LMFDB - Embedded newform 966.2.i.l.415.2

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:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	8.0.1768034304.4
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 2x^{7} - x^{6} - 6x^{5} + 14x^{4} + 18x^{3} - 31x^{2} - 14x + 49 $ x^8 - 2x^7 - x^6 - 6x^5 + 14x^4 + 18x^3 - 31x^2 - 14x + 49
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			415.2
Root			$2.09279 - 0.185573i$ of defining polynomial
Character	$\chi$	$=$	966.415
Dual form			966.2.i.l.277.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.914214 + 1.58346i) q^{5} +1.00000 q^{6} +(2.45965 + 0.974732i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.914214 + 1.58346i) q^{5} +1.00000 q^{6} +(2.45965 + 0.974732i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.914214 - 1.58346i) q^{10} +(-0.840244 - 1.45535i) q^{11} +(-0.500000 + 0.866025i) q^{12} +3.77137 q^{13} +(-2.07397 + 1.64276i) q^{14} +1.82843 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.29990 - 2.25149i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.545441 + 0.944731i) q^{19} +1.82843 q^{20} +(-0.385685 - 2.61749i) q^{21} +1.68049 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.828427 + 1.43488i) q^{25} +(-1.88568 + 3.26610i) q^{26} +1.00000 q^{27} +(-0.385685 - 2.61749i) q^{28} -0.771369 q^{29} +(-0.914214 + 1.58346i) q^{30} +(1.93113 + 3.34481i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.840244 + 1.45535i) q^{33} +2.59980 q^{34} +(-3.79210 + 3.00366i) q^{35} +1.00000 q^{36} +(-1.22593 + 2.12337i) q^{37} +(-0.545441 - 0.944731i) q^{38} +(-1.88568 - 3.26610i) q^{39} +(-0.914214 + 1.58346i) q^{40} -1.09088 q^{41} +(2.45965 + 0.974732i) q^{42} +10.2959 q^{43} +(-0.840244 + 1.45535i) q^{44} +(-0.914214 - 1.58346i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(1.11161 - 1.92537i) q^{47} +1.00000 q^{48} +(5.09980 + 4.79501i) q^{49} -1.65685 q^{50} +(-1.29990 + 2.25149i) q^{51} +(-1.88568 - 3.26610i) q^{52} +(3.68558 + 6.38362i) q^{53} +(-0.500000 + 0.866025i) q^{54} +3.07265 q^{55} +(2.45965 + 0.974732i) q^{56} +1.09088 q^{57} +(0.385685 - 0.668025i) q^{58} +(3.21411 + 5.56700i) q^{59} +(-0.914214 - 1.58346i) q^{60} +(-4.54274 + 7.86825i) q^{61} -3.86225 q^{62} +(-2.07397 + 1.64276i) q^{63} +1.00000 q^{64} +(-3.44784 + 5.97183i) q^{65} +(-0.840244 - 1.45535i) q^{66} +(6.44514 + 11.1633i) q^{67} +(-1.29990 + 2.25149i) q^{68} +1.00000 q^{69} +(-0.705196 - 4.78589i) q^{70} +8.22863 q^{71} +(-0.500000 + 0.866025i) q^{72} +(1.43113 + 2.47878i) q^{73} +(-1.22593 - 2.12337i) q^{74} +(0.828427 - 1.43488i) q^{75} +1.09088 q^{76} +(-0.648139 - 4.39866i) q^{77} +3.77137 q^{78} +(-0.385685 + 0.668025i) q^{79} +(-0.914214 - 1.58346i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.545441 - 0.944731i) q^{82} +3.33734 q^{83} +(-2.07397 + 1.64276i) q^{84} +4.75354 q^{85} +(-5.14794 + 8.91649i) q^{86} +(0.385685 + 0.668025i) q^{87} +(-0.840244 - 1.45535i) q^{88} +(-1.60250 + 2.77561i) q^{89} +1.82843 q^{90} +(9.27626 + 3.67607i) q^{91} +1.00000 q^{92} +(1.93113 - 3.34481i) q^{93} +(1.11161 + 1.92537i) q^{94} +(-0.997298 - 1.72737i) q^{95} +(-0.500000 + 0.866025i) q^{96} -10.4282 q^{97} +(-6.70249 + 2.01905i) q^{98} +1.68049 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9}+O(q^{10}) $ 8 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 - 4 * q^9	$ 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} + 12 q^{13} - 6 q^{14} - 8 q^{15} - 4 q^{16} + 10 q^{17} - 4 q^{18} + 4 q^{19} - 8 q^{20} + 6 q^{21} + 12 q^{22} - 4 q^{23} - 4 q^{24} - 16 q^{25} - 6 q^{26} + 8 q^{27} + 6 q^{28} + 12 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 6 q^{33} - 20 q^{34} - 10 q^{35} + 8 q^{36} + 4 q^{38} - 6 q^{39} + 4 q^{40} + 8 q^{41} + 40 q^{43} - 6 q^{44} + 4 q^{45} - 4 q^{46} - 10 q^{47} + 8 q^{48} + 32 q^{50} + 10 q^{51} - 6 q^{52} - 4 q^{54} + 20 q^{55} - 8 q^{57} - 6 q^{58} - 6 q^{59} + 4 q^{60} + 4 q^{62} - 6 q^{63} + 8 q^{64} + 14 q^{65} - 6 q^{66} - 18 q^{67} + 10 q^{68} + 8 q^{69} + 2 q^{70} + 84 q^{71} - 4 q^{72} - 6 q^{73} - 16 q^{75} - 8 q^{76} - 2 q^{77} + 12 q^{78} + 6 q^{79} + 4 q^{80} - 4 q^{81} - 4 q^{82} - 20 q^{83} - 6 q^{84} + 68 q^{85} - 20 q^{86} - 6 q^{87} - 6 q^{88} - 8 q^{90} + 10 q^{91} + 8 q^{92} - 2 q^{93} - 10 q^{94} + 20 q^{95} - 4 q^{96} - 20 q^{97} - 18 q^{98} + 12 q^{99}+O(q^{100}) $ 8 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 - 4 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 + 12 * q^13 - 6 * q^14 - 8 * q^15 - 4 * q^16 + 10 * q^17 - 4 * q^18 + 4 * q^19 - 8 * q^20 + 6 * q^21 + 12 * q^22 - 4 * q^23 - 4 * q^24 - 16 * q^25 - 6 * q^26 + 8 * q^27 + 6 * q^28 + 12 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 6 * q^33 - 20 * q^34 - 10 * q^35 + 8 * q^36 + 4 * q^38 - 6 * q^39 + 4 * q^40 + 8 * q^41 + 40 * q^43 - 6 * q^44 + 4 * q^45 - 4 * q^46 - 10 * q^47 + 8 * q^48 + 32 * q^50 + 10 * q^51 - 6 * q^52 - 4 * q^54 + 20 * q^55 - 8 * q^57 - 6 * q^58 - 6 * q^59 + 4 * q^60 + 4 * q^62 - 6 * q^63 + 8 * q^64 + 14 * q^65 - 6 * q^66 - 18 * q^67 + 10 * q^68 + 8 * q^69 + 2 * q^70 + 84 * q^71 - 4 * q^72 - 6 * q^73 - 16 * q^75 - 8 * q^76 - 2 * q^77 + 12 * q^78 + 6 * q^79 + 4 * q^80 - 4 * q^81 - 4 * q^82 - 20 * q^83 - 6 * q^84 + 68 * q^85 - 20 * q^86 - 6 * q^87 - 6 * q^88 - 8 * q^90 + 10 * q^91 + 8 * q^92 - 2 * q^93 - 10 * q^94 + 20 * q^95 - 4 * q^96 - 20 * q^97 - 18 * q^98 + 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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
$5$	−0.914214	+	1.58346i	−0.408849	+	0.708147i	−0.994761	−	0.102228i	$-0.967403\pi$
$5$	−0.914214	+	1.58346i	−0.408849	+	0.708147i	0.585912	+	0.810374i	$0.300736\pi$
$6$	1.00000			0.408248
$7$	2.45965	+	0.974732i	0.929662	+	0.368414i
$7$	2.45965	+	0.974732i	0.929662	+	0.368414i
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−0.914214	−	1.58346i	−0.289100	−	0.500735i
$11$	−0.840244	−	1.45535i	−0.253343	−	0.438803i	0.711101	−	0.703090i	$-0.248197\pi$
$11$	−0.840244	−	1.45535i	−0.253343	−	0.438803i	−0.964444	+	0.264287i	$0.914864\pi$
$12$	−0.500000	+	0.866025i	−0.144338	+	0.250000i
$13$	3.77137			1.04599			0.522995	−	0.852336i	$-0.324815\pi$
$13$	3.77137			1.04599			0.522995	+	0.852336i	$0.324815\pi$
$14$	−2.07397	+	1.64276i	−0.554292	+	0.439045i
$15$	1.82843			0.472098
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−1.29990	−	2.25149i	−0.315272	−	0.546066i	0.664224	−	0.747534i	$-0.268762\pi$
$17$	−1.29990	−	2.25149i	−0.315272	−	0.546066i	−0.979495	+	0.201467i	$0.935429\pi$
$18$	−0.500000	−	0.866025i	−0.117851	−	0.204124i
$19$	−0.545441	+	0.944731i	−0.125133	+	0.216736i	−0.921785	−	0.387702i	$-0.873269\pi$
$19$	−0.545441	+	0.944731i	−0.125133	+	0.216736i	0.796652	+	0.604438i	$0.206602\pi$
$20$	1.82843			0.408849
$21$	−0.385685	−	2.61749i	−0.0841633	−	0.571183i
$22$	1.68049			0.358281
$23$	−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
$25$	0.828427	+	1.43488i	0.165685	+	0.286976i
$26$	−1.88568	+	3.26610i	−0.369813	+	0.640535i
$27$	1.00000			0.192450
$28$	−0.385685	−	2.61749i	−0.0728876	−	0.494659i
$29$	−0.771369			−0.143240			−0.0716199	−	0.997432i	$-0.522817\pi$
$29$	−0.771369			−0.143240			−0.0716199	+	0.997432i	$0.522817\pi$
$30$	−0.914214	+	1.58346i	−0.166912	+	0.289100i
$31$	1.93113	+	3.34481i	0.346840	+	0.600745i	0.985686	−	0.168590i	$-0.0539212\pi$
$31$	1.93113	+	3.34481i	0.346840	+	0.600745i	−0.638846	+	0.769335i	$0.720588\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−0.840244	+	1.45535i	−0.146268	+	0.253343i
$34$	2.59980			0.445861
$35$	−3.79210	+	3.00366i	−0.640982	+	0.507711i
$36$	1.00000			0.166667
$37$	−1.22593	+	2.12337i	−0.201541	+	0.349080i	−0.949025	−	0.315200i	$-0.897928\pi$
$37$	−1.22593	+	2.12337i	−0.201541	+	0.349080i	0.747484	+	0.664280i	$0.231262\pi$
$38$	−0.545441	−	0.944731i	−0.0884821	−	0.153256i
$39$	−1.88568	−	3.26610i	−0.301951	−	0.522995i
$40$	−0.914214	+	1.58346i	−0.144550	+	0.250368i
$41$	−1.09088			−0.170367			−0.0851835	−	0.996365i	$-0.527148\pi$
$41$	−1.09088			−0.170367			−0.0851835	+	0.996365i	$0.527148\pi$
$42$	2.45965	+	0.974732i	0.379533	+	0.150404i
$43$	10.2959			1.57011			0.785053	−	0.619428i	$-0.212636\pi$
$43$	10.2959			1.57011			0.785053	+	0.619428i	$0.212636\pi$
$44$	−0.840244	+	1.45535i	−0.126672	+	0.219402i
$45$	−0.914214	−	1.58346i	−0.136283	−	0.236049i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	1.11161	−	1.92537i	0.162146	−	0.280844i	−0.773492	−	0.633806i	$-0.781492\pi$
$47$	1.11161	−	1.92537i	0.162146	−	0.280844i	0.935638	+	0.352961i	$0.114825\pi$
$48$	1.00000			0.144338
$49$	5.09980	+	4.79501i	0.728542	+	0.685001i
$50$	−1.65685			−0.234315
$51$	−1.29990	+	2.25149i	−0.182022	+	0.315272i
$52$	−1.88568	−	3.26610i	−0.261497	−	0.452927i
$53$	3.68558	+	6.38362i	0.506254	+	0.876857i	0.999974	+	0.00723633i	$0.00230342\pi$
$53$	3.68558	+	6.38362i	0.506254	+	0.876857i	−0.493720	+	0.869621i	$0.664363\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	3.07265			0.414316
