Properties

Label 546.2.l.k.211.1
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 211.1
Root \(-2.58945 - 2.07237i\) of defining polynomial
Character \(\chi\) \(=\) 546.211
Dual form 546.2.l.k.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} +(-3.08945 - 5.35109i) 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} +(4.08945 - 7.08314i) q^{19} +(1.00000 - 1.73205i) q^{20} +1.00000 q^{21} +(-3.08945 + 5.35109i) q^{22} +(-1.58945 - 2.75302i) q^{23} +(0.500000 + 0.866025i) q^{24} -1.00000 q^{25} +(3.58945 - 0.340322i) q^{26} -1.00000 q^{27} +(0.500000 + 0.866025i) q^{28} +(-4.08945 - 7.08314i) q^{29} +(-1.00000 + 1.73205i) q^{30} -7.17891 q^{31} +(-0.500000 + 0.866025i) q^{32} +(3.08945 - 5.35109i) q^{33} +5.00000 q^{34} +(-1.00000 + 1.73205i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-1.00000 - 1.73205i) q^{37} -8.17891 q^{38} +(-3.58945 + 0.340322i) q^{39} -2.00000 q^{40} +(-2.08945 - 3.61904i) q^{41} +(-0.500000 - 0.866025i) q^{42} +(-0.410546 + 0.711086i) q^{43} +6.17891 q^{44} +(1.00000 - 1.73205i) q^{45} +(-1.58945 + 2.75302i) q^{46} +4.17891 q^{47} +(0.500000 - 0.866025i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(0.500000 + 0.866025i) q^{50} -5.00000 q^{51} +(-2.08945 - 2.93840i) q^{52} -3.00000 q^{53} +(0.500000 + 0.866025i) q^{54} +(6.17891 + 10.7022i) q^{55} +(0.500000 - 0.866025i) q^{56} +8.17891 q^{57} +(-4.08945 + 7.08314i) q^{58} +(0.410546 - 0.711086i) q^{59} +2.00000 q^{60} +(1.50000 - 2.59808i) q^{61} +(3.58945 + 6.21712i) q^{62} +(0.500000 + 0.866025i) q^{63} +1.00000 q^{64} +(3.00000 - 6.55744i) q^{65} -6.17891 q^{66} +(7.58945 + 13.1453i) q^{67} +(-2.50000 - 4.33013i) q^{68} +(1.58945 - 2.75302i) q^{69} +2.00000 q^{70} +(-4.58945 + 7.94917i) q^{71} +(-0.500000 + 0.866025i) q^{72} +4.00000 q^{73} +(-1.00000 + 1.73205i) q^{74} +(-0.500000 - 0.866025i) q^{75} +(4.08945 + 7.08314i) q^{76} -6.17891 q^{77} +(2.08945 + 2.93840i) q^{78} +1.82109 q^{79} +(1.00000 + 1.73205i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.08945 + 3.61904i) q^{82} -5.17891 q^{83} +(-0.500000 + 0.866025i) q^{84} +(5.00000 - 8.66025i) q^{85} +0.821092 q^{86} +(4.08945 - 7.08314i) q^{87} +(-3.08945 - 5.35109i) q^{88} +(-4.50000 - 7.79423i) q^{89} -2.00000 q^{90} +(2.08945 + 2.93840i) q^{91} +3.17891 q^{92} +(-3.58945 - 6.21712i) q^{93} +(-2.08945 - 3.61904i) q^{94} +(-8.17891 + 14.1663i) q^{95} -1.00000 q^{96} +(-6.17891 + 10.7022i) q^{97} +(-0.500000 + 0.866025i) q^{98} +6.17891 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
\(11\) −3.08945 5.35109i −0.931505 1.61341i −0.780750 0.624844i \(-0.785163\pi\)
−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
\(19\) 4.08945 7.08314i 0.938185 1.62498i 0.169332 0.985559i \(-0.445839\pi\)
0.768853 0.639425i \(-0.220828\pi\)
\(20\) 1.00000 1.73205i 0.223607 0.387298i
\(21\) 1.00000 0.218218
\(22\) −3.08945 + 5.35109i −0.658674 + 1.14086i
\(23\) −1.58945 2.75302i −0.331424 0.574043i 0.651367 0.758763i \(-0.274196\pi\)
−0.982791 + 0.184719i \(0.940862\pi\)
\(24\) 0.500000 + 0.866025i 0.102062 + 0.176777i
\(25\) −1.00000 −0.200000
\(26\) 3.58945 0.340322i 0.703950 0.0667425i
\(27\) −1.00000 −0.192450
\(28\) 0.500000 + 0.866025i 0.0944911 + 0.163663i
\(29\) −4.08945 7.08314i −0.759393 1.31531i −0.943161 0.332337i \(-0.892163\pi\)
0.183768 0.982970i \(-0.441170\pi\)
\(30\) −1.00000 + 1.73205i −0.182574 + 0.316228i
\(31\) −7.17891 −1.28937 −0.644685 0.764448i \(-0.723011\pi\)
−0.644685 + 0.764448i \(0.723011\pi\)
\(32\) −0.500000 + 0.866025i −0.0883883 + 0.153093i
\(33\) 3.08945 5.35109i 0.537805 0.931505i
\(34\) 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 \(0.885902\pi\)
\(38\) −8.17891 −1.32679
\(39\) −3.58945 + 0.340322i −0.574773 + 0.0544951i
\(40\) −2.00000 −0.316228
\(41\) −2.08945 3.61904i −0.326318 0.565199i 0.655460 0.755230i \(-0.272475\pi\)
−0.981778 + 0.190030i \(0.939141\pi\)
\(42\) −0.500000 0.866025i −0.0771517 0.133631i
\(43\) −0.410546 + 0.711086i −0.0626077 + 0.108440i −0.895630 0.444799i \(-0.853275\pi\)
0.833023 + 0.553239i \(0.186608\pi\)
\(44\) 6.17891 0.931505
\(45\) 1.00000 1.73205i 0.149071 0.258199i
\(46\) −1.58945 + 2.75302i −0.234352 + 0.405910i
\(47\) 4.17891 0.609556 0.304778 0.952423i \(-0.401418\pi\)
0.304778 + 0.952423i \(0.401418\pi\)
\(48\) 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
\(52\) −2.08945 2.93840i −0.289755 0.407482i
\(53\) −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
\(55\) 6.17891 + 10.7022i 0.833164 + 1.44308i
\(56\) 0.500000 0.866025i 0.0668153 0.115728i
\(57\) 8.17891 1.08332
\(58\) −4.08945 + 7.08314i −0.536972 + 0.930062i
\(59\) 0.410546 0.711086i 0.0534485 0.0925755i −0.838063 0.545573i \(-0.816312\pi\)
0.891512 + 0.452998i \(0.149645\pi\)
\(60\) 2.00000 0.258199
\(61\) 1.50000 2.59808i 0.192055 0.332650i −0.753876 0.657017i \(-0.771818\pi\)
0.945931 + 0.324367i \(0.105151\pi\)
\(62\) 3.58945 + 6.21712i 0.455861 + 0.789575i
\(63\) 0.500000 + 0.866025i 0.0629941 + 0.109109i
\(64\) 1.00000 0.125000
\(65\) 3.00000 6.55744i 0.372104 0.813350i
\(66\) −6.17891 −0.760571
\(67\) 7.58945 + 13.1453i 0.927199 + 1.60596i 0.787985 + 0.615694i \(0.211124\pi\)
0.139214 + 0.990262i \(0.455542\pi\)
