LMFDB - Embedded newform 966.2.l.c.185.24

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(47,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 0]))

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

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

chi := DirichletCharacter("966.47");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.l (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$28$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			185.24
Character	$\chi$	$=$	966.185
Dual form			966.2.l.c.47.24

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.866025 - 0.500000i) q^{2} +(0.562211 - 1.63827i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.890465 - 1.54233i) q^{5} +(-0.332245 - 1.69989i) q^{6} +(-2.00001 + 1.73204i) q^{7} -1.00000i q^{8} +(-2.36784 - 1.84210i) q^{9} +O(q^{10})$	\(q+(0.866025 - 0.500000i) q^{2} +(0.562211 - 1.63827i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.890465 - 1.54233i) q^{5} +(-0.332245 - 1.69989i) q^{6} +(-2.00001 + 1.73204i) q^{7} -1.00000i q^{8} +(-2.36784 - 1.84210i) q^{9} +(-1.54233 - 0.890465i) q^{10} +(0.864424 + 0.499076i) q^{11} +(-1.13768 - 1.30602i) q^{12} -6.26372i q^{13} +(-0.866040 + 2.50000i) q^{14} +(-3.02738 + 0.591704i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.67970 + 2.90933i) q^{17} +(-2.97166 - 0.411389i) q^{18} +(-1.42779 + 0.824336i) q^{19} -1.78093 q^{20} +(1.71312 + 4.25032i) q^{21} +0.998151 q^{22} +(-0.866025 + 0.500000i) q^{23} +(-1.63827 - 0.562211i) q^{24} +(0.914144 - 1.58334i) q^{25} +(-3.13186 - 5.42454i) q^{26} +(-4.34908 + 2.84350i) q^{27} +(0.499985 + 2.59808i) q^{28} +1.24938i q^{29} +(-2.32593 + 2.02612i) q^{30} +(-6.98992 - 4.03563i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.30361 - 1.13557i) q^{33} +3.35941i q^{34} +(4.45232 + 1.54236i) q^{35} +(-2.77923 + 1.12956i) q^{36} +(0.235496 + 0.407891i) q^{37} +(-0.824336 + 1.42779i) q^{38} +(-10.2616 - 3.52153i) q^{39} +(-1.54233 + 0.890465i) q^{40} +4.34340 q^{41} +(3.60876 + 2.82433i) q^{42} +4.79063 q^{43} +(0.864424 - 0.499076i) q^{44} +(-0.732655 + 5.29232i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-4.22866 - 7.32426i) q^{47} +(-1.69989 + 0.332245i) q^{48} +(1.00008 - 6.92819i) q^{49} -1.82829i q^{50} +(3.82192 + 4.38746i) q^{51} +(-5.42454 - 3.13186i) q^{52} +(5.24099 + 3.02589i) q^{53} +(-2.34466 + 4.63708i) q^{54} -1.77764i q^{55} +(1.73204 + 2.00001i) q^{56} +(0.547762 + 2.80256i) q^{57} +(0.624691 + 1.08200i) q^{58} +(-0.600268 + 1.03970i) q^{59} +(-1.00126 + 2.91764i) q^{60} +(1.01927 - 0.588474i) q^{61} -8.07127 q^{62} +(7.92629 - 0.416965i) q^{63} -1.00000 q^{64} +(-9.66073 + 5.57762i) q^{65} +(0.561171 - 1.63524i) q^{66} +(4.81654 - 8.34250i) q^{67} +(1.67970 + 2.90933i) q^{68} +(0.332245 + 1.69989i) q^{69} +(4.62700 - 0.890439i) q^{70} +9.62306i q^{71} +(-1.84210 + 2.36784i) q^{72} +(9.57661 + 5.52906i) q^{73} +(0.407891 + 0.235496i) q^{74} +(-2.08000 - 2.38779i) q^{75} +1.64867i q^{76} +(-2.59328 + 0.499061i) q^{77} +(-10.6476 + 2.08109i) q^{78} +(0.576636 + 0.998763i) q^{79} +(-0.890465 + 1.54233i) q^{80} +(2.21331 + 8.72360i) q^{81} +(3.76149 - 2.17170i) q^{82} +7.53838 q^{83} +(4.53744 + 0.641559i) q^{84} +5.98287 q^{85} +(4.14881 - 2.39532i) q^{86} +(2.04682 + 0.702416i) q^{87} +(0.499076 - 0.864424i) q^{88} +(-4.81612 - 8.34177i) q^{89} +(2.01166 + 4.94961i) q^{90} +(10.8490 + 12.5275i) q^{91} +1.00000i q^{92} +(-10.5413 + 9.18248i) q^{93} +(-7.32426 - 4.22866i) q^{94} +(2.54280 + 1.46808i) q^{95} +(-1.30602 + 1.13768i) q^{96} -11.6654i q^{97} +(-2.59800 - 6.50003i) q^{98} +(-1.12747 - 2.77409i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	$ 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) $ 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$1$

Coefficient data

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

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

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

$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$2$	0.866025	−	0.500000i	0.612372	−	0.353553i
$3$	0.562211	−	1.63827i	0.324593	−	0.945854i
$3$	0.562211	−	1.63827i	0.324593	−	0.945854i
$4$	0.500000	−	0.866025i	0.250000	−	0.433013i
$5$	−0.890465	−	1.54233i	−0.398228	−	0.689751i	0.595279	−	0.803519i	$-0.297041\pi$
$5$	−0.890465	−	1.54233i	−0.398228	−	0.689751i	−0.993507	+	0.113768i	$0.963708\pi$
$6$	−0.332245	−	1.69989i	−0.135638	−	0.693976i
$7$	−2.00001	+	1.73204i	−0.755933	+	0.654649i
$7$	−2.00001	+	1.73204i	−0.755933	+	0.654649i
$8$		−	1.00000i		−	0.353553i
$9$	−2.36784	−	1.84210i	−0.789279	−	0.614034i
$10$	−1.54233	−	0.890465i	−0.487728	−	0.281590i
$11$	0.864424	+	0.499076i	0.260634	+	0.150477i	0.624624	−	0.780926i	$-0.285252\pi$
$11$	0.864424	+	0.499076i	0.260634	+	0.150477i	−0.363990	+	0.931403i	$0.618586\pi$
$12$	−1.13768	−	1.30602i	−0.328419	−	0.377016i
$13$		−	6.26372i		−	1.73724i	−0.495476	−	0.868622i	$-0.665006\pi$
$13$		−	6.26372i		−	1.73724i	0.495476	−	0.868622i	$-0.334994\pi$
$14$	−0.866040	+	2.50000i	−0.231459	+	0.668152i
$15$	−3.02738	+	0.591704i	−0.781666	+	0.152777i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	−1.67970	+	2.90933i	−0.407388	+	0.705617i	−0.994596	−	0.103819i	$-0.966894\pi$
$17$	−1.67970	+	2.90933i	−0.407388	+	0.705617i	0.587208	+	0.809436i	$0.300227\pi$
$18$	−2.97166	−	0.411389i	−0.700427	−	0.0969653i
$19$	−1.42779	+	0.824336i	−0.327558	+	0.189116i	−0.654756	−	0.755840i	$-0.727229\pi$
$19$	−1.42779	+	0.824336i	−0.327558	+	0.189116i	0.327198	+	0.944956i	$0.393895\pi$
$20$	−1.78093			−0.398228
$21$	1.71312	+	4.25032i	0.373833	+	0.927496i
$22$	0.998151			0.212807
$23$	−0.866025	+	0.500000i	−0.180579	+	0.104257i
$23$	−0.866025	+	0.500000i	−0.180579	+	0.104257i
$24$	−1.63827	−	0.562211i	−0.334410	−	0.114761i
$25$	0.914144	−	1.58334i	0.182829	−	0.316669i
$26$	−3.13186	−	5.42454i	−0.614208	−	1.06384i
$27$	−4.34908	+	2.84350i	−0.836981	+	0.547232i
$28$	0.499985	+	2.59808i	0.0944883	+	0.490991i
$29$			1.24938i			0.232004i	0.993249	+	0.116002i	$0.0370080\pi$
$29$			1.24938i			0.232004i	−0.993249	+	0.116002i	$0.962992\pi$
$30$	−2.32593	+	2.02612i	−0.424656	+	0.369917i
$31$	−6.98992	−	4.03563i	−1.25543	−	0.724821i	−0.283245	−	0.959048i	$-0.591411\pi$
$31$	−6.98992	−	4.03563i	−1.25543	−	0.724821i	−0.972182	+	0.234227i	$0.924744\pi$
$32$	−0.866025	−	0.500000i	−0.153093	−	0.0883883i
$33$	1.30361	−	1.13557i	0.226929	−	0.197678i
$34$			3.35941i			0.576134i
$35$	4.45232	+	1.54236i	0.752579	+	0.260706i
$36$	−2.77923	+	1.12956i	−0.463204	+	0.188259i
$37$	0.235496	+	0.407891i	0.0387153	+	0.0670569i	0.884734	−	0.466097i	$-0.154340\pi$
$37$	0.235496	+	0.407891i	0.0387153	+	0.0670569i	−0.846018	+	0.533154i	$0.821007\pi$
$38$	−0.824336	+	1.42779i	−0.133725	+	0.231618i
$39$	−10.2616	−	3.52153i	−1.64318	−	0.563896i
$40$	−1.54233	+	0.890465i	−0.243864	+	0.140795i
$41$	4.34340			0.678325			0.339162	−	0.940728i	$-0.389856\pi$
$41$	4.34340			0.678325			0.339162	+	0.940728i	$0.389856\pi$
$42$	3.60876	+	2.82433i	0.556844	+	0.435803i
$43$	4.79063			0.730565			0.365282	−	0.930897i	$-0.380972\pi$
$43$	4.79063			0.730565			0.365282	+	0.930897i	$0.380972\pi$
$44$	0.864424	−	0.499076i	0.130317	−	0.0752385i
$45$	−0.732655	+	5.29232i	−0.109218	+	0.788932i
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	−4.22866	−	7.32426i	−0.616814	−	1.06835i	−0.990063	−	0.140622i	$-0.955090\pi$
$47$	−4.22866	−	7.32426i	−0.616814	−	1.06835i	0.373250	−	0.927731i	$-0.378243\pi$
$48$	−1.69989	+	0.332245i	−0.245357	+	0.0479554i
$49$	1.00008	−	6.92819i	0.142868	−	0.989742i
$50$		−	1.82829i		−	0.258559i
$51$	3.82192	+	4.38746i	0.535175	+	0.614368i
$52$	−5.42454	−	3.13186i	−0.752248	−	0.434311i
$53$	5.24099	+	3.02589i	0.719906	+	0.415638i	0.814718	−	0.579857i	$-0.196892\pi$
$53$	5.24099	+	3.02589i	0.719906	+	0.415638i	−0.0948123	+	0.995495i	$0.530225\pi$
$54$	−2.34466	+	4.63708i	−0.319068	+	0.631027i
$55$		−	1.77764i		−	0.239697i
$56$	1.73204	+	2.00001i	0.231454	+	0.267263i
$57$	0.547762	+	2.80256i	0.0725529	+	0.371207i
$58$	0.624691	+	1.08200i	0.0820260	+	0.142073i
$59$	−0.600268	+	1.03970i	−0.0781483	+	0.135357i	−0.902451	−	0.430792i	$-0.858234\pi$
$59$	−0.600268	+	1.03970i	−0.0781483	+	0.135357i	0.824303	+	0.566149i	$0.191567\pi$
$60$	−1.00126	+	2.91764i	−0.129262	+	0.376666i
$61$	1.01927	−	0.588474i	0.130504	−	0.0753464i	−0.433327	−	0.901237i	$-0.642660\pi$
$61$	1.01927	−	0.588474i	0.130504	−	0.0753464i	0.563831	+	0.825890i	$0.309327\pi$
$62$	−8.07127			−1.02505
$63$	7.92629	−	0.416965i	0.998619	−	0.0525326i
$64$	−1.00000			−0.125000
$65$	−9.66073	+	5.57762i	−1.19827	+	0.691819i
$66$	0.561171	−	1.63524i	0.0690754	−	0.201284i
$67$	4.81654	−	8.34250i	0.588435	−	1.01920i	−0.406003	−	0.913872i	$-0.633078\pi$
$67$	4.81654	−	8.34250i	0.588435	−	1.01920i	0.994438	−	0.105327i	$-0.0335889\pi$
$68$	1.67970	+	2.90933i	0.203694	+	0.352809i
$69$	0.332245	+	1.69989i	0.0399976	+	0.204642i
$70$	4.62700	−	0.890439i	0.553032	−	0.106428i
$71$			9.62306i			1.14205i	0.820934	+	0.571023i	$0.193453\pi$
