LMFDB - Embedded newform 966.2.l.d.47.6

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			47.6
Character	$\chi$	$=$	966.47
Dual form			966.2.l.d.185.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.778308 - 1.54733i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.34998 + 2.33823i) q^{5} +(-0.0996314 + 1.72918i) q^{6} +(-2.25095 + 1.39041i) q^{7} -1.00000i q^{8} +(-1.78847 + 2.40860i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.778308 - 1.54733i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.34998 + 2.33823i) q^{5} +(-0.0996314 + 1.72918i) q^{6} +(-2.25095 + 1.39041i) q^{7} -1.00000i q^{8} +(-1.78847 + 2.40860i) q^{9} +(2.33823 - 1.34998i) q^{10} +(-1.91644 + 1.10646i) q^{11} +(0.950875 - 1.44770i) q^{12} +1.43276i q^{13} +(2.64458 - 0.0786570i) q^{14} +(4.66872 + 0.269000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.99316 - 5.18431i) q^{17} +(2.75316 - 1.19167i) q^{18} +(1.51456 + 0.874433i) q^{19} -2.69996 q^{20} +(3.90336 + 2.40079i) q^{21} +2.21292 q^{22} +(-0.866025 - 0.500000i) q^{23} +(-1.54733 + 0.778308i) q^{24} +(-1.14488 - 1.98299i) q^{25} +(0.716379 - 1.24080i) q^{26} +(5.11889 + 0.892727i) q^{27} +(-2.32960 - 1.25417i) q^{28} -9.35152i q^{29} +(-3.90873 - 2.56732i) q^{30} +(2.81858 - 1.62731i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.20364 + 2.10421i) q^{33} +5.98633i q^{34} +(-0.212370 - 7.14025i) q^{35} +(-2.98015 - 0.344562i) q^{36} +(5.10303 - 8.83871i) q^{37} +(-0.874433 - 1.51456i) q^{38} +(2.21695 - 1.11513i) q^{39} +(2.33823 + 1.34998i) q^{40} +9.83599 q^{41} +(-2.18001 - 4.03083i) q^{42} +3.30094 q^{43} +(-1.91644 - 1.10646i) q^{44} +(-3.21747 - 7.43342i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-3.28415 + 5.68832i) q^{47} +(1.72918 + 0.0996314i) q^{48} +(3.13352 - 6.25948i) q^{49} +2.28976i q^{50} +(-5.69225 + 8.66641i) q^{51} +(-1.24080 + 0.716379i) q^{52} +(-4.64160 + 2.67983i) q^{53} +(-3.98673 - 3.33257i) q^{54} -5.97477i q^{55} +(1.39041 + 2.25095i) q^{56} +(0.174242 - 3.02411i) q^{57} +(-4.67576 + 8.09865i) q^{58} +(6.27963 + 10.8766i) q^{59} +(2.10140 + 4.17773i) q^{60} +(-3.72233 - 2.14909i) q^{61} -3.25462 q^{62} +(0.676813 - 7.90835i) q^{63} -1.00000 q^{64} +(-3.35012 - 1.93419i) q^{65} +(-1.72233 - 3.42411i) q^{66} +(-6.30018 - 10.9122i) q^{67} +(2.99316 - 5.18431i) q^{68} +(-0.0996314 + 1.72918i) q^{69} +(-3.38621 + 6.28983i) q^{70} +1.18264i q^{71} +(2.40860 + 1.78847i) q^{72} +(3.33345 - 1.92457i) q^{73} +(-8.83871 + 5.10303i) q^{74} +(-2.17728 + 3.31489i) q^{75} +1.74887i q^{76} +(2.77538 - 5.15522i) q^{77} +(-2.47750 - 0.142748i) q^{78} +(-0.400950 + 0.694466i) q^{79} +(-1.34998 - 2.33823i) q^{80} +(-2.60273 - 8.61544i) q^{81} +(-8.51822 - 4.91800i) q^{82} -5.44986 q^{83} +(-0.127471 + 4.58080i) q^{84} +16.1628 q^{85} +(-2.85870 - 1.65047i) q^{86} +(-14.4699 + 7.27836i) q^{87} +(1.10646 + 1.91644i) q^{88} +(0.279618 - 0.484312i) q^{89} +(-0.930302 + 8.04626i) q^{90} +(-1.99212 - 3.22506i) q^{91} -1.00000i q^{92} +(-4.71171 - 3.09473i) q^{93} +(5.68832 - 3.28415i) q^{94} +(-4.08925 + 2.36093i) q^{95} +(-1.44770 - 0.950875i) q^{96} -2.70663i q^{97} +(-5.84345 + 3.85411i) q^{98} +(0.762486 - 6.59481i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	$ 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) $ 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$	$1$

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
$3$	−0.778308	−	1.54733i	−0.449356	−	0.893353i
$3$	−0.778308	−	1.54733i	−0.449356	−	0.893353i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	−1.34998	+	2.33823i	−0.603728	+	1.04569i	0.388523	+	0.921439i	$0.372986\pi$
$5$	−1.34998	+	2.33823i	−0.603728	+	1.04569i	−0.992251	+	0.124249i	$0.960348\pi$
$6$	−0.0996314	+	1.72918i	−0.0406744	+	0.705936i
$7$	−2.25095	+	1.39041i	−0.850778	+	0.525526i
$7$	−2.25095	+	1.39041i	−0.850778	+	0.525526i
$8$		−	1.00000i		−	0.353553i
$9$	−1.78847	+	2.40860i	−0.596158	+	0.802867i
$10$	2.33823	−	1.34998i	0.739413	−	0.426900i
$11$	−1.91644	+	1.10646i	−0.577829	+	0.333610i	−0.760270	−	0.649607i	$-0.774933\pi$
$11$	−1.91644	+	1.10646i	−0.577829	+	0.333610i	0.182441	+	0.983217i	$0.441600\pi$
$12$	0.950875	−	1.44770i	0.274494	−	0.417915i
$13$			1.43276i			0.397376i	0.980063	+	0.198688i	$0.0636680\pi$
$13$			1.43276i			0.397376i	−0.980063	+	0.198688i	$0.936332\pi$
$14$	2.64458	−	0.0786570i	0.706794	−	0.0210220i
$15$	4.66872	+	0.269000i	1.20546	+	0.0694556i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.99316	−	5.18431i	−0.725949	−	1.25738i	−0.958582	−	0.284816i	$-0.908067\pi$
$17$	−2.99316	−	5.18431i	−0.725949	−	1.25738i	0.232633	−	0.972565i	$-0.425266\pi$
$18$	2.75316	−	1.19167i	0.648927	−	0.280880i
$19$	1.51456	+	0.874433i	0.347465	+	0.200609i	0.663568	−	0.748116i	$-0.269041\pi$
$19$	1.51456	+	0.874433i	0.347465	+	0.200609i	−0.316103	+	0.948725i	$0.602375\pi$
$20$	−2.69996			−0.603728
$21$	3.90336	+	2.40079i	0.851782	+	0.523896i
$22$	2.21292			0.471795
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	−1.54733	+	0.778308i	−0.315848	+	0.158871i
$25$	−1.14488	−	1.98299i	−0.228976	−	0.396598i
$26$	0.716379	−	1.24080i	0.140493	−	0.243342i
$27$	5.11889	+	0.892727i	0.985131	+	0.171805i
$28$	−2.32960	−	1.25417i	−0.440254	−	0.237016i
$29$		−	9.35152i		−	1.73653i	−0.496097	−	0.868267i	$-0.665234\pi$
$29$		−	9.35152i		−	1.73653i	0.496097	−	0.868267i	$-0.334766\pi$
$30$	−3.90873	−	2.56732i	−0.713633	−	0.468726i
$31$	2.81858	−	1.62731i	0.506232	−	0.292273i	−0.225052	−	0.974347i	$-0.572255\pi$
$31$	2.81858	−	1.62731i	0.506232	−	0.292273i	0.731283	+	0.682074i	$0.238922\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	3.20364	+	2.10421i	0.557682	+	0.366295i
$34$			5.98633i			1.02665i
$35$	−0.212370	−	7.14025i	−0.0358971	−	1.20692i
$36$	−2.98015	−	0.344562i	−0.496691	−	0.0574270i
$37$	5.10303	−	8.83871i	0.838933	−	1.45307i	−0.0518542	−	0.998655i	$-0.516513\pi$
$37$	5.10303	−	8.83871i	0.838933	−	1.45307i	0.890787	−	0.454420i	$-0.150154\pi$
$38$	−0.874433	−	1.51456i	−0.141852	−	0.245695i
$39$	2.21695	−	1.11513i	0.354996	−	0.178563i
$40$	2.33823	+	1.34998i	0.369707	+	0.213450i
$41$	9.83599			1.53612			0.768062	−	0.640375i	$-0.221221\pi$
$41$	9.83599			1.53612			0.768062	+	0.640375i	$0.221221\pi$
$42$	−2.18001	−	4.03083i	−0.336383	−	0.621970i
$43$	3.30094			0.503389			0.251694	−	0.967807i	$-0.419012\pi$
$43$	3.30094			0.503389			0.251694	+	0.967807i	$0.419012\pi$
$44$	−1.91644	−	1.10646i	−0.288914	−	0.166805i
$45$	−3.21747	−	7.43342i	−0.479632	−	1.10811i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	−3.28415	+	5.68832i	−0.479043	+	0.829726i	−0.999711	−	0.0240327i	$-0.992349\pi$
$47$	−3.28415	+	5.68832i	−0.479043	+	0.829726i	0.520668	+	0.853759i	$0.325683\pi$
$48$	1.72918	+	0.0996314i	0.249586	+	0.0143806i
$49$	3.13352	−	6.25948i	0.447646	−	0.894211i
$50$			2.28976i			0.323821i
$51$	−5.69225	+	8.66641i	−0.797074	+	1.21354i
$52$	−1.24080	+	0.716379i	−0.172069	+	0.0993439i
$53$	−4.64160	+	2.67983i	−0.637573	+	0.368103i	−0.783679	−	0.621166i	$-0.786659\pi$
$53$	−4.64160	+	2.67983i	−0.637573	+	0.368103i	0.146106	+	0.989269i	$0.453326\pi$
$54$	−3.98673	−	3.33257i	−0.542525	−	0.453505i
$55$		−	5.97477i		−	0.805638i
$56$	1.39041	+	2.25095i	0.185801	+	0.300795i
$57$	0.174242	−	3.02411i	0.0230789	−	0.400553i
$58$	−4.67576	+	8.09865i	−0.613957	+	1.06341i
$59$	6.27963	+	10.8766i	0.817539	+	1.41602i	0.907491	+	0.420073i	$0.137995\pi$
$59$	6.27963	+	10.8766i	0.817539	+	1.41602i	−0.0899518	+	0.995946i	$0.528671\pi$
$60$	2.10140	+	4.17773i	0.271289	+	0.539342i
$61$	−3.72233	−	2.14909i	−0.476595	−	0.275162i	0.242401	−	0.970176i	$-0.422065\pi$
$61$	−3.72233	−	2.14909i	−0.476595	−	0.275162i	−0.718996	+	0.695014i	$0.755398\pi$
$62$	−3.25462			−0.413337
$63$	0.676813	−	7.90835i	0.0852704	−	0.996358i
$64$	−1.00000			−0.125000
$65$	−3.35012	−	1.93419i	−0.415531	−	0.239907i
$66$	−1.72233	−	3.42411i	−0.212004	−	0.421479i
$67$	−6.30018	−	10.9122i	−0.769690	−	1.33314i	−0.937731	−	0.347361i	$-0.887078\pi$
$67$	−6.30018	−	10.9122i	−0.769690	−	1.33314i	0.168042	−	0.985780i	$-0.446256\pi$
$68$	2.99316	−	5.18431i	0.362975	−	0.628690i
$69$	−0.0996314	+	1.72918i	−0.0119942	+	0.208169i
$70$	−3.38621	+	6.28983i	−0.404729	+	0.751778i
$71$			1.18264i			0.140353i	0.997535	+	0.0701765i	$0.0223562\pi$
$71$			1.18264i			0.140353i	−0.997535	+	0.0701765i	$0.977644\pi$
$72$	2.40860	+	1.78847i	0.283856	+	0.210774i
$73$	3.33345	−	1.92457i	0.390151	−	0.225254i	−0.292075	−	0.956395i	$-0.594346\pi$
$73$	3.33345	−	1.92457i	0.390151	−	0.225254i	0.682225	+	0.731142i	$0.261012\pi$
$74$	−8.83871	+	5.10303i	−1.02748	+	0.593215i
$75$	−2.17728	+	3.31489i	−0.251410	+	0.382770i
$76$			1.74887i			0.200609i
$77$	2.77538	−	5.15522i	0.316284	−	0.587491i
$78$	−2.47750	−	0.142748i	−0.280522	−	0.0161630i
$79$	−0.400950	+	0.694466i	−0.0451104	+	0.0781335i	−0.887699	−	0.460424i	$-0.847697\pi$
$79$	−0.400950	+	0.694466i	−0.0451104	+	0.0781335i	0.842589	+	0.538558i	$0.181031\pi$
