Properties

Label 546.2.l.d.211.1
Level $546$
Weight $2$
Character 546.211
Analytic conductor $4.360$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

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

Self dual: no
Analytic conductor: \(4.35983195036\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 211.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.d.295.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-0.500000 - 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -2.00000 q^{5} +(0.500000 - 0.866025i) q^{6} +(0.500000 - 0.866025i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(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} +(2.00000 + 3.46410i) q^{11} +1.00000 q^{12} +(-3.50000 + 0.866025i) q^{13} +1.00000 q^{14} +(1.00000 + 1.73205i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.50000 + 6.06218i) q^{17} -1.00000 q^{18} +(-1.00000 + 1.73205i) q^{19} +(1.00000 - 1.73205i) q^{20} -1.00000 q^{21} +(-2.00000 + 3.46410i) q^{22} +(0.500000 + 0.866025i) q^{23} +(0.500000 + 0.866025i) q^{24} -1.00000 q^{25} +(-2.50000 - 2.59808i) q^{26} +1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(1.00000 + 1.73205i) q^{29} +(-1.00000 + 1.73205i) q^{30} -9.00000 q^{31} +(0.500000 - 0.866025i) q^{32} +(2.00000 - 3.46410i) q^{33} -7.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(1.00000 + 1.73205i) q^{37} -2.00000 q^{38} +(2.50000 + 2.59808i) q^{39} +2.00000 q^{40} +(-1.00000 - 1.73205i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(2.50000 - 4.33013i) q^{43} -4.00000 q^{44} +(1.00000 - 1.73205i) q^{45} +(-0.500000 + 0.866025i) q^{46} +6.00000 q^{47} +(-0.500000 + 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(-0.500000 - 0.866025i) q^{50} +7.00000 q^{51} +(1.00000 - 3.46410i) q^{52} +3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(-4.00000 - 6.92820i) q^{55} +(-0.500000 + 0.866025i) q^{56} +2.00000 q^{57} +(-1.00000 + 1.73205i) q^{58} +(-7.50000 + 12.9904i) q^{59} -2.00000 q^{60} +(3.50000 - 6.06218i) q^{61} +(-4.50000 - 7.79423i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(7.00000 - 1.73205i) q^{65} +4.00000 q^{66} +(2.50000 + 4.33013i) q^{67} +(-3.50000 - 6.06218i) q^{68} +(0.500000 - 0.866025i) q^{69} -2.00000 q^{70} +(-0.500000 + 0.866025i) q^{71} +(0.500000 - 0.866025i) q^{72} +12.0000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(0.500000 + 0.866025i) q^{75} +(-1.00000 - 1.73205i) q^{76} +4.00000 q^{77} +(-1.00000 + 3.46410i) q^{78} -4.00000 q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(1.00000 - 1.73205i) q^{82} -1.00000 q^{83} +(0.500000 - 0.866025i) q^{84} +(7.00000 - 12.1244i) q^{85} +5.00000 q^{86} +(1.00000 - 1.73205i) q^{87} +(-2.00000 - 3.46410i) q^{88} +(-1.50000 - 2.59808i) q^{89} +2.00000 q^{90} +(-1.00000 + 3.46410i) q^{91} -1.00000 q^{92} +(4.50000 + 7.79423i) q^{93} +(3.00000 + 5.19615i) q^{94} +(2.00000 - 3.46410i) q^{95} -1.00000 q^{96} +(8.00000 - 13.8564i) q^{97} +(0.500000 - 0.866025i) q^{98} -4.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - q^{3} - q^{4} - 4q^{5} + q^{6} + q^{7} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - q^{3} - q^{4} - 4q^{5} + q^{6} + q^{7} - 2q^{8} - q^{9} - 2q^{10} + 4q^{11} + 2q^{12} - 7q^{13} + 2q^{14} + 2q^{15} - q^{16} - 7q^{17} - 2q^{18} - 2q^{19} + 2q^{20} - 2q^{21} - 4q^{22} + q^{23} + q^{24} - 2q^{25} - 5q^{26} + 2q^{27} + q^{28} + 2q^{29} - 2q^{30} - 18q^{31} + q^{32} + 4q^{33} - 14q^{34} - 2q^{35} - q^{36} + 2q^{37} - 4q^{38} + 5q^{39} + 4q^{40} - 2q^{41} - q^{42} + 5q^{43} - 8q^{44} + 2q^{45} - q^{46} + 12q^{47} - q^{48} - q^{49} - q^{50} + 14q^{51} + 2q^{52} + 6q^{53} + q^{54} - 8q^{55} - q^{56} + 4q^{57} - 2q^{58} - 15q^{59} - 4q^{60} + 7q^{61} - 9q^{62} + q^{63} + 2q^{64} + 14q^{65} + 8q^{66} + 5q^{67} - 7q^{68} + q^{69} - 4q^{70} - q^{71} + q^{72} + 24q^{73} - 2q^{74} + q^{75} - 2q^{76} + 8q^{77} - 2q^{78} - 8q^{79} + 2q^{80} - q^{81} + 2q^{82} - 2q^{83} + q^{84} + 14q^{85} + 10q^{86} + 2q^{87} - 4q^{88} - 3q^{89} + 4q^{90} - 2q^{91} - 2q^{92} + 9q^{93} + 6q^{94} + 4q^{95} - 2q^{96} + 16q^{97} + q^{98} - 8q^{99} + O(q^{100}) \)

Character values

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

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

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 \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.500000 + 0.866025i 0.353553 + 0.612372i
\(3\) −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 \(-0.647584\pi\)
−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
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) −1.00000 1.73205i −0.316228 0.547723i
\(11\) 2.00000 + 3.46410i 0.603023 + 1.04447i 0.992361 + 0.123371i \(0.0393705\pi\)
−0.389338 + 0.921095i \(0.627296\pi\)
\(12\) 1.00000 0.288675
\(13\) −3.50000 + 0.866025i −0.970725 + 0.240192i
\(14\) 1.00000 0.267261
\(15\) 1.00000 + 1.73205i 0.258199 + 0.447214i
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.50000 + 6.06218i −0.848875 + 1.47029i 0.0333386 + 0.999444i \(0.489386\pi\)
−0.882213 + 0.470850i \(0.843947\pi\)
\(18\) −1.00000 −0.235702
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 1.00000 1.73205i 0.223607 0.387298i
\(21\) −1.00000 −0.218218
\(22\) −2.00000 + 3.46410i −0.426401 + 0.738549i
\(23\) 0.500000 + 0.866025i 0.104257 + 0.180579i 0.913434 0.406986i \(-0.133420\pi\)
−0.809177 + 0.587565i \(0.800087\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −1.00000 −0.200000
\(26\) −2.50000 2.59808i −0.490290 0.509525i
\(27\) 1.00000 0.192450
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) 1.00000 + 1.73205i 0.185695 + 0.321634i 0.943811 0.330487i \(-0.107213\pi\)
