LMFDB - Embedded newform 21.3.f.a.19.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [21,3,Mod(10,21)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(21, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("21.10");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 21 = 3 \cdot 7 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	21.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:	$0.572208555157$
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			19.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	21.19
Dual form			21.3.f.a.10.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 + 2.59808i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-2.50000 - 4.33013i) q^{4} +(4.50000 + 2.59808i) q^{5} -5.19615i q^{6} +(6.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})$	\(q+(-1.50000 + 2.59808i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-2.50000 - 4.33013i) q^{4} +(4.50000 + 2.59808i) q^{5} -5.19615i q^{6} +(6.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-13.5000 + 7.79423i) q^{10} +(-7.50000 - 12.9904i) q^{11} +(7.50000 + 4.33013i) q^{12} +13.8564i q^{13} +(-3.00000 + 20.7846i) q^{14} -9.00000 q^{15} +(5.50000 - 9.52628i) q^{16} +(9.00000 - 5.19615i) q^{17} +(4.50000 + 7.79423i) q^{18} +(-9.00000 - 5.19615i) q^{19} -25.9808i q^{20} +(-7.50000 + 9.52628i) q^{21} +45.0000 q^{22} +(-4.50000 + 2.59808i) q^{24} +(1.00000 + 1.73205i) q^{25} +(-36.0000 - 20.7846i) q^{26} +5.19615i q^{27} +(-27.5000 - 21.6506i) q^{28} -9.00000 q^{29} +(13.5000 - 23.3827i) q^{30} +(-10.5000 + 6.06218i) q^{31} +(22.5000 + 38.9711i) q^{32} +(22.5000 + 12.9904i) q^{33} +31.1769i q^{34} +(36.0000 + 5.19615i) q^{35} -15.0000 q^{36} +(-5.00000 + 8.66025i) q^{37} +(27.0000 - 15.5885i) q^{38} +(-12.0000 - 20.7846i) q^{39} +(13.5000 + 7.79423i) q^{40} +10.3923i q^{41} +(-13.5000 - 33.7750i) q^{42} -74.0000 q^{43} +(-37.5000 + 64.9519i) q^{44} +(13.5000 - 7.79423i) q^{45} +19.0526i q^{48} +(35.5000 - 33.7750i) q^{49} -6.00000 q^{50} +(-9.00000 + 15.5885i) q^{51} +(60.0000 - 34.6410i) q^{52} +(-16.5000 - 28.5788i) q^{53} +(-13.5000 - 7.79423i) q^{54} -77.9423i q^{55} +(19.5000 - 7.79423i) q^{56} +18.0000 q^{57} +(13.5000 - 23.3827i) q^{58} +(13.5000 - 7.79423i) q^{59} +(22.5000 + 38.9711i) q^{60} +(78.0000 + 45.0333i) q^{61} -36.3731i q^{62} +(3.00000 - 20.7846i) q^{63} -91.0000 q^{64} +(-36.0000 + 62.3538i) q^{65} +(-67.5000 + 38.9711i) q^{66} +(38.0000 + 65.8179i) q^{67} +(-45.0000 - 25.9808i) q^{68} +(-67.5000 + 85.7365i) q^{70} +84.0000 q^{71} +(4.50000 - 7.79423i) q^{72} +(-54.0000 + 31.1769i) q^{73} +(-15.0000 - 25.9808i) q^{74} +(-3.00000 - 1.73205i) q^{75} +51.9615i q^{76} +(-82.5000 - 64.9519i) q^{77} +72.0000 q^{78} +(21.5000 - 37.2391i) q^{79} +(49.5000 - 28.5788i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-27.0000 - 15.5885i) q^{82} +119.512i q^{83} +(60.0000 + 8.66025i) q^{84} +54.0000 q^{85} +(111.000 - 192.258i) q^{86} +(13.5000 - 7.79423i) q^{87} +(-22.5000 - 38.9711i) q^{88} +(-63.0000 - 36.3731i) q^{89} +46.7654i q^{90} +(36.0000 + 90.0666i) q^{91} +(10.5000 - 18.1865i) q^{93} +(-27.0000 - 46.7654i) q^{95} +(-67.5000 - 38.9711i) q^{96} -185.329i q^{97} +(34.5000 + 142.894i) q^{98} -45.0000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} - 3 q^{3} - 5 q^{4} + 9 q^{5} + 13 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) $ 2 * q - 3 * q^2 - 3 * q^3 - 5 * q^4 + 9 * q^5 + 13 * q^7 + 6 * q^8 + 3 * q^9	$ 2 q - 3 q^{2} - 3 q^{3} - 5 q^{4} + 9 q^{5} + 13 q^{7} + 6 q^{8} + 3 q^{9} - 27 q^{10} - 15 q^{11} + 15 q^{12} - 6 q^{14} - 18 q^{15} + 11 q^{16} + 18 q^{17} + 9 q^{18} - 18 q^{19} - 15 q^{21} + 90 q^{22} - 9 q^{24} + 2 q^{25} - 72 q^{26} - 55 q^{28} - 18 q^{29} + 27 q^{30} - 21 q^{31} + 45 q^{32} + 45 q^{33} + 72 q^{35} - 30 q^{36} - 10 q^{37} + 54 q^{38} - 24 q^{39} + 27 q^{40} - 27 q^{42} - 148 q^{43} - 75 q^{44} + 27 q^{45} + 71 q^{49} - 12 q^{50} - 18 q^{51} + 120 q^{52} - 33 q^{53} - 27 q^{54} + 39 q^{56} + 36 q^{57} + 27 q^{58} + 27 q^{59} + 45 q^{60} + 156 q^{61} + 6 q^{63} - 182 q^{64} - 72 q^{65} - 135 q^{66} + 76 q^{67} - 90 q^{68} - 135 q^{70} + 168 q^{71} + 9 q^{72} - 108 q^{73} - 30 q^{74} - 6 q^{75} - 165 q^{77} + 144 q^{78} + 43 q^{79} + 99 q^{80} - 9 q^{81} - 54 q^{82} + 120 q^{84} + 108 q^{85} + 222 q^{86} + 27 q^{87} - 45 q^{88} - 126 q^{89} + 72 q^{91} + 21 q^{93} - 54 q^{95} - 135 q^{96} + 69 q^{98} - 90 q^{99}+O(q^{100}) $ 2 * q - 3 * q^2 - 3 * q^3 - 5 * q^4 + 9 * q^5 + 13 * q^7 + 6 * q^8 + 3 * q^9 - 27 * q^10 - 15 * q^11 + 15 * q^12 - 6 * q^14 - 18 * q^15 + 11 * q^16 + 18 * q^17 + 9 * q^18 - 18 * q^19 - 15 * q^21 + 90 * q^22 - 9 * q^24 + 2 * q^25 - 72 * q^26 - 55 * q^28 - 18 * q^29 + 27 * q^30 - 21 * q^31 + 45 * q^32 + 45 * q^33 + 72 * q^35 - 30 * q^36 - 10 * q^37 + 54 * q^38 - 24 * q^39 + 27 * q^40 - 27 * q^42 - 148 * q^43 - 75 * q^44 + 27 * q^45 + 71 * q^49 - 12 * q^50 - 18 * q^51 + 120 * q^52 - 33 * q^53 - 27 * q^54 + 39 * q^56 + 36 * q^57 + 27 * q^58 + 27 * q^59 + 45 * q^60 + 156 * q^61 + 6 * q^63 - 182 * q^64 - 72 * q^65 - 135 * q^66 + 76 * q^67 - 90 * q^68 - 135 * q^70 + 168 * q^71 + 9 * q^72 - 108 * q^73 - 30 * q^74 - 6 * q^75 - 165 * q^77 + 144 * q^78 + 43 * q^79 + 99 * q^80 - 9 * q^81 - 54 * q^82 + 120 * q^84 + 108 * q^85 + 222 * q^86 + 27 * q^87 - 45 * q^88 - 126 * q^89 + 72 * q^91 + 21 * q^93 - 54 * q^95 - 135 * q^96 + 69 * q^98 - 90 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/21\mathbb{Z}\right)^\times$.

$n$	$8$	$10$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$

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 $

$2$	−1.50000	+	2.59808i	−0.750000	+	1.29904i	0.197822	+	0.980238i	$0.436613\pi$
$2$	−1.50000	+	2.59808i	−0.750000	+	1.29904i	−0.947822	+	0.318800i	$0.896720\pi$
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$3$	−1.50000	+	0.866025i	−0.500000	+	0.288675i
$4$	−2.50000	−	4.33013i	−0.625000	−	1.08253i
$5$	4.50000	+	2.59808i	0.900000	+	0.519615i	0.877200	−	0.480125i	$-0.159409\pi$
$5$	4.50000	+	2.59808i	0.900000	+	0.519615i	0.0227998	+	0.999740i	$0.492742\pi$
$6$		−	5.19615i		−	0.866025i
$7$	6.50000	−	2.59808i	0.928571	−	0.371154i
$7$	6.50000	−	2.59808i	0.928571	−	0.371154i
$8$	3.00000			0.375000
$9$	1.50000	−	2.59808i	0.166667	−	0.288675i
$10$	−13.5000	+	7.79423i	−1.35000	+	0.779423i
$11$	−7.50000	−	12.9904i	−0.681818	−	1.18094i	−0.974425	−	0.224711i	$-0.927856\pi$
$11$	−7.50000	−	12.9904i	−0.681818	−	1.18094i	0.292607	−	0.956233i	$-0.405477\pi$
$12$	7.50000	+	4.33013i	0.625000	+	0.360844i
$13$			13.8564i			1.06588i	0.846154	+	0.532939i	$0.178912\pi$
$13$			13.8564i			1.06588i	−0.846154	+	0.532939i	$0.821088\pi$
$14$	−3.00000	+	20.7846i	−0.214286	+	1.48461i
$15$	−9.00000			−0.600000
$16$	5.50000	−	9.52628i	0.343750	−	0.595392i
$17$	9.00000	−	5.19615i	0.529412	−	0.305656i	−0.211365	−	0.977407i	$-0.567791\pi$
$17$	9.00000	−	5.19615i	0.529412	−	0.305656i	0.740777	+	0.671751i	$0.234458\pi$
$18$	4.50000	+	7.79423i	0.250000	+	0.433013i
$19$	−9.00000	−	5.19615i	−0.473684	−	0.273482i	0.244096	−	0.969751i	$-0.421509\pi$
$19$	−9.00000	−	5.19615i	−0.473684	−	0.273482i	−0.717781	+	0.696269i	$0.754842\pi$
$20$		−	25.9808i		−	1.29904i
$21$	−7.50000	+	9.52628i	−0.357143	+	0.453632i
$22$	45.0000			2.04545
$23$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$23$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$24$	−4.50000	+	2.59808i	−0.187500	+	0.108253i
$25$	1.00000	+	1.73205i	0.0400000	+	0.0692820i
$26$	−36.0000	−	20.7846i	−1.38462	−	0.799408i
$27$			5.19615i			0.192450i
$28$	−27.5000	−	21.6506i	−0.982143	−	0.773237i
$29$	−9.00000			−0.310345			−0.155172	−	0.987887i	$-0.549593\pi$
$29$	−9.00000			−0.310345			−0.155172	+	0.987887i	$0.549593\pi$
$30$	13.5000	−	23.3827i	0.450000	−	0.779423i
$31$	−10.5000	+	6.06218i	−0.338710	+	0.195554i	−0.659701	−	0.751528i	$-0.729317\pi$
$31$	−10.5000	+	6.06218i	−0.338710	+	0.195554i	0.320992	+	0.947082i	$0.395984\pi$
$32$	22.5000	+	38.9711i	0.703125	+	1.21785i
$33$	22.5000	+	12.9904i	0.681818	+	0.393648i
$34$			31.1769i			0.916968i
$35$	36.0000	+	5.19615i	1.02857	+	0.148461i
$36$	−15.0000			−0.416667
$37$	−5.00000	+	8.66025i	−0.135135	+	0.234061i	−0.925649	−	0.378383i	$-0.876480\pi$
$37$	−5.00000	+	8.66025i	−0.135135	+	0.234061i	0.790514	+	0.612444i	$0.209814\pi$
$38$	27.0000	−	15.5885i	0.710526	−	0.410223i
$39$	−12.0000	−	20.7846i	−0.307692	−	0.532939i
$40$	13.5000	+	7.79423i	0.337500	+	0.194856i
$41$			10.3923i			0.253471i	0.991937	+	0.126735i	$0.0404499\pi$
$41$			10.3923i			0.253471i	−0.991937	+	0.126735i	$0.959550\pi$
$42$	−13.5000	−	33.7750i	−0.321429	−	0.804166i
$43$	−74.0000			−1.72093			−0.860465	−	0.509509i	$-0.829827\pi$
$43$	−74.0000			−1.72093			−0.860465	+	0.509509i	$0.829827\pi$
$44$	−37.5000	+	64.9519i	−0.852273	+	1.47618i
$45$	13.5000	−	7.79423i	0.300000	−	0.173205i
$46$		0			0
$47$		0			0		0.500000	−	0.866025i	$-0.333333\pi$
$47$		0			0		−0.500000	+	0.866025i	$0.666667\pi$
$48$			19.0526i			0.396928i
