.235159i
$218$	−8.42649	+	7.07066i	−0.570714	+	0.478886i
$219$	5.36231	−	4.49951i	0.362351	−	0.304049i
$220$		0			0
$221$	7.50000	+	12.9904i	0.504505	+	0.873828i
$222$	−1.87939	−	0.684040i	−0.126136	−	0.0459098i
$223$	−4.51485	+	25.6050i	−0.302337	+	1.71464i	0.333445	+	0.942769i	$0.391789\pi$
$223$	−4.51485	+	25.6050i	−0.302337	+	1.71464i	−0.635782	+	0.771868i	$0.719322\pi$
$224$	−0.173648	−	0.984808i	−0.0116024	−	0.0658002i
$225$	−9.39693	+	3.42020i	−0.626462	+	0.228013i
$226$	−4.59627	−	3.85673i	−0.305739	−	0.256546i
$227$	15.0000			0.995585			0.497792	−	0.867296i	$-0.334144\pi$
$227$	15.0000			0.995585			0.497792	+	0.867296i	$0.334144\pi$
$228$		0			0
$229$	−22.0000			−1.45380			−0.726900	−	0.686743i	$-0.759040\pi$
$229$	−22.0000			−1.45380			−0.726900	+	0.686743i	$0.759040\pi$
$230$		0			0
$231$	5.63816	−	2.05212i	0.370963	−	0.135020i
$232$	−1.56283	−	8.86327i	−0.102605	−	0.581902i
$233$	−1.04189	+	5.90885i	−0.0682564	+	0.387101i	0.931472	+	0.363812i	$0.118525\pi$
$233$	−1.04189	+	5.90885i	−0.0682564	+	0.387101i	−0.999729	+	0.0232893i	$0.992586\pi$
$234$	−9.39693	−	3.42020i	−0.614296	−	0.223586i
$235$		0			0
$236$	4.50000	−	7.79423i	0.292925	−	0.507361i
$237$	−7.66044	+	6.42788i	−0.497599	+	0.417535i
$238$	−2.29813	+	1.92836i	−0.148966	+	0.124997i
$239$	10.5000	−	18.1865i	0.679189	−	1.17639i	−0.296037	−	0.955176i	$-0.595665\pi$
$239$	10.5000	−	18.1865i	0.679189	−	1.17639i	0.975226	−	0.221213i	$-0.0710015\pi$
$240$		0			0
$241$	7.51754	+	2.73616i	0.484247	+	0.176252i	0.572596	−	0.819838i	$-0.305937\pi$
$241$	7.51754	+	2.73616i	0.484247	+	0.176252i	−0.0883481	+	0.996090i	$0.528159\pi$
$242$	4.34120	−	24.6202i	0.279063	−	1.58265i
$243$	−2.77837	−	15.7569i	−0.178233	−	1.01081i
$244$	9.39693	−	3.42020i	0.601577	−	0.218956i
$245$		0			0
$246$		0			0
$247$		0			0
$248$	4.00000			0.254000
$249$	4.59627	+	3.85673i	0.291277	+	0.244410i
$250$		0			0
$251$	1.04189	+	5.90885i	0.0657635	+	0.372963i	0.999872	+	0.0159750i	$0.00508522\pi$
$251$	1.04189	+	5.90885i	0.0657635	+	0.372963i	−0.934109	+	0.356988i	$0.883804\pi$
$252$	0.347296	−	1.96962i	0.0218776	−	0.124074i
$253$	16.9145	+	6.15636i	1.06340	+	0.387047i
$254$	1.00000	+	1.73205i	0.0627456	+	0.108679i
$255$		0			0
$256$	0.766044	−	0.642788i	0.0478778	−	0.0401742i
$257$	−9.19253	+	7.71345i	−0.573414	+	0.481152i	−0.882777	−	0.469792i	$-0.844329\pi$
$257$	−9.19253	+	7.71345i	−0.573414	+	0.481152i	0.309362	+	0.950944i	$0.399884\pi$
$258$	4.00000	−	6.92820i	0.249029	−	0.431331i
$259$	−1.00000	−	1.73205i	−0.0621370	−	0.107624i
$260$		0			0
$261$	3.12567	−	17.7265i	0.193474	−	1.09725i
$262$		0			0
$263$	−22.5526	+	8.20848i	−1.39065	+	0.506157i	−0.925390	−	0.379015i	$-0.876263\pi$
$263$	−22.5526	+	8.20848i	−1.39065	+	0.506157i	−0.465264	+	0.885172i	$0.654041\pi$
$264$	4.59627	+	3.85673i	0.282881	+	0.237365i
$265$		0			0
$266$		0			0
$267$	−12.0000			−0.734388
$268$	−3.83022	−	3.21394i	−0.233968	−	0.196323i
$269$	−5.63816	+	2.05212i	−0.343764	+	0.125120i	−0.508132	−	0.861279i	$-0.669664\pi$
$269$	−5.63816	+	2.05212i	−0.343764	+	0.125120i	0.164368	+	0.986399i	$0.447442\pi$
$270$		0			0
$271$	1.91013	−	10.8329i	0.116032	−	0.658051i	−0.870202	−	0.492695i	$-0.836012\pi$
$271$	1.91013	−	10.8329i	0.116032	−	0.658051i	0.986234	−	0.165356i	$-0.0528772\pi$
$272$	−2.81908	−	1.02606i	−0.170932	−	0.0622141i
$273$	2.50000	+	4.33013i	0.151307	+	0.262071i
$274$	4.50000	−	7.79423i	0.271855	−	0.470867i
$275$	22.9813	−	19.2836i	1.38583	−	1.16285i
$276$	−2.29813	+	1.92836i	−0.138331	+	0.116074i
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	−0.960810	−	0.277207i	$-0.910591\pi$
$277$	−4.00000	+	6.92820i	−0.240337	+	0.416275i	0.720473	+	0.693482i	$0.243925\pi$
$278$	2.00000	+	3.46410i	0.119952	+	0.207763i
$279$	7.51754	+	2.73616i	0.450063	+	0.163810i
$280$		0			0
$281$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$281$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$282$		0			0
$283$	−16.8530	−	14.1413i	−1.00181	−	0.840615i	−0.0145720	−	0.999894i	$-0.504639\pi$
$283$	−16.8530	−	14.1413i	−1.00181	−	0.840615i	−0.987234	+	0.159279i	$0.949083\pi$
$284$	6.00000			0.356034
$285$		0			0
$286$	30.0000			1.77394
$287$		0			0
$288$	1.87939	−	0.684040i	0.110744	−	0.0403075i
$289$	−1.38919	−	7.87846i	−0.0817168	−	0.463439i
$290$		0			0
$291$	9.39693	+	3.42020i	0.550858	+	0.200496i
