Properties

Label 490.2.e.g.471.1
Level $490$
Weight $2$
Character 490.471
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 471.1
Root \(0.500000 - 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 490.471
Dual form 490.2.e.g.361.1

$q$-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 \(\left(\mathbb{Z}/490\mathbb{Z}\right)^\times\).

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

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 −0.995782 0.0917517i \(-0.970753\pi\)
0.418432 0.908248i \(-0.362580\pi\)
\(4\) −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 0.546259 0.837616i \(-0.316051\pi\)
−0.998526 + 0.0542666i \(0.982718\pi\)
\(12\) −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 −0.957892 0.287129i \(-0.907299\pi\)
0.230285 0.973123i \(-0.426034\pi\)
\(18\) 0.500000 + 0.866025i 0.117851 + 0.204124i
\(19\) −0.500000 + 0.866025i −0.114708 + 0.198680i −0.917663 0.397360i \(-0.869927\pi\)
0.802955 + 0.596040i \(0.203260\pi\)
\(20\) −1.00000 −0.223607
\(21\) 0 0
\(22\) −3.00000 −0.639602
\(23\) −4.50000 + 7.79423i −0.938315 + 1.62521i −0.169701 + 0.985496i \(0.554280\pi\)
−0.768613 + 0.639713i \(0.779053\pi\)
\(24\) 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 0.961625 + 0.274367i \(0.0884683\pi\)
−0.243204 + 0.969975i \(0.578198\pi\)
\(32\) 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 −0.420602 0.907245i \(-0.638181\pi\)
0.995998 0.0893706i \(-0.0284856\pi\)
\(38\) 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 −0.325150 0.945662i \(-0.605415\pi\)
0.981543 0.191243i \(-0.0612518\pi\)
\(48\) 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 −0.989828 0.142269i \(-0.954560\pi\)
0.371706 0.928351i \(-0.378773\pi\)
\(54\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(60\) 1.00000 + 1.73205i 0.129099 + 0.223607i
\(61\) 4.00000 6.92820i 0.512148 0.887066i −0.487753 0.872982i \(-0.662183\pi\)
0.999901 0.0140840i \(-0.00448323\pi\)
\(62\) 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 0.511237 0.859440i \(-0.329187\pi\)
−0.999915 + 0.0130248i \(0.995854\pi\)
\(68\) −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 0.724923 0.688830i \(-0.241875\pi\)
−0.959006 + 0.283387i \(0.908542\pi\)
\(74\) −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 −0.434730 0.900561i \(-0.643156\pi\)
0.997274 0.0737937i \(-0.0235106\pi\)
\(80\) 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 −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 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 0.993258 + 0.115924i \(0.0369830\pi\)
−0.396236 + 0.918149i \(0.629684\pi\)
\(102\) 6.00000 + 10.3923i 0.594089 + 1.02899i
\(103\) −2.00000 + 3.46410i −0.197066 + 0.341328i −0.947576 0.319531i \(-0.896475\pi\)
0.750510 + 0.660859i \(0.229808\pi\)
\(104\) −1.00000 −0.0980581
\(105\) 0 0
\(106\) −9.00000 −0.874157
\(107\) 6.00000 10.3923i 0.580042 1.00466i −0.415432 0.909624i \(-0.636370\pi\)
0.995474 0.0950377i \(-0.0302972\pi\)
\(108\) 2.00000 + 3.46410i 0.192450 + 0.333333i
\(109\) 8.00000 + 13.8564i 0.766261 + 1.32720i 0.939577 + 0.342337i \(0.111218\pi\)
−0.173316 + 0.984866i \(0.555448\pi\)
\(110\) −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 −0.793028 0.609185i \(-0.791497\pi\)
0.924084 + 0.382190i \(0.124830\pi\)
\(132\) 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 −0.999893 0.0146279i \(-0.995344\pi\)
0.487278 0.873247i \(-0.337990\pi\)
\(138\) 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 −0.716578 0.697507i \(-0.754293\pi\)
0.962348 + 0.271821i \(0.0876260\pi\)
\(150\) 1.00000 + 1.73205i 0.0816497 + 0.141421i
\(151\) 5.00000 + 8.66025i 0.406894 + 0.704761i 0.994540 0.104357i \(-0.0332784\pi\)
−0.587646 + 0.809118i \(0.699945\pi\)
\(152\) 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 0.802749 + 0.596316i \(0.203370\pi\)
0.115050 + 0.993360i \(0.463297\pi\)
\(158\) −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 0.146772 + 0.989170i \(0.453112\pi\)
−0.930033 + 0.367477i \(0.880222\pi\)
\(164\) 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 −0.642699 0.766119i \(-0.722185\pi\)
0.984828 + 0.173534i \(0.0555188\pi\)
\(174\) −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 0.916623 0.399753i \(-0.130904\pi\)
−0.804508 + 0.593942i \(0.797571\pi\)
\(180\) 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 −0.997225 0.0744412i \(-0.976283\pi\)
