LMFDB - Embedded newform 966.2.i.k.415.3

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			415.3
Root			$-2.56022 + 0.667305i$ of defining polynomial
Character	$\chi$	$=$	966.415
Dual form			966.2.i.k.277.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(1.85801 - 1.88356i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(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} +(1.85801 - 1.88356i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.202205 + 0.350229i) q^{11} +(0.500000 - 0.866025i) q^{12} +4.12043 q^{13} +(-0.702205 - 2.55086i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.65581 - 4.59999i) q^{17} +(0.500000 + 0.866025i) q^{18} +(1.35801 - 2.35214i) q^{19} +1.00000 q^{20} +(2.56022 + 0.667305i) q^{21} +0.404409 q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.06022 - 3.56840i) q^{26} -1.00000 q^{27} +(-2.56022 - 0.667305i) q^{28} +9.12043 q^{29} +(-0.500000 + 0.866025i) q^{30} +(4.91823 + 8.51862i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.202205 + 0.350229i) q^{33} -5.31161 q^{34} +(0.702205 + 2.55086i) q^{35} +1.00000 q^{36} +(3.95360 - 6.84784i) q^{37} +(-1.35801 - 2.35214i) q^{38} +(2.06022 + 3.56840i) q^{39} +(0.500000 - 0.866025i) q^{40} -10.7160 q^{41} +(1.85801 - 1.88356i) q^{42} +0.808819 q^{43} +(0.202205 - 0.350229i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(5.41823 - 9.38464i) q^{47} -1.00000 q^{48} +(-0.0955907 - 6.99935i) q^{49} +4.00000 q^{50} +(2.65581 - 4.59999i) q^{51} +(-2.06022 - 3.56840i) q^{52} +(0.0955907 + 0.165568i) q^{53} +(-0.500000 + 0.866025i) q^{54} -0.404409 q^{55} +(-1.85801 + 1.88356i) q^{56} +2.71602 q^{57} +(4.56022 - 7.89853i) q^{58} +(4.15581 + 7.19807i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-5.00000 + 8.66025i) q^{61} +9.83645 q^{62} +(0.702205 + 2.55086i) q^{63} +1.00000 q^{64} +(-2.06022 + 3.56840i) q^{65} +(0.202205 + 0.350229i) q^{66} +(-1.41823 - 2.45644i) q^{67} +(-2.65581 + 4.59999i) q^{68} +1.00000 q^{69} +(2.56022 + 0.667305i) q^{70} -6.92925 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.29780 - 3.97990i) q^{73} +(-3.95360 - 6.84784i) q^{74} +(-2.00000 + 3.46410i) q^{75} -2.71602 q^{76} +(1.03538 + 0.269864i) q^{77} +4.12043 q^{78} +(4.96462 - 8.59898i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.35801 + 9.28035i) q^{82} -4.40441 q^{83} +(-0.702205 - 2.55086i) q^{84} +5.31161 q^{85} +(0.404409 - 0.700458i) q^{86} +(4.56022 + 7.89853i) q^{87} +(-0.202205 - 0.350229i) q^{88} +(-3.95360 + 6.84784i) q^{89} -1.00000 q^{90} +(7.65581 - 7.76108i) q^{91} -1.00000 q^{92} +(-4.91823 + 8.51862i) q^{93} +(-5.41823 - 9.38464i) q^{94} +(1.35801 + 2.35214i) q^{95} +(-0.500000 + 0.866025i) q^{96} +15.3613 q^{97} +(-6.10941 - 3.41689i) q^{98} -0.404409 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 $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

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

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
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	−0.955901	−	0.293691i	$-0.905116\pi$
$5$	−0.500000	+	0.866025i	−0.223607	+	0.387298i	0.732294	+	0.680989i	$0.238450\pi$
$6$	1.00000			0.408248
$7$	1.85801	−	1.88356i	0.702262	−	0.711918i
$7$	1.85801	−	1.88356i	0.702262	−	0.711918i
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	+	0.866025i	0.158114	+	0.273861i
$11$	0.202205	+	0.350229i	0.0609670	+	0.105598i	0.894898	−	0.446271i	$-0.147248\pi$
$11$	0.202205	+	0.350229i	0.0609670	+	0.105598i	−0.833931	+	0.551869i	$0.813915\pi$
$12$	0.500000	−	0.866025i	0.144338	−	0.250000i
$13$	4.12043			1.14280			0.571401	−	0.820671i	$-0.306400\pi$
$13$	4.12043			1.14280			0.571401	+	0.820671i	$0.306400\pi$
$14$	−0.702205	−	2.55086i	−0.187672	−	0.681747i
$15$	−1.00000			−0.258199
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.65581	−	4.59999i	−0.644128	−	1.11566i	−0.984502	−	0.175372i	$-0.943887\pi$
$17$	−2.65581	−	4.59999i	−0.644128	−	1.11566i	0.340375	−	0.940290i	$-0.389446\pi$
$18$	0.500000	+	0.866025i	0.117851	+	0.204124i
$19$	1.35801	−	2.35214i	0.311549	−	0.539619i	−0.667149	−	0.744924i	$-0.732486\pi$
$19$	1.35801	−	2.35214i	0.311549	−	0.539619i	0.978698	+	0.205306i	$0.0658188\pi$
$20$	1.00000			0.223607
$21$	2.56022	+	0.667305i	0.558685	+	0.145618i
$22$	0.404409			0.0862204
$23$	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
$26$	2.06022	−	3.56840i	0.404042	−	0.699820i
$27$	−1.00000			−0.192450
$28$	−2.56022	−	0.667305i	−0.483835	−	0.126109i
$29$	9.12043			1.69362			0.846811	−	0.531894i	$-0.178520\pi$
$29$	9.12043			1.69362			0.846811	+	0.531894i	$0.178520\pi$
$30$	−0.500000	+	0.866025i	−0.0912871	+	0.158114i
$31$	4.91823	+	8.51862i	0.883340	+	1.52999i	0.847605	+	0.530628i	$0.178044\pi$
$31$	4.91823	+	8.51862i	0.883340	+	1.52999i	0.0357346	+	0.999361i	$0.488623\pi$
$32$	0.500000	+	0.866025i	0.0883883	+	0.153093i
$33$	−0.202205	+	0.350229i	−0.0351993	+	0.0609670i
$34$	−5.31161			−0.910934
$35$	0.702205	+	2.55086i	0.118694	+	0.431175i
$36$	1.00000			0.166667
$37$	3.95360	−	6.84784i	0.649968	−	1.12578i	−0.333162	−	0.942870i	$-0.608116\pi$
$37$	3.95360	−	6.84784i	0.649968	−	1.12578i	0.983130	−	0.182908i	$-0.0585511\pi$
$38$	−1.35801	−	2.35214i	−0.220298	−	0.381568i
$39$	2.06022	+	3.56840i	0.329899	+	0.571401i
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−10.7160			−1.67356			−0.836781	−	0.547538i	$-0.815565\pi$
$41$	−10.7160			−1.67356			−0.836781	+	0.547538i	$0.815565\pi$
$42$	1.85801	−	1.88356i	0.286697	−	0.290639i
$43$	0.808819			0.123344			0.0616718	−	0.998096i	$-0.480357\pi$
$43$	0.808819			0.123344			0.0616718	+	0.998096i	$0.480357\pi$
$44$	0.202205	−	0.350229i	0.0304835	−	0.0527990i
$45$	−0.500000	−	0.866025i	−0.0745356	−	0.129099i
$46$	−0.500000	−	0.866025i	−0.0737210	−	0.127688i
$47$	5.41823	−	9.38464i	0.790330	−	1.36889i	−0.135433	−	0.990786i	$-0.543243\pi$
$47$	5.41823	−	9.38464i	0.790330	−	1.36889i	0.925763	−	0.378105i	$-0.123424\pi$
$48$	−1.00000			−0.144338
$49$	−0.0955907	−	6.99935i	−0.0136558	−	0.999907i
$50$	4.00000			0.565685
$51$	2.65581	−	4.59999i	0.371887	−	0.644128i
$52$	−2.06022	−	3.56840i	−0.285701	−	0.494848i
$53$	0.0955907	+	0.165568i	0.0131304	+	0.0227425i	0.872516	−	0.488586i	$-0.162487\pi$
$53$	0.0955907	+	0.165568i	0.0131304	+	0.0227425i	−0.859386	+	0.511328i	$0.829154\pi$
$54$	−0.500000	+	0.866025i	−0.0680414	+	0.117851i
$55$	−0.404409			−0.0545305
$56$	−1.85801	+	1.88356i	−0.248287	+	0.251701i
$57$	2.71602			0.359746
$58$	4.56022	−	7.89853i	0.598786	−	1.03713i
$59$	4.15581	+	7.19807i	0.541040	+	0.937109i	0.998845	+	0.0480558i	$0.0153025\pi$
$59$	4.15581	+	7.19807i	0.541040	+	0.937109i	−0.457805	+	0.889053i	$0.651364\pi$
$60$	0.500000	+	0.866025i	0.0645497	+	0.111803i
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	0.345207	+	0.938527i	$0.387809\pi$
$61$	−5.00000	+	8.66025i	−0.640184	+	1.10883i	−0.985391	+	0.170305i	$0.945525\pi$
$62$	9.83645			1.24923
$63$	0.702205	+	2.55086i	0.0884695	+	0.321379i
$64$	1.00000			0.125000
$65$	−2.06022	+	3.56840i	−0.255538	+	0.442605i
$66$	0.202205	+	0.350229i	0.0248897	+	0.0431102i
$67$	−1.41823	−	2.45644i	−0.173264	−	0.300102i	0.766295	−	0.642489i	$-0.222098\pi$
$67$	−1.41823	−	2.45644i	−0.173264	−	0.300102i	−0.939559	+	0.342387i	$0.888765\pi$
$68$	−2.65581	+	4.59999i	−0.322064	+	0.557831i
$69$	1.00000			0.120386
$70$	2.56022	+	0.667305i	0.306004	+	0.0797582i
$71$	−6.92925			−0.822351			−0.411175	−	0.911556i	$-0.634882\pi$
$71$	−6.92925			−0.822351			−0.411175	+	0.911556i	$0.634882\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−2.29780	−	3.97990i	−0.268937	−	0.465812i	0.699651	−	0.714485i	$-0.253339\pi$
$73$	−2.29780	−	3.97990i	−0.268937	−	0.465812i	−0.968587	+	0.248673i	$0.920006\pi$
$74$	−3.95360	−	6.84784i	−0.459597	−	0.796045i
$75$	−2.00000	+	3.46410i	−0.230940	+	0.400000i
$76$	−2.71602			−0.311549
$77$	1.03538	+	0.269864i	0.117992	+	0.0307539i
$78$	4.12043			0.466547
$79$	4.96462	−	8.59898i	0.558564	−	0.967461i	−0.439053	−	0.898461i	$-0.644686\pi$
$79$	4.96462	−	8.59898i	0.558564	−	0.967461i	0.997617	−	0.0689998i	$-0.0219808\pi$
$80$	−0.500000	−	0.866025i	−0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−5.35801	+	9.28035i	−0.591693	+	1.02484i
$83$	−4.40441			−0.483447			−0.241723	−	0.970345i	$-0.577713\pi$
$83$	−4.40441			−0.483447			−0.241723	+	0.970345i	$0.577713\pi$