$292$	3.50000	+	6.06218i	0.204822	+	0.354762i
$293$	−10.5000	+	18.1865i	−0.613417	+	1.06247i	0.377244	+	0.926114i	$0.376872\pi$
$293$	−10.5000	+	18.1865i	−0.613417	+	1.06247i	−0.990660	+	0.136355i	$0.956461\pi$
$294$	4.59627	−	3.85673i	0.268060	−	0.224929i
$295$		0			0
$296$	1.00000	−	1.73205i	0.0581238	−	0.100673i
$297$	15.0000	+	25.9808i	0.870388	+	1.50756i
$298$		0			0
$299$	−2.60472	+	14.7721i	−0.150635	+	0.854294i
$300$	0.868241	+	4.92404i	0.0501279	+	0.284290i
$301$	7.51754	−	2.73616i	0.433304	−	0.157710i
$302$	7.66044	+	6.42788i	0.440809	+	0.369883i
$303$	−18.0000			−1.03407
$304$		0			0
$305$		0			0
$306$	−4.59627	−	3.85673i	−0.262751	−	0.220474i
$307$	18.7939	−	6.84040i	1.07262	−	0.390402i	0.255465	−	0.966818i	$-0.417771\pi$
$307$	18.7939	−	6.84040i	1.07262	−	0.390402i	0.817157	+	0.576416i	$0.195549\pi$
$308$	1.04189	+	5.90885i	0.0593671	+	0.336688i
$309$	2.43107	−	13.7873i	0.138299	−	0.784333i
$310$		0			0
$311$	10.5000	+	18.1865i	0.595400	+	1.03126i	0.993490	+	0.113917i	$0.0363399\pi$
$311$	10.5000	+	18.1865i	0.595400	+	1.03126i	−0.398090	+	0.917346i	$0.630327\pi$
$312$	−2.50000	+	4.33013i	−0.141535	+	0.245145i
$313$	−14.5548	+	12.2130i	−0.822688	+	0.690318i	−0.953600	−	0.301076i	$-0.902654\pi$
$313$	−14.5548	+	12.2130i	−0.822688	+	0.690318i	0.130912	+	0.991394i	$0.458210\pi$
$314$	−16.8530	+	14.1413i	−0.951069	+	0.798041i
$315$		0			0
$316$	−5.00000	−	8.66025i	−0.281272	−	0.487177i
$317$	−8.45723	−	3.07818i	−0.475006	−	0.172888i	0.0934130	−	0.995627i	$-0.470222\pi$
$317$	−8.45723	−	3.07818i	−0.475006	−	0.172888i	−0.568419	+	0.822740i	$0.692445\pi$
$318$	−0.520945	+	2.95442i	−0.0292131	+	0.165676i
$319$	9.37700	+	53.1796i	0.525011	+	2.97749i
$320$		0			0
$321$	−6.89440	−	5.78509i	−0.384808	−	0.322892i
$322$	−3.00000			−0.167183
$323$		0			0
$324$	1.00000			0.0555556
$325$	19.1511	+	16.0697i	1.06231	+	0.891386i
$326$	−18.7939	+	6.84040i	−1.04090	+	0.378855i
$327$	1.91013	+	10.8329i	0.105630	+	0.599060i
$328$		0			0
$329$		0			0
$330$		0			0
$331$	−0.500000	+	0.866025i	−0.0274825	+	0.0476011i	−0.879440	−	0.476011i	$-0.842082\pi$
$331$	−0.500000	+	0.866025i	−0.0274825	+	0.0476011i	0.851957	+	0.523612i	$0.175416\pi$
$332$	−4.59627	+	3.85673i	−0.252253	+	0.211665i
$333$	3.06418	−	2.57115i	0.167916	−	0.140898i
$334$	6.00000	−	10.3923i	0.328305	−	0.568642i
$335$		0			0
$336$	−0.939693	−	0.342020i	−0.0512644	−	0.0186587i
$337$	0.694593	−	3.93923i	0.0378369	−	0.214584i	−0.960027	−	0.279906i	$-0.909697\pi$
$337$	0.694593	−	3.93923i	0.0378369	−	0.214584i	0.997864	+	0.0653228i	$0.0208077\pi$
$338$	2.08378	+	11.8177i	0.113343	+	0.642798i
$339$	−5.63816	+	2.05212i	−0.306223	+	0.111456i
$340$		0			0
$341$	−24.0000			−1.29967
$342$		0			0
$343$	13.0000			0.701934
$344$	6.12836	+	5.14230i	0.330419	+	0.277254i
$345$		0			0
$346$	−1.04189	−	5.90885i	−0.0560123	−	0.317662i
$347$	3.12567	−	17.7265i	0.167795	−	0.951611i	−0.778341	−	0.627841i	$-0.783939\pi$
$347$	3.12567	−	17.7265i	0.167795	−	0.951611i	0.946136	−	0.323769i	$-0.104950\pi$
$348$	−8.45723	−	3.07818i	−0.453355	−	0.165008i
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	0.968253	−	0.249973i	$-0.0804216\pi$
$349$	5.00000	+	8.66025i	0.267644	+	0.463573i	−0.700609	+	0.713545i	$0.747088\pi$
$350$	−2.50000	+	4.33013i	−0.133631	+	0.231455i
$351$	−19.1511	+	16.0697i	−1.02221	+	0.857737i
$352$	−4.59627	+	3.85673i	−0.244982	+	0.205564i
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	−0.594441	−	0.804139i	$-0.702627\pi$
$353$	7.50000	−	12.9904i	0.399185	−	0.691408i	0.993626	+	0.112731i	$0.0359599\pi$
$354$	−4.50000	−	7.79423i	−0.239172	−	0.414259i
$355$		0			0
$356$	2.08378	−	11.8177i	0.110440	−	0.626336i
$357$	0.520945	+	2.95442i	0.0275713	+	0.156365i
$358$		0			0
$359$	16.0869	+	13.4985i	0.849036	+	0.712426i	0.959577	−	0.281446i	$-0.0908140\pi$
$359$	16.0869	+	13.4985i	0.849036	+	0.712426i	−0.110541	+	0.993872i	$0.535258\pi$
$360$		0			0
$361$		0			0
$362$	−2.00000			−0.105118
$363$	−19.1511	−	16.0697i	−1.00517	−	0.843440i
$364$	−4.69846	+	1.71010i	−0.246266	+	0.0896336i
$365$		0			0
$366$	1.73648	−	9.84808i	0.0907674	−	0.514767i
$367$	26.3114	+	9.57656i	1.37344	+	0.499893i	0.920184	−	0.391486i	$-0.128039\pi$
$367$	26.3114	+	9.57656i	1.37344	+	0.499893i	0.453260	+	0.891379i	$0.350261\pi$
