LMFDB - Embedded newform 966.2.i.k.277.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(277,966)]

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([0, 4, 0]))

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

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

chi := DirichletCharacter("966.277");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.i (of order $3$, 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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.29428272.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 6x^{4} - 4x^{3} - 42x^{2} + 343 $ x^6 - 6x^4 - 4x^3 - 42*x^2 + 343
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			277.1
Root			$-0.0741344 + 2.64471i$ of defining polynomial
Character	$\chi$	$=$	966.277
Dual form			966.2.i.k.415.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.25332 + 1.38656i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.25332 + 1.38656i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.82746 - 3.16525i) q^{11} +(0.500000 + 0.866025i) q^{12} -0.851731 q^{13} +(-2.32746 - 1.25815i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.08078 - 5.33606i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.75332 - 4.76889i) q^{19} +1.00000 q^{20} +(0.0741344 + 2.64471i) q^{21} +3.65491 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-0.425866 - 0.737621i) q^{26} -1.00000 q^{27} +(-0.0741344 - 2.64471i) q^{28} +4.14827 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-1.67919 + 2.90844i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.82746 - 3.16525i) q^{33} +6.16155 q^{34} +(2.32746 + 1.25815i) q^{35} +1.00000 q^{36} +(-3.40823 - 5.90323i) q^{37} +(2.75332 - 4.76889i) q^{38} +(-0.425866 + 0.737621i) q^{39} +(0.500000 + 0.866025i) q^{40} -2.49336 q^{41} +(-2.25332 + 1.38656i) q^{42} +7.30982 q^{43} +(1.82746 + 3.16525i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-1.17919 - 2.04241i) q^{47} -1.00000 q^{48} +(3.15491 - 6.24872i) q^{49} +4.00000 q^{50} +(-3.08078 - 5.33606i) q^{51} +(0.425866 - 0.737621i) q^{52} +(-3.15491 + 5.46447i) q^{53} +(-0.500000 - 0.866025i) q^{54} -3.65491 q^{55} +(2.25332 - 1.38656i) q^{56} -5.50664 q^{57} +(2.07413 + 3.59251i) q^{58} +(-1.58078 + 2.73799i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-5.00000 - 8.66025i) q^{61} -3.35837 q^{62} +(2.32746 + 1.25815i) q^{63} +1.00000 q^{64} +(0.425866 + 0.737621i) q^{65} +(1.82746 - 3.16525i) q^{66} +(5.17919 - 8.97061i) q^{67} +(3.08078 + 5.33606i) q^{68} +1.00000 q^{69} +(0.0741344 + 2.64471i) q^{70} -8.45809 q^{71} +(0.500000 + 0.866025i) q^{72} +(-0.672545 + 1.16488i) q^{73} +(3.40823 - 5.90323i) q^{74} +(-2.00000 - 3.46410i) q^{75} +5.50664 q^{76} +(0.270955 + 9.66619i) q^{77} -0.851731 q^{78} +(5.72905 + 9.92300i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.24668 - 2.15931i) q^{82} -7.65491 q^{83} +(-2.32746 - 1.25815i) q^{84} -6.16155 q^{85} +(3.65491 + 6.33049i) q^{86} +(2.07413 - 3.59251i) q^{87} +(-1.82746 + 3.16525i) q^{88} +(3.40823 + 5.90323i) q^{89} -1.00000 q^{90} +(1.91922 - 1.18098i) q^{91} -1.00000 q^{92} +(1.67919 + 2.90844i) q^{93} +(1.17919 - 2.04241i) q^{94} +(-2.75332 + 4.76889i) q^{95} +(-0.500000 - 0.866025i) q^{96} +0.444807 q^{97} +(6.98901 - 0.392129i) q^{98} -3.65491 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{12} - 6 q^{13} - 3 q^{14} - 6 q^{15} - 3 q^{16} - 3 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{23} - 3 q^{24} + 12 q^{25} - 3 q^{26} - 6 q^{27} + 24 q^{29} - 3 q^{30} + 3 q^{32} - 6 q^{34} + 3 q^{35} + 6 q^{36} + 12 q^{37} + 6 q^{38} - 3 q^{39} + 3 q^{40} - 36 q^{41} - 3 q^{42} - 3 q^{45} - 3 q^{46} + 3 q^{47} - 6 q^{48} - 3 q^{49} + 24 q^{50} + 3 q^{51} + 3 q^{52} + 3 q^{53} - 3 q^{54} + 3 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} + 3 q^{60} - 30 q^{61} + 3 q^{63} + 6 q^{64} + 3 q^{65} + 21 q^{67} - 3 q^{68} + 6 q^{69} - 6 q^{71} + 3 q^{72} - 15 q^{73} - 12 q^{74} - 12 q^{75} + 12 q^{76} + 24 q^{77} - 6 q^{78} + 12 q^{79} - 3 q^{80} - 3 q^{81} - 18 q^{82} - 24 q^{83} - 3 q^{84} + 6 q^{85} + 12 q^{87} - 12 q^{89} - 6 q^{90} + 33 q^{91} - 6 q^{92} - 3 q^{94} - 6 q^{95} - 3 q^{96} - 12 q^{98}+O(q^{100}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^12 - 6 * q^13 - 3 * q^14 - 6 * q^15 - 3 * q^16 - 3 * q^17 + 3 * q^18 - 6 * q^19 + 6 * q^20 + 3 * q^23 - 3 * q^24 + 12 * q^25 - 3 * q^26 - 6 * q^27 + 24 * q^29 - 3 * q^30 + 3 * q^32 - 6 * q^34 + 3 * q^35 + 6 * q^36 + 12 * q^37 + 6 * q^38 - 3 * q^39 + 3 * q^40 - 36 * q^41 - 3 * q^42 - 3 * q^45 - 3 * q^46 + 3 * q^47 - 6 * q^48 - 3 * q^49 + 24 * q^50 + 3 * q^51 + 3 * q^52 + 3 * q^53 - 3 * q^54 + 3 * q^56 - 12 * q^57 + 12 * q^58 + 12 * q^59 + 3 * q^60 - 30 * q^61 + 3 * q^63 + 6 * q^64 + 3 * q^65 + 21 * q^67 - 3 * q^68 + 6 * q^69 - 6 * q^71 + 3 * q^72 - 15 * q^73 - 12 * q^74 - 12 * q^75 + 12 * q^76 + 24 * q^77 - 6 * q^78 + 12 * q^79 - 3 * q^80 - 3 * q^81 - 18 * q^82 - 24 * q^83 - 3 * q^84 + 6 * q^85 + 12 * q^87 - 12 * q^89 - 6 * q^90 + 33 * q^91 - 6 * q^92 - 3 * q^94 - 6 * q^95 - 3 * q^96 - 12 * q^98

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	0.732294	−	0.680989i	$-0.238450\pi$
$5$	−0.500000	−	0.866025i	−0.223607	−	0.387298i	−0.955901	+	0.293691i	$0.905116\pi$
$6$	1.00000			0.408248
$7$	−2.25332	+	1.38656i	−0.851675	+	0.524070i
$7$	−2.25332	+	1.38656i	−0.851675	+	0.524070i
$8$	−1.00000			−0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	1.82746	−	3.16525i	0.550999	−	0.954357i	−0.447204	−	0.894432i	$-0.647580\pi$
$11$	1.82746	−	3.16525i	0.550999	−	0.954357i	0.998203	−	0.0599256i	$-0.0190864\pi$
$12$	0.500000	+	0.866025i	0.144338	+	0.250000i
$13$	−0.851731			−0.236228			−0.118114	−	0.993000i	$-0.537685\pi$
$13$	−0.851731			−0.236228			−0.118114	+	0.993000i	$0.537685\pi$
$14$	−2.32746	−	1.25815i	−0.622039	−	0.336256i
$15$	−1.00000			−0.258199
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	3.08078	−	5.33606i	0.747198	−	1.29418i	−0.201963	−	0.979393i	$-0.564732\pi$
$17$	3.08078	−	5.33606i	0.747198	−	1.29418i	0.949161	−	0.314792i	$-0.101935\pi$
$18$	0.500000	−	0.866025i	0.117851	−	0.204124i
$19$	−2.75332	−	4.76889i	−0.631655	−	1.09406i	−0.987213	−	0.159405i	$-0.949043\pi$
$19$	−2.75332	−	4.76889i	−0.631655	−	1.09406i	0.355558	−	0.934654i	$-0.384291\pi$
$20$	1.00000			0.223607
$21$	0.0741344	+	2.64471i	0.0161775	+	0.577124i
$22$	3.65491			0.779230
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$23$	0.500000	+	0.866025i	0.104257	+	0.180579i
$24$	−0.500000	+	0.866025i	−0.102062	+	0.176777i
$25$	2.00000	−	3.46410i	0.400000	−	0.692820i
$26$	−0.425866	−	0.737621i	−0.0835191	−	0.144659i
$27$	−1.00000			−0.192450
$28$	−0.0741344	−	2.64471i	−0.0140101	−	0.499804i
$29$	4.14827			0.770314			0.385157	−	0.922851i	$-0.374147\pi$
$29$	4.14827			0.770314			0.385157	+	0.922851i	$0.374147\pi$
$30$	−0.500000	−	0.866025i	−0.0912871	−	0.158114i
$31$	−1.67919	+	2.90844i	−0.301591	+	0.522371i	−0.976496	−	0.215533i	$-0.930851\pi$
$31$	−1.67919	+	2.90844i	−0.301591	+	0.522371i	0.674906	+	0.737904i	$0.264184\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	−1.82746	−	3.16525i	−0.318119	−	0.550999i
$34$	6.16155			1.05670
$35$	2.32746	+	1.25815i	0.393412	+	0.212667i
$36$	1.00000			0.166667
$37$	−3.40823	−	5.90323i	−0.560310	−	0.970485i	−0.997469	−	0.0711010i	$-0.977349\pi$
$37$	−3.40823	−	5.90323i	−0.560310	−	0.970485i	0.437159	−	0.899384i	$-0.355985\pi$
$38$	2.75332	−	4.76889i	0.446648	−	0.773616i
$39$	−0.425866	+	0.737621i	−0.0681931	+	0.118114i
$40$	0.500000	+	0.866025i	0.0790569	+	0.136931i
$41$	−2.49336			−0.389397			−0.194699	−	0.980863i	$-0.562373\pi$
$41$	−2.49336			−0.389397			−0.194699	+	0.980863i	$0.562373\pi$
$42$	−2.25332	+	1.38656i	−0.347695	+	0.213951i
$43$	7.30982			1.11474			0.557369	−	0.830265i	$-0.311811\pi$
$43$	7.30982			1.11474			0.557369	+	0.830265i	$0.311811\pi$
$44$	1.82746	+	3.16525i	0.275499	+	0.477179i
$45$	−0.500000	+	0.866025i	−0.0745356	+	0.129099i
$46$	−0.500000	+	0.866025i	−0.0737210	+	0.127688i
$47$	−1.17919	−	2.04241i	−0.172002	−	0.297916i	0.767118	−	0.641506i	$-0.221690\pi$
$47$	−1.17919	−	2.04241i	−0.172002	−	0.297916i	−0.939120	+	0.343590i	$0.888357\pi$
$48$	−1.00000			−0.144338
$49$	3.15491	−	6.24872i	0.450702	−	0.892675i
$50$	4.00000			0.565685
$51$	−3.08078	−	5.33606i	−0.431395	−	0.747198i
$52$	0.425866	−	0.737621i	0.0590569	−	0.102290i
$53$	−3.15491	+	5.46447i	−0.433360	+	0.750602i	−0.997160	−	0.0753093i	$-0.976006\pi$
$53$	−3.15491	+	5.46447i	−0.433360	+	0.750602i	0.563800	+	0.825911i	$0.309339\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	−3.65491			−0.492828
$56$	2.25332	−	1.38656i	0.301113	−	0.185287i
$57$	−5.50664			−0.729373
$58$	2.07413	+	3.59251i	0.272347	+	0.471719i
$59$	−1.58078	+	2.73799i	−0.205800	+	0.356455i	−0.950387	−	0.311069i	$-0.899313\pi$
$59$	−1.58078	+	2.73799i	−0.205800	+	0.356455i	0.744588	+	0.667525i	$0.232646\pi$
