LMFDB - Embedded newform 36.3.f.b.7.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,3,Mod(7,36)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 4]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("36.7");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	36.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.980928951697$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			7.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	36.7
Dual form			36.3.f.b.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000 q^{2} +(-1.50000 + 2.59808i) q^{3} +4.00000 q^{4} +(-2.00000 - 3.46410i) q^{5} +(-3.00000 + 5.19615i) q^{6} +(-3.00000 - 1.73205i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+2.00000 q^{2} +(-1.50000 + 2.59808i) q^{3} +4.00000 q^{4} +(-2.00000 - 3.46410i) q^{5} +(-3.00000 + 5.19615i) q^{6} +(-3.00000 - 1.73205i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-4.00000 - 6.92820i) q^{10} +(-10.5000 - 6.06218i) q^{11} +(-6.00000 + 10.3923i) q^{12} +(11.0000 + 19.0526i) q^{13} +(-6.00000 - 3.46410i) q^{14} +12.0000 q^{15} +16.0000 q^{16} -11.0000 q^{17} +(-9.00000 - 15.5885i) q^{18} +15.5885i q^{19} +(-8.00000 - 13.8564i) q^{20} +(9.00000 - 5.19615i) q^{21} +(-21.0000 - 12.1244i) q^{22} +(21.0000 - 12.1244i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(4.50000 - 7.79423i) q^{25} +(22.0000 + 38.1051i) q^{26} +27.0000 q^{27} +(-12.0000 - 6.92820i) q^{28} +(-17.0000 + 29.4449i) q^{29} +24.0000 q^{30} +(6.00000 - 3.46410i) q^{31} +32.0000 q^{32} +(31.5000 - 18.1865i) q^{33} -22.0000 q^{34} +13.8564i q^{35} +(-18.0000 - 31.1769i) q^{36} -16.0000 q^{37} +31.1769i q^{38} -66.0000 q^{39} +(-16.0000 - 27.7128i) q^{40} +(-6.50000 - 11.2583i) q^{41} +(18.0000 - 10.3923i) q^{42} +(-43.5000 - 25.1147i) q^{43} +(-42.0000 - 24.2487i) q^{44} +(-18.0000 + 31.1769i) q^{45} +(42.0000 - 24.2487i) q^{46} +(3.00000 + 1.73205i) q^{47} +(-24.0000 + 41.5692i) q^{48} +(-18.5000 - 32.0429i) q^{49} +(9.00000 - 15.5885i) q^{50} +(16.5000 - 28.5788i) q^{51} +(44.0000 + 76.2102i) q^{52} +52.0000 q^{53} +54.0000 q^{54} +48.4974i q^{55} +(-24.0000 - 13.8564i) q^{56} +(-40.5000 - 23.3827i) q^{57} +(-34.0000 + 58.8897i) q^{58} +(-46.5000 + 26.8468i) q^{59} +48.0000 q^{60} +(8.00000 - 13.8564i) q^{61} +(12.0000 - 6.92820i) q^{62} +31.1769i q^{63} +64.0000 q^{64} +(44.0000 - 76.2102i) q^{65} +(63.0000 - 36.3731i) q^{66} +(100.500 - 58.0237i) q^{67} -44.0000 q^{68} +72.7461i q^{69} +27.7128i q^{70} +(-36.0000 - 62.3538i) q^{72} -25.0000 q^{73} -32.0000 q^{74} +(13.5000 + 23.3827i) q^{75} +62.3538i q^{76} +(21.0000 + 36.3731i) q^{77} -132.000 q^{78} +(24.0000 + 13.8564i) q^{79} +(-32.0000 - 55.4256i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-13.0000 - 22.5167i) q^{82} +(30.0000 + 17.3205i) q^{83} +(36.0000 - 20.7846i) q^{84} +(22.0000 + 38.1051i) q^{85} +(-87.0000 - 50.2295i) q^{86} +(-51.0000 - 88.3346i) q^{87} +(-84.0000 - 48.4974i) q^{88} -2.00000 q^{89} +(-36.0000 + 62.3538i) q^{90} -76.2102i q^{91} +(84.0000 - 48.4974i) q^{92} +20.7846i q^{93} +(6.00000 + 3.46410i) q^{94} +(54.0000 - 31.1769i) q^{95} +(-48.0000 + 83.1384i) q^{96} +(21.5000 - 37.2391i) q^{97} +(-37.0000 - 64.0859i) q^{98} +109.119i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 4 q^{2} - 3 q^{3} + 8 q^{4} - 4 q^{5} - 6 q^{6} - 6 q^{7} + 16 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q + 4 * q^2 - 3 * q^3 + 8 * q^4 - 4 * q^5 - 6 * q^6 - 6 * q^7 + 16 * q^8 - 9 * q^9	\( 2 q + 4 q^{2} - 3 q^{3} + 8 q^{4} - 4 q^{5} - 6 q^{6} - 6 q^{7} + 16 q^{8} - 9 q^{9} - 8 q^{10} - 21 q^{11} - 12 q^{12} + 22 q^{13} - 12 q^{14} + 24 q^{15} + 32 q^{16} - 22 q^{17} - 18 q^{18} - 16 q^{20} + 18 q^{21} - 42 q^{22} + 42 q^{23} - 24 q^{24} + 9 q^{25} + 44 q^{26} + 54 q^{27} - 24 q^{28} - 34 q^{29} + 48 q^{30} + 12 q^{31} + 64 q^{32} + 63 q^{33} - 44 q^{34} - 36 q^{36} - 32 q^{37} - 132 q^{39} - 32 q^{40} - 13 q^{41} + 36 q^{42} - 87 q^{43} - 84 q^{44} - 36 q^{45} + 84 q^{46} + 6 q^{47} - 48 q^{48} - 37 q^{49} + 18 q^{50} + 33 q^{51} + 88 q^{52} + 104 q^{53} + 108 q^{54} - 48 q^{56} - 81 q^{57} - 68 q^{58} - 93 q^{59} + 96 q^{60} + 16 q^{61} + 24 q^{62} + 128 q^{64} + 88 q^{65} + 126 q^{66} + 201 q^{67} - 88 q^{68} - 72 q^{72} - 50 q^{73} - 64 q^{74} + 27 q^{75} + 42 q^{77} - 264 q^{78} + 48 q^{79} - 64 q^{80} - 81 q^{81} - 26 q^{82} + 60 q^{83} + 72 q^{84} + 44 q^{85} - 174 q^{86} - 102 q^{87} - 168 q^{88} - 4 q^{89} - 72 q^{90} + 168 q^{92} + 12 q^{94} + 108 q^{95} - 96 q^{96} + 43 q^{97} - 74 q^{98}+O(q^{100}) \) 2 * q + 4 * q^2 - 3 * q^3 + 8 * q^4 - 4 * q^5 - 6 * q^6 - 6 * q^7 + 16 * q^8 - 9 * q^9 - 8 * q^10 - 21 * q^11 - 12 * q^12 + 22 * q^13 - 12 * q^14 + 24 * q^15 + 32 * q^16 - 22 * q^17 - 18 * q^18 - 16 * q^20 + 18 * q^21 - 42 * q^22 + 42 * q^23 - 24 * q^24 + 9 * q^25 + 44 * q^26 + 54 * q^27 - 24 * q^28 - 34 * q^29 + 48 * q^30 + 12 * q^31 + 64 * q^32 + 63 * q^33 - 44 * q^34 - 36 * q^36 - 32 * q^37 - 132 * q^39 - 32 * q^40 - 13 * q^41 + 36 * q^42 - 87 * q^43 - 84 * q^44 - 36 * q^45 + 84 * q^46 + 6 * q^47 - 48 * q^48 - 37 * q^49 + 18 * q^50 + 33 * q^51 + 88 * q^52 + 104 * q^53 + 108 * q^54 - 48 * q^56 - 81 * q^57 - 68 * q^58 - 93 * q^59 + 96 * q^60 + 16 * q^61 + 24 * q^62 + 128 * q^64 + 88 * q^65 + 126 * q^66 + 201 * q^67 - 88 * q^68 - 72 * q^72 - 50 * q^73 - 64 * q^74 + 27 * q^75 + 42 * q^77 - 264 * q^78 + 48 * q^79 - 64 * q^80 - 81 * q^81 - 26 * q^82 + 60 * q^83 + 72 * q^84 + 44 * q^85 - 174 * q^86 - 102 * q^87 - 168 * q^88 - 4 * q^89 - 72 * q^90 + 168 * q^92 + 12 * q^94 + 108 * q^95 - 96 * q^96 + 43 * q^97 - 74 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.00000			1.00000
$2$	2.00000			1.00000
$3$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$3$	−1.50000	+	2.59808i	−0.500000	+	0.866025i
$4$	4.00000			1.00000
$5$	−2.00000	−	3.46410i	−0.400000	−	0.692820i	0.593725	−	0.804668i	$-0.297657\pi$
$5$	−2.00000	−	3.46410i	−0.400000	−	0.692820i	−0.993725	+	0.111847i	$0.964323\pi$
$6$	−3.00000	+	5.19615i	−0.500000	+	0.866025i
$7$	−3.00000	−	1.73205i	−0.428571	−	0.247436i	0.270166	−	0.962814i	$-0.412921\pi$
$7$	−3.00000	−	1.73205i	−0.428571	−	0.247436i	−0.698738	+	0.715378i	$0.746255\pi$
$8$	8.00000			1.00000
$9$	−4.50000	−	7.79423i	−0.500000	−	0.866025i
$10$	−4.00000	−	6.92820i	−0.400000	−	0.692820i
$11$	−10.5000	−	6.06218i	−0.954545	−	0.551107i	−0.0600555	−	0.998195i	$-0.519128\pi$
$11$	−10.5000	−	6.06218i	−0.954545	−	0.551107i	−0.894490	+	0.447088i	$0.852461\pi$
$12$	−6.00000	+	10.3923i	−0.500000	+	0.866025i
$13$	11.0000	+	19.0526i	0.846154	+	1.46558i	0.884615	+	0.466321i	$0.154421\pi$
$13$	11.0000	+	19.0526i	0.846154	+	1.46558i	−0.0384615	+	0.999260i	$0.512246\pi$
$14$	−6.00000	−	3.46410i	−0.428571	−	0.247436i
$15$	12.0000			0.800000
$16$	16.0000			1.00000
$17$	−11.0000			−0.647059			−0.323529	−	0.946218i	$-0.604869\pi$
$17$	−11.0000			−0.647059			−0.323529	+	0.946218i	$0.604869\pi$
$18$	−9.00000	−	15.5885i	−0.500000	−	0.866025i
$19$			15.5885i			0.820445i	0.911985	+	0.410223i	$0.134549\pi$
$19$			15.5885i			0.820445i	−0.911985	+	0.410223i	$0.865451\pi$
$20$	−8.00000	−	13.8564i	−0.400000	−	0.692820i
$21$	9.00000	−	5.19615i	0.428571	−	0.247436i
$22$	−21.0000	−	12.1244i	−0.954545	−	0.551107i
$23$	21.0000	−	12.1244i	0.913043	−	0.527146i	0.0316343	−	0.999500i	$-0.489929\pi$
$23$	21.0000	−	12.1244i	0.913043	−	0.527146i	0.881409	+	0.472354i	$0.156595\pi$
$24$	−12.0000	+	20.7846i	−0.500000	+	0.866025i
$25$	4.50000	−	7.79423i	0.180000	−	0.311769i
$26$	22.0000	+	38.1051i	0.846154	+	1.46558i
$27$	27.0000			1.00000
$28$	−12.0000	−	6.92820i	−0.428571	−	0.247436i
$29$	−17.0000	+	29.4449i	−0.586207	+	1.01534i	0.408517	+	0.912751i	$0.366046\pi$
$29$	−17.0000	+	29.4449i	−0.586207	+	1.01534i	−0.994724	+	0.102589i	$0.967287\pi$
$30$	24.0000			0.800000
$31$	6.00000	−	3.46410i	0.193548	−	0.111745i	−0.400094	−	0.916474i	$-0.631023\pi$
$31$	6.00000	−	3.46410i	0.193548	−	0.111745i	0.593643	+	0.804729i	$0.297689\pi$
$32$	32.0000			1.00000
$33$	31.5000	−	18.1865i	0.954545	−	0.551107i
$34$	−22.0000			−0.647059
$35$			13.8564i			0.395897i
$36$	−18.0000	−	31.1769i	−0.500000	−	0.866025i
$37$	−16.0000			−0.432432			−0.216216	−	0.976346i	$-0.569372\pi$
$37$	−16.0000			−0.432432			−0.216216	+	0.976346i	$0.569372\pi$
$38$			31.1769i			0.820445i
$39$	−66.0000			−1.69231
$40$	−16.0000	−	27.7128i	−0.400000	−	0.692820i
$41$	−6.50000	−	11.2583i	−0.158537	−	0.274593i	0.775805	−	0.630973i	$-0.217344\pi$
$41$	−6.50000	−	11.2583i	−0.158537	−	0.274593i	−0.934341	+	0.356380i	$0.884011\pi$
$42$	18.0000	−	10.3923i	0.428571	−	0.247436i
$43$	−43.5000	−	25.1147i	−1.01163	−	0.584064i	−0.0999600	−	0.994991i	$-0.531871\pi$
$43$	−43.5000	−	25.1147i	−1.01163	−	0.584064i	−0.911668	+	0.410928i	$0.865205\pi$
$44$	−42.0000	−	24.2487i	−0.954545	−	0.551107i
$45$	−18.0000	+	31.1769i	−0.400000	+	0.692820i
$46$	42.0000	−	24.2487i	0.913043	−	0.527146i
$47$	3.00000	+	1.73205i	0.0638298	+	0.0368521i	0.531575	−	0.847011i	$-0.321600\pi$
