LMFDB - Embedded newform 722.2.e.i.245.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [722,2,Mod(99,722)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("722.99"); S:= CuspForms(chi, 2); N := Newforms(S);

sage: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")

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:traces = [6,0,0,0,0,0,12,-3,0,0,-9,3,0] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(13)] == traces)

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			245.1
Root			$-0.766044 - 0.642788i$ of defining polynomial
Character	$\chi$	$=$	722.245
Dual form			722.2.e.i.389.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.173648 - 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(2.00000 + 3.46410i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.347296 - 1.96962i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.53209 + 1.28558i) q^{13} +(3.75877 - 1.36808i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-1.04189 + 5.90885i) q^{17} -2.00000 q^{18} +(0.694593 - 3.93923i) q^{21} +(2.29813 + 1.92836i) q^{22} +(5.63816 + 2.05212i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-3.83022 + 3.21394i) q^{25} +(1.00000 + 1.73205i) q^{26} +(-2.50000 + 4.33013i) q^{27} +(-0.694593 - 3.93923i) q^{28} +(1.00000 + 1.73205i) q^{31} +(0.766044 - 0.642788i) q^{32} +(2.81908 - 1.02606i) q^{33} +(5.63816 + 2.05212i) q^{34} +(-0.347296 + 1.96962i) q^{36} +10.0000 q^{37} +2.00000 q^{39} +(-6.89440 - 5.78509i) q^{41} +(-3.75877 - 1.36808i) q^{42} +(3.75877 - 1.36808i) q^{43} +(2.29813 - 1.92836i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-0.173648 - 0.984808i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(2.50000 + 4.33013i) q^{50} +(4.59627 - 3.85673i) q^{51} +(1.87939 - 0.684040i) q^{52} +(5.63816 + 2.05212i) q^{53} +(3.83022 + 3.21394i) q^{54} -4.00000 q^{56} +(1.56283 - 8.86327i) q^{59} +(3.75877 + 1.36808i) q^{61} +(1.87939 - 0.684040i) q^{62} +(6.12836 - 5.14230i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.520945 - 2.95442i) q^{66} +(1.21554 + 6.89365i) q^{67} +(3.00000 - 5.19615i) q^{68} +(-3.00000 - 5.19615i) q^{69} +(-5.63816 + 2.05212i) q^{71} +(1.87939 + 0.684040i) q^{72} +(-0.766044 - 0.642788i) q^{73} +(1.73648 - 9.84808i) q^{74} +5.00000 q^{75} -12.0000 q^{77} +(0.347296 - 1.96962i) q^{78} +(3.06418 + 2.57115i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(-6.89440 + 5.78509i) q^{82} +(-1.50000 - 2.59808i) q^{83} +(-2.00000 + 3.46410i) q^{84} +(-0.694593 - 3.93923i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(-4.59627 + 3.85673i) q^{89} +(-7.51754 - 2.73616i) q^{91} +(-4.59627 - 3.85673i) q^{92} +(0.347296 - 1.96962i) q^{93} -1.00000 q^{96} +(-2.95202 + 16.7417i) q^{97} +(6.89440 + 5.78509i) q^{98} +(5.63816 + 2.05212i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 12 q^{7} - 3 q^{8} - 9 q^{11} + 3 q^{12} - 12 q^{18} + 6 q^{26} - 15 q^{27} + 6 q^{31} + 60 q^{37} + 12 q^{39} + 18 q^{46} - 27 q^{49} + 15 q^{50} - 24 q^{56} - 3 q^{64} + 18 q^{68} - 18 q^{69} + 30 q^{75}+ \cdots - 6 q^{96}+O(q^{100}) $ 6 * q + 12 * q^7 - 3 * q^8 - 9 * q^11 + 3 * q^12 - 12 * q^18 + 6 * q^26 - 15 * q^27 + 6 * q^31 + 60 * q^37 + 12 * q^39 + 18 * q^46 - 27 * q^49 + 15 * q^50 - 24 * q^56 - 3 * q^64 + 18 * q^68 - 18 * q^69 + 30 * q^75 - 72 * q^77 - 9 * q^83 - 12 * q^84 - 9 * q^88 - 6 * q^96

Character values

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

$n$	$363$
$\chi(n)$	$e\left(\frac{5}{9}\right)$

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 $

$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$2$	0.173648	−	0.984808i	0.122788	−	0.696364i
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i	0.394284	−	0.918989i	$-0.370993\pi$
$3$	−0.766044	−	0.642788i	−0.442276	−	0.371114i	−0.836560	+	0.547875i	$0.815437\pi$
$4$	−0.939693	−	0.342020i	−0.469846	−	0.171010i
$5$		0			0		−0.342020	−	0.939693i	$-0.611111\pi$
$5$		0			0		0.342020	+	0.939693i	$0.388889\pi$
$6$	−0.766044	+	0.642788i	−0.312736	+	0.262417i
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	0.944911	+	0.327327i	$0.106148\pi$
$7$	2.00000	+	3.46410i	0.755929	+	1.30931i	−0.188982	+	0.981981i	$0.560519\pi$
$8$	−0.500000	+	0.866025i	−0.176777	+	0.306186i
$9$	−0.347296	−	1.96962i	−0.115765	−	0.656539i
$10$		0			0
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	−0.998526	−	0.0542666i	$-0.982718\pi$
$11$	−1.50000	+	2.59808i	−0.452267	+	0.783349i	0.546259	+	0.837616i	$0.316051\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−1.53209	+	1.28558i	−0.424925	+	0.356554i	−0.830033	−	0.557714i	$-0.811678\pi$
$13$	−1.53209	+	1.28558i	−0.424925	+	0.356554i	0.405108	+	0.914269i	$0.367234\pi$
$14$	3.75877	−	1.36808i	1.00457	−	0.365635i
$15$		0			0
$16$	0.766044	+	0.642788i	0.191511	+	0.160697i
$17$	−1.04189	+	5.90885i	−0.252695	+	1.43311i	0.549225	+	0.835675i	$0.314923\pi$
$17$	−1.04189	+	5.90885i	−0.252695	+	1.43311i	−0.801920	+	0.597431i	$0.796188\pi$
$18$	−2.00000			−0.471405
$19$		0			0
$19$		0			0
$20$		0			0
$21$	0.694593	−	3.93923i	0.151573	−	0.859611i
$22$	2.29813	+	1.92836i	0.489964	+	0.411128i
$23$	5.63816	+	2.05212i	1.17564	+	0.427897i	0.854659	−	0.519190i	$-0.173766\pi$
$23$	5.63816	+	2.05212i	1.17564	+	0.427897i	0.320978	+	0.947087i	$0.395988\pi$
$24$	0.939693	−	0.342020i	0.191814	−	0.0698146i
$25$	−3.83022	+	3.21394i	−0.766044	+	0.642788i
$26$	1.00000	+	1.73205i	0.196116	+	0.339683i
$27$	−2.50000	+	4.33013i	−0.481125	+	0.833333i
$28$	−0.694593	−	3.93923i	−0.131266	−	0.744445i
$29$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$29$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$30$		0			0
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	0.941745	−	0.336327i	$-0.109185\pi$
$31$	1.00000	+	1.73205i	0.179605	+	0.311086i	−0.762140	+	0.647412i	$0.775851\pi$
$32$	0.766044	−	0.642788i	0.135419	−	0.113630i
$33$	2.81908	−	1.02606i	0.490738	−	0.178614i
$34$	5.63816	+	2.05212i	0.966936	+	0.351936i
$35$		0			0
$36$	−0.347296	+	1.96962i	−0.0578827	+	0.328269i
$37$	10.0000			1.64399			0.821995	−	0.569495i	$-0.192861\pi$
$37$	10.0000			1.64399			0.821995	+	0.569495i	$0.192861\pi$
$38$		0			0
$39$	2.00000			0.320256
$40$		0			0
$41$	−6.89440	−	5.78509i	−1.07672	−	0.903479i	−0.0810797	−	0.996708i	$-0.525837\pi$
$41$	−6.89440	−	5.78509i	−1.07672	−	0.903479i	−0.995645	+	0.0932286i	$0.970281\pi$
$42$	−3.75877	−	1.36808i	−0.579991	−	0.211099i
$43$	3.75877	−	1.36808i	0.573207	−	0.208630i	−0.0391204	−	0.999235i	$-0.512456\pi$
$43$	3.75877	−	1.36808i	0.573207	−	0.208630i	0.612328	+	0.790604i	$0.290233\pi$
$44$	2.29813	−	1.92836i	0.346457	−	0.290712i
$45$		0			0
$46$	3.00000	−	5.19615i	0.442326	−	0.766131i
$47$		0			0		0.984808	−	0.173648i	$-0.0555556\pi$
$47$		0			0		−0.984808	+	0.173648i	$0.944444\pi$
$48$	−0.173648	−	0.984808i	−0.0250640	−	0.142145i
$49$	−4.50000	+	7.79423i	−0.642857	+	1.11346i
$50$	2.50000	+	4.33013i	0.353553	+	0.612372i
$51$	4.59627	−	3.85673i	0.643606	−	0.540050i
$52$	1.87939	−	0.684040i	0.260624	−	0.0948593i
$53$	5.63816	+	2.05212i	0.774460	+	0.281880i	0.698861	−	0.715258i	$-0.253691\pi$
$53$	5.63816	+	2.05212i	0.774460	+	0.281880i	0.0755995	+	0.997138i	$0.475913\pi$
$54$	3.83022	+	3.21394i	0.521227	+	0.437362i
$55$		0			0
$56$	−4.00000			−0.534522
$57$		0			0
$58$		0			0
$59$	1.56283	−	8.86327i	0.203464	−	1.15390i	−0.696376	−	0.717678i	$-0.745205\pi$
$59$	1.56283	−	8.86327i	0.203464	−	1.15390i	0.899839	−	0.436222i	$-0.143684\pi$
$60$		0			0
$61$	3.75877	+	1.36808i	0.481261	+	0.175165i	0.571247	−	0.820778i	$-0.306460\pi$
$61$	3.75877	+	1.36808i	0.481261	+	0.175165i	−0.0899856	+	0.995943i	$0.528682\pi$
$62$	1.87939	−	0.684040i	0.238682	−	0.0868732i
$63$	6.12836	−	5.14230i	0.772100	−	0.647869i
$64$	−0.500000	−	0.866025i	−0.0625000	−	0.108253i
$65$		0			0
$66$	−0.520945	−	2.95442i	−0.0641238	−	0.363664i
$67$	1.21554	+	6.89365i	0.148502	+	0.842194i	0.964489	+	0.264124i	$0.0850828\pi$
$67$	1.21554	+	6.89365i	0.148502	+	0.842194i	−0.815987	+	0.578070i	$0.803806\pi$
$68$	3.00000	−	5.19615i	0.363803	−	0.630126i
$69$	−3.00000	−	5.19615i	−0.361158	−	0.625543i
$70$		0			0