\(68\) −2.50000 4.33013i −0.303170 0.525105i
\(69\) 1.58945 2.75302i 0.191348 0.331424i
\(70\) 2.00000 0.239046
\(71\) −4.58945 + 7.94917i −0.544668 + 0.943393i 0.453960 + 0.891022i \(0.350011\pi\)
−0.998628 + 0.0523705i \(0.983322\pi\)
\(72\) −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
\(76\) 4.08945 + 7.08314i 0.469093 + 0.812492i
\(77\) −6.17891 −0.704152
\(78\) 2.08945 + 2.93840i 0.236584 + 0.332708i
\(79\) 1.82109 0.204889 0.102444 0.994739i \(-0.467334\pi\)
0.102444 + 0.994739i \(0.467334\pi\)
\(80\) 1.00000 + 1.73205i 0.111803 + 0.193649i
\(81\) −0.500000 0.866025i −0.0555556 0.0962250i
\(82\) −2.08945 + 3.61904i −0.230742 + 0.399656i
\(83\) −5.17891 −0.568459 −0.284230 0.958756i \(-0.591738\pi\)
−0.284230 + 0.958756i \(0.591738\pi\)
\(84\) −0.500000 + 0.866025i −0.0545545 + 0.0944911i
\(85\) 5.00000 8.66025i 0.542326 0.939336i
\(86\) 0.821092 0.0885406
\(87\) 4.08945 7.08314i 0.438436 0.759393i
\(88\) −3.08945 5.35109i −0.329337 0.570428i
\(89\) −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
\(91\) 2.08945 + 2.93840i 0.219034 + 0.308028i
\(92\) 3.17891 0.331424
\(93\) −3.58945 6.21712i −0.372209 0.644685i
\(94\) −2.08945 3.61904i −0.215511 0.373276i
\(95\) −8.17891 + 14.1663i −0.839138 + 1.45343i
\(96\) −1.00000 −0.102062
\(97\) −6.17891 + 10.7022i −0.627373 + 1.08664i 0.360704 + 0.932680i \(0.382537\pi\)
−0.988077 + 0.153962i \(0.950797\pi\)
\(98\) −0.500000 + 0.866025i −0.0505076 + 0.0874818i
\(99\) 6.17891 0.621004
\(100\) 0.500000 0.866025i 0.0500000 0.0866025i
\(101\) 8.17891 + 14.1663i 0.813832 + 1.40960i 0.910164 + 0.414249i \(0.135956\pi\)
−0.0963319 + 0.995349i \(0.530711\pi\)
\(102\) 2.50000 + 4.33013i 0.247537 + 0.428746i
\(103\) 3.17891 0.313227 0.156614 0.987660i \(-0.449942\pi\)
0.156614 + 0.987660i \(0.449942\pi\)
\(104\) −1.50000 + 3.27872i −0.147087 + 0.321505i
\(105\) −2.00000 −0.195180
\(106\) 1.50000 + 2.59808i 0.145693 + 0.252347i
\(107\) −3.91055 6.77326i −0.378047 0.654796i 0.612731 0.790291i \(-0.290071\pi\)
−0.990778 + 0.135495i \(0.956737\pi\)
\(108\) 0.500000 0.866025i 0.0481125 0.0833333i
\(109\) 4.00000 0.383131 0.191565 0.981480i \(-0.438644\pi\)
0.191565 + 0.981480i \(0.438644\pi\)
\(110\) 6.17891 10.7022i 0.589136 1.02041i
\(111\) 1.00000 1.73205i 0.0949158 0.164399i
\(112\) −1.00000 −0.0944911
\(113\) 2.17891 3.77398i 0.204974 0.355026i −0.745150 0.666897i \(-0.767622\pi\)
0.950125 + 0.311871i \(0.100956\pi\)
\(114\) −4.08945 7.08314i −0.383012 0.663397i
\(115\) 3.17891 + 5.50603i 0.296435 + 0.513440i
\(116\) 8.17891 0.759393
\(117\) −2.08945 2.93840i −0.193170 0.271655i
\(118\) −0.821092 −0.0755876
\(119\) 2.50000 + 4.33013i 0.229175 + 0.396942i
\(120\) −1.00000 1.73205i −0.0912871 0.158114i
\(121\) −13.5895 + 23.5376i −1.23540 + 2.13978i
\(122\) −3.00000 −0.271607
\(123\) 2.08945 3.61904i 0.188400 0.326318i
\(124\) 3.58945 6.21712i 0.322343 0.558314i
\(125\) 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
\(129\) −0.821092 −0.0722931
\(130\) −7.17891 + 0.680643i −0.629632 + 0.0596963i
\(131\) 19.5367 1.70693 0.853466 0.521149i \(-0.174496\pi\)
0.853466 + 0.521149i \(0.174496\pi\)
\(132\) 3.08945 + 5.35109i 0.268902 + 0.465753i
\(133\) −4.08945 7.08314i −0.354601 0.614186i
\(134\) 7.58945 13.1453i 0.655629 1.13558i
\(135\) 2.00000 0.172133
\(136\) −2.50000 + 4.33013i −0.214373 + 0.371305i
\(137\) 8.17891 14.1663i 0.698771 1.21031i −0.270121 0.962826i \(-0.587064\pi\)
0.968893 0.247481i \(-0.0796028\pi\)
\(138\) −3.17891 −0.270607
\(139\) 9.08945 15.7434i 0.770957 1.33534i −0.166081 0.986112i \(-0.553111\pi\)
0.937039 0.349225i \(-0.113555\pi\)
\(140\) −1.00000 1.73205i −0.0845154 0.146385i
\(141\) 2.08945 + 3.61904i 0.175964 + 0.304778i
\(142\) 9.17891 0.770277
\(143\) 22.1789 2.10282i 1.85469 0.175846i
\(144\) 1.00000 0.0833333
\(145\) 8.17891 + 14.1663i 0.679221 + 1.17645i
\(146\) −2.00000 3.46410i −0.165521 0.286691i
\(147\) 0.500000 0.866025i 0.0412393 0.0714286i
\(148\) 2.00000 0.164399
\(149\) −2.41055 + 4.17519i −0.197480 + 0.342045i −0.947711 0.319131i \(-0.896609\pi\)
0.750231 + 0.661176i \(0.229942\pi\)
\(150\) −0.500000 + 0.866025i −0.0408248 + 0.0707107i
\(151\) −14.5367 −1.18298 −0.591491 0.806312i \(-0.701460\pi\)
−0.591491 + 0.806312i \(0.701460\pi\)
\(152\) 4.08945 7.08314i 0.331699 0.574519i
\(153\) −2.50000 4.33013i −0.202113 0.350070i
\(154\) 3.08945 + 5.35109i 0.248955 + 0.431203i
\(155\) 14.3578 1.15325
\(156\) 1.50000 3.27872i 0.120096 0.262508i
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −0.910546 1.57711i −0.0724391 0.125468i
\(159\) −1.50000 2.59808i −0.118958 0.206041i
\(160\) 1.00000 1.73205i 0.0790569 0.136931i
\(161\) −3.17891 −0.250533
\(162\) −0.500000 + 0.866025i −0.0392837 + 0.0680414i
\(163\) 4.41055 7.63929i 0.345461 0.598355i −0.639977 0.768394i \(-0.721056\pi\)
0.985437 + 0.170039i \(0.0543894\pi\)
\(164\) 4.17891 0.326318
\(165\) −6.17891 + 10.7022i −0.481027 + 0.833164i
\(166\) 2.58945 + 4.48507i 0.200981 + 0.348109i
\(167\) 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
\(171\) 4.08945 + 7.08314i 0.312728 + 0.541661i
\(172\) −0.410546 0.711086i −0.0313038 0.0542198i
\(173\) −2.00000 + 3.46410i −0.152057 + 0.263371i −0.931984 0.362500i \(-0.881923\pi\)
