Properties

Label 98.2.c.b.79.1
Level 98
Weight 2
Character 98.79
Analytic conductor 0.783
Analytic rank 0
Dimension 2
CM no
Inner twists 2

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Newspace parameters

Level: \( N \) \(=\) \( 98 = 2 \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 98.c (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(0.782533939809\)
Analytic rank: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 14)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 79.1
Root \(0.500000 - 0.866025i\) of \(x^{2} - x + 1\)
Character \(\chi\) \(=\) 98.79
Dual form 98.2.c.b.67.1

$q$-expansion

\(f(q)\) \(=\) \(q+(0.500000 - 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\) \(q+(0.500000 - 0.866025i) q^{2} +(1.00000 + 1.73205i) q^{3} +(-0.500000 - 0.866025i) q^{4} +2.00000 q^{6} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(1.00000 - 1.73205i) q^{12} -4.00000 q^{13} +(-0.500000 + 0.866025i) q^{16} +(-3.00000 - 5.19615i) q^{17} +(0.500000 + 0.866025i) q^{18} +(-1.00000 + 1.73205i) q^{19} +(-1.00000 - 1.73205i) q^{24} +(2.50000 + 4.33013i) q^{25} +(-2.00000 + 3.46410i) q^{26} +4.00000 q^{27} -6.00000 q^{29} +(2.00000 + 3.46410i) q^{31} +(0.500000 + 0.866025i) q^{32} -6.00000 q^{34} +1.00000 q^{36} +(-1.00000 + 1.73205i) q^{37} +(1.00000 + 1.73205i) q^{38} +(-4.00000 - 6.92820i) q^{39} +6.00000 q^{41} +8.00000 q^{43} +(6.00000 - 10.3923i) q^{47} -2.00000 q^{48} +5.00000 q^{50} +(6.00000 - 10.3923i) q^{51} +(2.00000 + 3.46410i) q^{52} +(-3.00000 - 5.19615i) q^{53} +(2.00000 - 3.46410i) q^{54} -4.00000 q^{57} +(-3.00000 + 5.19615i) q^{58} +(3.00000 + 5.19615i) q^{59} +(-4.00000 + 6.92820i) q^{61} +4.00000 q^{62} +1.00000 q^{64} +(2.00000 + 3.46410i) q^{67} +(-3.00000 + 5.19615i) q^{68} +(0.500000 - 0.866025i) q^{72} +(-1.00000 - 1.73205i) q^{73} +(1.00000 + 1.73205i) q^{74} +(-5.00000 + 8.66025i) q^{75} +2.00000 q^{76} -8.00000 q^{78} +(-4.00000 + 6.92820i) q^{79} +(5.50000 + 9.52628i) q^{81} +(3.00000 - 5.19615i) q^{82} -6.00000 q^{83} +(4.00000 - 6.92820i) q^{86} +(-6.00000 - 10.3923i) q^{87} +(3.00000 - 5.19615i) q^{89} +(-4.00000 + 6.92820i) q^{93} +(-6.00000 - 10.3923i) q^{94} +(-1.00000 + 1.73205i) q^{96} -10.0000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q + q^{2} + 2q^{3} - q^{4} + 4q^{6} - 2q^{8} - q^{9} + O(q^{10}) \) \( 2q + q^{2} + 2q^{3} - q^{4} + 4q^{6} - 2q^{8} - q^{9} + 2q^{12} - 8q^{13} - q^{16} - 6q^{17} + q^{18} - 2q^{19} - 2q^{24} + 5q^{25} - 4q^{26} + 8q^{27} - 12q^{29} + 4q^{31} + q^{32} - 12q^{34} + 2q^{36} - 2q^{37} + 2q^{38} - 8q^{39} + 12q^{41} + 16q^{43} + 12q^{47} - 4q^{48} + 10q^{50} + 12q^{51} + 4q^{52} - 6q^{53} + 4q^{54} - 8q^{57} - 6q^{58} + 6q^{59} - 8q^{61} + 8q^{62} + 2q^{64} + 4q^{67} - 6q^{68} + q^{72} - 2q^{73} + 2q^{74} - 10q^{75} + 4q^{76} - 16q^{78} - 8q^{79} + 11q^{81} + 6q^{82} - 12q^{83} + 8q^{86} - 12q^{87} + 6q^{89} - 8q^{93} - 12q^{94} - 2q^{96} - 20q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/98\mathbb{Z}\right)^\times\).

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

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
\(3\) 1.00000 + 1.73205i 0.577350 + 1.00000i 0.995782 + 0.0917517i \(0.0292466\pi\)
−0.418432 + 0.908248i \(0.637420\pi\)
\(4\) −0.500000 0.866025i −0.250000 0.433013i
\(5\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(6\) 2.00000 0.816497
\(7\) 0 0
\(8\) −1.00000 −0.353553
\(9\) −0.500000 + 0.866025i −0.166667 + 0.288675i
\(10\) 0 0
\(11\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(12\) 1.00000 1.73205i 0.288675 0.500000i
\(13\) −4.00000 −1.10940 −0.554700 0.832050i \(-0.687167\pi\)
−0.554700 + 0.832050i \(0.687167\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −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
\(19\) −1.00000 + 1.73205i −0.229416 + 0.397360i −0.957635 0.287984i \(-0.907015\pi\)
0.728219 + 0.685344i \(0.240348\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) 0 0
\(23\) 0 0 −0.866025 0.500000i \(-0.833333\pi\)
0.866025 + 0.500000i \(0.166667\pi\)
\(24\) −1.00000 1.73205i −0.204124 0.353553i
\(25\) 2.50000 + 4.33013i 0.500000 + 0.866025i
\(26\) −2.00000 + 3.46410i −0.392232 + 0.679366i
\(27\) 4.00000 0.769800
\(28\) 0 0
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) 2.00000 + 3.46410i 0.359211 + 0.622171i 0.987829 0.155543i \(-0.0497126\pi\)
−0.628619 + 0.777714i \(0.716379\pi\)
\(32\) 0.500000 + 0.866025i 0.0883883 + 0.153093i
\(33\) 0 0