$71$	−5.63816	+	2.05212i	−0.669126	+	0.243542i	−0.654172	−	0.756346i	$-0.726983\pi$
$71$	−5.63816	+	2.05212i	−0.669126	+	0.243542i	−0.0149545	+	0.999888i	$0.504760\pi$
$72$	1.87939	+	0.684040i	0.221488	+	0.0806149i
$73$	−0.766044	−	0.642788i	−0.0896587	−	0.0752326i	0.596857	−	0.802348i	$-0.296416\pi$
$73$	−0.766044	−	0.642788i	−0.0896587	−	0.0752326i	−0.686515	+	0.727115i	$0.740861\pi$
$74$	1.73648	−	9.84808i	0.201862	−	1.14482i
$75$	5.00000			0.577350
$76$		0			0
$77$	−12.0000			−1.36753
$78$	0.347296	−	1.96962i	0.0393236	−	0.223015i
$79$	3.06418	+	2.57115i	0.344747	+	0.289277i	0.798677	−	0.601760i	$-0.205534\pi$
$79$	3.06418	+	2.57115i	0.344747	+	0.289277i	−0.453930	+	0.891038i	$0.649978\pi$
$80$		0			0
$81$	−0.939693	+	0.342020i	−0.104410	+	0.0380022i
$82$	−6.89440	+	5.78509i	−0.761359	+	0.638856i
$83$	−1.50000	−	2.59808i	−0.164646	−	0.285176i	0.771883	−	0.635764i	$-0.219315\pi$
$83$	−1.50000	−	2.59808i	−0.164646	−	0.285176i	−0.936530	+	0.350588i	$0.885982\pi$
$84$	−2.00000	+	3.46410i	−0.218218	+	0.377964i
$85$		0			0
$86$	−0.694593	−	3.93923i	−0.0748999	−	0.424778i
$87$		0			0
$88$	−1.50000	−	2.59808i	−0.159901	−	0.276956i
$89$	−4.59627	+	3.85673i	−0.487203	+	0.408812i	−0.853023	−	0.521874i	$-0.825233\pi$
$89$	−4.59627	+	3.85673i	−0.487203	+	0.408812i	0.365819	+	0.930686i	$0.380789\pi$
$90$		0			0
$91$	−7.51754	−	2.73616i	−0.788052	−	0.286828i
$92$	−4.59627	−	3.85673i	−0.479194	−	0.402091i
$93$	0.347296	−	1.96962i	0.0360130	−	0.204240i
$94$		0			0
$95$		0			0
$96$	−1.00000			−0.102062
$97$	−2.95202	+	16.7417i	−0.299732	+	1.69987i	0.347588	+	0.937647i	$0.387001\pi$
$97$	−2.95202	+	16.7417i	−0.299732	+	1.69987i	−0.647320	+	0.762218i	$0.724110\pi$
$98$	6.89440	+	5.78509i	0.696440	+	0.584382i
$99$	5.63816	+	2.05212i	0.566656	+	0.206246i
$100$	4.69846	−	1.71010i	0.469846	−	0.171010i
$101$		0			0		−0.642788	−	0.766044i	$-0.722222\pi$
$101$		0			0		0.642788	+	0.766044i	$0.277778\pi$
$102$	−3.00000	−	5.19615i	−0.297044	−	0.514496i
$103$	1.00000	−	1.73205i	0.0985329	−	0.170664i	−0.812545	−	0.582899i	$-0.801918\pi$
$103$	1.00000	−	1.73205i	0.0985329	−	0.170664i	0.911078	+	0.412235i	$0.135252\pi$
$104$	−0.347296	−	1.96962i	−0.0340552	−	0.193137i
$105$		0			0
$106$	3.00000	−	5.19615i	0.291386	−	0.504695i
$107$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$107$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$108$	3.83022	−	3.21394i	0.368563	−	0.309261i
$109$	−15.0351	+	5.47232i	−1.44010	+	0.524153i	−0.939808	−	0.341703i	$-0.888996\pi$
$109$	−15.0351	+	5.47232i	−1.44010	+	0.524153i	−0.500292	+	0.865857i	$0.666774\pi$
$110$		0			0
$111$	−7.66044	−	6.42788i	−0.727097	−	0.610107i
$112$	−0.694593	+	3.93923i	−0.0656328	+	0.372222i
$113$	−15.0000			−1.41108			−0.705541	−	0.708669i	$-0.749296\pi$
$113$	−15.0000			−1.41108			−0.705541	+	0.708669i	$0.749296\pi$
$114$		0			0
$115$		0			0
$116$		0			0
$117$	3.06418	+	2.57115i	0.283283	+	0.237703i
$118$	−8.45723	−	3.07818i	−0.778551	−	0.283370i
$119$	−22.5526	+	8.20848i	−2.06740	+	0.752470i
$120$		0			0
$121$	1.00000	+	1.73205i	0.0909091	+	0.157459i
$122$	2.00000	−	3.46410i	0.181071	−	0.313625i
$123$	1.56283	+	8.86327i	0.140916	+	0.799174i
$124$	−0.347296	−	1.96962i	−0.0311881	−	0.176877i
$125$		0			0
$126$	−4.00000	−	6.92820i	−0.356348	−	0.617213i
$127$	−1.53209	+	1.28558i	−0.135951	+	0.114076i	−0.708227	−	0.705984i	$-0.750505\pi$
$127$	−1.53209	+	1.28558i	−0.135951	+	0.114076i	0.572276	+	0.820061i	$0.306060\pi$
$128$	−0.939693	+	0.342020i	−0.0830579	+	0.0302306i
$129$	−3.75877	−	1.36808i	−0.330941	−	0.120453i
$130$		0			0
$131$	1.56283	−	8.86327i	0.136545	−	0.774387i	−0.837226	−	0.546858i	$-0.815824\pi$
$131$	1.56283	−	8.86327i	0.136545	−	0.774387i	0.973771	−	0.227530i	$-0.0730650\pi$
$132$	−3.00000			−0.261116
$133$		0			0
$134$	7.00000			0.604708
$135$		0			0
$136$	−4.59627	−	3.85673i	−0.394127	−	0.330711i
$137$	−8.45723	−	3.07818i	−0.722550	−	0.262987i	−0.0455422	−	0.998962i	$-0.514502\pi$
$137$	−8.45723	−	3.07818i	−0.722550	−	0.262987i	−0.677008	+	0.735976i	$0.736724\pi$
$138$	−5.63816	+	2.05212i	−0.479952	+	0.174688i
$139$	8.42649	−	7.07066i	0.714725	−	0.599726i	−0.211195	−	0.977444i	$-0.567736\pi$
$139$	8.42649	−	7.07066i	0.714725	−	0.599726i	0.925921	+	0.377718i	$0.123291\pi$
$140$		0			0
$141$		0			0
$142$	1.04189	+	5.90885i	0.0874334	+	0.495859i
$143$	−1.04189	−	5.90885i	−0.0871271	−	0.494123i
$144$	1.00000	−	1.73205i	0.0833333	−	0.144338i
$145$		0			0
$146$	−0.766044	+	0.642788i	−0.0633983	+	0.0531975i
$147$	8.45723	−	3.07818i	0.697541	−	0.253884i
$148$	−9.39693	−	3.42020i	−0.772423	−	0.281139i
$149$	13.7888	+	11.5702i	1.12962	+	0.947866i	0.999050	−	0.0435730i	$-0.0138741\pi$
$149$	13.7888	+	11.5702i	1.12962	+	0.947866i	0.130572	+	0.991439i	$0.458319\pi$
$150$	0.868241	−	4.92404i	0.0708916	−	0.402046i
$151$	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
$153$	12.0000			0.970143
$154$	−2.08378	+	11.8177i	−0.167916	+	0.952297i
$155$		0			0
$156$	−1.87939	−	0.684040i	−0.150471	−	0.0547671i
$157$	15.0351	−	5.47232i	1.19993	−	0.436739i	0.336730	−	0.941601i	$-0.390679\pi$
$157$	15.0351	−	5.47232i	1.19993	−	0.436739i	0.863200	+	0.504862i	$0.168457\pi$
$158$	3.06418	−	2.57115i	0.243773	−	0.204550i
$159$	−3.00000	−	5.19615i	−0.237915	−	0.412082i
$160$		0			0
$161$	4.16756	+	23.6354i	0.328449	+	1.86273i
$162$	0.173648	+	0.984808i	0.0136431	+	0.0773738i
$163$	9.50000	−	16.4545i	0.744097	−	1.28881i	−0.206518	−	0.978443i	$-0.566213\pi$
$163$	9.50000	−	16.4545i	0.744097	−	1.28881i	0.950615	−	0.310372i	$-0.100454\pi$
$164$	4.50000	+	7.79423i	0.351391	+	0.608627i
$165$		0			0
$166$	−2.81908	+	1.02606i	−0.218803	+	0.0796377i
$167$	−22.5526	−	8.20848i	−1.74517	−	0.635192i	−0.745659	−	0.666328i	$-0.767865\pi$
$167$	−22.5526	−	8.20848i	−1.74517	−	0.635192i	−0.999515	+	0.0311360i	$0.990088\pi$
$168$	3.06418	+	2.57115i	0.236406	+	0.198369i
$169$	−1.56283	+	8.86327i	−0.120218	+	0.681790i
$170$		0			0
$171$		0			0
$172$	−4.00000			−0.304997
$173$	−1.04189	+	5.90885i	−0.0792134	+	0.449241i	0.919243	+	0.393692i	$0.128802\pi$
$173$	−1.04189	+	5.90885i	−0.0792134	+	0.449241i	−0.998456	+	0.0555496i	$0.982309\pi$
$174$		0			0
$175$	−18.7939	−	6.84040i	−1.42068	−	0.517086i
$176$	−2.81908	+	1.02606i	−0.212496	+	0.0773422i
$177$	−6.89440	+	5.78509i	−0.518215	+	0.434834i
$178$	3.00000	+	5.19615i	0.224860	+	0.389468i
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	−0.647397	−	0.762153i	$-0.724142\pi$
$179$	4.50000	−	7.79423i	0.336346	−	0.582568i	0.983742	+	0.179585i	$0.0574756\pi$
$180$		0			0
$181$	−0.347296	−	1.96962i	−0.0258143	−	0.146400i	0.969176	−	0.246368i	$-0.0792372\pi$
$181$	−0.347296	−	1.96962i	−0.0258143	−	0.146400i	−0.994991	+	0.0999676i	$0.968126\pi$
$182$	−4.00000	+	6.92820i	−0.296500	+	0.513553i
$183$	−2.00000	−	3.46410i	−0.147844	−	0.256074i
$184$	−4.59627	+	3.85673i	−0.338841	+	0.284322i
$185$		0			0
$186$	−1.87939	−	0.684040i	−0.137803	−	0.0501563i
$187$	−13.7888	−	11.5702i	−1.00834	−	0.846095i
$188$		0			0
$189$	−20.0000			−1.45479
$190$		0			0
$191$	12.0000			0.868290			0.434145	−	0.900843i	$-0.357051\pi$
$191$	12.0000			0.868290			0.434145	+	0.900843i	$0.357051\pi$
$192$	−0.173648	+	0.984808i	−0.0125320	+	0.0710724i
$193$	−1.53209	−	1.28558i	−0.110282	−	0.0925377i	0.585979	−	0.810326i	$-0.300710\pi$
$193$	−1.53209	−	1.28558i	−0.110282	−	0.0925377i	−0.696261	+	0.717788i	$0.745155\pi$
$194$	15.9748	+	5.81434i	1.14692	+	0.417445i
$195$		0			0
$196$	6.89440	−	5.78509i	0.492457	−	0.413221i
$197$	−9.00000	−	15.5885i	−0.641223	−	1.11063i	−0.985160	−	0.171639i	$-0.945094\pi$
$197$	−9.00000	−	15.5885i	−0.641223	−	1.11063i	0.343937	−	0.938993i	$-0.388239\pi$
$198$	3.00000	−	5.19615i	0.213201	−	0.369274i
$199$	−1.73648	−	9.84808i	−0.123096	−	0.698112i	−0.982421	−	0.186681i	$-0.940227\pi$
$199$	−1.73648	−	9.84808i	−0.123096	−	0.698112i	0.859325	−	0.511431i	$-0.170884\pi$
$200$	−0.868241	−	4.92404i	−0.0613939	−	0.348182i
$201$	3.50000	−	6.06218i	0.246871	−	0.427593i
$202$		0			0
$203$		0			0
$204$	−5.63816	+	2.05212i	−0.394750	+	0.143677i
$205$		0			0
$206$	−1.53209	−	1.28558i	−0.106746	−	0.0895703i