$56$	2.45965	+	0.974732i	0.328685	+	0.130254i
$57$	1.09088			0.144491
$58$	0.385685	−	0.668025i	0.0506429	−	0.0877160i
$59$	3.21411	+	5.56700i	0.418442	+	0.724762i	0.995783	−	0.0917407i	$-0.0292431\pi$
$59$	3.21411	+	5.56700i	0.418442	+	0.724762i	−0.577341	+	0.816503i	$0.695910\pi$
$60$	−0.914214	−	1.58346i	−0.118024	−	0.204424i
$61$	−4.54274	+	7.86825i	−0.581638	+	1.00743i	0.413647	+	0.910437i	$0.364255\pi$
$61$	−4.54274	+	7.86825i	−0.581638	+	1.00743i	−0.995285	+	0.0969895i	$0.969079\pi$
$62$	−3.86225			−0.490506
$63$	−2.07397	+	1.64276i	−0.261296	+	0.206968i
$64$	1.00000			0.125000
$65$	−3.44784	+	5.97183i	−0.427652	+	0.740714i
$66$	−0.840244	−	1.45535i	−0.103427	−	0.179141i
$67$	6.44514	+	11.1633i	0.787399	+	1.36381i	0.927556	+	0.373685i	$0.121906\pi$
$67$	6.44514	+	11.1633i	0.787399	+	1.36381i	−0.140157	+	0.990129i	$0.544761\pi$
$68$	−1.29990	+	2.25149i	−0.157636	+	0.273033i
$69$	1.00000			0.120386
$70$	−0.705196	−	4.78589i	−0.0842871	−	0.572023i
$71$	8.22863			0.976559			0.488279	−	0.872687i	$-0.337625\pi$
$71$	8.22863			0.976559			0.488279	+	0.872687i	$0.337625\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	1.43113	+	2.47878i	0.167501	+	0.290119i	0.937540	−	0.347876i	$-0.113097\pi$
$73$	1.43113	+	2.47878i	0.167501	+	0.290119i	−0.770040	+	0.637996i	$0.779764\pi$
$74$	−1.22593	−	2.12337i	−0.142511	−	0.246837i
$75$	0.828427	−	1.43488i	0.0956585	−	0.165685i
$76$	1.09088			0.125133
$77$	−0.648139	−	4.39866i	−0.0738623	−	0.501274i
$78$	3.77137			0.427023
$79$	−0.385685	+	0.668025i	−0.0433929	+	0.0751587i	−0.886906	−	0.461950i	$-0.847150\pi$
$79$	−0.385685	+	0.668025i	−0.0433929	+	0.0751587i	0.843513	+	0.537108i	$0.180483\pi$
$80$	−0.914214	−	1.58346i	−0.102212	−	0.177037i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	0.545441	−	0.944731i	0.0602338	−	0.104328i
$83$	3.33734			0.366321			0.183160	−	0.983083i	$-0.441367\pi$
$83$	3.33734			0.366321			0.183160	+	0.983083i	$0.441367\pi$
$84$	−2.07397	+	1.64276i	−0.226289	+	0.179239i
$85$	4.75354			0.515594
$86$	−5.14794	+	8.91649i	−0.555117	+	0.961490i
$87$	0.385685	+	0.668025i	0.0413497	+	0.0716199i
$88$	−0.840244	−	1.45535i	−0.0895703	−	0.155140i
$89$	−1.60250	+	2.77561i	−0.169864	+	0.294214i	−0.938372	−	0.345627i	$-0.887666\pi$
$89$	−1.60250	+	2.77561i	−0.169864	+	0.294214i	0.768508	+	0.639841i	$0.221000\pi$
$90$	1.82843			0.192733
$91$	9.27626	+	3.67607i	0.972417	+	0.385357i
$92$	1.00000			0.104257
$93$	1.93113	−	3.34481i	0.200248	−	0.346840i
$94$	1.11161	+	1.92537i	0.114654	+	0.198587i
$95$	−0.997298	−	1.72737i	−0.102321	−	0.177225i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	−10.4282			−1.05883			−0.529413	−	0.848364i	$-0.677588\pi$
$97$	−10.4282			−1.05883			−0.529413	+	0.848364i	$0.677588\pi$
$98$	−6.70249	+	2.01905i	−0.677054	+	0.203955i
$99$	1.68049			0.168895
$100$	0.828427	−	1.43488i	0.0828427	−	0.143488i
$101$	3.23882	+	5.60980i	0.322275	+	0.558196i	0.980957	−	0.194225i	$-0.0622192\pi$
$101$	3.23882	+	5.60980i	0.322275	+	0.558196i	−0.658682	+	0.752421i	$0.728886\pi$
$102$	−1.29990	−	2.25149i	−0.128709	−	0.222931i
$103$	9.44514	−	16.3595i	0.930657	−	1.61194i	0.148456	−	0.988919i	$-0.452570\pi$
$103$	9.44514	−	16.3595i	0.930657	−	1.61194i	0.782201	−	0.623026i	$-0.214097\pi$
$104$	3.77137			0.369813
$105$	4.49730	+	1.78223i	0.438891	+	0.173927i
$106$	−7.37117			−0.715951
$107$	−6.90749	+	11.9641i	−0.667772	+	1.15662i	0.310753	+	0.950491i	$0.399419\pi$
$107$	−6.90749	+	11.9641i	−0.667772	+	1.15662i	−0.978526	+	0.206125i	$0.933915\pi$
$108$	−0.500000	−	0.866025i	−0.0481125	−	0.0833333i
$109$	−5.03382	−	8.71884i	−0.482153	−	0.835113i	0.517637	−	0.855600i	$-0.326812\pi$
$109$	−5.03382	−	8.71884i	−0.482153	−	0.835113i	−0.999790	+	0.0204870i	$0.993478\pi$
$110$	−1.53633	+	2.66099i	−0.146483	+	0.253716i
$111$	2.45186			0.232720
$112$	−2.07397	+	1.64276i	−0.195972	+	0.155226i
$113$	6.30392			0.593023			0.296511	−	0.955029i	$-0.404177\pi$
$113$	6.30392			0.593023			0.296511	+	0.955029i	$0.404177\pi$
$114$	−0.545441	+	0.944731i	−0.0510852	+	0.0884821i
$115$	−0.914214	−	1.58346i	−0.0852509	−	0.147659i
$116$	0.385685	+	0.668025i	0.0358099	+	0.0620246i
$117$	−1.88568	+	3.26610i	−0.174332	+	0.301951i
$118$	−6.42822			−0.591766
$119$	−1.00270	−	6.80494i	−0.0919175	−	0.623808i
$120$	1.82843			0.166912
$121$	4.08798	−	7.08059i	0.371634	−	0.643690i
$122$	−4.54274	−	7.86825i	−0.411280	−	0.712358i
$123$	0.545441	+	0.944731i	0.0491807	+	0.0851835i
$124$	1.93113	−	3.34481i	0.173420	−	0.300373i
$125$	−12.1716			−1.08866
$126$	−0.385685	−	2.61749i	−0.0343595	−	0.233184i
$127$	4.02363			0.357040			0.178520	−	0.983936i	$-0.442869\pi$
$127$	4.02363			0.357040			0.178520	+	0.983936i	$0.442869\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−5.14794	−	8.91649i	−0.453251	−	0.785053i
$130$	−3.44784	−	5.97183i	−0.302395	−	0.523764i
$131$	−5.49730	+	9.52160i	−0.480301	+	0.831906i	−0.999745	−	0.0225988i	$-0.992806\pi$
$131$	−5.49730	+	9.52160i	−0.480301	+	0.831906i	0.519443	+	0.854505i	$0.326139\pi$
$132$	1.68049			0.146268
$133$	−2.26245	+	1.79205i	−0.196180	+	0.155391i
$134$	−12.8903			−1.11355
$135$	−0.914214	+	1.58346i	−0.0786830	+	0.136283i
$136$	−1.29990	−	2.25149i	−0.111465	−	0.193064i
$137$	−2.07397	−	3.59222i	−0.177191	−	0.306904i	0.763726	−	0.645540i	$-0.223368\pi$
$137$	−2.07397	−	3.59222i	−0.177191	−	0.306904i	−0.940917	+	0.338636i	$0.890034\pi$
$138$	−0.500000	+	0.866025i	−0.0425628	+	0.0737210i
$139$	−13.3137			−1.12925			−0.564627	−	0.825346i	$-0.690980\pi$
$139$	−13.3137			−1.12925			−0.564627	+	0.825346i	$0.690980\pi$
$140$	4.49730	+	1.78223i	0.380091	+	0.150626i
$141$	−2.22323			−0.187229
$142$	−4.11432	+	7.12620i	−0.345266	+	0.598018i
$143$	−3.16887	−	5.48865i	−0.264994	−	0.458984i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	0.705196	−	1.22144i	0.0585634	−	0.101435i
$146$	−2.86225			−0.236882
$147$	1.60270	−	6.81406i	0.132188	−	0.562014i
$148$	2.45186			0.201541
$149$	5.93622	−	10.2818i	0.486314	−	0.842321i	−0.513562	−	0.858052i	$-0.671674\pi$
$149$	5.93622	−	10.2818i	0.486314	−	0.842321i	0.999876	+	0.0157317i	$0.00500776\pi$
$150$	0.828427	+	1.43488i	0.0676408	+	0.117157i
$151$	−0.536325	−	0.928943i	−0.0436455	−	0.0755963i	0.843377	−	0.537322i	$-0.180564\pi$
$151$	−0.536325	−	0.928943i	−0.0436455	−	0.0755963i	−0.887023	+	0.461725i	$0.847231\pi$
$152$	−0.545441	+	0.944731i	−0.0442411	+	0.0766278i
$153$	2.59980			0.210181
$154$	4.13342	+	1.63803i	0.333080	+	0.131996i
$155$	−7.06184			−0.567221
$156$	−1.88568	+	3.26610i	−0.150976	+	0.261497i
$157$	−10.6880	−	18.5121i	−0.852993	−	1.47743i	−0.878494	−	0.477753i	$-0.841451\pi$
$157$	−10.6880	−	18.5121i	−0.852993	−	1.47743i	0.0255009	−	0.999675i	$-0.491882\pi$
$158$	−0.385685	−	0.668025i	−0.0306834	−	0.0531453i
$159$	3.68558	−	6.38362i	0.292286	−	0.506254i
$160$	1.82843			0.144550
$161$	−2.07397	+	1.64276i	−0.163452	+	0.129467i
$162$	1.00000			0.0785674
$163$	−0.940241	+	1.62854i	−0.0736453	+	0.127557i	−0.900496	−	0.434864i	$-0.856797\pi$
$163$	−0.940241	+	1.62854i	−0.0736453	+	0.127557i	0.826851	+	0.562421i	$0.190130\pi$
$164$	0.545441	+	0.944731i	0.0425917	+	0.0737711i
$165$	−1.53633	−	2.66099i	−0.119603	−	0.207158i
$166$	−1.66867	+	2.89022i	−0.129514	+	0.224325i
$167$	−19.6511			−1.52064			−0.760322	−	0.649546i	$-0.774959\pi$
$167$	−19.6511			−1.52064			−0.760322	+	0.649546i	$0.774959\pi$
$168$	−0.385685	−	2.61749i	−0.0297562	−	0.201944i
$169$	1.22323			0.0940944
$170$	−2.37677	+	4.11669i	−0.182290	+	0.315735i
$171$	−0.545441	−	0.944731i	−0.0417109	−	0.0722454i
$172$	−5.14794	−	8.91649i	−0.392527	−	0.679876i
$173$	0.885485	−	1.53370i	0.0673222	−	0.116605i	−0.830400	−	0.557168i	$-0.811888\pi$
$173$	0.885485	−	1.53370i	0.0673222	−	0.116605i	0.897722	+	0.440563i	$0.145221\pi$
$174$	−0.771369			−0.0584774
$175$	0.639023	+	4.33680i	0.0483056	+	0.327831i
$176$	1.68049			0.126672
$177$	3.21411	−	5.56700i	0.241587	−	0.418442i
$178$	−1.60250	−	2.77561i	−0.120112	−	0.208041i
$179$	6.11161	+	10.5856i	0.456803	+	0.791207i	0.998790	−	0.0491804i	$-0.0156609\pi$
$179$	6.11161	+	10.5856i	0.456803	+	0.791207i	−0.541986	+	0.840387i	$0.682328\pi$
$180$	−0.914214	+	1.58346i	−0.0681415	+	0.118024i
$181$	0.820785			0.0610085			0.0305043	−	0.999535i	$-0.490289\pi$
$181$	0.820785			0.0610085			0.0305043	+	0.999535i	$0.490289\pi$
$182$	−7.82170	+	6.19544i	−0.579783	+	0.459237i
$183$	9.08548			0.671618
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	−2.24152	−	3.88243i	−0.164800	−	0.285442i
$186$	1.93113	+	3.34481i	0.141597	+	0.245253i
$187$	−2.18446	+	3.78360i	−0.159744	+	0.276684i
$188$	−2.22323			−0.162146
$189$	2.45965	+	0.974732i	0.178914	+	0.0709013i
$190$	1.99460			0.144703
$191$	6.22593	−	10.7836i	0.450492	−	0.780276i	−0.547924	−	0.836528i	$-0.684582\pi$
$191$	6.22593	−	10.7836i	0.450492	−	0.780276i	0.998417	+	0.0562523i	$0.0179151\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	−3.35206	−	5.80594i	−0.241287	−	0.417921i	0.719794	−	0.694187i	$-0.244236\pi$
