LMFDB - Embedded newform 722.2.e.r.595.1

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:	$24$
Relative dimension:	$4$ over $\Q(\zeta_{9})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			595.1
Character	$\chi$	$=$	722.595
Dual form			722.2.e.r.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.766044 - 0.642788i) q^{2} +(-2.62513 - 0.955469i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.407131 - 2.30896i) q^{5} +(-2.62513 + 0.955469i) q^{6} +(0.642040 - 1.11205i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(3.68025 + 3.08810i) q^{9} +O(q^{10})$	\(q+(0.766044 - 0.642788i) q^{2} +(-2.62513 - 0.955469i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.407131 - 2.30896i) q^{5} +(-2.62513 + 0.955469i) q^{6} +(0.642040 - 1.11205i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(3.68025 + 3.08810i) q^{9} +(-1.79605 - 1.50706i) q^{10} +(-2.87811 - 4.98503i) q^{11} +(-1.39680 + 2.41933i) q^{12} +(-0.285932 + 0.104071i) q^{13} +(-0.222978 - 1.26457i) q^{14} +(-1.13736 + 6.45031i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.20681 - 2.69083i) q^{17} +4.80423 q^{18} -2.34458 q^{20} +(-2.74796 + 2.30581i) q^{21} +(-5.40907 - 1.96874i) q^{22} +(-1.12469 + 6.37844i) q^{23} +(0.485104 + 2.75116i) q^{24} +(-0.467064 + 0.169997i) q^{25} +(-0.152141 + 0.263516i) q^{26} +(-2.52015 - 4.36502i) q^{27} +(-0.983662 - 0.825390i) q^{28} +(-2.39585 - 2.01036i) q^{29} +(3.27491 + 5.67231i) q^{30} +(-3.22123 + 5.57934i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(2.79236 + 15.8363i) q^{33} +(0.726925 - 4.12259i) q^{34} +(-2.82906 - 1.02969i) q^{35} +(3.68025 - 3.08810i) q^{36} -3.97980 q^{37} +0.850045 q^{39} +(-1.79605 + 1.50706i) q^{40} +(4.71461 + 1.71598i) q^{41} +(-0.622912 + 3.53271i) q^{42} +(-0.171804 - 0.974348i) q^{43} +(-5.40907 + 1.96874i) q^{44} +(5.63194 - 9.75480i) q^{45} +(3.23842 + 5.60910i) q^{46} +(-3.36635 - 2.82470i) q^{47} +(2.14003 + 1.79569i) q^{48} +(2.67557 + 4.63422i) q^{49} +(-0.248520 + 0.430448i) q^{50} +(-10.9893 + 3.99978i) q^{51} +(0.0528381 + 0.299660i) q^{52} +(0.571414 - 3.24065i) q^{53} +(-4.73633 - 1.72388i) q^{54} +(-10.3384 + 8.67499i) q^{55} -1.28408 q^{56} -3.12756 q^{58} +(2.53848 - 2.13004i) q^{59} +(6.15482 + 2.24017i) q^{60} +(-1.90344 + 10.7949i) q^{61} +(1.11872 + 6.34459i) q^{62} +(5.79697 - 2.10992i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.356707 + 0.617834i) q^{65} +(12.3184 + 10.3364i) q^{66} +(-3.35590 - 2.81593i) q^{67} +(-2.09310 - 3.62535i) q^{68} +(9.04686 - 15.6696i) q^{69} +(-2.82906 + 1.02969i) q^{70} +(-0.766777 - 4.34861i) q^{71} +(0.834245 - 4.73124i) q^{72} +(2.13018 + 0.775323i) q^{73} +(-3.04870 + 2.55816i) q^{74} +1.38853 q^{75} -7.39144 q^{77} +(0.651172 - 0.546398i) q^{78} +(-8.05936 - 2.93337i) q^{79} +(-0.407131 + 2.30896i) q^{80} +(-0.0576668 - 0.327045i) q^{81} +(4.71461 - 1.71598i) q^{82} +(4.88232 - 8.45643i) q^{83} +(1.79360 + 3.10661i) q^{84} +(-7.51861 - 6.30886i) q^{85} +(-0.757908 - 0.635960i) q^{86} +(4.36858 + 7.56661i) q^{87} +(-2.87811 + 4.98503i) q^{88} +(14.1673 - 5.15648i) q^{89} +(-1.95595 - 11.0928i) q^{90} +(-0.0678483 + 0.384787i) q^{91} +(6.08623 + 2.21521i) q^{92} +(13.7870 - 11.5687i) q^{93} -4.39445 q^{94} +2.79360 q^{96} +(13.2925 - 11.1538i) q^{97} +(5.02843 + 1.83020i) q^{98} +(4.80209 - 27.2340i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 6 q^{7} - 12 q^{8}+O(q^{10}) $ 24 * q + 6 * q^7 - 12 * q^8	$ 24 q + 6 q^{7} - 12 q^{8} - 6 q^{11} - 6 q^{12} + 24 q^{18} - 12 q^{20} - 54 q^{26} + 12 q^{27} - 12 q^{30} - 78 q^{31} + 24 q^{37} - 36 q^{39} + 66 q^{45} + 30 q^{46} + 36 q^{49} - 18 q^{50} - 12 q^{56} - 12 q^{58} - 12 q^{64} + 12 q^{65} - 18 q^{68} + 60 q^{69} + 48 q^{75} + 24 q^{77} + 36 q^{83} - 12 q^{84} + 78 q^{87} - 6 q^{88} - 72 q^{94} + 12 q^{96}+O(q^{100}) $ 24 * q + 6 * q^7 - 12 * q^8 - 6 * q^11 - 6 * q^12 + 24 * q^18 - 12 * q^20 - 54 * q^26 + 12 * q^27 - 12 * q^30 - 78 * q^31 + 24 * q^37 - 36 * q^39 + 66 * q^45 + 30 * q^46 + 36 * q^49 - 18 * q^50 - 12 * q^56 - 12 * q^58 - 12 * q^64 + 12 * q^65 - 18 * q^68 + 60 * q^69 + 48 * q^75 + 24 * q^77 + 36 * q^83 - 12 * q^84 + 78 * q^87 - 6 * q^88 - 72 * q^94 + 12 * q^96

Display 100 coefficients 10 coefficients

Character values

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

$n$	$363$
$\chi(n)$	$e\left(\frac{7}{9}\right)$

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
$3$	−2.62513	−	0.955469i	−1.51562	−	0.551640i	−0.555570	−	0.831470i	$-0.687500\pi$
$3$	−2.62513	−	0.955469i	−1.51562	−	0.551640i	−0.960050	+	0.279830i	$0.909722\pi$
$4$	0.173648	−	0.984808i	0.0868241	−	0.492404i
$5$	−0.407131	−	2.30896i	−0.182075	−	1.03260i	−0.929657	−	0.368427i	$-0.879896\pi$
$5$	−0.407131	−	2.30896i	−0.182075	−	1.03260i	0.747582	−	0.664170i	$-0.231215\pi$
$6$	−2.62513	+	0.955469i	−1.07170	+	0.390069i
$7$	0.642040	−	1.11205i	0.242668	−	0.420314i	−0.718805	−	0.695211i	$-0.755311\pi$
$7$	0.642040	−	1.11205i	0.242668	−	0.420314i	0.961473	+	0.274898i	$0.0886441\pi$
$8$	−0.500000	−	0.866025i	−0.176777	−	0.306186i
$9$	3.68025	+	3.08810i	1.22675	+	1.02937i
$10$	−1.79605	−	1.50706i	−0.567961	−	0.476576i
$11$	−2.87811	−	4.98503i	−0.867782	−	1.50304i	−0.864258	−	0.503049i	$-0.832212\pi$
$11$	−2.87811	−	4.98503i	−0.867782	−	1.50304i	−0.00352407	−	0.999994i	$-0.501122\pi$
$12$	−1.39680	+	2.41933i	−0.403222	+	0.698401i
$13$	−0.285932	+	0.104071i	−0.0793033	+	0.0288640i	−0.381367	−	0.924424i	$-0.624547\pi$
$13$	−0.285932	+	0.104071i	−0.0793033	+	0.0288640i	0.302064	+	0.953288i	$0.402324\pi$
$14$	−0.222978	−	1.26457i	−0.0595934	−	0.337971i
$15$	−1.13736	+	6.45031i	−0.293666	+	1.66546i
$16$	−0.939693	−	0.342020i	−0.234923	−	0.0855050i
$17$	3.20681	−	2.69083i	0.777765	−	0.652623i	−0.164919	−	0.986307i	$-0.552736\pi$
$17$	3.20681	−	2.69083i	0.777765	−	0.652623i	0.942685	+	0.333684i	$0.108292\pi$
$18$	4.80423			1.13237
$19$		0			0
$19$		0			0
$20$	−2.34458			−0.524263
$21$	−2.74796	+	2.30581i	−0.599654	+	0.503170i
$22$	−5.40907	−	1.96874i	−1.15322	−	0.419737i
$23$	−1.12469	+	6.37844i	−0.234514	+	1.33000i	0.609120	+	0.793078i	$0.291523\pi$
$23$	−1.12469	+	6.37844i	−0.234514	+	1.33000i	−0.843634	+	0.536918i	$0.819588\pi$
$24$	0.485104	+	2.75116i	0.0990215	+	0.561579i
$25$	−0.467064	+	0.169997i	−0.0934128	+	0.0339995i
$26$	−0.152141	+	0.263516i	−0.0298374	+	0.0516798i
$27$	−2.52015	−	4.36502i	−0.485003	−	0.840049i
$28$	−0.983662	−	0.825390i	−0.185895	−	0.155984i
$29$	−2.39585	−	2.01036i	−0.444898	−	0.373314i	0.392640	−	0.919692i	$-0.371562\pi$
$29$	−2.39585	−	2.01036i	−0.444898	−	0.373314i	−0.837539	+	0.546378i	$0.816006\pi$
$30$	3.27491	+	5.67231i	0.597914	+	1.03562i
$31$	−3.22123	+	5.57934i	−0.578550	+	1.00208i	0.417096	+	0.908863i	$0.363048\pi$
$31$	−3.22123	+	5.57934i	−0.578550	+	1.00208i	−0.995646	+	0.0932159i	$0.970285\pi$
$32$	−0.939693	+	0.342020i	−0.166116	+	0.0604612i
$33$	2.79236	+	15.8363i	0.486088	+	2.75674i
$34$	0.726925	−	4.12259i	0.124667	−	0.707019i
$35$	−2.82906	−	1.02969i	−0.478198	−	0.174050i
$36$	3.68025	−	3.08810i	0.613375	−	0.514683i
$37$	−3.97980			−0.654275			−0.327137	−	0.944977i	$-0.606084\pi$
$37$	−3.97980			−0.654275			−0.327137	+	0.944977i	$0.606084\pi$
$38$		0			0
$39$	0.850045			0.136116
$40$	−1.79605	+	1.50706i	−0.283980	+	0.238288i
$41$	4.71461	+	1.71598i	0.736299	+	0.267991i	0.682829	−	0.730579i	$-0.260750\pi$
$41$	4.71461	+	1.71598i	0.736299	+	0.267991i	0.0534702	+	0.998569i	$0.482972\pi$
$42$	−0.622912	+	3.53271i	−0.0961175	+	0.545109i
$43$	−0.171804	−	0.974348i	−0.0261998	−	0.148587i	0.968902	−	0.247447i	$-0.0795915\pi$
$43$	−0.171804	−	0.974348i	−0.0261998	−	0.148587i	−0.995101	+	0.0988600i	$0.968480\pi$
$44$	−5.40907	+	1.96874i	−0.815448	+	0.296799i
$45$	5.63194	−	9.75480i	0.839560	−	1.45416i
$46$	3.23842	+	5.60910i	0.477479	+	0.827017i
$47$	−3.36635	−	2.82470i	−0.491032	−	0.412025i	0.363364	−	0.931647i	$-0.381628\pi$
$47$	−3.36635	−	2.82470i	−0.491032	−	0.412025i	−0.854396	+	0.519622i	$0.826073\pi$
$48$	2.14003	+	1.79569i	0.308886	+	0.259186i
$49$	2.67557	+	4.63422i	0.382224	+	0.662032i
$50$	−0.248520	+	0.430448i	−0.0351460	+	0.0608746i
$51$	−10.9893	+	3.99978i	−1.53881	+	0.560081i
$52$	0.0528381	+	0.299660i	0.00732733	+	0.0415553i
$53$	0.571414	−	3.24065i	0.0784898	−	0.445138i	−0.920083	−	0.391724i	$-0.871879\pi$
$53$	0.571414	−	3.24065i	0.0784898	−	0.445138i	0.998572	−	0.0534135i	$-0.0170101\pi$
$54$	−4.73633	−	1.72388i	−0.644532	−	0.234591i
$55$	−10.3384	+	8.67499i	−1.39404	+	1.16974i
$56$	−1.28408			−0.171592
$57$		0			0
$58$	−3.12756			−0.410669
$59$	2.53848	−	2.13004i	0.330482	−	0.277307i	−0.462414	−	0.886664i	$-0.653017\pi$
$59$	2.53848	−	2.13004i	0.330482	−	0.277307i	0.792896	+	0.609357i	$0.208572\pi$
$60$	6.15482	+	2.24017i	0.794583	+	0.289205i
$61$	−1.90344	+	10.7949i	−0.243710	+	1.38215i	0.579759	+	0.814788i	$0.303147\pi$
$61$	−1.90344	+	10.7949i	−0.243710	+	1.38215i	−0.823469	+	0.567361i	$0.807964\pi$
$62$	1.11872	+	6.34459i	0.142078	+	0.805763i
$63$	5.79697	−	2.10992i	0.730349	−	0.265825i
$64$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$65$	0.356707	+	0.617834i	0.0442440	+	0.0766329i
$66$	12.3184	+	10.3364i	1.51630	+	1.27232i
$67$	−3.35590	−	2.81593i	−0.409988	−	0.344021i	0.414351	−	0.910117i	$-0.364009\pi$
