LMFDB - Embedded newform 966.2.l.d.47.14

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			47.14
Character	$\chi$	$=$	966.47
Dual form			966.2.l.d.185.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(1.71535 - 0.239977i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.203133 - 0.351837i) q^{5} +(-1.60552 - 0.649847i) q^{6} +(2.64215 + 0.138089i) q^{7} -1.00000i q^{8} +(2.88482 - 0.823286i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(1.71535 - 0.239977i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.203133 - 0.351837i) q^{5} +(-1.60552 - 0.649847i) q^{6} +(2.64215 + 0.138089i) q^{7} -1.00000i q^{8} +(2.88482 - 0.823286i) q^{9} +(-0.351837 + 0.203133i) q^{10} +(-0.507052 + 0.292747i) q^{11} +(1.06550 + 1.36554i) q^{12} -5.38874i q^{13} +(-2.21912 - 1.44066i) q^{14} +(0.264011 - 0.652269i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.37746 - 4.11789i) q^{17} +(-2.90997 - 0.729424i) q^{18} +(-2.00521 - 1.15771i) q^{19} +0.406266 q^{20} +(4.56533 - 0.397183i) q^{21} +0.585493 q^{22} +(-0.866025 - 0.500000i) q^{23} +(-0.239977 - 1.71535i) q^{24} +(2.41747 + 4.18719i) q^{25} +(-2.69437 + 4.66678i) q^{26} +(4.75090 - 2.10451i) q^{27} +(1.20148 + 2.35721i) q^{28} +4.66579i q^{29} +(-0.554774 + 0.432876i) q^{30} +(6.37174 - 3.67873i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.799517 + 0.623842i) q^{33} +4.75493i q^{34} +(0.585292 - 0.901553i) q^{35} +(2.15540 + 2.08669i) q^{36} +(-3.85694 + 6.68042i) q^{37} +(1.15771 + 2.00521i) q^{38} +(-1.29317 - 9.24354i) q^{39} +(-0.351837 - 0.203133i) q^{40} -2.48393 q^{41} +(-4.15228 - 1.93870i) q^{42} -0.0777633 q^{43} +(-0.507052 - 0.292747i) q^{44} +(0.296340 - 1.18222i) q^{45} +(0.500000 + 0.866025i) q^{46} +(5.12400 - 8.87503i) q^{47} +(-0.649847 + 1.60552i) q^{48} +(6.96186 + 0.729704i) q^{49} -4.83495i q^{50} +(-5.06637 - 6.49306i) q^{51} +(4.66678 - 2.69437i) q^{52} +(2.29429 - 1.32461i) q^{53} +(-5.16665 - 0.552889i) q^{54} +0.237866i q^{55} +(0.138089 - 2.64215i) q^{56} +(-3.71745 - 1.50467i) q^{57} +(2.33290 - 4.04070i) q^{58} +(5.50497 + 9.53488i) q^{59} +(0.696886 - 0.0974944i) q^{60} +(0.109261 + 0.0630820i) q^{61} -7.35745 q^{62} +(7.73581 - 1.77688i) q^{63} -1.00000 q^{64} +(-1.89595 - 1.09463i) q^{65} +(1.00432 - 0.140505i) q^{66} +(-0.572437 - 0.991489i) q^{67} +(2.37746 - 4.11789i) q^{68} +(-1.60552 - 0.649847i) q^{69} +(-0.957654 + 0.488122i) q^{70} +1.39096i q^{71} +(-0.823286 - 2.88482i) q^{72} +(-7.13315 + 4.11833i) q^{73} +(6.68042 - 3.85694i) q^{74} +(5.15163 + 6.60234i) q^{75} -2.31542i q^{76} +(-1.38013 + 0.703461i) q^{77} +(-3.50185 + 8.65173i) q^{78} +(-4.72544 + 8.18470i) q^{79} +(0.203133 + 0.351837i) q^{80} +(7.64440 - 4.75007i) q^{81} +(2.15115 + 1.24196i) q^{82} -10.8067 q^{83} +(2.62664 + 3.75510i) q^{84} -1.93176 q^{85} +(0.0673450 + 0.0388816i) q^{86} +(1.11968 + 8.00345i) q^{87} +(0.292747 + 0.507052i) q^{88} +(0.0584772 - 0.101285i) q^{89} +(-0.847749 + 0.875665i) q^{90} +(0.744126 - 14.2378i) q^{91} -1.00000i q^{92} +(10.0469 - 7.83936i) q^{93} +(-8.87503 + 5.12400i) q^{94} +(-0.814649 + 0.470338i) q^{95} +(1.36554 - 1.06550i) q^{96} -13.1555i q^{97} +(-5.66430 - 4.11287i) q^{98} +(-1.22174 + 1.26197i) 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
$3$	1.71535	−	0.239977i	0.990355	−	0.138551i
$3$	1.71535	−	0.239977i	0.990355	−	0.138551i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	0.203133	−	0.351837i	0.0908438	−	0.157346i	−0.817023	−	0.576606i	$-0.804377\pi$
$5$	0.203133	−	0.351837i	0.0908438	−	0.157346i	0.907866	+	0.419260i	$0.137710\pi$
$6$	−1.60552	−	0.649847i	−0.655451	−	0.265299i
$7$	2.64215	+	0.138089i	0.998637	+	0.0521928i
$7$	2.64215	+	0.138089i	0.998637	+	0.0521928i
$8$		−	1.00000i		−	0.353553i
$9$	2.88482	−	0.823286i	0.961607	−	0.274429i
$10$	−0.351837	+	0.203133i	−0.111260	+	0.0642363i
$11$	−0.507052	+	0.292747i	−0.152882	+	0.0882664i	−0.574489	−	0.818512i	$-0.694799\pi$
$11$	−0.507052	+	0.292747i	−0.152882	+	0.0882664i	0.421607	+	0.906778i	$0.361466\pi$
$12$	1.06550	+	1.36554i	0.307583	+	0.394199i
$13$		−	5.38874i		−	1.49457i	−0.664506	−	0.747283i	$-0.731358\pi$
$13$		−	5.38874i		−	1.49457i	0.664506	−	0.747283i	$-0.268642\pi$
$14$	−2.21912	−	1.44066i	−0.593085	−	0.385033i
$15$	0.264011	−	0.652269i	0.0681672	−	0.168415i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.37746	−	4.11789i	−0.576619	−	0.998734i	−0.995864	−	0.0908606i	$-0.971038\pi$
$17$	−2.37746	−	4.11789i	−0.576619	−	0.998734i	0.419244	−	0.907873i	$-0.362295\pi$
$18$	−2.90997	−	0.729424i	−0.685887	−	0.171927i
$19$	−2.00521	−	1.15771i	−0.460027	−	0.265597i	0.252029	−	0.967720i	$-0.418902\pi$
$19$	−2.00521	−	1.15771i	−0.460027	−	0.265597i	−0.712056	+	0.702123i	$0.752236\pi$
$20$	0.406266			0.0908438
$21$	4.56533	−	0.397183i	0.996237	−	0.0866724i
$22$	0.585493			0.124828
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$23$	−0.866025	−	0.500000i	−0.180579	−	0.104257i
$24$	−0.239977	−	1.71535i	−0.0489851	−	0.350143i
$25$	2.41747	+	4.18719i	0.483495	+	0.837438i
$26$	−2.69437	+	4.66678i	−0.528409	+	0.915231i
$27$	4.75090	−	2.10451i	0.914311	−	0.405013i
$28$	1.20148	+	2.35721i	0.227059	+	0.445471i
$29$			4.66579i			0.866416i	0.901294	+	0.433208i	$0.142619\pi$
$29$			4.66579i			0.866416i	−0.901294	+	0.433208i	$0.857381\pi$
$30$	−0.554774	+	0.432876i	−0.101287	+	0.0790320i
$31$	6.37174	−	3.67873i	1.14440	−	0.660719i	0.196882	−	0.980427i	$-0.436918\pi$
$31$	6.37174	−	3.67873i	1.14440	−	0.660719i	0.947516	+	0.319708i	$0.103585\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	−0.799517	+	0.623842i	−0.139178	+	0.108597i
$34$			4.75493i			0.815463i
$35$	0.585292	−	0.901553i	0.0989323	−	0.152390i
$36$	2.15540	+	2.08669i	0.359233	+	0.347781i
$37$	−3.85694	+	6.68042i	−0.634078	+	1.09825i	0.352632	+	0.935762i	$0.385287\pi$
$37$	−3.85694	+	6.68042i	−0.634078	+	1.09825i	−0.986710	+	0.162493i	$0.948047\pi$
$38$	1.15771	+	2.00521i	0.187805	+	0.325288i
$39$	−1.29317	−	9.24354i	−0.207073	−	1.48015i
$40$	−0.351837	−	0.203133i	−0.0556302	−	0.0321181i
$41$	−2.48393			−0.387925			−0.193962	−	0.981009i	$-0.562134\pi$
$41$	−2.48393			−0.387925			−0.193962	+	0.981009i	$0.562134\pi$
$42$	−4.15228	−	1.93870i	−0.640711	−	0.299147i
$43$	−0.0777633			−0.0118588			−0.00592940	−	0.999982i	$-0.501887\pi$
$43$	−0.0777633			−0.0118588			−0.00592940	+	0.999982i	$0.501887\pi$
$44$	−0.507052	−	0.292747i	−0.0764410	−	0.0441332i
$45$	0.296340	−	1.18222i	0.0441758	−	0.176235i
$46$	0.500000	+	0.866025i	0.0737210	+	0.127688i
$47$	5.12400	−	8.87503i	0.747412	−	1.29456i	−0.201647	−	0.979458i	$-0.564629\pi$
$47$	5.12400	−	8.87503i	0.747412	−	1.29456i	0.949059	−	0.315098i	$-0.102037\pi$
$48$	−0.649847	+	1.60552i	−0.0937973	+	0.231737i
$49$	6.96186	+	0.729704i	0.994552	+	0.104243i
$50$		−	4.83495i		−	0.683765i
$51$	−5.06637	−	6.49306i	−0.709433	−	0.909211i
$52$	4.66678	−	2.69437i	0.647166	−	0.373642i
$53$	2.29429	−	1.32461i	0.315145	−	0.181949i	−0.334081	−	0.942544i	$-0.608426\pi$
$53$	2.29429	−	1.32461i	0.315145	−	0.181949i	0.649227	+	0.760595i	$0.275093\pi$
$54$	−5.16665	−	0.552889i	−0.703093	−	0.0752386i
$55$			0.237866i			0.0320738i
$56$	0.138089	−	2.64215i	0.0184529	−	0.353072i
$57$	−3.71745	−	1.50467i	−0.492389	−	0.199298i
$58$	2.33290	−	4.04070i	0.306324	−	0.530569i
$59$	5.50497	+	9.53488i	0.716686	+	1.24134i	0.962306	+	0.271970i	$0.0876751\pi$
$59$	5.50497	+	9.53488i	0.716686	+	1.24134i	−0.245620	+	0.969366i	$0.578992\pi$
$60$	0.696886	−	0.0974944i	0.0899677	−	0.0125865i
$61$	0.109261	+	0.0630820i	0.0139895	+	0.00807682i	0.506978	−	0.861959i	$-0.330762\pi$
$61$	0.109261	+	0.0630820i	0.0139895	+	0.00807682i	−0.492989	+	0.870036i	$0.664096\pi$
$62$	−7.35745			−0.934397
$63$	7.73581	−	1.77688i	0.974620	−	0.223866i
$64$	−1.00000			−0.125000
$65$	−1.89595	−	1.09463i	−0.235164	−	0.135772i
$66$	1.00432	−	0.140505i	0.123624	−	0.0172949i
$67$	−0.572437	−	0.991489i	−0.0699343	−	0.121130i	0.828938	−	0.559341i	$-0.188946\pi$
$67$	−0.572437	−	0.991489i	−0.0699343	−	0.121130i	−0.898872	+	0.438211i	$0.855612\pi$
$68$	2.37746	−	4.11789i	0.288310	−	0.499367i
$69$	−1.60552	−	0.649847i	−0.193282	−	0.0782324i
$70$	−0.957654	+	0.488122i	−0.114462	+	0.0583417i
$71$			1.39096i			0.165077i	0.996588	+	0.0825384i	$0.0263027\pi$
$71$			1.39096i			0.165077i	−0.996588	+	0.0825384i	$0.973697\pi$
$72$	−0.823286	−	2.88482i	−0.0970252	−	0.339980i
$73$	−7.13315	+	4.11833i	−0.834872	+	0.482014i	−0.855518	−	0.517773i	$-0.826761\pi$
$73$	−7.13315	+	4.11833i	−0.834872	+	0.482014i	0.0206459	+	0.999787i	$0.493428\pi$
$74$	6.68042	−	3.85694i	0.776584	−	0.448361i
$75$	5.15163	+	6.60234i	0.594859	+	0.762372i
$76$		−	2.31542i		−	0.265597i
$77$	−1.38013	+	0.703461i	−0.157280	+	0.0801668i
$78$	−3.50185	+	8.65173i	−0.396507	+	0.979616i
$79$	−4.72544	+	8.18470i	−0.531653	+	0.920850i	0.467664	+	0.883906i	$0.345096\pi$
