Properties

Label 490.2.e.g.361.1
Level $490$
Weight $2$
Character 490.361
Analytic conductor $3.913$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 490 = 2 \cdot 5 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 490.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.91266969904\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 70)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 490.361
Dual form 490.2.e.g.471.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 + 0.866025i) q^{2} +(-1.00000 + 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(0.500000 + 0.866025i) q^{5} -2.00000 q^{6} -1.00000 q^{8} +(-0.500000 - 0.866025i) q^{9} +(-0.500000 + 0.866025i) q^{10} +(-1.50000 + 2.59808i) q^{11} +(-1.00000 - 1.73205i) q^{12} +1.00000 q^{13} -2.00000 q^{15} +(-0.500000 - 0.866025i) q^{16} +(-3.00000 + 5.19615i) q^{17} +(0.500000 - 0.866025i) q^{18} +(-0.500000 - 0.866025i) q^{19} -1.00000 q^{20} -3.00000 q^{22} +(-4.50000 - 7.79423i) q^{23} +(1.00000 - 1.73205i) q^{24} +(-0.500000 + 0.866025i) q^{25} +(0.500000 + 0.866025i) q^{26} -4.00000 q^{27} +6.00000 q^{29} +(-1.00000 - 1.73205i) q^{30} +(4.00000 - 6.92820i) q^{31} +(0.500000 - 0.866025i) q^{32} +(-3.00000 - 5.19615i) q^{33} -6.00000 q^{34} +1.00000 q^{36} +(3.50000 + 6.06218i) q^{37} +(0.500000 - 0.866025i) q^{38} +(-1.00000 + 1.73205i) q^{39} +(-0.500000 - 0.866025i) q^{40} -3.00000 q^{41} +2.00000 q^{43} +(-1.50000 - 2.59808i) q^{44} +(0.500000 - 0.866025i) q^{45} +(4.50000 - 7.79423i) q^{46} +(4.50000 + 7.79423i) q^{47} +2.00000 q^{48} -1.00000 q^{50} +(-6.00000 - 10.3923i) q^{51} +(-0.500000 + 0.866025i) q^{52} +(-4.50000 + 7.79423i) q^{53} +(-2.00000 - 3.46410i) q^{54} -3.00000 q^{55} +2.00000 q^{57} +(3.00000 + 5.19615i) q^{58} +(1.00000 - 1.73205i) q^{60} +(4.00000 + 6.92820i) q^{61} +8.00000 q^{62} +1.00000 q^{64} +(0.500000 + 0.866025i) q^{65} +(3.00000 - 5.19615i) q^{66} +(-4.00000 + 6.92820i) q^{67} +(-3.00000 - 5.19615i) q^{68} +18.0000 q^{69} +(0.500000 + 0.866025i) q^{72} +(-2.00000 + 3.46410i) q^{73} +(-3.50000 + 6.06218i) q^{74} +(-1.00000 - 1.73205i) q^{75} +1.00000 q^{76} -2.00000 q^{78} +(5.00000 + 8.66025i) q^{79} +(0.500000 - 0.866025i) q^{80} +(5.50000 - 9.52628i) q^{81} +(-1.50000 - 2.59808i) q^{82} -6.00000 q^{85} +(1.00000 + 1.73205i) q^{86} +(-6.00000 + 10.3923i) q^{87} +(1.50000 - 2.59808i) q^{88} +(3.00000 + 5.19615i) q^{89} +1.00000 q^{90} +9.00000 q^{92} +(8.00000 + 13.8564i) q^{93} +(-4.50000 + 7.79423i) q^{94} +(0.500000 - 0.866025i) q^{95} +(1.00000 + 1.73205i) q^{96} +10.0000 q^{97} +3.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} - 2q^{3} - q^{4} + q^{5} - 4q^{6} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} - 2q^{3} - q^{4} + q^{5} - 4q^{6} - 2q^{8} - q^{9} - q^{10} - 3q^{11} - 2q^{12} + 2q^{13} - 4q^{15} - q^{16} - 6q^{17} + q^{18} - q^{19} - 2q^{20} - 6q^{22} - 9q^{23} + 2q^{24} - q^{25} + q^{26} - 8q^{27} + 12q^{29} - 2q^{30} + 8q^{31} + q^{32} - 6q^{33} - 12q^{34} + 2q^{36} + 7q^{37} + q^{38} - 2q^{39} - q^{40} - 6q^{41} + 4q^{43} - 3q^{44} + q^{45} + 9q^{46} + 9q^{47} + 4q^{48} - 2q^{50} - 12q^{51} - q^{52} - 9q^{53} - 4q^{54} - 6q^{55} + 4q^{57} + 6q^{58} + 2q^{60} + 8q^{61} + 16q^{62} + 2q^{64} + q^{65} + 6q^{66} - 8q^{67} - 6q^{68} + 36q^{69} + q^{72} - 4q^{73} - 7q^{74} - 2q^{75} + 2q^{76} - 4q^{78} + 10q^{79} + q^{80} + 11q^{81} - 3q^{82} - 12q^{85} + 2q^{86} - 12q^{87} + 3q^{88} + 6q^{89} + 2q^{90} + 18q^{92} + 16q^{93} - 9q^{94} + q^{95} + 2q^{96} + 20q^{97} + 6q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

\(n\) \(101\) \(197\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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
\(3\) −1.00000 + 1.73205i −0.577350 + 1.00000i 0.418432 + 0.908248i \(0.362580\pi\)
−0.995782 + 0.0917517i \(0.970753\pi\)
\(4\) −0.500000 + 0.866025i −0.250000 + 0.433013i
\(5\) 0.500000 + 0.866025i 0.223607 + 0.387298i
\(6\) −2.00000 −0.816497
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −0.500000 0.866025i −0.166667 0.288675i
\(10\) −0.500000 + 0.866025i −0.158114 + 0.273861i
\(11\) −1.50000 + 2.59808i −0.452267 + 0.783349i −0.998526 0.0542666i \(-0.982718\pi\)
0.546259 + 0.837616i \(0.316051\pi\)
\(12\) −1.00000 1.73205i −0.288675 0.500000i
\(13\) 1.00000 0.277350 0.138675 0.990338i \(-0.455716\pi\)
0.138675 + 0.990338i \(0.455716\pi\)
\(14\) 0 0
\(15\) −2.00000 −0.516398
\(16\) −0.500000 0.866025i −0.125000 0.216506i
\(17\) −3.00000 + 5.19615i −0.727607 + 1.26025i 0.230285 + 0.973123i \(0.426034\pi\)
−0.957892 + 0.287129i \(0.907299\pi\)
\(18\) 0.500000 0.866025i 0.117851 0.204124i
\(19\) −0.500000 0.866025i −0.114708 0.198680i 0.802955 0.596040i \(-0.203260\pi\)
−0.917663 + 0.397360i \(0.869927\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −3.00000 −0.639602
\(23\) −4.50000 7.79423i −0.938315 1.62521i −0.768613 0.639713i \(-0.779053\pi\)
−0.169701 0.985496i \(-0.554280\pi\)
\(24\) 1.00000 1.73205i 0.204124 0.353553i
\(25\) −0.500000 + 0.866025i −0.100000 + 0.173205i
\(26\) 0.500000 + 0.866025i 0.0980581 + 0.169842i
