LMFDB - Embedded newform 546.2.l.k.295.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(211,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 0, 2]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("546.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.l (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-43})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 10x^{2} - 11x + 121 $ x^4 - x^3 - 10x^2 - 11x + 121
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			295.2
Root			$3.08945 - 1.20635i$ of defining polynomial
Character	$\chi$	$=$	546.295
Dual form			546.2.l.k.211.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})$	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{10} +(2.58945 - 4.48507i) q^{11} -1.00000 q^{12} +(-1.50000 + 3.27872i) q^{13} -1.00000 q^{14} +(-1.00000 + 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +1.00000 q^{18} +(-1.58945 - 2.75302i) q^{19} +(1.00000 + 1.73205i) q^{20} +1.00000 q^{21} +(2.58945 + 4.48507i) q^{22} +(4.08945 - 7.08314i) q^{23} +(0.500000 - 0.866025i) q^{24} -1.00000 q^{25} +(-2.08945 - 2.93840i) q^{26} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(1.58945 - 2.75302i) q^{29} +(-1.00000 - 1.73205i) q^{30} +4.17891 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.58945 - 4.48507i) q^{33} +5.00000 q^{34} +(-1.00000 - 1.73205i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.00000 + 1.73205i) q^{37} +3.17891 q^{38} +(2.08945 + 2.93840i) q^{39} -2.00000 q^{40} +(3.58945 - 6.21712i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-6.08945 - 10.5472i) q^{43} -5.17891 q^{44} +(1.00000 + 1.73205i) q^{45} +(4.08945 + 7.08314i) q^{46} -7.17891 q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} -5.00000 q^{51} +(3.58945 - 0.340322i) q^{52} -3.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(-5.17891 + 8.97013i) q^{55} +(0.500000 + 0.866025i) q^{56} -3.17891 q^{57} +(1.58945 + 2.75302i) q^{58} +(6.08945 + 10.5472i) q^{59} +2.00000 q^{60} +(1.50000 + 2.59808i) q^{61} +(-2.08945 + 3.61904i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(3.00000 - 6.55744i) q^{65} +5.17891 q^{66} +(1.91055 - 3.30916i) q^{67} +(-2.50000 + 4.33013i) q^{68} +(-4.08945 - 7.08314i) q^{69} +2.00000 q^{70} +(1.08945 + 1.88699i) q^{71} +(-0.500000 - 0.866025i) q^{72} +4.00000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-1.58945 + 2.75302i) q^{76} +5.17891 q^{77} +(-3.58945 + 0.340322i) q^{78} +13.1789 q^{79} +(1.00000 - 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.58945 + 6.21712i) q^{82} +6.17891 q^{83} +(-0.500000 - 0.866025i) q^{84} +(5.00000 + 8.66025i) q^{85} +12.1789 q^{86} +(-1.58945 - 2.75302i) q^{87} +(2.58945 - 4.48507i) q^{88} +(-4.50000 + 7.79423i) q^{89} -2.00000 q^{90} +(-3.58945 + 0.340322i) q^{91} -8.17891 q^{92} +(2.08945 - 3.61904i) q^{93} +(3.58945 - 6.21712i) q^{94} +(3.17891 + 5.50603i) q^{95} -1.00000 q^{96} +(5.17891 + 8.97013i) q^{97} +(-0.500000 - 0.866025i) q^{98} -5.17891 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 6 q^{13} - 4 q^{14} - 4 q^{15} - 2 q^{16} - 10 q^{17} + 4 q^{18} + 5 q^{19} + 4 q^{20} + 4 q^{21} - q^{22} + 5 q^{23} + 2 q^{24} - 4 q^{25} + 3 q^{26} - 4 q^{27} + 2 q^{28} - 5 q^{29} - 4 q^{30} - 6 q^{31} - 2 q^{32} + q^{33} + 20 q^{34} - 4 q^{35} - 2 q^{36} - 4 q^{37} - 10 q^{38} - 3 q^{39} - 8 q^{40} + 3 q^{41} - 2 q^{42} - 13 q^{43} + 2 q^{44} + 4 q^{45} + 5 q^{46} - 6 q^{47} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 20 q^{51} + 3 q^{52} - 12 q^{53} + 2 q^{54} + 2 q^{55} + 2 q^{56} + 10 q^{57} - 5 q^{58} + 13 q^{59} + 8 q^{60} + 6 q^{61} + 3 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{65} - 2 q^{66} + 19 q^{67} - 10 q^{68} - 5 q^{69} + 8 q^{70} - 7 q^{71} - 2 q^{72} + 16 q^{73} - 4 q^{74} - 2 q^{75} + 5 q^{76} - 2 q^{77} - 3 q^{78} + 30 q^{79} + 4 q^{80} - 2 q^{81} + 3 q^{82} + 2 q^{83} - 2 q^{84} + 20 q^{85} + 26 q^{86} + 5 q^{87} - q^{88} - 18 q^{89} - 8 q^{90} - 3 q^{91} - 10 q^{92} - 3 q^{93} + 3 q^{94} - 10 q^{95} - 4 q^{96} - 2 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 6 * q^13 - 4 * q^14 - 4 * q^15 - 2 * q^16 - 10 * q^17 + 4 * q^18 + 5 * q^19 + 4 * q^20 + 4 * q^21 - q^22 + 5 * q^23 + 2 * q^24 - 4 * q^25 + 3 * q^26 - 4 * q^27 + 2 * q^28 - 5 * q^29 - 4 * q^30 - 6 * q^31 - 2 * q^32 + q^33 + 20 * q^34 - 4 * q^35 - 2 * q^36 - 4 * q^37 - 10 * q^38 - 3 * q^39 - 8 * q^40 + 3 * q^41 - 2 * q^42 - 13 * q^43 + 2 * q^44 + 4 * q^45 + 5 * q^46 - 6 * q^47 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 20 * q^51 + 3 * q^52 - 12 * q^53 + 2 * q^54 + 2 * q^55 + 2 * q^56 + 10 * q^57 - 5 * q^58 + 13 * q^59 + 8 * q^60 + 6 * q^61 + 3 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^65 - 2 * q^66 + 19 * q^67 - 10 * q^68 - 5 * q^69 + 8 * q^70 - 7 * q^71 - 2 * q^72 + 16 * q^73 - 4 * q^74 - 2 * q^75 + 5 * q^76 - 2 * q^77 - 3 * q^78 + 30 * q^79 + 4 * q^80 - 2 * q^81 + 3 * q^82 + 2 * q^83 - 2 * q^84 + 20 * q^85 + 26 * q^86 + 5 * q^87 - q^88 - 18 * q^89 - 8 * q^90 - 3 * q^91 - 10 * q^92 - 3 * q^93 + 3 * q^94 - 10 * q^95 - 4 * q^96 - 2 * q^97 - 2 * q^98 + 2 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$1$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$2$	−0.500000	+	0.866025i	−0.353553	+	0.612372i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$3$	0.500000	−	0.866025i	0.288675	−	0.500000i
$4$	−0.500000	−	0.866025i	−0.250000	−	0.433013i
$5$	−2.00000			−0.894427			−0.447214	−	0.894427i	$-0.647584\pi$
$5$	−2.00000			−0.894427			−0.447214	+	0.894427i	$0.647584\pi$
$6$	0.500000	+	0.866025i	0.204124	+	0.353553i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$7$	0.500000	+	0.866025i	0.188982	+	0.327327i
$8$	1.00000			0.353553
$9$	−0.500000	−	0.866025i	−0.166667	−	0.288675i
$10$	1.00000	−	1.73205i	0.316228	−	0.547723i
$11$	2.58945	−	4.48507i	0.780750	−	1.35230i	−0.150756	−	0.988571i	$-0.548171\pi$
$11$	2.58945	−	4.48507i	0.780750	−	1.35230i	0.931505	−	0.363727i	$-0.118496\pi$
$12$	−1.00000			−0.288675
$13$	−1.50000	+	3.27872i	−0.416025	+	0.909353i
$13$	−1.50000	+	3.27872i	−0.416025	+	0.909353i
$14$	−1.00000			−0.267261
$15$	−1.00000	+	1.73205i	−0.258199	+	0.447214i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	−0.991838	−	0.127502i	$-0.959304\pi$
$17$	−2.50000	−	4.33013i	−0.606339	−	1.05021i	0.385499	−	0.922708i	$-0.374029\pi$
$18$	1.00000			0.235702
$19$	−1.58945	−	2.75302i	−0.364646	−	0.631585i	0.624073	−	0.781366i	$-0.285477\pi$
$19$	−1.58945	−	2.75302i	−0.364646	−	0.631585i	−0.988719	+	0.149781i	$0.952143\pi$
$20$	1.00000	+	1.73205i	0.223607	+	0.387298i
$21$	1.00000			0.218218
$22$	2.58945	+	4.48507i	0.552073	+	0.956219i
$23$	4.08945	−	7.08314i	0.852710	−	1.47694i	−0.0260431	−	0.999661i	$-0.508291\pi$
$23$	4.08945	−	7.08314i	0.852710	−	1.47694i	0.878753	−	0.477276i	$-0.158376\pi$
$24$	0.500000	−	0.866025i	0.102062	−	0.176777i
$25$	−1.00000			−0.200000
$26$	−2.08945	−	2.93840i	−0.409776	−	0.576267i
$27$	−1.00000			−0.192450
$28$	0.500000	−	0.866025i	0.0944911	−	0.163663i
$29$	1.58945	−	2.75302i	0.295154	−	0.511222i	−0.679867	−	0.733336i	$-0.737962\pi$
$29$	1.58945	−	2.75302i	0.295154	−	0.511222i	0.975021	+	0.222114i	$0.0712956\pi$
$30$	−1.00000	−	1.73205i	−0.182574	−	0.316228i
$31$	4.17891			0.750554			0.375277	−	0.926913i	$-0.377548\pi$
$31$	4.17891			0.750554			0.375277	+	0.926913i	$0.377548\pi$
$32$	−0.500000	−	0.866025i	−0.0883883	−	0.153093i
$33$	−2.58945	−	4.48507i	−0.450766	−	0.780750i
$34$	5.00000			0.857493
$35$	−1.00000	−	1.73205i	−0.169031	−	0.292770i
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	−0.936442	−	0.350823i	$-0.885902\pi$
$37$	−1.00000	+	1.73205i	−0.164399	+	0.284747i	0.772043	+	0.635571i	$0.219235\pi$
$38$	3.17891			0.515687
$39$	2.08945	+	2.93840i	0.334580	+	0.470520i
$40$	−2.00000			−0.316228
$41$	3.58945	−	6.21712i	0.560579	−	0.970951i	−0.436867	−	0.899526i	$-0.643912\pi$
$41$	3.58945	−	6.21712i	0.560579	−	0.970951i	0.997446	−	0.0714247i	$-0.0227545\pi$
$42$	−0.500000	+	0.866025i	−0.0771517	+	0.133631i
$43$	−6.08945	−	10.5472i	−0.928633	−	1.60844i	−0.785612	−	0.618720i	$-0.787652\pi$
$43$	−6.08945	−	10.5472i	−0.928633	−	1.60844i	−0.143022	−	0.989720i	$-0.545682\pi$
$44$	−5.17891			−0.780750
$45$	1.00000	+	1.73205i	0.149071	+	0.258199i
$46$	4.08945	+	7.08314i	0.602957	+	1.04435i
$47$	−7.17891			−1.04715			−0.523576	−	0.851979i	$-0.675402\pi$
$47$	−7.17891			−1.04715			−0.523576	+	0.851979i	$0.675402\pi$
$48$	0.500000	+	0.866025i	0.0721688	+	0.125000i
$49$	−0.500000	+	0.866025i	−0.0714286	+	0.123718i
$50$	0.500000	−	0.866025i	0.0707107	−	0.122474i
$51$	−5.00000			−0.700140
$52$	3.58945	−	0.340322i	0.497768	−	0.0471941i
$53$	−3.00000			−0.412082			−0.206041	−	0.978543i	$-0.566058\pi$
$53$	−3.00000			−0.412082			−0.206041	+	0.978543i	$0.566058\pi$
$54$	0.500000	−	0.866025i	0.0680414	−	0.117851i
$55$	−5.17891	+	8.97013i	−0.698324	+	1.20953i