$47$	3.00000	+	1.73205i	0.0638298	+	0.0368521i	−0.467745	+	0.883863i	$0.654934\pi$
$48$	−24.0000	+	41.5692i	−0.500000	+	0.866025i
$49$	−18.5000	−	32.0429i	−0.377551	−	0.653938i
$50$	9.00000	−	15.5885i	0.180000	−	0.311769i
$51$	16.5000	−	28.5788i	0.323529	−	0.560369i
$52$	44.0000	+	76.2102i	0.846154	+	1.46558i
$53$	52.0000			0.981132			0.490566	−	0.871404i	$-0.336790\pi$
$53$	52.0000			0.981132			0.490566	+	0.871404i	$0.336790\pi$
$54$	54.0000			1.00000
$55$			48.4974i			0.881771i
$56$	−24.0000	−	13.8564i	−0.428571	−	0.247436i
$57$	−40.5000	−	23.3827i	−0.710526	−	0.410223i
$58$	−34.0000	+	58.8897i	−0.586207	+	1.01534i
$59$	−46.5000	+	26.8468i	−0.788136	+	0.455030i	−0.839306	−	0.543660i	$-0.817038\pi$
$59$	−46.5000	+	26.8468i	−0.788136	+	0.455030i	0.0511702	+	0.998690i	$0.483705\pi$
$60$	48.0000			0.800000
$61$	8.00000	−	13.8564i	0.131148	−	0.227154i	−0.792972	−	0.609259i	$-0.791467\pi$
$61$	8.00000	−	13.8564i	0.131148	−	0.227154i	0.924119	+	0.382104i	$0.124801\pi$
$62$	12.0000	−	6.92820i	0.193548	−	0.111745i
$63$			31.1769i			0.494872i
$64$	64.0000			1.00000
$65$	44.0000	−	76.2102i	0.676923	−	1.17247i
$66$	63.0000	−	36.3731i	0.954545	−	0.551107i
$67$	100.500	−	58.0237i	1.50000	−	0.866025i	0.500000	−	0.866025i	$-0.333333\pi$
$67$	100.500	−	58.0237i	1.50000	−	0.866025i	1.00000			$0$
$68$	−44.0000			−0.647059
$69$			72.7461i			1.05429i
$70$			27.7128i			0.395897i
$71$		0			0		1.00000			$0$
$71$		0			0		−1.00000			$\pi$
$72$	−36.0000	−	62.3538i	−0.500000	−	0.866025i
$73$	−25.0000			−0.342466			−0.171233	−	0.985231i	$-0.554775\pi$
$73$	−25.0000			−0.342466			−0.171233	+	0.985231i	$0.554775\pi$
$74$	−32.0000			−0.432432
$75$	13.5000	+	23.3827i	0.180000	+	0.311769i
$76$			62.3538i			0.820445i
$77$	21.0000	+	36.3731i	0.272727	+	0.472377i
$78$	−132.000			−1.69231
$79$	24.0000	+	13.8564i	0.303797	+	0.175398i	0.644148	−	0.764901i	$-0.277212\pi$
$79$	24.0000	+	13.8564i	0.303797	+	0.175398i	−0.340350	+	0.940299i	$0.610546\pi$
$80$	−32.0000	−	55.4256i	−0.400000	−	0.692820i
$81$	−40.5000	+	70.1481i	−0.500000	+	0.866025i
$82$	−13.0000	−	22.5167i	−0.158537	−	0.274593i
$83$	30.0000	+	17.3205i	0.361446	+	0.208681i	0.669715	−	0.742618i	$-0.266416\pi$
$83$	30.0000	+	17.3205i	0.361446	+	0.208681i	−0.308269	+	0.951299i	$0.599750\pi$
$84$	36.0000	−	20.7846i	0.428571	−	0.247436i
$85$	22.0000	+	38.1051i	0.258824	+	0.448296i
$86$	−87.0000	−	50.2295i	−1.01163	−	0.584064i
$87$	−51.0000	−	88.3346i	−0.586207	−	1.01534i
$88$	−84.0000	−	48.4974i	−0.954545	−	0.551107i
$89$	−2.00000			−0.0224719			−0.0112360	−	0.999937i	$-0.503577\pi$
$89$	−2.00000			−0.0224719			−0.0112360	+	0.999937i	$0.503577\pi$
$90$	−36.0000	+	62.3538i	−0.400000	+	0.692820i
$91$		−	76.2102i		−	0.837475i
$92$	84.0000	−	48.4974i	0.913043	−	0.527146i
$93$			20.7846i			0.223490i
$94$	6.00000	+	3.46410i	0.0638298	+	0.0368521i
$95$	54.0000	−	31.1769i	0.568421	−	0.328178i
$96$	−48.0000	+	83.1384i	−0.500000	+	0.866025i
$97$	21.5000	−	37.2391i	0.221649	−	0.383908i	−0.733659	−	0.679517i	$-0.762189\pi$
$97$	21.5000	−	37.2391i	0.221649	−	0.383908i	0.955309	+	0.295609i	$0.0955226\pi$
$98$	−37.0000	−	64.0859i	−0.377551	−	0.653938i
$99$			109.119i			1.10221i
$100$	18.0000	−	31.1769i	0.180000	−	0.311769i
$101$	10.0000	−	17.3205i	0.0990099	−	0.171490i	−0.812265	−	0.583288i	$-0.801766\pi$
$101$	10.0000	−	17.3205i	0.0990099	−	0.171490i	0.911275	+	0.411798i	$0.135099\pi$
$102$	33.0000	−	57.1577i	0.323529	−	0.560369i
$103$	−21.0000	+	12.1244i	−0.203883	+	0.117712i	−0.598466	−	0.801148i	$-0.704223\pi$
$103$	−21.0000	+	12.1244i	−0.203883	+	0.117712i	0.394582	+	0.918861i	$0.370889\pi$
$104$	88.0000	+	152.420i	0.846154	+	1.46558i
$105$	−36.0000	−	20.7846i	−0.342857	−	0.197949i
$106$	104.000			0.981132
$107$			15.5885i			0.145687i	0.997343	+	0.0728433i	$0.0232073\pi$
$107$			15.5885i			0.145687i	−0.997343	+	0.0728433i	$0.976793\pi$
$108$	108.000			1.00000
$109$	−88.0000			−0.807339			−0.403670	−	0.914905i	$-0.632266\pi$
$109$	−88.0000			−0.807339			−0.403670	+	0.914905i	$0.632266\pi$
$110$			96.9948i			0.881771i
$111$	24.0000	−	41.5692i	0.216216	−	0.374497i
$112$	−48.0000	−	27.7128i	−0.428571	−	0.247436i
$113$	25.0000	+	43.3013i	0.221239	+	0.383197i	0.955184	−	0.296011i	$-0.0956566\pi$
$113$	25.0000	+	43.3013i	0.221239	+	0.383197i	−0.733946	+	0.679208i	$0.762323\pi$
$114$	−81.0000	−	46.7654i	−0.710526	−	0.410223i
$115$	−84.0000	−	48.4974i	−0.730435	−	0.421717i
$116$	−68.0000	+	117.779i	−0.586207	+	1.01534i
$117$	99.0000	−	171.473i	0.846154	−	1.46558i
$118$	−93.0000	+	53.6936i	−0.788136	+	0.455030i
$119$	33.0000	+	19.0526i	0.277311	+	0.160106i
$120$	96.0000			0.800000
$121$	13.0000	+	22.5167i	0.107438	+	0.186088i
$122$	16.0000	−	27.7128i	0.131148	−	0.227154i
$123$	39.0000			0.317073
$124$	24.0000	−	13.8564i	0.193548	−	0.111745i
$125$	−136.000			−1.08800
$126$			62.3538i			0.494872i
$127$			218.238i			1.71841i	0.511629	+	0.859206i	$0.329042\pi$
$127$			218.238i			1.71841i	−0.511629	+	0.859206i	$0.670958\pi$
$128$	128.000			1.00000
$129$	130.500	−	75.3442i	1.01163	−	0.584064i
$130$	88.0000	−	152.420i	0.676923	−	1.17247i
$131$	−168.000	+	96.9948i	−1.28244	+	0.740419i	−0.977294	−	0.211886i	$-0.932039\pi$
$131$	−168.000	+	96.9948i	−1.28244	+	0.740419i	−0.305148	+	0.952305i	$0.598706\pi$
$132$	126.000	−	72.7461i	0.954545	−	0.551107i
$133$	27.0000	−	46.7654i	0.203008	−	0.351619i
$134$	201.000	−	116.047i	1.50000	−	0.866025i
$135$	−54.0000	−	93.5307i	−0.400000	−	0.692820i
$136$	−88.0000			−0.647059
$137$	−84.5000	+	146.358i	−0.616788	+	1.06831i	0.373280	+	0.927719i	$0.378233\pi$
$137$	−84.5000	+	146.358i	−0.616788	+	1.06831i	−0.990068	+	0.140590i	$0.955100\pi$
$138$			145.492i			1.05429i
$139$	−169.500	+	97.8609i	−1.21942	+	0.704035i	−0.964795	−	0.263004i	$-0.915287\pi$
$139$	−169.500	+	97.8609i	−1.21942	+	0.704035i	−0.254630	+	0.967039i	$0.581954\pi$
$140$			55.4256i			0.395897i
$141$	−9.00000	+	5.19615i	−0.0638298	+	0.0368521i
$142$		0			0
$143$		−	266.736i		−	1.86529i
$144$	−72.0000	−	124.708i	−0.500000	−	0.866025i
$145$	136.000			0.937931
$146$	−50.0000			−0.342466
$147$	111.000			0.755102
$148$	−64.0000			−0.432432
$149$	−65.0000	−	112.583i	−0.436242	−	0.755593i	0.561154	−	0.827711i	$-0.310357\pi$
$149$	−65.0000	−	112.583i	−0.436242	−	0.755593i	−0.997396	+	0.0721185i	$0.977024\pi$
$150$	27.0000	+	46.7654i	0.180000	+	0.311769i
$151$	105.000	+	60.6218i	0.695364	+	0.401469i	0.805618	−	0.592435i	$-0.201833\pi$
$151$	105.000	+	60.6218i	0.695364	+	0.401469i	−0.110254	+	0.993903i	$0.535167\pi$
$152$			124.708i			0.820445i
$153$	49.5000	+	85.7365i	0.323529	+	0.560369i
$154$	42.0000	+	72.7461i	0.272727	+	0.472377i
$155$	−24.0000	−	13.8564i	−0.154839	−	0.0893962i
$156$	−264.000			−1.69231
$157$	2.00000	+	3.46410i	0.0127389	+	0.0220643i	0.872325	−	0.488927i	$-0.162612\pi$
$157$	2.00000	+	3.46410i	0.0127389	+	0.0220643i	−0.859586	+	0.510992i	$0.829278\pi$
$158$	48.0000	+	27.7128i	0.303797	+	0.175398i
$159$	−78.0000	+	135.100i	−0.490566	+	0.849685i
$160$	−64.0000	−	110.851i	−0.400000	−	0.692820i
$161$	−84.0000			−0.521739
$162$	−81.0000	+	140.296i	−0.500000	+	0.866025i
$163$		−	311.769i		−	1.91269i	−0.292233	−	0.956347i	$-0.594398\pi$
$163$		−	311.769i		−	1.91269i	0.292233	−	0.956347i	$-0.405602\pi$
$164$	−26.0000	−	45.0333i	−0.158537	−	0.274593i
$165$	−126.000	−	72.7461i	−0.763636	−	0.440886i
$166$	60.0000	+	34.6410i	0.361446	+	0.208681i
$167$	156.000	−	90.0666i	0.934132	−	0.539321i	0.0460158	−	0.998941i	$-0.485348\pi$
$167$	156.000	−	90.0666i	0.934132	−	0.539321i	0.888116	+	0.459620i	$0.152014\pi$
$168$	72.0000	−	41.5692i	0.428571	−	0.247436i
$169$	−157.500	+	272.798i	−0.931953	+	1.61419i
$170$	44.0000	+	76.2102i	0.258824	+	0.448296i
$171$	121.500	−	70.1481i	0.710526	−	0.410223i
$172$	−174.000	−	100.459i	−1.01163	−	0.584064i
$173$	1.00000	−	1.73205i	0.00578035	−	0.0100119i	−0.863121	−	0.504998i	$-0.831493\pi$
$173$	1.00000	−	1.73205i	0.00578035	−	0.0100119i	0.868901	+	0.494986i	$0.164827\pi$
$174$	−102.000	−	176.669i	−0.586207	−	1.01534i
$175$	−27.0000	+	15.5885i	−0.154286	+	0.0890769i
$176$	−168.000	−	96.9948i	−0.954545	−	0.551107i
$177$		−	161.081i		−	0.910061i
$178$	−4.00000			−0.0224719
$179$			187.061i			1.04504i	0.852628	+	0.522518i	$0.175007\pi$
$179$			187.061i			1.04504i	−0.852628	+	0.522518i	$0.824993\pi$
$180$	−72.0000	+	124.708i	−0.400000	+	0.692820i
$181$	254.000			1.40331			0.701657	−	0.712514i	$-0.252444\pi$
$181$	254.000			1.40331			0.701657	+	0.712514i	$0.252444\pi$
$182$		−	152.420i		−	0.837475i
$183$	24.0000	+	41.5692i	0.131148	+	0.227154i
$184$	168.000	−	96.9948i	0.913043	−	0.527146i
$185$	32.0000	+	55.4256i	0.172973	+	0.299598i
$186$			41.5692i			0.223490i
$187$	115.500	+	66.6840i	0.617647	+	0.356599i
$188$	12.0000	+	6.92820i	0.0638298	+	0.0368521i
$189$	−81.0000	−	46.7654i	−0.428571	−	0.247436i
$190$	108.000	−	62.3538i	0.568421	−	0.328178i
$191$	3.00000	+	1.73205i	0.0157068	+	0.00906833i	0.507833	−	0.861456i	$-0.330447\pi$
$191$	3.00000	+	1.73205i	0.0157068	+	0.00906833i	−0.492126	+	0.870524i	$0.663780\pi$