0.563081 + 0.826402i \(0.309616\pi\)
\(192\) −1.00000 1.73205i −0.0721688 0.125000i
\(193\) 8.00000 + 13.8564i 0.575853 + 0.997406i 0.995948 + 0.0899262i \(0.0286631\pi\)
−0.420096 + 0.907480i \(0.638004\pi\)
\(194\) 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 −0.996850 0.0793045i \(-0.974730\pi\)
0.429745 0.902950i \(-0.358603\pi\)
\(200\) 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 0.595274 0.803523i \(-0.297043\pi\)
−0.993508 + 0.113761i \(0.963710\pi\)
\(228\) −1.00000 1.73205i −0.0662266 0.114708i
\(229\) −2.00000 + 3.46410i −0.132164 + 0.228914i −0.924510 0.381157i \(-0.875526\pi\)
0.792347 + 0.610071i \(0.208859\pi\)
\(230\) 9.00000 0.593442
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) 3.00000 5.19615i 0.196537 0.340411i −0.750867 0.660454i \(-0.770364\pi\)
0.947403 + 0.320043i \(0.103697\pi\)
\(234\) 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 0.849472 0.527633i \(-0.176921\pi\)
−0.881680 + 0.471848i \(0.843587\pi\)
\(242\) −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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(258\) −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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(270\) 2.00000 + 3.46410i 0.121716 + 0.210819i
\(271\) −8.00000 + 13.8564i −0.485965 + 0.841717i −0.999870 0.0161307i \(-0.994865\pi\)
0.513905 + 0.857847i \(0.328199\pi\)
\(272\) 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 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) 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 0.995544 0.0942988i \(-0.0300609\pi\)
−0.579437 + 0.815017i \(0.696728\pi\)
\(284\) 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 −0.974841 0.222900i \(-0.928448\pi\)
0.294384 0.955687i \(-0.404886\pi\)
\(312\) 1.00000 + 1.73205i 0.0566139 + 0.0980581i
\(313\) −14.0000 + 24.2487i −0.791327 + 1.37062i 0.133819 + 0.991006i \(0.457276\pi\)
−0.925146 + 0.379612i \(0.876057\pi\)
\(314\) 23.0000 1.29797
\(315\) 0 0
\(316\) −10.0000 −0.562544
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) 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 −0.753660 0.657264i \(-0.771714\pi\)
0.946038 + 0.324057i \(0.105047\pi\)
\(332\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(348\) −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 0.980352 0.197256i \(-0.0632029\pi\)
−0.661004 + 0.750382i \(0.729870\pi\)
\(354\) 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 −0.999590 0.0286287i \(-0.990886\pi\)
0.524588 + 0.851356i \(0.324219\pi\)
\(360\) −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 0.504093 0.863649i \(-0.331827\pi\)
−0.999989 + 0.00473247i \(0.998494\pi\)
\(368\) −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 −0.890753 0.454488i \(-0.849822\pi\)
0.838975 + 0.544170i \(0.183156\pi\)
\(374\) 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 −0.462563 0.886586i \(-0.653070\pi\)
0.999088 0.0427020i \(-0.0135966\pi\)
\(384\) −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 0.977086 0.212847i \(-0.0682735\pi\)
−0.672874 + 0.739758i \(0.734940\pi\)
\(390\) −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 −0.635161 0.772380i \(-0.719066\pi\)
0.986481 + 0.163876i \(0.0523996\pi\)
\(398\) −16.0000 −0.802008
\(399\) 0 0
\(400\) 1.00000 0.0500000
\(401\) 13.5000 23.3827i 0.674158 1.16768i −0.302556 0.953131i \(-0.597840\pi\)
0.976714 0.214544i \(-0.0688266\pi\)
\(402\) 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 0.984803 + 0.173675i \(0.0555643\pi\)
−0.341994 + 0.939702i \(0.611102\pi\)
\(410\) 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 0.684564 0.728953i \(-0.259993\pi\)
−0.973574 + 0.228373i \(0.926659\pi\)
\(432\) 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 −0.368945 0.929451i \(-0.620281\pi\)
0.989401 0.145210i \(-0.0463858\pi\)
\(440\) 3.00000 0.143019
\(441\) 0 0
\(442\) −6.00000 −0.285391
\(443\) −6.00000 + 10.3923i −0.285069 + 0.493753i −0.972626 0.232377i \(-0.925350\pi\)
0.687557 + 0.726130i \(0.258683\pi\)
\(444\) 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 −0.982004 0.188858i \(-0.939521\pi\)
0.654558 + 0.756012i \(0.272855\pi\)
\(458\) 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 −0.927052 0.374934i \(-0.877665\pi\)
0.788228 + 0.615383i \(0.210999\pi\)
