LMFDB - Embedded newform 36.3.f.a.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:	$\Z[a_1, a_2, a_3]$
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.a.31.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.00000 - 3.46410i) q^{5} -6.00000 q^{6} +(3.00000 + 1.73205i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.00000 - 3.46410i) q^{5} -6.00000 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} -6.92820i q^{14} -12.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} -11.0000 q^{17} +(-9.00000 + 15.5885i) q^{18} -15.5885i q^{19} +16.0000 q^{20} +(9.00000 - 5.19615i) q^{21} -24.2487i 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} +(12.0000 + 20.7846i) q^{30} +(-6.00000 + 3.46410i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(31.5000 - 18.1865i) q^{33} +(11.0000 + 19.0526i) q^{34} -13.8564i q^{35} +36.0000 q^{36} -16.0000 q^{37} +(-27.0000 + 15.5885i) 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} -48.0000 q^{48} +(-18.5000 - 32.0429i) q^{49} -18.0000 q^{50} +(-16.5000 + 28.5788i) q^{51} -88.0000 q^{52} +52.0000 q^{53} +(27.0000 + 46.7654i) q^{54} -48.4974i q^{55} +(24.0000 + 13.8564i) q^{56} +(-40.5000 - 23.3827i) q^{57} +68.0000 q^{58} +(46.5000 - 26.8468i) q^{59} +(24.0000 - 41.5692i) 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} +(22.0000 - 38.1051i) q^{68} +72.7461i q^{69} +(-24.0000 + 13.8564i) q^{70} +(-36.0000 - 62.3538i) q^{72} -25.0000 q^{73} +(16.0000 + 27.7128i) q^{74} +(-13.5000 - 23.3827i) q^{75} +(54.0000 + 31.1769i) q^{76} +(21.0000 + 36.3731i) q^{77} +(-66.0000 - 114.315i) 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} +41.5692i q^{84} +(22.0000 + 38.1051i) q^{85} -100.459i q^{86} +(51.0000 + 88.3346i) q^{87} +(84.0000 + 48.4974i) q^{88} -2.00000 q^{89} +72.0000 q^{90} +76.2102i q^{91} -96.9948i q^{92} +20.7846i q^{93} +6.92820i 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 - 2 q^{2} + 3 q^{3} - 4 q^{4} - 4 q^{5} - 12 q^{6} + 6 q^{7} + 16 q^{8} - 9 q^{9}+O(q^{10}) $ 2 * q - 2 * q^2 + 3 * q^3 - 4 * q^4 - 4 * q^5 - 12 * q^6 + 6 * q^7 + 16 * q^8 - 9 * q^9	$ 2 q - 2 q^{2} + 3 q^{3} - 4 q^{4} - 4 q^{5} - 12 q^{6} + 6 q^{7} + 16 q^{8} - 9 q^{9} - 8 q^{10} + 21 q^{11} + 12 q^{12} + 22 q^{13} - 24 q^{15} - 16 q^{16} - 22 q^{17} - 18 q^{18} + 32 q^{20} + 18 q^{21} - 42 q^{23} + 24 q^{24} + 9 q^{25} + 44 q^{26} - 54 q^{27} - 24 q^{28} - 34 q^{29} + 24 q^{30} - 12 q^{31} - 32 q^{32} + 63 q^{33} + 22 q^{34} + 72 q^{36} - 32 q^{37} - 54 q^{38} + 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} - 96 q^{48} - 37 q^{49} - 36 q^{50} - 33 q^{51} - 176 q^{52} + 104 q^{53} + 54 q^{54} + 48 q^{56} - 81 q^{57} + 136 q^{58} + 93 q^{59} + 48 q^{60} + 16 q^{61} + 24 q^{62} + 128 q^{64} + 88 q^{65} - 126 q^{66} - 201 q^{67} + 44 q^{68} - 48 q^{70} - 72 q^{72} - 50 q^{73} + 32 q^{74} - 27 q^{75} + 108 q^{76} + 42 q^{77} - 132 q^{78} - 48 q^{79} - 64 q^{80} - 81 q^{81} - 26 q^{82} - 60 q^{83} + 44 q^{85} + 102 q^{87} + 168 q^{88} - 4 q^{89} + 144 q^{90} - 108 q^{95} + 96 q^{96} + 43 q^{97} - 74 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 + 3 * q^3 - 4 * q^4 - 4 * q^5 - 12 * q^6 + 6 * q^7 + 16 * q^8 - 9 * q^9 - 8 * q^10 + 21 * q^11 + 12 * q^12 + 22 * q^13 - 24 * q^15 - 16 * q^16 - 22 * q^17 - 18 * q^18 + 32 * q^20 + 18 * q^21 - 42 * q^23 + 24 * q^24 + 9 * q^25 + 44 * q^26 - 54 * q^27 - 24 * q^28 - 34 * q^29 + 24 * q^30 - 12 * q^31 - 32 * q^32 + 63 * q^33 + 22 * q^34 + 72 * q^36 - 32 * q^37 - 54 * q^38 + 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 - 96 * q^48 - 37 * q^49 - 36 * q^50 - 33 * q^51 - 176 * q^52 + 104 * q^53 + 54 * q^54 + 48 * q^56 - 81 * q^57 + 136 * q^58 + 93 * q^59 + 48 * q^60 + 16 * q^61 + 24 * q^62 + 128 * q^64 + 88 * q^65 - 126 * q^66 - 201 * q^67 + 44 * q^68 - 48 * q^70 - 72 * q^72 - 50 * q^73 + 32 * q^74 - 27 * q^75 + 108 * q^76 + 42 * q^77 - 132 * q^78 - 48 * q^79 - 64 * q^80 - 81 * q^81 - 26 * q^82 - 60 * q^83 + 44 * q^85 + 102 * q^87 + 168 * q^88 - 4 * q^89 + 144 * q^90 - 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 $

$2$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$2$	−1.00000	−	1.73205i	−0.500000	−	0.866025i
$3$	1.50000	−	2.59808i	0.500000	−	0.866025i
$3$	1.50000	−	2.59808i	0.500000	−	0.866025i
$4$	−2.00000	+	3.46410i	−0.500000	+	0.866025i
$5$	−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	$0.964323\pi$
$6$	−6.00000			−1.00000
$7$	3.00000	+	1.73205i	0.428571	+	0.247436i	0.698738	−	0.715378i	$-0.253745\pi$
$7$	3.00000	+	1.73205i	0.428571	+	0.247436i	−0.270166	+	0.962814i	$0.587079\pi$
$8$	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	0.894490	−	0.447088i	$-0.147539\pi$
$11$	10.5000	+	6.06218i	0.954545	+	0.551107i	0.0600555	+	0.998195i	$0.480872\pi$
$12$	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	$0.512246\pi$
$14$		−	6.92820i		−	0.494872i
$15$	−12.0000			−0.800000
$16$	−8.00000	−	13.8564i	−0.500000	−	0.866025i
$17$	−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	$-0.865451\pi$
$19$		−	15.5885i		−	0.820445i	0.911985	−	0.410223i	$-0.134549\pi$
$20$	16.0000			0.800000
$21$	9.00000	−	5.19615i	0.428571	−	0.247436i
$22$		−	24.2487i		−	1.10221i
$23$	−21.0000	+	12.1244i	−0.913043	+	0.527146i	−0.881409	−	0.472354i	$-0.843405\pi$
$23$	−21.0000	+	12.1244i	−0.913043	+	0.527146i	−0.0316343	+	0.999500i	$0.510071\pi$
$24$	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	$0.967287\pi$
$30$	12.0000	+	20.7846i	0.400000	+	0.692820i
$31$	−6.00000	+	3.46410i	−0.193548	+	0.111745i	−0.593643	−	0.804729i	$-0.702311\pi$
$31$	−6.00000	+	3.46410i	−0.193548	+	0.111745i	0.400094	+	0.916474i	$0.368977\pi$
$32$	−16.0000	+	27.7128i	−0.500000	+	0.866025i
$33$	31.5000	−	18.1865i	0.954545	−	0.551107i
$34$	11.0000	+	19.0526i	0.323529	+	0.560369i
$35$		−	13.8564i		−	0.395897i
$36$	36.0000			1.00000
$37$	−16.0000			−0.432432			−0.216216	−	0.976346i	$-0.569372\pi$