$71$			9.62306i			1.14205i	−0.820934	+	0.571023i	$0.806547\pi$
$72$	−1.84210	+	2.36784i	−0.217094	+	0.279052i
$73$	9.57661	+	5.52906i	1.12086	+	0.647128i	0.941620	−	0.336678i	$-0.109303\pi$
$73$	9.57661	+	5.52906i	1.12086	+	0.647128i	0.179238	+	0.983806i	$0.442637\pi$
$74$	0.407891	+	0.235496i	0.0474164	+	0.0273759i
$75$	−2.08000	−	2.38779i	−0.240178	−	0.275718i
$76$			1.64867i			0.189116i
$77$	−2.59328	+	0.499061i	−0.295531	+	0.0568733i
$78$	−10.6476	+	2.08109i	−1.20560	+	0.235637i
$79$	0.576636	+	0.998763i	0.0648766	+	0.112370i	0.896639	−	0.442762i	$-0.146001\pi$
$79$	0.576636	+	0.998763i	0.0648766	+	0.112370i	−0.831763	+	0.555131i	$0.812668\pi$
$80$	−0.890465	+	1.54233i	−0.0995570	+	0.172438i
$81$	2.21331	+	8.72360i	0.245924	+	0.969289i
$82$	3.76149	−	2.17170i	0.415387	−	0.239824i
$83$	7.53838			0.827445			0.413722	−	0.910403i	$-0.364228\pi$
$83$	7.53838			0.827445			0.413722	+	0.910403i	$0.364228\pi$
$84$	4.53744	+	0.641559i	0.495076	+	0.0699998i
$85$	5.98287			0.648934
$86$	4.14881	−	2.39532i	0.447378	−	0.258294i
$87$	2.04682	+	0.702416i	0.219442	+	0.0753069i
$88$	0.499076	−	0.864424i	0.0532016	−	0.0921480i
$89$	−4.81612	−	8.34177i	−0.510508	−	0.884225i	−0.999926	−	0.0121761i	$-0.996124\pi$
$89$	−4.81612	−	8.34177i	−0.510508	−	0.884225i	0.489418	−	0.872049i	$-0.337209\pi$
$90$	2.01166	+	4.94961i	0.212048	+	0.521735i
$91$	10.8490	+	12.5275i	1.13729	+	1.31324i
$92$			1.00000i			0.104257i
$93$	−10.5413	+	9.18248i	−1.09308	+	0.952179i
$94$	−7.32426	−	4.22866i	−0.755439	−	0.436153i
$95$	2.54280	+	1.46808i	0.260885	+	0.150622i
$96$	−1.30602	+	1.13768i	−0.133295	+	0.116114i
$97$		−	11.6654i		−	1.18444i	−0.805776	−	0.592220i	$-0.798252\pi$
$97$		−	11.6654i		−	1.18444i	0.805776	−	0.592220i	$-0.201748\pi$
$98$	−2.59800	−	6.50003i	−0.262438	−	0.656602i
$99$	−1.12747	−	2.77409i	−0.113315	−	0.278806i
$100$	−0.914144	−	1.58334i	−0.0914144	−	0.158334i
$101$	8.67140	−	15.0193i	0.862836	−	1.49448i	−0.00634380	−	0.999980i	$-0.502019\pi$
$101$	8.67140	−	15.0193i	0.862836	−	1.49448i	0.869180	−	0.494496i	$-0.164647\pi$
$102$	5.50361	+	1.88870i	0.544939	+	0.187009i
$103$	7.08086	−	4.08814i	0.697698	−	0.402816i	−0.108791	−	0.994065i	$-0.534698\pi$
$103$	7.08086	−	4.08814i	0.697698	−	0.402816i	0.806490	+	0.591248i	$0.201365\pi$
$104$	−6.26372			−0.614208
$105$	5.02993	−	6.42695i	0.490871	−	0.627206i
$106$	6.05178			0.587800
$107$	−17.0877	+	9.86556i	−1.65193	+	0.953740i	−0.675647	+	0.737226i	$0.736135\pi$
$107$	−17.0877	+	9.86556i	−1.65193	+	0.953740i	−0.976279	+	0.216514i	$0.930531\pi$
$108$	0.288003	+	5.18816i	0.0277131	+	0.499231i
$109$	7.96954	−	13.8036i	0.763343	−	1.32215i	−0.177775	−	0.984071i	$-0.556890\pi$
$109$	7.96954	−	13.8036i	0.763343	−	1.32215i	0.941118	−	0.338078i	$-0.109777\pi$
$110$	−0.888819	−	1.53948i	−0.0847455	−	0.146784i
$111$	0.800633	−	0.156485i	0.0759927	−	0.0148529i
$112$	2.50000	+	0.866040i	0.236227	+	0.0818330i
$113$		−	6.36516i		−	0.598784i	−0.954130	−	0.299392i	$-0.903216\pi$
$113$		−	6.36516i		−	0.598784i	0.954130	−	0.299392i	$-0.0967839\pi$
$114$	1.87565	+	2.15320i	0.175671	+	0.201666i
$115$	1.54233	+	0.890465i	0.143823	+	0.0830363i
$116$	1.08200	+	0.624691i	0.100461	+	0.0580011i
$117$	−11.5384	+	14.8315i	−1.06673	+	1.37117i
$118$			1.20054i			0.110518i
$119$	−1.67966	−	8.72801i	−0.153974	−	0.800095i
$120$	0.591704	+	3.02738i	0.0540150	+	0.276361i
$121$	−5.00185	−	8.66345i	−0.454713	−	0.787587i
$122$	0.588474	−	1.01927i	0.0532780	−	0.0922802i
$123$	2.44191	−	7.11564i	0.220179	−	0.641596i
$124$	−6.98992	+	4.03563i	−0.627713	+	0.362411i
$125$	−12.1607			−1.08769
$126$	6.65589	−	4.32425i	0.592954	−	0.385235i
$127$	−1.66680			−0.147904			−0.0739522	−	0.997262i	$-0.523561\pi$
$127$	−1.66680			−0.147904			−0.0739522	+	0.997262i	$0.523561\pi$
$128$	−0.866025	+	0.500000i	−0.0765466	+	0.0441942i
$129$	2.69335	−	7.84834i	0.237136	−	0.691008i
$130$	−5.57762	+	9.66073i	−0.489190	+	0.847302i
$131$	−0.963948	−	1.66961i	−0.0842205	−	0.145874i	0.820838	−	0.571161i	$-0.193507\pi$
$131$	−0.963948	−	1.66961i	−0.0842205	−	0.145874i	−0.905059	+	0.425286i	$0.860173\pi$
$132$	−0.331630	−	1.69674i	−0.0288647	−	0.147683i
$133$	1.42782	−	4.12167i	0.123807	−	0.357394i
$134$		−	9.63309i		−	0.832172i
$135$	8.25832	+	4.17568i	0.710763	+	0.359386i
$136$	2.90933	+	1.67970i	0.249473	+	0.144033i
$137$	7.54322	+	4.35508i	0.644461	+	0.372080i	0.786331	−	0.617806i	$-0.211978\pi$
$137$	7.54322	+	4.35508i	0.644461	+	0.372080i	−0.141870	+	0.989885i	$0.545312\pi$
$138$	1.13768	+	1.30602i	0.0968454	+	0.111176i
$139$		−	0.941550i		−	0.0798613i	−0.999202	−	0.0399306i	$-0.987286\pi$
$139$		−	0.941550i		−	0.0798613i	0.999202	−	0.0399306i	$-0.0127137\pi$
$140$	3.56188	−	3.08464i	0.301034	−	0.260700i
$141$	−14.3765	+	2.80990i	−1.21072	+	0.236636i
$142$	4.81153	+	8.33381i	0.403774	+	0.699358i
$143$	3.12607	−	5.41451i	0.261415	−	0.452784i
$144$	−0.411389	+	2.97166i	−0.0342824	+	0.247638i
$145$	1.92696	−	1.11253i	0.160025	−	0.0923907i
$146$	11.0581			0.915177
$147$	−10.7880	−	5.53350i	−0.889777	−	0.456395i
$148$	0.470992			0.0387153
$149$	−0.753321	+	0.434930i	−0.0617144	+	0.0356309i	−0.530540	−	0.847660i	$-0.678011\pi$
$149$	−0.753321	+	0.434930i	−0.0617144	+	0.0356309i	0.468825	+	0.883291i	$0.344677\pi$
$150$	−2.99523	−	1.02788i	−0.244559	−	0.0839264i
$151$	3.57086	−	6.18491i	0.290593	−	0.503321i	−0.683357	−	0.730084i	$-0.739481\pi$
$151$	3.57086	−	6.18491i	0.290593	−	0.503321i	0.973950	+	0.226763i	$0.0728142\pi$
$152$	0.824336	+	1.42779i	0.0668625	+	0.115809i
$153$	9.33656	−	3.79464i	0.754816	−	0.306779i
$154$	−1.99631	+	1.72884i	−0.160867	+	0.139314i
$155$			14.3744i			1.15458i
$156$	−8.18056	+	7.12608i	−0.654969	+	0.570543i
$157$	−11.8872	−	6.86308i	−0.948702	−	0.547733i	−0.0560243	−	0.998429i	$-0.517842\pi$
$157$	−11.8872	−	6.86308i	−0.948702	−	0.547733i	−0.892677	+	0.450696i	$0.851176\pi$
$158$	0.998763	+	0.576636i	0.0794573	+	0.0458747i
$159$	7.90376	−	6.88496i	0.626809	−	0.546013i
$160$			1.78093i			0.140795i
$161$	0.866040	−	2.50000i	0.0682535	−	0.197027i
$162$	6.27859	+	6.44821i	0.493292	+	0.506619i
$163$	4.67610	+	8.09924i	0.366260	+	0.634381i	0.988978	−	0.148066i	$-0.0473047\pi$
$163$	4.67610	+	8.09924i	0.366260	+	0.634381i	−0.622717	+	0.782447i	$0.713971\pi$
$164$	2.17170	−	3.76149i	0.169581	−	0.293723i
$165$	−2.91224	−	0.999407i	−0.226718	−	0.0778037i
$166$	6.52843	−	3.76919i	0.506704	−	0.292546i
$167$	24.8198			1.92061			0.960307	−	0.278945i	$-0.0899846\pi$
$167$	24.8198			1.92061			0.960307	+	0.278945i	$0.0899846\pi$
$168$	4.25032	−	1.71312i	0.327919	−	0.132170i
$169$	−26.2342			−2.01801
$170$	5.18132	−	2.99144i	0.397389	−	0.229433i
$171$	4.89929	+	0.678246i	0.374658	+	0.0518667i
$172$	2.39532	−	4.14881i	0.182641	−	0.316344i
$173$	1.64788	+	2.85421i	0.125286	+	0.217002i	0.921845	−	0.387560i	$-0.126682\pi$
$173$	1.64788	+	2.85421i	0.125286	+	0.217002i	−0.796559	+	0.604561i	$0.793349\pi$
$174$	2.12381	−	0.415101i	0.161005	−	0.0314687i
$175$	0.914118	+	4.75004i	0.0691008	+	0.359069i
$176$		−	0.998151i		−	0.0752385i
$177$	1.36582	+	1.56793i	0.102661	+	0.117853i
$178$	−8.34177	−	4.81612i	−0.625242	−	0.360984i
$179$	19.3860	+	11.1925i	1.44897	+	0.836566i	0.998420	−	0.0561832i	$-0.0178931\pi$
$179$	19.3860	+	11.1925i	1.44897	+	0.836566i	0.450554	+	0.892749i	$0.351226\pi$
$180$	4.21695	+	3.28066i	0.314313	+	0.244526i
$181$		−	2.62713i		−	0.195273i	−0.995222	−	0.0976366i	$-0.968872\pi$
$181$		−	2.62713i		−	0.195273i	0.995222	−	0.0976366i	$-0.0311283\pi$
$182$	15.6593	+	5.42463i	1.16074	+	0.402100i
$183$	−0.391035	−	2.00068i	−0.0289061	−	0.147894i
$184$	0.500000	+	0.866025i	0.0368605	+	0.0638442i
$185$	0.419402	−	0.726425i	0.0308350	−	0.0534079i
$186$	−4.53775	+	13.2229i	−0.332724	+	0.969549i
$187$	−2.90396	+	1.67660i	−0.212358	+	0.122605i
$188$	−8.45732			−0.616814
$189$	3.77315	−	13.2198i	0.274456	−	0.961600i
$190$	2.93617			0.213012
$191$	4.07616	−	2.35337i	0.294941	−	0.170284i	−0.345227	−	0.938519i	$-0.612198\pi$
$191$	4.07616	−	2.35337i	0.294941	−	0.170284i	0.640168	+	0.768235i	$0.278865\pi$
$192$	−0.562211	+	1.63827i	−0.0405741	+	0.118232i
$193$	0.532666	−	0.922605i	0.0383422	−	0.0664106i	−0.846218	−	0.532838i	$-0.821126\pi$
$193$	0.532666	−	0.922605i	0.0383422	−	0.0664106i	0.884560	+	0.466427i	$0.154459\pi$
$194$	−5.83269	−	10.1025i	−0.418763	−	0.725318i
$195$	3.70627	+	18.9626i	0.265412	+	1.35794i
$196$	−5.49995	−	4.33019i	−0.392854	−	0.309299i
$197$			16.9781i			1.20964i	0.796362	+	0.604820i	$0.206755\pi$
$197$			16.9781i			1.20964i	−0.796362	+	0.604820i	$0.793245\pi$
$198$	−2.36346	−	1.83870i	−0.167964	−	0.130671i
$199$	1.85652	+	1.07186i	0.131605	+	0.0759823i	0.564357	−	0.825531i	$-0.309124\pi$
$199$	1.85652	+	1.07186i	0.131605	+	0.0759823i	−0.432752	+	0.901513i	$0.642457\pi$
$200$	−1.58334	−	0.914144i	−0.111959	−	0.0646398i
$201$	−10.9593	−	12.5810i	−0.773012	−	0.887397i
$202$		−	17.3428i		−	1.22023i
$203$	−2.16398	−	2.49878i	−0.151882	−	0.175380i
$204$	5.71061	−	1.11615i	0.399823	−	0.0781458i
$205$	−3.86764	−	6.69895i	−0.270128	−	0.467875i
$206$	4.08814	−	7.08086i	0.284834	−	0.493347i