$84$	−0.702205	−	2.55086i	−0.0766168	−	0.278322i
$85$	5.31161			0.576125
$86$	0.404409	−	0.700458i	0.0436086	−	0.0755323i
$87$	4.56022	+	7.89853i	0.488906	+	0.846811i
$88$	−0.202205	−	0.350229i	−0.0215551	−	0.0373345i
$89$	−3.95360	+	6.84784i	−0.419081	+	0.725869i	−0.995847	−	0.0910397i	$-0.970981\pi$
$89$	−3.95360	+	6.84784i	−0.419081	+	0.725869i	0.576766	+	0.816909i	$0.304314\pi$
$90$	−1.00000			−0.105409
$91$	7.65581	−	7.76108i	0.802547	−	0.813582i
$92$	−1.00000			−0.104257
$93$	−4.91823	+	8.51862i	−0.509996	+	0.883340i
$94$	−5.41823	−	9.38464i	−0.558847	−	0.967952i
$95$	1.35801	+	2.35214i	0.139329	+	0.241325i
$96$	−0.500000	+	0.866025i	−0.0510310	+	0.0883883i
$97$	15.3613			1.55970			0.779852	−	0.625965i	$-0.215295\pi$
$97$	15.3613			1.55970			0.779852	+	0.625965i	$0.215295\pi$
$98$	−6.10941	−	3.41689i	−0.617143	−	0.345158i
$99$	−0.404409			−0.0406447
$100$	2.00000	−	3.46410i	0.200000	−	0.346410i
$101$	2.59559	+	4.49569i	0.258271	+	0.447338i	0.965779	−	0.259367i	$-0.0835139\pi$
$101$	2.59559	+	4.49569i	0.258271	+	0.447338i	−0.707508	+	0.706705i	$0.750181\pi$
$102$	−2.65581	−	4.59999i	−0.262964	−	0.455467i
$103$	−8.41823	+	14.5808i	−0.829473	+	1.43669i	0.0689801	+	0.997618i	$0.478025\pi$
$103$	−8.41823	+	14.5808i	−0.829473	+	1.43669i	−0.898453	+	0.439070i	$0.855308\pi$
$104$	−4.12043			−0.404042
$105$	−1.85801	+	1.88356i	−0.181323	+	0.183817i
$106$	0.191181			0.0185692
$107$	4.79780	−	8.31003i	0.463820	−	0.803360i	−0.535327	−	0.844645i	$-0.679812\pi$
$107$	4.79780	−	8.31003i	0.463820	−	0.803360i	0.999147	+	0.0412844i	$0.0131450\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	1.59559	+	2.76364i	0.152830	+	0.264709i	0.932267	−	0.361772i	$-0.117828\pi$
$109$	1.59559	+	2.76364i	0.152830	+	0.264709i	−0.779437	+	0.626481i	$0.784495\pi$
$110$	−0.202205	+	0.350229i	−0.0192795	+	0.0333930i
$111$	7.90720			0.750519
$112$	0.702205	+	2.55086i	0.0663521	+	0.241034i
$113$	−18.7437			−1.76325			−0.881627	−	0.471946i	$-0.843552\pi$
$113$	−18.7437			−1.76325			−0.881627	+	0.471946i	$0.843552\pi$
$114$	1.35801	−	2.35214i	0.127189	−	0.220298i
$115$	0.500000	+	0.866025i	0.0466252	+	0.0807573i
$116$	−4.56022	−	7.89853i	−0.423405	−	0.733360i
$117$	−2.06022	+	3.56840i	−0.190467	+	0.329899i
$118$	8.31161			0.765146
$119$	−13.5989	−	3.54447i	−1.24661	−	0.324921i
$120$	1.00000			0.0912871
$121$	5.41823	−	9.38464i	0.492566	−	0.853149i
$122$	5.00000	+	8.66025i	0.452679	+	0.784063i
$123$	−5.35801	−	9.28035i	−0.483116	−	0.836781i
$124$	4.91823	−	8.51862i	0.441670	−	0.764995i
$125$	−9.00000			−0.804984
$126$	2.56022	+	0.667305i	0.228082	+	0.0594483i
$127$	−11.5956			−1.02894			−0.514471	−	0.857508i	$-0.672012\pi$
$127$	−11.5956			−1.02894			−0.514471	+	0.857508i	$0.672012\pi$
$128$	0.500000	−	0.866025i	0.0441942	−	0.0765466i
$129$	0.404409	+	0.700458i	0.0356063	+	0.0616718i
$130$	2.06022	+	3.56840i	0.180693	+	0.312969i
$131$	−8.38285	+	14.5195i	−0.732413	+	1.26858i	0.223436	+	0.974719i	$0.428273\pi$
$131$	−8.38285	+	14.5195i	−0.732413	+	1.26858i	−0.955849	+	0.293858i	$0.905061\pi$
$132$	0.404409			0.0351993
$133$	−1.90720	−	6.92820i	−0.165375	−	0.600751i
$134$	−2.83645			−0.245032
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	2.65581	+	4.59999i	0.227734	+	0.394446i
$137$	4.82264	+	8.35305i	0.412026	+	0.713649i	0.995111	−	0.0987615i	$-0.0314881\pi$
$137$	4.82264	+	8.35305i	0.412026	+	0.713649i	−0.583086	+	0.812411i	$0.698155\pi$
$138$	0.500000	−	0.866025i	0.0425628	−	0.0737210i
$139$	−16.8641			−1.43039			−0.715197	−	0.698923i	$-0.753663\pi$
$139$	−16.8641			−1.43039			−0.715197	+	0.698923i	$0.753663\pi$
$140$	1.85801	−	1.88356i	0.157031	−	0.159190i
$141$	10.8365			0.912594
$142$	−3.46462	+	6.00091i	−0.290745	+	0.503585i
$143$	0.833170	+	1.44309i	0.0696732	+	0.120678i
$144$	−0.500000	−	0.866025i	−0.0416667	−	0.0721688i
$145$	−4.56022	+	7.89853i	−0.378705	+	0.655937i
$146$	−4.59559			−0.380334
$147$	6.01382	−	3.58246i	0.496011	−	0.295476i
$148$	−7.90720			−0.649968
$149$	5.10661	−	8.84491i	0.418350	−	0.724604i	−0.577424	−	0.816445i	$-0.695942\pi$
$149$	5.10661	−	8.84491i	0.418350	−	0.724604i	0.995774	+	0.0918411i	$0.0292752\pi$
$150$	2.00000	+	3.46410i	0.163299	+	0.282843i
$151$	−2.79780	−	4.84592i	−0.227681	−	0.394356i	0.729439	−	0.684046i	$-0.239781\pi$
$151$	−2.79780	−	4.84592i	−0.227681	−	0.394356i	−0.957121	+	0.289690i	$0.906448\pi$
$152$	−1.35801	+	2.35214i	−0.110149	+	0.190784i
$153$	5.31161			0.429418
$154$	0.751397	−	0.761729i	0.0605493	−	0.0613819i
$155$	−9.83645			−0.790083
$156$	2.06022	−	3.56840i	0.164949	−	0.285701i
$157$	−11.3856	−	19.7205i	−0.908673	−	1.57387i	−0.815909	−	0.578180i	$-0.803763\pi$
$157$	−11.3856	−	19.7205i	−0.908673	−	1.57387i	−0.0927645	−	0.995688i	$-0.529570\pi$
$158$	−4.96462	−	8.59898i	−0.394964	−	0.684098i
$159$	−0.0955907	+	0.165568i	−0.00758083	+	0.0131304i
$160$	−1.00000			−0.0790569
$161$	−0.702205	−	2.55086i	−0.0553415	−	0.201036i
$162$	−1.00000			−0.0785674
$163$	−12.3856	+	21.4526i	−0.970119	+	1.68029i	−0.274935	+	0.961463i	$0.588656\pi$
$163$	−12.3856	+	21.4526i	−0.970119	+	1.68029i	−0.695184	+	0.718832i	$0.744677\pi$
$164$	5.35801	+	9.28035i	0.418390	+	0.724673i
$165$	−0.202205	−	0.350229i	−0.0157416	−	0.0272653i
$166$	−2.20220	+	3.81433i	−0.170924	+	0.296049i
$167$	−19.0773			−1.47625			−0.738123	−	0.674666i	$-0.764288\pi$
$167$	−19.0773			−1.47625			−0.738123	+	0.674666i	$0.764288\pi$
$168$	−2.56022	−	0.667305i	−0.197525	−	0.0514837i
$169$	3.97795			0.305996
$170$	2.65581	−	4.59999i	0.203691	−	0.352803i
$171$	1.35801	+	2.35214i	0.103850	+	0.179873i
$172$	−0.404409	−	0.700458i	−0.0308359	−	0.0534094i
$173$	−3.12043	+	5.40475i	−0.237242	+	0.410915i	−0.959922	−	0.280268i	$-0.909577\pi$
$173$	−3.12043	+	5.40475i	−0.237242	+	0.410915i	0.722680	+	0.691183i	$0.242910\pi$
$174$	9.12043			0.691418
$175$	10.2409	+	2.66922i	0.774136	+	0.201774i
$176$	−0.404409			−0.0304835
$177$	−4.15581	+	7.19807i	−0.312370	+	0.541040i
$178$	3.95360	+	6.84784i	0.296335	+	0.513267i
$179$	5.60941	+	9.71578i	0.419267	+	0.726191i	0.995866	−	0.0908358i	$-0.0289538\pi$
$179$	5.60941	+	9.71578i	0.419267	+	0.726191i	−0.576599	+	0.817027i	$0.695621\pi$
$180$	−0.500000	+	0.866025i	−0.0372678	+	0.0645497i
$181$	8.24086			0.612538			0.306269	−	0.951945i	$-0.400919\pi$
$181$	8.24086			0.612538			0.306269	+	0.951945i	$0.400919\pi$
$182$	−2.89339	−	10.5107i	−0.214472	−	0.779102i
$183$	−10.0000			−0.739221
$184$	−0.500000	+	0.866025i	−0.0368605	+	0.0638442i
$185$	3.95360	+	6.84784i	0.290675	+	0.503463i
$186$	4.91823	+	8.51862i	0.360622	+	0.624615i
$187$	1.07403	−	1.86028i	0.0785411	−	0.136037i
$188$	−10.8365			−0.790330
$189$	−1.85801	+	1.88356i	−0.135150	+	0.137009i
$190$	2.71602			0.197041
$191$	−12.3856	+	21.4526i	−0.896194	+	1.55225i	−0.0638738	+	0.997958i	$0.520345\pi$
$191$	−12.3856	+	21.4526i	−0.896194	+	1.55225i	−0.832320	+	0.554295i	$0.812988\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	7.42925	+	12.8678i	0.534769	+	0.926247i	0.999174	+	0.0406245i	$0.0129347\pi$
$193$	7.42925	+	12.8678i	0.534769	+	0.926247i	−0.464405	+	0.885623i	$0.653732\pi$
$194$	7.68065	−	13.3033i	0.551438	−	0.955119i
$195$	−4.12043			−0.295070
$196$	−6.01382	+	3.58246i	−0.429558	+	0.255890i
$197$	−11.4320			−0.814499			−0.407250	−	0.913317i	$-0.633512\pi$
$197$	−11.4320			−0.814499			−0.407250	+	0.913317i	$0.633512\pi$
$198$	−0.202205	+	0.350229i	−0.0143701	+	0.0248897i
$199$	4.31161	+	7.46793i	0.305642	+	0.529388i	0.977404	−	0.211379i	$-0.0677956\pi$
$199$	4.31161	+	7.46793i	0.305642	+	0.529388i	−0.671762	+	0.740767i	$0.734462\pi$
$200$	−2.00000	−	3.46410i	−0.141421	−	0.244949i
$201$	1.41823	−	2.45644i	0.100034	−	0.173264i
$202$	5.19118			0.365250
$203$	16.9459	−	17.1789i	1.18937	−	1.20572i
$204$	−5.31161			−0.371887
$205$	5.35801	−	9.28035i	0.374220	−	0.648168i
$206$	8.41823	+	14.5808i	0.586526	+	1.01589i
$207$	0.500000	+	0.866025i	0.0347524	+	0.0601929i
$208$	−2.06022	+	3.56840i	−0.142850	+	0.247424i
$209$	1.09838			0.0759769
$210$	0.702205	+	2.55086i	0.0484567	+	0.176026i
$211$	7.43204			0.511643			0.255821	−	0.966724i	$-0.417654\pi$
$211$	7.43204			0.511643			0.255821	+	0.966724i	$0.417654\pi$
$212$	0.0955907	−	0.165568i	0.00656519	−	0.0113713i
$213$	−3.46462	−	6.00091i	−0.237392	−	0.411175i
$214$	−4.79780	−	8.31003i	−0.327971	−	0.568062i
$215$	−0.404409	+	0.700458i	−0.0275805	+	0.0477708i
$216$	1.00000			0.0680414