$37$	−16.0000			−0.432432			−0.216216	+	0.976346i	$0.569372\pi$
$38$	−27.0000	+	15.5885i	−0.710526	+	0.410223i
$39$	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	0.911668	−	0.410928i	$-0.134795\pi$
$43$	43.5000	+	25.1147i	1.01163	+	0.584064i	0.0999600	+	0.994991i	$0.468129\pi$
$44$	−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	0.467745	−	0.883863i	$-0.345066\pi$
$47$	−3.00000	−	1.73205i	−0.0638298	−	0.0368521i	−0.531575	+	0.847011i	$0.678400\pi$
$48$	−48.0000			−1.00000
$49$	−18.5000	−	32.0429i	−0.377551	−	0.653938i
$50$	−18.0000			−0.360000
$51$	−16.5000	+	28.5788i	−0.323529	+	0.560369i
$52$	−88.0000			−1.69231
$53$	52.0000			0.981132			0.490566	−	0.871404i	$-0.336790\pi$
$53$	52.0000			0.981132			0.490566	+	0.871404i	$0.336790\pi$
$54$	27.0000	+	46.7654i	0.500000	+	0.866025i
$55$		−	48.4974i		−	0.881771i
$56$	24.0000	+	13.8564i	0.428571	+	0.247436i
$57$	−40.5000	−	23.3827i	−0.710526	−	0.410223i
$58$	68.0000			1.17241
$59$	46.5000	−	26.8468i	0.788136	−	0.455030i	−0.0511702	−	0.998690i	$-0.516295\pi$
$59$	46.5000	−	26.8468i	0.788136	−	0.455030i	0.839306	+	0.543660i	$0.182962\pi$
$60$	24.0000	−	41.5692i	0.400000	−	0.692820i
$61$	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	$0.666667\pi$
$67$	−100.500	+	58.0237i	−1.50000	+	0.866025i	−1.00000			$\pi$
$68$	22.0000	−	38.1051i	0.323529	−	0.560369i
$69$			72.7461i			1.05429i
$70$	−24.0000	+	13.8564i	−0.342857	+	0.197949i
$71$		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	$0.554775\pi$
$74$	16.0000	+	27.7128i	0.216216	+	0.374497i
$75$	−13.5000	−	23.3827i	−0.180000	−	0.311769i
$76$	54.0000	+	31.1769i	0.710526	+	0.410223i
$77$	21.0000	+	36.3731i	0.272727	+	0.472377i
$78$	−66.0000	−	114.315i	−0.846154	−	1.46558i
$79$	−24.0000	−	13.8564i	−0.303797	−	0.175398i	0.340350	−	0.940299i	$-0.389454\pi$
$79$	−24.0000	−	13.8564i	−0.303797	−	0.175398i	−0.644148	+	0.764901i	$0.722788\pi$
$80$	−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	0.308269	−	0.951299i	$-0.400250\pi$
$83$	−30.0000	−	17.3205i	−0.361446	−	0.208681i	−0.669715	+	0.742618i	$0.733584\pi$
$84$			41.5692i			0.494872i
$85$	22.0000	+	38.1051i	0.258824	+	0.448296i
$86$		−	100.459i		−	1.16813i
$87$	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	$0.503577\pi$
$90$	72.0000			0.800000
$91$			76.2102i			0.837475i
$92$		−	96.9948i		−	1.05429i
$93$			20.7846i			0.223490i
$94$			6.92820i			0.0737043i
$95$	−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	$0.135099\pi$
$102$	66.0000			0.647059
$103$	21.0000	−	12.1244i	0.203883	−	0.117712i	−0.394582	−	0.918861i	$-0.629111\pi$
$103$	21.0000	−	12.1244i	0.203883	−	0.117712i	0.598466	+	0.801148i	$0.295777\pi$
$104$	88.0000	+	152.420i	0.846154	+	1.46558i
$105$	−36.0000	−	20.7846i	−0.342857	−	0.197949i
$106$	−52.0000	−	90.0666i	−0.490566	−	0.849685i
$107$		−	15.5885i		−	0.145687i	−0.997343	−	0.0728433i	$-0.976793\pi$
$107$		−	15.5885i		−	0.145687i	0.997343	−	0.0728433i	$-0.0232073\pi$
$108$	54.0000	−	93.5307i	0.500000	−	0.866025i
$109$	−88.0000			−0.807339			−0.403670	−	0.914905i	$-0.632266\pi$
$109$	−88.0000			−0.807339			−0.403670	+	0.914905i	$0.632266\pi$
$110$	−84.0000	+	48.4974i	−0.763636	+	0.440886i
$111$	−24.0000	+	41.5692i	−0.216216	+	0.374497i
$112$		−	55.4256i		−	0.494872i
$113$	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	$0.762323\pi$
$114$			93.5307i			0.820445i
$115$	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
$122$	−32.0000			−0.262295
$123$	−39.0000			−0.317073
$124$		−	27.7128i		−	0.223490i
$125$	−136.000			−1.08800
$126$	−54.0000	+	31.1769i	−0.428571	+	0.247436i
$127$		−	218.238i		−	1.71841i	−0.511629	−	0.859206i	$-0.670958\pi$
$127$		−	218.238i		−	1.71841i	0.511629	−	0.859206i	$-0.329042\pi$
$128$	−64.0000	−	110.851i	−0.500000	−	0.866025i
$129$	130.500	−	75.3442i	1.01163	−	0.584064i
$130$	−176.000			−1.35385
$131$	168.000	−	96.9948i	1.28244	−	0.740419i	0.305148	−	0.952305i	$-0.401294\pi$
$131$	168.000	−	96.9948i	1.28244	−	0.740419i	0.977294	+	0.211886i	$0.0679606\pi$
$132$			145.492i			1.10221i
$133$	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	$0.955100\pi$
$138$	126.000	−	72.7461i	0.913043	−	0.527146i
$139$	169.500	−	97.8609i	1.21942	−	0.704035i	0.254630	−	0.967039i	$-0.418046\pi$
$139$	169.500	−	97.8609i	1.21942	−	0.704035i	0.964795	+	0.263004i	$0.0847131\pi$
$140$	48.0000	+	27.7128i	0.342857	+	0.197949i
$141$	−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
$146$	25.0000	+	43.3013i	0.171233	+	0.296584i
$147$	−111.000			−0.755102
$148$	32.0000	−	55.4256i	0.216216	−	0.374497i
$149$	−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	0.110254	−	0.993903i	$-0.464833\pi$
$151$	−105.000	−	60.6218i	−0.695364	−	0.401469i	−0.805618	+	0.592435i	$0.798167\pi$
$152$		−	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
$156$	−132.000	+	228.631i	−0.846154	+	1.46558i
$157$	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	$0.829278\pi$
$158$			55.4256i			0.350795i
$159$	78.0000	−	135.100i	0.490566	−	0.849685i
$160$	128.000			0.800000
$161$	−84.0000			−0.521739
$162$	162.000			1.00000
$163$			311.769i			1.91269i	0.292233	+	0.956347i	$0.405602\pi$
$163$			311.769i			1.91269i	−0.292233	+	0.956347i	$0.594398\pi$
$164$	52.0000			0.317073
$165$	−126.000	−	72.7461i	−0.763636	−	0.440886i
$166$			69.2820i			0.417362i
$167$	−156.000	+	90.0666i	−0.934132	+	0.539321i	−0.888116	−	0.459620i	$-0.847986\pi$
$167$	−156.000	+	90.0666i	−0.934132	+	0.539321i	−0.0460158	+	0.998941i	$0.514652\pi$
$168$	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
$176$		−	193.990i		−	1.10221i
$177$		−	161.081i		−	0.910061i
$178$	2.00000	+	3.46410i	0.0112360	+	0.0194612i
$179$		−	187.061i		−	1.04504i	−0.852628	−	0.522518i	$-0.824993\pi$
$179$		−	187.061i		−	1.04504i	0.852628	−	0.522518i	$-0.175007\pi$
$180$	−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	$0.252444\pi$
$182$	132.000	−	76.2102i	0.725275	−	0.418738i