$207$	2.08378	−	11.8177i	0.144833	−	0.821386i
$208$	−2.00000			−0.138675
$209$		0			0
$210$		0			0
$211$	−3.47296	+	19.6962i	−0.239089	+	1.35594i	0.594741	+	0.803917i	$0.297255\pi$
$211$	−3.47296	+	19.6962i	−0.239089	+	1.35594i	−0.833830	+	0.552022i	$0.813856\pi$
$212$	−4.59627	−	3.85673i	−0.315673	−	0.264881i
$213$	5.63816	+	2.05212i	0.386320	+	0.140609i
$214$		0			0
$215$		0			0
$216$	−2.50000	−	4.33013i	−0.170103	−	0.294628i
$217$	−4.00000	+	6.92820i	−0.271538	+	0.470317i
$218$	2.77837	+	15.7569i	0.188175	+	1.06719i
$219$	0.173648	+	0.984808i	0.0117341	+	0.0665471i
$220$		0			0
$221$	−6.00000	−	10.3923i	−0.403604	−	0.699062i
$222$	−7.66044	+	6.42788i	−0.514135	+	0.431411i
$223$	13.1557	−	4.78828i	0.880971	−	0.320647i	0.138369	−	0.990381i	$-0.455814\pi$
$223$	13.1557	−	4.78828i	0.880971	−	0.320647i	0.742601	+	0.669734i	$0.233592\pi$
$224$	3.75877	+	1.36808i	0.251143	+	0.0914087i
$225$	7.66044	+	6.42788i	0.510696	+	0.428525i
$226$	−2.60472	+	14.7721i	−0.173264	+	0.982627i
$227$	−3.00000			−0.199117			−0.0995585	−	0.995032i	$-0.531743\pi$
$227$	−3.00000			−0.199117			−0.0995585	+	0.995032i	$0.531743\pi$
$228$		0			0
$229$	−16.0000			−1.05731			−0.528655	−	0.848837i	$-0.677303\pi$
$229$	−16.0000			−1.05731			−0.528655	+	0.848837i	$0.677303\pi$
$230$		0			0
$231$	9.19253	+	7.71345i	0.604824	+	0.507508i
$232$		0			0
$233$	−2.81908	+	1.02606i	−0.184684	+	0.0672195i	−0.432707	−	0.901535i	$-0.642441\pi$
$233$	−2.81908	+	1.02606i	−0.184684	+	0.0672195i	0.248023	+	0.968754i	$0.420219\pi$
$234$	3.06418	−	2.57115i	0.200312	−	0.168081i
$235$		0			0
$236$	−4.50000	+	7.79423i	−0.292925	+	0.507361i
$237$	−0.694593	−	3.93923i	−0.0451186	−	0.255881i
$238$	4.16756	+	23.6354i	0.270143	+	1.53205i
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	−0.604087	−	0.796918i	$-0.706462\pi$
$239$	6.00000	−	10.3923i	0.388108	−	0.672222i	0.992195	+	0.124696i	$0.0397955\pi$
$240$		0			0
$241$	−3.83022	+	3.21394i	−0.246726	+	0.207028i	−0.757761	−	0.652532i	$-0.773707\pi$
$241$	−3.83022	+	3.21394i	−0.246726	+	0.207028i	0.511035	+	0.859560i	$0.329262\pi$
$242$	1.87939	−	0.684040i	0.120811	−	0.0439718i
$243$	15.0351	+	5.47232i	0.964501	+	0.351050i
$244$	−3.06418	−	2.57115i	−0.196164	−	0.164601i
$245$		0			0
$246$	9.00000			0.573819
$247$		0			0
$248$	−2.00000			−0.127000
$249$	−0.520945	+	2.95442i	−0.0330135	+	0.187229i
$250$		0			0
$251$	2.81908	+	1.02606i	0.177939	+	0.0647644i	0.429453	−	0.903089i	$-0.358706\pi$
$251$	2.81908	+	1.02606i	0.177939	+	0.0647644i	−0.251514	+	0.967854i	$0.580929\pi$
$252$	−7.51754	+	2.73616i	−0.473561	+	0.172362i
$253$	−13.7888	+	11.5702i	−0.866894	+	0.727411i
$254$	1.00000	+	1.73205i	0.0627456	+	0.108679i
$255$		0			0
$256$	0.173648	+	0.984808i	0.0108530	+	0.0615505i
$257$	−0.520945	−	2.95442i	−0.0324956	−	0.184292i	0.964240	−	0.265032i	$-0.0853826\pi$
$257$	−0.520945	−	2.95442i	−0.0324956	−	0.184292i	−0.996735	+	0.0807404i	$0.974272\pi$
$258$	−2.00000	+	3.46410i	−0.124515	+	0.215666i
$259$	20.0000	+	34.6410i	1.24274	+	2.15249i
$260$		0			0
$261$		0			0
$262$	−8.45723	−	3.07818i	−0.522490	−	0.190171i
$263$	−9.19253	−	7.71345i	−0.566836	−	0.475632i	0.313758	−	0.949503i	$-0.398412\pi$
$263$	−9.19253	−	7.71345i	−0.566836	−	0.475632i	−0.880594	+	0.473871i	$0.842856\pi$
$264$	−0.520945	+	2.95442i	−0.0320619	+	0.181832i
$265$		0			0
$266$		0			0
$267$	6.00000			0.367194
$268$	1.21554	−	6.89365i	0.0742508	−	0.421097i
$269$	−9.19253	−	7.71345i	−0.560479	−	0.470297i	0.317992	−	0.948093i	$-0.396991\pi$
$269$	−9.19253	−	7.71345i	−0.560479	−	0.470297i	−0.878471	+	0.477796i	$0.841436\pi$
$270$		0			0
$271$	15.0351	−	5.47232i	0.913316	−	0.332420i	0.157740	−	0.987481i	$-0.449579\pi$
$271$	15.0351	−	5.47232i	0.913316	−	0.332420i	0.755576	+	0.655061i	$0.227357\pi$
$272$	−4.59627	+	3.85673i	−0.278690	+	0.233848i
$273$	4.00000	+	6.92820i	0.242091	+	0.419314i
$274$	−4.50000	+	7.79423i	−0.271855	+	0.470867i
$275$	−2.60472	−	14.7721i	−0.157071	−	0.890792i
$276$	1.04189	+	5.90885i	0.0627144	+	0.355671i
$277$	−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	$0.243925\pi$
$278$	−5.50000	−	9.52628i	−0.329868	−	0.571348i
$279$	3.06418	−	2.57115i	0.183448	−	0.153931i
$280$		0			0
$281$	25.3717	+	9.23454i	1.51355	+	0.550887i	0.959527	−	0.281616i	$-0.0908703\pi$
$281$	25.3717	+	9.23454i	1.51355	+	0.550887i	0.554021	+	0.832502i	$0.313093\pi$
$282$		0			0
$283$	0.868241	−	4.92404i	0.0516116	−	0.292704i	−0.948067	−	0.318072i	$-0.896965\pi$
$283$	0.868241	−	4.92404i	0.0516116	−	0.292704i	0.999678	+	0.0253681i	$0.00807579\pi$
$284$	6.00000			0.356034
$285$		0			0
$286$	−6.00000			−0.354787
$287$	6.25133	−	35.4531i	0.369005	−	2.09273i
$288$	−1.53209	−	1.28558i	−0.0902792	−	0.0757532i
$289$	−17.8542	−	6.49838i	−1.05024	−	0.382258i
$290$		0			0
$291$	13.0228	−	10.9274i	0.763407	−	0.640575i
$292$	0.500000	+	0.866025i	0.0292603	+	0.0506803i
$293$	12.0000	−	20.7846i	0.701047	−	1.21425i	−0.267052	−	0.963682i	$-0.586049\pi$
$293$	12.0000	−	20.7846i	0.701047	−	1.21425i	0.968099	−	0.250568i	$-0.0806172\pi$
$294$	−1.56283	−	8.86327i	−0.0911463	−	0.516916i
$295$		0			0
$296$	−5.00000	+	8.66025i	−0.290619	+	0.503367i
$297$	−7.50000	−	12.9904i	−0.435194	−	0.753778i
$298$	13.7888	−	11.5702i	0.798764	−	0.670242i
$299$	−11.2763	+	4.10424i	−0.652126	+	0.237354i
$300$	−4.69846	−	1.71010i	−0.271266	−	0.0987327i
$301$	12.2567	+	10.2846i	0.706465	+	0.592795i
$302$	1.73648	−	9.84808i	0.0999233	−	0.566693i
$303$		0			0
$304$		0			0
$305$		0			0
$306$	2.08378	−	11.8177i	0.119122	−	0.675573i
$307$	5.36231	+	4.49951i	0.306043	+	0.256801i	0.782854	−	0.622205i	$-0.213763\pi$
$307$	5.36231	+	4.49951i	0.306043	+	0.256801i	−0.476811	+	0.879006i	$0.658207\pi$
$308$	11.2763	+	4.10424i	0.642527	+	0.233861i
$309$	−1.87939	+	0.684040i	−0.106914	+	0.0389137i
$310$		0			0
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	0.880693	+	0.473688i	$0.157077\pi$
$311$	15.0000	+	25.9808i	0.850572	+	1.47323i	−0.0301210	+	0.999546i	$0.509589\pi$
$312$	−1.00000	+	1.73205i	−0.0566139	+	0.0980581i
$313$	−3.29932	−	18.7113i	−0.186488	−	1.05763i	−0.924028	−	0.382324i	$-0.875124\pi$
$313$	−3.29932	−	18.7113i	−0.186488	−	1.05763i	0.737540	−	0.675304i	$-0.235987\pi$
$314$	−2.77837	−	15.7569i	−0.156793	−	0.889215i
$315$		0			0
$316$	−2.00000	−	3.46410i	−0.112509	−	0.194871i
$317$	13.7888	−	11.5702i	0.774456	−	0.649846i	−0.167390	−	0.985891i	$-0.553534\pi$
$317$	13.7888	−	11.5702i	0.774456	−	0.649846i	0.941846	+	0.336045i	$0.109089\pi$
$318$	−5.63816	+	2.05212i	−0.316172	+	0.115077i
$319$		0			0
$320$		0			0
$321$		0			0
$322$	24.0000			1.33747
$323$		0			0
$324$	1.00000			0.0555556
$325$	1.73648	−	9.84808i	0.0963227	−	0.546273i
$326$	−14.5548	−	12.2130i	−0.806118	−	0.676414i
$327$	15.0351	+	5.47232i	0.831442	+	0.302620i
$328$	8.45723	−	3.07818i	0.466973	−	0.169964i
$329$		0			0
$330$		0			0
$331$	2.50000	−	4.33013i	0.137412	−	0.238005i	−0.789104	−	0.614260i	$-0.789455\pi$
$331$	2.50000	−	4.33013i	0.137412	−	0.238005i	0.926516	+	0.376254i	$0.122788\pi$
$332$	0.520945	+	2.95442i	0.0285905	+	0.162145i
$333$	−3.47296	−	19.6962i	−0.190317	−	1.07934i
$334$	−12.0000	+	20.7846i	−0.656611	+	1.13728i
$335$		0			0
$336$	3.06418	−	2.57115i	0.167165	−	0.140268i
$337$	10.3366	−	3.76222i	0.563072	−	0.204941i	−0.0447732	−	0.998997i	$-0.514257\pi$
$337$	10.3366	−	3.76222i	0.563072	−	0.204941i	0.607845	+	0.794056i	$0.292034\pi$
$338$	8.45723	+	3.07818i	0.460013	+	0.167431i
$339$	11.4907	+	9.64181i	0.624087	+	0.523671i
$340$		0			0
$341$	−6.00000			−0.324918
$342$		0			0
$343$	−8.00000			−0.431959
$344$	−0.694593	+	3.93923i	−0.0374499	+	0.212389i
$345$		0			0
$346$	5.63816	+	2.05212i	0.303109	+	0.110323i
$347$	8.45723	−	3.07818i	0.454008	−	0.165245i	−0.104886	−	0.994484i	$-0.533448\pi$
$347$	8.45723	−	3.07818i	0.454008	−	0.165245i	0.558894	+	0.829239i	$0.311226\pi$
$348$		0			0
$349$	2.00000	+	3.46410i	0.107058	+	0.185429i	0.914577	−	0.404412i	$-0.132524\pi$
$349$	2.00000	+	3.46410i	0.107058	+	0.185429i	−0.807519	+	0.589841i	$0.799190\pi$
$350$	−10.0000	+	17.3205i	−0.534522	+	0.925820i
$351$	−1.73648	−	9.84808i	−0.0926865	−	0.525651i