$193$	−3.35206	−	5.80594i	−0.241287	−	0.417921i	−0.961081	+	0.276267i	$0.910903\pi$
$194$	5.21411	−	9.03111i	0.374351	−	0.648396i
$195$	6.89567			0.493809
$196$	1.60270	−	6.81406i	0.114478	−	0.486718i
$197$	16.5606			1.17989			0.589946	−	0.807443i	$-0.299149\pi$
$197$	16.5606			1.17989			0.589946	+	0.807443i	$0.299149\pi$
$198$	−0.840244	+	1.45535i	−0.0597136	+	0.103427i
$199$	2.50892	+	4.34557i	0.177852	+	0.308049i	0.941145	−	0.338004i	$-0.109752\pi$
$199$	2.50892	+	4.34557i	0.177852	+	0.308049i	−0.763292	+	0.646053i	$0.776418\pi$
$200$	0.828427	+	1.43488i	0.0585786	+	0.101461i
$201$	6.44514	−	11.1633i	0.454605	−	0.787399i
$202$	−6.47764			−0.455765
$203$	−1.89730	−	0.751878i	−0.133164	−	0.0527715i
$204$	2.59980			0.182022
$205$	0.997298	−	1.72737i	0.0696543	−	0.120645i
$206$	9.44514	+	16.3595i	0.658074	+	1.13982i
$207$	−0.500000	−	0.866025i	−0.0347524	−	0.0601929i
$208$	−1.88568	+	3.26610i	−0.130749	+	0.226463i
$209$	1.83321			0.126806
$210$	−3.79210	+	3.00366i	−0.261680	+	0.207272i
$211$	17.1523			1.18081			0.590407	−	0.807105i	$-0.298967\pi$
$211$	17.1523			1.18081			0.590407	+	0.807105i	$0.298967\pi$
$212$	3.68558	−	6.38362i	0.253127	−	0.438429i
$213$	−4.11432	−	7.12620i	−0.281908	−	0.488279i
$214$	−6.90749	−	11.9641i	−0.472186	−	0.817851i
$215$	−9.41263	+	16.3032i	−0.641936	+	1.11187i
$216$	1.00000			0.0680414
$217$	1.48961	+	10.1094i	0.101121	+	0.686271i
$218$	10.0676			0.681867
$219$	1.43113	−	2.47878i	0.0967065	−	0.167501i
$220$	−1.53633	−	2.66099i	−0.103579	−	0.179404i
$221$	−4.90240	−	8.49120i	−0.329771	−	0.571180i
$222$	−1.22593	+	2.12337i	−0.0822790	+	0.142511i
$223$	4.42282			0.296174			0.148087	−	0.988974i	$-0.452688\pi$
$223$	4.42282			0.296174			0.148087	+	0.988974i	$0.452688\pi$
$224$	−0.385685	−	2.61749i	−0.0257696	−	0.174888i
$225$	−1.65685			−0.110457
$226$	−3.15196	+	5.45935i	−0.209665	+	0.363151i
$227$	6.04524	+	10.4707i	0.401237	+	0.694962i	0.993875	−	0.110506i	$-0.0352471\pi$
$227$	6.04524	+	10.4707i	0.401237	+	0.694962i	−0.592639	+	0.805468i	$0.701914\pi$
$228$	−0.545441	−	0.944731i	−0.0361227	−	0.0625663i
$229$	4.54544	−	7.87293i	0.300371	−	0.520258i	−0.675849	−	0.737040i	$-0.736223\pi$
$229$	4.54544	−	7.87293i	0.300371	−	0.520258i	0.976220	+	0.216782i	$0.0695561\pi$
$230$	1.82843			0.120563
$231$	−3.48528	+	2.76063i	−0.229315	+	0.181636i
$232$	−0.771369			−0.0506429
$233$	−3.37387	+	5.84371i	−0.221029	+	0.382834i	−0.955121	−	0.296216i	$-0.904275\pi$
$233$	−3.37387	+	5.84371i	−0.221029	+	0.382834i	0.734091	+	0.679051i	$0.237608\pi$
$234$	−1.88568	−	3.26610i	−0.123271	−	0.213512i
$235$	2.03250	+	3.52040i	0.132586	+	0.229646i
$236$	3.21411	−	5.56700i	0.209221	−	0.362381i
$237$	0.771369			0.0501058
$238$	6.39460	+	2.53410i	0.414500	+	0.164262i
$239$	20.5918			1.33197			0.665985	−	0.745965i	$-0.268011\pi$
$239$	20.5918			1.33197			0.665985	+	0.745965i	$0.268011\pi$
$240$	−0.914214	+	1.58346i	−0.0590122	+	0.102212i
$241$	−8.59068	−	14.8795i	−0.553374	−	0.958473i	−0.998028	−	0.0627700i	$-0.980007\pi$
$241$	−8.59068	−	14.8795i	−0.553374	−	0.958473i	0.444654	−	0.895703i	$-0.353327\pi$
$242$	4.08798	+	7.08059i	0.262785	+	0.455157i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	9.08548			0.581638
$245$	−12.2550	+	3.69169i	−0.782945	+	0.235853i
$246$	−1.09088			−0.0695520
$247$	−2.05706	+	3.56293i	−0.130887	+	0.226704i
$248$	1.93113	+	3.34481i	0.122627	+	0.212395i
$249$	−1.66867	−	2.89022i	−0.105748	−	0.183160i
$250$	6.08579	−	10.5409i	0.384899	−	0.666665i
$251$	−15.1760			−0.957898			−0.478949	−	0.877843i	$-0.658982\pi$
$251$	−15.1760			−0.957898			−0.478949	+	0.877843i	$0.658982\pi$
$252$	2.45965	+	0.974732i	0.154944	+	0.0614023i
$253$	1.68049			0.105651
$254$	−2.01182	+	3.48457i	−0.126233	+	0.218641i
$255$	−2.37677	−	4.11669i	−0.148839	−	0.257797i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	7.99730	−	13.8517i	0.498858	−	0.864047i	−0.501141	−	0.865365i	$-0.667086\pi$
$257$	7.99730	−	13.8517i	0.498858	−	0.864047i	0.999999	+	0.00131844i	$0.000419674\pi$
$258$	10.2959			0.640993
$259$	−5.08508	+	4.02781i	−0.315971	+	0.250276i
$260$	6.89567			0.427652
$261$	0.385685	−	0.668025i	0.0238733	−	0.0413497i
$262$	−5.49730	−	9.52160i	−0.339624	−	0.588246i
$263$	−10.8801	−	18.8449i	−0.670895	−	1.16202i	−0.977651	−	0.210235i	$-0.932577\pi$
$263$	−10.8801	−	18.8449i	−0.670895	−	1.16202i	0.306756	−	0.951788i	$-0.400756\pi$
$264$	−0.840244	+	1.45535i	−0.0517135	+	0.0895703i
$265$	−13.4776			−0.827925
$266$	−0.420736	−	2.85537i	−0.0257970	−	0.175074i
$267$	3.20500			0.196143
$268$	6.44514	−	11.1633i	0.393699	−	0.681907i
$269$	−10.2814	−	17.8078i	−0.626866	−	1.08576i	−0.988177	−	0.153318i	$-0.951004\pi$
$269$	−10.2814	−	17.8078i	−0.626866	−	1.08576i	0.361311	−	0.932445i	$-0.382329\pi$
$270$	−0.914214	−	1.58346i	−0.0556373	−	0.0963666i
$271$	−1.93113	+	3.34481i	−0.117308	+	0.203183i	−0.918700	−	0.394957i	$-0.870760\pi$
$271$	−1.93113	+	3.34481i	−0.117308	+	0.203183i	0.801392	+	0.598139i	$0.204093\pi$
$272$	2.59980			0.157636
$273$	−1.45456	−	9.87152i	−0.0880339	−	0.597451i
$274$	4.14794			0.250586
$275$	1.39216	−	2.41130i	0.0839505	−	0.145407i
$276$	−0.500000	−	0.866025i	−0.0300965	−	0.0521286i
$277$	−12.0647	−	20.8968i	−0.724900	−	1.25556i	−0.959015	−	0.283355i	$-0.908552\pi$
$277$	−12.0647	−	20.8968i	−0.724900	−	1.25556i	0.234115	−	0.972209i	$-0.424781\pi$
$278$	6.65685	−	11.5300i	0.399252	−	0.691524i
$279$	−3.86225			−0.231227
$280$	−3.79210	+	3.00366i	−0.226621	+	0.179503i
$281$	27.6853			1.65156			0.825782	−	0.563989i	$-0.190734\pi$
$281$	27.6853			1.65156			0.825782	+	0.563989i	$0.190734\pi$
$282$	1.11161	−	1.92537i	0.0661956	−	0.114654i
$283$	−2.98309	−	5.16686i	−0.177326	−	0.307138i	0.763638	−	0.645645i	$-0.223411\pi$
$283$	−2.98309	−	5.16686i	−0.177326	−	0.307138i	−0.940964	+	0.338507i	$0.890078\pi$
$284$	−4.11432	−	7.12620i	−0.244140	−	0.422862i
$285$	−0.997298	+	1.72737i	−0.0590749	+	0.102321i
$286$	6.33774			0.374759
$287$	−2.68319	−	1.06332i	−0.158384	−	0.0627656i
$288$	1.00000			0.0589256
$289$	5.12053	−	8.86902i	0.301208	−	0.521707i
$290$	0.705196	+	1.22144i	0.0414106	+	0.0717252i
$291$	5.21411	+	9.03111i	0.305657	+	0.529413i
$292$	1.43113	−	2.47878i	0.0837503	−	0.145060i
$293$	−31.4853			−1.83939			−0.919695	−	0.392634i	$-0.871564\pi$
$293$	−31.4853			−1.83939			−0.919695	+	0.392634i	$0.871564\pi$
$294$	5.09980	+	4.79501i	0.297426	+	0.279650i
$295$	−11.7535			−0.684317
$296$	−1.22593	+	2.12337i	−0.0712557	+	0.123418i
$297$	−0.840244	−	1.45535i	−0.0487559	−	0.0844477i
$298$	5.93622	+	10.2818i	0.343876	+	0.595611i
$299$	−1.88568	+	3.26610i	−0.109052	+	0.188884i
$300$	−1.65685			−0.0956585
$301$	25.3243	+	10.0357i	1.45967	+	0.578449i
$302$	1.07265			0.0617241
$303$	3.23882	−	5.60980i	0.186065	−	0.322275i
$304$	−0.545441	−	0.944731i	−0.0312832	−	0.0541840i
$305$	−8.30607	−	14.3865i	−0.475604	−	0.823770i
$306$	−1.29990	+	2.25149i	−0.0743102	+	0.128709i
$307$	5.13815			0.293250			0.146625	−	0.989192i	$-0.453159\pi$
$307$	5.13815			0.293250			0.146625	+	0.989192i	$0.453159\pi$
$308$	−3.48528	+	2.76063i	−0.198592	+	0.157302i
$309$	−18.8903			−1.07463
$310$	3.53092	−	6.11574i	0.200543	−	0.347350i
$311$	7.78136	+	13.4777i	0.441240	+	0.764251i	0.997782	−	0.0665691i	$-0.0212053\pi$
$311$	7.78136	+	13.4777i	0.441240	+	0.764251i	−0.556541	+	0.830820i	$0.687872\pi$
$312$	−1.88568	−	3.26610i	−0.106756	−	0.184907i
$313$	11.0764	−	19.1848i	0.626073	−	1.08439i	−0.362259	−	0.932077i	$-0.617995\pi$
$313$	11.0764	−	19.1848i	0.626073	−	1.08439i	0.988332	−	0.152313i	$-0.0486722\pi$
$314$	21.3760			1.20631
$315$	−0.705196	−	4.78589i	−0.0397333	−	0.269654i
$316$	0.771369			0.0433929
$317$	−9.28136	+	16.0758i	−0.521293	+	0.902906i	0.478400	+	0.878142i	$0.341217\pi$
$317$	−9.28136	+	16.0758i	−0.521293	+	0.902906i	−0.999693	+	0.0247642i	$0.992117\pi$
$318$	3.68558	+	6.38362i	0.206677	+	0.357975i
$319$	0.648139	+	1.12261i	0.0362888	+	0.0628540i
$320$	−0.914214	+	1.58346i	−0.0511061	+	0.0885183i
$321$	13.8150			0.771077
$322$	−0.385685	−	2.61749i	−0.0214934	−	0.145867i
$323$	2.83607			0.157803
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	3.12430	+	5.41145i	0.173305	+	0.300173i
$326$	−0.940241	−	1.62854i	−0.0520751	−	0.0901967i
$327$	−5.03382	+	8.71884i	−0.278371	+	0.482153i
$328$	−1.09088			−0.0602338
$329$	4.61091	−	3.65222i	0.254207	−	0.201354i
$330$	3.07265			0.169144
$331$	−1.43133	+	2.47913i	−0.0786727	+	0.136265i	−0.902678	−	0.430318i	$-0.858402\pi$
$331$	−1.43133	+	2.47913i	−0.0786727	+	0.136265i	0.824005	+	0.566583i	$0.191735\pi$
$332$	−1.66867	−	2.89022i	−0.0915802	−	0.158622i
$333$	−1.22593	−	2.12337i	−0.0671805	−	0.116360i
$334$	9.82553	−	17.0183i	0.537629	−	0.931200i
$335$	−23.5689			−1.28771
$336$	2.45965	+	0.974732i	0.134185	+	0.0531760i
$337$	−7.70627			−0.419787			−0.209894	−	0.977724i	$-0.567312\pi$
$337$	−7.70627			−0.419787			−0.209894	+	0.977724i	$0.567312\pi$
$338$	−0.611614	+	1.05935i	−0.0332674	+	0.0576208i
$339$	−3.15196	−	5.45935i	−0.171191	−	0.296511i