$183$	−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
$186$	36.0000	−	20.7846i	0.193548	−	0.111745i
$187$	−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	0.492126	−	0.870524i	$-0.336220\pi$
$191$	−3.00000	−	1.73205i	−0.0157068	−	0.00906833i	−0.507833	+	0.861456i	$0.669553\pi$
$192$	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	$0.777801\pi$
$194$	−86.0000			−0.443299
$195$	−132.000	−	228.631i	−0.676923	−	1.17247i
$196$	148.000			0.755102
$197$	268.000			1.36041			0.680203	−	0.733024i	$-0.261892\pi$
$197$	268.000			1.36041			0.680203	+	0.733024i	$0.261892\pi$
$198$	−189.000	+	109.119i	−0.954545	+	0.551107i
$199$			31.1769i			0.156668i	0.996927	+	0.0783340i	$0.0249600\pi$
$199$			31.1769i			0.156668i	−0.996927	+	0.0783340i	$0.975040\pi$
$200$	36.0000	−	62.3538i	0.180000	−	0.311769i
$201$			348.142i			1.73205i
$202$	−40.0000			−0.198020
$203$	−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
$210$			83.1384i			0.395897i
$211$	−114.000	+	65.8179i	−0.540284	+	0.311933i	−0.745194	−	0.666848i	$-0.767643\pi$
$211$	−114.000	+	65.8179i	−0.540284	+	0.311933i	0.204910	+	0.978781i	$0.434310\pi$
$212$	−104.000	+	180.133i	−0.490566	+	0.849685i
$213$		0			0
$214$	−27.0000	+	15.5885i	−0.126168	+	0.0728433i
$215$		−	200.918i		−	0.934502i
$216$	−216.000			−1.00000
$217$	−24.0000			−0.110599
$218$	88.0000	+	152.420i	0.403670	+	0.699176i
$219$	−37.5000	+	64.9519i	−0.171233	+	0.296584i
$220$	168.000	+	96.9948i	0.763636	+	0.440886i
$221$	−121.000	−	209.578i	−0.547511	−	0.948317i
$222$	96.0000			0.432432
$223$	−51.0000	−	29.4449i	−0.228700	−	0.132040i	0.381272	−	0.924463i	$-0.375486\pi$
$223$	−51.0000	−	29.4449i	−0.228700	−	0.132040i	−0.609972	+	0.792423i	$0.708819\pi$
$224$	−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	$0.117529\pi$
$227$	388.500	+	224.301i	1.71145	+	0.988108i	0.778847	+	0.627214i	$0.215805\pi$
$228$	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	$-0.519632\pi$
$230$		−	193.990i		−	0.843433i
$231$	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	$0.544545\pi$
$234$	−396.000			−1.69231
$235$			13.8564i			0.0589634i
$236$			214.774i			0.910061i
$237$	−72.0000	+	41.5692i	−0.303797	+	0.175398i
$238$			76.2102i			0.320211i
$239$	33.0000	−	19.0526i	0.138075	−	0.0797178i	−0.429371	−	0.903128i	$-0.641265\pi$
$239$	33.0000	−	19.0526i	0.138075	−	0.0797178i	0.567446	+	0.823410i	$0.307931\pi$
$240$	96.0000	+	166.277i	0.400000	+	0.692820i
$241$	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
$246$	39.0000	+	67.5500i	0.158537	+	0.274593i
$247$	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
$250$	136.000	+	235.559i	0.544000	+	0.942236i
$251$		−	109.119i		−	0.434738i	−0.976090	−	0.217369i	$-0.930253\pi$
$251$		−	109.119i		−	0.434738i	0.976090	−	0.217369i	$-0.0697475\pi$
$252$	108.000	+	62.3538i	0.428571	+	0.247436i
$253$	−294.000			−1.16206
$254$	−378.000	+	218.238i	−1.48819	+	0.859206i
$255$	132.000			0.517647
$256$	−128.000	+	221.703i	−0.500000	+	0.866025i
$257$	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	−0.118750	−	0.992924i	$-0.537889\pi$
$263$	−273.000	−	157.617i	−1.03802	−	0.599303i	−0.919273	+	0.393621i	$0.871222\pi$
$264$	252.000	−	145.492i	0.954545	−	0.551107i
$265$	−104.000	−	180.133i	−0.392453	−	0.679748i
$266$	−108.000			−0.406015
$267$	−3.00000	+	5.19615i	−0.0112360	+	0.0194612i
$268$		−	464.190i		−	1.73205i
$269$	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	$0.195083\pi$
$271$			311.769i			1.15044i	−0.817999	+	0.575220i	$0.804917\pi$
$272$	88.0000	+	152.420i	0.323529	+	0.560369i
$273$	198.000	+	114.315i	0.725275	+	0.418738i
$274$	338.000			1.23358
$275$	94.5000	−	54.5596i	0.343636	−	0.198399i
$276$	−252.000	−	145.492i	−0.913043	−	0.527146i
$277$	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	−0.510563	−	0.859840i	$-0.670563\pi$
$283$	−6.00000	+	3.46410i	−0.0212014	+	0.0122406i	0.489362	+	0.872081i	$0.337230\pi$
$284$		0			0
$285$			187.061i			0.656356i
$286$	462.000	−	266.736i	1.61538	−	0.932643i
$287$		−	45.0333i		−	0.156911i
$288$	288.000			1.00000
$289$	−168.000			−0.581315
$290$	−136.000	−	235.559i	−0.468966	−	0.812272i
$291$	−64.5000	−	111.717i	−0.221649	−	0.383908i
$292$	50.0000	−	86.6025i	0.171233	−	0.296584i
$293$	−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	$0.945356\pi$
$294$	111.000	+	192.258i	0.377551	+	0.653938i
$295$	−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
$300$	108.000			0.360000
$301$	87.0000	+	150.688i	0.289037	+	0.500626i
$302$			242.487i			0.802937i
$303$	−30.0000	−	51.9615i	−0.0990099	−	0.171490i
$304$	−216.000	+	124.708i	−0.710526	+	0.410223i
$305$	−64.0000			−0.209836
$306$	99.0000	−	171.473i	0.323529	−	0.560369i
$307$		−	109.119i		−	0.355437i	−0.984081	−	0.177719i	$-0.943128\pi$
$307$		−	109.119i		−	0.355437i	0.984081	−	0.177719i	$-0.0568717\pi$
$308$	−168.000			−0.545455
$309$		−	72.7461i		−	0.235424i
$310$		−	55.4256i		−	0.178792i
$311$	−237.000	+	136.832i	−0.762058	+	0.439974i	−0.830034	−	0.557713i	$-0.811679\pi$
$311$	−237.000	+	136.832i	−0.762058	+	0.439974i	0.0679762	+	0.997687i	$0.478346\pi$
$312$	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	$0.875812\pi$
$318$	−312.000			−0.981132
$319$	−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
$322$	84.0000	+	145.492i	0.260870	+	0.451839i
$323$			171.473i			0.530876i
$324$	−162.000	−	280.592i	−0.500000	−	0.866025i
$325$	198.000			0.609231
$326$	540.000	−	311.769i	1.65644	−	0.956347i
$327$	−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
$330$			290.985i			0.881771i
$331$	354.000	+	204.382i	1.06949	+	0.617468i	0.928041	−	0.372478i	$-0.121492\pi$
$331$	354.000	+	204.382i	1.06949	+	0.617468i	0.141445	+	0.989946i	$0.454825\pi$
$332$	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	$0.666667\pi$
$338$	630.000			1.86391
$339$	150.000			0.442478
$340$	−176.000			−0.517647
$341$	−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