$49$	35.5000	−	33.7750i	0.724490	−	0.689286i
$50$	−6.00000			−0.120000
$51$	−9.00000	+	15.5885i	−0.176471	+	0.305656i
$52$	60.0000	−	34.6410i	1.15385	−	0.666173i
$53$	−16.5000	−	28.5788i	−0.311321	−	0.539223i	0.667328	−	0.744764i	$-0.267438\pi$
$53$	−16.5000	−	28.5788i	−0.311321	−	0.539223i	−0.978649	+	0.205541i	$0.934105\pi$
$54$	−13.5000	−	7.79423i	−0.250000	−	0.144338i
$55$		−	77.9423i		−	1.41713i
$56$	19.5000	−	7.79423i	0.348214	−	0.139183i
$57$	18.0000			0.315789
$58$	13.5000	−	23.3827i	0.232759	−	0.403150i
$59$	13.5000	−	7.79423i	0.228814	−	0.132106i	−0.381211	−	0.924488i	$-0.624493\pi$
$59$	13.5000	−	7.79423i	0.228814	−	0.132106i	0.610025	+	0.792382i	$0.291160\pi$
$60$	22.5000	+	38.9711i	0.375000	+	0.649519i
$61$	78.0000	+	45.0333i	1.27869	+	0.738251i	0.976607	−	0.215031i	$-0.0689853\pi$
$61$	78.0000	+	45.0333i	1.27869	+	0.738251i	0.302081	+	0.953282i	$0.402319\pi$
$62$		−	36.3731i		−	0.586662i
$63$	3.00000	−	20.7846i	0.0476190	−	0.329914i
$64$	−91.0000			−1.42188
$65$	−36.0000	+	62.3538i	−0.553846	+	0.959290i
$66$	−67.5000	+	38.9711i	−1.02273	+	0.590472i
$67$	38.0000	+	65.8179i	0.567164	+	0.982357i	0.996845	+	0.0793762i	$0.0252928\pi$
$67$	38.0000	+	65.8179i	0.567164	+	0.982357i	−0.429681	+	0.902981i	$0.641374\pi$
$68$	−45.0000	−	25.9808i	−0.661765	−	0.382070i
$69$		0			0
$70$	−67.5000	+	85.7365i	−0.964286	+	1.22481i
$71$	84.0000			1.18310			0.591549	−	0.806269i	$-0.298517\pi$
$71$	84.0000			1.18310			0.591549	+	0.806269i	$0.298517\pi$
$72$	4.50000	−	7.79423i	0.0625000	−	0.108253i
$73$	−54.0000	+	31.1769i	−0.739726	+	0.427081i	−0.821970	−	0.569531i	$-0.807125\pi$
$73$	−54.0000	+	31.1769i	−0.739726	+	0.427081i	0.0822437	+	0.996612i	$0.473791\pi$
$74$	−15.0000	−	25.9808i	−0.202703	−	0.351091i
$75$	−3.00000	−	1.73205i	−0.0400000	−	0.0230940i
$76$			51.9615i			0.683704i
$77$	−82.5000	−	64.9519i	−1.07143	−	0.843531i
$78$	72.0000			0.923077
$79$	21.5000	−	37.2391i	0.272152	−	0.471381i	−0.697261	−	0.716818i	$-0.745598\pi$
$79$	21.5000	−	37.2391i	0.272152	−	0.471381i	0.969413	+	0.245437i	$0.0789313\pi$
$80$	49.5000	−	28.5788i	0.618750	−	0.357235i
$81$	−4.50000	−	7.79423i	−0.0555556	−	0.0962250i
$82$	−27.0000	−	15.5885i	−0.329268	−	0.190103i
$83$			119.512i			1.43990i	0.694027	+	0.719949i	$0.255835\pi$
$83$			119.512i			1.43990i	−0.694027	+	0.719949i	$0.744165\pi$
$84$	60.0000	+	8.66025i	0.714286	+	0.103098i
$85$	54.0000			0.635294
$86$	111.000	−	192.258i	1.29070	−	2.23555i
$87$	13.5000	−	7.79423i	0.155172	−	0.0895888i
$88$	−22.5000	−	38.9711i	−0.255682	−	0.442854i
$89$	−63.0000	−	36.3731i	−0.707865	−	0.408686i	0.102405	−	0.994743i	$-0.467346\pi$
$89$	−63.0000	−	36.3731i	−0.707865	−	0.408686i	−0.810270	+	0.586057i	$0.800680\pi$
$90$			46.7654i			0.519615i
$91$	36.0000	+	90.0666i	0.395604	+	0.989743i
$92$		0			0
$93$	10.5000	−	18.1865i	0.112903	−	0.195554i
$94$		0			0
$95$	−27.0000	−	46.7654i	−0.284211	−	0.492267i
$96$	−67.5000	−	38.9711i	−0.703125	−	0.405949i
$97$		−	185.329i		−	1.91061i	−0.295618	−	0.955306i	$-0.595525\pi$
$97$		−	185.329i		−	1.91061i	0.295618	−	0.955306i	$-0.404475\pi$
$98$	34.5000	+	142.894i	0.352041	+	1.45810i
$99$	−45.0000			−0.454545
$100$	5.00000	−	8.66025i	0.0500000	−	0.0866025i
$101$	−126.000	+	72.7461i	−1.24752	+	0.720259i	−0.970615	−	0.240637i	$-0.922644\pi$
$101$	−126.000	+	72.7461i	−1.24752	+	0.720259i	−0.276910	+	0.960896i	$0.589310\pi$
$102$	−27.0000	−	46.7654i	−0.264706	−	0.458484i
$103$	−60.0000	−	34.6410i	−0.582524	−	0.336321i	0.179612	−	0.983738i	$-0.442516\pi$
$103$	−60.0000	−	34.6410i	−0.582524	−	0.336321i	−0.762136	+	0.647417i	$0.775849\pi$
$104$			41.5692i			0.399704i
$105$	−58.5000	+	23.3827i	−0.557143	+	0.222692i
$106$	99.0000			0.933962
$107$	−46.5000	+	80.5404i	−0.434579	+	0.752714i	−0.997261	−	0.0739599i	$-0.976436\pi$
$107$	−46.5000	+	80.5404i	−0.434579	+	0.752714i	0.562682	+	0.826674i	$0.309770\pi$
$108$	22.5000	−	12.9904i	0.208333	−	0.120281i
$109$	4.00000	+	6.92820i	0.0366972	+	0.0635615i	0.883791	−	0.467882i	$-0.154983\pi$
$109$	4.00000	+	6.92820i	0.0366972	+	0.0635615i	−0.847093	+	0.531444i	$0.821650\pi$
$110$	202.500	+	116.913i	1.84091	+	1.06285i
$111$		−	17.3205i		−	0.156041i
$112$	11.0000	−	76.2102i	0.0982143	−	0.680449i
$113$	42.0000			0.371681			0.185841	−	0.982580i	$-0.440499\pi$
$113$	42.0000			0.371681			0.185841	+	0.982580i	$0.440499\pi$
$114$	−27.0000	+	46.7654i	−0.236842	+	0.410223i
$115$		0			0
$116$	22.5000	+	38.9711i	0.193966	+	0.335958i
$117$	36.0000	+	20.7846i	0.307692	+	0.177646i
$118$			46.7654i			0.396317i
$119$	45.0000	−	57.1577i	0.378151	−	0.480317i
$120$	−27.0000			−0.225000
$121$	−52.0000	+	90.0666i	−0.429752	+	0.744352i
$122$	−234.000	+	135.100i	−1.91803	+	1.10738i
$123$	−9.00000	−	15.5885i	−0.0731707	−	0.126735i
$124$	52.5000	+	30.3109i	0.423387	+	0.244443i
$125$		−	119.512i		−	0.956092i
$126$	49.5000	+	38.9711i	0.392857	+	0.309295i
$127$	35.0000			0.275591			0.137795	−	0.990461i	$-0.455998\pi$
$127$	35.0000			0.275591			0.137795	+	0.990461i	$0.455998\pi$
$128$	46.5000	−	80.5404i	0.363281	−	0.629222i
$129$	111.000	−	64.0859i	0.860465	−	0.496790i
$130$	−108.000	−	187.061i	−0.830769	−	1.43893i
$131$	148.500	+	85.7365i	1.13359	+	0.654477i	0.944835	−	0.327547i	$-0.106222\pi$
$131$	148.500	+	85.7365i	1.13359	+	0.654477i	0.188753	+	0.982025i	$0.439555\pi$
$132$		−	129.904i		−	0.984120i
$133$	−72.0000	−	10.3923i	−0.541353	−	0.0781376i
$134$	−228.000			−1.70149
$135$	−13.5000	+	23.3827i	−0.100000	+	0.173205i
$136$	27.0000	−	15.5885i	0.198529	−	0.114621i
$137$	48.0000	+	83.1384i	0.350365	+	0.606850i	0.986313	−	0.164882i	$-0.0527242\pi$
$137$	48.0000	+	83.1384i	0.350365	+	0.606850i	−0.635948	+	0.771732i	$0.719391\pi$
$138$		0			0
$139$			183.597i			1.32084i	0.750894	+	0.660422i	$0.229623\pi$
$139$			183.597i			1.32084i	−0.750894	+	0.660422i	$0.770377\pi$
$140$	−67.5000	−	168.875i	−0.482143	−	1.20625i
$141$		0			0
$142$	−126.000	+	218.238i	−0.887324	+	1.53689i
$143$	180.000	−	103.923i	1.25874	−	0.726735i
$144$	−16.5000	−	28.5788i	−0.114583	−	0.198464i
$145$	−40.5000	−	23.3827i	−0.279310	−	0.161260i
$146$		−	187.061i		−	1.28124i
$147$	−24.0000	+	81.4064i	−0.163265	+	0.553785i
$148$	50.0000			0.337838
$149$	93.0000	−	161.081i	0.624161	−	1.08108i	−0.364541	−	0.931187i	$-0.618774\pi$
$149$	93.0000	−	161.081i	0.624161	−	1.08108i	0.988702	−	0.149892i	$-0.0478924\pi$
$150$	9.00000	−	5.19615i	0.0600000	−	0.0346410i
$151$	−39.5000	−	68.4160i	−0.261589	−	0.453086i	0.705075	−	0.709133i	$-0.250913\pi$
$151$	−39.5000	−	68.4160i	−0.261589	−	0.453086i	−0.966664	+	0.256047i	$0.917580\pi$
$152$	−27.0000	−	15.5885i	−0.177632	−	0.102556i
$153$		−	31.1769i		−	0.203771i
$154$	292.500	−	116.913i	1.89935	−	0.759178i
$155$	−63.0000			−0.406452
$156$	−60.0000	+	103.923i	−0.384615	+	0.666173i
$157$	−18.0000	+	10.3923i	−0.114650	+	0.0661930i	−0.556228	−	0.831030i	$-0.687752\pi$
$157$	−18.0000	+	10.3923i	−0.114650	+	0.0661930i	0.441579	+	0.897223i	$0.354419\pi$
$158$	64.5000	+	111.717i	0.408228	+	0.707071i
$159$	49.5000	+	28.5788i	0.311321	+	0.179741i
$160$			233.827i			1.46142i
$161$		0			0
$162$	27.0000			0.166667
$163$	104.000	−	180.133i	0.638037	−	1.10511i	−0.347826	−	0.937559i	$-0.613080\pi$
$163$	104.000	−	180.133i	0.638037	−	1.10511i	0.985863	−	0.167553i	$-0.0535866\pi$
$164$	45.0000	−	25.9808i	0.274390	−	0.158419i
$165$	67.5000	+	116.913i	0.409091	+	0.708566i
$166$	−310.500	−	179.267i	−1.87048	−	1.07992i
$167$			249.415i			1.49350i	0.665102	+	0.746752i	$0.268388\pi$
$167$			249.415i			1.49350i	−0.665102	+	0.746752i	$0.731612\pi$
$168$	−22.5000	+	28.5788i	−0.133929	+	0.170112i
$169$	−23.0000			−0.136095
$170$	−81.0000	+	140.296i	−0.476471	+	0.825271i
$171$	−27.0000	+	15.5885i	−0.157895	+	0.0911606i
$172$	185.000	+	320.429i	1.07558	+	1.86296i
$173$	−198.000	−	114.315i	−1.14451	−	0.660782i	−0.196966	−	0.980410i	$-0.563109\pi$
$173$	−198.000	−	114.315i	−1.14451	−	0.660782i	−0.947543	+	0.319628i	$0.896442\pi$
$174$			46.7654i			0.268767i
$175$	11.0000	+	8.66025i	0.0628571	+	0.0494872i
$176$	−165.000			−0.937500
$177$	−13.5000	+	23.3827i	−0.0762712	+	0.132106i
$178$	189.000	−	109.119i	1.06180	−	0.613029i
$179$	−45.0000	−	77.9423i	−0.251397	−	0.435432i	0.712514	−	0.701658i	$-0.247557\pi$
$179$	−45.0000	−	77.9423i	−0.251397	−	0.435432i	−0.963911	+	0.266226i	$0.914223\pi$
$180$	−67.5000	−	38.9711i	−0.375000	−	0.216506i
$181$			10.3923i			0.0574160i	0.999588	+	0.0287080i	$0.00913930\pi$
$181$			10.3923i			0.0574160i	−0.999588	+	0.0287080i	$0.990861\pi$
$182$	−288.000	−	41.5692i	−1.58242	−	0.228402i
$183$	−156.000			−0.852459
$184$		0			0
$185$	−45.0000	+	25.9808i	−0.243243	+	0.140437i
$186$	31.5000	+	54.5596i	0.169355	+	0.293331i
$187$	−135.000	−	77.9423i	−0.721925	−	0.416804i
$188$		0			0
$189$	13.5000	+	33.7750i	0.0714286	+	0.178704i
$190$	162.000			0.852632
$191$	156.000	−	270.200i	0.816754	−	1.41466i	−0.0913077	−	0.995823i	$-0.529105\pi$
$191$	156.000	−	270.200i	0.816754	−	1.41466i	0.908062	−	0.418837i	$-0.137562\pi$