$60$	0.500000	−	0.866025i	0.0645497	−	0.111803i
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	−0.985391	−	0.170305i	$-0.945525\pi$
$61$	−5.00000	−	8.66025i	−0.640184	−	1.10883i	0.345207	−	0.938527i	$-0.387809\pi$
$62$	−3.35837			−0.426514
$63$	2.32746	+	1.25815i	0.293232	+	0.158512i
$64$	1.00000			0.125000
$65$	0.425866	+	0.737621i	0.0528221	+	0.0914906i
$66$	1.82746	−	3.16525i	0.224944	−	0.389615i
$67$	5.17919	−	8.97061i	0.632738	−	1.09593i	−0.354251	−	0.935150i	$-0.615264\pi$
$67$	5.17919	−	8.97061i	0.632738	−	1.09593i	0.986990	−	0.160785i	$-0.0514025\pi$
$68$	3.08078	+	5.33606i	0.373599	+	0.647092i
$69$	1.00000			0.120386
$70$	0.0741344	+	2.64471i	0.00886076	+	0.316104i
$71$	−8.45809			−1.00379			−0.501895	−	0.864928i	$-0.667364\pi$
$71$	−8.45809			−1.00379			−0.501895	+	0.864928i	$0.667364\pi$
$72$	0.500000	+	0.866025i	0.0589256	+	0.102062i
$73$	−0.672545	+	1.16488i	−0.0787154	+	0.136339i	−0.902696	−	0.430279i	$-0.858415\pi$
$73$	−0.672545	+	1.16488i	−0.0787154	+	0.136339i	0.823981	+	0.566618i	$0.191749\pi$
$74$	3.40823	−	5.90323i	0.396199	−	0.686237i
$75$	−2.00000	−	3.46410i	−0.230940	−	0.400000i
$76$	5.50664			0.631655
$77$	0.270955	+	9.66619i	0.0308782	+	1.10156i
$78$	−0.851731			−0.0964396
$79$	5.72905	+	9.92300i	0.644568	+	1.11642i	0.984401	+	0.175939i	$0.0562961\pi$
$79$	5.72905	+	9.92300i	0.644568	+	1.11642i	−0.339833	+	0.940486i	$0.610371\pi$
$80$	−0.500000	+	0.866025i	−0.0559017	+	0.0968246i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	−1.24668	−	2.15931i	−0.137673	−	0.238456i
$83$	−7.65491			−0.840236			−0.420118	−	0.907470i	$-0.638011\pi$
$83$	−7.65491			−0.840236			−0.420118	+	0.907470i	$0.638011\pi$
$84$	−2.32746	−	1.25815i	−0.253946	−	0.137276i
$85$	−6.16155			−0.668314
$86$	3.65491	+	6.33049i	0.394119	+	0.682634i
$87$	2.07413	−	3.59251i	0.222371	−	0.385157i
$88$	−1.82746	+	3.16525i	−0.194807	+	0.337416i
$89$	3.40823	+	5.90323i	0.361272	+	0.625741i	0.988170	−	0.153360i	$-0.0490093\pi$
$89$	3.40823	+	5.90323i	0.361272	+	0.625741i	−0.626899	+	0.779101i	$0.715676\pi$
$90$	−1.00000			−0.105409
$91$	1.91922	−	1.18098i	0.201189	−	0.123800i
$92$	−1.00000			−0.104257
$93$	1.67919	+	2.90844i	0.174124	+	0.301591i
$94$	1.17919	−	2.04241i	0.121624	−	0.210659i
$95$	−2.75332	+	4.76889i	−0.282485	+	0.489278i
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	0.444807			0.0451633			0.0225816	−	0.999745i	$-0.492811\pi$
$97$	0.444807			0.0451633			0.0225816	+	0.999745i	$0.492811\pi$
$98$	6.98901	−	0.392129i	0.705996	−	0.0396110i
$99$	−3.65491			−0.367332
$100$	2.00000	+	3.46410i	0.200000	+	0.346410i
$101$	−0.654911	+	1.13434i	−0.0651661	+	0.112871i	−0.896768	−	0.442502i	$-0.854091\pi$
$101$	−0.654911	+	1.13434i	−0.0651661	+	0.112871i	0.831602	+	0.555373i	$0.187424\pi$
$102$	3.08078	−	5.33606i	0.305042	−	0.528349i
$103$	−1.82081	−	3.15374i	−0.179410	−	0.310747i	0.762269	−	0.647261i	$-0.224086\pi$
$103$	−1.82081	−	3.15374i	−0.179410	−	0.310747i	−0.941679	+	0.336513i	$0.890752\pi$
$104$	0.851731			0.0835191
$105$	2.25332	−	1.38656i	0.219902	−	0.135314i
$106$	−6.30982			−0.612864
$107$	3.17254	+	5.49501i	0.306701	+	0.531223i	0.977639	−	0.210292i	$-0.0674413\pi$
$107$	3.17254	+	5.49501i	0.306701	+	0.531223i	−0.670937	+	0.741514i	$0.734108\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−1.65491	+	2.86639i	−0.158512	+	0.274550i	−0.934332	−	0.356403i	$-0.884003\pi$
$109$	−1.65491	+	2.86639i	−0.158512	+	0.274550i	0.775820	+	0.630954i	$0.217336\pi$
$110$	−1.82746	−	3.16525i	−0.174241	−	0.301794i
$111$	−6.81646			−0.646990
$112$	2.32746	+	1.25815i	0.219924	+	0.118884i
$113$	9.17484			0.863096			0.431548	−	0.902090i	$-0.357968\pi$
$113$	9.17484			0.863096			0.431548	+	0.902090i	$0.357968\pi$
$114$	−2.75332	−	4.76889i	−0.257872	−	0.446648i
$115$	0.500000	−	0.866025i	0.0466252	−	0.0807573i
$116$	−2.07413	+	3.59251i	−0.192579	+	0.333556i
$117$	0.425866	+	0.737621i	0.0393713	+	0.0681931i
$118$	−3.16155			−0.291045
$119$	0.456783	+	16.2955i	0.0418733	+	1.49381i
$120$	1.00000			0.0912871
$121$	−1.17919	−	2.04241i	−0.107199	−	0.185674i
$122$	5.00000	−	8.66025i	0.452679	−	0.784063i
$123$	−1.24668	+	2.15931i	−0.112409	+	0.194699i
$124$	−1.67919	−	2.90844i	−0.150795	−	0.261185i
$125$	−9.00000			−0.804984
$126$	0.0741344	+	2.64471i	0.00660442	+	0.235610i
$127$	−8.34509			−0.740507			−0.370253	−	0.928931i	$-0.620729\pi$
$127$	−8.34509			−0.740507			−0.370253	+	0.928931i	$0.620729\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	3.65491	−	6.33049i	0.321797	−	0.557369i
$130$	−0.425866	+	0.737621i	−0.0373509	+	0.0646936i
$131$	−2.54986	−	4.41648i	−0.222782	−	0.385870i	0.732870	−	0.680369i	$-0.238181\pi$
$131$	−2.54986	−	4.41648i	−0.222782	−	0.385870i	−0.955652	+	0.294499i	$0.904847\pi$
$132$	3.65491			0.318119
$133$	12.8165	+	6.92820i	1.11133	+	0.600751i
$134$	10.3584			0.894827
$135$	0.500000	+	0.866025i	0.0430331	+	0.0745356i
$136$	−3.08078	+	5.33606i	−0.264174	+	0.457563i
$137$	1.47572	−	2.55603i	0.126080	−	0.218376i	−0.796075	−	0.605198i	$-0.793094\pi$
$137$	1.47572	−	2.55603i	0.126080	−	0.218376i	0.922154	+	0.386822i	$0.126427\pi$
$138$	0.500000	+	0.866025i	0.0425628	+	0.0737210i
$139$	16.0266			1.35936			0.679678	−	0.733511i	$-0.262120\pi$
$139$	16.0266			1.35936			0.679678	+	0.733511i	$0.262120\pi$
$140$	−2.25332	+	1.38656i	−0.190440	+	0.117186i
$141$	−2.35837			−0.198611
$142$	−4.22905	−	7.32492i	−0.354894	−	0.614694i
$143$	−1.55650	+	2.69594i	−0.130161	+	0.225446i
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	−2.07413	−	3.59251i	−0.172247	−	0.298341i
$146$	−1.34509			−0.111320
$147$	−3.83410	−	5.85659i	−0.316231	−	0.483044i
$148$	6.81646			0.560310
$149$	9.98237	+	17.2900i	0.817787	+	1.41645i	0.907309	+	0.420464i	$0.138133\pi$
$149$	9.98237	+	17.2900i	0.817787	+	1.41645i	−0.0895218	+	0.995985i	$0.528534\pi$
$150$	2.00000	−	3.46410i	0.163299	−	0.282843i
$151$	−1.17254	+	2.03091i	−0.0954203	+	0.165273i	−0.909784	−	0.415082i	$-0.863753\pi$
$151$	−1.17254	+	2.03091i	−0.0954203	+	0.165273i	0.814364	+	0.580355i	$0.197086\pi$
$152$	2.75332	+	4.76889i	0.223324	+	0.386808i
$153$	−6.16155			−0.498132
$154$	−8.23569	+	5.06775i	−0.663651	+	0.408371i
$155$	3.35837			0.269751
$156$	−0.425866	−	0.737621i	−0.0340965	−	0.0590569i
$157$	12.4215	−	21.5147i	0.991345	−	1.71706i	0.381978	−	0.924172i	$-0.375243\pi$
$157$	12.4215	−	21.5147i	0.991345	−	1.71706i	0.609367	−	0.792888i	$-0.291424\pi$
$158$	−5.72905	+	9.92300i	−0.455778	+	0.789431i
$159$	3.15491	+	5.46447i	0.250201	+	0.433360i
$160$	−1.00000			−0.0790569
$161$	−2.32746	−	1.25815i	−0.183429	−	0.0991564i
$162$	−1.00000			−0.0785674
$163$	11.4215	+	19.7826i	0.894602	+	1.54950i	0.834296	+	0.551316i	$0.185874\pi$
$163$	11.4215	+	19.7826i	0.894602	+	1.54950i	0.0603059	+	0.998180i	$0.480792\pi$
$164$	1.24668	−	2.15931i	0.0973493	−	0.168614i
$165$	−1.82746	+	3.16525i	−0.142267	+	0.246414i
$166$	−3.82746	−	6.62935i	−0.297068	−	0.514537i
$167$	4.06184			0.314314			0.157157	−	0.987574i	$-0.449767\pi$
$167$	4.06184			0.314314			0.157157	+	0.987574i	$0.449767\pi$
$168$	−0.0741344	−	2.64471i	−0.00571960	−	0.204044i
$169$	−12.2746			−0.944196
$170$	−3.08078	−	5.33606i	−0.236285	−	0.409257i
$171$	−2.75332	+	4.76889i	−0.210552	+	0.364686i
$172$	−3.65491	+	6.33049i	−0.278684	+	0.482695i
$173$	1.85173	+	3.20729i	0.140785	+	0.243846i	0.927792	−	0.373097i	$-0.121704\pi$
$173$	1.85173	+	3.20729i	0.140785	+	0.243846i	−0.787008	+	0.616943i	$0.788371\pi$
$174$	4.14827			0.314479
$175$	0.296538	+	10.5788i	0.0224161	+	0.799686i
$176$	−3.65491			−0.275499
$177$	1.58078	+	2.73799i	0.118818	+	0.205800i
$178$	−3.40823	+	5.90323i	−0.255458	+	0.442466i
$179$	−7.48901	+	12.9713i	−0.559755	+	0.969524i	0.437762	+	0.899091i	$0.355771\pi$
$179$	−7.48901	+	12.9713i	−0.559755	+	0.969524i	−0.997517	+	0.0704327i	$0.977562\pi$
$180$	−0.500000	−	0.866025i	−0.0372678	−	0.0645497i
$181$	−1.70346			−0.126617			−0.0633087	−	0.997994i	$-0.520165\pi$
$181$	−1.70346			−0.126617			−0.0633087	+	0.997994i	$0.520165\pi$
$182$	1.98237	+	1.07161i	0.146943	+	0.0794329i
$183$	−10.0000			−0.739221
$184$	−0.500000	−	0.866025i	−0.0368605	−	0.0638442i
$185$	−3.40823	+	5.90323i	−0.250578	+	0.434014i
$186$	−1.67919	+	2.90844i	−0.123124	+	0.213257i
$187$	−11.2600	−	19.5028i	−0.823410	−	1.42619i
$188$	2.35837			0.172002
$189$	2.25332	−	1.38656i	0.163905	−	0.100857i
$190$	−5.50664			−0.399494
$191$	11.4215	+	19.7826i	0.826432	+	1.43142i	0.900820	+	0.434193i	$0.142966\pi$
$191$	11.4215	+	19.7826i	0.826432	+	1.43142i	−0.0743882	+	0.997229i	$0.523700\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	8.95809	−	15.5159i	0.644817	−	1.11686i	−0.339526	−	0.940597i	$-0.610267\pi$
$193$	8.95809	−	15.5159i	0.644817	−	1.11686i	0.984344	−	0.176260i	$-0.0563999\pi$
$194$	0.222403	+	0.385214i	0.0159676	+	0.0276567i
$195$	0.851731			0.0609937