$207$	2.97166	+	0.411389i	0.206545	+	0.0285935i
$208$	−5.42454	+	3.13186i	−0.376124	+	0.217155i
$209$	−1.64562			−0.113830
$210$	1.14257	−	8.08087i	0.0788449	−	0.557633i
$211$	−25.7800			−1.77477			−0.887385	−	0.461029i	$-0.847480\pi$
$211$	−25.7800			−1.77477			−0.887385	+	0.461029i	$0.847480\pi$
$212$	5.24099	−	3.02589i	0.359953	−	0.207819i
$213$	15.7651	+	5.41019i	1.08021	+	0.370700i
$214$	−9.86556	+	17.0877i	−0.674396	+	1.16809i
$215$	−4.26589	−	7.38874i	−0.290931	−	0.503908i
$216$	2.84350	+	4.34908i	0.193476	+	0.295917i
$217$	20.9698	−	4.03551i	1.42352	−	0.273949i
$218$		−	15.9391i		−	1.07953i
$219$	14.4422	−	12.5806i	0.975910	−	0.850115i
$220$	−1.53948	−	0.888819i	−0.103792	−	0.0599241i
$221$	18.2233	+	10.5212i	1.22583	+	0.707732i
$222$	0.615126	−	0.535836i	0.0412846	−	0.0359630i
$223$		−	10.0664i		−	0.674094i	−0.941488	−	0.337047i	$-0.890572\pi$
$223$		−	10.0664i		−	0.674094i	0.941488	−	0.337047i	$-0.109428\pi$
$224$	2.59808	−	0.499985i	0.173591	−	0.0334067i
$225$	−5.08123	+	2.06516i	−0.338749	+	0.137677i
$226$	−3.18258	−	5.51239i	−0.211702	−	0.366679i
$227$	−13.1471	+	22.7715i	−0.872604	+	1.51140i	−0.0133113	+	0.999911i	$0.504237\pi$
$227$	−13.1471	+	22.7715i	−0.872604	+	1.51140i	−0.859293	+	0.511484i	$0.829096\pi$
$228$	2.70097	+	0.926901i	0.178876	+	0.0613855i
$229$	−17.0205	+	9.82677i	−1.12474	+	0.649371i	−0.942608	−	0.333902i	$-0.891635\pi$
$229$	−17.0205	+	9.82677i	−1.12474	+	0.649371i	−0.182136	+	0.983273i	$0.558301\pi$
$230$	1.78093			0.117431
$231$	−0.640373	+	4.52906i	−0.0421334	+	0.297990i
$232$	1.24938			0.0820260
$233$	−2.78352	+	1.60706i	−0.182354	+	0.105282i	−0.588398	−	0.808571i	$-0.700241\pi$
$233$	−2.78352	+	1.60706i	−0.182354	+	0.105282i	0.406044	+	0.913853i	$0.366908\pi$
$234$	−2.57683	+	18.6136i	−0.168452	+	1.21681i
$235$	−7.53095	+	13.0440i	−0.491265	+	0.850896i
$236$	0.600268	+	1.03970i	0.0390741	+	0.0676784i
$237$	1.96043	−	0.383168i	0.127344	−	0.0248895i
$238$	−5.81863	−	6.71885i	−0.377166	−	0.435518i
$239$		−	8.42177i		−	0.544759i	−0.962190	−	0.272380i	$-0.912189\pi$
$239$		−	8.42177i		−	0.544759i	0.962190	−	0.272380i	$-0.0878106\pi$
$240$	2.02612	+	2.32593i	0.130785	+	0.150138i
$241$	7.66278	+	4.42411i	0.493603	+	0.284982i	0.726068	−	0.687623i	$-0.241346\pi$
$241$	7.66278	+	4.42411i	0.493603	+	0.284982i	−0.232465	+	0.972605i	$0.574679\pi$
$242$	−8.66345	−	5.00185i	−0.556908	−	0.321531i
$243$	15.5359	+	1.27851i	0.996631	+	0.0820162i
$244$		−	1.17695i		−	0.0753464i
$245$	−11.5761	+	4.62686i	−0.739570	+	0.295599i
$246$	−1.44307	−	7.38328i	−0.0920068	−	0.470741i
$247$	5.16341	+	8.94329i	0.328540	+	0.569048i
$248$	−4.03563	+	6.98992i	−0.256263	+	0.443860i
$249$	4.23816	−	12.3499i	0.268582	−	0.782642i
$250$	−10.5315	+	6.08035i	−0.666069	+	0.384555i
$251$	28.0228			1.76879			0.884393	−	0.466743i	$-0.154573\pi$
$251$	28.0228			1.76879			0.884393	+	0.466743i	$0.154573\pi$
$252$	3.60204	−	7.07285i	0.226908	−	0.445548i
$253$	−0.998151			−0.0627532
$254$	−1.44349	+	0.833399i	−0.0905726	+	0.0522921i
$255$	3.36364	−	9.80154i	0.210639	−	0.613796i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	−6.26044	−	10.8434i	−0.390516	−	0.676393i	0.602002	−	0.798495i	$-0.294370\pi$
$257$	−6.26044	−	10.8434i	−0.390516	−	0.676393i	−0.992518	+	0.122102i	$0.961037\pi$
$258$	−1.59166	−	8.14353i	−0.0990926	−	0.506994i
$259$	−1.17748	−	0.407898i	−0.0731649	−	0.0253455i
$260$			11.1552i			0.691819i
$261$	2.30149	−	2.95833i	0.142459	−	0.183116i
$262$	−1.66961	−	0.963948i	−0.103149	−	0.0595529i
$263$	7.36275	+	4.25089i	0.454007	+	0.262121i	0.709521	−	0.704684i	$-0.248911\pi$
$263$	7.36275	+	4.25089i	0.454007	+	0.262121i	−0.255514	+	0.966805i	$0.582245\pi$
$264$	−1.13557	−	1.30361i	−0.0698896	−	0.0802315i
$265$		−	10.7778i		−	0.662074i
$266$	−0.824312	−	4.28338i	−0.0505418	−	0.262631i
$267$	−16.3737	+	3.20026i	−1.00206	+	0.195853i
$268$	−4.81654	−	8.34250i	−0.294217	−	0.509599i
$269$	−5.33348	+	9.23785i	−0.325188	+	0.563242i	−0.981550	−	0.191204i	$-0.938761\pi$
$269$	−5.33348	+	9.23785i	−0.325188	+	0.563242i	0.656363	+	0.754446i	$0.272094\pi$
$270$	9.23976	−	0.512914i	0.562314	−	0.0312149i
$271$	10.1811	−	5.87807i	0.618459	−	0.357067i	−0.157810	−	0.987469i	$-0.550443\pi$
$271$	10.1811	−	5.87807i	0.618459	−	0.357067i	0.776269	+	0.630402i	$0.217110\pi$
$272$	3.35941			0.203694
$273$	26.6228	−	10.7305i	1.61129	−	0.649438i
$274$	8.71016			0.526200
$275$	1.58042	−	0.912454i	0.0953028	−	0.0550231i
$276$	1.63827	+	0.562211i	0.0986121	+	0.0338411i
$277$	8.89694	−	15.4099i	0.534565	−	0.925894i	−0.464619	−	0.885511i	$-0.653809\pi$
$277$	8.89694	−	15.4099i	0.534565	−	0.925894i	0.999184	−	0.0403832i	$-0.0128579\pi$
$278$	−0.470775	−	0.815407i	−0.0282352	−	0.0489048i
$279$	9.11695	+	22.4319i	0.545817	+	1.34296i
$280$	1.54236	−	4.45232i	0.0921734	−	0.266077i
$281$		−	1.55697i		−	0.0928810i	−0.998921	−	0.0464405i	$-0.985212\pi$
$281$		−	1.55697i		−	0.0928810i	0.998921	−	0.0464405i	$-0.0147878\pi$
$282$	−11.0455	+	9.62169i	−0.657747	+	0.572963i
$283$	24.6744	+	14.2458i	1.46674	+	0.846822i	0.999308	−	0.0372070i	$-0.0118461\pi$
$283$	24.6744	+	14.2458i	1.46674	+	0.846822i	0.467432	+	0.884029i	$0.345179\pi$
$284$	8.33381	+	4.81153i	0.494521	+	0.285512i
$285$	3.83470	−	3.34041i	0.227148	−	0.197869i
$286$		−	6.25214i		−	0.369697i
$287$	−8.68684	+	7.52294i	−0.512768	+	0.444065i
$288$	1.12956	+	2.77923i	0.0665597	+	0.163768i
$289$	2.85719	+	4.94879i	0.168070	+	0.291105i
$290$	1.11253	−	1.92696i	0.0653301	−	0.113155i
$291$	−19.1110	−	6.55840i	−1.12031	−	0.384460i
$292$	9.57661	−	5.52906i	0.560429	−	0.323564i
$293$	−13.8727			−0.810454			−0.405227	−	0.914216i	$-0.632807\pi$
$293$	−13.8727			−0.810454			−0.405227	+	0.914216i	$0.632807\pi$
$294$	−12.1094	+	0.601835i	−0.706235	+	0.0350998i
$295$	2.13807			0.124483
$296$	0.407891	−	0.235496i	0.0237082	−	0.0136879i
$297$	−5.17857	+	0.287471i	−0.300491	+	0.0166808i
$298$	−0.434930	+	0.753321i	−0.0251948	+	0.0436387i
$299$	3.13186	+	5.42454i	0.181120	+	0.313709i
$300$	−3.10788	+	0.607439i	−0.179434	+	0.0350705i
$301$	−9.58132	+	8.29757i	−0.552258	+	0.478264i
$302$		−	7.14172i		−	0.410960i
$303$	−19.7305	−	22.6501i	−1.13349	−	1.30121i
$304$	1.42779	+	0.824336i	0.0818895	+	0.0472789i
$305$	−1.81524	−	1.04803i	−0.103941	−	0.0600101i
$306$	6.18838	−	7.95454i	0.353766	−	0.454731i
$307$			26.0728i			1.48805i	0.668151	+	0.744025i	$0.267086\pi$
$307$			26.0728i			1.48805i	−0.668151	+	0.744025i	$0.732914\pi$
$308$	−0.864439	+	2.49537i	−0.0492560	+	0.142187i
$309$	−2.71652	−	13.8987i	−0.154538	−	0.790672i
$310$	7.18718	+	12.4486i	0.408204	+	0.707031i
$311$	4.89012	−	8.46993i	0.277293	−	0.480286i	−0.693418	−	0.720536i	$-0.743896\pi$
$311$	4.89012	−	8.46993i	0.277293	−	0.480286i	0.970711	+	0.240250i	$0.0772294\pi$
$312$	−3.52153	+	10.2616i	−0.199367	+	0.580951i
$313$	−14.9080	+	8.60715i	−0.842651	+	0.486505i	−0.858164	−	0.513375i	$-0.828395\pi$
$313$	−14.9080	+	8.60715i	−0.842651	+	0.486505i	0.0155136	+	0.999880i	$0.495062\pi$
$314$	−13.7262			−0.774612
$315$	−7.70118	−	11.8537i	−0.433913	−	0.667879i
$316$	1.15327			0.0648766
$317$	−7.16590	+	4.13723i	−0.402477	+	0.232370i	−0.687552	−	0.726135i	$-0.741315\pi$
$317$	−7.16590	+	4.13723i	−0.402477	+	0.232370i	0.285075	+	0.958505i	$0.407981\pi$
$318$	3.40237	−	9.91443i	0.190796	−	0.555973i
$319$	−0.623536	+	1.08000i	−0.0349113	+	0.0604682i
$320$	0.890465	+	1.54233i	0.0497785	+	0.0862189i
$321$	6.55556	+	33.5407i	0.365896	+	1.87206i
$322$	−0.499985	−	2.59808i	−0.0278631	−	0.144785i
$323$		−	5.53856i		−	0.308174i
$324$	8.66152	+	2.44502i	0.481195	+	0.135834i
$325$	−9.91763	−	5.72594i	−0.550131	−	0.317618i
$326$	8.09924	+	4.67610i	0.448575	+	0.258985i
$327$	−18.1335	−	20.8168i	−1.00278	−	1.15117i
$328$		−	4.34340i		−	0.239824i
$329$	21.1433	+	7.32438i	1.16567	+	0.403806i
$330$	−3.02178	+	0.590611i	−0.166344	+	0.0325120i
$331$	8.69571	+	15.0614i	0.477959	+	0.827850i	0.999681	−	0.0252659i	$-0.00804325\pi$
$331$	8.69571	+	15.0614i	0.477959	+	0.827850i	−0.521721	+	0.853116i	$0.674710\pi$
$332$	3.76919	−	6.52843i	0.206861	−	0.358294i
$333$	0.193761	−	1.39963i	0.0106180	−	0.0766991i
$334$	21.4946	−	12.4099i	1.17613	−	0.679040i
$335$	−17.1559			−0.937325
$336$	2.82433	−	3.60876i	0.154080	−	0.196874i
$337$	24.0061			1.30770			0.653848	−	0.756626i	$-0.273153\pi$
$337$	24.0061			1.30770			0.653848	+	0.756626i	$0.273153\pi$
$338$	−22.7195	+	13.1171i	−1.23578	+	0.713476i
$339$	−10.4278	−	3.57856i	−0.566362	−	0.194361i
$340$	2.99144	−	5.18132i	0.162233	−	0.280996i
$341$	−4.02817	−	6.97700i	−0.218138	−	0.377826i
$342$	4.58203	−	1.86227i	0.247768	−	0.100700i
$343$	9.99974	+	15.5886i	0.539935	+	0.841707i
$344$		−	4.79063i		−	0.258294i
$345$	2.32593	−	2.02612i	0.125224	−	0.109083i
$346$	2.85421	+	1.64788i	0.153443	+	0.0885905i
$347$	20.7550	+	11.9829i	1.11419	+	0.643276i	0.939911	−	0.341420i	$-0.110908\pi$
$347$	20.7550	+	11.9829i	1.11419	+	0.643276i	0.174277	+	0.984697i	$0.444241\pi$
$348$	1.63172	−	1.42139i	0.0874694	−	0.0761946i
$349$		−	25.6100i		−	1.37087i	−0.728132	−	0.685437i	$-0.759611\pi$