−0.758115 + 0.652121i \(0.773880\pi\)
\(30\) −1.00000 + 1.73205i −0.182574 + 0.316228i
\(31\) −9.00000 −1.61645 −0.808224 0.588875i \(-0.799571\pi\)
−0.808224 + 0.588875i \(0.799571\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) 2.00000 3.46410i 0.348155 0.603023i
\(34\) −7.00000 −1.20049
\(35\) −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 \(-0.114098\pi\)
−0.772043 + 0.635571i \(0.780765\pi\)
\(38\) −2.00000 −0.324443
\(39\) 2.50000 + 2.59808i 0.400320 + 0.416025i
\(40\) 2.00000 0.316228
\(41\) −1.00000 1.73205i −0.156174 0.270501i 0.777312 0.629115i \(-0.216583\pi\)
−0.933486 + 0.358614i \(0.883249\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) 2.50000 4.33013i 0.381246 0.660338i −0.609994 0.792406i \(-0.708828\pi\)
0.991241 + 0.132068i \(0.0421616\pi\)
\(44\) −4.00000 −0.603023
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) −0.500000 + 0.866025i −0.0737210 + 0.127688i
\(47\) 6.00000 0.875190 0.437595 0.899172i \(-0.355830\pi\)
0.437595 + 0.899172i \(0.355830\pi\)
\(48\) −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
\(51\) 7.00000 0.980196
\(52\) 1.00000 3.46410i 0.138675 0.480384i
\(53\) 3.00000 0.412082 0.206041 0.978543i \(-0.433942\pi\)
0.206041 + 0.978543i \(0.433942\pi\)
\(54\) 0.500000 + 0.866025i 0.0680414 + 0.117851i
\(55\) −4.00000 6.92820i −0.539360 0.934199i
\(56\) −0.500000 + 0.866025i −0.0668153 + 0.115728i
\(57\) 2.00000 0.264906
\(58\) −1.00000 + 1.73205i −0.131306 + 0.227429i
\(59\) −7.50000 + 12.9904i −0.976417 + 1.69120i −0.301239 + 0.953549i \(0.597400\pi\)
−0.675178 + 0.737655i \(0.735933\pi\)
\(60\) −2.00000 −0.258199
\(61\) 3.50000 6.06218i 0.448129 0.776182i −0.550135 0.835076i \(-0.685424\pi\)
0.998264 + 0.0588933i \(0.0187572\pi\)
\(62\) −4.50000 7.79423i −0.571501 0.989868i
\(63\) 0.500000 + 0.866025i 0.0629941 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) 7.00000 1.73205i 0.868243 0.214834i
\(66\) 4.00000 0.492366
\(67\) 2.50000 + 4.33013i 0.305424 + 0.529009i 0.977356 0.211604i \(-0.0678686\pi\)
−0.671932 + 0.740613i \(0.734535\pi\)
\(68\) −3.50000 6.06218i −0.424437 0.735147i
\(69\) 0.500000 0.866025i 0.0601929 0.104257i
\(70\) −2.00000 −0.239046
\(71\) −0.500000 + 0.866025i −0.0593391 + 0.102778i −0.894169 0.447730i \(-0.852233\pi\)
0.834830 + 0.550508i \(0.185566\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) 12.0000 1.40449 0.702247 0.711934i \(-0.252180\pi\)
0.702247 + 0.711934i \(0.252180\pi\)
\(74\) −1.00000 + 1.73205i −0.116248 + 0.201347i
\(75\) 0.500000 + 0.866025i 0.0577350 + 0.100000i
\(76\) −1.00000 1.73205i −0.114708 0.198680i
\(77\) 4.00000 0.455842
\(78\) −1.00000 + 3.46410i −0.113228 + 0.392232i
\(79\) −4.00000 −0.450035 −0.225018 0.974355i \(-0.572244\pi\)
−0.225018 + 0.974355i \(0.572244\pi\)
\(80\) 1.00000 + 1.73205i 0.111803 + 0.193649i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) 1.00000 1.73205i 0.110432 0.191273i
\(83\) −1.00000 −0.109764 −0.0548821 0.998493i \(-0.517478\pi\)
−0.0548821 + 0.998493i \(0.517478\pi\)
\(84\) 0.500000 0.866025i 0.0545545 0.0944911i
\(85\) 7.00000 12.1244i 0.759257 1.31507i
\(86\) 5.00000 0.539164
\(87\) 1.00000 1.73205i 0.107211 0.185695i
\(88\) −2.00000 3.46410i −0.213201 0.369274i
\(89\) −1.50000 2.59808i −0.159000 0.275396i 0.775509 0.631337i \(-0.217494\pi\)
−0.934508 + 0.355942i \(0.884160\pi\)
\(90\) 2.00000 0.210819
\(91\) −1.00000 + 3.46410i −0.104828 + 0.363137i
\(92\) −1.00000 −0.104257
\(93\) 4.50000 + 7.79423i 0.466628 + 0.808224i
\(94\) 3.00000 + 5.19615i 0.309426 + 0.535942i
\(95\) 2.00000 3.46410i 0.205196 0.355409i
\(96\) −1.00000 −0.102062
\(97\) 8.00000 13.8564i 0.812277 1.40690i −0.0989899 0.995088i \(-0.531561\pi\)
0.911267 0.411816i \(-0.135106\pi\)
\(98\) 0.500000 0.866025i 0.0505076 0.0874818i
\(99\) −4.00000 −0.402015
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) 3.50000 + 6.06218i 0.346552 + 0.600245i
\(103\) −11.0000 −1.08386 −0.541931 0.840423i \(-0.682307\pi\)
−0.541931 + 0.840423i \(0.682307\pi\)
\(104\) 3.50000 0.866025i 0.343203 0.0849208i
\(105\) 2.00000 0.195180
\(106\) 1.50000 + 2.59808i 0.145693 + 0.252347i
\(107\) 3.00000 + 5.19615i 0.290021 + 0.502331i 0.973814 0.227345i \(-0.0730044\pi\)
−0.683793 + 0.729676i \(0.739671\pi\)
\(108\) −0.500000 + 0.866025i −0.0481125 + 0.0833333i
\(109\) −16.0000 −1.53252 −0.766261 0.642529i \(-0.777885\pi\)
−0.766261 + 0.642529i \(0.777885\pi\)
\(110\) 4.00000 6.92820i 0.381385 0.660578i
\(111\) 1.00000 1.73205i 0.0949158 0.164399i
\(112\) −1.00000 −0.0944911
\(113\) 4.00000 6.92820i 0.376288 0.651751i −0.614231 0.789127i \(-0.710534\pi\)
0.990519 + 0.137376i \(0.0438669\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) −1.00000 1.73205i −0.0932505 0.161515i
\(116\) −2.00000 −0.185695
\(117\) 1.00000 3.46410i 0.0924500 0.320256i
\(118\) −15.0000 −1.38086
\(119\) 3.50000 + 6.06218i 0.320844 + 0.555719i
\(120\) −1.00000 1.73205i −0.0912871 0.158114i
\(121\) −2.50000 + 4.33013i −0.227273 + 0.393648i
\(122\) 7.00000 0.633750
\(123\) −1.00000 + 1.73205i −0.0901670 + 0.156174i
\(124\) 4.50000 7.79423i 0.404112 0.699942i
\(125\) 12.0000 1.07331
\(126\) −0.500000 + 0.866025i −0.0445435 + 0.0771517i
\(127\) −8.00000 13.8564i −0.709885 1.22956i −0.964899 0.262620i \(-0.915413\pi\)
0.255014 0.966937i \(-0.417920\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −5.00000 −0.440225
\(130\) 5.00000 + 5.19615i 0.438529 + 0.455733i
\(131\) 15.0000 1.31056 0.655278 0.755388i \(-0.272551\pi\)
0.655278 + 0.755388i \(0.272551\pi\)
\(132\) 2.00000 + 3.46410i 0.174078 + 0.301511i
\(133\) 1.00000 + 1.73205i 0.0867110 + 0.150188i
\(134\) −2.50000 + 4.33013i −0.215967 + 0.374066i