\(27\) −4.00000 −0.769800
\(28\) 0 0
\(29\) 6.00000 1.11417 0.557086 0.830455i \(-0.311919\pi\)
0.557086 + 0.830455i \(0.311919\pi\)
\(30\) −1.00000 1.73205i −0.182574 0.316228i
\(31\) 4.00000 6.92820i 0.718421 1.24434i −0.243204 0.969975i \(-0.578198\pi\)
0.961625 0.274367i \(-0.0884683\pi\)
\(32\) 0.500000 0.866025i 0.0883883 0.153093i
\(33\) −3.00000 5.19615i −0.522233 0.904534i
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) 3.50000 + 6.06218i 0.575396 + 0.996616i 0.995998 + 0.0893706i \(0.0284856\pi\)
−0.420602 + 0.907245i \(0.638181\pi\)
\(38\) 0.500000 0.866025i 0.0811107 0.140488i
\(39\) −1.00000 + 1.73205i −0.160128 + 0.277350i
\(40\) −0.500000 0.866025i −0.0790569 0.136931i
\(41\) −3.00000 −0.468521 −0.234261 0.972174i \(-0.575267\pi\)
−0.234261 + 0.972174i \(0.575267\pi\)
\(42\) 0 0
\(43\) 2.00000 0.304997 0.152499 0.988304i \(-0.451268\pi\)
0.152499 + 0.988304i \(0.451268\pi\)
\(44\) −1.50000 2.59808i −0.226134 0.391675i
\(45\) 0.500000 0.866025i 0.0745356 0.129099i
\(46\) 4.50000 7.79423i 0.663489 1.14920i
\(47\) 4.50000 + 7.79423i 0.656392 + 1.13691i 0.981543 + 0.191243i \(0.0612518\pi\)
−0.325150 + 0.945662i \(0.605415\pi\)
\(48\) 2.00000 0.288675
\(49\) 0 0
\(50\) −1.00000 −0.141421
\(51\) −6.00000 10.3923i −0.840168 1.45521i
\(52\) −0.500000 + 0.866025i −0.0693375 + 0.120096i
\(53\) −4.50000 + 7.79423i −0.618123 + 1.07062i 0.371706 + 0.928351i \(0.378773\pi\)
−0.989828 + 0.142269i \(0.954560\pi\)
\(54\) −2.00000 3.46410i −0.272166 0.471405i
\(55\) −3.00000 −0.404520
\(56\) 0 0
\(57\) 2.00000 0.264906
\(58\) 3.00000 + 5.19615i 0.393919 + 0.682288i
\(59\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(60\) 1.00000 1.73205i 0.129099 0.223607i
\(61\) 4.00000 + 6.92820i 0.512148 + 0.887066i 0.999901 + 0.0140840i \(0.00448323\pi\)
−0.487753 + 0.872982i \(0.662183\pi\)
\(62\) 8.00000 1.01600
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0.500000 + 0.866025i 0.0620174 + 0.107417i
\(66\) 3.00000 5.19615i 0.369274 0.639602i
\(67\) −4.00000 + 6.92820i −0.488678 + 0.846415i −0.999915 0.0130248i \(-0.995854\pi\)
0.511237 + 0.859440i \(0.329187\pi\)
\(68\) −3.00000 5.19615i −0.363803 0.630126i
\(69\) 18.0000 2.16695
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0.500000 + 0.866025i 0.0589256 + 0.102062i
\(73\) −2.00000 + 3.46410i −0.234082 + 0.405442i −0.959006 0.283387i \(-0.908542\pi\)
0.724923 + 0.688830i \(0.241875\pi\)
\(74\) −3.50000 + 6.06218i −0.406867 + 0.704714i
\(75\) −1.00000 1.73205i −0.115470 0.200000i
\(76\) 1.00000 0.114708
\(77\) 0 0
\(78\) −2.00000 −0.226455
\(79\) 5.00000 + 8.66025i 0.562544 + 0.974355i 0.997274 + 0.0737937i \(0.0235106\pi\)
−0.434730 + 0.900561i \(0.643156\pi\)
\(80\) 0.500000 0.866025i 0.0559017 0.0968246i
\(81\) 5.50000 9.52628i 0.611111 1.05848i
\(82\) −1.50000 2.59808i −0.165647 0.286910i
\(83\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(84\) 0 0
\(85\) −6.00000 −0.650791
\(86\) 1.00000 + 1.73205i 0.107833 + 0.186772i
\(87\) −6.00000 + 10.3923i −0.643268 + 1.11417i
\(88\) 1.50000 2.59808i 0.159901 0.276956i
\(89\) 3.00000 + 5.19615i 0.317999 + 0.550791i 0.980071 0.198650i \(-0.0636557\pi\)
−0.662071 + 0.749441i \(0.730322\pi\)
\(90\) 1.00000 0.105409
\(91\) 0 0
\(92\) 9.00000 0.938315
\(93\) 8.00000 + 13.8564i 0.829561 + 1.43684i
\(94\) −4.50000 + 7.79423i −0.464140 + 0.803913i
\(95\) 0.500000 0.866025i 0.0512989 0.0888523i
\(96\) 1.00000 + 1.73205i 0.102062 + 0.176777i
\(97\) 10.0000 1.01535 0.507673 0.861550i \(-0.330506\pi\)
0.507673 + 0.861550i \(0.330506\pi\)
\(98\) 0 0
\(99\) 3.00000 0.301511
\(100\) −0.500000 0.866025i −0.0500000 0.0866025i
\(101\) 6.00000 10.3923i 0.597022 1.03407i −0.396236 0.918149i \(-0.629684\pi\)
0.993258 0.115924i \(-0.0369830\pi\)
\(102\) 6.00000 10.3923i 0.594089 1.02899i
\(103\) −2.00000 3.46410i −0.197066 0.341328i 0.750510 0.660859i \(-0.229808\pi\)
−0.947576 + 0.319531i \(0.896475\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) 6.00000 + 10.3923i 0.580042 + 1.00466i 0.995474 + 0.0950377i \(0.0302972\pi\)
−0.415432 + 0.909624i \(0.636370\pi\)
\(108\) 2.00000 3.46410i 0.192450 0.333333i
\(109\) 8.00000 13.8564i 0.766261 1.32720i −0.173316 0.984866i \(-0.555448\pi\)
0.939577 0.342337i \(-0.111218\pi\)
\(110\) −1.50000 2.59808i −0.143019 0.247717i
\(111\) −14.0000 −1.32882
\(112\) 0 0
\(113\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(114\) 1.00000 + 1.73205i 0.0936586 + 0.162221i
\(115\) 4.50000 7.79423i 0.419627 0.726816i
\(116\) −3.00000 + 5.19615i −0.278543 + 0.482451i
\(117\) −0.500000 0.866025i −0.0462250 0.0800641i
\(118\) 0 0
\(119\) 0 0
\(120\) 2.00000 0.182574
\(121\) 1.00000 + 1.73205i 0.0909091 + 0.157459i
\(122\) −4.00000 + 6.92820i −0.362143 + 0.627250i
\(123\) 3.00000 5.19615i 0.270501 0.468521i
\(124\) 4.00000 + 6.92820i 0.359211 + 0.622171i
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −1.00000 −0.0887357 −0.0443678 0.999015i \(-0.514127\pi\)
−0.0443678 + 0.999015i \(0.514127\pi\)
\(128\) 0.500000 + 0.866025i 0.0441942 + 0.0765466i
\(129\) −2.00000 + 3.46410i −0.176090 + 0.304997i