$217$	25.1834	+	6.56391i	1.70956	+	0.445588i
$218$	3.19118			0.216134
$219$	2.29780	−	3.97990i	0.155271	−	0.268937i
$220$	0.202205	+	0.350229i	0.0136326	+	0.0236124i
$221$	−10.9431	−	18.9539i	−0.736110	−	1.27498i
$222$	3.95360	−	6.84784i	0.265348	−	0.459597i
$223$	10.2188			0.684303			0.342151	−	0.939645i	$-0.388844\pi$
$223$	10.2188			0.684303			0.342151	+	0.939645i	$0.388844\pi$
$224$	2.56022	+	0.667305i	0.171062	+	0.0445862i
$225$	−4.00000			−0.266667
$226$	−9.37183	+	16.2325i	−0.623405	+	1.07977i
$227$	−6.10941	−	10.5818i	−0.405496	−	0.702339i	0.588883	−	0.808218i	$-0.299568\pi$
$227$	−6.10941	−	10.5818i	−0.405496	−	0.702339i	−0.994379	+	0.105879i	$0.966234\pi$
$228$	−1.35801	−	2.35214i	−0.0899365	−	0.155775i
$229$	−1.92597	+	3.33587i	−0.127271	+	0.220441i	−0.922619	−	0.385714i	$-0.873955\pi$
$229$	−1.92597	+	3.33587i	−0.127271	+	0.220441i	0.795347	+	0.606154i	$0.207289\pi$
$230$	1.00000			0.0659380
$231$	0.283978	+	1.03159i	0.0186844	+	0.0678739i
$232$	−9.12043			−0.598786
$233$	13.2652	−	22.9760i	0.869033	−	1.50521i	0.00604701	−	0.999982i	$-0.498075\pi$
$233$	13.2652	−	22.9760i	0.869033	−	1.50521i	0.862986	−	0.505228i	$-0.168592\pi$
$234$	2.06022	+	3.56840i	0.134681	+	0.233273i
$235$	5.41823	+	9.38464i	0.353446	+	0.612187i
$236$	4.15581	−	7.19807i	0.270520	−	0.468554i
$237$	9.92925			0.644974
$238$	−9.86903	+	10.0047i	−0.639714	+	0.648511i
$239$	−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
$241$	7.39667	+	12.8114i	0.476461	+	0.825255i	0.999636	−	0.0269701i	$-0.00858590\pi$
$241$	7.39667	+	12.8114i	0.476461	+	0.825255i	−0.523175	+	0.852225i	$0.675253\pi$
$242$	−5.41823	−	9.38464i	−0.348297	−	0.603268i
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	10.0000			0.640184
$245$	6.10941	+	3.41689i	0.390316	+	0.218297i
$246$	−10.7160			−0.683229
$247$	5.59559	−	9.69185i	0.356039	−	0.616677i
$248$	−4.91823	−	8.51862i	−0.312308	−	0.540933i
$249$	−2.20220	−	3.81433i	−0.139559	−	0.241723i
$250$	−4.50000	+	7.79423i	−0.284605	+	0.492950i
$251$	14.0220			0.885064			0.442532	−	0.896753i	$-0.354080\pi$
$251$	14.0220			0.885064			0.442532	+	0.896753i	$0.354080\pi$
$252$	1.85801	−	1.88356i	0.117044	−	0.118653i
$253$	0.404409			0.0254250
$254$	−5.79780	+	10.0421i	−0.363786	+	0.630096i
$255$	2.65581	+	4.59999i	0.166313	+	0.288063i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	−3.54919	+	6.14738i	−0.221393	+	0.383463i	−0.955231	−	0.295861i	$-0.904394\pi$
$257$	−3.54919	+	6.14738i	−0.221393	+	0.383463i	0.733839	+	0.679324i	$0.237727\pi$
$258$	0.808819			0.0503548
$259$	−5.55247	−	20.1702i	−0.345014	−	1.25332i
$260$	4.12043			0.255538
$261$	−4.56022	+	7.89853i	−0.282270	+	0.488906i
$262$	8.38285	+	14.5195i	0.517894	+	0.897019i
$263$	4.40441	+	7.62866i	0.271588	+	0.470403i	0.969269	−	0.246005i	$-0.0791180\pi$
$263$	4.40441	+	7.62866i	0.271588	+	0.470403i	−0.697681	+	0.716409i	$0.745785\pi$
$264$	0.202205	−	0.350229i	0.0124448	−	0.0215551i
$265$	−0.191181			−0.0117442
$266$	−6.95360	−	1.81242i	−0.426353	−	0.111126i
$267$	−7.90720			−0.483913
$268$	−1.41823	+	2.45644i	−0.0866320	+	0.150051i
$269$	2.24860	+	3.89469i	0.137100	+	0.237464i	0.926398	−	0.376547i	$-0.122889\pi$
$269$	2.24860	+	3.89469i	0.137100	+	0.237464i	−0.789298	+	0.614010i	$0.789555\pi$
$270$	−0.500000	−	0.866025i	−0.0304290	−	0.0527046i
$271$	−7.63425	+	13.2229i	−0.463748	+	0.803234i	−0.999144	−	0.0413665i	$-0.986829\pi$
$271$	−7.63425	+	13.2229i	−0.463748	+	0.803234i	0.535396	+	0.844601i	$0.320162\pi$
$272$	5.31161			0.322064
$273$	10.5492	+	2.74958i	0.638466	+	0.166412i
$274$	9.64527			0.582692
$275$	−0.808819	+	1.40092i	−0.0487736	+	0.0844784i
$276$	−0.500000	−	0.866025i	−0.0300965	−	0.0521286i
$277$	1.10661	+	1.91671i	0.0664900	+	0.115164i	0.897354	−	0.441312i	$-0.145487\pi$
$277$	1.10661	+	1.91671i	0.0664900	+	0.115164i	−0.830864	+	0.556476i	$0.812153\pi$
$278$	−8.43204	+	14.6047i	−0.505720	+	0.875933i
$279$	−9.83645			−0.588893
$280$	−0.702205	−	2.55086i	−0.0419648	−	0.152443i
$281$	29.4110			1.75451			0.877256	−	0.480023i	$-0.159372\pi$
$281$	29.4110			1.75451			0.877256	+	0.480023i	$0.159372\pi$
$282$	5.41823	−	9.38464i	0.322651	−	0.558847i
$283$	−13.5387	−	23.4496i	−0.804790	−	1.39394i	−0.916433	−	0.400188i	$-0.868945\pi$
$283$	−13.5387	−	23.4496i	−0.804790	−	1.39394i	0.111643	−	0.993748i	$-0.464389\pi$
$284$	3.46462	+	6.00091i	0.205588	+	0.356088i
$285$	−1.35801	+	2.35214i	−0.0804416	+	0.139329i
$286$	1.66634			0.0985328
$287$	−19.9105	+	20.1843i	−1.17528	+	1.19144i
$288$	−1.00000			−0.0589256
$289$	−5.60661	+	9.71094i	−0.329801	+	0.571232i
$290$	4.56022	+	7.89853i	0.267785	+	0.463817i
$291$	7.68065	+	13.3033i	0.450247	+	0.779852i
$292$	−2.29780	+	3.97990i	−0.134468	+	0.232906i
$293$	−19.8641			−1.16047			−0.580236	−	0.814448i	$-0.697040\pi$
$293$	−19.8641			−1.16047			−0.580236	+	0.814448i	$0.697040\pi$
$294$	−0.0955907	−	6.99935i	−0.00557496	−	0.408210i
$295$	−8.31161			−0.483921
$296$	−3.95360	+	6.84784i	−0.229798	+	0.398023i
$297$	−0.202205	−	0.350229i	−0.0117331	−	0.0203223i
$298$	−5.10661	−	8.84491i	−0.295818	−	0.512372i
$299$	2.06022	−	3.56840i	0.119145	−	0.206366i
$300$	4.00000			0.230940
$301$	1.50279	−	1.52346i	0.0866196	−	0.0878106i
$302$	−5.59559			−0.321990
$303$	−2.59559	+	4.49569i	−0.149113	+	0.258271i
$304$	1.35801	+	2.35214i	0.0778873	+	0.134905i
$305$	−5.00000	−	8.66025i	−0.286299	−	0.495885i
$306$	2.65581	−	4.59999i	0.151822	−	0.262964i
$307$	−30.5745			−1.74498			−0.872490	−	0.488632i	$-0.837496\pi$
$307$	−30.5745			−1.74498			−0.872490	+	0.488632i	$0.837496\pi$
$308$	−0.283978	−	1.03159i	−0.0161812	−	0.0587805i
$309$	−16.8365			−0.957792
$310$	−4.91823	+	8.51862i	−0.279336	+	0.483825i
$311$	3.53538	+	6.12345i	0.200473	+	0.347229i	0.948681	−	0.316235i	$-0.102419\pi$
$311$	3.53538	+	6.12345i	0.200473	+	0.347229i	−0.748208	+	0.663464i	$0.769086\pi$
$312$	−2.06022	−	3.56840i	−0.116637	−	0.202021i
$313$	−3.84419	+	6.65834i	−0.217287	+	0.376352i	−0.953978	−	0.299878i	$-0.903054\pi$
$313$	−3.84419	+	6.65834i	−0.217287	+	0.376352i	0.736691	+	0.676230i	$0.236387\pi$
$314$	−22.7713			−1.28506
$315$	−2.56022	−	0.667305i	−0.144252	−	0.0375984i
$316$	−9.92925			−0.558564
$317$	11.3967	−	19.7396i	0.640101	−	1.10869i	−0.345309	−	0.938489i	$-0.612226\pi$
$317$	11.3967	−	19.7396i	0.640101	−	1.10869i	0.985410	−	0.170198i	$-0.0544407\pi$
$318$	0.0955907	+	0.165568i	0.00536046	+	0.00928459i
$319$	1.84419	+	3.19424i	0.103255	+	0.178843i
$320$	−0.500000	+	0.866025i	−0.0279508	+	0.0484123i
$321$	9.59559			0.535574
$322$	−2.56022	−	0.667305i	−0.142675	−	0.0371875i
$323$	−14.4265			−0.802709
$324$	−0.500000	+	0.866025i	−0.0277778	+	0.0481125i
$325$	8.24086	+	14.2736i	0.457121	+	0.791756i
$326$	12.3856	+	21.4526i	0.685977	+	1.18815i
$327$	−1.59559	+	2.76364i	−0.0882364	+	0.152830i
$328$	10.7160			0.591693
$329$	−7.60941	−	27.6423i	−0.419520	−	1.52397i
$330$	−0.404409			−0.0222620
$331$	10.2652	−	17.7799i	0.564227	−	0.977270i	−0.432894	−	0.901445i	$-0.642508\pi$
$331$	10.2652	−	17.7799i	0.564227	−	0.977270i	0.997121	−	0.0758253i	$-0.0241591\pi$
$332$	2.20220	+	3.81433i	0.120862	+	0.209339i
$333$	3.95360	+	6.84784i	0.216656	+	0.375259i
$334$	−9.53866	+	16.5214i	−0.521932	+	0.904013i
$335$	2.83645			0.154972
$336$	−1.85801	+	1.88356i	−0.101363	+	0.102757i
$337$	16.7933			0.914791			0.457396	−	0.889263i	$-0.348782\pi$
$337$	16.7933			0.914791			0.457396	+	0.889263i	$0.348782\pi$
$338$	1.98898	−	3.44501i	0.108186	−	0.187384i
$339$	−9.37183	−	16.2325i	−0.509008	−	0.881627i
$340$	−2.65581	−	4.59999i	−0.144031	−	0.249470i
$341$	−1.98898	+	3.44501i	−0.107709	+	0.186558i
$342$	2.71602			0.146866
$343$	−13.3613	−	12.8248i	−0.721442	−	0.692475i
$344$	−0.808819			−0.0436086
$345$	−0.500000	+	0.866025i	−0.0269191	+	0.0466252i
$346$	3.12043	+	5.40475i	0.167755	+	0.290561i
$347$	−0.177364	−	0.307204i	−0.00952141	−	0.0164916i	0.861225	−	0.508223i	$-0.169697\pi$
$347$	−0.177364	−	0.307204i	−0.00952141	−	0.0164916i	−0.870747	+	0.491732i	$0.836364\pi$
$348$	4.56022	−	7.89853i	0.244453	−	0.423405i
$349$	20.9292			1.12032			0.560159	−	0.828385i	$-0.310740\pi$
$349$	20.9292			1.12032			0.560159	+	0.828385i	$0.310740\pi$
$350$	7.43204	−	7.53424i	0.397259	−	0.402722i
$351$	−4.12043			−0.219932
$352$	−0.202205	+	0.350229i	−0.0107775	+	0.0186673i
$353$	13.2652	+	22.9760i	0.706036	+	1.22289i	0.966316	+	0.257357i	$0.0828517\pi$