$56$	0.500000	+	0.866025i	0.0668153	+	0.115728i
$57$	−3.17891			−0.421057
$58$	1.58945	+	2.75302i	0.208706	+	0.361489i
$59$	6.08945	+	10.5472i	0.792779	+	1.37313i	0.924240	+	0.381813i	$0.124700\pi$
$59$	6.08945	+	10.5472i	0.792779	+	1.37313i	−0.131460	+	0.991321i	$0.541967\pi$
$60$	2.00000			0.258199
$61$	1.50000	+	2.59808i	0.192055	+	0.332650i	0.945931	−	0.324367i	$-0.105151\pi$
$61$	1.50000	+	2.59808i	0.192055	+	0.332650i	−0.753876	+	0.657017i	$0.771818\pi$
$62$	−2.08945	+	3.61904i	−0.265361	+	0.459619i
$63$	0.500000	−	0.866025i	0.0629941	−	0.109109i
$64$	1.00000			0.125000
$65$	3.00000	−	6.55744i	0.372104	−	0.813350i
$66$	5.17891			0.637480
$67$	1.91055	−	3.30916i	0.233410	−	0.404279i	−0.725399	−	0.688328i	$-0.758345\pi$
$67$	1.91055	−	3.30916i	0.233410	−	0.404279i	0.958809	+	0.284050i	$0.0916781\pi$
$68$	−2.50000	+	4.33013i	−0.303170	+	0.525105i
$69$	−4.08945	−	7.08314i	−0.492312	−	0.852710i
$70$	2.00000			0.239046
$71$	1.08945	+	1.88699i	0.129294	+	0.223945i	0.923403	−	0.383831i	$-0.125395\pi$
$71$	1.08945	+	1.88699i	0.129294	+	0.223945i	−0.794109	+	0.607775i	$0.792062\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$	4.00000			0.468165			0.234082	−	0.972217i	$-0.424791\pi$
$73$	4.00000			0.468165			0.234082	+	0.972217i	$0.424791\pi$
$74$	−1.00000	−	1.73205i	−0.116248	−	0.201347i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	−1.58945	+	2.75302i	−0.182323	+	0.315793i
$77$	5.17891			0.590191
$78$	−3.58945	+	0.340322i	−0.406426	+	0.0385338i
$79$	13.1789			1.48274			0.741372	−	0.671095i	$-0.234176\pi$
$79$	13.1789			1.48274			0.741372	+	0.671095i	$0.234176\pi$
$80$	1.00000	−	1.73205i	0.111803	−	0.193649i
$81$	−0.500000	+	0.866025i	−0.0555556	+	0.0962250i
$82$	3.58945	+	6.21712i	0.396389	+	0.686566i
$83$	6.17891			0.678223			0.339112	−	0.940746i	$-0.389874\pi$
$83$	6.17891			0.678223			0.339112	+	0.940746i	$0.389874\pi$
$84$	−0.500000	−	0.866025i	−0.0545545	−	0.0944911i
$85$	5.00000	+	8.66025i	0.542326	+	0.939336i
$86$	12.1789			1.31329
$87$	−1.58945	−	2.75302i	−0.170407	−	0.295154i
$88$	2.58945	−	4.48507i	0.276037	−	0.478110i
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	−0.999653	−	0.0263586i	$-0.991609\pi$
$89$	−4.50000	+	7.79423i	−0.476999	+	0.826187i	0.522654	+	0.852545i	$0.324942\pi$
$90$	−2.00000			−0.210819
$91$	−3.58945	+	0.340322i	−0.376277	+	0.0356754i
$92$	−8.17891			−0.852710
$93$	2.08945	−	3.61904i	0.216666	−	0.375277i
$94$	3.58945	−	6.21712i	0.370224	−	0.641247i
$95$	3.17891	+	5.50603i	0.326149	+	0.564907i
$96$	−1.00000			−0.102062
$97$	5.17891	+	8.97013i	0.525838	+	0.910779i	0.999547	+	0.0300973i	$0.00958170\pi$
$97$	5.17891	+	8.97013i	0.525838	+	0.910779i	−0.473709	+	0.880682i	$0.657085\pi$
$98$	−0.500000	−	0.866025i	−0.0505076	−	0.0874818i
$99$	−5.17891			−0.520500
$100$	0.500000	+	0.866025i	0.0500000	+	0.0866025i
$101$	−3.17891	+	5.50603i	−0.316313	+	0.547871i	−0.979716	−	0.200392i	$-0.935778\pi$
$101$	−3.17891	+	5.50603i	−0.316313	+	0.547871i	0.663403	+	0.748263i	$0.269112\pi$
$102$	2.50000	−	4.33013i	0.247537	−	0.428746i
$103$	−8.17891			−0.805892			−0.402946	−	0.915224i	$-0.632014\pi$
$103$	−8.17891			−0.805892			−0.402946	+	0.915224i	$0.632014\pi$
$104$	−1.50000	+	3.27872i	−0.147087	+	0.321505i
$105$	−2.00000			−0.195180
$106$	1.50000	−	2.59808i	0.145693	−	0.252347i
$107$	−9.58945	+	16.6094i	−0.927048	+	1.60569i	−0.138813	+	0.990319i	$0.544329\pi$
$107$	−9.58945	+	16.6094i	−0.927048	+	1.60569i	−0.788235	+	0.615375i	$0.789005\pi$
$108$	0.500000	+	0.866025i	0.0481125	+	0.0833333i
$109$	4.00000			0.383131			0.191565	−	0.981480i	$-0.438644\pi$
$109$	4.00000			0.383131			0.191565	+	0.981480i	$0.438644\pi$
$110$	−5.17891	−	8.97013i	−0.493790	−	0.855269i
$111$	1.00000	+	1.73205i	0.0949158	+	0.164399i
$112$	−1.00000			−0.0944911
$113$	−9.17891	−	15.8983i	−0.863479	−	1.49559i	−0.868549	−	0.495602i	$-0.834947\pi$
$113$	−9.17891	−	15.8983i	−0.863479	−	1.49559i	0.00507042	−	0.999987i	$-0.498386\pi$
$114$	1.58945	−	2.75302i	0.148866	−	0.257844i
$115$	−8.17891	+	14.1663i	−0.762687	+	1.32101i
$116$	−3.17891			−0.295154
$117$	3.58945	−	0.340322i	0.331845	−	0.0314627i
$118$	−12.1789			−1.12116
$119$	2.50000	−	4.33013i	0.229175	−	0.396942i
$120$	−1.00000	+	1.73205i	−0.0912871	+	0.158114i
$121$	−7.91055	−	13.7015i	−0.719141	−	1.24559i
$122$	−3.00000			−0.271607
$123$	−3.58945	−	6.21712i	−0.323650	−	0.560579i
$124$	−2.08945	−	3.61904i	−0.187639	−	0.324999i
$125$	12.0000			1.07331
$126$	0.500000	+	0.866025i	0.0445435	+	0.0771517i
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	0.466870	+	0.884326i	$0.345382\pi$
$127$	−6.00000	+	10.3923i	−0.532414	+	0.922168i	−0.999284	+	0.0378419i	$0.987952\pi$
$128$	−0.500000	+	0.866025i	−0.0441942	+	0.0765466i
$129$	−12.1789			−1.07229
$130$	4.17891	+	5.87680i	0.366515	+	0.515429i
$131$	−14.5367			−1.27008			−0.635040	−	0.772479i	$-0.719016\pi$
$131$	−14.5367			−1.27008			−0.635040	+	0.772479i	$0.719016\pi$
$132$	−2.58945	+	4.48507i	−0.225383	+	0.390375i
$133$	1.58945	−	2.75302i	0.137823	−	0.238717i
$134$	1.91055	+	3.30916i	0.165046	+	0.285868i
$135$	2.00000			0.172133
$136$	−2.50000	−	4.33013i	−0.214373	−	0.371305i
$137$	−3.17891	−	5.50603i	−0.271592	−	0.470412i	0.697677	−	0.716412i	$-0.254217\pi$
$137$	−3.17891	−	5.50603i	−0.271592	−	0.470412i	−0.969270	+	0.246000i	$0.920884\pi$
$138$	8.17891			0.696235
$139$	3.41055	+	5.90724i	0.289279	+	0.501045i	0.973638	−	0.228100i	$-0.0732512\pi$
$139$	3.41055	+	5.90724i	0.289279	+	0.501045i	−0.684359	+	0.729145i	$0.739918\pi$
$140$	−1.00000	+	1.73205i	−0.0845154	+	0.146385i
$141$	−3.58945	+	6.21712i	−0.302287	+	0.523576i
$142$	−2.17891			−0.182850
$143$	10.8211	+	15.2177i	0.904905	+	1.27257i
$144$	1.00000			0.0833333
$145$	−3.17891	+	5.50603i	−0.263994	+	0.457251i
$146$	−2.00000	+	3.46410i	−0.165521	+	0.286691i
$147$	0.500000	+	0.866025i	0.0412393	+	0.0714286i
$148$	2.00000			0.164399
$149$	−8.08945	−	14.0113i	−0.662714	−	1.14785i	−0.979900	−	0.199491i	$-0.936071\pi$
$149$	−8.08945	−	14.0113i	−0.662714	−	1.14785i	0.317186	−	0.948363i	$-0.397262\pi$
$150$	−0.500000	−	0.866025i	−0.0408248	−	0.0707107i
$151$	19.5367			1.58988			0.794938	−	0.606691i	$-0.207503\pi$
$151$	19.5367			1.58988			0.794938	+	0.606691i	$0.207503\pi$
$152$	−1.58945	−	2.75302i	−0.128922	−	0.223299i
$153$	−2.50000	+	4.33013i	−0.202113	+	0.350070i
$154$	−2.58945	+	4.48507i	−0.208664	+	0.361417i
$155$	−8.35782			−0.671316
$156$	1.50000	−	3.27872i	0.120096	−	0.262508i
$157$	2.00000			0.159617			0.0798087	−	0.996810i	$-0.474569\pi$
$157$	2.00000			0.159617			0.0798087	+	0.996810i	$0.474569\pi$
$158$	−6.58945	+	11.4133i	−0.524229	+	0.907991i
$159$	−1.50000	+	2.59808i	−0.118958	+	0.206041i
$160$	1.00000	+	1.73205i	0.0790569	+	0.136931i
$161$	8.17891			0.644588
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	10.0895	+	17.4754i	0.790267	+	1.36878i	0.925801	+	0.378010i	$0.123392\pi$
$163$	10.0895	+	17.4754i	0.790267	+	1.36878i	−0.135534	+	0.990773i	$0.543275\pi$
$164$	−7.17891			−0.560579
$165$	5.17891	+	8.97013i	0.403177	+	0.698324i
$166$	−3.08945	+	5.35109i	−0.239788	+	0.415325i
$167$	4.00000	−	6.92820i	0.309529	−	0.536120i	−0.668730	−	0.743505i	$-0.733162\pi$
$167$	4.00000	−	6.92820i	0.309529	−	0.536120i	0.978259	+	0.207385i	$0.0664952\pi$
$168$	1.00000			0.0771517
$169$	−8.50000	−	9.83616i	−0.653846	−	0.756628i
$170$	−10.0000			−0.766965
$171$	−1.58945	+	2.75302i	−0.121549	+	0.210528i
$172$	−6.08945	+	10.5472i	−0.464317	+	0.804220i
$173$	−2.00000	−	3.46410i	−0.152057	−	0.263371i	0.779926	−	0.625871i	$-0.215256\pi$
$173$	−2.00000	−	3.46410i	−0.152057	−	0.263371i	−0.931984	+	0.362500i	$0.881923\pi$
$174$	3.17891			0.240992
$175$	−0.500000	−	0.866025i	−0.0377964	−	0.0654654i
$176$	2.58945	+	4.48507i	0.195187	+	0.338075i
$177$	12.1789			0.915423
$178$	−4.50000	−	7.79423i	−0.337289	−	0.584202i
$179$	−4.17891	+	7.23808i	−0.312346	+	0.541000i	−0.978870	−	0.204484i	$-0.934448\pi$
$179$	−4.17891	+	7.23808i	−0.312346	+	0.541000i	0.666524	+	0.745484i	$0.267782\pi$
$180$	1.00000	−	1.73205i	0.0745356	−	0.129099i
$181$	19.1789			1.42556			0.712779	−	0.701389i	$-0.247436\pi$
$181$	19.1789			1.42556			0.712779	+	0.701389i	$0.247436\pi$
$182$	1.50000	−	3.27872i	0.111187	−	0.243035i
$183$	3.00000			0.221766
$184$	4.08945	−	7.08314i	0.301479	−	0.522176i
$185$	2.00000	−	3.46410i	0.147043	−	0.254686i
$186$	2.08945	+	3.61904i	0.153206	+	0.265361i
$187$	−25.8945			−1.89360
$188$	3.58945	+	6.21712i	0.261788	+	0.453430i
$189$	−0.500000	−	0.866025i	−0.0363696	−	0.0629941i
$190$	−6.35782			−0.461245
$191$	3.26836	+	5.66097i	0.236490	+	0.409613i	0.959705	−	0.281010i	$-0.0906695\pi$
$191$	3.26836	+	5.66097i	0.236490	+	0.409613i	−0.723214	+	0.690624i	$0.757336\pi$
$192$	0.500000	−	0.866025i	0.0360844	−	0.0625000i
$193$	6.76836	−	11.7231i	0.487197	−	0.843851i	−0.512694	−	0.858571i	$-0.671353\pi$