\(130\) −0.500000 + 0.866025i −0.0438529 + 0.0759555i
\(131\) 1.50000 + 2.59808i 0.131056 + 0.226995i 0.924084 0.382190i \(-0.124830\pi\)
−0.793028 + 0.609185i \(0.791497\pi\)
\(132\) 6.00000 0.522233
\(133\) 0 0
\(134\) −8.00000 −0.691095
\(135\) −2.00000 3.46410i −0.172133 0.298142i
\(136\) 3.00000 5.19615i 0.257248 0.445566i
\(137\) −6.00000 + 10.3923i −0.512615 + 0.887875i 0.487278 + 0.873247i \(0.337990\pi\)
−0.999893 + 0.0146279i \(0.995344\pi\)
\(138\) 9.00000 + 15.5885i 0.766131 + 1.32698i
\(139\) 4.00000 0.339276 0.169638 0.985506i \(-0.445740\pi\)
0.169638 + 0.985506i \(0.445740\pi\)
\(140\) 0 0
\(141\) −18.0000 −1.51587
\(142\) 0 0
\(143\) −1.50000 + 2.59808i −0.125436 + 0.217262i
\(144\) −0.500000 + 0.866025i −0.0416667 + 0.0721688i
\(145\) 3.00000 + 5.19615i 0.249136 + 0.431517i
\(146\) −4.00000 −0.331042
\(147\) 0 0
\(148\) −7.00000 −0.575396
\(149\) 3.00000 + 5.19615i 0.245770 + 0.425685i 0.962348 0.271821i \(-0.0876260\pi\)
−0.716578 + 0.697507i \(0.754293\pi\)
\(150\) 1.00000 1.73205i 0.0816497 0.141421i
\(151\) 5.00000 8.66025i 0.406894 0.704761i −0.587646 0.809118i \(-0.699945\pi\)
0.994540 + 0.104357i \(0.0332784\pi\)
\(152\) 0.500000 + 0.866025i 0.0405554 + 0.0702439i
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 8.00000 0.642575
\(156\) −1.00000 1.73205i −0.0800641 0.138675i
\(157\) 11.5000 19.9186i 0.917800 1.58968i 0.115050 0.993360i \(-0.463297\pi\)
0.802749 0.596316i \(-0.203370\pi\)
\(158\) −5.00000 + 8.66025i −0.397779 + 0.688973i
\(159\) −9.00000 15.5885i −0.713746 1.23625i
\(160\) 1.00000 0.0790569
\(161\) 0 0
\(162\) 11.0000 0.864242
\(163\) −10.0000 17.3205i −0.783260 1.35665i −0.930033 0.367477i \(-0.880222\pi\)
0.146772 0.989170i \(-0.453112\pi\)
\(164\) 1.50000 2.59808i 0.117130 0.202876i
\(165\) 3.00000 5.19615i 0.233550 0.404520i
\(166\) 0 0
\(167\) −3.00000 −0.232147 −0.116073 0.993241i \(-0.537031\pi\)
−0.116073 + 0.993241i \(0.537031\pi\)
\(168\) 0 0
\(169\) −12.0000 −0.923077
\(170\) −3.00000 5.19615i −0.230089 0.398527i
\(171\) −0.500000 + 0.866025i −0.0382360 + 0.0662266i
\(172\) −1.00000 + 1.73205i −0.0762493 + 0.132068i
\(173\) 4.50000 + 7.79423i 0.342129 + 0.592584i 0.984828 0.173534i \(-0.0555188\pi\)
−0.642699 + 0.766119i \(0.722185\pi\)
\(174\) −12.0000 −0.909718
\(175\) 0 0
\(176\) 3.00000 0.226134
\(177\) 0 0
\(178\) −3.00000 + 5.19615i −0.224860 + 0.389468i
\(179\) 1.50000 2.59808i 0.112115 0.194189i −0.804508 0.593942i \(-0.797571\pi\)
0.916623 + 0.399753i \(0.130904\pi\)
\(180\) 0.500000 + 0.866025i 0.0372678 + 0.0645497i
\(181\) −2.00000 −0.148659 −0.0743294 0.997234i \(-0.523682\pi\)
−0.0743294 + 0.997234i \(0.523682\pi\)
\(182\) 0 0
\(183\) −16.0000 −1.18275
\(184\) 4.50000 + 7.79423i 0.331744 + 0.574598i
\(185\) −3.50000 + 6.06218i −0.257325 + 0.445700i
\(186\) −8.00000 + 13.8564i −0.586588 + 1.01600i
\(187\) −9.00000 15.5885i −0.658145 1.13994i
\(188\) −9.00000 −0.656392
\(189\) 0 0
\(190\) 1.00000 0.0725476
\(191\) −6.00000 10.3923i −0.434145 0.751961i 0.563081 0.826402i \(-0.309616\pi\)
−0.997225 + 0.0744412i \(0.976283\pi\)
\(192\) −1.00000 + 1.73205i −0.0721688 + 0.125000i
\(193\) 8.00000 13.8564i 0.575853 0.997406i −0.420096 0.907480i \(-0.638004\pi\)
0.995948 0.0899262i \(-0.0286631\pi\)
\(194\) 5.00000 + 8.66025i 0.358979 + 0.621770i
\(195\) −2.00000 −0.143223
\(196\) 0 0
\(197\) 15.0000 1.06871 0.534353 0.845262i \(-0.320555\pi\)
0.534353 + 0.845262i \(0.320555\pi\)
\(198\) 1.50000 + 2.59808i 0.106600 + 0.184637i
\(199\) −8.00000 + 13.8564i −0.567105 + 0.982255i 0.429745 + 0.902950i \(0.358603\pi\)
−0.996850 + 0.0793045i \(0.974730\pi\)
\(200\) 0.500000 0.866025i 0.0353553 0.0612372i
\(201\) −8.00000 13.8564i −0.564276 0.977356i
\(202\) 12.0000 0.844317
\(203\) 0 0
\(204\) 12.0000 0.840168
\(205\) −1.50000 2.59808i −0.104765 0.181458i
\(206\) 2.00000 3.46410i 0.139347 0.241355i
\(207\) −4.50000 + 7.79423i −0.312772 + 0.541736i
\(208\) −0.500000 0.866025i −0.0346688 0.0600481i
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) 23.0000 1.58339 0.791693 0.610920i \(-0.209200\pi\)
0.791693 + 0.610920i \(0.209200\pi\)
\(212\) −4.50000 7.79423i −0.309061 0.535310i
\(213\) 0 0
\(214\) −6.00000 + 10.3923i −0.410152 + 0.710403i
\(215\) 1.00000 + 1.73205i 0.0681994 + 0.118125i
\(216\) 4.00000 0.272166
\(217\) 0 0
\(218\) 16.0000 1.08366
\(219\) −4.00000 6.92820i −0.270295 0.468165i
\(220\) 1.50000 2.59808i 0.101130 0.175162i
\(221\) −3.00000 + 5.19615i −0.201802 + 0.349531i
\(222\) −7.00000 12.1244i −0.469809 0.813733i
\(223\) −8.00000 −0.535720 −0.267860 0.963458i \(-0.586316\pi\)
−0.267860 + 0.963458i \(0.586316\pi\)
\(224\) 0 0
\(225\) 1.00000 0.0666667
\(226\) 0 0
\(227\) −6.00000 + 10.3923i −0.398234 + 0.689761i −0.993508 0.113761i \(-0.963710\pi\)
0.595274 + 0.803523i \(0.297043\pi\)
\(228\) −1.00000 + 1.73205i −0.0662266 + 0.114708i
\(229\) −2.00000 3.46410i −0.132164 0.228914i 0.792347 0.610071i \(-0.208859\pi\)
−0.924510 + 0.381157i \(0.875526\pi\)
\(230\) 9.00000 0.593442
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 3.00000 + 5.19615i 0.196537 + 0.340411i 0.947403 0.320043i \(-0.103697\pi\)