$67$	−3.35590	−	2.81593i	−0.409988	−	0.344021i	−0.824339	+	0.566096i	$0.808453\pi$
$68$	−2.09310	−	3.62535i	−0.253825	−	0.439638i
$69$	9.04686	−	15.6696i	1.08911	−	1.88640i
$70$	−2.82906	+	1.02969i	−0.338137	+	0.123072i
$71$	−0.766777	−	4.34861i	−0.0909997	−	0.516085i	−0.995900	−	0.0904614i	$-0.971166\pi$
$71$	−0.766777	−	4.34861i	−0.0909997	−	0.516085i	0.904900	−	0.425624i	$-0.139945\pi$
$72$	0.834245	−	4.73124i	0.0983167	−	0.557582i
$73$	2.13018	+	0.775323i	0.249319	+	0.0907447i	0.463657	−	0.886015i	$-0.346537\pi$
$73$	2.13018	+	0.775323i	0.249319	+	0.0907447i	−0.214338	+	0.976760i	$0.568759\pi$
$74$	−3.04870	+	2.55816i	−0.354404	+	0.297381i
$75$	1.38853			0.160334
$76$		0			0
$77$	−7.39144			−0.842332
$78$	0.651172	−	0.546398i	0.0737307	−	0.0618674i
$79$	−8.05936	−	2.93337i	−0.906748	−	0.330029i	−0.153795	−	0.988103i	$-0.549149\pi$
$79$	−8.05936	−	2.93337i	−0.906748	−	0.330029i	−0.752954	+	0.658073i	$0.771372\pi$
$80$	−0.407131	+	2.30896i	−0.0455187	+	0.258149i
$81$	−0.0576668	−	0.327045i	−0.00640743	−	0.0363383i
$82$	4.71461	−	1.71598i	0.520642	−	0.189498i
$83$	4.88232	−	8.45643i	0.535904	−	0.928214i	−0.463214	−	0.886246i	$-0.653304\pi$
$83$	4.88232	−	8.45643i	0.535904	−	0.928214i	0.999119	−	0.0419676i	$-0.0133626\pi$
$84$	1.79360	+	3.10661i	0.195698	+	0.338959i
$85$	−7.51861	−	6.30886i	−0.815508	−	0.684292i
$86$	−0.757908	−	0.635960i	−0.0817273	−	0.0685774i
$87$	4.36858	+	7.56661i	0.468361	+	0.811225i
$88$	−2.87811	+	4.98503i	−0.306807	+	0.531406i
$89$	14.1673	−	5.15648i	1.50173	−	0.546586i	0.545223	−	0.838291i	$-0.316445\pi$
$89$	14.1673	−	5.15648i	1.50173	−	0.546586i	0.956508	+	0.291705i	$0.0942227\pi$
$90$	−1.95595	−	11.0928i	−0.206175	−	1.16928i
$91$	−0.0678483	+	0.384787i	−0.00711243	+	0.0403366i
$92$	6.08623	+	2.21521i	0.634534	+	0.230951i
$93$	13.7870	−	11.5687i	1.42965	−	1.19962i
$94$	−4.39445			−0.453253
$95$		0			0
$96$	2.79360			0.285121
$97$	13.2925	−	11.1538i	1.34965	−	1.13249i	0.370622	−	0.928784i	$-0.379145\pi$
$97$	13.2925	−	11.1538i	1.34965	−	1.13249i	0.979031	−	0.203710i	$-0.0652998\pi$
$98$	5.02843	+	1.83020i	0.507948	+	0.184878i
$99$	4.80209	−	27.2340i	0.482629	−	2.73712i
$100$	0.0863099	+	0.489488i	0.00863099	+	0.0489488i
$101$	−3.45494	+	1.25749i	−0.343779	+	0.125125i	−0.508139	−	0.861275i	$-0.669666\pi$
$101$	−3.45494	+	1.25749i	−0.343779	+	0.125125i	0.164360	+	0.986400i	$0.447444\pi$
$102$	−5.84728	+	10.1278i	−0.578967	+	1.00280i
$103$	−9.50676	−	16.4662i	−0.936729	−	1.62246i	−0.771521	−	0.636204i	$-0.780504\pi$
$103$	−9.50676	−	16.4662i	−0.936729	−	1.62246i	−0.165208	−	0.986259i	$-0.552830\pi$
$104$	0.233094	+	0.195589i	0.0228567	+	0.0191791i
$105$	6.44281	+	5.40616i	0.628753	+	0.527587i
$106$	−1.64532	−	2.84978i	−0.159808	−	0.276795i
$107$	−5.01864	+	8.69254i	−0.485170	+	0.840339i	−0.999855	−	0.0170403i	$-0.994576\pi$
$107$	−5.01864	+	8.69254i	−0.485170	+	0.840339i	0.514685	+	0.857380i	$0.327909\pi$
$108$	−4.73633	+	1.72388i	−0.455753	+	0.165881i
$109$	−1.53565	−	8.70913i	−0.147089	−	0.834183i	−0.965666	−	0.259786i	$-0.916348\pi$
$109$	−1.53565	−	8.70913i	−0.147089	−	0.834183i	0.818577	−	0.574397i	$-0.194763\pi$
$110$	−2.34354	+	13.2909i	−0.223447	+	1.26723i
$111$	10.4475	+	3.80257i	0.991631	+	0.360924i
$112$	−0.983662	+	0.825390i	−0.0929473	+	0.0779920i
$113$	−14.2502			−1.34055			−0.670275	−	0.742113i	$-0.733824\pi$
$113$	−14.2502			−1.34055			−0.670275	+	0.742113i	$0.733824\pi$
$114$		0			0
$115$	15.1854			1.41605
$116$	−2.39585	+	2.01036i	−0.222449	+	0.186657i
$117$	−1.37368	−	0.499979i	−0.126997	−	0.0462231i
$118$	0.575427	−	3.26341i	0.0529723	−	0.300421i
$119$	−0.933429	−	5.29374i	−0.0855673	−	0.485276i
$120$	6.15482	−	2.24017i	0.561855	−	0.204499i
$121$	−11.0670	+	19.1686i	−1.00609	+	1.74260i
$122$	5.48073	+	9.49290i	0.496202	+	0.859447i
$123$	−10.7369	−	9.00933i	−0.968114	−	0.812344i
$124$	4.93521	+	4.14114i	0.443195	+	0.371885i
$125$	−5.27877	−	9.14309i	−0.472147	−	0.817783i
$126$	3.08450	−	5.34252i	0.274789	−	0.475949i
$127$	−2.09565	+	0.762755i	−0.185959	+	0.0676836i	−0.433321	−	0.901240i	$-0.642658\pi$
$127$	−2.09565	+	0.762755i	−0.185959	+	0.0676836i	0.247362	+	0.968923i	$0.420436\pi$
$128$	0.173648	+	0.984808i	0.0153485	+	0.0870455i
$129$	−0.479952	+	2.72194i	−0.0422574	+	0.239654i
$130$	0.670389	+	0.244002i	0.0587970	+	0.0214004i
$131$	1.16642	−	0.978743i	0.101911	−	0.0855132i	−0.590409	−	0.807104i	$-0.701033\pi$
$131$	1.16642	−	0.978743i	0.101911	−	0.0855132i	0.692319	+	0.721591i	$0.256589\pi$
$132$	16.0806			1.39964
$133$		0			0
$134$	−4.38081			−0.378445
$135$	−9.05262	+	7.59605i	−0.779125	+	0.653764i
$136$	−3.93373	−	1.43176i	−0.337315	−	0.122773i
$137$	1.86008	−	10.5490i	0.158917	−	0.901263i	−0.796200	−	0.605034i	$-0.793160\pi$
$137$	1.86008	−	10.5490i	0.158917	−	0.901263i	0.955117	−	0.296229i	$-0.0957293\pi$
$138$	−3.14194	−	17.8188i	−0.267460	−	1.51684i
$139$	10.1622	−	3.69872i	0.861943	−	0.313721i	0.127043	−	0.991897i	$-0.459451\pi$
$139$	10.1622	−	3.69872i	0.861943	−	0.313721i	0.734900	+	0.678176i	$0.237229\pi$
$140$	−1.50531	+	2.60727i	−0.127222	+	0.220355i
$141$	6.13818	+	10.6316i	0.516928	+	0.895346i
$142$	−3.38262	−	2.83835i	−0.283863	−	0.238189i
$143$	1.34174	+	1.12585i	0.112202	+	0.0941485i
$144$	−2.40211	−	4.16058i	−0.200176	−	0.346715i
$145$	−3.66640	+	6.35039i	−0.304478	+	0.527371i
$146$	2.13018	−	0.775323i	0.176295	−	0.0641662i
$147$	−2.59586	−	14.7219i	−0.214103	−	1.21424i
$148$	−0.691084	+	3.91933i	−0.0568068	+	0.322167i
$149$	8.77094	+	3.19236i	0.718544	+	0.261528i	0.675307	−	0.737536i	$-0.264011\pi$
$149$	8.77094	+	3.19236i	0.718544	+	0.261528i	0.0432362	+	0.999065i	$0.486233\pi$
$150$	1.06368	−	0.892530i	0.0868488	−	0.0728748i
$151$	19.8232			1.61319			0.806593	−	0.591107i	$-0.201309\pi$
$151$	19.8232			1.61319			0.806593	+	0.591107i	$0.201309\pi$
$152$		0			0
$153$	20.1114			1.62591
$154$	−5.66217	+	4.75112i	−0.456270	+	0.382856i
$155$	14.1939	+	5.16616i	1.14008	+	0.414956i
$156$	0.147609	−	0.837131i	0.0118182	−	0.0670241i
$157$	2.40809	+	13.6569i	0.192186	+	1.08994i	0.916369	+	0.400335i	$0.131106\pi$
$157$	2.40809	+	13.6569i	0.192186	+	1.08994i	−0.724183	+	0.689608i	$0.757783\pi$
$158$	−8.05936	+	2.93337i	−0.641168	+	0.233366i
$159$	−4.59638	+	7.96116i	−0.364517	+	0.631361i
$160$	1.17229	+	2.03046i	0.0926775	+	0.160522i
$161$	6.37101	+	5.34592i	0.502106	+	0.421317i
$162$	−0.254396	−	0.213463i	−0.0199872	−	0.0167713i
$163$	−7.12480	−	12.3405i	−0.558057	−	0.966583i	−0.997659	−	0.0683904i	$-0.978214\pi$
$163$	−7.12480	−	12.3405i	−0.558057	−	0.966583i	0.439601	−	0.898193i	$-0.355120\pi$
$164$	2.50859	−	4.34501i	0.195888	−	0.339288i
$165$	35.4285	−	12.8949i	2.75810	−	1.00387i
$166$	−1.69561	−	9.61630i	−0.131605	−	0.746369i
$167$	2.01260	−	11.4140i	0.155740	−	0.883244i	−0.802366	−	0.596832i	$-0.796426\pi$
$167$	2.01260	−	11.4140i	0.155740	−	0.883244i	0.958106	−	0.286413i	$-0.0924629\pi$
$168$	3.37087	+	1.22690i	0.260069	+	0.0946572i
$169$	−9.88765	+	8.29672i	−0.760589	+	0.638210i
$170$	−9.81485			−0.752764
$171$		0			0
$172$	−0.989378			−0.0754394
$173$	3.05156	−	2.56056i	0.232006	−	0.194676i	−0.519372	−	0.854548i	$-0.673834\pi$
$173$	3.05156	−	2.56056i	0.232006	−	0.194676i	0.751378	+	0.659872i	$0.229390\pi$
$174$	8.21025	+	2.98829i	0.622417	+	0.226541i
$175$	−0.110829	+	0.628541i	−0.00837787	+	0.0475132i
$176$	0.999556	+	5.66877i	0.0753444	+	0.427299i
$177$	−8.69903	+	3.16619i	−0.653859	+	0.237985i
$178$	7.53827	−	13.0567i	0.565017	−	0.978638i
$179$	4.22545	+	7.31869i	0.315825	+	0.547024i	0.979612	−	0.200897i	$-0.0643855\pi$
$179$	4.22545	+	7.31869i	0.315825	+	0.547024i	−0.663788	+	0.747921i	$0.731052\pi$
$180$	−8.62863	−	7.24028i	−0.643140	−	0.539659i
$181$	6.50009	+	5.45422i	0.483148	+	0.405409i	0.851563	−	0.524252i	$-0.175655\pi$
$181$	6.50009	+	5.45422i	0.483148	+	0.405409i	−0.368415	+	0.929661i	$0.620100\pi$
$182$	0.195361	+	0.338376i	0.0144811	+	0.0250821i
$183$	15.3110	−	26.5194i	1.13182	−	1.96037i
$184$	6.08623	−	2.21521i	0.448683	−	0.163307i
$185$	1.62030	+	9.18918i	0.119127	+	0.675602i
$186$	3.12527	−	17.7243i	0.229156	−	1.29961i
$187$	−22.6434	−	8.24153i	−1.65585	−	0.602680i
$188$	−3.36635	+	2.82470i	−0.245516	+	0.206012i
$189$	−6.47214			−0.470779
$190$		0			0
$191$	−22.3790			−1.61929			−0.809644	−	0.586921i	$-0.800340\pi$
$191$	−22.3790			−1.61929			−0.809644	+	0.586921i	$0.800340\pi$
$192$	2.14003	−	1.79569i	0.154443	−	0.129593i
$193$	−6.98014	−	2.54056i	−0.502442	−	0.182874i	0.0783502	−	0.996926i	$-0.475035\pi$
$193$	−6.98014	−	2.54056i	−0.502442	−	0.182874i	−0.580792	+	0.814052i	$0.697257\pi$
$194$	3.01317	−	17.0886i	0.216333	−	1.22689i
$195$	−0.346080	−	1.96272i	−0.0247833	−	0.140553i
$196$	5.02843	−	1.83020i	0.359173	−	0.130728i
$197$	−4.26777	+	7.39199i	−0.304066	+	0.526658i	−0.977053	−	0.212997i	$-0.931678\pi$
$197$	−4.26777	+	7.39199i	−0.304066	+	0.526658i	0.672987	+	0.739654i	$0.265011\pi$
$198$	−13.8271	−	23.9492i	−0.982648	−	1.70200i
$199$	−4.87147	−	4.08765i	−0.345330	−	0.289766i	0.453582	−	0.891215i	$-0.350146\pi$
$199$	−4.87147	−	4.08765i	−0.345330	−	0.289766i	−0.798911	+	0.601449i	$0.794590\pi$
$200$	0.380754	+	0.319491i	0.0269234	+	0.0225914i
$201$	6.11913	+	10.5986i	0.431610	+	0.747571i