$368$	−1.50000	−	2.59808i	−0.0781929	−	0.135434i
$369$		0			0
$370$		0			0
$371$	−2.29813	+	1.92836i	−0.119313	+	0.100116i
$372$	2.00000	−	3.46410i	0.103695	−	0.179605i
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	0.993484	+	0.113975i	$0.0363585\pi$
$373$	11.5000	+	19.9186i	0.595447	+	1.03135i	−0.398036	+	0.917370i	$0.630308\pi$
$374$	16.9145	+	6.15636i	0.874626	+	0.318338i
$375$		0			0
$376$		0			0
$377$	−42.2862	+	15.3909i	−2.17785	+	0.792672i
$378$	−3.83022	−	3.21394i	−0.197005	−	0.165307i
$379$	7.00000			0.359566			0.179783	−	0.983706i	$-0.442460\pi$
$379$	7.00000			0.359566			0.179783	+	0.983706i	$0.442460\pi$
$380$		0			0
$381$	2.00000			0.102463
$382$	2.29813	+	1.92836i	0.117583	+	0.0986636i
$383$	16.9145	−	6.15636i	0.864289	−	0.314575i	0.128437	−	0.991718i	$-0.459004\pi$
$383$	16.9145	−	6.15636i	0.864289	−	0.314575i	0.735852	+	0.677142i	$0.236782\pi$
$384$	−0.173648	−	0.984808i	−0.00886145	−	0.0502558i
$385$		0			0
$386$	13.1557	+	4.78828i	0.669607	+	0.243717i
$387$	8.00000	+	13.8564i	0.406663	+	0.704361i
$388$	−5.00000	+	8.66025i	−0.253837	+	0.439658i
$389$	13.7888	−	11.5702i	0.699120	−	0.586631i	−0.222403	−	0.974955i	$-0.571390\pi$
$389$	13.7888	−	11.5702i	0.699120	−	0.586631i	0.921523	+	0.388324i	$0.126946\pi$
$390$		0			0
$391$	−4.50000	+	7.79423i	−0.227575	+	0.394171i
$392$	3.00000	+	5.19615i	0.151523	+	0.262445i
$393$		0			0
$394$		0			0
$395$		0			0
$396$	−11.2763	+	4.10424i	−0.566656	+	0.206246i
$397$	15.3209	+	12.8558i	0.768933	+	0.645212i	0.940436	−	0.339972i	$-0.110418\pi$
$397$	15.3209	+	12.8558i	0.768933	+	0.645212i	−0.171502	+	0.985184i	$0.554862\pi$
$398$	11.0000			0.551380
$399$		0			0
$400$	−5.00000			−0.250000
$401$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$401$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$402$	−4.69846	+	1.71010i	−0.234338	+	0.0852921i
$403$	−3.47296	−	19.6962i	−0.173001	−	0.981135i
$404$	3.12567	−	17.7265i	0.155508	−	0.881928i
$405$		0			0
$406$	−4.50000	−	7.79423i	−0.223331	−	0.386821i
$407$	−6.00000	+	10.3923i	−0.297409	+	0.515127i
$408$	−2.29813	+	1.92836i	−0.113775	+	0.0954682i
$409$	−24.5134	+	20.5692i	−1.21211	+	1.01708i	−0.212911	+	0.977072i	$0.568295\pi$
$409$	−24.5134	+	20.5692i	−1.21211	+	1.01708i	−0.999199	+	0.0400102i	$0.987261\pi$
$410$		0			0
$411$	−4.50000	−	7.79423i	−0.221969	−	0.384461i
$412$	13.1557	+	4.78828i	0.648135	+	0.235902i
$413$	1.56283	−	8.86327i	0.0769020	−	0.436133i
$414$	−1.04189	−	5.90885i	−0.0512061	−	0.290404i
$415$		0			0
$416$	−3.83022	−	3.21394i	−0.187792	−	0.157576i
$417$	4.00000			0.195881
$418$		0			0
$419$	−12.0000			−0.586238			−0.293119	−	0.956076i	$-0.594693\pi$
$419$	−12.0000			−0.586238			−0.293119	+	0.956076i	$0.594693\pi$
$420$		0			0
$421$	15.9748	−	5.81434i	0.778563	−	0.283374i	0.0779896	−	0.996954i	$-0.475150\pi$
$421$	15.9748	−	5.81434i	0.778563	−	0.283374i	0.700573	+	0.713580i	$0.252928\pi$
$422$	−0.868241	−	4.92404i	−0.0422653	−	0.239698i
$423$		0			0
$424$	−2.81908	−	1.02606i	−0.136907	−	0.0498299i
$425$	7.50000	+	12.9904i	0.363803	+	0.630126i
$426$	3.00000	−	5.19615i	0.145350	−	0.251754i
$427$	7.66044	−	6.42788i	0.370715	−	0.311067i
$428$	6.89440	−	5.78509i	0.333253	−	0.279633i
$429$	15.0000	−	25.9808i	0.724207	−	1.25436i
$430$		0			0
$431$	5.63816	+	2.05212i	0.271580	+	0.0988472i	0.474221	−	0.880406i	$-0.342730\pi$
$431$	5.63816	+	2.05212i	0.271580	+	0.0988472i	−0.202640	+	0.979253i	$0.564952\pi$
$432$	0.868241	−	4.92404i	0.0417733	−	0.236908i
$433$	−0.347296	−	1.96962i	−0.0166900	−	0.0946537i	0.975325	−	0.220774i	$-0.0708584\pi$
$433$	−0.347296	−	1.96962i	−0.0166900	−	0.0946537i	−0.992015	+	0.126121i	$0.959747\pi$
$434$	3.75877	−	1.36808i	0.180427	−	0.0656700i
$435$		0			0
$436$	−11.0000			−0.526804
$437$		0			0
$438$	7.00000			0.334473
$439$	21.4492	+	17.9981i	1.02372	+	0.859000i	0.990090	−	0.140434i	$-0.0448499\pi$
$439$	21.4492	+	17.9981i	1.02372	+	0.859000i	0.0336266	+	0.999434i	$0.489294\pi$
$440$		0			0
$441$	2.08378	+	11.8177i	0.0992275	+	0.562747i
$442$	−2.60472	+	14.7721i	−0.123894	+	0.702638i
$443$	16.9145	+	6.15636i	0.803631	+	0.292498i	0.710990	−	0.703202i	$-0.248247\pi$
$443$	16.9145	+	6.15636i	0.803631	+	0.292498i	0.0926405	+	0.995700i	$0.470469\pi$
$444$	−1.00000	−	1.73205i	−0.0474579	−	0.0821995i
$445$		0			0
$446$	−19.9172	+	16.7125i	−0.943105	+	0.791359i