$346$	−4.00000			−0.0115607
$347$	235.500	−	135.966i	0.678674	−	0.391833i	−0.120681	−	0.992691i	$-0.538508\pi$
$347$	235.500	−	135.966i	0.678674	−	0.391833i	0.799355	+	0.600859i	$0.205174\pi$
$348$	−408.000			−1.17241
$349$	−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	$-0.0598125\pi$
$354$	−279.000	+	161.081i	−0.788136	+	0.455030i
$355$		0			0
$356$	4.00000	−	6.92820i	0.0112360	−	0.0194612i
$357$	−99.0000	+	57.1577i	−0.277311	+	0.160106i
$358$	−324.000	+	187.061i	−0.905028	+	0.522518i
$359$			530.008i			1.47634i	0.674612	+	0.738172i	$0.264311\pi$
$359$			530.008i			1.47634i	−0.674612	+	0.738172i	$0.735689\pi$
$360$	−144.000	+	249.415i	−0.400000	+	0.692820i
$361$	118.000			0.326870
$362$	−254.000	−	439.941i	−0.701657	−	1.21531i
$363$	78.0000			0.214876
$364$	−264.000	−	152.420i	−0.725275	−	0.418738i
$365$	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	0.610057	−	0.792358i	$-0.291147\pi$
$367$	84.0000	+	48.4974i	0.228883	+	0.132146i	−0.381174	+	0.924503i	$0.624480\pi$
$368$	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
$372$	−72.0000	−	41.5692i	−0.193548	−	0.111745i
$373$	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	$0.679816\pi$
$374$			266.736i			0.713197i
$375$	−204.000	+	353.338i	−0.544000	+	0.942236i
$376$	−24.0000	−	13.8564i	−0.0638298	−	0.0368521i
$377$	−748.000			−1.98408
$378$			187.061i			0.494872i
$379$		−	327.358i		−	0.863740i	−0.901936	−	0.431870i	$-0.857854\pi$
$379$		−	327.358i		−	0.863740i	0.901936	−	0.431870i	$-0.142146\pi$
$380$		−	249.415i		−	0.656356i
$381$	−567.000	−	327.358i	−1.48819	−	0.859206i
$382$			6.92820i			0.0181367i
$383$	546.000	−	315.233i	1.42559	−	0.823063i	0.428819	−	0.903390i	$-0.358930\pi$
$383$	546.000	−	315.233i	1.42559	−	0.823063i	0.996769	+	0.0803272i	$0.0255965\pi$
$384$	−384.000			−1.00000
$385$	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
$394$	−268.000	−	464.190i	−0.680203	−	1.17815i
$395$			110.851i			0.280636i
$396$	378.000	+	218.238i	0.954545	+	0.551107i
$397$	488.000			1.22922			0.614610	−	0.788831i	$-0.289314\pi$
$397$	488.000			1.22922			0.614610	+	0.788831i	$0.289314\pi$
$398$	54.0000	−	31.1769i	0.135678	−	0.0783340i
$399$	−81.0000	−	140.296i	−0.203008	−	0.351619i
$400$	−144.000			−0.360000
$401$	−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	$-0.353896\pi$
$402$	603.000	−	348.142i	1.50000	−	0.866025i
$403$	−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	$0.807232\pi$
$410$	104.000			0.253659
$411$	253.500	+	439.075i	0.616788	+	1.06831i
$412$			96.9948i			0.235424i
$413$	186.000			0.450363
$414$		−	436.477i		−	1.05429i
$415$			138.564i			0.333889i
$416$	−704.000			−1.69231
$417$		−	587.165i		−	1.40807i
$418$	−378.000			−0.904306
$419$	−534.000	+	308.305i	−1.27446	+	0.735812i	−0.975825	−	0.218555i	$-0.929866\pi$
$419$	−534.000	+	308.305i	−1.27446	+	0.735812i	−0.298638	+	0.954366i	$0.596532\pi$
$420$	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
$428$	54.0000	+	31.1769i	0.126168	+	0.0728433i
$429$	693.000	+	400.104i	1.61538	+	0.932643i
$430$	−348.000	+	200.918i	−0.809302	+	0.467251i
$431$		−	405.300i		−	0.940371i	−0.882568	−	0.470185i	$-0.844187\pi$
$431$		−	405.300i		−	0.940371i	0.882568	−	0.470185i	$-0.155813\pi$
$432$	216.000	+	374.123i	0.500000	+	0.866025i
$433$	−439.000			−1.01386			−0.506928	−	0.861988i	$-0.669219\pi$
$433$	−439.000			−1.01386			−0.506928	+	0.861988i	$0.669219\pi$
$434$	24.0000	+	41.5692i	0.0552995	+	0.0957816i
$435$	204.000	−	353.338i	0.468966	−	0.812272i
$436$	176.000	−	304.841i	0.403670	−	0.699176i
$437$	189.000	+	327.358i	0.432494	+	0.749102i
$438$	150.000			0.342466
$439$	732.000	+	422.620i	1.66743	+	0.962689i	0.969018	+	0.246989i	$0.0794410\pi$
$439$	732.000	+	422.620i	1.66743	+	0.962689i	0.698408	+	0.715700i	$0.253892\pi$
$440$		−	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	0.140474	−	0.990084i	$-0.455137\pi$
$443$	−286.500	−	165.411i	−0.646727	−	0.373388i	−0.787201	+	0.616696i	$0.788471\pi$
$444$	−96.0000	−	166.277i	−0.216216	−	0.374497i
$445$	4.00000	+	6.92820i	0.00898876	+	0.0155690i
$446$			117.779i			0.264079i
$447$	−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	$0.516667\pi$
$450$	81.0000	+	140.296i	0.180000	+	0.311769i
$451$		−	157.617i		−	0.349483i
$452$	−200.000			−0.442478
$453$	−315.000	+	181.865i	−0.695364	+	0.401469i
$454$		−	897.202i		−	1.97622i
$455$	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	$0.968344\pi$
$462$	−126.000	−	218.238i	−0.272727	−	0.472377i
$463$	−492.000	+	284.056i	−1.06263	+	0.613513i	−0.926160	−	0.377131i	$-0.876911\pi$
$463$	−492.000	+	284.056i	−1.06263	+	0.613513i	−0.136475	+	0.990644i	$0.543577\pi$
$464$	544.000			1.17241
$465$	72.0000	−	41.5692i	0.154839	−	0.0893962i
$466$	65.0000	+	112.583i	0.139485	+	0.241595i
$467$			639.127i			1.36858i	0.729210	+	0.684290i	$0.239888\pi$
$467$			639.127i			1.36858i	−0.729210	+	0.684290i	$0.760112\pi$
$468$	396.000	+	685.892i	0.846154	+	1.46558i
$469$	−402.000			−0.857143
$470$	24.0000	−	13.8564i	0.0510638	−	0.0294817i
$471$	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	0.605583	−	0.795782i	$-0.292940\pi$
$479$	105.000	+	60.6218i	0.219207	+	0.126559i	−0.386376	+	0.922341i	$0.626273\pi$
$480$	192.000	−	332.554i	0.400000	−	0.692820i
$481$	−176.000	−	304.841i	−0.365904	−	0.633765i
$482$	−446.000			−0.925311
$483$	−126.000	+	218.238i	−0.260870	+	0.451839i
$484$	−104.000			−0.214876
$485$	−172.000			−0.354639
$486$	243.000	−	420.888i	0.500000	−	0.866025i
$487$		−	405.300i		−	0.832238i	−0.909310	−	0.416119i	$-0.863390\pi$
$487$		−	405.300i		−	0.832238i	0.909310	−	0.416119i	$-0.136610\pi$
$488$	64.0000	−	110.851i	0.131148	−	0.227154i
$489$	810.000	+	467.654i	1.65644	+	0.956347i
$490$	296.000			0.604082
$491$	−628.500	+	362.865i	−1.28004	+	0.739032i	−0.976856	−	0.213900i	$-0.931383\pi$
$491$	−628.500	+	362.865i	−1.28004	+	0.739032i	−0.303185	+	0.952932i	$0.598050\pi$