$352$	0.520945	+	2.95442i	0.0277664	+	0.157471i
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	−0.903179	−	0.429263i	$-0.858773\pi$
$353$	−1.50000	+	2.59808i	−0.0798369	+	0.138282i	0.823343	+	0.567545i	$0.192107\pi$
$354$	4.50000	+	7.79423i	0.239172	+	0.414259i
$355$		0			0
$356$	5.63816	−	2.05212i	0.298822	−	0.108762i
$357$	22.5526	+	8.20848i	1.19361	+	0.434439i
$358$	−6.89440	−	5.78509i	−0.364380	−	0.305751i
$359$	−1.04189	+	5.90885i	−0.0549888	+	0.311857i	−0.999879	−	0.0155292i	$-0.995057\pi$
$359$	−1.04189	+	5.90885i	−0.0549888	+	0.311857i	0.944891	+	0.327386i	$0.106168\pi$
$360$		0			0
$361$		0			0
$362$	−2.00000			−0.105118
$363$	0.347296	−	1.96962i	0.0182283	−	0.103378i
$364$	6.12836	+	5.14230i	0.321213	+	0.269530i
$365$		0			0
$366$	−3.75877	+	1.36808i	−0.196474	+	0.0715107i
$367$	−16.8530	+	14.1413i	−0.879718	+	0.738171i	−0.966121	−	0.258089i	$-0.916907\pi$
$367$	−16.8530	+	14.1413i	−0.879718	+	0.738171i	0.0864029	+	0.996260i	$0.472463\pi$
$368$	3.00000	+	5.19615i	0.156386	+	0.270868i
$369$	−9.00000	+	15.5885i	−0.468521	+	0.811503i
$370$		0			0
$371$	4.16756	+	23.6354i	0.216369	+	1.22709i
$372$	−1.00000	+	1.73205i	−0.0518476	+	0.0898027i
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	0.809591	−	0.586994i	$-0.199689\pi$
$373$	−2.00000	−	3.46410i	−0.103556	−	0.179364i	−0.913147	+	0.407630i	$0.866355\pi$
$374$	−13.7888	+	11.5702i	−0.713002	+	0.598280i
$375$		0			0
$376$		0			0
$377$		0			0
$378$	−3.47296	+	19.6962i	−0.178630	+	1.01306i
$379$	28.0000			1.43826			0.719132	−	0.694874i	$-0.244540\pi$
$379$	28.0000			1.43826			0.719132	+	0.694874i	$0.244540\pi$
$380$		0			0
$381$	2.00000			0.102463
$382$	2.08378	−	11.8177i	0.106615	−	0.604646i
$383$	27.5776	+	23.1404i	1.40915	+	1.18242i	0.956861	+	0.290545i	$0.0938366\pi$
$383$	27.5776	+	23.1404i	1.40915	+	1.18242i	0.452288	+	0.891872i	$0.350608\pi$
$384$	0.939693	+	0.342020i	0.0479535	+	0.0174536i
$385$		0			0
$386$	−1.53209	+	1.28558i	−0.0779813	+	0.0654341i
$387$	−4.00000	−	6.92820i	−0.203331	−	0.352180i
$388$	8.50000	−	14.7224i	0.431522	−	0.747418i
$389$	−6.25133	−	35.4531i	−0.316955	−	1.79754i	−0.561040	−	0.827789i	$-0.689599\pi$
$389$	−6.25133	−	35.4531i	−0.316955	−	1.79754i	0.244085	−	0.969754i	$-0.421512\pi$
$390$		0			0
$391$	−18.0000	+	31.1769i	−0.910299	+	1.57668i
$392$	−4.50000	−	7.79423i	−0.227284	−	0.393668i
$393$	−6.89440	+	5.78509i	−0.347776	+	0.291819i
$394$	−16.9145	+	6.15636i	−0.852139	+	0.310153i
$395$		0			0
$396$	−4.59627	−	3.85673i	−0.230971	−	0.193808i
$397$	−1.73648	+	9.84808i	−0.0871515	+	0.494261i	0.909720	+	0.415222i	$0.136296\pi$
$397$	−1.73648	+	9.84808i	−0.0871515	+	0.494261i	−0.996872	+	0.0790387i	$0.974815\pi$
$398$	−10.0000			−0.501255
$399$		0			0
$400$	−5.00000			−0.250000
$401$	4.68850	−	26.5898i	0.234133	−	1.32783i	−0.610300	−	0.792170i	$-0.708951\pi$
$401$	4.68850	−	26.5898i	0.234133	−	1.32783i	0.844433	−	0.535662i	$-0.179938\pi$
$402$	−5.36231	−	4.49951i	−0.267448	−	0.224415i
$403$	−3.75877	−	1.36808i	−0.187238	−	0.0681489i
$404$		0			0
$405$		0			0
$406$		0			0
$407$	−15.0000	+	25.9808i	−0.743522	+	1.28782i
$408$	1.04189	+	5.90885i	0.0515812	+	0.292531i
$409$	−0.868241	−	4.92404i	−0.0429317	−	0.243478i	0.955788	−	0.294055i	$-0.0950050\pi$
$409$	−0.868241	−	4.92404i	−0.0429317	−	0.243478i	−0.998720	+	0.0505773i	$0.983894\pi$
$410$		0			0
$411$	4.50000	+	7.79423i	0.221969	+	0.384461i
$412$	−1.53209	+	1.28558i	−0.0754806	+	0.0633357i
$413$	33.8289	−	12.3127i	1.66461	−	0.605870i
$414$	−11.2763	−	4.10424i	−0.554200	−	0.201712i
$415$		0			0
$416$	−0.347296	+	1.96962i	−0.0170276	+	0.0965683i
$417$	−11.0000			−0.538672
$418$		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
$421$	7.66044	+	6.42788i	0.373347	+	0.313276i	0.810084	−	0.586314i	$-0.199421\pi$
$421$	7.66044	+	6.42788i	0.373347	+	0.313276i	−0.436737	+	0.899589i	$0.643866\pi$
$422$	18.7939	+	6.84040i	0.914870	+	0.332986i
$423$		0			0
$424$	−4.59627	+	3.85673i	−0.223214	+	0.187299i
$425$	−15.0000	−	25.9808i	−0.727607	−	1.26025i
$426$	3.00000	−	5.19615i	0.145350	−	0.251754i
$427$	2.77837	+	15.7569i	0.134455	+	0.762531i
$428$		0			0
$429$	−3.00000	+	5.19615i	−0.144841	+	0.250873i
$430$		0			0
$431$	22.9813	−	19.2836i	1.10697	−	0.928860i	0.109098	−	0.994031i	$-0.465204\pi$
$431$	22.9813	−	19.2836i	1.10697	−	0.928860i	0.997874	+	0.0651713i	$0.0207594\pi$
$432$	−4.69846	+	1.71010i	−0.226055	+	0.0822773i
$433$	24.4320	+	8.89252i	1.17413	+	0.427347i	0.854124	−	0.520069i	$-0.174094\pi$
$433$	24.4320	+	8.89252i	1.17413	+	0.427347i	0.320003	+	0.947416i	$0.396316\pi$
$434$	6.12836	+	5.14230i	0.294170	+	0.246838i
$435$		0			0
$436$	16.0000			0.766261
$437$		0			0
$438$	1.00000			0.0477818
$439$	−2.43107	+	13.7873i	−0.116029	+	0.658032i	0.870207	+	0.492687i	$0.163985\pi$
$439$	−2.43107	+	13.7873i	−0.116029	+	0.658032i	−0.986236	+	0.165346i	$0.947126\pi$
$440$		0			0
$441$	16.9145	+	6.15636i	0.805451	+	0.293160i
$442$	−11.2763	+	4.10424i	−0.536359	+	0.195219i
$443$	6.89440	−	5.78509i	0.327563	−	0.274858i	−0.464143	−	0.885760i	$-0.653638\pi$
$443$	6.89440	−	5.78509i	0.327563	−	0.274858i	0.791706	+	0.610902i	$0.209193\pi$
$444$	5.00000	+	8.66025i	0.237289	+	0.410997i
$445$		0			0
$446$	−2.43107	−	13.7873i	−0.115115	−	0.652848i
$447$	−3.12567	−	17.7265i	−0.147839	−	0.838437i
$448$	2.00000	−	3.46410i	0.0944911	−	0.163663i
$449$	4.50000	+	7.79423i	0.212368	+	0.367832i	0.952455	−	0.304679i	$-0.0985491\pi$
$449$	4.50000	+	7.79423i	0.212368	+	0.367832i	−0.740087	+	0.672511i	$0.765216\pi$
$450$	7.66044	−	6.42788i	0.361117	−	0.303013i
$451$	25.3717	−	9.23454i	1.19471	−	0.434838i
$452$	14.0954	+	5.13030i	0.662991	+	0.241309i
$453$	−7.66044	−	6.42788i	−0.359919	−	0.302008i
$454$	−0.520945	+	2.95442i	−0.0244491	+	0.138658i
$455$		0			0
$456$		0			0
$457$	5.00000			0.233890			0.116945	−	0.993138i	$-0.462690\pi$
$457$	5.00000			0.233890			0.116945	+	0.993138i	$0.462690\pi$
$458$	−2.77837	+	15.7569i	−0.129825	+	0.736273i
$459$	−22.9813	−	19.2836i	−1.07268	−	0.900083i
$460$		0			0
$461$	−5.63816	+	2.05212i	−0.262595	+	0.0955768i	−0.469963	−	0.882686i	$-0.655733\pi$
$461$	−5.63816	+	2.05212i	−0.262595	+	0.0955768i	0.207368	+	0.978263i	$0.433510\pi$
$462$	9.19253	−	7.71345i	0.427675	−	0.358862i
$463$	17.0000	+	29.4449i	0.790057	+	1.36842i	0.925931	+	0.377693i	$0.123282\pi$
$463$	17.0000	+	29.4449i	0.790057	+	1.36842i	−0.135874	+	0.990726i	$0.543384\pi$
$464$		0			0
$465$		0			0
$466$	0.520945	+	2.95442i	0.0241323	+	0.136861i
$467$	13.5000	−	23.3827i	0.624705	−	1.08202i	−0.363892	−	0.931441i	$-0.618552\pi$
$467$	13.5000	−	23.3827i	0.624705	−	1.08202i	0.988598	−	0.150581i	$-0.0481143\pi$
$468$	−2.00000	−	3.46410i	−0.0924500	−	0.160128i
$469$	−21.4492	+	17.9981i	−0.990434	+	0.831073i
$470$		0			0
$471$	−15.0351	−	5.47232i	−0.692780	−	0.252151i
$472$	6.89440	+	5.78509i	0.317340	+	0.266280i
$473$	−2.08378	+	11.8177i	−0.0958122	+	0.543378i
$474$	−4.00000			−0.183726
$475$		0			0
$476$	24.0000			1.10004
$477$	2.08378	−	11.8177i	0.0954096	−	0.541095i
$478$	−9.19253	−	7.71345i	−0.420457	−	0.352805i
$479$	−33.8289	−	12.3127i	−1.54568	−	0.562583i	−0.578283	−	0.815836i	$-0.696277\pi$
$479$	−33.8289	−	12.3127i	−1.54568	−	0.562583i	−0.967400	+	0.253253i	$0.918499\pi$
$480$		0			0
$481$	−15.3209	+	12.8558i	−0.698572	+	0.586172i
$482$	2.50000	+	4.33013i	0.113872	+	0.197232i
$483$	12.0000	−	20.7846i	0.546019	−	0.945732i
$484$	−0.347296	−	1.96962i	−0.0157862	−	0.0895280i
$485$		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	$0.818904\pi$
$488$	−3.06418	+	2.57115i	−0.138709	+	0.116391i
$489$	−17.8542	+	6.49838i	−0.807393	+	0.293867i
$490$		0			0
$491$		0			0		0.642788	−	0.766044i	$-0.277778\pi$
$491$		0			0		−0.642788	+	0.766044i	$0.722222\pi$
$492$	1.56283	−	8.86327i	0.0704580	−	0.399587i
$493$		0			0
$494$		0			0
$495$		0			0
$496$	−0.347296	+	1.96962i	−0.0155941	+	0.0884383i
$497$	−18.3851	−	15.4269i	−0.824683	−	0.691991i
$498$	2.81908	+	1.02606i	0.126326	+	0.0459789i
$499$	23.4923	−	8.55050i	1.05166	−	0.382773i	0.242371	−	0.970184i	$-0.422075\pi$
$499$	23.4923	−	8.55050i	1.05166	−	0.382773i	0.809289	+	0.587410i	$0.199853\pi$
$500$		0			0