$79$	−4.72544	+	8.18470i	−0.531653	+	0.920850i	−0.999317	+	0.0369442i	$0.988238\pi$
$80$	0.203133	+	0.351837i	0.0227110	+	0.0393365i
$81$	7.64440	−	4.75007i	0.849378	−	0.527786i
$82$	2.15115	+	1.24196i	0.237554	+	0.137152i
$83$	−10.8067			−1.18619			−0.593097	−	0.805131i	$-0.702095\pi$
$83$	−10.8067			−1.18619			−0.593097	+	0.805131i	$0.702095\pi$
$84$	2.62664	+	3.75510i	0.286589	+	0.409715i
$85$	−1.93176			−0.209529
$86$	0.0673450	+	0.0388816i	0.00726200	+	0.00419272i
$87$	1.11968	+	8.00345i	0.120043	+	0.858060i
$88$	0.292747	+	0.507052i	0.0312069	+	0.0540519i
$89$	0.0584772	−	0.101285i	0.00619857	−	0.0107362i	−0.862909	−	0.505359i	$-0.831360\pi$
$89$	0.0584772	−	0.101285i	0.00619857	−	0.0107362i	0.869108	+	0.494622i	$0.164694\pi$
$90$	−0.847749	+	0.875665i	−0.0893606	+	0.0923032i
$91$	0.744126	−	14.2378i	0.0780056	−	1.49253i
$92$		−	1.00000i		−	0.104257i
$93$	10.0469	−	7.83936i	1.04182	−	0.812903i
$94$	−8.87503	+	5.12400i	−0.915389	+	0.528500i
$95$	−0.814649	+	0.470338i	−0.0835812	+	0.0482556i
$96$	1.36554	−	1.06550i	0.139370	−	0.108747i
$97$		−	13.1555i		−	1.33574i	−0.744280	−	0.667868i	$-0.767207\pi$
$97$		−	13.1555i		−	1.33574i	0.744280	−	0.667868i	$-0.232793\pi$
$98$	−5.66430	−	4.11287i	−0.572181	−	0.415463i
$99$	−1.22174	+	1.26197i	−0.122790	+	0.126833i
$100$	−2.41747	+	4.18719i	−0.241747	+	0.418719i
$101$	2.72865	+	4.72616i	0.271511	+	0.470270i	0.969249	−	0.246082i	$-0.0791434\pi$
$101$	2.72865	+	4.72616i	0.271511	+	0.470270i	−0.697738	+	0.716353i	$0.745810\pi$
$102$	1.14107	+	8.15634i	0.112983	+	0.807598i
$103$	6.54129	+	3.77662i	0.644533	+	0.372121i	0.786358	−	0.617770i	$-0.211964\pi$
$103$	6.54129	+	3.77662i	0.644533	+	0.372121i	−0.141826	+	0.989892i	$0.545297\pi$
$104$	−5.38874			−0.528409
$105$	0.787626	−	1.68693i	0.0768644	−	0.164628i
$106$	−2.64922			−0.257315
$107$	8.84917	+	5.10907i	0.855481	+	0.493912i	0.862497	−	0.506063i	$-0.168900\pi$
$107$	8.84917	+	5.10907i	0.855481	+	0.493912i	−0.00701511	+	0.999975i	$0.502233\pi$
$108$	4.19801	+	3.06214i	0.403954	+	0.294655i
$109$	0.800119	+	1.38585i	0.0766375	+	0.132740i	0.901797	−	0.432160i	$-0.142248\pi$
$109$	0.800119	+	1.38585i	0.0766375	+	0.132740i	−0.825160	+	0.564900i	$0.808915\pi$
$110$	0.118933	−	0.205998i	0.0113398	−	0.0196411i
$111$	−5.01285	+	12.3848i	−0.475798	+	1.17551i
$112$	−1.44066	+	2.21912i	−0.136130	+	0.209687i
$113$		−	15.2625i		−	1.43578i	−0.696158	−	0.717889i	$-0.745109\pi$
$113$		−	15.2625i		−	1.43578i	0.696158	−	0.717889i	$-0.254891\pi$
$114$	2.46707	+	3.16181i	0.231063	+	0.296130i
$115$	−0.351837	+	0.203133i	−0.0328089	+	0.0189422i
$116$	−4.04070	+	2.33290i	−0.375169	+	0.216604i
$117$	−4.43647	−	15.5455i	−0.410152	−	1.43719i
$118$		−	11.0099i		−	1.01355i
$119$	−5.71297	−	11.2084i	−0.523707	−	1.02747i
$120$	−0.652269	−	0.264011i	−0.0595437	−	0.0241008i
$121$	−5.32860	+	9.22940i	−0.484418	+	0.839037i
$122$	−0.0630820	−	0.109261i	−0.00571117	−	0.00989204i
$123$	−4.26080	+	0.596085i	−0.384183	+	0.0537472i
$124$	6.37174	+	3.67873i	0.572199	+	0.330359i
$125$	3.99560			0.357378
$126$	−7.58784	−	2.32908i	−0.675979	−	0.207491i
$127$	−16.1802			−1.43576			−0.717880	−	0.696167i	$-0.754887\pi$
$127$	−16.1802			−1.43576			−0.717880	+	0.696167i	$0.754887\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	−0.133391	+	0.0186614i	−0.0117444	+	0.00164304i
$130$	1.09463	+	1.89595i	0.0960054	+	0.166286i
$131$	2.96416	−	5.13407i	0.258980	−	0.448566i	−0.706989	−	0.707224i	$-0.749947\pi$
$131$	2.96416	−	5.13407i	0.258980	−	0.448566i	0.965969	+	0.258658i	$0.0832804\pi$
$132$	−0.940022	−	0.380481i	−0.0818184	−	0.0331166i
$133$	−5.13819	−	3.33573i	−0.445538	−	0.289245i
$134$			1.14487i			0.0989020i
$135$	0.224620	−	2.09904i	0.0193322	−	0.180656i
$136$	−4.11789	+	2.37746i	−0.353106	+	0.203866i
$137$	7.16011	−	4.13389i	0.611729	−	0.353182i	−0.161913	−	0.986805i	$-0.551766\pi$
$137$	7.16011	−	4.13389i	0.611729	−	0.353182i	0.773642	+	0.633623i	$0.218433\pi$
$138$	1.06550	+	1.36554i	0.0907013	+	0.116243i
$139$			7.61881i			0.646219i	0.946362	+	0.323109i	$0.104728\pi$
$139$			7.61881i			0.646219i	−0.946362	+	0.323109i	$0.895272\pi$
$140$	1.07341	+	0.0561009i	0.0907200	+	0.00474139i
$141$	6.65963	−	16.4534i	0.560842	−	1.38562i
$142$	0.695481	−	1.20461i	0.0583634	−	0.101088i
$143$	1.57753	+	2.73237i	0.131920	+	0.228492i
$144$	−0.729424	+	2.90997i	−0.0607853	+	0.242498i
$145$	1.64160	+	0.947777i	0.136327	+	0.0787086i
$146$	8.23665			0.681670
$147$	12.1171	−	0.418992i	0.999403	−	0.0345579i
$148$	−7.71389			−0.634078
$149$	16.3309	+	9.42866i	1.33788	+	0.772426i	0.986493	−	0.163804i	$-0.0523764\pi$
$149$	16.3309	+	9.42866i	1.33788	+	0.772426i	0.351388	+	0.936230i	$0.385710\pi$
$150$	−1.16028	−	8.29361i	−0.0947361	−	0.677170i
$151$	1.05175	+	1.82169i	0.0855903	+	0.148247i	0.905643	−	0.424042i	$-0.139389\pi$
$151$	1.05175	+	1.82169i	0.0855903	+	0.148247i	−0.820052	+	0.572289i	$0.806056\pi$
$152$	−1.15771	+	2.00521i	−0.0939026	+	0.162644i
$153$	−10.2488	−	9.92204i	−0.828563	−	0.802149i
$154$	1.54696	+	0.0808503i	0.124657	+	0.00651510i
$155$		−	2.98908i		−	0.240089i
$156$	7.35856	−	5.74169i	0.589156	−	0.459703i
$157$	−10.7257	+	6.19247i	−0.856002	+	0.494213i	−0.862671	−	0.505765i	$-0.831210\pi$
$157$	−10.7257	+	6.19247i	−0.856002	+	0.494213i	0.00666972	+	0.999978i	$0.497877\pi$
$158$	8.18470	−	4.72544i	0.651140	−	0.375936i
$159$	3.61763	−	2.82274i	0.286897	−	0.223858i
$160$		−	0.406266i		−	0.0321181i
$161$	−2.21912	−	1.44066i	−0.174891	−	0.113540i
$162$	−8.99528	+	0.291482i	−0.706736	+	0.0229010i
$163$	−4.56933	+	7.91431i	−0.357898	+	0.619897i	−0.987609	−	0.156932i	$-0.949840\pi$
$163$	−4.56933	+	7.91431i	−0.357898	+	0.619897i	0.629712	+	0.776829i	$0.283173\pi$
$164$	−1.24196	−	2.15115i	−0.0969811	−	0.167976i
$165$	0.0570823	+	0.408022i	0.00444385	+	0.0317645i
$166$	9.35891	+	5.40337i	0.726393	+	0.419383i
$167$	−24.0829			−1.86359			−0.931796	−	0.362983i	$-0.881758\pi$
$167$	−24.0829			−1.86359			−0.931796	+	0.362983i	$0.881758\pi$
$168$	−0.397183	−	4.56533i	−0.0306433	−	0.352223i
$169$	−16.0385			−1.23373
$170$	1.67296	+	0.965882i	0.128310	+	0.0740798i
$171$	−6.73780	−	1.68892i	−0.515253	−	0.129155i
$172$	−0.0388816	−	0.0673450i	−0.00296470	−	0.00513501i
$173$	−0.321290	+	0.556491i	−0.0244272	+	0.0423092i	−0.877981	−	0.478696i	$-0.841110\pi$
$173$	−0.321290	+	0.556491i	−0.0244272	+	0.0423092i	0.853553	+	0.521005i	$0.174443\pi$
$174$	3.03205	−	7.49103i	0.229859	−	0.567894i
$175$	5.80911	+	11.3970i	0.439128	+	0.861531i
$176$		−	0.585493i		−	0.0441332i
$177$	11.7311	+	15.0346i	0.881762	+	1.13007i
$178$	−0.101285	+	0.0584772i	−0.00759167	+	0.00438305i
$179$	18.4147	−	10.6317i	1.37638	−	0.794653i	0.384657	−	0.923059i	$-0.374320\pi$
$179$	18.4147	−	10.6317i	1.37638	−	0.794653i	0.991722	+	0.128407i	$0.0409863\pi$
$180$	1.17200	−	0.334473i	0.0873561	−	0.0249302i
$181$			13.7180i			1.01965i	0.860279	+	0.509824i	$0.170290\pi$
$181$			13.7180i			1.01965i	−0.860279	+	0.509824i	$0.829710\pi$
$182$	−7.76334	+	11.9583i	−0.575457	+	0.886405i
$183$	0.202559	+	0.0819873i	0.0149736	+	0.00606067i
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	1.56694	+	2.71403i	0.115204	+	0.199539i
$186$	−12.6206	+	1.76562i	−0.925385	+	0.129461i
$187$	2.41099	+	1.39199i	0.176309	+	0.101792i
$188$	10.2480			0.747412
$189$	12.8432	−	4.90438i	0.934203	−	0.356741i
$190$	0.940675			0.0682437
$191$	−12.9442	−	7.47336i	−0.936612	−	0.540753i	−0.0477154	−	0.998861i	$-0.515194\pi$
$191$	−12.9442	−	7.47336i	−0.936612	−	0.540753i	−0.888897	+	0.458108i	$0.848527\pi$
$192$	−1.71535	+	0.239977i	−0.123794	+	0.0173188i
$193$	−0.819707	−	1.41977i	−0.0590038	−	0.102198i	0.835015	−	0.550228i	$-0.185459\pi$
$193$	−0.819707	−	1.41977i	−0.0590038	−	0.102198i	−0.894018	+	0.448030i	$0.852126\pi$
$194$	−6.57773	+	11.3930i	−0.472254	+	0.817968i
$195$	−3.51490	−	1.42268i	−0.251707	−	0.101880i
$196$	2.84899	+	6.39400i	0.203499	+	0.456714i
$197$			21.1786i			1.50891i	0.656351	+	0.754456i	$0.272099\pi$
$197$			21.1786i			1.50891i	−0.656351	+	0.754456i	$0.727901\pi$
$198$	1.68904	−	0.482029i	0.120035	−	0.0342563i
$199$	9.57411	−	5.52761i	0.678690	−	0.391842i	−0.120671	−	0.992693i	$-0.538505\pi$
$199$	9.57411	−	5.52761i	0.678690	−	0.391842i	0.799361	+	0.600850i	$0.205171\pi$
$200$	4.18719	−	2.41747i	0.296079	−	0.170941i
$201$	−1.21986	−	1.56338i	−0.0860424	−	0.110272i
$202$		−	5.45730i		−	0.383974i
$203$	−0.644296	+	12.3277i	−0.0452207	+	0.865235i
$204$	3.08997	−	7.63413i	0.216341	−	0.534496i
$205$	−0.504568	+	0.873937i	−0.0352405	+	0.0610384i
$206$	−3.77662	−	6.54129i	−0.263129	−	0.455754i
$207$	−2.90997	−	0.729424i	−0.202257	−	0.0506985i
$208$	4.66678	+	2.69437i	0.323583	+	0.186821i
$209$	1.35566			0.0937730
$210$	−1.52557	+	1.06711i	−0.105274	+	0.0736378i
$211$	0.387624			0.0266851			0.0133426	−	0.999911i	$-0.495753\pi$
$211$	0.387624			0.0266851			0.0133426	+	0.999911i	$0.495753\pi$
