Properties

Label 546.2.l.k.211.2
Level $546$
Weight $2$
Character 546.211
Analytic conductor $4.360$
Analytic rank $0$
Dimension $4$
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: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{-43})\)
Defining polynomial: \(x^{4} - x^{3} - 10 x^{2} - 11 x + 121\)
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 211.2
Root \(3.08945 + 1.20635i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.k.295.2

$q$-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} +(2.58945 + 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})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 8q^{5} + 2q^{6} + 2q^{7} + 4q^{8} - 2q^{9} + O(q^{10}) \) \( 4q - 2q^{2} + 2q^{3} - 2q^{4} - 8q^{5} + 2q^{6} + 2q^{7} + 4q^{8} - 2q^{9} + 4q^{10} - q^{11} - 4q^{12} - 6q^{13} - 4q^{14} - 4q^{15} - 2q^{16} - 10q^{17} + 4q^{18} + 5q^{19} + 4q^{20} + 4q^{21} - q^{22} + 5q^{23} + 2q^{24} - 4q^{25} + 3q^{26} - 4q^{27} + 2q^{28} - 5q^{29} - 4q^{30} - 6q^{31} - 2q^{32} + q^{33} + 20q^{34} - 4q^{35} - 2q^{36} - 4q^{37} - 10q^{38} - 3q^{39} - 8q^{40} + 3q^{41} - 2q^{42} - 13q^{43} + 2q^{44} + 4q^{45} + 5q^{46} - 6q^{47} + 2q^{48} - 2q^{49} + 2q^{50} - 20q^{51} + 3q^{52} - 12q^{53} + 2q^{54} + 2q^{55} + 2q^{56} + 10q^{57} - 5q^{58} + 13q^{59} + 8q^{60} + 6q^{61} + 3q^{62} + 2q^{63} + 4q^{64} + 12q^{65} - 2q^{66} + 19q^{67} - 10q^{68} - 5q^{69} + 8q^{70} - 7q^{71} - 2q^{72} + 16q^{73} - 4q^{74} - 2q^{75} + 5q^{76} - 2q^{77} - 3q^{78} + 30q^{79} + 4q^{80} - 2q^{81} + 3q^{82} + 2q^{83} - 2q^{84} + 20q^{85} + 26q^{86} + 5q^{87} - q^{88} - 18q^{89} - 8q^{90} - 3q^{91} - 10q^{92} - 3q^{93} + 3q^{94} - 10q^{95} - 4q^{96} - 2q^{97} - 2q^{98} + 2q^{99} + O(q^{100}) \)

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
\(11\) 2.58945 + 4.48507i 0.780750 + 1.35230i 0.931505 + 0.363727i \(0.118496\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) −1.00000 −0.288675
\(13\) −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 0.385499 + 0.922708i \(0.374029\pi\)
−0.991838 + 0.127502i \(0.959304\pi\)
\(18\) 1.00000 0.235702
\(19\) −1.58945 + 2.75302i −0.364646 + 0.631585i −0.988719 0.149781i \(-0.952143\pi\)
0.624073 + 0.781366i \(0.285477\pi\)
\(20\) 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 0.878753 + 0.477276i \(0.158376\pi\)
−0.0260431 + 0.999661i \(0.508291\pi\)
\(24\) 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 0.975021 0.222114i \(-0.0712956\pi\)
−0.679867 + 0.733336i \(0.737962\pi\)
\(30\) −1.00000 + 1.73205i −0.182574 + 0.316228i
\(31\) 4.17891 0.750554 0.375277 0.926913i \(-0.377548\pi\)
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 0.772043 0.635571i \(-0.219235\pi\)
−0.936442 + 0.350823i \(0.885902\pi\)
\(38\) 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 0.997446 + 0.0714247i \(0.0227545\pi\)
−0.436867 + 0.899526i \(0.643912\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) −6.08945 + 10.5472i −0.928633 + 1.60844i −0.143022 + 0.989720i \(0.545682\pi\)
−0.785612 + 0.618720i \(0.787652\pi\)
\(44\) −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 \(-0.675402\pi\)
−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 \(-0.566058\pi\)
−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 −0.131460 0.991321i \(-0.541967\pi\)
0.924240 0.381813i \(-0.124700\pi\)
\(60\) 2.00000 0.258199
\(61\) 1.50000 2.59808i 0.192055 0.332650i −0.753876 0.657017i \(-0.771818\pi\)
0.945931 + 0.324367i \(0.105151\pi\)
\(62\) −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 0.958809 0.284050i \(-0.0916781\pi\)
−0.725399 + 0.688328i \(0.758345\pi\)
\(68\) −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 −0.794109 0.607775i \(-0.792062\pi\)
0.923403 + 0.383831i \(0.125395\pi\)
\(72\) −0.500000 + 0.866025i −0.0589256 + 0.102062i
\(73\) 4.00000 0.468165 0.234082 0.972217i \(-0.424791\pi\)
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 \(-0.234176\pi\)
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 \(-0.389874\pi\)
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 0.522654 0.852545i \(-0.324942\pi\)
−0.999653 + 0.0263586i \(0.991609\pi\)
\(90\) −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 −0.473709 0.880682i \(-0.657085\pi\)
0.999547 0.0300973i \(-0.00958170\pi\)
\(98\) −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 0.663403 0.748263i \(-0.269112\pi\)
−0.979716 + 0.200392i \(0.935778\pi\)
\(102\) 2.50000 + 4.33013i 0.247537 + 0.428746i
