Properties

Label 1323.2.h.h.802.8
Level $1323$
Weight $2$
Character 1323.802
Analytic conductor $10.564$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 1323 = 3^{3} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1323.h (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(10.5642081874\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: no (minimal twist has level 441)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 802.8
Character \(\chi\) \(=\) 1323.802
Dual form 1323.2.h.h.226.8

$q$-expansion

\(f(q)\) \(=\) \(q+1.10281 q^{2} -0.783802 q^{4} +(0.0527330 - 0.0913363i) q^{5} -3.07001 q^{8} +O(q^{10})\) \(q+1.10281 q^{2} -0.783802 q^{4} +(0.0527330 - 0.0913363i) q^{5} -3.07001 q^{8} +(0.0581547 - 0.100727i) q^{10} +(1.66866 + 2.89020i) q^{11} +(-1.23997 - 2.14770i) q^{13} -1.81805 q^{16} +(0.806594 - 1.39706i) q^{17} +(3.84133 + 6.65338i) q^{19} +(-0.0413323 + 0.0715896i) q^{20} +(1.84022 + 3.18735i) q^{22} +(-0.948593 + 1.64301i) q^{23} +(2.49444 + 4.32049i) q^{25} +(-1.36746 - 2.36851i) q^{26} +(-4.64521 + 8.04574i) q^{29} +9.26162 q^{31} +4.13506 q^{32} +(0.889523 - 1.54070i) q^{34} +(0.991268 + 1.71693i) q^{37} +(4.23627 + 7.33744i) q^{38} +(-0.161891 + 0.280404i) q^{40} +(-3.74268 - 6.48252i) q^{41} +(-3.77388 + 6.53655i) q^{43} +(-1.30790 - 2.26534i) q^{44} +(-1.04612 + 1.81194i) q^{46} +3.19560 q^{47} +(2.75090 + 4.76470i) q^{50} +(0.971894 + 1.68337i) q^{52} +(-4.98839 + 8.64015i) q^{53} +0.351974 q^{55} +(-5.12280 + 8.87296i) q^{58} -4.45986 q^{59} -5.67100 q^{61} +10.2138 q^{62} +8.19630 q^{64} -0.261550 q^{65} +9.97141 q^{67} +(-0.632210 + 1.09502i) q^{68} -3.29042 q^{71} +(2.36189 - 4.09091i) q^{73} +(1.09318 + 1.89345i) q^{74} +(-3.01084 - 5.21493i) q^{76} +7.69409 q^{79} +(-0.0958713 + 0.166054i) q^{80} +(-4.12748 - 7.14901i) q^{82} +(0.584428 - 1.01226i) q^{83} +(-0.0850683 - 0.147343i) q^{85} +(-4.16189 + 7.20860i) q^{86} +(-5.12280 - 8.87296i) q^{88} +(3.01477 + 5.22173i) q^{89} +(0.743509 - 1.28780i) q^{92} +3.52415 q^{94} +0.810260 q^{95} +(-1.90127 + 3.29310i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 8q^{2} + 24q^{4} + 24q^{8} + O(q^{10}) \) \( 24q + 8q^{2} + 24q^{4} + 24q^{8} - 20q^{11} + 24q^{16} - 32q^{23} - 12q^{25} - 16q^{29} + 96q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} + 120q^{65} + 24q^{67} + 112q^{71} - 68q^{74} - 24q^{79} + 12q^{85} - 76q^{86} - 16q^{92} + 128q^{95} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.10281 0.779807 0.389903 0.920856i \(-0.372508\pi\)
0.389903 + 0.920856i \(0.372508\pi\)
\(3\) 0 0
\(4\) −0.783802 −0.391901
\(5\) 0.0527330 0.0913363i 0.0235829 0.0408468i −0.853993 0.520284i \(-0.825826\pi\)
0.877576 + 0.479438i \(0.159159\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −3.07001 −1.08541
\(9\) 0 0
\(10\) 0.0581547 0.100727i 0.0183901 0.0318527i
\(11\) 1.66866 + 2.89020i 0.503119 + 0.871428i 0.999994 + 0.00360543i \(0.00114765\pi\)
−0.496874 + 0.867822i \(0.665519\pi\)
\(12\) 0 0
\(13\) −1.23997 2.14770i −0.343907 0.595664i 0.641248 0.767334i \(-0.278417\pi\)
−0.985155 + 0.171670i \(0.945084\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.81805 −0.454512
\(17\) 0.806594 1.39706i 0.195628 0.338837i −0.751478 0.659758i \(-0.770659\pi\)
0.947106 + 0.320921i \(0.103992\pi\)
\(18\) 0 0
\(19\) 3.84133 + 6.65338i 0.881262 + 1.52639i 0.849939 + 0.526880i \(0.176638\pi\)
0.0313221 + 0.999509i \(0.490028\pi\)
\(20\) −0.0413323 + 0.0715896i −0.00924218 + 0.0160079i
\(21\) 0 0
\(22\) 1.84022 + 3.18735i 0.392336 + 0.679546i
\(23\) −0.948593 + 1.64301i −0.197795 + 0.342592i −0.947813 0.318826i \(-0.896711\pi\)
0.750018 + 0.661417i \(0.230045\pi\)
\(24\) 0 0
\(25\) 2.49444 + 4.32049i 0.498888 + 0.864099i
\(26\) −1.36746 2.36851i −0.268181 0.464503i
\(27\) 0 0
\(28\) 0 0
\(29\) −4.64521 + 8.04574i −0.862594 + 1.49406i 0.00682200 + 0.999977i \(0.497828\pi\)
−0.869416 + 0.494080i \(0.835505\pi\)
\(30\) 0 0
\(31\) 9.26162 1.66344 0.831718 0.555199i \(-0.187358\pi\)
0.831718 + 0.555199i \(0.187358\pi\)
\(32\) 4.13506 0.730982
\(33\) 0 0
\(34\) 0.889523 1.54070i 0.152552 0.264228i
\(35\) 0 0
\(36\) 0 0
\(37\) 0.991268 + 1.71693i 0.162963 + 0.282261i 0.935930 0.352186i \(-0.114561\pi\)
−0.772967 + 0.634447i \(0.781228\pi\)
\(38\) 4.23627 + 7.33744i 0.687214 + 1.19029i
\(39\) 0 0
\(40\) −0.161891 + 0.280404i −0.0255973 + 0.0443357i
\(41\) −3.74268 6.48252i −0.584509 1.01240i −0.994936 0.100506i \(-0.967954\pi\)
0.410427 0.911893i \(-0.365379\pi\)