0.779926 + 0.625871i \(0.215256\pi\)
\(174\) −8.17891 −0.620041
\(175\) −0.500000 + 0.866025i −0.0377964 + 0.0654654i
\(176\) −3.08945 + 5.35109i −0.232876 + 0.403354i
\(177\) 0.821092 0.0617170
\(178\) −4.50000 + 7.79423i −0.337289 + 0.584202i
\(179\) 7.17891 + 12.4342i 0.536577 + 0.929378i 0.999085 + 0.0427634i \(0.0136162\pi\)
−0.462508 + 0.886615i \(0.653051\pi\)
\(180\) 1.00000 + 1.73205i 0.0745356 + 0.129099i
\(181\) 7.82109 0.581337 0.290669 0.956824i \(-0.406122\pi\)
0.290669 + 0.956824i \(0.406122\pi\)
\(182\) 1.50000 3.27872i 0.111187 0.243035i
\(183\) 3.00000 0.221766
\(184\) −1.58945 2.75302i −0.117176 0.202955i
\(185\) 2.00000 + 3.46410i 0.147043 + 0.254686i
\(186\) −3.58945 + 6.21712i −0.263192 + 0.455861i
\(187\) 30.8945 2.25923
\(188\) −2.08945 + 3.61904i −0.152389 + 0.263946i
\(189\) −0.500000 + 0.866025i −0.0363696 + 0.0629941i
\(190\) 16.3578 1.18672
\(191\) −13.7684 + 23.8475i −0.996244 + 1.72554i −0.423130 + 0.906069i \(0.639069\pi\)
−0.573114 + 0.819476i \(0.694265\pi\)
\(192\) 0.500000 + 0.866025i 0.0360844 + 0.0625000i
\(193\) −10.2684 17.7853i −0.739133 1.28022i −0.952886 0.303328i \(-0.901902\pi\)
0.213753 0.976888i \(-0.431431\pi\)
\(194\) 12.3578 0.887240
\(195\) 7.17891 0.680643i 0.514092 0.0487419i
\(196\) 1.00000 0.0714286
\(197\) −8.50000 14.7224i −0.605600 1.04893i −0.991956 0.126580i \(-0.959600\pi\)
0.386356 0.922350i \(-0.373733\pi\)
\(198\) −3.08945 5.35109i −0.219558 0.380286i
\(199\) −6.41055 + 11.1034i −0.454432 + 0.787099i −0.998655 0.0518416i \(-0.983491\pi\)
0.544224 + 0.838940i \(0.316824\pi\)
\(200\) −1.00000 −0.0707107
\(201\) −7.58945 + 13.1453i −0.535319 + 0.927199i
\(202\) 8.17891 14.1663i 0.575466 0.996736i
\(203\) −8.17891 −0.574047
\(204\) 2.50000 4.33013i 0.175035 0.303170i
\(205\) 4.17891 + 7.23808i 0.291868 + 0.505530i
\(206\) −1.58945 2.75302i −0.110743 0.191812i
\(207\) 3.17891 0.220949
\(208\) 3.58945 0.340322i 0.248884 0.0235971i
\(209\) −50.5367 −3.49570
\(210\) 1.00000 + 1.73205i 0.0690066 + 0.119523i
\(211\) −8.17891 14.1663i −0.563059 0.975247i −0.997227 0.0744154i \(-0.976291\pi\)
0.434168 0.900832i \(-0.357042\pi\)
\(212\) 1.50000 2.59808i 0.103020 0.178437i
\(213\) −9.17891 −0.628928
\(214\) −3.91055 + 6.77326i −0.267319 + 0.463011i
\(215\) 0.821092 1.42217i 0.0559980 0.0969914i
\(216\) −1.00000 −0.0680414
\(217\) −3.58945 + 6.21712i −0.243668 + 0.422045i
\(218\) −2.00000 3.46410i −0.135457 0.234619i
\(219\) 2.00000 + 3.46410i 0.135147 + 0.234082i
\(220\) −12.3578 −0.833164
\(221\) −10.4473 14.6920i −0.702759 0.988290i
\(222\) −2.00000 −0.134231
\(223\) −4.58945 7.94917i −0.307333 0.532316i 0.670445 0.741959i \(-0.266103\pi\)
−0.977778 + 0.209643i \(0.932770\pi\)
\(224\) 0.500000 + 0.866025i 0.0334077 + 0.0578638i
\(225\) 0.500000 0.866025i 0.0333333 0.0577350i
\(226\) −4.35782 −0.289878
\(227\) −4.17891 + 7.23808i −0.277364 + 0.480408i −0.970729 0.240178i \(-0.922794\pi\)
0.693365 + 0.720587i \(0.256127\pi\)
\(228\) −4.08945 + 7.08314i −0.270831 + 0.469093i
\(229\) 1.00000 0.0660819 0.0330409 0.999454i \(-0.489481\pi\)
0.0330409 + 0.999454i \(0.489481\pi\)
\(230\) 3.17891 5.50603i 0.209611 0.363057i
\(231\) −3.08945 5.35109i −0.203271 0.352076i
\(232\) −4.08945 7.08314i −0.268486 0.465031i
\(233\) −0.357817 −0.0234414 −0.0117207 0.999931i \(-0.503731\pi\)
−0.0117207 + 0.999931i \(0.503731\pi\)
\(234\) −1.50000 + 3.27872i −0.0980581 + 0.214337i
\(235\) −8.35782 −0.545204
\(236\) 0.410546 + 0.711086i 0.0267243 + 0.0462878i
\(237\) 0.910546 + 1.57711i 0.0591463 + 0.102444i
\(238\) 2.50000 4.33013i 0.162051 0.280680i
\(239\) −1.17891 −0.0762572 −0.0381286 0.999273i \(-0.512140\pi\)
−0.0381286 + 0.999273i \(0.512140\pi\)
\(240\) −1.00000 + 1.73205i −0.0645497 + 0.111803i
\(241\) 9.17891 15.8983i 0.591265 1.02410i −0.402797 0.915289i \(-0.631962\pi\)
0.994062 0.108812i \(-0.0347048\pi\)
\(242\) 27.1789 1.74713
\(243\) 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
\(246\) −4.17891 −0.266437
\(247\) 17.0895 + 24.0329i 1.08738 + 1.52918i
\(248\) −7.17891 −0.455861
\(249\) −2.58945 4.48507i −0.164100 0.284230i
\(250\) −6.00000 10.3923i −0.379473 0.657267i
\(251\) −5.41055 + 9.37134i −0.341511 + 0.591514i −0.984713 0.174182i \(-0.944272\pi\)
0.643203 + 0.765696i \(0.277605\pi\)
\(252\) −1.00000 −0.0629941
\(253\) −9.82109 + 17.0106i −0.617447 + 1.06945i
\(254\) −6.00000 + 10.3923i −0.376473 + 0.652071i
\(255\) 10.0000 0.626224
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) −12.8578 22.2704i −0.802049 1.38919i −0.918266 0.395965i \(-0.870410\pi\)
0.116217 0.993224i \(-0.462923\pi\)
\(258\) 0.410546 + 0.711086i 0.0255595 + 0.0442703i
\(259\) −2.00000 −0.124274
\(260\) 4.17891 + 5.87680i 0.259165 + 0.364463i
\(261\) 8.17891 0.506262
\(262\) −9.76836 16.9193i −0.603491 1.04528i
\(263\) 6.00000 + 10.3923i 0.369976 + 0.640817i 0.989561 0.144112i \(-0.0460326\pi\)
−0.619586 + 0.784929i \(0.712699\pi\)
\(264\) 3.08945 5.35109i 0.190143 0.329337i
\(265\) 6.00000 0.368577
\(266\) −4.08945 + 7.08314i −0.250741 + 0.434295i
\(267\) 4.50000 7.79423i 0.275396 0.476999i
\(268\) −15.1789 −0.927199
\(269\) −9.17891 + 15.8983i −0.559648 + 0.969339i 0.437878 + 0.899035i \(0.355730\pi\)