$193$	6.76836	−	11.7231i	0.487197	−	0.843851i	0.999892	+	0.0147206i	$0.00468589\pi$
$194$	−10.3578			−0.743648
$195$	−4.17891	−	5.87680i	−0.299258	−	0.420846i
$196$	1.00000			0.0714286
$197$	−8.50000	+	14.7224i	−0.605600	+	1.04893i	0.386356	+	0.922350i	$0.373733\pi$
$197$	−8.50000	+	14.7224i	−0.605600	+	1.04893i	−0.991956	+	0.126580i	$0.959600\pi$
$198$	2.58945	−	4.48507i	0.184024	−	0.318740i
$199$	−12.0895	−	20.9395i	−0.856999	−	1.48437i	−0.874778	−	0.484523i	$-0.838993\pi$
$199$	−12.0895	−	20.9395i	−0.856999	−	1.48437i	0.0177797	−	0.999842i	$-0.494340\pi$
$200$	−1.00000			−0.0707107
$201$	−1.91055	−	3.30916i	−0.134760	−	0.233410i
$202$	−3.17891	−	5.50603i	−0.223667	−	0.387403i
$203$	3.17891			0.223116
$204$	2.50000	+	4.33013i	0.175035	+	0.303170i
$205$	−7.17891	+	12.4342i	−0.501397	+	0.868445i
$206$	4.08945	−	7.08314i	0.284926	−	0.493506i
$207$	−8.17891			−0.568473
$208$	−2.08945	−	2.93840i	−0.144878	−	0.203741i
$209$	−16.4633			−1.13879
$210$	1.00000	−	1.73205i	0.0690066	−	0.119523i
$211$	3.17891	−	5.50603i	0.218845	−	0.379051i	−0.735610	−	0.677405i	$-0.763104\pi$
$211$	3.17891	−	5.50603i	0.218845	−	0.379051i	0.954455	+	0.298354i	$0.0964377\pi$
$212$	1.50000	+	2.59808i	0.103020	+	0.178437i
$213$	2.17891			0.149296
$214$	−9.58945	−	16.6094i	−0.655522	−	1.13540i
$215$	12.1789	+	21.0945i	0.830595	+	1.43863i
$216$	−1.00000			−0.0680414
$217$	2.08945	+	3.61904i	0.141841	+	0.245676i
$218$	−2.00000	+	3.46410i	−0.135457	+	0.234619i
$219$	2.00000	−	3.46410i	0.135147	−	0.234082i
$220$	10.3578			0.698324
$221$	17.9473	−	1.70161i	1.20726	−	0.114463i
$222$	−2.00000			−0.134231
$223$	1.08945	−	1.88699i	0.0729552	−	0.126362i	−0.827240	−	0.561849i	$-0.810090\pi$
$223$	1.08945	−	1.88699i	0.0729552	−	0.126362i	0.900195	+	0.435487i	$0.143424\pi$
$224$	0.500000	−	0.866025i	0.0334077	−	0.0578638i
$225$	0.500000	+	0.866025i	0.0333333	+	0.0577350i
$226$	18.3578			1.22114
$227$	7.17891	+	12.4342i	0.476481	+	0.825289i	0.999637	−	0.0269479i	$-0.00857881\pi$
$227$	7.17891	+	12.4342i	0.476481	+	0.825289i	−0.523156	+	0.852237i	$0.675245\pi$
$228$	1.58945	+	2.75302i	0.105264	+	0.182323i
$229$	1.00000			0.0660819			0.0330409	−	0.999454i	$-0.489481\pi$
$229$	1.00000			0.0660819			0.0330409	+	0.999454i	$0.489481\pi$
$230$	−8.17891	−	14.1663i	−0.539301	−	0.934097i
$231$	2.58945	−	4.48507i	0.170374	−	0.295096i
$232$	1.58945	−	2.75302i	0.104353	−	0.180744i
$233$	22.3578			1.46471			0.732355	−	0.680923i	$-0.238421\pi$
$233$	22.3578			1.46471			0.732355	+	0.680923i	$0.238421\pi$
$234$	−1.50000	+	3.27872i	−0.0980581	+	0.214337i
$235$	14.3578			0.936601
$236$	6.08945	−	10.5472i	0.396390	−	0.686567i
$237$	6.58945	−	11.4133i	0.428031	−	0.741372i
$238$	2.50000	+	4.33013i	0.162051	+	0.280680i
$239$	10.1789			0.658419			0.329209	−	0.944257i	$-0.393218\pi$
$239$	10.1789			0.658419			0.329209	+	0.944257i	$0.393218\pi$
$240$	−1.00000	−	1.73205i	−0.0645497	−	0.111803i
$241$	−2.17891	−	3.77398i	−0.140356	−	0.243103i	0.787275	−	0.616602i	$-0.211491\pi$
$241$	−2.17891	−	3.77398i	−0.140356	−	0.243103i	−0.927631	+	0.373499i	$0.878158\pi$
$242$	15.8211			1.01702
$243$	0.500000	+	0.866025i	0.0320750	+	0.0555556i
$244$	1.50000	−	2.59808i	0.0960277	−	0.166325i
$245$	1.00000	−	1.73205i	0.0638877	−	0.110657i
$246$	7.17891			0.457710
$247$	11.4105	−	1.08185i	0.726036	−	0.0688365i
$248$	4.17891			0.265361
$249$	3.08945	−	5.35109i	0.195786	−	0.339112i
$250$	−6.00000	+	10.3923i	−0.379473	+	0.657267i
$251$	−11.0895	−	19.2075i	−0.699960	−	1.21237i	−0.968480	−	0.249092i	$-0.919868\pi$
$251$	−11.0895	−	19.2075i	−0.699960	−	1.21237i	0.268520	−	0.963274i	$-0.413466\pi$
$252$	−1.00000			−0.0629941
$253$	−21.1789	−	36.6829i	−1.33151	−	2.30624i
$254$	−6.00000	−	10.3923i	−0.376473	−	0.652071i
$255$	10.0000			0.626224
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	9.85782	−	17.0742i	0.614914	−	1.06506i	−0.375486	−	0.926828i	$-0.622524\pi$
$257$	9.85782	−	17.0742i	0.614914	−	1.06506i	0.990400	−	0.138234i	$-0.0441425\pi$
$258$	6.08945	−	10.5472i	0.379113	−	0.656643i
$259$	−2.00000			−0.124274
$260$	−7.17891	+	0.680643i	−0.445217	+	0.0422117i
$261$	−3.17891			−0.196769
$262$	7.26836	−	12.5892i	0.449041	−	0.777762i
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	−0.619586	−	0.784929i	$-0.712699\pi$
$263$	6.00000	−	10.3923i	0.369976	−	0.640817i	0.989561	+	0.144112i	$0.0460326\pi$
$264$	−2.58945	−	4.48507i	−0.159370	−	0.276037i
$265$	6.00000			0.368577
$266$	1.58945	+	2.75302i	0.0974557	+	0.168798i
$267$	4.50000	+	7.79423i	0.275396	+	0.476999i
$268$	−3.82109			−0.233410
$269$	2.17891	+	3.77398i	0.132850	+	0.230104i	0.924774	−	0.380516i	$-0.124254\pi$
$269$	2.17891	+	3.77398i	0.132850	+	0.230104i	−0.791924	+	0.610620i	$0.790920\pi$
$270$	−1.00000	+	1.73205i	−0.0608581	+	0.105409i
$271$	−9.91055	+	17.1656i	−0.602023	+	1.04273i	0.390492	+	0.920606i	$0.372305\pi$
$271$	−9.91055	+	17.1656i	−0.602023	+	1.04273i	−0.992514	+	0.122128i	$0.961028\pi$
$272$	5.00000			0.303170
$273$	−1.50000	+	3.27872i	−0.0907841	+	0.198437i
$274$	6.35782			0.384090
$275$	−2.58945	+	4.48507i	−0.156150	+	0.270460i
$276$	−4.08945	+	7.08314i	−0.246156	+	0.426355i
$277$	−2.82109	−	4.88627i	−0.169503	−	0.293588i	0.768742	−	0.639559i	$-0.220883\pi$
$277$	−2.82109	−	4.88627i	−0.169503	−	0.293588i	−0.938245	+	0.345971i	$0.887550\pi$
$278$	−6.82109			−0.409102
$279$	−2.08945	−	3.61904i	−0.125092	−	0.216666i
$280$	−1.00000	−	1.73205i	−0.0597614	−	0.103510i
$281$	28.3578			1.69169			0.845843	−	0.533432i	$-0.179098\pi$
$281$	28.3578			1.69169			0.845843	+	0.533432i	$0.179098\pi$
$282$	−3.58945	−	6.21712i	−0.213749	−	0.370224i
$283$	−3.82109	+	6.61832i	−0.227140	+	0.393419i	−0.956959	−	0.290222i	$-0.906271\pi$
$283$	−3.82109	+	6.61832i	−0.227140	+	0.393419i	0.729819	+	0.683640i	$0.239604\pi$
$284$	1.08945	−	1.88699i	0.0646472	−	0.111972i
$285$	6.35782			0.376605
$286$	−18.5895	+	1.76249i	−1.09922	+	0.104218i
$287$	7.17891			0.423758
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−4.00000	+	6.92820i	−0.235294	+	0.407541i
$290$	−3.17891	−	5.50603i	−0.186672	−	0.323325i
$291$	10.3578			0.607186
$292$	−2.00000	−	3.46410i	−0.117041	−	0.202721i
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	0.635818	−	0.771839i	$-0.280663\pi$
$293$	−6.00000	−	10.3923i	−0.350524	−	0.607125i	−0.986341	+	0.164714i	$0.947330\pi$
$294$	−1.00000			−0.0583212
$295$	−12.1789	−	21.0945i	−0.709083	−	1.22817i
$296$	−1.00000	+	1.73205i	−0.0581238	+	0.100673i
$297$	−2.58945	+	4.48507i	−0.150255	+	0.260250i
$298$	16.1789			0.937219
$299$	17.0895	+	24.0329i	0.988309	+	1.38986i
$300$	1.00000			0.0577350
$301$	6.08945	−	10.5472i	0.350990	−	0.607933i
$302$	−9.76836	+	16.9193i	−0.562106	+	0.973596i
$303$	3.17891	+	5.50603i	0.182624	+	0.316313i
$304$	3.17891			0.182323
$305$	−3.00000	−	5.19615i	−0.171780	−	0.297531i
$306$	−2.50000	−	4.33013i	−0.142915	−	0.247537i
$307$	−31.8945			−1.82032			−0.910159	−	0.414259i	$-0.864041\pi$
$307$	−31.8945			−1.82032			−0.910159	+	0.414259i	$0.864041\pi$
$308$	−2.58945	−	4.48507i	−0.147548	−	0.255560i
$309$	−4.08945	+	7.08314i	−0.232641	+	0.402946i
$310$	4.17891	−	7.23808i	0.237346	−	0.411095i
$311$	25.5367			1.44805			0.724027	−	0.689771i	$-0.242289\pi$
$311$	25.5367			1.44805			0.724027	+	0.689771i	$0.242289\pi$
$312$	2.08945	+	2.93840i	0.118292	+	0.166354i
$313$	4.00000			0.226093			0.113047	−	0.993590i	$-0.463939\pi$
$313$	4.00000			0.226093			0.113047	+	0.993590i	$0.463939\pi$
$314$	−1.00000	+	1.73205i	−0.0564333	+	0.0977453i
$315$	−1.00000	+	1.73205i	−0.0563436	+	0.0975900i
$316$	−6.58945	−	11.4133i	−0.370686	−	0.642047i
$317$	−4.17891			−0.234711			−0.117355	−	0.993090i	$-0.537442\pi$
$317$	−4.17891			−0.234711			−0.117355	+	0.993090i	$0.537442\pi$
$318$	−1.50000	−	2.59808i	−0.0841158	−	0.145693i
$319$	−8.23164	−	14.2576i	−0.460883	−	0.798273i
$320$	−2.00000			−0.111803
$321$	9.58945	+	16.6094i	0.535231	+	0.927048i
$322$	−4.08945	+	7.08314i	−0.227896	+	0.394728i
$323$	−7.94727	+	13.7651i	−0.442198	+	0.765909i
$324$	1.00000			0.0555556
$325$	1.50000	−	3.27872i	0.0832050	−	0.181871i
$326$	−20.1789			−1.11761
$327$	2.00000	−	3.46410i	0.110600	−	0.191565i
$328$	3.58945	−	6.21712i	0.198194	−	0.343283i
$329$	−3.58945	−	6.21712i	−0.197893	−	0.342761i
$330$	−10.3578			−0.570179
$331$	0.821092	+	1.42217i	0.0451313	+	0.0781697i	0.887709	−	0.460406i	$-0.152296\pi$
$331$	0.821092	+	1.42217i	0.0451313	+	0.0781697i	−0.842577	+	0.538575i	$0.818963\pi$
$332$	−3.08945	−	5.35109i	−0.169556	−	0.293679i
$333$	2.00000			0.109599
$334$	4.00000	+	6.92820i	0.218870	+	0.379094i
$335$	−3.82109	+	6.61832i	−0.208769	+	0.361598i
$336$	−0.500000	+	0.866025i	−0.0272772	+	0.0472456i
$337$	33.5367			1.82686			0.913431	−	0.406994i	$-0.133423\pi$
$337$	33.5367			1.82686			0.913431	+	0.406994i	$0.133423\pi$
$338$	12.7684	−	2.44314i	0.694507	−	0.132889i
$339$	−18.3578			−0.997060
$340$	5.00000	−	8.66025i	0.271163	−	0.469668i