$192$	136.500	−	78.8083i	0.710938	−	0.410460i
$193$	92.5000	+	160.215i	0.479275	+	0.830128i	0.999717	−	0.0237685i	$-0.00756646\pi$
$193$	92.5000	+	160.215i	0.479275	+	0.830128i	−0.520443	+	0.853896i	$0.674233\pi$
$194$	481.500	+	277.994i	2.48196	+	1.43296i
$195$		−	124.708i		−	0.639526i
$196$	−235.000	−	69.2820i	−1.19898	−	0.353480i
$197$	330.000			1.67513			0.837563	−	0.546340i	$-0.183979\pi$
$197$	330.000			1.67513			0.837563	+	0.546340i	$0.183979\pi$
$198$	67.5000	−	116.913i	0.340909	−	0.590472i
$199$	6.00000	−	3.46410i	0.0301508	−	0.0174075i	−0.484849	−	0.874598i	$-0.661125\pi$
$199$	6.00000	−	3.46410i	0.0301508	−	0.0174075i	0.515000	+	0.857190i	$0.327792\pi$
$200$	3.00000	+	5.19615i	0.0150000	+	0.0259808i
$201$	−114.000	−	65.8179i	−0.567164	−	0.327452i
$202$		−	436.477i		−	2.16078i
$203$	−58.5000	+	23.3827i	−0.288177	+	0.115186i
$204$	90.0000			0.441176
$205$	−27.0000	+	46.7654i	−0.131707	+	0.228124i
$206$	180.000	−	103.923i	0.873786	−	0.504481i
$207$		0			0
$208$	132.000	+	76.2102i	0.634615	+	0.366395i
$209$			155.885i			0.745859i
$210$	27.0000	−	187.061i	0.128571	−	0.890769i
$211$	−248.000			−1.17536			−0.587678	−	0.809095i	$-0.699958\pi$
$211$	−248.000			−1.17536			−0.587678	+	0.809095i	$0.699958\pi$
$212$	−82.5000	+	142.894i	−0.389151	+	0.674029i
$213$	−126.000	+	72.7461i	−0.591549	+	0.341531i
$214$	−139.500	−	241.621i	−0.651869	−	1.12907i
$215$	−333.000	−	192.258i	−1.54884	−	0.894222i
$216$			15.5885i			0.0721688i
$217$	−52.5000	+	66.6840i	−0.241935	+	0.307299i
$218$	−24.0000			−0.110092
$219$	54.0000	−	93.5307i	0.246575	−	0.427081i
$220$	−337.500	+	194.856i	−1.53409	+	0.885708i
$221$	72.0000	+	124.708i	0.325792	+	0.564288i
$222$	45.0000	+	25.9808i	0.202703	+	0.117030i
$223$			192.258i			0.862142i	0.902318	+	0.431071i	$0.141864\pi$
$223$			192.258i			0.862142i	−0.902318	+	0.431071i	$0.858136\pi$
$224$	247.500	+	194.856i	1.10491	+	0.869892i
$225$	6.00000			0.0266667
$226$	−63.0000	+	109.119i	−0.278761	+	0.482828i
$227$	−76.5000	+	44.1673i	−0.337004	+	0.194570i	−0.658947	−	0.752190i	$-0.728998\pi$
$227$	−76.5000	+	44.1673i	−0.337004	+	0.194570i	0.321942	+	0.946759i	$0.395664\pi$
$228$	−45.0000	−	77.9423i	−0.197368	−	0.341852i
$229$	285.000	+	164.545i	1.24454	+	0.718536i	0.970015	−	0.243043i	$-0.0781457\pi$
$229$	285.000	+	164.545i	1.24454	+	0.718536i	0.274526	+	0.961580i	$0.411479\pi$
$230$		0			0
$231$	180.000	+	25.9808i	0.779221	+	0.112471i
$232$	−27.0000			−0.116379
$233$	−135.000	+	233.827i	−0.579399	+	1.00355i	0.416149	+	0.909296i	$0.363379\pi$
$233$	−135.000	+	233.827i	−0.579399	+	1.00355i	−0.995548	+	0.0942524i	$0.969954\pi$
$234$	−108.000	+	62.3538i	−0.461538	+	0.266469i
$235$		0			0
$236$	−67.5000	−	38.9711i	−0.286017	−	0.165132i
$237$			74.4782i			0.314254i
$238$	81.0000	+	202.650i	0.340336	+	0.851470i
$239$	−228.000			−0.953975			−0.476987	−	0.878910i	$-0.658271\pi$
$239$	−228.000			−0.953975			−0.476987	+	0.878910i	$0.658271\pi$
$240$	−49.5000	+	85.7365i	−0.206250	+	0.357235i
$241$	385.500	−	222.569i	1.59959	−	0.923521i	0.608018	−	0.793923i	$-0.291965\pi$
$241$	385.500	−	222.569i	1.59959	−	0.923521i	0.991567	−	0.129598i	$-0.0413687\pi$
$242$	−156.000	−	270.200i	−0.644628	−	1.11653i
$243$	13.5000	+	7.79423i	0.0555556	+	0.0320750i
$244$		−	450.333i		−	1.84563i
$245$	247.500	−	59.7558i	1.01020	−	0.243901i
$246$	54.0000			0.219512
$247$	72.0000	−	124.708i	0.291498	−	0.504889i
$248$	−31.5000	+	18.1865i	−0.127016	+	0.0733328i
$249$	−103.500	−	179.267i	−0.415663	−	0.719949i
$250$	310.500	+	179.267i	1.24200	+	0.717069i
$251$			5.19615i			0.0207018i	0.999946	+	0.0103509i	$0.00329485\pi$
$251$			5.19615i			0.0207018i	−0.999946	+	0.0103509i	$0.996705\pi$
$252$	−97.5000	+	38.9711i	−0.386905	+	0.154647i
$253$		0			0
$254$	−52.5000	+	90.9327i	−0.206693	+	0.358003i
$255$	−81.0000	+	46.7654i	−0.317647	+	0.183394i
$256$	−42.5000	−	73.6122i	−0.166016	−	0.287547i
$257$	99.0000	+	57.1577i	0.385214	+	0.222403i	0.680084	−	0.733134i	$-0.261943\pi$
$257$	99.0000	+	57.1577i	0.385214	+	0.222403i	−0.294870	+	0.955537i	$0.595276\pi$
$258$			384.515i			1.49037i
$259$	−10.0000	+	69.2820i	−0.0386100	+	0.267498i
$260$	360.000			1.38462
$261$	−13.5000	+	23.3827i	−0.0517241	+	0.0895888i
$262$	−445.500	+	257.210i	−1.70038	+	0.981716i
$263$	−93.0000	−	161.081i	−0.353612	−	0.612474i	0.633267	−	0.773933i	$-0.281713\pi$
$263$	−93.0000	−	161.081i	−0.353612	−	0.612474i	−0.986879	+	0.161459i	$0.948380\pi$
$264$	67.5000	+	38.9711i	0.255682	+	0.147618i
$265$		−	171.473i		−	0.647068i
$266$	135.000	−	171.473i	0.507519	−	0.644635i
$267$	126.000			0.471910
$268$	190.000	−	329.090i	0.708955	−	1.22795i
$269$	−292.500	+	168.875i	−1.08736	+	0.627788i	−0.932873	−	0.360207i	$-0.882706\pi$
$269$	−292.500	+	168.875i	−1.08736	+	0.627788i	−0.154488	+	0.987995i	$0.549373\pi$
$270$	−40.5000	−	70.1481i	−0.150000	−	0.259808i
$271$	79.5000	+	45.8993i	0.293358	+	0.169370i	0.639455	−	0.768828i	$-0.279160\pi$
$271$	79.5000	+	45.8993i	0.293358	+	0.169370i	−0.346097	+	0.938199i	$0.612493\pi$
$272$		−	114.315i		−	0.420277i
$273$	−132.000	−	103.923i	−0.483516	−	0.380671i
$274$	−288.000			−1.05109
$275$	15.0000	−	25.9808i	0.0545455	−	0.0944755i
$276$		0			0
$277$	−190.000	−	329.090i	−0.685921	−	1.18805i	−0.973147	−	0.230186i	$-0.926066\pi$
$277$	−190.000	−	329.090i	−0.685921	−	1.18805i	0.287226	−	0.957863i	$-0.407267\pi$
$278$	−477.000	−	275.396i	−1.71583	−	0.990633i
$279$			36.3731i			0.130369i
$280$	108.000	+	15.5885i	0.385714	+	0.0556731i
$281$	300.000			1.06762			0.533808	−	0.845606i	$-0.320761\pi$
$281$	300.000			1.06762			0.533808	+	0.845606i	$0.320761\pi$
$282$		0			0
$283$	177.000	−	102.191i	0.625442	−	0.361099i	−0.153543	−	0.988142i	$-0.549068\pi$
$283$	177.000	−	102.191i	0.625442	−	0.361099i	0.778985	+	0.627043i	$0.215735\pi$
$284$	−210.000	−	363.731i	−0.739437	−	1.28074i
$285$	81.0000	+	46.7654i	0.284211	+	0.164089i
$286$			623.538i			2.18020i
$287$	27.0000	+	67.5500i	0.0940767	+	0.235366i
$288$	135.000			0.468750
$289$	−90.5000	+	156.751i	−0.313149	+	0.542390i
$290$	121.500	−	70.1481i	0.418966	−	0.241890i
$291$	160.500	+	277.994i	0.551546	+	0.955306i
$292$	270.000	+	155.885i	0.924658	+	0.533851i
$293$		−	545.596i		−	1.86210i	−0.364889	−	0.931051i	$-0.618893\pi$
$293$		−	545.596i		−	1.86210i	0.364889	−	0.931051i	$-0.381107\pi$
$294$	−175.500	−	184.463i	−0.596939	−	0.627427i
$295$	81.0000			0.274576
$296$	−15.0000	+	25.9808i	−0.0506757	+	0.0877728i
$297$	67.5000	−	38.9711i	0.227273	−	0.131216i
$298$	279.000	+	483.242i	0.936242	+	1.62162i
$299$		0			0
$300$			17.3205i			0.0577350i
$301$	−481.000	+	192.258i	−1.59801	+	0.638730i
$302$	237.000			0.784768
$303$	126.000	−	218.238i	0.415842	−	0.720259i
$304$	−99.0000	+	57.1577i	−0.325658	+	0.188019i
$305$	234.000	+	405.300i	0.767213	+	1.32885i
$306$	81.0000	+	46.7654i	0.264706	+	0.152828i
$307$		−	173.205i		−	0.564186i	−0.959387	−	0.282093i	$-0.908971\pi$
$307$		−	173.205i		−	0.564186i	0.959387	−	0.282093i	$-0.0910287\pi$
$308$	−75.0000	+	519.615i	−0.243506	+	1.68706i
$309$	120.000			0.388350
$310$	94.5000	−	163.679i	0.304839	−	0.527996i
$311$	−153.000	+	88.3346i	−0.491961	+	0.284034i	−0.725388	−	0.688340i	$-0.758340\pi$
$311$	−153.000	+	88.3346i	−0.491961	+	0.284034i	0.233426	+	0.972374i	$0.425006\pi$
$312$	−36.0000	−	62.3538i	−0.115385	−	0.199852i
$313$	−184.500	−	106.521i	−0.589457	−	0.340323i	0.175426	−	0.984493i	$-0.443870\pi$
$313$	−184.500	−	106.521i	−0.589457	−	0.340323i	−0.764883	+	0.644170i	$0.777203\pi$
$314$		−	62.3538i		−	0.198579i
$315$	67.5000	−	85.7365i	0.214286	−	0.272179i
$316$	−215.000			−0.680380
$317$	−58.5000	+	101.325i	−0.184543	+	0.319637i	−0.943422	−	0.331594i	$-0.892414\pi$
$317$	−58.5000	+	101.325i	−0.184543	+	0.319637i	0.758880	+	0.651231i	$0.225747\pi$
$318$	−148.500	+	85.7365i	−0.466981	+	0.269612i
$319$	67.5000	+	116.913i	0.211599	+	0.366500i
$320$	−409.500	−	236.425i	−1.27969	−	0.738828i
$321$		−	161.081i		−	0.501809i
$322$		0			0
$323$	−108.000			−0.334365
$324$	−22.5000	+	38.9711i	−0.0694444	+	0.120281i
$325$	−24.0000	+	13.8564i	−0.0738462	+	0.0426351i
$326$	312.000	+	540.400i	0.957055	+	1.65767i
$327$	−12.0000	−	6.92820i	−0.0366972	−	0.0211872i
$328$			31.1769i			0.0950516i
$329$		0			0
$330$	−405.000			−1.22727
$331$	−20.0000	+	34.6410i	−0.0604230	+	0.104656i	−0.894655	−	0.446759i	$-0.852578\pi$
$331$	−20.0000	+	34.6410i	−0.0604230	+	0.104656i	0.834232	+	0.551414i	$0.185912\pi$
$332$	517.500	−	298.779i	1.55873	−	0.899936i
$333$	15.0000	+	25.9808i	0.0450450	+	0.0780203i
$334$	−648.000	−	374.123i	−1.94012	−	1.12013i
$335$			394.908i			1.17883i
$336$	49.5000	+	123.842i	0.147321	+	0.368576i
$337$	91.0000			0.270030			0.135015	−	0.990844i	$-0.456892\pi$
$337$	91.0000			0.270030			0.135015	+	0.990844i	$0.456892\pi$
$338$	34.5000	−	59.7558i	0.102071	−	0.176792i
$339$	−63.0000	+	36.3731i	−0.185841	+	0.107295i
$340$	−135.000	−	233.827i	−0.397059	−	0.687726i
$341$	157.500	+	90.9327i	0.461877	+	0.266665i
$342$		−	93.5307i		−	0.273482i