$349$		−	25.6100i		−	1.37087i	0.728132	−	0.685437i	$-0.240389\pi$
$350$	3.16667	+	3.65660i	0.169266	+	0.195453i
$351$	17.8109	+	27.2414i	0.950675	+	1.45404i
$352$	−0.499076	−	0.864424i	−0.0266008	−	0.0460740i
$353$	−3.17800	+	5.50445i	−0.169148	+	0.292972i	−0.938120	−	0.346309i	$-0.887435\pi$
$353$	−3.17800	+	5.50445i	−0.169148	+	0.292972i	0.768973	+	0.639281i	$0.220768\pi$
$354$	1.96680	+	0.674955i	0.104534	+	0.0358734i
$355$	14.8419	−	8.56899i	0.787728	−	0.454795i
$356$	−9.63224			−0.510508
$357$	−15.2431	−	2.15526i	−0.806752	−	0.114068i
$358$	22.3850			1.18308
$359$	−21.2047	+	12.2425i	−1.11914	+	0.646136i	−0.941181	−	0.337902i	$-0.890283\pi$
$359$	−21.2047	+	12.2425i	−1.11914	+	0.646136i	−0.177959	+	0.984038i	$0.556949\pi$
$360$	5.29232	+	0.732655i	0.278930	+	0.0386143i
$361$	−8.14094	+	14.1005i	−0.428471	+	0.742133i
$362$	−1.31357	−	2.27516i	−0.0690395	−	0.119580i
$363$	−17.0051	+	3.32367i	−0.892539	+	0.174448i
$364$	16.2736	−	3.13177i	0.852970	−	0.164149i
$365$		−	19.6937i		−	1.03082i
$366$	−1.33899	−	1.53712i	−0.0699899	−	0.0803466i
$367$	−25.7670	−	14.8766i	−1.34503	−	0.776552i	−0.357488	−	0.933918i	$-0.616367\pi$
$367$	−25.7670	−	14.8766i	−1.34503	−	0.776552i	−0.987540	+	0.157365i	$0.949700\pi$
$368$	0.866025	+	0.500000i	0.0451447	+	0.0260643i
$369$	−10.2845	−	8.00099i	−0.535388	−	0.416515i
$370$		−	0.838804i		−	0.0436073i
$371$	−15.7230	+	3.02580i	−0.816297	+	0.157092i
$372$	2.68163	+	13.7202i	0.139036	+	0.711361i
$373$	−4.84352	−	8.38922i	−0.250788	−	0.434377i	0.712955	−	0.701210i	$-0.247356\pi$
$373$	−4.84352	−	8.38922i	−0.250788	−	0.434377i	−0.963743	+	0.266832i	$0.914023\pi$
$374$	−1.67660	+	2.90396i	−0.0866949	+	0.150160i
$375$	−6.83688	+	19.9225i	−0.353055	+	1.02879i
$376$	−7.32426	+	4.22866i	−0.377720	+	0.218077i
$377$	7.82578			0.403048
$378$	−3.34226	−	13.3353i	−0.171907	−	0.685892i
$379$	−20.7752			−1.06715			−0.533576	−	0.845752i	$-0.679152\pi$
$379$	−20.7752			−1.06715			−0.533576	+	0.845752i	$0.679152\pi$
$380$	2.54280	−	1.46808i	0.130443	−	0.0753112i
$381$	−0.937092	+	2.73066i	−0.0480087	+	0.139896i
$382$	2.35337	−	4.07616i	0.120409	−	0.208555i
$383$	−4.36899	−	7.56732i	−0.223245	−	0.386672i	0.732546	−	0.680717i	$-0.238332\pi$
$383$	−4.36899	−	7.56732i	−0.223245	−	0.386672i	−0.955791	+	0.294045i	$0.904998\pi$
$384$	0.332245	+	1.69989i	0.0169548	+	0.0867470i
$385$	3.07894	+	3.55529i	0.156917	+	0.181194i
$386$		−	1.06533i		−	0.0542240i
$387$	−11.3434	−	8.82484i	−0.576620	−	0.448592i
$388$	−10.1025	−	5.83269i	−0.512878	−	0.296110i
$389$	20.6982	+	11.9501i	1.04944	+	0.605895i	0.922493	−	0.386015i	$-0.126149\pi$
$389$	20.6982	+	11.9501i	1.04944	+	0.605895i	0.126948	+	0.991909i	$0.459482\pi$
$390$	12.6910	+	14.5690i	0.642636	+	0.737730i
$391$		−	3.35941i		−	0.169893i
$392$	−6.92819	−	1.00008i	−0.349927	−	0.0505116i
$393$	−3.27720	+	0.640533i	−0.165313	+	0.0323106i
$394$	8.48905	+	14.7035i	0.427672	+	0.740750i
$395$	1.02695	−	1.77873i	0.0516714	−	0.0894974i
$396$	−2.96617	−	0.410628i	−0.149055	−	0.0206349i
$397$	26.7399	−	15.4383i	1.34204	−	0.774825i	0.354931	−	0.934893i	$-0.384504\pi$
$397$	26.7399	−	15.4383i	1.34204	−	0.774825i	0.987106	+	0.160067i	$0.0511711\pi$
$398$	2.14372			0.107455
$399$	−5.94967	−	4.65639i	−0.297856	−	0.233111i
$400$	−1.82829			−0.0914144
$401$	−28.6452	+	16.5383i	−1.43047	+	0.825883i	−0.997156	−	0.0753598i	$-0.975989\pi$
$401$	−28.6452	+	16.5383i	−1.43047	+	0.825883i	−0.433315	+	0.901243i	$0.642656\pi$
$402$	−15.7816	−	5.41583i	−0.787113	−	0.270117i
$403$	−25.2781	+	43.7829i	−1.25919	+	2.18098i
$404$	−8.67140	−	15.0193i	−0.431418	−	0.747238i
$405$	11.4838	−	11.1817i	0.570635	−	0.555624i
$406$	−3.12345	−	1.08201i	−0.155014	−	0.0536995i
$407$			0.470121i			0.0233031i
$408$	4.38746	−	3.82192i	0.217212	−	0.189213i
$409$	30.8832	+	17.8304i	1.52707	+	0.881657i	0.999483	+	0.0321581i	$0.0102380\pi$
$409$	30.8832	+	17.8304i	1.52707	+	0.881657i	0.527591	+	0.849498i	$0.323095\pi$
$410$	−6.69895	−	3.86764i	−0.330838	−	0.191009i
$411$	11.3757	−	9.90934i	0.561120	−	0.488791i
$412$		−	8.17628i		−	0.402816i
$413$	−0.600251	−	3.11909i	−0.0295364	−	0.153480i
$414$	2.77923	−	1.12956i	0.136592	−	0.0555147i
$415$	−6.71266	−	11.6267i	−0.329512	−	0.570731i
$416$	−3.13186	+	5.42454i	−0.153552	+	0.265960i
$417$	−1.54251	−	0.529350i	−0.0755371	−	0.0259224i
$418$	−1.42515	+	0.822812i	−0.0697065	+	0.0402451i
$419$	22.3712			1.09291			0.546454	−	0.837489i	$-0.315978\pi$
$419$	22.3712			1.09291			0.546454	+	0.837489i	$0.315978\pi$
$420$	−3.05094	−	7.56952i	−0.148871	−	0.369355i
$421$	−7.17807			−0.349838			−0.174919	−	0.984583i	$-0.555966\pi$
$421$	−7.17807			−0.349838			−0.174919	+	0.984583i	$0.555966\pi$
$422$	−22.3262	+	12.8900i	−1.08682	+	0.627476i
$423$	−3.47925	+	25.1323i	−0.169167	+	1.22197i
$424$	3.02589	−	5.24099i	0.146950	−	0.254525i
$425$	3.07099	+	5.31910i	0.148965	+	0.258014i
$426$	16.3581	−	3.19721i	0.792553	−	0.154905i
$427$	−1.01928	+	2.94237i	−0.0493266	+	0.142391i
$428$			19.7311i			0.953740i
$429$	−7.11291	−	8.16543i	−0.343414	−	0.394231i
$430$	−7.38874	−	4.26589i	−0.356317	−	0.205720i
$431$	−12.9486	−	7.47587i	−0.623712	−	0.360100i	0.154601	−	0.987977i	$-0.450591\pi$
$431$	−12.9486	−	7.47587i	−0.623712	−	0.360100i	−0.778313	+	0.627877i	$0.783924\pi$
$432$	4.63708	+	2.34466i	0.223102	+	0.112808i
$433$		−	15.7882i		−	0.758735i	−0.925246	−	0.379367i	$-0.876142\pi$
$433$		−	15.7882i		−	0.758735i	0.925246	−	0.379367i	$-0.123858\pi$
$434$	16.1426	−	13.9798i	0.774870	−	0.671050i
$435$	−0.739265	−	3.78235i	−0.0354450	−	0.181350i
$436$	−7.96954	−	13.8036i	−0.381672	−	0.661075i
$437$	0.824336	−	1.42779i	0.0394333	−	0.0683005i
$438$	6.21700	−	18.1162i	0.297060	−	0.865623i
$439$	−35.6172	+	20.5636i	−1.69992	+	0.981448i	−0.754094	+	0.656767i	$0.771924\pi$
$439$	−35.6172	+	20.5636i	−1.69992	+	0.981448i	−0.945824	+	0.324681i	$0.894743\pi$
$440$	−1.77764			−0.0847455
$441$	−15.1305	+	14.5626i	−0.720498	+	0.693457i
$442$	21.0424			1.00088
$443$	12.6002	−	7.27471i	0.598652	−	0.345632i	−0.169859	−	0.985468i	$-0.554331\pi$
$443$	12.6002	−	7.27471i	0.598652	−	0.345632i	0.768511	+	0.639837i	$0.220998\pi$
$444$	0.264797	−	0.771611i	0.0125667	−	0.0366190i
$445$	−8.57717	+	14.8561i	−0.406597	+	0.704247i
$446$	−5.03319	−	8.71774i	−0.238328	−	0.412797i
$447$	0.289006	+	1.47866i	0.0136695	+	0.0699384i
$448$	2.00001	−	1.73204i	0.0944916	−	0.0818312i
$449$			5.90954i			0.278889i	0.990230	+	0.139444i	$0.0445316\pi$
$449$			5.90954i			0.278889i	−0.990230	+	0.139444i	$0.955468\pi$
$450$	−3.36790	+	4.32909i	−0.158764	+	0.204075i
$451$	3.75454	+	2.16768i	0.176794	+	0.102072i
$452$	−5.51239	−	3.18258i	−0.259281	−	0.149696i
$453$	−8.12496	−	9.32725i	−0.381744	−	0.438233i
$454$			26.2942i			1.23405i
$455$	9.66088	−	27.8881i	0.452909	−	1.30741i
$456$	2.80256	−	0.547762i	0.131242	−	0.0256513i
$457$	3.47842	+	6.02479i	0.162713	+	0.281828i	0.935841	−	0.352423i	$-0.114642\pi$
$457$	3.47842	+	6.02479i	0.162713	+	0.281828i	−0.773127	+	0.634251i	$0.781309\pi$
$458$	−9.82677	+	17.0205i	−0.459175	+	0.795314i
$459$	−0.967521	−	17.4292i	−0.0451600	−	0.813524i
$460$	1.54233	−	0.890465i	0.0719115	−	0.0415181i
$461$	−18.8889			−0.879742			−0.439871	−	0.898061i	$-0.644976\pi$
$461$	−18.8889			−0.879742			−0.439871	+	0.898061i	$0.644976\pi$
$462$	1.70995	+	4.24246i	0.0795540	+	0.197377i
$463$	17.2700			0.802607			0.401304	−	0.915945i	$-0.368557\pi$
$463$	17.2700			0.802607			0.401304	+	0.915945i	$0.368557\pi$
$464$	1.08200	−	0.624691i	0.0502304	−	0.0290006i
$465$	23.5490	+	8.08142i	1.09206	+	0.374767i
$466$	−1.60706	+	2.78352i	−0.0744458	+	0.128944i
$467$	9.47185	+	16.4057i	0.438305	+	0.759166i	0.997559	−	0.0698300i	$-0.0222457\pi$
$467$	9.47185	+	16.4057i	0.438305	+	0.759166i	−0.559254	+	0.828996i	$0.688912\pi$
$468$	7.07522	+	17.4083i	0.327052	+	0.804699i
$469$	4.81640	+	25.0275i	0.222401	+	1.15566i
$470$			15.0619i			0.694754i
$471$	−17.9267	+	15.6159i	−0.826017	+	0.719543i
$472$	1.03970	+	0.600268i	0.0478558	+	0.0276296i
$473$	4.14114	+	2.39089i	0.190410	+	0.109933i
$474$	1.50620	−	1.31205i	0.0691820	−	0.0602644i
$475$			3.01425i			0.138303i
$476$	−8.39851	−	2.90938i	−0.384945	−	0.133351i
$477$	−6.83582	−	16.8193i	−0.312991	−	0.770101i
$478$	−4.21089	−	7.29347i	−0.192601	−	0.333595i
$479$	0.290036	−	0.502357i	0.0132521	−	0.0229533i	−0.859323	−	0.511433i	$-0.829115\pi$
$479$	0.290036	−	0.502357i	0.0132521	−	0.0229533i	0.872575	+	0.488479i	$0.162448\pi$
$480$	2.91764	+	1.00126i	0.133171	+	0.0457010i
$481$	2.55492	−	1.47508i	0.116494	−	0.0672579i
$482$	8.84821			0.403025
$483$	−3.60876	−	2.82433i	−0.164204	−	0.128511i
$484$	−10.0037			−0.454713
$485$	−17.9919	+	10.3876i	−0.816969	+	0.471677i
$486$	14.0938	−	6.66075i	0.639306	−	0.302138i
$487$	−7.33055	+	12.6969i	−0.332179	+	0.575351i	−0.982939	−	0.183933i	$-0.941117\pi$
$487$	−7.33055	+	12.6969i	−0.332179	+	0.575351i	0.650760	+	0.759284i	$0.274450\pi$
$488$	−0.588474	−	1.01927i	−0.0266390	−	0.0461401i
$489$	15.8977	−	3.10722i	0.718917	−	0.140513i
$490$	−7.71176	+	9.79503i	−0.348382	+	0.442494i