\(42\) 0 0
\(43\) −3.77388 + 6.53655i −0.575512 + 0.996815i 0.420474 + 0.907304i \(0.361864\pi\)
−0.995986 + 0.0895108i \(0.971470\pi\)
\(44\) −1.30790 2.26534i −0.197173 0.341514i
\(45\) 0 0
\(46\) −1.04612 + 1.81194i −0.154242 + 0.267155i
\(47\) 3.19560 0.466127 0.233063 0.972462i \(-0.425125\pi\)
0.233063 + 0.972462i \(0.425125\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.75090 + 4.76470i 0.389036 + 0.673830i
\(51\) 0 0
\(52\) 0.971894 + 1.68337i 0.134777 + 0.233441i
\(53\) −4.98839 + 8.64015i −0.685209 + 1.18682i 0.288163 + 0.957581i \(0.406956\pi\)
−0.973371 + 0.229234i \(0.926378\pi\)
\(54\) 0 0
\(55\) 0.351974 0.0474601
\(56\) 0 0
\(57\) 0 0
\(58\) −5.12280 + 8.87296i −0.672657 + 1.16508i
\(59\) −4.45986 −0.580625 −0.290312 0.956932i \(-0.593759\pi\)
−0.290312 + 0.956932i \(0.593759\pi\)
\(60\) 0 0
\(61\) −5.67100 −0.726097 −0.363048 0.931770i \(-0.618264\pi\)
−0.363048 + 0.931770i \(0.618264\pi\)
\(62\) 10.2138 1.29716
\(63\) 0 0
\(64\) 8.19630 1.02454
\(65\) −0.261550 −0.0324413
\(66\) 0 0
\(67\) 9.97141 1.21820 0.609101 0.793093i \(-0.291530\pi\)
0.609101 + 0.793093i \(0.291530\pi\)
\(68\) −0.632210 + 1.09502i −0.0766667 + 0.132791i
\(69\) 0 0
\(70\) 0 0
\(71\) −3.29042 −0.390502 −0.195251 0.980753i \(-0.562552\pi\)
−0.195251 + 0.980753i \(0.562552\pi\)
\(72\) 0 0
\(73\) 2.36189 4.09091i 0.276438 0.478805i −0.694059 0.719919i \(-0.744179\pi\)
0.970497 + 0.241113i \(0.0775125\pi\)
\(74\) 1.09318 + 1.89345i 0.127080 + 0.220109i
\(75\) 0 0
\(76\) −3.01084 5.21493i −0.345367 0.598194i
\(77\) 0 0
\(78\) 0 0
\(79\) 7.69409 0.865653 0.432827 0.901477i \(-0.357516\pi\)
0.432827 + 0.901477i \(0.357516\pi\)
\(80\) −0.0958713 + 0.166054i −0.0107187 + 0.0185654i
\(81\) 0 0
\(82\) −4.12748 7.14901i −0.455804 0.789476i
\(83\) 0.584428 1.01226i 0.0641493 0.111110i −0.832167 0.554525i \(-0.812900\pi\)
0.896316 + 0.443415i \(0.146233\pi\)
\(84\) 0 0
\(85\) −0.0850683 0.147343i −0.00922695 0.0159815i
\(86\) −4.16189 + 7.20860i −0.448788 + 0.777323i
\(87\) 0 0
\(88\) −5.12280 8.87296i −0.546093 0.945860i
\(89\) 3.01477 + 5.22173i 0.319565 + 0.553503i 0.980397 0.197031i \(-0.0631299\pi\)
−0.660832 + 0.750534i \(0.729797\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0.743509 1.28780i 0.0775162 0.134262i
\(93\) 0 0
\(94\) 3.52415 0.363489
\(95\) 0.810260 0.0831309
\(96\) 0 0
\(97\) −1.90127 + 3.29310i −0.193045 + 0.334364i −0.946258 0.323413i \(-0.895170\pi\)
0.753213 + 0.657777i \(0.228503\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.95515 3.38641i −0.195515 0.338641i
\(101\) 8.73512 + 15.1297i 0.869177 + 1.50546i 0.862839 + 0.505479i \(0.168684\pi\)
0.00633771 + 0.999980i \(0.497983\pi\)
\(102\) 0 0
\(103\) 4.36602 7.56217i 0.430197 0.745123i −0.566693 0.823929i \(-0.691777\pi\)
0.996890 + 0.0788062i \(0.0251108\pi\)
\(104\) 3.80674 + 6.59346i 0.373281 + 0.646542i
\(105\) 0 0
\(106\) −5.50127 + 9.52848i −0.534330 + 0.925487i
\(107\) −9.07316 15.7152i −0.877135 1.51924i −0.854471 0.519500i \(-0.826118\pi\)
−0.0226645 0.999743i \(-0.507215\pi\)
\(108\) 0 0
\(109\) 2.11124 3.65678i 0.202220 0.350256i −0.747023 0.664798i \(-0.768518\pi\)
0.949243 + 0.314542i \(0.101851\pi\)
\(110\) 0.388161 0.0370097
\(111\) 0 0
\(112\) 0 0
\(113\) −1.02824 1.78096i −0.0967285 0.167539i 0.813600 0.581425i \(-0.197505\pi\)
−0.910329 + 0.413886i \(0.864171\pi\)
\(114\) 0 0
\(115\) 0.100044 + 0.173282i 0.00932919 + 0.0161586i
\(116\) 3.64093 6.30627i 0.338052 0.585523i
\(117\) 0 0
\(118\) −4.91840 −0.452775
\(119\) 0 0
\(120\) 0 0
\(121\) −0.0688352 + 0.119226i −0.00625774 + 0.0108387i
\(122\) −6.25405 −0.566215
\(123\) 0 0
\(124\) −7.25928 −0.651902
\(125\) 1.05349 0.0942268
\(126\) 0 0
\(127\) 0.317159 0.0281433 0.0140717 0.999901i \(-0.495521\pi\)
0.0140717 + 0.999901i \(0.495521\pi\)
\(128\) 0.768871 0.0679592
\(129\) 0 0
\(130\) −0.288441 −0.0252980
\(131\) −7.47816 + 12.9525i −0.653370 + 1.13167i 0.328930 + 0.944354i \(0.393312\pi\)
−0.982300 + 0.187315i \(0.940021\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 10.9966 0.949962
\(135\) 0 0
\(136\) −2.47625 + 4.28900i −0.212337 + 0.367779i
\(137\) −7.62367 13.2046i −0.651334 1.12814i −0.982799 0.184676i \(-0.940876\pi\)
0.331466 0.943467i \(-0.392457\pi\)
\(138\) 0 0
\(139\) −4.05943 7.03114i −0.344316 0.596374i 0.640913 0.767614i \(-0.278556\pi\)
−0.985229 + 0.171240i \(0.945223\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −3.62872 −0.304516
\(143\) 4.13818 7.16754i 0.346052 0.599380i