$196$	3.83410	+	5.85659i	0.273864	+	0.418328i
$197$	5.01328			0.357182			0.178591	−	0.983923i	$-0.442846\pi$
$197$	5.01328			0.357182			0.178591	+	0.983923i	$0.442846\pi$
$198$	−1.82746	−	3.16525i	−0.129872	−	0.224944i
$199$	−7.16155	+	12.4042i	−0.507669	+	0.879309i	0.492292	+	0.870430i	$0.336159\pi$
$199$	−7.16155	+	12.4042i	−0.507669	+	0.879309i	−0.999961	+	0.00887817i	$0.997174\pi$
$200$	−2.00000	+	3.46410i	−0.141421	+	0.244949i
$201$	−5.17919	−	8.97061i	−0.365312	−	0.632738i
$202$	−1.30982			−0.0921587
$203$	−9.34738	+	5.75182i	−0.656058	+	0.403698i
$204$	6.16155			0.431395
$205$	1.24668	+	2.15931i	0.0870718	+	0.150813i
$206$	1.82081	−	3.15374i	0.126862	−	0.219732i
$207$	0.500000	−	0.866025i	0.0347524	−	0.0601929i
$208$	0.425866	+	0.737621i	0.0295285	+	0.0511448i
$209$	−20.1263			−1.39216
$210$	2.32746	+	1.25815i	0.160610	+	0.0868209i
$211$	−9.01328			−0.620500			−0.310250	−	0.950655i	$-0.600413\pi$
$211$	−9.01328			−0.620500			−0.310250	+	0.950655i	$0.600413\pi$
$212$	−3.15491	−	5.46447i	−0.216680	−	0.375301i
$213$	−4.22905	+	7.32492i	−0.289769	+	0.501895i
$214$	−3.17254	+	5.49501i	−0.216871	+	0.375631i
$215$	−3.65491	−	6.33049i	−0.249263	−	0.431736i
$216$	1.00000			0.0680414
$217$	−0.248971	−	8.88193i	−0.0169013	−	0.602945i
$218$	−3.30982			−0.224169
$219$	0.672545	+	1.16488i	0.0454464	+	0.0787154i
$220$	1.82746	−	3.16525i	0.123207	−	0.213401i
$221$	−2.62399	+	4.54489i	−0.176509	+	0.305722i
$222$	−3.40823	−	5.90323i	−0.228746	−	0.396199i
$223$	−15.9780			−1.06997			−0.534984	−	0.844862i	$-0.679682\pi$
$223$	−15.9780			−1.06997			−0.534984	+	0.844862i	$0.679682\pi$
$224$	0.0741344	+	2.64471i	0.00495332	+	0.176707i
$225$	−4.00000			−0.266667
$226$	4.58742	+	7.94564i	0.305151	+	0.528536i
$227$	6.98901	−	12.1053i	0.463877	−	0.803458i	−0.535273	−	0.844679i	$-0.679791\pi$
$227$	6.98901	−	12.1053i	0.463877	−	0.803458i	0.999150	+	0.0412208i	$0.0131247\pi$
$228$	2.75332	−	4.76889i	0.182343	−	0.315828i
$229$	−14.2600	−	24.6990i	−0.942325	−	1.63215i	−0.761021	−	0.648727i	$-0.775302\pi$
$229$	−14.2600	−	24.6990i	−0.942325	−	1.63215i	−0.181304	−	0.983427i	$-0.558032\pi$
$230$	1.00000			0.0659380
$231$	8.50664	+	4.59844i	0.559696	+	0.302555i
$232$	−4.14827			−0.272347
$233$	−5.56978	−	9.64715i	−0.364889	−	0.632006i	0.623870	−	0.781528i	$-0.285560\pi$
$233$	−5.56978	−	9.64715i	−0.364889	−	0.632006i	−0.988758	+	0.149523i	$0.952226\pi$
$234$	−0.425866	+	0.737621i	−0.0278397	+	0.0482198i
$235$	−1.17919	+	2.04241i	−0.0769216	+	0.133232i
$236$	−1.58078	−	2.73799i	−0.102900	−	0.178228i
$237$	11.4581			0.744283
$238$	−13.8840	+	8.54335i	−0.899963	+	0.553783i
$239$	−16.0000			−1.03495			−0.517477	−	0.855697i	$-0.673129\pi$
$239$	−16.0000			−1.03495			−0.517477	+	0.855697i	$0.673129\pi$
$240$	0.500000	+	0.866025i	0.0322749	+	0.0559017i
$241$	−8.28424	+	14.3487i	−0.533635	+	0.924282i	0.465593	+	0.884999i	$0.345841\pi$
$241$	−8.28424	+	14.3487i	−0.533635	+	0.924282i	−0.999228	+	0.0392837i	$0.987492\pi$
$242$	1.17919	−	2.04241i	0.0758010	−	0.131291i
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	10.0000			0.640184
$245$	−6.98901	+	0.392129i	−0.446511	+	0.0250522i
$246$	−2.49336			−0.158971
$247$	2.34509	+	4.06181i	0.149214	+	0.258447i
$248$	1.67919	−	2.90844i	0.106628	−	0.184686i
$249$	−3.82746	+	6.62935i	−0.242555	+	0.420118i
$250$	−4.50000	−	7.79423i	−0.284605	−	0.492950i
$251$	30.2746			1.91091			0.955456	−	0.295132i	$-0.0953637\pi$
$251$	30.2746			1.91091			0.955456	+	0.295132i	$0.0953637\pi$
$252$	−2.25332	+	1.38656i	−0.141946	+	0.0873450i
$253$	3.65491			0.229782
$254$	−4.17254	−	7.22706i	−0.261809	−	0.453466i
$255$	−3.08078	+	5.33606i	−0.192926	+	0.334157i
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	7.06314	+	12.2337i	0.440587	+	0.763119i	0.997733	−	0.0672957i	$-0.0214371\pi$
$257$	7.06314	+	12.2337i	0.440587	+	0.763119i	−0.557146	+	0.830414i	$0.688104\pi$
$258$	7.30982			0.455090
$259$	15.8650	+	8.57616i	0.985804	+	0.532897i
$260$	−0.851731			−0.0528221
$261$	−2.07413	−	3.59251i	−0.128386	−	0.222371i
$262$	2.54986	−	4.41648i	0.157531	−	0.272851i
$263$	7.65491	−	13.2587i	0.472022	−	0.817566i	−0.527466	−	0.849576i	$-0.676858\pi$
$263$	7.65491	−	13.2587i	0.472022	−	0.817566i	0.999488	+	0.0320103i	$0.0101909\pi$
$264$	1.82746	+	3.16525i	0.112472	+	0.194807i
$265$	6.30982			0.387609
$266$	0.408232	+	14.5635i	0.0250303	+	0.892945i
$267$	6.81646			0.417161
$268$	5.17919	+	8.97061i	0.316369	+	0.547967i
$269$	11.2357	−	19.4608i	0.685052	−	1.18654i	−0.288369	−	0.957519i	$-0.593113\pi$
$269$	11.2357	−	19.4608i	0.685052	−	1.18654i	0.973420	−	0.229025i	$-0.0735538\pi$
$270$	−0.500000	+	0.866025i	−0.0304290	+	0.0527046i
$271$	7.18583	+	12.4462i	0.436508	+	0.756054i	0.997417	−	0.0718232i	$-0.0228817\pi$
$271$	7.18583	+	12.4462i	0.436508	+	0.756054i	−0.560909	+	0.827877i	$0.689548\pi$
$272$	−6.16155			−0.373599
$273$	−0.0631426	−	2.25258i	−0.00382156	−	0.136333i
$274$	2.95145			0.178304
$275$	−7.30982	−	12.6610i	−0.440799	−	0.763486i
$276$	−0.500000	+	0.866025i	−0.0300965	+	0.0521286i
$277$	5.98237	−	10.3618i	0.359446	−	0.622578i	−0.628423	−	0.777872i	$-0.716299\pi$
$277$	5.98237	−	10.3618i	0.359446	−	0.622578i	0.987868	+	0.155294i	$0.0496325\pi$
$278$	8.01328	+	13.8794i	0.480605	+	0.832432i
$279$	3.35837			0.201061
$280$	−2.32746	−	1.25815i	−0.139092	−	0.0751891i
$281$	11.0512			0.659257			0.329629	−	0.944111i	$-0.393076\pi$
$281$	11.0512			0.659257			0.329629	+	0.944111i	$0.393076\pi$
$282$	−1.17919	−	2.04241i	−0.0702195	−	0.121624i
$283$	−1.96908	+	3.41055i	−0.117050	+	0.202736i	−0.918597	−	0.395195i	$-0.870677\pi$
$283$	−1.96908	+	3.41055i	−0.117050	+	0.202736i	0.801547	+	0.597931i	$0.204010\pi$
$284$	4.22905	−	7.32492i	0.250948	−	0.434654i
$285$	2.75332	+	4.76889i	0.163093	+	0.282485i
$286$	−3.11300			−0.184076
$287$	5.61834	−	3.45719i	0.331640	−	0.204071i
$288$	−1.00000			−0.0589256
$289$	−10.4824	−	18.1560i	−0.616610	−	1.06800i
$290$	2.07413	−	3.59251i	0.121797	−	0.210959i
$291$	0.222403	−	0.385214i	0.0130375	−	0.0225816i
$292$	−0.672545	−	1.16488i	−0.0393577	−	0.0681695i
$293$	13.0266			0.761020			0.380510	−	0.924777i	$-0.375748\pi$
$293$	13.0266			0.761020			0.380510	+	0.924777i	$0.375748\pi$
$294$	3.15491	−	6.24872i	0.183998	−	0.364433i
$295$	3.16155			0.184073
$296$	3.40823	+	5.90323i	0.198099	+	0.343118i
$297$	−1.82746	+	3.16525i	−0.106040	+	0.183666i
$298$	−9.98237	+	17.2900i	−0.578263	+	1.00158i
$299$	−0.425866	−	0.737621i	−0.0246284	−	0.0426577i
$300$	4.00000			0.230940
$301$	−16.4714	+	10.1355i	−0.949394	+	0.584200i
$302$	−2.34509			−0.134945
$303$	0.654911	+	1.13434i	0.0376236	+	0.0651661i
$304$	−2.75332	+	4.76889i	−0.157914	+	0.273515i
$305$	−5.00000	+	8.66025i	−0.286299	+	0.495885i
$306$	−3.08078	−	5.33606i	−0.176116	−	0.305042i
$307$	−25.4095			−1.45020			−0.725099	−	0.688644i	$-0.758206\pi$
$307$	−25.4095			−1.45020			−0.725099	+	0.688644i	$0.758206\pi$
$308$	−8.50664	−	4.59844i	−0.484711	−	0.262020i
$309$	−3.64163			−0.207165
$310$	1.67919	+	2.90844i	0.0953714	+	0.165188i
$311$	2.77095	−	4.79943i	0.157126	−	0.272151i	−0.776705	−	0.629865i	$-0.783110\pi$
$311$	2.77095	−	4.79943i	0.157126	−	0.272151i	0.933831	+	0.357714i	$0.116444\pi$
$312$	0.425866	−	0.737621i	0.0241099	−	0.0417596i
$313$	−9.58078	−	16.5944i	−0.541537	−	0.937970i	−0.998816	−	0.0486469i	$-0.984509\pi$
$313$	−9.58078	−	16.5944i	−0.541537	−	0.937970i	0.457279	−	0.889324i	$-0.348824\pi$
$314$	24.8430			1.40197
$315$	−0.0741344	−	2.64471i	−0.00417700	−	0.149013i
$316$	−11.4581			−0.644568
$317$	−4.28424	−	7.42052i	−0.240627	−	0.416778i	0.720266	−	0.693698i	$-0.244020\pi$
$317$	−4.28424	−	7.42052i	−0.240627	−	0.416778i	−0.960893	+	0.276920i	$0.910686\pi$
$318$	−3.15491	+	5.46447i	−0.176919	+	0.306432i
$319$	7.58078	−	13.1303i	0.424442	−	0.735155i
$320$	−0.500000	−	0.866025i	−0.0279508	−	0.0484123i
$321$	6.34509			0.354148
$322$	−0.0741344	−	2.64471i	−0.00413135	−	0.147384i
$323$	−33.9295			−1.88789
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$	−1.70346	+	2.95048i	−0.0944911	+	0.163663i
$326$	−11.4215	+	19.7826i	−0.632579	+	1.09566i
$327$	1.65491	+	2.86639i	0.0915168	+	0.158512i
$328$	2.49336			0.137673
$329$	5.48901	+	2.96720i	0.302619	+	0.163587i
$330$	−3.65491			−0.201196
$331$	−8.56978	−	14.8433i	−0.471038	−	0.815862i	0.528413	−	0.848987i	$-0.322787\pi$
$331$	−8.56978	−	14.8433i	−0.471038	−	0.815862i	−0.999451	+	0.0331256i	$0.989454\pi$
$332$	3.82746	−	6.62935i	0.210059	−	0.363833i
$333$	−3.40823	+	5.90323i	−0.186770	+	0.323495i
$334$	2.03092	+	3.51765i	0.111127	+	0.192477i
$335$	−10.3584			−0.565938
$336$	2.25332	−	1.38656i	0.122929	−	0.0756430i
$337$	−14.5685			−0.793596			−0.396798	−	0.917906i	$-0.629879\pi$
$337$	−14.5685			−0.793596			−0.396798	+	0.917906i	$0.629879\pi$
$338$	−6.13728	−	10.6301i	−0.333824	−	0.578200i
$339$	4.58742	−	7.94564i	0.249154	−	0.431548i