\(135\) −2.00000 −0.172133
\(136\) 3.50000 6.06218i 0.300123 0.519827i
\(137\) −2.00000 + 3.46410i −0.170872 + 0.295958i −0.938725 0.344668i \(-0.887992\pi\)
0.767853 + 0.640626i \(0.221325\pi\)
\(138\) 1.00000 0.0851257
\(139\) −8.00000 + 13.8564i −0.678551 + 1.17529i 0.296866 + 0.954919i \(0.404058\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(140\) −1.00000 1.73205i −0.0845154 0.146385i
\(141\) −3.00000 5.19615i −0.252646 0.437595i
\(142\) −1.00000 −0.0839181
\(143\) −10.0000 10.3923i −0.836242 0.869048i
\(144\) 1.00000 0.0833333
\(145\) −2.00000 3.46410i −0.166091 0.287678i
\(146\) 6.00000 + 10.3923i 0.496564 + 0.860073i
\(147\) −0.500000 + 0.866025i −0.0412393 + 0.0714286i
\(148\) −2.00000 −0.164399
\(149\) −10.5000 + 18.1865i −0.860194 + 1.48990i 0.0115483 + 0.999933i \(0.496324\pi\)
−0.871742 + 0.489966i \(0.837009\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) 20.0000 1.62758 0.813788 0.581161i \(-0.197401\pi\)
0.813788 + 0.581161i \(0.197401\pi\)
\(152\) 1.00000 1.73205i 0.0811107 0.140488i
\(153\) −3.50000 6.06218i −0.282958 0.490098i
\(154\) 2.00000 + 3.46410i 0.161165 + 0.279145i
\(155\) 18.0000 1.44579
\(156\) −3.50000 + 0.866025i −0.280224 + 0.0693375i
\(157\) 10.0000 0.798087 0.399043 0.916932i \(-0.369342\pi\)
0.399043 + 0.916932i \(0.369342\pi\)
\(158\) −2.00000 3.46410i −0.159111 0.275589i
\(159\) −1.50000 2.59808i −0.118958 0.206041i
\(160\) −1.00000 + 1.73205i −0.0790569 + 0.136931i
\(161\) 1.00000 0.0788110
\(162\) 0.500000 0.866025i 0.0392837 0.0680414i
\(163\) −10.5000 + 18.1865i −0.822423 + 1.42448i 0.0814491 + 0.996678i \(0.474045\pi\)
−0.903873 + 0.427802i \(0.859288\pi\)
\(164\) 2.00000 0.156174
\(165\) −4.00000 + 6.92820i −0.311400 + 0.539360i
\(166\) −0.500000 0.866025i −0.0388075 0.0672166i
\(167\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(168\) 1.00000 0.0771517
\(169\) 11.5000 6.06218i 0.884615 0.466321i
\(170\) 14.0000 1.07375
\(171\) −1.00000 1.73205i −0.0764719 0.132453i
\(172\) 2.50000 + 4.33013i 0.190623 + 0.330169i
\(173\) 8.00000 13.8564i 0.608229 1.05348i −0.383304 0.923622i \(-0.625214\pi\)
0.991532 0.129861i \(-0.0414530\pi\)
\(174\) 2.00000 0.151620
\(175\) −0.500000 + 0.866025i −0.0377964 + 0.0654654i
\(176\) 2.00000 3.46410i 0.150756 0.261116i
\(177\) 15.0000 1.12747
\(178\) 1.50000 2.59808i 0.112430 0.194734i
\(179\) −3.00000 5.19615i −0.224231 0.388379i 0.731858 0.681457i \(-0.238654\pi\)
−0.956088 + 0.293079i \(0.905320\pi\)
\(180\) 1.00000 + 1.73205i 0.0745356 + 0.129099i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) −3.50000 + 0.866025i −0.259437 + 0.0641941i
\(183\) −7.00000 −0.517455
\(184\) −0.500000 0.866025i −0.0368605 0.0638442i
\(185\) −2.00000 3.46410i −0.147043 0.254686i
\(186\) −4.50000 + 7.79423i −0.329956 + 0.571501i
\(187\) −28.0000 −2.04756
\(188\) −3.00000 + 5.19615i −0.218797 + 0.378968i
\(189\) 0.500000 0.866025i 0.0363696 0.0629941i
\(190\) 4.00000 0.290191
\(191\) −1.50000 + 2.59808i −0.108536 + 0.187990i −0.915177 0.403051i \(-0.867950\pi\)
0.806641 + 0.591041i \(0.201283\pi\)
\(192\) −0.500000 0.866025i −0.0360844 0.0625000i
\(193\) 11.0000 + 19.0526i 0.791797 + 1.37143i 0.924853 + 0.380325i \(0.124188\pi\)
−0.133056 + 0.991109i \(0.542479\pi\)
\(194\) 16.0000 1.14873
\(195\) −5.00000 5.19615i −0.358057 0.372104i
\(196\) 1.00000 0.0714286
\(197\) 4.50000 + 7.79423i 0.320612 + 0.555316i 0.980614 0.195947i \(-0.0627782\pi\)
−0.660003 + 0.751263i \(0.729445\pi\)
\(198\) −2.00000 3.46410i −0.142134 0.246183i
\(199\) 2.50000 4.33013i 0.177220 0.306955i −0.763707 0.645563i \(-0.776623\pi\)
0.940927 + 0.338608i \(0.109956\pi\)
\(200\) 1.00000 0.0707107
\(201\) 2.50000 4.33013i 0.176336 0.305424i
\(202\) 0 0
\(203\) 2.00000 0.140372
\(204\) −3.50000 + 6.06218i −0.245049 + 0.424437i
\(205\) 2.00000 + 3.46410i 0.139686 + 0.241943i
\(206\) −5.50000 9.52628i −0.383203 0.663727i
\(207\) −1.00000 −0.0695048
\(208\) 2.50000 + 2.59808i 0.173344 + 0.180144i
\(209\) −8.00000 −0.553372
\(210\) 1.00000 + 1.73205i 0.0690066 + 0.119523i
\(211\) −2.00000 3.46410i −0.137686 0.238479i 0.788935 0.614477i \(-0.210633\pi\)
−0.926620 + 0.375999i \(0.877300\pi\)
\(212\) −1.50000 + 2.59808i −0.103020 + 0.178437i
\(213\) 1.00000 0.0685189
\(214\) −3.00000 + 5.19615i −0.205076 + 0.355202i
\(215\) −5.00000 + 8.66025i −0.340997 + 0.590624i
\(216\) −1.00000 −0.0680414
\(217\) −4.50000 + 7.79423i −0.305480 + 0.529107i
\(218\) −8.00000 13.8564i −0.541828 0.938474i
\(219\) −6.00000 10.3923i −0.405442 0.702247i
\(220\) 8.00000 0.539360
\(221\) 7.00000 24.2487i 0.470871 1.63114i
\(222\) 2.00000 0.134231
\(223\) −1.50000 2.59808i −0.100447 0.173980i 0.811422 0.584461i \(-0.198694\pi\)
−0.911869 + 0.410481i \(0.865361\pi\)
\(224\) −0.500000 0.866025i −0.0334077 0.0578638i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) 8.00000 0.532152
\(227\) −14.0000 + 24.2487i −0.929213 + 1.60944i −0.144571 + 0.989494i \(0.546180\pi\)
−0.784642 + 0.619949i \(0.787153\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) 13.0000 0.859064 0.429532 0.903052i \(-0.358679\pi\)
0.429532 + 0.903052i \(0.358679\pi\)
\(230\) 1.00000 1.73205i 0.0659380 0.114208i
\(231\) −2.00000 3.46410i −0.131590 0.227921i
\(232\) −1.00000 1.73205i −0.0656532 0.113715i
\(233\) −16.0000 −1.04819 −0.524097 0.851658i \(-0.675597\pi\)
−0.524097 + 0.851658i \(0.675597\pi\)
\(234\) 3.50000 0.866025i 0.228802 0.0566139i
\(235\) −12.0000 −0.782794
\(236\) −7.50000 12.9904i −0.488208 0.845602i
\(237\) 2.00000 + 3.46410i 0.129914 + 0.225018i
\(238\) −3.50000 + 6.06218i −0.226871 + 0.392953i
\(239\) −9.00000 −0.582162 −0.291081 0.956698i \(-0.594015\pi\)