\(144\) 0 0
\(145\) 0.489912 + 0.848553i 0.0406850 + 0.0704685i
\(146\) 2.60473 4.51152i 0.215569 0.373376i
\(147\) 0 0
\(148\) −0.776958 1.34573i −0.0638656 0.110618i
\(149\) −5.57430 + 9.65497i −0.456664 + 0.790966i −0.998782 0.0493365i \(-0.984289\pi\)
0.542118 + 0.840303i \(0.317623\pi\)
\(150\) 0 0
\(151\) 5.63676 + 9.76315i 0.458713 + 0.794514i 0.998893 0.0470354i \(-0.0149774\pi\)
−0.540180 + 0.841549i \(0.681644\pi\)
\(152\) −11.7929 20.4260i −0.956534 1.65677i
\(153\) 0 0
\(154\) 0 0
\(155\) 0.488393 0.845922i 0.0392287 0.0679461i
\(156\) 0 0
\(157\) −12.2064 −0.974173 −0.487087 0.873354i \(-0.661940\pi\)
−0.487087 + 0.873354i \(0.661940\pi\)
\(158\) 8.48515 0.675042
\(159\) 0 0
\(160\) 0.218054 0.377681i 0.0172387 0.0298583i
\(161\) 0 0
\(162\) 0 0
\(163\) −4.48132 7.76187i −0.351004 0.607957i 0.635422 0.772165i \(-0.280826\pi\)
−0.986426 + 0.164209i \(0.947493\pi\)
\(164\) 2.93352 + 5.08101i 0.229070 + 0.396760i
\(165\) 0 0
\(166\) 0.644515 1.11633i 0.0500240 0.0866442i
\(167\) −8.70833 15.0833i −0.673871 1.16718i −0.976798 0.214165i \(-0.931297\pi\)
0.302927 0.953014i \(-0.402036\pi\)
\(168\) 0 0
\(169\) 3.42493 5.93216i 0.263456 0.456320i
\(170\) −0.0938145 0.162491i −0.00719524 0.0124625i
\(171\) 0 0
\(172\) 2.95798 5.12337i 0.225544 0.390653i
\(173\) 2.82933 0.215110 0.107555 0.994199i \(-0.465698\pi\)
0.107555 + 0.994199i \(0.465698\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.03370 5.25453i −0.228674 0.396075i
\(177\) 0 0
\(178\) 3.32473 + 5.75860i 0.249199 + 0.431625i
\(179\) −5.08135 + 8.80115i −0.379798 + 0.657829i −0.991033 0.133620i \(-0.957340\pi\)
0.611235 + 0.791449i \(0.290673\pi\)
\(180\) 0 0
\(181\) 17.0870 1.27006 0.635032 0.772486i \(-0.280987\pi\)
0.635032 + 0.772486i \(0.280987\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 2.91220 5.04407i 0.214690 0.371854i
\(185\) 0.209090 0.0153726
\(186\) 0 0
\(187\) 5.38371 0.393696
\(188\) −2.50472 −0.182676
\(189\) 0 0
\(190\) 0.893566 0.0648261
\(191\) 22.4000 1.62081 0.810404 0.585872i \(-0.199248\pi\)
0.810404 + 0.585872i \(0.199248\pi\)
\(192\) 0 0
\(193\) −0.256786 −0.0184839 −0.00924194 0.999957i \(-0.502942\pi\)
−0.00924194 + 0.999957i \(0.502942\pi\)
\(194\) −2.09675 + 3.63168i −0.150538 + 0.260739i
\(195\) 0 0
\(196\) 0 0
\(197\) 0.763370 0.0543878 0.0271939 0.999630i \(-0.491343\pi\)
0.0271939 + 0.999630i \(0.491343\pi\)
\(198\) 0 0
\(199\) −2.51561 + 4.35716i −0.178327 + 0.308871i −0.941307 0.337550i \(-0.890402\pi\)
0.762981 + 0.646421i \(0.223735\pi\)
\(200\) −7.65796 13.2640i −0.541500 0.937905i
\(201\) 0 0
\(202\) 9.63321 + 16.6852i 0.677790 + 1.17397i
\(203\) 0 0
\(204\) 0 0
\(205\) −0.789452 −0.0551377
\(206\) 4.81491 8.33966i 0.335470 0.581052i
\(207\) 0 0
\(208\) 2.25433 + 3.90462i 0.156310 + 0.270737i
\(209\) −12.8197 + 22.2044i −0.886759 + 1.53591i
\(210\) 0 0
\(211\) −3.60537 6.24468i −0.248204 0.429901i 0.714824 0.699305i \(-0.246507\pi\)
−0.963027 + 0.269403i \(0.913174\pi\)
\(212\) 3.90991 6.77217i 0.268534 0.465114i
\(213\) 0 0
\(214\) −10.0060 17.3309i −0.683996 1.18472i
\(215\) 0.398017 + 0.689385i 0.0271445 + 0.0470157i
\(216\) 0 0
\(217\) 0 0
\(218\) 2.32831 4.03274i 0.157693 0.273132i
\(219\) 0 0
\(220\) −0.275878 −0.0185997
\(221\) −4.00062 −0.269111
\(222\) 0 0
\(223\) −5.59106 + 9.68400i −0.374405 + 0.648488i −0.990238 0.139388i \(-0.955486\pi\)
0.615833 + 0.787877i \(0.288820\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1.13395 1.96407i −0.0754295 0.130648i
\(227\) −11.8853 20.5860i −0.788857 1.36634i −0.926668 0.375881i \(-0.877340\pi\)
0.137811 0.990459i \(-0.455993\pi\)
\(228\) 0 0
\(229\) −0.952737 + 1.65019i −0.0629586 + 0.109048i −0.895787 0.444484i \(-0.853387\pi\)
0.832828 + 0.553532i \(0.186720\pi\)
\(230\) 0.110330 + 0.191098i 0.00727497 + 0.0126006i
\(231\) 0 0
\(232\) 14.2609 24.7006i 0.936272 1.62167i
\(233\) 3.27092 + 5.66540i 0.214285 + 0.371153i 0.953051 0.302809i \(-0.0979245\pi\)
−0.738766 + 0.673962i \(0.764591\pi\)
\(234\) 0 0
\(235\) 0.168514 0.291875i 0.0109926 0.0190398i
\(236\) 3.49565 0.227547
\(237\) 0 0
\(238\) 0 0
\(239\) −10.6735 18.4870i −0.690409 1.19582i −0.971704 0.236202i \(-0.924097\pi\)
0.281295 0.959621i \(-0.409236\pi\)
\(240\) 0 0
\(241\) −10.0331 17.3778i −0.646288 1.11940i −0.984003 0.178155i \(-0.942987\pi\)
0.337715 0.941248i \(-0.390346\pi\)
\(242\) −0.0759124 + 0.131484i −0.00487983 + 0.00845212i
\(243\) 0 0
\(244\) 4.44494 0.284558
\(245\) 0 0
\(246\) 0 0