−0.997526 + 0.0703041i \(0.977603\pi\)
\(270\) −1.00000 1.73205i −0.0608581 0.105409i
\(271\) −15.5895 27.0017i −0.946992 1.64024i −0.751713 0.659490i \(-0.770772\pi\)
−0.195279 0.980748i \(-0.562561\pi\)
\(272\) 5.00000 0.303170
\(273\) −1.50000 + 3.27872i −0.0907841 + 0.198437i
\(274\) −16.3578 −0.988212
\(275\) 3.08945 + 5.35109i 0.186301 + 0.322683i
\(276\) 1.58945 + 2.75302i 0.0956739 + 0.165712i
\(277\) −14.1789 + 24.5586i −0.851928 + 1.47558i 0.0275379 + 0.999621i \(0.491233\pi\)
−0.879466 + 0.475962i \(0.842100\pi\)
\(278\) −18.1789 −1.09030
\(279\) 3.58945 6.21712i 0.214895 0.372209i
\(280\) −1.00000 + 1.73205i −0.0597614 + 0.103510i
\(281\) 5.64218 0.336584 0.168292 0.985737i \(-0.446175\pi\)
0.168292 + 0.985737i \(0.446175\pi\)
\(282\) 2.08945 3.61904i 0.124425 0.215511i
\(283\) −15.1789 26.2906i −0.902292 1.56282i −0.824511 0.565846i \(-0.808550\pi\)
−0.0777814 0.996970i \(-0.524784\pi\)
\(284\) −4.58945 7.94917i −0.272334 0.471696i
\(285\) −16.3578 −0.968953
\(286\) −12.9105 18.1561i −0.763417 1.07359i
\(287\) −4.17891 −0.246673
\(288\) −0.500000 0.866025i −0.0294628 0.0510310i
\(289\) −4.00000 6.92820i −0.235294 0.407541i
\(290\) 8.17891 14.1663i 0.480282 0.831873i
\(291\) −12.3578 −0.724428
\(292\) −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
\(295\) −0.821092 + 1.42217i −0.0478058 + 0.0828021i
\(296\) −1.00000 1.73205i −0.0581238 0.100673i
\(297\) 3.08945 + 5.35109i 0.179268 + 0.310502i
\(298\) 4.82109 0.279278
\(299\) 11.4105 1.08185i 0.659889 0.0625651i
\(300\) 1.00000 0.0577350
\(301\) 0.410546 + 0.711086i 0.0236635 + 0.0409863i
\(302\) 7.26836 + 12.5892i 0.418247 + 0.724426i
\(303\) −8.17891 + 14.1663i −0.469866 + 0.813832i
\(304\) −8.17891 −0.469093
\(305\) −3.00000 + 5.19615i −0.171780 + 0.297531i
\(306\) −2.50000 + 4.33013i −0.142915 + 0.247537i
\(307\) 24.8945 1.42081 0.710403 0.703795i \(-0.248513\pi\)
0.710403 + 0.703795i \(0.248513\pi\)
\(308\) 3.08945 5.35109i 0.176038 0.304907i
\(309\) 1.58945 + 2.75302i 0.0904209 + 0.156614i
\(310\) −7.17891 12.4342i −0.407735 0.706217i
\(311\) −8.53673 −0.484073 −0.242037 0.970267i \(-0.577815\pi\)
−0.242037 + 0.970267i \(0.577815\pi\)
\(312\) −3.58945 + 0.340322i −0.203213 + 0.0192669i
\(313\) 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
\(316\) −0.910546 + 1.57711i −0.0512222 + 0.0887195i
\(317\) 7.17891 0.403208 0.201604 0.979467i \(-0.435385\pi\)
0.201604 + 0.979467i \(0.435385\pi\)
\(318\) −1.50000 + 2.59808i −0.0841158 + 0.145693i
\(319\) −25.2684 + 43.7661i −1.41476 + 2.45043i
\(320\) −2.00000 −0.111803
\(321\) 3.91055 6.77326i 0.218265 0.378047i
\(322\) 1.58945 + 2.75302i 0.0885768 + 0.153420i
\(323\) 20.4473 + 35.4157i 1.13772 + 1.97058i
\(324\) 1.00000 0.0555556
\(325\) 1.50000 3.27872i 0.0832050 0.181871i
\(326\) −8.82109 −0.488555
\(327\) 2.00000 + 3.46410i 0.110600 + 0.191565i
\(328\) −2.08945 3.61904i −0.115371 0.199828i
\(329\) 2.08945 3.61904i 0.115195 0.199524i
\(330\) 12.3578 0.680275
\(331\) 12.1789 21.0945i 0.669413 1.15946i −0.308655 0.951174i \(-0.599879\pi\)
0.978068 0.208284i \(-0.0667878\pi\)
\(332\) 2.58945 4.48507i 0.142115 0.246150i
\(333\) 2.00000 0.109599
\(334\) 4.00000 6.92820i 0.218870 0.379094i
\(335\) −15.1789 26.2906i −0.829312 1.43641i
\(336\) −0.500000 0.866025i −0.0272772 0.0472456i
\(337\) −0.536725 −0.0292373 −0.0146186 0.999893i \(-0.504653\pi\)
−0.0146186 + 0.999893i \(0.504653\pi\)
\(338\) −4.26836 + 12.2793i −0.232168 + 0.667906i
\(339\) 4.35782 0.236684
\(340\) 5.00000 + 8.66025i 0.271163 + 0.469668i
\(341\) 22.1789 + 38.4150i 1.20106 + 2.08029i
\(342\) 4.08945 7.08314i 0.221132 0.383012i
\(343\) −1.00000 −0.0539949
\(344\) −0.410546 + 0.711086i −0.0221351 + 0.0383392i
\(345\) −3.17891 + 5.50603i −0.171147 + 0.296435i
\(346\) 4.00000 0.215041
\(347\) 3.91055 6.77326i 0.209929 0.363608i −0.741763 0.670662i \(-0.766010\pi\)
0.951692 + 0.307054i \(0.0993433\pi\)
\(348\) 4.08945 + 7.08314i 0.219218 + 0.379696i
\(349\) 1.58945 + 2.75302i 0.0850815 + 0.147366i 0.905426 0.424504i \(-0.139552\pi\)
−0.820344 + 0.571870i \(0.806218\pi\)
\(350\) 1.00000 0.0534522
\(351\) 1.50000 3.27872i 0.0800641 0.175005i
\(352\) 6.17891 0.329337
\(353\) 3.58945 + 6.21712i 0.191047 + 0.330904i 0.945598 0.325339i \(-0.105478\pi\)
−0.754550 + 0.656242i \(0.772145\pi\)
\(354\) −0.410546 0.711086i −0.0218203 0.0377938i
\(355\) 9.17891 15.8983i 0.487166 0.843796i
\(356\) 9.00000 0.476999
\(357\) −2.50000 + 4.33013i −0.132314 + 0.229175i
\(358\) 7.17891 12.4342i 0.379417 0.657170i
\(359\) 12.3578 0.652221 0.326110 0.945332i \(-0.394262\pi\)
0.326110 + 0.945332i \(0.394262\pi\)
\(360\) 1.00000 1.73205i 0.0527046 0.0912871i
\(361\) −23.9473 41.4779i −1.26038 2.18305i
\(362\) −3.91055 6.77326i −0.205534 0.355995i
\(363\) −27.1789 −1.42652
\(364\) −3.58945 + 0.340322i −0.188139 + 0.0178377i
\(365\) −8.00000 −0.418739
\(366\) −1.50000 2.59808i −0.0784063 0.135804i
\(367\) −1.58945 2.75302i −0.0829688 0.143706i 0.821555 0.570129i \(-0.193107\pi\)
−0.904524 + 0.426423i \(0.859774\pi\)
\(368\) −1.58945 + 2.75302i −0.0828560 + 0.143511i
\(369\) 4.17891 0.217545
\(370\) 2.00000 3.46410i 0.103975 0.180090i
\(371\) −1.50000 + 2.59808i −0.0778761 + 0.134885i