$340$	3.08078	−	5.33606i	0.167079	−	0.289389i
$341$	6.13728	+	10.6301i	0.332352	+	0.575651i
$342$	−5.50664			−0.297765
$343$	1.55519	+	18.4548i	0.0839725	+	0.996468i
$344$	−7.30982			−0.394119
$345$	−0.500000	−	0.866025i	−0.0269191	−	0.0466252i
$346$	−1.85173	+	3.20729i	−0.0995497	+	0.172425i
$347$	−3.52428	+	6.10422i	−0.189193	+	0.327692i	−0.944981	−	0.327124i	$-0.893921\pi$
$347$	−3.52428	+	6.10422i	−0.189193	+	0.327692i	0.755788	+	0.654816i	$0.227254\pi$
$348$	2.07413	+	3.59251i	0.111185	+	0.192579i
$349$	22.4581			1.20215			0.601077	−	0.799191i	$-0.294738\pi$
$349$	22.4581			1.20215			0.601077	+	0.799191i	$0.294738\pi$
$350$	−9.01328	+	5.54623i	−0.481780	+	0.296459i
$351$	0.851731			0.0454620
$352$	−1.82746	−	3.16525i	−0.0974037	−	0.168708i
$353$	−5.56978	+	9.64715i	−0.296450	+	0.513466i	−0.975321	−	0.220791i	$-0.929136\pi$
$353$	−5.56978	+	9.64715i	−0.296450	+	0.513466i	0.678871	+	0.734257i	$0.262469\pi$
$354$	−1.58078	+	2.73799i	−0.0840173	+	0.145522i
$355$	4.22905	+	7.32492i	0.224454	+	0.388766i
$356$	−6.81646			−0.361272
$357$	14.3407	+	7.75218i	0.758992	+	0.410289i
$358$	−14.9780			−0.791613
$359$	14.0133	+	24.2717i	0.739593	+	1.28101i	0.952679	+	0.303979i	$0.0983152\pi$
$359$	14.0133	+	24.2717i	0.739593	+	1.28101i	−0.213086	+	0.977033i	$0.568351\pi$
$360$	0.500000	−	0.866025i	0.0263523	−	0.0456435i
$361$	−5.66155	+	9.80610i	−0.297976	+	0.516110i
$362$	−0.851731	−	1.47524i	−0.0447660	−	0.0775370i
$363$	−2.35837			−0.123782
$364$	0.0631426	+	2.25258i	0.00330957	+	0.118067i
$365$	1.34509			0.0704052
$366$	−5.00000	−	8.66025i	−0.261354	−	0.452679i
$367$	3.89495	−	6.74625i	0.203315	−	0.352151i	−0.746280	−	0.665632i	$-0.768162\pi$
$367$	3.89495	−	6.74625i	0.203315	−	0.352151i	0.949594	+	0.313481i	$0.101495\pi$
$368$	0.500000	−	0.866025i	0.0260643	−	0.0451447i
$369$	1.24668	+	2.15931i	0.0648995	+	0.112409i
$370$	−6.81646			−0.354371
$371$	−0.467775	−	16.6877i	−0.0242857	−	0.866380i
$372$	−3.35837			−0.174124
$373$	−6.35837	−	11.0130i	−0.329224	−	0.570233i	0.653134	−	0.757242i	$-0.273454\pi$
$373$	−6.35837	−	11.0130i	−0.329224	−	0.570233i	−0.982358	+	0.187009i	$0.940120\pi$
$374$	11.2600	−	19.5028i	0.582239	−	1.00847i
$375$	−4.50000	+	7.79423i	−0.232379	+	0.402492i
$376$	1.17919	+	2.04241i	0.0608119	+	0.105329i
$377$	−3.53321			−0.181970
$378$	2.32746	+	1.25815i	0.119711	+	0.0647125i
$379$	−22.2613			−1.14348			−0.571742	−	0.820433i	$-0.693732\pi$
$379$	−22.2613			−1.14348			−0.571742	+	0.820433i	$0.693732\pi$
$380$	−2.75332	−	4.76889i	−0.141242	−	0.244639i
$381$	−4.17254	+	7.22706i	−0.213766	+	0.370253i
$382$	−11.4215	+	19.7826i	−0.584376	+	1.01217i
$383$	11.1117	+	19.2460i	0.567781	+	0.983426i	0.996785	+	0.0801230i	$0.0255313\pi$
$383$	11.1117	+	19.2460i	0.567781	+	0.983426i	−0.429004	+	0.903303i	$0.641135\pi$
$384$	1.00000			0.0510310
$385$	8.23569	−	5.06775i	0.419729	−	0.258276i
$386$	17.9162			0.911910
$387$	−3.65491	−	6.33049i	−0.185790	−	0.321797i
$388$	−0.222403	+	0.385214i	−0.0112908	+	0.0195563i
$389$	15.3717	−	26.6245i	0.779374	−	1.34992i	−0.152929	−	0.988237i	$-0.548871\pi$
$389$	15.3717	−	26.6245i	0.779374	−	1.34992i	0.932303	−	0.361678i	$-0.117796\pi$
$390$	0.425866	+	0.737621i	0.0215645	+	0.0373509i
$391$	6.16155			0.311603
$392$	−3.15491	+	6.24872i	−0.159347	+	0.315608i
$393$	−5.09972			−0.257247
$394$	2.50664	+	4.34163i	0.126283	+	0.218728i
$395$	5.72905	−	9.92300i	0.288260	−	0.499280i
$396$	1.82746	−	3.16525i	0.0918331	−	0.159060i
$397$	3.08078	+	5.33606i	0.154620	+	0.267809i	0.932920	−	0.360082i	$-0.117251\pi$
$397$	3.08078	+	5.33606i	0.154620	+	0.267809i	−0.778301	+	0.627892i	$0.783918\pi$
$398$	−14.3231			−0.717952
$399$	12.4082	−	7.63528i	0.621189	−	0.382242i
$400$	−4.00000			−0.200000
$401$	7.98237	+	13.8259i	0.398620	+	0.690431i	0.993556	−	0.113343i	$-0.0361558\pi$
$401$	7.98237	+	13.8259i	0.398620	+	0.690431i	−0.594936	+	0.803773i	$0.702822\pi$
$402$	5.17919	−	8.97061i	0.258314	−	0.447414i
$403$	1.43022	−	2.47721i	0.0712441	−	0.123398i
$404$	−0.654911	−	1.13434i	−0.0325830	−	0.0564355i
$405$	1.00000			0.0496904
$406$	−9.65491	−	5.21916i	−0.479165	−	0.259023i
$407$	−24.9136			−1.23492
$408$	3.08078	+	5.33606i	0.152521	+	0.264174i
$409$	7.36502	−	12.7566i	0.364177	−	0.630772i	−0.624467	−	0.781051i	$-0.714684\pi$
$409$	7.36502	−	12.7566i	0.364177	−	0.630772i	0.988644	+	0.150279i	$0.0480171\pi$
$410$	−1.24668	+	2.15931i	−0.0615691	+	0.106641i
$411$	−1.47572	−	2.55603i	−0.0727921	−	0.126080i
$412$	3.64163			0.179410
$413$	−0.234380	−	8.36140i	−0.0115331	−	0.411437i
$414$	1.00000			0.0491473
$415$	3.82746	+	6.62935i	0.187882	+	0.325422i
$416$	−0.425866	+	0.737621i	−0.0208798	+	0.0361648i
$417$	8.01328	−	13.8794i	0.392412	−	0.679678i
$418$	−10.0631	−	17.4299i	−0.492204	−	0.852523i
$419$	24.9427			1.21853			0.609267	−	0.792966i	$-0.291464\pi$
$419$	24.9427			1.21853			0.609267	+	0.792966i	$0.291464\pi$
$420$	0.0741344	+	2.64471i	0.00361739	+	0.129049i
$421$	32.3497			1.57663			0.788313	−	0.615274i	$-0.210955\pi$
$421$	32.3497			1.57663			0.788313	+	0.615274i	$0.210955\pi$
$422$	−4.50664	−	7.80573i	−0.219380	−	0.379977i
$423$	−1.17919	+	2.04241i	−0.0573340	+	0.0993054i
$424$	3.15491	−	5.46447i	0.153216	−	0.265378i
$425$	−12.3231	−	21.3442i	−0.597758	−	1.03535i
$426$	−8.45809			−0.409796
$427$	23.2746	+	12.5815i	1.12633	+	0.608863i
$428$	−6.34509			−0.306701
$429$	1.55650	+	2.69594i	0.0751486	+	0.130161i
$430$	3.65491	−	6.33049i	0.176255	−	0.305283i
$431$	−2.29654	+	3.97772i	−0.110620	+	0.191600i	−0.916021	−	0.401131i	$-0.868617\pi$
$431$	−2.29654	+	3.97772i	−0.110620	+	0.191600i	0.805400	+	0.592731i	$0.201950\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	27.2393			1.30904			0.654518	−	0.756046i	$-0.272871\pi$
$433$	27.2393			1.30904			0.654518	+	0.756046i	$0.272871\pi$
$434$	7.56749	−	4.65658i	0.363251	−	0.223523i
$435$	−4.14827			−0.198894
$436$	−1.65491	−	2.86639i	−0.0792559	−	0.137275i
$437$	2.75332	−	4.76889i	0.131709	−	0.228127i
$438$	−0.672545	+	1.16488i	−0.0321354	+	0.0556602i
$439$	7.97572	+	13.8144i	0.380661	+	0.659323i	0.991157	−	0.132696i	$-0.0423633\pi$
$439$	7.97572	+	13.8144i	0.380661	+	0.659323i	−0.610496	+	0.792019i	$0.709030\pi$
$440$	3.65491			0.174241
$441$	−6.98901	+	0.392129i	−0.332810	+	0.0186728i
$442$	−5.24799			−0.249621
$443$	14.5631	+	25.2241i	0.691916	+	1.19843i	0.971209	+	0.238228i	$0.0765664\pi$
$443$	14.5631	+	25.2241i	0.691916	+	1.19843i	−0.279294	+	0.960206i	$0.590100\pi$
$444$	3.40823	−	5.90323i	0.161748	−	0.280155i
$445$	3.40823	−	5.90323i	0.161566	−	0.279840i
$446$	−7.98901	−	13.8374i	−0.378291	−	0.655218i
$447$	19.9647			0.944299
$448$	−2.25332	+	1.38656i	−0.106459	+	0.0655087i
$449$	−18.2234			−0.860015			−0.430007	−	0.902825i	$-0.641489\pi$
$449$	−18.2234			−0.860015			−0.430007	+	0.902825i	$0.641489\pi$
$450$	−2.00000	−	3.46410i	−0.0942809	−	0.163299i
$451$	−4.55650	+	7.89209i	−0.214557	+	0.371624i
$452$	−4.58742	+	7.94564i	−0.215774	+	0.373732i
$453$	1.17254	+	2.03091i	0.0550910	+	0.0954203i
$454$	13.9780			0.656021
$455$	−1.98237	−	1.07161i	−0.0929348	−	0.0502378i
$456$	5.50664			0.257872
$457$	−5.13597	−	8.89576i	−0.240251	−	0.416126i	0.720535	−	0.693419i	$-0.243896\pi$
$457$	−5.13597	−	8.89576i	−0.240251	−	0.416126i	−0.960786	+	0.277292i	$0.910563\pi$
$458$	14.2600	−	24.6990i	0.666324	−	1.15411i
$459$	−3.08078	+	5.33606i	−0.143798	+	0.249066i
$460$	0.500000	+	0.866025i	0.0233126	+	0.0403786i
$461$	20.6196			0.960353			0.480176	−	0.877172i	$-0.340573\pi$
$461$	20.6196			0.960353			0.480176	+	0.877172i	$0.340573\pi$
$462$	0.270955	+	9.66619i	0.0126060	+	0.449712i
$463$	15.3098			0.711508			0.355754	−	0.934580i	$-0.384224\pi$
$463$	15.3098			0.711508			0.355754	+	0.934580i	$0.384224\pi$
$464$	−2.07413	−	3.59251i	−0.0962893	−	0.166778i
$465$	1.67919	−	2.90844i	0.0778704	−	0.134876i
$466$	5.56978	−	9.64715i	0.258015	−	0.446896i
$467$	−3.65491	−	6.33049i	−0.169129	−	0.292940i	0.768985	−	0.639267i	$-0.220762\pi$
$467$	−3.65491	−	6.33049i	−0.169129	−	0.292940i	−0.938114	+	0.346327i	$0.887429\pi$
$468$	−0.851731			−0.0393713
$469$	0.767912	+	27.3949i	0.0354589	+	1.26498i
$470$	−2.35837			−0.108784
$471$	−12.4215	−	21.5147i	−0.572353	−	0.991345i
$472$	1.58078	−	2.73799i	0.0727611	−	0.126026i
$473$	13.3584	−	23.1374i	0.614219	−	1.06386i
$474$	5.72905	+	9.92300i	0.263144	+	0.455778i
$475$	−22.0266			−1.01065
$476$	−14.3407	−	7.75218i	−0.657307	−	0.355321i
$477$	6.30982			0.288907
$478$	−8.00000	−	13.8564i	−0.365911	−	0.633777i
$479$	16.5565	−	28.6767i	0.756486	−	1.31027i	−0.188146	−	0.982141i	$-0.560248\pi$
$479$	16.5565	−	28.6767i	0.756486	−	1.31027i	0.944632	−	0.328131i	$-0.106419\pi$
$480$	−0.500000	+	0.866025i	−0.0228218	+	0.0395285i
$481$	2.90290	+	5.02797i	0.132361	+	0.229255i
$482$	−16.5685			−0.754673
$483$	−2.25332	+	1.38656i	−0.102530	+	0.0630906i
$484$	2.35837			0.107199