$492$	78.0000	−	135.100i	0.158537	−	0.274593i
$493$	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	−0.878758	−	0.477269i	$-0.841627\pi$
$499$	−451.500	+	260.674i	−0.904810	+	0.522392i	−0.0260521	+	0.999661i	$0.508294\pi$
$500$	272.000	−	471.118i	0.544000	−	0.942236i
$501$			540.400i			1.07864i
$502$	−189.000	+	109.119i	−0.376494	+	0.217369i
$503$		−	872.954i		−	1.73549i	−0.497006	−	0.867747i	$-0.665567\pi$
$503$		−	872.954i		−	1.73549i	0.497006	−	0.867747i	$-0.334433\pi$
$504$		−	249.415i		−	0.494872i
$505$	−80.0000			−0.158416
$506$	294.000	+	509.223i	0.581028	+	1.00637i
$507$	472.500	+	818.394i	0.931953	+	1.61419i
$508$	756.000	+	436.477i	1.48819	+	0.859206i
$509$	−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	$-0.434963\pi$
$510$	−132.000	−	228.631i	−0.258824	−	0.448296i
$511$	−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
$516$			602.754i			1.16813i
$517$	−21.0000	−	36.3731i	−0.0406190	−	0.0703541i
$518$			110.851i			0.213999i
$519$	−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	$0.246440\pi$
$522$	−306.000	−	530.008i	−0.586207	−	1.01534i
$523$		−	561.184i		−	1.07301i	−0.843897	−	0.536505i	$-0.819744\pi$
$523$		−	561.184i		−	1.07301i	0.843897	−	0.536505i	$-0.180256\pi$
$524$			775.959i			1.48084i
$525$		−	93.5307i		−	0.178154i
$526$			630.466i			1.19861i
$527$	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
$534$	12.0000			0.0224719
$535$	−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
$538$	−304.000	−	526.543i	−0.565056	−	0.978705i
$539$		−	448.601i		−	0.832284i
$540$	−432.000			−0.800000
$541$	−520.000			−0.961183			−0.480591	−	0.876945i	$-0.659578\pi$
$541$	−520.000			−0.961183			−0.480591	+	0.876945i	$0.659578\pi$
$542$	540.000	−	311.769i	0.996310	−	0.575220i
$543$	381.000	−	659.911i	0.701657	−	1.21531i
$544$	176.000	−	304.841i	0.323529	−	0.560369i
$545$	176.000	+	304.841i	0.322936	+	0.559341i
$546$		−	457.261i		−	0.837475i
$547$	−334.500	−	193.124i	−0.611517	−	0.353060i	0.162042	−	0.986784i	$-0.448192\pi$
$547$	−334.500	−	193.124i	−0.611517	−	0.353060i	−0.773559	+	0.633724i	$0.781525\pi$
$548$	−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
$554$	−68.0000			−0.122744
$555$	192.000			0.345946
$556$			782.887i			1.40807i
$557$	934.000			1.67684			0.838420	−	0.545025i	$-0.183480\pi$
$557$	934.000			1.67684			0.838420	+	0.545025i	$0.183480\pi$
$558$		−	124.708i		−	0.223490i
$559$			1105.05i			1.97683i
$560$	−192.000	+	110.851i	−0.342857	+	0.197949i
$561$	−346.500	+	200.052i	−0.617647	+	0.356599i
$562$	−436.000			−0.775801
$563$	613.500	−	354.204i	1.08970	−	0.629137i	0.156202	−	0.987725i	$-0.450075\pi$
$563$	613.500	−	354.204i	1.08970	−	0.629137i	0.933496	+	0.358588i	$0.116742\pi$
$564$		−	41.5692i		−	0.0737043i
$565$	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	$-0.0424535\pi$
$570$	324.000	−	187.061i	0.568421	−	0.328178i
$571$	466.500	−	269.334i	0.816988	−	0.471688i	−0.0323889	−	0.999475i	$-0.510311\pi$
$571$	466.500	−	269.334i	0.816988	−	0.471688i	0.849377	+	0.527787i	$0.176978\pi$
$572$	−924.000	−	533.472i	−1.61538	−	0.932643i
$573$	−9.00000	+	5.19615i	−0.0157068	+	0.00906833i
$574$	−78.0000	+	45.0333i	−0.135889	+	0.0784553i
$575$			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	$0.436975\pi$
$578$	168.000	+	290.985i	0.290657	+	0.503433i
$579$	201.000			0.347150
$580$	−272.000	+	471.118i	−0.468966	+	0.812272i
$581$	−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	0.390189	−	0.920735i	$-0.372410\pi$
$587$	−124.500	−	71.8801i	−0.212095	−	0.122453i	−0.602285	+	0.798281i	$0.705743\pi$
$588$	222.000	−	384.515i	0.377551	−	0.653938i
$589$	54.0000	+	93.5307i	0.0916808	+	0.158796i
$590$			429.549i			0.728048i
$591$	402.000	−	696.284i	0.680203	−	1.17815i
$592$	128.000	+	221.703i	0.216216	+	0.374497i
$593$	−506.000			−0.853288			−0.426644	−	0.904420i	$-0.640304\pi$
$593$	−506.000			−0.853288			−0.426644	+	0.904420i	$0.640304\pi$
$594$			654.715i			1.10221i
$595$			152.420i			0.256169i
$596$	520.000			0.872483
$597$	81.0000	+	46.7654i	0.135678	+	0.0783340i
$598$			1066.94i			1.78419i
$599$	−48.0000	+	27.7128i	−0.0801336	+	0.0462651i	−0.539531	−	0.841965i	$-0.681399\pi$
$599$	−48.0000	+	27.7128i	−0.0801336	+	0.0462651i	0.459398	+	0.888231i	$0.348065\pi$
$600$	−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	−0.877040	−	0.480418i	$-0.840485\pi$
$607$	−546.000	+	315.233i	−0.899506	+	0.519330i	−0.0224660	+	0.999748i	$0.507152\pi$
$608$	432.000	+	249.415i	0.710526	+	0.410223i
$609$			353.338i			0.580194i
$610$	64.0000	+	110.851i	0.104918	+	0.181723i
$611$		−	76.2102i		−	0.124730i
$612$	−396.000			−0.647059
$613$	−340.000			−0.554649			−0.277325	−	0.960776i	$-0.589448\pi$
$613$	−340.000			−0.554649			−0.277325	+	0.960776i	$0.589448\pi$
$614$	−189.000	+	109.119i	−0.307818	+	0.177719i
$615$	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	$0.935960\pi$
$618$	−126.000	+	72.7461i	−0.203883	+	0.117712i
$619$	−10.5000	−	6.06218i	−0.0169628	−	0.00979350i	0.491495	−	0.870881i	$-0.336451\pi$
$619$	−10.5000	−	6.06218i	−0.0169628	−	0.00979350i	−0.508457	+	0.861087i	$0.669784\pi$
$620$	−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
$624$	−528.000	−	914.523i	−0.846154	−	1.46558i
$625$	159.500	+	276.262i	0.255200	+	0.442019i
$626$	−158.000			−0.252396
$627$	−283.500	−	491.036i	−0.452153	−	0.783152i
$628$	−16.0000			−0.0254777
$629$	176.000			0.279809
$630$	216.000	+	124.708i	0.342857	+	0.197949i
$631$			436.477i			0.691722i	0.938286	+	0.345861i	$0.112413\pi$
$631$			436.477i			0.691722i	−0.938286	+	0.345861i	$0.887587\pi$
$632$	−192.000	−	110.851i	−0.303797	−	0.175398i
$633$			394.908i			0.623867i
$634$	1004.00			1.58360
$635$	−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	$0.273174\pi$
$642$			93.5307i			0.145687i
$643$	358.500	−	206.980i	0.557543	−	0.321897i	−0.194616	−	0.980880i	$-0.562346\pi$