\(247\) 9.52629 16.5000i 0.606144 1.04987i
\(248\) −28.4333 −1.80552
\(249\) 0 0
\(250\) 1.16180 0.0734787
\(251\) −6.81467 −0.430138 −0.215069 0.976599i \(-0.568998\pi\)
−0.215069 + 0.976599i \(0.568998\pi\)
\(252\) 0 0
\(253\) −6.33151 −0.398059
\(254\) 0.349767 0.0219464
\(255\) 0 0
\(256\) −15.5447 −0.971542
\(257\) 7.19415 12.4606i 0.448759 0.777273i −0.549546 0.835463i \(-0.685199\pi\)
0.998306 + 0.0581897i \(0.0185328\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.205004 0.0127138
\(261\) 0 0
\(262\) −8.24701 + 14.2842i −0.509502 + 0.882484i
\(263\) −0.769503 1.33282i −0.0474496 0.0821851i 0.841325 0.540529i \(-0.181776\pi\)
−0.888775 + 0.458344i \(0.848443\pi\)
\(264\) 0 0
\(265\) 0.526106 + 0.911243i 0.0323185 + 0.0559772i
\(266\) 0 0
\(267\) 0 0
\(268\) −7.81562 −0.477415
\(269\) 13.1285 22.7393i 0.800461 1.38644i −0.118852 0.992912i \(-0.537921\pi\)
0.919313 0.393527i \(-0.128745\pi\)
\(270\) 0 0
\(271\) 8.96673 + 15.5308i 0.544690 + 0.943431i 0.998626 + 0.0523969i \(0.0166861\pi\)
−0.453936 + 0.891034i \(0.649981\pi\)
\(272\) −1.46643 + 2.53993i −0.0889152 + 0.154006i
\(273\) 0 0
\(274\) −8.40748 14.5622i −0.507915 0.879734i
\(275\) −8.32473 + 14.4188i −0.502000 + 0.869489i
\(276\) 0 0
\(277\) 9.43563 + 16.3430i 0.566932 + 0.981955i 0.996867 + 0.0790954i \(0.0252032\pi\)
−0.429935 + 0.902860i \(0.641463\pi\)
\(278\) −4.47680 7.75404i −0.268500 0.465056i
\(279\) 0 0
\(280\) 0 0
\(281\) 2.49578 4.32283i 0.148886 0.257878i −0.781930 0.623366i \(-0.785765\pi\)
0.930816 + 0.365488i \(0.119098\pi\)
\(282\) 0 0
\(283\) −15.3927 −0.915000 −0.457500 0.889210i \(-0.651255\pi\)
−0.457500 + 0.889210i \(0.651255\pi\)
\(284\) 2.57904 0.153038
\(285\) 0 0
\(286\) 4.56364 7.90446i 0.269854 0.467401i
\(287\) 0 0
\(288\) 0 0
\(289\) 7.19881 + 12.4687i 0.423460 + 0.733454i
\(290\) 0.540282 + 0.935796i 0.0317265 + 0.0549518i
\(291\) 0 0
\(292\) −1.85126 + 3.20647i −0.108337 + 0.187644i
\(293\) 12.9013 + 22.3456i 0.753700 + 1.30545i 0.946018 + 0.324114i \(0.105066\pi\)
−0.192318 + 0.981333i \(0.561601\pi\)
\(294\) 0 0
\(295\) −0.235182 + 0.407347i −0.0136928 + 0.0237167i
\(296\) −3.04321 5.27099i −0.176883 0.306370i
\(297\) 0 0
\(298\) −6.14741 + 10.6476i −0.356110 + 0.616801i
\(299\) 4.70492 0.272093
\(300\) 0 0
\(301\) 0 0
\(302\) 6.21629 + 10.7669i 0.357707 + 0.619567i
\(303\) 0 0
\(304\) −6.98373 12.0962i −0.400544 0.693763i
\(305\) −0.299049 + 0.517968i −0.0171235 + 0.0296588i
\(306\) 0 0
\(307\) −22.2914 −1.27224 −0.636120 0.771590i \(-0.719462\pi\)
−0.636120 + 0.771590i \(0.719462\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.538607 0.932894i 0.0305908 0.0529848i
\(311\) 1.30986 0.0742755 0.0371377 0.999310i \(-0.488176\pi\)
0.0371377 + 0.999310i \(0.488176\pi\)
\(312\) 0 0
\(313\) 21.5770 1.21960 0.609802 0.792554i \(-0.291249\pi\)
0.609802 + 0.792554i \(0.291249\pi\)
\(314\) −13.4613 −0.759667
\(315\) 0 0
\(316\) −6.03065 −0.339250
\(317\) 24.7819 1.39189 0.695946 0.718094i \(-0.254985\pi\)
0.695946 + 0.718094i \(0.254985\pi\)
\(318\) 0 0
\(319\) −31.0051 −1.73595
\(320\) 0.432216 0.748620i 0.0241616 0.0418491i
\(321\) 0 0
\(322\) 0 0
\(323\) 12.3936 0.689597
\(324\) 0 0
\(325\) 6.18608 10.7146i 0.343142 0.594339i
\(326\) −4.94206 8.55990i −0.273715 0.474089i
\(327\) 0 0
\(328\) 11.4901 + 19.9014i 0.634434 + 1.09887i
\(329\) 0 0
\(330\) 0 0
\(331\) 13.8451 0.760996 0.380498 0.924782i \(-0.375753\pi\)
0.380498 + 0.924782i \(0.375753\pi\)
\(332\) −0.458076 + 0.793410i −0.0251402 + 0.0435440i
\(333\) 0 0
\(334\) −9.60367 16.6340i −0.525489 0.910174i
\(335\) 0.525823 0.910752i 0.0287288 0.0497597i
\(336\) 0 0
\(337\) 1.69444 + 2.93485i 0.0923018 + 0.159871i 0.908479 0.417930i \(-0.137244\pi\)
−0.816178 + 0.577801i \(0.803911\pi\)
\(338\) 3.77706 6.54206i 0.205445 0.355841i
\(339\) 0 0
\(340\) 0.0666767 + 0.115487i 0.00361605 + 0.00626319i
\(341\) 15.4545 + 26.7679i 0.836906 + 1.44956i
\(342\) 0 0
\(343\) 0 0
\(344\) 11.5859 20.0673i 0.624668 1.08196i
\(345\) 0 0
\(346\) 3.12022 0.167744
\(347\) 14.5148 0.779195 0.389597 0.920985i \(-0.372614\pi\)
0.389597 + 0.920985i \(0.372614\pi\)
\(348\) 0 0
\(349\) 7.86412 13.6211i 0.420957 0.729119i −0.575076 0.818100i \(-0.695028\pi\)
0.996033 + 0.0889810i \(0.0283610\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 6.90000 + 11.9511i 0.367771 + 0.636998i
\(353\) −2.07211 3.58900i −0.110287 0.191023i 0.805599 0.592462i \(-0.201844\pi\)
−0.915886 + 0.401438i \(0.868510\pi\)
\(354\) 0 0