\(372\) 7.17891 0.372209
\(373\) 10.0000 17.3205i 0.517780 0.896822i −0.482006 0.876168i \(-0.660092\pi\)
0.999787 0.0206542i \(-0.00657489\pi\)
\(374\) −15.4473 26.7555i −0.798759 1.38349i
\(375\) 6.00000 + 10.3923i 0.309839 + 0.536656i
\(376\) 4.17891 0.215511
\(377\) 29.3578 2.78346i 1.51200 0.143355i
\(378\) 1.00000 0.0514344
\(379\) −10.3578 17.9403i −0.532045 0.921530i −0.999300 0.0374068i \(-0.988090\pi\)
0.467255 0.884123i \(-0.345243\pi\)
\(380\) −8.17891 14.1663i −0.419569 0.726715i
\(381\) 6.00000 10.3923i 0.307389 0.532414i
\(382\) 27.5367 1.40890
\(383\) −4.91055 + 8.50531i −0.250917 + 0.434601i −0.963779 0.266704i \(-0.914066\pi\)
0.712861 + 0.701305i \(0.247399\pi\)
\(384\) 0.500000 0.866025i 0.0255155 0.0441942i
\(385\) 12.3578 0.629813
\(386\) −10.2684 + 17.7853i −0.522646 + 0.905249i
\(387\) −0.410546 0.711086i −0.0208692 0.0361465i
\(388\) −6.17891 10.7022i −0.313687 0.543321i
\(389\) −0.821092 −0.0416310 −0.0208155 0.999783i \(-0.506626\pi\)
−0.0208155 + 0.999783i \(0.506626\pi\)
\(390\) −4.17891 5.87680i −0.211607 0.297583i
\(391\) 15.8945 0.803822
\(392\) −0.500000 0.866025i −0.0252538 0.0437409i
\(393\) 9.76836 + 16.9193i 0.492749 + 0.853466i
\(394\) −8.50000 + 14.7224i −0.428224 + 0.741705i
\(395\) −3.64218 −0.183258
\(396\) −3.08945 + 5.35109i −0.155251 + 0.268902i
\(397\) −1.50000 + 2.59808i −0.0752828 + 0.130394i −0.901209 0.433384i \(-0.857319\pi\)
0.825926 + 0.563778i \(0.190653\pi\)
\(398\) 12.8211 0.642663
\(399\) 4.08945 7.08314i 0.204729 0.354601i
\(400\) 0.500000 + 0.866025i 0.0250000 + 0.0433013i
\(401\) −16.1789 28.0227i −0.807936 1.39939i −0.914291 0.405058i \(-0.867251\pi\)
0.106355 0.994328i \(-0.466082\pi\)
\(402\) 15.1789 0.757055
\(403\) 10.7684 23.5376i 0.536410 1.17249i
\(404\) −16.3578 −0.813832
\(405\) 1.00000 + 1.73205i 0.0496904 + 0.0860663i
\(406\) 4.08945 + 7.08314i 0.202956 + 0.351530i
\(407\) −6.17891 + 10.7022i −0.306277 + 0.530488i
\(408\) −5.00000 −0.247537
\(409\) 6.82109 11.8145i 0.337281 0.584188i −0.646639 0.762796i \(-0.723826\pi\)
0.983920 + 0.178608i \(0.0571593\pi\)
\(410\) 4.17891 7.23808i 0.206382 0.357463i
\(411\) 16.3578 0.806872
\(412\) −1.58945 + 2.75302i −0.0783068 + 0.135631i
\(413\) −0.410546 0.711086i −0.0202016 0.0349903i
\(414\) −1.58945 2.75302i −0.0781174 0.135303i
\(415\) 10.3578 0.508445
\(416\) −2.08945 2.93840i −0.102444 0.144067i
\(417\) 18.1789 0.890225
\(418\) 25.2684 + 43.7661i 1.23592 + 2.14067i
\(419\) −14.9473 25.8894i −0.730222 1.26478i −0.956788 0.290786i \(-0.906083\pi\)
0.226566 0.973996i \(-0.427250\pi\)
\(420\) 1.00000 1.73205i 0.0487950 0.0845154i
\(421\) −34.7156 −1.69194 −0.845968 0.533233i \(-0.820977\pi\)
−0.845968 + 0.533233i \(0.820977\pi\)
\(422\) −8.17891 + 14.1663i −0.398143 + 0.689604i
\(423\) −2.08945 + 3.61904i −0.101593 + 0.175964i
\(424\) −3.00000 −0.145693
\(425\) 2.50000 4.33013i 0.121268 0.210042i
\(426\) 4.58945 + 7.94917i 0.222360 + 0.385138i
\(427\) −1.50000 2.59808i −0.0725901 0.125730i
\(428\) 7.82109 0.378047
\(429\) 12.9105 + 18.1561i 0.623327 + 0.876584i
\(430\) −1.64218 −0.0791931
\(431\) 0.589454 + 1.02096i 0.0283930 + 0.0491781i 0.879873 0.475209i \(-0.157628\pi\)
−0.851480 + 0.524387i \(0.824294\pi\)
\(432\) 0.500000 + 0.866025i 0.0240563 + 0.0416667i
\(433\) −5.82109 + 10.0824i −0.279744 + 0.484530i −0.971321 0.237772i \(-0.923583\pi\)
0.691577 + 0.722303i \(0.256916\pi\)
\(434\) 7.17891 0.344599
\(435\) −8.17891 + 14.1663i −0.392149 + 0.679221i
\(436\) −2.00000 + 3.46410i −0.0957826 + 0.165900i
\(437\) −26.0000 −1.24375
\(438\) 2.00000 3.46410i 0.0955637 0.165521i
\(439\) 2.35782 + 4.08386i 0.112532 + 0.194912i 0.916791 0.399368i \(-0.130770\pi\)
−0.804258 + 0.594280i \(0.797437\pi\)
\(440\) 6.17891 + 10.7022i 0.294568 + 0.510207i
\(441\) 1.00000 0.0476190
\(442\) −7.50000 + 16.3936i −0.356739 + 0.779764i
\(443\) −8.17891 −0.388592 −0.194296 0.980943i \(-0.562242\pi\)
−0.194296 + 0.980943i \(0.562242\pi\)
\(444\) 1.00000 + 1.73205i 0.0474579 + 0.0821995i
\(445\) 9.00000 + 15.5885i 0.426641 + 0.738964i
\(446\) −4.58945 + 7.94917i −0.217317 + 0.376404i
\(447\) −4.82109 −0.228030
\(448\) 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
\(451\) −12.9105 + 22.3617i −0.607934 + 1.05297i
\(452\) 2.17891 + 3.77398i 0.102487 + 0.177513i
\(453\) −7.26836 12.5892i −0.341497 0.591491i
\(454\) 8.35782 0.392252
\(455\) −4.17891 5.87680i −0.195910 0.275508i
\(456\) 8.17891 0.383012
\(457\) 15.9473 + 27.6215i 0.745982 + 1.29208i 0.949735 + 0.313056i \(0.101353\pi\)
−0.203753 + 0.979022i \(0.565314\pi\)
\(458\) −0.500000 0.866025i −0.0233635 0.0404667i
\(459\) 2.50000 4.33013i 0.116690 0.202113i
\(460\) −6.35782 −0.296435
\(461\) 12.3578 21.4044i 0.575561 0.996901i −0.420420 0.907330i \(-0.638117\pi\)
0.995980 0.0895709i \(-0.0285496\pi\)
\(462\) −3.08945 + 5.35109i −0.143734 + 0.248955i
\(463\) −28.8945 −1.34284 −0.671422 0.741076i \(-0.734316\pi\)
−0.671422 + 0.741076i \(0.734316\pi\)
\(464\) −4.08945 + 7.08314i −0.189848 + 0.328827i
\(465\) 7.17891 + 12.4342i 0.332914 + 0.576624i
\(466\) 0.178908 + 0.309878i 0.00828777 + 0.0143548i
\(467\) 33.8945 1.56845 0.784226 0.620475i \(-0.213060\pi\)
0.784226 + 0.620475i \(0.213060\pi\)