−0.291081 + 0.956698i \(0.594015\pi\)
\(240\) 1.00000 1.73205i 0.0645497 0.111803i
\(241\) −7.00000 + 12.1244i −0.450910 + 0.780998i −0.998443 0.0557856i \(-0.982234\pi\)
0.547533 + 0.836784i \(0.315567\pi\)
\(242\) −5.00000 −0.321412
\(243\) −0.500000 + 0.866025i −0.0320750 + 0.0555556i
\(244\) 3.50000 + 6.06218i 0.224065 + 0.388091i
\(245\) 1.00000 + 1.73205i 0.0638877 + 0.110657i
\(246\) −2.00000 −0.127515
\(247\) 2.00000 6.92820i 0.127257 0.440831i
\(248\) 9.00000 0.571501
\(249\) 0.500000 + 0.866025i 0.0316862 + 0.0548821i
\(250\) 6.00000 + 10.3923i 0.379473 + 0.657267i
\(251\) −11.5000 + 19.9186i −0.725874 + 1.25725i 0.232740 + 0.972539i \(0.425231\pi\)
−0.958613 + 0.284711i \(0.908102\pi\)
\(252\) −1.00000 −0.0629941
\(253\) −2.00000 + 3.46410i −0.125739 + 0.217786i
\(254\) 8.00000 13.8564i 0.501965 0.869428i
\(255\) −14.0000 −0.876714
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −13.5000 23.3827i −0.842107 1.45857i −0.888110 0.459631i \(-0.847982\pi\)
0.0460033 0.998941i \(-0.485352\pi\)
\(258\) −2.50000 4.33013i −0.155643 0.269582i
\(259\) 2.00000 0.124274
\(260\) −2.00000 + 6.92820i −0.124035 + 0.429669i
\(261\) −2.00000 −0.123797
\(262\) 7.50000 + 12.9904i 0.463352 + 0.802548i
\(263\) −2.00000 3.46410i −0.123325 0.213606i 0.797752 0.602986i \(-0.206023\pi\)
−0.921077 + 0.389380i \(0.872689\pi\)
\(264\) −2.00000 + 3.46410i −0.123091 + 0.213201i
\(265\) −6.00000 −0.368577
\(266\) −1.00000 + 1.73205i −0.0613139 + 0.106199i
\(267\) −1.50000 + 2.59808i −0.0917985 + 0.159000i
\(268\) −5.00000 −0.305424
\(269\) −9.00000 + 15.5885i −0.548740 + 0.950445i 0.449622 + 0.893219i \(0.351559\pi\)
−0.998361 + 0.0572259i \(0.981774\pi\)
\(270\) −1.00000 1.73205i −0.0608581 0.105409i
\(271\) −4.50000 7.79423i −0.273356 0.473466i 0.696363 0.717689i \(-0.254800\pi\)
−0.969719 + 0.244224i \(0.921467\pi\)
\(272\) 7.00000 0.424437
\(273\) 3.50000 0.866025i 0.211830 0.0524142i
\(274\) −4.00000 −0.241649
\(275\) −2.00000 3.46410i −0.120605 0.208893i
\(276\) 0.500000 + 0.866025i 0.0300965 + 0.0521286i
\(277\) 4.00000 6.92820i 0.240337 0.416275i −0.720473 0.693482i \(-0.756075\pi\)
0.960810 + 0.277207i \(0.0894088\pi\)
\(278\) −16.0000 −0.959616
\(279\) 4.50000 7.79423i 0.269408 0.466628i
\(280\) 1.00000 1.73205i 0.0597614 0.103510i
\(281\) −26.0000 −1.55103 −0.775515 0.631329i \(-0.782510\pi\)
−0.775515 + 0.631329i \(0.782510\pi\)
\(282\) 3.00000 5.19615i 0.178647 0.309426i
\(283\) −7.00000 12.1244i −0.416107 0.720718i 0.579437 0.815017i \(-0.303272\pi\)
−0.995544 + 0.0942988i \(0.969939\pi\)
\(284\) −0.500000 0.866025i −0.0296695 0.0513892i
\(285\) −4.00000 −0.236940
\(286\) 4.00000 13.8564i 0.236525 0.819346i
\(287\) −2.00000 −0.118056
\(288\) 0.500000 + 0.866025i 0.0294628 + 0.0510310i
\(289\) −16.0000 27.7128i −0.941176 1.63017i
\(290\) 2.00000 3.46410i 0.117444 0.203419i
\(291\) −16.0000 −0.937937
\(292\) −6.00000 + 10.3923i −0.351123 + 0.608164i
\(293\) 8.00000 13.8564i 0.467365 0.809500i −0.531940 0.846782i \(-0.678537\pi\)
0.999305 + 0.0372823i \(0.0118701\pi\)
\(294\) −1.00000 −0.0583212
\(295\) 15.0000 25.9808i 0.873334 1.51266i
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) 2.00000 + 3.46410i 0.116052 + 0.201008i
\(298\) −21.0000 −1.21650
\(299\) −2.50000 2.59808i −0.144579 0.150251i
\(300\) −1.00000 −0.0577350
\(301\) −2.50000 4.33013i −0.144098 0.249584i
\(302\) 10.0000 + 17.3205i 0.575435 + 0.996683i
\(303\) 0 0
\(304\) 2.00000 0.114708
\(305\) −7.00000 + 12.1244i −0.400819 + 0.694239i
\(306\) 3.50000 6.06218i 0.200082 0.346552i
\(307\) 30.0000 1.71219 0.856095 0.516818i \(-0.172884\pi\)
0.856095 + 0.516818i \(0.172884\pi\)
\(308\) −2.00000 + 3.46410i −0.113961 + 0.197386i
\(309\) 5.50000 + 9.52628i 0.312884 + 0.541931i
\(310\) 9.00000 + 15.5885i 0.511166 + 0.885365i
\(311\) 30.0000 1.70114 0.850572 0.525859i \(-0.176256\pi\)
0.850572 + 0.525859i \(0.176256\pi\)
\(312\) −2.50000 2.59808i −0.141535 0.147087i
\(313\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(314\) 5.00000 + 8.66025i 0.282166 + 0.488726i
\(315\) −1.00000 1.73205i −0.0563436 0.0975900i
\(316\) 2.00000 3.46410i 0.112509 0.194871i
\(317\) 23.0000 1.29181 0.645904 0.763418i \(-0.276480\pi\)
0.645904 + 0.763418i \(0.276480\pi\)
\(318\) 1.50000 2.59808i 0.0841158 0.145693i
\(319\) −4.00000 + 6.92820i −0.223957 + 0.387905i
\(320\) −2.00000 −0.111803
\(321\) 3.00000 5.19615i 0.167444 0.290021i
\(322\) 0.500000 + 0.866025i 0.0278639 + 0.0482617i
\(323\) −7.00000 12.1244i −0.389490 0.674617i
\(324\) 1.00000 0.0555556
\(325\) 3.50000 0.866025i 0.194145 0.0480384i
\(326\) −21.0000 −1.16308
\(327\) 8.00000 + 13.8564i 0.442401 + 0.766261i
\(328\) 1.00000 + 1.73205i 0.0552158 + 0.0956365i
\(329\) 3.00000 5.19615i 0.165395 0.286473i
\(330\) −8.00000 −0.440386
\(331\) −18.0000 + 31.1769i −0.989369 + 1.71364i −0.368744 + 0.929531i \(0.620212\pi\)
−0.620625 + 0.784107i \(0.713121\pi\)
\(332\) 0.500000 0.866025i 0.0274411 0.0475293i
\(333\) −2.00000 −0.109599
\(334\) 0 0
\(335\) −5.00000 8.66025i −0.273179 0.473160i
\(336\) 0.500000 + 0.866025i 0.0272772 + 0.0472456i
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 11.0000 + 6.92820i 0.598321 + 0.376845i
\(339\) −8.00000 −0.434500
\(340\) 7.00000 + 12.1244i 0.379628 + 0.657536i
\(341\) −18.0000 31.1769i −0.974755 1.68832i
\(342\) 1.00000 1.73205i 0.0540738 0.0936586i
\(343\) −1.00000 −0.0539949
\(344\) −2.50000 + 4.33013i −0.134791 + 0.233465i
\(345\) −1.00000 + 1.73205i −0.0538382 + 0.0932505i
\(346\) 16.0000 0.860165
\(347\) −5.00000 + 8.66025i −0.268414 + 0.464907i −0.968452 0.249198i \(-0.919833\pi\)
0.700038 + 0.714105i \(0.253166\pi\)
\(348\) 1.00000 + 1.73205i 0.0536056 + 0.0928477i