$80$	−1.34998	−	2.33823i	−0.150932	−	0.261422i
$81$	−2.60273	−	8.61544i	−0.289192	−	0.957271i
$82$	−8.51822	−	4.91800i	−0.940680	−	0.543102i
$83$	−5.44986			−0.598200			−0.299100	−	0.954222i	$-0.596686\pi$
$83$	−5.44986			−0.598200			−0.299100	+	0.954222i	$0.596686\pi$
$84$	−0.127471	+	4.58080i	−0.0139082	+	0.499807i
$85$	16.1628			1.75310
$86$	−2.85870	−	1.65047i	−0.308261	−	0.177975i
$87$	−14.4699	+	7.27836i	−1.55134	+	0.780323i
$88$	1.10646	+	1.91644i	0.117949	+	0.204293i
$89$	0.279618	−	0.484312i	0.0296394	−	0.0513370i	−0.850825	−	0.525449i	$-0.823897\pi$
$89$	0.279618	−	0.484312i	0.0296394	−	0.0513370i	0.880465	+	0.474112i	$0.157231\pi$
$90$	−0.930302	+	8.04626i	−0.0980624	+	0.848151i
$91$	−1.99212	−	3.22506i	−0.208831	−	0.338078i
$92$		−	1.00000i		−	0.104257i
$93$	−4.71171	−	3.09473i	−0.488581	−	0.320909i
$94$	5.68832	−	3.28415i	0.586705	−	0.338734i
$95$	−4.08925	+	2.36093i	−0.419548	+	0.242226i
$96$	−1.44770	−	0.950875i	−0.147755	−	0.0970483i
$97$		−	2.70663i		−	0.274817i	−0.990514	−	0.137409i	$-0.956123\pi$
$97$		−	2.70663i		−	0.274817i	0.990514	−	0.137409i	$-0.0438773\pi$
$98$	−5.84345	+	3.85411i	−0.590277	+	0.389323i
$99$	0.762486	−	6.59481i	0.0766328	−	0.662804i
$100$	1.14488	−	1.98299i	0.114488	−	0.198299i
$101$	1.10312	+	1.91066i	0.109764	+	0.190117i	0.915675	−	0.401920i	$-0.131657\pi$
$101$	1.10312	+	1.91066i	0.109764	+	0.190117i	−0.805910	+	0.592038i	$0.798324\pi$
$102$	9.26284	−	4.65921i	0.917158	−	0.461330i
$103$	−10.8680	−	6.27464i	−1.07086	−	0.618259i	−0.142440	−	0.989803i	$-0.545495\pi$
$103$	−10.8680	−	6.27464i	−1.07086	−	0.618259i	−0.928415	+	0.371545i	$0.878828\pi$
$104$	1.43276			0.140493
$105$	−10.8831	+	5.88592i	−1.06208	+	0.574407i
$106$	5.35966			0.520576
$107$	16.3344	+	9.43070i	1.57911	+	0.911700i	0.994984	+	0.100038i	$0.0318963\pi$
$107$	16.3344	+	9.43070i	1.57911	+	0.911700i	0.584127	+	0.811662i	$0.301437\pi$
$108$	1.78632	+	4.87945i	0.171889	+	0.469526i
$109$	1.44820	+	2.50835i	0.138712	+	0.240256i	0.927009	−	0.375038i	$-0.122370\pi$
$109$	1.44820	+	2.50835i	0.138712	+	0.240256i	−0.788297	+	0.615294i	$0.789037\pi$
$110$	−2.98739	+	5.17431i	−0.284836	+	0.493351i
$111$	−17.6482	−	1.01684i	−1.67509	−	0.0965146i
$112$	−0.0786570	−	2.64458i	−0.00743239	−	0.249889i
$113$		−	20.6749i		−	1.94493i	−0.233047	−	0.972466i	$-0.574870\pi$
$113$		−	20.6749i		−	1.94493i	0.233047	−	0.972466i	$-0.425130\pi$
$114$	−1.66295	+	2.53184i	−0.155750	+	0.237128i
$115$	2.33823	−	1.34998i	0.218041	−	0.125886i
$116$	8.09865	−	4.67576i	0.751941	−	0.434133i
$117$	−3.45094	−	2.56245i	−0.319040	−	0.236898i
$118$		−	12.5593i		−	1.15617i
$119$	13.9458	+	7.50789i	1.27841	+	0.688247i
$120$	0.269000	−	4.66872i	0.0245563	−	0.426194i
$121$	−3.05150	+	5.28536i	−0.277409	+	0.480487i
$122$	2.14909	+	3.72233i	0.194569	+	0.337004i
$123$	−7.65543	−	15.2195i	−0.690267	−	1.37230i
$124$	2.81858	+	1.62731i	0.253116	+	0.146137i
$125$	−7.31753			−0.654500
$126$	−4.54031	+	6.51042i	−0.404483	+	0.579994i
$127$	−10.5122			−0.932804			−0.466402	−	0.884573i	$-0.654450\pi$
$127$	−10.5122			−0.932804			−0.466402	+	0.884573i	$0.654450\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−2.56915	−	5.10765i	−0.226201	−	0.449704i
$130$	1.93419	+	3.35012i	0.169640	+	0.293825i
$131$	−4.44059	+	7.69133i	−0.387976	+	0.671994i	−0.992177	−	0.124837i	$-0.960159\pi$
$131$	−4.44059	+	7.69133i	−0.387976	+	0.671994i	0.604201	+	0.796832i	$0.293492\pi$
$132$	−0.220476	+	3.82654i	−0.0191900	+	0.333057i
$133$	−4.62502	+	0.137561i	−0.401040	+	0.0119280i
$134$			12.6004i			1.08851i
$135$	−8.99779	+	10.7640i	−0.774406	+	0.926416i
$136$	−5.18431	+	2.99316i	−0.444551	+	0.256662i
$137$	16.1691	−	9.33525i	1.38142	−	0.797564i	0.389093	−	0.921198i	$-0.372788\pi$
$137$	16.1691	−	9.33525i	1.38142	−	0.797564i	0.992328	+	0.123634i	$0.0394550\pi$
$138$	0.950875	−	1.44770i	0.0809438	−	0.123236i
$139$		−	1.23068i		−	0.104385i	−0.998637	−	0.0521923i	$-0.983379\pi$
$139$		−	1.23068i		−	0.104385i	0.998637	−	0.0521923i	$-0.0166209\pi$
$140$	6.07746	−	3.75404i	0.513639	−	0.317275i
$141$	11.3578	+	0.654409i	0.956499	+	0.0551112i
$142$	0.591318	−	1.02419i	0.0496223	−	0.0859483i
$143$	−1.58529	−	2.74580i	−0.132568	−	0.229615i
$144$	−1.19167	−	2.75316i	−0.0993062	−	0.229430i
$145$	21.8660	+	12.6243i	1.81587	+	1.04839i
$146$	−3.84913			−0.318557
$147$	−12.1243	+	0.0232042i	−0.999998	+	0.00191385i
$148$	10.2061			0.838933
$149$	−13.1559	−	7.59558i	−1.07778	−	0.622254i	−0.147481	−	0.989065i	$-0.547116\pi$
$149$	−13.1559	−	7.59558i	−1.07778	−	0.622254i	−0.930296	+	0.366811i	$0.880450\pi$
$150$	3.54302	−	1.78214i	0.289286	−	0.145511i
$151$	6.71279	+	11.6269i	0.546279	+	0.946183i	0.998525	+	0.0542896i	$0.0172894\pi$
$151$	6.71279	+	11.6269i	0.546279	+	0.946183i	−0.452246	+	0.891893i	$0.649377\pi$
$152$	0.874433	−	1.51456i	0.0709259	−	0.122847i
$153$	17.8401	+	2.06266i	1.44229	+	0.166756i
$154$	−4.98115	+	3.07686i	−0.401393	+	0.247940i
$155$			8.78732i			0.705814i
$156$	2.07420	+	1.36237i	0.166069	+	0.109077i
$157$	7.41201	−	4.27933i	0.591543	−	0.341528i	−0.174164	−	0.984717i	$-0.555722\pi$
$157$	7.41201	−	4.27933i	0.591543	−	0.341528i	0.765707	+	0.643189i	$0.222389\pi$
$158$	0.694466	−	0.400950i	0.0552488	−	0.0318979i
$159$	7.75918	+	5.09636i	0.615343	+	0.404168i
$160$			2.69996i			0.213450i
$161$	2.64458	−	0.0786570i	0.208422	−	0.00619904i
$162$	−2.05369	+	8.76255i	−0.161353	+	0.688451i
$163$	10.4547	−	18.1081i	0.818875	−	1.41833i	−0.0876363	−	0.996153i	$-0.527931\pi$
$163$	10.4547	−	18.1081i	0.818875	−	1.41833i	0.906512	−	0.422181i	$-0.138735\pi$
$164$	4.91800	+	8.51822i	0.384031	+	0.665161i
$165$	−9.24496	+	4.65021i	−0.719719	+	0.362019i
$166$	4.71972	+	2.72493i	0.366321	+	0.211496i
$167$	9.12336			0.705987			0.352993	−	0.935626i	$-0.385164\pi$
$167$	9.12336			0.705987			0.352993	+	0.935626i	$0.385164\pi$
$168$	2.40079	−	3.90336i	0.185225	−	0.301150i
$169$	10.9472			0.842093
$170$	−13.9974	−	8.08141i	−1.07355	−	0.619816i
$171$	−4.81492	+	2.08408i	−0.368206	+	0.159374i
$172$	1.65047	+	2.85870i	0.125847	+	0.217974i
$173$	−11.3201	+	19.6070i	−0.860651	+	1.49069i	0.0106509	+	0.999943i	$0.496610\pi$
$173$	−11.3201	+	19.6070i	−0.860651	+	1.49069i	−0.871302	+	0.490748i	$0.836724\pi$
$174$	16.1705	+	0.931705i	1.22588	+	0.0706324i
$175$	5.33423	+	2.87175i	0.403230	+	0.217084i
$176$		−	2.21292i		−	0.166805i
$177$	11.9423	−	18.1821i	0.897638	−	1.36665i
$178$	−0.484312	+	0.279618i	−0.0363007	+	0.0209582i
$179$	10.2862	−	5.93874i	0.768826	−	0.443882i	−0.0636296	−	0.997974i	$-0.520268\pi$
$179$	10.2862	−	5.93874i	0.768826	−	0.443882i	0.832456	+	0.554092i	$0.186934\pi$
$180$	4.82880	−	6.50312i	0.359917	−	0.484714i
$181$		−	12.0424i		−	0.895105i	−0.894258	−	0.447553i	$-0.852296\pi$
$181$		−	12.0424i		−	0.895105i	0.894258	−	0.447553i	$-0.147704\pi$
$182$	0.112696	+	3.78905i	0.00835361	+	0.280863i
$183$	−0.428233	+	7.43232i	−0.0316559	+	0.549413i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	13.7780	+	23.8641i	1.01298	+	1.75453i
$186$	2.53309	+	5.03597i	0.185735	+	0.369255i
$187$	11.4724	+	6.62362i	0.838948	+	0.484367i
$188$	−6.56830			−0.479043
$189$	−12.7636	+	5.10788i	−0.928416	+	0.371543i
$190$	4.72186			0.342560
$191$	−13.9151	−	8.03387i	−1.00686	−	0.581311i	−0.0965890	−	0.995324i	$-0.530793\pi$
$191$	−13.9151	−	8.03387i	−1.00686	−	0.581311i	−0.910271	+	0.414014i	$0.864127\pi$
$192$	0.778308	+	1.54733i	0.0561695	+	0.111669i
$193$	−5.92008	−	10.2539i	−0.426137	−	0.738091i	0.570389	−	0.821375i	$-0.306792\pi$
$193$	−5.92008	−	10.2539i	−0.426137	−	0.738091i	−0.996526	+	0.0832841i	$0.973459\pi$
$194$	−1.35332	+	2.34401i	−0.0971625	+	0.168290i
$195$	−0.385412	+	6.68914i	−0.0276000	+	0.479019i
$196$	6.98763	−	0.416030i	0.499116	−	0.0297164i
$197$		−	11.5096i		−	0.820026i	−0.912080	−	0.410013i	$-0.865524\pi$
$197$		−	11.5096i		−	0.820026i	0.912080	−	0.410013i	$-0.134476\pi$
$198$	−3.95774	+	5.33003i	−0.281264	+	0.378789i
$199$	17.7947	−	10.2738i	1.26143	−	0.728289i	0.288082	−	0.957606i	$-0.406983\pi$
$199$	17.7947	−	10.2738i	1.26143	−	0.728289i	0.973352	+	0.229317i	$0.0736492\pi$
$200$	−1.98299	+	1.14488i	−0.140219	+	0.0809552i
$201$	−11.9814	+	18.2415i	−0.845100	+	1.28666i
$202$		−	2.20624i		−	0.155230i
$203$	13.0024	+	21.0498i	0.912593	+	1.47740i
$204$	−10.3515	−	0.596427i	−0.724747	−	0.0417582i
$205$	−13.2784	+	22.9988i	−0.927402	+	1.60631i
$206$	6.27464	+	10.8680i	0.437175	+	0.757209i
$207$	2.75316	−	1.19167i	0.191358	−	0.0828271i
$208$	−1.24080	−	0.716379i	−0.0860343	−	0.0496719i
$209$	−3.87009			−0.267700
$210$	12.3680	+	0.344166i	0.853471	+	0.0237497i
$211$	1.51663			0.104409			0.0522047	−	0.998636i	$-0.483375\pi$
$211$	1.51663			0.104409			0.0522047	+	0.998636i	$0.483375\pi$
$212$	−4.64160	−	2.67983i	−0.318786	−	0.184051i
$213$	1.82993	−	0.920455i	0.125385	−	0.0630685i
$214$	−9.43070	−	16.3344i	−0.644669	−	1.11660i
$215$	−4.45620	+	7.71836i	−0.303910	+	0.526388i
$216$	0.892727	−	5.11889i	0.0607424	−	0.348296i