$491$			21.9498i			0.990579i	0.868728	+	0.495290i	$0.164938\pi$
$491$			21.9498i			0.990579i	−0.868728	+	0.495290i	$0.835062\pi$
$492$	−4.94138	−	5.67257i	−0.222774	−	0.255739i
$493$	−3.63487	−	2.09859i	−0.163706	−	0.0945159i
$494$	8.94329	+	5.16341i	0.402378	+	0.232313i
$495$	−3.27459	+	4.20916i	−0.147182	+	0.189188i
$496$			8.07127i			0.362411i
$497$	−16.6675	−	19.2462i	−0.747640	−	0.863310i
$498$	−2.50459	−	12.8144i	−0.112233	−	0.574227i
$499$	−16.6874	−	28.9034i	−0.747029	−	1.29389i	−0.949241	−	0.314550i	$-0.898146\pi$
$499$	−16.6874	−	28.9034i	−0.747029	−	1.29389i	0.202212	−	0.979342i	$-0.435187\pi$
$500$	−6.08035	+	10.5315i	−0.271922	+	0.470982i
$501$	13.9540	−	40.6615i	0.623417	−	1.81662i
$502$	24.2685	−	14.0114i	1.08316	−	0.625360i
$503$	−13.0707			−0.582793			−0.291396	−	0.956602i	$-0.594120\pi$
$503$	−13.0707			−0.582793			−0.291396	+	0.956602i	$0.594120\pi$
$504$	−0.416965	−	7.92629i	−0.0185731	−	0.353065i
$505$	−30.8863			−1.37442
$506$	−0.864424	+	0.499076i	−0.0384284	+	0.0221866i
$507$	−14.7491	+	42.9786i	−0.655032	+	1.90875i
$508$	−0.833399	+	1.44349i	−0.0369761	+	0.0640445i
$509$	−7.51025	−	13.0081i	−0.332886	−	0.576575i	0.650190	−	0.759771i	$-0.274689\pi$
$509$	−7.51025	−	13.0081i	−0.332886	−	0.576575i	−0.983076	+	0.183196i	$0.941356\pi$
$510$	−1.98778	−	10.1702i	−0.0880203	−	0.450344i
$511$	−28.7299	+	5.52890i	−1.27093	+	0.244584i
$512$			1.00000i			0.0441942i
$513$	3.86558	−	7.64503i	0.170670	−	0.337536i
$514$	−10.8434	−	6.26044i	−0.478282	−	0.276136i
$515$	−12.6105	−	7.28069i	−0.555686	−	0.320825i
$516$	−5.45019	−	6.25668i	−0.239931	−	0.275435i
$517$		−	8.44169i		−	0.371265i
$518$	−1.22367	+	0.235489i	−0.0537652	+	0.0103468i
$519$	5.60241	−	1.09500i	0.245919	−	0.0480651i
$520$	5.57762	+	9.66073i	0.244595	+	0.423651i
$521$	1.62224	−	2.80981i	0.0710718	−	0.123100i	−0.828300	−	0.560286i	$-0.810691\pi$
$521$	1.62224	−	2.80981i	0.0710718	−	0.123100i	0.899371	+	0.437186i	$0.144025\pi$
$522$	0.513982	−	3.71274i	0.0224964	−	0.162502i
$523$	15.4763	−	8.93522i	0.676730	−	0.390710i	−0.121892	−	0.992543i	$-0.538896\pi$
$523$	15.4763	−	8.93522i	0.676730	−	0.390710i	0.798622	+	0.601833i	$0.205563\pi$
$524$	−1.92790			−0.0842205
$525$	8.29576	+	1.17295i	0.362057	+	0.0511919i
$526$	8.50177			0.370695
$527$	23.4820	−	13.5573i	1.02289	−	0.590567i
$528$	−1.63524	−	0.561171i	−0.0711646	−	0.0244219i
$529$	0.500000	−	0.866025i	0.0217391	−	0.0376533i
$530$	−5.38889	−	9.33384i	−0.234079	−	0.405436i
$531$	3.33656	−	1.35607i	0.144795	−	0.0588486i
$532$	−2.85557	−	3.29736i	−0.123804	−	0.142959i
$533$		−	27.2058i		−	1.17841i
$534$	−12.5799	+	10.9584i	−0.544387	+	0.474215i
$535$	30.4319	+	17.5699i	1.31569	+	0.759612i
$536$	−8.34250	−	4.81654i	−0.360341	−	0.208043i
$537$	29.2353	−	25.4668i	1.26160	−	1.09898i
$538$			10.6670i			0.459885i
$539$	4.32218	−	5.48978i	0.186170	−	0.236462i
$540$	7.74541	−	5.06408i	0.333309	−	0.217923i
$541$	−14.0263	−	24.2942i	−0.603037	−	1.04449i	−0.992358	−	0.123389i	$-0.960624\pi$
$541$	−14.0263	−	24.2942i	−0.603037	−	1.04449i	0.389321	−	0.921102i	$-0.372710\pi$
$542$	5.87807	−	10.1811i	0.252485	−	0.437316i
$543$	−4.30394	−	1.47700i	−0.184700	−	0.0633842i
$544$	2.90933	−	1.67970i	0.124737	−	0.0720167i
$545$	−28.3864			−1.21594
$546$	17.6908	−	22.6043i	0.757096	−	0.967374i
$547$	1.55799			0.0666150			0.0333075	−	0.999445i	$-0.489396\pi$
$547$	1.55799			0.0666150			0.0333075	+	0.999445i	$0.489396\pi$
$548$	7.54322	−	4.35508i	0.322230	−	0.186040i
$549$	−3.49749	−	0.484184i	−0.149269	−	0.0206645i
$550$	0.912454	−	1.58042i	0.0389072	−	0.0673892i
$551$	−1.02991	−	1.78386i	−0.0438757	−	0.0759949i
$552$	1.69989	−	0.332245i	0.0723520	−	0.0141413i
$553$	−2.88317	−	0.998779i	−0.122605	−	0.0424724i
$554$		−	17.7939i		−	0.755989i
$555$	−0.954287	−	1.09550i	−0.0405072	−	0.0465012i
$556$	−0.815407	−	0.470775i	−0.0345809	−	0.0199653i
$557$	−2.17616	−	1.25641i	−0.0922068	−	0.0532356i	0.453188	−	0.891415i	$-0.350287\pi$
$557$	−2.17616	−	1.25641i	−0.0922068	−	0.0532356i	−0.545394	+	0.838180i	$0.683620\pi$
$558$	19.1114	+	14.8681i	0.809052	+	0.629417i
$559$		−	30.0072i		−	1.26917i
$560$	−0.890439	−	4.62700i	−0.0376279	−	0.195526i
$561$	1.11408	+	5.70006i	0.0470366	+	0.240657i
$562$	−0.778484	−	1.34837i	−0.0328384	−	0.0568778i
$563$	−8.48717	+	14.7002i	−0.357691	+	0.619540i	−0.987575	−	0.157150i	$-0.949769\pi$
$563$	−8.48717	+	14.7002i	−0.357691	+	0.619540i	0.629883	+	0.776690i	$0.283103\pi$
$564$	−4.75480	+	13.8554i	−0.200213	+	0.583416i
$565$	−9.81719	+	5.66795i	−0.413012	+	0.238453i
$566$	28.4915			1.19759
$567$	−19.5363	−	13.6137i	−0.820446	−	0.571724i
$568$	9.62306			0.403774
$569$	11.0775	−	6.39562i	0.464395	−	0.268118i	−0.249496	−	0.968376i	$-0.580265\pi$
$569$	11.0775	−	6.39562i	0.464395	−	0.268118i	0.713890	+	0.700258i	$0.246932\pi$
$570$	1.65075	−	4.81023i	0.0691421	−	0.201478i
$571$	18.6681	−	32.3341i	0.781236	−	1.35314i	−0.149986	−	0.988688i	$-0.547923\pi$
$571$	18.6681	−	32.3341i	0.781236	−	1.35314i	0.931222	−	0.364452i	$-0.118744\pi$
$572$	−3.12607	−	5.41451i	−0.130708	−	0.226392i
$573$	−1.56379	−	8.00093i	−0.0653283	−	0.334244i
$574$	−3.76155	+	10.8585i	−0.157004	+	0.453224i
$575$			1.82829i			0.0762449i
$576$	2.36784	+	1.84210i	0.0986599	+	0.0767543i
$577$	1.30824	+	0.755315i	0.0544629	+	0.0314442i	0.526984	−	0.849875i	$-0.323323\pi$
$577$	1.30824	+	0.755315i	0.0544629	+	0.0314442i	−0.472521	+	0.881319i	$0.656656\pi$
$578$	4.94879	+	2.85719i	0.205843	+	0.118843i
$579$	−1.21200	−	1.39135i	−0.0503691	−	0.0578225i
$580$		−	2.22506i		−	0.0923907i
$581$	−15.0768	+	13.0568i	−0.625493	+	0.541686i
$582$	−19.8298	+	3.87576i	−0.821973	+	0.160655i
$583$	3.02029	+	5.23130i	0.125088	+	0.216658i
$584$	5.52906	−	9.57661i	0.228794	−	0.396283i
$585$	33.1496	+	4.58915i	1.37057	+	0.189738i
$586$	−12.0141	+	6.93637i	−0.496299	+	0.286539i
$587$	−19.3744			−0.799666			−0.399833	−	0.916588i	$-0.630932\pi$
$587$	−19.3744			−0.799666			−0.399833	+	0.916588i	$0.630932\pi$
$588$	−10.1861	+	6.57591i	−0.420069	+	0.271186i
$589$	13.3069			0.548300
$590$	1.85162	−	1.06904i	0.0762302	−	0.0440115i
$591$	27.8147	+	9.54528i	1.14414	+	0.392640i
$592$	0.235496	−	0.407891i	0.00967883	−	0.0167642i
$593$	−13.3874	−	23.1877i	−0.549756	−	0.952204i	−0.998291	−	0.0584394i	$-0.981388\pi$
$593$	−13.3874	−	23.1877i	−0.549756	−	0.952204i	0.448535	−	0.893765i	$-0.351946\pi$
$594$	−4.34104	+	2.83824i	−0.178115	+	0.116455i
$595$	−11.9658	+	10.3626i	−0.490550	+	0.424824i
$596$			0.869860i			0.0356309i
$597$	2.79975	−	2.43886i	0.114586	−	0.0998160i
$598$	5.42454	+	3.13186i	0.221826	+	0.128071i
$599$	−17.3871	−	10.0384i	−0.710417	−	0.410159i	0.100799	−	0.994907i	$-0.467860\pi$
$599$	−17.3871	−	10.0384i	−0.710417	−	0.410159i	−0.811215	+	0.584748i	$0.801194\pi$
$600$	−2.38779	+	2.08000i	−0.0974810	+	0.0849156i
$601$		−	1.39900i		−	0.0570663i	−0.999593	−	0.0285331i	$-0.990916\pi$
$601$		−	1.39900i		−	0.0570663i	0.999593	−	0.0285331i	$-0.00908361\pi$
$602$	−4.14888	+	11.9766i	−0.169096	+	0.488128i
$603$	−26.7725	+	10.8811i	−1.09026	+	0.443113i
$604$	−3.57086	−	6.18491i	−0.145296	−	0.251661i
$605$	−8.90794	+	15.4290i	−0.362159	+	0.627278i
$606$	−28.4121	−	9.75030i	−1.15416	−	0.396079i
$607$	−21.5959	+	12.4684i	−0.876553	+	0.506078i	−0.869520	−	0.493897i	$-0.835572\pi$
$607$	−21.5959	+	12.4684i	−0.876553	+	0.506078i	−0.00703239	+	0.999975i	$0.502238\pi$
$608$	1.64867			0.0668625
$609$	−5.31028	+	2.14034i	−0.215183	+	0.0867308i
$610$	−2.09606			−0.0848671
$611$	−45.8771	+	26.4872i	−1.85599	+	1.07156i
$612$	1.38202	−	9.98302i	0.0558650	−	0.403540i
$613$	−21.9558	+	38.0285i	−0.886785	+	1.53596i	−0.0431305	+	0.999069i	$0.513733\pi$
$613$	−21.9558	+	38.0285i	−0.886785	+	1.53596i	−0.843654	+	0.536887i	$0.819600\pi$
$614$	13.0364	+	22.5797i	0.526105	+	0.911241i
$615$	−13.1491	+	2.57001i	−0.530223	+	0.103633i
$616$	0.499061	+	2.59328i	0.0201077	+	0.104486i
$617$			39.3657i			1.58480i	0.609999	+	0.792402i	$0.291170\pi$
$617$			39.3657i			1.58480i	−0.609999	+	0.792402i	$0.708830\pi$
$618$	−9.30195	−	10.6784i	−0.374179	−	0.429548i
$619$	−3.83941	−	2.21668i	−0.154319	−	0.0890960i	0.420852	−	0.907129i	$-0.361731\pi$
$619$	−3.83941	−	2.21668i	−0.154319	−	0.0890960i	−0.575171	+	0.818033i	$0.695064\pi$
$620$	12.4486	+	7.18718i	0.499946	+	0.288644i
$621$	2.34466	−	4.63708i	0.0940881	−	0.186080i
$622$		−	9.78023i		−	0.392152i
$623$	24.0806	+	8.34190i	0.964767	+	0.334211i
$624$	2.08109	+	10.6476i	0.0833102	+	0.426246i
$625$	6.25796	+	10.8391i	0.250318	+	0.433564i
$626$	−8.60715	+	14.9080i	−0.344011	+	0.595844i
$627$	−0.925188	+	2.69597i	−0.0369484	+	0.107667i
$628$	−11.8872	+	6.86308i	−0.474351	+	0.273867i
$629$	−1.58226			−0.0630886
$630$	−12.5963	−	6.41499i	−0.501847	−	0.255579i
$631$	26.8091			1.06725			0.533626	−	0.845721i	$-0.320829\pi$
$631$	26.8091			1.06725			0.533626	+	0.845721i	$0.320829\pi$
$632$	0.998763	−	0.576636i	0.0397286	−	0.0229373i
$633$	−14.4938	+	42.2346i	−0.576077	+	1.67867i
$634$	−4.13723	+	7.16590i	−0.164310	+	0.284594i
$635$	1.48423	+	2.57075i	0.0588997	+	0.102017i
$636$	−2.01067	−	10.2873i	−0.0797283	−	0.407919i