$340$	−2.37677	−	4.11669i	−0.128898	−	0.223259i
$341$	3.24523	−	5.62091i	0.175739	−	0.304389i
$342$	1.09088			0.0589881
$343$	7.86989	+	16.7650i	0.424934	+	0.905224i
$344$	10.2959			0.555117
$345$	−0.914214	+	1.58346i	−0.0492196	+	0.0852509i
$346$	0.885485	+	1.53370i	0.0476040	+	0.0824525i
$347$	4.97386	+	8.61499i	0.267011	+	0.462477i	0.968089	−	0.250608i	$-0.0806307\pi$
$347$	4.97386	+	8.61499i	0.267011	+	0.462477i	−0.701078	+	0.713085i	$0.747297\pi$
$348$	0.385685	−	0.668025i	0.0206749	−	0.0358099i
$349$	−8.54489			−0.457397			−0.228699	−	0.973497i	$-0.573447\pi$
$349$	−8.54489			−0.457397			−0.228699	+	0.973497i	$0.573447\pi$
$350$	−4.07529	−	1.61499i	−0.217833	−	0.0863248i
$351$	3.77137			0.201301
$352$	−0.840244	+	1.45535i	−0.0447852	+	0.0775702i
$353$	0.997298	+	1.72737i	0.0530808	+	0.0919387i	0.891345	−	0.453326i	$-0.149763\pi$
$353$	0.997298	+	1.72737i	0.0530808	+	0.0919387i	−0.838264	+	0.545264i	$0.816429\pi$
$354$	3.21411	+	5.56700i	0.170828	+	0.295883i
$355$	−7.52273	+	13.0297i	−0.399265	+	0.691547i
$356$	3.20500			0.169864
$357$	−5.39190	+	4.27083i	−0.285370	+	0.226037i
$358$	−12.2232			−0.646018
$359$	13.8564	−	24.0001i	0.731315	−	1.26668i	−0.225006	−	0.974357i	$-0.572240\pi$
$359$	13.8564	−	24.0001i	0.731315	−	1.26668i	0.956321	−	0.292318i	$-0.0944265\pi$
$360$	−0.914214	−	1.58346i	−0.0481833	−	0.0834559i
$361$	8.90499	+	15.4239i	0.468684	+	0.811784i
$362$	−0.410393	+	0.710821i	−0.0215698	+	0.0373599i
$363$	−8.17596			−0.429127
$364$	−1.45456	−	9.87152i	−0.0762396	−	0.517408i
$365$	−5.23342			−0.273930
$366$	−4.54274	+	7.86825i	−0.237453	+	0.411280i
$367$	10.8879	+	18.8584i	0.568343	+	0.984398i	0.996730	+	0.0808031i	$0.0257485\pi$
$367$	10.8879	+	18.8584i	0.568343	+	0.984398i	−0.428387	+	0.903595i	$0.640918\pi$
$368$	−0.500000	−	0.866025i	−0.0260643	−	0.0451447i
$369$	0.545441	−	0.944731i	0.0283945	−	0.0491807i
$370$	4.48304			0.233062
$371$	2.84295	+	19.2939i	0.147598	+	1.00169i
$372$	−3.86225			−0.200248
$373$	−6.68049	+	11.5709i	−0.345903	+	0.599121i	−0.985517	−	0.169575i	$-0.945761\pi$
$373$	−6.68049	+	11.5709i	−0.345903	+	0.599121i	0.639615	+	0.768696i	$0.279094\pi$
$374$	−2.18446	−	3.78360i	−0.112956	−	0.195645i
$375$	6.08579	+	10.5409i	0.314269	+	0.544329i
$376$	1.11161	−	1.92537i	0.0573271	−	0.0992934i
$377$	−2.90912			−0.149827
$378$	−2.07397	+	1.64276i	−0.106673	+	0.0844943i
$379$	−3.50892			−0.180241			−0.0901204	−	0.995931i	$-0.528725\pi$
$379$	−3.50892			−0.180241			−0.0901204	+	0.995931i	$0.528725\pi$
$380$	−0.997298	+	1.72737i	−0.0511603	+	0.0886123i
$381$	−2.01182	−	3.48457i	−0.103069	−	0.178520i
$382$	6.22593	+	10.7836i	0.318546	+	0.551738i
$383$	−0.241522	+	0.418328i	−0.0123412	+	0.0213755i	−0.872130	−	0.489274i	$-0.837262\pi$
$383$	−0.241522	+	0.418328i	−0.0123412	+	0.0213755i	0.859789	+	0.510650i	$0.170595\pi$
$384$	1.00000			0.0510310
$385$	7.55766	+	2.99501i	0.385174	+	0.152640i
$386$	6.70412			0.341231
$387$	−5.14794	+	8.91649i	−0.261684	+	0.453251i
$388$	5.21411	+	9.03111i	0.264706	+	0.458485i
$389$	−9.31411	−	16.1325i	−0.472244	−	0.817951i	0.527252	−	0.849709i	$-0.323223\pi$
$389$	−9.31411	−	16.1325i	−0.472244	−	0.817951i	−0.999496	+	0.0317586i	$0.989889\pi$
$390$	−3.44784	+	5.97183i	−0.174588	+	0.302395i
$391$	2.59980			0.131477
$392$	5.09980	+	4.79501i	0.257579	+	0.242184i
$393$	10.9946			0.554604
$394$	−8.28028	+	14.3419i	−0.417155	+	0.722533i
$395$	−0.705196	−	1.22144i	−0.0354823	−	0.0614571i
$396$	−0.840244	−	1.45535i	−0.0422239	−	0.0731339i
$397$	−15.8722	+	27.4915i	−0.796605	+	1.37976i	0.125210	+	0.992130i	$0.460039\pi$
$397$	−15.8722	+	27.4915i	−0.796605	+	1.37976i	−0.921815	+	0.387630i	$0.873294\pi$
$398$	−5.01783			−0.251521
$399$	2.68319	+	1.06332i	0.134328	+	0.0532324i
$400$	−1.65685			−0.0828427
$401$	10.3881	−	17.9927i	0.518756	−	0.898511i	−0.481007	−	0.876717i	$-0.659729\pi$
$401$	10.3881	−	17.9927i	0.518756	−	0.898511i	0.999762	−	0.0217945i	$-0.00693796\pi$
$402$	6.44514	+	11.1633i	0.321454	+	0.556775i
$403$	7.28299	+	12.6145i	0.362791	+	0.628373i
$404$	3.23882	−	5.60980i	0.161137	−	0.279098i
$405$	1.82843			0.0908553
$406$	1.59980	−	1.26717i	0.0793966	−	0.0628887i
$407$	4.12032			0.204237
$408$	−1.29990	+	2.25149i	−0.0643546	+	0.111465i
$409$	−9.84753	−	17.0564i	−0.486929	−	0.843386i	0.512958	−	0.858414i	$-0.328550\pi$
$409$	−9.84753	−	17.0564i	−0.486929	−	0.843386i	−0.999887	+	0.0150278i	$0.995216\pi$
$410$	0.997298	+	1.72737i	0.0492531	+	0.0853088i
$411$	−2.07397	+	3.59222i	−0.102301	+	0.177191i
$412$	−18.8903			−0.930657
$413$	2.47927	+	16.8258i	0.121997	+	0.827944i
$414$	1.00000			0.0491473
$415$	−3.05104	+	5.28456i	−0.149770	+	0.259409i
$416$	−1.88568	−	3.26610i	−0.0924533	−	0.160134i
$417$	6.65685	+	11.5300i	0.325988	+	0.564627i
$418$	−0.916606	+	1.58761i	−0.0448327	+	0.0776525i
$419$	−1.70412			−0.0832518			−0.0416259	−	0.999133i	$-0.513254\pi$
$419$	−1.70412			−0.0832518			−0.0416259	+	0.999133i	$0.513254\pi$
$420$	−0.705196	−	4.78589i	−0.0344101	−	0.233527i
$421$	−12.8564			−0.626585			−0.313292	−	0.949657i	$-0.601432\pi$
$421$	−12.8564			−0.626585			−0.313292	+	0.949657i	$0.601432\pi$
$422$	−8.57616	+	14.8543i	−0.417481	+	0.723098i
$423$	1.11161	+	1.92537i	0.0540485	+	0.0936147i
$424$	3.68558	+	6.38362i	0.178988	+	0.310016i
$425$	2.15374	−	3.73039i	0.104472	−	0.180951i
$426$	8.22863			0.398678
$427$	−18.8430	+	14.9252i	−0.911877	+	0.722283i
$428$	13.8150			0.667772
$429$	−3.16887	+	5.48865i	−0.152995	+	0.264994i
$430$	−9.41263	−	16.3032i	−0.453917	−	0.786208i
$431$	5.77097	+	9.99561i	0.277978	+	0.481472i	0.970882	−	0.239558i	$-0.0770025\pi$
$431$	5.77097	+	9.99561i	0.277978	+	0.481472i	−0.692904	+	0.721030i	$0.743669\pi$
$432$	−0.500000	+	0.866025i	−0.0240563	+	0.0416667i
$433$	−24.7627			−1.19002			−0.595010	−	0.803718i	$-0.702852\pi$
$433$	−24.7627			−1.19002			−0.595010	+	0.803718i	$0.702852\pi$
$434$	−9.49980	−	3.76466i	−0.456005	−	0.180709i
$435$	−1.41039			−0.0676232
$436$	−5.03382	+	8.71884i	−0.241076	+	0.417557i
$437$	−0.545441	−	0.944731i	−0.0260920	−	0.0451926i
$438$	1.43113	+	2.47878i	0.0683818	+	0.118441i
$439$	3.91289	−	6.77733i	0.186752	−	0.323464i	−0.757413	−	0.652936i	$-0.773537\pi$
$439$	3.91289	−	6.77733i	0.186752	−	0.323464i	0.944166	+	0.329471i	$0.106870\pi$
$440$	3.07265			0.146483
$441$	−6.70249	+	2.01905i	−0.319166	+	0.0961453i
$442$	9.80479			0.466366
$443$	0.497298	−	0.861346i	0.0236274	−	0.0409238i	−0.853970	−	0.520322i	$-0.825812\pi$
$443$	0.497298	−	0.861346i	0.0236274	−	0.0409238i	0.877597	+	0.479399i	$0.159145\pi$
$444$	−1.22593	−	2.12337i	−0.0581800	−	0.100771i
$445$	−2.93005	−	5.07500i	−0.138898	−	0.240578i
$446$	−2.21141	+	3.83027i	−0.104713	+	0.181369i
$447$	−11.8724			−0.561547
$448$	2.45965	+	0.974732i	0.116208	+	0.0460517i
$449$	26.1291			1.23311			0.616554	−	0.787313i	$-0.288528\pi$
$449$	26.1291			1.23311			0.616554	+	0.787313i	$0.288528\pi$
$450$	0.828427	−	1.43488i	0.0390524	−	0.0676408i
$451$	0.916606	+	1.58761i	0.0431613	+	0.0747576i
$452$	−3.15196	−	5.45935i	−0.148256	−	0.256786i
$453$	−0.536325	+	0.928943i	−0.0251988	+	0.0436455i
$454$	−12.0905			−0.567434
$455$	−14.3014	+	11.3279i	−0.670461	+	0.531061i
$456$	1.09088			0.0510852
$457$	−9.37224	+	16.2332i	−0.438415	+	0.759357i	−0.997567	−	0.0697079i	$-0.977793\pi$
$457$	−9.37224	+	16.2332i	−0.438415	+	0.759357i	0.559153	+	0.829065i	$0.311127\pi$
$458$	4.54544	+	7.87293i	0.212394	+	0.367878i
$459$	−1.29990	−	2.25149i	−0.0606741	−	0.105091i
$460$	−0.914214	+	1.58346i	−0.0426254	+	0.0738294i
$461$	−5.63648			−0.262517			−0.131258	−	0.991348i	$-0.541902\pi$
$461$	−5.63648			−0.262517			−0.131258	+	0.991348i	$0.541902\pi$
$462$	−0.648139	−	4.39866i	−0.0301541	−	0.204644i
$463$	−20.5337			−0.954281			−0.477141	−	0.878827i	$-0.658327\pi$
$463$	−20.5337			−0.954281			−0.477141	+	0.878827i	$0.658327\pi$
$464$	0.385685	−	0.668025i	0.0179050	−	0.0310123i
$465$	3.53092	+	6.11574i	0.163743	+	0.283610i
$466$	−3.37387	−	5.84371i	−0.156291	−	0.270705i
$467$	0.589607	−	1.02123i	0.0272838	−	0.0472569i	−0.852061	−	0.523442i	$-0.824648\pi$
$467$	0.589607	−	1.02123i	0.0272838	−	0.0472569i	0.879345	+	0.476185i	$0.157981\pi$
$468$	3.77137			0.174332
$469$	4.97158	+	33.7401i	0.229566	+	1.55797i
$470$	−4.06501			−0.187505
$471$	−10.6880	+	18.5121i	−0.492476	+	0.852993i
$472$	3.21411	+	5.56700i	0.147941	+	0.256242i
$473$	−8.65105	−	14.9841i	−0.397776	−	0.688968i
$474$	−0.385685	+	0.668025i	−0.0177151	+	0.0306834i
$475$	−1.80743			−0.0829306
$476$	−5.39190	+	4.27083i	−0.247137	+	0.195753i
$477$	−7.37117			−0.337503
$478$	−10.2959	+	17.8330i	−0.470922	+	0.815662i
$479$	−0.841318	−	1.45721i	−0.0384408	−	0.0665814i	0.846165	−	0.532921i	$-0.178906\pi$
$479$	−0.841318	−	1.45721i	−0.0384408	−	0.0665814i	−0.884606	+	0.466340i	$0.845572\pi$
$480$	−0.914214	−	1.58346i	−0.0417279	−	0.0722749i
$481$	−4.62343	+	8.00802i	−0.210810	+	0.365134i
$482$	17.1814			0.782590
$483$	2.45965	+	0.974732i	0.111918	+	0.0443518i
$484$	−8.17596			−0.371634