$202$	−1.83833	+	3.18409i	−0.129345	+	0.224032i
$203$	−3.77384	+	1.37356i	−0.264871	+	0.0964053i
$204$	2.03074	+	11.5169i	0.142180	+	0.806344i
$205$	2.04265	−	11.5845i	0.142665	−	0.809094i
$206$	−17.8669	−	6.50301i	−1.24484	−	0.453086i
$207$	−23.8364	+	20.0011i	−1.65674	+	1.39017i
$208$	0.304282			0.0210982
$209$		0			0
$210$	8.41049			0.580379
$211$	−10.6923	+	8.97190i	−0.736088	+	0.617651i	−0.931784	−	0.363014i	$-0.881748\pi$
$211$	−10.6923	+	8.97190i	−0.736088	+	0.617651i	0.195696	+	0.980665i	$0.437303\pi$
$212$	−3.09219	−	1.12547i	−0.212373	−	0.0772973i
$213$	−2.14207	+	12.1483i	−0.146772	+	0.832388i
$214$	1.74295	+	9.88479i	0.119146	+	0.675710i
$215$	−2.17978	+	0.793375i	−0.148660	+	0.0541077i
$216$	−2.52015	+	4.36502i	−0.171474	+	0.297002i
$217$	4.13632	+	7.16431i	0.280791	+	0.486345i
$218$	−6.77450	−	5.68448i	−0.458827	−	0.385002i
$219$	−4.85121	−	4.07065i	−0.327814	−	0.275069i
$220$	6.74794	+	11.6878i	0.454946	+	0.787990i
$221$	−0.636892	+	1.10313i	−0.0428420	+	0.0742046i
$222$	10.4475	−	3.80257i	0.701189	−	0.255212i
$223$	1.54964	+	8.78842i	0.103771	+	0.588516i	0.991704	+	0.128543i	$0.0410300\pi$
$223$	1.54964	+	8.78842i	0.103771	+	0.588516i	−0.887933	+	0.459973i	$0.847859\pi$
$224$	−0.222978	+	1.26457i	−0.0148983	+	0.0844927i
$225$	−2.24388	−	0.816706i	−0.149592	−	0.0544471i
$226$	−10.9163	+	9.15988i	−0.726142	+	0.609306i
$227$	−0.659796			−0.0437922			−0.0218961	−	0.999760i	$-0.506970\pi$
$227$	−0.659796			−0.0437922			−0.0218961	+	0.999760i	$0.506970\pi$
$228$		0			0
$229$	−6.97208			−0.460728			−0.230364	−	0.973105i	$-0.573992\pi$
$229$	−6.97208			−0.460728			−0.230364	+	0.973105i	$0.573992\pi$
$230$	11.6327	−	9.76101i	0.767039	−	0.643622i
$231$	19.4035	+	7.06229i	1.27665	+	0.464664i
$232$	−0.543095	+	3.08004i	−0.0356559	+	0.202215i
$233$	−5.14167	−	29.1599i	−0.336842	−	1.91033i	−0.408234	−	0.912877i	$-0.633855\pi$
$233$	−5.14167	−	29.1599i	−0.336842	−	1.91033i	0.0713919	−	0.997448i	$-0.477256\pi$
$234$	−1.37368	+	0.499979i	−0.0898004	+	0.0326847i
$235$	−5.15156	+	8.92277i	−0.336051	+	0.582057i
$236$	−1.65688	−	2.86979i	−0.107853	−	0.186808i
$237$	18.3541	+	15.4009i	1.19223	+	1.00040i
$238$	−4.11780	−	3.45524i	−0.266917	−	0.223970i
$239$	12.3517	+	21.3938i	0.798965	+	1.38385i	0.920291	+	0.391235i	$0.127952\pi$
$239$	12.3517	+	21.3938i	0.798965	+	1.38385i	−0.121326	+	0.992613i	$0.538715\pi$
$240$	3.27491	−	5.67231i	0.211395	−	0.366146i
$241$	−25.8967	+	9.42561i	−1.66815	+	0.607157i	−0.991612	−	0.129250i	$-0.958743\pi$
$241$	−25.8967	+	9.42561i	−1.66815	+	0.607157i	−0.676538	+	0.736407i	$0.736521\pi$
$242$	3.84353	+	21.7977i	0.247072	+	1.40121i
$243$	−2.78681	+	15.8048i	−0.178774	+	1.01388i
$244$	10.3004	+	3.74904i	0.659416	+	0.240008i
$245$	9.61092	−	8.06452i	0.614019	−	0.515223i
$246$	−14.0160			−0.893630
$247$		0			0
$248$	6.44246			0.409097
$249$	−20.8966	+	17.5343i	−1.32427	+	1.11119i
$250$	−9.92084	−	3.61089i	−0.627449	−	0.228373i
$251$	−0.518957	+	2.94315i	−0.0327563	+	0.185770i	−0.996796	−	0.0799891i	$-0.974511\pi$
$251$	−0.518957	+	2.94315i	−0.0327563	+	0.185770i	0.964039	+	0.265759i	$0.0856226\pi$
$252$	−1.07124	−	6.07528i	−0.0674816	−	0.382707i
$253$	35.0337	−	12.7512i	2.20255	−	0.801662i
$254$	−1.11507	+	1.93136i	−0.0699659	+	0.121185i
$255$	13.7094	+	23.7454i	0.858516	+	1.48699i
$256$	0.766044	+	0.642788i	0.0478778	+	0.0401742i
$257$	10.8259	+	9.08404i	0.675303	+	0.566647i	0.914630	−	0.404292i	$-0.132482\pi$
$257$	10.8259	+	9.08404i	0.675303	+	0.566647i	−0.239326	+	0.970939i	$0.576927\pi$
$258$	1.38197	+	2.39364i	0.0860374	+	0.149021i
$259$	−2.55519	+	4.42571i	−0.158772	+	0.275000i
$260$	0.670389	−	0.244002i	0.0415758	−	0.0151323i
$261$	−2.60915	−	14.7972i	−0.161502	−	0.915926i
$262$	0.264406	−	1.49952i	0.0163351	−	0.0926408i
$263$	−7.11241	−	2.58871i	−0.438570	−	0.159626i	0.113292	−	0.993562i	$-0.463860\pi$
$263$	−7.11241	−	2.58871i	−0.438570	−	0.159626i	−0.551862	+	0.833935i	$0.686083\pi$
$264$	12.3184	−	10.3364i	0.758148	−	0.636162i
$265$	−7.71517			−0.473939
$266$		0			0
$267$	−42.1179			−2.57757
$268$	−3.35590	+	2.81593i	−0.204994	+	0.172010i
$269$	7.20814	+	2.62355i	0.439488	+	0.159961i	0.552281	−	0.833658i	$-0.313757\pi$
$269$	7.20814	+	2.62355i	0.439488	+	0.159961i	−0.112793	+	0.993619i	$0.535980\pi$
$270$	−2.05206	+	11.6378i	−0.124885	+	0.708255i
$271$	2.02559	+	11.4877i	0.123046	+	0.697827i	0.982449	+	0.186529i	$0.0597239\pi$
$271$	2.02559	+	11.4877i	0.123046	+	0.697827i	−0.859404	+	0.511298i	$0.829165\pi$
$272$	−3.93373	+	1.43176i	−0.238518	+	0.0868133i
$273$	0.545762	−	0.945288i	0.0330310	−	0.0572114i
$274$	−5.35588	−	9.27665i	−0.323560	−	0.560423i
$275$	2.19170	+	1.83906i	0.132165	+	0.110899i
$276$	−13.8606	−	11.6304i	−0.834310	−	0.700069i
$277$	−13.7202	−	23.7642i	−0.824370	−	1.42785i	−0.902400	−	0.430899i	$-0.858197\pi$
$277$	−13.7202	−	23.7642i	−0.824370	−	1.42785i	0.0780307	−	0.996951i	$-0.475137\pi$
$278$	5.40717	−	9.36549i	0.324300	−	0.561705i
$279$	−29.0845	+	10.5859i	−1.74124	+	0.633760i
$280$	0.522789	+	2.96488i	0.0312426	+	0.177186i
$281$	2.82551	−	16.0243i	0.168556	−	0.955928i	−0.776766	−	0.629789i	$-0.783141\pi$
$281$	2.82551	−	16.0243i	0.168556	−	0.955928i	0.945322	−	0.326139i	$-0.105748\pi$
$282$	11.5360	+	4.19876i	0.686959	+	0.250033i
$283$	2.59976	−	2.18145i	0.154539	−	0.129674i	−0.562240	−	0.826974i	$-0.690060\pi$
$283$	2.59976	−	2.18145i	0.154539	−	0.129674i	0.716779	+	0.697300i	$0.245616\pi$
$284$	−4.41570			−0.262023
$285$		0			0
$286$	1.75152			0.103569
$287$	4.93521	−	4.14114i	0.291316	−	0.244444i
$288$	−4.51450	−	1.64314i	−0.266019	−	0.0968231i
$289$	0.0910271	−	0.516240i	0.00535453	−	0.0303671i
$290$	1.27333	+	7.22140i	0.0747724	+	0.424055i
$291$	−45.5517	+	16.5795i	−2.67029	+	0.971906i
$292$	1.13345	−	1.96319i	0.0663299	−	0.114887i
$293$	−11.6892	−	20.2462i	−0.682888	−	1.18280i	−0.974096	−	0.226136i	$-0.927391\pi$
$293$	−11.6892	−	20.2462i	−0.682888	−	1.18280i	0.291208	−	0.956660i	$-0.405943\pi$
$294$	−11.4516	−	9.60901i	−0.667870	−	0.560409i
$295$	−5.95166	−	4.99404i	−0.346519	−	0.290764i
$296$	1.98990	+	3.44660i	0.115660	+	0.200330i
$297$	−14.5065	+	25.1260i	−0.841753	+	1.45796i
$298$	8.77094	−	3.19236i	0.508087	−	0.184929i
$299$	−0.342224	−	1.94085i	−0.0197913	−	0.112242i
$300$	0.241116	−	1.36744i	0.0139208	−	0.0789489i
$301$	−1.19382	−	0.434516i	−0.0688108	−	0.0250451i
$302$	15.1854	−	12.7421i	0.873823	−	0.733225i
$303$	10.2712			0.590062
$304$		0			0
$305$	25.7000			1.47158
$306$	15.4062	−	12.9274i	0.880716	−	0.739008i
$307$	1.30431	+	0.474731i	0.0744411	+	0.0270943i	0.378972	−	0.925408i	$-0.376278\pi$
$307$	1.30431	+	0.474731i	0.0744411	+	0.0270943i	−0.304531	+	0.952502i	$0.598500\pi$
$308$	−1.28351	+	7.27914i	−0.0731347	+	0.414768i
$309$	9.22354	+	52.3093i	0.524709	+	2.97577i
$310$	14.1939	−	5.16616i	0.806160	−	0.293418i
$311$	6.09512	−	10.5571i	0.345623	−	0.598636i	−0.639844	−	0.768505i	$-0.721001\pi$
$311$	6.09512	−	10.5571i	0.345623	−	0.598636i	0.985467	+	0.169869i	$0.0543343\pi$
$312$	−0.425022	−	0.736160i	−0.0240622	−	0.0416769i
$313$	12.6638	+	10.6262i	0.715800	+	0.600628i	0.926220	−	0.376984i	$-0.123039\pi$
$313$	12.6638	+	10.6262i	0.715800	+	0.600628i	−0.210420	+	0.977611i	$0.567483\pi$
$314$	10.6232	+	8.91394i	0.599503	+	0.503043i
$315$	−7.23185	−	12.5259i	−0.407469	−	0.705757i
$316$	−4.28829	+	7.42754i	−0.241235	+	0.417832i
$317$	−2.52600	+	0.919389i	−0.141874	+	0.0516380i	−0.411981	−	0.911192i	$-0.635163\pi$
$317$	−2.52600	+	0.919389i	−0.141874	+	0.0516380i	0.270107	+	0.962830i	$0.412941\pi$
$318$	1.59631	+	9.05310i	0.0895164	+	0.507673i
$319$	−3.12617	+	17.7294i	−0.175032	+	0.992656i
$320$	2.20318	+	0.801892i	0.123162	+	0.0448271i
$321$	21.4800	−	18.0239i	1.19890	−	1.00599i
$322$	8.31677			0.463475
$323$		0			0
$324$	−0.332090			−0.0184495
$325$	0.115857	−	0.0972154i	0.00642658	−	0.00539254i
$326$	−13.3902	−	4.87365i	−0.741617	−	0.269926i
$327$	−4.29001	+	24.3299i	−0.237238	+	1.34544i
$328$	−0.871225	−	4.94096i	−0.0481054	−	0.272819i
$329$	−5.30252	+	1.92996i	−0.292337	+	0.106402i
$330$	18.8511	−	32.6510i	1.03772	−	1.79738i
$331$	−2.60651	−	4.51462i	−0.143267	−	0.248146i	0.785458	−	0.618915i	$-0.212427\pi$
$331$	−2.60651	−	4.51462i	−0.143267	−	0.248146i	−0.928725	+	0.370769i	$0.879094\pi$
$332$	−7.48015	−	6.27659i	−0.410527	−	0.344473i
$333$	−14.6466	−	12.2900i	−0.802631	−	0.673488i
$334$	−5.79506	−	10.0373i	−0.317091	−	0.549218i
$335$	−5.13558	+	8.89508i	−0.280587	+	0.485990i
$336$	3.37087	−	1.22690i	0.183896	−	0.0669328i
$337$	−4.64118	−	26.3214i	−0.252821	−	1.43382i	−0.801605	−	0.597855i	$-0.796020\pi$
$337$	−4.64118	−	26.3214i	−0.252821	−	1.43382i	0.548784	−	0.835964i	$-0.315091\pi$
$338$	−2.24135	+	12.7113i	−0.121913	+	0.691405i
$339$	37.4087	+	13.6157i	2.03176	+	0.739501i
$340$	−7.51861	+	6.30886i	−0.407754	+	0.342146i
$341$	37.0842			2.00822
$342$		0			0
$343$	15.8598			0.856351
$344$	−0.757908	+	0.635960i	−0.0408637	+	0.0342887i
$345$	−39.8637	−	14.5092i	−2.14619	−	0.781150i
$346$	0.691732	−	3.92301i	0.0371877	−	0.210902i
$347$	−5.67277	−	32.1719i	−0.304530	−	1.72708i	−0.625707	−	0.780058i	$-0.715189\pi$
$347$	−5.67277	−	32.1719i	−0.304530	−	1.72708i	0.321177	−	0.947019i	$-0.395922\pi$
$348$	8.21025	−	2.98829i	0.440116	−	0.160189i