$485$	−0.222403	−	0.385214i	−0.0100988	−	0.0174917i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	13.6925	−	23.7161i	0.620465	−	1.07468i	−0.368934	−	0.929456i	$-0.620277\pi$
$487$	13.6925	−	23.7161i	0.620465	−	1.07468i	0.989399	−	0.145221i	$-0.0463895\pi$
$488$	5.00000	+	8.66025i	0.226339	+	0.392031i
$489$	22.8430			1.03300
$490$	−3.83410	−	5.85659i	−0.173207	−	0.264574i
$491$	19.8165			0.894304			0.447152	−	0.894458i	$-0.352438\pi$
$491$	19.8165			0.894304			0.447152	+	0.894458i	$0.352438\pi$
$492$	−1.24668	−	2.15931i	−0.0562046	−	0.0973493i
$493$	12.7799	−	22.1354i	0.575577	−	0.996929i
$494$	−2.34509	+	4.06181i	−0.105511	+	0.182750i
$495$	1.82746	+	3.16525i	0.0821380	+	0.142267i
$496$	3.35837			0.150795
$497$	19.0588	−	11.7276i	0.854904	−	0.526056i
$498$	−7.65491			−0.343025
$499$	18.1748	+	31.4797i	0.813617	+	1.40923i	0.910316	+	0.413913i	$0.135838\pi$
$499$	18.1748	+	31.4797i	0.813617	+	1.40923i	−0.0966990	+	0.995314i	$0.530828\pi$
$500$	4.50000	−	7.79423i	0.201246	−	0.348569i
$501$	2.03092	−	3.51765i	0.0907347	−	0.157157i
$502$	15.1373	+	26.2185i	0.675610	+	1.17019i
$503$	−38.9427			−1.73637			−0.868186	−	0.496239i	$-0.834714\pi$
$503$	−38.9427			−1.73637			−0.868186	+	0.496239i	$0.834714\pi$
$504$	−2.32746	−	1.25815i	−0.103673	−	0.0560426i
$505$	1.30982			0.0582863
$506$	1.82746	+	3.16525i	0.0812403	+	0.140712i
$507$	−6.13728	+	10.6301i	−0.272566	+	0.472098i
$508$	4.17254	−	7.22706i	0.185127	−	0.320649i
$509$	−8.08742	−	14.0078i	−0.358469	−	0.620886i	0.629237	−	0.777214i	$-0.283368\pi$
$509$	−8.08742	−	14.0078i	−0.358469	−	0.620886i	−0.987705	+	0.156328i	$0.950034\pi$
$510$	−6.16155			−0.272838
$511$	−0.0997174	−	3.55737i	−0.00441124	−	0.157369i
$512$	−1.00000			−0.0441942
$513$	2.75332	+	4.76889i	0.121562	+	0.210552i
$514$	−7.06314	+	12.2337i	−0.311542	+	0.539606i
$515$	−1.82081	+	3.15374i	−0.0802346	+	0.138970i
$516$	3.65491	+	6.33049i	0.160898	+	0.278684i
$517$	−8.61964			−0.379091
$518$	0.505335	+	18.0276i	0.0222031	+	0.792087i
$519$	3.70346			0.162564
$520$	−0.425866	−	0.737621i	−0.0186754	−	0.0323468i
$521$	10.4890	−	18.1675i	0.459532	−	0.795932i	−0.539404	−	0.842047i	$-0.681351\pi$
$521$	10.4890	−	18.1675i	0.459532	−	0.795932i	0.998936	+	0.0461145i	$0.0146839\pi$
$522$	2.07413	−	3.59251i	0.0907824	−	0.157240i
$523$	13.1306	+	22.7429i	0.574163	+	0.994479i	0.996132	+	0.0878687i	$0.0280056\pi$
$523$	13.1306	+	22.7429i	0.574163	+	0.994479i	−0.421969	+	0.906610i	$0.638661\pi$
$524$	5.09972			0.222782
$525$	9.30982	+	5.03262i	0.406314	+	0.219641i
$526$	15.3098			0.667540
$527$	10.3464	+	17.9205i	0.450696	+	0.780629i
$528$	−1.82746	+	3.16525i	−0.0795298	+	0.137750i
$529$	−0.500000	+	0.866025i	−0.0217391	+	0.0376533i
$530$	3.15491	+	5.46447i	0.137041	+	0.237361i
$531$	3.16155			0.137200
$532$	−12.4082	+	7.63528i	−0.537965	+	0.331031i
$533$	2.12367			0.0919864
$534$	3.40823	+	5.90323i	0.147489	+	0.255458i
$535$	3.17254	−	5.49501i	0.137161	−	0.237570i
$536$	−5.17919	+	8.97061i	−0.223707	+	0.387472i
$537$	7.48901	+	12.9713i	0.323175	+	0.559755i
$538$	22.4714			0.968810
$539$	−14.0133	−	21.4053i	−0.603595	−	0.921993i
$540$	−1.00000			−0.0430331
$541$	−4.08078	−	7.06811i	−0.175446	−	0.303882i	0.764869	−	0.644185i	$-0.222803\pi$
$541$	−4.08078	−	7.06811i	−0.175446	−	0.303882i	−0.940316	+	0.340304i	$0.889470\pi$
$542$	−7.18583	+	12.4462i	−0.308658	+	0.534611i
$543$	−0.851731	+	1.47524i	−0.0365513	+	0.0633087i
$544$	−3.08078	−	5.33606i	−0.132087	−	0.228782i
$545$	3.30982			0.141777
$546$	1.91922	−	1.18098i	0.0821352	−	0.0505411i
$547$	21.7326			0.929221			0.464610	−	0.885515i	$-0.346194\pi$
$547$	21.7326			0.929221			0.464610	+	0.885515i	$0.346194\pi$
$548$	1.47572	+	2.55603i	0.0630398	+	0.109188i
$549$	−5.00000	+	8.66025i	−0.213395	+	0.369611i
$550$	7.30982	−	12.6610i	0.311692	−	0.539866i
$551$	−11.4215	−	19.7826i	−0.486573	−	0.842769i
$552$	−1.00000			−0.0425628
$553$	−26.6682	−	14.4160i	−1.13405	−	0.613032i
$554$	11.9647			0.508333
$555$	3.40823	+	5.90323i	0.144671	+	0.250578i
$556$	−8.01328	+	13.8794i	−0.339839	+	0.588618i
$557$	18.2988	−	31.6945i	0.775346	−	1.34294i	−0.159253	−	0.987238i	$-0.550909\pi$
$557$	18.2988	−	31.6945i	0.775346	−	1.34294i	0.934600	−	0.355701i	$-0.115758\pi$
$558$	1.67919	+	2.90844i	0.0710856	+	0.123124i
$559$	−6.22600			−0.263332
$560$	−0.0741344	−	2.64471i	−0.00313275	−	0.111760i
$561$	−22.5199			−0.950792
$562$	5.52558	+	9.57059i	0.233083	+	0.403711i
$563$	−3.64392	+	6.31145i	−0.153573	+	0.265996i	−0.932538	−	0.361071i	$-0.882411\pi$
$563$	−3.64392	+	6.31145i	−0.153573	+	0.265996i	0.778966	+	0.627067i	$0.215745\pi$
$564$	1.17919	−	2.04241i	0.0496527	−	0.0860010i
$565$	−4.58742	−	7.94564i	−0.192994	−	0.334276i
$566$	−3.93816			−0.165533
$567$	−0.0741344	−	2.64471i	−0.00311335	−	0.111067i
$568$	8.45809			0.354894
$569$	6.67254	+	11.5572i	0.279728	+	0.484502i	0.971317	−	0.237788i	$-0.0764225\pi$
$569$	6.67254	+	11.5572i	0.279728	+	0.484502i	−0.691589	+	0.722291i	$0.743089\pi$
$570$	−2.75332	+	4.76889i	−0.115324	+	0.199747i
$571$	15.7975	−	27.3621i	0.661106	−	1.14507i	−0.319220	−	0.947681i	$-0.603421\pi$
$571$	15.7975	−	27.3621i	0.661106	−	1.14507i	0.980325	−	0.197388i	$-0.0632459\pi$
$572$	−1.55650	−	2.69594i	−0.0650806	−	0.112723i
$573$	22.8430			0.954281
$574$	5.80318	+	3.13703i	0.242220	+	0.130937i
$575$	4.00000			0.166812
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−0.369365	+	0.639759i	−0.0153769	+	0.0266335i	−0.873611	−	0.486624i	$-0.838228\pi$
$577$	−0.369365	+	0.639759i	−0.0153769	+	0.0266335i	0.858235	+	0.513258i	$0.171561\pi$
$578$	10.4824	−	18.1560i	0.436009	−	0.755190i
$579$	−8.95809	−	15.5159i	−0.372286	−	0.644817i
$580$	4.14827			0.172247
$581$	17.2490	−	10.6140i	0.715608	−	0.440342i
$582$	0.444807			0.0184378
$583$	11.5309	+	19.9721i	0.477562	+	0.827161i
$584$	0.672545	−	1.16488i	0.0278301	−	0.0482031i
$585$	0.425866	−	0.737621i	0.0176074	−	0.0304969i
$586$	6.51328	+	11.2813i	0.269061	+	0.466028i
$587$	−42.2367			−1.74329			−0.871647	−	0.490134i	$-0.836948\pi$
$587$	−42.2367			−1.74329			−0.871647	+	0.490134i	$0.836948\pi$
$588$	6.98901	−	0.392129i	0.288222	−	0.0161711i
$589$	18.4934			0.762006
$590$	1.58078	+	2.73799i	0.0650795	+	0.112721i
$591$	2.50664	−	4.34163i	0.103109	−	0.178591i
$592$	−3.40823	+	5.90323i	−0.140077	+	0.242621i
$593$	0.331805	+	0.574704i	0.0136256	+	0.0236002i	0.872758	−	0.488153i	$-0.162329\pi$
$593$	0.331805	+	0.574704i	0.0136256	+	0.0236002i	−0.859132	+	0.511754i	$0.828996\pi$
$594$	−3.65491			−0.149963
$595$	13.8840	−	8.54335i	0.569187	−	0.350243i
$596$	−19.9647			−0.817787
$597$	7.16155	+	12.4042i	0.293103	+	0.507669i
$598$	0.425866	−	0.737621i	0.0174149	−	0.0301636i
$599$	−14.9458	+	25.8869i	−0.610668	+	1.05771i	0.380459	+	0.924798i	$0.375766\pi$
$599$	−14.9458	+	25.8869i	−0.610668	+	1.05771i	−0.991128	+	0.132911i	$0.957567\pi$
$600$	2.00000	+	3.46410i	0.0816497	+	0.141421i
$601$	−18.9647			−0.773588			−0.386794	−	0.922166i	$-0.626417\pi$
$601$	−18.9647			−0.773588			−0.386794	+	0.922166i	$0.626417\pi$
$602$	−17.0133	−	9.19688i	−0.693410	−	0.374837i
$603$	−10.3584			−0.421826
$604$	−1.17254	−	2.03091i	−0.0477102	−	0.0826364i
$605$	−1.17919	+	2.04241i	−0.0479408	+	0.0830358i
$606$	−0.654911	+	1.13434i	−0.0266039	+	0.0460794i
$607$	−11.7789	−	20.4017i	−0.478091	−	0.828078i	0.521594	−	0.853194i	$-0.325338\pi$
$607$	−11.7789	−	20.4017i	−0.478091	−	0.828078i	−0.999685	+	0.0251162i	$0.992004\pi$
$608$	−5.50664			−0.223324
$609$	0.307530	+	10.9710i	0.0124617	+	0.444566i
$610$	−10.0000			−0.404888
$611$	1.00435	+	1.73959i	0.0406316	+	0.0703761i
$612$	3.08078	−	5.33606i	0.124533	−	0.215697i
$613$	21.9647	−	38.0440i	0.887147	−	1.53658i	0.0439145	−	0.999035i	$-0.486017\pi$
$613$	21.9647	−	38.0440i	0.887147	−	1.53658i	0.843233	−	0.537549i	$-0.180650\pi$
$614$	−12.7048	−	22.0053i	−0.512723	−	0.888062i
$615$	2.49336			0.100542
$616$	−0.270955	−	9.66619i	−0.0109171	−	0.389462i
$617$	30.2878			1.21934			0.609671	−	0.792654i	$-0.291301\pi$
$617$	30.2878			1.21934			0.609671	+	0.792654i	$0.291301\pi$
$618$	−1.82081	−	3.15374i	−0.0732439	−	0.126862i
$619$	12.4524	−	21.5682i	0.500506	−	0.866901i	−0.499494	−	0.866317i	$-0.666481\pi$
$619$	12.4524	−	21.5682i	0.500506	−	0.866901i	1.00000		0.000583862i	$-0.000185849\pi$
$620$	−1.67919	+	2.90844i	−0.0674378	+	0.116806i
$621$	−0.500000	−	0.866025i	−0.0200643	−	0.0347524i
$622$	5.54191			0.222210
$623$	−15.8650	−	8.57616i	−0.635618	−	0.343597i
$624$	0.851731			0.0340965
$625$	−5.50000	−	9.52628i	−0.220000	−	0.381051i
$626$	9.58078	−	16.5944i	0.382925	−	0.663245i
$627$	−10.0631	+	17.4299i	−0.401883	+	0.696082i
$628$	12.4215	+	21.5147i	0.495672	+	0.858530i
$629$	−42.0000			−1.67465
$630$	2.25332	−	1.38656i	0.0897745	−	0.0552418i
$631$	−28.4095			−1.13097			−0.565483	−	0.824760i	$-0.691310\pi$
$631$	−28.4095			−1.13097			−0.565483	+	0.824760i	$0.691310\pi$
$632$	−5.72905	−	9.92300i	−0.227889	−	0.394716i