$485$	9.53362	−	16.5127i	0.432900	−	0.749804i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	8.64504	+	14.9736i	0.391744	+	0.678521i	0.992680	−	0.120777i	$-0.0385385\pi$
$487$	8.64504	+	14.9736i	0.391744	+	0.678521i	−0.600936	+	0.799297i	$0.705205\pi$
$488$	−4.54274	+	7.86825i	−0.205640	+	0.356179i
$489$	1.88048			0.0850383
$490$	2.93042	−	12.4590i	0.132383	−	0.562840i
$491$	25.7361			1.16146			0.580728	−	0.814098i	$-0.302768\pi$
$491$	25.7361			1.16146			0.580728	+	0.814098i	$0.302768\pi$
$492$	0.545441	−	0.944731i	0.0245904	−	0.0425917i
$493$	1.00270	+	1.73673i	0.0451594	+	0.0782184i
$494$	−2.05706	−	3.56293i	−0.0925514	−	0.160304i
$495$	−1.53633	+	2.66099i	−0.0690527	+	0.119603i
$496$	−3.86225			−0.173420
$497$	20.2396	+	8.02071i	0.907869	+	0.359778i
$498$	3.33734			0.149550
$499$	11.5998	−	20.0914i	0.519278	−	0.899416i	−0.480471	−	0.877011i	$-0.659534\pi$
$499$	11.5998	−	20.0914i	0.519278	−	0.899416i	0.999749	−	0.0224055i	$-0.00713249\pi$
$500$	6.08579	+	10.5409i	0.272165	+	0.471403i
$501$	9.82553	+	17.0183i	0.438972	+	0.760322i
$502$	7.58798	−	13.1428i	0.338668	−	0.586590i
$503$	−42.3054			−1.88631			−0.943153	−	0.332358i	$-0.892156\pi$
$503$	−42.3054			−1.88631			−0.943153	+	0.332358i	$0.892156\pi$
$504$	−2.07397	+	1.64276i	−0.0923819	+	0.0731742i
$505$	−11.8439			−0.527046
$506$	−0.840244	+	1.45535i	−0.0373534	+	0.0646980i
$507$	−0.611614	−	1.05935i	−0.0271627	−	0.0470472i
$508$	−2.01182	−	3.48457i	−0.0892599	−	0.154603i
$509$	13.9517	−	24.1650i	0.618396	−	1.07109i	−0.371382	−	0.928480i	$-0.621116\pi$
$509$	13.9517	−	24.1650i	0.618396	−	1.07109i	0.989778	−	0.142614i	$-0.0455507\pi$
$510$	4.75354			0.210490
$511$	1.10393	+	7.49191i	0.0488348	+	0.331423i
$512$	1.00000			0.0441942
$513$	−0.545441	+	0.944731i	−0.0240818	+	0.0417109i
$514$	7.99730	+	13.8517i	0.352746	+	0.610973i
$515$	17.2697	+	29.9121i	0.760996	+	1.31808i
$516$	−5.14794	+	8.91649i	−0.226625	+	0.392527i
$517$	−3.73611			−0.164314
$518$	−0.945644	−	6.41771i	−0.0415492	−	0.281978i
$519$	−1.77097			−0.0777369
$520$	−3.44784	+	5.97183i	−0.151198	+	0.261882i
$521$	−8.97768	−	15.5498i	−0.393320	−	0.681249i	0.599566	−	0.800326i	$-0.295340\pi$
$521$	−8.97768	−	15.5498i	−0.393320	−	0.681249i	−0.992885	+	0.119076i	$0.962007\pi$
$522$	0.385685	+	0.668025i	0.0168810	+	0.0292387i
$523$	6.46877	−	11.2042i	0.282860	−	0.489927i	−0.689228	−	0.724544i	$-0.742050\pi$
$523$	6.46877	−	11.2042i	0.282860	−	0.489927i	0.972088	+	0.234617i	$0.0753836\pi$
$524$	10.9946			0.480301
$525$	3.43627	−	2.72181i	0.149971	−	0.118789i
$526$	21.7602			0.948788
$527$	5.02053	−	8.69582i	0.218698	−	0.378796i
$528$	−0.840244	−	1.45535i	−0.0365669	−	0.0633358i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	6.73882	−	11.6720i	0.292716	−	0.506998i
$531$	−6.42822			−0.278961
$532$	2.68319	+	1.06332i	0.116331	+	0.0461006i
$533$	−4.11412			−0.178202
$534$	−1.60250	+	2.77561i	−0.0693469	+	0.120112i
$535$	−12.6298	−	21.8755i	−0.546036	−	0.945762i
$536$	6.44514	+	11.1633i	0.278387	+	0.482181i
$537$	6.11161	−	10.5856i	0.263736	−	0.456803i
$538$	20.5627			0.886522
$539$	2.69332	−	11.4509i	0.116009	−	0.493227i
$540$	1.82843			0.0786830
$541$	−20.4899	+	35.4895i	−0.880928	+	1.52581i	−0.0306176	+	0.999531i	$0.509747\pi$
$541$	−20.4899	+	35.4895i	−0.880928	+	1.52581i	−0.850311	+	0.526281i	$0.823586\pi$
$542$	−1.93113	−	3.34481i	−0.0829489	−	0.143672i
$543$	−0.410393	−	0.710821i	−0.0176116	−	0.0305043i
$544$	−1.29990	+	2.25149i	−0.0557327	+	0.0965318i
$545$	18.4080			0.788510
$546$	9.27626	+	3.67607i	0.396987	+	0.157321i
$547$	−41.6515			−1.78089			−0.890444	−	0.455093i	$-0.849606\pi$
$547$	−41.6515			−1.78089			−0.890444	+	0.455093i	$0.849606\pi$
$548$	−2.07397	+	3.59222i	−0.0885956	+	0.153452i
$549$	−4.54274	−	7.86825i	−0.193879	−	0.335809i
$550$	1.39216	+	2.41130i	0.0593620	+	0.102818i
$551$	0.420736	−	0.728736i	0.0179240	−	0.0310452i
$552$	1.00000			0.0425628
$553$	−1.59980	+	1.26717i	−0.0680303	+	0.0538857i
$554$	24.1295			1.02516
$555$	−2.24152	+	3.88243i	−0.0951473	+	0.164800i
$556$	6.65685	+	11.5300i	0.282314	+	0.488981i
$557$	8.90789	+	15.4289i	0.377439	+	0.653744i	0.990689	−	0.136145i	$-0.0434713\pi$
$557$	8.90789	+	15.4289i	0.377439	+	0.653744i	−0.613249	+	0.789889i	$0.710138\pi$
$558$	1.93113	−	3.34481i	0.0817510	−	0.141597i
$559$	38.8296			1.64232
$560$	−0.705196	−	4.78589i	−0.0298000	−	0.202241i
$561$	4.36893			0.184456
$562$	−13.8426	+	23.9762i	−0.583916	+	1.01137i
$563$	0.445844	+	0.772224i	0.0187901	+	0.0325454i	0.875268	−	0.483639i	$-0.160685\pi$
$563$	0.445844	+	0.772224i	0.0187901	+	0.0325454i	−0.856477	+	0.516184i	$0.827352\pi$
$564$	1.11161	+	1.92537i	0.0468074	+	0.0810728i
$565$	−5.76313	+	9.98203i	−0.242457	+	0.419947i
$566$	5.96618			0.250777
$567$	−0.385685	−	2.61749i	−0.0161972	−	0.109924i
$568$	8.22863			0.345266
$569$	3.64575	−	6.31462i	0.152838	−	0.264723i	−0.779432	−	0.626487i	$-0.784492\pi$
$569$	3.64575	−	6.31462i	0.152838	−	0.264723i	0.932270	+	0.361764i	$0.117826\pi$
$570$	−0.997298	−	1.72737i	−0.0417722	−	0.0723516i
$571$	−16.1902	−	28.0422i	−0.677537	−	1.17353i	−0.975720	−	0.219021i	$-0.929714\pi$
$571$	−16.1902	−	28.0422i	−0.677537	−	1.17353i	0.298183	−	0.954509i	$-0.403620\pi$
$572$	−3.16887	+	5.48865i	−0.132497	+	0.229492i
$573$	−12.4519			−0.520184
$574$	2.26245	−	1.79205i	0.0944330	−	0.0747988i
$575$	−1.65685			−0.0690956
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	2.22700	+	3.85728i	0.0927113	+	0.160581i	0.908651	−	0.417556i	$-0.137113\pi$
$577$	2.22700	+	3.85728i	0.0927113	+	0.160581i	−0.815940	+	0.578137i	$0.803780\pi$
$578$	5.12053	+	8.86902i	0.212986	+	0.368902i
$579$	−3.35206	+	5.80594i	−0.139307	+	0.241287i
$580$	−1.41039			−0.0585634
$581$	8.20871	+	3.25301i	0.340555	+	0.134958i
$582$	−10.4282			−0.432264
$583$	6.19358	−	10.7276i	0.256512	−	0.444292i
$584$	1.43113	+	2.47878i	0.0592204	+	0.102573i
$585$	−3.44784	−	5.97183i	−0.142551	−	0.246905i
$586$	15.7426	−	27.2671i	0.650322	−	1.12639i
$587$	−13.6693			−0.564192			−0.282096	−	0.959386i	$-0.591030\pi$
$587$	−13.6693			−0.564192			−0.282096	+	0.959386i	$0.591030\pi$
$588$	−6.70249	+	2.01905i	−0.276406	+	0.0832642i
$589$	−4.21326			−0.173604
$590$	5.87677	−	10.1789i	0.241943	−	0.419057i
$591$	−8.28028	−	14.3419i	−0.340605	−	0.589946i
$592$	−1.22593	−	2.12337i	−0.0503854	−	0.0872700i
$593$	6.60520	−	11.4405i	0.271243	−	0.469807i	−0.697937	−	0.716159i	$-0.745899\pi$
$593$	6.60520	−	11.4405i	0.271243	−	0.469807i	0.969180	+	0.246352i	$0.0792319\pi$
$594$	1.68049			0.0689513
$595$	11.6921	+	4.63342i	0.479328	+	0.189952i
$596$	−11.8724			−0.486314
$597$	2.50892	−	4.34557i	0.102683	−	0.177852i
$598$	−1.88568	−	3.26610i	−0.0771114	−	0.133561i
$599$	−13.6567	−	23.6540i	−0.557996	−	0.966477i	−0.997664	−	0.0683166i	$-0.978237\pi$
$599$	−13.6567	−	23.6540i	−0.557996	−	0.966477i	0.439668	−	0.898160i	$-0.355096\pi$
$600$	0.828427	−	1.43488i	0.0338204	−	0.0585786i
$601$	39.7677			1.62216			0.811079	−	0.584936i	$-0.198880\pi$
$601$	39.7677			1.62216			0.811079	+	0.584936i	$0.198880\pi$
$602$	−21.3533	+	16.9136i	−0.870297	+	0.689348i
$603$	−12.8903			−0.524932
$604$	−0.536325	+	0.928943i	−0.0218228	+	0.0377981i
$605$	7.47457	+	12.9463i	0.303885	+	0.526344i
$606$	3.23882	+	5.60980i	0.131568	+	0.227883i
$607$	4.75955	−	8.24379i	0.193184	−	0.334605i	−0.753120	−	0.657884i	$-0.771452\pi$
$607$	4.75955	−	8.24379i	0.193184	−	0.334605i	0.946304	+	0.323279i	$0.104785\pi$
$608$	1.09088			0.0442411
$609$	0.297505	+	2.01905i	0.0120555	+	0.0818161i
$610$	16.6121			0.672606
$611$	4.19231	−	7.26129i	0.169603	−	0.293760i
$612$	−1.29990	−	2.25149i	−0.0525453	−	0.0910111i
$613$	22.8903	+	39.6471i	0.924529	+	1.60133i	0.792316	+	0.610110i	$0.208875\pi$
$613$	22.8903	+	39.6471i	0.924529	+	1.60133i	0.132213	+	0.991221i	$0.457792\pi$
$614$	−2.56907	+	4.44977i	−0.103679	+	0.179578i
$615$	−1.99460			−0.0804299
$616$	−0.648139	−	4.39866i	−0.0261142	−	0.177227i
$617$	−23.5293			−0.947254			−0.473627	−	0.880726i	$-0.657055\pi$
$617$	−23.5293			−0.947254			−0.473627	+	0.880726i	$0.657055\pi$
$618$	9.44514	−	16.3595i	0.379939	−	0.658074i
$619$	2.43224	+	4.21277i	0.0977602	+	0.169326i	0.910757	−	0.412942i	$-0.135499\pi$
$619$	2.43224	+	4.21277i	0.0977602	+	0.169326i	−0.812997	+	0.582268i	$0.802166\pi$
$620$	3.53092	+	6.11574i	0.141805	+	0.245614i
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$	−15.5627			−0.624008
$623$	−6.64706	+	5.26503i	−0.266309	+	0.210939i
$624$	3.77137			0.150976
$625$	6.98528	−	12.0989i	0.279411	−	0.483954i
$626$	11.0764	+	19.1848i	0.442700	+	0.766780i
$627$	−0.916606	−	1.58761i	−0.0366057	−	0.0634030i
$628$	−10.6880	+	18.5121i	−0.426497	+	0.738714i
$629$	6.37433			0.254161
$630$	4.49730	+	1.78223i	0.179177	+	0.0710056i
$631$	−25.5940			−1.01888			−0.509440	−	0.860506i	$-0.670148\pi$
$631$	−25.5940			−1.01888			−0.509440	+	0.860506i	$0.670148\pi$
$632$	−0.385685	+	0.668025i	−0.0153417	+	0.0265726i
$633$	−8.57616	−	14.8543i	−0.340872	−	0.590407i
$634$	−9.28136	−	16.0758i	−0.368610	−	0.638451i