$343$	143.000	−	311.769i	0.416910	−	0.908948i
$344$	−222.000			−0.645349
$345$		0			0
$346$	594.000	−	342.946i	1.71676	−	0.991174i
$347$	−105.000	−	181.865i	−0.302594	−	0.524108i	0.674129	−	0.738614i	$-0.264519\pi$
$347$	−105.000	−	181.865i	−0.302594	−	0.524108i	−0.976723	+	0.214506i	$0.931186\pi$
$348$	−67.5000	−	38.9711i	−0.193966	−	0.111986i
$349$			304.841i			0.873470i	0.899590	+	0.436735i	$0.143865\pi$
$349$			304.841i			0.873470i	−0.899590	+	0.436735i	$0.856135\pi$
$350$	−39.0000	+	15.5885i	−0.111429	+	0.0445384i
$351$	−72.0000			−0.205128
$352$	337.500	−	584.567i	0.958807	−	1.66070i
$353$	342.000	−	197.454i	0.968839	−	0.559359i	0.0699566	−	0.997550i	$-0.477714\pi$
$353$	342.000	−	197.454i	0.968839	−	0.559359i	0.898882	+	0.438191i	$0.144381\pi$
$354$	−40.5000	−	70.1481i	−0.114407	−	0.198158i
$355$	378.000	+	218.238i	1.06479	+	0.614756i
$356$			363.731i			1.02172i
$357$	−18.0000	+	124.708i	−0.0504202	+	0.349321i
$358$	270.000			0.754190
$359$	−246.000	+	426.084i	−0.685237	+	1.18686i	0.288126	+	0.957593i	$0.406968\pi$
$359$	−246.000	+	426.084i	−0.685237	+	1.18686i	−0.973362	+	0.229272i	$0.926365\pi$
$360$	40.5000	−	23.3827i	0.112500	−	0.0649519i
$361$	−126.500	−	219.104i	−0.350416	−	0.606937i
$362$	−27.0000	−	15.5885i	−0.0745856	−	0.0430620i
$363$		−	180.133i		−	0.496235i
$364$	300.000	−	381.051i	0.824176	−	1.04684i
$365$	−324.000			−0.887671
$366$	234.000	−	405.300i	0.639344	−	1.10738i
$367$	−283.500	+	163.679i	−0.772480	+	0.445991i	−0.833758	−	0.552129i	$-0.813815\pi$
$367$	−283.500	+	163.679i	−0.772480	+	0.445991i	0.0612789	+	0.998121i	$0.480482\pi$
$368$		0			0
$369$	27.0000	+	15.5885i	0.0731707	+	0.0422451i
$370$		−	155.885i		−	0.421310i
$371$	−181.500	−	142.894i	−0.489218	−	0.385160i
$372$	−105.000			−0.282258
$373$	−85.0000	+	147.224i	−0.227882	+	0.394703i	−0.957180	−	0.289493i	$-0.906513\pi$
$373$	−85.0000	+	147.224i	−0.227882	+	0.394703i	0.729298	+	0.684196i	$0.239847\pi$
$374$	405.000	−	233.827i	1.08289	−	0.625206i
$375$	103.500	+	179.267i	0.276000	+	0.478046i
$376$		0			0
$377$		−	124.708i		−	0.330790i
$378$	−108.000	−	15.5885i	−0.285714	−	0.0412393i
$379$	82.0000			0.216359			0.108179	−	0.994131i	$-0.465498\pi$
$379$	82.0000			0.216359			0.108179	+	0.994131i	$0.465498\pi$
$380$	−135.000	+	233.827i	−0.355263	+	0.615334i
$381$	−52.5000	+	30.3109i	−0.137795	+	0.0795561i
$382$	468.000	+	810.600i	1.22513	+	2.12199i
$383$	189.000	+	109.119i	0.493473	+	0.284907i	0.726014	−	0.687680i	$-0.241371\pi$
$383$	189.000	+	109.119i	0.493473	+	0.284907i	−0.232541	+	0.972587i	$0.574704\pi$
$384$			161.081i			0.419481i
$385$	−202.500	−	506.625i	−0.525974	−	1.31591i
$386$	−555.000			−1.43782
$387$	−111.000	+	192.258i	−0.286822	+	0.496790i
$388$	−802.500	+	463.324i	−2.06830	+	1.19413i
$389$	−153.000	−	265.004i	−0.393316	−	0.681244i	0.599568	−	0.800323i	$-0.295339\pi$
$389$	−153.000	−	265.004i	−0.393316	−	0.681244i	−0.992885	+	0.119080i	$0.962006\pi$
$390$	324.000	+	187.061i	0.830769	+	0.479645i
$391$		0			0
$392$	106.500	−	101.325i	0.271684	−	0.258482i
$393$	−297.000			−0.755725
$394$	−495.000	+	857.365i	−1.25635	+	2.17605i
$395$	193.500	−	111.717i	0.489873	−	0.282829i
$396$	112.500	+	194.856i	0.284091	+	0.492060i
$397$	−222.000	−	128.172i	−0.559194	−	0.322851i	0.193628	−	0.981075i	$-0.437975\pi$
$397$	−222.000	−	128.172i	−0.559194	−	0.322851i	−0.752822	+	0.658224i	$0.771308\pi$
$398$			20.7846i			0.0522226i
$399$	117.000	−	46.7654i	0.293233	−	0.117206i
$400$	22.0000			0.0550000
$401$	−66.0000	+	114.315i	−0.164589	+	0.285076i	−0.936509	−	0.350643i	$-0.885963\pi$
$401$	−66.0000	+	114.315i	−0.164589	+	0.285076i	0.771921	+	0.635719i	$0.219296\pi$
$402$	342.000	−	197.454i	0.850746	−	0.491179i
$403$	−84.0000	−	145.492i	−0.208437	−	0.361023i
$404$	630.000	+	363.731i	1.55941	+	0.900323i
$405$		−	46.7654i		−	0.115470i
$406$	27.0000	−	187.061i	0.0665025	−	0.460743i
$407$	150.000			0.368550
$408$	−27.0000	+	46.7654i	−0.0661765	+	0.114621i
$409$	−313.500	+	180.999i	−0.766504	+	0.442541i	−0.831626	−	0.555336i	$-0.812590\pi$
$409$	−313.500	+	180.999i	−0.766504	+	0.442541i	0.0651223	+	0.997877i	$0.479256\pi$
$410$	−81.0000	−	140.296i	−0.197561	−	0.342186i
$411$	−144.000	−	83.1384i	−0.350365	−	0.202283i
$412$			346.410i			0.840801i
$413$	67.5000	−	85.7365i	0.163438	−	0.207594i
$414$		0			0
$415$	−310.500	+	537.802i	−0.748193	+	1.29591i
$416$	−540.000	+	311.769i	−1.29808	+	0.749445i
$417$	−159.000	−	275.396i	−0.381295	−	0.660422i
$418$	−405.000	−	233.827i	−0.968900	−	0.559394i
$419$		−	644.323i		−	1.53776i	−0.639391	−	0.768882i	$-0.720813\pi$
$419$		−	644.323i		−	1.53776i	0.639391	−	0.768882i	$-0.279187\pi$
$420$	247.500	+	194.856i	0.589286	+	0.463942i
$421$	752.000			1.78622			0.893112	−	0.449835i	$-0.148517\pi$
$421$	752.000			1.78622			0.893112	+	0.449835i	$0.148517\pi$
$422$	372.000	−	644.323i	0.881517	−	1.52683i
$423$		0			0
$424$	−49.5000	−	85.7365i	−0.116745	−	0.202209i
$425$	18.0000	+	10.3923i	0.0423529	+	0.0244525i
$426$		−	436.477i		−	1.02459i
$427$	624.000	+	90.0666i	1.46136	+	0.210929i
$428$	465.000			1.08645
$429$	−180.000	+	311.769i	−0.419580	+	0.726735i
$430$	999.000	−	576.773i	2.32326	−	1.34133i
$431$	−81.0000	−	140.296i	−0.187935	−	0.325513i	0.756627	−	0.653847i	$-0.226846\pi$
$431$	−81.0000	−	140.296i	−0.187935	−	0.325513i	−0.944562	+	0.328334i	$0.893513\pi$
$432$	49.5000	+	28.5788i	0.114583	+	0.0661547i
$433$			339.482i			0.784023i	0.919960	+	0.392011i	$0.128221\pi$
$433$			339.482i			0.784023i	−0.919960	+	0.392011i	$0.871779\pi$
$434$	−94.5000	−	236.425i	−0.217742	−	0.544758i
$435$	81.0000			0.186207
$436$	20.0000	−	34.6410i	0.0458716	−	0.0794519i
$437$		0			0
$438$	162.000	+	280.592i	0.369863	+	0.640622i
$439$	337.500	+	194.856i	0.768793	+	0.443863i	0.832444	−	0.554110i	$-0.186941\pi$
$439$	337.500	+	194.856i	0.768793	+	0.443863i	−0.0636511	+	0.997972i	$0.520274\pi$
$440$		−	233.827i		−	0.531425i
$441$	−34.5000	−	142.894i	−0.0782313	−	0.324023i
$442$	−432.000			−0.977376
$443$	148.500	−	257.210i	0.335214	−	0.580608i	−0.648312	−	0.761375i	$-0.724525\pi$
$443$	148.500	−	257.210i	0.335214	−	0.580608i	0.983526	+	0.180767i	$0.0578579\pi$
$444$	−75.0000	+	43.3013i	−0.168919	+	0.0975254i
$445$	−189.000	−	327.358i	−0.424719	−	0.735635i
$446$	−499.500	−	288.386i	−1.11996	−	0.646606i
$447$			322.161i			0.720719i
$448$	−591.500	+	236.425i	−1.32031	+	0.527734i
$449$	−492.000			−1.09577			−0.547884	−	0.836554i	$-0.684567\pi$
$449$	−492.000			−1.09577			−0.547884	+	0.836554i	$0.684567\pi$
$450$	−9.00000	+	15.5885i	−0.0200000	+	0.0346410i
$451$	135.000	−	77.9423i	0.299335	−	0.172821i
$452$	−105.000	−	181.865i	−0.232301	−	0.402357i
$453$	118.500	+	68.4160i	0.261589	+	0.151029i
$454$		−	265.004i		−	0.583709i
$455$	−72.0000	+	498.831i	−0.158242	+	1.09633i
$456$	54.0000			0.118421
$457$	221.500	−	383.649i	0.484683	−	0.839495i	−0.515162	−	0.857093i	$-0.672268\pi$
$457$	221.500	−	383.649i	0.484683	−	0.839495i	0.999845	+	0.0175975i	$0.00560174\pi$
$458$	−855.000	+	493.634i	−1.86681	+	1.07780i
$459$	27.0000	+	46.7654i	0.0588235	+	0.101885i
$460$		0			0
$461$		−	415.692i		−	0.901718i	−0.892595	−	0.450859i	$-0.851118\pi$
$461$		−	415.692i		−	0.901718i	0.892595	−	0.450859i	$-0.148882\pi$
$462$	−337.500	+	428.683i	−0.730519	+	0.927884i
$463$	−82.0000			−0.177106			−0.0885529	−	0.996071i	$-0.528224\pi$
$463$	−82.0000			−0.177106			−0.0885529	+	0.996071i	$0.528224\pi$
$464$	−49.5000	+	85.7365i	−0.106681	+	0.184777i
$465$	94.5000	−	54.5596i	0.203226	−	0.117332i
$466$	−405.000	−	701.481i	−0.869099	−	1.50532i
$467$	234.000	+	135.100i	0.501071	+	0.289293i	0.729156	−	0.684348i	$-0.239913\pi$
$467$	234.000	+	135.100i	0.501071	+	0.289293i	−0.228085	+	0.973641i	$0.573246\pi$
$468$		−	207.846i		−	0.444116i
$469$	418.000	+	329.090i	0.891258	+	0.701684i
$470$		0			0
$471$	18.0000	−	31.1769i	0.0382166	−	0.0661930i
$472$	40.5000	−	23.3827i	0.0858051	−	0.0495396i
$473$	555.000	+	961.288i	1.17336	+	2.03232i
$474$	−193.500	−	111.717i	−0.408228	−	0.235690i
$475$		−	20.7846i		−	0.0437571i
$476$	−360.000	−	51.9615i	−0.756303	−	0.109163i
$477$	−99.0000			−0.207547
$478$	342.000	−	592.361i	0.715481	−	1.23925i
$479$	297.000	−	171.473i	0.620042	−	0.357981i	−0.156844	−	0.987623i	$-0.550132\pi$
$479$	297.000	−	171.473i	0.620042	−	0.357981i	0.776885	+	0.629642i	$0.216798\pi$
$480$	−202.500	−	350.740i	−0.421875	−	0.730709i
$481$	−120.000	−	69.2820i	−0.249480	−	0.144037i
$482$			1335.41i			2.77056i
$483$		0			0
$484$	520.000			1.07438
$485$	481.500	−	833.982i	0.992784	−	1.71955i
$486$	−40.5000	+	23.3827i	−0.0833333	+	0.0481125i
$487$	158.500	+	274.530i	0.325462	+	0.563717i	0.981606	−	0.190919i	$-0.0611468\pi$
$487$	158.500	+	274.530i	0.325462	+	0.563717i	−0.656144	+	0.754636i	$0.727814\pi$
$488$	234.000	+	135.100i	0.479508	+	0.276844i
$489$			360.267i			0.736741i
$490$	−216.000	+	732.657i	−0.440816	+	1.49522i
$491$	27.0000			0.0549898			0.0274949	−	0.999622i	$-0.491247\pi$
$491$	27.0000			0.0549898			0.0274949	+	0.999622i	$0.491247\pi$