$212$	2.29429	+	1.32461i	0.157573	+	0.0909746i
$213$	0.333799	+	2.38598i	0.0228715	+	0.163485i
$214$	−5.10907	−	8.84917i	−0.349249	−	0.604917i
$215$	−0.0157963	+	0.0273600i	−0.00107730	+	0.00186593i
$216$	−2.10451	−	4.75090i	−0.143194	−	0.323258i
$217$	17.3431	−	8.83986i	1.17732	−	0.600089i
$218$		−	1.60024i		−	0.108382i
$219$	−11.2475	+	8.77614i	−0.760037	+	0.593037i
$220$	−0.205998	+	0.118933i	−0.0138884	+	0.00801846i
$221$	−22.1902	+	12.8115i	−1.49267	+	0.861796i
$222$	10.5337	−	8.21914i	0.706973	−	0.551633i
$223$			11.4119i			0.764195i	0.924122	+	0.382097i	$0.124798\pi$
$223$			11.4119i			0.764195i	−0.924122	+	0.382097i	$0.875202\pi$
$224$	2.35721	−	1.20148i	0.157498	−	0.0802775i
$225$	10.4212	+	10.0890i	0.694749	+	0.672601i
$226$	−7.63126	+	13.2177i	−0.507624	+	0.879230i
$227$	−0.0712898	−	0.123478i	−0.00473167	−	0.00819550i	0.863650	−	0.504092i	$-0.168173\pi$
$227$	−0.0712898	−	0.123478i	−0.00473167	−	0.00819550i	−0.868382	+	0.495897i	$0.834839\pi$
$228$	−0.555646	−	3.97174i	−0.0367986	−	0.263035i
$229$	15.8683	+	9.16158i	1.04861	+	0.605414i	0.922259	−	0.386572i	$-0.126341\pi$
$229$	15.8683	+	9.16158i	1.04861	+	0.605414i	0.126349	+	0.991986i	$0.459674\pi$
$230$	0.406266			0.0267884
$231$	−2.19859	+	1.53788i	−0.144656	+	0.101185i
$232$	4.66579			0.306324
$233$	15.4278	+	8.90725i	1.01071	+	0.583533i	0.911399	−	0.411523i	$-0.135003\pi$
$233$	15.4278	+	8.90725i	1.01071	+	0.583533i	0.0993100	+	0.995057i	$0.468336\pi$
$234$	−3.93067	+	15.6811i	−0.256956	+	1.02510i
$235$	−2.08171	−	3.60562i	−0.135796	−	0.235205i
$236$	−5.50497	+	9.53488i	−0.358343	+	0.620668i
$237$	−6.14162	+	15.1736i	−0.398941	+	0.985630i
$238$	−0.656604	+	12.5632i	−0.0425613	+	0.814351i
$239$		−	19.6390i		−	1.27034i	−0.772373	−	0.635169i	$-0.780930\pi$
$239$		−	19.6390i		−	1.27034i	0.772373	−	0.635169i	$-0.219070\pi$
$240$	0.432876	+	0.554774i	0.0279420	+	0.0358105i
$241$	−14.5336	+	8.39100i	−0.936194	+	0.540512i	−0.888765	−	0.458363i	$-0.848436\pi$
$241$	−14.5336	+	8.39100i	−0.936194	+	0.540512i	−0.0474287	+	0.998875i	$0.515103\pi$
$242$	9.22940	−	5.32860i	0.593289	−	0.342535i
$243$	11.9729	−	9.98249i	0.768061	−	0.640377i
$244$			0.126164i			0.00807682i
$245$	1.67092	−	2.30121i	0.106751	−	0.147019i
$246$	3.98800	+	1.61417i	0.254266	+	0.102916i
$247$	−6.23859	+	10.8055i	−0.396952	+	0.687541i
$248$	−3.67873	−	6.37174i	−0.233599	−	0.404606i
$249$	−18.5373	+	2.59337i	−1.17475	+	0.164348i
$250$	−3.46029	−	1.99780i	−0.218848	−	0.126352i
$251$	−21.1221			−1.33321			−0.666606	−	0.745410i	$-0.732254\pi$
$251$	−21.1221			−1.33321			−0.666606	+	0.745410i	$0.732254\pi$
$252$	5.40673	+	5.81097i	0.340592	+	0.366056i
$253$	0.585493			0.0368096
$254$	14.0125	+	8.09010i	0.879220	+	0.507618i
$255$	−3.31364	+	0.463579i	−0.207508	+	0.0290304i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−6.35658	+	11.0099i	−0.396513	+	0.686780i	−0.993293	−	0.115624i	$-0.963113\pi$
$257$	−6.35658	+	11.0099i	−0.396513	+	0.686780i	0.596780	+	0.802405i	$0.296446\pi$
$258$	0.124851	+	0.0505342i	0.00777286	+	0.00314612i
$259$	−11.1131	+	17.1180i	−0.690535	+	1.06366i
$260$		−	2.18926i		−	0.135772i
$261$	3.84129	+	13.4600i	0.237770	+	0.833152i
$262$	−5.13407	+	2.96416i	−0.317184	+	0.183126i
$263$	−25.1549	+	14.5232i	−1.55112	+	0.895540i	−0.553069	+	0.833135i	$0.686544\pi$
$263$	−25.1549	+	14.5232i	−1.55112	+	0.895540i	−0.998051	+	0.0624046i	$0.980123\pi$
$264$	0.623842	+	0.799517i	0.0383948	+	0.0492069i
$265$		−	1.07629i		−	0.0661158i
$266$	2.78194	+	5.45792i	0.170571	+	0.334647i
$267$	0.0760025	−	0.187773i	0.00465128	−	0.0114915i
$268$	0.572437	−	0.991489i	0.0349671	−	0.0605649i
$269$	14.7781	+	25.5964i	0.901035	+	1.56064i	0.826153	+	0.563446i	$0.190525\pi$
$269$	14.7781	+	25.5964i	0.901035	+	1.56064i	0.0748820	+	0.997192i	$0.476142\pi$
$270$	−1.24404	+	1.70551i	−0.0757101	+	0.103794i
$271$	−5.12993	−	2.96177i	−0.311621	−	0.179914i	0.336031	−	0.941851i	$-0.390915\pi$
$271$	−5.12993	−	2.96177i	−0.311621	−	0.179914i	−0.647652	+	0.761937i	$0.724249\pi$
$272$	4.75493			0.288310
$273$	−2.14031	−	24.6014i	−0.129538	−	1.48894i
$274$	−8.26778			−0.499475
$275$	−2.45157	−	1.41541i	−0.147835	−	0.0853527i
$276$	−0.239977	−	1.71535i	−0.0144449	−	0.103252i
$277$	1.39945	+	2.42391i	0.0840846	+	0.145639i	0.905001	−	0.425410i	$-0.139870\pi$
$277$	1.39945	+	2.42391i	0.0840846	+	0.145639i	−0.820916	+	0.571049i	$0.806537\pi$
$278$	3.80940	−	6.59808i	0.228473	−	0.395727i
$279$	15.3527	−	15.8582i	0.919142	−	0.949408i
$280$	−0.901553	−	0.585292i	−0.0538781	−	0.0349779i
$281$			21.6031i			1.28873i	0.764717	+	0.644366i	$0.222879\pi$
$281$			21.6031i			1.28873i	−0.764717	+	0.644366i	$0.777121\pi$
$282$	−13.9941	+	10.9192i	−0.833337	+	0.650231i
$283$	−24.2466	+	13.9988i	−1.44131	+	0.832141i	−0.997937	−	0.0641963i	$-0.979552\pi$
$283$	−24.2466	+	13.9988i	−1.44131	+	0.832141i	−0.443373	+	0.896337i	$0.646218\pi$
$284$	−1.20461	+	0.695481i	−0.0714803	+	0.0412692i
$285$	−1.28453	+	1.00229i	−0.0760892	+	0.0593704i
$286$		−	3.15507i		−	0.186563i
$287$	−6.56290	−	0.343004i	−0.387396	−	0.0202469i
$288$	2.08669	−	2.15540i	0.122959	−	0.127008i
$289$	−2.80466	+	4.85781i	−0.164980	+	0.285753i
$290$	−0.947777	−	1.64160i	−0.0556554	−	0.0963979i
$291$	−3.15701	−	22.5662i	−0.185067	−	1.32285i
$292$	−7.13315	−	4.11833i	−0.417436	−	0.241007i
$293$	−3.94816			−0.230654			−0.115327	−	0.993328i	$-0.536792\pi$
$293$	−3.94816			−0.230654			−0.115327	+	0.993328i	$0.536792\pi$
$294$	−10.7032	−	5.69570i	−0.624225	−	0.332180i
$295$	4.47296			0.260426
$296$	6.68042	+	3.85694i	0.388292	+	0.224180i
$297$	−1.79286	+	2.45791i	−0.104032	+	0.142622i
$298$	−9.42866	−	16.3309i	−0.546188	−	0.946025i
$299$	−2.69437	+	4.66678i	−0.155819	+	0.269887i
$300$	−3.14198	+	7.76261i	−0.181402	+	0.448175i
$301$	−0.205462	−	0.0107383i	−0.0118426	−	0.000618944i
$302$		−	2.10350i		−	0.121043i
$303$	5.81475	+	7.45218i	0.334048	+	0.428117i
$304$	2.00521	−	1.15771i	0.115007	−	0.0663991i
$305$	0.0443891	−	0.0256281i	0.00254171	−	0.00146746i
$306$	3.91467	+	13.7171i	0.223787	+	0.784155i
$307$		−	3.35692i		−	0.191590i	−0.995401	−	0.0957948i	$-0.969461\pi$
$307$		−	3.35692i		−	0.191590i	0.995401	−	0.0957948i	$-0.0305393\pi$
$308$	−1.29928	−	0.843497i	−0.0740333	−	0.0480627i
$309$	12.1269	+	4.90845i	0.689874	+	0.279232i
$310$	−1.49454	+	2.58862i	−0.0848842	+	0.147024i
$311$	14.7966	+	25.6284i	0.839037	+	1.45325i	0.890701	+	0.454590i	$0.150214\pi$
$311$	14.7966	+	25.6284i	0.839037	+	1.45325i	−0.0516635	+	0.998665i	$0.516452\pi$
$312$	−9.24354	+	1.29317i	−0.523313	+	0.0732114i
$313$	−9.16888	−	5.29366i	−0.518256	−	0.299215i	0.217965	−	0.975957i	$-0.430058\pi$
$313$	−9.16888	−	5.29366i	−0.518256	−	0.299215i	−0.736221	+	0.676741i	$0.763391\pi$
$314$	12.3849			0.698922
$315$	0.946226	−	3.08268i	0.0533138	−	0.173689i
$316$	−9.45087			−0.531653
$317$	−15.3152	−	8.84225i	−0.860188	−	0.496630i	0.00388698	−	0.999992i	$-0.498763\pi$
$317$	−15.3152	−	8.84225i	−0.860188	−	0.496630i	−0.864075	+	0.503362i	$0.832096\pi$
$318$	−4.54433	+	0.635751i	−0.254833	+	0.0356512i
$319$	−1.36590	−	2.36580i	−0.0764755	−	0.132459i
$320$	−0.203133	+	0.351837i	−0.0113555	+	0.0196683i
$321$	16.4054	+	6.64023i	0.915663	+	0.370621i
$322$	1.20148	+	2.35721i	0.0669561	+	0.131362i
$323$			11.0096i			0.612593i
$324$	7.93588	+	4.24521i	0.440882	+	0.235845i
$325$	22.5636	−	13.0271i	1.25161	−	0.722615i
$326$	7.91431	−	4.56933i	0.438333	−	0.253072i
$327$	1.70505	+	2.18520i	0.0942895	+	0.120842i
$328$			2.48393i			0.137152i
$329$	14.7639	−	22.7415i	0.813960	−	1.25378i
$330$	0.154576	−	0.381899i	0.00850915	−	0.0210228i
$331$	1.24821	−	2.16196i	0.0686076	−	0.118832i	−0.829681	−	0.558238i	$-0.811478\pi$
$331$	1.24821	−	2.16196i	0.0686076	−	0.118832i	0.898289	+	0.439406i	$0.144811\pi$
$332$	−5.40337	−	9.35891i	−0.296549	−	0.513637i
$333$	−5.62670	+	22.4472i	−0.308341	+	1.23010i
$334$	20.8564	+	12.0415i	1.14121	+	0.658879i
$335$	−0.465123			−0.0254124
$336$	−1.93870	+	4.15228i	−0.105764	+	0.226526i
$337$	−18.4152			−1.00314			−0.501569	−	0.865118i	$-0.667244\pi$
$337$	−18.4152			−1.00314			−0.501569	+	0.865118i	$0.667244\pi$
$338$	13.8897	+	8.01923i	0.755501	+	0.436189i
$339$	−3.66265	−	26.1805i	−0.198928	−	1.42193i
$340$	−0.965882	−	1.67296i	−0.0523823	−	0.0907288i
$341$	−2.15387	+	3.73061i	−0.116639	+	0.202024i
$342$	4.99065	+	4.83155i	0.269863	+	0.261260i
$343$	18.2935	+	2.88934i	0.987756	+	0.156010i
$344$			0.0777633i			0.00419272i
$345$	−0.554774	+	0.432876i	−0.0298680	+	0.0233053i
$346$	0.556491	−	0.321290i	0.0299171	−	0.0172727i
$347$	20.0140	−	11.5551i	1.07441	−	0.620310i	0.145025	−	0.989428i	$-0.453674\pi$
$347$	20.0140	−	11.5551i	1.07441	−	0.620310i	0.929382	+	0.369118i	$0.120340\pi$
$348$	−6.37135	+	4.97140i	−0.341540	+	0.266495i
$349$		−	10.8767i		−	0.582216i	−0.956690	−	0.291108i	$-0.905976\pi$