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 1.00000 0.166667
\(37\) −1.00000 + 1.73205i −0.164399 + 0.284747i −0.936442 0.350823i \(-0.885902\pi\)
0.772043 + 0.635571i \(0.219235\pi\)
\(38\) 1.00000 + 1.73205i 0.162221 + 0.280976i
\(39\) −4.00000 6.92820i −0.640513 1.10940i
\(40\) 0 0
\(41\) 6.00000 0.937043 0.468521 0.883452i \(-0.344787\pi\)
0.468521 + 0.883452i \(0.344787\pi\)
\(42\) 0 0
\(43\) 8.00000 1.21999 0.609994 0.792406i \(-0.291172\pi\)
0.609994 + 0.792406i \(0.291172\pi\)
\(44\) 0 0
\(45\) 0 0
\(46\) 0 0
\(47\) 6.00000 10.3923i 0.875190 1.51587i 0.0186297 0.999826i \(-0.494070\pi\)
0.856560 0.516047i \(-0.172597\pi\)
\(48\) −2.00000 −0.288675
\(49\) 0 0
\(50\) 5.00000 0.707107
\(51\) 6.00000 10.3923i 0.840168 1.45521i
\(52\) 2.00000 + 3.46410i 0.277350 + 0.480384i
\(53\) −3.00000 5.19615i −0.412082 0.713746i 0.583036 0.812447i \(-0.301865\pi\)
−0.995117 + 0.0987002i \(0.968532\pi\)
\(54\) 2.00000 3.46410i 0.272166 0.471405i
\(55\) 0 0
\(56\) 0 0
\(57\) −4.00000 −0.529813
\(58\) −3.00000 + 5.19615i −0.393919 + 0.682288i
\(59\) 3.00000 + 5.19615i 0.390567 + 0.676481i 0.992524 0.122047i \(-0.0389457\pi\)
−0.601958 + 0.798528i \(0.705612\pi\)
\(60\) 0 0
\(61\) −4.00000 + 6.92820i −0.512148 + 0.887066i 0.487753 + 0.872982i \(0.337817\pi\)
−0.999901 + 0.0140840i \(0.995517\pi\)
\(62\) 4.00000 0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 2.00000 + 3.46410i 0.244339 + 0.423207i 0.961946 0.273241i \(-0.0880957\pi\)
−0.717607 + 0.696449i \(0.754762\pi\)
\(68\) −3.00000 + 5.19615i −0.363803 + 0.630126i
\(69\) 0 0
\(70\) 0 0
\(71\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(72\) 0.500000 0.866025i 0.0589256 0.102062i
\(73\) −1.00000 1.73205i −0.117041 0.202721i 0.801553 0.597924i \(-0.204008\pi\)
−0.918594 + 0.395203i \(0.870674\pi\)
\(74\) 1.00000 + 1.73205i 0.116248 + 0.201347i
\(75\) −5.00000 + 8.66025i −0.577350 + 1.00000i
\(76\) 2.00000 0.229416
\(77\) 0 0
\(78\) −8.00000 −0.905822
\(79\) −4.00000 + 6.92820i −0.450035 + 0.779484i −0.998388 0.0567635i \(-0.981922\pi\)
0.548352 + 0.836247i \(0.315255\pi\)
\(80\) 0 0
\(81\) 5.50000 + 9.52628i 0.611111 + 1.05848i
\(82\) 3.00000 5.19615i 0.331295 0.573819i
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 4.00000 6.92820i 0.431331 0.747087i
\(87\) −6.00000 10.3923i −0.643268 1.11417i
\(88\) 0 0
\(89\) 3.00000 5.19615i 0.317999 0.550791i −0.662071 0.749441i \(-0.730322\pi\)
0.980071 + 0.198650i \(0.0636557\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) −4.00000 + 6.92820i −0.414781 + 0.718421i
\(94\) −6.00000 10.3923i −0.618853 1.07188i
\(95\) 0 0
\(96\) −1.00000 + 1.73205i −0.102062 + 0.176777i
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 2.50000 4.33013i 0.250000 0.433013i
\(101\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(102\) −6.00000 10.3923i −0.594089 1.02899i
\(103\) 2.00000 3.46410i 0.197066 0.341328i −0.750510 0.660859i \(-0.770192\pi\)
0.947576 + 0.319531i \(0.103525\pi\)
\(104\) 4.00000 0.392232
\(105\) 0 0
\(106\) −6.00000 −0.582772
\(107\) −6.00000 + 10.3923i −0.580042 + 1.00466i 0.415432 + 0.909624i \(0.363630\pi\)
−0.995474 + 0.0950377i \(0.969703\pi\)
\(108\) −2.00000 3.46410i −0.192450 0.333333i
\(109\) −1.00000 1.73205i −0.0957826 0.165900i 0.814152 0.580651i \(-0.197202\pi\)
−0.909935 + 0.414751i \(0.863869\pi\)
\(110\) 0 0
\(111\) −4.00000 −0.379663
\(112\) 0 0
\(113\) 6.00000 0.564433 0.282216 0.959351i \(-0.408930\pi\)
0.282216 + 0.959351i \(0.408930\pi\)
\(114\) −2.00000 + 3.46410i −0.187317 + 0.324443i
\(115\) 0 0
\(116\) 3.00000 + 5.19615i 0.278543 + 0.482451i
\(117\) 2.00000 3.46410i 0.184900 0.320256i
\(118\) 6.00000 0.552345
\(119\) 0 0
\(120\) 0 0
\(121\) 5.50000 9.52628i 0.500000 0.866025i
\(122\) 4.00000 + 6.92820i 0.362143 + 0.627250i
\(123\) 6.00000 + 10.3923i 0.541002 + 0.937043i
\(124\) 2.00000 3.46410i 0.179605 0.311086i
\(125\) 0 0
\(126\) 0 0
\(127\) −16.0000 −1.41977 −0.709885 0.704317i \(-0.751253\pi\)
−0.709885 + 0.704317i \(0.751253\pi\)
\(128\) 0.500000 0.866025i 0.0441942 0.0765466i
\(129\) 8.00000 + 13.8564i 0.704361 + 1.21999i
\(130\) 0 0
\(131\) −9.00000 + 15.5885i −0.786334 + 1.36197i 0.141865 + 0.989886i \(0.454690\pi\)
−0.928199 + 0.372084i \(0.878643\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 4.00000 0.345547
\(135\) 0 0
\(136\) 3.00000 + 5.19615i 0.257248 + 0.445566i
\(137\) −9.00000 15.5885i −0.768922 1.33181i −0.938148 0.346235i \(-0.887460\pi\)