$492$	−45.0000	+	77.9423i	−0.0914634	+	0.158419i
$493$	−81.0000	+	46.7654i	−0.164300	+	0.0948588i
$494$	216.000	+	374.123i	0.437247	+	0.757334i
$495$	−202.500	−	116.913i	−0.409091	−	0.236189i
$496$			133.368i			0.268887i
$497$	546.000	−	218.238i	1.09859	−	0.439111i
$498$	621.000			1.24699
$499$	223.000	−	386.247i	0.446894	−	0.774043i	−0.551288	−	0.834315i	$-0.685864\pi$
$499$	223.000	−	386.247i	0.446894	−	0.774043i	0.998182	+	0.0602721i	$0.0191969\pi$
$500$	−517.500	+	298.779i	−1.03500	+	0.597558i
$501$	−216.000	−	374.123i	−0.431138	−	0.746752i
$502$	−13.5000	−	7.79423i	−0.0268924	−	0.0155264i
$503$			488.438i			0.971050i	0.874223	+	0.485525i	$0.161372\pi$
$503$			488.438i			0.971050i	−0.874223	+	0.485525i	$0.838628\pi$
$504$	9.00000	−	62.3538i	0.0178571	−	0.123718i
$505$	−756.000			−1.49703
$506$		0			0
$507$	34.5000	−	19.9186i	0.0680473	−	0.0392871i
$508$	−87.5000	−	151.554i	−0.172244	−	0.298336i
$509$	85.5000	+	49.3634i	0.167976	+	0.0969812i	0.581631	−	0.813453i	$-0.302415\pi$
$509$	85.5000	+	49.3634i	0.167976	+	0.0969812i	−0.413655	+	0.910434i	$0.635748\pi$
$510$		−	280.592i		−	0.550181i
$511$	−270.000	+	342.946i	−0.528376	+	0.671127i
$512$	627.000			1.22461
$513$	27.0000	−	46.7654i	0.0526316	−	0.0911606i
$514$	−297.000	+	171.473i	−0.577821	+	0.333605i
$515$	−180.000	−	311.769i	−0.349515	−	0.605377i
$516$	−555.000	−	320.429i	−1.07558	−	0.620987i
$517$		0			0
$518$	−165.000	−	129.904i	−0.318533	−	0.250780i
$519$	396.000			0.763006
$520$	−108.000	+	187.061i	−0.207692	+	0.359734i
$521$	−783.000	+	452.065i	−1.50288	+	0.867688i	−0.502885	+	0.864354i	$0.667728\pi$
$521$	−783.000	+	452.065i	−1.50288	+	0.867688i	−0.999994	+	0.00333410i	$0.998939\pi$
$522$	−40.5000	−	70.1481i	−0.0775862	−	0.134383i
$523$	−606.000	−	349.874i	−1.15870	−	0.668976i	−0.207708	−	0.978191i	$-0.566600\pi$
$523$	−606.000	−	349.874i	−1.15870	−	0.668976i	−0.950992	+	0.309215i	$0.899934\pi$
$524$		−	857.365i		−	1.63619i
$525$	−24.0000	−	3.46410i	−0.0457143	−	0.00659829i
$526$	558.000			1.06084
$527$	−63.0000	+	109.119i	−0.119545	+	0.207057i
$528$	247.500	−	142.894i	0.468750	−	0.270633i
$529$	264.500	+	458.127i	0.500000	+	0.866025i
$530$	445.500	+	257.210i	0.840566	+	0.485301i
$531$		−	46.7654i		−	0.0880704i
$532$	135.000	+	337.750i	0.253759	+	0.634868i
$533$	−144.000			−0.270169
$534$	−189.000	+	327.358i	−0.353933	+	0.613029i
$535$	−418.500	+	241.621i	−0.782243	+	0.451628i
$536$	114.000	+	197.454i	0.212687	+	0.368384i
$537$	135.000	+	77.9423i	0.251397	+	0.145144i
$538$		−	1013.25i		−	1.88336i
$539$	−705.000	−	207.846i	−1.30798	−	0.385614i
$540$	135.000			0.250000
$541$	−37.0000	+	64.0859i	−0.0683919	+	0.118458i	−0.898194	−	0.439600i	$-0.855120\pi$
$541$	−37.0000	+	64.0859i	−0.0683919	+	0.118458i	0.829802	+	0.558058i	$0.188453\pi$
$542$	−238.500	+	137.698i	−0.440037	+	0.254055i
$543$	−9.00000	−	15.5885i	−0.0165746	−	0.0287080i
$544$	405.000	+	233.827i	0.744485	+	0.429829i
$545$			41.5692i			0.0762738i
$546$	468.000	−	187.061i	0.857143	−	0.342603i
$547$	−934.000			−1.70750			−0.853748	−	0.520687i	$-0.825676\pi$
$547$	−934.000			−1.70750			−0.853748	+	0.520687i	$0.825676\pi$
$548$	240.000	−	415.692i	0.437956	−	0.758562i
$549$	234.000	−	135.100i	0.426230	−	0.246084i
$550$	45.0000	+	77.9423i	0.0818182	+	0.141713i
$551$	81.0000	+	46.7654i	0.147005	+	0.0848736i
$552$		0			0
$553$	43.0000	−	297.913i	0.0777577	−	0.538721i
$554$	1140.00			2.05776
$555$	45.0000	−	77.9423i	0.0810811	−	0.140437i
$556$	795.000	−	458.993i	1.42986	−	0.825528i
$557$	−421.500	−	730.059i	−0.756732	−	1.31070i	−0.944508	−	0.328487i	$-0.893461\pi$
$557$	−421.500	−	730.059i	−0.756732	−	1.31070i	0.187776	−	0.982212i	$-0.439872\pi$
$558$	−94.5000	−	54.5596i	−0.169355	−	0.0977771i
$559$		−	1025.37i		−	1.83430i
$560$	247.500	−	314.367i	0.441964	−	0.561370i
$561$	270.000			0.481283
$562$	−450.000	+	779.423i	−0.800712	+	1.38687i
$563$	823.500	−	475.448i	1.46270	−	0.844490i	0.463564	−	0.886063i	$-0.346570\pi$
$563$	823.500	−	475.448i	1.46270	−	0.844490i	0.999135	+	0.0415731i	$0.0132369\pi$
$564$		0			0
$565$	189.000	+	109.119i	0.334513	+	0.193131i
$566$			613.146i			1.08330i
$567$	−49.5000	−	38.9711i	−0.0873016	−	0.0687322i
$568$	252.000			0.443662
$569$	−111.000	+	192.258i	−0.195079	+	0.337887i	−0.946926	−	0.321450i	$-0.895830\pi$
$569$	−111.000	+	192.258i	−0.195079	+	0.337887i	0.751847	+	0.659337i	$0.229163\pi$
$570$	−243.000	+	140.296i	−0.426316	+	0.246134i
$571$	−220.000	−	381.051i	−0.385289	−	0.667340i	0.606520	−	0.795068i	$-0.292565\pi$
$571$	−220.000	−	381.051i	−0.385289	−	0.667340i	−0.991809	+	0.127728i	$0.959232\pi$
$572$	−900.000	−	519.615i	−1.57343	−	0.908418i
$573$			540.400i			0.943106i
$574$	−216.000	−	31.1769i	−0.376307	−	0.0543152i
$575$		0			0
$576$	−136.500	+	236.425i	−0.236979	+	0.410460i
$577$	568.500	−	328.224i	0.985269	−	0.568845i	0.0814120	−	0.996681i	$-0.474057\pi$
$577$	568.500	−	328.224i	0.985269	−	0.568845i	0.903857	+	0.427835i	$0.140724\pi$
$578$	−271.500	−	470.252i	−0.469723	−	0.813584i
$579$	−277.500	−	160.215i	−0.479275	−	0.276709i
$580$			233.827i			0.403150i
$581$	310.500	+	776.825i	0.534423	+	1.33705i
$582$	−963.000			−1.65464
$583$	−247.500	+	428.683i	−0.424528	+	0.735305i
$584$	−162.000	+	93.5307i	−0.277397	+	0.160155i
$585$	108.000	+	187.061i	0.184615	+	0.319763i
$586$	1417.50	+	818.394i	2.41894	+	1.39658i
$587$			1054.82i			1.79697i	0.439008	+	0.898483i	$0.355330\pi$
$587$			1054.82i			1.79697i	−0.439008	+	0.898483i	$0.644670\pi$
$588$	412.500	−	99.5929i	0.701531	−	0.169376i
$589$	126.000			0.213922
$590$	−121.500	+	210.444i	−0.205932	+	0.356685i
$591$	−495.000	+	285.788i	−0.837563	+	0.483567i
$592$	55.0000	+	95.2628i	0.0929054	+	0.160917i
$593$	612.000	+	353.338i	1.03204	+	0.595849i	0.917569	−	0.397578i	$-0.130149\pi$
$593$	612.000	+	353.338i	1.03204	+	0.595849i	0.114472	+	0.993426i	$0.463482\pi$
$594$			233.827i			0.393648i
$595$	351.000	−	140.296i	0.589916	−	0.235792i
$596$	−930.000			−1.56040
$597$	−6.00000	+	10.3923i	−0.0100503	+	0.0174075i
$598$		0			0
$599$	−258.000	−	446.869i	−0.430718	−	0.746025i	0.566217	−	0.824256i	$-0.308406\pi$
$599$	−258.000	−	446.869i	−0.430718	−	0.746025i	−0.996935	+	0.0782307i	$0.975073\pi$
$600$	−9.00000	−	5.19615i	−0.0150000	−	0.00866025i
$601$			247.683i			0.412119i	0.978540	+	0.206059i	$0.0660640\pi$
$601$			247.683i			0.412119i	−0.978540	+	0.206059i	$0.933936\pi$
$602$	222.000	−	1538.06i	0.368771	−	2.55492i
$603$	228.000			0.378109
$604$	−197.500	+	342.080i	−0.326987	+	0.566358i
$605$	−468.000	+	270.200i	−0.773554	+	0.446611i
$606$	378.000	+	654.715i	0.623762	+	1.08039i
$607$	−562.500	−	324.760i	−0.926689	−	0.535024i	−0.0409259	−	0.999162i	$-0.513031\pi$
$607$	−562.500	−	324.760i	−0.926689	−	0.535024i	−0.885763	+	0.464138i	$0.846364\pi$
$608$		−	467.654i		−	0.769167i
$609$	67.5000	−	85.7365i	0.110837	−	0.140782i
$610$	−1404.00			−2.30164
$611$		0			0
$612$	−135.000	+	77.9423i	−0.220588	+	0.127357i
$613$	446.000	+	772.495i	0.727569	+	1.26019i	0.957908	+	0.287076i	$0.0926834\pi$
$613$	446.000	+	772.495i	0.727569	+	1.26019i	−0.230338	+	0.973111i	$0.573983\pi$
$614$	450.000	+	259.808i	0.732899	+	0.423139i
$615$		−	93.5307i		−	0.152083i
$616$	−247.500	−	194.856i	−0.401786	−	0.316324i
$617$	−1224.00			−1.98379			−0.991896	−	0.127050i	$-0.959449\pi$
$617$	−1224.00			−1.98379			−0.991896	+	0.127050i	$0.959449\pi$
$618$	−180.000	+	311.769i	−0.291262	+	0.504481i
$619$	−348.000	+	200.918i	−0.562197	+	0.324585i	−0.754027	−	0.656844i	$-0.771891\pi$
$619$	−348.000	+	200.918i	−0.562197	+	0.324585i	0.191830	+	0.981428i	$0.438558\pi$
$620$	157.500	+	272.798i	0.254032	+	0.439997i
$621$		0			0
$622$		−	530.008i		−	0.852102i
$623$	−504.000	−	72.7461i	−0.808989	−	0.116767i
$624$	−264.000			−0.423077
$625$	335.500	−	581.103i	0.536800	−	0.929765i
$626$	553.500	−	319.563i	0.884185	−	0.510485i
$627$	−135.000	−	233.827i	−0.215311	−	0.372930i
$628$	90.0000	+	51.9615i	0.143312	+	0.0827413i
$629$			103.923i			0.165219i
$630$	121.500	+	303.975i	0.192857	+	0.482500i
$631$	1115.00			1.76704			0.883518	−	0.468397i	$-0.155168\pi$
$631$	1115.00			1.76704			0.883518	+	0.468397i	$0.155168\pi$
$632$	64.5000	−	111.717i	0.102057	−	0.176768i
$633$	372.000	−	214.774i	0.587678	−	0.339296i
$634$	−175.500	−	303.975i	−0.276814	−	0.479456i
$635$	157.500	+	90.9327i	0.248031	+	0.143201i
$636$		−	285.788i		−	0.449353i
$637$	468.000	+	491.902i	0.734694	+	0.772217i
$638$	−405.000			−0.634796
$639$	126.000	−	218.238i	0.197183	−	0.341531i
$640$	418.500	−	241.621i	0.653906	−	0.377533i
$641$	192.000	+	332.554i	0.299532	+	0.518805i	0.976029	−	0.217641i	$-0.0698361\pi$
$641$	192.000	+	332.554i	0.299532	+	0.518805i	−0.676497	+	0.736445i	$0.736503\pi$
$642$	418.500	+	241.621i	0.651869	+	0.376357i
$643$			6.92820i			0.0107748i	0.999985	+	0.00538741i	$0.00171487\pi$
$643$			6.92820i			0.0107748i	−0.999985	+	0.00538741i	$0.998285\pi$
$644$		0			0
$645$	666.000			1.03256
$646$	162.000	−	280.592i	0.250774	−	0.434353i