$353$	13.2652	+	22.9760i	0.706036	+	1.22289i	−0.260280	+	0.965533i	$0.583815\pi$
$354$	4.15581	+	7.19807i	0.220879	+	0.382573i
$355$	3.46462	−	6.00091i	0.183883	−	0.318495i
$356$	7.90720			0.419081
$357$	−3.72984	−	13.5492i	−0.197404	−	0.717100i
$358$	11.2188			0.592933
$359$	−2.43204	+	4.21242i	−0.128358	+	0.222323i	−0.923041	−	0.384702i	$-0.874304\pi$
$359$	−2.43204	+	4.21242i	−0.128358	+	0.222323i	0.794682	+	0.607026i	$0.207637\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	5.81161	+	10.0660i	0.305874	+	0.529790i
$362$	4.12043	−	7.13680i	0.216565	−	0.375102i
$363$	10.8365			0.568766
$364$	−10.5492	−	2.74958i	−0.552928	−	0.144117i
$365$	4.59559			0.240544
$366$	−5.00000	+	8.66025i	−0.261354	+	0.452679i
$367$	12.9784	+	22.4793i	0.677469	+	1.17341i	0.975741	+	0.218930i	$0.0702566\pi$
$367$	12.9784	+	22.4793i	0.677469	+	1.17341i	−0.298271	+	0.954481i	$0.596410\pi$
$368$	0.500000	+	0.866025i	0.0260643	+	0.0451447i
$369$	5.35801	−	9.28035i	0.278927	−	0.483116i
$370$	7.90720			0.411076
$371$	0.489465	+	0.127576i	0.0254118	+	0.00662343i
$372$	9.83645			0.509996
$373$	6.83645	−	11.8411i	0.353978	−	0.613108i	−0.632964	−	0.774181i	$-0.718162\pi$
$373$	6.83645	−	11.8411i	0.353978	−	0.613108i	0.986943	+	0.161073i	$0.0514954\pi$
$374$	−1.07403	−	1.86028i	−0.0555369	−	0.0961928i
$375$	−4.50000	−	7.79423i	−0.232379	−	0.402492i
$376$	−5.41823	+	9.38464i	−0.279424	+	0.483976i
$377$	37.5801			1.93547
$378$	0.702205	+	2.55086i	0.0361175	+	0.131202i
$379$	−22.4541			−1.15339			−0.576695	−	0.816960i	$-0.695658\pi$
$379$	−22.4541			−1.15339			−0.576695	+	0.816960i	$0.695658\pi$
$380$	1.35801	−	2.35214i	0.0696645	−	0.120662i
$381$	−5.79780	−	10.0421i	−0.297030	−	0.514471i
$382$	12.3856	+	21.4526i	0.633705	+	1.09761i
$383$	−6.19446	+	10.7291i	−0.316522	+	0.548233i	−0.979760	−	0.200176i	$-0.935849\pi$
$383$	−6.19446	+	10.7291i	−0.316522	+	0.548233i	0.663238	+	0.748409i	$0.269182\pi$
$384$	1.00000			0.0510310
$385$	−0.751397	+	0.761729i	−0.0382947	+	0.0388213i
$386$	14.8585			0.756278
$387$	−0.404409	+	0.700458i	−0.0205573	+	0.0356063i
$388$	−7.68065	−	13.3033i	−0.389926	−	0.675371i
$389$	−14.2685	−	24.7138i	−0.723442	−	1.25304i	−0.959612	−	0.281326i	$-0.909226\pi$
$389$	−14.2685	−	24.7138i	−0.723442	−	1.25304i	0.236171	−	0.971712i	$-0.424108\pi$
$390$	−2.06022	+	3.56840i	−0.104323	+	0.180693i
$391$	−5.31161			−0.268620
$392$	0.0955907	+	6.99935i	0.00482806	+	0.353520i
$393$	−16.7657			−0.845718
$394$	−5.71602	+	9.90044i	−0.287969	+	0.498777i
$395$	4.96462	+	8.59898i	0.249797	+	0.432662i
$396$	0.202205	+	0.350229i	0.0101612	+	0.0175997i
$397$	−2.65581	+	4.59999i	−0.133291	+	0.230867i	−0.924943	−	0.380105i	$-0.875888\pi$
$397$	−2.65581	+	4.59999i	−0.133291	+	0.230867i	0.791652	+	0.610972i	$0.209221\pi$
$398$	8.62323			0.432243
$399$	5.04640	−	5.11579i	0.252636	−	0.256110i
$400$	−4.00000			−0.200000
$401$	3.10661	−	5.38081i	0.155137	−	0.268705i	−0.777972	−	0.628299i	$-0.783751\pi$
$401$	3.10661	−	5.38081i	0.155137	−	0.268705i	0.933109	+	0.359594i	$0.117085\pi$
$402$	−1.41823	−	2.45644i	−0.0707347	−	0.122516i
$403$	20.2652	+	35.1004i	1.00948	+	1.74847i
$404$	2.59559	−	4.49569i	0.129135	−	0.223669i
$405$	1.00000			0.0496904
$406$	−6.40441	−	23.2650i	−0.317845	−	1.15462i
$407$	3.19775			0.158506
$408$	−2.65581	+	4.59999i	−0.131482	+	0.227734i
$409$	−14.0525	−	24.3396i	−0.694850	−	1.20352i	−0.970231	−	0.242181i	$-0.922137\pi$
$409$	−14.0525	−	24.3396i	−0.694850	−	1.20352i	0.275381	−	0.961335i	$-0.411196\pi$
$410$	−5.35801	−	9.28035i	−0.264613	−	0.458324i
$411$	−4.82264	+	8.35305i	−0.237883	+	0.412026i
$412$	16.8365			0.829473
$413$	21.2795	+	5.54638i	1.04710	+	0.272920i
$414$	1.00000			0.0491473
$415$	2.20220	−	3.81433i	0.108102	−	0.187238i
$416$	2.06022	+	3.56840i	0.101010	+	0.174955i
$417$	−8.43204	−	14.6047i	−0.412919	−	0.715197i
$418$	0.549192	−	0.951229i	0.0268619	−	0.0465261i
$419$	−11.0056			−0.537658			−0.268829	−	0.963188i	$-0.586637\pi$
$419$	−11.0056			−0.537658			−0.268829	+	0.963188i	$0.586637\pi$
$420$	2.56022	+	0.667305i	0.124926	+	0.0325612i
$421$	−23.4873			−1.14470			−0.572351	−	0.820009i	$-0.693968\pi$
$421$	−23.4873			−1.14470			−0.572351	+	0.820009i	$0.693968\pi$
$422$	3.71602	−	6.43634i	0.180893	−	0.313316i
$423$	5.41823	+	9.38464i	0.263443	+	0.456297i
$424$	−0.0955907	−	0.165568i	−0.00464229	−	0.00804069i
$425$	10.6232	−	18.4000i	0.515302	−	0.892529i
$426$	−6.92925			−0.335723
$427$	7.02205	+	25.5086i	0.339821	+	1.23445i
$428$	−9.59559			−0.463820
$429$	−0.833170	+	1.44309i	−0.0402258	+	0.0696732i
$430$	0.404409	+	0.700458i	0.0195023	+	0.0337791i
$431$	−12.2409	−	21.2018i	−0.589622	−	1.02125i	−0.994282	−	0.106787i	$-0.965944\pi$
$431$	−12.2409	−	21.2018i	−0.589622	−	1.02125i	0.404660	−	0.914467i	$-0.367390\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	1.23527			0.0593635			0.0296818	−	0.999559i	$-0.490551\pi$
$433$	1.23527			0.0593635			0.0296818	+	0.999559i	$0.490551\pi$
$434$	18.2762	−	18.5275i	0.877287	−	0.889350i
$435$	−9.12043			−0.437291
$436$	1.59559	−	2.76364i	0.0764149	−	0.132355i
$437$	−1.35801	−	2.35214i	−0.0649625	−	0.112518i
$438$	−2.29780	−	3.97990i	−0.109793	−	0.190167i
$439$	11.3226	−	19.6114i	0.540400	−	0.936000i	−0.458481	−	0.888704i	$-0.651606\pi$
$439$	11.3226	−	19.6114i	0.540400	−	0.936000i	0.998881	−	0.0472959i	$-0.0150604\pi$
$440$	0.404409			0.0192795
$441$	6.10941	+	3.41689i	0.290924	+	0.162709i
$442$	−21.8861			−1.04102
$443$	3.95081	−	6.84300i	0.187709	−	0.325121i	−0.756777	−	0.653673i	$-0.773227\pi$
$443$	3.95081	−	6.84300i	0.187709	−	0.325121i	0.944486	+	0.328552i	$0.106561\pi$
$444$	−3.95360	−	6.84784i	−0.187630	−	0.324984i
$445$	−3.95360	−	6.84784i	−0.187419	−	0.324619i
$446$	5.10941	−	8.84975i	0.241937	−	0.419048i
$447$	10.2132			0.483069
$448$	1.85801	−	1.88356i	0.0877828	−	0.0889898i
$449$	16.3889			0.773441			0.386721	−	0.922197i	$-0.373608\pi$
$449$	16.3889			0.773441			0.386721	+	0.922197i	$0.373608\pi$
$450$	−2.00000	+	3.46410i	−0.0942809	+	0.163299i
$451$	−2.16683	−	3.75306i	−0.102032	−	0.176725i
$452$	9.37183	+	16.2325i	0.440814	+	0.763512i
$453$	2.79780	−	4.84592i	0.131452	−	0.227681i
$454$	−12.2188			−0.573457
$455$	2.89339	+	10.5107i	0.135644	+	0.492747i
$456$	−2.71602			−0.127189
$457$	15.5171	−	26.8764i	0.725859	−	1.25723i	−0.232760	−	0.972534i	$-0.574776\pi$
$457$	15.5171	−	26.8764i	0.725859	−	1.25723i	0.958619	−	0.284691i	$-0.0918910\pi$
$458$	1.92597	+	3.33587i	0.0899945	+	0.155875i
$459$	2.65581	+	4.59999i	0.123962	+	0.214709i
$460$	0.500000	−	0.866025i	0.0233126	−	0.0403786i
$461$	7.61764			0.354789			0.177394	−	0.984140i	$-0.443233\pi$
$461$	7.61764			0.354789			0.177394	+	0.984140i	$0.443233\pi$
$462$	1.03538	+	0.269864i	0.0481700	+	0.0125552i
$463$	8.80882			0.409381			0.204690	−	0.978827i	$-0.434381\pi$
$463$	8.80882			0.409381			0.204690	+	0.978827i	$0.434381\pi$
$464$	−4.56022	+	7.89853i	−0.211703	+	0.366680i
$465$	−4.91823	−	8.51862i	−0.228077	−	0.395041i
$466$	−13.2652	−	22.9760i	−0.614499	−	1.06434i
$467$	−0.404409	+	0.700458i	−0.0187138	+	0.0324133i	−0.875231	−	0.483706i	$-0.839290\pi$
$467$	−0.404409	+	0.700458i	−0.0187138	+	0.0324133i	0.856517	+	0.516119i	$0.172624\pi$
$468$	4.12043			0.190467
$469$	−7.26193	−	1.89278i	−0.335325	−	0.0874004i
$470$	10.8365			0.499848
$471$	11.3856	−	19.7205i	0.524623	−	0.908673i
$472$	−4.15581	−	7.19807i	−0.191286	−	0.331318i
$473$	0.163547	+	0.283272i	0.00751989	+	0.0130248i
$474$	4.96462	−	8.59898i	0.228033	−	0.394964i
$475$	10.8641			0.498479
$476$	3.72984	+	13.5492i	0.170957	+	0.621027i
$477$	−0.191181			−0.00875359
$478$	−8.00000	+	13.8564i	−0.365911	+	0.633777i
$479$	14.1668	+	24.5377i	0.647299	+	1.12115i	0.983765	+	0.179459i	$0.0574348\pi$
$479$	14.1668	+	24.5377i	0.647299	+	1.12115i	−0.336466	+	0.941695i	$0.609232\pi$
$480$	−0.500000	−	0.866025i	−0.0228218	−	0.0395285i
$481$	16.2905	−	28.2160i	0.742785	−	1.28654i
$482$	14.7933			0.673818
$483$	1.85801	−	1.88356i	0.0845424	−	0.0857049i
$484$	−10.8365			−0.492566
$485$	−7.68065	+	13.3033i	−0.348760	+	0.604070i
$486$	−0.500000	−	0.866025i	−0.0226805	−	0.0392837i
$487$	−9.35027	−	16.1951i	−0.423701	−	0.733872i	0.572597	−	0.819837i	$-0.305936\pi$
$487$	−9.35027	−	16.1951i	−0.423701	−	0.733872i	−0.996298	+	0.0859650i	$0.972603\pi$
$488$	5.00000	−	8.66025i	0.226339	−	0.392031i
$489$	−24.7713			−1.12020