$349$		−	10.8767i		−	0.582216i	0.956690	−	0.291108i	$-0.0940239\pi$
$350$	0.667654	−	12.7746i	0.0356876	−	0.682833i
$351$	−11.3407	−	25.6013i	−0.605319	−	1.36650i
$352$	−0.292747	+	0.507052i	−0.0156034	+	0.0270260i
$353$	1.42070	+	2.46072i	0.0756162	+	0.130971i	0.901354	−	0.433083i	$-0.142574\pi$
$353$	1.42070	+	2.46072i	0.0756162	+	0.130971i	−0.825738	+	0.564054i	$0.809241\pi$
$354$	−2.64213	−	18.8858i	−0.140428	−	1.00377i
$355$	0.489391	+	0.282550i	0.0259742	+	0.0149962i
$356$	0.116954			0.00619857
$357$	−12.4895	−	17.8552i	−0.661012	−	0.944999i
$358$	−21.2635			−1.12381
$359$	−3.64211	−	2.10277i	−0.192223	−	0.110980i	0.400800	−	0.916166i	$-0.368732\pi$
$359$	−3.64211	−	2.10277i	−0.192223	−	0.110980i	−0.593023	+	0.805186i	$0.702066\pi$
$360$	−1.18222	−	0.296340i	−0.0623086	−	0.0156185i
$361$	−6.81942	−	11.8116i	−0.358917	−	0.621662i
$362$	6.85898	−	11.8801i	0.360500	−	0.624405i
$363$	−6.92555	+	17.1104i	−0.363497	+	0.898061i
$364$	12.7024	−	6.47448i	0.665786	−	0.339355i
$365$			3.34627i			0.175152i
$366$	−0.134428	−	0.172283i	−0.00702664	−	0.00900535i
$367$	23.8692	−	13.7809i	1.24596	−	0.719356i	0.275660	−	0.961255i	$-0.411104\pi$
$367$	23.8692	−	13.7809i	1.24596	−	0.719356i	0.970301	+	0.241899i	$0.0777703\pi$
$368$	0.866025	−	0.500000i	0.0451447	−	0.0260643i
$369$	−7.16569	+	2.04499i	−0.373031	+	0.106458i
$370$		−	3.13389i		−	0.162923i
$371$	6.24477	−	3.18300i	0.324212	−	0.165253i
$372$	11.8125	+	4.78122i	0.612452	+	0.247895i
$373$	7.64112	−	13.2348i	0.395642	−	0.685272i	−0.597541	−	0.801838i	$-0.703855\pi$
$373$	7.64112	−	13.2348i	0.395642	−	0.685272i	0.993183	+	0.116566i	$0.0371888\pi$
$374$	−1.39199	−	2.41099i	−0.0719780	−	0.124670i
$375$	6.85384	−	0.958852i	0.353931	−	0.0495149i
$376$	−8.87503	−	5.12400i	−0.457695	−	0.264250i
$377$	25.1427			1.29492
$378$	−13.5747	−	2.17427i	−0.698207	−	0.111832i
$379$	−20.3504			−1.04533			−0.522666	−	0.852537i	$-0.675063\pi$
$379$	−20.3504			−1.04533			−0.522666	+	0.852537i	$0.675063\pi$
$380$	−0.814649	−	0.470338i	−0.0417906	−	0.0241278i
$381$	−27.7546	+	3.88287i	−1.42191	+	0.198926i
$382$	7.47336	+	12.9442i	0.382370	+	0.662285i
$383$	−5.03853	+	8.72699i	−0.257457	+	0.445928i	−0.965560	−	0.260181i	$-0.916218\pi$
$383$	−5.03853	+	8.72699i	−0.257457	+	0.445928i	0.708103	+	0.706109i	$0.249551\pi$
$384$	1.60552	+	0.649847i	0.0819314	+	0.0331624i
$385$	−0.0328467	+	0.628476i	−0.00167402	+	0.0320301i
$386$			1.63941i			0.0834440i
$387$	−0.224333	+	0.0640215i	−0.0114035	+	0.00325439i
$388$	11.3930	−	6.57773i	0.578390	−	0.333934i
$389$	−28.2398	+	16.3043i	−1.43182	+	0.826659i	−0.997259	−	0.0739855i	$-0.976428\pi$
$389$	−28.2398	+	16.3043i	−1.43182	+	0.826659i	−0.434556	+	0.900645i	$0.643095\pi$
$390$	2.33265	+	2.98953i	0.118118	+	0.151381i
$391$			4.75493i			0.240467i
$392$	0.729704	−	6.96186i	0.0368556	−	0.351627i
$393$	3.85250	−	9.51804i	0.194333	−	0.480121i
$394$	10.5893	−	18.3412i	0.533481	−	0.924016i
$395$	1.91978	+	3.32516i	0.0965948	+	0.167307i
$396$	−1.70377	−	0.427073i	−0.0856176	−	0.0214612i
$397$	30.8171	+	17.7923i	1.54667	+	0.892967i	0.998393	+	0.0566673i	$0.0180474\pi$
$397$	30.8171	+	17.7923i	1.54667	+	0.892967i	0.548272	+	0.836300i	$0.315286\pi$
$398$	−11.0552			−0.554148
$399$	−9.61427	−	4.48889i	−0.481316	−	0.224725i
$400$	−4.83495			−0.241747
$401$	−16.9434	−	9.78228i	−0.846114	−	0.488504i	0.0132241	−	0.999913i	$-0.495791\pi$
$401$	−16.9434	−	9.78228i	−0.846114	−	0.488504i	−0.859338	+	0.511409i	$0.829124\pi$
$402$	0.274743	+	1.96385i	0.0137029	+	0.0979481i
$403$	−19.8237	−	34.3356i	−0.987488	−	1.71038i
$404$	−2.72865	+	4.72616i	−0.135755	+	0.235135i
$405$	−0.118419	−	3.65447i	−0.00588429	−	0.181592i
$406$	6.72183	−	10.3540i	0.333599	−	0.513858i
$407$		−	4.51643i		−	0.223871i
$408$	−6.49306	+	5.06637i	−0.321454	+	0.250823i
$409$	27.7344	−	16.0125i	1.37138	−	0.791765i	0.380276	−	0.924873i	$-0.375829\pi$
$409$	27.7344	−	16.0125i	1.37138	−	0.791765i	0.991102	+	0.133108i	$0.0424958\pi$
$410$	0.873937	−	0.504568i	0.0431607	−	0.0249188i
$411$	11.2900	−	8.80931i	0.556896	−	0.434531i
$412$			7.55324i			0.372121i
$413$	13.2283	+	25.9527i	0.650920	+	1.27705i
$414$	2.15540	+	2.08669i	0.105932	+	0.102555i
$415$	−2.19521	+	3.80221i	−0.107758	+	0.186643i
$416$	−2.69437	−	4.66678i	−0.132102	−	0.228808i
$417$	1.82834	+	13.0689i	0.0895340	+	0.639986i
$418$	−1.17404	−	0.677830i	−0.0574240	−	0.0331538i
$419$	−23.7491			−1.16022			−0.580109	−	0.814539i	$-0.696990\pi$
$419$	−23.7491			−1.16022			−0.580109	+	0.814539i	$0.696990\pi$
$420$	1.85474	−	0.161362i	0.0905020	−	0.00787365i
$421$	28.2913			1.37883			0.689416	−	0.724365i	$-0.257867\pi$
$421$	28.2913			1.37883			0.689416	+	0.724365i	$0.257867\pi$
$422$	−0.335692	−	0.193812i	−0.0163412	−	0.00943461i
$423$	7.47514	−	29.8214i	0.363454	−	1.44997i
$424$	−1.32461	−	2.29429i	−0.0643288	−	0.111421i
$425$	11.4949	−	19.9098i	0.557585	−	0.965765i
$426$	0.903912	−	2.23322i	0.0437947	−	0.108200i
$427$	0.279973	+	0.181760i	0.0135488	+	0.00879596i
$428$			10.2181i			0.493912i
$429$	3.36172	+	4.30839i	0.162305	+	0.208011i
$430$	0.0273600	−	0.0157963i	0.00131942	−	0.000761765i
$431$	−29.3468	+	16.9434i	−1.41358	+	0.816133i	−0.995724	−	0.0923784i	$-0.970553\pi$
$431$	−29.3468	+	16.9434i	−1.41358	+	0.816133i	−0.417860	+	0.908511i	$0.637220\pi$
$432$	−0.552889	+	5.16665i	−0.0266009	+	0.248581i
$433$		−	29.8369i		−	1.43387i	−0.697139	−	0.716936i	$-0.745544\pi$
$433$		−	29.8369i		−	1.43387i	0.697139	−	0.716936i	$-0.254456\pi$
$434$	−19.4395	−	1.01598i	−0.933124	−	0.0487688i
$435$	3.04335	+	1.23182i	0.145918	+	0.0590612i
$436$	−0.800119	+	1.38585i	−0.0383187	+	0.0663700i
$437$	1.15771	+	2.00521i	0.0553807	+	0.0959222i
$438$	14.1287	−	1.97661i	0.675096	−	0.0944458i
$439$	−8.60849	−	4.97012i	−0.410861	−	0.237211i	0.280299	−	0.959913i	$-0.409567\pi$
$439$	−8.60849	−	4.97012i	−0.410861	−	0.237211i	−0.691160	+	0.722702i	$0.742900\pi$
$440$	0.237866			0.0113398
$441$	20.6845	−	3.62654i	0.984976	−	0.172692i
$442$	25.6230			1.21876
$443$	−13.6991	−	7.90916i	−0.650862	−	0.375775i	0.137924	−	0.990443i	$-0.455957\pi$
$443$	−13.6991	−	7.90916i	−0.650862	−	0.375775i	−0.788786	+	0.614667i	$0.789290\pi$
$444$	−13.2320	+	1.85115i	−0.627962	+	0.0878519i
$445$	−0.0237573	−	0.0411488i	−0.00112620	−	0.00195064i
$446$	5.70593	−	9.88296i	0.270184	−	0.467972i
$447$	30.2758	+	12.2544i	1.43200	+	0.579612i
$448$	−2.64215	−	0.138089i	−0.124830	−	0.00652410i
$449$		−	5.00300i		−	0.236106i	−0.993007	−	0.118053i	$-0.962335\pi$
$449$		−	5.00300i		−	0.236106i	0.993007	−	0.118053i	$-0.0376653\pi$
$450$	−3.98055	−	13.9480i	−0.187645	−	0.657513i
$451$	1.25948	−	0.727162i	0.0593066	−	0.0342407i
$452$	13.2177	−	7.63126i	0.621710	−	0.358944i
$453$	2.24128	+	2.87243i	0.105304	+	0.134958i
$454$			0.142580i			0.00669160i
$455$	−4.85823	−	3.15398i	−0.227757	−	0.147861i
$456$	−1.50467	+	3.71745i	−0.0704625	+	0.174086i
$457$	10.8973	−	18.8747i	0.509756	−	0.882922i	−0.490181	−	0.871621i	$-0.663069\pi$
$457$	10.8973	−	18.8747i	0.509756	−	0.882922i	0.999936	−	0.0113016i	$-0.00359747\pi$
$458$	−9.16158	−	15.8683i	−0.428093	−	0.741478i
$459$	−19.9612	−	14.5603i	−0.931710	−	0.679615i
$460$	−0.351837	−	0.203133i	−0.0164045	−	0.00947112i
$461$	3.52446			0.164150			0.0820752	−	0.996626i	$-0.473845\pi$
$461$	3.52446			0.164150			0.0820752	+	0.996626i	$0.473845\pi$
$462$	2.67297	−	0.232548i	0.124358	−	0.0108191i
$463$	−24.8392			−1.15438			−0.577189	−	0.816611i	$-0.695850\pi$
$463$	−24.8392			−1.15438			−0.577189	+	0.816611i	$0.695850\pi$
$464$	−4.04070	−	2.33290i	−0.187585	−	0.108302i
$465$	−0.717310	−	5.12731i	−0.0332645	−	0.237773i
$466$	−8.90725	−	15.4278i	−0.412620	−	0.714679i
$467$	7.49542	−	12.9824i	0.346847	−	0.600756i	−0.638841	−	0.769339i	$-0.720586\pi$
$467$	7.49542	−	12.9824i	0.346847	−	0.600756i	0.985687	+	0.168583i	$0.0539191\pi$
$468$	11.2446	−	11.6149i	0.519782	−	0.536898i
$469$	−1.37555	−	2.69871i	−0.0635169	−	0.124615i
$470$			4.16341i			0.192044i
$471$	−16.9122	+	13.1961i	−0.779272	+	0.608046i
$472$	9.53488	−	5.50497i	0.438879	−	0.253387i
$473$	0.0394300	−	0.0227649i	0.00181299	−	0.00104673i
$474$	12.9056	−	10.0699i	0.592773	−	0.462526i
$475$		−	11.1949i		−	0.513658i
$476$	6.85024	−	10.5518i	0.313980	−	0.483639i
$477$	5.52809	−	5.71012i	0.253114	−	0.261449i
$478$	−9.81948	+	17.0078i	−0.449133	+	0.777920i
$479$	−10.3127	−	17.8622i	−0.471200	−	0.816143i	0.528257	−	0.849085i	$-0.322846\pi$
$479$	−10.3127	−	17.8622i	−0.471200	−	0.816143i	−0.999457	+	0.0329416i	$0.989512\pi$
$480$	−0.0974944	−	0.696886i	−0.00444999	−	0.0318084i
$481$	35.9990	+	20.7841i	1.64141	+	0.947671i
$482$	16.7820			0.764399
$483$	−4.15228	−	1.93870i	−0.188935	−	0.0882137i
$484$	−10.6572			−0.484418
$485$	−4.62858	−	2.67231i	−0.210173	−	0.121343i
$486$	−15.3601	+	2.65865i	−0.696747	+	0.120599i
$487$	0.537720	+	0.931359i	0.0243664	+	0.0422039i	0.877951	−	0.478750i	$-0.158910\pi$