$349$	14.5529	−	25.2063i	0.778998	−	1.34926i	−0.153521	−	0.988145i	$-0.549061\pi$
$349$	14.5529	−	25.2063i	0.778998	−	1.34926i	0.932520	−	0.361119i	$-0.117605\pi$
$350$	0.319119	+	0.552730i	0.0170576	+	0.0295447i
$351$	1.17486	+	0.985826i	0.0627095	+	0.0526195i
$352$	4.40952	+	3.70002i	0.235028	+	0.197212i
$353$	7.15244	+	12.3884i	0.380686	+	0.659368i	0.991160	−	0.132668i	$-0.0423545\pi$
$353$	7.15244	+	12.3884i	0.380686	+	0.659368i	−0.610474	+	0.792036i	$0.709021\pi$
$354$	−4.62866	+	8.01707i	−0.246010	+	0.426102i
$355$	−9.72858	+	3.54091i	−0.516339	+	0.187932i
$356$	−2.61801	−	14.8475i	−0.138754	−	0.786915i
$357$	−2.60763	+	14.7886i	−0.138010	+	0.782696i
$358$	7.94124	+	2.89038i	0.419708	+	0.152761i
$359$	15.0686	−	12.6441i	0.795292	−	0.667329i	−0.151757	−	0.988418i	$-0.548493\pi$
$359$	15.0686	−	12.6441i	0.795292	−	0.667329i	0.947049	+	0.321089i	$0.104049\pi$
$360$	−11.2639			−0.593658
$361$		0			0
$362$	8.48526			0.445976
$363$	47.3673	−	39.7459i	2.48614	−	2.08612i
$364$	0.367159	+	0.133635i	0.0192444	+	0.00700438i
$365$	0.922923	−	5.23416i	0.0483080	−	0.273968i
$366$	−5.31745	−	30.1568i	−0.277948	−	1.57632i
$367$	−8.97456	+	3.26647i	−0.468468	+	0.170509i	−0.565458	−	0.824777i	$-0.691301\pi$
$367$	−8.97456	+	3.26647i	−0.468468	+	0.170509i	0.0969900	+	0.995285i	$0.469079\pi$
$368$	3.23842	−	5.60910i	0.168814	−	0.292395i
$369$	12.0518	+	20.8744i	0.627394	+	1.08668i
$370$	7.14791	+	5.99781i	0.371602	+	0.311811i
$371$	−3.23688	−	2.71606i	−0.168050	−	0.141011i
$372$	−8.99885	−	15.5865i	−0.466569	−	0.808120i
$373$	−1.82005	+	3.15242i	−0.0942387	+	0.163226i	−0.909291	−	0.416162i	$-0.863375\pi$
$373$	−1.82005	+	3.15242i	−0.0942387	+	0.163226i	0.815052	+	0.579388i	$0.196708\pi$
$374$	−22.6434	+	8.24153i	−1.17086	+	0.426159i
$375$	5.12151	+	29.0455i	0.264473	+	1.49990i
$376$	−0.763089	+	4.32769i	−0.0393533	+	0.223184i
$377$	0.894269	+	0.325487i	0.0460572	+	0.0167635i
$378$	−4.95794	+	4.16021i	−0.255009	+	0.213978i
$379$	8.34741			0.428778			0.214389	−	0.976748i	$-0.431224\pi$
$379$	8.34741			0.428778			0.214389	+	0.976748i	$0.431224\pi$
$380$		0			0
$381$	6.23015			0.319180
$382$	−17.1433	+	14.3850i	−0.877129	+	0.735998i
$383$	8.91361	+	3.24429i	0.455464	+	0.165775i	0.559556	−	0.828792i	$-0.310972\pi$
$383$	8.91361	+	3.24429i	0.455464	+	0.165775i	−0.104092	+	0.994568i	$0.533194\pi$
$384$	0.485104	−	2.75116i	0.0247554	−	0.140395i
$385$	3.00929	+	17.0665i	0.153367	+	0.869790i
$386$	−6.98014	+	2.54056i	−0.355280	+	0.129311i
$387$	2.37660	−	4.11639i	0.120809	−	0.209248i
$388$	−8.67609	−	15.0274i	−0.440462	−	0.762902i
$389$	27.6143	+	23.1712i	1.40010	+	1.17483i	0.961053	+	0.276363i	$0.0891292\pi$
$389$	27.6143	+	23.1712i	1.40010	+	1.17483i	0.439050	+	0.898463i	$0.355315\pi$
$390$	−1.52672	−	1.28107i	−0.0773086	−	0.0648696i
$391$	13.5566	+	23.4808i	0.685589	+	1.18747i
$392$	2.67557	−	4.63422i	0.135137	−	0.234064i
$393$	−3.99717	+	1.45485i	−0.201630	+	0.0733874i
$394$	1.48218	+	8.40586i	0.0746712	+	0.423481i
$395$	−3.49180	+	19.8030i	−0.175691	+	0.996396i
$396$	−25.9864	−	9.45828i	−1.30587	−	0.475296i
$397$	−4.90963	+	4.11967i	−0.246407	+	0.206760i	−0.757623	−	0.652692i	$-0.773640\pi$
$397$	−4.90963	+	4.11967i	−0.246407	+	0.206760i	0.511216	+	0.859452i	$0.329195\pi$
$398$	−6.35926			−0.318761
$399$		0			0
$400$	0.497039			0.0248520
$401$	0.143756	−	0.120625i	0.00717882	−	0.00602374i	−0.639191	−	0.769048i	$-0.720731\pi$
$401$	0.143756	−	0.120625i	0.00717882	−	0.00602374i	0.646370	+	0.763024i	$0.276286\pi$
$402$	11.5002	+	4.18573i	0.573578	+	0.208765i
$403$	0.340408	−	1.93055i	0.0169569	−	0.0961674i
$404$	0.638446	+	3.62081i	0.0317639	+	0.180142i
$405$	−0.731655	+	0.266301i	−0.0363562	+	0.0132326i
$406$	−2.00802	+	3.47799i	−0.0996562	+	0.172610i
$407$	11.4543	+	19.8394i	0.567768	+	0.983402i
$408$	8.95856	+	7.51712i	0.443515	+	0.372153i
$409$	13.2267	+	11.0985i	0.654020	+	0.548788i	0.908288	−	0.418346i	$-0.137390\pi$
$409$	13.2267	+	11.0985i	0.654020	+	0.548788i	−0.254268	+	0.967134i	$0.581835\pi$
$410$	−5.88159	−	10.1872i	−0.290471	−	0.503110i
$411$	−14.9622	+	25.9153i	−0.738031	+	1.27831i
$412$	−17.8669	+	6.50301i	−0.880238	+	0.320380i
$413$	−0.738894	−	4.19047i	−0.0363586	−	0.206200i
$414$	−5.40327	+	30.6435i	−0.265556	+	1.50604i
$415$	−21.5133	−	7.83019i	−1.05605	−	0.384369i
$416$	0.233094	−	0.195589i	0.0114284	−	0.00958954i
$417$	−30.2110			−1.47944
$418$		0			0
$419$	−1.72572			−0.0843068			−0.0421534	−	0.999111i	$-0.513422\pi$
$419$	−1.72572			−0.0843068			−0.0421534	+	0.999111i	$0.513422\pi$
$420$	6.44281	−	5.40616i	0.314377	−	0.263793i
$421$	−30.7792	−	11.2027i	−1.50009	−	0.545987i	−0.544004	−	0.839083i	$-0.683092\pi$
$421$	−30.7792	−	11.2027i	−1.50009	−	0.545987i	−0.956083	+	0.293096i	$0.905315\pi$
$422$	−2.42375	+	13.7457i	−0.117986	+	0.669133i
$423$	−3.66605	−	20.7912i	−0.178249	−	1.01090i
$424$	−3.09219	+	1.12547i	−0.150170	+	0.0546575i
$425$	−1.04035	+	1.80194i	−0.0504644	+	0.0874069i
$426$	6.16785	+	10.6830i	0.298833	+	0.517595i
$427$	10.7824	+	9.04748i	0.521795	+	0.437838i
$428$	7.68900	+	6.45184i	0.371662	+	0.311861i
$429$	−2.44652	−	4.23750i	−0.118119	−	0.204588i
$430$	−1.15984	+	2.00890i	−0.0559323	+	0.0968776i
$431$	23.9734	−	8.72559i	1.15476	−	0.420297i	0.307535	−	0.951537i	$-0.400496\pi$
$431$	23.9734	−	8.72559i	1.15476	−	0.420297i	0.847221	+	0.531240i	$0.178274\pi$
$432$	0.875238	+	4.96372i	0.0421099	+	0.238817i
$433$	4.25150	−	24.1114i	0.204314	−	1.15872i	−0.694202	−	0.719781i	$-0.744242\pi$
$433$	4.25150	−	24.1114i	0.204314	−	1.15872i	0.898516	−	0.438941i	$-0.144646\pi$
$434$	7.77373	+	2.82941i	0.373151	+	0.135816i
$435$	15.6924	−	13.1675i	0.752392	−	0.631332i
$436$	−8.84348			−0.423526
$437$		0			0
$438$	−6.33280			−0.302593
$439$	−23.6239	+	19.8228i	−1.12751	+	0.946091i	−0.998959	−	0.0456128i	$-0.985476\pi$
$439$	−23.6239	+	19.8228i	−1.12751	+	0.946091i	−0.128548	+	0.991703i	$0.541032\pi$
$440$	12.6820	+	4.61587i	0.604590	+	0.220053i
$441$	−4.46416	+	25.3175i	−0.212579	+	1.20560i
$442$	0.221190	+	1.25443i	0.0105210	+	0.0596673i
$443$	−10.0591	+	3.66122i	−0.477923	+	0.173950i	−0.569738	−	0.821826i	$-0.692955\pi$
$443$	−10.0591	+	3.66122i	−0.477923	+	0.173950i	0.0918153	+	0.995776i	$0.470733\pi$
$444$	5.55899	−	9.62845i	0.263818	−	0.456946i
$445$	−17.6740	−	30.6123i	−0.837830	−	1.45116i
$446$	6.83618	+	5.73624i	0.323702	+	0.271619i
$447$	−19.9747	−	16.7607i	−0.944769	−	0.792755i
$448$	0.642040	+	1.11205i	0.0303335	+	0.0525392i
$449$	−1.15781	+	2.00538i	−0.0546403	+	0.0946399i	−0.892052	−	0.451933i	$-0.850735\pi$
$449$	−1.15781	+	2.00538i	−0.0546403	+	0.0946399i	0.837411	+	0.546573i	$0.184068\pi$
$450$	−2.24388	+	0.816706i	−0.105778	+	0.0384999i
$451$	−5.01496	−	28.4412i	−0.236145	−	1.33925i
$452$	−2.47453	+	14.0337i	−0.116392	+	0.660092i
$453$	−52.0384	−	18.9404i	−2.44498	−	0.889899i
$454$	−0.505433	+	0.424109i	−0.0237211	+	0.0199044i
$455$	0.916079			0.0429465
$456$		0			0
$457$	−0.0521810			−0.00244092			−0.00122046	−	0.999999i	$-0.500388\pi$
$457$	−0.0521810			−0.00244092			−0.00122046	+	0.999999i	$0.500388\pi$
$458$	−5.34092	+	4.48157i	−0.249565	+	0.209410i
$459$	−19.8272	−	7.21650i	−0.925453	−	0.336837i
$460$	2.63692	−	14.9547i	0.122947	−	0.697268i
$461$	6.85424	+	38.8724i	0.319234	+	1.81047i	0.547431	+	0.836851i	$0.315606\pi$
$461$	6.85424	+	38.8724i	0.319234	+	1.81047i	−0.228197	+	0.973615i	$0.573283\pi$
$462$	19.4035	−	7.06229i	0.902731	−	0.328567i
$463$	3.09528	−	5.36119i	0.143850	−	0.249155i	−0.785093	−	0.619377i	$-0.787385\pi$
$463$	3.09528	−	5.36119i	0.143850	−	0.249155i	0.928943	+	0.370222i	$0.120718\pi$
$464$	1.56378	+	2.70855i	0.0725967	+	0.125741i
$465$	−32.3248	−	27.1237i	−1.49902	−	1.25783i
$466$	−22.6823	−	19.0327i	−1.05074	−	0.881675i
$467$	10.4981	+	18.1832i	0.485793	+	0.841418i	0.999867	−	0.0163277i	$-0.00519750\pi$
$467$	10.4981	+	18.1832i	0.485793	+	0.841418i	−0.514074	+	0.857746i	$0.671864\pi$
$468$	−0.730921	+	1.26599i	−0.0337868	+	0.0585205i
$469$	−5.28606	+	1.92397i	−0.244088	+	0.0888407i
$470$	1.78912	+	10.1466i	0.0825259	+	0.468028i
$471$	6.72725	−	38.1521i	0.309975	−	1.75796i
$472$	−3.11391	−	1.13337i	−0.143329	−	0.0521676i
$473$	−4.36268	+	3.66072i	−0.200596	+	0.168320i
$474$	23.9596			1.10050
$475$		0			0
$476$	−5.37540			−0.246381
$477$	12.1104	−	10.1618i	0.554497	−	0.465278i
$478$	23.2136	+	8.44906i	1.06177	+	0.386451i
$479$	2.69553	−	15.2871i	0.123162	−	0.698486i	−0.859221	−	0.511605i	$-0.829051\pi$
$479$	2.69553	−	15.2871i	0.123162	−	0.698486i	0.982383	−	0.186881i	$-0.0598378\pi$
$480$	−1.13736	−	6.45031i	−0.0519133	−	0.294415i
$481$	1.13795	−	0.414180i	0.0518861	−	0.0188850i
$482$	−13.7793	+	23.8665i	−0.627631	+	1.08709i
$483$	−11.6169	−	20.1210i	−0.528586	−	0.915539i
$484$	16.9556	+	14.2275i	0.770711	+	0.646703i
$485$	−31.1654	−	26.1509i	−1.41515	−	1.18745i
$486$	8.02431	+	13.8985i	0.363990	+	0.630449i
$487$	14.3033	−	24.7740i	0.648143	−	1.12262i	−0.335423	−	0.942068i	$-0.608879\pi$
$487$	14.3033	−	24.7740i	0.648143	−	1.12262i	0.983566	−	0.180549i	$-0.0577875\pi$
$488$	10.3004	−	3.74904i	0.466277	−	0.169711i
$489$	6.91254	+	39.2030i	0.312596	+	1.77282i
$490$	2.17862	−	12.3556i	0.0984199	−	0.558167i
$491$	28.5186	+	10.3799i	1.28703	+	0.468439i	0.892750	−	0.450553i	$-0.148773\pi$