$490$	6.01382	−	3.58246i	0.271677	−	0.161839i
$491$	5.09280			0.229835			0.114917	−	0.993375i	$-0.463340\pi$
$491$	5.09280			0.229835			0.114917	+	0.993375i	$0.463340\pi$
$492$	−5.35801	+	9.28035i	−0.241558	+	0.418390i
$493$	−24.2221	−	41.9539i	−1.09091	−	1.88951i
$494$	−5.59559	−	9.69185i	−0.251758	−	0.436057i
$495$	0.202205	−	0.350229i	0.00908842	−	0.0157416i
$496$	−9.83645			−0.441670
$497$	−12.8746	+	13.0517i	−0.577506	+	0.585447i
$498$	−4.40441			−0.197366
$499$	−9.74366	+	16.8765i	−0.436186	+	0.755496i	−0.997392	−	0.0721801i	$-0.977004\pi$
$499$	−9.74366	+	16.8765i	−0.436186	+	0.755496i	0.561206	+	0.827676i	$0.310338\pi$
$500$	4.50000	+	7.79423i	0.201246	+	0.348569i
$501$	−9.53866	−	16.5214i	−0.426156	−	0.738123i
$502$	7.01102	−	12.1434i	0.312917	−	0.541989i
$503$	−2.99441			−0.133514			−0.0667571	−	0.997769i	$-0.521265\pi$
$503$	−2.99441			−0.133514			−0.0667571	+	0.997769i	$0.521265\pi$
$504$	−0.702205	−	2.55086i	−0.0312787	−	0.113625i
$505$	−5.19118			−0.231005
$506$	0.202205	−	0.350229i	0.00898909	−	0.0155696i
$507$	1.98898	+	3.44501i	0.0883336	+	0.152998i
$508$	5.79780	+	10.0421i	0.257236	+	0.445545i
$509$	5.87183	−	10.1703i	0.260264	−	0.450791i	−0.706048	−	0.708164i	$-0.749524\pi$
$509$	5.87183	−	10.1703i	0.260264	−	0.450791i	0.966312	+	0.257373i	$0.0828570\pi$
$510$	5.31161			0.235202
$511$	−11.7657	−	3.06666i	−0.520484	−	0.135661i
$512$	−1.00000			−0.0441942
$513$	−1.35801	+	2.35214i	−0.0599576	+	0.103850i
$514$	3.54919	+	6.14738i	0.156548	+	0.271149i
$515$	−8.41823	−	14.5808i	−0.370951	−	0.642507i
$516$	0.404409	−	0.700458i	0.0178031	−	0.0308359i
$517$	4.38236			0.192736
$518$	−20.2441	−	5.27652i	−0.889477	−	0.231837i
$519$	−6.24086			−0.273943
$520$	2.06022	−	3.56840i	0.0903464	−	0.156485i
$521$	−2.60941	−	4.51963i	−0.114320	−	0.198008i	0.803188	−	0.595726i	$-0.203136\pi$
$521$	−2.60941	−	4.51963i	−0.114320	−	0.198008i	−0.917508	+	0.397718i	$0.869802\pi$
$522$	4.56022	+	7.89853i	0.199595	+	0.345709i
$523$	13.2270	−	22.9099i	0.578378	−	1.00178i	−0.417287	−	0.908775i	$-0.637019\pi$
$523$	13.2270	−	22.9099i	0.578378	−	1.00178i	0.995666	−	0.0930060i	$-0.0296476\pi$
$524$	16.7657			0.732413
$525$	2.80882	+	10.2035i	0.122587	+	0.445315i
$526$	8.80882			0.384083
$527$	26.1237	−	45.2476i	1.13797	−	1.97102i
$528$	−0.202205	−	0.350229i	−0.00879983	−	0.0152417i
$529$	−0.500000	−	0.866025i	−0.0217391	−	0.0376533i
$530$	−0.0955907	+	0.165568i	−0.00415219	+	0.00719181i
$531$	−8.31161			−0.360693
$532$	−5.04640	+	5.11579i	−0.218789	+	0.221798i
$533$	−44.1546			−1.91255
$534$	−3.95360	+	6.84784i	−0.171089	+	0.296335i
$535$	4.79780	+	8.31003i	0.207427	+	0.359274i
$536$	1.41823	+	2.45644i	0.0612581	+	0.106102i
$537$	−5.60941	+	9.71578i	−0.242064	+	0.419267i
$538$	4.49721			0.193888
$539$	2.43204	−	1.44878i	0.104756	−	0.0624033i
$540$	−1.00000			−0.0430331
$541$	1.65581	−	2.86794i	0.0711887	−	0.123302i	−0.828234	−	0.560383i	$-0.810654\pi$
$541$	1.65581	−	2.86794i	0.0711887	−	0.123302i	0.899423	+	0.437080i	$0.143987\pi$
$542$	7.63425	+	13.2229i	0.327919	+	0.567972i
$543$	4.12043	+	7.13680i	0.176825	+	0.306269i
$544$	2.65581	−	4.59999i	0.113867	−	0.197223i
$545$	−3.19118			−0.136695
$546$	7.65581	−	7.76108i	0.327638	−	0.332143i
$547$	3.95130			0.168945			0.0844726	−	0.996426i	$-0.473079\pi$
$547$	3.95130			0.168945			0.0844726	+	0.996426i	$0.473079\pi$
$548$	4.82264	−	8.35305i	0.206013	−	0.356825i
$549$	−5.00000	−	8.66025i	−0.213395	−	0.369611i
$550$	0.808819	+	1.40092i	0.0344881	+	0.0597352i
$551$	12.3856	−	21.4526i	0.527646	−	0.913910i
$552$	−1.00000			−0.0425628
$553$	−6.97237	−	25.3282i	−0.296495	−	1.07706i
$554$	2.21323			0.0940310
$555$	−3.95360	+	6.84784i	−0.167821	+	0.290675i
$556$	8.43204	+	14.6047i	0.357598	+	0.619378i
$557$	−1.30059	−	2.25269i	−0.0551077	−	0.0954494i	0.837156	−	0.546965i	$-0.184217\pi$
$557$	−1.30059	−	2.25269i	−0.0551077	−	0.0954494i	−0.892263	+	0.451516i	$0.850884\pi$
$558$	−4.91823	+	8.51862i	−0.208205	+	0.360622i
$559$	3.33268			0.140957
$560$	−2.56022	−	0.667305i	−0.108189	−	0.0281988i
$561$	2.14807			0.0906914
$562$	14.7055	−	25.4707i	0.620314	−	1.07441i
$563$	12.7050	+	22.0057i	0.535452	+	0.927430i	0.999141	+	0.0414320i	$0.0131920\pi$
$563$	12.7050	+	22.0057i	0.535452	+	0.927430i	−0.463689	+	0.885998i	$0.653475\pi$
$564$	−5.41823	−	9.38464i	−0.228148	−	0.395165i
$565$	9.37183	−	16.2325i	0.394276	−	0.682906i
$566$	−27.0773			−1.13814
$567$	−2.56022	−	0.667305i	−0.107519	−	0.0280242i
$568$	6.92925			0.290745
$569$	8.29780	−	14.3722i	0.347862	−	0.602514i	−0.638008	−	0.770030i	$-0.720241\pi$
$569$	8.29780	−	14.3722i	0.347862	−	0.602514i	0.985869	+	0.167516i	$0.0535745\pi$
$570$	1.35801	+	2.35214i	0.0568808	+	0.0985205i
$571$	−16.3287	−	28.2822i	−0.683335	−	1.18357i	−0.973957	−	0.226733i	$-0.927195\pi$
$571$	−16.3287	−	28.2822i	−0.683335	−	1.18357i	0.290621	−	0.956838i	$-0.406138\pi$
$572$	0.833170	−	1.44309i	0.0348366	−	0.0603388i
$573$	−24.7713			−1.03484
$574$	7.52484	+	27.3351i	0.314081	+	1.14095i
$575$	4.00000			0.166812
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	−0.272955	−	0.472772i	−0.0113633	−	0.0196817i	0.860288	−	0.509809i	$-0.170284\pi$
$577$	−0.272955	−	0.472772i	−0.0113633	−	0.0196817i	−0.871651	+	0.490127i	$0.836950\pi$
$578$	5.60661	+	9.71094i	0.233204	+	0.403922i
$579$	−7.42925	+	12.8678i	−0.308749	+	0.534769i
$580$	9.12043			0.378705
$581$	−8.18344	+	8.29597i	−0.339506	+	0.344175i
$582$	15.3613			0.636746
$583$	−0.0386578	+	0.0669572i	−0.00160104	+	0.00277308i
$584$	2.29780	+	3.97990i	0.0950834	+	0.164689i
$585$	−2.06022	−	3.56840i	−0.0851794	−	0.147535i
$586$	−9.93204	+	17.2028i	−0.410289	+	0.710641i
$587$	8.82097			0.364080			0.182040	−	0.983291i	$-0.441730\pi$
$587$	8.82097			0.364080			0.182040	+	0.983291i	$0.441730\pi$
$588$	−6.10941	−	3.41689i	−0.251948	−	0.140910i
$589$	26.7160			1.10081
$590$	−4.15581	+	7.19807i	−0.171092	+	0.296340i
$591$	−5.71602	−	9.90044i	−0.235126	−	0.407250i
$592$	3.95360	+	6.84784i	0.162492	+	0.281444i
$593$	20.0276	−	34.6889i	0.822436	−	1.42450i	−0.0814265	−	0.996679i	$-0.525948\pi$
$593$	20.0276	−	34.6889i	0.822436	−	1.42450i	0.903863	−	0.427822i	$-0.140719\pi$
$594$	−0.404409			−0.0165931
$595$	9.86903	−	10.0047i	0.404591	−	0.410154i
$596$	−10.2132			−0.418350
$597$	−4.31161	+	7.46793i	−0.176463	+	0.305642i
$598$	−2.06022	−	3.56840i	−0.0842485	−	0.145923i
$599$	12.2083	+	21.1454i	0.498817	+	0.863976i	0.999999	−	0.00136565i	$-0.000434699\pi$
$599$	12.2083	+	21.1454i	0.498817	+	0.863976i	−0.501182	+	0.865342i	$0.667101\pi$
$600$	2.00000	−	3.46410i	0.0816497	−	0.141421i
$601$	−9.21323			−0.375815			−0.187908	−	0.982187i	$-0.560171\pi$
$601$	−9.21323			−0.375815			−0.187908	+	0.982187i	$0.560171\pi$
$602$	−0.567956	−	2.06319i	−0.0231482	−	0.0840892i
$603$	2.83645			0.115509
$604$	−2.79780	+	4.84592i	−0.113841	+	0.197178i
$605$	5.41823	+	9.38464i	0.220282	+	0.381540i
$606$	2.59559	+	4.49569i	0.105439	+	0.182625i
$607$	−16.8475	+	29.1807i	−0.683818	+	1.18441i	0.289989	+	0.957030i	$0.406348\pi$
$607$	−16.8475	+	29.1807i	−0.683818	+	1.18441i	−0.973807	+	0.227377i	$0.926985\pi$
$608$	2.71602			0.110149
$609$	23.3503	+	6.08611i	0.946201	+	0.246622i
$610$	−10.0000			−0.404888
$611$	22.3254	−	38.6688i	0.903190	−	1.56437i
$612$	−2.65581	−	4.59999i	−0.107355	−	0.185944i
$613$	12.2132	+	21.1539i	0.493288	+	0.854399i	0.999970	−	0.00773351i	$-0.00246168\pi$
$613$	12.2132	+	21.1539i	0.493288	+	0.854399i	−0.506682	+	0.862133i	$0.669128\pi$
$614$	−15.2873	+	26.4783i	−0.616944	+	1.06858i
$615$	10.7160			0.432112
$616$	−1.03538	−	0.269864i	−0.0417165	−	0.0108731i
$617$	−2.41000			−0.0970228			−0.0485114	−	0.998823i	$-0.515448\pi$
$617$	−2.41000			−0.0970228			−0.0485114	+	0.998823i	$0.515448\pi$
$618$	−8.41823	+	14.5808i	−0.338631	+	0.586526i
$619$	−22.9243	−	39.7061i	−0.921406	−	1.59592i	−0.797242	−	0.603659i	$-0.793709\pi$
$619$	−22.9243	−	39.7061i	−0.921406	−	1.59592i	−0.124163	−	0.992262i	$-0.539625\pi$
$620$	4.91823	+	8.51862i	0.197521	+	0.342116i
$621$	−0.500000	+	0.866025i	−0.0200643	+	0.0347524i
$622$	7.07075			0.283511
$623$	5.55247	+	20.1702i	0.222455	+	0.808102i
$624$	−4.12043			−0.164949
$625$	−5.50000	+	9.52628i	−0.220000	+	0.381051i
$626$	3.84419	+	6.65834i	0.153645	+	0.266121i
$627$	0.549192	+	0.951229i	0.0219326	+	0.0379884i
$628$	−11.3856	+	19.7205i	−0.454337	+	0.786934i
$629$	−42.0000			−1.67465