\(349\) 12.5000 + 21.6506i 0.669110 + 1.15893i 0.978153 + 0.207884i \(0.0666577\pi\)
−0.309044 + 0.951048i \(0.600009\pi\)
\(350\) −1.00000 −0.0534522
\(351\) −3.50000 + 0.866025i −0.186816 + 0.0462250i
\(352\) 4.00000 0.213201
\(353\) 17.5000 + 30.3109i 0.931431 + 1.61329i 0.780878 + 0.624684i \(0.214772\pi\)
0.150553 + 0.988602i \(0.451894\pi\)
\(354\) 7.50000 + 12.9904i 0.398621 + 0.690431i
\(355\) 1.00000 1.73205i 0.0530745 0.0919277i
\(356\) 3.00000 0.159000
\(357\) 3.50000 6.06218i 0.185240 0.320844i
\(358\) 3.00000 5.19615i 0.158555 0.274625i
\(359\) −24.0000 −1.26667 −0.633336 0.773877i \(-0.718315\pi\)
−0.633336 + 0.773877i \(0.718315\pi\)
\(360\) −1.00000 + 1.73205i −0.0527046 + 0.0912871i
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) −1.00000 1.73205i −0.0525588 0.0910346i
\(363\) 5.00000 0.262432
\(364\) −2.50000 2.59808i −0.131036 0.136176i
\(365\) −24.0000 −1.25622
\(366\) −3.50000 6.06218i −0.182948 0.316875i
\(367\) 1.50000 + 2.59808i 0.0782994 + 0.135618i 0.902516 0.430656i \(-0.141718\pi\)
−0.824217 + 0.566274i \(0.808384\pi\)
\(368\) 0.500000 0.866025i 0.0260643 0.0451447i
\(369\) 2.00000 0.104116
\(370\) 2.00000 3.46410i 0.103975 0.180090i
\(371\) 1.50000 2.59808i 0.0778761 0.134885i
\(372\) −9.00000 −0.466628
\(373\) −2.00000 + 3.46410i −0.103556 + 0.179364i −0.913147 0.407630i \(-0.866355\pi\)
0.809591 + 0.586994i \(0.199689\pi\)
\(374\) −14.0000 24.2487i −0.723923 1.25387i
\(375\) −6.00000 10.3923i −0.309839 0.536656i
\(376\) −6.00000 −0.309426
\(377\) −5.00000 5.19615i −0.257513 0.267615i
\(378\) 1.00000 0.0514344
\(379\) 10.0000 + 17.3205i 0.513665 + 0.889695i 0.999874 + 0.0158521i \(0.00504609\pi\)
−0.486209 + 0.873843i \(0.661621\pi\)
\(380\) 2.00000 + 3.46410i 0.102598 + 0.177705i
\(381\) −8.00000 + 13.8564i −0.409852 + 0.709885i
\(382\) −3.00000 −0.153493
\(383\) −12.0000 + 20.7846i −0.613171 + 1.06204i 0.377531 + 0.925997i \(0.376773\pi\)
−0.990702 + 0.136047i \(0.956560\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) −8.00000 −0.407718
\(386\) −11.0000 + 19.0526i −0.559885 + 0.969750i
\(387\) 2.50000 + 4.33013i 0.127082 + 0.220113i
\(388\) 8.00000 + 13.8564i 0.406138 + 0.703452i
\(389\) −1.00000 −0.0507020 −0.0253510 0.999679i \(-0.508070\pi\)
−0.0253510 + 0.999679i \(0.508070\pi\)
\(390\) 2.00000 6.92820i 0.101274 0.350823i
\(391\) −7.00000 −0.354005
\(392\) 0.500000 + 0.866025i 0.0252538 + 0.0437409i
\(393\) −7.50000 12.9904i −0.378325 0.655278i
\(394\) −4.50000 + 7.79423i −0.226707 + 0.392668i
\(395\) 8.00000 0.402524
\(396\) 2.00000 3.46410i 0.100504 0.174078i
\(397\) 0.500000 0.866025i 0.0250943 0.0434646i −0.853206 0.521575i \(-0.825345\pi\)
0.878300 + 0.478110i \(0.158678\pi\)
\(398\) 5.00000 0.250627
\(399\) 1.00000 1.73205i 0.0500626 0.0867110i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −16.0000 27.7128i −0.799002 1.38391i −0.920267 0.391292i \(-0.872028\pi\)
0.121265 0.992620i \(-0.461305\pi\)
\(402\) 5.00000 0.249377
\(403\) 31.5000 7.79423i 1.56913 0.388258i
\(404\) 0 0
\(405\) 1.00000 + 1.73205i 0.0496904 + 0.0860663i
\(406\) 1.00000 + 1.73205i 0.0496292 + 0.0859602i
\(407\) −4.00000 + 6.92820i −0.198273 + 0.343418i
\(408\) −7.00000 −0.346552
\(409\) −7.00000 + 12.1244i −0.346128 + 0.599511i −0.985558 0.169338i \(-0.945837\pi\)
0.639430 + 0.768849i \(0.279170\pi\)
\(410\) −2.00000 + 3.46410i −0.0987730 + 0.171080i
\(411\) 4.00000 0.197305
\(412\) 5.50000 9.52628i 0.270966 0.469326i
\(413\) 7.50000 + 12.9904i 0.369051 + 0.639215i
\(414\) −0.500000 0.866025i −0.0245737 0.0425628i
\(415\) 2.00000 0.0981761
\(416\) −1.00000 + 3.46410i −0.0490290 + 0.169842i
\(417\) 16.0000 0.783523
\(418\) −4.00000 6.92820i −0.195646 0.338869i
\(419\) 15.5000 + 26.8468i 0.757225 + 1.31155i 0.944261 + 0.329198i \(0.106778\pi\)
−0.187036 + 0.982353i \(0.559888\pi\)
\(420\) −1.00000 + 1.73205i −0.0487950 + 0.0845154i
\(421\) 34.0000 1.65706 0.828529 0.559946i \(-0.189178\pi\)
0.828529 + 0.559946i \(0.189178\pi\)
\(422\) 2.00000 3.46410i 0.0973585 0.168630i
\(423\) −3.00000 + 5.19615i −0.145865 + 0.252646i
\(424\) −3.00000 −0.145693
\(425\) 3.50000 6.06218i 0.169775 0.294059i
\(426\) 0.500000 + 0.866025i 0.0242251 + 0.0419591i
\(427\) −3.50000 6.06218i −0.169377 0.293369i
\(428\) −6.00000 −0.290021
\(429\) −4.00000 + 13.8564i −0.193122 + 0.668994i
\(430\) −10.0000 −0.482243
\(431\) 0.500000 + 0.866025i 0.0240842 + 0.0417150i 0.877816 0.478997i \(-0.159000\pi\)
−0.853732 + 0.520712i \(0.825666\pi\)
\(432\) −0.500000 0.866025i −0.0240563 0.0416667i
\(433\) −6.00000 + 10.3923i −0.288342 + 0.499422i −0.973414 0.229053i \(-0.926437\pi\)
0.685072 + 0.728475i \(0.259771\pi\)
\(434\) −9.00000 −0.432014
\(435\) −2.00000 + 3.46410i −0.0958927 + 0.166091i
\(436\) 8.00000 13.8564i 0.383131 0.663602i
\(437\) −2.00000 −0.0956730
\(438\) 6.00000 10.3923i 0.286691 0.496564i
\(439\) −2.00000 3.46410i −0.0954548 0.165333i 0.814344 0.580383i \(-0.197097\pi\)
−0.909798 + 0.415051i \(0.863764\pi\)
\(440\) 4.00000 + 6.92820i 0.190693 + 0.330289i
\(441\) 1.00000 0.0476190
\(442\) 24.5000 6.06218i 1.16535 0.288348i
\(443\) −6.00000 −0.285069 −0.142534 0.989790i \(-0.545525\pi\)
−0.142534 + 0.989790i \(0.545525\pi\)
\(444\) 1.00000 + 1.73205i 0.0474579 + 0.0821995i
\(445\) 3.00000 + 5.19615i 0.142214 + 0.246321i
\(446\) 1.50000 2.59808i 0.0710271 0.123022i
\(447\) 21.0000 0.993266
\(448\) 0.500000 0.866025i 0.0236228 0.0409159i
\(449\) −9.00000 + 15.5885i −0.424736 + 0.735665i −0.996396 0.0848262i \(-0.972967\pi\)
0.571660 + 0.820491i \(0.306300\pi\)
\(450\) 1.00000 0.0471405
\(451\) 4.00000 6.92820i 0.188353 0.326236i