\(103\) −8.17891 −0.805892 −0.402946 0.915224i \(-0.632014\pi\)
−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 −0.788235 0.615375i \(-0.789005\pi\)
−0.138813 0.990319i \(-0.544329\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
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 0.00507042 + 0.999987i \(0.498386\pi\)
−0.868549 + 0.495602i \(0.834947\pi\)
\(114\) 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 −0.999284 0.0378419i \(-0.987952\pi\)
0.466870 0.884326i \(-0.345382\pi\)
\(128\) −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 \(-0.719016\pi\)
−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 −0.969270 0.246000i \(-0.920884\pi\)
0.697677 + 0.716412i \(0.254217\pi\)
\(138\) 8.17891 0.696235
\(139\) 3.41055 5.90724i 0.289279 0.501045i −0.684359 0.729145i \(-0.739918\pi\)
0.973638 + 0.228100i \(0.0732512\pi\)
\(140\) −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 0.317186 + 0.948363i \(0.397262\pi\)
−0.979900 + 0.199491i \(0.936071\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) 19.5367 1.58988 0.794938 0.606691i \(-0.207503\pi\)
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 \(-0.474569\pi\)
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 −0.135534 0.990773i \(-0.543275\pi\)
0.925801 0.378010i \(-0.123392\pi\)
\(164\) −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 0.978259 0.207385i \(-0.0664952\pi\)
−0.668730 + 0.743505i \(0.733162\pi\)
\(168\) 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 −0.931984 0.362500i \(-0.881923\pi\)
0.779926 + 0.625871i \(0.215256\pi\)
\(174\) 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 0.666524 0.745484i \(-0.267782\pi\)
−0.978870 + 0.204484i \(0.934448\pi\)
\(180\) 1.00000 + 1.73205i 0.0745356 + 0.129099i
\(181\) 19.1789 1.42556 0.712779 0.701389i \(-0.247436\pi\)
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 −0.723214 0.690624i \(-0.757336\pi\)
0.959705 + 0.281010i \(0.0906695\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) 6.76836 + 11.7231i 0.487197 + 0.843851i 0.999892 0.0147206i \(-0.00468589\pi\)
−0.512694 + 0.858571i \(0.671353\pi\)
\(194\) −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 −0.991956 0.126580i \(-0.959600\pi\)
0.386356 0.922350i \(-0.373733\pi\)
\(198\) 2.58945 + 4.48507i 0.184024 + 0.318740i
\(199\) −12.0895 + 20.9395i −0.856999 + 1.48437i 0.0177797 + 0.999842i \(0.494340\pi\)
−0.874778 + 0.484523i \(0.838993\pi\)
\(200\) −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 0.954455 0.298354i \(-0.0964377\pi\)
−0.735610 + 0.677405i \(0.763104\pi\)
\(212\) 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 0.900195 0.435487i \(-0.143424\pi\)
−0.827240 + 0.561849i \(0.810090\pi\)
\(224\) 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 −0.523156 0.852237i \(-0.675245\pi\)
0.999637 + 0.0269479i \(0.00857881\pi\)
\(228\) 1.58945 2.75302i 0.105264 0.182323i
\(229\) 1.00000 0.0660819 0.0330409 0.999454i \(-0.489481\pi\)
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 \(-0.238421\pi\)
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 \(-0.393218\pi\)
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 −0.927631 0.373499i \(-0.878158\pi\)
0.787275 + 0.616602i \(0.211491\pi\)
\(242\) 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 0.268520 + 0.963274i \(0.413466\pi\)
−0.968480 + 0.249092i \(0.919868\pi\)
\(252\) −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 0.990400 + 0.138234i \(0.0441425\pi\)
−0.375486 + 0.926828i \(0.622524\pi\)
\(258\) 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 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) −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 −0.791924 0.610620i \(-0.790920\pi\)
0.924774 + 0.380516i \(0.124254\pi\)
\(270\) −1.00000 1.73205i −0.0608581 0.105409i
\(271\) −9.91055 17.1656i −0.602023 1.04273i −0.992514 0.122128i \(-0.961028\pi\)
0.390492 0.920606i \(-0.372305\pi\)
\(272\) 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 −0.938245 0.345971i \(-0.887550\pi\)
0.768742 + 0.639559i \(0.220883\pi\)
\(278\) −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 \(-0.179098\pi\)
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 0.729819 0.683640i \(-0.239604\pi\)
−0.956959 + 0.290222i \(0.906271\pi\)
\(284\) 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 −0.986341 0.164714i \(-0.947330\pi\)
0.635818 + 0.771839i \(0.280663\pi\)
\(294\) −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 \(-0.864041\pi\)