$635$	−3.67846	+	6.37128i	−0.145975	+	0.252837i
$636$	−7.37117			−0.292286
$637$	19.2332	+	18.0837i	0.762048	+	0.716504i
$638$	−1.29628			−0.0513201
$639$	−4.11432	+	7.12620i	−0.162760	+	0.281908i
$640$	−0.914214	−	1.58346i	−0.0361375	−	0.0625919i
$641$	7.31773	+	12.6747i	0.289033	+	0.500620i	0.973579	−	0.228350i	$-0.0733330\pi$
$641$	7.31773	+	12.6747i	0.289033	+	0.500620i	−0.684546	+	0.728969i	$0.740000\pi$
$642$	−6.90749	+	11.9641i	−0.272617	+	0.472186i
$643$	41.6246			1.64151			0.820756	−	0.571279i	$-0.193552\pi$
$643$	41.6246			1.64151			0.820756	+	0.571279i	$0.193552\pi$
$644$	2.45965	+	0.974732i	0.0969239	+	0.0384098i
$645$	18.8253			0.741244
$646$	−1.41803	+	2.45611i	−0.0557918	+	0.0966343i
$647$	15.8096	+	27.3830i	0.621539	+	1.07654i	0.989199	+	0.146577i	$0.0468255\pi$
$647$	15.8096	+	27.3830i	0.621539	+	1.07654i	−0.367661	+	0.929960i	$0.619841\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	5.40128	−	9.35529i	0.212019	−	0.367227i
$650$	−6.24861			−0.245091
$651$	8.01019	−	6.34474i	0.313944	−	0.248670i
$652$	1.88048			0.0736453
$653$	1.64814	−	2.85466i	0.0644966	−	0.111711i	−0.831974	−	0.554815i	$-0.812789\pi$
$653$	1.64814	−	2.85466i	0.0644966	−	0.111711i	0.896471	+	0.443103i	$0.146122\pi$
$654$	−5.03382	−	8.71884i	−0.196838	−	0.340934i
$655$	−10.0514	−	17.4096i	−0.392741	−	0.680247i
$656$	0.545441	−	0.944731i	0.0212959	−	0.0368855i
$657$	−2.86225			−0.111667
$658$	0.857465	+	5.81927i	0.0334275	+	0.226859i
$659$	0.0203785			0.000793834			0.000396917	−	1.00000i	$-0.499874\pi$
$659$	0.0203785			0.000793834			0.000396917		1.00000i	$0.499874\pi$
$660$	−1.53633	+	2.66099i	−0.0598014	+	0.103579i
$661$	−21.1007	−	36.5474i	−0.820721	−	1.42153i	−0.905146	−	0.425101i	$-0.860239\pi$
$661$	−21.1007	−	36.5474i	−0.820721	−	1.42153i	0.0844251	−	0.996430i	$-0.473095\pi$
$662$	−1.43133	−	2.47913i	−0.0556300	−	0.0963540i
$663$	−4.90240	+	8.49120i	−0.190393	+	0.329771i
$664$	3.33734			0.129514
$665$	−0.769285	−	5.22083i	−0.0298316	−	0.202455i
$666$	2.45186			0.0950076
$667$	0.385685	−	0.668025i	0.0149338	−	0.0258661i
$668$	9.82553	+	17.0183i	0.380161	+	0.658458i
$669$	−2.21141	−	3.83027i	−0.0854981	−	0.148087i
$670$	11.7845	−	20.4113i	0.455273	−	0.788557i
$671$	15.2680			0.589416
$672$	−2.07397	+	1.64276i	−0.0800051	+	0.0633707i
$673$	−16.4540			−0.634255			−0.317128	−	0.948383i	$-0.602718\pi$
$673$	−16.4540			−0.634255			−0.317128	+	0.948383i	$0.602718\pi$
$674$	3.85314	−	6.67383i	0.148417	−	0.257066i
$675$	0.828427	+	1.43488i	0.0318862	+	0.0552285i
$676$	−0.611614	−	1.05935i	−0.0235236	−	0.0407441i
$677$	11.9422	−	20.6846i	0.458977	−	0.794972i	−0.539930	−	0.841710i	$-0.681549\pi$
$677$	11.9422	−	20.6846i	0.458977	−	0.794972i	0.998907	+	0.0467380i	$0.0148826\pi$
$678$	6.30392			0.242101
$679$	−25.6498	−	10.1647i	−0.984350	−	0.390086i
$680$	4.75354			0.182290
$681$	6.04524	−	10.4707i	0.231654	−	0.401237i
$682$	3.24523	+	5.62091i	0.124266	+	0.215236i
$683$	−5.54671	−	9.60719i	−0.212239	−	0.367609i	0.740176	−	0.672413i	$-0.234742\pi$
$683$	−5.54671	−	9.60719i	−0.212239	−	0.367609i	−0.952415	+	0.304804i	$0.901409\pi$
$684$	−0.545441	+	0.944731i	−0.0208554	+	0.0361227i
$685$	7.58420			0.289778
$686$	−18.4539	−	1.56697i	−0.704571	−	0.0598271i
$687$	−9.09088			−0.346839
$688$	−5.14794	+	8.91649i	−0.196263	+	0.339938i
$689$	13.8997	+	24.0750i	0.529536	+	0.917184i
$690$	−0.914214	−	1.58346i	−0.0348035	−	0.0602815i
$691$	3.31641	−	5.74419i	0.126162	−	0.218519i	−0.796024	−	0.605264i	$-0.793067\pi$
$691$	3.31641	−	5.74419i	0.126162	−	0.218519i	0.922187	+	0.386745i	$0.126401\pi$
$692$	−1.77097			−0.0673222
$693$	4.13342	+	1.63803i	0.157016	+	0.0622234i
$694$	−9.94773			−0.377611
$695$	12.1716	−	21.0818i	0.461694	−	0.799678i
$696$	0.385685	+	0.668025i	0.0146193	+	0.0253214i
$697$	1.41803	+	2.45611i	0.0537119	+	0.0930317i
$698$	4.27244	−	7.40009i	0.161714	−	0.280097i
$699$	6.74774			0.255223
$700$	3.43627	−	2.72181i	0.129879	−	0.102875i
$701$	−8.07784			−0.305096			−0.152548	−	0.988296i	$-0.548748\pi$
$701$	−8.07784			−0.305096			−0.152548	+	0.988296i	$0.548748\pi$
$702$	−1.88568	+	3.26610i	−0.0711706	+	0.123271i
$703$	−1.33734	−	2.31635i	−0.0504388	−	0.0873626i
$704$	−0.840244	−	1.45535i	−0.0316679	−	0.0548504i
$705$	2.03250	−	3.52040i	0.0765485	−	0.132586i
$706$	−1.99460			−0.0750676
$707$	2.49833	+	16.9551i	0.0939592	+	0.637664i
$708$	−6.42822			−0.241587
$709$	−18.7446	+	32.4667i	−0.703970	+	1.21931i	0.263093	+	0.964771i	$0.415258\pi$
$709$	−18.7446	+	32.4667i	−0.703970	+	1.21931i	−0.967062	+	0.254540i	$0.918076\pi$
$710$	−7.52273	−	13.0297i	−0.282323	−	0.488998i
$711$	−0.385685	−	0.668025i	−0.0144643	−	0.0250529i
$712$	−1.60250	+	2.77561i	−0.0600562	+	0.104020i
$713$	−3.86225			−0.144642
$714$	−1.00270	−	6.80494i	−0.0375252	−	0.254668i
$715$	11.5881			0.433370
$716$	6.11161	−	10.5856i	0.228402	−	0.395603i
$717$	−10.2959	−	17.8330i	−0.384507	−	0.665985i
$718$	13.8564	+	24.0001i	0.517118	+	0.895675i
$719$	−2.70122	+	4.67865i	−0.100739	+	0.174484i	−0.911989	−	0.410214i	$-0.865454\pi$
$719$	−2.70122	+	4.67865i	−0.100739	+	0.174484i	0.811251	+	0.584699i	$0.198787\pi$
$720$	1.82843			0.0681415
$721$	39.1778	−	31.0321i	1.45906	−	1.15570i
$722$	−17.8100			−0.662819
$723$	−8.59068	+	14.8795i	−0.319491	+	0.553374i
$724$	−0.410393	−	0.710821i	−0.0152521	−	0.0264175i
$725$	−0.639023	−	1.10682i	−0.0237327	−	0.0411063i
$726$	4.08798	−	7.08059i	0.151719	−	0.262785i
$727$	15.4461			0.572862			0.286431	−	0.958101i	$-0.407531\pi$
$727$	15.4461			0.572862			0.286431	+	0.958101i	$0.407531\pi$
$728$	9.27626	+	3.67607i	0.343801	+	0.136244i
$729$	1.00000			0.0370370
$730$	2.61671	−	4.53227i	0.0968487	−	0.167747i
$731$	−13.3836	−	23.1811i	−0.495010	−	0.857383i
$732$	−4.54274	−	7.86825i	−0.167904	−	0.290819i
$733$	−2.75084	+	4.76459i	−0.101604	+	0.175984i	−0.912346	−	0.409420i	$-0.865731\pi$
$733$	−2.75084	+	4.76459i	−0.101604	+	0.175984i	0.810741	+	0.585404i	$0.199064\pi$
$734$	−21.7758			−0.803758
$735$	9.32461	+	8.76732i	0.343943	+	0.323387i
$736$	1.00000			0.0368605
$737$	10.8310	−	18.7598i	0.398964	−	0.691026i
$738$	0.545441	+	0.944731i	0.0200779	+	0.0347760i
$739$	19.9710	+	34.5907i	0.734644	+	1.27244i	0.954879	+	0.296994i	$0.0959840\pi$
$739$	19.9710	+	34.5907i	0.734644	+	1.27244i	−0.220236	+	0.975447i	$0.570683\pi$
$740$	−2.24152	+	3.88243i	−0.0824000	+	0.142721i
$741$	4.11412			0.151136
$742$	−18.1305	−	7.18491i	−0.665592	−	0.263766i
$743$	21.5889			0.792020			0.396010	−	0.918246i	$-0.370395\pi$
$743$	21.5889			0.792020			0.396010	+	0.918246i	$0.370395\pi$
$744$	1.93113	−	3.34481i	0.0707985	−	0.122627i
$745$	10.8539	+	18.7996i	0.397658	+	0.688763i
$746$	−6.68049	−	11.5709i	−0.244590	−	0.423642i
$747$	−1.66867	+	2.89022i	−0.0610535	+	0.105748i
$748$	4.36893			0.159744
$749$	−28.6519	+	22.6947i	−1.04692	+	0.829245i
$750$	−12.1716			−0.444443
$751$	8.11559	−	14.0566i	0.296142	−	0.512933i	−0.679108	−	0.734038i	$-0.737633\pi$
$751$	8.11559	−	14.0566i	0.296142	−	0.512933i	0.975250	+	0.221105i	$0.0709665\pi$
$752$	1.11161	+	1.92537i	0.0405364	+	0.0702111i
$753$	7.58798	+	13.1428i	0.276521	+	0.478949i
$754$	1.45456	−	2.51937i	0.0529719	−	0.0917501i
$755$	1.96126			0.0713777
$756$	−0.385685	−	2.61749i	−0.0140272	−	0.0951971i
$757$	−25.4632			−0.925475			−0.462737	−	0.886495i	$-0.653133\pi$
$757$	−25.4632			−0.925475			−0.462737	+	0.886495i	$0.653133\pi$
$758$	1.75446	−	3.03881i	0.0637248	−	0.110375i
$759$	−0.840244	−	1.45535i	−0.0304989	−	0.0528257i
$760$	−0.997298	−	1.72737i	−0.0361758	−	0.0626583i
$761$	26.5992	−	46.0712i	0.964222	−	1.67008i	0.252530	−	0.967589i	$-0.418737\pi$
$761$	26.5992	−	46.0712i	0.964222	−	1.67008i	0.711691	−	0.702492i	$-0.247929\pi$
$762$	4.02363			0.145761
$763$	−3.88294	−	26.3520i	−0.140572	−	0.954005i
$764$	−12.4519			−0.450492
$765$	−2.37677	+	4.11669i	−0.0859323	+	0.148839i
$766$	−0.241522	−	0.418328i	−0.00872653	−	0.0151148i
$767$	12.1216	+	20.9952i	0.437686	+	0.758094i
$768$	−0.500000	+	0.866025i	−0.0180422	+	0.0312500i
$769$	1.70627			0.0615297			0.0307648	−	0.999527i	$-0.490206\pi$
$769$	1.70627			0.0615297			0.0307648	+	0.999527i	$0.490206\pi$
$770$	−6.37258	+	5.04762i	−0.229652	+	0.181904i
$771$	−15.9946			−0.576031
$772$	−3.35206	+	5.80594i	−0.120643	+	0.208960i
$773$	−13.5258	−	23.4274i	−0.486490	−	0.842626i	0.513389	−	0.858156i	$-0.328390\pi$
$773$	−13.5258	−	23.4274i	−0.486490	−	0.842626i	−0.999879	+	0.0155302i	$0.995056\pi$
$774$	−5.14794	−	8.91649i	−0.185039	−	0.320497i
$775$	−3.19959	+	5.54186i	−0.114933	+	0.199069i
$776$	−10.4282			−0.374351
$777$	6.03072	+	2.38990i	0.216351	+	0.0857373i
$778$	18.6282			0.667854
$779$	0.595011	−	1.03059i	0.0213185	−	0.0369247i
$780$	−3.44784	−	5.97183i	−0.123452	−	0.213826i
$781$	−6.91406	−	11.9755i	−0.247404	−	0.428517i
$782$	−1.29990	+	2.25149i	−0.0464843	+	0.0805131i
$783$	−0.771369			−0.0275665
$784$	−6.70249	+	2.01905i	−0.239375	+	0.0721090i
$785$	39.0844			1.39498
$786$	−5.49730	+	9.52160i	−0.196082	+	0.339624i