\(355\) −0.173514 + 0.300535i −0.00920917 + 0.0159508i
\(356\) −2.36298 4.09281i −0.125238 0.216918i
\(357\) 0 0
\(358\) −5.60378 + 9.70603i −0.296169 + 0.512979i
\(359\) 3.96994 + 6.87614i 0.209525 + 0.362909i 0.951565 0.307447i \(-0.0994748\pi\)
−0.742040 + 0.670356i \(0.766141\pi\)
\(360\) 0 0
\(361\) −20.0116 + 34.6612i −1.05324 + 1.82427i
\(362\) 18.8437 0.990405
\(363\) 0 0
\(364\) 0 0
\(365\) −0.249099 0.431453i −0.0130385 0.0225833i
\(366\) 0 0
\(367\) 6.57455 + 11.3875i 0.343189 + 0.594420i 0.985023 0.172423i \(-0.0551596\pi\)
−0.641834 + 0.766843i \(0.721826\pi\)
\(368\) 1.72459 2.98708i 0.0899004 0.155712i
\(369\) 0 0
\(370\) 0.230588 0.0119877
\(371\) 0 0
\(372\) 0 0
\(373\) −3.90543 + 6.76441i −0.202216 + 0.350248i −0.949242 0.314547i \(-0.898147\pi\)
0.747026 + 0.664794i \(0.231481\pi\)
\(374\) 5.93723 0.307007
\(375\) 0 0
\(376\) −9.81055 −0.505940
\(377\) 23.0398 1.18661
\(378\) 0 0
\(379\) −31.6147 −1.62394 −0.811968 0.583702i \(-0.801604\pi\)
−0.811968 + 0.583702i \(0.801604\pi\)
\(380\) −0.635084 −0.0325791
\(381\) 0 0
\(382\) 24.7030 1.26392
\(383\) −5.36593 + 9.29407i −0.274186 + 0.474905i −0.969930 0.243386i \(-0.921742\pi\)
0.695743 + 0.718291i \(0.255075\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.283187 −0.0144139
\(387\) 0 0
\(388\) 1.49022 2.58114i 0.0756546 0.131038i
\(389\) 12.0734 + 20.9118i 0.612147 + 1.06027i 0.990878 + 0.134763i \(0.0430272\pi\)
−0.378731 + 0.925507i \(0.623639\pi\)
\(390\) 0 0
\(391\) 1.53026 + 2.65049i 0.0773885 + 0.134041i
\(392\) 0 0
\(393\) 0 0
\(394\) 0.841854 0.0424120
\(395\) 0.405733 0.702750i 0.0204146 0.0353592i
\(396\) 0 0
\(397\) −12.0285 20.8339i −0.603691 1.04562i −0.992257 0.124203i \(-0.960363\pi\)
0.388566 0.921421i \(-0.372971\pi\)
\(398\) −2.77424 + 4.80513i −0.139060 + 0.240860i
\(399\) 0 0
\(400\) −4.53501 7.85487i −0.226751 0.392744i
\(401\) −0.781158 + 1.35301i −0.0390092 + 0.0675659i −0.884871 0.465836i \(-0.845753\pi\)
0.845862 + 0.533402i \(0.179087\pi\)
\(402\) 0 0
\(403\) −11.4842 19.8911i −0.572067 0.990849i
\(404\) −6.84661 11.8587i −0.340631 0.589991i
\(405\) 0 0
\(406\) 0 0
\(407\) −3.30817 + 5.72992i −0.163980 + 0.284022i
\(408\) 0 0
\(409\) −22.3456 −1.10492 −0.552460 0.833539i \(-0.686311\pi\)
−0.552460 + 0.833539i \(0.686311\pi\)
\(410\) −0.870619 −0.0429968
\(411\) 0 0
\(412\) −3.42210 + 5.92725i −0.168595 + 0.292014i
\(413\) 0 0
\(414\) 0 0
\(415\) −0.0616373 0.106759i −0.00302566 0.00524059i
\(416\) −5.12736 8.88086i −0.251390 0.435420i
\(417\) 0 0
\(418\) −14.1378 + 24.4873i −0.691501 + 1.19771i
\(419\) −2.98648 5.17273i −0.145899 0.252704i 0.783809 0.621002i \(-0.213274\pi\)
−0.929708 + 0.368298i \(0.879941\pi\)
\(420\) 0 0
\(421\) 7.31594 12.6716i 0.356557 0.617575i −0.630826 0.775924i \(-0.717284\pi\)
0.987383 + 0.158349i \(0.0506172\pi\)
\(422\) −3.97605 6.88672i −0.193551 0.335240i
\(423\) 0 0
\(424\) 15.3144 26.5254i 0.743735 1.28819i
\(425\) 8.04799 0.390385
\(426\) 0 0
\(427\) 0 0
\(428\) 7.11156 + 12.3176i 0.343750 + 0.595393i
\(429\) 0 0
\(430\) 0.438938 + 0.760263i 0.0211675 + 0.0366631i
\(431\) −9.70169 + 16.8038i −0.467314 + 0.809411i −0.999303 0.0373401i \(-0.988112\pi\)
0.531989 + 0.846751i \(0.321445\pi\)
\(432\) 0 0
\(433\) 1.35217 0.0649810 0.0324905 0.999472i \(-0.489656\pi\)
0.0324905 + 0.999472i \(0.489656\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1.65480 + 2.86619i −0.0792503 + 0.137266i
\(437\) −14.5754 −0.697238
\(438\) 0 0
\(439\) 17.3412 0.827650 0.413825 0.910356i \(-0.364193\pi\)
0.413825 + 0.910356i \(0.364193\pi\)
\(440\) −1.08056 −0.0515139
\(441\) 0 0
\(442\) −4.41194 −0.209854
\(443\) −19.6100 −0.931698 −0.465849 0.884864i \(-0.654251\pi\)
−0.465849 + 0.884864i \(0.654251\pi\)
\(444\) 0 0
\(445\) 0.635912 0.0301451
\(446\) −6.16590 + 10.6796i −0.291964 + 0.505696i
\(447\) 0 0
\(448\) 0 0
\(449\) 17.7345 0.836942 0.418471 0.908230i \(-0.362566\pi\)
0.418471 + 0.908230i \(0.362566\pi\)
\(450\) 0 0
\(451\) 12.4905 21.6342i 0.588155 1.01871i
\(452\) 0.805935 + 1.39592i 0.0379080 + 0.0656586i
\(453\) 0 0
\(454\) −13.1073 22.7025i −0.615156 1.06548i
\(455\) 0 0
\(456\) 0 0
\(457\) 0.485451 0.0227084 0.0113542 0.999936i \(-0.496386\pi\)
0.0113542 + 0.999936i \(0.496386\pi\)
\(458\) −1.05069 + 1.81985i −0.0490956 + 0.0850361i
\(459\) 0 0
\(460\) −0.0784150 0.135819i −0.00365612 0.00633259i
\(461\) −3.99687 + 6.92279i −0.186153 + 0.322426i −0.943964 0.330047i \(-0.892935\pi\)
0.757811 + 0.652474i \(0.226269\pi\)
\(462\) 0 0