$643$	358.500	−	206.980i	0.557543	−	0.321897i	0.752159	+	0.658982i	$0.229013\pi$
$644$	168.000	−	290.985i	0.260870	−	0.451839i
$645$	−522.000	−	301.377i	−0.809302	−	0.467251i
$646$	297.000	−	171.473i	0.459752	−	0.265438i
$647$		−	405.300i		−	0.626430i	−0.949682	−	0.313215i	$-0.898594\pi$
$647$		−	405.300i		−	0.626430i	0.949682	−	0.313215i	$-0.101406\pi$
$648$	−324.000	+	561.184i	−0.500000	+	0.866025i
$649$	651.000			1.00308
$650$	−198.000	−	342.946i	−0.304615	−	0.527609i
$651$	−36.0000	+	62.3538i	−0.0552995	+	0.0957816i
$652$	−1080.00	−	623.538i	−1.65644	−	0.956347i
$653$	−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	$-0.403996\pi$
$654$	528.000			0.807339
$655$	−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	0.936659	−	0.350243i	$-0.113901\pi$
$659$	726.000	+	419.156i	1.10167	+	0.636049i	0.165010	+	0.986292i	$0.447234\pi$
$660$	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	$0.893402\pi$
$662$		−	817.528i		−	1.23494i
$663$	−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
$668$		−	720.533i		−	1.07864i
$669$	−153.000	+	88.3346i	−0.228700	+	0.132040i
$670$		−	928.379i		−	1.38564i
$671$	168.000	−	96.9948i	0.250373	−	0.144553i
$672$			332.554i			0.494872i
$673$	−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	$0.851531\pi$
$678$	−150.000	−	259.808i	−0.221239	−	0.383197i
$679$	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
$682$	84.0000	+	145.492i	0.123167	+	0.213332i
$683$			795.011i			1.16400i	0.813189	+	0.582000i	$0.197729\pi$
$683$			795.011i			1.16400i	−0.813189	+	0.582000i	$0.802271\pi$
$684$		−	561.184i		−	0.820445i
$685$	676.000			0.986861
$686$	−516.000	+	297.913i	−0.752187	+	0.434275i
$687$	−1230.00			−1.79039
$688$		−	803.672i		−	1.16813i
$689$	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	−0.185166	−	0.982707i	$-0.559282\pi$
$691$	−780.000	−	450.333i	−1.12880	−	0.651712i	−0.943633	+	0.330995i	$0.892616\pi$
$692$	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
$698$	544.000			0.779370
$699$	−97.5000	+	168.875i	−0.139485	+	0.241595i
$700$			124.708i			0.178154i
$701$	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
$706$	−922.000			−1.30595
$707$	60.0000	−	34.6410i	0.0848656	−	0.0489972i
$708$	558.000	+	322.161i	0.788136	+	0.455030i
$709$	−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
$716$	648.000	+	374.123i	0.905028	+	0.522518i
$717$		−	114.315i		−	0.159436i
$718$	918.000	−	530.008i	1.27855	−	0.738172i
$719$		−	124.708i		−	0.173446i	−0.996232	−	0.0867230i	$-0.972360\pi$
$719$		−	124.708i		−	0.173446i	0.996232	−	0.0867230i	$-0.0276395\pi$
$720$	576.000			0.800000
$721$	84.0000			0.116505
$722$	−118.000	−	204.382i	−0.163435	−	0.283078i
$723$	−334.500	−	579.371i	−0.462656	−	0.801343i
$724$	−508.000	+	879.882i	−0.701657	+	1.21531i
$725$	153.000	+	265.004i	0.211034	+	0.365522i
$726$	−78.0000	−	135.100i	−0.107438	−	0.186088i
$727$	705.000	+	407.032i	0.969739	+	0.559879i	0.899157	−	0.437627i	$-0.144181\pi$
$727$	705.000	+	407.032i	0.969739	+	0.559879i	0.0705821	+	0.997506i	$0.477514\pi$
$728$			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
$732$	192.000			0.262295
$733$	−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	$-0.380942\pi$
$734$		−	193.990i		−	0.264291i
$735$	222.000	+	384.515i	0.302041	+	0.523150i
$736$		−	775.959i		−	1.05429i
$737$	−1407.00			−1.90909
$738$	234.000			0.317073
$739$			358.535i			0.485162i	0.970131	+	0.242581i	$0.0779940\pi$
$739$			358.535i			0.485162i	−0.970131	+	0.242581i	$0.922006\pi$
$740$	−256.000			−0.345946
$741$		−	1028.84i		−	1.38845i
$742$		−	360.267i		−	0.485534i
$743$	−345.000	+	199.186i	−0.464334	+	0.268083i	−0.713865	−	0.700284i	$-0.753057\pi$
$743$	−345.000	+	199.186i	−0.464334	+	0.268083i	0.249531	+	0.968367i	$0.419724\pi$
$744$			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
$750$	816.000			1.08800
$751$	966.000	−	557.720i	1.28628	−	0.742637i	0.308295	−	0.951291i	$-0.400241\pi$
$751$	966.000	−	557.720i	1.28628	−	0.742637i	0.977990	+	0.208654i	$0.0669082\pi$
$752$			55.4256i			0.0737043i
$753$	−283.500	−	163.679i	−0.376494	−	0.217369i
$754$	748.000	+	1295.57i	0.992042	+	1.71827i
$755$			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	$0.333091\pi$
$758$	−567.000	+	327.358i	−0.748021	+	0.431870i
$759$	−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	$0.754306\pi$
$762$			1309.43i			1.71841i
$763$	−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	$0.828780\pi$
$770$	−336.000			−0.436364
$771$	1311.00			1.70039
$772$	−268.000			−0.347150
$773$	−1334.00			−1.72574			−0.862872	−	0.505423i	$-0.831337\pi$
$773$	−1334.00			−1.72574			−0.862872	+	0.505423i	$0.831337\pi$
$774$	−783.000	+	452.065i	−1.01163	+	0.584064i
$775$			62.3538i			0.0804566i
$776$	172.000	−	297.913i	0.221649	−	0.383908i
$777$	−144.000	+	83.1384i	−0.185328	+	0.106999i
$778$	−292.000			−0.375321
$779$	−175.500	+	101.325i	−0.225289	+	0.130071i
$780$	1056.00			1.35385
$781$		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
$786$	−1008.00	+	581.969i	−1.28244	+	0.740419i
$787$	−762.000	+	439.941i	−0.968234	+	0.559010i	−0.898697	−	0.438569i	$-0.855485\pi$
$787$	−762.000	+	439.941i	−0.968234	+	0.559010i	−0.0695365	+	0.997579i	$0.522152\pi$
$788$	−536.000	+	928.379i	−0.680203	+	1.17815i
$789$	−819.000	+	472.850i	−1.03802	+	0.599303i
$790$	192.000	−	110.851i	0.243038	−	0.140318i
$791$			173.205i			0.218970i
$792$		−	872.954i		−	1.10221i
$793$	352.000			0.443884
$794$	−488.000	−	845.241i	−0.614610	−	1.06454i
$795$	−624.000			−0.784906
$796$	−108.000	−	62.3538i	−0.135678	−	0.0783340i
$797$	−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
$804$	−1206.00	−	696.284i	−1.50000	−	0.866025i
$805$	168.000	+	290.985i	0.208696	+	0.361471i
$806$			304.841i			0.378215i
$807$	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	$0.401445\pi$
$810$	−324.000	−	561.184i	−0.400000	−	0.692820i
$811$			327.358i			0.403647i	0.979422	+	0.201823i	$0.0646867\pi$