$787$	−17.1929	−	29.7789i	−0.612860	−	1.06150i	−0.990756	−	0.135656i	$-0.956686\pi$
$787$	−17.1929	−	29.7789i	−0.612860	−	1.06150i	0.377896	−	0.925848i	$-0.376648\pi$
$788$	−8.28028	−	14.3419i	−0.294973	−	0.510908i
$789$	−10.8801	+	18.8449i	−0.387341	+	0.670895i
$790$	1.41039			0.0501795
$791$	15.5055	+	6.14463i	0.551311	+	0.218478i
$792$	1.68049			0.0597136
$793$	−17.1323	+	29.6741i	−0.608387	+	1.05376i
$794$	−15.8722	−	27.4915i	−0.563285	−	0.975638i
$795$	6.73882	+	11.6720i	0.239001	+	0.413962i
$796$	2.50892	−	4.34557i	0.0889262	−	0.154025i
$797$	−7.25705			−0.257058			−0.128529	−	0.991706i	$-0.541026\pi$
$797$	−7.25705			−0.257058			−0.128529	+	0.991706i	$0.541026\pi$
$798$	−2.26245	+	1.79205i	−0.0800900	+	0.0634380i
$799$	−5.77994			−0.204480
$800$	0.828427	−	1.43488i	0.0292893	−	0.0507306i
$801$	−1.60250	−	2.77561i	−0.0566215	−	0.0980713i
$802$	10.3881	+	17.9927i	0.366816	+	0.635344i
$803$	2.40499	−	4.16556i	0.0848702	−	0.147000i
$804$	−12.8903			−0.454605
$805$	−0.705196	−	4.78589i	−0.0248549	−	0.168680i
$806$	−14.5660			−0.513065
$807$	−10.2814	+	17.8078i	−0.361921	+	0.626866i
$808$	3.23882	+	5.60980i	0.113941	+	0.197352i
$809$	3.22053	+	5.57811i	0.113228	+	0.196116i	0.917070	−	0.398727i	$-0.130548\pi$
$809$	3.22053	+	5.57811i	0.113228	+	0.196116i	−0.803842	+	0.594843i	$0.797214\pi$
$810$	−0.914214	+	1.58346i	−0.0321222	+	0.0556373i
$811$	21.6925			0.761727			0.380864	−	0.924631i	$-0.375627\pi$
$811$	21.6925			0.761727			0.380864	+	0.924631i	$0.375627\pi$
$812$	0.297505	+	2.01905i	0.0104404	+	0.0708548i
$813$	3.86225			0.135455
$814$	−2.06016	+	3.56830i	−0.0722085	+	0.125069i
$815$	−1.71916	−	2.97767i	−0.0602196	−	0.104303i
$816$	−1.29990	−	2.25149i	−0.0455055	−	0.0788179i
$817$	−5.61579	+	9.72683i	−0.196472	+	0.340299i
$818$	19.6951			0.688622
$819$	−7.82170	+	6.19544i	−0.273312	+	0.216486i
$820$	−1.99460			−0.0696543
$821$	2.53903	−	4.39772i	0.0886127	−	0.153482i	−0.818312	−	0.574774i	$-0.805090\pi$
$821$	2.53903	−	4.39772i	0.0886127	−	0.153482i	0.906925	+	0.421292i	$0.138423\pi$
$822$	−2.07397	−	3.59222i	−0.0723380	−	0.125293i
$823$	−27.1861	−	47.0878i	−0.947650	−	1.64138i	−0.750357	−	0.661032i	$-0.770119\pi$
$823$	−27.1861	−	47.0878i	−0.947650	−	1.64138i	−0.197292	−	0.980345i	$-0.563215\pi$
$824$	9.44514	−	16.3595i	0.329037	−	0.569909i
$825$	−2.78432			−0.0969377
$826$	−15.8112	−	6.26579i	−0.550142	−	0.218015i
$827$	−23.8979			−0.831012			−0.415506	−	0.909590i	$-0.636395\pi$
$827$	−23.8979			−0.831012			−0.415506	+	0.909590i	$0.636395\pi$
$828$	−0.500000	+	0.866025i	−0.0173762	+	0.0300965i
$829$	4.66995	+	8.08858i	0.162194	+	0.280928i	0.935655	−	0.352915i	$-0.114810\pi$
$829$	4.66995	+	8.08858i	0.162194	+	0.280928i	−0.773461	+	0.633843i	$0.781476\pi$
$830$	−3.05104	−	5.28456i	−0.105903	−	0.183430i
$831$	−12.0647	+	20.8968i	−0.418521	+	0.724900i
$832$	3.77137			0.130749
$833$	4.16669	−	17.7152i	0.144367	−	0.613794i
$834$	−13.3137			−0.461016
$835$	17.9653	−	31.1167i	0.621713	−	1.07684i
$836$	−0.916606	−	1.58761i	−0.0317015	−	0.0549086i
$837$	1.93113	+	3.34481i	0.0667495	+	0.115613i
$838$	0.852061	−	1.47581i	0.0294340	−	0.0509811i
$839$	56.1851			1.93973			0.969863	−	0.243651i	$-0.0783450\pi$
$839$	56.1851			1.93973			0.969863	+	0.243651i	$0.0783450\pi$
$840$	4.49730	+	1.78223i	0.155172	+	0.0614926i
$841$	−28.4050			−0.979482
$842$	6.42822	−	11.1340i	0.221531	−	0.383703i
$843$	−13.8426	−	23.9762i	−0.476766	−	0.825782i
$844$	−8.57616	−	14.8543i	−0.295204	−	0.511308i
$845$	−1.11829	+	1.93694i	−0.0384704	+	0.0666326i
$846$	−2.22323			−0.0764361
$847$	16.9567	−	13.4311i	0.582639	−	0.461499i
$848$	−7.37117			−0.253127
$849$	−2.98309	+	5.16686i	−0.102379	+	0.177326i
$850$	2.15374	+	3.73039i	0.0738727	+	0.127951i
$851$	−1.22593	−	2.12337i	−0.0420243	−	0.0727882i
$852$	−4.11432	+	7.12620i	−0.140954	+	0.244140i
$853$	32.1818			1.10188			0.550941	−	0.834544i	$-0.314269\pi$
$853$	32.1818			1.10188			0.550941	+	0.834544i	$0.314269\pi$
$854$	−3.50413	−	23.7811i	−0.119909	−	0.813774i
$855$	1.99460			0.0682138
$856$	−6.90749	+	11.9641i	−0.236093	+	0.408925i
$857$	−7.19465	−	12.4615i	−0.245765	−	0.425677i	0.716582	−	0.697503i	$-0.245706\pi$
$857$	−7.19465	−	12.4615i	−0.245765	−	0.425677i	−0.962346	+	0.271826i	$0.912372\pi$
$858$	−3.16887	−	5.48865i	−0.108183	−	0.187379i
$859$	14.4121	−	24.9624i	0.491734	−	0.851708i	−0.508221	−	0.861227i	$-0.669697\pi$
$859$	14.4121	−	24.9624i	0.491734	−	0.851708i	0.999955	+	0.00951892i	$0.00303001\pi$
$860$	18.8253			0.641936
$861$	0.420736	+	2.85537i	0.0143386	+	0.0973107i
$862$	−11.5419			−0.393120
$863$	19.6797	−	34.0862i	0.669904	−	1.16031i	−0.308027	−	0.951378i	$-0.599669\pi$
$863$	19.6797	−	34.0862i	0.669904	−	1.16031i	0.977931	−	0.208930i	$-0.0669980\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	1.61904	+	2.80427i	0.0550492	+	0.0953480i
$866$	12.3814	−	21.4451i	0.420736	−	0.728735i
$867$	−10.2411			−0.347805
$868$	8.01019	−	6.34474i	0.271884	−	0.215354i
$869$	1.29628			0.0439732
$870$	0.705196	−	1.22144i	0.0239084	−	0.0414106i
$871$	24.3070	+	42.1009i	0.823611	+	1.42654i
$872$	−5.03382	−	8.71884i	−0.170467	−	0.295257i
$873$	5.21411	−	9.03111i	0.176471	−	0.305657i
$874$	1.09088			0.0368996
$875$	−29.9379	−	11.8640i	−1.01208	−	0.401077i
$876$	−2.86225			−0.0967065
$877$	−15.9191	+	27.5727i	−0.537550	+	0.931064i	0.461485	+	0.887148i	$0.347317\pi$
$877$	−15.9191	+	27.5727i	−0.537550	+	0.931064i	−0.999035	+	0.0439161i	$0.986017\pi$
$878$	3.91289	+	6.77733i	0.132054	+	0.228724i
$879$	15.7426	+	27.2671i	0.530986	+	0.919695i
$880$	−1.53633	+	2.66099i	−0.0517895	+	0.0897021i
$881$	−3.69068			−0.124342			−0.0621710	−	0.998066i	$-0.519802\pi$
$881$	−3.69068			−0.124342			−0.0621710	+	0.998066i	$0.519802\pi$
$882$	1.60270	−	6.81406i	0.0539657	−	0.229441i
$883$	50.0034			1.68275			0.841374	−	0.540454i	$-0.181747\pi$
$883$	50.0034			1.68275			0.841374	+	0.540454i	$0.181747\pi$
$884$	−4.90240	+	8.49120i	−0.164885	+	0.285590i
$885$	5.87677	+	10.1789i	0.197545	+	0.342159i
$886$	0.497298	+	0.861346i	0.0167071	+	0.0289375i
$887$	−20.0668	+	34.7568i	−0.673779	+	1.16702i	0.303045	+	0.952976i	$0.401997\pi$
$887$	−20.0668	+	34.7568i	−0.673779	+	1.16702i	−0.976824	+	0.214043i	$0.931337\pi$
$888$	2.45186			0.0822790
$889$	9.89675	+	3.92196i	0.331926	+	0.131538i
$890$	5.86010			0.196431
$891$	−0.840244	+	1.45535i	−0.0281492	+	0.0487559i
$892$	−2.21141	−	3.83027i	−0.0740435	−	0.128247i
$893$	1.21264	+	2.10035i	0.0405794	+	0.0702856i
$894$	5.93622	−	10.2818i	0.198537	−	0.343876i
$895$	−22.3493			−0.747054
$896$	−2.07397	+	1.64276i	−0.0692865	+	0.0548807i
$897$	3.77137			0.125922
$898$	−13.0645	+	22.6285i	−0.435970	+	0.755121i
$899$	−1.48961	−	2.58008i	−0.0496813	−	0.0860505i
$900$	0.828427	+	1.43488i	0.0276142	+	0.0478293i
$901$	9.58177	−	16.5961i	0.319215	−	0.552896i
$902$	−1.83321			−0.0610393
$903$	−3.97096	−	26.9493i	−0.132145	−	0.896818i
$904$	6.30392			0.209665
$905$	−0.750373	+	1.29968i	−0.0249432	+	0.0432030i
$906$	−0.536325	−	0.928943i	−0.0178182	−	0.0308620i
$907$	−8.32792	−	14.4244i	−0.276524	−	0.478954i	0.693994	−	0.719980i	$-0.255849\pi$
$907$	−8.32792	−	14.4244i	−0.276524	−	0.478954i	−0.970518	+	0.241027i	$0.922516\pi$
$908$	6.04524	−	10.4707i	0.200618	−	0.347481i
$909$	−6.47764			−0.214850
$910$	−2.65956	−	18.0493i	−0.0881634	−	0.598330i
$911$	−59.6860			−1.97749			−0.988743	−	0.149625i	$-0.952193\pi$
$911$	−59.6860			−1.97749			−0.988743	+	0.149625i	$0.952193\pi$
$912$	−0.545441	+	0.944731i	−0.0180613	+	0.0312832i
$913$	−2.80418	−	4.85699i	−0.0928049	−	0.160743i
$914$	−9.37224	−	16.2332i	−0.310006	−	0.536946i
$915$	−8.30607	+	14.3865i	−0.274590	+	0.475604i
$916$	−9.09088			−0.300371
$917$	−22.8025	+	18.0615i	−0.753003	+	0.596442i
$918$	2.59980			0.0858061
$919$	18.8061	−	32.5731i	0.620356	−	1.07449i	−0.369063	−	0.929404i	$-0.620321\pi$
$919$	18.8061	−	32.5731i	0.620356	−	1.07449i	0.989419	−	0.145084i	$-0.0463454\pi$
$920$	−0.914214	−	1.58346i	−0.0301407	−	0.0522053i
$921$	−2.56907	−	4.44977i	−0.0846539	−	0.146625i
$922$	2.81824	−	4.88133i	0.0928137	−	0.160758i
$923$	31.0332			1.02147
$924$	4.13342	+	1.63803i	0.135980	+	0.0538871i
$925$	−4.06237			−0.133570
$926$	10.2668	−	17.7827i	0.337389	−	0.584375i
$927$	9.44514	+	16.3595i	0.310219	+	0.537315i
$928$	0.385685	+	0.668025i	0.0126607	+	0.0219290i
$929$	7.85476	−	13.6048i	0.257706	−	0.446361i	−0.707921	−	0.706292i	$-0.750367\pi$
$929$	7.85476	−	13.6048i	0.257706	−	0.446361i	0.965627	+	0.259931i	$0.0836999\pi$
$930$	−7.06184			−0.231567
$931$	−7.31162	+	2.20254i	−0.239629	+	0.0721855i
$932$	6.74774			0.221029
$933$	7.78136	−	13.4777i	0.254750	−	0.441240i
$934$	0.589607	+	1.02123i	0.0192925	+	0.0334157i
$935$	−3.99413	−	6.91804i	−0.130622	−	0.226244i
$936$	−1.88568	+	3.26610i	−0.0616355	+	0.106756i
$937$	−42.2196			−1.37925			−0.689627	−	0.724165i	$-0.742225\pi$
$937$	−42.2196			−1.37925			−0.689627	+	0.724165i	$0.742225\pi$
$938$	−31.7056	−	12.5646i	−1.03522	−	0.410247i
$939$	−22.1527			−0.722927