$630$	−1.85801	+	1.88356i	−0.0740249	+	0.0750428i
$631$	−33.5745			−1.33658			−0.668290	−	0.743901i	$-0.732974\pi$
$631$	−33.5745			−1.33658			−0.668290	+	0.743901i	$0.732974\pi$
$632$	−4.96462	+	8.59898i	−0.197482	+	0.342049i
$633$	3.71602	+	6.43634i	0.147699	+	0.255821i
$634$	−11.3967	−	19.7396i	−0.452620	−	0.783960i
$635$	5.79780	−	10.0421i	0.230078	−	0.398508i
$636$	0.191181			0.00758083
$637$	−0.393875	−	28.8403i	−0.0156059	−	1.14270i
$638$	3.68839			0.146025
$639$	3.46462	−	6.00091i	0.137058	−	0.237392i
$640$	0.500000	+	0.866025i	0.0197642	+	0.0342327i
$641$	16.7055	+	28.9348i	0.659827	+	1.14285i	0.980660	+	0.195718i	$0.0627038\pi$
$641$	16.7055	+	28.9348i	0.659827	+	1.14285i	−0.320833	+	0.947136i	$0.603963\pi$
$642$	4.79780	−	8.31003i	0.189354	−	0.327971i
$643$	11.5248			0.454495			0.227248	−	0.973837i	$-0.427027\pi$
$643$	11.5248			0.454495			0.227248	+	0.973837i	$0.427027\pi$
$644$	−1.85801	+	1.88356i	−0.0732159	+	0.0742226i
$645$	−0.808819			−0.0318472
$646$	−7.21323	+	12.4937i	−0.283801	+	0.491557i
$647$	24.1701	+	41.8639i	0.950225	+	1.64584i	0.744935	+	0.667137i	$0.232480\pi$
$647$	24.1701	+	41.8639i	0.950225	+	1.64584i	0.205290	+	0.978701i	$0.434186\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−1.68065	+	2.91097i	−0.0659712	+	0.114265i
$650$	16.4817			0.646466
$651$	6.90720	+	25.0915i	0.270715	+	0.983412i
$652$	24.7713			0.970119
$653$	−12.8995	+	22.3425i	−0.504795	+	0.874331i	0.495190	+	0.868785i	$0.335099\pi$
$653$	−12.8995	+	22.3425i	−0.504795	+	0.874331i	−0.999985	+	0.00554564i	$0.998235\pi$
$654$	1.59559	+	2.76364i	0.0623925	+	0.108067i
$655$	−8.38285	−	14.5195i	−0.327545	−	0.567325i
$656$	5.35801	−	9.28035i	0.209195	−	0.362337i
$657$	4.59559			0.179291
$658$	−27.7437	−	7.23122i	−1.08156	−	0.281902i
$659$	−14.1856			−0.552592			−0.276296	−	0.961073i	$-0.589107\pi$
$659$	−14.1856			−0.552592			−0.276296	+	0.961073i	$0.589107\pi$
$660$	−0.202205	+	0.350229i	−0.00787081	+	0.0136326i
$661$	23.6509	+	40.9645i	0.919912	+	1.59333i	0.799546	+	0.600604i	$0.205073\pi$
$661$	23.6509	+	40.9645i	0.919912	+	1.59333i	0.120365	+	0.992730i	$0.461593\pi$
$662$	−10.2652	−	17.7799i	−0.398969	−	0.691034i
$663$	10.9431	−	18.9539i	0.424994	−	0.736110i
$664$	4.40441			0.170924
$665$	6.95360	+	1.81242i	0.269649	+	0.0702824i
$666$	7.90720			0.306398
$667$	4.56022	−	7.89853i	0.176572	−	0.305832i
$668$	9.53866	+	16.5214i	0.369062	+	0.639234i
$669$	5.10941	+	8.84975i	0.197541	+	0.342151i
$670$	1.41823	−	2.45644i	0.0547909	−	0.0949006i
$671$	−4.04409			−0.156120
$672$	0.702205	+	2.55086i	0.0270881	+	0.0984017i
$673$	0.448503			0.0172885			0.00864425	−	0.999963i	$-0.497248\pi$
$673$	0.448503			0.0172885			0.00864425	+	0.999963i	$0.497248\pi$
$674$	8.39667	−	14.5435i	0.323428	−	0.560193i
$675$	−2.00000	−	3.46410i	−0.0769800	−	0.133333i
$676$	−1.98898	−	3.44501i	−0.0764991	−	0.132500i
$677$	8.30882	−	14.3913i	0.319334	−	0.553102i	−0.661015	−	0.750372i	$-0.729874\pi$
$677$	8.30882	−	14.3913i	0.319334	−	0.553102i	0.980349	+	0.197270i	$0.0632075\pi$
$678$	−18.7437			−0.719846
$679$	28.5415	−	28.9339i	1.09532	−	1.11038i
$680$	−5.31161			−0.203691
$681$	6.10941	−	10.5818i	0.234113	−	0.405496i
$682$	1.98898	+	3.44501i	0.0761619	+	0.131916i
$683$	13.6017	+	23.5588i	0.520453	+	0.901452i	0.999717	+	0.0237808i	$0.00757036\pi$
$683$	13.6017	+	23.5588i	0.520453	+	0.901452i	−0.479264	+	0.877671i	$0.659096\pi$
$684$	1.35801	−	2.35214i	0.0519248	−	0.0899365i
$685$	−9.64527			−0.368527
$686$	−17.7873	+	5.15881i	−0.679121	+	0.196964i
$687$	−3.85193			−0.146960
$688$	−0.404409	+	0.700458i	−0.0154180	+	0.0267047i
$689$	0.393875	+	0.682211i	0.0150054	+	0.0259902i
$690$	0.500000	+	0.866025i	0.0190347	+	0.0329690i
$691$	−22.5061	+	38.9817i	−0.856172	+	1.48293i	0.0193824	+	0.999812i	$0.493830\pi$
$691$	−22.5061	+	38.9817i	−0.856172	+	1.48293i	−0.875554	+	0.483120i	$0.839503\pi$
$692$	6.24086			0.237242
$693$	−0.751397	+	0.761729i	−0.0285432	+	0.0289357i
$694$	−0.354728			−0.0134653
$695$	8.43204	−	14.6047i	0.319846	−	0.553989i
$696$	−4.56022	−	7.89853i	−0.172855	−	0.299393i
$697$	28.4597	+	49.2936i	1.07799	+	1.86713i
$698$	10.4646	−	18.1253i	0.396092	−	0.686051i
$699$	26.5304			1.00347
$700$	−2.80882	−	10.2035i	−0.106163	−	0.385654i
$701$	−35.6232			−1.34547			−0.672735	−	0.739883i	$-0.734881\pi$
$701$	−35.6232			−1.34547			−0.672735	+	0.739883i	$0.734881\pi$
$702$	−2.06022	+	3.56840i	−0.0777578	+	0.134681i
$703$	−10.7381	−	18.5989i	−0.404994	−	0.701470i
$704$	0.202205	+	0.350229i	0.00762087	+	0.0131997i
$705$	−5.41823	+	9.38464i	−0.204062	+	0.353446i
$706$	26.5304			0.998486
$707$	13.2905	+	3.46410i	0.499842	+	0.130281i
$708$	8.31161			0.312370
$709$	10.0961	−	17.4869i	0.379166	−	0.656735i	−0.611775	−	0.791032i	$-0.709544\pi$
$709$	10.0961	−	17.4869i	0.379166	−	0.656735i	0.990941	+	0.134297i	$0.0428775\pi$
$710$	−3.46462	−	6.00091i	−0.130025	−	0.225210i
$711$	4.96462	+	8.59898i	0.186188	+	0.322487i
$712$	3.95360	−	6.84784i	0.148167	−	0.256634i
$713$	9.83645			0.368378
$714$	−13.5989	−	3.54447i	−0.508925	−	0.132648i
$715$	−1.66634			−0.0623176
$716$	5.60941	−	9.71578i	0.209633	−	0.363096i
$717$	−8.00000	−	13.8564i	−0.298765	−	0.517477i
$718$	2.43204	+	4.21242i	0.0907631	+	0.157206i
$719$	−0.488977	+	0.846932i	−0.0182358	+	0.0315853i	−0.874999	−	0.484124i	$-0.839138\pi$
$719$	−0.488977	+	0.846932i	−0.0182358	+	0.0315853i	0.856764	+	0.515709i	$0.172472\pi$
$720$	1.00000			0.0372678
$721$	11.8226	+	42.9475i	0.440298	+	1.59945i
$722$	11.6232			0.432572
$723$	−7.39667	+	12.8114i	−0.275085	+	0.476461i
$724$	−4.12043	−	7.13680i	−0.153135	−	0.265237i
$725$	18.2409	+	31.5941i	0.677449	+	1.17338i
$726$	5.41823	−	9.38464i	0.201089	−	0.348297i
$727$	−36.9348			−1.36984			−0.684919	−	0.728620i	$-0.740162\pi$
$727$	−36.9348			−1.36984			−0.684919	+	0.728620i	$0.740162\pi$
$728$	−7.65581	+	7.76108i	−0.283743	+	0.287645i
$729$	1.00000			0.0370370
$730$	2.29780	−	3.97990i	0.0850452	−	0.147303i
$731$	−2.14807	−	3.72056i	−0.0794491	−	0.137610i
$732$	5.00000	+	8.66025i	0.184805	+	0.320092i
$733$	17.8177	−	30.8611i	0.658111	−	1.13988i	−0.322993	−	0.946401i	$-0.604689\pi$
$733$	17.8177	−	30.8611i	0.658111	−	1.13988i	0.981104	−	0.193481i	$-0.0619777\pi$
$734$	25.9569			0.958086
$735$	0.0955907	+	6.99935i	0.00352592	+	0.258175i
$736$	1.00000			0.0368605
$737$	0.573544	−	0.993407i	0.0211268	−	0.0365926i
$738$	−5.35801	−	9.28035i	−0.197231	−	0.341614i
$739$	16.9348	+	29.3320i	0.622958	+	1.07900i	0.988932	+	0.148370i	$0.0474026\pi$
$739$	16.9348	+	29.3320i	0.622958	+	1.07900i	−0.365974	+	0.930625i	$0.619264\pi$
$740$	3.95360	−	6.84784i	0.145337	−	0.251732i
$741$	11.1912			0.411118
$742$	0.355217	−	0.360101i	0.0130404	−	0.0132197i
$743$	21.1537			0.776052			0.388026	−	0.921648i	$-0.373157\pi$
$743$	21.1537			0.776052			0.388026	+	0.921648i	$0.373157\pi$
$744$	4.91823	−	8.51862i	0.180311	−	0.312308i
$745$	5.10661	+	8.84491i	0.187092	+	0.324053i
$746$	−6.83645	−	11.8411i	−0.250300	−	0.433533i
$747$	2.20220	−	3.81433i	0.0805745	−	0.139559i
$748$	−2.14807			−0.0785411
$749$	−6.73807	−	24.4770i	−0.246204	−	0.894372i
$750$	−9.00000			−0.328634
$751$	−10.4895	+	18.1683i	−0.382766	+	0.662970i	−0.991457	−	0.130438i	$-0.958362\pi$
$751$	−10.4895	+	18.1683i	−0.382766	+	0.662970i	0.608690	+	0.793408i	$0.291695\pi$
$752$	5.41823	+	9.38464i	0.197582	+	0.342223i
$753$	7.01102	+	12.1434i	0.255496	+	0.442532i
$754$	18.7901	−	32.5453i	0.684293	−	1.18523i
$755$	5.59559			0.203644
$756$	2.56022	+	0.667305i	0.0931141	+	0.0242697i
$757$	−4.95688			−0.180161			−0.0900805	−	0.995934i	$-0.528712\pi$
$757$	−4.95688			−0.180161			−0.0900805	+	0.995934i	$0.528712\pi$
$758$	−11.2270	+	19.4458i	−0.407785	+	0.706304i
$759$	0.202205	+	0.350229i	0.00733956	+	0.0127125i
$760$	−1.35801	−	2.35214i	−0.0492602	−	0.0853212i
$761$	−9.78447	+	16.9472i	−0.354687	+	0.614335i	−0.987064	−	0.160325i	$-0.948746\pi$
$761$	−9.78447	+	16.9472i	−0.354687	+	0.614335i	0.632378	+	0.774660i	$0.282079\pi$
$762$	−11.5956			−0.420064
$763$	8.17011	+	2.12949i	0.295778	+	0.0770928i
$764$	24.7713			0.896194
$765$	−2.65581	+	4.59999i	−0.0960209	+	0.166313i
$766$	6.19446	+	10.7291i	0.223815	+	0.387659i
$767$	17.1237	+	29.6591i	0.618301	+	1.07093i
$768$	0.500000	−	0.866025i	0.0180422	−	0.0312500i
$769$	4.92366			0.177552			0.0887759	−	0.996052i	$-0.471705\pi$
$769$	4.92366			0.177552			0.0887759	+	0.996052i	$0.471705\pi$