$192$	−96.0000	+	166.277i	−0.500000	+	0.866025i
$193$	33.5000	+	58.0237i	0.173575	+	0.300641i	0.939667	−	0.342090i	$-0.111135\pi$
$193$	33.5000	+	58.0237i	0.173575	+	0.300641i	−0.766092	+	0.642731i	$0.777801\pi$
$194$	43.0000	−	74.4782i	0.221649	−	0.383908i
$195$	132.000	+	228.631i	0.676923	+	1.17247i
$196$	−74.0000	−	128.172i	−0.377551	−	0.653938i
$197$	268.000			1.36041			0.680203	−	0.733024i	$-0.261892\pi$
$197$	268.000			1.36041			0.680203	+	0.733024i	$0.261892\pi$
$198$			218.238i			1.10221i
$199$		−	31.1769i		−	0.156668i	−0.996927	−	0.0783340i	$-0.975040\pi$
$199$		−	31.1769i		−	0.156668i	0.996927	−	0.0783340i	$-0.0249600\pi$
$200$	36.0000	−	62.3538i	0.180000	−	0.311769i
$201$			348.142i			1.73205i
$202$	20.0000	−	34.6410i	0.0990099	−	0.171490i
$203$	102.000	−	58.8897i	0.502463	−	0.290097i
$204$	66.0000	−	114.315i	0.323529	−	0.560369i
$205$	−26.0000	+	45.0333i	−0.126829	+	0.219675i
$206$	−42.0000	+	24.2487i	−0.203883	+	0.117712i
$207$	−189.000	−	109.119i	−0.913043	−	0.527146i
$208$	176.000	+	304.841i	0.846154	+	1.46558i
$209$	94.5000	−	163.679i	0.452153	−	0.783152i
$210$	−72.0000	−	41.5692i	−0.342857	−	0.197949i
$211$	114.000	−	65.8179i	0.540284	−	0.311933i	−0.204910	−	0.978781i	$-0.565690\pi$
$211$	114.000	−	65.8179i	0.540284	−	0.311933i	0.745194	+	0.666848i	$0.232357\pi$
$212$	208.000			0.981132
$213$		0			0
$214$			31.1769i			0.145687i
$215$			200.918i			0.934502i
$216$	216.000			1.00000
$217$	−24.0000			−0.110599
$218$	−176.000			−0.807339
$219$	37.5000	−	64.9519i	0.171233	−	0.296584i
$220$			193.990i			0.881771i
$221$	−121.000	−	209.578i	−0.547511	−	0.948317i
$222$	48.0000	−	83.1384i	0.216216	−	0.374497i
$223$	51.0000	+	29.4449i	0.228700	+	0.132040i	0.609972	−	0.792423i	$-0.291181\pi$
$223$	51.0000	+	29.4449i	0.228700	+	0.132040i	−0.381272	+	0.924463i	$0.624514\pi$
$224$	−96.0000	−	55.4256i	−0.428571	−	0.247436i
$225$	−81.0000			−0.360000
$226$	50.0000	+	86.6025i	0.221239	+	0.383197i
$227$	−388.500	−	224.301i	−1.71145	−	0.988108i	−0.932607	−	0.360894i	$-0.882471\pi$
$227$	−388.500	−	224.301i	−1.71145	−	0.988108i	−0.778847	−	0.627214i	$-0.784195\pi$
$228$	−162.000	−	93.5307i	−0.710526	−	0.410223i
$229$	−205.000	−	355.070i	−0.895197	−	1.55053i	−0.833561	−	0.552427i	$-0.813702\pi$
$229$	−205.000	−	355.070i	−0.895197	−	1.55053i	−0.0616353	−	0.998099i	$-0.519632\pi$
$230$	−168.000	−	96.9948i	−0.730435	−	0.421717i
$231$	−126.000			−0.545455
$232$	−136.000	+	235.559i	−0.586207	+	1.01534i
$233$	−65.0000			−0.278970			−0.139485	−	0.990224i	$-0.544545\pi$
$233$	−65.0000			−0.278970			−0.139485	+	0.990224i	$0.544545\pi$
$234$	198.000	−	342.946i	0.846154	−	1.46558i
$235$		−	13.8564i		−	0.0589634i
$236$	−186.000	+	107.387i	−0.788136	+	0.455030i
$237$	−72.0000	+	41.5692i	−0.303797	+	0.175398i
$238$	66.0000	+	38.1051i	0.277311	+	0.160106i
$239$	−33.0000	+	19.0526i	−0.138075	+	0.0797178i	−0.567446	−	0.823410i	$-0.692069\pi$
$239$	−33.0000	+	19.0526i	−0.138075	+	0.0797178i	0.429371	+	0.903128i	$0.358735\pi$
$240$	192.000			0.800000
$241$	111.500	−	193.124i	0.462656	−	0.801343i	−0.536437	−	0.843941i	$-0.680230\pi$
$241$	111.500	−	193.124i	0.462656	−	0.801343i	0.999092	+	0.0425975i	$0.0135633\pi$
$242$	26.0000	+	45.0333i	0.107438	+	0.186088i
$243$	−121.500	−	210.444i	−0.500000	−	0.866025i
$244$	32.0000	−	55.4256i	0.131148	−	0.227154i
$245$	−74.0000	+	128.172i	−0.302041	+	0.523150i
$246$	78.0000			0.317073
$247$	−297.000	+	171.473i	−1.20243	+	0.694223i
$248$	48.0000	−	27.7128i	0.193548	−	0.111745i
$249$	−90.0000	+	51.9615i	−0.361446	+	0.208681i
$250$	−272.000			−1.08800
$251$			109.119i			0.434738i	0.976090	+	0.217369i	$0.0697475\pi$
$251$			109.119i			0.434738i	−0.976090	+	0.217369i	$0.930253\pi$
$252$			124.708i			0.494872i
$253$	−294.000			−1.16206
$254$			436.477i			1.71841i
$255$	−132.000			−0.517647
$256$	256.000			1.00000
$257$	218.500	+	378.453i	0.850195	+	1.47258i	0.881032	+	0.473056i	$0.156849\pi$
$257$	218.500	+	378.453i	0.850195	+	1.47258i	−0.0308379	+	0.999524i	$0.509818\pi$
$258$	261.000	−	150.688i	1.01163	−	0.584064i
$259$	48.0000	+	27.7128i	0.185328	+	0.106999i
$260$	176.000	−	304.841i	0.676923	−	1.17247i
$261$	306.000			1.17241
$262$	−336.000	+	193.990i	−1.28244	+	0.740419i
$263$	273.000	+	157.617i	1.03802	+	0.599303i	0.919273	−	0.393621i	$-0.128778\pi$
$263$	273.000	+	157.617i	1.03802	+	0.599303i	0.118750	+	0.992924i	$0.462111\pi$
$264$	252.000	−	145.492i	0.954545	−	0.551107i
$265$	−104.000	−	180.133i	−0.392453	−	0.679748i
$266$	54.0000	−	93.5307i	0.203008	−	0.351619i
$267$	3.00000	−	5.19615i	0.0112360	−	0.0194612i
$268$	402.000	−	232.095i	1.50000	−	0.866025i
$269$	304.000			1.13011			0.565056	−	0.825053i	$-0.308855\pi$
$269$	304.000			1.13011			0.565056	+	0.825053i	$0.308855\pi$
$270$	−108.000	−	187.061i	−0.400000	−	0.692820i
$271$		−	311.769i		−	1.15044i	−0.817999	−	0.575220i	$-0.804917\pi$
$271$		−	311.769i		−	1.15044i	0.817999	−	0.575220i	$-0.195083\pi$
$272$	−176.000			−0.647059
$273$	198.000	+	114.315i	0.725275	+	0.418738i
$274$	−169.000	+	292.717i	−0.616788	+	1.06831i
$275$	−94.5000	+	54.5596i	−0.343636	+	0.198399i
$276$			290.985i			1.05429i
$277$	17.0000	−	29.4449i	0.0613718	−	0.106299i	−0.833707	−	0.552207i	$-0.813786\pi$
$277$	17.0000	−	29.4449i	0.0613718	−	0.106299i	0.895079	+	0.445908i	$0.147119\pi$
$278$	−339.000	+	195.722i	−1.21942	+	0.704035i
$279$	−54.0000	−	31.1769i	−0.193548	−	0.111745i
$280$			110.851i			0.395897i
$281$	109.000	−	188.794i	0.387900	−	0.671863i	−0.604267	−	0.796782i	$-0.706534\pi$
$281$	109.000	−	188.794i	0.387900	−	0.671863i	0.992167	+	0.124919i	$0.0398671\pi$
$282$	−18.0000	+	10.3923i	−0.0638298	+	0.0368521i
$283$	6.00000	−	3.46410i	0.0212014	−	0.0122406i	−0.489362	−	0.872081i	$-0.662770\pi$
$283$	6.00000	−	3.46410i	0.0212014	−	0.0122406i	0.510563	+	0.859840i	$0.329437\pi$
$284$		0			0
$285$			187.061i			0.656356i
$286$		−	533.472i		−	1.86529i
$287$			45.0333i			0.156911i
$288$	−144.000	−	249.415i	−0.500000	−	0.866025i
$289$	−168.000			−0.581315
$290$	272.000			0.937931
$291$	64.5000	+	111.717i	0.221649	+	0.383908i
$292$	−100.000			−0.342466
$293$	−101.000	−	174.937i	−0.344710	−	0.597055i	0.640591	−	0.767882i	$-0.278689\pi$
$293$	−101.000	−	174.937i	−0.344710	−	0.597055i	−0.985301	+	0.170827i	$0.945356\pi$
$294$	222.000			0.755102
$295$	186.000	+	107.387i	0.630508	+	0.364024i
$296$	−128.000			−0.432432
$297$	−283.500	−	163.679i	−0.954545	−	0.551107i
$298$	−130.000	−	225.167i	−0.436242	−	0.755593i
$299$	462.000	+	266.736i	1.54515	+	0.892093i
$300$	54.0000	+	93.5307i	0.180000	+	0.311769i
$301$	87.0000	+	150.688i	0.289037	+	0.500626i
$302$	210.000	+	121.244i	0.695364	+	0.401469i
$303$	30.0000	+	51.9615i	0.0990099	+	0.171490i
$304$			249.415i			0.820445i
$305$	−64.0000			−0.209836
$306$	99.0000	+	171.473i	0.323529	+	0.560369i
$307$			109.119i			0.355437i	0.984081	+	0.177719i	$0.0568717\pi$
$307$			109.119i			0.355437i	−0.984081	+	0.177719i	$0.943128\pi$
$308$	84.0000	+	145.492i	0.272727	+	0.472377i
$309$		−	72.7461i		−	0.235424i
$310$	−48.0000	−	27.7128i	−0.154839	−	0.0893962i
$311$	237.000	−	136.832i	0.762058	−	0.439974i	−0.0679762	−	0.997687i	$-0.521654\pi$
$311$	237.000	−	136.832i	0.762058	−	0.439974i	0.830034	+	0.557713i	$0.188321\pi$
$312$	−528.000			−1.69231
$313$	39.5000	−	68.4160i	0.126198	−	0.218581i	−0.796003	−	0.605293i	$-0.793056\pi$
$313$	39.5000	−	68.4160i	0.126198	−	0.218581i	0.922201	+	0.386712i	$0.126389\pi$
$314$	4.00000	+	6.92820i	0.0127389	+	0.0220643i
$315$	108.000	−	62.3538i	0.342857	−	0.197949i
$316$	96.0000	+	55.4256i	0.303797	+	0.175398i
$317$	−251.000	+	434.745i	−0.791798	+	1.37143i	0.133054	+	0.991109i	$0.457521\pi$
$317$	−251.000	+	434.745i	−0.791798	+	1.37143i	−0.924853	+	0.380326i	$0.875812\pi$
$318$	−156.000	+	270.200i	−0.490566	+	0.849685i
$319$	357.000	−	206.114i	1.11912	−	0.646126i
$320$	−128.000	−	221.703i	−0.400000	−	0.692820i
$321$	−40.5000	−	23.3827i	−0.126168	−	0.0728433i
$322$	−168.000			−0.521739
$323$		−	171.473i		−	0.530876i
$324$	−162.000	+	280.592i	−0.500000	+	0.866025i
$325$	198.000			0.609231
$326$		−	623.538i		−	1.91269i
$327$	132.000	−	228.631i	0.403670	−	0.699176i
$328$	−52.0000	−	90.0666i	−0.158537	−	0.274593i
$329$	−6.00000	−	10.3923i	−0.0182371	−	0.0315876i
$330$	−252.000	−	145.492i	−0.763636	−	0.440886i
$331$	−354.000	−	204.382i	−1.06949	−	0.617468i	−0.141445	−	0.989946i	$-0.545175\pi$
$331$	−354.000	−	204.382i	−1.06949	−	0.617468i	−0.928041	+	0.372478i	$0.878508\pi$
$332$	120.000	+	69.2820i	0.361446	+	0.208681i
$333$	72.0000	+	124.708i	0.216216	+	0.374497i
$334$	312.000	−	180.133i	0.934132	−	0.539321i
$335$	−402.000	−	232.095i	−1.20000	−	0.692820i
$336$	144.000	−	83.1384i	0.428571	−	0.247436i
$337$	168.500	+	291.851i	0.500000	+	0.866025i	1.00000			$0$
$337$	168.500	+	291.851i	0.500000	+	0.866025i	−0.500000	+	0.866025i	$0.666667\pi$
$338$	−315.000	+	545.596i	−0.931953	+	1.61419i
$339$	−150.000			−0.442478
$340$	88.0000	+	152.420i	0.258824	+	0.448296i
$341$	−84.0000			−0.246334