−0.750867 + 0.660454i \(0.770364\pi\)
\(234\) 0.500000 0.866025i 0.0326860 0.0566139i
\(235\) −4.50000 + 7.79423i −0.293548 + 0.508439i
\(236\) 0 0
\(237\) −20.0000 −1.29914
\(238\) 0 0
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) 1.00000 + 1.73205i 0.0645497 + 0.111803i
\(241\) −0.500000 + 0.866025i −0.0322078 + 0.0557856i −0.881680 0.471848i \(-0.843587\pi\)
0.849472 + 0.527633i \(0.176921\pi\)
\(242\) −1.00000 + 1.73205i −0.0642824 + 0.111340i
\(243\) 5.00000 + 8.66025i 0.320750 + 0.555556i
\(244\) −8.00000 −0.512148
\(245\) 0 0
\(246\) 6.00000 0.382546
\(247\) −0.500000 0.866025i −0.0318142 0.0551039i
\(248\) −4.00000 + 6.92820i −0.254000 + 0.439941i
\(249\) 0 0
\(250\) −0.500000 0.866025i −0.0316228 0.0547723i
\(251\) 15.0000 0.946792 0.473396 0.880850i \(-0.343028\pi\)
0.473396 + 0.880850i \(0.343028\pi\)
\(252\) 0 0
\(253\) 27.0000 1.69748
\(254\) −0.500000 0.866025i −0.0313728 0.0543393i
\(255\) 6.00000 10.3923i 0.375735 0.650791i
\(256\) −0.500000 + 0.866025i −0.0312500 + 0.0541266i
\(257\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(258\) −4.00000 −0.249029
\(259\) 0 0
\(260\) −1.00000 −0.0620174
\(261\) −3.00000 5.19615i −0.185695 0.321634i
\(262\) −1.50000 + 2.59808i −0.0926703 + 0.160510i
\(263\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(264\) 3.00000 + 5.19615i 0.184637 + 0.319801i
\(265\) −9.00000 −0.552866
\(266\) 0 0
\(267\) −12.0000 −0.734388
\(268\) −4.00000 6.92820i −0.244339 0.423207i
\(269\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(270\) 2.00000 3.46410i 0.121716 0.210819i
\(271\) −8.00000 13.8564i −0.485965 0.841717i 0.513905 0.857847i \(-0.328199\pi\)
−0.999870 + 0.0161307i \(0.994865\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) −12.0000 −0.724947
\(275\) −1.50000 2.59808i −0.0904534 0.156670i
\(276\) −9.00000 + 15.5885i −0.541736 + 0.938315i
\(277\) 5.00000 8.66025i 0.300421 0.520344i −0.675810 0.737075i \(-0.736206\pi\)
0.976231 + 0.216731i \(0.0695395\pi\)
\(278\) 2.00000 + 3.46410i 0.119952 + 0.207763i
\(279\) −8.00000 −0.478947
\(280\) 0 0
\(281\) −27.0000 −1.61068 −0.805342 0.592810i \(-0.798019\pi\)
−0.805342 + 0.592810i \(0.798019\pi\)
\(282\) −9.00000 15.5885i −0.535942 0.928279i
\(283\) 7.00000 12.1244i 0.416107 0.720718i −0.579437 0.815017i \(-0.696728\pi\)
0.995544 + 0.0942988i \(0.0300609\pi\)
\(284\) 0 0
\(285\) 1.00000 + 1.73205i 0.0592349 + 0.102598i
\(286\) −3.00000 −0.177394
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −9.50000 16.4545i −0.558824 0.967911i
\(290\) −3.00000 + 5.19615i −0.176166 + 0.305129i
\(291\) −10.0000 + 17.3205i −0.586210 + 1.01535i
\(292\) −2.00000 3.46410i −0.117041 0.202721i
\(293\) 9.00000 0.525786 0.262893 0.964825i \(-0.415323\pi\)
0.262893 + 0.964825i \(0.415323\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −3.50000 6.06218i −0.203433 0.352357i
\(297\) 6.00000 10.3923i 0.348155 0.603023i
\(298\) −3.00000 + 5.19615i −0.173785 + 0.301005i
\(299\) −4.50000 7.79423i −0.260242 0.450752i
\(300\) 2.00000 0.115470
\(301\) 0 0
\(302\) 10.0000 0.575435
\(303\) 12.0000 + 20.7846i 0.689382 + 1.19404i
\(304\) −0.500000 + 0.866025i −0.0286770 + 0.0496700i
\(305\) −4.00000 + 6.92820i −0.229039 + 0.396708i
\(306\) 3.00000 + 5.19615i 0.171499 + 0.297044i
\(307\) −14.0000 −0.799022 −0.399511 0.916728i \(-0.630820\pi\)
−0.399511 + 0.916728i \(0.630820\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 4.00000 + 6.92820i 0.227185 + 0.393496i
\(311\) −12.0000 + 20.7846i −0.680458 + 1.17859i 0.294384 + 0.955687i \(0.404886\pi\)
−0.974841 + 0.222900i \(0.928448\pi\)
\(312\) 1.00000 1.73205i 0.0566139 0.0980581i
\(313\) −14.0000 24.2487i −0.791327 1.37062i −0.925146 0.379612i \(-0.876057\pi\)
0.133819 0.991006i \(-0.457276\pi\)
\(314\) 23.0000 1.29797
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −3.00000 5.19615i −0.168497 0.291845i 0.769395 0.638774i \(-0.220558\pi\)
−0.937892 + 0.346929i \(0.887225\pi\)
\(318\) 9.00000 15.5885i 0.504695 0.874157i
\(319\) −9.00000 + 15.5885i −0.503903 + 0.872786i
\(320\) 0.500000 + 0.866025i 0.0279508 + 0.0484123i
\(321\) −24.0000 −1.33955
\(322\) 0 0
\(323\) 6.00000 0.333849
\(324\) 5.50000 + 9.52628i 0.305556 + 0.529238i
\(325\) −0.500000 + 0.866025i −0.0277350 + 0.0480384i
\(326\) 10.0000 17.3205i 0.553849 0.959294i
\(327\) 16.0000 + 27.7128i 0.884802 + 1.53252i
\(328\) 3.00000 0.165647
\(329\) 0 0
\(330\) 6.00000 0.330289
\(331\) 3.50000 + 6.06218i 0.192377 + 0.333207i 0.946038 0.324057i \(-0.105047\pi\)
−0.753660 + 0.657264i \(0.771714\pi\)
\(332\) 0 0
\(333\) 3.50000 6.06218i 0.191799 0.332205i
\(334\) −1.50000 2.59808i −0.0820763 0.142160i
\(335\) −8.00000 −0.437087
\(336\) 0 0
\(337\) −22.0000 −1.19842 −0.599208 0.800593i \(-0.704518\pi\)
−0.599208 + 0.800593i \(0.704518\pi\)
\(338\) −6.00000 10.3923i −0.326357 0.565267i
\(339\) 0 0
\(340\) 3.00000 5.19615i 0.162698 0.281801i
\(341\) 12.0000 + 20.7846i 0.649836 + 1.12555i
\(342\) −1.00000 −0.0540738
\(343\) 0 0
\(344\) −2.00000 −0.107833