\(463\) 5.24280 + 9.08080i 0.243654 + 0.422021i 0.961752 0.273921i \(-0.0883206\pi\)
−0.718098 + 0.695942i \(0.754987\pi\)
\(464\) 8.44523 14.6276i 0.392060 0.679068i
\(465\) 0 0
\(466\) 3.60721 + 6.24788i 0.167101 + 0.289427i
\(467\) 10.9489 + 18.9640i 0.506653 + 0.877549i 0.999970 + 0.00769944i \(0.00245083\pi\)
−0.493317 + 0.869849i \(0.664216\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0.185839 0.321883i 0.00857213 0.0148474i
\(471\) 0 0
\(472\) 13.6918 0.630218
\(473\) −25.1893 −1.15820
\(474\) 0 0
\(475\) −19.1639 + 33.1929i −0.879301 + 1.52299i
\(476\) 0 0
\(477\) 0 0
\(478\) −11.7708 20.3877i −0.538386 0.932512i
\(479\) 2.00085 + 3.46557i 0.0914210 + 0.158346i 0.908109 0.418733i \(-0.137526\pi\)
−0.816688 + 0.577079i \(0.804192\pi\)
\(480\) 0 0
\(481\) 2.45829 4.25789i 0.112088 0.194143i
\(482\) −11.0646 19.1645i −0.503980 0.872918i
\(483\) 0 0
\(484\) 0.0539532 0.0934496i 0.00245242 0.00424771i
\(485\) 0.200520 + 0.347311i 0.00910514 + 0.0157706i
\(486\) 0 0
\(487\) 13.2377 22.9284i 0.599859 1.03899i −0.392982 0.919546i \(-0.628557\pi\)
0.992841 0.119440i \(-0.0381100\pi\)
\(488\) 17.4100 0.788116
\(489\) 0 0
\(490\) 0 0
\(491\) −14.2149 24.6210i −0.641511 1.11113i −0.985096 0.172008i \(-0.944975\pi\)
0.343584 0.939122i \(-0.388359\pi\)
\(492\) 0 0
\(493\) 7.49360 + 12.9793i 0.337495 + 0.584558i
\(494\) 10.5057 18.1965i 0.472675 0.818697i
\(495\) 0 0
\(496\) −16.8381 −0.756052
\(497\) 0 0
\(498\) 0 0
\(499\) 3.71559 6.43559i 0.166333 0.288097i −0.770795 0.637083i \(-0.780141\pi\)
0.937128 + 0.348986i \(0.113474\pi\)
\(500\) −0.825726 −0.0369276
\(501\) 0 0
\(502\) −7.51531 −0.335425
\(503\) 10.1610 0.453057 0.226529 0.974004i \(-0.427262\pi\)
0.226529 + 0.974004i \(0.427262\pi\)
\(504\) 0 0
\(505\) 1.84252 0.0819910
\(506\) −6.98247 −0.310409
\(507\) 0 0
\(508\) −0.248590 −0.0110294
\(509\) 14.4532 25.0336i 0.640625 1.10960i −0.344668 0.938725i \(-0.612009\pi\)
0.985293 0.170871i \(-0.0546581\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −18.6806 −0.825575
\(513\) 0 0
\(514\) 7.93381 13.7418i 0.349945 0.606123i
\(515\) −0.460467 0.797553i −0.0202906 0.0351444i
\(516\) 0 0
\(517\) 5.33237 + 9.23593i 0.234517 + 0.406196i
\(518\) 0 0
\(519\) 0 0
\(520\) 0.802963 0.0352123
\(521\) −16.8995 + 29.2708i −0.740381 + 1.28238i 0.211941 + 0.977283i \(0.432022\pi\)
−0.952322 + 0.305095i \(0.901312\pi\)
\(522\) 0 0
\(523\) −7.18895 12.4516i −0.314351 0.544471i 0.664949 0.746889i \(-0.268453\pi\)
−0.979299 + 0.202418i \(0.935120\pi\)
\(524\) 5.86140 10.1522i 0.256056 0.443502i
\(525\) 0 0
\(526\) −0.848618 1.46985i −0.0370015 0.0640885i
\(527\) 7.47036 12.9390i 0.325414 0.563634i
\(528\) 0 0
\(529\) 9.70034 + 16.8015i 0.421754 + 0.730499i
\(530\) 0.580197 + 1.00493i 0.0252022 + 0.0436514i
\(531\) 0 0
\(532\) 0 0
\(533\) −9.28166 + 16.0763i −0.402033 + 0.696342i
\(534\) 0 0
\(535\) −1.91382 −0.0827417
\(536\) −30.6124 −1.32225
\(537\) 0 0
\(538\) 14.4783 25.0772i 0.624205 1.08116i
\(539\) 0 0
\(540\) 0 0
\(541\) 12.5882 + 21.8034i 0.541210 + 0.937403i 0.998835 + 0.0482577i \(0.0153669\pi\)
−0.457625 + 0.889145i \(0.651300\pi\)
\(542\) 9.88863 + 17.1276i 0.424753 + 0.735694i
\(543\) 0 0
\(544\) 3.33531 5.77693i 0.143000 0.247684i
\(545\) −0.222664 0.385666i −0.00953789 0.0165201i
\(546\) 0 0
\(547\) 1.59011 2.75416i 0.0679883 0.117759i −0.830027 0.557723i \(-0.811675\pi\)
0.898016 + 0.439963i \(0.145009\pi\)
\(548\) 5.97545 + 10.3498i 0.255258 + 0.442121i
\(549\) 0 0
\(550\) −9.18062 + 15.9013i −0.391463 + 0.678034i
\(551\) −71.3752 −3.04068
\(552\) 0 0
\(553\) 0 0
\(554\) 10.4057 + 18.0233i 0.442098 + 0.765736i
\(555\) 0 0
\(556\) 3.18179 + 5.51102i 0.134938 + 0.233719i
\(557\) 10.0229 17.3602i 0.424686 0.735577i −0.571705 0.820459i \(-0.693718\pi\)
0.996391 + 0.0848820i \(0.0270513\pi\)
\(558\) 0 0
\(559\) 18.7181 0.791689
\(560\) 0 0
\(561\) 0 0
\(562\) 2.75238 4.76727i 0.116102 0.201095i
\(563\) 39.8013 1.67743 0.838713 0.544574i \(-0.183309\pi\)
0.838713 + 0.544574i \(0.183309\pi\)
\(564\) 0 0
\(565\) −0.216888 −0.00912457
\(566\) −16.9753 −0.713523
\(567\) 0 0
\(568\) 10.1017 0.423856
\(569\) −13.8159 −0.579194 −0.289597 0.957149i \(-0.593521\pi\)
−0.289597 + 0.957149i \(0.593521\pi\)
\(570\) 0 0
\(571\) 10.4387 0.436846 0.218423 0.975854i \(-0.429909\pi\)
0.218423 + 0.975854i \(0.429909\pi\)
\(572\) −3.24352 + 5.61793i −0.135618 + 0.234898i
\(573\) 0 0
\(574\) 0 0
\(575\) −9.46483 −0.394711
\(576\) 0 0