$491$	28.5186	+	10.3799i	1.28703	+	0.468439i	0.394276	+	0.918992i	$0.370995\pi$
$492$	−10.7369	+	9.00933i	−0.484057	+	0.406172i
$493$	−13.0926			−0.589659
$494$		0			0
$495$	−64.8373			−2.91422
$496$	4.93521	−	4.14114i	0.221598	−	0.185942i
$497$	−5.32815	−	1.93929i	−0.239000	−	0.0869890i
$498$	−4.73687	+	26.8641i	−0.212264	+	1.20381i
$499$	1.52398	+	8.64291i	0.0682226	+	0.386910i	0.999731	+	0.0231900i	$0.00738226\pi$
$499$	1.52398	+	8.64291i	0.0682226	+	0.386910i	−0.931508	+	0.363720i	$0.881507\pi$
$500$	−9.92084	+	3.61089i	−0.443673	+	0.161484i
$501$	−16.1891	+	28.0403i	−0.723275	+	1.25275i
$502$	1.49428	+	2.58816i	0.0666928	+	0.115515i
$503$	−16.1669	−	13.5656i	−0.720845	−	0.604861i	0.206774	−	0.978389i	$-0.433703\pi$
$503$	−16.1669	−	13.5656i	−0.720845	−	0.604861i	−0.927619	+	0.373528i	$0.878148\pi$
$504$	−4.72573	−	3.96536i	−0.210501	−	0.176631i
$505$	4.31011	+	7.46533i	0.191798	+	0.332203i
$506$	18.6410	−	32.2872i	0.828695	−	1.43534i
$507$	33.8836	−	12.3326i	1.50482	−	0.547711i
$508$	0.387261	+	2.19627i	0.0171819	+	0.0974435i
$509$	3.85866	−	21.8836i	0.171032	−	0.969972i	−0.771592	−	0.636118i	$-0.780539\pi$
$509$	3.85866	−	21.8836i	0.171032	−	0.969972i	0.942624	−	0.333855i	$-0.108350\pi$
$510$	25.7652	+	9.37778i	1.14090	+	0.415255i
$511$	2.22986	−	1.87107i	0.0986430	−	0.0827713i
$512$	1.00000			0.0441942
$513$		0			0
$514$	14.1323			0.623347
$515$	−34.1492	+	28.6546i	−1.50480	+	1.26267i
$516$	2.59725	+	0.945320i	0.114337	+	0.0416154i
$517$	−4.39250	+	24.9111i	−0.193182	+	1.09559i
$518$	0.887407	+	5.03274i	0.0389904	+	0.221126i
$519$	−10.4573	+	3.80614i	−0.459023	+	0.167071i
$520$	0.356707	−	0.617834i	0.0156426	−	0.0270938i
$521$	−5.01661	−	8.68902i	−0.219782	−	0.380673i	0.734959	−	0.678111i	$-0.237201\pi$
$521$	−5.01661	−	8.68902i	−0.219782	−	0.380673i	−0.954741	+	0.297438i	$0.903868\pi$
$522$	−11.5102	−	9.65821i	−0.503788	−	0.422728i
$523$	22.4315	+	18.8223i	0.980862	+	0.823041i	0.984219	−	0.176953i	$-0.0566241\pi$
$523$	22.4315	+	18.8223i	0.980862	+	0.823041i	−0.00335692	+	0.999994i	$0.501069\pi$
$524$	−0.761327	−	1.31866i	−0.0332587	−	0.0576058i
$525$	0.891491	−	1.54411i	0.0389079	−	0.0673904i
$526$	−7.11241	+	2.58871i	−0.310116	+	0.112873i
$527$	4.68319	+	26.5597i	0.204003	+	1.15696i
$528$	2.79236	−	15.8363i	0.121522	−	0.689186i
$529$	−17.8066	−	6.48108i	−0.774200	−	0.281786i
$530$	−5.91016	+	4.95921i	−0.256721	+	0.215414i
$531$	15.9200			0.690870
$532$		0			0
$533$	−1.52664			−0.0661262
$534$	−32.2642	+	27.0728i	−1.39621	+	1.17156i
$535$	22.1139	+	8.04882i	0.956069	+	0.347981i
$536$	−0.760720	+	4.31426i	−0.0328581	+	0.186348i
$537$	−4.09956	−	23.2498i	−0.176909	−	1.00330i
$538$	7.20814	−	2.62355i	0.310765	−	0.113109i
$539$	15.4012	−	26.6756i	0.663375	−	1.14900i
$540$	5.90868	+	10.2341i	0.254269	+	0.440407i
$541$	−28.9874	−	24.3233i	−1.24627	−	1.04574i	−0.997008	−	0.0773035i	$-0.975369\pi$
$541$	−28.9874	−	24.3233i	−1.24627	−	1.04574i	−0.249258	−	0.968437i	$-0.580187\pi$
$542$	8.93583	+	7.49805i	0.383827	+	0.322069i
$543$	−11.8522	−	20.5287i	−0.508628	−	0.880970i
$544$	−2.09310	+	3.62535i	−0.0897408	+	0.155436i
$545$	−19.4838	+	7.09152i	−0.834594	+	0.303767i
$546$	−0.189541	−	1.07494i	−0.00811162	−	0.0460033i
$547$	−2.51748	+	14.2773i	−0.107640	+	0.610454i	0.882494	+	0.470324i	$0.155863\pi$
$547$	−2.51748	+	14.2773i	−0.107640	+	0.610454i	−0.990133	+	0.140130i	$0.955248\pi$
$548$	−10.0658	−	3.66363i	−0.429988	−	0.156503i
$549$	−40.3409	+	33.8500i	−1.72171	+	1.44468i
$550$	2.86106			0.121996
$551$		0			0
$552$	−18.0937			−0.770120
$553$	−8.43646	+	7.07903i	−0.358755	+	0.301031i
$554$	−25.7856	−	9.38520i	−1.09553	−	0.398739i
$555$	4.52648	−	25.6709i	0.192138	−	1.08967i
$556$	−1.87789	−	10.6500i	−0.0796403	−	0.451662i
$557$	4.07640	−	1.48369i	0.172723	−	0.0628659i	−0.254211	−	0.967149i	$-0.581816\pi$
$557$	4.07640	−	1.48369i	0.172723	−	0.0628659i	0.426934	+	0.904283i	$0.359594\pi$
$558$	−15.4755	+	26.8044i	−0.655131	+	1.13472i
$559$	0.150525	+	0.260717i	0.00636654	+	0.0110272i
$560$	2.30627	+	1.93519i	0.0974577	+	0.0817767i
$561$	51.5674	+	43.2702i	2.17718	+	1.82687i
$562$	−8.13574	−	14.0915i	−0.343185	−	0.594415i
$563$	13.6468	−	23.6370i	0.575144	−	0.996179i	−0.420882	−	0.907116i	$-0.638279\pi$
$563$	13.6468	−	23.6370i	0.575144	−	0.996179i	0.996026	−	0.0890637i	$-0.0283875\pi$
$564$	11.5360	−	4.19876i	0.485754	−	0.176800i
$565$	5.80172	+	32.9032i	0.244080	+	1.38425i
$566$	0.589317	−	3.34218i	0.0247708	−	0.140482i
$567$	−0.400713	−	0.145848i	−0.0168284	−	0.00612502i
$568$	−3.38262	+	2.83835i	−0.141932	+	0.119095i
$569$	−7.19043			−0.301439			−0.150719	−	0.988577i	$-0.548159\pi$
$569$	−7.19043			−0.301439			−0.150719	+	0.988577i	$0.548159\pi$
$570$		0			0
$571$	42.0134			1.75821			0.879103	−	0.476631i	$-0.158142\pi$
$571$	42.0134			1.75821			0.879103	+	0.476631i	$0.158142\pi$
$572$	1.34174	−	1.12585i	0.0561009	−	0.0470743i
$573$	58.7478	+	21.3825i	2.45423	+	0.893265i
$574$	1.11872	−	6.34459i	0.0466946	−	0.264818i
$575$	−0.559015	−	3.17033i	−0.0233125	−	0.132212i
$576$	−4.51450	+	1.64314i	−0.188104	+	0.0684643i
$577$	−10.8357	+	18.7679i	−0.451095	+	0.781319i	−0.998454	−	0.0555783i	$-0.982300\pi$
$577$	−10.8357	+	18.7679i	−0.451095	+	0.781319i	0.547359	+	0.836898i	$0.315633\pi$
$578$	−0.262102	−	0.453974i	−0.0109020	−	0.0188828i
$579$	15.8963	+	13.3386i	0.660630	+	0.554334i
$580$	5.61725	+	4.71343i	0.233244	+	0.195715i
$581$	−6.26929	−	10.8587i	−0.260094	−	0.450496i
$582$	−24.2376	+	41.9807i	−1.00468	+	1.74016i
$583$	−17.7993	+	6.47843i	−0.737173	+	0.268309i
$584$	−0.393642	−	2.23245i	−0.0162890	−	0.0923796i
$585$	−0.595162	+	3.37533i	−0.0246069	+	0.139553i
$586$	−21.9684	−	7.99585i	−0.907507	−	0.330306i
$587$	−0.971838	+	0.815469i	−0.0401121	+	0.0336580i	−0.662623	−	0.748953i	$-0.730557\pi$
$587$	−0.971838	+	0.815469i	−0.0401121	+	0.0336580i	0.622511	+	0.782611i	$0.286112\pi$
$588$	−14.9490			−0.616485
$589$		0			0
$590$	−7.76934			−0.319859
$591$	18.2663	−	15.3272i	0.751374	−	0.630477i
$592$	3.73979	+	1.36117i	0.153704	+	0.0559438i
$593$	3.74385	−	21.2325i	0.153742	−	0.871912i	−0.806185	−	0.591663i	$-0.798472\pi$
$593$	3.74385	−	21.2325i	0.153742	−	0.871912i	0.959927	−	0.280250i	$-0.0904172\pi$
$594$	5.03806	+	28.5722i	0.206714	+	1.17233i
$595$	−11.8430	+	4.31049i	−0.485515	+	0.176713i
$596$	4.66692	−	8.08334i	0.191165	−	0.331107i
$597$	8.88262	+	15.3852i	0.363542	+	0.629672i
$598$	−1.50971	−	1.26680i	−0.0617367	−	0.0518032i
$599$	−21.9408	−	18.4106i	−0.896479	−	0.752235i	0.0730202	−	0.997330i	$-0.476736\pi$
$599$	−21.9408	−	18.4106i	−0.896479	−	0.752235i	−0.969499	+	0.245096i	$0.921181\pi$
$600$	−0.694265	−	1.20250i	−0.0283433	−	0.0490920i
$601$	−3.77932	+	6.54598i	−0.154162	+	0.267016i	−0.932754	−	0.360515i	$-0.882601\pi$
$601$	−3.77932	+	6.54598i	−0.154162	+	0.267016i	0.778592	+	0.627531i	$0.215934\pi$
$602$	−1.19382	+	0.434516i	−0.0486566	+	0.0177096i
$603$	−3.65467	−	20.7267i	−0.148830	−	0.844055i
$604$	3.44226	−	19.5220i	0.140063	−	0.794339i
$605$	48.7652	+	17.7491i	1.98259	+	0.721603i
$606$	7.86816	−	6.60217i	0.319622	−	0.268195i
$607$	1.72737			0.0701117			0.0350558	−	0.999385i	$-0.488839\pi$
$607$	1.72737			0.0701117			0.0350558	+	0.999385i	$0.488839\pi$
$608$		0			0
$609$	11.2192			0.454625
$610$	19.6873	−	16.5196i	0.797116	−	0.668860i
$611$	1.25651	+	0.457334i	0.0508331	+	0.0185017i
$612$	3.49231	−	19.8059i	0.141168	−	0.800605i
$613$	−4.76090	−	27.0004i	−0.192291	−	1.09054i	−0.916224	−	0.400666i	$-0.868779\pi$
$613$	−4.76090	−	27.0004i	−0.192291	−	1.09054i	0.723933	−	0.689870i	$-0.242332\pi$
$614$	1.30431	−	0.474731i	0.0526378	−	0.0191586i
$615$	−16.4308	+	28.4590i	−0.662555	+	1.14758i
$616$	3.69572	+	6.40117i	0.148905	+	0.257911i
$617$	8.14114	+	6.83123i	0.327750	+	0.275015i	0.791782	−	0.610803i	$-0.209153\pi$
$617$	8.14114	+	6.83123i	0.327750	+	0.275015i	−0.464032	+	0.885818i	$0.653598\pi$
$618$	40.6894	+	34.1425i	1.63677	+	1.37341i
$619$	−4.18004	−	7.24004i	−0.168010	−	0.291002i	0.769710	−	0.638394i	$-0.220401\pi$
$619$	−4.18004	−	7.24004i	−0.168010	−	0.291002i	−0.937720	+	0.347392i	$0.887067\pi$
$620$	7.55242	−	13.0812i	0.303313	−	0.525353i
$621$	30.6764	−	11.1653i	1.23100	−	0.448048i
$622$	−2.11681	−	12.0051i	−0.0848765	−	0.481359i
$623$	3.36173	−	19.0653i	0.134685	−	0.763837i
$624$	−0.798781	−	0.290732i	−0.0319768	−	0.0116386i
$625$	−20.8656	+	17.5083i	−0.834625	+	0.700334i
$626$	16.5314			0.660728
$627$		0			0
$628$	13.8676			0.553379
$629$	−12.7624	+	10.7090i	−0.508872	+	0.426994i
$630$	−13.5914	−	4.94688i	−0.541496	−	0.197088i
$631$	4.25962	−	24.1575i	0.169573	−	0.961694i	−0.774651	−	0.632389i	$-0.782074\pi$
$631$	4.25962	−	24.1575i	0.169573	−	0.961694i	0.944224	−	0.329305i	$-0.106814\pi$
$632$	1.48931	+	8.44629i	0.0592415	+	0.335975i
$633$	36.6410	−	13.3362i	1.45635	−	0.530068i
$634$	−1.34406	+	2.32797i	−0.0533793	+	0.0924557i
$635$	2.61437	+	4.52823i	0.103748	+	0.179697i
$636$	7.04206	+	5.90899i	0.279236	+	0.234307i
$637$	−1.24732	−	1.04662i	−0.0494206	−	0.0414688i
$638$	9.00145	+	15.5910i	0.356371	+	0.617253i
$639$	10.6070	−	18.3719i	0.419606	−	0.726780i
$640$	2.20318	−	0.801892i	0.0870884	−	0.0316976i
$641$	−1.21080	−	6.86677i	−0.0478236	−	0.271221i	0.951514	−	0.307605i	$-0.0995274\pi$