0.169226 0.985577i \(-0.445873\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 24.0000 2.02116
\(142\) 0 0
\(143\) 0 0
\(144\) −0.500000 0.866025i −0.0416667 0.0721688i
\(145\) 0 0
\(146\) −2.00000 −0.165521
\(147\) 0 0
\(148\) 2.00000 0.164399
\(149\) 9.00000 15.5885i 0.737309 1.27706i −0.216394 0.976306i \(-0.569430\pi\)
0.953703 0.300750i \(-0.0972370\pi\)
\(150\) 5.00000 + 8.66025i 0.408248 + 0.707107i
\(151\) −4.00000 6.92820i −0.325515 0.563809i 0.656101 0.754673i \(-0.272204\pi\)
−0.981617 + 0.190864i \(0.938871\pi\)
\(152\) 1.00000 1.73205i 0.0811107 0.140488i
\(153\) 6.00000 0.485071
\(154\) 0 0
\(155\) 0 0
\(156\) −4.00000 + 6.92820i −0.320256 + 0.554700i
\(157\) 2.00000 + 3.46410i 0.159617 + 0.276465i 0.934731 0.355357i \(-0.115641\pi\)
−0.775113 + 0.631822i \(0.782307\pi\)
\(158\) 4.00000 + 6.92820i 0.318223 + 0.551178i
\(159\) 6.00000 10.3923i 0.475831 0.824163i
\(160\) 0 0
\(161\) 0 0
\(162\) 11.0000 0.864242
\(163\) 8.00000 13.8564i 0.626608 1.08532i −0.361619 0.932326i \(-0.617776\pi\)
0.988227 0.152992i \(-0.0488907\pi\)
\(164\) −3.00000 5.19615i −0.234261 0.405751i
\(165\) 0 0
\(166\) −3.00000 + 5.19615i −0.232845 + 0.403300i
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 0 0
\(169\) 3.00000 0.230769
\(170\) 0 0
\(171\) −1.00000 1.73205i −0.0764719 0.132453i
\(172\) −4.00000 6.92820i −0.304997 0.528271i
\(173\) 6.00000 10.3923i 0.456172 0.790112i −0.542583 0.840002i \(-0.682554\pi\)
0.998755 + 0.0498898i \(0.0158870\pi\)
\(174\) −12.0000 −0.909718
\(175\) 0 0
\(176\) 0 0
\(177\) −6.00000 + 10.3923i −0.450988 + 0.781133i
\(178\) −3.00000 5.19615i −0.224860 0.389468i
\(179\) 6.00000 + 10.3923i 0.448461 + 0.776757i 0.998286 0.0585225i \(-0.0186389\pi\)
−0.549825 + 0.835280i \(0.685306\pi\)
\(180\) 0 0
\(181\) 20.0000 1.48659 0.743294 0.668965i \(-0.233262\pi\)
0.743294 + 0.668965i \(0.233262\pi\)
\(182\) 0 0
\(183\) −16.0000 −1.18275
\(184\) 0 0
\(185\) 0 0
\(186\) 4.00000 + 6.92820i 0.293294 + 0.508001i
\(187\) 0 0
\(188\) −12.0000 −0.875190
\(189\) 0 0
\(190\) 0 0
\(191\) −12.0000 + 20.7846i −0.868290 + 1.50392i −0.00454614 + 0.999990i \(0.501447\pi\)
−0.863743 + 0.503932i \(0.831886\pi\)
\(192\) 1.00000 + 1.73205i 0.0721688 + 0.125000i
\(193\) −7.00000 12.1244i −0.503871 0.872730i −0.999990 0.00447566i \(-0.998575\pi\)
0.496119 0.868255i \(-0.334758\pi\)
\(194\) −5.00000 + 8.66025i −0.358979 + 0.621770i
\(195\) 0 0
\(196\) 0 0
\(197\) −18.0000 −1.28245 −0.641223 0.767354i \(-0.721573\pi\)
−0.641223 + 0.767354i \(0.721573\pi\)
\(198\) 0 0
\(199\) −10.0000 17.3205i −0.708881 1.22782i −0.965272 0.261245i \(-0.915867\pi\)
0.256391 0.966573i \(-0.417466\pi\)
\(200\) −2.50000 4.33013i −0.176777 0.306186i
\(201\) −4.00000 + 6.92820i −0.282138 + 0.488678i
\(202\) 0 0
\(203\) 0 0
\(204\) −12.0000 −0.840168
\(205\) 0 0
\(206\) −2.00000 3.46410i −0.139347 0.241355i
\(207\) 0 0
\(208\) 2.00000 3.46410i 0.138675 0.240192i
\(209\) 0 0
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) −3.00000 + 5.19615i −0.206041 + 0.356873i
\(213\) 0 0
\(214\) 6.00000 + 10.3923i 0.410152 + 0.710403i
\(215\) 0 0
\(216\) −4.00000 −0.272166
\(217\) 0 0
\(218\) −2.00000 −0.135457
\(219\) 2.00000 3.46410i 0.135147 0.234082i
\(220\) 0 0
\(221\) 12.0000 + 20.7846i 0.807207 + 1.39812i
\(222\) −2.00000 + 3.46410i −0.134231 + 0.232495i
\(223\) 8.00000 0.535720 0.267860 0.963458i \(-0.413684\pi\)
0.267860 + 0.963458i \(0.413684\pi\)
\(224\) 0 0
\(225\) −5.00000 −0.333333
\(226\) 3.00000 5.19615i 0.199557 0.345643i
\(227\) −9.00000 15.5885i −0.597351 1.03464i −0.993210 0.116331i \(-0.962887\pi\)
0.395860 0.918311i \(-0.370447\pi\)
\(228\) 2.00000 + 3.46410i 0.132453 + 0.229416i
\(229\) 2.00000 3.46410i 0.132164 0.228914i −0.792347 0.610071i \(-0.791141\pi\)
0.924510 + 0.381157i \(0.124474\pi\)
\(230\) 0 0
\(231\) 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 \(0.103697\pi\)
\(234\) −2.00000 3.46410i −0.130744 0.226455i
\(235\) 0 0
\(236\) 3.00000 5.19615i 0.195283 0.338241i
\(237\) −16.0000 −1.03931
\(238\) 0 0
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 5.00000 + 8.66025i 0.322078 + 0.557856i 0.980917 0.194429i \(-0.0622852\pi\)
−0.658838 + 0.752285i \(0.728952\pi\)
\(242\) −5.50000 9.52628i −0.353553 0.612372i
\(243\) −5.00000 + 8.66025i −0.320750 + 0.555556i
\(244\) 8.00000 0.512148
\(245\) 0 0
\(246\) 12.0000 0.765092
\(247\) 4.00000 6.92820i 0.254514 0.440831i
\(248\) −2.00000 3.46410i −0.127000 0.219971i