\(345\) 9.00000 + 15.5885i 0.484544 + 0.839254i
\(346\) −4.50000 + 7.79423i −0.241921 + 0.419020i
\(347\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(348\) −6.00000 10.3923i −0.321634 0.557086i
\(349\) −26.0000 −1.39175 −0.695874 0.718164i \(-0.744983\pi\)
−0.695874 + 0.718164i \(0.744983\pi\)
\(350\) 0 0
\(351\) −4.00000 −0.213504
\(352\) 1.50000 + 2.59808i 0.0799503 + 0.138478i
\(353\) 6.00000 10.3923i 0.319348 0.553127i −0.661004 0.750382i \(-0.729870\pi\)
0.980352 + 0.197256i \(0.0632029\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 3.00000 0.158555
\(359\) −9.00000 15.5885i −0.475002 0.822727i 0.524588 0.851356i \(-0.324219\pi\)
−0.999590 + 0.0286287i \(0.990886\pi\)
\(360\) −0.500000 + 0.866025i −0.0263523 + 0.0456435i
\(361\) 9.00000 15.5885i 0.473684 0.820445i
\(362\) −1.00000 1.73205i −0.0525588 0.0910346i
\(363\) −4.00000 −0.209946
\(364\) 0 0
\(365\) −4.00000 −0.209370
\(366\) −8.00000 13.8564i −0.418167 0.724286i
\(367\) −9.50000 + 16.4545i −0.495896 + 0.858917i −0.999989 0.00473247i \(-0.998494\pi\)
0.504093 + 0.863649i \(0.331827\pi\)
\(368\) −4.50000 + 7.79423i −0.234579 + 0.406302i
\(369\) 1.50000 + 2.59808i 0.0780869 + 0.135250i
\(370\) −7.00000 −0.363913
\(371\) 0 0
\(372\) −16.0000 −0.829561
\(373\) −1.00000 1.73205i −0.0517780 0.0896822i 0.838975 0.544170i \(-0.183156\pi\)
−0.890753 + 0.454488i \(0.849822\pi\)
\(374\) 9.00000 15.5885i 0.465379 0.806060i
\(375\) 1.00000 1.73205i 0.0516398 0.0894427i
\(376\) −4.50000 7.79423i −0.232070 0.401957i
\(377\) 6.00000 0.309016
\(378\) 0 0
\(379\) 23.0000 1.18143 0.590715 0.806880i \(-0.298846\pi\)
0.590715 + 0.806880i \(0.298846\pi\)
\(380\) 0.500000 + 0.866025i 0.0256495 + 0.0444262i
\(381\) 1.00000 1.73205i 0.0512316 0.0887357i
\(382\) 6.00000 10.3923i 0.306987 0.531717i
\(383\) 10.5000 + 18.1865i 0.536525 + 0.929288i 0.999088 + 0.0427020i \(0.0135966\pi\)
−0.462563 + 0.886586i \(0.653070\pi\)
\(384\) −2.00000 −0.102062
\(385\) 0 0
\(386\) 16.0000 0.814379
\(387\) −1.00000 1.73205i −0.0508329 0.0880451i
\(388\) −5.00000 + 8.66025i −0.253837 + 0.439658i
\(389\) 6.00000 10.3923i 0.304212 0.526911i −0.672874 0.739758i \(-0.734940\pi\)
0.977086 + 0.212847i \(0.0682735\pi\)
\(390\) −1.00000 1.73205i −0.0506370 0.0877058i
\(391\) 54.0000 2.73090
\(392\) 0 0
\(393\) −6.00000 −0.302660
\(394\) 7.50000 + 12.9904i 0.377845 + 0.654446i
\(395\) −5.00000 + 8.66025i −0.251577 + 0.435745i
\(396\) −1.50000 + 2.59808i −0.0753778 + 0.130558i
\(397\) 7.00000 + 12.1244i 0.351320 + 0.608504i 0.986481 0.163876i \(-0.0523996\pi\)
−0.635161 + 0.772380i \(0.719066\pi\)
\(398\) −16.0000 −0.802008
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 13.5000 + 23.3827i 0.674158 + 1.16768i 0.976714 + 0.214544i \(0.0688266\pi\)
−0.302556 + 0.953131i \(0.597840\pi\)
\(402\) 8.00000 13.8564i 0.399004 0.691095i
\(403\) 4.00000 6.92820i 0.199254 0.345118i
\(404\) 6.00000 + 10.3923i 0.298511 + 0.517036i
\(405\) 11.0000 0.546594
\(406\) 0 0
\(407\) −21.0000 −1.04093
\(408\) 6.00000 + 10.3923i 0.297044 + 0.514496i
\(409\) 13.0000 22.5167i 0.642809 1.11338i −0.341994 0.939702i \(-0.611102\pi\)
0.984803 0.173675i \(-0.0555643\pi\)
\(410\) 1.50000 2.59808i 0.0740797 0.128310i
\(411\) −12.0000 20.7846i −0.591916 1.02523i
\(412\) 4.00000 0.197066
\(413\) 0 0
\(414\) −9.00000 −0.442326
\(415\) 0 0
\(416\) 0.500000 0.866025i 0.0245145 0.0424604i
\(417\) −4.00000 + 6.92820i −0.195881 + 0.339276i
\(418\) 1.50000 + 2.59808i 0.0733674 + 0.127076i
\(419\) 9.00000 0.439679 0.219839 0.975536i \(-0.429447\pi\)
0.219839 + 0.975536i \(0.429447\pi\)
\(420\) 0 0
\(421\) 2.00000 0.0974740 0.0487370 0.998812i \(-0.484480\pi\)
0.0487370 + 0.998812i \(0.484480\pi\)
\(422\) 11.5000 + 19.9186i 0.559811 + 0.969622i
\(423\) 4.50000 7.79423i 0.218797 0.378968i
\(424\) 4.50000 7.79423i 0.218539 0.378521i
\(425\) −3.00000 5.19615i −0.145521 0.252050i
\(426\) 0 0
\(427\) 0 0
\(428\) −12.0000 −0.580042
\(429\) −3.00000 5.19615i −0.144841 0.250873i
\(430\) −1.00000 + 1.73205i −0.0482243 + 0.0835269i
\(431\) −6.00000 + 10.3923i −0.289010 + 0.500580i −0.973574 0.228373i \(-0.926659\pi\)
0.684564 + 0.728953i \(0.259993\pi\)
\(432\) 2.00000 + 3.46410i 0.0962250 + 0.166667i
\(433\) 40.0000 1.92228 0.961139 0.276066i \(-0.0890309\pi\)
0.961139 + 0.276066i \(0.0890309\pi\)
\(434\) 0 0
\(435\) −12.0000 −0.575356
\(436\) 8.00000 + 13.8564i 0.383131 + 0.663602i
\(437\) −4.50000 + 7.79423i −0.215264 + 0.372849i
\(438\) 4.00000 6.92820i 0.191127 0.331042i
\(439\) 13.0000 + 22.5167i 0.620456 + 1.07466i 0.989401 + 0.145210i \(0.0463858\pi\)
−0.368945 + 0.929451i \(0.620281\pi\)
\(440\) 3.00000 0.143019
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) −6.00000 10.3923i −0.285069 0.493753i 0.687557 0.726130i \(-0.258683\pi\)
−0.972626 + 0.232377i \(0.925350\pi\)
\(444\) 7.00000 12.1244i 0.332205 0.575396i
\(445\) −3.00000 + 5.19615i −0.142214 + 0.246321i
\(446\) −4.00000 6.92820i −0.189405 0.328060i
\(447\) −12.0000 −0.567581
\(448\) 0 0
\(449\) 21.0000 0.991051 0.495526 0.868593i \(-0.334975\pi\)
0.495526 + 0.868593i \(0.334975\pi\)