$770$	0.283978	+	1.03159i	0.0102339	+	0.0371760i
$771$	−7.09838			−0.255642
$772$	7.42925	−	12.8678i	0.267385	−	0.463124i
$773$	1.01382	+	1.75598i	0.0364645	+	0.0631583i	0.883682	−	0.468088i	$-0.155057\pi$
$773$	1.01382	+	1.75598i	0.0364645	+	0.0631583i	−0.847217	+	0.531247i	$0.821724\pi$
$774$	0.404409	+	0.700458i	0.0145362	+	0.0251774i
$775$	−19.6729	+	34.0745i	−0.706672	+	1.22399i
$776$	−15.3613			−0.551438
$777$	14.6917	−	14.8937i	0.527061	−	0.534308i
$778$	−28.5370			−1.02310
$779$	−14.5525	+	25.2056i	−0.521397	+	0.903085i
$780$	2.06022	+	3.56840i	0.0737676	+	0.127769i
$781$	−1.40113	−	2.42682i	−0.0501363	−	0.0868385i
$782$	−2.65581	+	4.59999i	−0.0949714	+	0.164495i
$783$	−9.12043			−0.325938
$784$	6.10941	+	3.41689i	0.218193	+	0.122032i
$785$	22.7713			0.812742
$786$	−8.38285	+	14.5195i	−0.299006	+	0.517894i
$787$	0.134248	+	0.232525i	0.00478544	+	0.00828862i	0.868408	−	0.495850i	$-0.165143\pi$
$787$	0.134248	+	0.232525i	0.00478544	+	0.00828862i	−0.863623	+	0.504139i	$0.831810\pi$
$788$	5.71602	+	9.90044i	0.203625	+	0.352689i
$789$	−4.40441	+	7.62866i	−0.156801	+	0.271588i
$790$	9.92925			0.353267
$791$	−34.8259	+	35.3048i	−1.23827	+	1.25529i
$792$	0.404409			0.0143701
$793$	−20.6022	+	35.6840i	−0.731604	+	1.26718i
$794$	2.65581	+	4.59999i	0.0942510	+	0.163248i
$795$	−0.0955907	−	0.165568i	−0.00339025	−	0.00587209i
$796$	4.31161	−	7.46793i	0.152821	−	0.264694i
$797$	−16.0497			−0.568509			−0.284254	−	0.958749i	$-0.591746\pi$
$797$	−16.0497			−0.568509			−0.284254	+	0.958749i	$0.591746\pi$
$798$	−1.90720	−	6.92820i	−0.0675143	−	0.245256i
$799$	−57.5590			−2.03629
$800$	−2.00000	+	3.46410i	−0.0707107	+	0.122474i
$801$	−3.95360	−	6.84784i	−0.139694	−	0.241956i
$802$	−3.10661	−	5.38081i	−0.109698	−	0.190003i
$803$	0.929250	−	1.60951i	0.0327925	−	0.0567983i
$804$	−2.83645			−0.100034
$805$	2.56022	+	0.667305i	0.0902357	+	0.0235194i
$806$	40.5304			1.42762
$807$	−2.24860	+	3.89469i	−0.0791546	+	0.137100i
$808$	−2.59559	−	4.49569i	−0.0913126	−	0.158158i
$809$	3.86080	+	6.68711i	0.135739	+	0.235106i	0.925879	−	0.377819i	$-0.123326\pi$
$809$	3.86080	+	6.68711i	0.135739	+	0.235106i	−0.790141	+	0.612925i	$0.789993\pi$
$810$	0.500000	−	0.866025i	0.0175682	−	0.0304290i
$811$	−23.2465			−0.816293			−0.408147	−	0.912916i	$-0.633825\pi$
$811$	−23.2465			−0.816293			−0.408147	+	0.912916i	$0.633825\pi$
$812$	−23.3503	−	6.08611i	−0.819434	−	0.213581i
$813$	−15.2685			−0.535490
$814$	1.59887	−	2.76933i	0.0560405	−	0.0970650i
$815$	−12.3856	−	21.4526i	−0.433850	−	0.751451i
$816$	2.65581	+	4.59999i	0.0929718	+	0.161032i
$817$	1.09838	−	1.90246i	0.0384276	−	0.0665586i
$818$	−28.1049			−0.982667
$819$	2.89339	+	10.5107i	0.101103	+	0.367272i
$820$	−10.7160			−0.374220
$821$	19.5602	−	33.8793i	0.682656	−	1.18240i	−0.291511	−	0.956567i	$-0.594158\pi$
$821$	19.5602	−	33.8793i	0.682656	−	1.18240i	0.974167	−	0.225828i	$-0.0725087\pi$
$822$	4.82264	+	8.35305i	0.168209	+	0.291346i
$823$	−21.0773	−	36.5070i	−0.734709	−	1.27255i	−0.954851	−	0.297086i	$-0.903985\pi$
$823$	−21.0773	−	36.5070i	−0.734709	−	1.27255i	0.220142	−	0.975468i	$-0.429348\pi$
$824$	8.41823	−	14.5808i	0.293263	−	0.507946i
$825$	−1.61764			−0.0563189
$826$	15.4431	−	15.6554i	0.537333	−	0.544722i
$827$	54.3294			1.88922			0.944608	−	0.328200i	$-0.106442\pi$
$827$	54.3294			1.88922			0.944608	+	0.328200i	$0.106442\pi$
$828$	0.500000	−	0.866025i	0.0173762	−	0.0300965i
$829$	−9.31984	−	16.1424i	−0.323691	−	0.560650i	0.657555	−	0.753406i	$-0.271591\pi$
$829$	−9.31984	−	16.1424i	−0.323691	−	0.560650i	−0.981247	+	0.192756i	$0.938257\pi$
$830$	−2.20220	−	3.81433i	−0.0764396	−	0.132397i
$831$	−1.10661	+	1.91671i	−0.0383880	+	0.0664900i
$832$	4.12043			0.142850
$833$	−31.9431	+	19.0286i	−1.10676	+	0.659303i
$834$	−16.8641			−0.583956
$835$	9.53866	−	16.5214i	0.330099	−	0.571748i
$836$	−0.549192	−	0.951229i	−0.0189942	−	0.0328989i
$837$	−4.91823	−	8.51862i	−0.169999	−	0.294447i
$838$	−5.50279	+	9.53112i	−0.190091	+	0.329247i
$839$	32.9569			1.13780			0.568899	−	0.822407i	$-0.307370\pi$
$839$	32.9569			1.13780			0.568899	+	0.822407i	$0.307370\pi$
$840$	1.85801	−	1.88356i	0.0641075	−	0.0649890i
$841$	54.1823			1.86835
$842$	−11.7437	+	20.3406i	−0.404713	+	0.700984i
$843$	14.7055	+	25.4707i	0.506484	+	0.877256i
$844$	−3.71602	−	6.43634i	−0.127911	−	0.221548i
$845$	−1.98898	+	3.44501i	−0.0684229	+	0.118512i
$846$	10.8365			0.372565
$847$	−7.60941	−	27.6423i	−0.261462	−	0.949801i
$848$	−0.191181			−0.00656519
$849$	13.5387	−	23.4496i	0.464646	−	0.804790i
$850$	−10.6232	−	18.4000i	−0.364374	−	0.631114i
$851$	−3.95360	−	6.84784i	−0.135528	−	0.234741i
$852$	−3.46462	+	6.00091i	−0.118696	+	0.205588i
$853$	−25.0497			−0.857685			−0.428842	−	0.903379i	$-0.641078\pi$
$853$	−25.0497			−0.857685			−0.428842	+	0.903379i	$0.641078\pi$
$854$	25.6022	+	6.67305i	0.876088	+	0.228347i
$855$	−2.71602			−0.0928860
$856$	−4.79780	+	8.31003i	−0.163985	+	0.284031i
$857$	2.02435	+	3.50628i	0.0691505	+	0.119772i	0.898528	−	0.438917i	$-0.144638\pi$
$857$	2.02435	+	3.50628i	0.0691505	+	0.119772i	−0.829377	+	0.558689i	$0.811304\pi$
$858$	0.833170	+	1.44309i	0.0284440	+	0.0492664i
$859$	−23.8884	+	41.3760i	−0.815063	+	1.41173i	0.0942196	+	0.995551i	$0.469964\pi$
$859$	−23.8884	+	41.3760i	−0.815063	+	1.41173i	−0.909283	+	0.416179i	$0.863369\pi$
$860$	0.808819			0.0275805
$861$	−27.4353	−	7.15086i	−0.934993	−	0.243701i
$862$	−24.4817			−0.833851
$863$	12.4426	−	21.5512i	0.423550	−	0.733611i	−0.572734	−	0.819742i	$-0.694117\pi$
$863$	12.4426	−	21.5512i	0.423550	−	0.733611i	0.996284	+	0.0861310i	$0.0274504\pi$
$864$	−0.500000	−	0.866025i	−0.0170103	−	0.0294628i
$865$	−3.12043	−	5.40475i	−0.106098	−	0.183767i
$866$	0.617637	−	1.06978i	0.0209882	−	0.0363526i
$867$	−11.2132			−0.380821
$868$	−6.90720	−	25.0915i	−0.234446	−	0.851660i
$869$	4.01548			0.136216
$870$	−4.56022	+	7.89853i	−0.154606	+	0.267785i
$871$	−5.84370	−	10.1216i	−0.198006	−	0.342957i
$872$	−1.59559	−	2.76364i	−0.0540335	−	0.0935888i
$873$	−7.68065	+	13.3033i	−0.259951	+	0.450247i
$874$	−2.71602			−0.0918708
$875$	−16.7221	+	16.9520i	−0.565310	+	0.573083i
$876$	−4.59559			−0.155271
$877$	2.03258	−	3.52053i	0.0686354	−	0.118880i	−0.829665	−	0.558261i	$-0.811469\pi$
$877$	2.03258	−	3.52053i	0.0686354	−	0.118880i	0.898301	+	0.439381i	$0.144802\pi$
$878$	−11.3226	−	19.6114i	−0.382120	−	0.661852i
$879$	−9.93204	−	17.2028i	−0.335000	−	0.580236i
$880$	0.202205	−	0.350229i	0.00681632	−	0.0118062i
$881$	−12.2132			−0.411474			−0.205737	−	0.978607i	$-0.565959\pi$
$881$	−12.2132			−0.411474			−0.205737	+	0.978607i	$0.565959\pi$
$882$	6.01382	−	3.58246i	0.202496	−	0.120628i
$883$	−5.14248			−0.173058			−0.0865291	−	0.996249i	$-0.527578\pi$
$883$	−5.14248			−0.173058			−0.0865291	+	0.996249i	$0.527578\pi$
$884$	−10.9431	+	18.9539i	−0.368055	+	0.637490i
$885$	−4.15581	−	7.19807i	−0.139696	−	0.241960i
$886$	−3.95081	−	6.84300i	−0.132730	−	0.229895i
$887$	−15.1912	+	26.3119i	−0.510070	+	0.883467i	0.489862	+	0.871800i	$0.337047\pi$
$887$	−15.1912	+	26.3119i	−0.510070	+	0.883467i	−0.999932	+	0.0116671i	$0.996286\pi$
$888$	−7.90720			−0.265348
$889$	−21.5447	+	21.8410i	−0.722587	+	0.732523i
$890$	−7.90720			−0.265050
$891$	0.202205	−	0.350229i	0.00677411	−	0.0117331i
$892$	−5.10941	−	8.84975i	−0.171076	−	0.296312i
$893$	−14.7160	−	25.4889i	−0.492453	−	0.852953i
$894$	5.10661	−	8.84491i	0.170791	−	0.295818i
$895$	−11.2188			−0.375004
$896$	−0.702205	−	2.55086i	−0.0234590	−	0.0852184i
$897$	4.12043			0.137577
$898$	8.19446	−	14.1932i	0.273453	−	0.473634i
$899$	44.8563	+	77.6935i	1.49604	+	2.59122i
$900$	2.00000	+	3.46410i	0.0666667	+	0.115470i
$901$	0.507741	−	0.879433i	0.0169153	−	0.0292981i
$902$	−4.33366			−0.144295
$903$	2.07075	+	0.539729i	0.0689102	+	0.0179610i
$904$	18.7437			0.623405
$905$	−4.12043	+	7.13680i	−0.136968	+	0.237235i
$906$	−2.79780	−	4.84592i	−0.0929505	−	0.160995i
$907$	6.93978	+	12.0201i	0.230432	+	0.399120i	0.957935	−	0.286984i	$-0.0926528\pi$
$907$	6.93978	+	12.0201i	0.230432	+	0.399120i	−0.727503	+	0.686104i	$0.759319\pi$
$908$	−6.10941	+	10.5818i	−0.202748	+	0.351170i
$909$	−5.19118			−0.172181
$910$	10.5492	+	2.74958i	0.349702	+	0.0911478i
$911$	−27.3017			−0.904546			−0.452273	−	0.891879i	$-0.649387\pi$
$911$	−27.3017			−0.904546			−0.452273	+	0.891879i	$0.649387\pi$
$912$	−1.35801	+	2.35214i	−0.0449682	+	0.0778873i