\(452\) 4.00000 + 6.92820i 0.188144 + 0.325875i
\(453\) −10.0000 17.3205i −0.469841 0.813788i
\(454\) −28.0000 −1.31411
\(455\) 2.00000 6.92820i 0.0937614 0.324799i
\(456\) −2.00000 −0.0936586
\(457\) 4.50000 + 7.79423i 0.210501 + 0.364599i 0.951871 0.306497i \(-0.0991571\pi\)
−0.741370 + 0.671096i \(0.765824\pi\)
\(458\) 6.50000 + 11.2583i 0.303725 + 0.526067i
\(459\) −3.50000 + 6.06218i −0.163366 + 0.282958i
\(460\) 2.00000 0.0932505
\(461\) 10.0000 17.3205i 0.465746 0.806696i −0.533488 0.845807i \(-0.679119\pi\)
0.999235 + 0.0391109i \(0.0124526\pi\)
\(462\) 2.00000 3.46410i 0.0930484 0.161165i
\(463\) 18.0000 0.836531 0.418265 0.908325i \(-0.362638\pi\)
0.418265 + 0.908325i \(0.362638\pi\)
\(464\) 1.00000 1.73205i 0.0464238 0.0804084i
\(465\) −9.00000 15.5885i −0.417365 0.722897i
\(466\) −8.00000 13.8564i −0.370593 0.641886i
\(467\) 37.0000 1.71216 0.856078 0.516847i \(-0.172894\pi\)
0.856078 + 0.516847i \(0.172894\pi\)
\(468\) 2.50000 + 2.59808i 0.115563 + 0.120096i
\(469\) 5.00000 0.230879
\(470\) −6.00000 10.3923i −0.276759 0.479361i
\(471\) −5.00000 8.66025i −0.230388 0.399043i
\(472\) 7.50000 12.9904i 0.345215 0.597931i
\(473\) 20.0000 0.919601
\(474\) −2.00000 + 3.46410i −0.0918630 + 0.159111i
\(475\) 1.00000 1.73205i 0.0458831 0.0794719i
\(476\) −7.00000 −0.320844
\(477\) −1.50000 + 2.59808i −0.0686803 + 0.118958i
\(478\) −4.50000 7.79423i −0.205825 0.356500i
\(479\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) 2.00000 0.0912871
\(481\) −5.00000 5.19615i −0.227980 0.236924i
\(482\) −14.0000 −0.637683
\(483\) −0.500000 0.866025i −0.0227508 0.0394055i
\(484\) −2.50000 4.33013i −0.113636 0.196824i
\(485\) −16.0000 + 27.7128i −0.726523 + 1.25837i
\(486\) −1.00000 −0.0453609
\(487\) 14.0000 24.2487i 0.634401 1.09881i −0.352241 0.935909i \(-0.614580\pi\)
0.986642 0.162905i \(-0.0520863\pi\)
\(488\) −3.50000 + 6.06218i −0.158438 + 0.274422i
\(489\) 21.0000 0.949653
\(490\) −1.00000 + 1.73205i −0.0451754 + 0.0782461i
\(491\) 4.00000 + 6.92820i 0.180517 + 0.312665i 0.942057 0.335453i \(-0.108889\pi\)
−0.761539 + 0.648119i \(0.775556\pi\)
\(492\) −1.00000 1.73205i −0.0450835 0.0780869i
\(493\) −14.0000 −0.630528
\(494\) 7.00000 1.73205i 0.314945 0.0779287i
\(495\) 8.00000 0.359573
\(496\) 4.50000 + 7.79423i 0.202056 + 0.349971i
\(497\) 0.500000 + 0.866025i 0.0224281 + 0.0388465i
\(498\) −0.500000 + 0.866025i −0.0224055 + 0.0388075i
\(499\) 7.00000 0.313363 0.156682 0.987649i \(-0.449920\pi\)
0.156682 + 0.987649i \(0.449920\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) 0 0
\(502\) −23.0000 −1.02654
\(503\) 2.00000 3.46410i 0.0891756 0.154457i −0.817987 0.575236i \(-0.804910\pi\)
0.907163 + 0.420780i \(0.138243\pi\)
\(504\) −0.500000 0.866025i −0.0222718 0.0385758i
\(505\) 0 0
\(506\) −4.00000 −0.177822
\(507\) −11.0000 6.92820i −0.488527 0.307692i
\(508\) 16.0000 0.709885
\(509\) 6.00000 + 10.3923i 0.265945 + 0.460631i 0.967811 0.251679i \(-0.0809826\pi\)
−0.701866 + 0.712309i \(0.747649\pi\)
\(510\) −7.00000 12.1244i −0.309965 0.536875i
\(511\) 6.00000 10.3923i 0.265424 0.459728i
\(512\) −1.00000 −0.0441942
\(513\) −1.00000 + 1.73205i −0.0441511 + 0.0764719i
\(514\) 13.5000 23.3827i 0.595459 1.03137i
\(515\) 22.0000 0.969436
\(516\) 2.50000 4.33013i 0.110056 0.190623i
\(517\) 12.0000 + 20.7846i 0.527759 + 0.914106i
\(518\) 1.00000 + 1.73205i 0.0439375 + 0.0761019i
\(519\) −16.0000 −0.702322
\(520\) −7.00000 + 1.73205i −0.306970 + 0.0759555i
\(521\) −42.0000 −1.84005 −0.920027 0.391856i \(-0.871833\pi\)
−0.920027 + 0.391856i \(0.871833\pi\)
\(522\) −1.00000 1.73205i −0.0437688 0.0758098i
\(523\) 12.0000 + 20.7846i 0.524723 + 0.908848i 0.999586 + 0.0287874i \(0.00916457\pi\)
−0.474862 + 0.880060i \(0.657502\pi\)
\(524\) −7.50000 + 12.9904i −0.327639 + 0.567487i
\(525\) 1.00000 0.0436436
\(526\) 2.00000 3.46410i 0.0872041 0.151042i
\(527\) 31.5000 54.5596i 1.37216 2.37665i
\(528\) −4.00000 −0.174078
\(529\) 11.0000 19.0526i 0.478261 0.828372i
\(530\) −3.00000 5.19615i −0.130312 0.225706i
\(531\) −7.50000 12.9904i −0.325472 0.563735i
\(532\) −2.00000 −0.0867110
\(533\) 5.00000 + 5.19615i 0.216574 + 0.225070i
\(534\) −3.00000 −0.129823
\(535\) −6.00000 10.3923i −0.259403 0.449299i
\(536\) −2.50000 4.33013i −0.107984 0.187033i
\(537\) −3.00000 + 5.19615i −0.129460 + 0.224231i
\(538\) −18.0000 −0.776035
\(539\) 2.00000 3.46410i 0.0861461 0.149209i
\(540\) 1.00000 1.73205i 0.0430331 0.0745356i
\(541\) 34.0000 1.46177 0.730887 0.682498i \(-0.239107\pi\)
0.730887 + 0.682498i \(0.239107\pi\)
\(542\) 4.50000 7.79423i 0.193292 0.334791i
\(543\) 1.00000 + 1.73205i 0.0429141 + 0.0743294i
\(544\) 3.50000 + 6.06218i 0.150061 + 0.259914i
\(545\) 32.0000 1.37073
\(546\) 2.50000 + 2.59808i 0.106990 + 0.111187i
\(547\) −4.00000 −0.171028 −0.0855138 0.996337i \(-0.527253\pi\)
−0.0855138 + 0.996337i \(0.527253\pi\)
\(548\) −2.00000 3.46410i −0.0854358 0.147979i
\(549\) 3.50000 + 6.06218i 0.149376 + 0.258727i
\(550\) 2.00000 3.46410i 0.0852803 0.147710i
\(551\) −4.00000 −0.170406
\(552\) −0.500000 + 0.866025i −0.0212814 + 0.0368605i
\(553\) −2.00000 + 3.46410i −0.0850487 + 0.147309i
\(554\) 8.00000 0.339887
\(555\) −2.00000 + 3.46410i −0.0848953 + 0.147043i
\(556\) −8.00000 13.8564i −0.339276 0.587643i
\(557\) −6.50000 11.2583i −0.275414 0.477031i 0.694826 0.719178i \(-0.255482\pi\)
−0.970239 + 0.242147i \(0.922148\pi\)
\(558\) 9.00000 0.381000
\(559\) −5.00000 + 17.3205i −0.211477 + 0.732579i
\(560\) 2.00000 0.0845154
\(561\) 14.0000 + 24.2487i 0.591080 + 1.02378i
\(562\) −13.0000 22.5167i −0.548372 0.949808i
\(563\) 20.0000 34.6410i 0.842900 1.45994i −0.0445334 0.999008i \(-0.514180\pi\)
0.887433 0.460937i \(-0.152487\pi\)