$647$	774.000	−	446.869i	1.19629	−	0.690679i	0.236564	−	0.971616i	$-0.423979\pi$
$647$	774.000	−	446.869i	1.19629	−	0.690679i	0.959726	+	0.280937i	$0.0906452\pi$
$648$	−13.5000	−	23.3827i	−0.0208333	−	0.0360844i
$649$	−202.500	−	116.913i	−0.312018	−	0.180144i
$650$		−	83.1384i		−	0.127905i
$651$	21.0000	−	145.492i	0.0322581	−	0.223490i
$652$	−1040.00			−1.59509
$653$	−37.5000	+	64.9519i	−0.0574273	+	0.0994669i	−0.893310	−	0.449441i	$-0.851623\pi$
$653$	−37.5000	+	64.9519i	−0.0574273	+	0.0994669i	0.835883	+	0.548908i	$0.184956\pi$
$654$	36.0000	−	20.7846i	0.0550459	−	0.0317807i
$655$	445.500	+	771.629i	0.680153	+	1.17806i
$656$	99.0000	+	57.1577i	0.150915	+	0.0871306i
$657$			187.061i			0.284721i
$658$		0			0
$659$	642.000			0.974203			0.487102	−	0.873345i	$-0.338054\pi$
$659$	642.000			0.974203			0.487102	+	0.873345i	$0.338054\pi$
$660$	337.500	−	584.567i	0.511364	−	0.885708i
$661$	−243.000	+	140.296i	−0.367625	+	0.212248i	−0.672420	−	0.740170i	$-0.734745\pi$
$661$	−243.000	+	140.296i	−0.367625	+	0.212248i	0.304795	+	0.952418i	$0.401412\pi$
$662$	−60.0000	−	103.923i	−0.0906344	−	0.156983i
$663$	−216.000	−	124.708i	−0.325792	−	0.188096i
$664$			358.535i			0.539962i
$665$	−297.000	−	233.827i	−0.446617	−	0.351619i
$666$	−90.0000			−0.135135
$667$		0			0
$668$	1080.00	−	623.538i	1.61677	−	0.933441i
$669$	−166.500	−	288.386i	−0.248879	−	0.431071i
$670$	−1026.00	−	592.361i	−1.53134	−	0.884121i
$671$		−	1351.00i		−	2.01341i
$672$	−540.000	−	77.9423i	−0.803571	−	0.115986i
$673$	13.0000			0.0193165			0.00965825	−	0.999953i	$-0.496926\pi$
$673$	13.0000			0.0193165			0.00965825	+	0.999953i	$0.496926\pi$
$674$	−136.500	+	236.425i	−0.202522	+	0.350779i
$675$	−9.00000	+	5.19615i	−0.0133333	+	0.00769800i
$676$	57.5000	+	99.5929i	0.0850592	+	0.147327i
$677$	−1093.50	−	631.333i	−1.61521	−	0.932544i	−0.988135	−	0.153589i	$-0.950917\pi$
$677$	−1093.50	−	631.333i	−1.61521	−	0.932544i	−0.627079	−	0.778955i	$-0.715750\pi$
$678$		−	218.238i		−	0.321886i
$679$	−481.500	−	1204.64i	−0.709131	−	1.77414i
$680$	162.000			0.238235
$681$	76.5000	−	132.502i	0.112335	−	0.194570i
$682$	−472.500	+	272.798i	−0.692815	+	0.399997i
$683$	484.500	+	839.179i	0.709370	+	1.22867i	0.965091	+	0.261915i	$0.0843540\pi$
$683$	484.500	+	839.179i	0.709370	+	1.22867i	−0.255721	+	0.966751i	$0.582313\pi$
$684$	135.000	+	77.9423i	0.197368	+	0.113951i
$685$			498.831i			0.728220i
$686$	595.500	+	839.179i	0.868076	+	1.22329i
$687$	−570.000			−0.829694
$688$	−407.000	+	704.945i	−0.591570	+	1.02463i
$689$	396.000	−	228.631i	0.574746	−	0.331830i
$690$		0			0
$691$	−87.0000	−	50.2295i	−0.125904	−	0.0726910i	0.435725	−	0.900080i	$-0.356492\pi$
$691$	−87.0000	−	50.2295i	−0.125904	−	0.0726910i	−0.561629	+	0.827389i	$0.689825\pi$
$692$			1143.15i			1.65196i
$693$	−292.500	+	116.913i	−0.422078	+	0.168706i
$694$	630.000			0.907781
$695$	−477.000	+	826.188i	−0.686331	+	1.18876i
$696$	40.5000	−	23.3827i	0.0581897	−	0.0335958i
$697$	54.0000	+	93.5307i	0.0774749	+	0.134190i
$698$	−792.000	−	457.261i	−1.13467	−	0.655102i
$699$		−	467.654i		−	0.669033i
$700$	10.0000	−	69.2820i	0.0142857	−	0.0989743i
$701$	597.000			0.851641			0.425820	−	0.904808i	$-0.359986\pi$
$701$	597.000			0.851641			0.425820	+	0.904808i	$0.359986\pi$
$702$	108.000	−	187.061i	0.153846	−	0.266469i
$703$	90.0000	−	51.9615i	0.128023	−	0.0739140i
$704$	682.500	+	1182.12i	0.969460	+	1.67915i
$705$		0			0
$706$			1184.72i			1.67808i
$707$	−630.000	+	800.207i	−0.891089	+	1.13184i
$708$	135.000			0.190678
$709$	415.000	−	718.801i	0.585331	−	1.01382i	−0.409503	−	0.912309i	$-0.634298\pi$
$709$	415.000	−	718.801i	0.585331	−	1.01382i	0.994834	−	0.101515i	$-0.0323689\pi$
$710$	−1134.00	+	654.715i	−1.59718	+	0.922134i
$711$	−64.5000	−	111.717i	−0.0907173	−	0.157127i
$712$	−189.000	−	109.119i	−0.265449	−	0.153257i
$713$		0			0
$714$	−297.000	−	233.827i	−0.415966	−	0.327489i
$715$	1080.00			1.51049
$716$	−225.000	+	389.711i	−0.314246	+	0.544290i
$717$	342.000	−	197.454i	0.476987	−	0.275389i
$718$	−738.000	−	1278.25i	−1.02786	−	1.78030i
$719$	297.000	+	171.473i	0.413074	+	0.238488i	0.692110	−	0.721792i	$-0.256681\pi$
$719$	297.000	+	171.473i	0.413074	+	0.238488i	−0.279036	+	0.960281i	$0.590015\pi$
$720$		−	171.473i		−	0.238157i
$721$	−480.000	−	69.2820i	−0.665742	−	0.0960916i
$722$	759.000			1.05125
$723$	−385.500	+	667.706i	−0.533195	+	0.923521i
$724$	45.0000	−	25.9808i	0.0621547	−	0.0358850i
$725$	−9.00000	−	15.5885i	−0.0124138	−	0.0215013i
$726$	468.000	+	270.200i	0.644628	+	0.372176i
$727$		−	50.2295i		−	0.0690914i	−0.999403	−	0.0345457i	$-0.989002\pi$
$727$		−	50.2295i		−	0.0690914i	0.999403	−	0.0345457i	$-0.0109984\pi$
$728$	108.000	+	270.200i	0.148352	+	0.371154i
$729$	−27.0000			−0.0370370
$730$	486.000	−	841.777i	0.665753	−	1.15312i
$731$	−666.000	+	384.515i	−0.911081	+	0.526013i
$732$	390.000	+	675.500i	0.532787	+	0.922814i
$733$	−159.000	−	91.7987i	−0.216917	−	0.125237i	0.387605	−	0.921826i	$-0.373302\pi$
$733$	−159.000	−	91.7987i	−0.216917	−	0.125237i	−0.604522	+	0.796589i	$0.706636\pi$
$734$		−	982.073i		−	1.33797i
$735$	−319.500	+	303.975i	−0.434694	+	0.413571i
$736$		0			0
$737$	570.000	−	987.269i	0.773406	−	1.33958i
$738$	−81.0000	+	46.7654i	−0.109756	+	0.0633677i
$739$	167.000	+	289.252i	0.225981	+	0.391411i	0.956613	−	0.291361i	$-0.0941079\pi$
$739$	167.000	+	289.252i	0.225981	+	0.391411i	−0.730632	+	0.682771i	$0.760775\pi$
$740$	225.000	+	129.904i	0.304054	+	0.175546i
$741$			249.415i			0.336593i
$742$	643.500	−	257.210i	0.867251	−	0.346644i
$743$	84.0000			0.113055			0.0565276	−	0.998401i	$-0.481997\pi$
$743$	84.0000			0.113055			0.0565276	+	0.998401i	$0.481997\pi$
$744$	31.5000	−	54.5596i	0.0423387	−	0.0733328i
$745$	837.000	−	483.242i	1.12349	−	0.648647i
$746$	−255.000	−	441.673i	−0.341823	−	0.592055i
$747$	310.500	+	179.267i	0.415663	+	0.239983i
$748$			779.423i			1.04201i
$749$	−93.0000	+	644.323i	−0.124166	+	0.860244i
$750$	−621.000			−0.828000
$751$	179.500	−	310.903i	0.239015	−	0.413986i	−0.721417	−	0.692501i	$-0.756509\pi$
$751$	179.500	−	310.903i	0.239015	−	0.413986i	0.960432	+	0.278515i	$0.0898423\pi$
$752$		0			0
$753$	−4.50000	−	7.79423i	−0.00597610	−	0.0103509i
$754$	324.000	+	187.061i	0.429708	+	0.248092i
$755$		−	410.496i		−	0.543703i
$756$	112.500	−	142.894i	0.148810	−	0.189013i
$757$	−80.0000			−0.105680			−0.0528402	−	0.998603i	$-0.516827\pi$
$757$	−80.0000			−0.105680			−0.0528402	+	0.998603i	$0.516827\pi$
$758$	−123.000	+	213.042i	−0.162269	+	0.281058i
$759$		0			0
$760$	−81.0000	−	140.296i	−0.106579	−	0.184600i
$761$	−702.000	−	405.300i	−0.922470	−	0.532589i	−0.0380481	−	0.999276i	$-0.512114\pi$
$761$	−702.000	−	405.300i	−0.922470	−	0.532589i	−0.884422	+	0.466687i	$0.845447\pi$
$762$		−	181.865i		−	0.238668i
$763$	44.0000	+	34.6410i	0.0576671	+	0.0454011i
$764$	−1560.00			−2.04188
$765$	81.0000	−	140.296i	0.105882	−	0.183394i
$766$	−567.000	+	327.358i	−0.740209	+	0.427360i
$767$	108.000	+	187.061i	0.140808	+	0.243887i
$768$	127.500	+	73.6122i	0.166016	+	0.0958492i
$769$			774.227i			1.00680i	0.864054	+	0.503398i	$0.167917\pi$
$769$			774.227i			1.00680i	−0.864054	+	0.503398i	$0.832083\pi$
$770$	1620.00	+	233.827i	2.10390	+	0.303671i
$771$	−198.000			−0.256809
$772$	462.500	−	801.073i	0.599093	−	1.03766i
$773$	−630.000	+	363.731i	−0.815006	+	0.470544i	−0.848691	−	0.528888i	$-0.822609\pi$
$773$	−630.000	+	363.731i	−0.815006	+	0.470544i	0.0336850	+	0.999433i	$0.489276\pi$
$774$	−333.000	−	576.773i	−0.430233	−	0.745185i
$775$	−21.0000	−	12.1244i	−0.0270968	−	0.0156443i
$776$		−	555.988i		−	0.716480i
$777$	−45.0000	−	112.583i	−0.0579151	−	0.144895i
$778$	918.000			1.17995
$779$	54.0000	−	93.5307i	0.0693196	−	0.120065i
$780$	−540.000	+	311.769i	−0.692308	+	0.399704i
$781$	−630.000	−	1091.19i	−0.806658	−	1.39717i
$782$		0			0
$783$		−	46.7654i		−	0.0597259i
$784$	−126.500	−	523.945i	−0.161352	−	0.668298i
$785$	−108.000			−0.137580
$786$	445.500	−	771.629i	0.566794	−	0.981716i
$787$	−1236.00	+	713.605i	−1.57052	+	0.906741i	−0.574416	+	0.818563i	$0.694771\pi$
$787$	−1236.00	+	713.605i	−1.57052	+	0.906741i	−0.996105	+	0.0881773i	$0.971896\pi$
$788$	−825.000	−	1428.94i	−1.04695	−	1.81338i
$789$	279.000	+	161.081i	0.353612	+	0.204158i
$790$			670.304i			0.848486i
$791$	273.000	−	109.119i	0.345133	−	0.137951i
$792$	−135.000			−0.170455
$793$	−624.000	+	1080.80i	−0.786885	+	1.36293i
$794$	666.000	−	384.515i	0.838791	−	0.484276i
$795$	148.500	+	257.210i	0.186792	+	0.323534i
$796$	−30.0000	−	17.3205i	−0.0376884	−	0.0217594i
$797$		−	607.950i		−	0.762798i	−0.924411	−	0.381399i	$-0.875442\pi$
$797$		−	607.950i		−	0.762798i	0.924411	−	0.381399i	$-0.124558\pi$
$798$	−54.0000	+	374.123i	−0.0676692	+	0.468826i
$799$		0			0
$800$	−45.0000	+	77.9423i	−0.0562500	+	0.0974279i
$801$	−189.000	+	109.119i	−0.235955	+	0.136229i
$802$	−198.000	−	342.946i	−0.246883	−	0.427614i
$803$	810.000	+	467.654i	1.00872	+	0.582383i
$804$			658.179i			0.818631i