$342$	243.000	−	140.296i	0.710526	−	0.410223i
$343$			297.913i			0.868550i
$344$	−348.000	−	200.918i	−1.01163	−	0.584064i
$345$	252.000	−	145.492i	0.730435	−	0.421717i
$346$	2.00000	−	3.46410i	0.00578035	−	0.0100119i
$347$	−235.500	+	135.966i	−0.678674	+	0.391833i	−0.799355	−	0.600859i	$-0.794826\pi$
$347$	−235.500	+	135.966i	−0.678674	+	0.391833i	0.120681	+	0.992691i	$0.461492\pi$
$348$	−204.000	−	353.338i	−0.586207	−	1.01534i
$349$	−136.000	+	235.559i	−0.389685	+	0.674954i	−0.992407	−	0.122997i	$-0.960749\pi$
$349$	−136.000	+	235.559i	−0.389685	+	0.674954i	0.602722	+	0.797951i	$0.294083\pi$
$350$	−54.0000	+	31.1769i	−0.154286	+	0.0890769i
$351$	297.000	+	514.419i	0.846154	+	1.46558i
$352$	−336.000	−	193.990i	−0.954545	−	0.551107i
$353$	230.500	−	399.238i	0.652975	−	1.13099i	−0.329423	−	0.944182i	$-0.606854\pi$
$353$	230.500	−	399.238i	0.652975	−	1.13099i	0.982397	−	0.186803i	$-0.0598125\pi$
$354$		−	322.161i		−	0.910061i
$355$		0			0
$356$	−8.00000			−0.0224719
$357$	−99.0000	+	57.1577i	−0.277311	+	0.160106i
$358$			374.123i			1.04504i
$359$		−	530.008i		−	1.47634i	−0.674612	−	0.738172i	$-0.735689\pi$
$359$		−	530.008i		−	1.47634i	0.674612	−	0.738172i	$-0.264311\pi$
$360$	−144.000	+	249.415i	−0.400000	+	0.692820i
$361$	118.000			0.326870
$362$	508.000			1.40331
$363$	−78.0000			−0.214876
$364$		−	304.841i		−	0.837475i
$365$	50.0000	+	86.6025i	0.136986	+	0.237267i
$366$	48.0000	+	83.1384i	0.131148	+	0.227154i
$367$	−84.0000	−	48.4974i	−0.228883	−	0.132146i	0.381174	−	0.924503i	$-0.375520\pi$
$367$	−84.0000	−	48.4974i	−0.228883	−	0.132146i	−0.610057	+	0.792358i	$0.708853\pi$
$368$	336.000	−	193.990i	0.913043	−	0.527146i
$369$	−58.5000	+	101.325i	−0.158537	+	0.274593i
$370$	64.0000	+	110.851i	0.172973	+	0.299598i
$371$	−156.000	−	90.0666i	−0.420485	−	0.242767i
$372$			83.1384i			0.223490i
$373$	173.000	+	299.645i	0.463807	+	0.803337i	0.999147	−	0.0412995i	$-0.0131498\pi$
$373$	173.000	+	299.645i	0.463807	+	0.803337i	−0.535340	+	0.844637i	$0.679816\pi$
$374$	231.000	+	133.368i	0.617647	+	0.356599i
$375$	204.000	−	353.338i	0.544000	−	0.942236i
$376$	24.0000	+	13.8564i	0.0638298	+	0.0368521i
$377$	−748.000			−1.98408
$378$	−162.000	−	93.5307i	−0.428571	−	0.247436i
$379$			327.358i			0.863740i	0.901936	+	0.431870i	$0.142146\pi$
$379$			327.358i			0.863740i	−0.901936	+	0.431870i	$0.857854\pi$
$380$	216.000	−	124.708i	0.568421	−	0.328178i
$381$	−567.000	−	327.358i	−1.48819	−	0.859206i
$382$	6.00000	+	3.46410i	0.0157068	+	0.00906833i
$383$	−546.000	+	315.233i	−1.42559	+	0.823063i	−0.996769	−	0.0803272i	$-0.974403\pi$
$383$	−546.000	+	315.233i	−1.42559	+	0.823063i	−0.428819	+	0.903390i	$0.641070\pi$
$384$	−192.000	+	332.554i	−0.500000	+	0.866025i
$385$	84.0000	−	145.492i	0.218182	−	0.377902i
$386$	67.0000	+	116.047i	0.173575	+	0.300641i
$387$			452.065i			1.16813i
$388$	86.0000	−	148.956i	0.221649	−	0.383908i
$389$	73.0000	−	126.440i	0.187661	−	0.325038i	−0.756809	−	0.653636i	$-0.773243\pi$
$389$	73.0000	−	126.440i	0.187661	−	0.325038i	0.944470	+	0.328598i	$0.106576\pi$
$390$	264.000	+	457.261i	0.676923	+	1.17247i
$391$	−231.000	+	133.368i	−0.590793	+	0.341094i
$392$	−148.000	−	256.344i	−0.377551	−	0.653938i
$393$		−	581.969i		−	1.48084i
$394$	536.000			1.36041
$395$		−	110.851i		−	0.280636i
$396$			436.477i			1.10221i
$397$	488.000			1.22922			0.614610	−	0.788831i	$-0.289314\pi$
$397$	488.000			1.22922			0.614610	+	0.788831i	$0.289314\pi$
$398$		−	62.3538i		−	0.156668i
$399$	81.0000	+	140.296i	0.203008	+	0.351619i
$400$	72.0000	−	124.708i	0.180000	−	0.311769i
$401$	−222.500	−	385.381i	−0.554863	−	0.961051i	−0.997914	−	0.0645544i	$-0.979437\pi$
$401$	−222.500	−	385.381i	−0.554863	−	0.961051i	0.443051	−	0.896496i	$-0.353896\pi$
$402$			696.284i			1.73205i
$403$	132.000	+	76.2102i	0.327543	+	0.189107i
$404$	40.0000	−	69.2820i	0.0990099	−	0.171490i
$405$	324.000			0.800000
$406$	204.000	−	117.779i	0.502463	−	0.290097i
$407$	168.000	+	96.9948i	0.412776	+	0.238317i
$408$	132.000	−	228.631i	0.323529	−	0.560369i
$409$	33.5000	+	58.0237i	0.0819071	+	0.141867i	0.904069	−	0.427386i	$-0.140566\pi$
$409$	33.5000	+	58.0237i	0.0819071	+	0.141867i	−0.822162	+	0.569254i	$0.807232\pi$
$410$	−52.0000	+	90.0666i	−0.126829	+	0.219675i
$411$	−253.500	−	439.075i	−0.616788	−	1.06831i
$412$	−84.0000	+	48.4974i	−0.203883	+	0.117712i
$413$	186.000			0.450363
$414$	−378.000	−	218.238i	−0.913043	−	0.527146i
$415$		−	138.564i		−	0.333889i
$416$	352.000	+	609.682i	0.846154	+	1.46558i
$417$		−	587.165i		−	1.40807i
$418$	189.000	−	327.358i	0.452153	−	0.783152i
$419$	534.000	−	308.305i	1.27446	−	0.735812i	0.298638	−	0.954366i	$-0.403468\pi$
$419$	534.000	−	308.305i	1.27446	−	0.735812i	0.975825	+	0.218555i	$0.0701342\pi$
$420$	−144.000	−	83.1384i	−0.342857	−	0.197949i
$421$	−136.000	+	235.559i	−0.323040	+	0.559522i	−0.981114	−	0.193431i	$-0.938038\pi$
$421$	−136.000	+	235.559i	−0.323040	+	0.559522i	0.658073	+	0.752954i	$0.271372\pi$
$422$	228.000	−	131.636i	0.540284	−	0.311933i
$423$		−	31.1769i		−	0.0737043i
$424$	416.000			0.981132
$425$	−49.5000	+	85.7365i	−0.116471	+	0.201733i
$426$		0			0
$427$	−48.0000	+	27.7128i	−0.112412	+	0.0649012i
$428$			62.3538i			0.145687i
$429$	693.000	+	400.104i	1.61538	+	0.932643i
$430$			401.836i			0.934502i
$431$			405.300i			0.940371i	0.882568	+	0.470185i	$0.155813\pi$
$431$			405.300i			0.940371i	−0.882568	+	0.470185i	$0.844187\pi$
$432$	432.000			1.00000
$433$	−439.000			−1.01386			−0.506928	−	0.861988i	$-0.669219\pi$
$433$	−439.000			−1.01386			−0.506928	+	0.861988i	$0.669219\pi$
$434$	−48.0000			−0.110599
$435$	−204.000	+	353.338i	−0.468966	+	0.812272i
$436$	−352.000			−0.807339
$437$	189.000	+	327.358i	0.432494	+	0.749102i
$438$	75.0000	−	129.904i	0.171233	−	0.296584i
$439$	−732.000	−	422.620i	−1.66743	−	0.962689i	−0.969018	−	0.246989i	$-0.920559\pi$
$439$	−732.000	−	422.620i	−1.66743	−	0.962689i	−0.698408	−	0.715700i	$-0.746108\pi$
$440$			387.979i			0.881771i
$441$	−166.500	+	288.386i	−0.377551	+	0.653938i
$442$	−242.000	−	419.156i	−0.547511	−	0.948317i
$443$	286.500	+	165.411i	0.646727	+	0.373388i	0.787201	−	0.616696i	$-0.211529\pi$
$443$	286.500	+	165.411i	0.646727	+	0.373388i	−0.140474	+	0.990084i	$0.544863\pi$
$444$	96.0000	−	166.277i	0.216216	−	0.374497i
$445$	4.00000	+	6.92820i	0.00898876	+	0.0155690i
$446$	102.000	+	58.8897i	0.228700	+	0.132040i
$447$	390.000			0.872483
$448$	−192.000	−	110.851i	−0.428571	−	0.247436i
$449$	−47.0000			−0.104677			−0.0523385	−	0.998629i	$-0.516667\pi$
$449$	−47.0000			−0.104677			−0.0523385	+	0.998629i	$0.516667\pi$
$450$	−162.000			−0.360000
$451$			157.617i			0.349483i
$452$	100.000	+	173.205i	0.221239	+	0.383197i
$453$	−315.000	+	181.865i	−0.695364	+	0.401469i
$454$	−777.000	−	448.601i	−1.71145	−	0.988108i
$455$	−264.000	+	152.420i	−0.580220	+	0.334990i
$456$	−324.000	−	187.061i	−0.710526	−	0.410223i
$457$	165.500	−	286.654i	0.362144	−	0.627253i	−0.626169	−	0.779687i	$-0.715378\pi$
$457$	165.500	−	286.654i	0.362144	−	0.627253i	0.988314	+	0.152435i	$0.0487114\pi$
$458$	−410.000	−	710.141i	−0.895197	−	1.55053i
$459$	−297.000			−0.647059
$460$	−336.000	−	193.990i	−0.730435	−	0.421717i
$461$	−269.000	+	465.922i	−0.583514	+	1.01068i	0.411545	+	0.911390i	$0.364989\pi$
$461$	−269.000	+	465.922i	−0.583514	+	1.01068i	−0.995059	+	0.0992865i	$0.968344\pi$
$462$	−252.000			−0.545455
$463$	492.000	−	284.056i	1.06263	−	0.613513i	0.136475	−	0.990644i	$-0.456423\pi$
$463$	492.000	−	284.056i	1.06263	−	0.613513i	0.926160	+	0.377131i	$0.123089\pi$
$464$	−272.000	+	471.118i	−0.586207	+	1.01534i
$465$	72.0000	−	41.5692i	0.154839	−	0.0893962i
$466$	−130.000			−0.278970
$467$		−	639.127i		−	1.36858i	−0.729210	−	0.684290i	$-0.760112\pi$
$467$		−	639.127i		−	1.36858i	0.729210	−	0.684290i	$-0.239888\pi$
$468$	396.000	−	685.892i	0.846154	−	1.46558i
$469$	−402.000			−0.857143
$470$		−	27.7128i		−	0.0589634i
$471$	−12.0000			−0.0254777
$472$	−372.000	+	214.774i	−0.788136	+	0.455030i
$473$	304.500	+	527.409i	0.643763	+	1.11503i
$474$	−144.000	+	83.1384i	−0.303797	+	0.175398i
$475$	121.500	+	70.1481i	0.255789	+	0.147680i
$476$	132.000	+	76.2102i	0.277311	+	0.160106i
$477$	−234.000	−	405.300i	−0.490566	−	0.849685i
$478$	−66.0000	+	38.1051i	−0.138075	+	0.0797178i
$479$	−105.000	−	60.6218i	−0.219207	−	0.126559i	0.386376	−	0.922341i	$-0.373727\pi$
$479$	−105.000	−	60.6218i	−0.219207	−	0.126559i	−0.605583	+	0.795782i	$0.707060\pi$
$480$	384.000			0.800000
$481$	−176.000	−	304.841i	−0.365904	−	0.633765i
$482$	223.000	−	386.247i	0.462656	−	0.801343i
$483$	126.000	−	218.238i	0.260870	−	0.451839i
$484$	52.0000	+	90.0666i	0.107438	+	0.186088i
$485$	−172.000			−0.354639
$486$	−243.000	−	420.888i	−0.500000	−	0.866025i
$487$			405.300i			0.832238i	0.909310	+	0.416119i	$0.136610\pi$
$487$			405.300i			0.832238i	−0.909310	+	0.416119i	$0.863390\pi$
$488$	64.0000	−	110.851i	0.131148	−	0.227154i
$489$	810.000	+	467.654i	1.65644	+	0.956347i
$490$	−148.000	+	256.344i	−0.302041	+	0.523150i