$487$	0.537720	+	0.931359i	0.0243664	+	0.0422039i	−0.853585	+	0.520953i	$0.825576\pi$
$488$	0.0630820	−	0.109261i	0.00285559	−	0.00494602i
$489$	−5.93873	+	14.6723i	−0.268559	+	0.663505i
$490$	−2.59766	+	1.15745i	−0.117351	+	0.0522881i
$491$		−	18.8484i		−	0.850615i	−0.905049	−	0.425308i	$-0.860166\pi$
$491$		−	18.8484i		−	0.850615i	0.905049	−	0.425308i	$-0.139834\pi$
$492$	−2.64662	−	3.39192i	−0.119319	−	0.152919i
$493$	19.2132	−	11.0928i	0.865320	−	0.499592i
$494$	10.8055	−	6.23859i	0.486165	−	0.280687i
$495$	0.195832	+	0.686201i	0.00880198	+	0.0308424i
$496$			7.35745i			0.330359i
$497$	−0.192077	+	3.67512i	−0.00861582	+	0.164852i
$498$	17.3505	+	7.02273i	0.777493	+	0.314696i
$499$	9.04070	−	15.6589i	0.404717	−	0.700991i	−0.589571	−	0.807716i	$-0.700703\pi$
$499$	9.04070	−	15.6589i	0.404717	−	0.700991i	0.994289	+	0.106726i	$0.0340367\pi$
$500$	1.99780	+	3.46029i	0.0893444	+	0.154749i
$501$	−41.3105	+	5.77934i	−1.84562	+	0.258202i
$502$	18.2922	+	10.5610i	0.816423	+	0.471362i
$503$	−19.1137			−0.852236			−0.426118	−	0.904668i	$-0.640119\pi$
$503$	−19.1137			−0.852236			−0.426118	+	0.904668i	$0.640119\pi$
$504$	−1.77688	−	7.73581i	−0.0791485	−	0.344580i
$505$	2.21711			0.0986603
$506$	−0.507052	−	0.292747i	−0.0225412	−	0.0130142i
$507$	−27.5115	+	3.84886i	−1.22183	+	0.170934i
$508$	−8.09010	−	14.0125i	−0.358940	−	0.621702i
$509$	16.0857	−	27.8612i	0.712985	−	1.23493i	−0.250747	−	0.968053i	$-0.580676\pi$
$509$	16.0857	−	27.8612i	0.712985	−	1.23493i	0.963732	−	0.266873i	$-0.0859904\pi$
$510$	3.10149	+	1.25535i	0.137336	+	0.0555879i
$511$	−19.4155	+	9.89620i	−0.858892	+	0.437782i
$512$			1.00000i			0.0441942i
$513$	−11.9630	−	1.28017i	−0.528178	−	0.0565208i
$514$	11.0099	−	6.35658i	0.485627	−	0.280377i
$515$	2.65750	−	1.53431i	0.117104	−	0.0676098i
$516$	−0.0828567	−	0.106189i	−0.00364756	−	0.00467472i
$517$			6.00013i			0.263886i
$518$	18.1833	−	9.26811i	0.798926	−	0.407218i
$519$	−0.417579	+	1.03168i	−0.0183297	+	0.0452856i
$520$	−1.09463	+	1.89595i	−0.0480027	+	0.0831431i
$521$	10.7930	+	18.6941i	0.472852	+	0.819004i	0.999517	−	0.0310690i	$-0.00989116\pi$
$521$	10.7930	+	18.6941i	0.472852	+	0.819004i	−0.526665	+	0.850073i	$0.676558\pi$
$522$	3.40334	−	13.5773i	0.148960	−	0.594264i
$523$	35.9473	+	20.7542i	1.57187	+	0.907517i	0.995940	+	0.0900146i	$0.0286914\pi$
$523$	35.9473	+	20.7542i	1.57187	+	0.907517i	0.575925	+	0.817502i	$0.304642\pi$
$524$	5.92832			0.258980
$525$	12.6996	+	18.1557i	0.554258	+	0.792381i
$526$	29.0464			1.26648
$527$	−30.2971	−	17.4921i	−1.31976	−	0.761966i
$528$	−0.140505	−	1.00432i	−0.00611469	−	0.0437076i
$529$	0.500000	+	0.866025i	0.0217391	+	0.0376533i
$530$	−0.538144	+	0.932093i	−0.0233755	+	0.0404875i
$531$	23.7308	+	22.9743i	1.02983	+	0.996999i
$532$	0.319734	−	6.11767i	0.0138622	−	0.265235i
$533$			13.3852i			0.579779i
$534$	−0.159706	+	0.124615i	−0.00691118	+	0.00539261i
$535$	3.59512	−	2.07564i	0.155430	−	0.0897378i
$536$	−0.991489	+	0.572437i	−0.0428258	+	0.0247255i
$537$	29.0362	−	22.6562i	1.25300	−	0.977687i
$538$		−	29.5561i		−	1.27426i
$539$	−3.74364	+	1.66806i	−0.161250	+	0.0718486i
$540$	1.93013	−	0.854991i	0.0830595	−	0.0367930i
$541$	−11.3328	+	19.6290i	−0.487235	+	0.843916i	−0.999892	−	0.0146776i	$-0.995328\pi$
$541$	−11.3328	+	19.6290i	−0.487235	+	0.843916i	0.512657	+	0.858593i	$0.328661\pi$
$542$	2.96177	+	5.12993i	0.127219	+	0.220349i
$543$	3.29199	+	23.5311i	0.141273	+	1.00981i
$544$	−4.11789	−	2.37746i	−0.176553	−	0.101933i
$545$	0.650122			0.0278482
$546$	−10.4471	+	22.3756i	−0.447095	+	0.957586i
$547$	33.9822			1.45297			0.726486	−	0.687181i	$-0.241152\pi$
$547$	33.9822			1.45297			0.726486	+	0.687181i	$0.241152\pi$
$548$	7.16011	+	4.13389i	0.305865	+	0.176591i
$549$	0.367134	+	0.0920270i	0.0156689	+	0.00392762i
$550$	1.41541	+	2.45157i	0.0603535	+	0.104535i
$551$	5.40163	−	9.35590i	0.230117	−	0.398575i
$552$	−0.649847	+	1.60552i	−0.0276593	+	0.0683355i
$553$	−13.6155	+	20.9726i	−0.578990	+	0.891847i
$554$		−	2.79889i		−	0.118914i
$555$	3.33916	+	4.27947i	0.141739	+	0.181653i
$556$	−6.59808	+	3.80940i	−0.279821	+	0.161555i
$557$	17.9322	−	10.3532i	0.759813	−	0.438678i	−0.0694156	−	0.997588i	$-0.522113\pi$
$557$	17.9322	−	10.3532i	0.759813	−	0.438678i	0.829229	+	0.558910i	$0.188780\pi$
$558$	−21.2249	+	6.05729i	−0.898523	+	0.256426i
$559$			0.419046i			0.0177238i
$560$	0.488122	+	0.957654i	0.0206269	+	0.0404683i
$561$	4.46973	+	1.80916i	0.188712	+	0.0763827i
$562$	10.8015	−	18.7088i	0.455635	−	0.789184i
$563$	−13.8909	−	24.0598i	−0.585433	−	1.01400i	−0.994821	−	0.101640i	$-0.967591\pi$
$563$	−13.8909	−	24.0598i	−0.585433	−	1.01400i	0.409388	−	0.912360i	$-0.365742\pi$
$564$	17.5789	−	2.45928i	0.740204	−	0.103554i
$565$	−5.36991	−	3.10032i	−0.225914	−	0.130431i
$566$	27.9976			1.17682
$567$	20.8535	−	11.4948i	0.875767	−	0.482735i
$568$	1.39096			0.0583634
$569$	19.7439	+	11.3992i	0.827709	+	0.477878i	0.853068	−	0.521800i	$-0.174739\pi$
$569$	19.7439	+	11.3992i	0.827709	+	0.477878i	−0.0253587	+	0.999678i	$0.508073\pi$
$570$	1.61358	−	0.225740i	0.0675856	−	0.00945522i
$571$	−0.706116	−	1.22303i	−0.0295501	−	0.0511822i	0.850872	−	0.525373i	$-0.176074\pi$
$571$	−0.706116	−	1.22303i	−0.0295501	−	0.0511822i	−0.880422	+	0.474191i	$0.842741\pi$
$572$	−1.57753	+	2.73237i	−0.0659600	+	0.114246i
$573$	−23.9973	−	9.71308i	−1.00250	−	0.405770i
$574$	5.51214	+	3.57850i	0.230072	+	0.149364i
$575$		−	4.83495i		−	0.201631i
$576$	−2.88482	+	0.823286i	−0.120201	+	0.0343036i
$577$	6.83950	−	3.94879i	0.284732	−	0.164390i	−0.350832	−	0.936439i	$-0.614101\pi$
$577$	6.83950	−	3.94879i	0.284732	−	0.164390i	0.635564	+	0.772048i	$0.280768\pi$
$578$	4.85781	−	2.80466i	0.202058	−	0.116658i
$579$	−1.74679	−	2.23869i	−0.0725943	−	0.0930369i
$580$			1.89555i			0.0787086i
$581$	−28.5530	−	1.49229i	−1.18458	−	0.0619108i
$582$	−8.54904	+	21.1214i	−0.354369	+	0.875510i
$583$	−0.775550	+	1.34329i	−0.0321200	+	0.0556335i
$584$	4.11833	+	7.13315i	0.170418	+	0.295172i
$585$	−6.37068	−	1.59690i	−0.263395	−	0.0660236i
$586$	3.41920	+	1.97408i	0.141246	+	0.0815484i
$587$	−11.4539			−0.472752			−0.236376	−	0.971662i	$-0.575960\pi$
$587$	−11.4539			−0.472752			−0.236376	+	0.971662i	$0.575960\pi$
$588$	6.42141	+	10.2842i	0.264815	+	0.424115i
$589$	−17.0356			−0.701939
$590$	−3.87370	−	2.23648i	−0.159478	−	0.0920744i
$591$	5.08237	+	36.3286i	0.209061	+	1.49436i
$592$	−3.85694	−	6.68042i	−0.158519	−	0.274564i
$593$	6.94997	−	12.0377i	0.285401	−	0.494329i	−0.687305	−	0.726369i	$-0.741207\pi$
$593$	6.94997	−	12.0377i	0.285401	−	0.494329i	0.972706	+	0.232039i	$0.0745398\pi$
$594$	2.78162	−	1.23218i	0.114131	−	0.0505568i
$595$	−5.10400	−	0.266756i	−0.209244	−	0.0109359i
$596$			18.8573i			0.772426i
$597$	15.0964	−	11.7793i	0.617855	−	0.482096i
$598$	4.66678	−	2.69437i	0.190839	−	0.110181i
$599$	−27.3830	+	15.8096i	−1.11884	+	0.645963i	−0.941105	−	0.338115i	$-0.890211\pi$
$599$	−27.3830	+	15.8096i	−1.11884	+	0.645963i	−0.177736	+	0.984078i	$0.556877\pi$
$600$	6.60234	−	5.15163i	0.269539	−	0.210314i
$601$		−	45.8527i		−	1.87037i	−0.354156	−	0.935186i	$-0.615232\pi$
$601$		−	45.8527i		−	1.87037i	0.354156	−	0.935186i	$-0.384768\pi$
$602$	0.172566	+	0.112031i	0.00703327	+	0.00456603i
$603$	−2.46766	−	2.38899i	−0.100491	−	0.0972873i
$604$	−1.05175	+	1.82169i	−0.0427951	+	0.0741233i
$605$	2.16483	+	3.74959i	0.0880128	+	0.152443i
$606$	−1.30963	−	9.36115i	−0.0531999	−	0.380271i
$607$	21.2390	+	12.2624i	0.862065	+	0.497714i	0.864703	−	0.502283i	$-0.167506\pi$
$607$	21.2390	+	12.2624i	0.862065	+	0.497714i	−0.00263806	+	0.999997i	$0.500840\pi$
$608$	−2.31542			−0.0939026
$609$	1.85317	+	21.3009i	0.0750944	+	0.863156i
$610$	−0.0512561			−0.00207530
$611$	−47.8252	−	27.6119i	−1.93480	−	1.11706i
$612$	3.46836	−	13.8367i	0.140200	−	0.559316i
$613$	2.23926	+	3.87851i	0.0904428	+	0.156651i	0.907698	−	0.419625i	$-0.137838\pi$
$613$	2.23926	+	3.87851i	0.0904428	+	0.156651i	−0.817255	+	0.576277i	$0.804505\pi$
$614$	−1.67846	+	2.90718i	−0.0677372	+	0.117324i
$615$	−0.655784	+	1.62019i	−0.0264437	+	0.0653323i
$616$	0.703461	+	1.38013i	0.0283432	+	0.0556070i
$617$		−	13.1049i		−	0.527583i	−0.964580	−	0.263792i	$-0.915027\pi$
$617$		−	13.1049i		−	0.527583i	0.964580	−	0.263792i	$-0.0849731\pi$
$618$	−8.04796	−	10.3143i	−0.323737	−	0.414901i
$619$	−10.9882	+	6.34407i	−0.441655	+	0.254990i	−0.704299	−	0.709903i	$-0.748739\pi$
$619$	−10.9882	+	6.34407i	−0.441655	+	0.254990i	0.262645	+	0.964893i	$0.415405\pi$
$620$	2.58862	−	1.49454i	0.103962	−	0.0600222i
$621$	−5.16665	−	0.552889i	−0.207331	−	0.0221867i
$622$		−	29.5932i		−	1.18658i
$623$	0.168492	−	0.259536i	0.00675048	−	0.0103981i
$624$	8.65173	+	3.50185i	0.346346	+	0.140186i
$625$	−11.2757	+	19.5301i	−0.451029	+	0.781206i
$626$	5.29366	+	9.16888i	0.211577	+	0.366462i
$627$	2.32543	−	0.325327i	0.0928686	−	0.0129923i