$341$	10.8211	−	18.7427i	0.585995	−	1.01497i
$342$	−1.58945	−	2.75302i	−0.0859478	−	0.148866i
$343$	−1.00000			−0.0539949
$344$	−6.08945	−	10.5472i	−0.328321	−	0.568669i
$345$	8.17891	+	14.1663i	0.440338	+	0.762687i
$346$	4.00000			0.215041
$347$	9.58945	+	16.6094i	0.514789	+	0.891640i	0.999853	+	0.0171617i	$0.00546302\pi$
$347$	9.58945	+	16.6094i	0.514789	+	0.891640i	−0.485064	+	0.874479i	$0.661204\pi$
$348$	−1.58945	+	2.75302i	−0.0852037	+	0.147577i
$349$	−4.08945	+	7.08314i	−0.218903	+	0.379152i	−0.954473	−	0.298297i	$-0.903581\pi$
$349$	−4.08945	+	7.08314i	−0.218903	+	0.379152i	0.735570	+	0.677449i	$0.236915\pi$
$350$	1.00000			0.0534522
$351$	1.50000	−	3.27872i	0.0800641	−	0.175005i
$352$	−5.17891			−0.276037
$353$	−2.08945	+	3.61904i	−0.111210	+	0.192622i	−0.916259	−	0.400587i	$-0.868806\pi$
$353$	−2.08945	+	3.61904i	−0.111210	+	0.192622i	0.805048	+	0.593209i	$0.202139\pi$
$354$	−6.08945	+	10.5472i	−0.323651	+	0.560580i
$355$	−2.17891	−	3.77398i	−0.115644	−	0.200302i
$356$	9.00000			0.476999
$357$	−2.50000	−	4.33013i	−0.132314	−	0.229175i
$358$	−4.17891	−	7.23808i	−0.220862	−	0.382544i
$359$	−10.3578			−0.546665			−0.273332	−	0.961920i	$-0.588126\pi$
$359$	−10.3578			−0.546665			−0.273332	+	0.961920i	$0.588126\pi$
$360$	1.00000	+	1.73205i	0.0527046	+	0.0912871i
$361$	4.44727	−	7.70290i	0.234067	−	0.405416i
$362$	−9.58945	+	16.6094i	−0.504011	+	0.872972i
$363$	−15.8211			−0.830392
$364$	2.08945	+	2.93840i	0.109517	+	0.154014i
$365$	−8.00000			−0.418739
$366$	−1.50000	+	2.59808i	−0.0784063	+	0.135804i
$367$	4.08945	−	7.08314i	0.213468	−	0.369737i	−0.739330	−	0.673344i	$-0.764857\pi$
$367$	4.08945	−	7.08314i	0.213468	−	0.369737i	0.952797	+	0.303607i	$0.0981908\pi$
$368$	4.08945	+	7.08314i	0.213178	+	0.369234i
$369$	−7.17891			−0.373719
$370$	2.00000	+	3.46410i	0.103975	+	0.180090i
$371$	−1.50000	−	2.59808i	−0.0778761	−	0.134885i
$372$	−4.17891			−0.216666
$373$	10.0000	+	17.3205i	0.517780	+	0.896822i	0.999787	+	0.0206542i	$0.00657489\pi$
$373$	10.0000	+	17.3205i	0.517780	+	0.896822i	−0.482006	+	0.876168i	$0.660092\pi$
$374$	12.9473	−	22.4253i	0.669487	−	1.15959i
$375$	6.00000	−	10.3923i	0.309839	−	0.536656i
$376$	−7.17891			−0.370224
$377$	6.64218	+	9.34090i	0.342090	+	0.481081i
$378$	1.00000			0.0514344
$379$	12.3578	−	21.4044i	0.634778	−	1.09947i	−0.351784	−	0.936081i	$-0.614425\pi$
$379$	12.3578	−	21.4044i	0.634778	−	1.09947i	0.986562	−	0.163387i	$-0.0522420\pi$
$380$	3.17891	−	5.50603i	0.163075	−	0.282453i
$381$	6.00000	+	10.3923i	0.307389	+	0.532414i
$382$	−6.53673			−0.334448
$383$	−10.5895	−	18.3415i	−0.541096	−	0.937205i	−0.998841	−	0.0481223i	$-0.984676\pi$
$383$	−10.5895	−	18.3415i	−0.541096	−	0.937205i	0.457746	−	0.889083i	$-0.348657\pi$
$384$	0.500000	+	0.866025i	0.0255155	+	0.0441942i
$385$	−10.3578			−0.527883
$386$	6.76836	+	11.7231i	0.344501	+	0.596693i
$387$	−6.08945	+	10.5472i	−0.309544	+	0.536147i
$388$	5.17891	−	8.97013i	0.262919	−	0.455389i
$389$	−12.1789			−0.617495			−0.308748	−	0.951144i	$-0.599910\pi$
$389$	−12.1789			−0.617495			−0.308748	+	0.951144i	$0.599910\pi$
$390$	7.17891	−	0.680643i	0.363518	−	0.0344657i
$391$	−40.8945			−2.06813
$392$	−0.500000	+	0.866025i	−0.0252538	+	0.0437409i
$393$	−7.26836	+	12.5892i	−0.366640	+	0.635040i
$394$	−8.50000	−	14.7224i	−0.428224	−	0.741705i
$395$	−26.3578			−1.32621
$396$	2.58945	+	4.48507i	0.130125	+	0.225383i
$397$	−1.50000	−	2.59808i	−0.0752828	−	0.130394i	0.825926	−	0.563778i	$-0.190653\pi$
$397$	−1.50000	−	2.59808i	−0.0752828	−	0.130394i	−0.901209	+	0.433384i	$0.857319\pi$
$398$	24.1789			1.21198
$399$	−1.58945	−	2.75302i	−0.0795722	−	0.137823i
$400$	0.500000	−	0.866025i	0.0250000	−	0.0433013i
$401$	−4.82109	+	8.35038i	−0.240754	+	0.416998i	−0.960929	−	0.276794i	$-0.910728\pi$
$401$	−4.82109	+	8.35038i	−0.240754	+	0.416998i	0.720175	+	0.693792i	$0.244061\pi$
$402$	3.82109			0.190579
$403$	−6.26836	+	13.7015i	−0.312249	+	0.682519i
$404$	6.35782			0.316313
$405$	1.00000	−	1.73205i	0.0496904	−	0.0860663i
$406$	−1.58945	+	2.75302i	−0.0788833	+	0.136630i
$407$	5.17891	+	8.97013i	0.256709	+	0.444633i
$408$	−5.00000			−0.247537
$409$	18.1789	+	31.4868i	0.898889	+	1.55692i	0.828916	+	0.559373i	$0.188958\pi$
$409$	18.1789	+	31.4868i	0.898889	+	1.55692i	0.0699730	+	0.997549i	$0.477709\pi$
$410$	−7.17891	−	12.4342i	−0.354541	−	0.614083i
$411$	−6.35782			−0.313608
$412$	4.08945	+	7.08314i	0.201473	+	0.348961i
$413$	−6.08945	+	10.5472i	−0.299642	+	0.518996i
$414$	4.08945	−	7.08314i	0.200986	−	0.348117i
$415$	−12.3578			−0.606621
$416$	3.58945	−	0.340322i	0.175987	−	0.0166856i
$417$	6.82109			0.334030
$418$	8.23164	−	14.2576i	0.402623	−	0.697363i
$419$	13.4473	−	23.2914i	0.656942	−	1.13786i	−0.324461	−	0.945899i	$-0.605183\pi$
$419$	13.4473	−	23.2914i	0.656942	−	1.13786i	0.981403	−	0.191958i	$-0.0614838\pi$
$420$	1.00000	+	1.73205i	0.0487950	+	0.0845154i
$421$	10.7156			0.522248			0.261124	−	0.965305i	$-0.415907\pi$
$421$	10.7156			0.522248			0.261124	+	0.965305i	$0.415907\pi$
$422$	3.17891	+	5.50603i	0.154747	+	0.268029i
$423$	3.58945	+	6.21712i	0.174525	+	0.302287i
$424$	−3.00000			−0.145693
$425$	2.50000	+	4.33013i	0.121268	+	0.210042i
$426$	−1.08945	+	1.88699i	−0.0527842	+	0.0914250i
$427$	−1.50000	+	2.59808i	−0.0725901	+	0.125730i
$428$	19.1789			0.927048
$429$	18.5895	−	1.76249i	0.897507	−	0.0850940i
$430$	−24.3578			−1.17464
$431$	−5.08945	+	8.81519i	−0.245150	+	0.424613i	−0.962174	−	0.272436i	$-0.912171\pi$
$431$	−5.08945	+	8.81519i	−0.245150	+	0.424613i	0.717024	+	0.697049i	$0.245504\pi$
$432$	0.500000	−	0.866025i	0.0240563	−	0.0416667i
$433$	−17.1789	−	29.7547i	−0.825566	−	1.42992i	−0.901486	−	0.432808i	$-0.857523\pi$
$433$	−17.1789	−	29.7547i	−0.825566	−	1.42992i	0.0759206	−	0.997114i	$-0.475810\pi$
$434$	−4.17891			−0.200594
$435$	3.17891	+	5.50603i	0.152417	+	0.263994i
$436$	−2.00000	−	3.46410i	−0.0957826	−	0.165900i
$437$	−26.0000			−1.24375
$438$	2.00000	+	3.46410i	0.0955637	+	0.165521i
$439$	−20.3578	+	35.2608i	−0.971626	+	1.68290i	−0.280977	+	0.959715i	$0.590658\pi$
$439$	−20.3578	+	35.2608i	−0.971626	+	1.68290i	−0.690649	+	0.723190i	$0.742675\pi$
$440$	−5.17891	+	8.97013i	−0.246895	+	0.427634i
$441$	1.00000			0.0476190
$442$	−7.50000	+	16.3936i	−0.356739	+	0.779764i
$443$	3.17891			0.151034			0.0755172	−	0.997144i	$-0.475939\pi$
$443$	3.17891			0.151034			0.0755172	+	0.997144i	$0.475939\pi$
$444$	1.00000	−	1.73205i	0.0474579	−	0.0821995i
$445$	9.00000	−	15.5885i	0.426641	−	0.738964i
$446$	1.08945	+	1.88699i	0.0515872	+	0.0893516i
$447$	−16.1789			−0.765236
$448$	0.500000	+	0.866025i	0.0236228	+	0.0409159i
$449$	7.00000	+	12.1244i	0.330350	+	0.572184i	0.982581	−	0.185837i	$-0.0594997\pi$
$449$	7.00000	+	12.1244i	0.330350	+	0.572184i	−0.652230	+	0.758021i	$0.726166\pi$
$450$	−1.00000			−0.0471405
$451$	−18.5895	−	32.1979i	−0.875343	−	1.51614i
$452$	−9.17891	+	15.8983i	−0.431740	+	0.747795i
$453$	9.76836	−	16.9193i	0.458958	−	0.794938i
$454$	−14.3578			−0.673846
$455$	7.17891	−	0.680643i	0.336552	−	0.0319090i
$456$	−3.17891			−0.148866
$457$	−12.4473	+	21.5593i	−0.582259	+	1.00850i	0.412952	+	0.910753i	$0.364498\pi$
$457$	−12.4473	+	21.5593i	−0.582259	+	1.00850i	−0.995211	+	0.0977491i	$0.968836\pi$
$458$	−0.500000	+	0.866025i	−0.0233635	+	0.0404667i
$459$	2.50000	+	4.33013i	0.116690	+	0.202113i
$460$	16.3578			0.762687
$461$	−10.3578	−	17.9403i	−0.482412	−	0.835561i	0.517385	−	0.855753i	$-0.326906\pi$
$461$	−10.3578	−	17.9403i	−0.482412	−	0.835561i	−0.999796	+	0.0201916i	$0.993572\pi$
$462$	2.58945	+	4.48507i	0.120472	+	0.208664i
$463$	27.8945			1.29637			0.648185	−	0.761483i	$-0.275528\pi$
$463$	27.8945			1.29637			0.648185	+	0.761483i	$0.275528\pi$
$464$	1.58945	+	2.75302i	0.0737886	+	0.127806i
$465$	−4.17891	+	7.23808i	−0.193792	+	0.335658i
$466$	−11.1789	+	19.3624i	−0.517853	+	0.896948i
$467$	−22.8945			−1.05943			−0.529717	−	0.848175i	$-0.677702\pi$
$467$	−22.8945			−1.05943			−0.529717	+	0.848175i	$0.677702\pi$
$468$	−2.08945	−	2.93840i	−0.0965851	−	0.135827i
$469$	3.82109			0.176442
$470$	−7.17891	+	12.4342i	−0.331138	+	0.573548i
$471$	1.00000	−	1.73205i	0.0460776	−	0.0798087i
$472$	6.08945	+	10.5472i	0.280290	+	0.485476i
$473$	−63.0735			−2.90012
$474$	6.58945	+	11.4133i	0.302664	+	0.524229i
$475$	1.58945	+	2.75302i	0.0729292	+	0.126317i
$476$	−5.00000			−0.229175
$477$	1.50000	+	2.59808i	0.0686803	+	0.118958i
$478$	−5.08945	+	8.81519i	−0.232786	+	0.403198i
$479$	20.5895	−	35.6620i	0.940756	−	1.62944i	0.176723	−	0.984261i	$-0.443450\pi$
$479$	20.5895	−	35.6620i	0.940756	−	1.62944i	0.764033	−	0.645177i	$-0.223216\pi$
$480$	2.00000			0.0912871
$481$	−4.17891	−	5.87680i	−0.190542	−	0.267959i
$482$	4.35782			0.198493
$483$	4.08945	−	7.08314i	0.186077	−	0.322294i
$484$	−7.91055	+	13.7015i	−0.359570	+	0.622794i
$485$	−10.3578	−	17.9403i	−0.470324	−	0.814625i