$805$		0			0
$806$	504.000			0.625310
$807$	292.500	−	506.625i	0.362454	−	0.627788i
$808$	−378.000	+	218.238i	−0.467822	+	0.270097i
$809$	84.0000	+	145.492i	0.103832	+	0.179842i	0.913260	−	0.407376i	$-0.133556\pi$
$809$	84.0000	+	145.492i	0.103832	+	0.179842i	−0.809428	+	0.587218i	$0.800223\pi$
$810$	121.500	+	70.1481i	0.150000	+	0.0866025i
$811$		−	353.338i		−	0.435682i	−0.975984	−	0.217841i	$-0.930099\pi$
$811$		−	353.338i		−	0.435682i	0.975984	−	0.217841i	$-0.0699015\pi$
$812$	247.500	+	194.856i	0.304803	+	0.239970i
$813$	−159.000			−0.195572
$814$	−225.000	+	389.711i	−0.276413	+	0.478761i
$815$	936.000	−	540.400i	1.14847	−	0.663067i
$816$	99.0000	+	171.473i	0.121324	+	0.210139i
$817$	666.000	+	384.515i	0.815177	+	0.470643i
$818$		−	1086.00i		−	1.32762i
$819$	288.000	+	41.5692i	0.351648	+	0.0507561i
$820$	270.000			0.329268
$821$	−142.500	+	246.817i	−0.173569	+	0.300630i	−0.939665	−	0.342096i	$-0.888863\pi$
$821$	−142.500	+	246.817i	−0.173569	+	0.300630i	0.766096	+	0.642726i	$0.222197\pi$
$822$	432.000	−	249.415i	0.525547	−	0.303425i
$823$	137.000	+	237.291i	0.166464	+	0.288324i	0.937174	−	0.348862i	$-0.113432\pi$
$823$	137.000	+	237.291i	0.166464	+	0.288324i	−0.770710	+	0.637186i	$0.780098\pi$
$824$	−180.000	−	103.923i	−0.218447	−	0.126120i
$825$			51.9615i			0.0629837i
$826$	121.500	+	303.975i	0.147094	+	0.368008i
$827$	429.000			0.518742			0.259371	−	0.965778i	$-0.416485\pi$
$827$	429.000			0.518742			0.259371	+	0.965778i	$0.416485\pi$
$828$		0			0
$829$	−819.000	+	472.850i	−0.987937	+	0.570386i	−0.904657	−	0.426140i	$-0.859873\pi$
$829$	−819.000	+	472.850i	−0.987937	+	0.570386i	−0.0832802	+	0.996526i	$0.526540\pi$
$830$	−931.500	−	1613.41i	−1.12229	−	1.94386i
$831$	570.000	+	329.090i	0.685921	+	0.396016i
$832$		−	1260.93i		−	1.51554i
$833$	144.000	−	488.438i	0.172869	−	0.586361i
$834$	954.000			1.14388
$835$	−648.000	+	1122.37i	−0.776048	+	1.34415i
$836$	675.000	−	389.711i	0.807416	−	0.466162i
$837$	−31.5000	−	54.5596i	−0.0376344	−	0.0651847i
$838$	1674.00	+	966.484i	1.99761	+	1.15332i
$839$		−	259.808i		−	0.309663i	−0.987941	−	0.154832i	$-0.950516\pi$
$839$		−	259.808i		−	0.309663i	0.987941	−	0.154832i	$-0.0494835\pi$
$840$	−175.500	+	70.1481i	−0.208929	+	0.0835096i
$841$	−760.000			−0.903686
$842$	−1128.00	+	1953.75i	−1.33967	+	2.32037i
$843$	−450.000	+	259.808i	−0.533808	+	0.308194i
$844$	620.000	+	1073.87i	0.734597	+	1.27236i
$845$	−103.500	−	59.7558i	−0.122485	−	0.0707169i
$846$		0			0
$847$	−104.000	+	720.533i	−0.122786	+	0.850688i
$848$	−363.000			−0.428066
$849$	−177.000	+	306.573i	−0.208481	+	0.361099i
$850$	−54.0000	+	31.1769i	−0.0635294	+	0.0366787i
$851$		0			0
$852$	630.000	+	363.731i	0.739437	+	0.426914i
$853$		−	997.661i		−	1.16959i	−0.811181	−	0.584796i	$-0.801175\pi$
$853$		−	997.661i		−	1.16959i	0.811181	−	0.584796i	$-0.198825\pi$
$854$	−1170.00	+	1486.10i	−1.37002	+	1.74016i
$855$	−162.000			−0.189474
$856$	−139.500	+	241.621i	−0.162967	+	0.282268i
$857$	378.000	−	218.238i	0.441074	−	0.254654i	−0.262979	−	0.964801i	$-0.584705\pi$
$857$	378.000	−	218.238i	0.441074	−	0.254654i	0.704053	+	0.710148i	$0.251372\pi$
$858$	−540.000	−	935.307i	−0.629371	−	1.09010i
$859$	−393.000	−	226.899i	−0.457509	−	0.264143i	0.253487	−	0.967339i	$-0.418422\pi$
$859$	−393.000	−	226.899i	−0.457509	−	0.264143i	−0.710996	+	0.703196i	$0.751756\pi$
$860$			1922.58i			2.23555i
$861$	−99.0000	−	77.9423i	−0.114983	−	0.0905253i
$862$	486.000			0.563805
$863$	195.000	−	337.750i	0.225956	−	0.391367i	−0.730650	−	0.682752i	$-0.760783\pi$
$863$	195.000	−	337.750i	0.225956	−	0.391367i	0.956606	+	0.291385i	$0.0941161\pi$
$864$	−202.500	+	116.913i	−0.234375	+	0.135316i
$865$	−594.000	−	1028.84i	−0.686705	−	1.18941i
$866$	−882.000	−	509.223i	−1.01848	−	0.588017i
$867$		−	313.501i		−	0.361593i
$868$	420.000	+	60.6218i	0.483871	+	0.0698408i
$869$	−645.000			−0.742232
$870$	−121.500	+	210.444i	−0.139655	+	0.241890i
$871$	−912.000	+	526.543i	−1.04707	+	0.604527i
$872$	12.0000	+	20.7846i	0.0137615	+	0.0238356i
$873$	−481.500	−	277.994i	−0.551546	−	0.318435i
$874$		0			0
$875$	−310.500	−	776.825i	−0.354857	−	0.887800i
$876$	−540.000			−0.616438
$877$	272.000	−	471.118i	0.310148	−	0.537192i	−0.668246	−	0.743940i	$-0.732955\pi$
$877$	272.000	−	471.118i	0.310148	−	0.537192i	0.978394	+	0.206748i	$0.0662880\pi$
$878$	−1012.50	+	584.567i	−1.15319	+	0.665794i
$879$	472.500	+	818.394i	0.537543	+	0.931051i
$880$	−742.500	−	428.683i	−0.843750	−	0.487139i
$881$			187.061i			0.212329i	0.994349	+	0.106164i	$0.0338569\pi$
$881$			187.061i			0.212329i	−0.994349	+	0.106164i	$0.966143\pi$
$882$	423.000	+	124.708i	0.479592	+	0.141392i
$883$	322.000			0.364666			0.182333	−	0.983237i	$-0.441635\pi$
$883$	322.000			0.364666			0.182333	+	0.983237i	$0.441635\pi$
$884$	360.000	−	623.538i	0.407240	−	0.705360i
$885$	−121.500	+	70.1481i	−0.137288	+	0.0792633i
$886$	445.500	+	771.629i	0.502822	+	0.870913i
$887$	612.000	+	353.338i	0.689966	+	0.398352i	0.803599	−	0.595171i	$-0.202916\pi$
$887$	612.000	+	353.338i	0.689966	+	0.398352i	−0.113633	+	0.993523i	$0.536249\pi$
$888$		−	51.9615i		−	0.0585152i
$889$	227.500	−	90.9327i	0.255906	−	0.102286i
$890$	1134.00			1.27416
$891$	−67.5000	+	116.913i	−0.0757576	+	0.131216i
$892$	832.500	−	480.644i	0.933296	−	0.538839i
$893$		0			0
$894$	−837.000	−	483.242i	−0.936242	−	0.540539i
$895$		−	467.654i		−	0.522518i
$896$	93.0000	−	644.323i	0.103795	−	0.719110i
$897$		0			0
$898$	738.000	−	1278.25i	0.821826	−	1.42344i
$899$	94.5000	−	54.5596i	0.105117	−	0.0606892i
$900$	−15.0000	−	25.9808i	−0.0166667	−	0.0288675i
$901$	−297.000	−	171.473i	−0.329634	−	0.190314i
$902$			467.654i			0.518463i
$903$	555.000	−	704.945i	0.614618	−	0.780670i
$904$	126.000			0.139381
$905$	−27.0000	+	46.7654i	−0.0298343	+	0.0516744i
$906$	−355.500	+	205.248i	−0.392384	+	0.226543i
$907$	550.000	+	952.628i	0.606395	+	1.05031i	0.991829	+	0.127571i	$0.0407182\pi$
$907$	550.000	+	952.628i	0.606395	+	1.05031i	−0.385435	+	0.922735i	$0.625948\pi$
$908$	382.500	+	220.836i	0.421256	+	0.243212i
$909$			436.477i			0.480173i
$910$	−1188.00	−	935.307i	−1.30549	−	1.02781i
$911$	900.000			0.987925			0.493963	−	0.869483i	$-0.335548\pi$
$911$	900.000			0.987925			0.493963	+	0.869483i	$0.335548\pi$
$912$	99.0000	−	171.473i	0.108553	−	0.188019i
$913$	1552.50	−	896.336i	1.70044	−	0.981748i
$914$	664.500	+	1150.95i	0.727024	+	1.25924i
$915$	−702.000	−	405.300i	−0.767213	−	0.442951i
$916$		−	1645.45i		−	1.79634i
$917$	1188.00	+	171.473i	1.29553	+	0.186993i
$918$	−162.000			−0.176471
$919$	859.000	−	1487.83i	0.934712	−	1.61897i	0.159564	−	0.987188i	$-0.448991\pi$
$919$	859.000	−	1487.83i	0.934712	−	1.61897i	0.775147	−	0.631781i	$-0.217676\pi$
$920$		0			0
$921$	150.000	+	259.808i	0.162866	+	0.282093i
$922$	1080.00	+	623.538i	1.17137	+	0.676289i
$923$			1163.94i			1.26104i
$924$	−337.500	−	844.375i	−0.365260	−	0.913826i
$925$	−20.0000			−0.0216216
$926$	123.000	−	213.042i	0.132829	−	0.230067i
$927$	−180.000	+	103.923i	−0.194175	+	0.112107i
$928$	−202.500	−	350.740i	−0.218211	−	0.377953i
$929$	−1287.00	−	743.050i	−1.38536	−	0.799838i	−0.392573	−	0.919721i	$-0.628415\pi$
$929$	−1287.00	−	743.050i	−1.38536	−	0.799838i	−0.992788	+	0.119883i	$0.961748\pi$
$930$			327.358i			0.351997i
$931$	−495.000	+	119.512i	−0.531686	+	0.128369i
$932$	1350.00			1.44850
$933$	153.000	−	265.004i	0.163987	−	0.284034i
$934$	−702.000	+	405.300i	−0.751606	+	0.433940i
$935$	−405.000	−	701.481i	−0.433155	−	0.750247i
$936$	108.000	+	62.3538i	0.115385	+	0.0666173i
$937$			957.824i			1.02222i	0.859514	+	0.511112i	$0.170766\pi$
$937$			957.824i			1.02222i	−0.859514	+	0.511112i	$0.829234\pi$
$938$	−1482.00	+	592.361i	−1.57996	+	0.631515i
$939$	369.000			0.392971
$940$		0			0
$941$	310.500	−	179.267i	0.329968	−	0.190507i	−0.325859	−	0.945418i	$-0.605653\pi$
$941$	310.500	−	179.267i	0.329968	−	0.190507i	0.655827	+	0.754911i	$0.272320\pi$
$942$	54.0000	+	93.5307i	0.0573248	+	0.0992895i
$943$		0			0
$944$		−	171.473i		−	0.181645i
$945$	−27.0000	+	187.061i	−0.0285714	+	0.197949i
$946$	−3330.00			−3.52008
$947$	−81.0000	+	140.296i	−0.0855333	+	0.148148i	−0.905618	−	0.424094i	$-0.860593\pi$
$947$	−81.0000	+	140.296i	−0.0855333	+	0.148148i	0.820085	+	0.572242i	$0.193926\pi$
$948$	322.500	−	186.195i	0.340190	−	0.196409i
$949$	−432.000	−	748.246i	−0.455216	−	0.788457i
$950$	54.0000	+	31.1769i	0.0568421	+	0.0328178i
$951$		−	202.650i		−	0.213091i
$952$	135.000	−	171.473i	0.141807	−	0.180119i
$953$	−954.000			−1.00105			−0.500525	−	0.865722i	$-0.666860\pi$
$953$	−954.000			−1.00105			−0.500525	+	0.865722i	$0.666860\pi$
$954$	148.500	−	257.210i	0.155660	−	0.269612i
$955$	1404.00	−	810.600i	1.47016	−	0.848796i
$956$	570.000	+	987.269i	0.596234	+	1.03271i
$957$	−202.500	−	116.913i	−0.211599	−	0.122167i
$958$			1028.84i			1.07394i
$959$	528.000	+	415.692i	0.550574	+	0.433464i
$960$	819.000			0.853125
$961$	−407.000	+	704.945i	−0.423517	+	0.733553i