$447$		0			0
$448$	0.500000	−	0.866025i	0.0236228	−	0.0409159i
$449$	−9.00000	−	15.5885i	−0.424736	−	0.735665i	0.571660	−	0.820491i	$-0.306300\pi$
$449$	−9.00000	−	15.5885i	−0.424736	−	0.735665i	−0.996396	+	0.0848262i	$0.972967\pi$
$450$	−9.39693	−	3.42020i	−0.442975	−	0.161230i
$451$		0			0
$452$	−1.04189	−	5.90885i	−0.0490063	−	0.277929i
$453$	9.39693	−	3.42020i	0.441506	−	0.160695i
$454$	11.4907	+	9.64181i	0.539284	+	0.452513i
$455$		0			0
$456$		0			0
$457$	17.0000			0.795226			0.397613	−	0.917553i	$-0.369839\pi$
$457$	17.0000			0.795226			0.397613	+	0.917553i	$0.369839\pi$
$458$	−16.8530	−	14.1413i	−0.787488	−	0.660781i
$459$	−14.0954	+	5.13030i	−0.657916	+	0.239462i
$460$		0			0
$461$	−2.08378	+	11.8177i	−0.0970512	+	0.550405i	0.897048	+	0.441933i	$0.145707\pi$
$461$	−2.08378	+	11.8177i	−0.0970512	+	0.550405i	−0.994099	+	0.108472i	$0.965404\pi$
$462$	5.63816	+	2.05212i	0.262311	+	0.0954733i
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	0.908750	−	0.417340i	$-0.137038\pi$
$463$	2.00000	+	3.46410i	0.0929479	+	0.160990i	−0.815802	+	0.578331i	$0.803704\pi$
$464$	4.50000	−	7.79423i	0.208907	−	0.361838i
$465$		0			0
$466$	−4.59627	+	3.85673i	−0.212918	+	0.178659i
$467$	−9.00000	+	15.5885i	−0.416470	+	0.721348i	−0.995582	−	0.0939008i	$-0.970066\pi$
$467$	−9.00000	+	15.5885i	−0.416470	+	0.721348i	0.579111	+	0.815249i	$0.303400\pi$
$468$	−5.00000	−	8.66025i	−0.231125	−	0.400320i
$469$	−4.69846	−	1.71010i	−0.216955	−	0.0789651i
$470$		0			0
$471$	3.82026	+	21.6658i	0.176028	+	0.998306i
$472$	8.45723	−	3.07818i	0.389276	−	0.141685i
$473$	−36.7701	−	30.8538i	−1.69069	−	1.41866i
$474$	−10.0000			−0.459315
$475$		0			0
$476$	−3.00000			−0.137505
$477$	−4.59627	−	3.85673i	−0.210449	−	0.176587i
$478$	19.7335	−	7.18242i	0.902591	−	0.328516i
$479$	6.25133	+	35.4531i	0.285631	+	1.61989i	0.703024	+	0.711166i	$0.251833\pi$
$479$	6.25133	+	35.4531i	0.285631	+	1.61989i	−0.417393	+	0.908726i	$0.637056\pi$
$480$		0			0
$481$	−9.39693	−	3.42020i	−0.428463	−	0.155948i
$482$	4.00000	+	6.92820i	0.182195	+	0.315571i
$483$	−1.50000	+	2.59808i	−0.0682524	+	0.118217i
$484$	19.1511	−	16.0697i	0.870505	−	0.730440i
$485$		0			0
$486$	8.00000	−	13.8564i	0.362887	−	0.628539i
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	0.887793	−	0.460243i	$-0.152238\pi$
$487$	1.00000	+	1.73205i	0.0453143	+	0.0784867i	−0.842479	+	0.538730i	$0.818904\pi$
$488$	9.39693	+	3.42020i	0.425379	+	0.154825i
$489$	−3.47296	+	19.6962i	−0.157053	+	0.890691i
$490$		0			0
$491$	33.8289	−	12.3127i	1.52668	−	0.555666i	0.563873	−	0.825861i	$-0.309311\pi$
$491$	33.8289	−	12.3127i	1.52668	−	0.555666i	0.962805	+	0.270196i	$0.0870885\pi$
$492$		0			0
$493$	−27.0000			−1.21602
$494$		0			0
$495$		0			0
$496$	3.06418	+	2.57115i	0.137586	+	0.115448i
$497$	5.63816	−	2.05212i	0.252906	−	0.0920502i
$498$	1.04189	+	5.90885i	0.0466882	+	0.264782i
$499$	−0.694593	+	3.93923i	−0.0310942	+	0.176344i	−0.996400	−	0.0847787i	$-0.972982\pi$
$499$	−0.694593	+	3.93923i	−0.0310942	+	0.176344i	0.965306	+	0.261123i	$0.0840928\pi$
$500$		0			0
$501$	−6.00000	−	10.3923i	−0.268060	−	0.464294i
$502$	−3.00000	+	5.19615i	−0.133897	+	0.231916i
$503$	−16.0869	+	13.4985i	−0.717281	+	0.601870i	−0.926632	−	0.375970i	$-0.877309\pi$
$503$	−16.0869	+	13.4985i	−0.717281	+	0.601870i	0.209351	+	0.977841i	$0.432865\pi$
$504$	1.53209	−	1.28558i	0.0682447	−	0.0572641i
$505$		0			0
$506$	9.00000	+	15.5885i	0.400099	+	0.692991i
$507$	11.2763	+	4.10424i	0.500799	+	0.182276i
$508$	−0.347296	+	1.96962i	−0.0154088	+	0.0873876i
$509$	−5.20945	−	29.5442i	−0.230905	−	1.30953i	−0.851069	−	0.525053i	$-0.824045\pi$
$509$	−5.20945	−	29.5442i	−0.230905	−	1.30953i	0.620165	−	0.784472i	$-0.287066\pi$
$510$		0			0
$511$	5.36231	+	4.49951i	0.237215	+	0.199047i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−12.0000			−0.529297
$515$		0			0
$516$	7.51754	−	2.73616i	0.330941	−	0.120453i
$517$		0			0
$518$	0.347296	−	1.96962i	0.0152593	−	0.0865399i
$519$	−5.63816	−	2.05212i	−0.247488	−	0.0900781i
$520$		0			0
$521$	−18.0000	+	31.1769i	−0.788594	+	1.36589i	0.138234	+	0.990400i	$0.455857\pi$
$521$	−18.0000	+	31.1769i	−0.788594	+	1.36589i	−0.926828	+	0.375486i	$0.877476\pi$
$522$	13.7888	−	11.5702i	0.603519	−	0.506413i
$523$	−8.42649	+	7.07066i	−0.368465	+	0.309179i	−0.808154	−	0.588971i	$-0.799533\pi$