$217$	−4.08185	+	7.58196i	−0.277094	+	0.514697i
$218$		−	2.89639i		−	0.196168i
$219$	−5.57240	−	3.66005i	−0.376548	−	0.247323i
$220$	5.17431	−	2.98739i	0.348852	−	0.201410i
$221$	7.42786	−	4.28848i	0.499652	−	0.288474i
$222$	14.7753	+	9.70469i	0.991655	+	0.651336i
$223$			5.35523i			0.358613i	0.983793	+	0.179306i	$0.0573853\pi$
$223$			5.35523i			0.358613i	−0.983793	+	0.179306i	$0.942615\pi$
$224$	−1.25417	+	2.32960i	−0.0837979	+	0.155653i
$225$	6.82382	+	0.788964i	0.454921	+	0.0525976i
$226$	−10.3375	+	17.9050i	−0.687637	+	1.19102i
$227$	−4.09072	−	7.08533i	−0.271511	−	0.470270i	0.697738	−	0.716353i	$-0.254190\pi$
$227$	−4.09072	−	7.08533i	−0.271511	−	0.470270i	−0.969249	+	0.246083i	$0.920857\pi$
$228$	2.70608	−	1.36116i	0.179214	−	0.0901448i
$229$	15.9535	+	9.21073i	1.05423	+	0.608662i	0.923832	−	0.382799i	$-0.125040\pi$
$229$	15.9535	+	9.21073i	1.05423	+	0.608662i	0.130402	+	0.991461i	$0.458373\pi$
$230$	−2.69996			−0.178030
$231$	−10.1369	−	0.282083i	−0.666961	−	0.0185597i
$232$	−9.35152			−0.613957
$233$	−13.4516	−	7.76627i	−0.881241	−	0.508785i	−0.0101739	−	0.999948i	$-0.503239\pi$
$233$	−13.4516	−	7.76627i	−0.881241	−	0.508785i	−0.871068	+	0.491163i	$0.836572\pi$
$234$	1.70738	+	3.94462i	0.111615	+	0.257868i
$235$	−8.86706	−	15.3582i	−0.578423	−	1.00186i
$236$	−6.27963	+	10.8766i	−0.408769	+	0.708009i
$237$	1.38663	+	0.0798945i	0.0900715	+	0.00518970i
$238$	−8.32345	−	13.4749i	−0.539529	−	0.873448i
$239$			6.79571i			0.439578i	0.975547	+	0.219789i	$0.0705369\pi$
$239$			6.79571i			0.439578i	−0.975547	+	0.219789i	$0.929463\pi$
$240$	−2.56732	+	3.90873i	−0.165720	+	0.252307i
$241$	−5.90306	+	3.40814i	−0.380250	+	0.219537i	−0.677927	−	0.735129i	$-0.737121\pi$
$241$	−5.90306	+	3.40814i	−0.380250	+	0.219537i	0.297677	+	0.954667i	$0.403788\pi$
$242$	5.28536	−	3.05150i	0.339756	−	0.196158i
$243$	−11.3052	+	10.7328i	−0.725230	+	0.688506i
$244$		−	4.29817i		−	0.275162i
$245$	10.4059	+	15.7770i	0.664809	+	1.00796i
$246$	−0.979974	+	17.0082i	−0.0624809	+	1.08441i
$247$	−1.25285	+	2.17000i	−0.0797170	+	0.138074i
$248$	−1.62731	−	2.81858i	−0.103334	−	0.178980i
$249$	4.24167	+	8.43274i	0.268805	+	0.534403i
$250$	6.33716	+	3.65876i	0.400797	+	0.231401i
$251$	1.41997			0.0896280			0.0448140	−	0.998995i	$-0.485730\pi$
$251$	1.41997			0.0896280			0.0448140	+	0.998995i	$0.485730\pi$
$252$	7.18723	−	3.36804i	0.452753	−	0.212166i
$253$	2.21292			0.139125
$254$	9.10380	+	5.25608i	0.571223	+	0.329796i
$255$	−12.5797	−	25.0093i	−0.787769	−	1.56614i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	5.02436	−	8.70244i	0.313411	−	0.542843i	−0.665688	−	0.746231i	$-0.731862\pi$
$257$	5.02436	−	8.70244i	0.313411	−	0.542843i	0.979098	+	0.203387i	$0.0651950\pi$
$258$	−0.328878	+	5.70793i	−0.0204750	+	0.355360i
$259$	0.802778	+	26.9908i	0.0498822	+	1.67712i
$260$		−	3.86838i		−	0.239907i
$261$	22.5241	+	16.7249i	1.39421	+	1.03525i
$262$	7.69133	−	4.44059i	0.475172	−	0.274341i
$263$	4.21685	−	2.43460i	0.260022	−	0.150124i	−0.364322	−	0.931273i	$-0.618699\pi$
$263$	4.21685	−	2.43460i	0.260022	−	0.150124i	0.624345	+	0.781149i	$0.285366\pi$
$264$	2.10421	−	3.20364i	0.129505	−	0.197170i
$265$		−	14.4708i		−	0.888937i
$266$	4.07417	+	2.19338i	0.249803	+	0.134485i
$267$	−0.967021	−	0.0557174i	−0.0591807	−	0.00340985i
$268$	6.30018	−	10.9122i	0.384845	−	0.666571i
$269$	14.2913	+	24.7533i	0.871358	+	1.50924i	0.860592	+	0.509295i	$0.170094\pi$
$269$	14.2913	+	24.7533i	0.871358	+	1.50924i	0.0107666	+	0.999942i	$0.496573\pi$
$270$	13.1743	−	4.82299i	0.801763	−	0.293518i
$271$	−9.53797	−	5.50675i	−0.579391	−	0.334511i	0.181501	−	0.983391i	$-0.441905\pi$
$271$	−9.53797	−	5.50675i	−0.579391	−	0.334511i	−0.760891	+	0.648879i	$0.775238\pi$
$272$	5.98633			0.362975
$273$	−3.43976	+	5.59256i	−0.208184	+	0.338477i
$274$	−18.6705			−1.12793
$275$	4.38819	+	2.53352i	0.264618	+	0.152777i
$276$	−1.54733	+	0.778308i	−0.0931384	+	0.0468486i
$277$	9.09879	+	15.7596i	0.546693	+	0.946900i	0.998498	+	0.0547837i	$0.0174469\pi$
$277$	9.09879	+	15.7596i	0.546693	+	0.946900i	−0.451805	+	0.892117i	$0.649220\pi$
$278$	−0.615338	+	1.06580i	−0.0369055	+	0.0639222i
$279$	−1.12142	+	9.69923i	−0.0671375	+	0.580678i
$280$	−7.14025	+	0.212370i	−0.426712	+	0.0126916i
$281$		−	23.0462i		−	1.37482i	−0.726269	−	0.687411i	$-0.758747\pi$
$281$		−	23.0462i		−	1.37482i	0.726269	−	0.687411i	$-0.241253\pi$
$282$	−9.50894	−	6.24563i	−0.566249	−	0.371922i
$283$	−7.96753	+	4.60005i	−0.473620	+	0.273445i	−0.717754	−	0.696297i	$-0.754830\pi$
$283$	−7.96753	+	4.60005i	−0.473620	+	0.273445i	0.244134	+	0.969742i	$0.421496\pi$
$284$	−1.02419	+	0.591318i	−0.0607746	+	0.0350882i
$285$	6.83584	+	4.48990i	0.404920	+	0.265959i
$286$			3.17057i			0.187480i
$287$	−22.1403	+	13.6761i	−1.30690	+	0.807272i
$288$	−0.344562	+	2.98015i	−0.0203035	+	0.175607i
$289$	−9.41807	+	16.3126i	−0.554004	+	0.959563i
$290$	−12.6243	−	21.8660i	−0.741327	−	1.28402i
$291$	−4.18806	+	2.10660i	−0.245509	+	0.123491i
$292$	3.33345	+	1.92457i	0.195075	+	0.112627i
$293$	−0.830396			−0.0485122			−0.0242561	−	0.999706i	$-0.507722\pi$
$293$	−0.830396			−0.0485122			−0.0242561	+	0.999706i	$0.507722\pi$
$294$	10.5116	+	6.04207i	0.613048	+	0.352381i
$295$	−33.9095			−1.97429
$296$	−8.83871	−	5.10303i	−0.513740	−	0.296608i
$297$	−10.7978	+	3.95298i	−0.626553	+	0.229375i
$298$	7.59558	+	13.1559i	0.440000	+	0.762103i
$299$	0.716379	−	1.24080i	0.0414293	−	0.0717576i
$300$	−3.95941	−	0.228132i	−0.228597	−	0.0131712i
$301$	−7.43024	+	4.58966i	−0.428272	+	0.264544i
$302$		−	13.4256i		−	0.772555i
$303$	2.09785	−	3.19397i	0.120519	−	0.183489i
$304$	−1.51456	+	0.874433i	−0.0868661	+	0.0501522i
$305$	10.0501	−	5.80244i	0.575468	−	0.332246i
$306$	−14.4187	−	10.7064i	−0.824261	−	0.612043i
$307$		−	11.4880i		−	0.655658i	−0.944737	−	0.327829i	$-0.893683\pi$
$307$		−	11.4880i		−	0.655658i	0.944737	−	0.327829i	$-0.106317\pi$
$308$	5.85224	−	0.174061i	0.333462	−	0.00991806i
$309$	−1.25030	+	21.7000i	−0.0711272	+	1.23447i
$310$	4.39366	−	7.61004i	0.249543	−	0.432221i
$311$	−6.67985	−	11.5698i	−0.378779	−	0.656065i	0.612106	−	0.790776i	$-0.290323\pi$
$311$	−6.67985	−	11.5698i	−0.378779	−	0.656065i	−0.990885	+	0.134711i	$0.956989\pi$
$312$	−1.11513	−	2.21695i	−0.0631316	−	0.125510i
$313$	−14.4388	−	8.33627i	−0.816131	−	0.471194i	0.0329493	−	0.999457i	$-0.489510\pi$
$313$	−14.4388	−	8.33627i	−0.816131	−	0.471194i	−0.849081	+	0.528263i	$0.822843\pi$
$314$	−8.55866			−0.482993
$315$	17.5778	+	12.2586i	0.990400	+	0.690696i
$316$	−0.801900			−0.0451104
$317$	9.04580	+	5.22260i	0.508063	+	0.293330i	0.732037	−	0.681265i	$-0.238570\pi$
$317$	9.04580	+	5.22260i	0.508063	+	0.293330i	−0.223974	+	0.974595i	$0.571903\pi$
$318$	−4.17147	−	8.29317i	−0.233924	−	0.465058i
$319$	10.3471	+	17.9216i	0.579324	+	1.00342i
$320$	1.34998	−	2.33823i	0.0754661	−	0.130711i
$321$	1.87919	−	32.6148i	0.104886	−	1.82038i
$322$	−2.32960	−	1.25417i	−0.129824	−	0.0698923i
$323$		−	10.4693i		−	0.582527i
$324$	6.15983	−	6.56175i	0.342213	−	0.364542i
$325$	2.84114	−	1.64034i	0.157598	−	0.0909895i
$326$	−18.1081	+	10.4547i	−1.00291	+	0.579032i
$327$	2.75411	−	4.19311i	0.152302	−	0.231879i
$328$		−	9.83599i		−	0.543102i
$329$	−0.516643	−	17.3704i	−0.0284834	−	0.957662i
$330$	10.3315	+	0.595275i	0.568729	+	0.0327688i
$331$	4.48257	−	7.76405i	0.246385	−	0.426751i	−0.716135	−	0.697961i	$-0.754091\pi$
$331$	4.48257	−	7.76405i	0.246385	−	0.426751i	0.962520	+	0.271211i	$0.0874241\pi$
$332$	−2.72493	−	4.71972i	−0.149550	−	0.259028i
$333$	12.1623	+	28.0990i	0.666490	+	1.53981i
$334$	−7.90106	−	4.56168i	−0.432327	−	0.249604i
$335$	34.0204			1.85873
$336$	−4.03083	+	2.18001i	−0.219900	+	0.118929i
$337$	−24.5860			−1.33929			−0.669643	−	0.742683i	$-0.733553\pi$
$337$	−24.5860			−1.33929			−0.669643	+	0.742683i	$0.733553\pi$
$338$	−9.48056	−	5.47360i	−0.515674	−	0.297725i
$339$	−31.9909	+	16.0914i	−1.73751	+	0.873967i
$340$	8.08141	+	13.9974i	0.438276	+	0.759116i
$341$	−3.60109	+	6.23728i	−0.195010	+	0.337768i
$342$	5.21188	+	0.602593i	0.281826	+	0.0325845i
$343$	1.64985	+	18.4466i	0.0890835	+	0.996024i
$344$		−	3.30094i		−	0.177975i
$345$	−3.90873	−	2.56732i	−0.210439	−	0.138220i
$346$	19.6070	−	11.3201i	1.05408	−	0.608572i
$347$	18.7255	−	10.8111i	1.00523	−	0.580373i	0.0954419	−	0.995435i	$-0.469574\pi$
$347$	18.7255	−	10.8111i	1.00523	−	0.580373i	0.909793	+	0.415062i	$0.136240\pi$
$348$	−13.5382	−	8.89213i	−0.725724	−	0.476668i
$349$		−	27.7476i		−	1.48530i	−0.669682	−	0.742648i	$-0.733570\pi$
$349$		−	27.7476i		−	1.48530i	0.669682	−	0.742648i	$-0.266430\pi$
$350$	−3.18370	−	5.15413i	−0.170176	−	0.275500i
$351$	−1.27906	+	7.33413i	−0.0682712	+	0.391467i
$352$	−1.10646	+	1.91644i	−0.0589744	+	0.102147i
$353$	1.11081	+	1.92398i	0.0591223	+	0.102403i	0.894072	−	0.447924i	$-0.147836\pi$
$353$	1.11081	+	1.92398i	0.0591223	+	0.102403i	−0.834949	+	0.550327i	$0.814503\pi$
$354$	−19.4334	+	9.77498i	−1.03287	+	0.519534i