$633$	−4.50664	+	7.80573i	−0.179123	+	0.310250i
$634$	4.28424	−	7.42052i	0.170149	−	0.294706i
$635$	4.17254	+	7.22706i	0.165582	+	0.286797i
$636$	−6.30982			−0.250201
$637$	−2.68714	+	5.32223i	−0.106468	+	0.210875i
$638$	15.1616			0.600252
$639$	4.22905	+	7.32492i	0.167298	+	0.289769i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	7.52558	−	13.0347i	0.297243	−	0.514839i	−0.678261	−	0.734821i	$-0.737266\pi$
$641$	7.52558	−	13.0347i	0.297243	−	0.514839i	0.975504	+	0.219981i	$0.0705996\pi$
$642$	3.17254	+	5.49501i	0.125210	+	0.216871i
$643$	9.80318			0.386600			0.193300	−	0.981140i	$-0.438081\pi$
$643$	9.80318			0.386600			0.193300	+	0.981140i	$0.438081\pi$
$644$	2.25332	−	1.38656i	0.0887933	−	0.0546381i
$645$	−7.30982			−0.287824
$646$	−16.9647	−	29.3838i	−0.667468	−	1.15609i
$647$	15.7546	−	27.2878i	0.619378	−	1.07279i	−0.370221	−	0.928944i	$-0.620718\pi$
$647$	15.7546	−	27.2878i	0.619378	−	1.07279i	0.989599	−	0.143851i	$-0.0459486\pi$
$648$	0.500000	−	0.866025i	0.0196419	−	0.0340207i
$649$	5.77760	+	10.0071i	0.226791	+	0.392813i
$650$	−3.40692			−0.133631
$651$	−7.81646	−	4.22535i	−0.306351	−	0.165605i
$652$	−22.8430			−0.894602
$653$	20.7556	+	35.9498i	0.812230	+	1.40682i	0.911300	+	0.411743i	$0.135080\pi$
$653$	20.7556	+	35.9498i	0.812230	+	1.40682i	−0.0990701	+	0.995080i	$0.531587\pi$
$654$	−1.65491	+	2.86639i	−0.0647121	+	0.112085i
$655$	−2.54986	+	4.41648i	−0.0996312	+	0.172566i
$656$	1.24668	+	2.15931i	0.0486746	+	0.0843069i
$657$	1.34509			0.0524769
$658$	0.174837	+	6.23722i	0.00681584	+	0.243152i
$659$	−43.6329			−1.69970			−0.849849	−	0.527027i	$-0.823307\pi$
$659$	−43.6329			−1.69970			−0.849849	+	0.527027i	$0.823307\pi$
$660$	−1.82746	−	3.16525i	−0.0711336	−	0.123207i
$661$	−18.9913	+	32.8939i	−0.738676	+	1.27942i	0.214416	+	0.976742i	$0.431215\pi$
$661$	−18.9913	+	32.8939i	−0.738676	+	1.27942i	−0.953092	+	0.302682i	$0.902118\pi$
$662$	8.56978	−	14.8433i	0.333074	−	0.576901i
$663$	2.62399	+	4.54489i	0.101907	+	0.176509i
$664$	7.65491			0.297068
$665$	−0.408232	−	14.5635i	−0.0158305	−	0.564748i
$666$	−6.81646			−0.264133
$667$	2.07413	+	3.59251i	0.0803108	+	0.139102i
$668$	−2.03092	+	3.51765i	−0.0785786	+	0.136102i
$669$	−7.98901	+	13.8374i	−0.308873	+	0.534984i
$670$	−5.17919	−	8.97061i	−0.200089	−	0.346565i
$671$	−36.5491			−1.41096
$672$	2.32746	+	1.25815i	0.0897835	+	0.0485343i
$673$	36.2040			1.39556			0.697781	−	0.716311i	$-0.254171\pi$
$673$	36.2040			1.39556			0.697781	+	0.716311i	$0.254171\pi$
$674$	−7.28424	−	12.6167i	−0.280578	−	0.485976i
$675$	−2.00000	+	3.46410i	−0.0769800	+	0.133333i
$676$	6.13728	−	10.6301i	0.236049	−	0.408849i
$677$	14.8098	+	25.6514i	0.569188	+	0.985862i	0.996647	+	0.0818272i	$0.0260756\pi$
$677$	14.8098	+	25.6514i	0.569188	+	0.985862i	−0.427459	+	0.904035i	$0.640591\pi$
$678$	9.17484			0.352357
$679$	−1.00229	+	0.616750i	−0.0384644	+	0.0236687i
$680$	6.16155			0.236285
$681$	−6.98901	−	12.1053i	−0.267819	−	0.463877i
$682$	−6.13728	+	10.6301i	−0.235008	+	0.407047i
$683$	−18.4282	+	31.9185i	−0.705134	+	1.22133i	0.261509	+	0.965201i	$0.415780\pi$
$683$	−18.4282	+	31.9185i	−0.705134	+	1.22133i	−0.966643	+	0.256127i	$0.917554\pi$
$684$	−2.75332	−	4.76889i	−0.105276	−	0.182343i
$685$	−2.95145			−0.112769
$686$	−15.2048	+	10.5743i	−0.580521	+	0.403727i
$687$	−28.5199			−1.08810
$688$	−3.65491	−	6.33049i	−0.139342	−	0.241348i
$689$	2.68714	−	4.65426i	0.102372	−	0.177313i
$690$	0.500000	−	0.866025i	0.0190347	−	0.0329690i
$691$	6.27325	+	10.8656i	0.238646	+	0.413346i	0.960326	−	0.278880i	$-0.0899633\pi$
$691$	6.27325	+	10.8656i	0.238646	+	0.413346i	−0.721680	+	0.692226i	$0.756630\pi$
$692$	−3.70346			−0.140785
$693$	8.23569	−	5.06775i	0.312848	−	0.192508i
$694$	−7.04855			−0.267559
$695$	−8.01328	−	13.8794i	−0.303961	−	0.526476i
$696$	−2.07413	+	3.59251i	−0.0786199	+	0.136174i
$697$	−7.68148	+	13.3047i	−0.290957	+	0.503952i
$698$	11.2290	+	19.4493i	0.425026	+	0.736166i
$699$	−11.1396			−0.421337
$700$	−9.30982	−	5.03262i	−0.351878	−	0.190215i
$701$	−12.6769			−0.478800			−0.239400	−	0.970921i	$-0.576951\pi$
$701$	−12.6769			−0.478800			−0.239400	+	0.970921i	$0.576951\pi$
$702$	0.425866	+	0.737621i	0.0160733	+	0.0278397i
$703$	−18.7679	+	32.5070i	−0.707845	+	1.22602i
$704$	1.82746	−	3.16525i	0.0688748	−	0.119295i
$705$	1.17919	+	2.04241i	0.0444107	+	0.0769216i
$706$	−11.1396			−0.419243
$707$	−0.0971029	−	3.46410i	−0.00365193	−	0.130281i
$708$	−3.16155			−0.118818
$709$	14.0146	+	24.2740i	0.526329	+	0.911629i	0.999529	+	0.0306738i	$0.00976531\pi$
$709$	14.0146	+	24.2740i	0.526329	+	0.911629i	−0.473200	+	0.880955i	$0.656901\pi$
$710$	−4.22905	+	7.32492i	−0.158713	+	0.274899i
$711$	5.72905	−	9.92300i	0.214856	−	0.372141i
$712$	−3.40823	−	5.90323i	−0.127729	−	0.221233i
$713$	−3.35837			−0.125772
$714$	0.456783	+	16.2955i	0.0170947	+	0.609845i
$715$	3.11300			0.116420
$716$	−7.48901	−	12.9713i	−0.279877	−	0.484762i
$717$	−8.00000	+	13.8564i	−0.298765	+	0.517477i
$718$	−14.0133	+	24.2717i	−0.522971	+	0.905813i
$719$	7.63728	+	13.2282i	0.284822	+	0.493327i	0.972566	−	0.232627i	$-0.0747320\pi$
$719$	7.63728	+	13.2282i	0.284822	+	0.493327i	−0.687744	+	0.725954i	$0.741399\pi$
$720$	1.00000			0.0372678
$721$	8.47572	+	4.58173i	0.315652	+	0.170632i
$722$	−11.3231			−0.421402
$723$	8.28424	+	14.3487i	0.308094	+	0.533635i
$724$	0.851731	−	1.47524i	0.0316543	−	0.0548269i
$725$	8.29654	−	14.3700i	0.308126	−	0.533689i
$726$	−1.17919	−	2.04241i	−0.0437637	−	0.0758010i
$727$	−2.51534			−0.0932889			−0.0466444	−	0.998912i	$-0.514853\pi$
$727$	−2.51534			−0.0932889			−0.0466444	+	0.998912i	$0.514853\pi$
$728$	−1.91922	+	1.18098i	−0.0711312	+	0.0437698i
$729$	1.00000			0.0370370
$730$	0.672545	+	1.16488i	0.0248920	+	0.0431142i
$731$	22.5199	−	39.0057i	0.832930	−	1.44268i
$732$	5.00000	−	8.66025i	0.184805	−	0.320092i
$733$	−22.4348	−	38.8582i	−0.828648	−	1.43526i	−0.899099	−	0.437746i	$-0.855777\pi$
$733$	−22.4348	−	38.8582i	−0.828648	−	1.43526i	0.0704507	−	0.997515i	$-0.477556\pi$
$734$	7.78990			0.287530
$735$	−3.15491	+	6.24872i	−0.116371	+	0.230488i
$736$	1.00000			0.0368605
$737$	−18.9295	−	32.7868i	−0.697276	−	1.20772i
$738$	−1.24668	+	2.15931i	−0.0458909	+	0.0794854i
$739$	−17.4847	+	30.2843i	−0.643184	+	1.11403i	0.341534	+	0.939869i	$0.389053\pi$
$739$	−17.4847	+	30.2843i	−0.643184	+	1.11403i	−0.984718	+	0.174157i	$0.944280\pi$
$740$	−3.40823	−	5.90323i	−0.125289	−	0.217007i
$741$	4.69018			0.172298
$742$	14.2181	−	8.74894i	0.521961	−	0.321184i
$743$	−39.4627			−1.44775			−0.723873	−	0.689934i	$-0.757640\pi$
$743$	−39.4627			−1.44775			−0.723873	+	0.689934i	$0.757640\pi$
$744$	−1.67919	−	2.90844i	−0.0615620	−	0.106628i
$745$	9.98237	−	17.2900i	0.365726	−	0.633455i
$746$	6.35837	−	11.0130i	0.232797	−	0.403216i
$747$	3.82746	+	6.62935i	0.140039	+	0.242555i
$748$	22.5199			0.823410
$749$	−14.7679	−	7.98310i	−0.539608	−	0.291696i
$750$	−9.00000			−0.328634
$751$	−9.53222	−	16.5103i	−0.347836	−	0.602469i	0.638029	−	0.770012i	$-0.279750\pi$
$751$	−9.53222	−	16.5103i	−0.347836	−	0.602469i	−0.985865	+	0.167543i	$0.946417\pi$
$752$	−1.17919	+	2.04241i	−0.0430005	+	0.0744791i
$753$	15.1373	−	26.2185i	0.551633	−	0.955456i
$754$	−1.76660	−	3.05985i	−0.0643360	−	0.111433i
$755$	2.34509			0.0853465
$756$	0.0741344	+	2.64471i	0.00269624	+	0.0961873i
$757$	13.2101			0.480129			0.240065	−	0.970757i	$-0.422831\pi$
$757$	13.2101			0.480129			0.240065	+	0.970757i	$0.422831\pi$
$758$	−11.1306	−	19.2788i	−0.404283	−	0.700238i
$759$	1.82746	−	3.16525i	0.0663324	−	0.114891i
$760$	2.75332	−	4.76889i	0.0998734	−	0.172986i
$761$	−25.1761	−	43.6064i	−0.912635	−	1.58073i	−0.810328	−	0.585976i	$-0.800711\pi$
$761$	−25.1761	−	43.6064i	−0.912635	−	1.58073i	−0.102306	−	0.994753i	$-0.532622\pi$
$762$	−8.34509			−0.302311
$763$	−0.245372	−	8.75353i	−0.00888305	−	0.316899i
$764$	−22.8430			−0.826432
$765$	3.08078	+	5.33606i	0.111386	+	0.192926i
$766$	−11.1117	+	19.2460i	−0.401482	+	0.695387i
$767$	1.34640	−	2.33203i	0.0486156	−	0.0842046i
$768$	0.500000	+	0.866025i	0.0180422	+	0.0312500i
$769$	42.4008			1.52901			0.764507	−	0.644616i	$-0.222983\pi$
$769$	42.4008			1.52901			0.764507	+	0.644616i	$0.222983\pi$
$770$	8.50664	+	4.59844i	0.306558	+	0.165716i
$771$	14.1263			0.508746
$772$	8.95809	+	15.5159i	0.322409	+	0.558428i
$773$	−8.83410	+	15.3011i	−0.317740	+	0.550343i	−0.980016	−	0.198918i	$-0.936257\pi$
$773$	−8.83410	+	15.3011i	−0.317740	+	0.550343i	0.662276	+	0.749260i	$0.269591\pi$
$774$	3.65491	−	6.33049i	0.131373	−	0.227545i
$775$	6.71675	+	11.6337i	0.241273	+	0.417896i
$776$	−0.444807			−0.0159676
$777$	15.3597	−	9.45143i	0.551025	−	0.339068i
$778$	30.7433			1.10220
$779$	6.86502	+	11.8906i	0.245965	+	0.426023i
$780$	−0.425866	+	0.737621i	−0.0152484	+	0.0264111i
$781$	−15.4568	+	26.7719i	−0.553087	+	0.957975i
$782$	3.08078	+	5.33606i	0.110168	+	0.190817i