$501$	12.0000	+	20.7846i	0.536120	+	0.928588i
$502$	1.50000	−	2.59808i	0.0669483	−	0.115958i
$503$	1.04189	+	5.90885i	0.0464555	+	0.263462i	0.999185	−	0.0403564i	$-0.0128493\pi$
$503$	1.04189	+	5.90885i	0.0464555	+	0.263462i	−0.952730	+	0.303819i	$0.901738\pi$
$504$	1.38919	+	7.87846i	0.0618792	+	0.350935i
$505$		0			0
$506$	9.00000	+	15.5885i	0.400099	+	0.692991i
$507$	6.89440	−	5.78509i	0.306191	−	0.256925i
$508$	1.87939	−	0.684040i	0.0833842	−	0.0303494i
$509$	−22.5526	−	8.20848i	−0.999627	−	0.363835i	−0.210187	−	0.977661i	$-0.567407\pi$
$509$	−22.5526	−	8.20848i	−0.999627	−	0.363835i	−0.789441	+	0.613827i	$0.789629\pi$
$510$		0			0
$511$	0.694593	−	3.93923i	0.0307270	−	0.174261i
$512$	1.00000			0.0441942
$513$		0			0
$514$	−3.00000			−0.132324
$515$		0			0
$516$	3.06418	+	2.57115i	0.134893	+	0.113189i
$517$		0			0
$518$	37.5877	−	13.6808i	1.65151	−	0.601100i
$519$	4.59627	−	3.85673i	0.201754	−	0.169291i
$520$		0			0
$521$	4.50000	−	7.79423i	0.197149	−	0.341471i	−0.750454	−	0.660922i	$-0.770165\pi$
$521$	4.50000	−	7.79423i	0.197149	−	0.341471i	0.947603	+	0.319451i	$0.103499\pi$
$522$		0			0
$523$	4.86215	+	27.5746i	0.212607	+	1.20575i	0.885011	+	0.465570i	$0.154151\pi$
$523$	4.86215	+	27.5746i	0.212607	+	1.20575i	−0.672404	+	0.740184i	$0.734738\pi$
$524$	−4.50000	+	7.79423i	−0.196583	+	0.340492i
$525$	10.0000	+	17.3205i	0.436436	+	0.755929i
$526$	−9.19253	+	7.71345i	−0.400813	+	0.336322i
$527$	−11.2763	+	4.10424i	−0.491204	+	0.178784i
$528$	2.81908	+	1.02606i	0.122685	+	0.0446535i
$529$	9.95858	+	8.35624i	0.432982	+	0.363315i
$530$		0			0
$531$	−18.0000			−0.781133
$532$		0			0
$533$	18.0000			0.779667
$534$	1.04189	−	5.90885i	0.0450869	−	0.255701i
$535$		0			0
$536$	−6.57785	−	2.39414i	−0.284120	−	0.103411i
$537$	−8.45723	+	3.07818i	−0.364957	+	0.132833i
$538$	−9.19253	+	7.71345i	−0.396318	+	0.332550i
$539$	−13.5000	−	23.3827i	−0.581486	−	1.00716i
$540$		0			0
$541$	7.64052	+	43.3315i	0.328492	+	1.86297i	0.483907	+	0.875119i	$0.339217\pi$
$541$	7.64052	+	43.3315i	0.328492	+	1.86297i	−0.155416	+	0.987849i	$0.549672\pi$
$542$	−2.77837	−	15.7569i	−0.119341	−	0.676818i
$543$	−1.00000	+	1.73205i	−0.0429141	+	0.0743294i
$544$	3.00000	+	5.19615i	0.128624	+	0.222783i
$545$		0			0
$546$	7.51754	−	2.73616i	0.321721	−	0.117097i
$547$	−3.75877	−	1.36808i	−0.160713	−	0.0584949i	0.260411	−	0.965498i	$-0.416142\pi$
$547$	−3.75877	−	1.36808i	−0.160713	−	0.0584949i	−0.421124	+	0.907003i	$0.638364\pi$
$548$	6.89440	+	5.78509i	0.294514	+	0.247127i
$549$	1.38919	−	7.87846i	0.0592890	−	0.336245i
$550$	−15.0000			−0.639602
$551$		0			0
$552$	6.00000			0.255377
$553$	−2.77837	+	15.7569i	−0.118148	+	0.670053i
$554$	6.12836	+	5.14230i	0.260369	+	0.218475i
$555$		0			0
$556$	−10.3366	+	3.76222i	−0.438370	+	0.159554i
$557$	18.3851	−	15.4269i	0.779000	−	0.653659i	−0.163996	−	0.986461i	$-0.552439\pi$
$557$	18.3851	−	15.4269i	0.779000	−	0.653659i	0.942997	+	0.332802i	$0.107994\pi$
$558$	−2.00000	−	3.46410i	−0.0846668	−	0.146647i
$559$	−4.00000	+	6.92820i	−0.169182	+	0.293032i
$560$		0			0
$561$	3.12567	+	17.7265i	0.131966	+	0.748415i
$562$	13.5000	−	23.3827i	0.569463	−	0.986339i
$563$	−10.5000	−	18.1865i	−0.442522	−	0.766471i	0.555354	−	0.831614i	$-0.312583\pi$
$563$	−10.5000	−	18.1865i	−0.442522	−	0.766471i	−0.997876	+	0.0651433i	$0.979250\pi$
$564$		0			0
$565$		0			0
$566$	−4.69846	−	1.71010i	−0.197491	−	0.0718809i
$567$	−3.06418	−	2.57115i	−0.128683	−	0.107978i
$568$	1.04189	−	5.90885i	0.0437167	−	0.247930i
$569$	6.00000			0.251533			0.125767	−	0.992060i	$-0.459861\pi$
$569$	6.00000			0.251533			0.125767	+	0.992060i	$0.459861\pi$
$570$		0			0
$571$	−7.00000			−0.292941			−0.146470	−	0.989215i	$-0.546791\pi$
$571$	−7.00000			−0.292941			−0.146470	+	0.989215i	$0.546791\pi$
$572$	−1.04189	+	5.90885i	−0.0435636	+	0.247061i
$573$	−9.19253	−	7.71345i	−0.384024	−	0.322234i
$574$	−33.8289	−	12.3127i	−1.41199	−	0.513923i
$575$	−28.1908	+	10.2606i	−1.17564	+	0.427897i
$576$	−1.53209	+	1.28558i	−0.0638370	+	0.0535656i
$577$	−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	$0.906868\pi$
$578$	−9.50000	+	16.4545i	−0.395148	+	0.684416i
$579$	0.347296	+	1.96962i	0.0144331	+	0.0818544i
$580$		0			0
$581$	6.00000	−	10.3923i	0.248922	−	0.431145i
$582$	−8.50000	−	14.7224i	−0.352336	−	0.610264i
$583$	−13.7888	+	11.5702i	−0.571074	+	0.479188i
$584$	0.939693	−	0.342020i	0.0388848	−	0.0141529i
$585$		0			0
$586$	−18.3851	−	15.4269i	−0.759480	−	0.637279i
$587$	−2.08378	+	11.8177i	−0.0860067	+	0.487768i	0.911128	+	0.412123i	$0.135213\pi$
$587$	−2.08378	+	11.8177i	−0.0860067	+	0.487768i	−0.997135	+	0.0756451i	$0.975898\pi$
$588$	−9.00000			−0.371154
$589$		0			0
$590$		0			0
$591$	−3.12567	+	17.7265i	−0.128573	+	0.729172i
$592$	7.66044	+	6.42788i	0.314842	+	0.264184i
$593$	19.7335	+	7.18242i	0.810360	+	0.294947i	0.713772	−	0.700378i	$-0.246985\pi$
$593$	19.7335	+	7.18242i	0.810360	+	0.294947i	0.0965872	+	0.995325i	$0.469207\pi$
$594$	−14.0954	+	5.13030i	−0.578341	+	0.210499i
$595$		0			0
$596$	−9.00000	−	15.5885i	−0.368654	−	0.638528i
$597$	−5.00000	+	8.66025i	−0.204636	+	0.354441i
$598$	2.08378	+	11.8177i	0.0852120	+	0.483261i
$599$	1.04189	+	5.90885i	0.0425704	+	0.241429i	0.998667	−	0.0516242i	$-0.0164398\pi$
$599$	1.04189	+	5.90885i	0.0425704	+	0.241429i	−0.956096	+	0.293053i	$0.905329\pi$
$600$	−2.50000	+	4.33013i	−0.102062	+	0.176777i
$601$	−6.50000	−	11.2583i	−0.265141	−	0.459237i	0.702460	−	0.711723i	$-0.252085\pi$
$601$	−6.50000	−	11.2583i	−0.265141	−	0.459237i	−0.967600	+	0.252486i	$0.918752\pi$
$602$	12.2567	−	10.2846i	0.499546	−	0.419169i
$603$	13.1557	−	4.78828i	0.535741	−	0.194994i
$604$	−9.39693	−	3.42020i	−0.382356	−	0.139166i
$605$		0			0
$606$		0			0
$607$	−20.0000			−0.811775			−0.405887	−	0.913923i	$-0.633038\pi$
$607$	−20.0000			−0.811775			−0.405887	+	0.913923i	$0.633038\pi$
$608$		0			0
$609$		0			0
$610$		0			0
$611$		0			0
$612$	−11.2763	−	4.10424i	−0.455818	−	0.165904i
$613$	−1.87939	+	0.684040i	−0.0759077	+	0.0276281i	−0.379695	−	0.925112i	$-0.623971\pi$
$613$	−1.87939	+	0.684040i	−0.0759077	+	0.0276281i	0.303787	+	0.952740i	$0.401749\pi$
$614$	5.36231	−	4.49951i	0.216405	−	0.181586i
$615$		0			0
$616$	6.00000	−	10.3923i	0.241747	−	0.418718i
$617$	0.520945	+	2.95442i	0.0209724	+	0.118941i	0.993497	−	0.113861i	$-0.0363218\pi$
$617$	0.520945	+	2.95442i	0.0209724	+	0.118941i	−0.972524	+	0.232802i	$0.925211\pi$
$618$	0.347296	+	1.96962i	0.0139703	+	0.0792296i
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	−0.823029	−	0.567999i	$-0.807718\pi$
$619$	2.00000	−	3.46410i	0.0803868	−	0.139234i	0.903416	+	0.428765i	$0.141051\pi$
$620$		0			0
$621$	−22.9813	+	19.2836i	−0.922209	+	0.773825i
$622$	28.1908	−	10.2606i	1.13035	−	0.411413i
$623$	−22.5526	−	8.20848i	−0.903552	−	0.328866i
$624$	1.53209	+	1.28558i	0.0613326	+	0.0514642i
$625$	4.34120	−	24.6202i	0.173648	−	0.984808i
$626$	−19.0000			−0.759393
$627$		0			0
$628$	−16.0000			−0.638470
$629$	−10.4189	+	59.0885i	−0.415428	+	2.35601i
$630$		0			0
$631$	26.3114	+	9.57656i	1.04744	+	0.381237i	0.807696	−	0.589599i	$-0.200714\pi$
$631$	26.3114	+	9.57656i	1.04744	+	0.381237i	0.239744	+	0.970836i	$0.422936\pi$
$632$	−3.75877	+	1.36808i	−0.149516	+	0.0544193i
$633$	15.3209	−	12.8558i	0.608951	−	0.510970i
$634$	−9.00000	−	15.5885i	−0.357436	−	0.619097i
$635$		0			0
$636$	1.04189	+	5.90885i	0.0413136	+	0.234301i
$637$	−3.12567	−	17.7265i	−0.123843	−	0.702351i
$638$		0			0
$639$	6.00000	+	10.3923i	0.237356	+	0.411113i
$640$		0			0
$641$	−36.6480	+	13.3388i	−1.44751	+	0.526850i	−0.941894	−	0.335909i	$-0.890957\pi$
$641$	−36.6480	+	13.3388i	−1.44751	+	0.526850i	−0.505615	+	0.862759i	$0.668734\pi$
$642$		0			0
$643$	−32.9399	−	27.6399i	−1.29902	−	1.09001i	−0.990313	−	0.138854i	$-0.955658\pi$
$643$	−32.9399	−	27.6399i	−1.29902	−	1.09001i	−0.308710	−	0.951156i	$-0.599897\pi$
$644$	4.16756	−	23.6354i	0.164225	−	0.931365i
$645$		0			0
$646$		0			0
$647$	18.0000			0.707653			0.353827	−	0.935311i	$-0.384880\pi$
$647$	18.0000			0.707653			0.353827	+	0.935311i	$0.384880\pi$
$648$	0.173648	−	0.984808i	0.00682154	−	0.0386869i