\(577\) −12.7461 + 22.0769i −0.530628 + 0.919075i 0.468733 + 0.883340i \(0.344711\pi\)
−0.999361 + 0.0357353i \(0.988623\pi\)
\(578\) 7.93895 + 13.7507i 0.330217 + 0.571952i
\(579\) 0 0
\(580\) −0.383994 0.665098i −0.0159445 0.0276167i
\(581\) 0 0
\(582\) 0 0
\(583\) −33.2957 −1.37897
\(584\) −7.25104 + 12.5592i −0.300050 + 0.519702i
\(585\) 0 0
\(586\) 14.2277 + 24.6431i 0.587740 + 1.01800i
\(587\) 17.5168 30.3401i 0.722998 1.25227i −0.236795 0.971560i \(-0.576097\pi\)
0.959793 0.280709i \(-0.0905697\pi\)
\(588\) 0 0
\(589\) 35.5769 + 61.6210i 1.46592 + 2.53905i
\(590\) −0.259362 + 0.449228i −0.0106778 + 0.0184944i
\(591\) 0 0
\(592\) −1.80217 3.12146i −0.0740689 0.128291i
\(593\) −18.0646 31.2888i −0.741824 1.28488i −0.951664 0.307141i \(-0.900628\pi\)
0.209840 0.977736i \(-0.432706\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 4.36915 7.56759i 0.178967 0.309980i
\(597\) 0 0
\(598\) 5.18865 0.212180
\(599\) 40.9484 1.67310 0.836552 0.547887i \(-0.184568\pi\)
0.836552 + 0.547887i \(0.184568\pi\)
\(600\) 0 0
\(601\) 12.8547 22.2650i 0.524354 0.908207i −0.475244 0.879854i \(-0.657640\pi\)
0.999598 0.0283533i \(-0.00902635\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −4.41810 7.65238i −0.179770 0.311371i
\(605\) 0.00725978 + 0.0125743i 0.000295152 + 0.000511218i
\(606\) 0 0
\(607\) −3.42258 + 5.92808i −0.138918 + 0.240613i −0.927087 0.374845i \(-0.877696\pi\)
0.788169 + 0.615459i \(0.211029\pi\)
\(608\) 15.8841 + 27.5121i 0.644187 + 1.11576i
\(609\) 0 0
\(610\) −0.329795 + 0.571222i −0.0133530 + 0.0231281i
\(611\) −3.96246 6.86319i −0.160304 0.277655i
\(612\) 0 0
\(613\) 14.5648 25.2271i 0.588269 1.01891i −0.406191 0.913788i \(-0.633143\pi\)
0.994459 0.105123i \(-0.0335235\pi\)
\(614\) −24.5833 −0.992101
\(615\) 0 0
\(616\) 0 0
\(617\) 10.3395 + 17.9085i 0.416252 + 0.720969i 0.995559 0.0941404i \(-0.0300102\pi\)
−0.579307 + 0.815109i \(0.696677\pi\)
\(618\) 0 0
\(619\) 4.43178 + 7.67606i 0.178128 + 0.308527i 0.941239 0.337740i \(-0.109663\pi\)
−0.763111 + 0.646267i \(0.776329\pi\)
\(620\) −0.382804 + 0.663035i −0.0153738 + 0.0266281i
\(621\) 0 0
\(622\) 1.44453 0.0579205
\(623\) 0 0
\(624\) 0 0
\(625\) −12.4166 + 21.5062i −0.496666 + 0.860250i
\(626\) 23.7954 0.951055
\(627\) 0 0
\(628\) 9.56737 0.381779
\(629\) 3.19820 0.127521
\(630\) 0 0
\(631\) 26.4661 1.05360 0.526799 0.849990i \(-0.323392\pi\)
0.526799 + 0.849990i \(0.323392\pi\)
\(632\) −23.6210 −0.939592
\(633\) 0 0
\(634\) 27.3299 1.08541
\(635\) 0.0167248 0.0289681i 0.000663702 0.00114957i
\(636\) 0 0
\(637\) 0 0
\(638\) −34.1928 −1.35371
\(639\) 0 0
\(640\) 0.0405449 0.0702258i 0.00160268 0.00277592i
\(641\) −8.26595 14.3171i −0.326486 0.565489i 0.655326 0.755346i \(-0.272531\pi\)
−0.981812 + 0.189856i \(0.939198\pi\)
\(642\) 0 0
\(643\) −15.4460 26.7532i −0.609130 1.05504i −0.991384 0.130987i \(-0.958185\pi\)
0.382254 0.924057i \(-0.375148\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 13.6678 0.537752
\(647\) −0.649903 + 1.12567i −0.0255503 + 0.0442545i −0.878518 0.477710i \(-0.841467\pi\)
0.852968 + 0.521964i \(0.174800\pi\)
\(648\) 0 0
\(649\) −7.44198 12.8899i −0.292123 0.505972i
\(650\) 6.82209 11.8162i 0.267584 0.463470i
\(651\) 0 0
\(652\) 3.51247 + 6.08377i 0.137559 + 0.238259i
\(653\) −22.4435 + 38.8733i −0.878281 + 1.52123i −0.0250558 + 0.999686i \(0.507976\pi\)
−0.853226 + 0.521542i \(0.825357\pi\)
\(654\) 0 0
\(655\) 0.788692 + 1.36605i 0.0308167 + 0.0533762i
\(656\) 6.80438 + 11.7855i 0.265667 + 0.460148i
\(657\) 0 0
\(658\) 0 0
\(659\) −8.96167 + 15.5221i −0.349097 + 0.604654i −0.986089 0.166216i \(-0.946845\pi\)
0.636992 + 0.770870i \(0.280178\pi\)
\(660\) 0 0
\(661\) 33.0256 1.28455 0.642274 0.766475i \(-0.277991\pi\)
0.642274 + 0.766475i \(0.277991\pi\)
\(662\) 15.2686 0.593430
\(663\) 0 0
\(664\) −1.79420 + 3.10765i −0.0696285 + 0.120600i
\(665\) 0 0
\(666\) 0 0
\(667\) −8.81283 15.2643i −0.341234 0.591035i
\(668\) 6.82561 + 11.8223i 0.264091 + 0.457419i
\(669\) 0 0
\(670\) 0.579885 1.00439i 0.0224029 0.0388030i
\(671\) −9.46295 16.3903i −0.365313 0.632741i
\(672\) 0 0
\(673\) −10.6758 + 18.4909i −0.411520 + 0.712774i −0.995056 0.0993135i \(-0.968335\pi\)
0.583536 + 0.812087i \(0.301669\pi\)
\(674\) 1.86865 + 3.23659i 0.0719776 + 0.124669i
\(675\) 0 0
\(676\) −2.68447 + 4.64964i −0.103249 + 0.178832i
\(677\) −8.30167 −0.319059 −0.159530 0.987193i \(-0.550998\pi\)
−0.159530 + 0.987193i \(0.550998\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.261161 + 0.452344i 0.0100151 + 0.0173466i