$628$	−10.7257	−	6.19247i	−0.428001	−	0.247106i
$629$	36.6790			1.46249
$630$	−2.36080	+	2.19657i	−0.0940564	+	0.0875134i
$631$	−7.97881			−0.317631			−0.158816	−	0.987308i	$-0.550768\pi$
$631$	−7.97881			−0.317631			−0.158816	+	0.987308i	$0.550768\pi$
$632$	8.18470	+	4.72544i	0.325570	+	0.187968i
$633$	0.664908	−	0.0930207i	0.0264277	−	0.00369724i
$634$	8.84225	+	15.3152i	0.351170	+	0.608245i
$635$	−3.28673	+	5.69278i	−0.130430	+	0.225911i
$636$	4.25338	+	1.72159i	0.168657	+	0.0682654i
$637$	3.93218	−	37.5156i	0.155799	−	1.48642i
$638$			2.73179i			0.108153i
$639$	1.14516	+	4.01268i	0.0453018	+	0.158739i
$640$	0.351837	−	0.203133i	0.0139076	−	0.00802953i
$641$	−34.0659	+	19.6680i	−1.34552	+	0.776838i	−0.987612	−	0.156918i	$-0.949844\pi$
$641$	−34.0659	+	19.6680i	−1.34552	+	0.776838i	−0.357911	+	0.933756i	$0.616511\pi$
$642$	−10.8874	−	13.9533i	−0.429692	−	0.550694i
$643$		−	40.7213i		−	1.60589i	−0.596051	−	0.802946i	$-0.703265\pi$
$643$		−	40.7213i		−	1.60589i	0.596051	−	0.802946i	$-0.296735\pi$
$644$	0.138089	−	2.64215i	0.00544148	−	0.104115i
$645$	−0.0205303	+	0.0507226i	−0.000808381	+	0.00199720i
$646$	5.50482	−	9.53462i	0.216584	−	0.375135i
$647$	−0.873285	−	1.51257i	−0.0343324	−	0.0594654i	0.848349	−	0.529438i	$-0.177597\pi$
$647$	−0.873285	−	1.51257i	−0.0343324	−	0.0594654i	−0.882681	+	0.469973i	$0.844264\pi$
$648$	−4.75007	−	7.64440i	−0.186600	−	0.300300i
$649$	−5.58261	−	3.22312i	−0.219137	−	0.126519i
$650$	−26.0543			−1.02193
$651$	27.6280	−	19.3253i	1.08283	−	0.757420i
$652$	−9.13866			−0.357898
$653$	39.3930	+	22.7436i	1.54157	+	0.890025i	0.998740	+	0.0501806i	$0.0159797\pi$
$653$	39.3930	+	22.7436i	1.54157	+	0.890025i	0.542828	+	0.839844i	$0.317354\pi$
$654$	−0.384020	−	2.74496i	−0.0150164	−	0.107336i
$655$	−1.20424	−	2.08580i	−0.0470534	−	0.0814989i
$656$	1.24196	−	2.15115i	0.0484906	−	0.0839881i
$657$	−17.1873	+	17.7533i	−0.670541	+	0.692621i
$658$	−24.1567	+	12.3128i	−0.941725	+	0.480003i
$659$		−	0.910507i		−	0.0354683i	−0.999843	−	0.0177342i	$-0.994355\pi$
$659$		−	0.910507i		−	0.0354683i	0.999843	−	0.0177342i	$-0.00564526\pi$
$660$	−0.324816	+	0.253446i	−0.0126435	+	0.00986537i
$661$	−24.0696	+	13.8966i	−0.936198	+	0.540514i	−0.888766	−	0.458361i	$-0.848437\pi$
$661$	−24.0696	+	13.8966i	−0.936198	+	0.540514i	−0.0474313	+	0.998875i	$0.515104\pi$
$662$	−2.16196	+	1.24821i	−0.0840268	+	0.0485129i
$663$	−34.9894	+	27.3013i	−1.35888	+	1.06030i
$664$			10.8067i			0.419383i
$665$	−2.21737	+	1.13021i	−0.0859859	+	0.0438275i
$666$	16.0965	−	16.6265i	0.623725	−	0.644264i
$667$	2.33290	−	4.04070i	0.0903301	−	0.156456i
$668$	−12.0415	−	20.8564i	−0.465898	−	0.806959i
$669$	2.73858	+	19.5753i	0.105880	+	0.756824i
$670$	0.402808	+	0.232562i	0.0155618	+	0.00898463i
$671$	−0.0738681			−0.00285165
$672$	3.75510	−	2.62664i	0.144856	−	0.101325i
$673$	−27.8552			−1.07374			−0.536870	−	0.843665i	$-0.680393\pi$
$673$	−27.8552			−1.07374			−0.536870	+	0.843665i	$0.680393\pi$
$674$	15.9480	+	9.20759i	0.614294	+	0.354663i
$675$	20.2972	+	14.8053i	0.781238	+	0.569856i
$676$	−8.01923	−	13.8897i	−0.308432	−	0.534220i
$677$	0.0979180	−	0.169599i	0.00376329	−	0.00651822i	−0.864138	−	0.503256i	$-0.832135\pi$
$677$	0.0979180	−	0.169599i	0.00376329	−	0.00651822i	0.867901	+	0.496737i	$0.165469\pi$
$678$	−9.91830	+	24.5043i	−0.380910	+	0.941082i
$679$	1.81663	−	34.7587i	0.0697158	−	1.33391i
$680$			1.93176i			0.0740798i
$681$	−0.151918	−	0.194699i	−0.00582153	−	0.00746088i
$682$	3.73061	−	2.15387i	0.142852	−	0.0824759i
$683$	21.4492	−	12.3837i	0.820730	−	0.473849i	−0.0299381	−	0.999552i	$-0.509531\pi$
$683$	21.4492	−	12.3837i	0.820730	−	0.473849i	0.850668	+	0.525703i	$0.176198\pi$
$684$	−1.90625	−	6.67957i	−0.0728874	−	0.255400i
$685$		−	3.35892i		−	0.128338i
$686$	−14.3980	−	11.6490i	−0.549716	−	0.444760i
$687$	29.4182	+	11.9072i	1.12238	+	0.454290i
$688$	0.0388816	−	0.0673450i	0.00148235	−	0.00256750i
$689$	−7.13797	−	12.3633i	−0.271935	−	0.471005i
$690$	0.696886	−	0.0974944i	0.0265300	−	0.00371155i
$691$	−27.5920	−	15.9302i	−1.04965	−	0.606015i	−0.127097	−	0.991890i	$-0.540566\pi$
$691$	−27.5920	−	15.9302i	−1.04965	−	0.606015i	−0.922551	+	0.385876i	$0.873899\pi$
$692$	−0.642580			−0.0244272
$693$	−3.40228	+	3.16560i	−0.129242	+	0.120251i
$694$	−23.1102			−0.877250
$695$	2.68057	+	1.54763i	0.101680	+	0.0587050i
$696$	8.00345	−	1.11968i	0.303370	−	0.0424415i
$697$	5.90545	+	10.2285i	0.223685	+	0.387433i
$698$	−5.43835	+	9.41949i	−0.205844	+	0.356533i
$699$	28.6016	+	11.5767i	1.08181	+	0.437871i
$700$	−6.96552	+	10.7293i	−0.263272	+	0.405531i
$701$			39.0106i			1.47341i	0.676214	+	0.736705i	$0.263619\pi$
$701$			39.0106i			1.47341i	−0.676214	+	0.736705i	$0.736381\pi$
$702$	−2.97937	+	27.8417i	−0.112449	+	1.05082i
$703$	15.4680	−	8.93044i	0.583386	−	0.336818i
$704$	0.507052	−	0.292747i	0.0191102	−	0.0110333i
$705$	−4.43611	−	5.68533i	−0.167074	−	0.214122i
$706$		−	2.84140i		−	0.106937i
$707$	6.55686	+	12.8640i	0.246596	+	0.483800i
$708$	−7.15477	+	17.6767i	−0.268893	+	0.664331i
$709$	−3.75196	+	6.49859i	−0.140908	+	0.244060i	−0.927839	−	0.372982i	$-0.878335\pi$
$709$	−3.75196	+	6.49859i	−0.140908	+	0.244060i	0.786931	+	0.617041i	$0.211669\pi$
$710$	−0.282550	−	0.489391i	−0.0106039	−	0.0183665i
$711$	−6.89370	+	27.5018i	−0.258534	+	1.03140i
$712$	−0.101285	−	0.0584772i	−0.00379583	−	0.00219153i
$713$	−7.35745			−0.275539
$714$	1.88857	+	21.7078i	0.0706781	+	0.812394i
$715$	1.28180			0.0479365
$716$	18.4147	+	10.6317i	0.688189	+	0.397326i
$717$	−4.71289	−	33.6876i	−0.176006	−	1.25809i
$718$	2.10277	+	3.64211i	0.0784748	+	0.135922i
$719$	−20.0402	+	34.7106i	−0.747372	+	1.29449i	0.201706	+	0.979446i	$0.435351\pi$
$719$	−20.0402	+	34.7106i	−0.747372	+	1.29449i	−0.949078	+	0.315041i	$0.897982\pi$
$720$	0.875665	+	0.847749i	0.0326341	+	0.0315938i
$721$	16.7615	+	10.8817i	0.624232	+	0.405254i
$722$			13.6388i			0.507585i
$723$	−22.9166	+	17.8812i	−0.852276	+	0.665009i
$724$	−11.8801	+	6.85898i	−0.441521	+	0.254912i
$725$	−19.5366	+	11.2794i	−0.725570	+	0.418908i
$726$	14.5529	−	11.3552i	0.540108	−	0.421432i
$727$		−	22.0145i		−	0.816474i	−0.912876	−	0.408237i	$-0.866144\pi$
$727$		−	22.0145i		−	0.816474i	0.912876	−	0.408237i	$-0.133856\pi$
$728$	−14.2378	−	0.744126i	−0.527689	−	0.0275792i
$729$	18.1421	−	19.9966i	0.671928	−	0.740616i
$730$	1.67314	−	2.89795i	0.0619255	−	0.107258i
$731$	0.184879	+	0.320220i	0.00683801	+	0.0118438i
$732$	0.0302764	+	0.216415i	0.00111905	+	0.00799892i
$733$	−39.0061	−	22.5202i	−1.44072	−	0.831801i	−0.442824	−	0.896609i	$-0.646023\pi$
$733$	−39.0061	−	22.5202i	−1.44072	−	0.831801i	−0.997898	+	0.0648077i	$0.979357\pi$
$734$	−27.5618			−1.01732
$735$	2.31397	−	4.34835i	0.0853520	−	0.160391i
$736$	−1.00000			−0.0368605
$737$	0.580510	+	0.335158i	0.0213834	+	0.0123457i
$738$	7.22817	+	1.81184i	0.266072	+	0.0666947i
$739$	8.69977	+	15.0684i	0.320026	+	0.554302i	0.980493	−	0.196554i	$-0.0629750\pi$
$739$	8.69977	+	15.0684i	0.320026	+	0.554302i	−0.660467	+	0.750855i	$0.729642\pi$
$740$	−1.56694	+	2.71403i	−0.0576020	+	0.0997697i
$741$	−8.10825	+	20.0324i	−0.297864	+	0.735907i
$742$	−6.99963	−	0.365829i	−0.256964	−	0.0134300i
$743$		−	0.441530i		−	0.0161982i	−0.999967	−	0.00809908i	$-0.997422\pi$
$743$		−	0.441530i		−	0.0161982i	0.999967	−	0.00809908i	$-0.00257805\pi$
$744$	−7.83936	−	10.0469i	−0.287405	−	0.368338i
$745$	6.63470	−	3.83054i	0.243076	−	0.140340i
$746$	−13.2348	+	7.64112i	−0.484561	+	0.279761i
$747$	−31.1755	+	8.89705i	−1.14065	+	0.325526i
$748$			2.78398i			0.101792i
$749$	22.6753	+	14.7209i	0.828537	+	0.537889i
$750$	−6.41503	−	2.59653i	−0.234244	−	0.0948119i
$751$	−20.5835	+	35.6516i	−0.751101	+	1.30095i	0.196188	+	0.980566i	$0.437144\pi$
$751$	−20.5835	+	35.6516i	−0.751101	+	1.30095i	−0.947289	+	0.320379i	$0.896190\pi$
$752$	5.12400	+	8.87503i	0.186853	+	0.323639i
$753$	−36.2316	+	5.06881i	−1.32035	+	0.184718i
$754$	−21.7742	−	12.5714i	−0.792971	−	0.457822i
$755$	0.854581			0.0311014
$756$	10.6689	+	8.67033i	0.388024	+	0.315337i
$757$	25.8843			0.940779			0.470390	−	0.882459i	$-0.344113\pi$
$757$	25.8843			0.940779			0.470390	+	0.882459i	$0.344113\pi$
$758$	17.6240	+	10.1752i	0.640133	+	0.369581i
$759$	1.00432	−	0.140505i	0.0364546	−	0.00510000i
$760$	0.470338	+	0.814649i	0.0170609	+	0.0295504i
$761$	8.88046	−	15.3814i	0.321916	−	0.557575i	−0.658967	−	0.752172i	$-0.729006\pi$
$761$	8.88046	−	15.3814i	0.321916	−	0.557575i	0.980883	+	0.194596i	$0.0623397\pi$
$762$	25.9776	+	10.5146i	0.941071	+	0.380906i
$763$	1.92266	+	3.77209i	0.0696049	+	0.136559i
$764$		−	14.9467i		−	0.540753i
$765$	−5.57280	+	1.59039i	−0.201485	+	0.0575009i
$766$	8.72699	−	5.03853i	0.315319	−	0.182049i
$767$	51.3810	−	29.6648i	1.85526	−	1.07113i
$768$	−1.06550	−	1.36554i	−0.0384479	−	0.0492748i
$769$			36.1276i			1.30279i	0.758737	+	0.651397i	$0.225817\pi$