−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 \(-0.242289\pi\)
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 \(-0.463939\pi\)
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 \(-0.537442\pi\)
−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 −0.842577 0.538575i \(-0.818963\pi\)
0.887709 + 0.460406i \(0.152296\pi\)
\(332\) −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 \(-0.133423\pi\)
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 −0.485064 0.874479i \(-0.661204\pi\)
0.999853 0.0171617i \(-0.00546302\pi\)
\(348\) −1.58945 2.75302i −0.0852037 0.147577i
\(349\) −4.08945 7.08314i −0.218903 0.379152i 0.735570 0.677449i \(-0.236915\pi\)
−0.954473 + 0.298297i \(0.903581\pi\)
\(350\) 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 0.805048 0.593209i \(-0.202139\pi\)
−0.916259 + 0.400587i \(0.868806\pi\)
\(354\) −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 \(-0.588126\pi\)
−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 0.952797 0.303607i \(-0.0981908\pi\)
−0.739330 + 0.673344i \(0.764857\pi\)
\(368\) 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 −0.482006 0.876168i \(-0.660092\pi\)
0.999787 0.0206542i \(-0.00657489\pi\)
\(374\) 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 0.986562 + 0.163387i \(0.0522420\pi\)
−0.351784 + 0.936081i \(0.614425\pi\)
\(380\) 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 0.457746 + 0.889083i \(0.348657\pi\)
−0.998841 + 0.0481223i \(0.984676\pi\)
\(384\) 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 \(-0.599910\pi\)
−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 −0.901209 0.433384i \(-0.857319\pi\)
0.825926 + 0.563778i \(0.190653\pi\)
\(398\) 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 0.720175 0.693792i \(-0.244061\pi\)
−0.960929 + 0.276794i \(0.910728\pi\)
\(402\) 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 0.0699730 0.997549i \(-0.477709\pi\)
0.828916 0.559373i \(-0.188958\pi\)
\(410\) −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 0.981403 + 0.191958i \(0.0614838\pi\)
−0.324461 + 0.945899i \(0.605183\pi\)
\(420\) 1.00000 1.73205i 0.0487950 0.0845154i
\(421\) 10.7156 0.522248 0.261124 0.965305i \(-0.415907\pi\)
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 0.717024 0.697049i \(-0.245504\pi\)
−0.962174 + 0.272436i \(0.912171\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −17.1789 + 29.7547i −0.825566 + 1.42992i 0.0759206 + 0.997114i \(0.475810\pi\)
−0.901486 + 0.432808i \(0.857523\pi\)
\(434\) −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 −0.690649 0.723190i \(-0.742675\pi\)
−0.280977 0.959715i \(-0.590658\pi\)
\(440\) −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 \(-0.475939\pi\)
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 −0.652230 0.758021i \(-0.726166\pi\)
0.982581 + 0.185837i \(0.0594997\pi\)
\(450\) −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 −0.995211 0.0977491i \(-0.968836\pi\)
0.412952 0.910753i \(-0.364498\pi\)
\(458\) −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 −0.999796 0.0201916i \(-0.993572\pi\)
0.517385 + 0.855753i \(0.326906\pi\)
\(462\) 2.58945 4.48507i 0.120472 0.208664i
\(463\) 27.8945 1.29637 0.648185 0.761483i \(-0.275528\pi\)
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 \(-0.677702\pi\)
−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 0.764033 + 0.645177i \(0.223216\pi\)
0.176723 + 0.984261i \(0.443450\pi\)
\(480\) 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 −0.383930 0.923362i \(-0.625430\pi\)
0.991620 0.129188i \(-0.0412369\pi\)
\(488\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) −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 \(-0.441397\pi\)
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 −0.464107 0.885779i \(-0.653625\pi\)
0.999161 0.0409609i \(-0.0130419\pi\)
\(504\) 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 0.989635 0.143603i \(-0.0458689\pi\)
−0.619182 + 0.785248i \(0.712536\pi\)
\(510\) −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 \(-0.449735\pi\)
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 0.711907 0.702273i \(-0.247832\pi\)
−0.964140 + 0.265393i \(0.914498\pi\)
\(524\) 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 \(-0.644180\pi\)
−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 \(-0.220443\pi\)
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 −0.999996 0.00281030i \(-0.999105\pi\)