\(249\) −6.00000 10.3923i −0.380235 0.658586i
\(250\) 0 0
\(251\) −18.0000 −1.13615 −0.568075 0.822977i \(-0.692312\pi\)
−0.568075 + 0.822977i \(0.692312\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −8.00000 + 13.8564i −0.501965 + 0.869428i
\(255\) 0 0
\(256\) −0.500000 0.866025i −0.0312500 0.0541266i
\(257\) −9.00000 + 15.5885i −0.561405 + 0.972381i 0.435970 + 0.899961i \(0.356405\pi\)
−0.997374 + 0.0724199i \(0.976928\pi\)
\(258\) 16.0000 0.996116
\(259\) 0 0
\(260\) 0 0
\(261\) 3.00000 5.19615i 0.185695 0.321634i
\(262\) 9.00000 + 15.5885i 0.556022 + 0.963058i
\(263\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 0 0
\(267\) 12.0000 0.734388
\(268\) 2.00000 3.46410i 0.122169 0.211604i
\(269\) 6.00000 + 10.3923i 0.365826 + 0.633630i 0.988908 0.148527i \(-0.0474530\pi\)
−0.623082 + 0.782157i \(0.714120\pi\)
\(270\) 0 0
\(271\) 8.00000 13.8564i 0.485965 0.841717i −0.513905 0.857847i \(-0.671801\pi\)
0.999870 + 0.0161307i \(0.00513477\pi\)
\(272\) 6.00000 0.363803
\(273\) 0 0
\(274\) −18.0000 −1.08742
\(275\) 0 0
\(276\) 0 0
\(277\) 5.00000 + 8.66025i 0.300421 + 0.520344i 0.976231 0.216731i \(-0.0695395\pi\)
−0.675810 + 0.737075i \(0.736206\pi\)
\(278\) 7.00000 12.1244i 0.419832 0.727171i
\(279\) −4.00000 −0.239474
\(280\) 0 0
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) 12.0000 20.7846i 0.714590 1.23771i
\(283\) 11.0000 + 19.0526i 0.653882 + 1.13256i 0.982173 + 0.187980i \(0.0601941\pi\)
−0.328291 + 0.944577i \(0.606473\pi\)
\(284\) 0 0
\(285\) 0 0
\(286\) 0 0
\(287\) 0 0
\(288\) −1.00000 −0.0589256
\(289\) −9.50000 + 16.4545i −0.558824 + 0.967911i
\(290\) 0 0
\(291\) −10.0000 17.3205i −0.586210 1.01535i
\(292\) −1.00000 + 1.73205i −0.0585206 + 0.101361i
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 1.73205i 0.0581238 0.100673i
\(297\) 0 0
\(298\) −9.00000 15.5885i −0.521356 0.903015i
\(299\) 0 0
\(300\) 10.0000 0.577350
\(301\) 0 0
\(302\) −8.00000 −0.460348
\(303\) 0 0
\(304\) −1.00000 1.73205i −0.0573539 0.0993399i
\(305\) 0 0
\(306\) 3.00000 5.19615i 0.171499 0.297044i
\(307\) 2.00000 0.114146 0.0570730 0.998370i \(-0.481823\pi\)
0.0570730 + 0.998370i \(0.481823\pi\)
\(308\) 0 0
\(309\) 8.00000 0.455104
\(310\) 0 0
\(311\) 12.0000 + 20.7846i 0.680458 + 1.17859i 0.974841 + 0.222900i \(0.0715523\pi\)
−0.294384 + 0.955687i \(0.595114\pi\)
\(312\) 4.00000 + 6.92820i 0.226455 + 0.392232i
\(313\) 5.00000 8.66025i 0.282617 0.489506i −0.689412 0.724370i \(-0.742131\pi\)
0.972028 + 0.234863i \(0.0754642\pi\)
\(314\) 4.00000 0.225733
\(315\) 0 0
\(316\) 8.00000 0.450035
\(317\) −3.00000 + 5.19615i −0.168497 + 0.291845i −0.937892 0.346929i \(-0.887225\pi\)
0.769395 + 0.638774i \(0.220558\pi\)
\(318\) −6.00000 10.3923i −0.336463 0.582772i
\(319\) 0 0
\(320\) 0 0
\(321\) −24.0000 −1.33955
\(322\) 0 0
\(323\) 12.0000 0.667698
\(324\) 5.50000 9.52628i 0.305556 0.529238i
\(325\) −10.0000 17.3205i −0.554700 0.960769i
\(326\) −8.00000 13.8564i −0.443079 0.767435i
\(327\) 2.00000 3.46410i 0.110600 0.191565i
\(328\) −6.00000 −0.331295
\(329\) 0 0
\(330\) 0 0
\(331\) −4.00000 + 6.92820i −0.219860 + 0.380808i −0.954765 0.297361i \(-0.903893\pi\)
0.734905 + 0.678170i \(0.237227\pi\)
\(332\) 3.00000 + 5.19615i 0.164646 + 0.285176i
\(333\) −1.00000 1.73205i −0.0547997 0.0949158i
\(334\) −6.00000 + 10.3923i −0.328305 + 0.568642i
\(335\) 0 0
\(336\) 0 0
\(337\) 14.0000 0.762629 0.381314 0.924445i \(-0.375472\pi\)
0.381314 + 0.924445i \(0.375472\pi\)
\(338\) 1.50000 2.59808i 0.0815892 0.141317i
\(339\) 6.00000 + 10.3923i 0.325875 + 0.564433i
\(340\) 0 0
\(341\) 0 0
\(342\) −2.00000 −0.108148
\(343\) 0 0
\(344\) −8.00000 −0.431331
\(345\) 0 0
\(346\) −6.00000 10.3923i −0.322562 0.558694i
\(347\) 12.0000 + 20.7846i 0.644194 + 1.11578i 0.984487 + 0.175457i \(0.0561403\pi\)
−0.340293 + 0.940319i \(0.610526\pi\)
\(348\) −6.00000 + 10.3923i −0.321634 + 0.557086i
\(349\) −28.0000 −1.49881 −0.749403 0.662114i \(-0.769659\pi\)
−0.749403 + 0.662114i \(0.769659\pi\)
\(350\) 0 0
\(351\) −16.0000 −0.854017
\(352\) 0 0
\(353\) −9.00000 15.5885i −0.479022 0.829690i 0.520689 0.853746i \(-0.325675\pi\)
−0.999711 + 0.0240566i \(0.992342\pi\)
\(354\) 6.00000 + 10.3923i 0.318896 + 0.552345i
\(355\) 0 0
\(356\) −6.00000 −0.317999
\(357\) 0 0
\(358\) 12.0000 0.634220
\(359\) 12.0000 20.7846i 0.633336 1.09697i −0.353529 0.935423i \(-0.615019\pi\)
0.986865 0.161546i \(-0.0516481\pi\)
\(360\) 0 0
\(361\) 7.50000 + 12.9904i 0.394737 + 0.683704i