$491$	628.500	−	362.865i	1.28004	−	0.739032i	0.303185	−	0.952932i	$-0.401950\pi$
$491$	628.500	−	362.865i	1.28004	−	0.739032i	0.976856	+	0.213900i	$0.0686166\pi$
$492$	156.000			0.317073
$493$	187.000	−	323.894i	0.379310	−	0.656985i
$494$	−594.000	+	342.946i	−1.20243	+	0.694223i
$495$	378.000	−	218.238i	0.763636	−	0.440886i
$496$	96.0000	−	55.4256i	0.193548	−	0.111745i
$497$		0			0
$498$	−180.000	+	103.923i	−0.361446	+	0.208681i
$499$	451.500	−	260.674i	0.904810	−	0.522392i	0.0260521	−	0.999661i	$-0.491706\pi$
$499$	451.500	−	260.674i	0.904810	−	0.522392i	0.878758	+	0.477269i	$0.158373\pi$
$500$	−544.000			−1.08800
$501$			540.400i			1.07864i
$502$			218.238i			0.434738i
$503$			872.954i			1.73549i	0.497006	+	0.867747i	$0.334433\pi$
$503$			872.954i			1.73549i	−0.497006	+	0.867747i	$0.665567\pi$
$504$			249.415i			0.494872i
$505$	−80.0000			−0.158416
$506$	−588.000			−1.16206
$507$	−472.500	−	818.394i	−0.931953	−	1.61419i
$508$			872.954i			1.71841i
$509$	−380.000	−	658.179i	−0.746562	−	1.29308i	−0.949461	−	0.313884i	$-0.898370\pi$
$509$	−380.000	−	658.179i	−0.746562	−	1.29308i	0.202900	−	0.979200i	$-0.434963\pi$
$510$	−264.000			−0.517647
$511$	75.0000	+	43.3013i	0.146771	+	0.0847383i
$512$	512.000			1.00000
$513$			420.888i			0.820445i
$514$	437.000	+	756.906i	0.850195	+	1.47258i
$515$	84.0000	+	48.4974i	0.163107	+	0.0941698i
$516$	522.000	−	301.377i	1.01163	−	0.584064i
$517$	−21.0000	−	36.3731i	−0.0406190	−	0.0703541i
$518$	96.0000	+	55.4256i	0.185328	+	0.106999i
$519$	3.00000	+	5.19615i	0.00578035	+	0.0100119i
$520$	352.000	−	609.682i	0.676923	−	1.17247i
$521$	745.000			1.42994			0.714971	−	0.699154i	$-0.246440\pi$
$521$	745.000			1.42994			0.714971	+	0.699154i	$0.246440\pi$
$522$	612.000			1.17241
$523$			561.184i			1.07301i	0.843897	+	0.536505i	$0.180256\pi$
$523$			561.184i			1.07301i	−0.843897	+	0.536505i	$0.819744\pi$
$524$	−672.000	+	387.979i	−1.28244	+	0.740419i
$525$		−	93.5307i		−	0.178154i
$526$	546.000	+	315.233i	1.03802	+	0.599303i
$527$	−66.0000	+	38.1051i	−0.125237	+	0.0723057i
$528$	504.000	−	290.985i	0.954545	−	0.551107i
$529$	29.5000	−	51.0955i	0.0557656	−	0.0965888i
$530$	−208.000	−	360.267i	−0.392453	−	0.679748i
$531$	418.500	+	241.621i	0.788136	+	0.455030i
$532$	108.000	−	187.061i	0.203008	−	0.351619i
$533$	143.000	−	247.683i	0.268293	−	0.464697i
$534$	6.00000	−	10.3923i	0.0112360	−	0.0194612i
$535$	54.0000	−	31.1769i	0.100935	−	0.0582746i
$536$	804.000	−	464.190i	1.50000	−	0.866025i
$537$	−486.000	−	280.592i	−0.905028	−	0.522518i
$538$	608.000			1.13011
$539$			448.601i			0.832284i
$540$	−216.000	−	374.123i	−0.400000	−	0.692820i
$541$	−520.000			−0.961183			−0.480591	−	0.876945i	$-0.659578\pi$
$541$	−520.000			−0.961183			−0.480591	+	0.876945i	$0.659578\pi$
$542$		−	623.538i		−	1.15044i
$543$	−381.000	+	659.911i	−0.701657	+	1.21531i
$544$	−352.000			−0.647059
$545$	176.000	+	304.841i	0.322936	+	0.559341i
$546$	396.000	+	228.631i	0.725275	+	0.418738i
$547$	334.500	+	193.124i	0.611517	+	0.353060i	0.773559	−	0.633724i	$-0.218475\pi$
$547$	334.500	+	193.124i	0.611517	+	0.353060i	−0.162042	+	0.986784i	$0.551808\pi$
$548$	−338.000	+	585.433i	−0.616788	+	1.06831i
$549$	−144.000			−0.262295
$550$	−189.000	+	109.119i	−0.343636	+	0.198399i
$551$	−459.000	−	265.004i	−0.833031	−	0.480951i
$552$			581.969i			1.05429i
$553$	−48.0000	−	83.1384i	−0.0867993	−	0.150341i
$554$	34.0000	−	58.8897i	0.0613718	−	0.106299i
$555$	−192.000			−0.345946
$556$	−678.000	+	391.443i	−1.21942	+	0.704035i
$557$	934.000			1.67684			0.838420	−	0.545025i	$-0.183480\pi$
$557$	934.000			1.67684			0.838420	+	0.545025i	$0.183480\pi$
$558$	−108.000	−	62.3538i	−0.193548	−	0.111745i
$559$		−	1105.05i		−	1.97683i
$560$			221.703i			0.395897i
$561$	−346.500	+	200.052i	−0.617647	+	0.356599i
$562$	218.000	−	377.587i	0.387900	−	0.671863i
$563$	−613.500	+	354.204i	−1.08970	+	0.629137i	−0.933496	−	0.358588i	$-0.883258\pi$
$563$	−613.500	+	354.204i	−1.08970	+	0.629137i	−0.156202	+	0.987725i	$0.549925\pi$
$564$	−36.0000	+	20.7846i	−0.0638298	+	0.0368521i
$565$	100.000	−	173.205i	0.176991	−	0.306558i
$566$	12.0000	−	6.92820i	0.0212014	−	0.0122406i
$567$	243.000	−	140.296i	0.428571	−	0.247436i
$568$		0			0
$569$	347.500	−	601.888i	0.610721	−	1.05780i	−0.380399	−	0.924823i	$-0.624213\pi$
$569$	347.500	−	601.888i	0.610721	−	1.05780i	0.991119	−	0.132976i	$-0.0424535\pi$
$570$			374.123i			0.656356i
$571$	−466.500	+	269.334i	−0.816988	+	0.471688i	−0.849377	−	0.527787i	$-0.823022\pi$
$571$	−466.500	+	269.334i	−0.816988	+	0.471688i	0.0323889	+	0.999475i	$0.489689\pi$
$572$		−	1066.94i		−	1.86529i
$573$	−9.00000	+	5.19615i	−0.0157068	+	0.00906833i
$574$			90.0666i			0.156911i
$575$		−	218.238i		−	0.379545i
$576$	−288.000	−	498.831i	−0.500000	−	0.866025i
$577$	227.000			0.393414			0.196707	−	0.980462i	$-0.436975\pi$
$577$	227.000			0.393414			0.196707	+	0.980462i	$0.436975\pi$
$578$	−336.000			−0.581315
$579$	−201.000			−0.347150
$580$	544.000			0.937931
$581$	−60.0000	−	103.923i	−0.103270	−	0.178869i
$582$	129.000	+	223.435i	0.221649	+	0.383908i
$583$	−546.000	−	315.233i	−0.936535	−	0.540709i
$584$	−200.000			−0.342466
$585$	−792.000			−1.35385
$586$	−202.000	−	349.874i	−0.344710	−	0.597055i
$587$	124.500	+	71.8801i	0.212095	+	0.122453i	0.602285	−	0.798281i	$-0.294257\pi$
$587$	124.500	+	71.8801i	0.212095	+	0.122453i	−0.390189	+	0.920735i	$0.627590\pi$
$588$	444.000			0.755102
$589$	54.0000	+	93.5307i	0.0916808	+	0.158796i
$590$	372.000	+	214.774i	0.630508	+	0.364024i
$591$	−402.000	+	696.284i	−0.680203	+	1.17815i
$592$	−256.000			−0.432432
$593$	−506.000			−0.853288			−0.426644	−	0.904420i	$-0.640304\pi$
$593$	−506.000			−0.853288			−0.426644	+	0.904420i	$0.640304\pi$
$594$	−567.000	−	327.358i	−0.954545	−	0.551107i
$595$		−	152.420i		−	0.256169i
$596$	−260.000	−	450.333i	−0.436242	−	0.755593i
$597$	81.0000	+	46.7654i	0.135678	+	0.0783340i
$598$	924.000	+	533.472i	1.54515	+	0.892093i
$599$	48.0000	−	27.7128i	0.0801336	−	0.0462651i	−0.459398	−	0.888231i	$-0.651935\pi$
$599$	48.0000	−	27.7128i	0.0801336	−	0.0462651i	0.539531	+	0.841965i	$0.318601\pi$
$600$	108.000	+	187.061i	0.180000	+	0.311769i
$601$	−167.500	+	290.119i	−0.278702	+	0.482726i	−0.971062	−	0.238826i	$-0.923238\pi$
$601$	−167.500	+	290.119i	−0.278702	+	0.482726i	0.692360	+	0.721552i	$0.256571\pi$
$602$	174.000	+	301.377i	0.289037	+	0.500626i
$603$	−904.500	−	522.213i	−1.50000	−	0.866025i
$604$	420.000	+	242.487i	0.695364	+	0.401469i
$605$	52.0000	−	90.0666i	0.0859504	−	0.148870i
$606$	60.0000	+	103.923i	0.0990099	+	0.171490i
$607$	546.000	−	315.233i	0.899506	−	0.519330i	0.0224660	−	0.999748i	$-0.492848\pi$
$607$	546.000	−	315.233i	0.899506	−	0.519330i	0.877040	+	0.480418i	$0.159515\pi$
$608$			498.831i			0.820445i
$609$			353.338i			0.580194i
$610$	−128.000			−0.209836
$611$			76.2102i			0.124730i
$612$	198.000	+	342.946i	0.323529	+	0.560369i
$613$	−340.000			−0.554649			−0.277325	−	0.960776i	$-0.589448\pi$
$613$	−340.000			−0.554649			−0.277325	+	0.960776i	$0.589448\pi$
$614$			218.238i			0.355437i
$615$	−78.0000	−	135.100i	−0.126829	−	0.219675i
$616$	168.000	+	290.985i	0.272727	+	0.472377i
$617$	−195.500	−	338.616i	−0.316856	−	0.548810i	0.662974	−	0.748642i	$-0.269294\pi$
$617$	−195.500	−	338.616i	−0.316856	−	0.548810i	−0.979830	+	0.199832i	$0.935960\pi$
$618$		−	145.492i		−	0.235424i
$619$	10.5000	+	6.06218i	0.0169628	+	0.00979350i	0.508457	−	0.861087i	$-0.330216\pi$
$619$	10.5000	+	6.06218i	0.0169628	+	0.00979350i	−0.491495	+	0.870881i	$0.663549\pi$
$620$	−96.0000	−	55.4256i	−0.154839	−	0.0893962i
$621$	567.000	−	327.358i	0.913043	−	0.527146i
$622$	474.000	−	273.664i	0.762058	−	0.439974i
$623$	6.00000	+	3.46410i	0.00963082	+	0.00556036i
$624$	−1056.00			−1.69231
$625$	159.500	+	276.262i	0.255200	+	0.442019i
$626$	79.0000	−	136.832i	0.126198	−	0.218581i
$627$	283.500	+	491.036i	0.452153	+	0.783152i
$628$	8.00000	+	13.8564i	0.0127389	+	0.0220643i
$629$	176.000			0.279809
$630$	216.000	−	124.708i	0.342857	−	0.197949i
$631$		−	436.477i		−	0.691722i	−0.938286	−	0.345861i	$-0.887587\pi$
$631$		−	436.477i		−	0.691722i	0.938286	−	0.345861i	$-0.112413\pi$
$632$	192.000	+	110.851i	0.303797	+	0.175398i
$633$			394.908i			0.623867i
$634$	−502.000	+	869.490i	−0.791798	+	1.37143i
$635$	756.000	−	436.477i	1.19055	−	0.687365i
$636$	−312.000	+	540.400i	−0.490566	+	0.849685i
$637$	407.000	−	704.945i	0.638932	−	1.10666i
$638$	714.000	−	412.228i	1.11912	−	0.646126i
$639$		0			0
$640$	−256.000	−	443.405i	−0.400000	−	0.692820i
$641$	−210.500	+	364.597i	−0.328393	+	0.568794i	−0.982193	−	0.187874i	$-0.939840\pi$
$641$	−210.500	+	364.597i	−0.328393	+	0.568794i	0.653800	+	0.756667i	$0.273174\pi$
$642$	−81.0000	−	46.7654i	−0.126168	−	0.0728433i
$643$	−358.500	+	206.980i	−0.557543	+	0.321897i	−0.752159	−	0.658982i	$-0.770987\pi$
$643$	−358.500	+	206.980i	−0.557543	+	0.321897i	0.194616	+	0.980880i	$0.437654\pi$
$644$	−336.000			−0.521739
$645$	−522.000	−	301.377i	−0.809302	−	0.467251i