$962$	360.000	−	207.846i	0.374220	−	0.216056i
$963$	139.500	+	241.621i	0.144860	+	0.250905i
$964$	−1927.50	−	1112.84i	−1.99948	−	1.15440i
$965$			961.288i			0.996154i
$966$		0			0
$967$	−751.000			−0.776629			−0.388314	−	0.921527i	$-0.626943\pi$
$967$	−751.000			−0.776629			−0.388314	+	0.921527i	$0.626943\pi$
$968$	−156.000	+	270.200i	−0.161157	+	0.279132i
$969$	162.000	−	93.5307i	0.167183	−	0.0965230i
$970$	1444.50	+	2501.95i	1.48918	+	2.57933i
$971$	−247.500	−	142.894i	−0.254892	−	0.147162i	0.367110	−	0.930177i	$-0.380347\pi$
$971$	−247.500	−	142.894i	−0.254892	−	0.147162i	−0.622002	+	0.783016i	$0.713680\pi$
$972$		−	77.9423i		−	0.0801875i
$973$	477.000	+	1193.38i	0.490236	+	1.22650i
$974$	−951.000			−0.976386
$975$	24.0000	−	41.5692i	0.0246154	−	0.0426351i
$976$	858.000	−	495.367i	0.879098	−	0.507548i
$977$	9.00000	+	15.5885i	0.00921187	+	0.0159554i	0.870595	−	0.492001i	$-0.163734\pi$
$977$	9.00000	+	15.5885i	0.00921187	+	0.0159554i	−0.861383	+	0.507957i	$0.830401\pi$
$978$	−936.000	−	540.400i	−0.957055	−	0.552556i
$979$			1091.19i			1.11460i
$980$	−877.500	−	922.317i	−0.895408	−	0.941140i
$981$	24.0000			0.0244648
$982$	−40.5000	+	70.1481i	−0.0412424	+	0.0714339i
$983$	−855.000	+	493.634i	−0.869786	+	0.502171i	−0.867277	−	0.497825i	$-0.834132\pi$
$983$	−855.000	+	493.634i	−0.869786	+	0.502171i	−0.00250913	+	0.999997i	$0.500799\pi$
$984$	−27.0000	−	46.7654i	−0.0274390	−	0.0475258i
$985$	1485.00	+	857.365i	1.50761	+	0.870421i
$986$		−	280.592i		−	0.284576i
$987$		0			0
$988$	−720.000			−0.728745
$989$		0			0
$990$	607.500	−	350.740i	0.613636	−	0.354283i
$991$	−351.500	−	608.816i	−0.354692	−	0.614345i	0.632373	−	0.774664i	$-0.282081\pi$
$991$	−351.500	−	608.816i	−0.354692	−	0.614345i	−0.987065	+	0.160319i	$0.948748\pi$
$992$	−472.500	−	272.798i	−0.476310	−	0.274998i
$993$		−	69.2820i		−	0.0697704i
$994$	−252.000	+	1745.91i	−0.253521	+	1.75645i
$995$	36.0000			0.0361809
$996$	−517.500	+	896.336i	−0.519578	+	0.899936i
$997$	186.000	−	107.387i	0.186560	−	0.107710i	−0.403811	−	0.914842i	$-0.632315\pi$
$997$	186.000	−	107.387i	0.186560	−	0.107710i	0.590371	+	0.807132i	$0.298981\pi$
$998$	669.000	+	1158.74i	0.670341	+	1.16106i
$999$	−45.0000	−	25.9808i	−0.0450450	−	0.0260068i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	21.3.f.a.19.1	yes	2
3.2	odd	2		63.3.m.d.19.1		2
4.3	odd	2		336.3.bh.d.145.1		2
5.2	odd	4		525.3.s.e.124.1		4
5.3	odd	4		525.3.s.e.124.2		4
5.4	even	2		525.3.o.h.376.1		2
7.2	even	3		147.3.d.c.97.1		2
7.3	odd	6	inner	21.3.f.a.10.1	✓	2
7.4	even	3		147.3.f.a.31.1		2
7.5	odd	6		147.3.d.c.97.2		2
7.6	odd	2		147.3.f.a.19.1		2
12.11	even	2		1008.3.cg.a.145.1		2
21.2	odd	6		441.3.d.a.244.2		2
21.5	even	6		441.3.d.a.244.1		2
21.11	odd	6		441.3.m.g.325.1		2
21.17	even	6		63.3.m.d.10.1		2
21.20	even	2		441.3.m.g.19.1		2
28.3	even	6		336.3.bh.d.241.1		2
28.19	even	6		2352.3.f.a.97.1		2
28.23	odd	6		2352.3.f.a.97.2		2
35.3	even	12		525.3.s.e.199.1		4
35.17	even	12		525.3.s.e.199.2		4
35.24	odd	6		525.3.o.h.451.1		2
84.59	odd	6		1008.3.cg.a.577.1		2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
21.3.f.a.10.1	✓	2	7.3	odd	6	inner
21.3.f.a.19.1	yes	2	1.1	even	1	trivial
63.3.m.d.10.1		2	21.17	even	6
63.3.m.d.19.1		2	3.2	odd	2
147.3.d.c.97.1		2	7.2	even	3
147.3.d.c.97.2		2	7.5	odd	6
147.3.f.a.19.1		2	7.6	odd	2
147.3.f.a.31.1		2	7.4	even	3
336.3.bh.d.145.1		2	4.3	odd	2
336.3.bh.d.241.1		2	28.3	even	6
441.3.d.a.244.1		2	21.5	even	6
441.3.d.a.244.2		2	21.2	odd	6
441.3.m.g.19.1		2	21.20	even	2
441.3.m.g.325.1		2	21.11	odd	6
525.3.o.h.376.1		2	5.4	even	2
525.3.o.h.451.1		2	35.24	odd	6
525.3.s.e.124.1		4	5.2	odd	4
525.3.s.e.124.2		4	5.3	odd	4
525.3.s.e.199.1		4	35.3	even	12
525.3.s.e.199.2		4	35.17	even	12
1008.3.cg.a.145.1		2	12.11	even	2
1008.3.cg.a.577.1		2	84.59	odd	6
2352.3.f.a.97.1		2	28.19	even	6
2352.3.f.a.97.2		2	28.23	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:	\( N \)	\(=\)	\( 21 = 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	21.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 + 2.59808i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-2.50000 - 4.33013i) q^{4} +(4.50000 + 2.59808i) q^{5} -5.19615i q^{6} +(6.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +O(q^{10})\)	\(q+(-1.50000 + 2.59808i) q^{2} +(-1.50000 + 0.866025i) q^{3} +(-2.50000 - 4.33013i) q^{4} +(4.50000 + 2.59808i) q^{5} -5.19615i q^{6} +(6.50000 - 2.59808i) q^{7} +3.00000 q^{8} +(1.50000 - 2.59808i) q^{9} +(-13.5000 + 7.79423i) q^{10} +(-7.50000 - 12.9904i) q^{11} +(7.50000 + 4.33013i) q^{12} +13.8564i q^{13} +(-3.00000 + 20.7846i) q^{14} -9.00000 q^{15} +(5.50000 - 9.52628i) q^{16} +(9.00000 - 5.19615i) q^{17} +(4.50000 + 7.79423i) q^{18} +(-9.00000 - 5.19615i) q^{19} -25.9808i q^{20} +(-7.50000 + 9.52628i) q^{21} +45.0000 q^{22} +(-4.50000 + 2.59808i) q^{24} +(1.00000 + 1.73205i) q^{25} +(-36.0000 - 20.7846i) q^{26} +5.19615i q^{27} +(-27.5000 - 21.6506i) q^{28} -9.00000 q^{29} +(13.5000 - 23.3827i) q^{30} +(-10.5000 + 6.06218i) q^{31} +(22.5000 + 38.9711i) q^{32} +(22.5000 + 12.9904i) q^{33} +31.1769i q^{34} +(36.0000 + 5.19615i) q^{35} -15.0000 q^{36} +(-5.00000 + 8.66025i) q^{37} +(27.0000 - 15.5885i) q^{38} +(-12.0000 - 20.7846i) q^{39} +(13.5000 + 7.79423i) q^{40} +10.3923i q^{41} +(-13.5000 - 33.7750i) q^{42} -74.0000 q^{43} +(-37.5000 + 64.9519i) q^{44} +(13.5000 - 7.79423i) q^{45} +19.0526i q^{48} +(35.5000 - 33.7750i) q^{49} -6.00000 q^{50} +(-9.00000 + 15.5885i) q^{51} +(60.0000 - 34.6410i) q^{52} +(-16.5000 - 28.5788i) q^{53} +(-13.5000 - 7.79423i) q^{54} -77.9423i q^{55} +(19.5000 - 7.79423i) q^{56} +18.0000 q^{57} +(13.5000 - 23.3827i) q^{58} +(13.5000 - 7.79423i) q^{59} +(22.5000 + 38.9711i) q^{60} +(78.0000 + 45.0333i) q^{61} -36.3731i q^{62} +(3.00000 - 20.7846i) q^{63} -91.0000 q^{64} +(-36.0000 + 62.3538i) q^{65} +(-67.5000 + 38.9711i) q^{66} +(38.0000 + 65.8179i) q^{67} +(-45.0000 - 25.9808i) q^{68} +(-67.5000 + 85.7365i) q^{70} +84.0000 q^{71} +(4.50000 - 7.79423i) q^{72} +(-54.0000 + 31.1769i) q^{73} +(-15.0000 - 25.9808i) q^{74} +(-3.00000 - 1.73205i) q^{75} +51.9615i q^{76} +(-82.5000 - 64.9519i) q^{77} +72.0000 q^{78} +(21.5000 - 37.2391i) q^{79} +(49.5000 - 28.5788i) q^{80} +(-4.50000 - 7.79423i) q^{81} +(-27.0000 - 15.5885i) q^{82} +119.512i q^{83} +(60.0000 + 8.66025i) q^{84} +54.0000 q^{85} +(111.000 - 192.258i) q^{86} +(13.5000 - 7.79423i) q^{87} +(-22.5000 - 38.9711i) q^{88} +(-63.0000 - 36.3731i) q^{89} +46.7654i q^{90} +(36.0000 + 90.0666i) q^{91} +(10.5000 - 18.1865i) q^{93} +(-27.0000 - 46.7654i) q^{95} +(-67.5000 - 38.9711i) q^{96} -185.329i q^{97} +(34.5000 + 142.894i) q^{98} -45.0000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} - 3 q^{3} - 5 q^{4} + 9 q^{5} + 13 q^{7} + 6 q^{8} + 3 q^{9}+O(q^{10}) \) 2 * q - 3 * q^2 - 3 * q^3 - 5 * q^4 + 9 * q^5 + 13 * q^7 + 6 * q^8 + 3 * q^9	\( 2 q - 3 q^{2} - 3 q^{3} - 5 q^{4} + 9 q^{5} + 13 q^{7} + 6 q^{8} + 3 q^{9} - 27 q^{10} - 15 q^{11} + 15 q^{12} - 6 q^{14} - 18 q^{15} + 11 q^{16} + 18 q^{17} + 9 q^{18} - 18 q^{19} - 15 q^{21} + 90 q^{22} - 9 q^{24} + 2 q^{25} - 72 q^{26} - 55 q^{28} - 18 q^{29} + 27 q^{30} - 21 q^{31} + 45 q^{32} + 45 q^{33} + 72 q^{35} - 30 q^{36} - 10 q^{37} + 54 q^{38} - 24 q^{39} + 27 q^{40} - 27 q^{42} - 148 q^{43} - 75 q^{44} + 27 q^{45} + 71 q^{49} - 12 q^{50} - 18 q^{51} + 120 q^{52} - 33 q^{53} - 27 q^{54} + 39 q^{56} + 36 q^{57} + 27 q^{58} + 27 q^{59} + 45 q^{60} + 156 q^{61} + 6 q^{63} - 182 q^{64} - 72 q^{65} - 135 q^{66} + 76 q^{67} - 90 q^{68} - 135 q^{70} + 168 q^{71} + 9 q^{72} - 108 q^{73} - 30 q^{74} - 6 q^{75} - 165 q^{77} + 144 q^{78} + 43 q^{79} + 99 q^{80} - 9 q^{81} - 54 q^{82} + 120 q^{84} + 108 q^{85} + 222 q^{86} + 27 q^{87} - 45 q^{88} - 126 q^{89} + 72 q^{91} + 21 q^{93} - 54 q^{95} - 135 q^{96} + 69 q^{98} - 90 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 - 3 * q^3 - 5 * q^4 + 9 * q^5 + 13 * q^7 + 6 * q^8 + 3 * q^9 - 27 * q^10 - 15 * q^11 + 15 * q^12 - 6 * q^14 - 18 * q^15 + 11 * q^16 + 18 * q^17 + 9 * q^18 - 18 * q^19 - 15 * q^21 + 90 * q^22 - 9 * q^24 + 2 * q^25 - 72 * q^26 - 55 * q^28 - 18 * q^29 + 27 * q^30 - 21 * q^31 + 45 * q^32 + 45 * q^33 + 72 * q^35 - 30 * q^36 - 10 * q^37 + 54 * q^38 - 24 * q^39 + 27 * q^40 - 27 * q^42 - 148 * q^43 - 75 * q^44 + 27 * q^45 + 71 * q^49 - 12 * q^50 - 18 * q^51 + 120 * q^52 - 33 * q^53 - 27 * q^54 + 39 * q^56 + 36 * q^57 + 27 * q^58 + 27 * q^59 + 45 * q^60 + 156 * q^61 + 6 * q^63 - 182 * q^64 - 72 * q^65 - 135 * q^66 + 76 * q^67 - 90 * q^68 - 135 * q^70 + 168 * q^71 + 9 * q^72 - 108 * q^73 - 30 * q^74 - 6 * q^75 - 165 * q^77 + 144 * q^78 + 43 * q^79 + 99 * q^80 - 9 * q^81 - 54 * q^82 + 120 * q^84 + 108 * q^85 + 222 * q^86 + 27 * q^87 - 45 * q^88 - 126 * q^89 + 72 * q^91 + 21 * q^93 - 54 * q^95 - 135 * q^96 + 69 * q^98 - 90 * q^99

Introduction

L-functions

Modular forms

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Database

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