\(564\) 6.00000 0.252646
\(565\) −8.00000 + 13.8564i −0.336563 + 0.582943i
\(566\) 7.00000 12.1244i 0.294232 0.509625i
\(567\) −1.00000 −0.0419961
\(568\) 0.500000 0.866025i 0.0209795 0.0363376i
\(569\) −13.0000 22.5167i −0.544988 0.943948i −0.998608 0.0527519i \(-0.983201\pi\)
0.453619 0.891196i \(-0.350133\pi\)
\(570\) −2.00000 3.46410i −0.0837708 0.145095i
\(571\) 23.0000 0.962520 0.481260 0.876578i \(-0.340179\pi\)
0.481260 + 0.876578i \(0.340179\pi\)
\(572\) 14.0000 3.46410i 0.585369 0.144841i
\(573\) 3.00000 0.125327
\(574\) −1.00000 1.73205i −0.0417392 0.0722944i
\(575\) −0.500000 0.866025i −0.0208514 0.0361158i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) 6.00000 0.249783 0.124892 0.992170i \(-0.460142\pi\)
0.124892 + 0.992170i \(0.460142\pi\)
\(578\) 16.0000 27.7128i 0.665512 1.15270i
\(579\) 11.0000 19.0526i 0.457144 0.791797i
\(580\) 4.00000 0.166091
\(581\) −0.500000 + 0.866025i −0.0207435 + 0.0359288i
\(582\) −8.00000 13.8564i −0.331611 0.574367i
\(583\) 6.00000 + 10.3923i 0.248495 + 0.430405i
\(584\) −12.0000 −0.496564
\(585\) −2.00000 + 6.92820i −0.0826898 + 0.286446i
\(586\) 16.0000 0.660954
\(587\) −22.5000 38.9711i −0.928674 1.60851i −0.785543 0.618808i \(-0.787616\pi\)
−0.143132 0.989704i \(-0.545717\pi\)
\(588\) −0.500000 0.866025i −0.0206197 0.0357143i
\(589\) 9.00000 15.5885i 0.370839 0.642311i
\(590\) 30.0000 1.23508
\(591\) 4.50000 7.79423i 0.185105 0.320612i
\(592\) 1.00000 1.73205i 0.0410997 0.0711868i
\(593\) 29.0000 1.19089 0.595444 0.803397i \(-0.296976\pi\)
0.595444 + 0.803397i \(0.296976\pi\)
\(594\) −2.00000 + 3.46410i −0.0820610 + 0.142134i
\(595\) −7.00000 12.1244i −0.286972 0.497050i
\(596\) −10.5000 18.1865i −0.430097 0.744949i
\(597\) −5.00000 −0.204636
\(598\) 1.00000 3.46410i 0.0408930 0.141658i
\(599\) 9.00000 0.367730 0.183865 0.982952i \(-0.441139\pi\)
0.183865 + 0.982952i \(0.441139\pi\)
\(600\) −0.500000 0.866025i −0.0204124 0.0353553i
\(601\) −19.0000 32.9090i −0.775026 1.34238i −0.934780 0.355228i \(-0.884403\pi\)
0.159754 0.987157i \(-0.448930\pi\)
\(602\) 2.50000 4.33013i 0.101892 0.176483i
\(603\) −5.00000 −0.203616
\(604\) −10.0000 + 17.3205i −0.406894 + 0.704761i
\(605\) 5.00000 8.66025i 0.203279 0.352089i
\(606\) 0 0
\(607\) −23.5000 + 40.7032i −0.953836 + 1.65209i −0.216825 + 0.976210i \(0.569570\pi\)
−0.737011 + 0.675881i \(0.763763\pi\)
\(608\) 1.00000 + 1.73205i 0.0405554 + 0.0702439i
\(609\) −1.00000 1.73205i −0.0405220 0.0701862i
\(610\) −14.0000 −0.566843
\(611\) −21.0000 + 5.19615i −0.849569 + 0.210214i
\(612\) 7.00000 0.282958
\(613\) −7.00000 12.1244i −0.282727 0.489698i 0.689328 0.724449i \(-0.257906\pi\)
−0.972056 + 0.234751i \(0.924572\pi\)
\(614\) 15.0000 + 25.9808i 0.605351 + 1.04850i
\(615\) 2.00000 3.46410i 0.0806478 0.139686i
\(616\) −4.00000 −0.161165
\(617\) 10.0000 17.3205i 0.402585 0.697297i −0.591452 0.806340i \(-0.701445\pi\)
0.994037 + 0.109043i \(0.0347785\pi\)
\(618\) −5.50000 + 9.52628i −0.221242 + 0.383203i
\(619\) −22.0000 −0.884255 −0.442127 0.896952i \(-0.645776\pi\)
−0.442127 + 0.896952i \(0.645776\pi\)
\(620\) −9.00000 + 15.5885i −0.361449 + 0.626048i
\(621\) 0.500000 + 0.866025i 0.0200643 + 0.0347524i
\(622\) 15.0000 + 25.9808i 0.601445 + 1.04173i
\(623\) −3.00000 −0.120192
\(624\) 1.00000 3.46410i 0.0400320 0.138675i
\(625\) −19.0000 −0.760000
\(626\) 0 0
\(627\) 4.00000 + 6.92820i 0.159745 + 0.276686i
\(628\) −5.00000 + 8.66025i −0.199522 + 0.345582i
\(629\) −14.0000 −0.558217
\(630\) 1.00000 1.73205i 0.0398410 0.0690066i
\(631\) 10.0000 17.3205i 0.398094 0.689519i −0.595397 0.803432i \(-0.703005\pi\)
0.993491 + 0.113913i \(0.0363385\pi\)
\(632\) 4.00000 0.159111
\(633\) −2.00000 + 3.46410i −0.0794929 + 0.137686i
\(634\) 11.5000 + 19.9186i 0.456723 + 0.791068i
\(635\) 16.0000 + 27.7128i 0.634941 + 1.09975i
\(636\) 3.00000 0.118958
\(637\) 2.50000 + 2.59808i 0.0990536 + 0.102940i
\(638\) −8.00000 −0.316723
\(639\) −0.500000 0.866025i −0.0197797 0.0342594i
\(640\) −1.00000 1.73205i −0.0395285 0.0684653i
\(641\) −16.0000 + 27.7128i −0.631962 + 1.09459i 0.355188 + 0.934795i \(0.384417\pi\)
−0.987150 + 0.159795i \(0.948917\pi\)
\(642\) 6.00000 0.236801
\(643\) −7.00000 + 12.1244i −0.276053 + 0.478138i −0.970400 0.241502i \(-0.922360\pi\)
0.694347 + 0.719640i \(0.255693\pi\)
\(644\) −0.500000 + 0.866025i −0.0197028 + 0.0341262i
\(645\) 10.0000 0.393750
\(646\) 7.00000 12.1244i 0.275411 0.477026i
\(647\) 3.00000 + 5.19615i 0.117942 + 0.204282i 0.918952 0.394369i \(-0.129037\pi\)
−0.801010 + 0.598651i \(0.795704\pi\)
\(648\) 0.500000 + 0.866025i 0.0196419 + 0.0340207i
\(649\) −60.0000 −2.35521
\(650\) 2.50000 + 2.59808i 0.0980581 + 0.101905i
\(651\) 9.00000 0.352738
\(652\) −10.5000 18.1865i −0.411212 0.712240i
\(653\) −13.5000 23.3827i −0.528296 0.915035i −0.999456 0.0329874i \(-0.989498\pi\)
0.471160 0.882048i \(-0.343835\pi\)
\(654\) −8.00000 + 13.8564i −0.312825 + 0.541828i
\(655\) −30.0000 −1.17220
\(656\) −1.00000 + 1.73205i −0.0390434 + 0.0676252i
\(657\) −6.00000 + 10.3923i −0.234082 + 0.405442i
\(658\) 6.00000 0.233904
\(659\) 3.00000 5.19615i 0.116863 0.202413i −0.801660 0.597781i \(-0.796049\pi\)
0.918523 + 0.395367i \(0.129383\pi\)
\(660\) −4.00000 6.92820i −0.155700 0.269680i
\(661\) 17.5000 + 30.3109i 0.680671 + 1.17896i 0.974776 + 0.223184i \(0.0716450\pi\)
−0.294105 + 0.955773i \(0.595022\pi\)
\(662\) −36.0000 −1.39918
\(663\) −24.5000 + 6.06218i −0.951501 + 0.235435i
\(664\) 1.00000 0.0388075
\(665\) −2.00000 3.46410i −0.0775567 0.134332i
\(666\) −1.00000 1.73205i −0.0387492 0.0671156i
\(667\) −1.00000 + 1.73205i −0.0387202 + 0.0670653i
\(668\) 0 0