$637$	−43.3963	−	6.26421i	−1.71942	−	0.248197i
$638$			1.24707i			0.0493721i
$639$	17.7267	−	22.7858i	0.701256	−	0.901394i
$640$	1.54233	+	0.890465i	0.0609660	+	0.0351987i
$641$	13.7645	+	7.94693i	0.543664	+	0.313885i	0.746563	−	0.665315i	$-0.231703\pi$
$641$	13.7645	+	7.94693i	0.543664	+	0.313885i	−0.202898	+	0.979200i	$0.565036\pi$
$642$	22.4476	+	25.7693i	0.885937	+	1.01703i
$643$			35.5512i			1.40200i	0.713161	+	0.701001i	$0.247263\pi$
$643$			35.5512i			1.40200i	−0.713161	+	0.701001i	$0.752737\pi$
$644$	−1.73204	−	2.00001i	−0.0682519	−	0.0788114i
$645$	−14.5031	+	2.83464i	−0.571058	+	0.111614i
$646$	−2.76928	−	4.79654i	−0.108956	−	0.188717i
$647$	0.832081	−	1.44121i	0.0327125	−	0.0566596i	−0.849206	−	0.528062i	$-0.822919\pi$
$647$	0.832081	−	1.44121i	0.0327125	−	0.0566596i	0.881918	+	0.471403i	$0.156252\pi$
$648$	8.72360	−	2.21331i	0.342695	−	0.0869472i
$649$	−1.03777	+	0.599159i	−0.0407362	+	0.0235190i
$650$	−11.4519			−0.449180
$651$	5.17819	−	36.6229i	0.202949	−	1.43537i
$652$	9.35219			0.366260
$653$	29.9085	−	17.2677i	1.17041	−	0.675737i	0.216634	−	0.976253i	$-0.430492\pi$
$653$	29.9085	−	17.2677i	1.17041	−	0.675737i	0.953777	+	0.300516i	$0.0971587\pi$
$654$	−26.1125	−	8.96112i	−1.02108	−	0.350407i
$655$	−1.71672	+	2.97345i	−0.0670780	+	0.116182i
$656$	−2.17170	−	3.76149i	−0.0847906	−	0.146862i
$657$	−12.4908	−	30.7330i	−0.487311	−	1.19901i
$658$	21.9728	−	4.22854i	0.856589	−	0.164846i
$659$			9.87817i			0.384799i	0.981317	+	0.192399i	$0.0616269\pi$
$659$			9.87817i			0.384799i	−0.981317	+	0.192399i	$0.938373\pi$
$660$	−2.32163	+	2.02237i	−0.0903695	+	0.0787208i
$661$	−33.4283	−	19.2999i	−1.30021	−	0.750678i	−0.319772	−	0.947495i	$-0.603606\pi$
$661$	−33.4283	−	19.2999i	−1.30021	−	0.750678i	−0.980440	+	0.196817i	$0.936940\pi$
$662$	15.0614	+	8.69571i	0.585378	+	0.337968i
$663$	27.4818	−	23.9394i	1.06731	−	0.929730i
$664$		−	7.53838i		−	0.292546i
$665$	−7.62840	+	1.46804i	−0.295817	+	0.0569282i
$666$	−0.532012	−	1.30899i	−0.0206150	−	0.0507225i
$667$	−0.624691	−	1.08200i	−0.0241881	−	0.0418951i
$668$	12.4099	−	21.4946i	0.480154	−	0.831650i
$669$	−16.4914	−	5.65943i	−0.637595	−	0.218806i
$670$	−14.8574	+	8.57793i	−0.573992	+	0.331394i
$671$	1.17477			0.0453516
$672$	0.641559	−	4.53744i	0.0247487	−	0.175036i
$673$	31.5214			1.21506			0.607531	−	0.794296i	$-0.292160\pi$
$673$	31.5214			1.21506			0.607531	+	0.794296i	$0.292160\pi$
$674$	20.7899	−	12.0031i	0.800797	−	0.462341i
$675$	0.526553	+	9.48546i	0.0202670	+	0.365096i
$676$	−13.1171	+	22.7195i	−0.504504	+	0.873826i
$677$	25.3117	+	43.8411i	0.972807	+	1.68495i	0.686990	+	0.726667i	$0.258932\pi$
$677$	25.3117	+	43.8411i	0.972807	+	1.68495i	0.285817	+	0.958284i	$0.407735\pi$
$678$	−10.8201	+	2.11479i	−0.415542	+	0.0812181i
$679$	20.2049	+	23.3309i	0.775393	+	0.895357i
$680$		−	5.98287i		−	0.229433i
$681$	29.9143	+	34.3408i	1.14632	+	1.31594i
$682$	−6.97700	−	4.02817i	−0.267163	−	0.154247i
$683$	−31.2495	−	18.0419i	−1.19573	−	0.690355i	−0.236130	−	0.971722i	$-0.575879\pi$
$683$	−31.2495	−	18.0419i	−1.19573	−	0.690355i	−0.959600	+	0.281367i	$0.909212\pi$
$684$	3.03702	−	3.90379i	0.116124	−	0.149265i
$685$		−	15.5122i		−	0.592690i
$686$	16.4543	+	8.50028i	0.628230	+	0.324542i
$687$	6.52978	+	33.4088i	0.249127	+	1.27462i
$688$	−2.39532	−	4.14881i	−0.0913206	−	0.158172i
$689$	18.9533	−	32.8281i	0.722064	−	1.25065i
$690$	1.00126	−	2.91764i	0.0381172	−	0.111073i
$691$	−19.7530	+	11.4044i	−0.751441	+	0.433845i	−0.826214	−	0.563356i	$-0.809510\pi$
$691$	−19.7530	+	11.4044i	−0.751441	+	0.433845i	0.0747732	+	0.997201i	$0.476177\pi$
$692$	3.29576			0.125286
$693$	7.05978	+	3.59539i	0.268179	+	0.136577i
$694$	23.9658			0.909730
$695$	−1.45218	+	0.838418i	−0.0550844	+	0.0318030i
$696$	0.702416	−	2.04682i	0.0266250	−	0.0775846i
$697$	−7.29562	+	12.6364i	−0.276341	+	0.478637i
$698$	−12.8050	−	22.1789i	−0.484677	−	0.839485i
$699$	1.06788	+	5.46365i	0.0403908	+	0.206654i
$700$	4.57071	+	1.58337i	0.172757	+	0.0598458i
$701$		−	9.21264i		−	0.347956i	−0.984749	−	0.173978i	$-0.944338\pi$
$701$		−	9.21264i		−	0.347956i	0.984749	−	0.173978i	$-0.0556622\pi$
$702$	29.0454	+	14.6863i	1.09625	+	0.554299i
$703$	−0.672479	−	0.388256i	−0.0253630	−	0.0146433i
$704$	−0.864424	−	0.499076i	−0.0325792	−	0.0188096i
$705$	17.1356	+	19.6712i	0.645362	+	0.740859i
$706$			6.35599i			0.239211i
$707$	8.67114	+	45.0579i	0.326112	+	1.69458i
$708$	2.04078	−	0.398872i	0.0766970	−	0.0149905i
$709$	4.44249	+	7.69463i	0.166841	+	0.288978i	0.937308	−	0.348503i	$-0.113310\pi$
$709$	4.44249	+	7.69463i	0.166841	+	0.288978i	−0.770466	+	0.637481i	$0.779977\pi$
$710$	8.56899	−	14.8419i	0.321589	−	0.557008i
$711$	0.474443	−	3.42713i	0.0177930	−	0.128527i
$712$	−8.34177	+	4.81612i	−0.312621	+	0.180492i
$713$	8.07127			0.302271
$714$	−14.2786	+	5.75506i	−0.534362	+	0.215378i
$715$	−11.1346			−0.416411
$716$	19.3860	−	11.1925i	0.724487	−	0.418283i
$717$	−13.7971	−	4.73481i	−0.515262	−	0.176825i
$718$	−12.2425	+	21.2047i	−0.456887	+	0.791352i
$719$	−16.2393	−	28.1273i	−0.605624	−	1.04897i	−0.991953	−	0.126610i	$-0.959590\pi$
$719$	−16.2393	−	28.1273i	−0.605624	−	1.04897i	0.386329	−	0.922361i	$-0.373743\pi$
$720$	4.94961	−	2.01166i	0.184461	−	0.0749702i
$721$	−7.08098	+	20.4406i	−0.263709	+	0.761250i
$722$			16.2819i			0.605949i
$723$	11.5560	−	10.0664i	0.429771	−	0.374373i
$724$	−2.27516	−	1.31357i	−0.0845558	−	0.0488183i
$725$	1.97820	+	1.14212i	0.0734686	+	0.0424171i
$726$	−13.0650	+	11.3810i	−0.484889	+	0.422387i
$727$			45.2760i			1.67919i	0.543210	+	0.839597i	$0.317209\pi$
$727$			45.2760i			1.67919i	−0.543210	+	0.839597i	$0.682791\pi$
$728$	12.5275	−	10.8490i	0.464300	−	0.402091i
$729$	10.8290	−	24.7332i	0.401074	−	0.916045i
$730$	−9.84687	−	17.0553i	−0.364449	−	0.631244i
$731$	−8.04685	+	13.9376i	−0.297624	+	0.515499i
$732$	−1.92816	−	0.661693i	−0.0712667	−	0.0244569i
$733$	−36.8605	+	21.2814i	−1.36147	+	0.786048i	−0.989820	−	0.142324i	$-0.954543\pi$
$733$	−36.8605	+	21.2814i	−1.36147	+	0.786048i	−0.371654	+	0.928371i	$0.621209\pi$
$734$	−29.7532			−1.09821
$735$	1.07183	+	21.5660i	0.0395349	+	0.795474i
$736$	1.00000			0.0368605
$737$	8.32708	−	4.80764i	0.306732	−	0.177092i
$738$	−12.9071	−	1.78683i	−0.475117	−	0.0657740i
$739$	15.0275	−	26.0284i	0.552795	−	0.957469i	−0.445277	−	0.895393i	$-0.646895\pi$
$739$	15.0275	−	26.0284i	0.552795	−	0.957469i	0.998071	−	0.0620755i	$-0.0197720\pi$
$740$	−0.419402	−	0.726425i	−0.0154175	−	0.0267039i
$741$	17.5544	−	3.43103i	0.644878	−	0.126042i
$742$	−12.1036	+	10.4819i	−0.444338	+	0.384803i
$743$		−	21.1026i		−	0.774179i	−0.922042	−	0.387090i	$-0.873480\pi$
$743$		−	21.1026i		−	0.774179i	0.922042	−	0.387090i	$-0.126520\pi$
$744$	9.18248	+	10.5413i	0.336646	+	0.386461i
$745$	1.34161	+	0.774580i	0.0491528	+	0.0283784i
$746$	−8.38922	−	4.84352i	−0.307151	−	0.177334i
$747$	−17.8497	−	13.8865i	−0.653085	−	0.508080i
$748$			3.35320i			0.122605i
$749$	17.0879	−	49.3277i	0.624380	−	1.80240i
$750$	4.04033	+	20.6718i	0.147532	+	0.754828i
$751$	3.69047	+	6.39208i	0.134667	+	0.233250i	0.925470	−	0.378820i	$-0.123670\pi$
$751$	3.69047	+	6.39208i	0.134667	+	0.233250i	−0.790803	+	0.612071i	$0.790337\pi$
$752$	−4.22866	+	7.32426i	−0.154203	+	0.267088i
$753$	15.7547	−	45.9089i	0.574135	−	1.67301i
$754$	6.77732	−	3.91289i	0.246816	−	0.142499i
$755$	−12.7189			−0.462889
$756$	−9.56212	−	9.87755i	−0.347771	−	0.359243i
$757$	39.1757			1.42386			0.711932	−	0.702248i	$-0.247820\pi$
$757$	39.1757			1.42386			0.711932	+	0.702248i	$0.247820\pi$
$758$	−17.9919	+	10.3876i	−0.653494	+	0.377295i
$759$	−0.561171	+	1.63524i	−0.0203692	+	0.0593554i
$760$	1.46808	−	2.54280i	0.0532530	−	0.0922369i
$761$	−24.8222	−	42.9934i	−0.899805	−	1.55851i	−0.827742	−	0.561109i	$-0.810375\pi$
$761$	−24.8222	−	42.9934i	−0.899805	−	1.55851i	−0.0720632	−	0.997400i	$-0.522958\pi$
$762$	0.553785	+	2.83337i	0.0200615	+	0.102642i
$763$	7.96930	+	41.4110i	0.288508	+	1.49918i
$764$		−	4.70674i		−	0.170284i
$765$	−14.1665	−	11.0211i	−0.512190	−	0.398467i
$766$	−7.56732	−	4.36899i	−0.273418	−	0.157858i
$767$	6.51236	+	3.75991i	0.235148	+	0.135763i
$768$	1.13768	+	1.30602i	0.0410523	+	0.0471270i
$769$		−	26.5055i		−	0.955814i	−0.878411	−	0.477907i	$-0.841396\pi$
$769$		−	26.5055i		−	0.955814i	0.878411	−	0.477907i	$-0.158604\pi$
$770$	4.44408	+	1.53950i	0.160154	+	0.0554799i
$771$	−21.2841	+	4.16000i	−0.766528	+	0.149819i
$772$	−0.532666	−	0.922605i	−0.0191711	−	0.0332053i
$773$	20.2511	−	35.0760i	0.728382	−	1.26160i	−0.229184	−	0.973383i	$-0.573606\pi$
$773$	20.2511	−	35.0760i	0.728382	−	1.26160i	0.957567	−	0.288212i	$-0.0930608\pi$
$774$	−14.2361	−	1.97081i	−0.511707	−	0.0708395i
$775$	−12.7796	+	7.37830i	−0.459057	+	0.265036i
$776$	−11.6654			−0.418763
$777$	−1.33024	+	1.69970i	−0.0477220	+	0.0609764i
$778$	23.9002			0.856864
$779$	−6.20147	+	3.58042i	−0.222191	+	0.128282i
$780$	18.2753	+	6.27160i	0.654360	+	0.224559i
$781$	−4.80263	+	8.31840i	−0.171852	+	0.297656i
$782$	−1.67970	−	2.90933i	−0.0600661	−	0.104038i