$355$	−2.76527	−	1.59653i	−0.146765	−	0.0847351i
$356$	0.559236			0.0296394
$357$	0.763084	−	27.4222i	0.0403867	−	1.45134i
$358$	−11.8775			−0.627744
$359$	−31.9954	−	18.4725i	−1.68865	−	0.974944i	−0.955552	−	0.294823i	$-0.904739\pi$
$359$	−31.9954	−	18.4725i	−1.68865	−	0.974944i	−0.733100	−	0.680121i	$-0.761927\pi$
$360$	−7.43342	+	3.21747i	−0.391776	+	0.169575i
$361$	−7.97073	−	13.8057i	−0.419512	−	0.726617i
$362$	−6.02121	+	10.4290i	−0.316468	+	0.548138i
$363$	10.5532	+	0.608051i	0.553900	+	0.0319144i
$364$	1.79692	−	3.33776i	0.0941844	−	0.174946i
$365$			10.3925i			0.543968i
$366$	4.08702	−	6.22247i	0.213632	−	0.325253i
$367$	3.33189	−	1.92367i	0.173923	−	0.100415i	−0.410511	−	0.911856i	$-0.634650\pi$
$367$	3.33189	−	1.92367i	0.173923	−	0.100415i	0.584434	+	0.811441i	$0.301316\pi$
$368$	0.866025	−	0.500000i	0.0451447	−	0.0260643i
$369$	−17.5914	+	23.6910i	−0.915772	+	1.23330i
$370$		−	27.5559i		−	1.43256i
$371$	6.72193	−	12.4859i	0.348985	−	0.648235i
$372$	0.324262	−	5.62783i	0.0168122	−	0.291789i
$373$	12.3397	−	21.3729i	0.638923	−	1.10665i	−0.346747	−	0.937959i	$-0.612714\pi$
$373$	12.3397	−	21.3729i	0.638923	−	1.10665i	0.985669	−	0.168688i	$-0.0539530\pi$
$374$	−6.62362	−	11.4724i	−0.342499	−	0.593226i
$375$	5.69529	+	11.3226i	0.294104	+	0.584699i
$376$	5.68832	+	3.28415i	0.293353	+	0.169367i
$377$	13.3985			0.690056
$378$	13.6075	+	1.95825i	0.699897	+	0.100722i
$379$	8.48598			0.435895			0.217948	−	0.975960i	$-0.430064\pi$
$379$	8.48598			0.435895			0.217948	+	0.975960i	$0.430064\pi$
$380$	−4.08925	−	2.36093i	−0.209774	−	0.121113i
$381$	8.18170	+	16.2658i	0.419161	+	0.833323i
$382$	8.03387	+	13.9151i	0.411049	+	0.711957i
$383$	1.21052	−	2.09667i	0.0618545	−	0.107135i	−0.833440	−	0.552610i	$-0.813632\pi$
$383$	1.21052	−	2.09667i	0.0618545	−	0.107135i	0.895294	+	0.445475i	$0.146965\pi$
$384$	0.0996314	−	1.72918i	0.00508429	−	0.0882420i
$385$	8.30738	+	13.4489i	0.423383	+	0.685419i
$386$			11.8402i			0.602648i
$387$	−5.90364	+	7.95065i	−0.300099	+	0.404155i
$388$	2.34401	−	1.35332i	0.118999	−	0.0687043i
$389$	4.08956	−	2.36111i	0.207349	−	0.119713i	−0.392730	−	0.919654i	$-0.628469\pi$
$389$	4.08956	−	2.36111i	0.207349	−	0.119713i	0.600079	+	0.799941i	$0.295136\pi$
$390$	3.67835	−	5.60026i	0.186260	−	0.283580i
$391$			5.98633i			0.302742i
$392$	−6.25948	−	3.13352i	−0.316151	−	0.158267i
$393$	15.3572	+	0.884845i	0.774668	+	0.0446345i
$394$	−5.75481	+	9.96762i	−0.289923	+	0.502161i
$395$	−1.08255	−	1.87503i	−0.0544689	−	0.0943429i
$396$	6.09252	−	2.63707i	0.306161	−	0.132518i
$397$	24.6115	+	14.2095i	1.23522	+	0.713152i	0.968113	−	0.250516i	$-0.0806002\pi$
$397$	24.6115	+	14.2095i	1.23522	+	0.713152i	0.267103	+	0.963668i	$0.413934\pi$
$398$	−20.5476			−1.02996
$399$	3.81254	+	7.04938i	0.190866	+	0.352910i
$400$	2.28976			0.114488
$401$	−20.3620	−	11.7560i	−1.01683	−	0.587067i	−0.103646	−	0.994614i	$-0.533051\pi$
$401$	−20.3620	−	11.7560i	−1.01683	−	0.587067i	−0.913184	+	0.407547i	$0.866384\pi$
$402$	19.4969	−	9.80696i	0.972419	−	0.489127i
$403$	2.33154	+	4.03834i	0.116142	+	0.201164i
$404$	−1.10312	+	1.91066i	−0.0548822	+	0.0950587i
$405$	23.6585	+	5.54487i	1.17560	+	0.275527i
$406$	−0.735562	−	24.7309i	−0.0365053	−	1.22737i
$407$			22.5852i			1.11950i
$408$	8.66641	+	5.69225i	0.429051	+	0.281808i
$409$	−9.76750	+	5.63927i	−0.482972	+	0.278844i	−0.721654	−	0.692254i	$-0.756618\pi$
$409$	−9.76750	+	5.63927i	−0.482972	+	0.278844i	0.238682	+	0.971098i	$0.423285\pi$
$410$	22.9988	−	13.2784i	1.13583	−	0.655772i
$411$	−27.0293	−	17.7533i	−1.33326	−	0.875706i
$412$		−	12.5493i		−	0.618259i
$413$	−29.2581	−	15.7515i	−1.43970	−	0.775080i
$414$	−2.98015	−	0.344562i	−0.146466	−	0.0169343i
$415$	7.35719	−	12.7430i	0.361150	−	0.625530i
$416$	0.716379	+	1.24080i	0.0351234	+	0.0608355i
$417$	−1.90426	+	0.957845i	−0.0932522	+	0.0469059i
$418$	3.35160	+	1.93505i	0.163932	+	0.0946462i
$419$	5.27392			0.257648			0.128824	−	0.991667i	$-0.458880\pi$
$419$	5.27392			0.257648			0.128824	+	0.991667i	$0.458880\pi$
$420$	−10.5389	−	6.48204i	−0.514245	−	0.316291i
$421$	18.0881			0.881559			0.440779	−	0.897615i	$-0.354702\pi$
$421$	18.0881			0.881559			0.440779	+	0.897615i	$0.354702\pi$
$422$	−1.31344	−	0.758317i	−0.0639374	−	0.0369143i
$423$	−7.82728	−	18.0836i	−0.380575	−	0.879255i
$424$	2.67983	+	4.64160i	0.130144	+	0.225416i
$425$	−6.85363	+	11.8708i	−0.332450	+	0.575820i
$426$	−2.04499	−	0.117828i	−0.0990802	−	0.00570877i
$427$	11.3669	−	0.338081i	0.550081	−	0.0163609i
$428$			18.8614i			0.911700i
$429$	−3.01482	+	4.59004i	−0.145557	+	0.221609i
$430$	7.71836	−	4.45620i	0.372212	−	0.214897i
$431$	−7.93784	+	4.58291i	−0.382352	+	0.220751i	−0.678841	−	0.734285i	$-0.737518\pi$
$431$	−7.93784	+	4.58291i	−0.382352	+	0.220751i	0.296489	+	0.955036i	$0.404184\pi$
$432$	−3.33257	+	3.98673i	−0.160338	+	0.191811i
$433$			12.7359i			0.612047i	0.952024	+	0.306024i	$0.0989987\pi$
$433$			12.7359i			0.612047i	−0.952024	+	0.306024i	$0.901001\pi$
$434$	7.32597	−	4.52525i	0.351658	−	0.217219i
$435$	2.51556	−	43.6596i	0.120612	−	2.09332i
$436$	−1.44820	+	2.50835i	−0.0693560	+	0.120128i
$437$	−0.874433	−	1.51456i	−0.0418298	−	0.0724514i
$438$	2.99581	+	5.95589i	0.143145	+	0.284583i
$439$	−15.8389	−	9.14462i	−0.755951	−	0.436449i	0.0718889	−	0.997413i	$-0.477097\pi$
$439$	−15.8389	−	9.14462i	−0.755951	−	0.436449i	−0.827840	+	0.560964i	$0.810431\pi$
$440$	−5.97477			−0.284836
$441$	9.47237	+	18.7423i	0.451065	+	0.892491i
$442$	−8.57696			−0.407964
$443$	−8.54180	−	4.93161i	−0.405833	−	0.234308i	0.283165	−	0.959071i	$-0.408616\pi$
$443$	−8.54180	−	4.93161i	−0.405833	−	0.234308i	−0.688998	+	0.724763i	$0.741949\pi$
$444$	−7.94346	−	15.7922i	−0.376980	−	0.749463i
$445$	0.754956	+	1.30762i	0.0357883	+	0.0619872i
$446$	2.67762	−	4.63777i	0.126789	−	0.219605i
$447$	−1.51352	+	26.2683i	−0.0715869	+	1.24245i
$448$	2.25095	−	1.39041i	0.106347	−	0.0656907i
$449$		−	16.7458i		−	0.790283i	−0.918620	−	0.395141i	$-0.870696\pi$
$449$		−	16.7458i		−	0.790283i	0.918620	−	0.395141i	$-0.129304\pi$
$450$	−5.51512	−	4.09517i	−0.259985	−	0.193048i
$451$	−18.8501	+	10.8831i	−0.887617	+	0.512466i
$452$	17.9050	−	10.3375i	0.842180	−	0.486233i
$453$	12.7660	−	19.4362i	0.599801	−	0.913193i
$454$			8.18144i			0.383974i
$455$	10.2303	−	0.304275i	0.479602	−	0.0142646i
$456$	−3.02411	−	0.174242i	−0.141617	−	0.00815963i
$457$	10.0451	−	17.3985i	0.469888	−	0.813870i	−0.529519	−	0.848298i	$-0.677628\pi$
$457$	10.0451	−	17.3985i	0.469888	−	0.813870i	0.999407	+	0.0344283i	$0.0109610\pi$
$458$	−9.21073	−	15.9535i	−0.430389	−	0.745456i
$459$	−10.6935	−	29.2100i	−0.499130	−	1.36341i
$460$	2.33823	+	1.34998i	0.109021	+	0.0629430i
$461$	29.6900			1.38280			0.691401	−	0.722471i	$-0.256994\pi$
$461$	29.6900			1.38280			0.691401	+	0.722471i	$0.256994\pi$
$462$	8.63780	+	5.31276i	0.401867	+	0.247172i
$463$	−17.7289			−0.823933			−0.411967	−	0.911199i	$-0.635158\pi$
$463$	−17.7289			−0.823933			−0.411967	+	0.911199i	$0.635158\pi$
$464$	8.09865	+	4.67576i	0.375971	+	0.217067i
$465$	13.5969	−	6.83924i	0.630541	−	0.317162i
$466$	7.76627	+	13.4516i	0.359765	+	0.623132i
$467$	11.5346	−	19.9785i	0.533758	−	0.924496i	−0.465464	−	0.885067i	$-0.654113\pi$
$467$	11.5346	−	19.9785i	0.533758	−	0.924496i	0.999222	−	0.0394293i	$-0.0125540\pi$
$468$	0.493674	−	4.26983i	0.0228201	−	0.197373i
$469$	29.3538	+	15.8030i	1.35543	+	0.729716i
$470$			17.7341i			0.818014i
$471$	−12.3904	−	8.13821i	−0.570918	−	0.374989i
$472$	10.8766	−	6.27963i	0.500638	−	0.289044i
$473$	−6.32606	+	3.65235i	−0.290873	+	0.167935i
$474$	−1.16091	−	0.762507i	−0.0533224	−	0.0350231i
$475$		−	4.00448i		−	0.183738i
$476$	0.470867	+	15.8313i	0.0215821	+	0.725628i
$477$	1.84673	−	15.9726i	0.0845561	−	0.731334i
$478$	3.39786	−	5.88526i	0.155414	−	0.269186i
$479$	0.974816	+	1.68843i	0.0445405	+	0.0771464i	0.887436	−	0.460931i	$-0.152484\pi$
$479$	0.974816	+	1.68843i	0.0445405	+	0.0771464i	−0.842896	+	0.538077i	$0.819151\pi$
$480$	4.17773	−	2.10140i	0.190686	−	0.0959152i
$481$	12.6637	+	7.31141i	0.577416	+	0.333372i
$482$	6.81627			0.310473
$483$	−2.18001	−	4.03083i	−0.0991938	−	0.183409i
$484$	−6.10301			−0.277409
$485$	6.32873	+	3.65390i	0.287373	+	0.165915i
$486$	15.1570	−	3.64223i	0.687535	−	0.165215i
$487$	−12.2520	−	21.2211i	−0.555192	−	0.961621i	−0.997889	−	0.0649496i	$-0.979311\pi$
$487$	−12.2520	−	21.2211i	−0.555192	−	0.961621i	0.442696	−	0.896672i	$-0.354022\pi$
$488$	−2.14909	+	3.72233i	−0.0972845	+	0.168502i
$489$	−36.1562	−	2.08323i	−1.63504	−	0.0942071i
$490$	−1.12326	−	18.8663i	−0.0507438	−	0.852292i
$491$		−	28.2864i		−	1.27655i	−0.769809	−	0.638274i	$-0.779649\pi$
$491$		−	28.2864i		−	1.27655i	0.769809	−	0.638274i	$-0.220351\pi$
$492$	9.35280	−	14.2396i	0.421657	−	0.641970i
$493$	−48.4812	+	27.9906i	−2.18348	+	1.26064i
$494$	2.17000	−	1.25285i	0.0976330	−	0.0563684i
$495$	14.3909	+	10.6857i	0.646821	+	0.480287i
$496$			3.25462i			0.146137i
$497$	−1.64435	−	2.66205i	−0.0737591	−	0.119409i