$811$			327.358i			0.403647i	−0.979422	+	0.201823i	$0.935313\pi$
$812$		−	471.118i		−	0.580194i
$813$	810.000	+	467.654i	0.996310	+	0.575220i
$814$			387.979i			0.476633i
$815$	1080.00	−	623.538i	1.32515	−	0.765078i
$816$	528.000			0.647059
$817$	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	0.0304509	−	0.999536i	$-0.490306\pi$
$823$	750.000	−	433.013i	0.911300	−	0.526139i	0.880849	+	0.473397i	$0.156972\pi$
$824$	168.000	−	96.9948i	0.203883	−	0.117712i
$825$		−	327.358i		−	0.396797i
$826$	−186.000	−	322.161i	−0.225182	−	0.390026i
$827$		−	436.477i		−	0.527783i	−0.964552	−	0.263892i	$-0.914994\pi$
$827$		−	436.477i		−	0.527783i	0.964552	−	0.263892i	$-0.0850061\pi$
$828$	−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	$0.642563\pi$
$830$	240.000	−	138.564i	0.289157	−	0.166945i
$831$	−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
$834$	−1017.00	+	587.165i	−1.21942	+	0.704035i
$835$	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	−0.0478645	−	0.998854i	$-0.515242\pi$
$839$	−786.000	−	453.797i	−0.936830	−	0.540879i	−0.888965	+	0.457975i	$0.848575\pi$
$840$	−288.000	−	166.277i	−0.342857	−	0.197949i
$841$	−157.500	−	272.798i	−0.187277	−	0.324373i
$842$	544.000			0.646081
$843$	−327.000	−	566.381i	−0.387900	−	0.671863i
$844$		−	526.543i		−	0.623867i
$845$	1260.00			1.49112
$846$	54.0000	−	31.1769i	0.0638298	−	0.0368521i
$847$			90.0666i			0.106336i
$848$	−416.000	−	720.533i	−0.490566	−	0.849685i
$849$			20.7846i			0.0244813i
$850$	198.000			0.232941
$851$	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	$0.139520\pi$
$858$		−	1600.41i		−	1.86529i
$859$	−73.5000	+	42.4352i	−0.0855646	+	0.0494008i	−0.542172	−	0.840268i	$-0.682398\pi$
$859$	−73.5000	+	42.4352i	−0.0855646	+	0.0494008i	0.456607	+	0.889668i	$0.349064\pi$
$860$	696.000	+	401.836i	0.809302	+	0.467251i
$861$	−117.000	−	67.5500i	−0.135889	−	0.0784553i
$862$	−702.000	+	405.300i	−0.814385	+	0.470185i
$863$			1184.72i			1.37280i	0.727226	+	0.686398i	$0.240809\pi$
$863$			1184.72i			1.37280i	−0.727226	+	0.686398i	$0.759191\pi$
$864$	432.000	−	748.246i	0.500000	−	0.866025i
$865$	−8.00000			−0.00924855
$866$	439.000	+	760.370i	0.506928	+	0.878026i
$867$	−252.000	+	436.477i	−0.290657	+	0.503433i
$868$	48.0000	−	83.1384i	0.0552995	−	0.0957816i
$869$	−168.000	−	290.985i	−0.193326	−	0.334850i
$870$	−816.000			−0.937931
$871$	−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	$0.513655\pi$
$878$		−	1690.48i		−	1.92538i
$879$	−606.000			−0.689420
$880$	−672.000	+	387.979i	−0.763636	+	0.440886i
$881$	142.000			0.161180			0.0805902	−	0.996747i	$-0.474319\pi$
$881$	142.000			0.161180			0.0805902	+	0.996747i	$0.474319\pi$
$882$	666.000			0.755102
$883$			1200.31i			1.35936i	0.733511	+	0.679678i	$0.237880\pi$
$883$			1200.31i			1.35936i	−0.733511	+	0.679678i	$0.762120\pi$
$884$	968.000			1.09502
$885$	−558.000	+	322.161i	−0.630508	+	0.364024i
$886$			661.643i			0.746776i
$887$	546.000	−	315.233i	0.615558	−	0.355393i	−0.159580	−	0.987185i	$-0.551014\pi$
$887$	546.000	−	315.233i	0.615558	−	0.355393i	0.775138	+	0.631792i	$0.217681\pi$
$888$	−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
$894$	390.000	+	675.500i	0.436242	+	0.755593i
$895$	−648.000	+	374.123i	−0.724022	+	0.418014i
$896$		−	443.405i		−	0.494872i
$897$	−1386.00	+	800.207i	−1.54515	+	0.892093i
$898$	47.0000	+	81.4064i	0.0523385	+	0.0906530i
$899$		−	235.559i		−	0.262023i
$900$	162.000	−	280.592i	0.180000	−	0.311769i
$901$	−572.000			−0.634850
$902$	−273.000	+	157.617i	−0.302661	+	0.174741i
$903$	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	0.774358	−	0.632748i	$-0.218073\pi$
$907$	556.500	+	321.295i	0.613561	+	0.354240i	−0.160797	+	0.986988i	$0.551406\pi$
$908$	−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	0.678687	−	0.734428i	$-0.262549\pi$
$911$	348.000	+	200.918i	0.381998	+	0.220547i	−0.296689	+	0.954974i	$0.595883\pi$
$912$			748.246i			0.820445i
$913$	−210.000	−	363.731i	−0.230011	−	0.398391i
$914$	−662.000			−0.724289
$915$	−96.0000	+	166.277i	−0.104918	+	0.181723i
$916$	1640.00			1.79039
$917$	672.000			0.732824
$918$	−297.000	−	514.419i	−0.323529	−	0.560369i
$919$		−	779.423i		−	0.848121i	−0.905634	−	0.424060i	$-0.860604\pi$
$919$		−	779.423i		−	0.848121i	0.905634	−	0.424060i	$-0.139396\pi$
$920$	672.000	+	387.979i	0.730435	+	0.421717i
$921$	−283.500	−	163.679i	−0.307818	−	0.177719i
$922$	1076.00			1.16703
$923$		0			0
$924$	−252.000	+	436.477i	−0.272727	+	0.472377i
$925$	−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
$932$	130.000	−	225.167i	0.139485	−	0.241595i
$933$			820.992i			0.879949i
$934$	1107.00	−	639.127i	1.18522	−	0.684290i
$935$			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	$0.631806\pi$
$938$	402.000	+	696.284i	0.428571	+	0.742307i
$939$	−118.500	−	205.248i	−0.126198	−	0.218581i
$940$	−48.0000	−	27.7128i	−0.0510638	−	0.0294817i
$941$	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	$0.429932\pi$
$942$	−12.0000	−	20.7846i	−0.0127389	−	0.0220643i
$943$	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	0.547532	−	0.836785i	$-0.315567\pi$
$947$	91.5000	+	52.8275i	0.0966209	+	0.0557841i	−0.450911	+	0.892569i	$0.648901\pi$
$948$		−	332.554i		−	0.350795i
$949$	−275.000	−	476.314i	−0.289779	−	0.501911i
$950$			280.592i			0.295360i
$951$	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
$956$			152.420i			0.159436i
$957$			1236.68i			1.29225i
$958$		−	242.487i		−	0.253118i
$959$	−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
$966$	504.000			0.521739
$967$	−303.000	+	174.937i	−0.313340	+	0.180907i	−0.648420	−	0.761283i	$-0.724570\pi$
$967$	−303.000	+	174.937i	−0.313340	+	0.180907i	0.335080	+	0.942190i	$0.391237\pi$
$968$	104.000	+	180.133i	0.107438	+	0.186088i
$969$	445.500	+	257.210i	0.459752	+	0.265438i
$970$	172.000	+	297.913i	0.177320	+	0.307127i
$971$		−	1434.14i		−	1.47697i	−0.674270	−	0.738485i	$-0.735542\pi$