$783$	−3.55262	−	5.43366i	−0.126960	−	0.194183i
$784$	−6.50003	+	2.59800i	−0.232144	+	0.0927858i
$785$			24.4453i			0.872491i
$786$	−2.51788	+	2.19332i	−0.0898097	+	0.0782331i
$787$	23.1463	+	13.3636i	0.825078	+	0.476359i	0.852165	−	0.523274i	$-0.175290\pi$
$787$	23.1463	+	13.3636i	0.825078	+	0.476359i	−0.0270863	+	0.999633i	$0.508623\pi$
$788$	14.7035	+	8.48905i	0.523790	+	0.302410i
$789$	11.1035	−	9.67226i	0.395295	−	0.344341i
$790$		−	2.05390i		−	0.0730743i
$791$	11.0247	+	12.7304i	0.391994	+	0.452641i
$792$	−2.77409	+	1.12747i	−0.0985730	+	0.0400628i
$793$	−3.68604	−	6.38441i	−0.130895	−	0.226717i
$794$	15.4383	−	26.7399i	0.547884	−	0.948963i
$795$	−17.6569	−	6.05939i	−0.626226	−	0.214904i
$796$	1.85652	−	1.07186i	0.0658026	−	0.0379912i
$797$	30.0145			1.06317			0.531584	−	0.847006i	$-0.321597\pi$
$797$	30.0145			1.06317			0.531584	+	0.847006i	$0.321597\pi$
$798$	−7.48076	−	1.05772i	−0.264816	−	0.0374429i
$799$	28.4116			1.00513
$800$	−1.58334	+	0.914144i	−0.0559797	+	0.0323199i
$801$	−3.96260	+	28.6237i	−0.140012	+	1.01137i
$802$	−16.5383	+	28.6452i	−0.583987	+	1.01150i
$803$	5.51884	+	9.55891i	0.194756	+	0.337327i
$804$	−16.3752	+	3.20054i	−0.577507	+	0.112874i
$805$	−4.62700	+	0.890439i	−0.163080	+	0.0313838i
$806$			50.5561i			1.78076i
$807$	12.1355	+	13.9313i	0.427191	+	0.490404i
$808$	−15.0193	−	8.67140i	−0.528377	−	0.305059i
$809$	−24.3548	−	14.0613i	−0.856271	−	0.494368i	0.00649108	−	0.999979i	$-0.497934\pi$
$809$	−24.3548	−	14.0613i	−0.856271	−	0.494368i	−0.862762	+	0.505611i	$0.831267\pi$
$810$	4.35440	−	15.4256i	0.152998	−	0.541999i
$811$		−	32.9090i		−	1.15559i	−0.816182	−	0.577795i	$-0.803913\pi$
$811$		−	32.9090i		−	1.15559i	0.816182	−	0.577795i	$-0.196087\pi$
$812$	−3.24599	+	0.624673i	−0.113912	+	0.0219217i
$813$	−3.90591	−	19.9841i	−0.136986	−	0.700873i
$814$	0.235061	+	0.407137i	0.00823887	+	0.0142701i
$815$	8.32780	−	14.4242i	0.291710	−	0.505257i
$816$	1.88870	−	5.50361i	0.0661176	−	0.192665i
$817$	−6.84003	+	3.94909i	−0.239302	+	0.138161i
$818$	35.6608			1.24685
$819$	−2.61175	−	49.6481i	−0.0912620	−	1.73484i
$820$	−7.73529			−0.270128
$821$	13.1079	−	7.56785i	0.457469	−	0.264120i	−0.253510	−	0.967333i	$-0.581585\pi$
$821$	13.1079	−	7.56785i	0.457469	−	0.264120i	0.710979	+	0.703213i	$0.248252\pi$
$822$	4.89695	−	14.2696i	0.170801	−	0.497708i
$823$	15.9647	−	27.6517i	0.556494	−	0.963876i	−0.441291	−	0.897364i	$-0.645479\pi$
$823$	15.9647	−	27.6517i	0.556494	−	0.963876i	0.997786	−	0.0665125i	$-0.0211872\pi$
$824$	−4.08814	−	7.08086i	−0.142417	−	0.246674i
$825$	−0.606316	−	3.10214i	−0.0211092	−	0.108003i
$826$	−2.07938	−	2.40108i	−0.0723508	−	0.0835444i
$827$		−	47.2478i		−	1.64297i	−0.570233	−	0.821483i	$-0.693147\pi$
$827$		−	47.2478i		−	1.64297i	0.570233	−	0.821483i	$-0.306853\pi$
$828$	1.84210	−	2.36784i	0.0640175	−	0.0822881i
$829$	−8.53322	−	4.92666i	−0.296371	−	0.171110i	0.344440	−	0.938808i	$-0.388069\pi$
$829$	−8.53322	−	4.92666i	−0.296371	−	0.171110i	−0.640811	+	0.767698i	$0.721402\pi$
$830$	−11.6267	−	6.71266i	−0.403568	−	0.233000i
$831$	−20.2437	−	23.2392i	−0.702244	−	0.806159i
$832$			6.26372i			0.217155i
$833$	18.4766	+	14.5469i	0.640176	+	0.504019i
$834$	−1.60053	+	0.312825i	−0.0554218	+	0.0108322i
$835$	−22.1012	−	38.2803i	−0.764842	−	1.32475i
$836$	−0.822812	+	1.42515i	−0.0284576	+	0.0492899i
$837$	41.8751	−	2.32455i	1.44741	−	0.0803483i
$838$	19.3741	−	11.1856i	0.669266	−	0.386401i
$839$	8.06261			0.278352			0.139176	−	0.990268i	$-0.455555\pi$
$839$	8.06261			0.278352			0.139176	+	0.990268i	$0.455555\pi$
$840$	−6.42695	−	5.02993i	−0.221751	−	0.173549i
$841$	27.4390			0.946174
$842$	−6.21639	+	3.58904i	−0.214231	+	0.123686i
$843$	−2.55073	−	0.875345i	−0.0878518	−	0.0301485i
$844$	−12.8900	+	22.3262i	−0.443692	+	0.768498i
$845$	23.3606	+	40.4618i	0.803630	+	1.39193i
$846$	9.55302	+	23.5048i	0.328440	+	0.808112i
$847$	25.0092	+	8.66359i	0.859326	+	0.297685i
$848$		−	6.05178i		−	0.207819i
$849$	37.2106	−	32.4141i	1.27706	−	1.11245i
$850$	5.31910	+	3.07099i	0.182444	+	0.105334i
$851$	−0.407891	−	0.235496i	−0.0139823	−	0.00807270i
$852$	12.5679	−	10.9479i	0.430570	−	0.375069i
$853$			28.1001i			0.962128i	0.876686	+	0.481064i	$0.159749\pi$
$853$			28.1001i			0.962128i	−0.876686	+	0.481064i	$0.840251\pi$
$854$	0.588457	+	3.05781i	0.0201366	+	0.104636i
$855$	−3.31657	−	8.16028i	−0.113424	−	0.279076i
$856$	9.86556	+	17.0877i	0.337198	+	0.584044i
$857$	8.71262	−	15.0907i	0.297618	−	0.515489i	−0.677973	−	0.735087i	$-0.737141\pi$
$857$	8.71262	−	15.0907i	0.297618	−	0.515489i	0.975590	+	0.219598i	$0.0704746\pi$
$858$	−10.2427	−	3.51502i	−0.349679	−	0.120001i
$859$	−15.1009	+	8.71853i	−0.515237	+	0.297472i	−0.734984	−	0.678085i	$-0.762810\pi$
$859$	−15.1009	+	8.71853i	−0.515237	+	0.297472i	0.219747	+	0.975557i	$0.429477\pi$
$860$	−8.53178			−0.290931
$861$	7.44074	+	18.4608i	0.253580	+	0.629144i
$862$	−14.9517			−0.509258
$863$	33.8050	−	19.5173i	1.15074	−	0.664378i	0.201669	−	0.979454i	$-0.435363\pi$
$863$	33.8050	−	19.5173i	1.15074	−	0.664378i	0.949066	+	0.315076i	$0.102030\pi$
$864$	5.18816	−	0.288003i	0.176505	−	0.00979807i
$865$	2.93476	−	5.08315i	0.0997847	−	0.172832i
$866$	−7.89412	−	13.6730i	−0.268253	−	0.464628i
$867$	9.71378	−	1.89857i	0.329897	−	0.0644788i
$868$	6.99004	−	20.1781i	0.237257	−	0.684890i
$869$			1.15114i			0.0390497i
$870$	−2.53140	−	2.90598i	−0.0858225	−	0.0985220i
$871$	−52.2551	−	30.1695i	−1.77060	−	1.02225i
$872$	−13.8036	−	7.96954i	−0.467450	−	0.269883i
$873$	−21.4888	+	27.6217i	−0.727287	+	0.934854i
$874$		−	1.64867i		−	0.0557672i
$875$	24.3215	−	21.0628i	0.822218	−	0.712053i
$876$	−3.67400	−	18.7975i	−0.124133	−	0.635110i
$877$	0.839003	+	1.45320i	0.0283311	+	0.0490710i	0.879843	−	0.475264i	$-0.157647\pi$
$877$	0.839003	+	1.45320i	0.0283311	+	0.0490710i	−0.851512	+	0.524335i	$0.824314\pi$
$878$	−20.5636	+	35.6172i	−0.693988	+	1.20202i
$879$	−7.79940	+	22.7272i	−0.263067	+	0.766571i
$880$	−1.53948	+	0.888819i	−0.0518958	+	0.0299621i
$881$	−41.0614			−1.38339			−0.691696	−	0.722189i	$-0.743136\pi$
$881$	−41.0614			−1.38339			−0.691696	+	0.722189i	$0.743136\pi$
$882$	−5.82207	+	20.1768i	−0.196039	+	0.679388i
$883$	−51.3510			−1.72810			−0.864049	−	0.503408i	$-0.832079\pi$
$883$	−51.3510			−1.72810			−0.864049	+	0.503408i	$0.832079\pi$
$884$	18.2233	−	10.5212i	0.612914	−	0.353866i
$885$	1.20205	−	3.50273i	0.0404064	−	0.117743i
$886$	7.27471	−	12.6002i	0.244399	−	0.423311i
$887$	21.8703	+	37.8805i	0.734334	+	1.27190i	0.955015	+	0.296558i	$0.0958388\pi$
$887$	21.8703	+	37.8805i	0.734334	+	1.27190i	−0.220681	+	0.975346i	$0.570828\pi$
$888$	−0.156485	−	0.800633i	−0.00525128	−	0.0268675i
$889$	3.33361	−	2.88696i	0.111806	−	0.0968256i
$890$			17.1543i			0.575015i
$891$	−2.44050	+	8.64551i	−0.0817597	+	0.289635i
$892$	−8.71774	−	5.03319i	−0.291891	−	0.168524i
$893$	12.0753	+	6.97168i	0.404084	+	0.233298i
$894$	0.989618	+	1.13606i	0.0330978	+	0.0379954i
$895$		−	39.8661i		−	1.33258i
$896$	0.866040	−	2.50000i	0.0289324	−	0.0835190i
$897$	10.6476	−	2.08109i	0.355513	−	0.0694855i
$898$	2.95477	+	5.11782i	0.0986020	+	0.170784i
$899$	5.04205	−	8.73308i	0.168162	−	0.291265i
$900$	−0.752138	+	5.43305i	−0.0250713	+	0.181102i
$901$	−17.6066	+	10.1652i	−0.586562	+	0.338652i
$902$	4.33537			0.144352
$903$	8.20691	+	20.3617i	0.273109	+	0.677596i
$904$	−6.36516			−0.211702
$905$	−4.05191	+	2.33937i	−0.134690	+	0.0777633i
$906$	−11.7001	−	4.01515i	−0.388708	−	0.133395i
$907$	24.9311	−	43.1819i	0.827824	−	1.43383i	−0.0719181	−	0.997411i	$-0.522912\pi$
$907$	24.9311	−	43.1819i	0.827824	−	1.43383i	0.899742	−	0.436422i	$-0.143755\pi$
$908$	13.1471	+	22.7715i	0.436302	+	0.755698i
$909$	−48.1996	+	19.5897i	−1.59868	+	0.649748i
$910$	−5.57746	−	28.9822i	−0.184891	−	0.960751i
$911$			35.8440i			1.18757i	0.804625	+	0.593783i	$0.202366\pi$
$911$			35.8440i			1.18757i	−0.804625	+	0.593783i	$0.797634\pi$
$912$	2.15320	−	1.87565i	0.0712997	−	0.0621091i
$913$	6.51636	+	3.76222i	0.215660	+	0.124511i
$914$	6.02479	+	3.47842i	0.199282	+	0.115056i
$915$	−2.73751	+	2.38464i	−0.0904991	+	0.0788338i
$916$			19.6535i			0.649371i
$917$	4.81973	+	1.66963i	0.159162	+	0.0551362i
$918$	−9.55248	−	14.6103i	−0.315279	−	0.482213i
$919$	−13.3474	−	23.1183i	−0.440289	−	0.762603i	0.557422	−	0.830229i	$-0.311791\pi$
$919$	−13.3474	−	23.1183i	−0.440289	−	0.762603i	−0.997711	+	0.0676268i	$0.978457\pi$
$920$	0.890465	−	1.54233i	0.0293578	−	0.0508491i
$921$	42.7141	+	14.6584i	1.40748	+	0.483010i
$922$	−16.3582	+	9.44443i	−0.538729	+	0.311036i
$923$	60.2761			1.98401
$924$	3.60209	+	2.81911i	0.118500	+	0.0927418i
$925$	0.861110			0.0283131
$926$	14.9563	−	8.63502i	0.491495	−	0.283764i
$927$	−24.2971	−	3.36363i	−0.798022	−	0.110476i
$928$	0.624691	−	1.08200i	0.0205065	−	0.0355183i
$929$	11.2304	+	19.4516i	0.368457	+	0.638186i	0.989325	−	0.145729i	$-0.0465528\pi$
$929$	11.2304	+	19.4516i	0.368457	+	0.638186i	−0.620867	+	0.783916i	$0.713219\pi$
$930$	24.4348	−	4.77580i	0.801248	−	0.156605i
$931$	4.28325	+	10.7164i	0.140378	+	0.351216i
$932$			3.21413i			0.105282i