$940$	2.03250	−	3.52040i	0.0662930	−	0.114823i
$941$	−13.3361	−	23.0988i	−0.434745	−	0.753000i	0.562530	−	0.826777i	$-0.309828\pi$
$941$	−13.3361	−	23.0988i	−0.434745	−	0.753000i	−0.997275	+	0.0737767i	$0.976495\pi$
$942$	−10.6880	−	18.5121i	−0.348233	−	0.603157i
$943$	0.545441	−	0.944731i	0.0177620	−	0.0307647i
$944$	−6.42822			−0.209221
$945$	−3.79210	+	3.00366i	−0.123357	+	0.0977091i
$946$	17.3021			0.562540
$947$	20.5394	−	35.5753i	0.667442	−	1.15604i	−0.311175	−	0.950353i	$-0.600723\pi$
$947$	20.5394	−	35.5753i	0.667442	−	1.15604i	0.978617	−	0.205691i	$-0.0659441\pi$
$948$	−0.385685	−	0.668025i	−0.0125265	−	0.0216965i
$949$	5.39730	+	9.34840i	0.175204	+	0.303462i
$950$	0.903715	−	1.56528i	0.0293204	−	0.0507844i
$951$	18.5627			0.601937
$952$	−1.00270	−	6.80494i	−0.0324977	−	0.220549i
$953$	−35.0374			−1.13497			−0.567487	−	0.823383i	$-0.692084\pi$
$953$	−35.0374			−1.13497			−0.567487	+	0.823383i	$0.692084\pi$
$954$	3.68558	−	6.38362i	0.119325	−	0.206677i
$955$	11.3837	+	19.7171i	0.368366	+	0.638029i
$956$	−10.2959	−	17.8330i	−0.332992	−	0.576760i
$957$	0.648139	−	1.12261i	0.0209513	−	0.0362888i
$958$	1.68264			0.0543635
$959$	−1.59980	−	10.8572i	−0.0516601	−	0.350597i
$960$	1.82843			0.0590122
$961$	8.04151	−	13.9283i	0.259404	−	0.449300i
$962$	−4.62343	−	8.00802i	−0.149065	−	0.258189i
$963$	−6.90749	−	11.9641i	−0.222591	−	0.385539i
$964$	−8.59068	+	14.8795i	−0.276687	+	0.479236i
$965$	12.2580			0.394599
$966$	−2.07397	+	1.64276i	−0.0667289	+	0.0528548i
$967$	6.28833			0.202219			0.101109	−	0.994875i	$-0.467761\pi$
$967$	6.28833			0.202219			0.101109	+	0.994875i	$0.467761\pi$
$968$	4.08798	−	7.08059i	0.131393	−	0.227579i
$969$	−1.41803	−	2.45611i	−0.0455538	−	0.0789015i
$970$	9.53362	+	16.5127i	0.306106	+	0.530191i
$971$	−17.4971	+	30.3059i	−0.561509	+	0.972561i	0.435857	+	0.900016i	$0.356446\pi$
$971$	−17.4971	+	30.3059i	−0.561509	+	0.972561i	−0.997365	+	0.0725453i	$0.976888\pi$
$972$	1.00000			0.0320750
$973$	−32.7471	−	12.9773i	−1.04982	−	0.416033i
$974$	−17.2901			−0.554010
$975$	3.12430	−	5.41145i	0.100058	−	0.173305i
$976$	−4.54274	−	7.86825i	−0.145410	−	0.251857i
$977$	−6.08161	−	10.5337i	−0.194568	−	0.337002i	0.752191	−	0.658945i	$-0.228997\pi$
$977$	−6.08161	−	10.5337i	−0.194568	−	0.337002i	−0.946759	+	0.321944i	$0.895664\pi$
$978$	−0.940241	+	1.62854i	−0.0300656	+	0.0520751i
$979$	5.38596			0.172136
$980$	9.32461	+	8.76732i	0.297864	+	0.280062i
$981$	10.0676			0.321435
$982$	−12.8681	+	22.2881i	−0.410636	+	0.711243i
$983$	15.6542	+	27.1138i	0.499290	+	0.864796i	1.00000		0.000819731i	$-0.000260929\pi$
$983$	15.6542	+	27.1138i	0.499290	+	0.864796i	−0.500710	+	0.865615i	$0.666928\pi$
$984$	0.545441	+	0.944731i	0.0173880	+	0.0301169i
$985$	−15.1399	+	26.2231i	−0.482397	+	0.835537i
$986$	−2.00540			−0.0638651
$987$	−5.46837	−	2.16705i	−0.174060	−	0.0689780i
$988$	4.11412			0.130887
$989$	−5.14794	+	8.91649i	−0.163695	+	0.283528i
$990$	−1.53633	−	2.66099i	−0.0488276	−	0.0845719i
$991$	22.1980	+	38.4480i	0.705142	+	1.22134i	0.966640	+	0.256137i	$0.0824499\pi$
$991$	22.1980	+	38.4480i	0.705142	+	1.22134i	−0.261499	+	0.965204i	$0.584217\pi$
$992$	1.93113	−	3.34481i	0.0613133	−	0.106198i
$993$	2.86265			0.0908435
$994$	−17.0659	+	13.5176i	−0.541298	+	0.428754i
$995$	−9.17474			−0.290859
$996$	−1.66867	+	2.89022i	−0.0528739	+	0.0915802i
$997$	−22.6407	−	39.2149i	−0.717038	−	1.24195i	−0.962168	−	0.272457i	$-0.912164\pi$
$997$	−22.6407	−	39.2149i	−0.717038	−	1.24195i	0.245130	−	0.969490i	$-0.421169\pi$
$998$	11.5998	+	20.0914i	0.367185	+	0.635983i
$999$	−1.22593	+	2.12337i	−0.0387867	+	0.0671805i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.l.415.2	yes	8
7.2	even	3		6762.2.a.cp.1.3		4
7.4	even	3	inner	966.2.i.l.277.2	✓	8
7.5	odd	6		6762.2.a.cm.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.l.277.2	✓	8	7.4	even	3	inner
966.2.i.l.415.2	yes	8	1.1	even	1	trivial
6762.2.a.cm.1.1		4	7.5	odd	6
6762.2.a.cp.1.3		4	7.2	even	3

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)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.914214 + 1.58346i) q^{5} +1.00000 q^{6} +(2.45965 + 0.974732i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.914214 + 1.58346i) q^{5} +1.00000 q^{6} +(2.45965 + 0.974732i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-0.914214 - 1.58346i) q^{10} +(-0.840244 - 1.45535i) q^{11} +(-0.500000 + 0.866025i) q^{12} +3.77137 q^{13} +(-2.07397 + 1.64276i) q^{14} +1.82843 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-1.29990 - 2.25149i) q^{17} +(-0.500000 - 0.866025i) q^{18} +(-0.545441 + 0.944731i) q^{19} +1.82843 q^{20} +(-0.385685 - 2.61749i) q^{21} +1.68049 q^{22} +(-0.500000 + 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(0.828427 + 1.43488i) q^{25} +(-1.88568 + 3.26610i) q^{26} +1.00000 q^{27} +(-0.385685 - 2.61749i) q^{28} -0.771369 q^{29} +(-0.914214 + 1.58346i) q^{30} +(1.93113 + 3.34481i) q^{31} +(-0.500000 - 0.866025i) q^{32} +(-0.840244 + 1.45535i) q^{33} +2.59980 q^{34} +(-3.79210 + 3.00366i) q^{35} +1.00000 q^{36} +(-1.22593 + 2.12337i) q^{37} +(-0.545441 - 0.944731i) q^{38} +(-1.88568 - 3.26610i) q^{39} +(-0.914214 + 1.58346i) q^{40} -1.09088 q^{41} +(2.45965 + 0.974732i) q^{42} +10.2959 q^{43} +(-0.840244 + 1.45535i) q^{44} +(-0.914214 - 1.58346i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(1.11161 - 1.92537i) q^{47} +1.00000 q^{48} +(5.09980 + 4.79501i) q^{49} -1.65685 q^{50} +(-1.29990 + 2.25149i) q^{51} +(-1.88568 - 3.26610i) q^{52} +(3.68558 + 6.38362i) q^{53} +(-0.500000 + 0.866025i) q^{54} +3.07265 q^{55} +(2.45965 + 0.974732i) q^{56} +1.09088 q^{57} +(0.385685 - 0.668025i) q^{58} +(3.21411 + 5.56700i) q^{59} +(-0.914214 - 1.58346i) q^{60} +(-4.54274 + 7.86825i) q^{61} -3.86225 q^{62} +(-2.07397 + 1.64276i) q^{63} +1.00000 q^{64} +(-3.44784 + 5.97183i) q^{65} +(-0.840244 - 1.45535i) q^{66} +(6.44514 + 11.1633i) q^{67} +(-1.29990 + 2.25149i) q^{68} +1.00000 q^{69} +(-0.705196 - 4.78589i) q^{70} +8.22863 q^{71} +(-0.500000 + 0.866025i) q^{72} +(1.43113 + 2.47878i) q^{73} +(-1.22593 - 2.12337i) q^{74} +(0.828427 - 1.43488i) q^{75} +1.09088 q^{76} +(-0.648139 - 4.39866i) q^{77} +3.77137 q^{78} +(-0.385685 + 0.668025i) q^{79} +(-0.914214 - 1.58346i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(0.545441 - 0.944731i) q^{82} +3.33734 q^{83} +(-2.07397 + 1.64276i) q^{84} +4.75354 q^{85} +(-5.14794 + 8.91649i) q^{86} +(0.385685 + 0.668025i) q^{87} +(-0.840244 - 1.45535i) q^{88} +(-1.60250 + 2.77561i) q^{89} +1.82843 q^{90} +(9.27626 + 3.67607i) q^{91} +1.00000 q^{92} +(1.93113 - 3.34481i) q^{93} +(1.11161 + 1.92537i) q^{94} +(-0.997298 - 1.72737i) q^{95} +(-0.500000 + 0.866025i) q^{96} -10.4282 q^{97} +(-6.70249 + 2.01905i) q^{98} +1.68049 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9}+O(q^{10}) \) 8 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 - 4 * q^9	\( 8 q - 4 q^{2} - 4 q^{3} - 4 q^{4} + 4 q^{5} + 8 q^{6} + 8 q^{8} - 4 q^{9} + 4 q^{10} - 6 q^{11} - 4 q^{12} + 12 q^{13} - 6 q^{14} - 8 q^{15} - 4 q^{16} + 10 q^{17} - 4 q^{18} + 4 q^{19} - 8 q^{20} + 6 q^{21} + 12 q^{22} - 4 q^{23} - 4 q^{24} - 16 q^{25} - 6 q^{26} + 8 q^{27} + 6 q^{28} + 12 q^{29} + 4 q^{30} - 2 q^{31} - 4 q^{32} - 6 q^{33} - 20 q^{34} - 10 q^{35} + 8 q^{36} + 4 q^{38} - 6 q^{39} + 4 q^{40} + 8 q^{41} + 40 q^{43} - 6 q^{44} + 4 q^{45} - 4 q^{46} - 10 q^{47} + 8 q^{48} + 32 q^{50} + 10 q^{51} - 6 q^{52} - 4 q^{54} + 20 q^{55} - 8 q^{57} - 6 q^{58} - 6 q^{59} + 4 q^{60} + 4 q^{62} - 6 q^{63} + 8 q^{64} + 14 q^{65} - 6 q^{66} - 18 q^{67} + 10 q^{68} + 8 q^{69} + 2 q^{70} + 84 q^{71} - 4 q^{72} - 6 q^{73} - 16 q^{75} - 8 q^{76} - 2 q^{77} + 12 q^{78} + 6 q^{79} + 4 q^{80} - 4 q^{81} - 4 q^{82} - 20 q^{83} - 6 q^{84} + 68 q^{85} - 20 q^{86} - 6 q^{87} - 6 q^{88} - 8 q^{90} + 10 q^{91} + 8 q^{92} - 2 q^{93} - 10 q^{94} + 20 q^{95} - 4 q^{96} - 20 q^{97} - 18 q^{98} + 12 q^{99}+O(q^{100}) \) 8 * q - 4 * q^2 - 4 * q^3 - 4 * q^4 + 4 * q^5 + 8 * q^6 + 8 * q^8 - 4 * q^9 + 4 * q^10 - 6 * q^11 - 4 * q^12 + 12 * q^13 - 6 * q^14 - 8 * q^15 - 4 * q^16 + 10 * q^17 - 4 * q^18 + 4 * q^19 - 8 * q^20 + 6 * q^21 + 12 * q^22 - 4 * q^23 - 4 * q^24 - 16 * q^25 - 6 * q^26 + 8 * q^27 + 6 * q^28 + 12 * q^29 + 4 * q^30 - 2 * q^31 - 4 * q^32 - 6 * q^33 - 20 * q^34 - 10 * q^35 + 8 * q^36 + 4 * q^38 - 6 * q^39 + 4 * q^40 + 8 * q^41 + 40 * q^43 - 6 * q^44 + 4 * q^45 - 4 * q^46 - 10 * q^47 + 8 * q^48 + 32 * q^50 + 10 * q^51 - 6 * q^52 - 4 * q^54 + 20 * q^55 - 8 * q^57 - 6 * q^58 - 6 * q^59 + 4 * q^60 + 4 * q^62 - 6 * q^63 + 8 * q^64 + 14 * q^65 - 6 * q^66 - 18 * q^67 + 10 * q^68 + 8 * q^69 + 2 * q^70 + 84 * q^71 - 4 * q^72 - 6 * q^73 - 16 * q^75 - 8 * q^76 - 2 * q^77 + 12 * q^78 + 6 * q^79 + 4 * q^80 - 4 * q^81 - 4 * q^82 - 20 * q^83 - 6 * q^84 + 68 * q^85 - 20 * q^86 - 6 * q^87 - 6 * q^88 - 8 * q^90 + 10 * q^91 + 8 * q^92 - 2 * q^93 - 10 * q^94 + 20 * q^95 - 4 * q^96 - 20 * q^97 - 18 * q^98 + 12 * q^99

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