\(362\) 10.0000 17.3205i 0.525588 0.910346i
\(363\) 22.0000 1.15470
\(364\) 0 0
\(365\) 0 0
\(366\) −8.00000 + 13.8564i −0.418167 + 0.724286i
\(367\) −4.00000 6.92820i −0.208798 0.361649i 0.742538 0.669804i \(-0.233622\pi\)
−0.951336 + 0.308155i \(0.900289\pi\)
\(368\) 0 0
\(369\) −3.00000 + 5.19615i −0.156174 + 0.270501i
\(370\) 0 0
\(371\) 0 0
\(372\) 8.00000 0.414781
\(373\) −7.00000 + 12.1244i −0.362446 + 0.627775i −0.988363 0.152115i \(-0.951392\pi\)
0.625917 + 0.779890i \(0.284725\pi\)
\(374\) 0 0
\(375\) 0 0
\(376\) −6.00000 + 10.3923i −0.309426 + 0.535942i
\(377\) 24.0000 1.23606
\(378\) 0 0
\(379\) −16.0000 −0.821865 −0.410932 0.911666i \(-0.634797\pi\)
−0.410932 + 0.911666i \(0.634797\pi\)
\(380\) 0 0
\(381\) −16.0000 27.7128i −0.819705 1.41977i
\(382\) 12.0000 + 20.7846i 0.613973 + 1.06343i
\(383\) −18.0000 + 31.1769i −0.919757 + 1.59307i −0.119974 + 0.992777i \(0.538281\pi\)
−0.799783 + 0.600289i \(0.795052\pi\)
\(384\) 2.00000 0.102062
\(385\) 0 0
\(386\) −14.0000 −0.712581
\(387\) −4.00000 + 6.92820i −0.203331 + 0.352180i
\(388\) 5.00000 + 8.66025i 0.253837 + 0.439658i
\(389\) −9.00000 15.5885i −0.456318 0.790366i 0.542445 0.840091i \(-0.317499\pi\)
−0.998763 + 0.0497253i \(0.984165\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) −36.0000 −1.81596
\(394\) −9.00000 + 15.5885i −0.453413 + 0.785335i
\(395\) 0 0
\(396\) 0 0
\(397\) −10.0000 + 17.3205i −0.501886 + 0.869291i 0.498112 + 0.867113i \(0.334027\pi\)
−0.999998 + 0.00217869i \(0.999307\pi\)
\(398\) −20.0000 −1.00251
\(399\) 0 0
\(400\) −5.00000 −0.250000
\(401\) 9.00000 15.5885i 0.449439 0.778450i −0.548911 0.835881i \(-0.684957\pi\)
0.998350 + 0.0574304i \(0.0182907\pi\)
\(402\) 4.00000 + 6.92820i 0.199502 + 0.345547i
\(403\) −8.00000 13.8564i −0.398508 0.690237i
\(404\) 0 0
\(405\) 0 0
\(406\) 0 0
\(407\) 0 0
\(408\) −6.00000 + 10.3923i −0.297044 + 0.514496i
\(409\) −7.00000 12.1244i −0.346128 0.599511i 0.639430 0.768849i \(-0.279170\pi\)
−0.985558 + 0.169338i \(0.945837\pi\)
\(410\) 0 0
\(411\) 18.0000 31.1769i 0.887875 1.53784i
\(412\) −4.00000 −0.197066
\(413\) 0 0
\(414\) 0 0
\(415\) 0 0
\(416\) −2.00000 3.46410i −0.0980581 0.169842i
\(417\) 14.0000 + 24.2487i 0.685583 + 1.18746i
\(418\) 0 0
\(419\) 6.00000 0.293119 0.146560 0.989202i \(-0.453180\pi\)
0.146560 + 0.989202i \(0.453180\pi\)
\(420\) 0 0
\(421\) −10.0000 −0.487370 −0.243685 0.969854i \(-0.578356\pi\)
−0.243685 + 0.969854i \(0.578356\pi\)
\(422\) −2.00000 + 3.46410i −0.0973585 + 0.168630i
\(423\) 6.00000 + 10.3923i 0.291730 + 0.505291i
\(424\) 3.00000 + 5.19615i 0.145693 + 0.252347i
\(425\) 15.0000 25.9808i 0.727607 1.26025i
\(426\) 0 0
\(427\) 0 0
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) −12.0000 20.7846i −0.578020 1.00116i −0.995706 0.0925683i \(-0.970492\pi\)
0.417687 0.908591i \(-0.362841\pi\)
\(432\) −2.00000 + 3.46410i −0.0962250 + 0.166667i
\(433\) −34.0000 −1.63394 −0.816968 0.576683i \(-0.804347\pi\)
−0.816968 + 0.576683i \(0.804347\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.00000 + 1.73205i −0.0478913 + 0.0829502i
\(437\) 0 0
\(438\) −2.00000 3.46410i −0.0955637 0.165521i
\(439\) −4.00000 + 6.92820i −0.190910 + 0.330665i −0.945552 0.325471i \(-0.894477\pi\)
0.754642 + 0.656136i \(0.227810\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 24.0000 1.14156
\(443\) 6.00000 10.3923i 0.285069 0.493753i −0.687557 0.726130i \(-0.741317\pi\)
0.972626 + 0.232377i \(0.0746503\pi\)
\(444\) 2.00000 + 3.46410i 0.0949158 + 0.164399i
\(445\) 0 0
\(446\) 4.00000 6.92820i 0.189405 0.328060i
\(447\) 36.0000 1.70274
\(448\) 0 0
\(449\) 18.0000 0.849473 0.424736 0.905317i \(-0.360367\pi\)
0.424736 + 0.905317i \(0.360367\pi\)
\(450\) −2.50000 + 4.33013i −0.117851 + 0.204124i
\(451\) 0 0
\(452\) −3.00000 5.19615i −0.141108 0.244406i
\(453\) 8.00000 13.8564i 0.375873 0.651031i
\(454\) −18.0000 −0.844782
\(455\) 0 0
\(456\) 4.00000 0.187317
\(457\) 5.00000 8.66025i 0.233890 0.405110i −0.725059 0.688686i \(-0.758188\pi\)
0.958950 + 0.283577i \(0.0915211\pi\)
\(458\) −2.00000 3.46410i −0.0934539 0.161867i
\(459\) −12.0000 20.7846i −0.560112 0.970143i
\(460\) 0 0
\(461\) 12.0000 0.558896 0.279448 0.960161i \(-0.409849\pi\)
0.279448 + 0.960161i \(0.409849\pi\)
\(462\) 0 0
\(463\) 32.0000 1.48717 0.743583 0.668644i \(-0.233125\pi\)
0.743583 + 0.668644i \(0.233125\pi\)
\(464\) 3.00000 5.19615i 0.139272 0.241225i
\(465\) 0 0
\(466\) −3.00000 5.19615i −0.138972 0.240707i