$646$		−	342.946i		−	0.530876i
$647$			405.300i			0.626430i	0.949682	+	0.313215i	$0.101406\pi$
$647$			405.300i			0.626430i	−0.949682	+	0.313215i	$0.898594\pi$
$648$	−324.000	+	561.184i	−0.500000	+	0.866025i
$649$	651.000			1.00308
$650$	396.000			0.609231
$651$	36.0000	−	62.3538i	0.0552995	−	0.0957816i
$652$		−	1247.08i		−	1.91269i
$653$	−443.000	−	767.299i	−0.678407	−	1.17504i	−0.975460	−	0.220175i	$-0.929337\pi$
$653$	−443.000	−	767.299i	−0.678407	−	1.17504i	0.297053	−	0.954861i	$-0.403996\pi$
$654$	264.000	−	457.261i	0.403670	−	0.699176i
$655$	672.000	+	387.979i	1.02595	+	0.592335i
$656$	−104.000	−	180.133i	−0.158537	−	0.274593i
$657$	112.500	+	194.856i	0.171233	+	0.296584i
$658$	−12.0000	−	20.7846i	−0.0182371	−	0.0315876i
$659$	−726.000	−	419.156i	−1.10167	−	0.636049i	−0.165010	−	0.986292i	$-0.552766\pi$
$659$	−726.000	−	419.156i	−1.10167	−	0.636049i	−0.936659	+	0.350243i	$0.886099\pi$
$660$	−504.000	−	290.985i	−0.763636	−	0.440886i
$661$	−124.000	−	214.774i	−0.187595	−	0.324923i	0.756853	−	0.653585i	$-0.226736\pi$
$661$	−124.000	−	214.774i	−0.187595	−	0.324923i	−0.944448	+	0.328662i	$0.893402\pi$
$662$	−708.000	−	408.764i	−1.06949	−	0.617468i
$663$	726.000			1.09502
$664$	240.000	+	138.564i	0.361446	+	0.208681i
$665$	−216.000			−0.324812
$666$	144.000	+	249.415i	0.216216	+	0.374497i
$667$			824.456i			1.23607i
$668$	624.000	−	360.267i	0.934132	−	0.539321i
$669$	−153.000	+	88.3346i	−0.228700	+	0.132040i
$670$	−804.000	−	464.190i	−1.20000	−	0.692820i
$671$	−168.000	+	96.9948i	−0.250373	+	0.144553i
$672$	288.000	−	166.277i	0.428571	−	0.247436i
$673$	−577.000	+	999.393i	−0.857355	+	1.48498i	0.0170877	+	0.999854i	$0.494561\pi$
$673$	−577.000	+	999.393i	−0.857355	+	1.48498i	−0.874443	+	0.485129i	$0.838773\pi$
$674$	337.000	+	583.701i	0.500000	+	0.866025i
$675$	121.500	−	210.444i	0.180000	−	0.311769i
$676$	−630.000	+	1091.19i	−0.931953	+	1.61419i
$677$	−566.000	+	980.341i	−0.836041	+	1.44807i	0.0571384	+	0.998366i	$0.481802\pi$
$677$	−566.000	+	980.341i	−0.836041	+	1.44807i	−0.893180	+	0.449700i	$0.851531\pi$
$678$	−300.000			−0.442478
$679$	−129.000	+	74.4782i	−0.189985	+	0.109688i
$680$	176.000	+	304.841i	0.258824	+	0.448296i
$681$	1165.50	−	672.902i	1.71145	−	0.988108i
$682$	−168.000			−0.246334
$683$		−	795.011i		−	1.16400i	−0.813189	−	0.582000i	$-0.802271\pi$
$683$		−	795.011i		−	1.16400i	0.813189	−	0.582000i	$-0.197729\pi$
$684$	486.000	−	280.592i	0.710526	−	0.410223i
$685$	676.000			0.986861
$686$			595.825i			0.868550i
$687$	1230.00			1.79039
$688$	−696.000	−	401.836i	−1.01163	−	0.584064i
$689$	572.000	+	990.733i	0.830189	+	1.43793i
$690$	504.000	−	290.985i	0.730435	−	0.421717i
$691$	780.000	+	450.333i	1.12880	+	0.651712i	0.943633	−	0.330995i	$-0.107384\pi$
$691$	780.000	+	450.333i	1.12880	+	0.651712i	0.185166	+	0.982707i	$0.440718\pi$
$692$	4.00000	−	6.92820i	0.00578035	−	0.0100119i
$693$	189.000	−	327.358i	0.272727	−	0.472377i
$694$	−471.000	+	271.932i	−0.678674	+	0.391833i
$695$	678.000	+	391.443i	0.975540	+	0.563228i
$696$	−408.000	−	706.677i	−0.586207	−	1.01534i
$697$	71.5000	+	123.842i	0.102582	+	0.177678i
$698$	−272.000	+	471.118i	−0.389685	+	0.674954i
$699$	97.5000	−	168.875i	0.139485	−	0.241595i
$700$	−108.000	+	62.3538i	−0.154286	+	0.0890769i
$701$	142.000			0.202568			0.101284	−	0.994858i	$-0.467705\pi$
$701$	142.000			0.202568			0.101284	+	0.994858i	$0.467705\pi$
$702$	594.000	+	1028.84i	0.846154	+	1.46558i
$703$		−	249.415i		−	0.354787i
$704$	−672.000	−	387.979i	−0.954545	−	0.551107i
$705$	36.0000	+	20.7846i	0.0510638	+	0.0294817i
$706$	461.000	−	798.475i	0.652975	−	1.13099i
$707$	−60.0000	+	34.6410i	−0.0848656	+	0.0489972i
$708$		−	644.323i		−	0.910061i
$709$	−370.000	+	640.859i	−0.521862	+	0.903891i	0.477815	+	0.878461i	$0.341429\pi$
$709$	−370.000	+	640.859i	−0.521862	+	0.903891i	−0.999677	+	0.0254305i	$0.991904\pi$
$710$		0			0
$711$		−	249.415i		−	0.350795i
$712$	−16.0000			−0.0224719
$713$	84.0000	−	145.492i	0.117812	−	0.204056i
$714$	−198.000	+	114.315i	−0.277311	+	0.160106i
$715$	−924.000	+	533.472i	−1.29231	+	0.746114i
$716$			748.246i			1.04504i
$717$		−	114.315i		−	0.159436i
$718$		−	1060.02i		−	1.47634i
$719$			124.708i			0.173446i	0.996232	+	0.0867230i	$0.0276395\pi$
$719$			124.708i			0.173446i	−0.996232	+	0.0867230i	$0.972360\pi$
$720$	−288.000	+	498.831i	−0.400000	+	0.692820i
$721$	84.0000			0.116505
$722$	236.000			0.326870
$723$	334.500	+	579.371i	0.462656	+	0.801343i
$724$	1016.00			1.40331
$725$	153.000	+	265.004i	0.211034	+	0.365522i
$726$	−156.000			−0.214876
$727$	−705.000	−	407.032i	−0.969739	−	0.559879i	−0.0705821	−	0.997506i	$-0.522486\pi$
$727$	−705.000	−	407.032i	−0.969739	−	0.559879i	−0.899157	+	0.437627i	$0.855819\pi$
$728$		−	609.682i		−	0.837475i
$729$	729.000			1.00000
$730$	100.000	+	173.205i	0.136986	+	0.237267i
$731$	478.500	+	276.262i	0.654583	+	0.377924i
$732$	96.0000	+	166.277i	0.131148	+	0.227154i
$733$	−457.000	−	791.547i	−0.623465	−	1.07987i	−0.988836	−	0.149011i	$-0.952391\pi$
$733$	−457.000	−	791.547i	−0.623465	−	1.07987i	0.365370	−	0.930862i	$-0.380942\pi$
$734$	−168.000	−	96.9948i	−0.228883	−	0.132146i
$735$	−222.000	−	384.515i	−0.302041	−	0.523150i
$736$	672.000	−	387.979i	0.913043	−	0.527146i
$737$	−1407.00			−1.90909
$738$	−117.000	+	202.650i	−0.158537	+	0.274593i
$739$		−	358.535i		−	0.485162i	−0.970131	−	0.242581i	$-0.922006\pi$
$739$		−	358.535i		−	0.485162i	0.970131	−	0.242581i	$-0.0779940\pi$
$740$	128.000	+	221.703i	0.172973	+	0.299598i
$741$		−	1028.84i		−	1.38845i
$742$	−312.000	−	180.133i	−0.420485	−	0.242767i
$743$	345.000	−	199.186i	0.464334	−	0.268083i	−0.249531	−	0.968367i	$-0.580276\pi$
$743$	345.000	−	199.186i	0.464334	−	0.268083i	0.713865	+	0.700284i	$0.246943\pi$
$744$			166.277i			0.223490i
$745$	−260.000	+	450.333i	−0.348993	+	0.604474i
$746$	346.000	+	599.290i	0.463807	+	0.803337i
$747$		−	311.769i		−	0.417362i
$748$	462.000	+	266.736i	0.617647	+	0.356599i
$749$	27.0000	−	46.7654i	0.0360481	−	0.0624371i
$750$	408.000	−	706.677i	0.544000	−	0.942236i
$751$	−966.000	+	557.720i	−1.28628	+	0.742637i	−0.977990	−	0.208654i	$-0.933092\pi$
$751$	−966.000	+	557.720i	−1.28628	+	0.742637i	−0.308295	+	0.951291i	$0.599759\pi$
$752$	48.0000	+	27.7128i	0.0638298	+	0.0368521i
$753$	−283.500	−	163.679i	−0.376494	−	0.217369i
$754$	−1496.00			−1.98408
$755$		−	484.974i		−	0.642350i
$756$	−324.000	−	187.061i	−0.428571	−	0.247436i
$757$	758.000			1.00132			0.500661	−	0.865644i	$-0.333091\pi$
$757$	758.000			1.00132			0.500661	+	0.865644i	$0.333091\pi$
$758$			654.715i			0.863740i
$759$	441.000	−	763.834i	0.581028	−	1.00637i
$760$	432.000	−	249.415i	0.568421	−	0.328178i
$761$	187.000	+	323.894i	0.245729	+	0.425616i	0.962336	−	0.271861i	$-0.0876392\pi$
$761$	187.000	+	323.894i	0.245729	+	0.425616i	−0.716607	+	0.697477i	$0.754306\pi$
$762$	−1134.00	−	654.715i	−1.48819	−	0.859206i
$763$	264.000	+	152.420i	0.346003	+	0.199765i
$764$	12.0000	+	6.92820i	0.0157068	+	0.00906833i
$765$	198.000	−	342.946i	0.258824	−	0.448296i
$766$	−1092.00	+	630.466i	−1.42559	+	0.823063i
$767$	−1023.00	−	590.629i	−1.33377	−	0.770051i
$768$	−384.000	+	665.108i	−0.500000	+	0.866025i
$769$	11.0000	+	19.0526i	0.0143043	+	0.0247758i	0.873089	−	0.487561i	$-0.162113\pi$
$769$	11.0000	+	19.0526i	0.0143043	+	0.0247758i	−0.858785	+	0.512337i	$0.828780\pi$
$770$	168.000	−	290.985i	0.218182	−	0.377902i
$771$	−1311.00			−1.70039
$772$	134.000	+	232.095i	0.173575	+	0.300641i
$773$	−1334.00			−1.72574			−0.862872	−	0.505423i	$-0.831337\pi$
$773$	−1334.00			−1.72574			−0.862872	+	0.505423i	$0.831337\pi$
$774$			904.131i			1.16813i
$775$		−	62.3538i		−	0.0804566i
$776$	172.000	−	297.913i	0.221649	−	0.383908i
$777$	−144.000	+	83.1384i	−0.185328	+	0.106999i
$778$	146.000	−	252.879i	0.187661	−	0.325038i
$779$	175.500	−	101.325i	0.225289	−	0.130071i
$780$	528.000	+	914.523i	0.676923	+	1.17247i
$781$		0			0
$782$	−462.000	+	266.736i	−0.590793	+	0.341094i
$783$	−459.000	+	795.011i	−0.586207	+	1.01534i
$784$	−296.000	−	512.687i	−0.377551	−	0.653938i
$785$	8.00000	−	13.8564i	0.0101911	−	0.0176515i
$786$		−	1163.94i		−	1.48084i
$787$	762.000	−	439.941i	0.968234	−	0.559010i	0.0695365	−	0.997579i	$-0.477848\pi$
$787$	762.000	−	439.941i	0.968234	−	0.559010i	0.898697	+	0.438569i	$0.144515\pi$
$788$	1072.00			1.36041
$789$	−819.000	+	472.850i	−1.03802	+	0.599303i
$790$		−	221.703i		−	0.280636i
$791$		−	173.205i		−	0.218970i
$792$			872.954i			1.10221i
$793$	352.000			0.443884
$794$	976.000			1.22922
$795$	624.000			0.784906
$796$		−	124.708i		−	0.156668i
$797$	−416.000	−	720.533i	−0.521957	−	0.904057i	−0.999674	−	0.0255425i	$-0.991869\pi$
$797$	−416.000	−	720.533i	−0.521957	−	0.904057i	0.477716	−	0.878514i	$-0.341465\pi$
$798$	162.000	+	280.592i	0.203008	+	0.351619i
$799$	−33.0000	−	19.0526i	−0.0413016	−	0.0238455i
$800$	144.000	−	249.415i	0.180000	−	0.311769i
$801$	9.00000	+	15.5885i	0.0112360	+	0.0194612i
$802$	−445.000	−	770.763i	−0.554863	−	0.961051i
$803$	262.500	+	151.554i	0.326899	+	0.188735i