$523$	−8.42649	+	7.07066i	−0.368465	+	0.309179i	0.439689	+	0.898150i	$0.355089\pi$
$524$		0			0
$525$	2.50000	+	4.33013i	0.109109	+	0.188982i
$526$	−22.5526	−	8.20848i	−0.983341	−	0.357907i
$527$	2.08378	−	11.8177i	0.0907708	−	0.514787i
$528$	1.04189	+	5.90885i	0.0453424	+	0.257150i
$529$	13.1557	−	4.78828i	0.571987	−	0.208186i
$530$		0			0
$531$	18.0000			0.781133
$532$		0			0
$533$		0			0
$534$	−9.19253	−	7.71345i	−0.397800	−	0.333794i
$535$		0			0
$536$	−0.868241	−	4.92404i	−0.0375023	−	0.212686i
$537$		0			0
$538$	−5.63816	−	2.05212i	−0.243078	−	0.0884732i
$539$	−18.0000	−	31.1769i	−0.775315	−	1.34288i
$540$		0			0
$541$	1.53209	−	1.28558i	0.0658696	−	0.0552712i	−0.609258	−	0.792972i	$-0.708533\pi$
$541$	1.53209	−	1.28558i	0.0658696	−	0.0552712i	0.675128	+	0.737701i	$0.264088\pi$
$542$	8.42649	−	7.07066i	0.361949	−	0.303711i
$543$	−1.00000	+	1.73205i	−0.0429141	+	0.0743294i
$544$	−1.50000	−	2.59808i	−0.0643120	−	0.111392i
$545$		0			0
$546$	−0.868241	+	4.92404i	−0.0371573	+	0.210729i
$547$	−7.64052	−	43.3315i	−0.326685	−	1.85272i	−0.497559	−	0.867430i	$-0.665770\pi$
$547$	−7.64052	−	43.3315i	−0.326685	−	1.85272i	0.170874	−	0.985293i	$-0.445341\pi$
$548$	8.45723	−	3.07818i	0.361275	−	0.131493i
$549$	15.3209	+	12.8558i	0.653880	+	0.548670i
$550$	30.0000			1.27920
$551$		0			0
$552$	−3.00000			−0.127688
$553$	−7.66044	−	6.42788i	−0.325755	−	0.273341i
$554$	−7.51754	+	2.73616i	−0.319390	+	0.116248i
$555$		0			0
$556$	−0.694593	+	3.93923i	−0.0294573	+	0.167061i
$557$	−22.5526	−	8.20848i	−0.955585	−	0.347805i	−0.183283	−	0.983060i	$-0.558673\pi$
$557$	−22.5526	−	8.20848i	−0.955585	−	0.347805i	−0.772302	+	0.635256i	$0.780895\pi$
$558$	4.00000	+	6.92820i	0.169334	+	0.293294i
$559$	20.0000	−	34.6410i	0.845910	−	1.46516i
$560$		0			0
$561$	13.7888	−	11.5702i	0.582164	−	0.488493i
$562$		0			0
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	0.711445	−	0.702742i	$-0.248041\pi$
$563$	−6.00000	−	10.3923i	−0.252870	−	0.437983i	−0.964315	+	0.264758i	$0.914708\pi$
$564$		0			0
$565$		0			0
$566$	−3.82026	−	21.6658i	−0.160578	−	0.910680i
$567$	0.939693	−	0.342020i	0.0394634	−	0.0143635i
$568$	4.59627	+	3.85673i	0.192855	+	0.161825i
$569$	24.0000			1.00613			0.503066	−	0.864248i	$-0.332205\pi$
$569$	24.0000			1.00613			0.503066	+	0.864248i	$0.332205\pi$
$570$		0			0
$571$	−4.00000			−0.167395			−0.0836974	−	0.996491i	$-0.526673\pi$
$571$	−4.00000			−0.167395			−0.0836974	+	0.996491i	$0.526673\pi$
$572$	22.9813	+	19.2836i	0.960898	+	0.806289i
$573$	2.81908	−	1.02606i	0.117769	−	0.0428643i
$574$		0			0
$575$	−2.60472	+	14.7721i	−0.108624	+	0.616040i
$576$	1.87939	+	0.684040i	0.0783077	+	0.0285017i
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	0.728535	−	0.685009i	$-0.240202\pi$
$577$	−5.50000	−	9.52628i	−0.228968	−	0.396584i	−0.957503	+	0.288425i	$0.906868\pi$
$578$	4.00000	−	6.92820i	0.166378	−	0.288175i
$579$	10.7246	−	8.99903i	0.445700	−	0.373987i
$580$		0			0
$581$	−3.00000	+	5.19615i	−0.124461	+	0.215573i
$582$	5.00000	+	8.66025i	0.207257	+	0.358979i
$583$	16.9145	+	6.15636i	0.700526	+	0.254970i
$584$	−1.21554	+	6.89365i	−0.0502993	+	0.285261i
$585$		0			0
$586$	−19.7335	+	7.18242i	−0.815185	+	0.296703i
$587$	−9.19253	−	7.71345i	−0.379416	−	0.318368i	0.433057	−	0.901367i	$-0.357435\pi$
$587$	−9.19253	−	7.71345i	−0.379416	−	0.318368i	−0.812473	+	0.582998i	$0.801879\pi$
$588$	6.00000			0.247436
$589$		0			0
$590$		0			0
$591$		0			0
$592$	1.87939	−	0.684040i	0.0772423	−	0.0281139i
$593$	−5.20945	−	29.5442i	−0.213926	−	1.21324i	−0.882760	−	0.469824i	$-0.844317\pi$
$593$	−5.20945	−	29.5442i	−0.213926	−	1.21324i	0.668834	−	0.743412i	$-0.266794\pi$
$594$	−5.20945	+	29.5442i	−0.213746	+	1.21221i
$595$		0			0
$596$		0			0
$597$	5.50000	−	9.52628i	0.225100	−	0.389885i
$598$	−11.4907	+	9.64181i	−0.469888	+	0.394283i
$599$	18.3851	−	15.4269i	0.751193	−	0.630326i	−0.184625	−	0.982809i	$-0.559107\pi$
$599$	18.3851	−	15.4269i	0.751193	−	0.630326i	0.935818	+	0.352483i	$0.114663\pi$
$600$	−2.50000	+	4.33013i	−0.102062	+	0.176777i
$601$	−14.0000	−	24.2487i	−0.571072	−	0.989126i	−0.996456	−	0.0841128i	$-0.973194\pi$
$601$	−14.0000	−	24.2487i	−0.571072	−	0.989126i	0.425384	−	0.905013i	$-0.360139\pi$
$602$	7.51754	+	2.73616i	0.306392	+	0.111518i
$603$	1.73648	−	9.84808i	0.0707150	−	0.401045i