\(681\) 0 0
\(682\) 17.0434 + 29.5200i 0.652625 + 1.13038i
\(683\) 1.24728 2.16036i 0.0477259 0.0826637i −0.841176 0.540762i \(-0.818136\pi\)
0.888902 + 0.458098i \(0.151469\pi\)
\(684\) 0 0
\(685\) −1.60808 −0.0614414
\(686\) 0 0
\(687\) 0 0
\(688\) 6.86110 11.8838i 0.261577 0.453065i
\(689\) 24.7419 0.942591
\(690\) 0 0
\(691\) −16.8691 −0.641731 −0.320865 0.947125i \(-0.603974\pi\)
−0.320865 + 0.947125i \(0.603974\pi\)
\(692\) −2.21763 −0.0843017
\(693\) 0 0
\(694\) 16.0071 0.607621
\(695\) −0.856265 −0.0324800
\(696\) 0 0
\(697\) −12.0753 −0.457385
\(698\) 8.67266 15.0215i 0.328265 0.568572i
\(699\) 0 0
\(700\) 0 0
\(701\) −16.4806 −0.622465 −0.311232 0.950334i \(-0.600742\pi\)
−0.311232 + 0.950334i \(0.600742\pi\)
\(702\) 0 0
\(703\) −7.61558 + 13.1906i −0.287227 + 0.497492i
\(704\) 13.6768 + 23.6889i 0.515464 + 0.892811i
\(705\) 0 0
\(706\) −2.28515 3.95800i −0.0860029 0.148961i
\(707\) 0 0
\(708\) 0 0
\(709\) −29.4925 −1.10761 −0.553807 0.832645i \(-0.686825\pi\)
−0.553807 + 0.832645i \(0.686825\pi\)
\(710\) −0.191354 + 0.331434i −0.00718138 + 0.0124385i
\(711\) 0 0
\(712\) −9.25539 16.0308i −0.346860 0.600780i
\(713\) −8.78551 + 15.2169i −0.329020 + 0.569879i
\(714\) 0 0
\(715\) −0.436438 0.755933i −0.0163219 0.0282703i
\(716\) 3.98277 6.89836i 0.148843 0.257804i
\(717\) 0 0
\(718\) 4.37810 + 7.58310i 0.163389 + 0.282999i
\(719\) −0.217311 0.376394i −0.00810433 0.0140371i 0.861945 0.507002i \(-0.169246\pi\)
−0.870049 + 0.492965i \(0.835913\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −22.0691 + 38.2248i −0.821327 + 1.42258i
\(723\) 0 0
\(724\) −13.3928 −0.497740
\(725\) −46.3488 −1.72135
\(726\) 0 0
\(727\) 13.5839 23.5280i 0.503799 0.872605i −0.496192 0.868213i \(-0.665269\pi\)
0.999990 0.00439187i \(-0.00139798\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −0.274710 0.475812i −0.0101675 0.0176106i
\(731\) 6.08798 + 10.5447i 0.225172 + 0.390009i
\(732\) 0 0
\(733\) 2.83307 4.90702i 0.104642 0.181245i −0.808950 0.587878i \(-0.799964\pi\)
0.913592 + 0.406632i \(0.133297\pi\)
\(734\) 7.25050 + 12.5582i 0.267621 + 0.463533i
\(735\) 0 0
\(736\) −3.92249 + 6.79395i −0.144585 + 0.250428i
\(737\) 16.6389 + 28.8194i 0.612901 + 1.06158i
\(738\) 0 0
\(739\) 6.80540 11.7873i 0.250341 0.433603i −0.713279 0.700880i \(-0.752791\pi\)
0.963620 + 0.267278i \(0.0861241\pi\)
\(740\) −0.163885 −0.00602455
\(741\) 0 0
\(742\) 0 0
\(743\) 6.33421 + 10.9712i 0.232380 + 0.402493i 0.958508 0.285066i \(-0.0920155\pi\)
−0.726128 + 0.687559i \(0.758682\pi\)
\(744\) 0 0
\(745\) 0.587900 + 1.01827i 0.0215390 + 0.0373066i
\(746\) −4.30696 + 7.45988i −0.157689 + 0.273126i
\(747\) 0 0
\(748\) −4.21977 −0.154290
\(749\) 0 0
\(750\) 0 0
\(751\) 3.57269 6.18808i 0.130369 0.225806i −0.793450 0.608636i \(-0.791717\pi\)
0.923819 + 0.382830i \(0.125050\pi\)
\(752\) −5.80977 −0.211860
\(753\) 0 0
\(754\) 25.4086 0.925325
\(755\) 1.18897 0.0432712
\(756\) 0 0
\(757\) 37.6446 1.36822 0.684108 0.729381i \(-0.260192\pi\)
0.684108 + 0.729381i \(0.260192\pi\)
\(758\) −34.8651 −1.26636
\(759\) 0 0
\(760\) −2.48751 −0.0902315
\(761\) 5.02358 8.70109i 0.182104 0.315414i −0.760493 0.649347i \(-0.775042\pi\)
0.942597 + 0.333933i \(0.108376\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −17.5572 −0.635196
\(765\) 0 0
\(766\) −5.91762 + 10.2496i −0.213812 + 0.370334i
\(767\) 5.53011 + 9.57843i 0.199681 + 0.345857i
\(768\) 0 0
\(769\) 16.1463 + 27.9663i 0.582252 + 1.00849i 0.995212 + 0.0977407i \(0.0311616\pi\)
−0.412960 + 0.910749i \(0.635505\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.201270 0.00724385
\(773\) −24.2939 + 42.0783i −0.873792 + 1.51345i −0.0157473 + 0.999876i \(0.505013\pi\)
−0.858044 + 0.513576i \(0.828321\pi\)
\(774\) 0 0
\(775\) 23.1025 + 40.0148i 0.829867 + 1.43737i
\(776\) 5.83694 10.1099i 0.209534 0.362923i
\(777\) 0 0
\(778\) 13.3147 + 23.0618i 0.477356 + 0.826806i
\(779\) 28.7538 49.8030i 1.03021 1.78438i
\(780\) 0 0
\(781\) −5.49059 9.50998i −0.196469 0.340294i
\(782\) 1.68759 + 2.92299i 0.0603481 + 0.104526i
\(783\) 0 0
\(784\) 0 0
\(785\) −0.643678 + 1.11488i −0.0229739 + 0.0397919i
\(786\) 0 0
\(787\) 48.9551 1.74506 0.872531 0.488560i \(-0.162478\pi\)
0.872531 + 0.488560i \(0.162478\pi\)
\(788\) −0.598331 −0.0213147
\(789\) 0 0
\(790\) 0.447448 0.775003i 0.0159195 0.0275734i
\(791\) 0 0
\(792\) 0 0
\(793\) 7.03188 + 12.1796i 0.249710 + 0.432510i
\(794\) −13.2652 22.9759i −0.470763 0.815385i
\(795\) 0 0
\(796\) 1.97174 3.41515i