$804$			1392.57i			1.73205i
$805$	168.000	+	290.985i	0.208696	+	0.361471i
$806$	264.000	+	152.420i	0.327543	+	0.189107i
$807$	−456.000	+	789.815i	−0.565056	+	0.978705i
$808$	80.0000	−	138.564i	0.0990099	−	0.171490i
$809$	493.000			0.609394			0.304697	−	0.952449i	$-0.401445\pi$
$809$	493.000			0.609394			0.304697	+	0.952449i	$0.401445\pi$
$810$	648.000			0.800000
$811$		−	327.358i		−	0.403647i	−0.979422	−	0.201823i	$-0.935313\pi$
$811$		−	327.358i		−	0.403647i	0.979422	−	0.201823i	$-0.0646867\pi$
$812$	408.000	−	235.559i	0.502463	−	0.290097i
$813$	810.000	+	467.654i	0.996310	+	0.575220i
$814$	336.000	+	193.990i	0.412776	+	0.238317i
$815$	−1080.00	+	623.538i	−1.32515	+	0.765078i
$816$	264.000	−	457.261i	0.323529	−	0.560369i
$817$	391.500	−	678.098i	0.479192	−	0.829985i
$818$	67.0000	+	116.047i	0.0819071	+	0.141867i
$819$	−594.000	+	342.946i	−0.725275	+	0.418738i
$820$	−104.000	+	180.133i	−0.126829	+	0.219675i
$821$	379.000	−	656.447i	0.461632	−	0.799570i	−0.537410	−	0.843321i	$-0.680597\pi$
$821$	379.000	−	656.447i	0.461632	−	0.799570i	0.999042	+	0.0437505i	$0.0139307\pi$
$822$	−507.000	−	878.150i	−0.616788	−	1.06831i
$823$	−750.000	+	433.013i	−0.911300	+	0.526139i	−0.880849	−	0.473397i	$-0.843028\pi$
$823$	−750.000	+	433.013i	−0.911300	+	0.526139i	−0.0304509	+	0.999536i	$0.509694\pi$
$824$	−168.000	+	96.9948i	−0.203883	+	0.117712i
$825$		−	327.358i		−	0.396797i
$826$	372.000			0.450363
$827$			436.477i			0.527783i	0.964552	+	0.263892i	$0.0850061\pi$
$827$			436.477i			0.527783i	−0.964552	+	0.263892i	$0.914994\pi$
$828$	−756.000	−	436.477i	−0.913043	−	0.527146i
$829$	−718.000			−0.866104			−0.433052	−	0.901369i	$-0.642563\pi$
$829$	−718.000			−0.866104			−0.433052	+	0.901369i	$0.642563\pi$
$830$		−	277.128i		−	0.333889i
$831$	51.0000	+	88.3346i	0.0613718	+	0.106299i
$832$	704.000	+	1219.36i	0.846154	+	1.46558i
$833$	203.500	+	352.472i	0.244298	+	0.423136i
$834$		−	1174.33i		−	1.40807i
$835$	−624.000	−	360.267i	−0.747305	−	0.431457i
$836$	378.000	−	654.715i	0.452153	−	0.783152i
$837$	162.000	−	93.5307i	0.193548	−	0.111745i
$838$	1068.00	−	616.610i	1.27446	−	0.735812i
$839$	786.000	+	453.797i	0.936830	+	0.540879i	0.888965	−	0.457975i	$-0.151425\pi$
$839$	786.000	+	453.797i	0.936830	+	0.540879i	0.0478645	+	0.998854i	$0.484758\pi$
$840$	−288.000	−	166.277i	−0.342857	−	0.197949i
$841$	−157.500	−	272.798i	−0.187277	−	0.324373i
$842$	−272.000	+	471.118i	−0.323040	+	0.559522i
$843$	327.000	+	566.381i	0.387900	+	0.671863i
$844$	456.000	−	263.272i	0.540284	−	0.311933i
$845$	1260.00			1.49112
$846$		−	62.3538i		−	0.0737043i
$847$		−	90.0666i		−	0.106336i
$848$	832.000			0.981132
$849$			20.7846i			0.0244813i
$850$	−99.0000	+	171.473i	−0.116471	+	0.201733i
$851$	−336.000	+	193.990i	−0.394830	+	0.227955i
$852$		0			0
$853$	−73.0000	+	126.440i	−0.0855803	+	0.148229i	−0.905638	−	0.424051i	$-0.860608\pi$
$853$	−73.0000	+	126.440i	−0.0855803	+	0.148229i	0.820058	+	0.572280i	$0.193941\pi$
$854$	−96.0000	+	55.4256i	−0.112412	+	0.0649012i
$855$	−486.000	−	280.592i	−0.568421	−	0.328178i
$856$			124.708i			0.145687i
$857$	73.0000	−	126.440i	0.0851809	−	0.147538i	−0.820287	−	0.571952i	$-0.806187\pi$
$857$	73.0000	−	126.440i	0.0851809	−	0.147538i	0.905468	+	0.424414i	$0.139520\pi$
$858$	1386.00	+	800.207i	1.61538	+	0.932643i
$859$	73.5000	−	42.4352i	0.0855646	−	0.0494008i	−0.456607	−	0.889668i	$-0.650936\pi$
$859$	73.5000	−	42.4352i	0.0855646	−	0.0494008i	0.542172	+	0.840268i	$0.317602\pi$
$860$			803.672i			0.934502i
$861$	−117.000	−	67.5500i	−0.135889	−	0.0784553i
$862$			810.600i			0.940371i
$863$		−	1184.72i		−	1.37280i	−0.727226	−	0.686398i	$-0.759191\pi$
$863$		−	1184.72i		−	1.37280i	0.727226	−	0.686398i	$-0.240809\pi$
$864$	864.000			1.00000
$865$	−8.00000			−0.00924855
$866$	−878.000			−1.01386
$867$	252.000	−	436.477i	0.290657	−	0.503433i
$868$	−96.0000			−0.110599
$869$	−168.000	−	290.985i	−0.193326	−	0.334850i
$870$	−408.000	+	706.677i	−0.468966	+	0.812272i
$871$	2211.00	+	1276.52i	2.53846	+	1.46558i
$872$	−704.000			−0.807339
$873$	−387.000			−0.443299
$874$	378.000	+	654.715i	0.432494	+	0.749102i
$875$	408.000	+	235.559i	0.466286	+	0.269210i
$876$	150.000	−	259.808i	0.171233	−	0.296584i
$877$	740.000	+	1281.72i	0.843786	+	1.46148i	0.886672	+	0.462400i	$0.153011\pi$
$877$	740.000	+	1281.72i	0.843786	+	1.46148i	−0.0428860	+	0.999080i	$0.513655\pi$
$878$	−1464.00	−	845.241i	−1.66743	−	0.962689i
$879$	606.000			0.689420
$880$			775.959i			0.881771i
$881$	142.000			0.161180			0.0805902	−	0.996747i	$-0.474319\pi$
$881$	142.000			0.161180			0.0805902	+	0.996747i	$0.474319\pi$
$882$	−333.000	+	576.773i	−0.377551	+	0.653938i
$883$		−	1200.31i		−	1.35936i	−0.733511	−	0.679678i	$-0.762120\pi$
$883$		−	1200.31i		−	1.35936i	0.733511	−	0.679678i	$-0.237880\pi$
$884$	−484.000	−	838.313i	−0.547511	−	0.948317i
$885$	−558.000	+	322.161i	−0.630508	+	0.364024i
$886$	573.000	+	330.822i	0.646727	+	0.373388i
$887$	−546.000	+	315.233i	−0.615558	+	0.355393i	−0.775138	−	0.631792i	$-0.782319\pi$
$887$	−546.000	+	315.233i	−0.615558	+	0.355393i	0.159580	+	0.987185i	$0.448986\pi$
$888$	192.000	−	332.554i	0.216216	−	0.374497i
$889$	378.000	−	654.715i	0.425197	−	0.736463i
$890$	8.00000	+	13.8564i	0.00898876	+	0.0155690i
$891$	850.500	−	491.036i	0.954545	−	0.551107i
$892$	204.000	+	117.779i	0.228700	+	0.132040i
$893$	−27.0000	+	46.7654i	−0.0302352	+	0.0523688i
$894$	780.000			0.872483
$895$	648.000	−	374.123i	0.724022	−	0.418014i
$896$	−384.000	−	221.703i	−0.428571	−	0.247436i
$897$	−1386.00	+	800.207i	−1.54515	+	0.892093i
$898$	−94.0000			−0.104677
$899$			235.559i			0.262023i
$900$	−324.000			−0.360000
$901$	−572.000			−0.634850
$902$			315.233i			0.349483i
$903$	−522.000			−0.578073
$904$	200.000	+	346.410i	0.221239	+	0.383197i
$905$	−508.000	−	879.882i	−0.561326	−	0.972245i
$906$	−630.000	+	363.731i	−0.695364	+	0.401469i
$907$	−556.500	−	321.295i	−0.613561	−	0.354240i	0.160797	−	0.986988i	$-0.448594\pi$
$907$	−556.500	−	321.295i	−0.613561	−	0.354240i	−0.774358	+	0.632748i	$0.781927\pi$
$908$	−1554.00	−	897.202i	−1.71145	−	0.988108i
$909$	−180.000			−0.198020
$910$	−528.000	+	304.841i	−0.580220	+	0.334990i
$911$	−348.000	−	200.918i	−0.381998	−	0.220547i	0.296689	−	0.954974i	$-0.404117\pi$
$911$	−348.000	−	200.918i	−0.381998	−	0.220547i	−0.678687	+	0.734428i	$0.737451\pi$
$912$	−648.000	−	374.123i	−0.710526	−	0.410223i
$913$	−210.000	−	363.731i	−0.230011	−	0.398391i
$914$	331.000	−	573.309i	0.362144	−	0.627253i
$915$	96.0000	−	166.277i	0.104918	−	0.181723i
$916$	−820.000	−	1420.28i	−0.895197	−	1.55053i
$917$	672.000			0.732824
$918$	−594.000			−0.647059
$919$			779.423i			0.848121i	0.905634	+	0.424060i	$0.139396\pi$
$919$			779.423i			0.848121i	−0.905634	+	0.424060i	$0.860604\pi$
$920$	−672.000	−	387.979i	−0.730435	−	0.421717i
$921$	−283.500	−	163.679i	−0.307818	−	0.177719i
$922$	−538.000	+	931.843i	−0.583514	+	1.01068i
$923$		0			0
$924$	−504.000			−0.545455
$925$	−72.0000	+	124.708i	−0.0778378	+	0.134819i
$926$	984.000	−	568.113i	1.06263	−	0.613513i
$927$	189.000	+	109.119i	0.203883	+	0.117712i
$928$	−544.000	+	942.236i	−0.586207	+	1.01534i
$929$	379.000	−	656.447i	0.407966	−	0.706617i	−0.586696	−	0.809807i	$-0.699572\pi$
$929$	379.000	−	656.447i	0.407966	−	0.706617i	0.994662	+	0.103190i	$0.0329050\pi$
$930$	144.000	−	83.1384i	0.154839	−	0.0893962i
$931$	499.500	−	288.386i	0.536520	−	0.309760i
$932$	−260.000			−0.278970
$933$			820.992i			0.879949i
$934$		−	1278.25i		−	1.36858i
$935$		−	533.472i		−	0.570558i
$936$	792.000	−	1371.78i	0.846154	−	1.46558i
$937$	−754.000			−0.804696			−0.402348	−	0.915487i	$-0.631806\pi$
$937$	−754.000			−0.804696			−0.402348	+	0.915487i	$0.631806\pi$
$938$	−804.000			−0.857143
$939$	118.500	+	205.248i	0.126198	+	0.218581i
$940$		−	55.4256i		−	0.0589634i
$941$	898.000	+	1555.38i	0.954304	+	1.65290i	0.735953	+	0.677033i	$0.236734\pi$
$941$	898.000	+	1555.38i	0.954304	+	1.65290i	0.218351	+	0.975870i	$0.429932\pi$
$942$	−24.0000			−0.0254777
$943$	−273.000	−	157.617i	−0.289502	−	0.167144i
$944$	−744.000	+	429.549i	−0.788136	+	0.455030i
$945$			374.123i			0.395897i
$946$	609.000	+	1054.82i	0.643763	+	1.11503i
$947$	−91.5000	−	52.8275i	−0.0966209	−	0.0557841i	0.450911	−	0.892569i	$-0.351099\pi$
$947$	−91.5000	−	52.8275i	−0.0966209	−	0.0557841i	−0.547532	+	0.836785i	$0.684433\pi$
$948$	−288.000	+	166.277i	−0.303797	+	0.175398i
$949$	−275.000	−	476.314i	−0.289779	−	0.501911i
$950$	243.000	+	140.296i	0.255789	+	0.147680i
$951$	−753.000	−	1304.23i	−0.791798	−	1.37143i
$952$	264.000	+	152.420i	0.277311	+	0.160106i
$953$	1213.00			1.27282			0.636411	−	0.771350i	$-0.280418\pi$
$953$	1213.00			1.27282			0.636411	+	0.771350i	$0.280418\pi$
$954$	−468.000	−	810.600i	−0.490566	−	0.849685i
$955$		−	13.8564i		−	0.0145093i
$956$	−132.000	+	76.2102i	−0.138075	+	0.0797178i
$957$			1236.68i			1.29225i
$958$	−210.000	−	121.244i	−0.219207	−	0.126559i
$959$	507.000	−	292.717i	0.528676	−	0.305231i