\(450\) 0.500000 + 0.866025i 0.0235702 + 0.0408248i
\(451\) 4.50000 7.79423i 0.211897 0.367016i
\(452\) 0 0
\(453\) 10.0000 + 17.3205i 0.469841 + 0.813788i
\(454\) −12.0000 −0.563188
\(455\) 0 0
\(456\) −2.00000 −0.0936586
\(457\) −7.00000 12.1244i −0.327446 0.567153i 0.654558 0.756012i \(-0.272855\pi\)
−0.982004 + 0.188858i \(0.939521\pi\)
\(458\) 2.00000 3.46410i 0.0934539 0.161867i
\(459\) 12.0000 20.7846i 0.560112 0.970143i
\(460\) 4.50000 + 7.79423i 0.209814 + 0.363408i
\(461\) 30.0000 1.39724 0.698620 0.715493i \(-0.253798\pi\)
0.698620 + 0.715493i \(0.253798\pi\)
\(462\) 0 0
\(463\) −1.00000 −0.0464739 −0.0232370 0.999730i \(-0.507397\pi\)
−0.0232370 + 0.999730i \(0.507397\pi\)
\(464\) −3.00000 5.19615i −0.139272 0.241225i
\(465\) −8.00000 + 13.8564i −0.370991 + 0.642575i
\(466\) −3.00000 + 5.19615i −0.138972 + 0.240707i
\(467\) −3.00000 5.19615i −0.138823 0.240449i 0.788228 0.615383i \(-0.210999\pi\)
−0.927052 + 0.374934i \(0.877665\pi\)
\(468\) 1.00000 0.0462250
\(469\) 0 0
\(470\) −9.00000 −0.415139
\(471\) 23.0000 + 39.8372i 1.05978 + 1.83560i
\(472\) 0 0
\(473\) −3.00000 + 5.19615i −0.137940 + 0.238919i
\(474\) −10.0000 17.3205i −0.459315 0.795557i
\(475\) 1.00000 0.0458831
\(476\) 0 0
\(477\) 9.00000 0.412082
\(478\) −3.00000 5.19615i −0.137217 0.237666i
\(479\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(480\) −1.00000 + 1.73205i −0.0456435 + 0.0790569i
\(481\) 3.50000 + 6.06218i 0.159586 + 0.276412i
\(482\) −1.00000 −0.0455488
\(483\) 0 0
\(484\) −2.00000 −0.0909091
\(485\) 5.00000 + 8.66025i 0.227038 + 0.393242i
\(486\) −5.00000 + 8.66025i −0.226805 + 0.392837i
\(487\) 8.00000 13.8564i 0.362515 0.627894i −0.625859 0.779936i \(-0.715252\pi\)
0.988374 + 0.152042i \(0.0485850\pi\)
\(488\) −4.00000 6.92820i −0.181071 0.313625i
\(489\) 40.0000 1.80886
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 3.00000 + 5.19615i 0.135250 + 0.234261i
\(493\) −18.0000 + 31.1769i −0.810679 + 1.40414i
\(494\) 0.500000 0.866025i 0.0224961 0.0389643i
\(495\) 1.50000 + 2.59808i 0.0674200 + 0.116775i
\(496\) −8.00000 −0.359211
\(497\) 0 0
\(498\) 0 0
\(499\) 2.00000 + 3.46410i 0.0895323 + 0.155074i 0.907314 0.420455i \(-0.138129\pi\)
−0.817781 + 0.575529i \(0.804796\pi\)
\(500\) 0.500000 0.866025i 0.0223607 0.0387298i
\(501\) 3.00000 5.19615i 0.134030 0.232147i
\(502\) 7.50000 + 12.9904i 0.334741 + 0.579789i
\(503\) −24.0000 −1.07011 −0.535054 0.844818i \(-0.679709\pi\)
−0.535054 + 0.844818i \(0.679709\pi\)
\(504\) 0 0
\(505\) 12.0000 0.533993
\(506\) 13.5000 + 23.3827i 0.600148 + 1.03949i
\(507\) 12.0000 20.7846i 0.532939 0.923077i
\(508\) 0.500000 0.866025i 0.0221839 0.0384237i
\(509\) −21.0000 36.3731i −0.930809 1.61221i −0.781943 0.623350i \(-0.785771\pi\)
−0.148866 0.988857i \(-0.547562\pi\)
\(510\) 12.0000 0.531369
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) 2.00000 + 3.46410i 0.0883022 + 0.152944i
\(514\) 0 0
\(515\) 2.00000 3.46410i 0.0881305 0.152647i
\(516\) −2.00000 3.46410i −0.0880451 0.152499i
\(517\) −27.0000 −1.18746
\(518\) 0 0
\(519\) −18.0000 −0.790112
\(520\) −0.500000 0.866025i −0.0219265 0.0379777i
\(521\) −7.50000 + 12.9904i −0.328581 + 0.569119i −0.982231 0.187678i \(-0.939904\pi\)
0.653650 + 0.756797i \(0.273237\pi\)
\(522\) 3.00000 5.19615i 0.131306 0.227429i
\(523\) −14.0000 24.2487i −0.612177 1.06032i −0.990873 0.134801i \(-0.956961\pi\)
0.378695 0.925521i \(-0.376373\pi\)
\(524\) −3.00000 −0.131056
\(525\) 0 0
\(526\) 0 0
\(527\) 24.0000 + 41.5692i 1.04546 + 1.81078i
\(528\) −3.00000 + 5.19615i −0.130558 + 0.226134i
\(529\) −29.0000 + 50.2295i −1.26087 + 2.18389i
\(530\) −4.50000 7.79423i −0.195468 0.338560i
\(531\) 0 0
\(532\) 0 0
\(533\) −3.00000 −0.129944
\(534\) −6.00000 10.3923i −0.259645 0.449719i
\(535\) −6.00000 + 10.3923i −0.259403 + 0.449299i
\(536\) 4.00000 6.92820i 0.172774 0.299253i
\(537\) 3.00000 + 5.19615i 0.129460 + 0.224231i
\(538\) 0 0
\(539\) 0 0
\(540\) 4.00000 0.172133
\(541\) −4.00000 6.92820i −0.171973 0.297867i 0.767136 0.641484i \(-0.221681\pi\)
−0.939110 + 0.343617i \(0.888348\pi\)
\(542\) 8.00000 13.8564i 0.343629 0.595184i
\(543\) 2.00000 3.46410i 0.0858282 0.148659i
\(544\) 3.00000 + 5.19615i 0.128624 + 0.222783i
\(545\) 16.0000 0.685365
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −6.00000 10.3923i −0.256307 0.443937i
\(549\) 4.00000 6.92820i 0.170716 0.295689i
\(550\) 1.50000 2.59808i 0.0639602 0.110782i
\(551\) −3.00000 5.19615i −0.127804 0.221364i
\(552\) −18.0000 −0.766131
\(553\) 0 0
\(554\) 10.0000 0.424859
\(555\) −7.00000 12.1244i −0.297133 0.514650i
\(556\) −2.00000 + 3.46410i −0.0848189 + 0.146911i
\(557\) 4.50000 7.79423i 0.190671 0.330252i −0.754802 0.655953i \(-0.772267\pi\)
0.945473 + 0.325701i \(0.105600\pi\)
\(558\) −4.00000 6.92820i −0.169334 0.293294i
\(559\) 2.00000 0.0845910
\(560\) 0 0
\(561\) 36.0000 1.51992
\(562\) −13.5000 23.3827i −0.569463 0.986339i
\(563\) 21.0000 36.3731i 0.885044 1.53294i 0.0393818 0.999224i \(-0.487461\pi\)
0.845663 0.533718i \(-0.179206\pi\)
\(564\) 9.00000 15.5885i 0.378968 0.656392i
\(565\) 0 0