$604$	1.73648	+	9.84808i	0.0706564	+	0.400713i
$605$		0			0
$606$	−13.7888	−	11.5702i	−0.560132	−	0.470006i
$607$	22.0000			0.892952			0.446476	−	0.894795i	$-0.352679\pi$
$607$	22.0000			0.892952			0.446476	+	0.894795i	$0.352679\pi$
$608$		0			0
$609$	−9.00000			−0.364698
$610$		0			0
$611$		0			0
$612$	−1.04189	−	5.90885i	−0.0421159	−	0.238851i
$613$	0.347296	−	1.96962i	0.0140272	−	0.0795520i	−0.976991	−	0.213282i	$-0.931585\pi$
$613$	0.347296	−	1.96962i	0.0140272	−	0.0795520i	0.991018	+	0.133730i	$0.0426956\pi$
$614$	18.7939	+	6.84040i	0.758458	+	0.276056i
$615$		0			0
$616$	−3.00000	+	5.19615i	−0.120873	+	0.209359i
$617$	−4.59627	+	3.85673i	−0.185039	+	0.155266i	−0.730602	−	0.682804i	$-0.760760\pi$
$617$	−4.59627	+	3.85673i	−0.185039	+	0.155266i	0.545563	+	0.838070i	$0.316316\pi$
$618$	10.7246	−	8.99903i	0.431408	−	0.361994i
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	−0.747873	−	0.663842i	$-0.768925\pi$
$619$	5.00000	−	8.66025i	0.200967	−	0.348085i	0.948840	+	0.315757i	$0.102258\pi$
$620$		0			0
$621$	−14.0954	−	5.13030i	−0.565628	−	0.205872i
$622$	−3.64661	+	20.6810i	−0.146216	+	0.829231i
$623$	−2.08378	−	11.8177i	−0.0834848	−	0.473466i
$624$	−4.69846	+	1.71010i	−0.188089	+	0.0684588i
$625$	19.1511	+	16.0697i	0.766044	+	0.642788i
$626$	−19.0000			−0.759393
$627$		0			0
$628$	−22.0000			−0.877896
$629$	−4.59627	−	3.85673i	−0.183265	−	0.153778i
$630$		0			0
$631$	−2.77837	−	15.7569i	−0.110605	−	0.627273i	−0.988833	−	0.149030i	$-0.952385\pi$
$631$	−2.77837	−	15.7569i	−0.110605	−	0.627273i	0.878227	−	0.478243i	$-0.158726\pi$
$632$	1.73648	−	9.84808i	0.0690735	−	0.391735i
$633$	−4.69846	−	1.71010i	−0.186747	−	0.0679704i
$634$	−4.50000	−	7.79423i	−0.178718	−	0.309548i
$635$		0			0
$636$	−2.29813	+	1.92836i	−0.0911269	+	0.0764646i
$637$	22.9813	−	19.2836i	0.910554	−	0.764045i
$638$	−27.0000	+	46.7654i	−1.06894	+	1.85146i
$639$	6.00000	+	10.3923i	0.237356	+	0.411113i
$640$		0			0
$641$	−1.04189	+	5.90885i	−0.0411521	+	0.233385i	−0.998446	−	0.0557321i	$-0.982251\pi$
$641$	−1.04189	+	5.90885i	−0.0411521	+	0.233385i	0.957294	+	0.289118i	$0.0933618\pi$
$642$	−1.56283	−	8.86327i	−0.0616801	−	0.349805i
$643$	20.6732	−	7.52444i	0.815273	−	0.296735i	0.0994728	−	0.995040i	$-0.468284\pi$
$643$	20.6732	−	7.52444i	0.815273	−	0.296735i	0.715800	+	0.698305i	$0.246062\pi$
$644$	−2.29813	−	1.92836i	−0.0905591	−	0.0759881i
$645$		0			0
$646$		0			0
$647$	27.0000			1.06148			0.530740	−	0.847535i	$-0.321914\pi$
$647$	27.0000			1.06148			0.530740	+	0.847535i	$0.321914\pi$
$648$	0.766044	+	0.642788i	0.0300931	+	0.0252511i
$649$	−50.7434	+	18.4691i	−1.99185	+	0.724975i
$650$	4.34120	+	24.6202i	0.170276	+	0.965683i
$651$	0.694593	−	3.93923i	0.0272232	−	0.154391i
$652$	−18.7939	−	6.84040i	−0.736024	−	0.267891i
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	0.529799	−	0.848123i	$-0.322267\pi$
$653$	−12.0000	−	20.7846i	−0.469596	−	0.813365i	−0.999396	+	0.0347583i	$0.988934\pi$
$654$	−5.50000	+	9.52628i	−0.215067	+	0.372507i
$655$		0			0
$656$		0			0
$657$	−7.00000	+	12.1244i	−0.273096	+	0.473016i
$658$		0			0
$659$	−42.2862	−	15.3909i	−1.64724	−	0.599545i	−0.658953	−	0.752184i	$-0.729001\pi$
$659$	−42.2862	−	15.3909i	−1.64724	−	0.599545i	−0.988282	+	0.152639i	$0.951223\pi$
$660$		0			0
$661$	2.25743	+	12.8025i	0.0878037	+	0.497960i	0.996716	+	0.0809729i	$0.0258027\pi$
$661$	2.25743	+	12.8025i	0.0878037	+	0.497960i	−0.908913	+	0.416987i	$0.863086\pi$
$662$	−0.939693	+	0.342020i	−0.0365222	+	0.0132930i
$663$	11.4907	+	9.64181i	0.446261	+	0.374457i
$664$	−6.00000			−0.232845
$665$		0			0
$666$	4.00000			0.154997
$667$	−20.6832	−	17.3553i	−0.800857	−	0.671999i
$668$	11.2763	−	4.10424i	0.436294	−	0.158798i
$669$	4.51485	+	25.6050i	0.174554	+	0.989947i
$670$		0			0
$671$	−56.3816	−	20.5212i	−2.17659	−	0.792212i
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	22.0000	−	38.1051i	0.848038	−	1.46884i	−0.0349191	−	0.999390i	$-0.511117\pi$
$673$	22.0000	−	38.1051i	0.848038	−	1.46884i	0.882957	−	0.469454i	$-0.155549\pi$
$674$	3.06418	−	2.57115i	0.118028	−	0.0990370i
$675$	−19.1511	+	16.0697i	−0.737127	+	0.618523i
$676$	−6.00000	+	10.3923i	−0.230769	+	0.399704i
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	−0.986695	−	0.162581i	$-0.948018\pi$
$677$	−16.5000	−	28.5788i	−0.634147	−	1.09837i	0.352549	−	0.935793i	$-0.385315\pi$