$649$	20.6832	+	17.3553i	0.811887	+	0.681254i
$650$	−9.39693	−	3.42020i	−0.368578	−	0.134151i
$651$	7.51754	−	2.73616i	0.294636	−	0.107239i
$652$	−14.5548	+	12.2130i	−0.570012	+	0.478297i
$653$	6.00000	+	10.3923i	0.234798	+	0.406682i	0.959214	−	0.282681i	$-0.0912238\pi$
$653$	6.00000	+	10.3923i	0.234798	+	0.406682i	−0.724416	+	0.689363i	$0.757890\pi$
$654$	8.00000	−	13.8564i	0.312825	−	0.541828i
$655$		0			0
$656$	−1.56283	−	8.86327i	−0.0610184	−	0.346053i
$657$	−1.00000	+	1.73205i	−0.0390137	+	0.0675737i
$658$		0			0
$659$	−27.5776	+	23.1404i	−1.07427	+	0.901420i	−0.995433	−	0.0954672i	$-0.969565\pi$
$659$	−27.5776	+	23.1404i	−1.07427	+	0.901420i	−0.0788382	+	0.996887i	$0.525121\pi$
$660$		0			0
$661$	−37.5877	−	13.6808i	−1.46199	−	0.532122i	−0.516079	−	0.856541i	$-0.672609\pi$
$661$	−37.5877	−	13.6808i	−1.46199	−	0.532122i	−0.945913	+	0.324419i	$0.894831\pi$
$662$	−3.83022	−	3.21394i	−0.148866	−	0.124913i
$663$	−2.08378	+	11.8177i	−0.0809272	+	0.458961i
$664$	3.00000			0.116423
$665$		0			0
$666$	−20.0000			−0.774984
$667$		0			0
$668$	18.3851	+	15.4269i	0.711340	+	0.596885i
$669$	−13.1557	−	4.78828i	−0.508629	−	0.185126i
$670$		0			0
$671$	−9.19253	+	7.71345i	−0.354874	+	0.297774i
$672$	−2.00000	−	3.46410i	−0.0771517	−	0.133631i
$673$	7.00000	−	12.1244i	0.269830	−	0.467360i	−0.698988	−	0.715134i	$-0.746366\pi$
$673$	7.00000	−	12.1244i	0.269830	−	0.467360i	0.968818	+	0.247774i	$0.0796991\pi$
$674$	−1.91013	−	10.8329i	−0.0735755	−	0.417267i
$675$	−4.34120	−	24.6202i	−0.167093	−	0.947632i
$676$	4.50000	−	7.79423i	0.173077	−	0.299778i
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	−0.914867	−	0.403755i	$-0.867705\pi$
$677$	−21.0000	−	36.3731i	−0.807096	−	1.39793i	0.107772	−	0.994176i	$-0.465628\pi$
$678$	11.4907	−	9.64181i	0.441296	−	0.370292i
$679$	−63.8991	+	23.2574i	−2.45222	+	0.892536i
$680$		0			0
$681$	2.29813	+	1.92836i	0.0880647	+	0.0738950i
$682$	−1.04189	+	5.90885i	−0.0398960	+	0.226261i
$683$	36.0000			1.37750			0.688751	−	0.724998i	$-0.258159\pi$
$683$	36.0000			1.37750			0.688751	+	0.724998i	$0.258159\pi$
$684$		0			0
$685$		0			0
$686$	−1.38919	+	7.87846i	−0.0530393	+	0.300801i
$687$	12.2567	+	10.2846i	0.467623	+	0.392382i
$688$	3.75877	+	1.36808i	0.143302	+	0.0521576i
$689$	−11.2763	+	4.10424i	−0.429593	+	0.156359i
$690$		0			0
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	−0.892458	−	0.451130i	$-0.851021\pi$
$691$	−22.0000	−	38.1051i	−0.836919	−	1.44959i	0.0555386	−	0.998457i	$-0.482312\pi$
$692$	3.00000	−	5.19615i	0.114043	−	0.197528i
$693$	4.16756	+	23.6354i	0.158312	+	0.897834i
$694$	−1.56283	−	8.86327i	−0.0593244	−	0.336445i
$695$		0			0
$696$		0			0
$697$	41.3664	−	34.7105i	1.56686	−	1.31476i
$698$	3.75877	−	1.36808i	0.142272	−	0.0517826i
$699$	2.81908	+	1.02606i	0.106627	+	0.0388092i
$700$	15.3209	+	12.8558i	0.579075	+	0.485902i
$701$	−4.16756	+	23.6354i	−0.157406	+	0.892696i	0.799146	+	0.601137i	$0.205285\pi$
$701$	−4.16756	+	23.6354i	−0.157406	+	0.892696i	−0.956553	+	0.291560i	$0.905826\pi$
$702$	−10.0000			−0.377426
$703$		0			0
$704$	3.00000			0.113067
$705$		0			0
$706$	2.29813	+	1.92836i	0.0864914	+	0.0725749i
$707$		0			0
$708$	8.45723	−	3.07818i	0.317842	−	0.115685i
$709$	10.7246	−	8.99903i	0.402772	−	0.337966i	−0.418792	−	0.908082i	$-0.637546\pi$
$709$	10.7246	−	8.99903i	0.402772	−	0.337966i	0.821564	+	0.570117i	$0.193102\pi$
$710$		0			0
$711$	4.00000	−	6.92820i	0.150012	−	0.259828i
$712$	−1.04189	−	5.90885i	−0.0390464	−	0.221443i
$713$	2.08378	+	11.8177i	0.0780381	+	0.442576i
$714$	12.0000	−	20.7846i	0.449089	−	0.777844i
$715$		0			0
$716$	−6.89440	+	5.78509i	−0.257656	+	0.216199i
$717$	−11.2763	+	4.10424i	−0.421122	+	0.153276i
$718$	5.63816	+	2.05212i	0.210414	+	0.0765845i
$719$	22.9813	+	19.2836i	0.857059	+	0.719158i	0.961332	−	0.275391i	$-0.0888072\pi$
$719$	22.9813	+	19.2836i	0.857059	+	0.719158i	−0.104273	+	0.994549i	$0.533252\pi$
$720$		0			0
$721$	8.00000			0.297936
$722$		0			0
$723$	5.00000			0.185952
$724$	−0.347296	+	1.96962i	−0.0129072	+	0.0732002i
$725$		0			0
$726$	−1.87939	−	0.684040i	−0.0697505	−	0.0253871i
$727$	−30.0702	+	10.9446i	−1.11524	+	0.405914i	−0.832913	−	0.553404i	$-0.813329\pi$
$727$	−30.0702	+	10.9446i	−1.11524	+	0.405914i	−0.282327	+	0.959318i	$0.591106\pi$
$728$	6.12836	−	5.14230i	0.227132	−	0.190586i
$729$	−6.50000	−	11.2583i	−0.240741	−	0.416975i
$730$		0			0
$731$	4.16756	+	23.6354i	0.154143	+	0.874186i
$732$	0.694593	+	3.93923i	0.0256729	+	0.145598i
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	−0.588177	−	0.808732i	$-0.700154\pi$
$733$	11.0000	−	19.0526i	0.406294	−	0.703722i	0.994471	+	0.105010i	$0.0334875\pi$
$734$	11.0000	+	19.0526i	0.406017	+	0.703243i
$735$		0			0
$736$	5.63816	−	2.05212i	0.207825	−	0.0756422i
$737$	−19.7335	−	7.18242i	−0.726894	−	0.264568i
$738$	13.7888	+	11.5702i	0.507573	+	0.425904i
$739$	6.07769	−	34.4683i	0.223571	−	1.26794i	−0.641826	−	0.766850i	$-0.721823\pi$
$739$	6.07769	−	34.4683i	0.223571	−	1.26794i	0.865398	−	0.501086i	$-0.167066\pi$
$740$		0			0
$741$		0			0
$742$	24.0000			0.881068
$743$	3.12567	−	17.7265i	0.114670	−	0.650324i	−0.872244	−	0.489072i	$-0.837336\pi$
$743$	3.12567	−	17.7265i	0.114670	−	0.650324i	0.986913	−	0.161252i	$-0.0515532\pi$
$744$	1.53209	+	1.28558i	0.0561691	+	0.0471315i
$745$		0			0
$746$	−3.75877	+	1.36808i	−0.137618	+	0.0500890i
$747$	−4.59627	+	3.85673i	−0.168169	+	0.141110i
$748$	9.00000	+	15.5885i	0.329073	+	0.569970i
$749$		0			0
$750$		0			0
$751$	−6.59863	−	37.4227i	−0.240787	−	1.36557i	−0.830076	−	0.557651i	$-0.811703\pi$
$751$	−6.59863	−	37.4227i	−0.240787	−	1.36557i	0.589288	−	0.807923i	$-0.299408\pi$
$752$		0			0
$753$	−1.50000	−	2.59808i	−0.0546630	−	0.0946792i
$754$		0			0
$755$		0			0
$756$	18.7939	+	6.84040i	0.683526	+	0.248783i
$757$	−7.66044	−	6.42788i	−0.278424	−	0.233625i	0.492873	−	0.870101i	$-0.335947\pi$
$757$	−7.66044	−	6.42788i	−0.278424	−	0.233625i	−0.771296	+	0.636476i	$0.780391\pi$
$758$	4.86215	−	27.5746i	0.176601	−	1.00156i
$759$	18.0000			0.653359
$760$		0			0
$761$	−39.0000			−1.41375			−0.706874	−	0.707339i	$-0.749895\pi$
$761$	−39.0000			−1.41375			−0.706874	+	0.707339i	$0.749895\pi$
$762$	0.347296	−	1.96962i	0.0125812	−	0.0713516i
$763$	−49.0268	−	41.1384i	−1.77489	−	1.48931i
$764$	−11.2763	−	4.10424i	−0.407963	−	0.148486i
$765$		0			0
$766$	27.5776	−	23.1404i	0.996419	−	0.836095i
$767$	9.00000	+	15.5885i	0.324971	+	0.562867i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	0.347296	+	1.96962i	0.0125238	+	0.0710262i	0.990429	−	0.138022i	$-0.0440745\pi$
$769$	0.347296	+	1.96962i	0.0125238	+	0.0710262i	−0.977905	+	0.209048i	$0.932963\pi$
$770$		0			0
$771$	−1.50000	+	2.59808i	−0.0540212	+	0.0935674i
$772$	1.00000	+	1.73205i	0.0359908	+	0.0623379i
$773$	36.7701	−	30.8538i	1.32253	−	1.10973i	0.336768	−	0.941588i	$-0.390666\pi$
$773$	36.7701	−	30.8538i	1.32253	−	1.10973i	0.985762	−	0.168146i	$-0.0537782\pi$
$774$	−7.51754	+	2.73616i	−0.270212	+	0.0983493i
$775$	−9.39693	−	3.42020i	−0.337548	−	0.122857i
$776$	−13.0228	−	10.9274i	−0.467490	−	0.392270i
$777$	6.94593	−	39.3923i	0.249184	−	1.41319i
$778$	−36.0000			−1.29066
$779$		0			0
$780$		0			0
$781$	3.12567	−	17.7265i	0.111845	−	0.634305i
$782$	27.5776	+	23.1404i	0.986173	+	0.827497i
$783$		0			0
$784$	−8.45723	+	3.07818i	−0.302044	+	0.109935i
$785$		0			0
$786$	4.50000	+	7.79423i	0.160510	+	0.278011i
$787$	−3.50000	+	6.06218i	−0.124762	+	0.216093i	−0.921640	−	0.388047i	$-0.873150\pi$
$787$	−3.50000	+	6.06218i	−0.124762	+	0.216093i	0.796878	+	0.604140i	$0.206483\pi$
$788$	3.12567	+	17.7265i	0.111347	+	0.631482i
$789$	2.08378	+	11.8177i	0.0741845	+	0.420721i
$790$		0			0
$791$	−30.0000	−	51.9615i	−1.06668	−	1.84754i
$792$	−4.59627	+	3.85673i	−0.163321	+	0.137043i
$793$	−7.51754	+	2.73616i	−0.266956	+	0.0971639i
$794$	9.39693	+	3.42020i	0.333484	+	0.121378i
$795$		0			0
$796$	−1.73648	+	9.84808i	−0.0615480	+	0.349056i
$797$	−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
$800$	−0.868241	+	4.92404i	−0.0306970	+	0.174091i
$801$	9.19253	+	7.71345i	0.324802	+	0.272541i
$802$	−25.3717	−	9.23454i	−0.895906	−	0.326083i