\(467\) 3.00000 5.19615i 0.138823 0.240449i −0.788228 0.615383i \(-0.789001\pi\)
0.927052 + 0.374934i \(0.122335\pi\)
\(468\) −4.00000 −0.184900
\(469\) 0 0
\(470\) 0 0
\(471\) −4.00000 + 6.92820i −0.184310 + 0.319235i
\(472\) −3.00000 5.19615i −0.138086 0.239172i
\(473\) 0 0
\(474\) −8.00000 + 13.8564i −0.367452 + 0.636446i
\(475\) −10.0000 −0.458831
\(476\) 0 0
\(477\) 6.00000 0.274721
\(478\) 12.0000 20.7846i 0.548867 0.950666i
\(479\) 18.0000 + 31.1769i 0.822441 + 1.42451i 0.903859 + 0.427830i \(0.140722\pi\)
−0.0814184 + 0.996680i \(0.525945\pi\)
\(480\) 0 0
\(481\) 4.00000 6.92820i 0.182384 0.315899i
\(482\) 10.0000 0.455488
\(483\) 0 0
\(484\) −11.0000 −0.500000
\(485\) 0 0
\(486\) 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
\(489\) 32.0000 1.44709
\(490\) 0 0
\(491\) −12.0000 −0.541552 −0.270776 0.962642i \(-0.587280\pi\)
−0.270776 + 0.962642i \(0.587280\pi\)
\(492\) 6.00000 10.3923i 0.270501 0.468521i
\(493\) 18.0000 + 31.1769i 0.810679 + 1.40414i
\(494\) −4.00000 6.92820i −0.179969 0.311715i
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) 0 0
\(498\) −12.0000 −0.537733
\(499\) 2.00000 3.46410i 0.0895323 0.155074i −0.817781 0.575529i \(-0.804796\pi\)
0.907314 + 0.420455i \(0.138129\pi\)
\(500\) 0 0
\(501\) −12.0000 20.7846i −0.536120 0.928588i
\(502\) −9.00000 + 15.5885i −0.401690 + 0.695747i
\(503\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 0 0
\(507\) 3.00000 + 5.19615i 0.133235 + 0.230769i
\(508\) 8.00000 + 13.8564i 0.354943 + 0.614779i
\(509\) −18.0000 + 31.1769i −0.797836 + 1.38189i 0.123187 + 0.992384i \(0.460689\pi\)
−0.921023 + 0.389509i \(0.872645\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −1.00000 −0.0441942
\(513\) −4.00000 + 6.92820i −0.176604 + 0.305888i
\(514\) 9.00000 + 15.5885i 0.396973 + 0.687577i
\(515\) 0 0
\(516\) 8.00000 13.8564i 0.352180 0.609994i
\(517\) 0 0
\(518\) 0 0
\(519\) 24.0000 1.05348
\(520\) 0 0
\(521\) −3.00000 5.19615i −0.131432 0.227648i 0.792797 0.609486i \(-0.208624\pi\)
−0.924229 + 0.381839i \(0.875291\pi\)
\(522\) −3.00000 5.19615i −0.131306 0.227429i
\(523\) −1.00000 + 1.73205i −0.0437269 + 0.0757373i −0.887061 0.461653i \(-0.847256\pi\)
0.843334 + 0.537390i \(0.180590\pi\)
\(524\) 18.0000 0.786334
\(525\) 0 0
\(526\) 0 0
\(527\) 12.0000 20.7846i 0.522728 0.905392i
\(528\) 0 0
\(529\) 11.5000 + 19.9186i 0.500000 + 0.866025i
\(530\) 0 0
\(531\) −6.00000 −0.260378
\(532\) 0 0
\(533\) −24.0000 −1.03956
\(534\) 6.00000 10.3923i 0.259645 0.449719i
\(535\) 0 0
\(536\) −2.00000 3.46410i −0.0863868 0.149626i
\(537\) −12.0000 + 20.7846i −0.517838 + 0.896922i
\(538\) 12.0000 0.517357
\(539\) 0 0
\(540\) 0 0
\(541\) −19.0000 + 32.9090i −0.816874 + 1.41487i 0.0911008 + 0.995842i \(0.470961\pi\)
−0.907975 + 0.419025i \(0.862372\pi\)
\(542\) −8.00000 13.8564i −0.343629 0.595184i
\(543\) 20.0000 + 34.6410i 0.858282 + 1.48659i
\(544\) 3.00000 5.19615i 0.128624 0.222783i
\(545\) 0 0
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) −9.00000 + 15.5885i −0.384461 + 0.665906i
\(549\) −4.00000 6.92820i −0.170716 0.295689i
\(550\) 0 0
\(551\) 6.00000 10.3923i 0.255609 0.442727i
\(552\) 0 0
\(553\) 0 0
\(554\) 10.0000 0.424859
\(555\) 0 0
\(556\) −7.00000 12.1244i −0.296866 0.514187i
\(557\) −3.00000 5.19615i −0.127114 0.220168i 0.795443 0.606028i \(-0.207238\pi\)
−0.922557 + 0.385860i \(0.873905\pi\)
\(558\) −2.00000 + 3.46410i −0.0846668 + 0.146647i
\(559\) −32.0000 −1.35346
\(560\) 0 0
\(561\) 0 0
\(562\) −3.00000 + 5.19615i −0.126547 + 0.219186i
\(563\) −15.0000 25.9808i −0.632175 1.09496i −0.987106 0.160066i \(-0.948829\pi\)
0.354932 0.934892i \(-0.384504\pi\)
\(564\) −12.0000 20.7846i −0.505291 0.875190i
\(565\) 0 0
\(566\) 22.0000 0.924729
\(567\) 0 0
\(568\) 0 0
\(569\) −3.00000 + 5.19615i −0.125767 + 0.217834i −0.922032 0.387113i \(-0.873472\pi\)
0.796266 + 0.604947i \(0.206806\pi\)
\(570\) 0 0
\(571\) −16.0000 27.7128i −0.669579 1.15975i −0.978022 0.208502i \(-0.933141\pi\)
0.308443 0.951243i \(-0.400192\pi\)
\(572\) 0 0
\(573\) −48.0000 −2.00523
\(574\) 0 0
\(575\) 0 0
\(576\) −0.500000 + 0.866025i −0.0208333 + 0.0360844i
\(577\) −1.00000 1.73205i −0.0416305 0.0721062i 0.844459 0.535620i \(-0.179922\pi\)
−0.886090 + 0.463513i \(0.846589\pi\)
\(578\) 9.50000 + 16.4545i 0.395148 + 0.684416i
\(579\) 14.0000 24.2487i 0.581820 1.00774i
\(580\) 0 0
\(581\) 0 0
\(582\) −20.0000 −0.829027
\(583\) 0 0
\(584\) 1.00000 + 1.73205i 0.0413803 + 0.0716728i