$486$	−1.00000			−0.0453609
$487$	13.4105	+	23.2277i	0.607690	+	1.05255i	0.991620	+	0.129188i	$0.0412369\pi$
$487$	13.4105	+	23.2277i	0.607690	+	1.05255i	−0.383930	+	0.923362i	$0.625430\pi$
$488$	1.50000	+	2.59808i	0.0679018	+	0.117609i
$489$	20.1789			0.912522
$490$	1.00000	+	1.73205i	0.0451754	+	0.0782461i
$491$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$491$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$492$	−3.58945	+	6.21712i	−0.161825	+	0.280289i
$493$	−15.8945			−0.715854
$494$	−4.76836	+	10.4227i	−0.214539	+	0.468942i
$495$	10.3578			0.465549
$496$	−2.08945	+	3.61904i	−0.0938193	+	0.162500i
$497$	−1.08945	+	1.88699i	−0.0488687	+	0.0846431i
$498$	3.08945	+	5.35109i	0.138442	+	0.239788i
$499$	8.17891			0.366138			0.183069	−	0.983100i	$-0.441397\pi$
$499$	8.17891			0.366138			0.183069	+	0.983100i	$0.441397\pi$
$500$	−6.00000	−	10.3923i	−0.268328	−	0.464758i
$501$	−4.00000	−	6.92820i	−0.178707	−	0.309529i
$502$	22.1789			0.989893
$503$	12.0000	+	20.7846i	0.535054	+	0.926740i	0.999161	+	0.0409609i	$0.0130419\pi$
$503$	12.0000	+	20.7846i	0.535054	+	0.926740i	−0.464107	+	0.885779i	$0.653625\pi$
$504$	0.500000	−	0.866025i	0.0222718	−	0.0385758i
$505$	6.35782	−	11.0121i	0.282919	−	0.490030i
$506$	42.3578			1.88303
$507$	−12.7684	+	2.44314i	−0.567063	+	0.108504i
$508$	12.0000			0.532414
$509$	8.35782	−	14.4762i	0.370454	−	0.641645i	−0.619182	−	0.785248i	$-0.712536\pi$
$509$	8.35782	−	14.4762i	0.370454	−	0.641645i	0.989635	+	0.143603i	$0.0458689\pi$
$510$	−5.00000	+	8.66025i	−0.221404	+	0.383482i
$511$	2.00000	+	3.46410i	0.0884748	+	0.153243i
$512$	1.00000			0.0441942
$513$	1.58945	+	2.75302i	0.0701761	+	0.121549i
$514$	9.85782	+	17.0742i	0.434810	+	0.753112i
$515$	16.3578			0.720812
$516$	6.08945	+	10.5472i	0.268073	+	0.464317i
$517$	−18.5895	+	32.1979i	−0.817563	+	1.41606i
$518$	1.00000	−	1.73205i	0.0439375	−	0.0761019i
$519$	−4.00000			−0.175581
$520$	3.00000	−	6.55744i	0.131559	−	0.287563i
$521$	7.17891			0.314514			0.157257	−	0.987558i	$-0.449735\pi$
$521$	7.17891			0.314514			0.157257	+	0.987558i	$0.449735\pi$
$522$	1.58945	−	2.75302i	0.0695685	−	0.120496i
$523$	−5.76836	+	9.99110i	−0.252233	+	0.436880i	−0.964140	−	0.265393i	$-0.914498\pi$
$523$	−5.76836	+	9.99110i	−0.252233	+	0.436880i	0.711907	+	0.702273i	$0.247832\pi$
$524$	7.26836	+	12.5892i	0.317520	+	0.549961i
$525$	−1.00000			−0.0436436
$526$	6.00000	+	10.3923i	0.261612	+	0.453126i
$527$	−10.4473	−	18.0952i	−0.455090	−	0.788239i
$528$	5.17891			0.225383
$529$	−21.9473	−	38.0138i	−0.954229	−	1.65277i
$530$	−3.00000	+	5.19615i	−0.130312	+	0.225706i
$531$	6.08945	−	10.5472i	0.264260	−	0.457711i
$532$	−3.17891			−0.137823
$533$	15.0000	+	21.0945i	0.649722	+	0.913704i
$534$	−9.00000			−0.389468
$535$	19.1789	−	33.2188i	0.829177	−	1.43618i
$536$	1.91055	−	3.30916i	0.0825230	−	0.142934i
$537$	4.17891	+	7.23808i	0.180333	+	0.312346i
$538$	−4.35782			−0.187879
$539$	2.58945	+	4.48507i	0.111536	+	0.193185i
$540$	−1.00000	−	1.73205i	−0.0430331	−	0.0745356i
$541$	−20.3578			−0.875251			−0.437625	−	0.899157i	$-0.644180\pi$
$541$	−20.3578			−0.875251			−0.437625	+	0.899157i	$0.644180\pi$
$542$	−9.91055	−	17.1656i	−0.425694	−	0.737324i
$543$	9.58945	−	16.6094i	0.411523	−	0.712779i
$544$	−2.50000	+	4.33013i	−0.107187	+	0.185653i
$545$	−8.00000			−0.342682
$546$	−2.08945	−	2.93840i	−0.0894204	−	0.125752i
$547$	36.0000			1.53925			0.769624	−	0.638497i	$-0.220443\pi$
$547$	36.0000			1.53925			0.769624	+	0.638497i	$0.220443\pi$
$548$	−3.17891	+	5.50603i	−0.135796	+	0.235206i
$549$	1.50000	−	2.59808i	0.0640184	−	0.110883i
$550$	−2.58945	−	4.48507i	−0.110415	−	0.191244i
$551$	−10.1055			−0.430507
$552$	−4.08945	−	7.08314i	−0.174059	−	0.301479i
$553$	6.58945	+	11.4133i	0.280212	+	0.485342i
$554$	5.64218			0.239713
$555$	−2.00000	−	3.46410i	−0.0848953	−	0.147043i
$556$	3.41055	−	5.90724i	0.144639	−	0.250523i
$557$	−11.8578	+	20.5383i	−0.502432	+	0.870237i	0.497564	+	0.867427i	$0.334228\pi$
$557$	−11.8578	+	20.5383i	−0.502432	+	0.870237i	−0.999996	+	0.00281030i	$0.999105\pi$
$558$	4.17891			0.176907
$559$	43.7156	−	4.14474i	1.84897	−	0.175304i
$560$	2.00000			0.0845154
$561$	−12.9473	+	22.4253i	−0.546634	+	0.946798i
$562$	−14.1789	+	24.5586i	−0.598101	+	1.03594i
$563$	9.17891	+	15.8983i	0.386845	+	0.670035i	0.992023	−	0.126055i	$-0.0402316\pi$
$563$	9.17891	+	15.8983i	0.386845	+	0.670035i	−0.605178	+	0.796090i	$0.706898\pi$
$564$	7.17891			0.302287
$565$	18.3578	+	31.7967i	0.772319	+	1.33770i
$566$	−3.82109	−	6.61832i	−0.160612	−	0.278189i
$567$	−1.00000			−0.0419961
$568$	1.08945	+	1.88699i	0.0457125	+	0.0791763i
$569$	1.82109	−	3.15422i	0.0763441	−	0.132232i	−0.825326	−	0.564657i	$-0.809009\pi$
$569$	1.82109	−	3.15422i	0.0763441	−	0.132232i	0.901670	+	0.432425i	$0.142342\pi$
$570$	−3.17891	+	5.50603i	−0.133150	+	0.230622i
$571$	−34.1789			−1.43034			−0.715171	−	0.698949i	$-0.753651\pi$
$571$	−34.1789			−1.43034			−0.715171	+	0.698949i	$0.753651\pi$
$572$	7.76836	−	16.9802i	0.324812	−	0.709977i
$573$	6.53673			0.273076
$574$	−3.58945	+	6.21712i	−0.149821	+	0.259497i
$575$	−4.08945	+	7.08314i	−0.170542	+	0.295387i
$576$	−0.500000	−	0.866025i	−0.0208333	−	0.0360844i
$577$	−28.3578			−1.18055			−0.590276	−	0.807202i	$-0.700981\pi$
$577$	−28.3578			−1.18055			−0.590276	+	0.807202i	$0.700981\pi$
$578$	−4.00000	−	6.92820i	−0.166378	−	0.288175i
$579$	−6.76836	−	11.7231i	−0.281284	−	0.487197i
$580$	6.35782			0.263994
$581$	3.08945	+	5.35109i	0.128172	+	0.222001i
$582$	−5.17891	+	8.97013i	−0.214673	+	0.371824i
$583$	−7.76836	+	13.4552i	−0.321733	+	0.557257i
$584$	4.00000			0.165521
$585$	−7.17891	+	0.680643i	−0.296811	+	0.0281411i
$586$	12.0000			0.495715
$587$	−0.0894542	+	0.154939i	−0.00369217	+	0.00639502i	−0.867866	−	0.496799i	$-0.834509\pi$
$587$	−0.0894542	+	0.154939i	−0.00369217	+	0.00639502i	0.864173	+	0.503194i	$0.167842\pi$
$588$	0.500000	−	0.866025i	0.0206197	−	0.0357143i
$589$	−6.64218	−	11.5046i	−0.273686	−	0.474039i
$590$	24.3578			1.00280
$591$	8.50000	+	14.7224i	0.349643	+	0.605600i
$592$	−1.00000	−	1.73205i	−0.0410997	−	0.0711868i
$593$	−33.0000			−1.35515			−0.677574	−	0.735455i	$-0.736969\pi$
$593$	−33.0000			−1.35515			−0.677574	+	0.735455i	$0.736969\pi$
$594$	−2.58945	−	4.48507i	−0.106247	−	0.184024i
$595$	−5.00000	+	8.66025i	−0.204980	+	0.355036i
$596$	−8.08945	+	14.0113i	−0.331357	+	0.573927i
$597$	−24.1789			−0.989577
$598$	−29.3578	+	2.78346i	−1.20053	+	0.113824i
$599$	40.1789			1.64167			0.820833	−	0.571168i	$-0.193510\pi$
$599$	40.1789			1.64167			0.820833	+	0.571168i	$0.193510\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	−0.549602	−	0.835426i	$-0.685221\pi$
$601$	11.0000	−	19.0526i	0.448699	−	0.777170i	0.998302	+	0.0582563i	$0.0185541\pi$
$602$	6.08945	+	10.5472i	0.248188	+	0.429874i
$603$	−3.82109			−0.155607
$604$	−9.76836	−	16.9193i	−0.397469	−	0.688437i
$605$	15.8211	+	27.4029i	0.643219	+	1.11409i
$606$	−6.35782			−0.258269
$607$	0.268363	+	0.464818i	0.0108925	+	0.0188664i	0.871420	−	0.490537i	$-0.163199\pi$
$607$	0.268363	+	0.464818i	0.0108925	+	0.0188664i	−0.860528	+	0.509404i	$0.829866\pi$
$608$	−1.58945	+	2.75302i	−0.0644609	+	0.111650i
$609$	1.58945	−	2.75302i	0.0644079	−	0.111558i
$610$	6.00000			0.242933
$611$	10.7684	−	23.5376i	0.435641	−	0.952230i
$612$	5.00000			0.202113
$613$	−7.82109	+	13.5465i	−0.315891	+	0.547139i	−0.979626	−	0.200828i	$-0.935637\pi$
$613$	−7.82109	+	13.5465i	−0.315891	+	0.547139i	0.663736	+	0.747967i	$0.268970\pi$
$614$	15.9473	−	27.6215i	0.643579	−	1.11471i
$615$	7.17891	+	12.4342i	0.289482	+	0.501397i
$616$	5.17891			0.208664
$617$	−16.0000	−	27.7128i	−0.644136	−	1.11568i	−0.984500	−	0.175382i	$-0.943884\pi$
$617$	−16.0000	−	27.7128i	−0.644136	−	1.11568i	0.340365	−	0.940294i	$-0.389449\pi$
$618$	−4.08945	−	7.08314i	−0.164502	−	0.284926i
$619$	25.5367			1.02641			0.513204	−	0.858267i	$-0.328458\pi$
$619$	25.5367			1.02641			0.513204	+	0.858267i	$0.328458\pi$
$620$	4.17891	+	7.23808i	0.167829	+	0.290688i
$621$	−4.08945	+	7.08314i	−0.164104	+	0.284237i
$622$	−12.7684	+	22.1155i	−0.511965	+	0.886749i
$623$	−9.00000			−0.360577
$624$	−3.58945	+	0.340322i	−0.143693	+	0.0136238i
$625$	−19.0000			−0.760000
$626$	−2.00000	+	3.46410i	−0.0799361	+	0.138453i
$627$	−8.23164	+	14.2576i	−0.328740	+	0.569394i
$628$	−1.00000	−	1.73205i	−0.0399043	−	0.0691164i
$629$	10.0000			0.398726
$630$	−1.00000	−	1.73205i	−0.0398410	−	0.0690066i
$631$	−12.9473	−	22.4253i	−0.515423	−	0.892738i	−0.999840	−	0.0179011i	$-0.994302\pi$
$631$	−12.9473	−	22.4253i	−0.515423	−	0.892738i	0.484417	−	0.874837i	$-0.339032\pi$
$632$	13.1789			0.524229
$633$	−3.17891	−	5.50603i	−0.126350	−	0.218845i
$634$	2.08945	−	3.61904i	0.0829828	−	0.143730i
$635$	12.0000	−	20.7846i	0.476205	−	0.824812i
$636$	3.00000			0.118958
$637$	−2.08945	−	2.93840i	−0.0827872	−	0.116424i
$638$	16.4633			0.651787