$960$	768.000			0.800000
$961$	−456.500	+	790.681i	−0.475026	+	0.822769i
$962$	−352.000	−	609.682i	−0.365904	−	0.633765i
$963$	121.500	−	70.1481i	0.126168	−	0.0728433i
$964$	446.000	−	772.495i	0.462656	−	0.801343i
$965$	134.000	−	232.095i	0.138860	−	0.240513i
$966$	252.000	−	436.477i	0.260870	−	0.451839i
$967$	303.000	−	174.937i	0.313340	−	0.180907i	−0.335080	−	0.942190i	$-0.608763\pi$
$967$	303.000	−	174.937i	0.313340	−	0.180907i	0.648420	+	0.761283i	$0.275430\pi$
$968$	104.000	+	180.133i	0.107438	+	0.186088i
$969$	445.500	+	257.210i	0.459752	+	0.265438i
$970$	−344.000			−0.354639
$971$			1434.14i			1.47697i	0.674270	+	0.738485i	$0.264458\pi$
$971$			1434.14i			1.47697i	−0.674270	+	0.738485i	$0.735542\pi$
$972$	−486.000	−	841.777i	−0.500000	−	0.866025i
$973$	678.000			0.696814
$974$			810.600i			0.832238i
$975$	−297.000	+	514.419i	−0.304615	+	0.527609i
$976$	128.000	−	221.703i	0.131148	−	0.227154i
$977$	−78.5000	−	135.966i	−0.0803480	−	0.139167i	0.823051	−	0.567967i	$-0.192270\pi$
$977$	−78.5000	−	135.966i	−0.0803480	−	0.139167i	−0.903399	+	0.428800i	$0.858936\pi$
$978$	1620.00	+	935.307i	1.65644	+	0.956347i
$979$	21.0000	+	12.1244i	0.0214505	+	0.0123844i
$980$	−296.000	+	512.687i	−0.302041	+	0.523150i
$981$	396.000	+	685.892i	0.403670	+	0.699176i
$982$	1257.00	−	725.729i	1.28004	−	0.739032i
$983$	1218.00	+	703.213i	1.23906	+	0.715374i	0.968903	−	0.247441i	$-0.0795897\pi$
$983$	1218.00	+	703.213i	1.23906	+	0.715374i	0.270161	+	0.962815i	$0.412923\pi$
$984$	312.000			0.317073
$985$	−536.000	−	928.379i	−0.544162	−	0.942517i
$986$	374.000	−	647.787i	0.379310	−	0.656985i
$987$	36.0000			0.0364742
$988$	−1188.00	+	685.892i	−1.20243	+	0.694223i
$989$	−1218.00			−1.23155
$990$	756.000	−	436.477i	0.763636	−	0.440886i
$991$		−	249.415i		−	0.251680i	−0.992051	−	0.125840i	$-0.959837\pi$
$991$		−	249.415i		−	0.251680i	0.992051	−	0.125840i	$-0.0401627\pi$
$992$	192.000	−	110.851i	0.193548	−	0.111745i
$993$	1062.00	−	613.146i	1.06949	−	0.617468i
$994$		0			0
$995$	−108.000	+	62.3538i	−0.108543	+	0.0626672i
$996$	−360.000	+	207.846i	−0.361446	+	0.208681i
$997$	206.000	−	356.802i	0.206620	−	0.357876i	−0.744028	−	0.668149i	$-0.767087\pi$
$997$	206.000	−	356.802i	0.206620	−	0.357876i	0.950648	+	0.310273i	$0.100420\pi$
$998$	903.000	−	521.347i	0.904810	−	0.522392i
$999$	−432.000			−0.432432

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.3.f.b.7.1	yes	2
3.2	odd	2		108.3.f.a.19.1		2
4.3	odd	2		36.3.f.a.7.1	✓	2
8.3	odd	2		576.3.o.a.511.1		2
8.5	even	2		576.3.o.b.511.1		2
9.2	odd	6		324.3.d.c.163.2		2
9.4	even	3		36.3.f.a.31.1	yes	2
9.5	odd	6		108.3.f.b.91.1		2
9.7	even	3		324.3.d.b.163.1		2
12.11	even	2		108.3.f.b.19.1		2
24.5	odd	2		1728.3.o.a.127.1		2
24.11	even	2		1728.3.o.b.127.1		2
36.7	odd	6		324.3.d.b.163.2		2
36.11	even	6		324.3.d.c.163.1		2
36.23	even	6		108.3.f.a.91.1		2
36.31	odd	6	inner	36.3.f.b.31.1	yes	2
72.5	odd	6		1728.3.o.b.1279.1		2
72.13	even	6		576.3.o.a.319.1		2
72.59	even	6		1728.3.o.a.1279.1		2
72.67	odd	6		576.3.o.b.319.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.3.f.a.7.1	✓	2	4.3	odd	2
36.3.f.a.31.1	yes	2	9.4	even	3
36.3.f.b.7.1	yes	2	1.1	even	1	trivial
36.3.f.b.31.1	yes	2	36.31	odd	6	inner
108.3.f.a.19.1		2	3.2	odd	2
108.3.f.a.91.1		2	36.23	even	6
108.3.f.b.19.1		2	12.11	even	2
108.3.f.b.91.1		2	9.5	odd	6
324.3.d.b.163.1		2	9.7	even	3
324.3.d.b.163.2		2	36.7	odd	6
324.3.d.c.163.1		2	36.11	even	6
324.3.d.c.163.2		2	9.2	odd	6
576.3.o.a.319.1		2	72.13	even	6
576.3.o.a.511.1		2	8.3	odd	2
576.3.o.b.319.1		2	72.67	odd	6
576.3.o.b.511.1		2	8.5	even	2
1728.3.o.a.127.1		2	24.5	odd	2
1728.3.o.a.1279.1		2	72.59	even	6
1728.3.o.b.127.1		2	24.11	even	2
1728.3.o.b.1279.1		2	72.5	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:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	36.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000 q^{2} +(-1.50000 + 2.59808i) q^{3} +4.00000 q^{4} +(-2.00000 - 3.46410i) q^{5} +(-3.00000 + 5.19615i) q^{6} +(-3.00000 - 1.73205i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+2.00000 q^{2} +(-1.50000 + 2.59808i) q^{3} +4.00000 q^{4} +(-2.00000 - 3.46410i) q^{5} +(-3.00000 + 5.19615i) q^{6} +(-3.00000 - 1.73205i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-4.00000 - 6.92820i) q^{10} +(-10.5000 - 6.06218i) q^{11} +(-6.00000 + 10.3923i) q^{12} +(11.0000 + 19.0526i) q^{13} +(-6.00000 - 3.46410i) q^{14} +12.0000 q^{15} +16.0000 q^{16} -11.0000 q^{17} +(-9.00000 - 15.5885i) q^{18} +15.5885i q^{19} +(-8.00000 - 13.8564i) q^{20} +(9.00000 - 5.19615i) q^{21} +(-21.0000 - 12.1244i) q^{22} +(21.0000 - 12.1244i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(4.50000 - 7.79423i) q^{25} +(22.0000 + 38.1051i) q^{26} +27.0000 q^{27} +(-12.0000 - 6.92820i) q^{28} +(-17.0000 + 29.4449i) q^{29} +24.0000 q^{30} +(6.00000 - 3.46410i) q^{31} +32.0000 q^{32} +(31.5000 - 18.1865i) q^{33} -22.0000 q^{34} +13.8564i q^{35} +(-18.0000 - 31.1769i) q^{36} -16.0000 q^{37} +31.1769i q^{38} -66.0000 q^{39} +(-16.0000 - 27.7128i) q^{40} +(-6.50000 - 11.2583i) q^{41} +(18.0000 - 10.3923i) q^{42} +(-43.5000 - 25.1147i) q^{43} +(-42.0000 - 24.2487i) q^{44} +(-18.0000 + 31.1769i) q^{45} +(42.0000 - 24.2487i) q^{46} +(3.00000 + 1.73205i) q^{47} +(-24.0000 + 41.5692i) q^{48} +(-18.5000 - 32.0429i) q^{49} +(9.00000 - 15.5885i) q^{50} +(16.5000 - 28.5788i) q^{51} +(44.0000 + 76.2102i) q^{52} +52.0000 q^{53} +54.0000 q^{54} +48.4974i q^{55} +(-24.0000 - 13.8564i) q^{56} +(-40.5000 - 23.3827i) q^{57} +(-34.0000 + 58.8897i) q^{58} +(-46.5000 + 26.8468i) q^{59} +48.0000 q^{60} +(8.00000 - 13.8564i) q^{61} +(12.0000 - 6.92820i) q^{62} +31.1769i q^{63} +64.0000 q^{64} +(44.0000 - 76.2102i) q^{65} +(63.0000 - 36.3731i) q^{66} +(100.500 - 58.0237i) q^{67} -44.0000 q^{68} +72.7461i q^{69} +27.7128i q^{70} +(-36.0000 - 62.3538i) q^{72} -25.0000 q^{73} -32.0000 q^{74} +(13.5000 + 23.3827i) q^{75} +62.3538i q^{76} +(21.0000 + 36.3731i) q^{77} -132.000 q^{78} +(24.0000 + 13.8564i) q^{79} +(-32.0000 - 55.4256i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-13.0000 - 22.5167i) q^{82} +(30.0000 + 17.3205i) q^{83} +(36.0000 - 20.7846i) q^{84} +(22.0000 + 38.1051i) q^{85} +(-87.0000 - 50.2295i) q^{86} +(-51.0000 - 88.3346i) q^{87} +(-84.0000 - 48.4974i) q^{88} -2.00000 q^{89} +(-36.0000 + 62.3538i) q^{90} -76.2102i q^{91} +(84.0000 - 48.4974i) q^{92} +20.7846i q^{93} +(6.00000 + 3.46410i) q^{94} +(54.0000 - 31.1769i) q^{95} +(-48.0000 + 83.1384i) q^{96} +(21.5000 - 37.2391i) q^{97} +(-37.0000 - 64.0859i) q^{98} +109.119i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 4 q^{2} - 3 q^{3} + 8 q^{4} - 4 q^{5} - 6 q^{6} - 6 q^{7} + 16 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q + 4 * q^2 - 3 * q^3 + 8 * q^4 - 4 * q^5 - 6 * q^6 - 6 * q^7 + 16 * q^8 - 9 * q^9	\( 2 q + 4 q^{2} - 3 q^{3} + 8 q^{4} - 4 q^{5} - 6 q^{6} - 6 q^{7} + 16 q^{8} - 9 q^{9} - 8 q^{10} - 21 q^{11} - 12 q^{12} + 22 q^{13} - 12 q^{14} + 24 q^{15} + 32 q^{16} - 22 q^{17} - 18 q^{18} - 16 q^{20} + 18 q^{21} - 42 q^{22} + 42 q^{23} - 24 q^{24} + 9 q^{25} + 44 q^{26} + 54 q^{27} - 24 q^{28} - 34 q^{29} + 48 q^{30} + 12 q^{31} + 64 q^{32} + 63 q^{33} - 44 q^{34} - 36 q^{36} - 32 q^{37} - 132 q^{39} - 32 q^{40} - 13 q^{41} + 36 q^{42} - 87 q^{43} - 84 q^{44} - 36 q^{45} + 84 q^{46} + 6 q^{47} - 48 q^{48} - 37 q^{49} + 18 q^{50} + 33 q^{51} + 88 q^{52} + 104 q^{53} + 108 q^{54} - 48 q^{56} - 81 q^{57} - 68 q^{58} - 93 q^{59} + 96 q^{60} + 16 q^{61} + 24 q^{62} + 128 q^{64} + 88 q^{65} + 126 q^{66} + 201 q^{67} - 88 q^{68} - 72 q^{72} - 50 q^{73} - 64 q^{74} + 27 q^{75} + 42 q^{77} - 264 q^{78} + 48 q^{79} - 64 q^{80} - 81 q^{81} - 26 q^{82} + 60 q^{83} + 72 q^{84} + 44 q^{85} - 174 q^{86} - 102 q^{87} - 168 q^{88} - 4 q^{89} - 72 q^{90} + 168 q^{92} + 12 q^{94} + 108 q^{95} - 96 q^{96} + 43 q^{97} - 74 q^{98}+O(q^{100}) \) 2 * q + 4 * q^2 - 3 * q^3 + 8 * q^4 - 4 * q^5 - 6 * q^6 - 6 * q^7 + 16 * q^8 - 9 * q^9 - 8 * q^10 - 21 * q^11 - 12 * q^12 + 22 * q^13 - 12 * q^14 + 24 * q^15 + 32 * q^16 - 22 * q^17 - 18 * q^18 - 16 * q^20 + 18 * q^21 - 42 * q^22 + 42 * q^23 - 24 * q^24 + 9 * q^25 + 44 * q^26 + 54 * q^27 - 24 * q^28 - 34 * q^29 + 48 * q^30 + 12 * q^31 + 64 * q^32 + 63 * q^33 - 44 * q^34 - 36 * q^36 - 32 * q^37 - 132 * q^39 - 32 * q^40 - 13 * q^41 + 36 * q^42 - 87 * q^43 - 84 * q^44 - 36 * q^45 + 84 * q^46 + 6 * q^47 - 48 * q^48 - 37 * q^49 + 18 * q^50 + 33 * q^51 + 88 * q^52 + 104 * q^53 + 108 * q^54 - 48 * q^56 - 81 * q^57 - 68 * q^58 - 93 * q^59 + 96 * q^60 + 16 * q^61 + 24 * q^62 + 128 * q^64 + 88 * q^65 + 126 * q^66 + 201 * q^67 - 88 * q^68 - 72 * q^72 - 50 * q^73 - 64 * q^74 + 27 * q^75 + 42 * q^77 - 264 * q^78 + 48 * q^79 - 64 * q^80 - 81 * q^81 - 26 * q^82 + 60 * q^83 + 72 * q^84 + 44 * q^85 - 174 * q^86 - 102 * q^87 - 168 * q^88 - 4 * q^89 - 72 * q^90 + 168 * q^92 + 12 * q^94 + 108 * q^95 - 96 * q^96 + 43 * q^97 - 74 * q^98

Introduction

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