\(566\) 14.0000 0.588464
\(567\) 0 0
\(568\) 0 0
\(569\) −10.5000 18.1865i −0.440183 0.762419i 0.557520 0.830164i \(-0.311753\pi\)
−0.997703 + 0.0677445i \(0.978420\pi\)
\(570\) −1.00000 + 1.73205i −0.0418854 + 0.0725476i
\(571\) −10.0000 + 17.3205i −0.418487 + 0.724841i −0.995788 0.0916910i \(-0.970773\pi\)
0.577301 + 0.816532i \(0.304106\pi\)
\(572\) −1.50000 2.59808i −0.0627182 0.108631i
\(573\) 24.0000 1.00261
\(574\) 0 0
\(575\) 9.00000 0.375326
\(576\) −0.500000 0.866025i −0.0208333 0.0360844i
\(577\) 22.0000 38.1051i 0.915872 1.58634i 0.110252 0.993904i \(-0.464834\pi\)
0.805620 0.592433i \(-0.201833\pi\)
\(578\) 9.50000 16.4545i 0.395148 0.684416i
\(579\) 16.0000 + 27.7128i 0.664937 + 1.15171i
\(580\) −6.00000 −0.249136
\(581\) 0 0
\(582\) −20.0000 −0.829027
\(583\) −13.5000 23.3827i −0.559113 0.968412i
\(584\) 2.00000 3.46410i 0.0827606 0.143346i
\(585\) 0.500000 0.866025i 0.0206725 0.0358057i
\(586\) 4.50000 + 7.79423i 0.185893 + 0.321977i
\(587\) 24.0000 0.990586 0.495293 0.868726i \(-0.335061\pi\)
0.495293 + 0.868726i \(0.335061\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) −15.0000 + 25.9808i −0.617018 + 1.06871i
\(592\) 3.50000 6.06218i 0.143849 0.249154i
\(593\) 12.0000 + 20.7846i 0.492781 + 0.853522i 0.999965 0.00831589i \(-0.00264706\pi\)
−0.507184 + 0.861838i \(0.669314\pi\)
\(594\) 12.0000 0.492366
\(595\) 0 0
\(596\) −6.00000 −0.245770
\(597\) −16.0000 27.7128i −0.654836 1.13421i
\(598\) 4.50000 7.79423i 0.184019 0.318730i
\(599\) 21.0000 36.3731i 0.858037 1.48616i −0.0157622 0.999876i \(-0.505017\pi\)
0.873799 0.486287i \(-0.161649\pi\)
\(600\) 1.00000 + 1.73205i 0.0408248 + 0.0707107i
\(601\) −26.0000 −1.06056 −0.530281 0.847822i \(-0.677914\pi\)
−0.530281 + 0.847822i \(0.677914\pi\)
\(602\) 0 0
\(603\) 8.00000 0.325785
\(604\) 5.00000 + 8.66025i 0.203447 + 0.352381i
\(605\) −1.00000 + 1.73205i −0.0406558 + 0.0704179i
\(606\) −12.0000 + 20.7846i −0.487467 + 0.844317i
\(607\) −0.500000 0.866025i −0.0202944 0.0351509i 0.855700 0.517472i \(-0.173127\pi\)
−0.875994 + 0.482322i \(0.839794\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 0 0
\(610\) −8.00000 −0.323911
\(611\) 4.50000 + 7.79423i 0.182051 + 0.315321i
\(612\) −3.00000 + 5.19615i −0.121268 + 0.210042i
\(613\) −14.5000 + 25.1147i −0.585649 + 1.01437i 0.409145 + 0.912470i \(0.365827\pi\)
−0.994794 + 0.101905i \(0.967506\pi\)
\(614\) −7.00000 12.1244i −0.282497 0.489299i
\(615\) 6.00000 0.241943
\(616\) 0 0
\(617\) −18.0000 −0.724653 −0.362326 0.932051i \(-0.618017\pi\)
−0.362326 + 0.932051i \(0.618017\pi\)
\(618\) 4.00000 + 6.92820i 0.160904 + 0.278693i
\(619\) 11.5000 19.9186i 0.462224 0.800595i −0.536847 0.843679i \(-0.680385\pi\)
0.999071 + 0.0430838i \(0.0137183\pi\)
\(620\) −4.00000 + 6.92820i −0.160644 + 0.278243i
\(621\) 18.0000 + 31.1769i 0.722315 + 1.25109i
\(622\) −24.0000 −0.962312
\(623\) 0 0
\(624\) 2.00000 0.0800641
\(625\) −0.500000 0.866025i −0.0200000 0.0346410i
\(626\) 14.0000 24.2487i 0.559553 0.969173i
\(627\) −3.00000 + 5.19615i −0.119808 + 0.207514i
\(628\) 11.5000 + 19.9186i 0.458900 + 0.794838i
\(629\) −42.0000 −1.67465
\(630\) 0 0
\(631\) 20.0000 0.796187 0.398094 0.917345i \(-0.369672\pi\)
0.398094 + 0.917345i \(0.369672\pi\)
\(632\) −5.00000 8.66025i −0.198889 0.344486i
\(633\) −23.0000 + 39.8372i −0.914168 + 1.58339i
\(634\) 3.00000 5.19615i 0.119145 0.206366i
\(635\) −0.500000 0.866025i −0.0198419 0.0343672i
\(636\) 18.0000 0.713746
\(637\) 0 0
\(638\) −18.0000 −0.712627
\(639\) 0 0
\(640\) −0.500000 + 0.866025i −0.0197642 + 0.0342327i
\(641\) −13.5000 + 23.3827i −0.533218 + 0.923561i 0.466029 + 0.884769i \(0.345684\pi\)
−0.999247 + 0.0387913i \(0.987649\pi\)
\(642\) −12.0000 20.7846i −0.473602 0.820303i
\(643\) −2.00000 −0.0788723 −0.0394362 0.999222i \(-0.512556\pi\)
−0.0394362 + 0.999222i \(0.512556\pi\)
\(644\) 0 0
\(645\) −4.00000 −0.157500
\(646\) 3.00000 + 5.19615i 0.118033 + 0.204440i
\(647\) 16.5000 28.5788i 0.648682 1.12355i −0.334756 0.942305i \(-0.608654\pi\)
0.983438 0.181245i \(-0.0580128\pi\)
\(648\) −5.50000 + 9.52628i −0.216060 + 0.374228i
\(649\) 0 0
\(650\) −1.00000 −0.0392232
\(651\) 0 0
\(652\) 20.0000 0.783260
\(653\) 4.50000 + 7.79423i 0.176099 + 0.305012i 0.940541 0.339680i \(-0.110319\pi\)
−0.764442 + 0.644692i \(0.776986\pi\)
\(654\) −16.0000 + 27.7128i −0.625650 + 1.08366i
\(655\) −1.50000 + 2.59808i −0.0586098 + 0.101515i
\(656\) 1.50000 + 2.59808i 0.0585652 + 0.101438i
\(657\) 4.00000 0.156055
\(658\) 0 0
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 3.00000 + 5.19615i 0.116775 + 0.202260i
\(661\) −14.0000 + 24.2487i −0.544537 + 0.943166i 0.454099 + 0.890951i \(0.349961\pi\)
−0.998636 + 0.0522143i \(0.983372\pi\)
\(662\) −3.50000 + 6.06218i −0.136031 + 0.235613i
\(663\) −6.00000 10.3923i −0.233021 0.403604i
\(664\) 0 0
\(665\) 0 0
\(666\) 7.00000 0.271244
\(667\) −27.0000 46.7654i −1.04544 1.81076i
\(668\) 1.50000 2.59808i 0.0580367 0.100523i
\(669\) 8.00000 13.8564i 0.309298 0.535720i
\(670\) −4.00000 6.92820i −0.154533 0.267660i
\(671\) −24.0000 −0.926510
\(672\) 0 0