$678$	−5.63816	−	2.05212i	−0.216532	−	0.0788112i
$679$	−1.73648	+	9.84808i	−0.0666401	+	0.377935i
$680$		0			0
$681$	14.0954	−	5.13030i	0.540136	−	0.196594i
$682$	−18.3851	−	15.4269i	−0.704001	−	0.590727i
$683$	−36.0000			−1.37750			−0.688751	−	0.724998i	$-0.741841\pi$
$683$	−36.0000			−1.37750			−0.688751	+	0.724998i	$0.741841\pi$
$684$		0			0
$685$		0			0
$686$	9.95858	+	8.35624i	0.380220	+	0.319043i
$687$	−20.6732	+	7.52444i	−0.788733	+	0.287075i
$688$	1.38919	+	7.87846i	0.0529622	+	0.300364i
$689$	−2.60472	+	14.7721i	−0.0992320	+	0.562773i
$690$		0			0
$691$	5.00000	+	8.66025i	0.190209	+	0.329452i	0.945319	−	0.326146i	$-0.105750\pi$
$691$	5.00000	+	8.66025i	0.190209	+	0.329452i	−0.755110	+	0.655598i	$0.772417\pi$
$692$	3.00000	−	5.19615i	0.114043	−	0.197528i
$693$	−9.19253	+	7.71345i	−0.349195	+	0.293010i
$694$	13.7888	−	11.5702i	0.523416	−	0.439198i
$695$		0			0
$696$	−4.50000	−	7.79423i	−0.170572	−	0.295439i
$697$		0			0
$698$	−1.73648	+	9.84808i	−0.0657268	+	0.372755i
$699$	1.04189	+	5.90885i	0.0394079	+	0.223493i
$700$	−4.69846	+	1.71010i	−0.177585	+	0.0646357i
$701$	9.19253	+	7.71345i	0.347197	+	0.291333i	0.799663	−	0.600448i	$-0.205011\pi$
$701$	9.19253	+	7.71345i	0.347197	+	0.291333i	−0.452466	+	0.891782i	$0.649456\pi$
$702$	−25.0000			−0.943564
$703$		0			0
$704$	−6.00000			−0.226134
$705$		0			0
$706$	14.0954	−	5.13030i	0.530487	−	0.193081i
$707$	−3.12567	−	17.7265i	−0.117553	−	0.666675i
$708$	1.56283	−	8.86327i	0.0587349	−	0.333102i
$709$	9.39693	+	3.42020i	0.352909	+	0.128448i	0.512391	−	0.858753i	$-0.328760\pi$
$709$	9.39693	+	3.42020i	0.352909	+	0.128448i	−0.159482	+	0.987201i	$0.550982\pi$
$710$		0			0
$711$	10.0000	−	17.3205i	0.375029	−	0.649570i
$712$	9.19253	−	7.71345i	0.344505	−	0.289074i
$713$	9.19253	−	7.71345i	0.344263	−	0.288871i
$714$	−1.50000	+	2.59808i	−0.0561361	+	0.0972306i
$715$		0			0
$716$		0			0
$717$	3.64661	−	20.6810i	0.136185	−	0.772345i
$718$	3.64661	+	20.6810i	0.136090	+	0.771807i
$719$	−36.6480	+	13.3388i	−1.36674	+	0.497453i	−0.918132	−	0.396276i	$-0.870302\pi$
$719$	−36.6480	+	13.3388i	−1.36674	+	0.497453i	−0.448609	+	0.893728i	$0.648080\pi$
$720$		0			0
$721$	14.0000			0.521387
$722$		0			0
$723$	8.00000			0.297523
$724$	−1.53209	−	1.28558i	−0.0569396	−	0.0477780i
$725$	−42.2862	+	15.3909i	−1.57047	+	0.571604i
$726$	−4.34120	−	24.6202i	−0.161117	−	0.913741i
$727$	−6.42498	+	36.4379i	−0.238289	+	1.35141i	0.597285	+	0.802029i	$0.296246\pi$
$727$	−6.42498	+	36.4379i	−0.238289	+	1.35141i	−0.835574	+	0.549377i	$0.814865\pi$
$728$	−4.69846	−	1.71010i	−0.174137	−	0.0633805i
$729$	−6.50000	−	11.2583i	−0.240741	−	0.416975i
$730$		0			0
$731$	18.3851	−	15.4269i	0.679996	−	0.570585i
$732$	7.66044	−	6.42788i	0.283138	−	0.237581i
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	0.403128	+	0.915144i	$0.367923\pi$
$733$	−16.0000	+	27.7128i	−0.590973	+	1.02360i	−0.994102	+	0.108453i	$0.965410\pi$
$734$	14.0000	+	24.2487i	0.516749	+	0.895036i
$735$		0			0
$736$	0.520945	−	2.95442i	0.0192023	−	0.108901i
$737$	5.20945	+	29.5442i	0.191892	+	1.08828i
$738$		0			0
$739$	−12.2567	−	10.2846i	−0.450870	−	0.378325i	0.388888	−	0.921285i	$-0.372859\pi$
$739$	−12.2567	−	10.2846i	−0.450870	−	0.378325i	−0.839759	+	0.542960i	$0.817304\pi$
$740$		0			0
$741$		0			0
$742$	−3.00000			−0.110133
$743$	27.5776	+	23.1404i	1.01172	+	0.848937i	0.988565	−	0.150795i	$-0.0481832\pi$
$743$	27.5776	+	23.1404i	1.01172	+	0.848937i	0.0231589	+	0.999732i	$0.492628\pi$
$744$	3.75877	−	1.36808i	0.137803	−	0.0501563i
$745$		0			0
$746$	−3.99391	+	22.6506i	−0.146227	+	0.829297i
$747$	−11.2763	−	4.10424i	−0.412579	−	0.150166i
$748$	9.00000	+	15.5885i	0.329073	+	0.569970i
$749$	4.50000	−	7.79423i	0.164426	−	0.284795i
$750$		0			0
$751$	30.6418	−	25.7115i	1.11813	−	0.938226i	0.119626	−	0.992819i	$-0.461831\pi$
$751$	30.6418	−	25.7115i	1.11813	−	0.938226i	0.998509	+	0.0545929i	$0.0173861\pi$
$752$		0			0
$753$	3.00000	+	5.19615i	0.109326	+	0.189358i
$754$	−42.2862	−	15.3909i	−1.53997	−	0.560504i
$755$		0			0
$756$	−0.868241	−	4.92404i	−0.0315776	−	0.179086i
$757$	−1.87939	+	0.684040i	−0.0683074	+	0.0248619i	−0.375948	−	0.926641i	$-0.622683\pi$
$757$	−1.87939	+	0.684040i	−0.0683074	+	0.0248619i	0.307640	+	0.951503i	$0.400461\pi$
$758$	5.36231	+	4.49951i	0.194768	+	0.163430i