$769$			36.1276i			1.30279i	−0.758737	+	0.651397i	$0.774183\pi$
$770$	0.342684	−	0.527853i	0.0123495	−	0.0190225i
$771$	−8.26161	+	20.4113i	−0.297535	+	0.735094i
$772$	0.819707	−	1.41977i	0.0295019	−	0.0510988i
$773$	10.5167	+	18.2155i	0.378261	+	0.655167i	0.990809	−	0.135266i	$-0.0431889\pi$
$773$	10.5167	+	18.2155i	0.378261	+	0.655167i	−0.612548	+	0.790433i	$0.709856\pi$
$774$	0.226289	+	0.0567224i	0.00813379	+	0.00203885i
$775$	30.8070	+	17.7864i	1.10662	+	0.638908i
$776$	−13.1555			−0.472254
$777$	−14.9549	+	32.0303i	−0.536503	+	1.14908i
$778$	32.6085			1.16907
$779$	4.98080	+	2.87567i	0.178456	+	0.103031i
$780$	−0.525371	−	3.75534i	−0.0188113	−	0.134463i
$781$	−0.407199	−	0.705290i	−0.0145707	−	0.0252373i
$782$	2.37746	−	4.11789i	0.0850179	−	0.147255i
$783$	9.81922	+	22.1667i	0.350910	+	0.792174i
$784$	−4.11287	+	5.66430i	−0.146888	+	0.202296i
$785$			5.03158i			0.179585i
$786$	−8.09538	+	6.31661i	−0.288753	+	0.225306i
$787$	26.6021	−	15.3587i	0.948261	−	0.547479i	0.0557207	−	0.998446i	$-0.482254\pi$
$787$	26.6021	−	15.3587i	0.948261	−	0.547479i	0.892540	+	0.450968i	$0.148921\pi$
$788$	−18.3412	+	10.5893i	−0.653378	+	0.377228i
$789$	−39.6642	+	30.9489i	−1.41208	+	1.10181i
$790$		−	3.83957i		−	0.136606i
$791$	2.10759	−	40.3258i	0.0749373	−	1.43382i
$792$	1.26197	+	1.22174i	0.0448422	+	0.0434127i
$793$	0.339932	−	0.588780i	0.0120713	−	0.0209082i
$794$	−17.7923	−	30.8171i	−0.631423	−	1.09366i
$795$	−0.258284	−	1.84621i	−0.00916039	−	0.0654782i
$796$	9.57411	+	5.52761i	0.339345	+	0.195921i
$797$	42.8074			1.51631			0.758157	−	0.652072i	$-0.226100\pi$
$797$	42.8074			1.51631			0.758157	+	0.652072i	$0.226100\pi$
$798$	6.08176	+	8.69463i	0.215292	+	0.307786i
$799$	−48.7285			−1.72389
$800$	4.18719	+	2.41747i	0.148039	+	0.0854706i
$801$	0.0853094	−	0.340334i	0.00301426	−	0.0120251i
$802$	9.78228	+	16.9434i	0.345424	+	0.598293i
$803$	2.41125	−	4.17641i	0.0850912	−	0.147382i
$804$	0.743992	−	1.83812i	0.0262386	−	0.0648255i
$805$	−0.957654	+	0.488122i	−0.0337529	+	0.0172040i
$806$			39.6474i			1.39652i
$807$	31.4920	+	40.3602i	1.10857	+	1.42075i
$808$	4.72616	−	2.72865i	0.166266	−	0.0959936i
$809$	26.6417	−	15.3816i	0.936674	−	0.540789i	0.0477575	−	0.998859i	$-0.484793\pi$
$809$	26.6417	−	15.3816i	0.936674	−	0.540789i	0.888916	+	0.458070i	$0.151459\pi$
$810$	−1.72468	+	3.22408i	−0.0605992	+	0.113283i
$811$		−	20.2543i		−	0.711225i	−0.934634	−	0.355612i	$-0.884272\pi$
$811$		−	20.2543i		−	0.711225i	0.934634	−	0.355612i	$-0.115728\pi$
$812$	−10.9983	+	5.60588i	−0.385963	+	0.196728i
$813$	−9.51035	−	3.84939i	−0.333543	−	0.135004i
$814$	−2.25821	+	3.91134i	−0.0791504	+	0.137092i
$815$	1.85636	+	3.21531i	0.0650256	+	0.112628i
$816$	8.15634	−	1.14107i	0.285529	−	0.0399455i
$817$	0.155932	+	0.0900272i	0.00545536	+	0.00314965i
$818$	−32.0249			−1.11972
$819$	−9.57513	−	41.6862i	−0.334582	−	1.45663i
$820$	−1.00914			−0.0352405
$821$	−19.6555	−	11.3481i	−0.685980	−	0.396051i	0.116124	−	0.993235i	$-0.462953\pi$
$821$	−19.6555	−	11.3481i	−0.685980	−	0.396051i	−0.802104	+	0.597184i	$0.796286\pi$
$822$	−14.1821	+	1.98408i	−0.494658	+	0.0692026i
$823$	17.3084	+	29.9791i	0.603333	+	1.04500i	0.992312	+	0.123757i	$0.0394945\pi$
$823$	17.3084	+	29.9791i	0.603333	+	1.04500i	−0.388979	+	0.921247i	$0.627172\pi$
$824$	3.77662	−	6.54129i	0.131565	−	0.227877i
$825$	−4.54496	−	1.83961i	−0.158235	−	0.0640468i
$826$	1.52035	−	29.0898i	0.0528999	−	1.01217i
$827$		−	25.3952i		−	0.883079i	−0.897242	−	0.441540i	$-0.854432\pi$
$827$		−	25.3952i		−	0.883079i	0.897242	−	0.441540i	$-0.145568\pi$
$828$	−0.823286	−	2.88482i	−0.0286112	−	0.100255i
$829$	0.262675	−	0.151656i	0.00912309	−	0.00526722i	−0.495432	−	0.868647i	$-0.664990\pi$
$829$	0.262675	−	0.151656i	0.00912309	−	0.00526722i	0.504555	+	0.863380i	$0.331657\pi$
$830$	3.80221	−	2.19521i	0.131977	−	0.0761967i
$831$	2.98222	+	3.82201i	0.103452	+	0.132584i
$832$			5.38874i			0.186821i
$833$	−13.5467	−	30.4030i	−0.469366	−	1.05340i
$834$	4.95106	−	12.2322i	0.171441	−	0.423565i
$835$	−4.89203	+	8.47325i	−0.169296	+	0.293229i
$836$	0.677830	+	1.17404i	0.0234433	+	0.0406049i
$837$	22.5296	−	30.8867i	0.778736	−	1.06760i
$838$	20.5673	+	11.8745i	0.710485	+	0.410199i
$839$	16.7002			0.576554			0.288277	−	0.957547i	$-0.406918\pi$
$839$	16.7002			0.576554			0.288277	+	0.957547i	$0.406918\pi$
$840$	−1.68693	−	0.787626i	−0.0582047	−	0.0271757i
$841$	7.23036			0.249323
$842$	−24.5010	−	14.1456i	−0.844359	−	0.487491i
$843$	5.18424	+	37.0568i	0.178555	+	1.27630i
$844$	0.193812	+	0.335692i	0.00667128	+	0.0115550i
$845$	−3.25794	+	5.64292i	−0.112077	+	0.194122i
$846$	−21.3844	+	22.0885i	−0.735209	+	0.759419i
$847$	−15.3534	+	23.6496i	−0.527550	+	0.812610i
$848$			2.64922i			0.0909746i
$849$	−38.2319	+	29.8314i	−1.31212	+	1.02381i
$850$	−19.9098	+	11.4949i	−0.682899	+	0.394272i
$851$	6.68042	−	3.85694i	0.229002	−	0.132214i
$852$	−1.89942	+	1.48207i	−0.0650731	+	0.0507748i
$853$		−	51.3211i		−	1.75720i	−0.477559	−	0.878600i	$-0.658478\pi$
$853$		−	51.3211i		−	1.75720i	0.477559	−	0.878600i	$-0.341522\pi$
$854$	−0.151584	−	0.297395i	−0.00518710	−	0.0101766i
$855$	−1.96289	+	2.02753i	−0.0671295	+	0.0693400i
$856$	5.10907	−	8.84917i	0.174624	−	0.302458i
$857$	19.7321	+	34.1770i	0.674036	+	1.16747i	0.976750	+	0.214384i	$0.0687743\pi$
$857$	19.7321	+	34.1770i	0.674036	+	1.16747i	−0.302713	+	0.953082i	$0.597892\pi$
$858$	−0.757143	−	5.41203i	−0.0258484	−	0.184764i
$859$	1.73674	+	1.00271i	0.0592569	+	0.0342120i	0.529336	−	0.848412i	$-0.322441\pi$
$859$	1.73674	+	1.00271i	0.0592569	+	0.0342120i	−0.470079	+	0.882624i	$0.655775\pi$
$860$	−0.0315926			−0.00107730
$861$	−11.3400	+	0.986574i	−0.386465	+	0.0336224i
$862$	33.8867			1.15419
$863$	−27.7733	−	16.0349i	−0.945413	−	0.545834i	−0.0537599	−	0.998554i	$-0.517121\pi$
$863$	−27.7733	−	16.0349i	−0.945413	−	0.545834i	−0.891653	+	0.452720i	$0.850454\pi$
$864$	3.06214	−	4.19801i	0.104176	−	0.142819i
$865$	0.130529	+	0.226083i	0.00443813	+	0.00768706i
$866$	−14.9185	+	25.8396i	−0.506950	+	0.878064i
$867$	−3.64519	+	9.00587i	−0.123797	+	0.305855i
$868$	16.3271	+	10.5996i	0.554177	+	0.359774i
$869$		−	5.53342i		−	0.187709i
$870$	−2.01971	−	2.58846i	−0.0684746	−	0.0877571i
$871$	−5.34287	+	3.08471i	−0.181036	+	0.104521i
$872$	1.38585	−	0.800119i	0.0469307	−	0.0270954i
$873$	−10.8307	−	37.9512i	−0.366564	−	1.28445i
$874$		−	2.31542i		−	0.0783202i
$875$	10.5570	+	0.551750i	0.356891	+	0.0186525i
$876$	−13.2241	−	5.35256i	−0.446802	−	0.180846i
$877$	21.7549	−	37.6806i	0.734611	−	1.27238i	−0.220283	−	0.975436i	$-0.570698\pi$
$877$	21.7549	−	37.6806i	0.734611	−	1.27238i	0.954894	−	0.296948i	$-0.0959687\pi$
$878$	4.97012	+	8.60849i	0.167733	+	0.290523i
$879$	−6.77245	+	0.947466i	−0.228429	+	0.0319572i
$880$	−0.205998	−	0.118933i	−0.00694419	−	0.00400923i
$881$	35.9054			1.20968			0.604842	−	0.796345i	$-0.293236\pi$
$881$	35.9054			1.20968			0.604842	+	0.796345i	$0.293236\pi$
$882$	−19.7266	−	7.20157i	−0.664228	−	0.242489i
$883$	5.39993			0.181722			0.0908611	−	0.995864i	$-0.471038\pi$
$883$	5.39993			0.181722			0.0908611	+	0.995864i	$0.471038\pi$
$884$	−22.1902	−	12.8115i	−0.746337	−	0.430898i
$885$	7.67267	−	1.07341i	0.257914	−	0.0360822i
$886$	7.90916	+	13.6991i	0.265713	+	0.460229i
$887$	−18.5994	+	32.2151i	−0.624507	+	1.08168i	0.364129	+	0.931348i	$0.381367\pi$
$887$	−18.5994	+	32.2151i	−0.624507	+	1.08168i	−0.988636	+	0.150329i	$0.951967\pi$
$888$	12.3848	+	5.01285i	0.415607	+	0.168220i
$889$	−42.7504	−	2.23431i	−1.43380	−	0.0749364i
$890$			0.0475146i			0.00159269i
$891$	−2.48554	+	4.64640i	−0.0832687	+	0.155660i
$892$	−9.88296	+	5.70593i	−0.330906	+	0.191049i
$893$	−20.5494	+	11.8642i	−0.687659	+	0.397020i
$894$	−20.0925	−	25.7505i	−0.671992	−	0.861226i
$895$		−	8.63862i		−	0.288757i
$896$	2.21912	+	1.44066i	0.0741356	+	0.0481291i
$897$	−3.50185	+	8.65173i	−0.116923	+	0.288873i
$898$	−2.50150	+	4.33273i	−0.0834761	+	0.144585i
$899$	17.1642	+	29.7292i	0.572458	+	0.991525i
$900$	−3.52673	+	14.0696i	−0.117558	+	0.468986i
$901$	−10.9092	−	6.29842i	−0.363438	−	0.209831i
$902$	−1.45432			−0.0484237
$903$	−0.355015	+	0.0308862i	−0.0118142	+	0.00102783i
$904$	−15.2625			−0.507624
$905$	4.82648	+	2.78657i	0.160438	+	0.0926288i
$906$	−0.504792	−	3.60823i	−0.0167706	−	0.119875i
$907$	−0.234451	−	0.406081i	−0.00778481	−	0.0134837i	0.862107	−	0.506727i	$-0.169145\pi$
$907$	−0.234451	−	0.406081i	−0.00778481	−	0.0134837i	−0.869892	+	0.493243i	$0.835811\pi$
$908$	0.0712898	−	0.123478i	0.00236584	−	0.00409775i
$909$	11.7627	+	11.3877i	0.390143	+	0.377705i
$910$	2.63036	+	5.16054i	0.0871956	+	0.171070i
$911$		−	57.1124i		−	1.89222i	−0.323848	−	0.946109i	$-0.604977\pi$
$911$		−	57.1124i		−	1.89222i	0.323848	−	0.946109i	$-0.395023\pi$
$912$	3.16181	−	2.46707i	0.104698	−	0.0816930i
$913$	5.47958	−	3.16364i	0.181348	−	0.104701i