$639$	1.08945	−	1.88699i	0.0430981	−	0.0746482i
$640$	1.00000	−	1.73205i	0.0395285	−	0.0684653i
$641$	−13.5367	−	23.4463i	−0.534668	−	0.926073i	−0.999179	−	0.0405056i	$-0.987103\pi$
$641$	−13.5367	−	23.4463i	−0.534668	−	0.926073i	0.464511	−	0.885567i	$-0.346230\pi$
$642$	−19.1789			−0.756931
$643$	4.41055	+	7.63929i	0.173935	+	0.301264i	0.939792	−	0.341746i	$-0.111018\pi$
$643$	4.41055	+	7.63929i	0.173935	+	0.301264i	−0.765857	+	0.643011i	$0.777685\pi$
$644$	−4.08945	−	7.08314i	−0.161147	−	0.279115i
$645$	24.3578			0.959088
$646$	−7.94727	−	13.7651i	−0.312681	−	0.541580i
$647$	−23.9473	+	41.4779i	−0.941464	+	1.63066i	−0.178784	+	0.983888i	$0.557216\pi$
$647$	−23.9473	+	41.4779i	−0.941464	+	1.63066i	−0.762680	+	0.646776i	$0.776117\pi$
$648$	−0.500000	+	0.866025i	−0.0196419	+	0.0340207i
$649$	63.0735			2.47585
$650$	2.08945	+	2.93840i	0.0819551	+	0.115253i
$651$	4.17891			0.163784
$652$	10.0895	−	17.4754i	0.395134	−	0.684391i
$653$	−10.5000	+	18.1865i	−0.410897	+	0.711694i	−0.994988	−	0.0999939i	$-0.968118\pi$
$653$	−10.5000	+	18.1865i	−0.410897	+	0.711694i	0.584091	+	0.811688i	$0.301451\pi$
$654$	2.00000	+	3.46410i	0.0782062	+	0.135457i
$655$	29.0735			1.13599
$656$	3.58945	+	6.21712i	0.140145	+	0.242738i
$657$	−2.00000	−	3.46410i	−0.0780274	−	0.135147i
$658$	7.17891			0.279863
$659$	−8.76836	−	15.1872i	−0.341567	−	0.591611i	0.643157	−	0.765734i	$-0.277624\pi$
$659$	−8.76836	−	15.1872i	−0.341567	−	0.591611i	−0.984724	+	0.174123i	$0.944291\pi$
$660$	5.17891	−	8.97013i	0.201589	−	0.349162i
$661$	−8.26836	+	14.3212i	−0.321602	+	0.557031i	−0.980819	−	0.194922i	$-0.937555\pi$
$661$	−8.26836	+	14.3212i	−0.321602	+	0.557031i	0.659217	+	0.751953i	$0.270888\pi$
$662$	−1.64218			−0.0638253
$663$	7.50000	−	16.3936i	0.291276	−	0.636675i
$664$	6.17891			0.239788
$665$	−3.17891	+	5.50603i	−0.123273	+	0.213515i
$666$	−1.00000	+	1.73205i	−0.0387492	+	0.0671156i
$667$	−13.0000	−	22.5167i	−0.503362	−	0.871849i
$668$	−8.00000			−0.309529
$669$	−1.08945	−	1.88699i	−0.0421207	−	0.0729552i
$670$	−3.82109	−	6.61832i	−0.147622	−	0.255688i
$671$	15.5367			0.599789
$672$	−0.500000	−	0.866025i	−0.0192879	−	0.0334077i
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	−0.856228	−	0.516599i	$-0.827198\pi$
$673$	0.500000	−	0.866025i	0.0192736	−	0.0333828i	0.875501	+	0.483216i	$0.160531\pi$
$674$	−16.7684	+	29.0437i	−0.645893	+	1.11872i
$675$	1.00000			0.0384900
$676$	−4.26836	+	12.2793i	−0.164168	+	0.472281i
$677$	12.0000			0.461197			0.230599	−	0.973049i	$-0.425932\pi$
$677$	12.0000			0.461197			0.230599	+	0.973049i	$0.425932\pi$
$678$	9.17891	−	15.8983i	0.352514	−	0.610572i
$679$	−5.17891	+	8.97013i	−0.198748	+	0.344242i
$680$	5.00000	+	8.66025i	0.191741	+	0.332106i
$681$	14.3578			0.550193
$682$	10.8211	+	18.7427i	0.414361	+	0.717694i
$683$	−4.17891	−	7.23808i	−0.159901	−	0.276957i	0.774931	−	0.632045i	$-0.217784\pi$
$683$	−4.17891	−	7.23808i	−0.159901	−	0.276957i	−0.934833	+	0.355088i	$0.884451\pi$
$684$	3.17891			0.121549
$685$	6.35782	+	11.0121i	0.242920	+	0.420749i
$686$	0.500000	−	0.866025i	0.0190901	−	0.0330650i
$687$	0.500000	−	0.866025i	0.0190762	−	0.0330409i
$688$	12.1789			0.464317
$689$	4.50000	−	9.83616i	0.171436	−	0.374728i
$690$	−16.3578			−0.622731
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	−0.181584	−	0.983375i	$-0.558123\pi$
$691$	20.0000	−	34.6410i	0.760836	−	1.31781i	0.942420	−	0.334431i	$-0.108544\pi$
$692$	−2.00000	+	3.46410i	−0.0760286	+	0.131685i
$693$	−2.58945	−	4.48507i	−0.0983652	−	0.170374i
$694$	−19.1789			−0.728021
$695$	−6.82109	−	11.8145i	−0.258739	−	0.448149i
$696$	−1.58945	−	2.75302i	−0.0602481	−	0.104353i
$697$	−35.8945			−1.35960
$698$	−4.08945	−	7.08314i	−0.154788	−	0.268101i
$699$	11.1789	−	19.3624i	0.422825	−	0.732355i
$700$	−0.500000	+	0.866025i	−0.0188982	+	0.0327327i
$701$	−21.7156			−0.820188			−0.410094	−	0.912043i	$-0.634504\pi$
$701$	−21.7156			−0.820188			−0.410094	+	0.912043i	$0.634504\pi$
$702$	2.08945	+	2.93840i	0.0788614	+	0.110903i
$703$	6.35782			0.239790
$704$	2.58945	−	4.48507i	0.0975937	−	0.169037i
$705$	7.17891	−	12.4342i	0.270373	−	0.468300i
$706$	−2.08945	−	3.61904i	−0.0786376	−	0.136204i
$707$	−6.35782			−0.239110
$708$	−6.08945	−	10.5472i	−0.228856	−	0.396390i
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	0.976237	−	0.216705i	$-0.0695310\pi$
$709$	8.00000	+	13.8564i	0.300446	+	0.520388i	−0.675791	+	0.737093i	$0.736198\pi$
$710$	4.35782			0.163546
$711$	−6.58945	−	11.4133i	−0.247124	−	0.428031i
$712$	−4.50000	+	7.79423i	−0.168645	+	0.292101i
$713$	17.0895	−	29.5998i	0.640005	−	1.10852i
$714$	5.00000			0.187120
$715$	−21.6422	−	30.4354i	−0.809372	−	1.13822i
$716$	8.35782			0.312346
$717$	5.08945	−	8.81519i	0.190069	−	0.329209i
$718$	5.17891	−	8.97013i	0.193275	−	0.334762i
$719$	18.5895	+	32.1979i	0.693270	+	1.20078i	0.970761	+	0.240050i	$0.0771638\pi$
$719$	18.5895	+	32.1979i	0.693270	+	1.20078i	−0.277491	+	0.960728i	$0.589503\pi$
$720$	−2.00000			−0.0745356
$721$	−4.08945	−	7.08314i	−0.152299	−	0.263790i
$722$	4.44727	+	7.70290i	0.165510	+	0.286672i
$723$	−4.35782			−0.162069
$724$	−9.58945	−	16.6094i	−0.356389	−	0.617284i
$725$	−1.58945	+	2.75302i	−0.0590308	+	0.102244i
$726$	7.91055	−	13.7015i	0.293588	−	0.508509i
$727$	34.5367			1.28090			0.640448	−	0.768001i	$-0.278749\pi$
$727$	34.5367			1.28090			0.640448	+	0.768001i	$0.278749\pi$
$728$	−3.58945	+	0.340322i	−0.133034	+	0.0126132i
$729$	1.00000			0.0370370
$730$	4.00000	−	6.92820i	0.148047	−	0.256424i
$731$	−30.4473	+	52.7362i	−1.12613	+	1.95052i
$732$	−1.50000	−	2.59808i	−0.0554416	−	0.0960277i
$733$	19.7156			0.728214			0.364107	−	0.931357i	$-0.381374\pi$
$733$	19.7156			0.728214			0.364107	+	0.931357i	$0.381374\pi$
$734$	4.08945	+	7.08314i	0.150945	+	0.261444i
$735$	−1.00000	−	1.73205i	−0.0368856	−	0.0638877i
$736$	−8.17891			−0.301479
$737$	−9.89454	−	17.1378i	−0.364470	−	0.631281i
$738$	3.58945	−	6.21712i	0.132130	−	0.228855i
$739$	8.08945	−	14.0113i	0.297575	−	0.515416i	−0.678005	−	0.735057i	$-0.737155\pi$
$739$	8.08945	−	14.0113i	0.297575	−	0.515416i	0.975581	+	0.219641i	$0.0704887\pi$
$740$	−4.00000			−0.147043
$741$	4.76836	−	10.4227i	0.175170	−	0.382889i
$742$	3.00000			0.110133
$743$	−15.9105	+	27.5579i	−0.583701	+	1.01100i	0.411335	+	0.911484i	$0.365063\pi$
$743$	−15.9105	+	27.5579i	−0.583701	+	1.01100i	−0.995036	+	0.0995159i	$0.968271\pi$
$744$	2.08945	−	3.61904i	0.0766031	−	0.132680i
$745$	16.1789	+	28.0227i	0.592749	+	1.02667i
$746$	−20.0000			−0.732252
$747$	−3.08945	−	5.35109i	−0.113037	−	0.195786i
$748$	12.9473	+	22.4253i	0.473399	+	0.819951i
$749$	−19.1789			−0.700782
$750$	6.00000	+	10.3923i	0.219089	+	0.379473i
$751$	17.9473	−	31.0856i	0.654905	−	1.13433i	−0.327012	−	0.945020i	$-0.606042\pi$
$751$	17.9473	−	31.0856i	0.654905	−	1.13433i	0.981918	−	0.189309i	$-0.0606248\pi$
$752$	3.58945	−	6.21712i	0.130894	−	0.226715i
$753$	−22.1789			−0.808244
$754$	−11.4105	+	1.08185i	−0.415548	+	0.0393987i
$755$	−39.0735			−1.42203
$756$	−0.500000	+	0.866025i	−0.0181848	+	0.0314970i
$757$	10.1789	−	17.6304i	0.369959	−	0.640787i	−0.619600	−	0.784918i	$-0.712705\pi$
$757$	10.1789	−	17.6304i	0.369959	−	0.640787i	0.989559	+	0.144130i	$0.0460385\pi$
$758$	12.3578	+	21.4044i	0.448856	+	0.777442i
$759$	−42.3578			−1.53749
$760$	3.17891	+	5.50603i	0.115311	+	0.199725i
$761$	21.7156	+	37.6126i	0.787191	+	1.36345i	0.927681	+	0.373373i	$0.121799\pi$
$761$	21.7156	+	37.6126i	0.787191	+	1.36345i	−0.140490	+	0.990082i	$0.544868\pi$
$762$	−12.0000			−0.434714
$763$	2.00000	+	3.46410i	0.0724049	+	0.125409i
$764$	3.26836	−	5.66097i	0.118245	−	0.204807i
$765$	5.00000	−	8.66025i	0.180775	−	0.313112i
$766$	21.1789			0.765225
$767$	−43.7156	+	4.14474i	−1.57848	+	0.149658i
$768$	−1.00000			−0.0360844
$769$	−9.17891	+	15.8983i	−0.331000	+	0.573309i	−0.982708	−	0.185161i	$-0.940719\pi$
$769$	−9.17891	+	15.8983i	−0.331000	+	0.573309i	0.651708	+	0.758470i	$0.274053\pi$
$770$	5.17891	−	8.97013i	0.186635	−	0.323261i
$771$	−9.85782	−	17.0742i	−0.355021	−	0.614914i
$772$	−13.5367			−0.487197
$773$	−7.35782	−	12.7441i	−0.264642	−	0.458374i	0.702828	−	0.711360i	$-0.251921\pi$
$773$	−7.35782	−	12.7441i	−0.264642	−	0.458374i	−0.967470	+	0.252986i	$0.918587\pi$
$774$	−6.08945	−	10.5472i	−0.218881	−	0.379113i
$775$	−4.17891			−0.150111
$776$	5.17891	+	8.97013i	0.185912	+	0.322009i
$777$	−1.00000	+	1.73205i	−0.0358748	+	0.0621370i
$778$	6.08945	−	10.5472i	0.218318	−	0.378137i
$779$	−22.8211			−0.817650
$780$	−3.00000	+	6.55744i	−0.107417	+	0.234794i
$781$	11.2844			0.403786
$782$	20.4473	−	35.4157i	0.731193	−	1.26646i
$783$	−1.58945	+	2.75302i	−0.0568025	+	0.0983847i
$784$	−0.500000	−	0.866025i	−0.0178571	−	0.0309295i
$785$	−4.00000			−0.142766
$786$	−7.26836	−	12.5892i	−0.259254	−	0.449041i
$787$	5.41055	+	9.37134i	0.192865	+	0.334052i	0.946199	−	0.323587i	$-0.104889\pi$