$641$	−1.21080	−	6.86677i	−0.0478236	−	0.271221i	−0.999338	+	0.0363834i	$0.988416\pi$
$642$	4.86913	−	27.6142i	0.192169	−	1.08985i
$643$	8.54203	+	3.10905i	0.336865	+	0.122609i	0.504914	−	0.863170i	$-0.331524\pi$
$643$	8.54203	+	3.10905i	0.336865	+	0.122609i	−0.168049	+	0.985779i	$0.553747\pi$
$644$	6.37101	−	5.34592i	0.251053	−	0.210659i
$645$	6.48025			0.255160
$646$		0			0
$647$	30.0074			1.17971			0.589856	−	0.807509i	$-0.299185\pi$
$647$	30.0074			1.17971			0.589856	+	0.807509i	$0.299185\pi$
$648$	−0.254396	+	0.213463i	−0.00999361	+	0.00838563i
$649$	−17.9243	−	6.52392i	−0.703591	−	0.256086i
$650$	0.0262626	−	0.148943i	0.00103010	−	0.00584201i
$651$	−4.01309	−	22.7594i	−0.157285	−	0.892010i
$652$	−13.3902	+	4.87365i	−0.524402	+	0.190867i
$653$	−5.20956	+	9.02323i	−0.203866	+	0.353106i	−0.949771	−	0.312946i	$-0.898684\pi$
$653$	−5.20956	+	9.02323i	−0.203866	+	0.353106i	0.745905	+	0.666053i	$0.232017\pi$
$654$	12.3526	+	21.3953i	0.483025	+	0.836623i
$655$	−2.73476	−	2.29474i	−0.106856	−	0.0896629i
$656$	−3.84339	−	3.22499i	−0.150059	−	0.125915i
$657$	5.44533	+	9.43159i	0.212443	+	0.367962i
$658$	−2.82141	+	4.88683i	−0.109990	+	0.190508i
$659$	24.7850	−	9.02099i	0.965485	−	0.351408i	0.189304	−	0.981918i	$-0.439377\pi$
$659$	24.7850	−	9.02099i	0.965485	−	0.351408i	0.776181	+	0.630511i	$0.217154\pi$
$660$	−6.54691	−	37.1294i	−0.254838	−	1.44526i
$661$	−4.28806	+	24.3188i	−0.166786	+	0.945891i	0.780418	+	0.625259i	$0.215007\pi$
$661$	−4.28806	+	24.3188i	−0.166786	+	0.945891i	−0.947204	+	0.320632i	$0.896105\pi$
$662$	−4.89865	−	1.78296i	−0.190391	−	0.0692968i
$663$	2.72593	−	2.28733i	0.105866	−	0.0888325i
$664$	−9.76464			−0.378942
$665$		0			0
$666$	−19.1198			−0.740879
$667$	15.5175	−	13.0207i	0.600841	−	0.504165i
$668$	−10.8911	−	3.96405i	−0.421391	−	0.153374i
$669$	4.32907	−	24.5514i	0.167372	−	0.949211i
$670$	1.78357	+	10.1151i	0.0689052	+	0.390781i
$671$	59.2913	−	21.5803i	2.28892	−	0.833097i
$672$	1.79360	−	3.10661i	0.0691898	−	0.119840i
$673$	4.88690	+	8.46436i	0.188376	+	0.326277i	0.944709	−	0.327910i	$-0.106344\pi$
$673$	4.88690	+	8.46436i	0.188376	+	0.326277i	−0.756333	+	0.654187i	$0.773011\pi$
$674$	−20.4744	−	17.1801i	−0.788646	−	0.661752i
$675$	1.91911	+	1.61033i	0.0738667	+	0.0619815i
$676$	6.45371	+	11.1781i	0.248219	+	0.429929i
$677$	10.7874	−	18.6843i	0.414592	−	0.718094i	−0.580794	−	0.814051i	$-0.697258\pi$
$677$	10.7874	−	18.6843i	0.414592	−	0.718094i	0.995386	+	0.0959565i	$0.0305910\pi$
$678$	37.4087	−	13.6157i	1.43667	−	0.522906i
$679$	−3.86915	−	21.9431i	−0.148485	−	0.842098i
$680$	−1.70433	+	9.66574i	−0.0653581	+	0.370664i
$681$	1.73205	+	0.630414i	0.0663723	+	0.0241575i
$682$	28.4081	−	23.8373i	1.08780	−	0.912776i
$683$	33.2509			1.27231			0.636155	−	0.771561i	$-0.280524\pi$
$683$	33.2509			1.27231			0.636155	+	0.771561i	$0.280524\pi$
$684$		0			0
$685$	−25.1145			−0.959576
$686$	12.1493	−	10.1945i	0.463864	−	0.389228i
$687$	18.3026	+	6.66161i	0.698288	+	0.254156i
$688$	−0.171804	+	0.974348i	−0.00654996	+	0.0371467i
$689$	0.173871	+	0.986073i	0.00662397	+	0.0375664i
$690$	−39.8637	+	14.5092i	−1.51759	+	0.552356i
$691$	−2.40466	+	4.16500i	−0.0914776	+	0.158444i	−0.908133	−	0.418682i	$-0.862492\pi$
$691$	−2.40466	+	4.16500i	−0.0914776	+	0.158444i	0.816655	+	0.577126i	$0.195826\pi$
$692$	−1.99176	−	3.44983i	−0.0757155	−	0.131143i
$693$	−27.2023	−	22.8255i	−1.03333	−	0.867068i
$694$	−25.0253	−	20.9987i	−0.949947	−	0.797100i
$695$	−12.6775	−	21.9581i	−0.480886	−	0.832919i
$696$	4.36858	−	7.56661i	0.165591	−	0.286811i
$697$	19.7363	−	7.18342i	0.747565	−	0.272091i
$698$	−5.05416	−	28.6636i	−0.191303	−	1.08493i
$699$	−14.3638	+	81.4611i	−0.543288	+	3.08114i
$700$	0.599747	+	0.218290i	0.0226683	+	0.00825059i
$701$	2.65409	−	2.22704i	0.100243	−	0.0841143i	−0.591289	−	0.806460i	$-0.701381\pi$
$701$	2.65409	−	2.22704i	0.100243	−	0.0841143i	0.691532	+	0.722346i	$0.256936\pi$
$702$	1.53367			0.0578848
$703$		0			0
$704$	5.75621			0.216946
$705$	22.0490	−	18.5013i	0.830412	−	0.696798i
$706$	13.4422	+	4.89256i	0.505904	+	0.184134i
$707$	−0.819816	+	4.64941i	−0.0308323	+	0.174859i
$708$	1.60752	+	9.11667i	0.0604141	+	0.342626i
$709$	−19.3335	+	7.03682i	−0.726085	+	0.264273i	−0.678507	−	0.734594i	$-0.737373\pi$
$709$	−19.3335	+	7.03682i	−0.726085	+	0.264273i	−0.0475785	+	0.998868i	$0.515150\pi$
$710$	−5.17647	+	8.96591i	−0.194269	+	0.336484i
$711$	−20.6019	−	35.6836i	−0.772633	−	1.33824i
$712$	−11.5493	−	9.69101i	−0.432828	−	0.363186i
$713$	−31.9646	−	26.8215i	−1.19708	−	1.00447i
$714$	7.50837	+	13.0049i	0.280994	+	0.486696i
$715$	2.05328	−	3.55639i	0.0767884	−	0.133001i
$716$	7.94124	−	2.89038i	0.296778	−	0.108018i
$717$	−11.9837	−	67.9631i	−0.447540	−	2.53813i
$718$	3.41578	−	19.3719i	0.127476	−	0.722951i
$719$	−22.7298	−	8.27297i	−0.847678	−	0.308530i	−0.118585	−	0.992944i	$-0.537836\pi$
$719$	−22.7298	−	8.27297i	−0.847678	−	0.308530i	−0.729093	+	0.684414i	$0.760058\pi$
$720$	−8.62863	+	7.24028i	−0.321570	+	0.269829i
$721$	−24.4149			−0.909257
$722$		0			0
$723$	76.9880			2.86321
$724$	6.50009	−	5.45422i	0.241574	−	0.202705i
$725$	1.46077	+	0.531677i	0.0542516	+	0.0197460i
$726$	10.7373	−	60.8943i	0.398499	−	2.26000i
$727$	3.14783	+	17.8522i	0.116747	+	0.662103i	0.985871	+	0.167508i	$0.0535722\pi$
$727$	3.14783	+	17.8522i	0.116747	+	0.662103i	−0.869124	+	0.494594i	$0.835317\pi$
$728$	0.367159	−	0.133635i	0.0136078	−	0.00495284i
$729$	21.9186	−	37.9641i	0.811800	−	1.40608i
$730$	−2.65745	−	4.60284i	−0.0983567	−	0.170359i
$731$	−3.17275	−	2.66225i	−0.117348	−	0.0984669i
$732$	−23.4578	−	19.6834i	−0.867025	−	0.727520i
$733$	−11.3682	−	19.6902i	−0.419893	−	0.727275i	0.576036	−	0.817425i	$-0.304599\pi$
$733$	−11.3682	−	19.6902i	−0.419893	−	0.727275i	−0.995928	+	0.0901491i	$0.971266\pi$
$734$	−4.77527	+	8.27100i	−0.176258	+	0.305288i
$735$	−32.9353	+	11.9875i	−1.21484	+	0.442164i
$736$	−1.12469	−	6.37844i	−0.0414566	−	0.235112i
$737$	−4.37887	+	24.8338i	−0.161298	+	0.914765i
$738$	22.6501	+	8.24395i	0.833760	+	0.303464i
$739$	11.6275	−	9.75665i	0.427725	−	0.358904i	−0.403367	−	0.915038i	$-0.632160\pi$
$739$	11.6275	−	9.75665i	0.427725	−	0.358904i	0.831093	+	0.556134i	$0.187716\pi$
$740$	9.33094			0.343012
$741$		0			0
$742$	−4.22545			−0.155121
$743$	−2.50975	+	2.10593i	−0.0920739	+	0.0772592i	−0.687663	−	0.726030i	$-0.741363\pi$
$743$	−2.50975	+	2.10593i	−0.0920739	+	0.0772592i	0.595589	+	0.803289i	$0.296919\pi$
$744$	−16.9123	−	6.15557i	−0.620035	−	0.225674i
$745$	3.80010	−	21.5514i	0.139225	−	0.789584i
$746$	0.632097	+	3.58480i	0.0231427	+	0.131249i
$747$	44.0824	−	16.0447i	1.61289	−	0.587045i
$748$	−12.0483	+	20.8683i	−0.440530	+	0.763020i
$749$	6.44433	+	11.1619i	0.235471	+	0.407847i
$750$	22.5934	+	18.9581i	0.824994	+	0.692252i
$751$	40.0123	+	33.5743i	1.46007	+	1.22514i	0.924796	+	0.380464i	$0.124236\pi$
$751$	40.0123	+	33.5743i	1.46007	+	1.22514i	0.535273	+	0.844679i	$0.320209\pi$
$752$	2.19723	+	3.80571i	0.0801246	+	0.138780i
$753$	4.17442	−	7.23030i	0.152124	−	0.263487i
$754$	0.894269	−	0.325487i	0.0325674	−	0.0118536i
$755$	−8.07063	−	45.7708i	−0.293720	−	1.66577i
$756$	−1.12387	+	6.37381i	−0.0408749	+	0.231813i
$757$	22.7727	+	8.28859i	0.827688	+	0.301254i	0.720910	−	0.693029i	$-0.243724\pi$
$757$	22.7727	+	8.28859i	0.827688	+	0.301254i	0.106778	+	0.994283i	$0.465946\pi$
$758$	6.39449	−	5.36561i	0.232258	−	0.194888i
$759$	−104.151			−3.78045
$760$		0			0
$761$	−24.8054			−0.899195			−0.449597	−	0.893231i	$-0.648433\pi$
$761$	−24.8054			−0.899195			−0.449597	+	0.893231i	$0.648433\pi$
$762$	4.77257	−	4.00466i	0.172892	−	0.145074i
$763$	−10.6709	−	3.88389i	−0.386312	−	0.140606i
$764$	−3.88608	+	22.0390i	−0.140593	+	0.797344i
$765$	−8.18799	−	46.4364i	−0.296037	−	1.67891i
$766$	8.91361	−	3.24429i	0.322062	−	0.117221i
$767$	−0.504158	+	0.873228i	−0.0182041	+	0.0315304i
$768$	−1.39680	−	2.41933i	−0.0504028	−	0.0873001i
$769$	7.38689	+	6.19833i	0.266378	+	0.223518i	0.766186	−	0.642618i	$-0.222152\pi$
$769$	7.38689	+	6.19833i	0.266378	+	0.223518i	−0.499809	+	0.866136i	$0.666596\pi$
$770$	13.2754	+	11.1394i	0.478412	+	0.401435i
$771$	−19.7400	−	34.1906i	−0.710918	−	1.23135i
$772$	−3.71406	+	6.43293i	−0.133672	+	0.231526i
$773$	−1.20968	+	0.440286i	−0.0435090	+	0.0158360i	−0.363683	−	0.931523i	$-0.618481\pi$
$773$	−1.20968	+	0.440286i	−0.0435090	+	0.0158360i	0.320174	+	0.947359i	$0.396259\pi$
$774$	−0.825384	−	4.68099i	−0.0296678	−	0.168255i
$775$	0.556049	−	3.15351i	0.0199739	−	0.113277i
$776$	−16.3057	−	5.93480i	−0.585341	−	0.213047i
$777$	10.9363	−	9.17667i	0.392339	−	0.329211i
$778$	36.0480			1.29238
$779$		0			0
$780$	−1.99300			−0.0713607
$781$	−19.4711	+	16.3382i	−0.696730	+	0.584626i
$782$	25.4781	+	9.27329i	0.911097	+	0.331612i
$783$	−2.73736	+	15.5243i	−0.0978252	+	0.554794i
$784$	−0.929216	−	5.26985i	−0.0331863	−	0.188209i
$785$	30.5529	−	11.1203i	1.09048	−	0.396902i
$786$	−2.12685	+	3.68381i	−0.0758621	+	0.131397i
$787$	8.17232	+	14.1549i	0.291312	+	0.504567i	0.974120	−	0.226031i	$-0.0725749\pi$
$787$	8.17232	+	14.1549i	0.291312	+	0.504567i	−0.682808	+	0.730598i	$0.739242\pi$
$788$	6.53860	+	5.48654i	0.232928	+	0.195450i
$789$	16.1976	+	13.5914i	0.576649	+	0.483866i
$790$	10.0542	+	17.4144i	0.357714	+	0.619578i