$914$	−18.8747	+	10.8973i	−0.624320	+	0.360452i
$915$	0.0699925	−	0.0546133i	0.00231388	−	0.00180546i
$916$			18.3232i			0.605414i
$917$	8.54069	−	13.1556i	0.282039	−	0.434438i
$918$	10.0068	+	22.5902i	0.330273	+	0.745587i
$919$	−3.71794	+	6.43966i	−0.122643	+	0.212425i	−0.920809	−	0.390013i	$-0.872470\pi$
$919$	−3.71794	+	6.43966i	−0.122643	+	0.212425i	0.798166	+	0.602438i	$0.205804\pi$
$920$	0.203133	+	0.351837i	0.00669709	+	0.0115997i
$921$	−0.805583	−	5.75828i	−0.0265449	−	0.189742i
$922$	−3.05227	−	1.76223i	−0.100521	−	0.0580359i
$923$	7.49552			0.246718
$924$	−2.43113	−	1.13509i	−0.0799784	−	0.0373418i
$925$	−37.2963			−1.22629
$926$	21.5114	+	12.4196i	0.706909	+	0.408134i
$927$	21.9797	+	5.50951i	0.721908	+	0.180956i
$928$	2.33290	+	4.04070i	0.0765811	+	0.132642i
$929$	7.53211	−	13.0460i	0.247121	−	0.428025i	−0.715605	−	0.698505i	$-0.753849\pi$
$929$	7.53211	−	13.0460i	0.247121	−	0.428025i	0.962726	+	0.270480i	$0.0871823\pi$
$930$	−1.94245	+	4.79903i	−0.0636953	+	0.157367i
$931$	−13.1152	−	9.52302i	−0.429834	−	0.312104i
$932$			17.8145i			0.583533i
$933$	31.5315	+	40.4108i	1.03229	+	1.32299i
$934$	−12.9824	+	7.49542i	−0.424799	+	0.245258i
$935$	0.979505	−	0.565517i	0.0320332	−	0.0184944i
$936$	−15.5455	+	4.43647i	−0.508122	+	0.145011i
$937$			34.3021i			1.12060i	0.828290	+	0.560300i	$0.189314\pi$
$937$			34.3021i			1.12060i	−0.828290	+	0.560300i	$0.810686\pi$
$938$	−0.158095	+	3.02492i	−0.00516197	+	0.0987672i
$939$	−16.9982	−	6.88013i	−0.554714	−	0.224525i
$940$	2.08171	−	3.60562i	0.0678978	−	0.117602i
$941$	−3.08626	−	5.34555i	−0.100609	−	0.174260i	0.811327	−	0.584593i	$-0.198746\pi$
$941$	−3.08626	−	5.34555i	−0.100609	−	0.174260i	−0.911936	+	0.410333i	$0.865412\pi$
$942$	21.2444	−	2.97210i	0.692181	−	0.0968362i
$943$	2.15115	+	1.24196i	0.0700509	+	0.0404439i
$944$	−11.0099			−0.358343
$945$	0.883332	−	5.51494i	0.0287348	−	0.179401i
$946$	−0.0455299			−0.00148030
$947$	6.93114	+	4.00170i	0.225232	+	0.130038i	0.608370	−	0.793653i	$-0.291823\pi$
$947$	6.93114	+	4.00170i	0.225232	+	0.130038i	−0.383139	+	0.923691i	$0.625157\pi$
$948$	−16.2115	+	2.26799i	−0.526526	+	0.0736609i
$949$	22.1926	+	38.4387i	0.720401	+	1.24777i
$950$	−5.59746	+	9.69509i	−0.181606	+	0.314550i
$951$	−28.3928	−	11.4922i	−0.920701	−	0.372660i
$952$	−11.2084	+	5.71297i	−0.363265	+	0.185158i
$953$		−	0.810105i		−	0.0262419i	−0.999914	−	0.0131209i	$-0.995823\pi$
$953$		−	0.810105i		−	0.0262419i	0.999914	−	0.0131209i	$-0.00417664\pi$
$954$	−7.64253	+	2.18107i	−0.247436	+	0.0706147i
$955$	−5.25880	+	3.03617i	−0.170171	+	0.0982482i
$956$	17.0078	−	9.81948i	0.550073	−	0.317585i
$957$	−2.91072	−	3.73038i	−0.0940902	−	0.120586i
$958$			20.6254i			0.666378i
$959$	19.4889	−	9.93360i	0.629329	−	0.320773i
$960$	−0.264011	+	0.652269i	−0.00852091	+	0.0210519i
$961$	11.5661	−	20.0330i	0.373098	−	0.646225i
$962$	−20.7841	−	35.9990i	−0.670105	−	1.16066i
$963$	29.7345	+	7.45336i	0.958181	+	0.240181i
$964$	−14.5336	−	8.39100i	−0.468097	−	0.270256i
$965$	−0.666038			−0.0214405
$966$	2.62664	+	3.75510i	0.0845106	+	0.120818i
$967$	28.2558			0.908644			0.454322	−	0.890838i	$-0.349882\pi$
$967$	28.2558			0.908644			0.454322	+	0.890838i	$0.349882\pi$
$968$	9.22940	+	5.32860i	0.296644	+	0.171268i
$969$	2.64206	+	18.8853i	0.0848751	+	0.606684i
$970$	2.67231	+	4.62858i	0.0858027	+	0.148615i
$971$	12.2205	−	21.1666i	0.392175	−	0.679267i	−0.600561	−	0.799579i	$-0.705056\pi$
$971$	12.2205	−	21.1666i	0.392175	−	0.679267i	0.992736	+	0.120312i	$0.0383895\pi$
$972$	14.6315	+	5.37757i	0.469307	+	0.172486i
$973$	−1.05208	+	20.1300i	−0.0337280	+	0.645338i
$974$		−	1.07544i		−	0.0344593i
$975$	35.5782	−	27.7608i	1.13942	−	0.889057i
$976$	−0.109261	+	0.0630820i	−0.00349737	+	0.00201921i
$977$	31.7058	−	18.3053i	1.01436	−	0.585640i	0.101893	−	0.994795i	$-0.467510\pi$
$977$	31.7058	−	18.3053i	1.01436	−	0.585640i	0.912465	+	0.409155i	$0.134177\pi$
$978$	12.4792	−	9.73723i	0.399042	−	0.311362i
$979$			0.0684760i			0.00218850i
$980$	2.82837	+	0.296454i	0.0903489	+	0.00946986i
$981$	3.44915	+	3.33919i	0.110123	+	0.106612i
$982$	−9.42419	+	16.3232i	−0.300738	+	0.520893i
$983$	−3.10273	−	5.37408i	−0.0989617	−	0.171407i	0.812293	−	0.583249i	$-0.198219\pi$
$983$	−3.10273	−	5.37408i	−0.0989617	−	0.171407i	−0.911255	+	0.411842i	$0.864885\pi$
$984$	0.596085	+	4.26080i	0.0190025	+	0.135829i
$985$	7.45140	+	4.30207i	0.237421	+	0.137075i
$986$	−22.1855			−0.706530
$987$	19.8677	−	42.5526i	0.632397	−	1.35446i
$988$	−12.4772			−0.396952
$989$	0.0673450	+	0.0388816i	0.00214145	+	0.00123636i
$990$	0.173505	−	0.692183i	0.00551435	−	0.0219990i
$991$	−18.5311	−	32.0968i	−0.588659	−	1.01959i	−0.994408	−	0.105603i	$-0.966323\pi$
$991$	−18.5311	−	32.0968i	−0.588659	−	1.01959i	0.405749	−	0.913984i	$-0.367011\pi$
$992$	3.67873	−	6.37174i	0.116800	−	0.202303i
$993$	1.62229	−	4.00804i	0.0514817	−	0.127191i
$994$	2.00390	−	3.08671i	0.0635600	−	0.0979045i
$995$		−	4.49136i		−	0.142386i
$996$	−11.5146	−	14.7571i	−0.364853	−	0.467596i
$997$	−7.83464	+	4.52333i	−0.248126	+	0.143255i	−0.618906	−	0.785465i	$-0.712424\pi$
$997$	−7.83464	+	4.52333i	−0.248126	+	0.143255i	0.370780	+	0.928721i	$0.379090\pi$
$998$	−15.6589	+	9.04070i	−0.495675	+	0.286178i
$999$	−4.26492	+	39.8550i	−0.134936	+	1.26096i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.l.d.47.14	✓	56
3.2	odd	2	inner	966.2.l.d.47.25	yes	56
7.3	odd	6	inner	966.2.l.d.185.25	yes	56
21.17	even	6	inner	966.2.l.d.185.14	yes	56

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.l.d.47.14	✓	56	1.1	even	1	trivial
966.2.l.d.47.25	yes	56	3.2	odd	2	inner
966.2.l.d.185.14	yes	56	21.17	even	6	inner
966.2.l.d.185.25	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)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.71535 - 0.239977i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.203133 - 0.351837i) q^{5} +(-1.60552 - 0.649847i) q^{6} +(2.64215 + 0.138089i) q^{7} -1.00000i q^{8} +(2.88482 - 0.823286i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(1.71535 - 0.239977i) q^{3} +(0.500000 + 0.866025i) q^{4} +(0.203133 - 0.351837i) q^{5} +(-1.60552 - 0.649847i) q^{6} +(2.64215 + 0.138089i) q^{7} -1.00000i q^{8} +(2.88482 - 0.823286i) q^{9} +(-0.351837 + 0.203133i) q^{10} +(-0.507052 + 0.292747i) q^{11} +(1.06550 + 1.36554i) q^{12} -5.38874i q^{13} +(-2.21912 - 1.44066i) q^{14} +(0.264011 - 0.652269i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.37746 - 4.11789i) q^{17} +(-2.90997 - 0.729424i) q^{18} +(-2.00521 - 1.15771i) q^{19} +0.406266 q^{20} +(4.56533 - 0.397183i) q^{21} +0.585493 q^{22} +(-0.866025 - 0.500000i) q^{23} +(-0.239977 - 1.71535i) q^{24} +(2.41747 + 4.18719i) q^{25} +(-2.69437 + 4.66678i) q^{26} +(4.75090 - 2.10451i) q^{27} +(1.20148 + 2.35721i) q^{28} +4.66579i q^{29} +(-0.554774 + 0.432876i) q^{30} +(6.37174 - 3.67873i) q^{31} +(0.866025 - 0.500000i) q^{32} +(-0.799517 + 0.623842i) q^{33} +4.75493i q^{34} +(0.585292 - 0.901553i) q^{35} +(2.15540 + 2.08669i) q^{36} +(-3.85694 + 6.68042i) q^{37} +(1.15771 + 2.00521i) q^{38} +(-1.29317 - 9.24354i) q^{39} +(-0.351837 - 0.203133i) q^{40} -2.48393 q^{41} +(-4.15228 - 1.93870i) q^{42} -0.0777633 q^{43} +(-0.507052 - 0.292747i) q^{44} +(0.296340 - 1.18222i) q^{45} +(0.500000 + 0.866025i) q^{46} +(5.12400 - 8.87503i) q^{47} +(-0.649847 + 1.60552i) q^{48} +(6.96186 + 0.729704i) q^{49} -4.83495i q^{50} +(-5.06637 - 6.49306i) q^{51} +(4.66678 - 2.69437i) q^{52} +(2.29429 - 1.32461i) q^{53} +(-5.16665 - 0.552889i) q^{54} +0.237866i q^{55} +(0.138089 - 2.64215i) q^{56} +(-3.71745 - 1.50467i) q^{57} +(2.33290 - 4.04070i) q^{58} +(5.50497 + 9.53488i) q^{59} +(0.696886 - 0.0974944i) q^{60} +(0.109261 + 0.0630820i) q^{61} -7.35745 q^{62} +(7.73581 - 1.77688i) q^{63} -1.00000 q^{64} +(-1.89595 - 1.09463i) q^{65} +(1.00432 - 0.140505i) q^{66} +(-0.572437 - 0.991489i) q^{67} +(2.37746 - 4.11789i) q^{68} +(-1.60552 - 0.649847i) q^{69} +(-0.957654 + 0.488122i) q^{70} +1.39096i q^{71} +(-0.823286 - 2.88482i) q^{72} +(-7.13315 + 4.11833i) q^{73} +(6.68042 - 3.85694i) q^{74} +(5.15163 + 6.60234i) q^{75} -2.31542i q^{76} +(-1.38013 + 0.703461i) q^{77} +(-3.50185 + 8.65173i) q^{78} +(-4.72544 + 8.18470i) q^{79} +(0.203133 + 0.351837i) q^{80} +(7.64440 - 4.75007i) q^{81} +(2.15115 + 1.24196i) q^{82} -10.8067 q^{83} +(2.62664 + 3.75510i) q^{84} -1.93176 q^{85} +(0.0673450 + 0.0388816i) q^{86} +(1.11968 + 8.00345i) q^{87} +(0.292747 + 0.507052i) q^{88} +(0.0584772 - 0.101285i) q^{89} +(-0.847749 + 0.875665i) q^{90} +(0.744126 - 14.2378i) q^{91} -1.00000i q^{92} +(10.0469 - 7.83936i) q^{93} +(-8.87503 + 5.12400i) q^{94} +(-0.814649 + 0.470338i) q^{95} +(1.36554 - 1.06550i) q^{96} -13.1555i q^{97} +(-5.66430 - 4.11287i) q^{98} +(-1.22174 + 1.26197i) 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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