$787$	5.41055	+	9.37134i	0.192865	+	0.334052i	−0.753333	+	0.657639i	$0.771555\pi$
$788$	17.0000			0.605600
$789$	−6.00000	−	10.3923i	−0.213606	−	0.369976i
$790$	13.1789	−	22.8265i	0.468885	−	0.812132i
$791$	9.17891	−	15.8983i	0.326364	−	0.565280i
$792$	−5.17891			−0.184024
$793$	−10.7684	+	1.02096i	−0.382396	+	0.0362555i
$794$	3.00000			0.106466
$795$	3.00000	−	5.19615i	0.106399	−	0.184289i
$796$	−12.0895	+	20.9395i	−0.428499	+	0.742183i
$797$		0			0		0.866025	−	0.500000i	$-0.166667\pi$
$797$		0			0		−0.866025	+	0.500000i	$0.833333\pi$
$798$	3.17891			0.112532
$799$	17.9473	+	31.0856i	0.634929	+	1.09973i
$800$	0.500000	+	0.866025i	0.0176777	+	0.0306186i
$801$	9.00000			0.317999
$802$	−4.82109	−	8.35038i	−0.170239	−	0.294862i
$803$	10.3578	−	17.9403i	0.365519	−	0.633098i
$804$	−1.91055	+	3.30916i	−0.0673798	+	0.116705i
$805$	−16.3578			−0.576537
$806$	−8.73164	−	12.2793i	−0.307559	−	0.432520i
$807$	4.35782			0.153402
$808$	−3.17891	+	5.50603i	−0.111834	+	0.193701i
$809$	10.0000	−	17.3205i	0.351581	−	0.608957i	−0.634945	−	0.772557i	$-0.718977\pi$
$809$	10.0000	−	17.3205i	0.351581	−	0.608957i	0.986527	+	0.163600i	$0.0523108\pi$
$810$	1.00000	+	1.73205i	0.0351364	+	0.0608581i
$811$	−12.7156			−0.446506			−0.223253	−	0.974761i	$-0.571668\pi$
$811$	−12.7156			−0.446506			−0.223253	+	0.974761i	$0.571668\pi$
$812$	−1.58945	−	2.75302i	−0.0557789	−	0.0966119i
$813$	9.91055	+	17.1656i	0.347578	+	0.602023i
$814$	−10.3578			−0.363041
$815$	−20.1789	−	34.9509i	−0.706836	−	1.22428i
$816$	2.50000	−	4.33013i	0.0875175	−	0.151585i
$817$	−19.3578	+	33.5287i	−0.677244	+	1.17302i
$818$	−36.3578			−1.27122
$819$	2.08945	+	2.93840i	0.0730114	+	0.102676i
$820$	14.3578			0.501397
$821$	−0.142183	+	0.246269i	−0.00496223	+	0.00859484i	−0.868496	−	0.495696i	$-0.834913\pi$
$821$	−0.142183	+	0.246269i	−0.00496223	+	0.00859484i	0.863534	+	0.504291i	$0.168246\pi$
$822$	3.17891	−	5.50603i	0.110877	−	0.192045i
$823$	−16.3578	−	28.3326i	−0.570198	−	0.987611i	−0.996545	−	0.0830519i	$-0.973533\pi$
$823$	−16.3578	−	28.3326i	−0.570198	−	0.987611i	0.426348	−	0.904559i	$-0.359800\pi$
$824$	−8.17891			−0.284926
$825$	2.58945	+	4.48507i	0.0901532	+	0.156150i
$826$	−6.08945	−	10.5472i	−0.211879	−	0.366986i
$827$	−40.7156			−1.41582			−0.707911	−	0.706302i	$-0.750362\pi$
$827$	−40.7156			−1.41582			−0.707911	+	0.706302i	$0.750362\pi$
$828$	4.08945	+	7.08314i	0.142118	+	0.246156i
$829$	1.58945	−	2.75302i	0.0552040	−	0.0956162i	−0.837103	−	0.547046i	$-0.815752\pi$
$829$	1.58945	−	2.75302i	0.0552040	−	0.0956162i	0.892307	+	0.451429i	$0.149086\pi$
$830$	6.17891	−	10.7022i	0.214473	−	0.371478i
$831$	−5.64218			−0.195725
$832$	−1.50000	+	3.27872i	−0.0520031	+	0.113669i
$833$	5.00000			0.173240
$834$	−3.41055	+	5.90724i	−0.118098	+	0.204551i
$835$	−8.00000	+	13.8564i	−0.276851	+	0.479521i
$836$	8.23164	+	14.2576i	0.284697	+	0.493110i
$837$	−4.17891			−0.144444
$838$	13.4473	+	23.2914i	0.464528	+	0.804587i
$839$	−5.82109	−	10.0824i	−0.200966	−	0.348084i	0.747874	−	0.663841i	$-0.231075\pi$
$839$	−5.82109	−	10.0824i	−0.200966	−	0.348084i	−0.948840	+	0.315757i	$0.897742\pi$
$840$	−2.00000			−0.0690066
$841$	9.44727	+	16.3632i	0.325768	+	0.564247i
$842$	−5.35782	+	9.28001i	−0.184643	+	0.319810i
$843$	14.1789	−	24.5586i	0.488348	−	0.845843i
$844$	−6.35782			−0.218845
$845$	17.0000	+	19.6723i	0.584818	+	0.676748i
$846$	−7.17891			−0.246816
$847$	7.91055	−	13.7015i	0.271810	−	0.470788i
$848$	1.50000	−	2.59808i	0.0515102	−	0.0892183i
$849$	3.82109	+	6.61832i	0.131140	+	0.227140i
$850$	−5.00000			−0.171499
$851$	8.17891	+	14.1663i	0.280369	+	0.485614i
$852$	−1.08945	−	1.88699i	−0.0373241	−	0.0646472i
$853$	27.7156			0.948965			0.474483	−	0.880265i	$-0.342635\pi$
$853$	27.7156			0.948965			0.474483	+	0.880265i	$0.342635\pi$
$854$	−1.50000	−	2.59808i	−0.0513289	−	0.0889043i
$855$	3.17891	−	5.50603i	0.108716	−	0.188302i
$856$	−9.58945	+	16.6094i	−0.327761	+	0.567698i
$857$	−10.7156			−0.366039			−0.183020	−	0.983109i	$-0.558587\pi$
$857$	−10.7156			−0.366039			−0.183020	+	0.983109i	$0.558587\pi$
$858$	−7.76836	+	16.9802i	−0.265208	+	0.579694i
$859$	19.8945			0.678793			0.339397	−	0.940643i	$-0.389777\pi$
$859$	19.8945			0.678793			0.339397	+	0.940643i	$0.389777\pi$
$860$	12.1789	−	21.0945i	0.415297	−	0.719316i
$861$	3.58945	−	6.21712i	0.122328	−	0.211879i
$862$	−5.08945	−	8.81519i	−0.173347	−	0.300247i
$863$	13.6422			0.464385			0.232193	−	0.972670i	$-0.425410\pi$
$863$	13.6422			0.464385			0.232193	+	0.972670i	$0.425410\pi$
$864$	0.500000	+	0.866025i	0.0170103	+	0.0294628i
$865$	4.00000	+	6.92820i	0.136004	+	0.235566i
$866$	34.3578			1.16753
$867$	4.00000	+	6.92820i	0.135847	+	0.235294i
$868$	2.08945	−	3.61904i	0.0709207	−	0.122838i
$869$	34.1262	−	59.1083i	1.15765	−	2.00511i
$870$	−6.35782			−0.215550
$871$	7.98400	+	11.2279i	0.270527	+	0.380442i
$872$	4.00000			0.135457
$873$	5.17891	−	8.97013i	0.175279	−	0.303593i
$874$	13.0000	−	22.5167i	0.439732	−	0.761637i
$875$	6.00000	+	10.3923i	0.202837	+	0.351324i
$876$	−4.00000			−0.135147
$877$	20.1789	+	34.9509i	0.681393	+	1.18021i	0.974556	+	0.224145i	$0.0719590\pi$
$877$	20.1789	+	34.9509i	0.681393	+	1.18021i	−0.293162	+	0.956063i	$0.594708\pi$
$878$	−20.3578	−	35.2608i	−0.687043	−	1.18999i
$879$	−12.0000			−0.404750
$880$	−5.17891	−	8.97013i	−0.174581	−	0.302383i
$881$	−5.73164	+	9.92749i	−0.193104	+	0.334466i	−0.946277	−	0.323356i	$-0.895189\pi$
$881$	−5.73164	+	9.92749i	−0.193104	+	0.334466i	0.753173	+	0.657822i	$0.228522\pi$
$882$	−0.500000	+	0.866025i	−0.0168359	+	0.0291606i
$883$	−3.46327			−0.116548			−0.0582742	−	0.998301i	$-0.518560\pi$
$883$	−3.46327			−0.116548			−0.0582742	+	0.998301i	$0.518560\pi$
$884$	−10.4473	−	14.6920i	−0.351380	−	0.494145i
$885$	−24.3578			−0.818779
$886$	−1.58945	+	2.75302i	−0.0533988	+	0.0924894i
$887$	22.7684	−	39.4360i	0.764487	−	1.32413i	−0.176031	−	0.984385i	$-0.556326\pi$
$887$	22.7684	−	39.4360i	0.764487	−	1.32413i	0.940517	−	0.339745i	$-0.110341\pi$
$888$	1.00000	+	1.73205i	0.0335578	+	0.0581238i
$889$	−12.0000			−0.402467
$890$	9.00000	+	15.5885i	0.301681	+	0.522526i
$891$	2.58945	+	4.48507i	0.0867500	+	0.150255i
$892$	−2.17891			−0.0729552
$893$	11.4105	+	19.7636i	0.381839	+	0.661365i
$894$	8.08945	−	14.0113i	0.270552	−	0.468609i
$895$	8.35782	−	14.4762i	0.279371	−	0.483885i
$896$	−1.00000			−0.0334077
$897$	29.3578	−	2.78346i	0.980229	−	0.0929370i
$898$	−14.0000			−0.467186
$899$	6.64218	−	11.5046i	0.221529	−	0.383700i
$900$	0.500000	−	0.866025i	0.0166667	−	0.0288675i
$901$	7.50000	+	12.9904i	0.249861	+	0.432772i
$902$	37.1789			1.23792
$903$	−6.08945	−	10.5472i	−0.202644	−	0.350990i
$904$	−9.17891	−	15.8983i	−0.305286	−	0.528771i
$905$	−38.3578			−1.27506
$906$	9.76836	+	16.9193i	0.324532	+	0.562106i
$907$	−24.8051	+	42.9637i	−0.823639	+	1.42659i	0.0793153	+	0.996850i	$0.474727\pi$
$907$	−24.8051	+	42.9637i	−0.823639	+	1.42659i	−0.902955	+	0.429736i	$0.858607\pi$
$908$	7.17891	−	12.4342i	0.238240	−	0.412645i
$909$	6.35782			0.210875
$910$	−3.00000	+	6.55744i	−0.0994490	+	0.217377i
$911$	28.7156			0.951391			0.475696	−	0.879610i	$-0.342196\pi$
$911$	28.7156			0.951391			0.475696	+	0.879610i	$0.342196\pi$
$912$	1.58945	−	2.75302i	0.0526321	−	0.0911614i
$913$	16.0000	−	27.7128i	0.529523	−	0.917160i
$914$	−12.4473	−	21.5593i	−0.411719	−	0.713118i
$915$	−6.00000			−0.198354
$916$	−0.500000	−	0.866025i	−0.0165205	−	0.0286143i
$917$	−7.26836	−	12.5892i	−0.240022	−	0.415731i
$918$	−5.00000			−0.165025
$919$	29.1262	+	50.4480i	0.960784	+	1.66413i	0.720539	+	0.693414i	$0.243894\pi$
$919$	29.1262	+	50.4480i	0.960784	+	1.66413i	0.240245	+	0.970712i	$0.422772\pi$
$920$	−8.17891	+	14.1663i	−0.269651	+	0.467049i
$921$	−15.9473	+	27.6215i	−0.525480	+	0.910159i
$922$	20.7156			0.682233
$923$	−7.82109	+	0.741529i	−0.257434	+	0.0244077i
$924$	−5.17891			−0.170374
$925$	1.00000	−	1.73205i	0.0328798	−	0.0569495i
$926$	−13.9473	+	24.1574i	−0.458336	+	0.793861i
$927$	4.08945	+	7.08314i	0.134315	+	0.232641i
$928$	−3.17891			−0.104353
$929$	−19.5000	−	33.7750i	−0.639774	−	1.10812i	−0.985482	−	0.169779i	$-0.945695\pi$
$929$	−19.5000	−	33.7750i	−0.639774	−	1.10812i	0.345708	−	0.938342i	$-0.387639\pi$
$930$	−4.17891	−	7.23808i	−0.137032	−	0.237346i
$931$	3.17891			0.104185
$932$	−11.1789	−	19.3624i	−0.366177	−	0.634238i
$933$	12.7684	−	22.1155i	0.418017	−	0.724027i
$934$	11.4473	−	19.8273i	0.374566	−	0.648768i
$935$	51.7891			1.69368
$936$	3.58945	−	0.340322i	0.117325	−	0.0111238i
$937$	21.0735			0.688440			0.344220	−	0.938889i	$-0.388143\pi$
$937$	21.0735			0.688440			0.344220	+	0.938889i	$0.388143\pi$
$938$	−1.91055	+	3.30916i	−0.0623815	+	0.108048i
$939$	2.00000	−	3.46410i	0.0652675	−	0.113047i
$940$	−7.17891	−	12.4342i	−0.234150	−	0.405560i
$941$	−20.0000			−0.651981			−0.325991	−	0.945373i	$-0.605698\pi$
$941$	−20.0000			−0.651981			−0.325991	+	0.945373i	$0.605698\pi$