$803$	2.81908	−	1.02606i	0.0994831	−	0.0362089i
$804$	−5.36231	+	4.49951i	−0.189114	+	0.158686i
$805$		0			0
$806$	−2.00000	+	3.46410i	−0.0704470	+	0.122018i
$807$	2.08378	+	11.8177i	0.0733525	+	0.416002i
$808$		0			0
$809$	−22.5000	+	38.9711i	−0.791058	+	1.37015i	0.134255	+	0.990947i	$0.457136\pi$
$809$	−22.5000	+	38.9711i	−0.791058	+	1.37015i	−0.925312	+	0.379206i	$0.876197\pi$
$810$		0			0
$811$	12.2567	−	10.2846i	0.430391	−	0.361141i	−0.401708	−	0.915768i	$-0.631583\pi$
$811$	12.2567	−	10.2846i	0.430391	−	0.361141i	0.832099	+	0.554627i	$0.187139\pi$
$812$		0			0
$813$	−15.0351	−	5.47232i	−0.527303	−	0.191923i
$814$	22.9813	+	19.2836i	0.805495	+	0.675891i
$815$		0			0
$816$	6.00000			0.210042
$817$		0			0
$818$	−5.00000			−0.174821
$819$	−2.77837	+	15.7569i	−0.0970841	+	0.550591i
$820$		0			0
$821$	−16.9145	−	6.15636i	−0.590319	−	0.214859i	0.0295507	−	0.999563i	$-0.490592\pi$
$821$	−16.9145	−	6.15636i	−0.590319	−	0.214859i	−0.619870	+	0.784705i	$0.712815\pi$
$822$	8.45723	−	3.07818i	0.294980	−	0.107364i
$823$	10.7246	−	8.99903i	0.373837	−	0.313686i	−0.436440	−	0.899733i	$-0.643761\pi$
$823$	10.7246	−	8.99903i	0.373837	−	0.313686i	0.810277	+	0.586047i	$0.199317\pi$
$824$	1.00000	+	1.73205i	0.0348367	+	0.0603388i
$825$	−7.50000	+	12.9904i	−0.261116	+	0.452267i
$826$	−6.25133	−	35.4531i	−0.217512	−	1.23357i
$827$	6.77228	+	38.4075i	0.235495	+	1.33556i	0.841568	+	0.540151i	$0.181633\pi$
$827$	6.77228	+	38.4075i	0.235495	+	1.33556i	−0.606073	+	0.795409i	$0.707256\pi$
$828$	−6.00000	+	10.3923i	−0.208514	+	0.361158i
$829$	22.0000	+	38.1051i	0.764092	+	1.32345i	0.940726	+	0.339169i	$0.110146\pi$
$829$	22.0000	+	38.1051i	0.764092	+	1.32345i	−0.176634	+	0.984277i	$0.556521\pi$
$830$		0			0
$831$	7.51754	−	2.73616i	0.260781	−	0.0949164i
$832$	1.87939	+	0.684040i	0.0651560	+	0.0237148i
$833$	−41.3664	−	34.7105i	−1.43326	−	1.20265i
$834$	−1.91013	+	10.8329i	−0.0661424	+	0.375112i
$835$		0			0
$836$		0			0
$837$	−10.0000			−0.345651
$838$	−2.08378	+	11.8177i	−0.0719829	+	0.408235i
$839$	9.19253	+	7.71345i	0.317361	+	0.266298i	0.787527	−	0.616280i	$-0.211361\pi$
$839$	9.19253	+	7.71345i	0.317361	+	0.266298i	−0.470165	+	0.882578i	$0.655806\pi$
$840$		0			0
$841$	27.2511	−	9.91858i	0.939693	−	0.342020i
$842$	7.66044	−	6.42788i	0.263996	−	0.221519i
$843$	−13.5000	−	23.3827i	−0.464965	−	0.805342i
$844$	10.0000	−	17.3205i	0.344214	−	0.596196i
$845$		0			0
$846$		0			0
$847$	−4.00000	+	6.92820i	−0.137442	+	0.238056i
$848$	3.00000	+	5.19615i	0.103020	+	0.178437i
$849$	−3.83022	+	3.21394i	−0.131453	+	0.110302i
$850$	−28.1908	+	10.2606i	−0.966936	+	0.351936i
$851$	56.3816	+	20.5212i	1.93273	+	0.703458i
$852$	−4.59627	−	3.85673i	−0.157466	−	0.132129i
$853$	−3.82026	+	21.6658i	−0.130803	+	0.741822i	0.846887	+	0.531772i	$0.178474\pi$
$853$	−3.82026	+	21.6658i	−0.130803	+	0.741822i	−0.977691	+	0.210050i	$0.932637\pi$
$854$	16.0000			0.547509
$855$		0			0
$856$		0			0
$857$	0.520945	−	2.95442i	0.0177951	−	0.100921i	−0.974617	−	0.223881i	$-0.928127\pi$
$857$	0.520945	−	2.95442i	0.0177951	−	0.100921i	0.992412	+	0.122959i	$0.0392385\pi$
$858$	4.59627	+	3.85673i	0.156914	+	0.131666i
$859$	40.4068	+	14.7069i	1.37866	+	0.501792i	0.921772	−	0.387732i	$-0.126741\pi$
$859$	40.4068	+	14.7069i	1.37866	+	0.501792i	0.456889	+	0.889524i	$0.348964\pi$
$860$		0			0
$861$	−27.5776	+	23.1404i	−0.939842	+	0.788621i
$862$	−15.0000	−	25.9808i	−0.510902	−	0.884908i
$863$	9.00000	−	15.5885i	0.306364	−	0.530637i	−0.671200	−	0.741276i	$-0.734221\pi$
$863$	9.00000	−	15.5885i	0.306364	−	0.530637i	0.977564	+	0.210639i	$0.0675543\pi$
$864$	0.868241	+	4.92404i	0.0295382	+	0.167519i
$865$		0			0
$866$	13.0000	−	22.5167i	0.441758	−	0.765147i
$867$	9.50000	+	16.4545i	0.322637	+	0.558824i
$868$	6.12836	−	5.14230i	0.208010	−	0.174541i
$869$	−11.2763	+	4.10424i	−0.382523	+	0.139227i
$870$		0			0
$871$	−10.7246	−	8.99903i	−0.363390	−	0.304920i
$872$	2.77837	−	15.7569i	0.0940875	−	0.533597i
$873$	34.0000			1.15073
$874$		0			0
$875$		0			0
$876$	0.173648	−	0.984808i	0.00586703	−	0.0332736i
$877$	−15.3209	−	12.8558i	−0.517350	−	0.434108i	0.346357	−	0.938103i	$-0.387419\pi$
$877$	−15.3209	−	12.8558i	−0.517350	−	0.434108i	−0.863707	+	0.503995i	$0.831863\pi$
$878$	13.1557	+	4.78828i	0.443983	+	0.161597i
$879$	−22.5526	+	8.20848i	−0.760681	+	0.276865i
$880$		0			0
$881$	4.50000	+	7.79423i	0.151609	+	0.262594i	0.931819	−	0.362923i	$-0.118221\pi$
$881$	4.50000	+	7.79423i	0.151609	+	0.262594i	−0.780210	+	0.625517i	$0.784888\pi$
$882$	9.00000	−	15.5885i	0.303046	−	0.524891i
$883$	−3.29932	−	18.7113i	−0.111031	−	0.629687i	−0.988639	−	0.150309i	$-0.951973\pi$
$883$	−3.29932	−	18.7113i	−0.111031	−	0.629687i	0.877608	−	0.479378i	$-0.159138\pi$
$884$	2.08378	+	11.8177i	0.0700850	+	0.397472i
$885$		0			0
$886$	−4.50000	−	7.79423i	−0.151180	−	0.261852i
$887$	−36.7701	+	30.8538i	−1.23462	+	1.03597i	−0.236695	+	0.971584i	$0.576064\pi$
$887$	−36.7701	+	30.8538i	−1.23462	+	1.03597i	−0.997925	+	0.0643854i	$0.979491\pi$
$888$	9.39693	−	3.42020i	0.315340	−	0.114774i
$889$	−7.51754	−	2.73616i	−0.252130	−	0.0917679i
$890$		0			0
$891$	0.520945	−	2.95442i	0.0174523	−	0.0989769i
$892$	−14.0000			−0.468755
$893$		0			0
$894$	−18.0000			−0.602010
$895$		0			0
$896$	−3.06418	−	2.57115i	−0.102367	−	0.0858961i
$897$	11.2763	+	4.10424i	0.376505	+	0.137037i
$898$	8.45723	−	3.07818i	0.282222	−	0.102720i
$899$		0			0
$900$	−5.00000	−	8.66025i	−0.166667	−	0.288675i
$901$	−18.0000	+	31.1769i	−0.599667	+	1.03865i
$902$	−4.68850	−	26.5898i	−0.156110	−	0.885344i
$903$	−2.77837	−	15.7569i	−0.0924584	−	0.524358i
$904$	7.50000	−	12.9904i	0.249446	−	0.432054i
$905$		0			0
$906$	−7.66044	+	6.42788i	−0.254501	+	0.213552i
$907$	15.9748	−	5.81434i	0.530434	−	0.193062i	−0.0628983	−	0.998020i	$-0.520034\pi$
$907$	15.9748	−	5.81434i	0.530434	−	0.193062i	0.593332	+	0.804958i	$0.297812\pi$
$908$	2.81908	+	1.02606i	0.0935544	+	0.0340510i
$909$		0			0
$910$		0			0
$911$	−30.0000			−0.993944			−0.496972	−	0.867766i	$-0.665555\pi$
$911$	−30.0000			−0.993944			−0.496972	+	0.867766i	$0.665555\pi$
$912$		0			0
$913$	9.00000			0.297857
$914$	0.868241	−	4.92404i	0.0287189	−	0.162873i
$915$		0			0
$916$	15.0351	+	5.47232i	0.496773	+	0.180811i
$917$	33.8289	−	12.3127i	1.11713	−	0.406602i
$918$	−22.9813	+	19.2836i	−0.758497	+	0.636455i
$919$	5.00000	+	8.66025i	0.164935	+	0.285675i	0.936632	−	0.350315i	$-0.113925\pi$
$919$	5.00000	+	8.66025i	0.164935	+	0.285675i	−0.771697	+	0.635990i	$0.780592\pi$
$920$		0			0
$921$	−1.21554	−	6.89365i	−0.0400533	−	0.227154i
$922$	1.04189	+	5.90885i	0.0343128	+	0.194597i
$923$	6.00000	−	10.3923i	0.197492	−	0.342067i
$924$	−6.00000	−	10.3923i	−0.197386	−	0.341882i
$925$	−38.3022	+	32.1394i	−1.25937	+	1.05674i
$926$	31.9495	−	11.6287i	1.04993	−	0.382142i
$927$	−3.75877	−	1.36808i	−0.123454	−	0.0449337i
$928$		0			0
$929$	−0.520945	+	2.95442i	−0.0170916	+	0.0969315i	−0.992160	−	0.124972i	$-0.960116\pi$
$929$	−0.520945	+	2.95442i	−0.0170916	+	0.0969315i	0.975069	+	0.221904i	$0.0712270\pi$
$930$		0			0
$931$		0			0
$932$	3.00000			0.0982683
$933$	5.20945	−	29.5442i	0.170550	−	0.967235i
$934$	−20.6832	−	17.3553i	−0.676775	−	0.567882i
$935$		0			0
$936$	−3.75877	+	1.36808i	−0.122859	+	0.0447171i
$937$	26.8116	−	22.4976i	0.875895	−	0.734963i	−0.0894356	−	0.995993i	$-0.528506\pi$
$937$	26.8116	−	22.4976i	0.875895	−	0.734963i	0.965331	+	0.261029i	$0.0840619\pi$
$938$	14.0000	+	24.2487i	0.457116	+	0.791748i
$939$	−9.50000	+	16.4545i	−0.310021	+	0.536972i
$940$		0			0
$941$	7.29322	+	41.3619i	0.237752	+	1.34836i	0.836739	+	0.547601i	$0.184459\pi$
$941$	7.29322	+	41.3619i	0.237752	+	1.34836i	−0.598987	+	0.800759i	$0.704430\pi$
$942$	−8.00000	+	13.8564i	−0.260654	+	0.451466i
$943$	−27.0000	−	46.7654i	−0.879241	−	1.52289i
$944$	6.89440	−	5.78509i	0.224394	−	0.188289i
$945$		0			0
$946$	11.2763	+	4.10424i	0.366625	+	0.133440i
$947$	45.9627	+	38.5673i	1.49359	+	1.25327i	0.889992	+	0.455975i	$0.150709\pi$
$947$	45.9627	+	38.5673i	1.49359	+	1.25327i	0.603594	+	0.797292i	$0.293735\pi$
$948$	−0.694593	+	3.93923i	−0.0225593	+	0.127940i
$949$	2.00000			0.0649227