$498$	0.542977	−	9.42380i	0.0243314	−	0.422291i
$499$	−11.8933	+	20.5997i	−0.532415	+	0.922170i	0.466869	+	0.884327i	$0.345382\pi$
$499$	−11.8933	+	20.5997i	−0.532415	+	0.922170i	−0.999284	+	0.0378434i	$0.987951\pi$
$500$	−3.65876	−	6.33716i	−0.163625	−	0.283407i
$501$	−7.10079	−	14.1169i	−0.317240	−	0.630695i
$502$	−1.22973	−	0.709987i	−0.0548857	−	0.0316883i
$503$	−17.9415			−0.799972			−0.399986	−	0.916521i	$-0.630985\pi$
$503$	−17.9415			−0.799972			−0.399986	+	0.916521i	$0.630985\pi$
$504$	−7.90835	−	0.676813i	−0.352266	−	0.0301476i
$505$	−5.95674			−0.265071
$506$	−1.91644	−	1.10646i	−0.0851962	−	0.0491880i
$507$	−8.52030	−	16.9390i	−0.378400	−	0.752286i
$508$	−5.25608	−	9.10380i	−0.233201	−	0.403916i
$509$	−5.32786	+	9.22812i	−0.236153	+	0.409029i	−0.959607	−	0.281343i	$-0.909220\pi$
$509$	−5.32786	+	9.22812i	−0.236153	+	0.409029i	0.723454	+	0.690373i	$0.242553\pi$
$510$	−1.61033	+	27.9485i	−0.0713064	+	1.23758i
$511$	−4.82748	+	8.96696i	−0.213555	+	0.396675i
$512$			1.00000i			0.0441942i
$513$	6.97225	+	5.82822i	0.307832	+	0.257322i
$514$	−8.70244	+	5.02436i	−0.383848	+	0.221615i
$515$	29.3431	−	16.9413i	1.29301	−	0.746521i
$516$	3.13878	−	4.77878i	0.138177	−	0.210374i
$517$		−	14.5351i		−	0.639253i
$518$	12.8002	−	23.7761i	0.562407	−	1.04466i
$519$	39.1490	+	2.25567i	1.71845	+	0.0990131i
$520$	−1.93419	+	3.35012i	−0.0848199	+	0.146912i
$521$	−2.08649	−	3.61391i	−0.0914109	−	0.158328i	0.816694	−	0.577071i	$-0.195804\pi$
$521$	−2.08649	−	3.61391i	−0.0914109	−	0.158328i	−0.908105	+	0.418742i	$0.862471\pi$
$522$	−11.1440	−	25.7463i	−0.487758	−	1.12688i
$523$	−19.0773	−	11.0143i	−0.834191	−	0.481620i	0.0210944	−	0.999777i	$-0.493285\pi$
$523$	−19.0773	−	11.0143i	−0.834191	−	0.481620i	−0.855285	+	0.518157i	$0.826618\pi$
$524$	−8.88118			−0.387976
$525$	0.291878	−	10.4889i	0.0127386	−	0.457775i
$526$	−4.86920			−0.212307
$527$	−16.8729	−	9.74160i	−0.734997	−	0.424351i
$528$	−3.42411	+	1.72233i	−0.149015	+	0.0749548i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	−7.23542	+	12.5321i	−0.314287	+	0.544360i
$531$	−37.4285	−	4.32745i	−1.62426	−	0.187795i
$532$	−2.43164	−	3.93660i	−0.105425	−	0.170673i
$533$			14.0926i			0.610418i
$534$	0.809606	+	0.531763i	0.0350351	+	0.0230116i
$535$	−44.1023	+	25.4625i	−1.90671	+	1.10084i
$536$	−10.9122	+	6.30018i	−0.471337	+	0.272126i
$537$	−17.1950	−	11.2940i	−0.742020	−	0.487372i
$538$		−	28.5827i		−	1.23229i
$539$	0.920638	+	15.4630i	0.0396547	+	0.666040i
$540$	−13.8208	−	2.41032i	−0.594752	−	0.103724i
$541$	−2.23499	+	3.87112i	−0.0960899	+	0.166433i	−0.910063	−	0.414470i	$-0.863967\pi$
$541$	−2.23499	+	3.87112i	−0.0960899	+	0.166433i	0.813973	+	0.580903i	$0.197300\pi$
$542$	5.50675	+	9.53797i	0.236535	+	0.409691i
$543$	−18.6336	+	9.37271i	−0.799645	+	0.402221i
$544$	−5.18431	−	2.99316i	−0.222276	−	0.128331i
$545$	−7.82013			−0.334977
$546$	5.77520	−	3.12342i	0.247156	−	0.133670i
$547$	−3.32163			−0.142023			−0.0710114	−	0.997476i	$-0.522623\pi$
$547$	−3.32163			−0.142023			−0.0710114	+	0.997476i	$0.522623\pi$
$548$	16.1691	+	9.33525i	0.690711	+	0.398782i
$549$	11.8336	−	5.12202i	0.505044	−	0.218602i
$550$	−2.53352	−	4.38819i	−0.108030	−	0.187113i
$551$	8.17728	−	14.1635i	0.348364	−	0.603384i
$552$	1.72918	+	0.0996314i	0.0735989	+	0.00424060i
$553$	−0.0630751	−	2.12069i	−0.00268222	−	0.0901810i
$554$		−	18.1976i		−	0.773141i
$555$	26.2022	−	39.8927i	1.11222	−	1.69335i
$556$	1.06580	−	0.615338i	0.0451998	−	0.0260961i
$557$	24.4754	−	14.1309i	1.03706	−	0.598745i	0.118059	−	0.993007i	$-0.462333\pi$
$557$	24.4754	−	14.1309i	1.03706	−	0.598745i	0.918998	+	0.394262i	$0.129000\pi$
$558$	5.82079	−	7.83907i	0.246414	−	0.331854i
$559$			4.72945i			0.200034i
$560$	6.28983	+	3.38621i	0.265794	+	0.143093i
$561$	1.31984	−	22.9069i	0.0557237	−	0.967130i
$562$	−11.5231	+	19.9586i	−0.486073	+	0.841903i
$563$	17.2943	+	29.9546i	0.728868	+	1.26244i	0.957362	+	0.288891i	$0.0932864\pi$
$563$	17.2943	+	29.9546i	0.728868	+	1.26244i	−0.228494	+	0.973545i	$0.573380\pi$
$564$	5.11216	+	10.1633i	0.215261	+	0.427954i
$565$	48.3427	+	27.9107i	2.03379	+	1.17421i
$566$	9.20011			0.386709
$567$	17.8376	+	15.7740i	0.749109	+	0.662447i
$568$	1.18264			0.0496223
$569$	2.07211	+	1.19633i	0.0868672	+	0.0501528i	0.542804	−	0.839859i	$-0.317362\pi$
$569$	2.07211	+	1.19633i	0.0868672	+	0.0501528i	−0.455937	+	0.890012i	$0.650696\pi$
$570$	−3.67506	−	7.30629i	−0.153931	−	0.306027i
$571$	17.9656	+	31.1174i	0.751838	+	1.30222i	0.946931	+	0.321438i	$0.104166\pi$
$571$	17.9656	+	31.1174i	0.751838	+	1.30222i	−0.195092	+	0.980785i	$0.562501\pi$
$572$	1.58529	−	2.74580i	0.0662841	−	0.114807i
$573$	−1.60085	+	27.7841i	−0.0668766	+	1.16070i
$574$	26.0121	−	0.773670i	1.08572	−	0.0322923i
$575$			2.28976i			0.0954896i
$576$	1.78847	−	2.40860i	0.0745197	−	0.100358i
$577$	5.26476	−	3.03961i	0.219175	−	0.126541i	−0.386393	−	0.922334i	$-0.626279\pi$
$577$	5.26476	−	3.03961i	0.219175	−	0.126541i	0.605568	+	0.795793i	$0.292946\pi$
$578$	16.3126	−	9.41807i	0.678514	−	0.391740i
$579$	−11.2585	+	17.1410i	−0.467888	+	0.712356i
$580$			25.2487i			1.04839i
$581$	12.2673	−	7.57754i	0.508935	−	0.314369i
$582$	4.68027	+	0.269666i	0.194003	+	0.0111780i
$583$	5.93023	−	10.2715i	0.245605	−	0.425401i
$584$	−1.92457	−	3.33345i	−0.0796392	−	0.137939i
$585$	10.6503	−	4.60985i	0.440335	−	0.190594i
$586$	0.719144	+	0.415198i	0.0297076	+	0.0171517i
$587$	13.6143			0.561922			0.280961	−	0.959719i	$-0.409347\pi$
$587$	13.6143			0.561922			0.280961	+	0.959719i	$0.409347\pi$
$588$	−6.08226	−	10.4884i	−0.250828	−	0.432533i
$589$	5.69189			0.234530
$590$	29.3665	+	16.9547i	1.20900	+	0.698015i
$591$	−17.8092	+	8.95802i	−0.732572	+	0.368484i
$592$	5.10303	+	8.83871i	0.209733	+	0.363269i
$593$	−9.66516	+	16.7406i	−0.396901	+	0.687452i	−0.993342	−	0.115205i	$-0.963248\pi$
$593$	−9.66516	+	16.7406i	−0.396901	+	0.687452i	0.596441	+	0.802657i	$0.296581\pi$
$594$	11.3277	+	1.97553i	0.464780	+	0.0810569i
$595$	−36.3817	+	22.4729i	−1.49150	+	0.921301i
$596$		−	15.1912i		−	0.622254i
$597$	−29.7467	−	19.5382i	−1.21745	−	0.799643i
$598$	−1.24080	+	0.716379i	−0.0507403	+	0.0292949i
$599$	−15.2450	+	8.80172i	−0.622895	+	0.359629i	−0.777995	−	0.628270i	$-0.783763\pi$
$599$	−15.2450	+	8.80172i	−0.622895	+	0.359629i	0.155100	+	0.987899i	$0.450430\pi$
$600$	3.31489	+	2.17728i	0.135330	+	0.0888869i
$601$			43.6783i			1.78167i	0.454323	+	0.890837i	$0.349881\pi$
$601$			43.6783i			1.78167i	−0.454323	+	0.890837i	$0.650119\pi$
$602$	8.72961	−	0.259642i	0.355792	−	0.0105822i
$603$	37.5509	+	4.34160i	1.52919	+	0.176804i
$604$	−6.71279	+	11.6269i	−0.273139	+	0.473091i
$605$	−8.23892	−	14.2702i	−0.334960	−	0.580167i
$606$	−3.41378	+	1.71713i	−0.138675	+	0.0697537i
$607$	−23.9305	−	13.8163i	−0.971309	−	0.560786i	−0.0716741	−	0.997428i	$-0.522834\pi$
$607$	−23.9305	−	13.8163i	−0.971309	−	0.560786i	−0.899635	+	0.436642i	$0.856167\pi$
$608$	1.74887			0.0709259
$609$	22.4511	−	36.5023i	0.909764	−	1.47915i
$610$	−11.6049			−0.469868
$611$	−8.14998	−	4.70539i	−0.329713	−	0.190360i
$612$	7.13375	+	16.4813i	0.288365	+	0.666219i
$613$	−7.82250	−	13.5490i	−0.315948	−	0.547238i	0.663691	−	0.748007i	$-0.268989\pi$
$613$	−7.82250	−	13.5490i	−0.315948	−	0.547238i	−0.979639	+	0.200769i	$0.935656\pi$
$614$	−5.74402	+	9.94894i	−0.231810	+	0.401507i
$615$	45.9215	+	2.64589i	1.85173	+	0.106692i
$616$	−5.15522	−	2.77538i	−0.207710	−	0.111823i
$617$			19.4854i			0.784451i	0.919869	+	0.392226i	$0.128295\pi$
$617$			19.4854i			0.784451i	−0.919869	+	0.392226i	$0.871705\pi$
$618$	11.9328	−	18.1676i	0.480007	−	0.730808i
$619$	−13.9471	+	8.05237i	−0.560582	+	0.323652i	−0.753379	−	0.657587i	$-0.771577\pi$
$619$	−13.9471	+	8.05237i	−0.560582	+	0.323652i	0.192797	+	0.981239i	$0.438244\pi$
$620$	−7.61004	+	4.39366i	−0.305627	+	0.176454i
$621$	−3.98673	−	3.33257i	−0.159982	−	0.133731i
$622$			13.3597i			0.535675i
$623$	0.0439878	+	1.47894i	0.00176233	+	0.0592527i
$624$	−0.142748	+	2.47750i	−0.00571448	+	0.0991794i
$625$	15.6029	−	27.0250i	0.624116	−	1.08100i
$626$	8.33627	+	14.4388i	0.333184	+	0.577092i
$627$	3.01213	+	5.98832i	0.120293	+	0.239150i
$628$	7.41201	+	4.27933i	0.295772	+	0.170764i
$629$	−61.0969			−2.43609
$630$	−9.09355	−	19.4052i	−0.362296	−	0.773122i
$631$	−45.4746			−1.81032			−0.905158	−	0.425075i	$-0.860248\pi$
$631$	−45.4746			−1.81032			−0.905158	+	0.425075i	$0.860248\pi$
$632$	0.694466	+	0.400950i	0.0276244	+	0.0159489i
$633$	−1.18041	−	2.34674i	−0.0469170	−	0.0932744i
$634$	−5.22260	−	9.04580i	−0.207416	−	0.359255i
$635$	14.1912	−	24.5799i	0.563160	−	0.975422i
$636$	−0.533990	+	9.26783i	−0.0211741	+	0.367493i
$637$	8.96831	+	4.48958i	0.355338	+	0.177883i
$638$		−	20.6941i		−	0.819288i
$639$	−2.84850	−	2.11511i	−0.112685	−	0.0836725i
$640$	−2.33823	+	1.34998i	−0.0924267	+	0.0533626i
$641$	3.61910	−	2.08949i	0.142946	−	0.0825299i	−0.426821	−	0.904336i	$-0.640367\pi$
$641$	3.61910	−	2.08949i	0.142946	−	0.0825299i	0.569767	+	0.821806i	$0.307033\pi$