0.497564 0.867427i \(-0.334228\pi\)
\(558\) 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 −0.605178 0.796090i \(-0.706898\pi\)
0.992023 + 0.126055i \(0.0402316\pi\)
\(564\) 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 0.901670 0.432425i \(-0.142342\pi\)
−0.825326 + 0.564657i \(0.809009\pi\)
\(570\) −3.17891 5.50603i −0.133150 0.230622i
\(571\) −34.1789 −1.43034 −0.715171 0.698949i \(-0.753651\pi\)
−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 \(-0.700981\pi\)
−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 0.864173 0.503194i \(-0.167842\pi\)
−0.867866 + 0.496799i \(0.834509\pi\)
\(588\) 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 \(-0.736969\pi\)
−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 \(-0.193510\pi\)
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 0.998302 0.0582563i \(-0.0185541\pi\)
−0.549602 + 0.835426i \(0.685221\pi\)
\(602\) 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 −0.860528 0.509404i \(-0.829866\pi\)
0.871420 + 0.490537i \(0.163199\pi\)
\(608\) −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 0.663736 0.747967i \(-0.268970\pi\)
−0.979626 + 0.200828i \(0.935637\pi\)
\(614\) 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 0.340365 + 0.940294i \(0.389449\pi\)
−0.984500 + 0.175382i \(0.943884\pi\)
\(618\) −4.08945 + 7.08314i −0.164502 + 0.284926i
\(619\) 25.5367 1.02641 0.513204 0.858267i \(-0.328458\pi\)
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 0.484417 + 0.874837i \(0.339032\pi\)
−0.999840 + 0.0179011i \(0.994302\pi\)
\(632\) 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 0.464511 + 0.885567i \(0.346230\pi\)
−0.999179 + 0.0405056i \(0.987103\pi\)
\(642\) −19.1789 −0.756931
\(643\) 4.41055 7.63929i 0.173935 0.301264i −0.765857 0.643011i \(-0.777685\pi\)
0.939792 + 0.341746i \(0.111018\pi\)
\(644\) −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 −0.762680 0.646776i \(-0.776117\pi\)
−0.178784 0.983888i \(-0.557216\pi\)
\(648\) −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 0.584091 0.811688i \(-0.301451\pi\)
−0.994988 + 0.0999939i \(0.968118\pi\)
\(654\) 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 −0.984724 0.174123i \(-0.944291\pi\)
0.643157 + 0.765734i \(0.277624\pi\)
\(660\) 5.17891 + 8.97013i 0.201589 + 0.349162i
\(661\) −8.26836 14.3212i −0.321602 0.557031i 0.659217 0.751953i \(-0.270888\pi\)
−0.980819 + 0.194922i \(0.937555\pi\)
\(662\) −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 0.875501 0.483216i \(-0.160531\pi\)
−0.856228 + 0.516599i \(0.827198\pi\)
\(674\) −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 \(-0.425932\pi\)
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 −0.934833 0.355088i \(-0.884451\pi\)
0.774931 + 0.632045i \(0.217784\pi\)
\(684\) 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 0.942420 + 0.334431i \(0.108544\pi\)
−0.181584 + 0.983375i \(0.558123\pi\)
\(692\) −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 \(-0.634504\pi\)
−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 −0.675791 0.737093i \(-0.736198\pi\)
0.976237 + 0.216705i \(0.0695310\pi\)
\(710\) 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 −0.277491 0.960728i \(-0.589503\pi\)
0.970761 0.240050i \(-0.0771638\pi\)
\(720\) −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 \(-0.278749\pi\)
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 \(-0.381374\pi\)
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 0.975581 0.219641i \(-0.0704887\pi\)
−0.678005 + 0.735057i \(0.737155\pi\)
\(740\) −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 −0.995036 0.0995159i \(-0.968271\pi\)
0.411335 0.911484i \(-0.365063\pi\)
\(744\) 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 0.981918 + 0.189309i \(0.0606248\pi\)
−0.327012 + 0.945020i \(0.606042\pi\)
\(752\) 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 0.989559 0.144130i \(-0.0460385\pi\)
−0.619600 + 0.784918i \(0.712705\pi\)
\(758\) 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 −0.140490 0.990082i \(-0.544868\pi\)
0.927681 0.373373i \(-0.121799\pi\)
\(762\) −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 0.651708 0.758470i \(-0.274053\pi\)
−0.982708 + 0.185161i \(0.940719\pi\)
\(770\) 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 −0.967470 0.252986i \(-0.918587\pi\)
0.702828 + 0.711360i \(0.251921\pi\)
\(774\) −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 <