\(585\) 0 0
\(586\) 12.0000 20.7846i 0.495715 0.858604i
\(587\) −42.0000 −1.73353 −0.866763 0.498721i \(-0.833803\pi\)
−0.866763 + 0.498721i \(0.833803\pi\)
\(588\) 0 0
\(589\) −8.00000 −0.329634
\(590\) 0 0
\(591\) −18.0000 31.1769i −0.740421 1.28245i
\(592\) −1.00000 1.73205i −0.0410997 0.0711868i
\(593\) 3.00000 5.19615i 0.123195 0.213380i −0.797831 0.602881i \(-0.794019\pi\)
0.921026 + 0.389501i \(0.127353\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) 20.0000 34.6410i 0.818546 1.41776i
\(598\) 0 0
\(599\) 12.0000 + 20.7846i 0.490307 + 0.849236i 0.999938 0.0111569i \(-0.00355143\pi\)
−0.509631 + 0.860393i \(0.670218\pi\)
\(600\) 5.00000 8.66025i 0.204124 0.353553i
\(601\) 26.0000 1.06056 0.530281 0.847822i \(-0.322086\pi\)
0.530281 + 0.847822i \(0.322086\pi\)
\(602\) 0 0
\(603\) −4.00000 −0.162893
\(604\) −4.00000 + 6.92820i −0.162758 + 0.281905i
\(605\) 0 0
\(606\) 0 0
\(607\) −16.0000 + 27.7128i −0.649420 + 1.12483i 0.333842 + 0.942629i \(0.391655\pi\)
−0.983262 + 0.182199i \(0.941678\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) −24.0000 + 41.5692i −0.970936 + 1.68171i
\(612\) −3.00000 5.19615i −0.121268 0.210042i
\(613\) −1.00000 1.73205i −0.0403896 0.0699569i 0.845124 0.534570i \(-0.179527\pi\)
−0.885514 + 0.464614i \(0.846193\pi\)
\(614\) 1.00000 1.73205i 0.0403567 0.0698999i
\(615\) 0 0
\(616\) 0 0
\(617\) 6.00000 0.241551 0.120775 0.992680i \(-0.461462\pi\)
0.120775 + 0.992680i \(0.461462\pi\)
\(618\) 4.00000 6.92820i 0.160904 0.278693i
\(619\) −13.0000 22.5167i −0.522514 0.905021i −0.999657 0.0261952i \(-0.991661\pi\)
0.477143 0.878826i \(-0.341672\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 24.0000 0.962312
\(623\) 0 0
\(624\) 8.00000 0.320256
\(625\) −12.5000 + 21.6506i −0.500000 + 0.866025i
\(626\) −5.00000 8.66025i −0.199840 0.346133i
\(627\) 0 0
\(628\) 2.00000 3.46410i 0.0798087 0.138233i
\(629\) 12.0000 0.478471
\(630\) 0 0
\(631\) −16.0000 −0.636950 −0.318475 0.947931i \(-0.603171\pi\)
−0.318475 + 0.947931i \(0.603171\pi\)
\(632\) 4.00000 6.92820i 0.159111 0.275589i
\(633\) −4.00000 6.92820i −0.158986 0.275371i
\(634\) 3.00000 + 5.19615i 0.119145 + 0.206366i
\(635\) 0 0
\(636\) −12.0000 −0.475831
\(637\) 0 0
\(638\) 0 0
\(639\) 0 0
\(640\) 0 0
\(641\) 9.00000 + 15.5885i 0.355479 + 0.615707i 0.987200 0.159489i \(-0.0509845\pi\)
−0.631721 + 0.775196i \(0.717651\pi\)
\(642\) −12.0000 + 20.7846i −0.473602 + 0.820303i
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 6.00000 10.3923i 0.236067 0.408880i
\(647\) 6.00000 + 10.3923i 0.235884 + 0.408564i 0.959529 0.281609i \(-0.0908680\pi\)
−0.723645 + 0.690172i \(0.757535\pi\)
\(648\) −5.50000 9.52628i −0.216060 0.374228i
\(649\) 0 0
\(650\) −20.0000 −0.784465
\(651\) 0 0
\(652\) −16.0000 −0.626608
\(653\) −9.00000 + 15.5885i −0.352197 + 0.610023i −0.986634 0.162951i \(-0.947899\pi\)
0.634437 + 0.772975i \(0.281232\pi\)
\(654\) −2.00000 3.46410i −0.0782062 0.135457i
\(655\) 0 0
\(656\) −3.00000 + 5.19615i −0.117130 + 0.202876i
\(657\) 2.00000 0.0780274
\(658\) 0 0
\(659\) −24.0000 −0.934907 −0.467454 0.884018i \(-0.654829\pi\)
−0.467454 + 0.884018i \(0.654829\pi\)
\(660\) 0 0
\(661\) 20.0000 + 34.6410i 0.777910 + 1.34738i 0.933144 + 0.359502i \(0.117053\pi\)
−0.155235 + 0.987878i \(0.549613\pi\)
\(662\) 4.00000 + 6.92820i 0.155464 + 0.269272i
\(663\) −24.0000 + 41.5692i −0.932083 + 1.61441i
\(664\) 6.00000 0.232845
\(665\) 0 0
\(666\) −2.00000 −0.0774984
\(667\) 0 0
\(668\) 6.00000 + 10.3923i 0.232147 + 0.402090i
\(669\) 8.00000 + 13.8564i 0.309298 + 0.535720i
\(670\) 0 0
\(671\) 0 0
\(672\) 0 0
\(673\) 26.0000 1.00223 0.501113 0.865382i \(-0.332924\pi\)
0.501113 + 0.865382i \(0.332924\pi\)
\(674\) 7.00000 12.1244i 0.269630 0.467013i
\(675\) 10.0000 + 17.3205i 0.384900 + 0.666667i
\(676\) −1.50000 2.59808i −0.0576923 0.0999260i
\(677\) 6.00000 10.3923i 0.230599 0.399409i −0.727386 0.686229i \(-0.759265\pi\)
0.957984 + 0.286820i \(0.0925982\pi\)
\(678\) 12.0000 0.460857
\(679\) 0 0
\(680\) 0 0
\(681\) 18.0000 31.1769i 0.689761 1.19470i
\(682\) 0 0
\(683\) 6.00000 + 10.3923i 0.229584 + 0.397650i 0.957685 0.287819i \(-0.0929302\pi\)
−0.728101 + 0.685470i \(0.759597\pi\)
\(684\) −1.00000 + 1.73205i −0.0382360 + 0.0662266i
\(685\) 0 0
\(686\) 0 0
\(687\) 8.00000 0.305219
\(688\) −4.00000 + 6.92820i −0.152499 + 0.264135i
\(689\) 12.0000 + 20.7846i 0.457164 + 0.791831i
\(690\) 0 0
\(691\) 23.0000 39.8372i 0.874961 1.51548i 0.0181572 0.999835i \(-0.494220\pi\)