\(673\) −34.0000 −1.31060 −0.655302 0.755367i \(-0.727459\pi\)
−0.655302 + 0.755367i \(0.727459\pi\)
\(674\) −11.0000 19.0526i −0.423704 0.733877i
\(675\) 2.00000 3.46410i 0.0769800 0.133333i
\(676\) 6.00000 10.3923i 0.230769 0.399704i
\(677\) −4.50000 7.79423i −0.172949 0.299557i 0.766501 0.642244i \(-0.221996\pi\)
−0.939450 + 0.342687i \(0.888663\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 6.00000 0.230089
\(681\) −12.0000 20.7846i −0.459841 0.796468i
\(682\) −12.0000 + 20.7846i −0.459504 + 0.795884i
\(683\) −6.00000 + 10.3923i −0.229584 + 0.397650i −0.957685 0.287819i \(-0.907070\pi\)
0.728101 + 0.685470i \(0.240403\pi\)
\(684\) −0.500000 0.866025i −0.0191180 0.0331133i
\(685\) −12.0000 −0.458496
\(686\) 0 0
\(687\) 8.00000 0.305219
\(688\) −1.00000 1.73205i −0.0381246 0.0660338i
\(689\) −4.50000 + 7.79423i −0.171436 + 0.296936i
\(690\) −9.00000 + 15.5885i −0.342624 + 0.593442i
\(691\) 16.0000 + 27.7128i 0.608669 + 1.05425i 0.991460 + 0.130410i \(0.0416295\pi\)
−0.382791 + 0.923835i \(0.625037\pi\)
\(692\) −9.00000 −0.342129
\(693\) 0 0
\(694\) 0 0
\(695\) 2.00000 + 3.46410i 0.0758643 + 0.131401i
\(696\) 6.00000 10.3923i 0.227429 0.393919i
\(697\) 9.00000 15.5885i 0.340899 0.590455i
\(698\) −13.0000 22.5167i −0.492057 0.852268i
\(699\) −12.0000 −0.453882
\(700\) 0 0
\(701\) −30.0000 −1.13308 −0.566542 0.824033i \(-0.691719\pi\)
−0.566542 + 0.824033i \(0.691719\pi\)
\(702\) −2.00000 3.46410i −0.0754851 0.130744i
\(703\) 3.50000 6.06218i 0.132005 0.228639i
\(704\) −1.50000 + 2.59808i −0.0565334 + 0.0979187i
\(705\) −9.00000 15.5885i −0.338960 0.587095i
\(706\) 12.0000 0.451626
\(707\) 0 0
\(708\) 0 0
\(709\) 23.0000 + 39.8372i 0.863783 + 1.49612i 0.868250 + 0.496126i \(0.165245\pi\)
−0.00446726 + 0.999990i \(0.501422\pi\)
\(710\) 0 0
\(711\) 5.00000 8.66025i 0.187515 0.324785i
\(712\) −3.00000 5.19615i −0.112430 0.194734i
\(713\) −72.0000 −2.69642
\(714\) 0 0
\(715\) −3.00000 −0.112194
\(716\) 1.50000 + 2.59808i 0.0560576 + 0.0970947i
\(717\) 6.00000 10.3923i 0.224074 0.388108i
\(718\) 9.00000 15.5885i 0.335877 0.581756i
\(719\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 0 0
\(722\) 18.0000 0.669891
\(723\) −1.00000 1.73205i −0.0371904 0.0644157i
\(724\) 1.00000 1.73205i 0.0371647 0.0643712i
\(725\) −3.00000 + 5.19615i −0.111417 + 0.192980i
\(726\) −2.00000 3.46410i −0.0742270 0.128565i
\(727\) 1.00000 0.0370879 0.0185440 0.999828i \(-0.494097\pi\)
0.0185440 + 0.999828i \(0.494097\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) −2.00000 3.46410i −0.0740233 0.128212i
\(731\) −6.00000 + 10.3923i −0.221918 + 0.384373i
\(732\) 8.00000 13.8564i 0.295689 0.512148i
\(733\) −21.5000 37.2391i −0.794121 1.37546i −0.923396 0.383849i \(-0.874598\pi\)
0.129275 0.991609i \(-0.458735\pi\)
\(734\) −19.0000 −0.701303
\(735\) 0 0
\(736\) −9.00000 −0.331744
\(737\) −12.0000 20.7846i −0.442026 0.765611i
\(738\) −1.50000 + 2.59808i −0.0552158 + 0.0956365i
\(739\) −17.5000 + 30.3109i −0.643748 + 1.11500i 0.340841 + 0.940121i \(0.389288\pi\)
−0.984589 + 0.174883i \(0.944045\pi\)
\(740\) −3.50000 6.06218i −0.128663 0.222850i
\(741\) 2.00000 0.0734718
\(742\) 0 0
\(743\) −45.0000 −1.65089 −0.825445 0.564483i \(-0.809076\pi\)
−0.825445 + 0.564483i \(0.809076\pi\)
\(744\) −8.00000 13.8564i −0.293294 0.508001i
\(745\) −3.00000 + 5.19615i −0.109911 + 0.190372i
\(746\) 1.00000 1.73205i 0.0366126 0.0634149i
\(747\) 0 0
\(748\) 18.0000 0.658145
\(749\) 0 0
\(750\) 2.00000 0.0730297
\(751\) 5.00000 + 8.66025i 0.182453 + 0.316017i 0.942715 0.333599i \(-0.108263\pi\)
−0.760263 + 0.649616i \(0.774930\pi\)
\(752\) 4.50000 7.79423i 0.164098 0.284226i
\(753\) −15.0000 + 25.9808i −0.546630 + 0.946792i
\(754\) 3.00000 + 5.19615i 0.109254 + 0.189233i
\(755\) 10.0000 0.363937
\(756\) 0 0
\(757\) 38.0000 1.38113 0.690567 0.723269i \(-0.257361\pi\)
0.690567 + 0.723269i \(0.257361\pi\)
\(758\) 11.5000 + 19.9186i 0.417699 + 0.723476i
\(759\) −27.0000 + 46.7654i −0.980038 + 1.69748i
\(760\) −0.500000 + 0.866025i −0.0181369 + 0.0314140i
\(761\) −13.5000 23.3827i −0.489375 0.847622i 0.510551 0.859848i \(-0.329442\pi\)
−0.999925 + 0.0122260i \(0.996108\pi\)
\(762\) 2.00000 0.0724524
\(763\) 0 0
\(764\) 12.0000 0.434145
\(765\) 3.00000 + 5.19615i 0.108465 + 0.187867i
\(766\) −10.5000 + 18.1865i −0.379380 + 0.657106i
\(767\) 0 0
\(768\) −1.00000 1.73205i −0.0360844 0.0625000i
\(769\) −23.0000 −0.829401 −0.414701 0.909958i \(-0.636114\pi\)
−0.414701 + 0.909958i \(0.636114\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 8.00000 + 13.8564i 0.287926 + 0.498703i
\(773\) −25.5000 + 44.1673i −0.917171 + 1.58859i −0.113480 + 0.993540i \(0.536200\pi\)
−0.803691 + 0.595047i \(0.797133\pi\)
\(774\) 1.00000 1.73205i 0.0359443 0.0622573i
\(775\) 4.00000 + 6.92820i 0.143684 + 0.248868i
\(776\) −10.0000 −0.358979
\(777\) 0 0
\(778\) 12.0000 0.430221
\(779\) 1.50000 + 2.59808i 0.0537431 + 0.0930857i
\(780\) 1.00000 1.73205i 0.0358057 0.0620174i
\(781\) 0 0
\(782\) 27.0000 + 46.7654i 0.965518 + 1.67233i
\(783\) −24.0000 −0.857690
\(784\) 0 0
\(785\) 23.0000