\(468\) 3.58945 0.340322i 0.165923 0.0157314i
\(469\) 15.1789 0.700897
\(470\) 4.17891 + 7.23808i 0.192759 + 0.333868i
\(471\) 1.00000 + 1.73205i 0.0460776 + 0.0798087i
\(472\) 0.410546 0.711086i 0.0188969 0.0327304i
\(473\) 5.07345 0.233277
\(474\) 0.910546 1.57711i 0.0418228 0.0724391i
\(475\) −4.08945 + 7.08314i −0.187637 + 0.324997i
\(476\) −5.00000 −0.229175
\(477\) 1.50000 2.59808i 0.0686803 0.118958i
\(478\) 0.589454 + 1.02096i 0.0269610 + 0.0466978i
\(479\) 14.9105 + 25.8258i 0.681280 + 1.18001i 0.974590 + 0.223995i \(0.0719098\pi\)
−0.293310 + 0.956017i \(0.594757\pi\)
\(480\) 2.00000 0.0912871
\(481\) 7.17891 0.680643i 0.327330 0.0310347i
\(482\) −18.3578 −0.836176
\(483\) −1.58945 2.75302i −0.0723227 0.125267i
\(484\) −13.5895 23.5376i −0.617702 1.06989i
\(485\) 12.3578 21.4044i 0.561140 0.971922i
\(486\) −1.00000 −0.0453609
\(487\) 19.0895 33.0639i 0.865026 1.49827i −0.00199588 0.999998i \(-0.500635\pi\)
0.867022 0.498271i \(-0.166031\pi\)
\(488\) 1.50000 2.59808i 0.0679018 0.117609i
\(489\) 8.82109 0.398904
\(490\) 1.00000 1.73205i 0.0451754 0.0782461i
\(491\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(492\) 2.08945 + 3.61904i 0.0941999 + 0.163159i
\(493\) 40.8945 1.84180
\(494\) 12.2684 26.8163i 0.551980 1.20652i
\(495\) −12.3578 −0.555443
\(496\) 3.58945 + 6.21712i 0.161171 + 0.279157i
\(497\) 4.58945 + 7.94917i 0.205865 + 0.356569i
\(498\) −2.58945 + 4.48507i −0.116036 + 0.200981i
\(499\) −3.17891 −0.142307 −0.0711537 0.997465i \(-0.522668\pi\)
−0.0711537 + 0.997465i \(0.522668\pi\)
\(500\) −6.00000 + 10.3923i −0.268328 + 0.464758i
\(501\) −4.00000 + 6.92820i −0.178707 + 0.309529i
\(502\) 10.8211 0.482969
\(503\) 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
\(505\) −16.3578 28.3326i −0.727913 1.26078i
\(506\) 19.6422 0.873202
\(507\) 4.26836 12.2793i 0.189565 0.545343i
\(508\) 12.0000 0.532414
\(509\) −14.3578 24.8685i −0.636399 1.10228i −0.986217 0.165458i \(-0.947090\pi\)
0.349818 0.936818i \(-0.386243\pi\)
\(510\) −5.00000 8.66025i −0.221404 0.383482i
\(511\) 2.00000 3.46410i 0.0884748 0.153243i
\(512\) 1.00000 0.0441942
\(513\) −4.08945 + 7.08314i −0.180554 + 0.312728i
\(514\) −12.8578 + 22.2704i −0.567134 + 0.982305i
\(515\) −6.35782 −0.280159
\(516\) 0.410546 0.711086i 0.0180733 0.0313038i
\(517\) −12.9105 22.3617i −0.567805 0.983467i
\(518\) 1.00000 + 1.73205i 0.0439375 + 0.0761019i
\(519\) −4.00000 −0.175581
\(520\) 3.00000 6.55744i 0.131559 0.287563i
\(521\) −4.17891 −0.183081 −0.0915406 0.995801i \(-0.529179\pi\)
−0.0915406 + 0.995801i \(0.529179\pi\)
\(522\) −4.08945 7.08314i −0.178991 0.310021i
\(523\) 11.2684 + 19.5174i 0.492731 + 0.853435i 0.999965 0.00837317i \(-0.00266530\pi\)
−0.507234 + 0.861808i \(0.669332\pi\)
\(524\) −9.76836 + 16.9193i −0.426733 + 0.739123i
\(525\) −1.00000 −0.0436436
\(526\) 6.00000 10.3923i 0.261612 0.453126i
\(527\) 17.9473 31.0856i 0.781795 1.35411i
\(528\) −6.17891 −0.268902
\(529\) 6.44727 11.1670i 0.280316 0.485522i
\(530\) −3.00000 5.19615i −0.130312 0.225706i
\(531\) 0.410546 + 0.711086i 0.0178162 + 0.0308585i
\(532\) 8.17891 0.354601
\(533\) 15.0000 1.42217i 0.649722 0.0616011i
\(534\) −9.00000 −0.389468
\(535\) 7.82109 + 13.5465i 0.338135 + 0.585667i
\(536\) 7.58945 + 13.1453i 0.327814 + 0.567791i
\(537\) −7.17891 + 12.4342i −0.309793 + 0.536577i
\(538\) 18.3578 0.791462
\(539\) −3.08945 + 5.35109i −0.133072 + 0.230488i
\(540\) −1.00000 + 1.73205i −0.0430331 + 0.0745356i
\(541\) 2.35782 0.101370 0.0506852 0.998715i \(-0.483859\pi\)
0.0506852 + 0.998715i \(0.483859\pi\)
\(542\) −15.5895 + 27.0017i −0.669624 + 1.15982i
\(543\) 3.91055 + 6.77326i 0.167818 + 0.290669i
\(544\) −2.50000 4.33013i −0.107187 0.185653i
\(545\) −8.00000 −0.342682
\(546\) 3.58945 0.340322i 0.153614 0.0145644i
\(547\) 36.0000 1.53925 0.769624 0.638497i \(-0.220443\pi\)
0.769624 + 0.638497i \(0.220443\pi\)
\(548\) 8.17891 + 14.1663i 0.349386 + 0.605154i
\(549\) 1.50000 + 2.59808i 0.0640184 + 0.110883i
\(550\) 3.08945 5.35109i 0.131735 0.228171i
\(551\) −66.8945 −2.84980
\(552\) 1.58945 2.75302i 0.0676517 0.117176i
\(553\) 0.910546 1.57711i 0.0387203 0.0670656i
\(554\) 28.3578 1.20481
\(555\) −2.00000 + 3.46410i −0.0848953 + 0.147043i
\(556\) 9.08945 + 15.7434i 0.385479 + 0.667669i
\(557\) 10.8578 + 18.8063i 0.460060 + 0.796848i 0.998963 0.0455198i \(-0.0144944\pi\)
−0.538903 + 0.842368i \(0.681161\pi\)
\(558\) −7.17891 −0.303907
\(559\) −1.71563 2.41269i −0.0725636 0.102046i
\(560\) 2.00000 0.0845154
\(561\) 15.4473 + 26.7555i 0.652184 + 1.12962i
\(562\) −2.82109 4.88627i −0.119001 0.206115i
\(563\) −2.17891 + 3.77398i −0.0918300 + 0.159054i −0.908281 0.418360i \(-0.862605\pi\)
0.816451 + 0.577414i \(0.195938\pi\)
\(564\) −4.17891 −0.175964
\(565\) −4.35782 + 7.54796i −0.183335 + 0.317545i
\(566\) −15.1789 + 26.2906i −0.638017 + 1.10508i
\(567\) −1.00000 −0.0419961
\(568\) −4.58945 + 7.94917i −0.192569 + 0.333540i
\(569\) 13.1789 + 22.8265i 0.552489 + 0.956938i 0.998094 + 0.0617089i \(0.0196550\pi\)
−0.445606 + 0.895229i \(0.647012\pi\)
\(570\) 8.17891 + 14.1663i 0.342577 + 0.593360i
\(571\) −22.8211 −0.955033 −0.477516 0.878623i \(-0.658463\pi\)
−0.477516 + 0.878623i \(0.658463\pi\)