$950$		0			0
$951$	−18.0000			−0.583690
$952$	4.16756	−	23.6354i	0.135071	−	0.766027i
$953$	11.4907	+	9.64181i	0.372219	+	0.312329i	0.809639	−	0.586929i	$-0.199663\pi$
$953$	11.4907	+	9.64181i	0.372219	+	0.312329i	−0.437420	+	0.899258i	$0.644108\pi$
$954$	−11.2763	−	4.10424i	−0.365084	−	0.132880i
$955$		0			0
$956$	−9.19253	+	7.71345i	−0.297308	+	0.249471i
$957$		0			0
$958$	−18.0000	+	31.1769i	−0.581554	+	1.00728i
$959$	−6.25133	−	35.4531i	−0.201866	−	1.14484i
$960$		0			0
$961$	13.5000	−	23.3827i	0.435484	−	0.754280i
$962$	10.0000	+	17.3205i	0.322413	+	0.558436i
$963$		0			0
$964$	4.69846	−	1.71010i	0.151327	−	0.0550786i
$965$		0			0
$966$	−18.3851	−	15.4269i	−0.591530	−	0.496352i
$967$	−5.90404	+	33.4835i	−0.189861	+	1.07676i	0.729688	+	0.683780i	$0.239665\pi$
$967$	−5.90404	+	33.4835i	−0.189861	+	1.07676i	−0.919549	+	0.392975i	$0.871446\pi$
$968$	−2.00000			−0.0642824
$969$		0			0
$970$		0			0
$971$	−3.64661	+	20.6810i	−0.117025	+	0.663684i	0.868702	+	0.495335i	$0.164955\pi$
$971$	−3.64661	+	20.6810i	−0.117025	+	0.663684i	−0.985727	+	0.168349i	$0.946156\pi$
$972$	−12.2567	−	10.2846i	−0.393134	−	0.329879i
$973$	41.3465	+	15.0489i	1.32551	+	0.482445i
$974$	1.87939	−	0.684040i	0.0602194	−	0.0219181i
$975$	−7.66044	+	6.42788i	−0.245331	+	0.205857i
$976$	2.00000	+	3.46410i	0.0640184	+	0.110883i
$977$	16.5000	−	28.5788i	0.527882	−	0.914318i	−0.471590	−	0.881818i	$-0.656320\pi$
$977$	16.5000	−	28.5788i	0.527882	−	0.914318i	0.999472	−	0.0325001i	$-0.0103469\pi$
$978$	3.29932	+	18.7113i	0.105500	+	0.598323i
$979$	−3.12567	−	17.7265i	−0.0998968	−	0.566543i
$980$		0			0
$981$	16.0000	+	27.7128i	0.510841	+	0.884802i
$982$		0			0
$983$	22.5526	−	8.20848i	0.719317	−	0.261810i	0.0436812	−	0.999046i	$-0.486091\pi$
$983$	22.5526	−	8.20848i	0.719317	−	0.261810i	0.675636	+	0.737236i	$0.263869\pi$
$984$	−8.45723	−	3.07818i	−0.269607	−	0.0981288i
$985$		0			0
$986$		0			0
$987$		0			0
$988$		0			0
$989$	24.0000			0.763156
$990$		0			0
$991$	−6.12836	−	5.14230i	−0.194674	−	0.163351i	0.540241	−	0.841511i	$-0.318333\pi$
$991$	−6.12836	−	5.14230i	−0.194674	−	0.163351i	−0.734914	+	0.678160i	$0.762778\pi$
$992$	1.87939	+	0.684040i	0.0596705	+	0.0217183i
$993$	−4.69846	+	1.71010i	−0.149101	+	0.0542684i
$994$	−18.3851	+	15.4269i	−0.583139	+	0.489312i
$995$		0			0
$996$	1.50000	−	2.59808i	0.0475293	−	0.0823232i
$997$	−0.694593	−	3.93923i	−0.0219980	−	0.124757i	0.971831	−	0.235678i	$-0.0757310\pi$
$997$	−0.694593	−	3.93923i	−0.0219980	−	0.124757i	−0.993829	+	0.110921i	$0.964620\pi$
$998$	−4.34120	−	24.6202i	−0.137418	−	0.779339i
$999$	−25.0000	+	43.3013i	−0.790965	+	1.36999i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.i.245.1		6
19.2	odd	18		38.2.c.a.11.1	yes	2
19.3	odd	18		722.2.a.c.1.1		1
19.4	even	9	inner	722.2.e.i.595.1		6
19.5	even	9		722.2.c.b.653.1		2
19.6	even	9	inner	722.2.e.i.99.1		6
19.7	even	3	inner	722.2.e.i.415.1		6
19.8	odd	6		722.2.e.j.423.1		6
19.9	even	9	inner	722.2.e.i.389.1		6
19.10	odd	18		722.2.e.j.389.1		6
19.11	even	3	inner	722.2.e.i.423.1		6
19.12	odd	6		722.2.e.j.415.1		6
19.13	odd	18		722.2.e.j.99.1		6
19.14	odd	18		38.2.c.a.7.1	✓	2
19.15	odd	18		722.2.e.j.595.1		6
19.16	even	9		722.2.a.d.1.1		1
19.17	even	9		722.2.c.b.429.1		2
19.18	odd	2		722.2.e.j.245.1		6
57.2	even	18		342.2.g.b.163.1		2
57.14	even	18		342.2.g.b.235.1		2
57.35	odd	18		6498.2.a.e.1.1		1
57.41	even	18		6498.2.a.s.1.1		1
76.3	even	18		5776.2.a.g.1.1		1
76.35	odd	18		5776.2.a.n.1.1		1
76.59	even	18		304.2.i.c.49.1		2
76.71	even	18		304.2.i.c.273.1		2
95.2	even	36		950.2.j.e.49.2		4
95.14	odd	18		950.2.e.d.501.1		2
95.33	even	36		950.2.j.e.349.2		4
95.52	even	36		950.2.j.e.349.1		4
95.59	odd	18		950.2.e.d.201.1		2
95.78	even	36		950.2.j.e.49.1		4
152.21	odd	18		1216.2.i.h.961.1		2
152.59	even	18		1216.2.i.d.961.1		2
152.109	odd	18		1216.2.i.h.577.1		2
152.147	even	18		1216.2.i.d.577.1		2
228.59	odd	18		2736.2.s.m.1873.1		2
228.71	odd	18		2736.2.s.m.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
38.2.c.a.7.1	✓	2	19.14	odd	18
38.2.c.a.11.1	yes	2	19.2	odd	18
304.2.i.c.49.1		2	76.59	even	18
304.2.i.c.273.1		2	76.71	even	18
342.2.g.b.163.1		2	57.2	even	18
342.2.g.b.235.1		2	57.14	even	18
722.2.a.c.1.1		1	19.3	odd	18
722.2.a.d.1.1		1	19.16	even	9
722.2.c.b.429.1		2	19.17	even	9
722.2.c.b.653.1		2	19.5	even	9
722.2.e.i.99.1		6	19.6	even	9	inner
722.2.e.i.245.1		6	1.1	even	1	trivial
722.2.e.i.389.1		6	19.9	even	9	inner
722.2.e.i.415.1		6	19.7	even	3	inner
722.2.e.i.423.1		6	19.11	even	3	inner
722.2.e.i.595.1		6	19.4	even	9	inner
722.2.e.j.99.1		6	19.13	odd	18
722.2.e.j.245.1		6	19.18	odd	2
722.2.e.j.389.1		6	19.10	odd	18
722.2.e.j.415.1		6	19.12	odd	6
722.2.e.j.423.1		6	19.8	odd	6
722.2.e.j.595.1		6	19.15	odd	18
950.2.e.d.201.1		2	95.59	odd	18
950.2.e.d.501.1		2	95.14	odd	18
950.2.j.e.49.1		4	95.78	even	36
950.2.j.e.49.2		4	95.2	even	36
950.2.j.e.349.1		4	95.52	even	36
950.2.j.e.349.2		4	95.33	even	36
1216.2.i.d.577.1		2	152.147	even	18
1216.2.i.d.961.1		2	152.59	even	18
1216.2.i.h.577.1		2	152.109	odd	18
1216.2.i.h.961.1		2	152.21	odd	18
2736.2.s.m.577.1		2	228.71	odd	18
2736.2.s.m.1873.1		2	228.59	odd	18
5776.2.a.g.1.1		1	76.3	even	18
5776.2.a.n.1.1		1	76.35	odd	18
6498.2.a.e.1.1		1	57.35	odd	18
6498.2.a.s.1.1		1	57.41	even	18

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+(0.173648 - 0.984808i) q^{2} +(-0.766044 - 0.642788i) q^{3} +(-0.939693 - 0.342020i) q^{4} +(-0.766044 + 0.642788i) q^{6} +(2.00000 + 3.46410i) q^{7} +(-0.500000 + 0.866025i) q^{8} +(-0.347296 - 1.96962i) q^{9} +(-1.50000 + 2.59808i) q^{11} +(0.500000 + 0.866025i) q^{12} +(-1.53209 + 1.28558i) q^{13} +(3.75877 - 1.36808i) q^{14} +(0.766044 + 0.642788i) q^{16} +(-1.04189 + 5.90885i) q^{17} -2.00000 q^{18} +(0.694593 - 3.93923i) q^{21} +(2.29813 + 1.92836i) q^{22} +(5.63816 + 2.05212i) q^{23} +(0.939693 - 0.342020i) q^{24} +(-3.83022 + 3.21394i) q^{25} +(1.00000 + 1.73205i) q^{26} +(-2.50000 + 4.33013i) q^{27} +(-0.694593 - 3.93923i) q^{28} +(1.00000 + 1.73205i) q^{31} +(0.766044 - 0.642788i) q^{32} +(2.81908 - 1.02606i) q^{33} +(5.63816 + 2.05212i) q^{34} +(-0.347296 + 1.96962i) q^{36} +10.0000 q^{37} +2.00000 q^{39} +(-6.89440 - 5.78509i) q^{41} +(-3.75877 - 1.36808i) q^{42} +(3.75877 - 1.36808i) q^{43} +(2.29813 - 1.92836i) q^{44} +(3.00000 - 5.19615i) q^{46} +(-0.173648 - 0.984808i) q^{48} +(-4.50000 + 7.79423i) q^{49} +(2.50000 + 4.33013i) q^{50} +(4.59627 - 3.85673i) q^{51} +(1.87939 - 0.684040i) q^{52} +(5.63816 + 2.05212i) q^{53} +(3.83022 + 3.21394i) q^{54} -4.00000 q^{56} +(1.56283 - 8.86327i) q^{59} +(3.75877 + 1.36808i) q^{61} +(1.87939 - 0.684040i) q^{62} +(6.12836 - 5.14230i) q^{63} +(-0.500000 - 0.866025i) q^{64} +(-0.520945 - 2.95442i) q^{66} +(1.21554 + 6.89365i) q^{67} +(3.00000 - 5.19615i) q^{68} +(-3.00000 - 5.19615i) q^{69} +(-5.63816 + 2.05212i) q^{71} +(1.87939 + 0.684040i) q^{72} +(-0.766044 - 0.642788i) q^{73} +(1.73648 - 9.84808i) q^{74} +5.00000 q^{75} -12.0000 q^{77} +(0.347296 - 1.96962i) q^{78} +(3.06418 + 2.57115i) q^{79} +(-0.939693 + 0.342020i) q^{81} +(-6.89440 + 5.78509i) q^{82} +(-1.50000 - 2.59808i) q^{83} +(-2.00000 + 3.46410i) q^{84} +(-0.694593 - 3.93923i) q^{86} +(-1.50000 - 2.59808i) q^{88} +(-4.59627 + 3.85673i) q^{89} +(-7.51754 - 2.73616i) q^{91} +(-4.59627 - 3.85673i) q^{92} +(0.347296 - 1.96962i) q^{93} -1.00000 q^{96} +(-2.95202 + 16.7417i) q^{97} +(6.89440 + 5.78509i) q^{98} +(5.63816 + 2.05212i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 12 q^{7} - 3 q^{8} - 9 q^{11} + 3 q^{12} - 12 q^{18} + 6 q^{26} - 15 q^{27} + 6 q^{31} + 60 q^{37} + 12 q^{39} + 18 q^{46} - 27 q^{49} + 15 q^{50} - 24 q^{56} - 3 q^{64} + 18 q^{68} - 18 q^{69} + 30 q^{75}+ \cdots - 6 q^{96}+O(q^{100}) \) 6 * q + 12 * q^7 - 3 * q^8 - 9 * q^11 + 3 * q^12 - 12 * q^18 + 6 * q^26 - 15 * q^27 + 6 * q^31 + 60 * q^37 + 12 * q^39 + 18 * q^46 - 27 * q^49 + 15 * q^50 - 24 * q^56 - 3 * q^64 + 18 * q^68 - 18 * q^69 + 30 * q^75 - 72 * q^77 - 9 * q^83 - 12 * q^84 - 9 * q^88 - 6 * q^96

Introduction

L-functions

Modular forms

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