$971$		−	1434.14i		−	1.47697i	0.674270	−	0.738485i	$-0.264458\pi$
$972$	−972.000			−1.00000
$973$	678.000			0.696814
$974$	−702.000	+	405.300i	−0.720739	+	0.416119i
$975$	297.000	−	514.419i	0.304615	−	0.527609i
$976$	−256.000			−0.262295
$977$	−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	$0.858936\pi$
$978$		−	1870.61i		−	1.91269i
$979$	−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	−0.270161	−	0.962815i	$-0.587077\pi$
$983$	−1218.00	−	703.213i	−1.23906	−	0.715374i	−0.968903	+	0.247441i	$0.920410\pi$
$984$	−312.000			−0.317073
$985$	−536.000	−	928.379i	−0.544162	−	0.942517i
$986$	−748.000			−0.758621
$987$	−36.0000			−0.0364742
$988$			1371.78i			1.38845i
$989$	−1218.00			−1.23155
$990$	756.000	+	436.477i	0.763636	+	0.440886i
$991$			249.415i			0.251680i	0.992051	+	0.125840i	$0.0401627\pi$
$991$			249.415i			0.251680i	−0.992051	+	0.125840i	$0.959837\pi$
$992$		−	221.703i		−	0.223490i
$993$	1062.00	−	613.146i	1.06949	−	0.617468i
$994$		0			0
$995$	108.000	−	62.3538i	0.108543	−	0.0626672i
$996$		−	415.692i		−	0.417362i
$997$	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.a.7.1	✓	2
3.2	odd	2		108.3.f.b.19.1		2
4.3	odd	2		36.3.f.b.7.1	yes	2
8.3	odd	2		576.3.o.b.511.1		2
8.5	even	2		576.3.o.a.511.1		2
9.2	odd	6		324.3.d.c.163.1		2
9.4	even	3		36.3.f.b.31.1	yes	2
9.5	odd	6		108.3.f.a.91.1		2
9.7	even	3		324.3.d.b.163.2		2
12.11	even	2		108.3.f.a.19.1		2
24.5	odd	2		1728.3.o.b.127.1		2
24.11	even	2		1728.3.o.a.127.1		2
36.7	odd	6		324.3.d.b.163.1		2
36.11	even	6		324.3.d.c.163.2		2
36.23	even	6		108.3.f.b.91.1		2
36.31	odd	6	inner	36.3.f.a.31.1	yes	2
72.5	odd	6		1728.3.o.a.1279.1		2
72.13	even	6		576.3.o.b.319.1		2
72.59	even	6		1728.3.o.b.1279.1		2
72.67	odd	6		576.3.o.a.319.1		2

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

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.00000 - 3.46410i) q^{5} -6.00000 q^{6} +(3.00000 + 1.73205i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(-2.00000 - 3.46410i) q^{5} -6.00000 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} -6.92820i q^{14} -12.0000 q^{15} +(-8.00000 - 13.8564i) q^{16} -11.0000 q^{17} +(-9.00000 + 15.5885i) q^{18} -15.5885i q^{19} +16.0000 q^{20} +(9.00000 - 5.19615i) q^{21} -24.2487i 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} +(12.0000 + 20.7846i) q^{30} +(-6.00000 + 3.46410i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(31.5000 - 18.1865i) q^{33} +(11.0000 + 19.0526i) q^{34} -13.8564i q^{35} +36.0000 q^{36} -16.0000 q^{37} +(-27.0000 + 15.5885i) 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} -48.0000 q^{48} +(-18.5000 - 32.0429i) q^{49} -18.0000 q^{50} +(-16.5000 + 28.5788i) q^{51} -88.0000 q^{52} +52.0000 q^{53} +(27.0000 + 46.7654i) q^{54} -48.4974i q^{55} +(24.0000 + 13.8564i) q^{56} +(-40.5000 - 23.3827i) q^{57} +68.0000 q^{58} +(46.5000 - 26.8468i) q^{59} +(24.0000 - 41.5692i) 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} +(22.0000 - 38.1051i) q^{68} +72.7461i q^{69} +(-24.0000 + 13.8564i) q^{70} +(-36.0000 - 62.3538i) q^{72} -25.0000 q^{73} +(16.0000 + 27.7128i) q^{74} +(-13.5000 - 23.3827i) q^{75} +(54.0000 + 31.1769i) q^{76} +(21.0000 + 36.3731i) q^{77} +(-66.0000 - 114.315i) 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} +41.5692i q^{84} +(22.0000 + 38.1051i) q^{85} -100.459i q^{86} +(51.0000 + 88.3346i) q^{87} +(84.0000 + 48.4974i) q^{88} -2.00000 q^{89} +72.0000 q^{90} +76.2102i q^{91} -96.9948i q^{92} +20.7846i q^{93} +6.92820i 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})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} + 3 q^{3} - 4 q^{4} - 4 q^{5} - 12 q^{6} + 6 q^{7} + 16 q^{8} - 9 q^{9}+O(q^{10}) \) 2 * q - 2 * q^2 + 3 * q^3 - 4 * q^4 - 4 * q^5 - 12 * q^6 + 6 * q^7 + 16 * q^8 - 9 * q^9	\( 2 q - 2 q^{2} + 3 q^{3} - 4 q^{4} - 4 q^{5} - 12 q^{6} + 6 q^{7} + 16 q^{8} - 9 q^{9} - 8 q^{10} + 21 q^{11} + 12 q^{12} + 22 q^{13} - 24 q^{15} - 16 q^{16} - 22 q^{17} - 18 q^{18} + 32 q^{20} + 18 q^{21} - 42 q^{23} + 24 q^{24} + 9 q^{25} + 44 q^{26} - 54 q^{27} - 24 q^{28} - 34 q^{29} + 24 q^{30} - 12 q^{31} - 32 q^{32} + 63 q^{33} + 22 q^{34} + 72 q^{36} - 32 q^{37} - 54 q^{38} + 132 q^{39} - 32 q^{40} - 13 q^{41} - 36 q^{42} + 87 q^{43} - 84 q^{44} - 36 q^{45} + 84 q^{46} - 6 q^{47} - 96 q^{48} - 37 q^{49} - 36 q^{50} - 33 q^{51} - 176 q^{52} + 104 q^{53} + 54 q^{54} + 48 q^{56} - 81 q^{57} + 136 q^{58} + 93 q^{59} + 48 q^{60} + 16 q^{61} + 24 q^{62} + 128 q^{64} + 88 q^{65} - 126 q^{66} - 201 q^{67} + 44 q^{68} - 48 q^{70} - 72 q^{72} - 50 q^{73} + 32 q^{74} - 27 q^{75} + 108 q^{76} + 42 q^{77} - 132 q^{78} - 48 q^{79} - 64 q^{80} - 81 q^{81} - 26 q^{82} - 60 q^{83} + 44 q^{85} + 102 q^{87} + 168 q^{88} - 4 q^{89} + 144 q^{90} - 108 q^{95} + 96 q^{96} + 43 q^{97} - 74 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 + 3 * q^3 - 4 * q^4 - 4 * q^5 - 12 * q^6 + 6 * q^7 + 16 * q^8 - 9 * q^9 - 8 * q^10 + 21 * q^11 + 12 * q^12 + 22 * q^13 - 24 * q^15 - 16 * q^16 - 22 * q^17 - 18 * q^18 + 32 * q^20 + 18 * q^21 - 42 * q^23 + 24 * q^24 + 9 * q^25 + 44 * q^26 - 54 * q^27 - 24 * q^28 - 34 * q^29 + 24 * q^30 - 12 * q^31 - 32 * q^32 + 63 * q^33 + 22 * q^34 + 72 * q^36 - 32 * q^37 - 54 * q^38 + 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 - 96 * q^48 - 37 * q^49 - 36 * q^50 - 33 * q^51 - 176 * q^52 + 104 * q^53 + 54 * q^54 + 48 * q^56 - 81 * q^57 + 136 * q^58 + 93 * q^59 + 48 * q^60 + 16 * q^61 + 24 * q^62 + 128 * q^64 + 88 * q^65 - 126 * q^66 - 201 * q^67 + 44 * q^68 - 48 * q^70 - 72 * q^72 - 50 * q^73 + 32 * q^74 - 27 * q^75 + 108 * q^76 + 42 * q^77 - 132 * q^78 - 48 * q^79 - 64 * q^80 - 81 * q^81 - 26 * q^82 - 60 * q^83 + 44 * q^85 + 102 * q^87 + 168 * q^88 - 4 * q^89 + 144 * q^90 - 108 * q^95 + 96 * q^96 + 43 * q^97 - 74 * q^98

Introduction

L-functions

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