\(572\) −9.26836 + 20.2589i −0.387530 + 0.847067i
\(573\) −27.5367 −1.15036
\(574\) 2.08945 + 3.61904i 0.0872121 + 0.151056i
\(575\) 1.58945 + 2.75302i 0.0662848 + 0.114809i
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −5.64218 −0.234887 −0.117444 0.993080i \(-0.537470\pi\)
−0.117444 + 0.993080i \(0.537470\pi\)
\(578\) −4.00000 + 6.92820i −0.166378 + 0.288175i
\(579\) 10.2684 17.7853i 0.426739 0.739133i
\(580\) −16.3578 −0.679221
\(581\) −2.58945 + 4.48507i −0.107429 + 0.186072i
\(582\) 6.17891 + 10.7022i 0.256124 + 0.443620i
\(583\) 9.26836 + 16.0533i 0.383856 + 0.664859i
\(584\) 4.00000 0.165521
\(585\) 4.17891 + 5.87680i 0.172777 + 0.242976i
\(586\) 12.0000 0.495715
\(587\) 5.58945 + 9.68122i 0.230701 + 0.399587i 0.958015 0.286719i \(-0.0925646\pi\)
−0.727313 + 0.686306i \(0.759231\pi\)
\(588\) 0.500000 + 0.866025i 0.0206197 + 0.0357143i
\(589\) −29.3578 + 50.8492i −1.20967 + 2.09521i
\(590\) 1.64218 0.0676076
\(591\) 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 \(0.736969\pi\)
\(594\) 3.08945 5.35109i 0.126762 0.219558i
\(595\) −5.00000 8.66025i −0.204980 0.355036i
\(596\) −2.41055 4.17519i −0.0987398 0.171022i
\(597\) −12.8211 −0.524732
\(598\) −6.64218 9.34090i −0.271619 0.381978i
\(599\) 28.8211 1.17760 0.588799 0.808280i \(-0.299601\pi\)
0.588799 + 0.808280i \(0.299601\pi\)
\(600\) −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 \(0.685221\pi\)
\(602\) 0.410546 0.711086i 0.0167326 0.0289817i
\(603\) −15.1789 −0.618133
\(604\) 7.26836 12.5892i 0.295745 0.512246i
\(605\) 27.1789 47.0753i 1.10498 1.91388i
\(606\) 16.3578 0.664491
\(607\) −16.7684 + 29.0437i −0.680607 + 1.17885i 0.294189 + 0.955747i \(0.404950\pi\)
−0.974796 + 0.223098i \(0.928383\pi\)
\(608\) 4.08945 + 7.08314i 0.165849 + 0.287259i
\(609\) −4.08945 7.08314i −0.165713 0.287023i
\(610\) 6.00000 0.242933
\(611\) −6.26836 + 13.7015i −0.253591 + 0.554302i
\(612\) 5.00000 0.202113
\(613\) −19.1789 33.2188i −0.774629 1.34170i −0.935003 0.354640i \(-0.884603\pi\)
0.160374 0.987056i \(-0.448730\pi\)
\(614\) −12.4473 21.5593i −0.502331 0.870063i
\(615\) −4.17891 + 7.23808i −0.168510 + 0.291868i
\(616\) −6.17891 −0.248955
\(617\) −16.0000 + 27.7128i −0.644136 + 1.11568i 0.340365 + 0.940294i \(0.389449\pi\)
−0.984500 + 0.175382i \(0.943884\pi\)
\(618\) 1.58945 2.75302i 0.0639372 0.110743i
\(619\) −8.53673 −0.343120 −0.171560 0.985174i \(-0.554881\pi\)
−0.171560 + 0.985174i \(0.554881\pi\)
\(620\) −7.17891 + 12.4342i −0.288312 + 0.499371i
\(621\) 1.58945 + 2.75302i 0.0637826 + 0.110475i
\(622\) 4.26836 + 7.39302i 0.171146 + 0.296433i
\(623\) −9.00000 −0.360577
\(624\) 2.08945 + 2.93840i 0.0836451 + 0.117630i
\(625\) −19.0000 −0.760000
\(626\) −2.00000 3.46410i −0.0799361 0.138453i
\(627\) −25.2684 43.7661i −1.00912 1.74785i
\(628\) −1.00000 + 1.73205i −0.0399043 + 0.0691164i
\(629\) 10.0000 0.398726
\(630\) −1.00000 + 1.73205i −0.0398410 + 0.0690066i
\(631\) 15.4473 26.7555i 0.614946 1.06512i −0.375448 0.926844i \(-0.622511\pi\)
0.990394 0.138274i \(-0.0441556\pi\)
\(632\) 1.82109 0.0724391
\(633\) 8.17891 14.1663i 0.325082 0.563059i
\(634\) −3.58945 6.21712i −0.142555 0.246913i
\(635\) 12.0000 + 20.7846i 0.476205 + 0.824812i
\(636\) 3.00000 0.118958
\(637\) 3.58945 0.340322i 0.142219 0.0134840i
\(638\) 50.5367 2.00077
\(639\) −4.58945 7.94917i −0.181556 0.314464i
\(640\) 1.00000 + 1.73205i 0.0395285 + 0.0684653i
\(641\) 20.5367 35.5707i 0.811152 1.40496i −0.100907 0.994896i \(-0.532174\pi\)
0.912058 0.410060i \(-0.134492\pi\)
\(642\) −7.82109 −0.308674
\(643\) 10.0895 17.4754i 0.397889 0.689164i −0.595576 0.803299i \(-0.703076\pi\)
0.993465 + 0.114135i \(0.0364095\pi\)
\(644\) 1.58945 2.75302i 0.0626333 0.108484i
\(645\) 1.64218 0.0646609
\(646\) 20.4473 35.4157i 0.804487 1.39341i
\(647\) 4.44727 + 7.70290i 0.174840 + 0.302832i 0.940106 0.340882i \(-0.110726\pi\)
−0.765266 + 0.643715i \(0.777392\pi\)
\(648\) −0.500000 0.866025i −0.0196419 0.0340207i
\(649\) −5.07345 −0.199150
\(650\) −3.58945 + 0.340322i −0.140790 + 0.0133485i
\(651\) −7.17891 −0.281364
\(652\) 4.41055 + 7.63929i 0.172730 + 0.299178i
\(653\) −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
\(655\) −39.0735 −1.52673
\(656\) −2.08945 + 3.61904i −0.0815795 + 0.141300i
\(657\) −2.00000 + 3.46410i −0.0780274 + 0.135147i
\(658\) −4.17891 −0.162911
\(659\) 8.26836 14.3212i 0.322090 0.557876i −0.658829 0.752292i \(-0.728948\pi\)
0.980919 + 0.194417i \(0.0622814\pi\)
\(660\) −6.17891 10.7022i −0.240514 0.416582i
\(661\) 8.76836 + 15.1872i 0.341050 + 0.590716i 0.984628 0.174665i \(-0.0558842\pi\)
−0.643578 + 0.765380i \(0.722551\pi\)
\(662\) −24.3578 −0.946693
\(663\) 7.50000 16.3936i 0.291276 0.636675i
\(664\) −5.17891 −0.200981
\(665\) 8.17891 + 14.1663i 0.317164 + 0.549345i
\(666\) −1.00000 1.73205i −0.0387492 0.0671156i
\(667\) −13.0000 + 22.5167i −0.503362 + 0.871849i
\(668\) −8.00000 −0.309529
\(669\) 4.58945 7.94917i 0.177439 0.307333i
\(670\) −15.1789 + 26.2906i −0.586412 + 1.01570i
\(671\) −18.5367 −0.715602
\(672\) −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 \(0.827198\pi\)
\(674\) 0.268363 + 0.464818i 0.0103369 + 0.0179041i
\(675\) 1.00000 0.0384900