$791$	−9.14922	+	15.8469i	−0.325309	+	0.563451i
$792$	−25.9864	+	9.45828i	−0.923387	+	0.336085i
$793$	−0.579183	−	3.28471i	−0.0205674	−	0.116643i
$794$	−1.11292	+	6.31169i	−0.0394961	+	0.223994i
$795$	20.2533	+	7.37160i	0.718311	+	0.261444i
$796$	−4.87147	+	4.08765i	−0.172665	+	0.144883i
$797$	−15.6884			−0.555712			−0.277856	−	0.960623i	$-0.589624\pi$
$797$	−15.6884			−0.555712			−0.277856	+	0.960623i	$0.589624\pi$
$798$		0			0
$799$	−18.3960			−0.650804
$800$	0.380754	−	0.319491i	0.0134617	−	0.0112957i
$801$	68.0629	+	24.7729i	2.40489	+	0.875307i
$802$	0.0325868	−	0.184809i	0.00115068	−	0.00652583i
$803$	−2.26589	−	12.8505i	−0.0799614	−	0.453484i
$804$	11.5002	−	4.18573i	0.405581	−	0.147619i
$805$	9.74965	−	16.8869i	0.343630	−	0.595185i
$806$	−0.980164	−	1.69769i	−0.0345248	−	0.0597987i
$807$	−16.4156	−	13.7743i	−0.577856	−	0.484879i
$808$	2.81649	+	2.36332i	0.0990838	+	0.0831412i
$809$	5.76242	+	9.98080i	0.202596	+	0.350906i	0.949364	−	0.314178i	$-0.101729\pi$
$809$	5.76242	+	9.98080i	0.202596	+	0.350906i	−0.746768	+	0.665084i	$0.768396\pi$
$810$	−0.389305	+	0.674297i	−0.0136788	+	0.0236924i
$811$	7.80041	−	2.83912i	0.273909	−	0.0996948i	−0.201413	−	0.979506i	$-0.564553\pi$
$811$	7.80041	−	2.83912i	0.273909	−	0.0996948i	0.475323	+	0.879811i	$0.342331\pi$
$812$	0.697377	+	3.95502i	0.0244731	+	0.138794i
$813$	5.65869	−	32.0920i	0.198459	−	1.12552i
$814$	21.5270	+	7.83519i	0.754521	+	0.274623i
$815$	−25.5930	+	21.4751i	−0.896483	+	0.752239i
$816$	11.6946			0.409392
$817$		0			0
$818$	17.2663			0.603701
$819$	−1.43796	+	1.20659i	−0.0502463	+	0.0421617i
$820$	−11.0538	−	4.02324i	−0.386014	−	0.140498i
$821$	−5.85390	+	33.1991i	−0.204302	+	1.15866i	0.694231	+	0.719752i	$0.255744\pi$
$821$	−5.85390	+	33.1991i	−0.204302	+	1.15866i	−0.898534	+	0.438904i	$0.855367\pi$
$822$	5.19632	+	29.4698i	0.181242	+	1.02788i
$823$	−20.5490	+	7.47921i	−0.716292	+	0.260709i	−0.674351	−	0.738411i	$-0.735576\pi$
$823$	−20.5490	+	7.47921i	−0.716292	+	0.260709i	−0.0419413	+	0.999120i	$0.513354\pi$
$824$	−9.50676	+	16.4662i	−0.331184	+	0.573627i
$825$	−3.99634	−	6.92186i	−0.139135	−	0.240988i
$826$	−3.25961	−	2.73514i	−0.113416	−	0.0951676i
$827$	30.0056	+	25.1777i	1.04340	+	0.875513i	0.992384	−	0.123185i	$-0.0393108\pi$
$827$	30.0056	+	25.1777i	1.04340	+	0.875513i	0.0510122	+	0.998698i	$0.483755\pi$
$828$	15.5581	+	26.9474i	0.540681	+	0.936487i
$829$	7.20878	−	12.4860i	0.250371	−	0.433656i	−0.713257	−	0.700903i	$-0.752781\pi$
$829$	7.20878	−	12.4860i	0.250371	−	0.433656i	0.963628	+	0.267247i	$0.0861140\pi$
$830$	−21.5133	+	7.83019i	−0.746737	+	0.271790i
$831$	13.3115	+	75.4933i	0.461771	+	2.61883i
$832$	0.0528381	−	0.299660i	0.00183183	−	0.0103888i
$833$	21.0500	+	7.66156i	0.729338	+	0.265457i
$834$	−23.1430	+	19.4192i	−0.801375	+	0.672433i
$835$	−27.1739			−0.940392
$836$		0			0
$837$	32.4719			1.12239
$838$	−1.32198	+	1.10927i	−0.0456669	+	0.0383191i
$839$	−19.6896	−	7.16642i	−0.679760	−	0.247412i	−0.0210154	−	0.999779i	$-0.506690\pi$
$839$	−19.6896	−	7.16642i	−0.679760	−	0.247412i	−0.658744	+	0.752367i	$0.728912\pi$
$840$	1.46047	−	8.28271i	0.0503908	−	0.285781i
$841$	−3.33724	−	18.9264i	−0.115077	−	0.652635i
$842$	−30.7792	+	11.2027i	−1.06072	+	0.386071i
$843$	−22.7280	+	39.3661i	−0.782795	+	1.35584i
$844$	6.97890	+	12.0878i	0.240224	+	0.416079i
$845$	23.1824	+	19.4523i	0.797497	+	0.669180i
$846$	−16.1727	−	13.5705i	−0.556028	−	0.466563i
$847$	14.2109	+	24.6140i	0.488293	+	0.845748i
$848$	−1.64532	+	2.84978i	−0.0565006	+	0.0978619i
$849$	−8.90901	+	3.24261i	−0.305756	+	0.111286i
$850$	0.361310	+	2.04909i	0.0123928	+	0.0702832i
$851$	4.47604	−	25.3849i	0.153437	−	0.870183i
$852$	11.5918	+	4.21906i	0.397128	+	0.144543i
$853$	39.8001	−	33.3962i	1.36273	−	1.14347i	0.387599	−	0.921828i	$-0.373304\pi$
$853$	39.8001	−	33.3962i	1.36273	−	1.14347i	0.975129	−	0.221637i	$-0.0711401\pi$
$854$	14.0754			0.481650
$855$		0			0
$856$	10.0373			0.343067
$857$	22.3558	−	18.7588i	0.763660	−	0.640787i	−0.175416	−	0.984494i	$-0.556127\pi$
$857$	22.3558	−	18.7588i	0.763660	−	0.640787i	0.939077	+	0.343707i	$0.111683\pi$
$858$	−4.59795	−	1.67352i	−0.156972	−	0.0571330i
$859$	3.81876	−	21.6572i	0.130294	−	0.738936i	−0.847727	−	0.530432i	$-0.822030\pi$
$859$	3.81876	−	21.6572i	0.130294	−	0.738936i	0.978022	−	0.208503i	$-0.0668593\pi$
$860$	0.402807	+	2.28443i	0.0137356	+	0.0778985i
$861$	−16.9123	+	6.15557i	−0.576370	+	0.209781i
$862$	12.7560	−	22.0940i	0.434470	−	0.752524i
$863$	17.9079	+	31.0173i	0.609590	+	1.05584i	0.991308	+	0.131562i	$0.0419994\pi$
$863$	17.9079	+	31.0173i	0.609590	+	1.05584i	−0.381717	+	0.924279i	$0.624667\pi$
$864$	3.86109	+	3.23984i	0.131357	+	0.110222i
$865$	−7.15461	−	6.00343i	−0.243264	−	0.204123i
$866$	−12.2417	−	21.2032i	−0.415990	−	0.720516i
$867$	−0.732209	+	1.26822i	−0.0248671	+	0.0430711i
$868$	7.77373	−	2.82941i	0.263858	−	0.0960363i
$869$	8.57278	+	48.6187i	0.290812	+	1.64928i
$870$	3.55717	−	20.1737i	0.120599	−	0.683954i
$871$	1.25261	+	0.455914i	0.0424432	+	0.0154481i
$872$	−6.77450	+	5.68448i	−0.229413	+	0.192501i
$873$	83.3638			2.82144
$874$		0			0
$875$	−13.5567			−0.458300
$876$	−4.85121	+	4.07065i	−0.163907	+	0.137534i
$877$	−7.35293	−	2.67625i	−0.248291	−	0.0903705i	0.214877	−	0.976641i	$-0.431065\pi$
$877$	−7.35293	−	2.67625i	−0.248291	−	0.0903705i	−0.463168	+	0.886271i	$0.653287\pi$
$878$	−5.35510	+	30.3703i	−0.180726	+	1.02495i
$879$	11.3409	+	64.3175i	0.382520	+	2.16938i
$880$	12.6820	−	4.61587i	0.427510	−	0.155601i
$881$	7.24145	−	12.5426i	0.243970	−	0.422569i	−0.717871	−	0.696176i	$-0.754883\pi$
$881$	7.24145	−	12.5426i	0.243970	−	0.422569i	0.961842	+	0.273607i	$0.0882167\pi$
$882$	12.8540	+	22.2639i	0.432818	+	0.749663i
$883$	−18.0426	−	15.1395i	−0.607181	−	0.509486i	0.286563	−	0.958061i	$-0.407487\pi$
$883$	−18.0426	−	15.1395i	−0.607181	−	0.509486i	−0.893745	+	0.448576i	$0.851932\pi$
$884$	0.975776	+	0.818773i	0.0328189	+	0.0275383i
$885$	10.8522	+	18.7966i	0.364794	+	0.631842i
$886$	−5.35234	+	9.27052i	−0.179815	+	0.311449i
$887$	14.9163	−	5.42908i	0.500840	−	0.182291i	−0.0792320	−	0.996856i	$-0.525247\pi$
$887$	14.9163	−	5.42908i	0.500840	−	0.182291i	0.580072	+	0.814566i	$0.303025\pi$
$888$	−1.93062	−	10.9491i	−0.0647872	−	0.367427i
$889$	−0.497273	+	2.82018i	−0.0166780	+	0.0945857i
$890$	−33.2163	−	12.0898i	−1.11341	−	0.405250i
$891$	−1.46436	+	1.22874i	−0.0490578	+	0.0411644i
$892$	8.92400			0.298798
$893$		0			0
$894$	−26.0751			−0.872081
$895$	15.1782	−	12.7360i	0.507352	−	0.425719i
$896$	1.20664	+	0.439181i	0.0403110	+	0.0146720i
$897$	−0.956038	+	5.42196i	−0.0319212	+	0.181034i
$898$	0.402103	+	2.28044i	0.0134183	+	0.0760992i
$899$	18.9340	−	6.89143i	0.631486	−	0.229842i
$900$	−1.19394	+	2.06797i	−0.0397981	+	0.0689324i
$901$	−6.88763	−	11.9297i	−0.229460	−	0.397437i
$902$	−22.1234	−	18.5637i	−0.736627	−	0.618104i
$903$	2.71877	+	2.28132i	0.0904751	+	0.0759176i
$904$	7.12512	+	12.3411i	0.236978	+	0.410458i
$905$	9.94718	−	17.2290i	0.330655	−	0.572712i
$906$	−52.0384	+	18.9404i	−1.72886	+	0.629253i
$907$	7.81637	+	44.3289i	0.259538	+	1.47192i	0.784149	+	0.620573i	$0.213100\pi$
$907$	7.81637	+	44.3289i	0.259538	+	1.47192i	−0.524610	+	0.851343i	$0.675789\pi$
$908$	−0.114572	+	0.649772i	−0.00380222	+	0.0215634i
$909$	−16.5983	−	6.04129i	−0.550531	−	0.200377i
$910$	0.701758	−	0.588844i	0.0232630	−	0.0195200i
$911$	−2.75901			−0.0914100			−0.0457050	−	0.998955i	$-0.514553\pi$
$911$	−2.75901			−0.0914100			−0.0457050	+	0.998955i	$0.514553\pi$
$912$		0			0
$913$	−56.2074			−1.86019
$914$	−0.0399729	+	0.0335413i	−0.00132219	+	0.00110945i
$915$	−67.4658	−	24.5555i	−2.23035	−	0.811781i
$916$	−1.21069	+	6.86616i	−0.0400023	+	0.226864i
$917$	−0.339518	−	1.92550i	−0.0112119	−	0.0635858i
$918$	−19.8272	+	7.21650i	−0.654394	+	0.238180i
$919$	19.6542	−	34.0420i	0.648331	−	1.12294i	−0.335191	−	0.942150i	$-0.608801\pi$
$919$	19.6542	−	34.0420i	0.648331	−	1.12294i	0.983521	−	0.180792i	$-0.0578660\pi$
$920$	−7.59272	−	13.1510i	−0.250325	−	0.433575i
$921$	−2.97040	−	2.49246i	−0.0978780	−	0.0821294i
$922$	30.2373	+	25.3721i	0.995813	+	0.835587i
$923$	0.671809	+	1.16361i	0.0221129	+	0.0383006i
$924$	10.3244	−	17.8823i	0.339647	−	0.588286i
$925$	1.85882	−	0.676555i	0.0611176	−	0.0222450i
$926$	−1.07498	−	6.09652i	−0.0353260	−	0.200344i
$927$	15.8619	−	89.9575i	0.520974	−	2.95459i
$928$	2.93894	+	1.06969i	0.0964756	+	0.0351142i
$929$	−22.7835	+	19.1176i	−0.747502	+	0.627229i	−0.934841	−	0.355067i	$-0.884458\pi$
$929$	−22.7835	+	19.1176i	−0.747502	+	0.627229i	0.187339	+	0.982295i	$0.440014\pi$
$930$	−42.1970			−1.38369
$931$		0			0
$932$	−29.6097			−0.969898
$933$	−26.0874	+	21.8900i	−0.854064	+	0.716645i
$934$	19.7299	+	7.18111i	0.645583	+	0.234973i
$935$	−9.81049	+	55.6381i	−0.320837	+	1.81956i
$936$	0.253846	+	1.43963i	0.00829722	+	0.0470559i
$937$	−35.4462	+	12.9014i	−1.15798	+	0.421470i	−0.848375	−	0.529396i	$-0.822419\pi$
$937$	−35.4462	+	12.9014i	−1.15798	+	0.421470i	−0.309604	+	0.950866i	$0.600196\pi$
$938$	−2.81266	+	4.87166i	−0.0918365	+	0.159065i
$939$	−23.0911	−	39.9950i	−0.753550	−	1.30519i
$940$	7.89266	+	6.62272i	0.257430	+	0.216009i
$941$	−4.96130	−	4.16303i	−0.161734	−	0.135711i	0.558329	−	0.829620i	$-0.311443\pi$