$759$	18.0000			0.653359
$760$		0			0
$761$	−21.0000			−0.761249			−0.380625	−	0.924730i	$-0.624291\pi$
$761$	−21.0000			−0.761249			−0.380625	+	0.924730i	$0.624291\pi$
$762$	1.53209	+	1.28558i	0.0555017	+	0.0465715i
$763$	−10.3366	+	3.76222i	−0.374211	+	0.136202i
$764$	0.520945	+	2.95442i	0.0188471	+	0.106887i
$765$		0			0
$766$	16.9145	+	6.15636i	0.611145	+	0.222438i
$767$	−22.5000	−	38.9711i	−0.812428	−	1.40717i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	3.83022	−	3.21394i	0.138121	−	0.115898i	−0.571109	−	0.820874i	$-0.693487\pi$
$769$	3.83022	−	3.21394i	0.138121	−	0.115898i	0.709231	+	0.704976i	$0.249042\pi$
$770$		0			0
$771$	−6.00000	+	10.3923i	−0.216085	+	0.374270i
$772$	7.00000	+	12.1244i	0.251936	+	0.436365i
$773$	47.9243	+	17.4430i	1.72372	+	0.627382i	0.998152	−	0.0607702i	$-0.0193557\pi$
$773$	47.9243	+	17.4430i	1.72372	+	0.627382i	0.725566	+	0.688152i	$0.241578\pi$
$774$	−2.77837	+	15.7569i	−0.0998665	+	0.566371i
$775$	−3.47296	−	19.6962i	−0.124753	−	0.707507i
$776$	−9.39693	+	3.42020i	−0.337330	+	0.122778i
$777$	−1.53209	−	1.28558i	−0.0549634	−	0.0461198<

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:	\( N \)	\(=\)	\( 722 = 2 \cdot 19^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	722.e (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.53209 + 1.28558i) q^{9} +O(q^{10})\)	\(q+(0.766044 + 0.642788i) q^{2} +(0.939693 - 0.342020i) q^{3} +(0.173648 + 0.984808i) q^{4} +(0.939693 + 0.342020i) q^{6} +(0.500000 + 0.866025i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-1.53209 + 1.28558i) q^{9} +(3.00000 - 5.19615i) q^{11} +(0.500000 + 0.866025i) q^{12} +(4.69846 + 1.71010i) q^{13} +(-0.173648 + 0.984808i) q^{14} +(-0.939693 + 0.342020i) q^{16} +(2.29813 + 1.92836i) q^{17} -2.00000 q^{18} +(0.766044 + 0.642788i) q^{21} +(5.63816 - 2.05212i) q^{22} +(0.520945 + 2.95442i) q^{23} +(-0.173648 + 0.984808i) q^{24} +(4.69846 + 1.71010i) q^{25} +(2.50000 + 4.33013i) q^{26} +(-2.50000 + 4.33013i) q^{27} +(-0.766044 + 0.642788i) q^{28} +(-6.89440 + 5.78509i) q^{29} +(-2.00000 - 3.46410i) q^{31} +(-0.939693 - 0.342020i) q^{32} +(1.04189 - 5.90885i) q^{33} +(0.520945 + 2.95442i) q^{34} +(-1.53209 - 1.28558i) q^{36} -2.00000 q^{37} +5.00000 q^{39} +(0.173648 + 0.984808i) q^{42} +(1.38919 - 7.87846i) q^{43} +(5.63816 + 2.05212i) q^{44} +(-1.50000 + 2.59808i) q^{46} +(-0.766044 + 0.642788i) q^{48} +(3.00000 - 5.19615i) q^{49} +(2.50000 + 4.33013i) q^{50} +(2.81908 + 1.02606i) q^{51} +(-0.868241 + 4.92404i) q^{52} +(0.520945 + 2.95442i) q^{53} +(-4.69846 + 1.71010i) q^{54} -1.00000 q^{56} -9.00000 q^{58} +(-6.89440 - 5.78509i) q^{59} +(-1.73648 - 9.84808i) q^{61} +(0.694593 - 3.93923i) q^{62} +(-1.87939 - 0.684040i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(4.59627 - 3.85673i) q^{66} +(-3.83022 + 3.21394i) q^{67} +(-1.50000 + 2.59808i) q^{68} +(1.50000 + 2.59808i) q^{69} +(1.04189 - 5.90885i) q^{71} +(-0.347296 - 1.96962i) q^{72} +(6.57785 - 2.39414i) q^{73} +(-1.53209 - 1.28558i) q^{74} +5.00000 q^{75} +6.00000 q^{77} +(3.83022 + 3.21394i) q^{78} +(-9.39693 + 3.42020i) q^{79} +(0.173648 - 0.984808i) q^{81} +(3.00000 + 5.19615i) q^{83} +(-0.500000 + 0.866025i) q^{84} +(6.12836 - 5.14230i) q^{86} +(-4.50000 + 7.79423i) q^{87} +(3.00000 + 5.19615i) q^{88} +(-11.2763 - 4.10424i) q^{89} +(0.868241 + 4.92404i) q^{91} +(-2.81908 + 1.02606i) q^{92} +(-3.06418 - 2.57115i) q^{93} -1.00000 q^{96} +(7.66044 + 6.42788i) q^{97} +(5.63816 - 2.05212i) q^{98} +(2.08378 + 11.8177i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{7} - 3 q^{8}+O(q^{10}) \) 6 * q + 3 * q^7 - 3 * q^8	\( 6 q + 3 q^{7} - 3 q^{8} + 18 q^{11} + 3 q^{12} - 12 q^{18} + 15 q^{26} - 15 q^{27} - 12 q^{31} - 12 q^{37} + 30 q^{39} - 9 q^{46} + 18 q^{49} + 15 q^{50} - 6 q^{56} - 54 q^{58} - 3 q^{64} - 9 q^{68} + 9 q^{69} + 30 q^{75} + 36 q^{77} + 18 q^{83} - 3 q^{84} - 27 q^{87} + 18 q^{88} - 6 q^{96}+O(q^{100}) \) 6 * q + 3 * q^7 - 3 * q^8 + 18 * q^11 + 3 * q^12 - 12 * q^18 + 15 * q^26 - 15 * q^27 - 12 * q^31 - 12 * q^37 + 30 * q^39 - 9 * q^46 + 18 * q^49 + 15 * q^50 - 6 * q^56 - 54 * q^58 - 3 * q^64 - 9 * q^68 + 9 * q^69 + 30 * q^75 + 36 * q^77 + 18 * q^83 - 3 * q^84 - 27 * q^87 + 18 * q^88 - 6 * q^96

Introduction

L-functions

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