\(468\) 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 \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(480\) −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 0.988374 0.152042i \(-0.0485850\pi\)
−0.625859 + 0.779936i \(0.715252\pi\)
\(488\) −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 −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 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 −0.148866 + 0.988857i \(0.547562\pi\)
−0.781943 + 0.623350i \(0.785771\pi\)
\(510\) 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 0.653650 0.756797i \(-0.273237\pi\)
−0.982231 + 0.187678i \(0.939904\pi\)
\(522\) 3.00000 + 5.19615i 0.131306 + 0.227429i
\(523\) −14.0000 + 24.2487i −0.612177 + 1.06032i 0.378695 + 0.925521i \(0.376373\pi\)
−0.990873 + 0.134801i \(0.956961\pi\)
\(524\) −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 −0.939110 0.343617i \(-0.888348\pi\)
0.767136 + 0.641484i \(0.221681\pi\)
\(542\) 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 0.945473 0.325701i \(-0.105600\pi\)
−0.754802 + 0.655953i \(0.772267\pi\)
\(558\) −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 0.845663 + 0.533718i \(0.179206\pi\)
0.0393818 + 0.999224i \(0.487461\pi\)
\(564\) 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 −0.997703 0.0677445i \(-0.978420\pi\)
0.557520 + 0.830164i \(0.311753\pi\)
\(570\) −1.00000 1.73205i −0.0418854 0.0725476i
\(571\) −10.0000 17.3205i −0.418487 0.724841i 0.577301 0.816532i \(-0.304106\pi\)
−0.995788 + 0.0916910i \(0.970773\pi\)
\(572\) −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 0.805620 + 0.592433i \(0.201833\pi\)
0.110252 + 0.993904i \(0.464834\pi\)
\(578\) 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 −0.507184 0.861838i \(-0.669314\pi\)
0.999965 + 0.00831589i \(0.00264706\pi\)
\(594\) 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 0.873799 + 0.486287i \(0.161649\pi\)
−0.0157622 + 0.999876i \(0.505017\pi\)
\(600\) 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 −0.875994 0.482322i \(-0.839794\pi\)
0.855700 + 0.517472i \(0.173127\pi\)
\(608\) −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 −0.994794 0.101905i \(-0.967506\pi\)
0.409145 0.912470i \(-0.365827\pi\)
\(614\) −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 0.999071 0.0430838i \(-0.0137183\pi\)
−0.536847 + 0.843679i \(0.680385\pi\)
\(620\) −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 −0.999247 0.0387913i \(-0.987649\pi\)
0.466029 0.884769i \(-0.345684\pi\)
\(642\) −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 0.983438 + 0.181245i \(0.0580128\pi\)
−0.334756 + 0.942305i \(0.608654\pi\)
\(648\) −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 −0.764442 0.644692i \(-0.776986\pi\)
0.940541 + 0.339680i \(0.110319\pi\)
\(654\) −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 −0.998636 0.0522143i \(-0.983372\pi\)
0.454099 0.890951i \(-0.349961\pi\)
\(662\) −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 −0.939450 0.342687i \(-0.888663\pi\)
0.766501 + 0.642244i \(0.221996\pi\)
\(678\) 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 0.728101 0.685470i \(-0.240403\pi\)
−0.957685 + 0.287819i \(0.907070\pi\)
\(684\) −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 −0.382791 0.923835i \(-0.625037\pi\)
0.991460 0.130410i \(-0.0416295\pi\)
\(692\) −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 −0.00446726 0.999990i \(-0.501422\pi\)
0.868250 0.496126i \(-0.165245\pi\)
\(710\) 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 \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(720\) −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 0.129275 + 0.991609i \(0.458735\pi\)
−0.923396 + 0.383849i \(0.874598\pi\)
\(734\) −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 −0.984589 0.174883i \(-0.944045\pi\)
0.340841 0.940121i \(-0.389288\pi\)
\(740\) −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 −0.760263 0.649616i \(-0.774930\pi\)
0.942715 + 0.333599i \(0.108263\pi\)
\(752\) 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 −0.999925 0.0122260i \(-0.996108\pi\)
0.510551 + 0.859848i \(0.329442\pi\)
\(762\) 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 −0.803691 0.595047i \(-0.797133\pi\)
−0.113480 0.993540i \(-0.536200\pi\)
\(774\) 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