$783$	−4.14827			−0.148247
$784$	−6.98901	+	0.392129i	−0.249607	+	0.0140046i
$785$	−24.8430			−0.886686
$786$	−2.54986	−	4.41648i	−0.0909504	−	0.157531i
$787$	−14.6858	+	25.4366i	−0.523493	+	0.906717i	0.476133	+	0.879373i	$0.342038\pi$
$787$	−14.6858	+	25.4366i	−0.523493	+	0.906717i	−0.999626	+	0.0273435i	$0.991295\pi$
$788$	−2.50664	+	4.34163i	−0.0892954	+	0.154664i
$789$	−7.65491	−	13.2587i	−0.272522	−	0.472022i
$790$	11.4581			0.407661
$791$	−20.6739	+	12.7214i	−0.735078	+	0.452323i
$792$	3.65491			0.129872
$793$	4.25866	+	7.37621i	0.151229	+	0.261937i
$794$	−3.08078	+	5.33606i	−0.109333	+	0.189370i
$795$	3.15491	−	5.46447i	0.111893	−	0.193805i
$796$	−7.16155	−	12.4042i	−0.253835	−	0.439654i
$797$	−12.6064			−0.446540			−0.223270	−	0.974757i	$-0.571673\pi$
$797$	−12.6064			−0.446540			−0.223270	+	0.974757i	$0.571673\pi$
$798$	12.8165	+	6.92820i	0.453698	+	0.245256i
$799$	−14.5312			−0.514078
$800$	−2.00000	−	3.46410i	−0.0707107	−	0.122474i
$801$	3.40823	−	5.90323i	0.120424	−	0.208580i
$802$	−7.98237	+	13.8259i	−0.281867	+	0.488208i
$803$	2.45809	+	4.25754i	0.0867441	+	0.150245i
$804$	10.3584			0.365312
$805$	0.0741344	+	2.64471i	0.00261290	+	0.0932139i
$806$	2.86043			0.100754
$807$	−11.2357	−	19.4608i	−0.395515	−	0.685052i
$808$	0.654911	−	1.13434i	0.0230397	−	0.0399059i
$809$	−18.2247	+	31.5661i	−0.640746	+	1.10980i	0.344520	+	0.938779i	$0.388042\pi$
$809$	−18.2247	+	31.5661i	−0.640746	+	1.10980i	−0.985267	+	0.171026i	$0.945292\pi$
$810$	0.500000	+	0.866025i	0.0175682	+	0.0304290i
$811$	22.6462			0.795216			0.397608	−	0.917555i	$-0.369840\pi$
$811$	22.6462			0.795216			0.397608	+	0.917555i	$0.369840\pi$
$812$	−0.307530	−	10.9710i	−0.0107922	−	0.385006i
$813$	14.3717			0.504036
$814$	−12.4568	−	21.5758i	−0.436610	−	0.756231i
$815$	11.4215	−	19.7826i	0.400078	−	0.692956i
$816$	−3.08078	+	5.33606i	−0.107849	+	0.186800i
$817$	−20.1263	−	34.8597i	−0.704130	−	1.21959i
$818$	14.7300			0.515023
$819$	−1.98237	−	1.07161i	−0.0692695	−	0.0374450i
$820$	−2.49336			−0.0870718
$821$	17.0741	+	29.5733i	0.595891	+	1.03211i	0.993420	+	0.114525i	$0.0365345\pi$
$821$	17.0741	+	29.5733i	0.595891	+	1.03211i	−0.397529	+	0.917590i	$0.630132\pi$
$822$	1.47572	−	2.55603i	0.0514718	−	0.0891518i
$823$	2.06184	−	3.57120i	0.0718711	−	0.124484i	−0.827850	−	0.560949i	$-0.810436\pi$
$823$	2.06184	−	3.57120i	0.0718711	−	0.124484i	0.899721	+	0.436465i	$0.143770\pi$
$824$	1.82081	+	3.15374i	0.0634310	+	0.109866i
$825$	−14.6196			−0.508991
$826$	7.12399	−	4.38368i	0.247875	−	0.152528i
$827$	−50.6508			−1.76130			−0.880650	−	0.473767i	$-0.842894\pi$
$827$	−50.6508			−1.76130			−0.880650	+	0.473767i	$0.842894\pi$
$828$	0.500000	+	0.866025i	0.0173762	+	0.0300965i
$829$	−23.9471	+	41.4776i	−0.831717	+	1.44058i	0.0649584	+	0.997888i	$0.479309\pi$
$829$	−23.9471	+	41.4776i	−0.831717	+	1.44058i	−0.896676	+	0.442688i	$0.854025\pi$
$830$	−3.82746	+	6.62935i	−0.132853	+	0.230108i
$831$	−5.98237	−	10.3618i	−0.207526	−	0.359446i
$832$	−0.851731			−0.0295285
$833$	−23.6240	−	36.0857i	−0.818523	−	1.25030i
$834$	16.0266			0.554955
$835$	−2.03092	−	3.51765i	−0.0702828	−	0.121733i
$836$	10.0631	−	17.4299i	0.348041	−	0.602825i
$837$	1.67919	−	2.90844i	0.0580412	−	0.100530i
$838$	12.4714	+	21.6011i	0.430816	+	0.746196i
$839$	14.7899			0.510604			0.255302	−	0.966861i	$-0.417825\pi$
$839$	14.7899			0.510604			0.255302	+	0.966861i	$0.417825\pi$
$840$	−2.25332	+	1.38656i	−0.0777470	+	0.0478408i
$841$	−11.7919			−0.406616
$842$	16.1748	+	28.0156i	0.557422	+	0.965483i
$843$	5.52558	−	9.57059i	0.190311	−	0.329629i
$844$	4.50664	−	7.80573i	0.155125	−	0.268684i
$845$	6.13728	+	10.6301i	0.211129	+	0.365686i
$846$	−2.35837			−0.0810825
$847$	5.48901	+	2.96720i	0.188605	+	0.101954i
$848$	6.30982			0.216680
$849$	1.96908	+	3.41055i	0.0675787	+	0.117050i
$850$	12.3231	−	21.3442i	0.422679	−	0.732102i
$851$	3.40823	−	5.90323i	0.116833	−	0.202360i
$852$	−4.22905	−	7.32492i	−0.144885	−	0.250948i
$853$	−21.6064			−0.739788			−0.369894	−	0.929074i	$-0.620606\pi$
$853$	−21.6064			−0.739788			−0.369894	+	0.929074i	$0.620606\pi$
$854$	0.741344	+	26.4471i	0.0253683	+	0.905002i
$855$	5.50664			0.188323
$856$	−3.17254	−	5.49501i	−0.108435	−	0.187816i
$857$	−6.86632	+	11.8928i	−0.234549	+	0.406251i	−0.959142	−	0.282927i	$-0.908695\pi$
$857$	−6.86632	+	11.8928i	−0.234549	+	0.406251i	0.724592	+	0.689178i	$0.242028\pi$
$858$	−1.55650	+	2.69594i	−0.0531381	+	0.0920378i
$859$	17.8929	+	30.9914i	0.610498	+	1.05741i	0.991157	+	0.132697i	$0.0423638\pi$
$859$	17.8929	+	30.9914i	0.610498	+	1.05741i	−0.380659	+	0.924715i	$0.624303\pi$
$860$	7.30982			0.249263
$861$	−0.184844	−	6.59422i	−0.00629946	−	0.224730i
$862$	−4.59308			−0.156441
$863$	−3.04551	−	5.27498i	−0.103670	−	0.179562i	0.809524	−	0.587087i	$-0.199725\pi$
$863$	−3.04551	−	5.27498i	−0.103670	−	0.179562i	−0.913194	+	0.407525i	$0.866392\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	1.85173	−	3.20729i	0.0629607	−	0.109051i
$866$	13.6196	+	23.5899i	0.462814	+	0.801618i
$867$	−20.9647			−0.712000
$868$	7.81646	+	4.22535i	0.265308	+	0.143418i
$869$	41.8783			1.42062
$870$	−2.07413	−	3.59251i	−0.0703197	−	0.121797i
$871$	−4.41127	+	7.64055i	−0.149470	+	0.258890i
$872$	1.65491	−	2.86639i	0.0560424	−	0.0970682i
$873$	−0.222403	−	0.385214i	−0.00752721	−	0.0130375i
$874$	5.50664			0.186265
$875$	20.2799	−	12.4790i	0.685585	−	0.421868i
$876$	−1.34509			−0.0454464
$877$	19.2423	+	33.3287i	0.649767	+	1.12543i	0.983178	+	0.182648i	$0.0584670\pi$
$877$	19.2423	+	33.3287i	0.649767	+	1.12543i	−0.333411	+	0.942782i	$0.608200\pi$
$878$	−7.97572	+	13.8144i	−0.269168	+	0.466212i
$879$	6.51328	−	11.2813i	0.219688	−	0.380510i
$880$	1.82746	+	3.16525i	0.0616035	+	0.106700i
$881$	−21.9647			−0.740011			−0.370005	−	0.929030i	$-0.620644\pi$
$881$	−21.9647			−0.740011			−0.370005	+	0.929030i	$0.620644\pi$
$882$	−3.83410	−	5.85659i	−0.129101	−	0.197202i
$883$	−16.4228			−0.552672			−0.276336	−	0.961061i	$-0.589120\pi$
$883$	−16.4228			−0.552672			−0.276336	+	0.961061i	$0.589120\pi$
$884$	−2.62399	−	4.54489i	−0.0882544	−	0.152861i
$885$	1.58078	−	2.73799i	0.0531372	−	0.0920364i
$886$	−14.5631	+	25.2241i	−0.489258	+	0.847420i
$887$	−8.69018	−	15.0518i	−0.291788	−	0.505391i	0.682445	−	0.730937i	$-0.260917\pi$
$887$	−8.69018	−	15.0518i	−0.291788	−	0.505391i	−0.974233	+	0.225546i	$0.927583\pi$
$888$	6.81646			0.228746
$889$	18.8042	−	11.5710i	0.630671	−	0.388077i
$890$	6.81646			0.228488
$891$	1.82746	+	3.16525i	0.0612221	+	0.106040i
$892$	7.98901	−	13.8374i	0.267492	−	0.463309i
$893$	−6.49336	+	11.2468i	−0.217292	+	0.376361i
$894$	9.98237	+	17.2900i	0.333860	+	0.578263i
$895$	14.9780			0.500660
$896$	−2.32746	−	1.25815i	−0.0777548	−	0.0420320i
$897$	−0.851731			−0.0284385
$898$	−9.11169	−	15.7819i	−0.304061	−	0.526649i
$899$	−6.96572	+	12.0650i	−0.232320	+	0.402389i
$900$	2.00000	−	3.46410i	0.0666667	−	0.115470i
$901$	19.4391	+	33.6696i	0.647612	+	1.12170i
$902$	−9.11300			−0.303430
$903$	0.541909	+	19.3324i	0.0180336	+	0.643341i
$904$	−9.17484			−0.305151
$905$	0.851731	+	1.47524i	0.0283125	+	0.0490387i
$906$	−1.17254	+	2.03091i	−0.0389552	+	0.0674724i
$907$	9.42587	−	16.3261i	0.312981	−	0.542099i	−0.666025	−	0.745929i	$-0.732006\pi$
$907$	9.42587	−	16.3261i	0.312981	−	0.542099i	0.979006	+	0.203830i	$0.0653391\pi$
$908$	6.98901	+	12.1053i	0.231938	+	0.401729i
$909$	1.30982			0.0434440
$910$	−0.0631426	−	2.25258i	−0.00209316	−	0.0746724i
$911$	57.9826			1.92105			0.960525	−	0.278195i	$-0.0897361\pi$
$911$	57.9826			1.92105			0.960525	+	0.278195i	$0.0897361\pi$
$912$	2.75332	+	4.76889i	0.0911716	+	0.157914i
$913$	−13.9890	+	24.2297i	−0.462969	+	0.801885i
$914$	5.13597	−	8.89576i	0.169883	−	0.294246i
$915$	5.00000	+	8.66025i	0.165295	+	0.286299i
$916$	28.5199			0.942325
$917$	11.8694	+	6.41623i	0.391961	+	0.211883i
$918$	−6.16155			−0.203362
$919$	−19.1306	−	33.1352i	−0.631061	−	1.09303i	−0.987335	−	0.158649i	$-0.949286\pi$
$919$	−19.1306	−	33.1352i	−0.631061	−	1.09303i	0.356274	−	0.934382i	$-0.384047\pi$
$920$	−0.500000	+	0.866025i	−0.0164845	+	0.0285520i
$921$	−12.7048	+	22.0053i	−0.418636	+	0.725099i
$922$	10.3098	+	17.8571i	0.339536	+	0.588093i
$923$	7.20402			0.237123
$924$	−8.23569	+	5.06775i	−0.270934	+	0.166717i
$925$	−27.2659			−0.896496
$926$	7.65491	+	13.2587i	0.251556	+	0.435708i
$927$	−1.82081	+	3.15374i	−0.0598034	+	0.103582i
$928$	2.07413	−	3.59251i	0.0680868	−	0.117930i
$929$	21.9414	+	38.0037i	0.719875	+	1.24686i	0.961049	+	0.276379i	$0.0891344\pi$
$929$	21.9414	+	38.0037i	0.719875	+	1.24686i	−0.241173	+	0.970482i	$0.577532\pi$
$930$	3.35837			0.110125
$931$	−38.4860	+	2.15931i	−1.26133	+	0.0707686i
$932$	11.1396			0.364889
$933$	−2.77095	−	4.79943i	−0.0907170	−	0.157126i
$934$	3.65491	−	6.33049i	0.119592	−	0.207140i
$935$	−11.2600	+	19.5028i	−0.368240	+	0.637811i