$642$	−17.9348	+	27.3057i	−0.707831	+	1.07767i
$643$		−	48.0129i		−	1.89344i	−0.322054	−	0.946721i	$-0.604373\pi$
$643$		−	48.0129i		−	1.89344i	0.322054	−	0.946721i	$-0.395627\pi$
$644$	1.39041	+	2.25095i	0.0547898	+	0.0886997i
$645$	15.4112	+	0.887955i	0.606814	+	0.0349632i
$646$	−5.23465	+	9.06667i	−0.205954	+	0.356723i
$647$	−8.04212	−	13.9294i	−0.316168	−	0.547620i	0.663517	−	0.748161i	$-0.269063\pi$
$647$	−8.04212	−	13.9294i	−0.316168	−	0.547620i	−0.979685	+	0.200542i	$0.935730\pi$
$648$	−8.61544	+	2.60273i	−0.338446	+	0.102245i
$649$	−24.0691	−	13.8963i	−0.944795	−	0.545477i
$650$	−3.28067			−0.128679
$651$	14.9088	+	0.414870i	0.584320	+	0.0162600i
$652$	20.9094			0.818875
$653$	−22.2469	−	12.8442i	−0.870587	−	0.502634i	−0.00304393	−	0.999995i	$-0.500969\pi$
$653$	−22.2469	−	12.8442i	−0.870587	−	0.502634i	−0.867543	+	0.497362i	$0.834302\pi$
$654$	−4.48168	+	2.25428i	−0.175248	+	0.0881495i
$655$	−11.9894	−	20.7662i	−0.468464	−	0.811404i
$656$	−4.91800	+	8.51822i	−0.192016	+	0.332581i
$657$	−1.32627	+	11.4710i	−0.0517425	+	0.447526i
$658$	−8.23778	+	15.3015i	−0.321142	+	0.596516i
$659$			44.1564i			1.72009i	0.510218	+	0.860045i	$0.329565\pi$
$659$			44.1564i			1.72009i	−0.510218	+	0.860045i	$0.670435\pi$
$660$	−8.64968	−	5.68126i	−0.336688	−	0.221143i
$661$	−19.4527	+	11.2310i	−0.756621	+	0.436835i	−0.828081	−	0.560608i	$-0.810567\pi$
$661$	−19.4527	+	11.2310i	−0.756621	+	0.436835i	0.0714604	+	0.997443i	$0.477234\pi$
$662$	−7.76405	+	4.48257i	−0.301758	+	0.174220i
$663$	−12.4169	−	8.15561i	−0.482231	−	0.316738i
$664$			5.44986i			0.211496i
$665$	5.92203	−	11.0001i	0.229646	−	0.426564i
$666$	3.51662	−	30.4156i	0.136266	−	1.17858i
$667$	−4.67576	+	8.09865i	−0.181046	+	0.313581i
$668$	4.56168	+	7.90106i	0.176497	+	0.305701i
$669$	8.28632	−	4.16802i	0.320368	−	0.161145i
$670$	−29.4625	−	17.0102i	−1.13824	−	0.657162i
$671$	9.51149			0.367187
$672$	4.58080	+	0.127471i	0.176708	+	0.00491731i
$673$	−38.5037			−1.48421			−0.742104	−	0.670284i	$-0.766172\pi$
$673$	−38.5037			−1.48421			−0.742104	+	0.670284i	$0.766172\pi$
$674$	21.2921	+	12.2930i	0.820141	+	0.473509i
$675$	−4.09025	−	11.1728i	−0.157434	−	0.430040i
$676$	5.47360	+	9.48056i	0.210523	+	0.364637i
$677$	16.8208	−	29.1345i	0.646476	−	1.11973i	−0.337483	−	0.941332i	$-0.609576\pi$
$677$	16.8208	−	29.1345i	0.646476	−	1.11973i	0.983959	−	0.178397i	$-0.0570911\pi$
$678$	35.7507	+	2.05987i	1.37300	+	0.0791088i
$679$	3.76333	+	6.09249i	0.144423	+	0.233808i
$680$		−	16.1628i		−	0.619816i
$681$	−7.77952	+	11.8443i	−0.298112	+	0.453874i
$682$	6.23728	−	3.60109i	0.238838	−	0.137893i
$683$	26.2370	−	15.1480i	1.00393	−	0.579620i	0.0945228	−	0.995523i	$-0.469867\pi$
$683$	26.2370	−	15.1480i	1.00393	−	0.579620i	0.909409	+	0.415902i	$0.136534\pi$
$684$	−4.21232	−	3.12780i	−0.161062	−	0.119594i
$685$			50.4095i			1.92605i
$686$	7.79450	−	16.8002i	0.297595	−	0.641434i
$687$	1.83536	−	31.8541i	0.0700232	−	1.21531i
$688$	−1.65047	+	2.85870i	−0.0629236	+	0.108987i
$689$	−3.83955	−	6.65029i	−0.146275	−	0.253356i
$690$	2.10140	+	4.17773i	0.0799988	+	0.159043i
$691$	8.16682	+	4.71512i	0.310681	+	0.179372i	0.647231	−	0.762294i	$-0.275927\pi$
$691$	8.16682	+	4.71512i	0.310681	+	0.179372i	−0.336550	+	0.941665i	$0.609260\pi$
$692$	−22.6402			−0.860651
$693$	7.45318	+	15.9047i	0.283123	+	0.604171i
$694$	−21.6223			−0.820771
$695$	2.87760	+	1.66139i	0.109154	+	0.0630199i
$696$	7.27836	+	14.4699i	0.275886	+	0.548480i
$697$	−29.4407	−	50.9929i	−1.11515	−	1.93149i
$698$	−13.8738	+	24.0301i	−0.525131	+	0.909554i
$699$	−1.54753	+	26.8586i	−0.0585329	+	1.01589i
$700$	0.180106	+	6.05546i	0.00680735	+	0.228875i
$701$		−	10.1563i		−	0.383599i	−0.981434	−	0.191800i	$-0.938568\pi$
$701$		−	10.1563i		−	0.383599i	0.981434	−	0.191800i	$-0.0614324\pi$
$702$	4.77476	−	5.71201i	0.180212	−	0.215586i
$703$	15.4577	−	8.92452i	0.582999	−	0.336595i
$704$	1.91644	−	1.10646i	0.0722286	−	0.0417012i
$705$	−16.8629	+	25.6737i	−0.635095	+	0.966928i
$706$		−	2.22162i		−	0.0836116i
$707$	−5.13965	−	2.76700i	−0.193297	−	0.104064i
$708$	21.7173	+	1.25130i	0.816185	+	0.0470267i
$709$	−13.5322	+	23.4385i	−0.508213	+	0.880250i	0.491742	+	0.870741i	$0.336360\pi$
$709$	−13.5322	+	23.4385i	−0.508213	+	0.880250i	−0.999955	+	0.00950924i	$0.996973\pi$
$710$	1.59653	+	2.76527i	0.0599168	+	0.103779i
$711$	−0.955604	−	2.20776i	−0.0358379	−	0.0827976i
$712$	−0.484312	−	0.279618i	−0.0181504	−	0.0104791i
$713$	−3.25462			−0.121886
$714$	−14.3719	+	23.3668i	−0.537857	+	0.874479i
$715$	8.56040			0.320141
$716$	10.2862	+	5.93874i	0.384413	+	0.221941i
$717$	10.5152	−	5.28916i	0.392698	−	0.197527i
$718$	18.4725	+	31.9954i	0.689389	+	1.19406i
$719$	18.8769	−	32.6958i	0.703991	−	1.21935i	−0.263064	−	0.964778i	$-0.584733\pi$
$719$	18.8769	−	32.6958i	0.703991	−	1.21935i	0.967055	−	0.254569i	$-0.0819336\pi$
$720$	8.04626	+	0.930302i	0.299867	+	0.0346703i
$721$	33.1876	−	0.987089i	1.23597	−	0.0367611i
$722$			15.9415i			0.593280i
$723$	9.86792	+	6.48142i	0.366992	+	0.241047i
$724$	10.4290	−	6.02121i	0.387592	−	0.223776i
$725$	−18.5440	+	10.7064i	−0.688706	+	0.397625i
$726$	−8.83532	−	5.80319i	−0.327910	−	0.215377i
$727$		−	4.36254i		−	0.161798i	−0.996722	−	0.0808988i	$-0.974221\pi$
$727$		−	4.36254i		−	0.161798i	0.996722	−	0.0808988i	$-0.0257791\pi$
$728$	−3.22506	+	1.99212i	−0.119529	+	0.0738329i
$729$	25.4061	+	9.13954i	0.940966	+	0.338502i
$730$	5.19625	−	9.00016i	0.192322	−	0.333111i
$731$	−9.88026	−	17.1131i	−0.365435	−	0.632951i
$732$	−6.65070	+	3.34530i	−0.245817	+	0.123646i
$733$	15.9256	+	9.19463i	0.588224	+	0.339611i	0.764395	−	0.644748i	$-0.223038\pi$
$733$	15.9256	+	9.19463i	0.588224	+	0.339611i	−0.176171	+	0.984360i	$0.556371\pi$
$734$	−3.84733			−0.142008
$735$	16.3133	−	28.3808i	0.601726	−	1.04684i
$736$	−1.00000			−0.0368605
$737$	24.1478	+	13.9418i	0.889497	+	0.513552i
$738$	27.0801	−	11.7213i	0.996832	−	0.431467i
$739$	−7.39594	−	12.8102i	−0.272064	−	0.471229i	0.697326	−	0.716754i	$-0.254373\pi$
$739$	−7.39594	−	12.8102i	−0.272064	−	0.471229i	−0.969390	+	0.245525i	$0.921040\pi$
$740$	−13.7780	+	23.8641i	−0.506488	+	0.877263i
$741$	4.33282	+	0.249647i	0.159170	+	0.00917100i
$742$	−12.0643	+	7.45212i	−0.442895	+	0.273576i
$743$			41.7216i			1.53062i	0.643664	+	0.765308i	$0.277413\pi$
$743$			41.7216i			1.53062i	−0.643664	+	0.765308i	$0.722587\pi$
$744$	−3.09473	+	4.71171i	−0.113458	+	0.172740i
$745$	35.5204	−	20.5077i	1.30137	−	0.751345i
$746$	−21.3729	+	12.3397i	−0.782518	+	0.451787i
$747$	9.74692	−	13.1265i	0.356621	−	0.480275i
$748$			13.2472i			0.484367i
$749$	−49.8805	+	1.48358i	−1.82259	+	0.0542088i
$750$	0.729056	−	12.6533i	0.0266213	−	0.462035i
$751$	−2.71160	+	4.69662i	−0.0989475	+	0.171382i	−0.911249	−	0.411855i	$-0.864881\pi$
$751$	−2.71160	+	4.69662i	−0.0989475	+	0.171382i	0.812302	+	0.583237i	$0.198214\pi$
$752$	−3.28415	−	5.68832i	−0.119761	−	0.207432i
$753$	−1.10518	−	2.19717i	−0.0402749	−	0.0800694i
$754$	−11.6034	−	6.69923i	−0.422571	−	0.243972i
$755$	−36.2484			−1.31922
$756$	−10.8054	−	8.49967i	−0.392987	−	0.309130i
$757$	25.2623			0.918172			0.459086	−	0.888392i	$-0.348177\pi$
$757$	25.2623			0.918172			0.459086	+	0.888392i	$0.348177\pi$
$758$	−7.34907	−	4.24299i	−0.266930	−	0.154112i
$759$	−1.72233	−	3.42411i	−0.0625166	−	0.124287i
$760$	2.36093	+	4.08925i	0.0856400	+	0.148333i
$761$	−26.4849	+	45.8732i	−0.960077	+	1.66290i	−0.237779	+	0.971319i	$0.576419\pi$
$761$	−26.4849	+	45.8732i	−0.960077	+	1.66290i	−0.722298	+	0.691582i	$0.756914\pi$
$762$	1.04734	−	18.1775i	0.0379412	−	0.658500i
$763$	−6.74744	−	3.63257i	−0.244274	−	0.131508i
$764$		−	16.0677i		−	0.581311i
$765$	−28.9068	+	38.9298i	−1.04513	+	1.40751i
$766$	−2.09667	+	1.21052i	−0.0757559	+	0.0437377i
$767$	−15.5836	+	8.99719i	−0.562691	+	0.324870i
$768$	−0.950875	+	1.44770i	−0.0343117	+	0.0522394i
$769$		−	29.2565i		−	1.05502i	−0.849550	−	0.527508i	$-0.823126\pi$
$769$		−	29.2565i		−	1.05502i	0.849550	−	0.527508i	$-0.176874\pi$
$770$	−0.469958	−	15.8008i	−0.0169361	−	0.569420i
$771$	−17.3761	−	1.00117i	−0.625784	−	0.0360562i
$772$	5.92008	−	10.2539i	0.213068	−	0.369045i
$773$	13.9391	+	24.1432i	0.501354	+	0.868370i	0.999999	+	0.00156396i	$0.000497824\pi$
$773$	13.9391	+	24.1432i	0.501354	+	0.868370i	−0.498645	+	0.866806i	$0.666169\pi$
$774$	9.08803	−	3.93365i	0.326663	−	0.141392i
$775$	−6.45387	−	3.72614i	−0.231830	−	0.133847i
$776$	−2.70663			−0.0971625
$777$	41.1389	−	22.2493i	1.47585	−	0.798189i
$778$	−4.72222			−0.169300
$779$	14.8972	+	8.60092i	0.533749	+	0.308160i
$780$	−5.98567	+	3.01079i	−0.214321	+	0.107804i
$781$	−1.30854	−	2.26645i	−0.0468231	−	0.0811000i
$782$	2.99316	−	5.18431i	0.107035	−	0.185391i
$783$	8.34835	−	47.8694i	0.298346	−	1.71071i
$784$	3.85411	+	5.84345i	0.137647	+	0.208695i
$785$			23.1080i			0.824760i
$786$	−12.8573	−	8.44489i	−0.458604	−	0.301219i
$787$	18.3547	−	10.5971i	0.654274	−	0.377745i	−0.135818	−	0.990734i	$-0.543366\pi$