$933$	−11.1267	−	12.7732i	−0.364273	−	0.418176i
$934$	16.4057	+	9.47185i	0.536812	+	0.309928i
$935$	5.17174	+	2.98591i	0.169134	+	0.0976496i
$936$	14.8315	+	11.5384i	0.484782	+	0.377145i
$937$			36.9477i			1.20703i	0.797353	+	0.603514i	$0.206233\pi$
$937$			36.9477i			1.20703i	−0.797353	+	0.603514i	$0.793767\pi$
$938$	16.6849	+	19.2663i	0.544781	+	0.629066i
$939$	5.71936	+	29.2623i	0.186644	+	0.954940i
$940$	7.53095	+	13.0440i	0.245633	+	0.425448i
$941$	25.9527	−	44.9514i	0.846034	−	1.46537i	−0.0386864	−	0.999251i	$-0.512317\pi$
$941$	25.9527	−	44.9514i	0.846034	−	1.46537i	0.884720	−	0.466122i	$-0.154349\pi$
$942$	−7.71699	+	22.4871i	−0.251433	+	0.732670i
$943$	−3.76149	+	2.17170i	−0.122491	+	0.0707202i
$944$	1.20054			0.0390741
$945$	−23.7492	+	5.95233i	−0.772561	+	0.193629i
$946$	4.78178			0.155469
$947$	3.70407	−	2.13855i	0.120366	−	0.0694934i	−0.438608	−	0.898678i	$-0.644528\pi$
$947$	3.70407	−	2.13855i	0.120366	−	0.0694934i	0.558974	+	0.829185i	$0.311195\pi$
$948$	0.648382	−	1.88937i	0.0210585	−	0.0613638i
$949$	34.6325	−	59.9852i	1.12422	−	1.94720i
$950$	1.50712	+	2.61042i	0.0488976	+	0.0846931i
$951$	2.74915	+	14.0656i	0.0891472	+	0.456110i
$952$	−8.72801	+	1.67966i	−0.282876	+	0.0544379i
$953$		−	28.0861i		−	0.909798i	−0.890543	−	0.454899i	$-0.849675\pi$
$953$		−	28.0861i		−	0.909798i	0.890543	−	0.454899i	$-0.150325\pi$
$954$	−14.3296	−	11.1480i	−0.463939	−	0.360930i
$955$	−7.25936	−	4.19119i	−0.234907	−	0.135624i
$956$	−7.29347	−	4.21089i	−0.235888	−	0.136190i
$957$	1.41876	+	1.62870i	0.0458621	+	0.0526486i
$958$		−	0.580072i		−	0.0187413i
$959$	−22.6297	+	4.35495i	−0.730751	+	0.140629i
$960$	3.02738	−	0.591704i	0.0977082	−	0.0190972i
$961$	17.0727	+	29.5707i	0.550731	+	0.953894i
$962$	1.47508	−	2.55492i	0.0475585	−	0.0823738i
$963$	58.6342	+	8.11717i	1.88946	+	0.261572i
$964$	7.66278	−	4.42411i	0.246801	−	0.142491i
$965$	−1.89728			−0.0610757
$966$	−4.53744	−	0.641559i	−0.145990	−	0.0206418i
$967$	41.1377			1.32290			0.661450	−	0.749989i	$-0.269941\pi$
$967$	41.1377			1.32290			0.661450	+	0.749989i	$0.269941\pi$
$968$	−8.66345	+	5.00185i	−0.278454	+	0.160765i
$969$	−9.07365	−	3.11384i	−0.291488	−	0.100031i
$970$	−10.3876	+	17.9919i	−0.333526	+	0.577684i
$971$	10.4551	+	18.1087i	0.335519	+	0.581135i	0.983584	−	0.180449i	$-0.0577551\pi$
$971$	10.4551	+	18.1087i	0.335519	+	0.581135i	−0.648066	+	0.761584i	$0.724422\pi$
$972$	8.87519	−	12.8153i	0.284672	−	0.411050i
$973$	1.63080	+	1.88311i	0.0522811	+	0.0603697i
$974$			14.6611i			0.469772i
$975$	−14.9564	+	13.0285i	−0.478989	+	0.417247i
$976$	−1.01927	−	0.588474i	−0.0326260	−	0.0188366i
$977$	24.0409	+	13.8800i	0.769137	+	0.444062i	0.832567	−	0.553925i	$-0.186870\pi$
$977$	24.0409	+	13.8800i	0.769137	+	0.444062i	−0.0634294	+	0.997986i	$0.520204\pi$
$978$	12.2142	−	10.6398i	0.390566	−	0.340222i
$979$		−	9.61443i		−	0.307279i
$980$	−1.78107	+	12.3386i	−0.0568942	+	0.394143i
$981$	−44.2983	+	18.0041i	−1.41434	+	0.574826i
$982$	10.9749	+	19.0091i	0.350223	+	0.606604i
$983$	9.28941	−	16.0897i	0.296286	−	0.513183i	−0.678997	−	0.734141i	$-0.737585\pi$
$983$	9.28941	−	16.0897i	0.296286	−	0.513183i	0.975283	+	0.220958i	$0.0709185\pi$
$984$	−7.11564	−	2.44191i	−0.226838	−	0.0778451i
$985$	26.1859	−	15.1184i	0.834351	−	0.481713i
$986$	−4.19719			−0.133666
$987$	23.8863	−	30.5205i	0.760308	−	0.971477i
$988$	10.3268			0.328540
$989$	−4.14881	+	2.39532i	−0.131925	+	0.0761667i
$990$	−0.731301	+	5.28253i	−0.0232423	+	0.167890i
$991$	4.39574	−	7.61365i	0.139635	−	0.241856i	−0.787723	−	0.616029i	$-0.788740\pi$
$991$	4.39574	−	7.61365i	0.139635	−	0.241856i	0.927359	+	0.374174i	$0.122074\pi$
$992$	4.03563	+	6.98992i	0.128131	+	0.221930i
$993$	29.5634	−	5.77821i	0.938167	−	0.183366i
$994$	−24.0576	−	8.33395i	−0.763061	−	0.264337i
$995$		−	3.81782i		−	0.121033i
$996$	−8.57623	−	9.84529i	−0.271748	−	0.311960i
$997$	3.42951	+	1.98003i	0.108614	+	0.0627081i	0.553323	−	0.832967i	$-0.313360\pi$
$997$	3.42951	+	1.98003i	0.108614	+	0.0627081i	−0.444709	+	0.895675i	$0.646693\pi$
$998$	−28.9034	−	16.6874i	−0.914920	−	0.528229i
$999$	−2.18403	−	1.10432i	−0.0690996	−	0.0349391i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.c.185.24	yes	56
3.2	odd	2	inner	966.2.l.c.185.5	yes	56
7.5	odd	6	inner	966.2.l.c.47.5	✓	56
21.5	even	6	inner	966.2.l.c.47.24	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.c.47.5	✓	56	7.5	odd	6	inner
966.2.l.c.47.24	yes	56	21.5	even	6	inner
966.2.l.c.185.5	yes	56	3.2	odd	2	inner
966.2.l.c.185.24	yes	56	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.l (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.562211 - 1.63827i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.890465 - 1.54233i) q^{5} +(-0.332245 - 1.69989i) q^{6} +(-2.00001 + 1.73204i) q^{7} -1.00000i q^{8} +(-2.36784 - 1.84210i) q^{9} +O(q^{10})\)	\(q+(0.866025 - 0.500000i) q^{2} +(0.562211 - 1.63827i) q^{3} +(0.500000 - 0.866025i) q^{4} +(-0.890465 - 1.54233i) q^{5} +(-0.332245 - 1.69989i) q^{6} +(-2.00001 + 1.73204i) q^{7} -1.00000i q^{8} +(-2.36784 - 1.84210i) q^{9} +(-1.54233 - 0.890465i) q^{10} +(0.864424 + 0.499076i) q^{11} +(-1.13768 - 1.30602i) q^{12} -6.26372i q^{13} +(-0.866040 + 2.50000i) q^{14} +(-3.02738 + 0.591704i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-1.67970 + 2.90933i) q^{17} +(-2.97166 - 0.411389i) q^{18} +(-1.42779 + 0.824336i) q^{19} -1.78093 q^{20} +(1.71312 + 4.25032i) q^{21} +0.998151 q^{22} +(-0.866025 + 0.500000i) q^{23} +(-1.63827 - 0.562211i) q^{24} +(0.914144 - 1.58334i) q^{25} +(-3.13186 - 5.42454i) q^{26} +(-4.34908 + 2.84350i) q^{27} +(0.499985 + 2.59808i) q^{28} +1.24938i q^{29} +(-2.32593 + 2.02612i) q^{30} +(-6.98992 - 4.03563i) q^{31} +(-0.866025 - 0.500000i) q^{32} +(1.30361 - 1.13557i) q^{33} +3.35941i q^{34} +(4.45232 + 1.54236i) q^{35} +(-2.77923 + 1.12956i) q^{36} +(0.235496 + 0.407891i) q^{37} +(-0.824336 + 1.42779i) q^{38} +(-10.2616 - 3.52153i) q^{39} +(-1.54233 + 0.890465i) q^{40} +4.34340 q^{41} +(3.60876 + 2.82433i) q^{42} +4.79063 q^{43} +(0.864424 - 0.499076i) q^{44} +(-0.732655 + 5.29232i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-4.22866 - 7.32426i) q^{47} +(-1.69989 + 0.332245i) q^{48} +(1.00008 - 6.92819i) q^{49} -1.82829i q^{50} +(3.82192 + 4.38746i) q^{51} +(-5.42454 - 3.13186i) q^{52} +(5.24099 + 3.02589i) q^{53} +(-2.34466 + 4.63708i) q^{54} -1.77764i q^{55} +(1.73204 + 2.00001i) q^{56} +(0.547762 + 2.80256i) q^{57} +(0.624691 + 1.08200i) q^{58} +(-0.600268 + 1.03970i) q^{59} +(-1.00126 + 2.91764i) q^{60} +(1.01927 - 0.588474i) q^{61} -8.07127 q^{62} +(7.92629 - 0.416965i) q^{63} -1.00000 q^{64} +(-9.66073 + 5.57762i) q^{65} +(0.561171 - 1.63524i) q^{66} +(4.81654 - 8.34250i) q^{67} +(1.67970 + 2.90933i) q^{68} +(0.332245 + 1.69989i) q^{69} +(4.62700 - 0.890439i) q^{70} +9.62306i q^{71} +(-1.84210 + 2.36784i) q^{72} +(9.57661 + 5.52906i) q^{73} +(0.407891 + 0.235496i) q^{74} +(-2.08000 - 2.38779i) q^{75} +1.64867i q^{76} +(-2.59328 + 0.499061i) q^{77} +(-10.6476 + 2.08109i) q^{78} +(0.576636 + 0.998763i) q^{79} +(-0.890465 + 1.54233i) q^{80} +(2.21331 + 8.72360i) q^{81} +(3.76149 - 2.17170i) q^{82} +7.53838 q^{83} +(4.53744 + 0.641559i) q^{84} +5.98287 q^{85} +(4.14881 - 2.39532i) q^{86} +(2.04682 + 0.702416i) q^{87} +(0.499076 - 0.864424i) q^{88} +(-4.81612 - 8.34177i) q^{89} +(2.01166 + 4.94961i) q^{90} +(10.8490 + 12.5275i) q^{91} +1.00000i q^{92} +(-10.5413 + 9.18248i) q^{93} +(-7.32426 - 4.22866i) q^{94} +(2.54280 + 1.46808i) q^{95} +(-1.30602 + 1.13768i) q^{96} -11.6654i q^{97} +(-2.59800 - 6.50003i) q^{98} +(-1.12747 - 2.77409i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9}+O(q^{10}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9	\( 56 q - 6 q^{3} + 28 q^{4} + 20 q^{7} - 2 q^{9} - 6 q^{10} - 6 q^{12} - 36 q^{15} - 28 q^{16} + 8 q^{18} - 36 q^{19} + 34 q^{21} + 16 q^{22} - 46 q^{25} + 4 q^{28} - 6 q^{30} - 6 q^{31} + 30 q^{33} - 4 q^{36} - 8 q^{37} + 42 q^{39} - 6 q^{40} + 18 q^{42} + 64 q^{43} - 6 q^{45} - 28 q^{46} - 40 q^{49} - 24 q^{51} - 36 q^{52} - 60 q^{57} - 16 q^{58} - 18 q^{60} + 12 q^{61} + 36 q^{63} - 56 q^{64} + 48 q^{66} - 16 q^{67} - 34 q^{70} - 8 q^{72} - 102 q^{73} + 18 q^{75} - 16 q^{78} + 24 q^{79} + 54 q^{81} + 12 q^{82} - 4 q^{84} + 128 q^{85} + 102 q^{87} + 8 q^{88} + 68 q^{91} - 32 q^{93} + 6 q^{94} - 112 q^{99}+O(q^{100}) \) 56 * q - 6 * q^3 + 28 * q^4 + 20 * q^7 - 2 * q^9 - 6 * q^10 - 6 * q^12 - 36 * q^15 - 28 * q^16 + 8 * q^18 - 36 * q^19 + 34 * q^21 + 16 * q^22 - 46 * q^25 + 4 * q^28 - 6 * q^30 - 6 * q^31 + 30 * q^33 - 4 * q^36 - 8 * q^37 + 42 * q^39 - 6 * q^40 + 18 * q^42 + 64 * q^43 - 6 * q^45 - 28 * q^46 - 40 * q^49 - 24 * q^51 - 36 * q^52 - 60 * q^57 - 16 * q^58 - 18 * q^60 + 12 * q^61 + 36 * q^63 - 56 * q^64 + 48 * q^66 - 16 * q^67 - 34 * q^70 - 8 * q^72 - 102 * q^73 + 18 * q^75 - 16 * q^78 + 24 * q^79 + 54 * q^81 + 12 * q^82 - 4 * q^84 + 128 * q^85 + 102 * q^87 + 8 * q^88 + 68 * q^91 - 32 * q^93 + 6 * q^94 - 112 * q^99

Introduction

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