\(669\) −1.50000 + 2.59808i −0.0579934 + 0.100447i
\(670\) 5.00000 8.66025i 0.193167 0.334575i
\(671\) 28.0000 1.08093
\(672\) −0.500000 + 0.866025i −0.0192879 + 0.0334077i
\(673\) 16.5000 + 28.5788i 0.636028 + 1.10163i 0.986296 + 0.164984i \(0.0527572\pi\)
−0.350268 + 0.936650i \(0.613909\pi\)
\(674\) 9.00000 + 15.5885i 0.346667 + 0.600445i
\(675\) −1.00000 −0.0384900
\(676\) −0.500000 + 12.9904i −0.0192308 + 0.499630i
\(677\) 28.0000 1.07613 0.538064 0.842904i \(-0.319156\pi\)
0.538064 + 0.842904i \(0.319156\pi\)
\(678\) −4.00000 6.92820i −0.153619 0.266076i
\(679\) −8.00000 13.8564i −0.307012 0.531760i
\(680\) −7.00000 + 12.1244i −0.268438 + 0.464948i
\(681\) 28.0000 1.07296
\(682\) 18.0000 31.1769i 0.689256 1.19383i
\(683\) −11.0000 + 19.0526i −0.420903 + 0.729026i −0.996028 0.0890398i \(-0.971620\pi\)
0.575125 + 0.818066i \(0.304953\pi\)
\(684\) 2.00000 0.0764719
\(685\) 4.00000 6.92820i 0.152832 0.264713i
\(686\) −0.500000 0.866025i −0.0190901 0.0330650i
\(687\) −6.50000 11.2583i −0.247990 0.429532i
\(688\) −5.00000 −0.190623
\(689\) −10.5000 + 2.59808i −0.400018 + 0.0989788i
\(690\) −2.00000 −0.0761387
\(691\) 22.0000 + 38.1051i 0.836919 + 1.44959i 0.892458 + 0.451130i \(0.148979\pi\)
−0.0555386 + 0.998457i \(0.517688\pi\)
\(692\) 8.00000 + 13.8564i 0.304114 + 0.526742i
\(693\) −2.00000 + 3.46410i −0.0759737 + 0.131590i
\(694\) −10.0000 −0.379595
\(695\) 16.0000 27.7128i 0.606915 1.05121i
\(696\) −1.00000 + 1.73205i −0.0379049 + 0.0656532i
\(697\) 14.0000 0.530288
\(698\) −12.5000 + 21.6506i −0.473132 + 0.819489i
\(699\) 8.00000 + 13.8564i 0.302588 + 0.524097i
\(700\) −0.500000 0.866025i −0.0188982 0.0327327i
\(701\) −15.0000 −0.566542 −0.283271 0.959040i \(-0.591420\pi\)
−0.283271 + 0.959040i \(0.591420\pi\)
\(702\) −2.50000 2.59808i −0.0943564 0.0980581i
\(703\) −4.00000 −0.150863
\(704\) 2.00000 + 3.46410i 0.0753778 + 0.130558i
\(705\) 6.00000 + 10.3923i 0.225973 + 0.391397i
\(706\) −17.5000 + 30.3109i −0.658621 + 1.14077i
\(707\) 0 0
\(708\) −7.50000 + 12.9904i −0.281867 + 0.488208i
\(709\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(710\) 2.00000 0.0750587
\(711\) 2.00000 3.46410i 0.0750059 0.129914i
\(712\) 1.50000 + 2.59808i 0.0562149 + 0.0973670i
\(713\) −4.50000 7.79423i −0.168526 0.291896i
\(714\) 7.00000 0.261968
\(715\) 20.0000 + 20.7846i 0.747958 + 0.777300i
\(716\) 6.00000 0.224231
\(717\) 4.50000 + 7.79423i 0.168056 + 0.291081i
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) −10.0000 + 17.3205i −0.372937 + 0.645946i −0.990016 0.140955i \(-0.954983\pi\)
0.617079 + 0.786901i \(0.288316\pi\)
\(720\) −2.00000 −0.0745356
\(721\) −5.50000 + 9.52628i −0.204831 + 0.354777i
\(722\) −7.50000 + 12.9904i −0.279121 + 0.483452i
\(723\) 14.0000 0.520666
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) −1.00000 1.73205i −0.0371391 0.0643268i
\(726\) 2.50000 + 4.33013i 0.0927837 + 0.160706i
\(727\) −21.0000 −0.778847 −0.389423 0.921059i \(-0.627326\pi\)
−0.389423 + 0.921059i \(0.627326\pi\)
\(728\) 1.00000 3.46410i 0.0370625 0.128388i
\(729\) 1.00000 0.0370370
\(730\) −12.0000 20.7846i −0.444140 0.769273i
\(731\) 17.5000 + 30.3109i 0.647261 + 1.12109i
\(732\) 3.50000 6.06218i 0.129364 0.224065i
\(733\) −21.0000 −0.775653 −0.387826 0.921732i \(-0.626774\pi\)
−0.387826 + 0.921732i \(0.626774\pi\)
\(734\) −1.50000 + 2.59808i −0.0553660 + 0.0958967i
\(735\) 1.00000 1.73205i 0.0368856 0.0638877i
\(736\) 1.00000 0.0368605
\(737\) −10.0000 + 17.3205i −0.368355 + 0.638009i
\(738\) 1.00000 + 1.73205i 0.0368105 + 0.0637577i
\(739\) −24.5000 42.4352i −0.901247 1.56101i −0.825877 0.563850i \(-0.809320\pi\)
−0.0753699 0.997156i \(-0.524014\pi\)
\(740\) 4.00000 0.147043
\(741\) −7.00000 + 1.73205i −0.257151 + 0.0636285i
\(742\) 3.00000 0.110133
\(743\) 20.5000 + 35.5070i 0.752072 + 1.30263i 0.946817 + 0.321773i \(0.104279\pi\)
−0.194745 + 0.980854i \(0.562388\pi\)
\(744\) −4.50000 7.79423i −0.164978 0.285750i
\(745\) 21.0000 36.3731i 0.769380 1.33261i
\(746\) −4.00000 −0.146450
\(747\) 0.500000 0.866025i 0.0182940 0.0316862i
\(748\) 14.0000 24.2487i 0.511891 0.886621i
\(749\) 6.00000 0.219235
\(750\) 6.00000 10.3923i 0.219089 0.379473i
\(751\) 13.0000 + 22.5167i 0.474377 + 0.821645i 0.999570 0.0293387i \(-0.00934013\pi\)
−0.525193 + 0.850983i \(0.676007\pi\)
\(752\) −3.00000 5.19615i −0.109399 0.189484i
\(753\) 23.0000 0.838167
\(754\) 2.00000 6.92820i 0.0728357 0.252310i
\(755\) −40.0000 −1.45575
\(756\) 0.500000 + 0.866025i 0.0181848 + 0.0314970i
\(757\) −23.0000 39.8372i −0.835949 1.44791i −0.893255 0.449550i \(-0.851584\pi\)
0.0573060 0.998357i \(-0.481749\pi\)
\(758\) −10.0000 + 17.3205i −0.363216 + 0.629109i
\(759\) 4.00000 0.145191
\(760\) −2.00000 + 3.46410i −0.0725476 + 0.125656i
\(761\) −5.00000 + 8.66025i −0.181250 + 0.313934i −0.942306 0.334752i \(-0.891348\pi\)
0.761057 + 0.648686i \(0.224681\pi\)
\(762\) −16.0000 −0.579619
\(763\) −8.00000 + 13.8564i −0.289619 + 0.501636i
\(764\) −1.50000 2.59808i −0.0542681 0.0939951i
\(765\) 7.00000 + 12.1244i 0.253086 + 0.438357i
\(766\) −24.0000 −0.867155
\(767\) 15.0000 51.9615i 0.541619 1.87622i
\(768\) 1.00000 0.0360844
\(769\) −2.00000 3.46410i −0.0721218 0.124919i 0.827709 0.561157i \(-0.189644\pi\)
−0.899831 + 0.436239i \(0.856310\pi\)
\(770\) −4.00000 6.92820i −0.144150 0.249675i
\(771\) −13.5000 + 23.3827i −0.486191 + 0.842107i
\(772\) −22.0000 −0.791797
\(773\) 5.00000 8.66025i 0.179838 0.311488i −0.761987 0.647592i \(-0.775776\pi\)
0.941825 + 0.336104i \(0.109109\pi\)
\(774\) −2.50000 + 4.33013i −0.0898606 + 0.155643i
\(775\) 9.00000 0.323290
\(776\) −8.00000 + 13.8564i −0.287183 + 0.497416i
\(777\) −1.00000 1.73205i −0.0358748