$941$	−4.96130	−	4.16303i	−0.161734	−	0.135711i	−0.720063	+	0.693909i	$0.755887\pi$
$942$	−19.3703	−	33.5504i	−0.631120	−	1.09313i
$943$	−16.2477	+	28.1419i	−0.529099	+	0.916427i
$944$	−3.11391	+	1.13337i	−0.101349	+	0.0368880i
$945$	2.63501	+	14.9439i	0.0857169	+	0.486125i
$946$	−0.988939	+	5.60855i	−0.0321532	+	0.182350i
$947$	−15.3088	−	5.57195i	−0.497469	−	0.181064i	0.0810862	−	0.996707i	$-0.474161\pi$
$947$	−15.3088	−	5.57195i	−0.497469	−	0.181064i	−0.578555	+	0.815643i	$0.696383\pi$
$948$	18.3541	−	15.4009i	0.596114	−	0.500199i
$949$	−0.689776			−0.0223911
$950$		0			0
$951$	7.50953			0.243513
$952$	−4.11780	+	3.45524i	−0.133459	+	0.111985i
$953$	32.5334	+	11.8412i	1.05386	+	0.383574i	0.810118	−	0.586266i	$-0.199403\pi$
$953$	32.5334	+	11.8412i	1.05386	+	0.383574i	0.243742	+	0.969840i	$0.421625\pi$
$954$	2.74520	−	15.5688i	0.0888792	−	0.504059i
$955$	9.11120	+	51.6722i	0.294832	+	1.67207i
$956$	23.2136	−	8.44906i	0.750781	−	0.273262i
$957$	25.1465	−	43.5550i	0.812871	−	1.40793i
$958$	−7.76147	−	13.4433i	−0.250762	−	0.434332i
$959$	−10.5367	−	8.84137i	−0.340249	−	0.285503i
$960$	−5.01745	−	4.21014i	−0.161938	−	0.135882i
$961$	−5.25267	−	9.09789i	−0.169441	−	0.293480i
$962$	0.605491	−	1.04874i	0.0195218	−	0.0338128i
$963$	−45.3132	+	16.4927i	−1.46020	+	0.531469i
$964$	4.78551	+	27.1400i	0.154131	+	0.874120i
$965$	−3.02422	+	17.1512i	−0.0973530	+	0.552116i
$966$	−21.8326	−	7.94641i	−0.702452	−	0.255672i
$967$	−37.4676	+	31.4391i	−1.20488	+	1.01101i	−0.205400	+	0.978678i	$0.565850\pi$
$967$	−37.4676	+	31.4391i	−1.20488	+	1.01101i	−0.999477	+	0.0323340i	$0.989706\pi$
$968$	22.1340			0.711414
$969$		0			0
$970$	−40.6835			−1.30627
$971$	4.65442	−	3.90553i	0.149368	−	0.125334i	−0.565042	−	0.825062i	$-0.691140\pi$
$971$	4.65442	−	3.90553i	0.149368	−	0.125334i	0.714409	+	0.699728i	$0.246695\pi$
$972$	15.0808	+	5.48895i	0.483716	+	0.176058i
$973$	2.41136	−	13.6755i	0.0773046	−	0.438416i
$974$	−4.96747	−	28.1719i	−0.159168	−	0.902687i
$975$	−0.397025	+	0.144505i	−0.0127150	+	0.00462788i
$976$	5.48073	−	9.49290i	0.175434	−	0.303860i
$977$	−28.5239	−	49.4048i	−0.912559	−	1.58060i	−0.810436	−	0.585828i	$-0.800770\pi$
$977$	−28.5239	−	49.4048i	−0.912559	−	1.58060i	−0.102124	−	0.994772i	$-0.532564\pi$
$978$	30.4945	+	25.5879i	0.975106	+	0.818211i
$979$	−66.4802	−	55.7835i	−2.12472	−	1.78285i
$980$	−6.27308	−	10.8653i	−0.200386	−	0.347079i
$981$	21.2430	−	36.7940i	0.678238	−	1.17474i
$982$	28.5186	−	10.3799i	0.910064	−	0.331236i
$983$	0.0323888	+	0.183686i	0.00103304	+	0.00585867i	0.985320	−	0.170718i	$-0.0546087\pi$
$983$	0.0323888	+	0.183686i	0.00103304	+	0.00585867i	−0.984287	+	0.176577i	$0.943498\pi$
$984$	−2.43386	+	13.8031i	−0.0775886	+	0.440027i
$985$	18.8053	+	6.84458i	0.599188	+	0.218087i
$986$	−10.0295	+	8.41574i	−0.319404	+	0.268012i
$987$	15.7638			0.501768
$988$		0			0
$989$	6.40804			0.203764
$990$	−49.6682	+	41.6766i	−1.57856	+	1.32457i
$991$	43.4512	+	15.8150i	1.38027	+	0.502379i	0.922261	−	0.386567i	$-0.126339\pi$
$991$	43.4512	+	15.8150i	1.38027	+	0.502379i	0.458012	+	0.888946i	$0.348561\pi$
$992$	1.11872	−	6.34459i	0.0355195	−	0.201441i
$993$	2.52886	+	14.3419i	0.0802511	+	0.455126i
$994$	−5.32815	+	1.93929i	−0.168999	+	0.0615105i
$995$	−7.45488	+	12.9122i	−0.236336	+	0.409345i
$996$	13.6393	+	23.6239i	0.432177	+	0.748553i
$997$	−15.9713	−	13.4015i	−0.505815	−	0.424429i	0.353839	−	0.935306i	$-0.384876\pi$
$997$	−15.9713	−	13.4015i	−0.505815	−	0.424429i	−0.859654	+	0.510877i	$0.829321\pi$
$998$	6.72299	+	5.64126i	0.212812	+	0.178571i
$999$	10.0297	+	17.3719i	0.317325	+	0.549623i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	722.2.e.r.595.1		24
19.2	odd	18		722.2.e.s.423.1		24
19.3	odd	18		722.2.e.s.415.4		24
19.4	even	9		722.2.a.n.1.4	yes	4
19.5	even	9	inner	722.2.e.r.245.4		24
19.6	even	9		722.2.c.m.653.1		8
19.7	even	3	inner	722.2.e.r.389.4		24
19.8	odd	6		722.2.e.s.99.1		24
19.9	even	9		722.2.c.m.429.1		8
19.10	odd	18		722.2.c.n.429.4		8
19.11	even	3	inner	722.2.e.r.99.4		24
19.12	odd	6		722.2.e.s.389.1		24
19.13	odd	18		722.2.c.n.653.4		8
19.14	odd	18		722.2.e.s.245.1		24
19.15	odd	18		722.2.a.m.1.1	✓	4
19.16	even	9	inner	722.2.e.r.415.1		24
19.17	even	9	inner	722.2.e.r.423.4		24
19.18	odd	2		722.2.e.s.595.4		24
57.23	odd	18		6498.2.a.bx.1.3		4
57.53	even	18		6498.2.a.ca.1.3		4
76.15	even	18		5776.2.a.bv.1.4		4
76.23	odd	18		5776.2.a.bt.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
722.2.a.m.1.1	✓	4	19.15	odd	18
722.2.a.n.1.4	yes	4	19.4	even	9
722.2.c.m.429.1		8	19.9	even	9
722.2.c.m.653.1		8	19.6	even	9
722.2.c.n.429.4		8	19.10	odd	18
722.2.c.n.653.4		8	19.13	odd	18
722.2.e.r.99.4		24	19.11	even	3	inner
722.2.e.r.245.4		24	19.5	even	9	inner
722.2.e.r.389.4		24	19.7	even	3	inner
722.2.e.r.415.1		24	19.16	even	9	inner
722.2.e.r.423.4		24	19.17	even	9	inner
722.2.e.r.595.1		24	1.1	even	1	trivial
722.2.e.s.99.1		24	19.8	odd	6
722.2.e.s.245.1		24	19.14	odd	18
722.2.e.s.389.1		24	19.12	odd	6
722.2.e.s.415.4		24	19.3	odd	18
722.2.e.s.423.1		24	19.2	odd	18
722.2.e.s.595.4		24	19.18	odd	2
5776.2.a.bt.1.1		4	76.23	odd	18
5776.2.a.bv.1.4		4	76.15	even	18
6498.2.a.bx.1.3		4	57.23	odd	18
6498.2.a.ca.1.3		4	57.53	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 $\F_{q}$

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

\(f(q)\)	\(=\)	\(q+(0.766044 - 0.642788i) q^{2} +(-2.62513 - 0.955469i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.407131 - 2.30896i) q^{5} +(-2.62513 + 0.955469i) q^{6} +(0.642040 - 1.11205i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(3.68025 + 3.08810i) q^{9} +O(q^{10})\)	\(q+(0.766044 - 0.642788i) q^{2} +(-2.62513 - 0.955469i) q^{3} +(0.173648 - 0.984808i) q^{4} +(-0.407131 - 2.30896i) q^{5} +(-2.62513 + 0.955469i) q^{6} +(0.642040 - 1.11205i) q^{7} +(-0.500000 - 0.866025i) q^{8} +(3.68025 + 3.08810i) q^{9} +(-1.79605 - 1.50706i) q^{10} +(-2.87811 - 4.98503i) q^{11} +(-1.39680 + 2.41933i) q^{12} +(-0.285932 + 0.104071i) q^{13} +(-0.222978 - 1.26457i) q^{14} +(-1.13736 + 6.45031i) q^{15} +(-0.939693 - 0.342020i) q^{16} +(3.20681 - 2.69083i) q^{17} +4.80423 q^{18} -2.34458 q^{20} +(-2.74796 + 2.30581i) q^{21} +(-5.40907 - 1.96874i) q^{22} +(-1.12469 + 6.37844i) q^{23} +(0.485104 + 2.75116i) q^{24} +(-0.467064 + 0.169997i) q^{25} +(-0.152141 + 0.263516i) q^{26} +(-2.52015 - 4.36502i) q^{27} +(-0.983662 - 0.825390i) q^{28} +(-2.39585 - 2.01036i) q^{29} +(3.27491 + 5.67231i) q^{30} +(-3.22123 + 5.57934i) q^{31} +(-0.939693 + 0.342020i) q^{32} +(2.79236 + 15.8363i) q^{33} +(0.726925 - 4.12259i) q^{34} +(-2.82906 - 1.02969i) q^{35} +(3.68025 - 3.08810i) q^{36} -3.97980 q^{37} +0.850045 q^{39} +(-1.79605 + 1.50706i) q^{40} +(4.71461 + 1.71598i) q^{41} +(-0.622912 + 3.53271i) q^{42} +(-0.171804 - 0.974348i) q^{43} +(-5.40907 + 1.96874i) q^{44} +(5.63194 - 9.75480i) q^{45} +(3.23842 + 5.60910i) q^{46} +(-3.36635 - 2.82470i) q^{47} +(2.14003 + 1.79569i) q^{48} +(2.67557 + 4.63422i) q^{49} +(-0.248520 + 0.430448i) q^{50} +(-10.9893 + 3.99978i) q^{51} +(0.0528381 + 0.299660i) q^{52} +(0.571414 - 3.24065i) q^{53} +(-4.73633 - 1.72388i) q^{54} +(-10.3384 + 8.67499i) q^{55} -1.28408 q^{56} -3.12756 q^{58} +(2.53848 - 2.13004i) q^{59} +(6.15482 + 2.24017i) q^{60} +(-1.90344 + 10.7949i) q^{61} +(1.11872 + 6.34459i) q^{62} +(5.79697 - 2.10992i) q^{63} +(-0.500000 + 0.866025i) q^{64} +(0.356707 + 0.617834i) q^{65} +(12.3184 + 10.3364i) q^{66} +(-3.35590 - 2.81593i) q^{67} +(-2.09310 - 3.62535i) q^{68} +(9.04686 - 15.6696i) q^{69} +(-2.82906 + 1.02969i) q^{70} +(-0.766777 - 4.34861i) q^{71} +(0.834245 - 4.73124i) q^{72} +(2.13018 + 0.775323i) q^{73} +(-3.04870 + 2.55816i) q^{74} +1.38853 q^{75} -7.39144 q^{77} +(0.651172 - 0.546398i) q^{78} +(-8.05936 - 2.93337i) q^{79} +(-0.407131 + 2.30896i) q^{80} +(-0.0576668 - 0.327045i) q^{81} +(4.71461 - 1.71598i) q^{82} +(4.88232 - 8.45643i) q^{83} +(1.79360 + 3.10661i) q^{84} +(-7.51861 - 6.30886i) q^{85} +(-0.757908 - 0.635960i) q^{86} +(4.36858 + 7.56661i) q^{87} +(-2.87811 + 4.98503i) q^{88} +(14.1673 - 5.15648i) q^{89} +(-1.95595 - 11.0928i) q^{90} +(-0.0678483 + 0.384787i) q^{91} +(6.08623 + 2.21521i) q^{92} +(13.7870 - 11.5687i) q^{93} -4.39445 q^{94} +2.79360 q^{96} +(13.2925 - 11.1538i) q^{97} +(5.02843 + 1.83020i) q^{98} +(4.80209 - 27.2340i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 6 q^{7} - 12 q^{8}+O(q^{10}) \) 24 * q + 6 * q^7 - 12 * q^8	\( 24 q + 6 q^{7} - 12 q^{8} - 6 q^{11} - 6 q^{12} + 24 q^{18} - 12 q^{20} - 54 q^{26} + 12 q^{27} - 12 q^{30} - 78 q^{31} + 24 q^{37} - 36 q^{39} + 66 q^{45} + 30 q^{46} + 36 q^{49} - 18 q^{50} - 12 q^{56} - 12 q^{58} - 12 q^{64} + 12 q^{65} - 18 q^{68} + 60 q^{69} + 48 q^{75} + 24 q^{77} + 36 q^{83} - 12 q^{84} + 78 q^{87} - 6 q^{88} - 72 q^{94} + 12 q^{96}+O(q^{100}) \) 24 * q + 6 * q^7 - 12 * q^8 - 6 * q^11 - 6 * q^12 + 24 * q^18 - 12 * q^20 - 54 * q^26 + 12 * q^27 - 12 * q^30 - 78 * q^31 + 24 * q^37 - 36 * q^39 + 66 * q^45 + 30 * q^46 + 36 * q^49 - 18 * q^50 - 12 * q^56 - 12 * q^58 - 12 * q^64 + 12 * q^65 - 18 * q^68 + 60 * q^69 + 48 * q^75 + 24 * q^77 + 36 * q^83 - 12 * q^84 + 78 * q^87 - 6 * q^88 - 72 * q^94 + 12 * q^96

Introduction

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