$787$	18.3547	−	10.5971i	0.654274	−	0.377745i	0.790092	+	0.612989i	$0.210033\pi$
$788$	9.96762	−	5.75481i	0.355082	−	0.205006i
$789$	−7.04915	−	4.63000i	−0.250956	−	0.164832i
$790$			2.16510i			0.0770306i
$791$	28.7466	+	46.5381i	1.02211	+	1.65470i
$792$	−6.59481	−	0.762486i	−0.234336	−	0.0270938i
$793$	3.07912	−	5.33319i	0.109343	−	0.189387i
$794$	−14.2095	−	24.6115i	−0.504275	−	0.873429i
$795$	−22.3912	+	11.2628i	−0.794134	+	0.399449i
$796$	17.7947	+	10.2738i	0.630717	+	0.364144i
$797$	−46.7554			−1.65616			−0.828081	−	0.560608i	$-0.810567\pi$
$797$	−46.7554			−1.65616			−0.828081	+	0.560608i	$0.810567\pi$
$798$	0.222930	−	8.01121i	0.00789164	−	0.283594i
$799$	39.3200			1.39104
$800$	−1.98299	−	1.14488i	−0.0701093	−	0.0404776i
$801$	0.666427	+	1.53967i	0.0235470	+	0.0544015i
$802$	11.7560	+	20.3620i	0.415119	+	0.719007i
$803$	−4.25890	+	7.37664i	−0.150293	+	0.260316i
$804$	−21.7883	−	1.25539i	−0.768415	−	0.0442743i
$805$	−3.38621	+	6.28983i	−0.119348	+	0.221687i
$806$		−	4.66308i		−	0.164250i
$807$	27.1786	−	41.3792i	0.956730	−	1.45662i
$808$	1.91066	−	1.10312i	0.0672167	−	0.0388076i
$809$	29.0513	−	16.7728i	1.02139	−	0.589699i	0.106883	−	0.994272i	$-0.465913\pi$
$809$	29.0513	−	16.7728i	1.02139	−	0.589699i	0.914506	+	0.404572i	$0.132580\pi$
$810$	−17.7164	−	16.6313i	−0.622492	−	0.584363i
$811$			45.9917i			1.61499i	0.589878	+	0.807493i	$0.299176\pi$
$811$			45.9917i			1.61499i	−0.589878	+	0.807493i	$0.700824\pi$
$812$	−11.7284	+	21.7853i	−0.411587	+	0.764515i
$813$	−1.09729	+	19.0444i	−0.0384837	+	0.667915i
$814$	11.2926	−	19.5593i	0.395805	−	0.685554i
$815$	28.2272	+	48.8910i	0.988757	+	1.71258i
$816$	−4.65921	−	9.26284i	−0.163105	−	0.324264i
$817$	4.99948	+	2.88645i	0.174910	+	0.100984i
$818$	11.2785			0.394345
$819$	11.3307	+	0.969709i	0.395928	+	0.0338844i
$820$	−26.5567			−0.927402
$821$	−24.6895	−	14.2545i	−0.861671	−	0.497486i	0.00290076	−	0.999996i	$-0.499077\pi$
$821$	−24.6895	−	14.2545i	−0.861671	−	0.497486i	−0.864571	+	0.502510i	$0.832410\pi$
$822$	14.5314	+	28.8895i	0.506841	+	1.00764i
$823$	26.9171	+	46.6218i	0.938271	+	1.62513i	0.768694	+	0.639617i	$0.220907\pi$
$823$	26.9171	+	46.6218i	0.938271	+	1.62513i	0.169577	+	0.985517i	$0.445760\pi$
$824$	−6.27464	+	10.8680i	−0.218587	+	0.378605i
$825$	0.504837	−	8.76185i	0.0175762	−	0.305048i
$826$	17.4625	+	28.2702i	0.607599	+	0.983648i
$827$		−	17.8833i		−	0.621864i	−0.950432	−	0.310932i	$-0.899359\pi$
$827$		−	17.8833i		−	0.621864i	0.950432	−	0.310932i	$-0.100641\pi$
$828$	2.40860	+	1.78847i	0.0837047	+	0.0621537i
$829$	−23.2212	+	13.4068i	−0.806507	+	0.465637i	−0.845741	−	0.533593i	$-0.820841\pi$
$829$	−23.2212	+	13.4068i	−0.806507	+	0.465637i	0.0392346	+	0.999230i	$0.487508\pi$
$830$	−12.7430	+	7.35719i	−0.442317	+	0.255372i
$831$	17.3036	−	26.3446i	0.600256	−	0.913886i
$832$		−	1.43276i		−	0.0496719i
$833$	−41.8302	+	2.49049i	−1.44933	+	0.0862904i
$834$	2.12806	+	0.122614i	0.0736888	+	0.00424578i
$835$	−12.3163	+	21.3325i	−0.426224	+	0.738242i
$836$	−1.93505	−	3.35160i	−0.0669250	−	0.115917i
$837$	15.8807	−	5.81379i	0.548919	−	0.200954i
$838$	−4.56735	−	2.63696i	−0.157776	−	0.0910922i
$839$	−6.24432			−0.215578			−0.107789	−	0.994174i	$-0.534377\pi$
$839$	−6.24432			−0.215578			−0.107789	+	0.994174i	$0.534377\pi$
$840$	5.88592	+	10.8831i	0.203084	+	0.375501i
$841$	−58.4509			−2.01555
$842$	−15.6647	−	9.04404i	−0.539842	−	0.311678i
$843$	−35.6601	+	17.9371i	−1.22820	+	0.617785i
$844$	0.758317	+	1.31344i	0.0261024	+	0.0452106i
$845$	−14.7785	+	25.5971i	−0.508395	+	0.880566i
$846$	−2.26319	+	19.5745i	−0.0778100	+	0.672985i
$847$	−0.480044	−	16.1399i	−0.0164945	−	0.554573i
$848$		−	5.35966i		−	0.184051i
$849$	13.3190	+	8.74815i	0.457107	+	0.300236i
$850$	11.8708	−	6.85363i	0.407166	−	0.235078i
$851$	−8.83871	+	5.10303i	−0.302987	+	0.174930i
$852$	1.71210	+	1.12454i	0.0586556	+	0.0385260i
$853$		−	4.20086i		−	0.143835i	−0.997411	−	0.0719174i	$-0.977088\pi$
$853$		−	4.20086i		−	0.143835i	0.997411	−	0.0719174i	$-0.0229118\pi$
$854$	−10.0130	−	5.39065i	−0.342639	−	0.184464i
$855$	1.62697	−	14.0718i	0.0556413	−	0.481247i
$856$	9.43070	−	16.3344i	0.322335	−	0.558300i
$857$	10.4215	+	18.0506i	0.355992	+	0.616596i	0.987287	−	0.158947i	$-0.0508097\pi$
$857$	10.4215	+	18.0506i	0.355992	+	0.616596i	−0.631295	+	0.775543i	$0.717476\pi$
$858$	4.90593	−	2.46768i	0.167486	−	0.0842453i
$859$	28.8371	+	16.6491i	0.983911	+	0.568061i	0.903449	−	0.428697i	$-0.141027\pi$
$859$	28.8371	+	16.6491i	0.983911	+	0.568061i	0.0804622	+	0.996758i	$0.474360\pi$
$860$	−8.91240			−0.303910
$861$	38.3934	+	23.6142i	1.30844	+	0.804770i
$862$	9.16583			0.312189
$863$	17.2537	+	9.96145i	0.587324	+	0.339092i	0.764039	−	0.645170i	$-0.223214\pi$
$863$	17.2537	+	9.96145i	0.587324	+	0.339092i	−0.176715	+	0.984262i	$0.556547\pi$
$864$	4.87945	−	1.78632i	0.166002	−	0.0607719i
$865$	−30.5638	−	52.9380i	−1.03920	−	1.79994i
$866$	6.36794	−	11.0296i	0.216391	−	0.374801i
$867$	32.5711	+	1.87667i	1.10617	+	0.0637351i
$868$	−8.60710	+	0.255998i	−0.292144	+	0.00868915i
$869$		−	1.77454i		−	0.0601971i
$870$	−24.0083	+	36.5525i	−0.813959	+	1.23925i
$871$	15.6346	−	9.02663i	0.529758	−	0.305856i
$872$	2.50835	−	1.44820i	0.0849434	−	0.0490421i
$873$	6.51921	+	4.84074i	0.220642	+	0.163834i
$874$			1.74887i			0.0591563i
$875$	16.4714	−	10.1744i	0.556834	−	0.343956i
$876$	0.383495	−	6.65586i	0.0129571	−	0.224881i
$877$	7.82765	−	13.5579i	0.264321	−	0.457817i	−0.703065	−	0.711126i	$-0.748186\pi$
$877$	7.82765	−	13.5579i	0.264321	−	0.457817i	0.967385	+	0.253309i	$0.0815189\pi$
$878$	9.14462	+	15.8389i	0.308616	+	0.534538i
$879$	0.646304	+	1.28490i	0.0217993	+	0.0433385i
$880$	5.17431	+	2.98739i	0.174426	+	0.100705i
$881$	34.3328			1.15670			0.578351	−	0.815788i	$-0.303697\pi$
$881$	34.3328			1.15670			0.578351	+	0.815788i	$0.303697\pi$
$882$	1.16784	−	20.9675i	0.0393232	−	0.706013i
$883$	−1.59342			−0.0536230			−0.0268115	−	0.999641i	$-0.508535\pi$
$883$	−1.59342			−0.0536230			−0.0268115	+	0.999641i	$0.508535\pi$
$884$	7.42786	+	4.28848i	0.249826	+	0.144237i
$885$	26.3920	+	52.4692i	0.887158	+	1.76373i
$886$	4.93161	+	8.54180i	0.165681	+	0.286967i
$887$	−2.38456	+	4.13018i	−0.0800658	+	0.138678i	−0.903278	−	0.429056i	$-0.858846\pi$
$887$	−2.38456	+	4.13018i	−0.0800658	+	0.138678i	0.823212	+	0.567734i	$0.192180\pi$
$888$	−1.01684	+	17.6482i	−0.0341231	+	0.592233i
$889$	23.6623	−	14.6162i	0.793609	−	0.490212i
$890$		−	1.50991i		−	0.0506123i
$891$	14.5206	+	13.6312i	0.486458	+	0.456661i
$892$	−4.63777	+	2.67762i	−0.155284	+	0.0896532i
$893$	−9.94811	+	5.74354i	−0.332901	+	0.192200i
$894$	14.4449	−	21.9923i	0.483110	−	0.735531i
$895$			32.0686i			1.07194i
$896$	−2.64458	+	0.0786570i	−0.0883493	+	0.00262775i
$897$	−2.47750	−	0.142748i	−0.0827213	−	0.00476621i
$898$	−8.37289	+	14.5023i	−0.279407	+	0.483947i
$899$	−15.2178	−	26.3580i	−0.507542	−	0.879089i
$900$	2.72865	+	6.30409i	0.0909549	+	0.210136i
$901$	27.7861	+	16.0423i	0.925691	+	0.534448i
$902$	21.7662			0.724736
$903$	12.8847	+	7.92488i	0.428778	+	0.263724i
$904$	−20.6749			−0.687637
$905$	28.1579	+	16.2570i	0.936001	+	0.540401i
$906$	−20.7738	+	10.4492i	−0.690164	+	0.347152i
$907$	15.4107	+	26.6920i	0.511702	+	0.886294i	0.999908	+	0.0135658i	$0.00431825\pi$
$907$	15.4107	+	26.6920i	0.511702	+	0.886294i	−0.488206	+	0.872729i	$0.662348\pi$
$908$	4.09072	−	7.08533i	0.135755	−	0.235135i
$909$	−6.57491	−	0.760185i	−0.218076	−	0.0252137i
$910$	−9.01180	−	4.85162i	−0.298738	−	0.160830i
$911$			24.7319i			0.819404i	0.912220	+	0.409702i	$0.134367\pi$
$911$			24.7319i			0.819404i	−0.912220	+	0.409702i	$0.865633\pi$
$912$	2.53184	+	1.66295i	0.0838374	+	0.0550659i
$913$	10.4443	−	6.03004i	0.345657	−	0.199565i
$914$	−17.3985	+	10.0451i	−0.575493	+	0.332261i
$915$	−16.8004	−	11.0348i	−0.555403	−	0.364799i
$916$			18.4215i			0.608662i
$917$	−0.698567	−	23.4870i	−0.0230687	−	0.775609i
$918$	−5.34416	+	30.6434i	−0.176383	+	1.01138i
$919$	24.3606	−	42.1939i	0.803583	−	1.39185i	−0.113660	−	0.993520i	$-0.536257\pi$
$919$	24.3606	−	42.1939i	0.803583	−	1.39185i	0.917243	−	0.398327i	$-0.130409\pi$
$920$	−1.34998	−	2.33823i	−0.0445074	−	0.0770892i
$921$	−17.7758	+	8.94124i	−0.585733	+	0.294624i
$922$	−25.7123	−	14.8450i	−0.846790	−	0.488895i
$923$	−1.69443			−0.0557728
$924$	−4.82417	−	8.91988i	−0.158704	−	0.293442i
$925$	−23.3694			−0.768382
$926$	15.3537	+	8.86447i	0.504554	+	0.291304i
$927$	34.5502	−	14.9547i	1.13478	−	0.491175i
$928$	−4.67576	−	8.09865i	−0.153489	−	0.265851i
$929$	24.6796	−	42.7463i	0.809710	−	1.40246i	−0.103355	−	0.994645i	$-0.532958\pi$
$929$	24.6796	−	42.7463i	0.809710	−	1.40246i	0.913065	−	0.407814i	$-0.133709\pi$
$930$	−15.1949	−	0.875493i	−0.498260	−	0.0287085i
$931$	10.2194	−	6.74032i	0.334928	−	0.220905i
$932$		−	15.5325i		−	0.508785i
$933$	−12.7034	+	19.3408i	−0.415891	+	0.633191i
$934$	−19.9785	+	11.5346i	−0.653717	+	0.377424i
$935$	−30.9751	+	17.8835i	−1.01299	+	0.584852i