$913$	−0.890592	−	1.54255i	−0.0294743	−	0.0510510i
$914$	−15.5171	−	26.8764i	−0.513260	−	0.888992i
$915$	5.00000	−	8.66025i	0.165295	−	0.286299i
$916$	3.85193			0.127271
$917$	11.7730	+	42.7670i	0.388777	+	1.41229i
$918$	5.31161			0.175309
$919$	−19.2270	+	33.3022i	−0.634242	+	1.09854i	0.352434	+	0.935837i	$0.385354\pi$
$919$	−19.2270	+	33.3022i	−0.634242	+	1.09854i	−0.986675	+	0.162702i	$0.947979\pi$
$920$	−0.500000	−	0.866025i	−0.0164845	−	0.0285520i
$921$	−15.2873	−	26.4783i	−0.503732	−	0.872490i
$922$	3.80882	−	6.59707i	0.125437	−	0.217263i
$923$	−28.5515			−0.939784
$924$	0.751397	−	0.761729i	0.0247191	−	0.0250590i
$925$	31.6288			1.03995
$926$	4.40441	−	7.62866i	0.144738	−	0.250693i
$927$	−8.41823	−	14.5808i	−0.276491	−	0.478896i
$928$	4.56022	+	7.89853i	0.149696	+	0.259282i
$929$	−26.5337	+	45.9577i	−0.870543	+	1.50782i	−0.00910666	+	0.999959i	$0.502899\pi$
$929$	−26.5337	+	45.9577i	−0.870543	+	1.50782i	−0.861436	+	0.507866i	$0.830435\pi$
$930$	−9.83645			−0.322550
$931$	−16.5933	−	9.28035i	−0.543823	−	0.304151i
$932$	−26.5304			−0.869033
$933$	−3.53538	+	6.12345i	−0.115743	+	0.200473i
$934$	0.404409	+	0.700458i	0.0132327	+	0.0229197i
$935$	1.07403	+	1.86028i	0.0351246	+	0.0608376i
$936$	2.06022	−	3.56840i	0.0673403	−	0.116637i
$937$	−29.1645			−0.952763			−0.476382	−	0.879239i	$-0.658052\pi$
$937$	−29.1645			−0.952763			−0.476382	+	0.879239i	$0.658052\pi$
$938$	−5.27016	+	5.34263i	−0.172077	+	0.174443i
$939$	−7.68839			−0.250901
$940$	5.41823	−	9.38464i	0.176723	−	0.306093i
$941$	−13.0110	−	22.5358i	−0.424147	−	0.734645i	0.572193	−	0.820119i	$-0.306093\pi$
$941$	−13.0110	−	22.5358i	−0.424147	−	0.734645i	−0.996340	+	0.0854743i	$0.972759\pi$
$942$	−11.3856	−	19.7205i	−0.370964	−	0.642529i
$943$	−5.35801	+	9.28035i	−0.174481	+	0.302210i
$944$	−8.31161			−0.270520
$945$	−0.702205	−	2.55086i	−0.0228427	−	0.0829796i
$946$	0.327094			0.0106347
$947$	6.46134	−	11.1914i	0.209965	−	0.363671i	−0.741738	−	0.670690i	$-0.765998\pi$
$947$	6.46134	−	11.1914i	0.209965	−	0.363671i	0.951703	+	0.307019i	$0.0993315\pi$
$948$	−4.96462	−	8.59898i	−0.161244	−	0.279282i
$949$	−9.46791	−	16.3989i	−0.307341	−	0.532331i
$950$	5.43204	−	9.40858i	0.176239	−	0.305255i
$951$	22.7933			0.739125
$952$	13.5989	+	3.54447i	0.440742	+	0.114877i
$953$	12.5680			0.407116			0.203558	−	0.979063i	$-0.434749\pi$
$953$	12.5680			0.407116			0.203558	+	0.979063i	$0.434749\pi$
$954$	−0.0955907	+	0.165568i	−0.00309486	+	0.00536046i
$955$	−12.3856	−	21.4526i	−0.400790	−	0.694189i
$956$	8.00000	+	13.8564i	0.258738	+	0.448148i
$957$	−1.84419	+	3.19424i	−0.0596143	+	0.103255i
$958$	28.3337			0.915419
$959$	24.6940	+	6.43634i	0.797410	+	0.207840i
$960$	−1.00000			−0.0322749
$961$	−32.8779	+	56.9462i	−1.06058	+	1.83697i
$962$	−16.2905	−	28.2160i	−0.525228	−	0.909722i
$963$	4.79780	+	8.31003i	0.154607	+	0.267787i
$964$	7.39667	−	12.8114i	0.238231	−	0.412628i
$965$	−14.8585			−0.478312
$966$	−0.702205	−	2.55086i	−0.0225931	−	0.0820727i
$967$	12.8309			0.412613			0.206306	−	0.978487i	$-0.433856\pi$
$967$	12.8309			0.412613			0.206306	+	0.978487i	$0.433856\pi$
$968$	−5.41823	+	9.38464i	−0.174148	+	0.301634i
$969$	−7.21323	−	12.4937i	−0.231722	−	0.401355i
$970$	7.68065	+	13.3033i	0.246611	+	0.427142i
$971$	11.2022	−	19.4028i	0.359496	−	0.622665i	−0.628381	−	0.777906i	$-0.716282\pi$
$971$	11.2022	−	19.4028i	0.359496	−	0.622665i	0.987877	+	0.155241i	$0.0496153\pi$
$972$	−1.00000			−0.0320750
$973$	−31.3337	+	31.7645i	−1.00451	+	1.01832i
$974$	−18.7005			−0.599204
$975$	−8.24086	+	14.2736i	−0.263919	+	0.457121i
$976$	−5.00000	−	8.66025i	−0.160046	−	0.277208i
$977$	10.2547	+	17.7616i	0.328076	+	0.568245i	0.982130	−	0.188203i	$-0.0602664\pi$
$977$	10.2547	+	17.7616i	0.328076	+	0.568245i	−0.654054	+	0.756448i	$0.726933\pi$
$978$	−12.3856	+	21.4526i	−0.396049	+	0.685977i
$979$	−3.19775			−0.102200
$980$	−0.0955907	−	6.99935i	−0.00305353	−	0.223586i
$981$	−3.19118			−0.101887
$982$	2.54640	−	4.41049i	0.0812588	−	0.140744i
$983$	−2.26521	−	3.92347i	−0.0722491	−	0.125139i	0.827638	−	0.561263i	$-0.189684\pi$
$983$	−2.26521	−	3.92347i	−0.0722491	−	0.125139i	−0.899887	+	0.436124i	$0.856351\pi$
$984$	5.35801	+	9.28035i	0.170807	+	0.295847i
$985$	5.71602	−	9.90044i	0.182128	−	0.315454i
$986$	−48.4442			−1.54278
$987$	20.1342	−	20.4111i	0.640880	−	0.649693i
$988$	−11.1912			−0.356039
$989$	0.404409	−	0.700458i	0.0128595	−	0.0222733i
$990$	−0.202205	−	0.350229i	−0.00642649	−	0.0111310i
$991$	15.7050	+	27.2019i	0.498886	+	0.864095i	0.999999	−	0.00128618i	$-0.000409404\pi$
$991$	15.7050	+	27.2019i	0.498886	+	0.864095i	−0.501113	+	0.865382i	$0.667076\pi$
$992$	−4.91823	+	8.51862i	−0.156154	+	0.270466i
$993$	20.5304			0.651513
$994$	4.86575	+	17.6756i	0.154332	+	0.560635i
$995$	−8.62323			−0.273375
$996$	−2.20220	+	3.81433i	−0.0697795	+	0.120862i
$997$	−9.23758	−	16.0000i	−0.292557	−	0.506724i	0.681857	−	0.731486i	$-0.261173\pi$
$997$	−9.23758	−	16.0000i	−0.292557	−	0.506724i	−0.974414	+	0.224762i	$0.927839\pi$
$998$	9.74366	+	16.8765i	0.308430	+	0.534217i
$999$	−3.95360	+	6.84784i	−0.125086	+	0.216656i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.i.k.415.3	yes	6
7.2	even	3		6762.2.a.ce.1.2		3
7.4	even	3	inner	966.2.i.k.277.3	✓	6
7.5	odd	6		6762.2.a.cf.1.2		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.i.k.277.3	✓	6	7.4	even	3	inner
966.2.i.k.415.3	yes	6	1.1	even	1	trivial
6762.2.a.ce.1.2		3	7.2	even	3
6762.2.a.cf.1.2		3	7.5	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)

\(f(q)\)	\(=\)	\(q+(0.500000 - 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} +(-0.500000 + 0.866025i) q^{5} +1.00000 q^{6} +(1.85801 - 1.88356i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(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} +(1.85801 - 1.88356i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 + 0.866025i) q^{10} +(0.202205 + 0.350229i) q^{11} +(0.500000 - 0.866025i) q^{12} +4.12043 q^{13} +(-0.702205 - 2.55086i) q^{14} -1.00000 q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.65581 - 4.59999i) q^{17} +(0.500000 + 0.866025i) q^{18} +(1.35801 - 2.35214i) q^{19} +1.00000 q^{20} +(2.56022 + 0.667305i) q^{21} +0.404409 q^{22} +(0.500000 - 0.866025i) q^{23} +(-0.500000 - 0.866025i) q^{24} +(2.00000 + 3.46410i) q^{25} +(2.06022 - 3.56840i) q^{26} -1.00000 q^{27} +(-2.56022 - 0.667305i) q^{28} +9.12043 q^{29} +(-0.500000 + 0.866025i) q^{30} +(4.91823 + 8.51862i) q^{31} +(0.500000 + 0.866025i) q^{32} +(-0.202205 + 0.350229i) q^{33} -5.31161 q^{34} +(0.702205 + 2.55086i) q^{35} +1.00000 q^{36} +(3.95360 - 6.84784i) q^{37} +(-1.35801 - 2.35214i) q^{38} +(2.06022 + 3.56840i) q^{39} +(0.500000 - 0.866025i) q^{40} -10.7160 q^{41} +(1.85801 - 1.88356i) q^{42} +0.808819 q^{43} +(0.202205 - 0.350229i) q^{44} +(-0.500000 - 0.866025i) q^{45} +(-0.500000 - 0.866025i) q^{46} +(5.41823 - 9.38464i) q^{47} -1.00000 q^{48} +(-0.0955907 - 6.99935i) q^{49} +4.00000 q^{50} +(2.65581 - 4.59999i) q^{51} +(-2.06022 - 3.56840i) q^{52} +(0.0955907 + 0.165568i) q^{53} +(-0.500000 + 0.866025i) q^{54} -0.404409 q^{55} +(-1.85801 + 1.88356i) q^{56} +2.71602 q^{57} +(4.56022 - 7.89853i) q^{58} +(4.15581 + 7.19807i) q^{59} +(0.500000 + 0.866025i) q^{60} +(-5.00000 + 8.66025i) q^{61} +9.83645 q^{62} +(0.702205 + 2.55086i) q^{63} +1.00000 q^{64} +(-2.06022 + 3.56840i) q^{65} +(0.202205 + 0.350229i) q^{66} +(-1.41823 - 2.45644i) q^{67} +(-2.65581 + 4.59999i) q^{68} +1.00000 q^{69} +(2.56022 + 0.667305i) q^{70} -6.92925 q^{71} +(0.500000 - 0.866025i) q^{72} +(-2.29780 - 3.97990i) q^{73} +(-3.95360 - 6.84784i) q^{74} +(-2.00000 + 3.46410i) q^{75} -2.71602 q^{76} +(1.03538 + 0.269864i) q^{77} +4.12043 q^{78} +(4.96462 - 8.59898i) q^{79} +(-0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-5.35801 + 9.28035i) q^{82} -4.40441 q^{83} +(-0.702205 - 2.55086i) q^{84} +5.31161 q^{85} +(0.404409 - 0.700458i) q^{86} +(4.56022 + 7.89853i) q^{87} +(-0.202205 - 0.350229i) q^{88} +(-3.95360 + 6.84784i) q^{89} -1.00000 q^{90} +(7.65581 - 7.76108i) q^{91} -1.00000 q^{92} +(-4.91823 + 8.51862i) q^{93} +(-5.41823 - 9.38464i) q^{94} +(1.35801 + 2.35214i) q^{95} +(-0.500000 + 0.866025i) q^{96} +15.3613 q^{97} +(-6.10941 - 3.41689i) q^{98} -0.404409 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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