0.856804 0.515642i \(-0.172447\pi\)
\(692\) −12.0000 −0.456172
\(693\) 0 0
\(694\) 24.0000 0.911028
\(695\) 0 0
\(696\) 6.00000 + 10.3923i 0.227429 + 0.393919i
\(697\) −18.0000 31.1769i −0.681799 1.18091i
\(698\) −14.0000 + 24.2487i −0.529908 + 0.917827i
\(699\) 12.0000 0.453882
\(700\) 0 0
\(701\) 18.0000 0.679851 0.339925 0.940452i \(-0.389598\pi\)
0.339925 + 0.940452i \(0.389598\pi\)
\(702\) −8.00000 + 13.8564i −0.301941 + 0.522976i
\(703\) −2.00000 3.46410i −0.0754314 0.130651i
\(704\) 0 0
\(705\) 0 0
\(706\) −18.0000 −0.677439
\(707\) 0 0
\(708\) 12.0000 0.450988
\(709\) 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
\(711\) −4.00000 6.92820i −0.150012 0.259828i
\(712\) −3.00000 + 5.19615i −0.112430 + 0.194734i
\(713\) 0 0
\(714\) 0 0
\(715\) 0 0
\(716\) 6.00000 10.3923i 0.224231 0.388379i
\(717\) 24.0000 + 41.5692i 0.896296 + 1.55243i
\(718\) −12.0000 20.7846i −0.447836 0.775675i
\(719\) −6.00000 + 10.3923i −0.223762 + 0.387568i −0.955947 0.293538i \(-0.905167\pi\)
0.732185 + 0.681106i \(0.238501\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 15.0000 0.558242
\(723\) −10.0000 + 17.3205i −0.371904 + 0.644157i
\(724\) −10.0000 17.3205i −0.371647 0.643712i
\(725\) −15.0000 25.9808i −0.557086 0.964901i
\(726\) 11.0000 19.0526i 0.408248 0.707107i
\(727\) 44.0000 1.63187 0.815935 0.578144i \(-0.196223\pi\)
0.815935 + 0.578144i \(0.196223\pi\)
\(728\) 0 0
\(729\) 13.0000 0.481481
\(730\) 0 0
\(731\) −24.0000 41.5692i −0.887672 1.53749i
\(732\) 8.00000 + 13.8564i 0.295689 + 0.512148i
\(733\) 20.0000 34.6410i 0.738717 1.27950i −0.214356 0.976756i \(-0.568765\pi\)
0.953073 0.302740i \(-0.0979013\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) 0 0
\(737\) 0 0
\(738\) 3.00000 + 5.19615i 0.110432 + 0.191273i
\(739\) 8.00000 + 13.8564i 0.294285 + 0.509716i 0.974818 0.223001i \(-0.0715853\pi\)
−0.680534 + 0.732717i \(0.738252\pi\)
\(740\) 0 0
\(741\) 16.0000 0.587775
\(742\) 0 0
\(743\) 24.0000 0.880475 0.440237 0.897881i \(-0.354894\pi\)
0.440237 + 0.897881i \(0.354894\pi\)
\(744\) 4.00000 6.92820i 0.146647 0.254000i
\(745\) 0 0
\(746\) 7.00000 + 12.1244i 0.256288 + 0.443904i
\(747\) 3.00000 5.19615i 0.109764 0.190117i
\(748\) 0 0
\(749\) 0 0
\(750\) 0 0
\(751\) 20.0000 34.6410i 0.729810 1.26407i −0.227153 0.973859i \(-0.572942\pi\)
0.956963 0.290209i \(-0.0937250\pi\)
\(752\) 6.00000 + 10.3923i 0.218797 + 0.378968i
\(753\) −18.0000 31.1769i −0.655956 1.13615i
\(754\) 12.0000 20.7846i 0.437014 0.756931i
\(755\) 0 0
\(756\) 0 0
\(757\) 2.00000 0.0726912 0.0363456 0.999339i \(-0.488428\pi\)
0.0363456 + 0.999339i \(0.488428\pi\)
\(758\) −8.00000 + 13.8564i −0.290573 + 0.503287i
\(759\) 0 0
\(760\) 0 0
\(761\) 9.00000 15.5885i 0.326250 0.565081i −0.655515 0.755182i \(-0.727548\pi\)
0.981764 + 0.190101i \(0.0608816\pi\)
\(762\) −32.0000 −1.15924
\(763\) 0 0
\(764\) 24.0000 0.868290
\(765\) 0 0
\(766\) 18.0000 + 31.1769i 0.650366 + 1.12647i
\(767\) −12.0000 20.7846i −0.433295 0.750489i
\(768\) 1.00000 1.73205i 0.0360844 0.0625000i
\(769\) 14.0000 0.504853 0.252426 0.967616i \(-0.418771\pi\)
0.252426 + 0.967616i \(0.418771\pi\)
\(770\) 0 0
\(771\) −36.0000 −1.29651
\(772\) −7.00000 + 12.1244i −0.251936 + 0.436365i
\(773\) −12.0000 20.7846i −0.431610 0.747570i 0.565402 0.824815i \(-0.308721\pi\)
−0.997012 + 0.0772449i \(0.975388\pi\)
\(774\) 4.00000 + 6.92820i 0.143777 + 0.249029i
\(775\) −10.0000 + 17.3205i −0.359211 + 0.622171i
\(776\) 10.0000 0.358979
\(777\) 0 0
\(778\) −18.0000 −0.645331
\(779\) −6.00000 + 10.3923i −0.214972 + 0.372343i
\(780\) 0 0
\(781\) 0 0
\(782\) 0 0
\(783\) −24.0000 −0.857690
\(784\) 0 0
\(785\) 0 0
\(786\) −18.0000 + 31.1769i −0.642039 + 1.11204i
\(787\) 11.0000 + 19.0526i 0.392108 + 0.679150i 0.992727 0.120384i \(-0.0384127\pi\)
−0.600620 + 0.799535i \(0.705079\pi\)
\(788\) 9.00000 + 15.5885i 0.320612 + 0.555316i
\(789\) 0 0
\(790\) 0 0
\(791\) 0 0
\(792\) 0 0
\(793\) 16.0000 27.7128i 0.568177 0.984111i
\(794\) 10.0000 + 17.3205i 0.354887 + 0.614682i
\(795\) 0 0
\(796\) −10.0000 + 17.3205i −0.354441 + 0.613909i
\(797\) −12.0000 −0.425062 −0.212531 0.977154i \(-0.568171\pi\)
−0.212531 + 0.977154i \(0.568171\pi\)
\(798\) 0 0
\(799\) −72.0000 −2.54718
\(800\) −2.50000 + 4.33013i −0.0883883 + 0.153093i
\(801\) 3.00000 + 5.19615i 0.106000 + 0.183597i
\(802\) −9.00000 15.5885i −0.317801 0.550448i
\(803\) 0 0
\(804\) 8.00000 0.282138
\(805\) 0 0
\(806\) −16.0000