$936$	−2.56245	+	3.45094i	−0.0837562	+	0.112798i
$937$		−	3.85492i		−	0.125935i	−0.998016	−	0.0629674i	$-0.979944\pi$
$937$		−	3.85492i		−	0.125935i	0.998016	−	0.0629674i	$-0.0200564\pi$
$938$	−17.5197	−	28.3627i	−0.572037	−	0.926076i
$939$	−1.66111	+	28.8299i	−0.0542082	+	0.940827i
$940$	8.86706	−	15.3582i	0.289212	−	0.500929i
$941$	13.1368	+	22.7536i	0.428247	+	0.741745i	0.996717	−	0.0809585i	$-0.0257981\pi$
$941$	13.1368	+	22.7536i	0.428247	+	0.741745i	−0.568471	+	0.822703i	$0.692465\pi$
$942$	6.66127	+	13.2431i	0.217036	+	0.431483i
$943$	−8.51822	−	4.91800i	−0.277391	−	0.160152i
$944$	−12.5593			−0.408769
$945$	5.28720	−	36.7398i	0.171992	−	1.19514i
$946$	7.30470			0.237496
$947$	46.3376	+	26.7530i	1.50577	+	0.869357i	0.999978	+	0.00670213i	$0.00213337\pi$
$947$	46.3376	+	26.7530i	1.50577	+	0.869357i	0.505793	+	0.862655i	$0.331200\pi$
$948$	0.624126	+	1.24081i	0.0202707	+	0.0402995i
$949$	2.75744	+	4.77602i	0.0895103	+	0.155036i
$950$	−2.00224	+	3.46799i	−0.0649613	+	0.112516i
$951$	1.04067	−	18.0616i	0.0337460	−	0.585689i
$952$	7.50789	−	13.9458i	0.243332	−	0.451985i
$953$		−	28.8393i		−	0.934197i	−0.884205	−	0.467099i	$-0.845299\pi$
$953$		−	28.8393i		−	0.934197i	0.884205	−	0.467099i	$-0.154701\pi$
$954$	−9.58560	+	12.9093i	−0.310345	+	0.417954i
$955$	37.5701	−	21.6911i	1.21574	−	0.701908i
$956$	−5.88526	+	3.39786i	−0.190343	+	0.109895i
$957$	19.6775	−	29.9589i	0.636084	−	0.968434i
$958$		−	1.94963i		−	0.0629897i
$959$	−23.4160	+	43.4948i	−0.756142	+	1.40452i
$960$	−4.66872	−	0.269000i	−0.150682	−	0.00868195i
$961$	−10.2037	+	17.6734i	−0.329153	+	0.570110i
$962$	−7.31141	−	12.6637i	−0.235729	−	0.408295i
$963$	−51.9285	+	22.4766i	−1.67337	+	0.724300i
$964$	−5.90306	−	3.40814i	−0.190125	−	0.109769i
$965$	31.9679			1.02908
$966$	−0.127471	+	4.58080i	−0.00410132	+	0.147385i
$967$	−55.1973			−1.77503			−0.887513	−	0.460783i	$-0.847569\pi$
$967$	−55.1973			−1.77503			−0.887513	+	0.460783i	$0.847569\pi$
$968$	5.28536	+	3.05150i	0.169878	+	0.0980790i
$969$	−16.1995	+	8.14833i	−0.520402	+	0.261762i
$970$	−3.65390	−	6.32873i	−0.117320	−	0.203203i
$971$	11.2634	−	19.5088i	0.361460	−	0.626068i	−0.626741	−	0.779228i	$-0.715612\pi$
$971$	11.2634	−	19.5088i	0.361460	−	0.626068i	0.988201	+	0.153160i	$0.0489450\pi$
$972$	−14.9474	−	4.42423i	−0.479440	−	0.141907i
$973$	1.71114	+	2.77019i	0.0548568	+	0.0888081i
$974$			24.5041i			0.785160i
$975$	−4.74943	−	3.11951i	−0.152103	−	0.0999042i
$976$	3.72233	−	2.14909i	0.119149	−	0.0687906i
$977$	17.7901	−	10.2711i	0.569157	−	0.328603i	−0.187656	−	0.982235i	$-0.560089\pi$
$977$	17.7901	−	10.2711i	0.569157	−	0.328603i	0.756812	+	0.653632i	$0.226756\pi$
$978$	30.2706	+	19.8822i	0.967945	+	0.635763i
$979$			1.23754i			0.0395520i
$980$	−8.46037	+	16.9003i	−0.270257	+	0.539861i
$981$	−8.63167	−	0.997986i	−0.275588	−	0.0318632i
$982$	−14.1432	+	24.4968i	−0.451328	+	0.781723i
$983$	−15.3037	−	26.5068i	−0.488112	−	0.845434i	0.511795	−	0.859108i	$-0.328981\pi$
$983$	−15.3037	−	26.5068i	−0.488112	−	0.845434i	−0.999907	+	0.0136734i	$0.995647\pi$
$984$	−15.2195	+	7.65543i	−0.485181	+	0.244046i
$985$	26.9121	+	15.5377i	0.857492	+	0.495073i
$986$	55.9813			1.78281
$987$	−26.4757	+	14.3190i	−0.842730	+	0.455777i
$988$	−2.50570			−0.0797170
$989$	−2.85870	−	1.65047i	−0.0909013	−	0.0524819i
$990$	−7.11998	−	16.4495i	−0.226288	−	0.522800i
$991$	10.0709	+	17.4433i	0.319913	+	0.554105i	0.980470	−	0.196671i	$-0.0630131\pi$
$991$	10.0709	+	17.4433i	0.319913	+	0.554105i	−0.660557	+	0.750776i	$0.729680\pi$
$992$	1.62731	−	2.81858i	0.0516671	−	0.0894900i
$993$	−15.5024	−	0.893210i	−0.491953	−	0.0283452i
$994$	0.0930225	+	3.12758i	0.00295050	+	0.0992007i
$995$			55.4775i			1.75875i
$996$	−5.18213	+	7.88976i	−0.164202	+	0.249997i
$997$	−21.2780	+	12.2849i	−0.673881	+	0.389066i	−0.797546	−	0.603259i	$-0.793869\pi$
$997$	−21.2780	+	12.2849i	−0.673881	+	0.389066i	0.123664	+	0.992324i	$0.460535\pi$
$998$	20.5997	−	11.8933i	0.652073	−	0.376474i
$999$	34.0124	−	40.6888i	1.07611	−	1.28734i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.d.47.6	✓	56
3.2	odd	2	inner	966.2.l.d.47.24	yes	56
7.3	odd	6	inner	966.2.l.d.185.24	yes	56
21.17	even	6	inner	966.2.l.d.185.6	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.d.47.6	✓	56	1.1	even	1	trivial
966.2.l.d.47.24	yes	56	3.2	odd	2	inner
966.2.l.d.185.6	yes	56	21.17	even	6	inner
966.2.l.d.185.24	yes	56	7.3	odd	6	inner

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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.778308 - 1.54733i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.34998 + 2.33823i) q^{5} +(-0.0996314 + 1.72918i) q^{6} +(-2.25095 + 1.39041i) q^{7} -1.00000i q^{8} +(-1.78847 + 2.40860i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.778308 - 1.54733i) q^{3} +(0.500000 + 0.866025i) q^{4} +(-1.34998 + 2.33823i) q^{5} +(-0.0996314 + 1.72918i) q^{6} +(-2.25095 + 1.39041i) q^{7} -1.00000i q^{8} +(-1.78847 + 2.40860i) q^{9} +(2.33823 - 1.34998i) q^{10} +(-1.91644 + 1.10646i) q^{11} +(0.950875 - 1.44770i) q^{12} +1.43276i q^{13} +(2.64458 - 0.0786570i) q^{14} +(4.66872 + 0.269000i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.99316 - 5.18431i) q^{17} +(2.75316 - 1.19167i) q^{18} +(1.51456 + 0.874433i) q^{19} -2.69996 q^{20} +(3.90336 + 2.40079i) q^{21} +2.21292 q^{22} +(-0.866025 - 0.500000i) q^{23} +(-1.54733 + 0.778308i) q^{24} +(-1.14488 - 1.98299i) q^{25} +(0.716379 - 1.24080i) q^{26} +(5.11889 + 0.892727i) q^{27} +(-2.32960 - 1.25417i) q^{28} -9.35152i q^{29} +(-3.90873 - 2.56732i) q^{30} +(2.81858 - 1.62731i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.20364 + 2.10421i) q^{33} +5.98633i q^{34} +(-0.212370 - 7.14025i) q^{35} +(-2.98015 - 0.344562i) q^{36} +(5.10303 - 8.83871i) q^{37} +(-0.874433 - 1.51456i) q^{38} +(2.21695 - 1.11513i) q^{39} +(2.33823 + 1.34998i) q^{40} +9.83599 q^{41} +(-2.18001 - 4.03083i) q^{42} +3.30094 q^{43} +(-1.91644 - 1.10646i) q^{44} +(-3.21747 - 7.43342i) q^{45} +(0.500000 + 0.866025i) q^{46} +(-3.28415 + 5.68832i) q^{47} +(1.72918 + 0.0996314i) q^{48} +(3.13352 - 6.25948i) q^{49} +2.28976i q^{50} +(-5.69225 + 8.66641i) q^{51} +(-1.24080 + 0.716379i) q^{52} +(-4.64160 + 2.67983i) q^{53} +(-3.98673 - 3.33257i) q^{54} -5.97477i q^{55} +(1.39041 + 2.25095i) q^{56} +(0.174242 - 3.02411i) q^{57} +(-4.67576 + 8.09865i) q^{58} +(6.27963 + 10.8766i) q^{59} +(2.10140 + 4.17773i) q^{60} +(-3.72233 - 2.14909i) q^{61} -3.25462 q^{62} +(0.676813 - 7.90835i) q^{63} -1.00000 q^{64} +(-3.35012 - 1.93419i) q^{65} +(-1.72233 - 3.42411i) q^{66} +(-6.30018 - 10.9122i) q^{67} +(2.99316 - 5.18431i) q^{68} +(-0.0996314 + 1.72918i) q^{69} +(-3.38621 + 6.28983i) q^{70} +1.18264i q^{71} +(2.40860 + 1.78847i) q^{72} +(3.33345 - 1.92457i) q^{73} +(-8.83871 + 5.10303i) q^{74} +(-2.17728 + 3.31489i) q^{75} +1.74887i q^{76} +(2.77538 - 5.15522i) q^{77} +(-2.47750 - 0.142748i) q^{78} +(-0.400950 + 0.694466i) q^{79} +(-1.34998 - 2.33823i) q^{80} +(-2.60273 - 8.61544i) q^{81} +(-8.51822 - 4.91800i) q^{82} -5.44986 q^{83} +(-0.127471 + 4.58080i) q^{84} +16.1628 q^{85} +(-2.85870 - 1.65047i) q^{86} +(-14.4699 + 7.27836i) q^{87} +(1.10646 + 1.91644i) q^{88} +(0.279618 - 0.484312i) q^{89} +(-0.930302 + 8.04626i) q^{90} +(-1.99212 - 3.22506i) q^{91} -1.00000i q^{92} +(-4.71171 - 3.09473i) q^{93} +(5.68832 - 3.28415i) q^{94} +(-4.08925 + 2.36093i) q^{95} +(-1.44770 - 0.950875i) q^{96} -2.70663i q^{97} +(-5.84345 + 3.85411i) q^{98} +(0.762486 - 6.59481i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9}+O(q^{10}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9	\( 56 q + 28 q^{4} + 8 q^{7} + 10 q^{9} + 12 q^{10} + 8 q^{15} - 28 q^{16} - 8 q^{18} - 24 q^{19} - 4 q^{21} - 12 q^{22} + 6 q^{24} - 8 q^{25} + 10 q^{28} + 6 q^{30} - 6 q^{31} + 30 q^{33} + 20 q^{36} + 4 q^{37} - 10 q^{39} + 12 q^{40} + 8 q^{42} - 104 q^{43} - 6 q^{45} + 28 q^{46} + 40 q^{49} - 22 q^{51} - 6 q^{52} + 18 q^{54} + 68 q^{57} - 30 q^{58} + 4 q^{60} - 84 q^{61} - 6 q^{63} - 56 q^{64} - 30 q^{66} + 2 q^{67} + 30 q^{70} + 8 q^{72} + 54 q^{73} - 24 q^{75} + 68 q^{78} - 6 q^{79} + 22 q^{81} + 4 q^{84} - 108 q^{85} - 126 q^{87} - 6 q^{88} - 42 q^{91} + 36 q^{93} - 18 q^{94} + 6 q^{96} + 48 q^{99}+O(q^{100}) \) 56 * q + 28 * q^4 + 8 * q^7 + 10 * q^9 + 12 * q^10 + 8 * q^15 - 28 * q^16 - 8 * q^18 - 24 * q^19 - 4 * q^21 - 12 * q^22 + 6 * q^24 - 8 * q^25 + 10 * q^28 + 6 * q^30 - 6 * q^31 + 30 * q^33 + 20 * q^36 + 4 * q^37 - 10 * q^39 + 12 * q^40 + 8 * q^42 - 104 * q^43 - 6 * q^45 + 28 * q^46 + 40 * q^49 - 22 * q^51 - 6 * q^52 + 18 * q^54 + 68 * q^57 - 30 * q^58 + 4 * q^60 - 84 * q^61 - 6 * q^63 - 56 * q^64 - 30 * q^66 + 2 * q^67 + 30 * q^70 + 8 * q^72 + 54 * q^73 - 24 * q^75 + 68 * q^78 - 6 * q^79 + 22 * q^81 + 4 * q^84 - 108 * q^85 - 126 * q^87 - 6 * q^88 - 42 * q^91 + 36 * q^93 - 18 * q^94 + 6 * q^96 + 48 * q^99

Introduction

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