$942$	1.00000	+	1.73205i	0.0325818	+	0.0564333i
$943$	−29.3578	−	50.8492i	−0.956022	−	1.65588i
$944$	−12.1789			−0.396390
$945$	1.00000	+	1.73205i	0.0325300	+	0.0563436i
$946$	31.5367	−	54.6232i	1.02535	−	1.77595i
$947$	20.1262	−	34.8596i	0.654013	−	1.13278i	−0.328127	−	0.944634i	$-0.606418\pi$
$947$	20.1262	−	34.8596i	0.654013	−	1.13278i	0.982140	−	0.188150i	$-0.0602492\pi$
$948$	−13.1789			−0.428031
$949$	−6.00000	+	13.1149i	−0.194768	+	0.425727i
$950$	−3.17891			−0.103137
$951$	−2.08945	+	3.61904i	−0.0677552	+	0.117355i
$952$	2.50000	−	4.33013i	0.0810255	−	0.140340i
$953$	1.35782	+	2.35181i	0.0439840	+	0.0761825i	0.887179	−	0.461425i	$-0.152662\pi$
$953$	1.35782	+	2.35181i	0.0439840	+	0.0761825i	−0.843195	+	0.537607i	$0.819328\pi$
$954$	−3.00000			−0.0971286
$955$	−6.53673	−	11.3219i	−0.211523	−	0.366369i
$956$	−5.08945	−	8.81519i	−0.164605	−	0.285104i
$957$	−16.4633			−0.532182
$958$	20.5895	+	35.6620i	0.665215	+	1.15219i
$959$	3.17891	−	5.50603i	0.102652	−	0.177799i
$960$	−1.00000	+	1.73205i	−0.0322749	+	0.0559017i
$961$	−13.5367			−0.436669
$962$	7.17891	−	0.680643i	0.231457	−	0.0219448i
$963$	19.1789			0.618032
$964$	−2.17891	+	3.77398i	−0.0701779	+	0.121552i
$965$	−13.5367	+	23.4463i	−0.435763	+	0.754763i
$966$	4.08945	+	7.08314i	0.131576	+	0.227896i
$967$	11.6422			0.374387			0.187194	−	0.982323i	$-0.440061\pi$
$967$	11.6422			0.374387			0.187194	+	0.982323i	$0.440061\pi$
$968$	−7.91055	−	13.7015i	−0.254255	−	0.440382i
$969$	7.94727	+	13.7651i	0.255303	+	0.442198i
$970$	20.7156			0.665139
$971$	14.0895	+	24.4037i	0.452152	+	0.783150i	0.998519	−	0.0543952i	$-0.0173231\pi$
$971$	14.0895	+	24.4037i	0.452152	+	0.783150i	−0.546367	+	0.837546i	$0.683990\pi$
$972$	0.500000	−	0.866025i	0.0160375	−	0.0277778i
$973$	−3.41055	+	5.90724i	−0.109337	+	0.189377i
$974$	−26.8211			−0.859403
$975$	−2.08945	−	2.93840i	−0.0669161	−	0.0941040i
$976$	−3.00000			−0.0960277
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	−0.945899	−	0.324462i	$-0.894817\pi$
$977$	−6.00000	+	10.3923i	−0.191957	+	0.332479i	0.753942	+	0.656941i	$0.228150\pi$
$978$	−10.0895	+	17.4754i	−0.322625	+	0.558803i
$979$	23.3051	+	40.3656i	0.744834	+	1.29009i
$980$	−2.00000			−0.0638877
$981$	−2.00000	−	3.46410i	−0.0638551	−	0.110600i
$982$		0			0
$983$	−13.0735			−0.416978			−0.208489	−	0.978025i	$-0.566855\pi$
$983$	−13.0735			−0.416978			−0.208489	+	0.978025i	$0.566855\pi$
$984$	−3.58945	−	6.21712i	−0.114428	−	0.198194i
$985$	17.0000	−	29.4449i	0.541665	−	0.938191i
$986$	7.94727	−	13.7651i	0.253093	−	0.438369i
$987$	−7.17891			−0.228507
$988$	−6.64218	−	9.34090i	−0.211316	−	0.297174i
$989$	−99.6102			−3.16742
$990$	−5.17891	+	8.97013i	−0.164597	+	0.285090i
$991$	24.7684	−	42.9001i	0.786793	−	1.36277i	−0.141129	−	0.989991i	$-0.545073\pi$
$991$	24.7684	−	42.9001i	0.786793	−	1.36277i	0.927922	−	0.372774i	$-0.121593\pi$
$992$	−2.08945	−	3.61904i	−0.0663402	−	0.114905i
$993$	1.64218			0.0521131
$994$	−1.08945	−	1.88699i	−0.0345554	−	0.0598517i
$995$	24.1789	+	41.8791i	0.766523	+	1.32766i
$996$	−6.17891			−0.195786
$997$	−6.14218	−	10.6386i	−0.194525	−	0.336927i	0.752220	−	0.658912i	$-0.228983\pi$
$997$	−6.14218	−	10.6386i	−0.194525	−	0.336927i	−0.946745	+	0.321985i	$0.895650\pi$
$998$	−4.08945	+	7.08314i	−0.129449	+	0.224213i
$999$	1.00000	−	1.73205i	0.0316386	−	0.0547997i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.l.k.295.2	yes	4
3.2	odd	2		1638.2.r.ba.1387.1		4
13.3	even	3	inner	546.2.l.k.211.2	✓	4
13.4	even	6		7098.2.a.bk.1.2		2
13.9	even	3		7098.2.a.br.1.1		2
39.29	odd	6		1638.2.r.ba.757.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.l.k.211.2	✓	4	13.3	even	3	inner
546.2.l.k.295.2	yes	4	1.1	even	1	trivial
1638.2.r.ba.757.1		4	39.29	odd	6
1638.2.r.ba.1387.1		4	3.2	odd	2
7098.2.a.bk.1.2		2	13.4	even	6
7098.2.a.br.1.1		2	13.9	even	3

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.l (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\)	\(q+(-0.500000 + 0.866025i) q^{2} +(0.500000 - 0.866025i) q^{3} +(-0.500000 - 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 + 0.866025i) q^{6} +(0.500000 + 0.866025i) q^{7} +1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{10} +(2.58945 - 4.48507i) q^{11} -1.00000 q^{12} +(-1.50000 + 3.27872i) q^{13} -1.00000 q^{14} +(-1.00000 + 1.73205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(-2.50000 - 4.33013i) q^{17} +1.00000 q^{18} +(-1.58945 - 2.75302i) q^{19} +(1.00000 + 1.73205i) q^{20} +1.00000 q^{21} +(2.58945 + 4.48507i) q^{22} +(4.08945 - 7.08314i) q^{23} +(0.500000 - 0.866025i) q^{24} -1.00000 q^{25} +(-2.08945 - 2.93840i) q^{26} -1.00000 q^{27} +(0.500000 - 0.866025i) q^{28} +(1.58945 - 2.75302i) q^{29} +(-1.00000 - 1.73205i) q^{30} +4.17891 q^{31} +(-0.500000 - 0.866025i) q^{32} +(-2.58945 - 4.48507i) q^{33} +5.00000 q^{34} +(-1.00000 - 1.73205i) q^{35} +(-0.500000 + 0.866025i) q^{36} +(-1.00000 + 1.73205i) q^{37} +3.17891 q^{38} +(2.08945 + 2.93840i) q^{39} -2.00000 q^{40} +(3.58945 - 6.21712i) q^{41} +(-0.500000 + 0.866025i) q^{42} +(-6.08945 - 10.5472i) q^{43} -5.17891 q^{44} +(1.00000 + 1.73205i) q^{45} +(4.08945 + 7.08314i) q^{46} -7.17891 q^{47} +(0.500000 + 0.866025i) q^{48} +(-0.500000 + 0.866025i) q^{49} +(0.500000 - 0.866025i) q^{50} -5.00000 q^{51} +(3.58945 - 0.340322i) q^{52} -3.00000 q^{53} +(0.500000 - 0.866025i) q^{54} +(-5.17891 + 8.97013i) q^{55} +(0.500000 + 0.866025i) q^{56} -3.17891 q^{57} +(1.58945 + 2.75302i) q^{58} +(6.08945 + 10.5472i) q^{59} +2.00000 q^{60} +(1.50000 + 2.59808i) q^{61} +(-2.08945 + 3.61904i) q^{62} +(0.500000 - 0.866025i) q^{63} +1.00000 q^{64} +(3.00000 - 6.55744i) q^{65} +5.17891 q^{66} +(1.91055 - 3.30916i) q^{67} +(-2.50000 + 4.33013i) q^{68} +(-4.08945 - 7.08314i) q^{69} +2.00000 q^{70} +(1.08945 + 1.88699i) q^{71} +(-0.500000 - 0.866025i) q^{72} +4.00000 q^{73} +(-1.00000 - 1.73205i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(-1.58945 + 2.75302i) q^{76} +5.17891 q^{77} +(-3.58945 + 0.340322i) q^{78} +13.1789 q^{79} +(1.00000 - 1.73205i) q^{80} +(-0.500000 + 0.866025i) q^{81} +(3.58945 + 6.21712i) q^{82} +6.17891 q^{83} +(-0.500000 - 0.866025i) q^{84} +(5.00000 + 8.66025i) q^{85} +12.1789 q^{86} +(-1.58945 - 2.75302i) q^{87} +(2.58945 - 4.48507i) q^{88} +(-4.50000 + 7.79423i) q^{89} -2.00000 q^{90} +(-3.58945 + 0.340322i) q^{91} -8.17891 q^{92} +(2.08945 - 3.61904i) q^{93} +(3.58945 - 6.21712i) q^{94} +(3.17891 + 5.50603i) q^{95} -1.00000 q^{96} +(5.17891 + 8.97013i) q^{97} +(-0.500000 - 0.866025i) q^{98} -5.17891 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q - 2 q^{2} + 2 q^{3} - 2 q^{4} - 8 q^{5} + 2 q^{6} + 2 q^{7} + 4 q^{8} - 2 q^{9} + 4 q^{10} - q^{11} - 4 q^{12} - 6 q^{13} - 4 q^{14} - 4 q^{15} - 2 q^{16} - 10 q^{17} + 4 q^{18} + 5 q^{19} + 4 q^{20} + 4 q^{21} - q^{22} + 5 q^{23} + 2 q^{24} - 4 q^{25} + 3 q^{26} - 4 q^{27} + 2 q^{28} - 5 q^{29} - 4 q^{30} - 6 q^{31} - 2 q^{32} + q^{33} + 20 q^{34} - 4 q^{35} - 2 q^{36} - 4 q^{37} - 10 q^{38} - 3 q^{39} - 8 q^{40} + 3 q^{41} - 2 q^{42} - 13 q^{43} + 2 q^{44} + 4 q^{45} + 5 q^{46} - 6 q^{47} + 2 q^{48} - 2 q^{49} + 2 q^{50} - 20 q^{51} + 3 q^{52} - 12 q^{53} + 2 q^{54} + 2 q^{55} + 2 q^{56} + 10 q^{57} - 5 q^{58} + 13 q^{59} + 8 q^{60} + 6 q^{61} + 3 q^{62} + 2 q^{63} + 4 q^{64} + 12 q^{65} - 2 q^{66} + 19 q^{67} - 10 q^{68} - 5 q^{69} + 8 q^{70} - 7 q^{71} - 2 q^{72} + 16 q^{73} - 4 q^{74} - 2 q^{75} + 5 q^{76} - 2 q^{77} - 3 q^{78} + 30 q^{79} + 4 q^{80} - 2 q^{81} + 3 q^{82} + 2 q^{83} - 2 q^{84} + 20 q^{85} + 26 q^{86} + 5 q^{87} - q^{88} - 18 q^{89} - 8 q^{90} - 3 q^{91} - 10 q^{92} - 3 q^{93} + 3 q^{94} - 10 q^{95} - 4 q^{96} - 2 q^{97} - 2 q^{98} + 2 q^{99}+O(q^{100}) \) 4 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 - 8 * q^5 + 2 * q^6 + 2 * q^7 + 4 * q^8 - 2 * q^9 + 4 * q^10 - q^11 - 4 * q^12 - 6 * q^13 - 4 * q^14 - 4 * q^15 - 2 * q^16 - 10 * q^17 + 4 * q^18 + 5 * q^19 + 4 * q^20 + 4 * q^21 - q^22 + 5 * q^23 + 2 * q^24 - 4 * q^25 + 3 * q^26 - 4 * q^27 + 2 * q^28 - 5 * q^29 - 4 * q^30 - 6 * q^31 - 2 * q^32 + q^33 + 20 * q^34 - 4 * q^35 - 2 * q^36 - 4 * q^37 - 10 * q^38 - 3 * q^39 - 8 * q^40 + 3 * q^41 - 2 * q^42 - 13 * q^43 + 2 * q^44 + 4 * q^45 + 5 * q^46 - 6 * q^47 + 2 * q^48 - 2 * q^49 + 2 * q^50 - 20 * q^51 + 3 * q^52 - 12 * q^53 + 2 * q^54 + 2 * q^55 + 2 * q^56 + 10 * q^57 - 5 * q^58 + 13 * q^59 + 8 * q^60 + 6 * q^61 + 3 * q^62 + 2 * q^63 + 4 * q^64 + 12 * q^65 - 2 * q^66 + 19 * q^67 - 10 * q^68 - 5 * q^69 + 8 * q^70 - 7 * q^71 - 2 * q^72 + 16 * q^73 - 4 * q^74 - 2 * q^75 + 5 * q^76 - 2 * q^77 - 3 * q^78 + 30 * q^79 + 4 * q^80 - 2 * q^81 + 3 * q^82 + 2 * q^83 - 2 * q^84 + 20 * q^85 + 26 * q^86 + 5 * q^87 - q^88 - 18 * q^89 - 8 * q^90 - 3 * q^91 - 10 * q^92 - 3 * q^93 + 3 * q^94 - 10 * q^95 - 4 * q^96 - 2 * q^97 - 2 * q^98 + 2 * q^99

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