\(676\) 12.7684 2.44314i 0.491091 0.0939668i
\(677\) 12.0000 0.461197 0.230599 0.973049i \(-0.425932\pi\)
0.230599 + 0.973049i \(0.425932\pi\)
\(678\) −2.17891 3.77398i −0.0836805 0.144939i
\(679\) 6.17891 + 10.7022i 0.237125 + 0.410712i
\(680\) 5.00000 8.66025i 0.191741 0.332106i
\(681\) −8.35782 −0.320272
\(682\) 22.1789 38.4150i 0.849274 1.47099i
\(683\) 7.17891 12.4342i 0.274693 0.475783i −0.695364 0.718657i \(-0.744757\pi\)
0.970058 + 0.242875i \(0.0780903\pi\)
\(684\) −8.17891 −0.312728
\(685\) −16.3578 + 28.3326i −0.625000 + 1.08253i
\(686\) 0.500000 + 0.866025i 0.0190901 + 0.0330650i
\(687\) 0.500000 + 0.866025i 0.0190762 + 0.0330409i
\(688\) 0.821092 0.0313038
\(689\) 4.50000 9.83616i 0.171436 0.374728i
\(690\) 6.35782 0.242038
\(691\) 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
\(693\) 3.08945 5.35109i 0.117359 0.203271i
\(694\) −7.82109 −0.296885
\(695\) −18.1789 + 31.4868i −0.689565 + 1.19436i
\(696\) 4.08945 7.08314i 0.155010 0.268486i
\(697\) 20.8945 0.791437
\(698\) 1.58945 2.75302i 0.0601617 0.104203i
\(699\) −0.178908 0.309878i −0.00676694 0.0117207i
\(700\) −0.500000 0.866025i −0.0188982 0.0327327i
\(701\) 23.7156 0.895727 0.447864 0.894102i \(-0.352185\pi\)
0.447864 + 0.894102i \(0.352185\pi\)
\(702\) −3.58945 + 0.340322i −0.135475 + 0.0128446i
\(703\) −16.3578 −0.616947
\(704\) −3.08945 5.35109i −0.116438 0.201677i
\(705\) −4.17891 7.23808i −0.157387 0.272602i
\(706\) 3.58945 6.21712i 0.135091 0.233984i
\(707\) 16.3578 0.615199
\(708\) −0.410546 + 0.711086i −0.0154293 + 0.0267243i
\(709\) 8.00000 13.8564i 0.300446 0.520388i −0.675791 0.737093i \(-0.736198\pi\)
0.976237 + 0.216705i \(0.0695310\pi\)
\(710\) −18.3578 −0.688957
\(711\) −0.910546 + 1.57711i −0.0341481 + 0.0591463i
\(712\) −4.50000 7.79423i −0.168645 0.292101i
\(713\) 11.4105 + 19.7636i 0.427328 + 0.740154i
\(714\) 5.00000 0.187120
\(715\) −44.3578 + 4.20563i −1.65889 + 0.157282i
\(716\) −14.3578 −0.536577
\(717\) −0.589454 1.02096i −0.0220136 0.0381286i
\(718\) −6.17891 10.7022i −0.230595 0.399402i
\(719\) 12.9105 22.3617i 0.481482 0.833951i −0.518292 0.855204i \(-0.673432\pi\)
0.999774 + 0.0212522i \(0.00676530\pi\)
\(720\) −2.00000 −0.0745356
\(721\) 1.58945 2.75302i 0.0591944 0.102528i
\(722\) −23.9473 + 41.4779i −0.891225 + 1.54365i
\(723\) 18.3578 0.682735
\(724\) −3.91055 + 6.77326i −0.145334 + 0.251726i
\(725\) 4.08945 + 7.08314i 0.151879 + 0.263061i
\(726\) 13.5895 + 23.5376i 0.504352 + 0.873563i
\(727\) 0.463275 0.0171819 0.00859096 0.999963i \(-0.497265\pi\)
0.00859096 + 0.999963i \(0.497265\pi\)
\(728\) 2.08945 + 2.93840i 0.0774403 + 0.108904i
\(729\) 1.00000 0.0370370
\(730\) 4.00000 + 6.92820i 0.148047 + 0.256424i
\(731\) −2.05273 3.55543i −0.0759229 0.131502i
\(732\) −1.50000 + 2.59808i −0.0554416 + 0.0960277i
\(733\) −25.7156 −0.949829 −0.474914 0.880032i \(-0.657521\pi\)
−0.474914 + 0.880032i \(0.657521\pi\)
\(734\) −1.58945 + 2.75302i −0.0586678 + 0.101616i
\(735\) −1.00000 + 1.73205i −0.0368856 + 0.0638877i
\(736\) 3.17891 0.117176
\(737\) 46.8945 81.2237i 1.72738 2.99191i
\(738\) −2.08945 3.61904i −0.0769139 0.133219i
\(739\) 2.41055 + 4.17519i 0.0886734 + 0.153587i 0.906951 0.421237i \(-0.138404\pi\)
−0.818277 + 0.574824i \(0.805071\pi\)
\(740\) −4.00000 −0.147043
\(741\) −12.2684 + 26.8163i −0.450690 + 0.985123i
\(742\) 3.00000 0.110133
\(743\) −21.5895 37.3940i −0.792040 1.37185i −0.924702 0.380693i \(-0.875686\pi\)
0.132661 0.991161i \(-0.457648\pi\)
\(744\) −3.58945 6.21712i −0.131596 0.227931i
\(745\) 4.82109 8.35038i 0.176631 0.305934i
\(746\) −20.0000 −0.732252
\(747\) 2.58945 4.48507i 0.0947432 0.164100i
\(748\) −15.4473 + 26.7555i −0.564808 + 0.978276i
\(749\) −7.82109 −0.285776
\(750\) 6.00000 10.3923i 0.219089 0.379473i
\(751\) −10.4473 18.0952i −0.381226 0.660303i 0.610012 0.792393i \(-0.291165\pi\)
−0.991238 + 0.132089i \(0.957831\pi\)
\(752\) −2.08945 3.61904i −0.0761946 0.131973i
\(753\) −10.8211 −0.394343
\(754\) −17.0895 24.0329i −0.622361 0.875226i
\(755\) 29.0735 1.05809
\(756\) −0.500000 0.866025i −0.0181848 0.0314970i
\(757\) −1.17891 2.04193i −0.0428482 0.0742152i 0.843806 0.536648i \(-0.180310\pi\)
−0.886654 + 0.462433i \(0.846977\pi\)
\(758\) −10.3578 + 17.9403i −0.376213 + 0.651620i
\(759\) −19.6422 −0.712966
\(760\) −8.17891 + 14.1663i −0.296680 + 0.513865i
\(761\) −23.7156 + 41.0767i −0.859691 + 1.48903i 0.0125327 + 0.999921i \(0.496011\pi\)
−0.872224 + 0.489107i \(0.837323\pi\)
\(762\) −12.0000 −0.434714
\(763\) 2.00000 3.46410i 0.0724049 0.125409i
\(764\) −13.7684 23.8475i −0.498122 0.862772i
\(765\) 5.00000 + 8.66025i 0.180775 + 0.313112i
\(766\) 9.82109 0.354850
\(767\) 1.71563 + 2.41269i 0.0619479 + 0.0871173i
\(768\) −1.00000 −0.0360844
\(769\) 2.17891 + 3.77398i 0.0785734 + 0.136093i 0.902635 0.430408i \(-0.141630\pi\)
−0.824061 + 0.566501i \(0.808297\pi\)
\(770\) −6.17891 10.7022i −0.222672 0.385680i
\(771\) 12.8578 22.2704i 0.463063 0.802049i
\(772\) 20.5367 0.739133
\(773\) 15.3578 26.6005i 0.552382 0.956754i −0.445720 0.895173i \(-0.647052\pi\)
0.998102 0.0615816i \(-0.0196144\pi\)
\(774\) −0.410546 + 0.711086i −0.0147568 + 0.0255595i
\(775\) 7.17891 0.257874
\(776\) −6.17891 + 10.7022i −0.221810 + 0.384186i
\(777\)