$936$	−0.425866	−	0.737621i	−0.0139199	−	0.0241099i
$937$	−56.6974			−1.85222			−0.926111	−	0.377250i	$-0.876870\pi$
$937$	−56.6974			−1.85222			−0.926111	+	0.377250i	$0.876870\pi$
$938$	−23.3407	+	14.3625i	−0.762102	+	0.468952i
$939$	−19.1616			−0.625314
$940$	−1.17919	−	2.04241i	−0.0384608	−	0.0666161i
$941$	−21.1373	+	36.6108i	−0.689056	+	1.19348i	0.283088	+	0.959094i	$0.408641\pi$
$941$	−21.1373	+	36.6108i	−0.689056	+	1.19348i	−0.972144	+	0.234385i	$0.924692\pi$
$942$	12.4215	−	21.5147i	0.404715	−	0.700987i
$943$	−1.24668	−	2.15931i	−0.0405975	−	0.0703169i
$944$	3.16155			0.102900
$945$	−2.32746	−	1.25815i	−0.0757121	−	0.0409278i
$946$	26.7167			0.868636
$947$	18.0309	+	31.2305i	0.585926	+	1.01485i	0.994759	+	0.102245i	$0.0326025\pi$
$947$	18.0309	+	31.2305i	0.585926	+	1.01485i	−0.408833	+	0.912609i	$0.634064\pi$
$948$	−5.72905	+	9.92300i	−0.186071	+	0.322284i
$949$	0.572827	−	0.992166i	0.0185948	−	0.0322071i
$950$	−11.0133	−	19.0756i	−0.357318	−	0.618893i
$951$	−8.56848			−0.277852
$952$	−0.456783	−	16.2955i	−0.0148044	−	0.528141i
$953$	29.0133			0.939832			0.469916	−	0.882711i	$-0.344284\pi$
$953$	29.0133			0.939832			0.469916	+	0.882711i	$0.344284\pi$
$954$	3.15491	+	5.46447i	0.102144	+	0.176919i
$955$	11.4215	−	19.7826i	0.369592	−	0.640151i
$956$	8.00000	−	13.8564i	0.258738	−	0.448148i
$957$	−7.58078	−	13.1303i	−0.245052	−	0.424442i
$958$	33.1130			1.06983
$959$	0.218804	+	7.80573i	0.00706555	+	0.252060i
$960$	−1.00000			−0.0322749
$961$	9.86067	+	17.0792i	0.318086	+	0.550941i
$962$	−2.90290	+	5.02797i	−0.0935932	+	0.162108i
$963$	3.17254	−	5.49501i	0.102234	−	0.177074i
$964$	−8.28424	−	14.3487i	−0.266817	−	0.462141i
$965$	−17.9162			−0.576742
$966$	−2.32746	−	1.25815i	−0.0748847	−	0.0404804i
$967$	35.5844			1.14432			0.572158	−	0.820143i	$-0.306106\pi$
$967$	35.5844			1.14432			0.572158	+	0.820143i	$0.306106\pi$
$968$	1.17919	+	2.04241i	0.0379005	+	0.0656456i
$969$	−16.9647	+	29.3838i	−0.544986	+	0.943943i
$970$	0.222403	−	0.385214i	0.00714094	−	0.0123685i
$971$	12.8275	+	22.2178i	0.411653	+	0.713003i	0.995071	−	0.0991688i	$-0.0316184\pi$
$971$	12.8275	+	22.2178i	0.411653	+	0.713003i	−0.583418	+	0.812172i	$0.698285\pi$
$972$	−1.00000			−0.0320750
$973$	−36.1130	+	22.2218i	−1.15773	+	0.712397i
$974$	27.3849			0.877470
$975$	1.70346	+	2.95048i	0.0545545	+	0.0944911i
$976$	−5.00000	+	8.66025i	−0.160046	+	0.277208i
$977$	−9.53756	+	16.5195i	−0.305134	+	0.528507i	−0.977291	−	0.211901i	$-0.932034\pi$
$977$	−9.53756	+	16.5195i	−0.305134	+	0.528507i	0.672157	+	0.740408i	$0.265368\pi$
$978$	11.4215	+	19.7826i	0.365220	+	0.632579i
$979$	24.9136			0.796241
$980$	3.15491	−	6.24872i	0.100780	−	0.199608i
$981$	3.30982			0.105674
$982$	9.90823	+	17.1616i	0.316184	+	0.547647i
$983$	16.5698	−	28.6997i	0.528494	−	0.915379i	−0.470954	−	0.882158i	$-0.656090\pi$
$983$	16.5698	−	28.6997i	0.528494	−	0.915379i	0.999448	−	0.0332208i	$-0.0105764\pi$
$984$	1.24668	−	2.15931i	0.0397427	−	0.0688363i
$985$	−2.50664	−	4.34163i	−0.0798683	−	0.138336i
$986$	25.5598			0.813989
$987$	5.31417	−	3.27002i	0.169152	−	0.104086i
$988$	−4.69018			−0.149214
$989$	3.65491	+	6.33049i	0.116219	+	0.201298i
$990$	−1.82746	+	3.16525i	−0.0580803	+	0.100598i
$991$	−0.643919	+	1.11530i	−0.0204548	+	0.0354287i	−0.876072	−	0.482181i	$-0.839845\pi$
$991$	−0.643919	+	1.11530i	−0.0204548	+	0.0354287i	0.855617	+	0.517610i	$0.173178\pi$
$992$	1.67919	+	2.90844i	0.0533142	+	0.0923429i
$993$	−17.1396			−0.543908
$994$	19.6858	+	10.6416i	0.624397	+	0.337530i
$995$	14.3231			0.454073
$996$	−3.82746	−	6.62935i	−0.121278	−	0.210059i
$997$	−10.0984	+	17.4910i	−0.319820	+	0.553944i	−0.980450	−	0.196767i	$-0.936956\pi$
$997$	−10.0984	+	17.4910i	−0.319820	+	0.553944i	0.660630	+	0.750711i	$0.270289\pi$
$998$	−18.1748	+	31.4797i	−0.575314	+	0.996474i
$999$	3.40823	+	5.90323i	0.107832	+	0.186770i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.k.277.1	✓	6
7.2	even	3	inner	966.2.i.k.415.1	yes	6
7.3	odd	6		6762.2.a.cf.1.1		3
7.4	even	3		6762.2.a.ce.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.k.277.1	✓	6	1.1	even	1	trivial
966.2.i.k.415.1	yes	6	7.2	even	3	inner
6762.2.a.ce.1.1		3	7.4	even	3
6762.2.a.cf.1.1		3	7.3	odd	6

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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.25332 + 1.38656i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-0.500000 - 0.866025i) q^{5} +1.00000 q^{6} +(-2.25332 + 1.38656i) q^{7} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(1.82746 - 3.16525i) q^{11} +(0.500000 + 0.866025i) q^{12} -0.851731 q^{13} +(-2.32746 - 1.25815i) q^{14} -1.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(3.08078 - 5.33606i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-2.75332 - 4.76889i) q^{19} +1.00000 q^{20} +(0.0741344 + 2.64471i) q^{21} +3.65491 q^{22} +(0.500000 + 0.866025i) q^{23} +(-0.500000 + 0.866025i) q^{24} +(2.00000 - 3.46410i) q^{25} +(-0.425866 - 0.737621i) q^{26} -1.00000 q^{27} +(-0.0741344 - 2.64471i) q^{28} +4.14827 q^{29} +(-0.500000 - 0.866025i) q^{30} +(-1.67919 + 2.90844i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-1.82746 - 3.16525i) q^{33} +6.16155 q^{34} +(2.32746 + 1.25815i) q^{35} +1.00000 q^{36} +(-3.40823 - 5.90323i) q^{37} +(2.75332 - 4.76889i) q^{38} +(-0.425866 + 0.737621i) q^{39} +(0.500000 + 0.866025i) q^{40} -2.49336 q^{41} +(-2.25332 + 1.38656i) q^{42} +7.30982 q^{43} +(1.82746 + 3.16525i) q^{44} +(-0.500000 + 0.866025i) q^{45} +(-0.500000 + 0.866025i) q^{46} +(-1.17919 - 2.04241i) q^{47} -1.00000 q^{48} +(3.15491 - 6.24872i) q^{49} +4.00000 q^{50} +(-3.08078 - 5.33606i) q^{51} +(0.425866 - 0.737621i) q^{52} +(-3.15491 + 5.46447i) q^{53} +(-0.500000 - 0.866025i) q^{54} -3.65491 q^{55} +(2.25332 - 1.38656i) q^{56} -5.50664 q^{57} +(2.07413 + 3.59251i) q^{58} +(-1.58078 + 2.73799i) q^{59} +(0.500000 - 0.866025i) q^{60} +(-5.00000 - 8.66025i) q^{61} -3.35837 q^{62} +(2.32746 + 1.25815i) q^{63} +1.00000 q^{64} +(0.425866 + 0.737621i) q^{65} +(1.82746 - 3.16525i) q^{66} +(5.17919 - 8.97061i) q^{67} +(3.08078 + 5.33606i) q^{68} +1.00000 q^{69} +(0.0741344 + 2.64471i) q^{70} -8.45809 q^{71} +(0.500000 + 0.866025i) q^{72} +(-0.672545 + 1.16488i) q^{73} +(3.40823 - 5.90323i) q^{74} +(-2.00000 - 3.46410i) q^{75} +5.50664 q^{76} +(0.270955 + 9.66619i) q^{77} -0.851731 q^{78} +(5.72905 + 9.92300i) q^{79} +(-0.500000 + 0.866025i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(-1.24668 - 2.15931i) q^{82} -7.65491 q^{83} +(-2.32746 - 1.25815i) q^{84} -6.16155 q^{85} +(3.65491 + 6.33049i) q^{86} +(2.07413 - 3.59251i) q^{87} +(-1.82746 + 3.16525i) q^{88} +(3.40823 + 5.90323i) q^{89} -1.00000 q^{90} +(1.91922 - 1.18098i) q^{91} -1.00000 q^{92} +(1.67919 + 2.90844i) q^{93} +(1.17919 - 2.04241i) q^{94} +(-2.75332 + 4.76889i) q^{95} +(-0.500000 - 0.866025i) q^{96} +0.444807 q^{97} +(6.98901 - 0.392129i) q^{98} -3.65491 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 3 q^{5} + 6 q^{6} - 3 q^{7} - 6 q^{8} - 3 q^{9} + 3 q^{10} + 3 q^{12} - 6 q^{13} - 3 q^{14} - 6 q^{15} - 3 q^{16} - 3 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} + 3 q^{23} - 3 q^{24} + 12 q^{25} - 3 q^{26} - 6 q^{27} + 24 q^{29} - 3 q^{30} + 3 q^{32} - 6 q^{34} + 3 q^{35} + 6 q^{36} + 12 q^{37} + 6 q^{38} - 3 q^{39} + 3 q^{40} - 36 q^{41} - 3 q^{42} - 3 q^{45} - 3 q^{46} + 3 q^{47} - 6 q^{48} - 3 q^{49} + 24 q^{50} + 3 q^{51} + 3 q^{52} + 3 q^{53} - 3 q^{54} + 3 q^{56} - 12 q^{57} + 12 q^{58} + 12 q^{59} + 3 q^{60} - 30 q^{61} + 3 q^{63} + 6 q^{64} + 3 q^{65} + 21 q^{67} - 3 q^{68} + 6 q^{69} - 6 q^{71} + 3 q^{72} - 15 q^{73} - 12 q^{74} - 12 q^{75} + 12 q^{76} + 24 q^{77} - 6 q^{78} + 12 q^{79} - 3 q^{80} - 3 q^{81} - 18 q^{82} - 24 q^{83} - 3 q^{84} + 6 q^{85} + 12 q^{87} - 12 q^{89} - 6 q^{90} + 33 q^{91} - 6 q^{92} - 3 q^{94} - 6 q^{95} - 3 q^{96} - 12 q^{98}+O(q^{100}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 3 * q^5 + 6 * q^6 - 3 * q^7 - 6 * q^8 - 3 * q^9 + 3 * q^10 + 3 * q^12 - 6 * q^13 - 3 * q^14 - 6 * q^15 - 3 * q^16 - 3 * q^17 + 3 * q^18 - 6 * q^19 + 6 * q^20 + 3 * q^23 - 3 * q^24 + 12 * q^25 - 3 * q^26 - 6 * q^27 + 24 * q^29 - 3 * q^30 + 3 * q^32 - 6 * q^34 + 3 * q^35 + 6 * q^36 + 12 * q^37 + 6 * q^38 - 3 * q^39 + 3 * q^40 - 36 * q^41 - 3 * q^42 - 3 * q^45 - 3 * q^46 + 3 * q^47 - 6 * q^48 - 3 * q^49 + 24 * q^50 + 3 * q^51 + 3 * q^52 + 3 * q^53 - 3 * q^54 + 3 * q^56 - 12 * q^57 + 12 * q^58 + 12 * q^59 + 3 * q^60 - 30 * q^61 + 3 * q^63 + 6 * q^64 + 3 * q^65 + 21 * q^67 - 3 * q^68 + 6 * q^69 - 6 * q^71 + 3 * q^72 - 15 * q^73 - 12 * q^74 - 12 * q^75 + 12 * q^76 + 24 * q^77 - 6 * q^78 + 12 * q^79 - 3 * q^80 - 3 * q^81 - 18 * q^82 - 24 * q^83 - 3 * q^84 + 6 * q^85 + 12 * q^87 - 12 * q^89 - 6 * q^90 + 33 * q^91 - 6 * q^92 - 3 * q^94 - 6 * q^95 - 3 * q^96 - 12 * q^98

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