Properties

Label 1323.2.h.h.802.7
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 802.7
Character \(\chi\) \(=\) 1323.802
Dual form 1323.2.h.h.226.7

$q$-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 −0.877576 0.479438i \(-0.840841\pi\)
0.853993 + 0.520284i \(0.174174\pi\)
\(6\) 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 0.985155 0.171670i \(-0.0549162\pi\)
−0.641248 + 0.767334i \(0.721583\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −1.81805 −0.454512
\(17\) −0.806594 + 1.39706i −0.195628 + 0.338837i −0.947106 0.320921i \(-0.896008\pi\)
0.751478 + 0.659758i \(0.229341\pi\)
\(18\) 0 0
\(19\) −3.84133 6.65338i −0.881262 1.52639i −0.849939 0.526880i \(-0.823362\pi\)
−0.0313221 0.999509i \(-0.509972\pi\)
\(20\) 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 \(-0.812642\pi\)
−0.831718 + 0.555199i \(0.812642\pi\)
\(32\) 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 \(0.0320462\pi\)
−0.410427 + 0.911893i \(0.634621\pi\)
\(42\) 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 \(-0.574875\pi\)
−0.233063 + 0.972462i \(0.574875\pi\)
\(48\) 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 \(-0.406241\pi\)
0.290312 + 0.956932i \(0.406241\pi\)
\(60\) 0 0
\(61\) 5.67100 0.726097 0.363048 0.931770i \(-0.381736\pi\)
0.363048 + 0.931770i \(0.381736\pi\)
\(62\) −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 −0.970497 0.241113i \(-0.922488\pi\)
0.694059 + 0.719919i \(0.255821\pi\)
\(74\) 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 −0.896316 0.443415i \(-0.853767\pi\)
0.832167 + 0.554525i \(0.187100\pi\)
\(84\) 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 0.660832 0.750534i \(-0.270203\pi\)
−0.980397 + 0.197031i \(0.936870\pi\)
\(90\) 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 −0.753213 0.657777i \(-0.771497\pi\)
0.946258 + 0.323413i \(0.104830\pi\)
\(98\) 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 \(-0.831316\pi\)
−0.00633771 0.999980i \(-0.502017\pi\)
\(102\) 0 0
\(103\) −4.36602 + 7.56217i −0.430197 + 0.745123i −0.996890 0.0788062i \(-0.974889\pi\)
0.566693 + 0.823929i \(0.308223\pi\)
\(104\) −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 \(-0.606688\pi\)
0.982300 0.187315i \(-0.0599786\pi\)
\(132\) 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 0.985229 0.171240i \(-0.0547774\pi\)
−0.640913 + 0.767614i \(0.721444\pi\)
\(140\) 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 \(-0.338060\pi\)
0.487087 + 0.873354i \(0.338060\pi\)
\(158\) 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 \(0.0687030\pi\)
−0.302927 + 0.953014i \(0.597964\pi\)
\(168\) 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 \(-0.534302\pi\)
−0.107555 + 0.994199i \(0.534302\pi\)
\(174\) 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 \(-0.719013\pi\)
−0.635032 + 0.772486i \(0.719013\pi\)
\(182\) 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 −0.762981 0.646421i \(-0.776265\pi\)
0.941307 + 0.337550i \(0.109598\pi\)
\(200\) −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 −0.615833 0.787877i \(-0.711180\pi\)
0.990238 + 0.139388i \(0.0445137\pi\)
\(224\) 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 \(0.122660\pi\)
−0.137811 + 0.990459i \(0.544007\pi\)
\(228\) 0 0
\(229\) 0.952737 1.65019i 0.0629586 0.109048i −0.832828 0.553532i \(-0.813280\pi\)
0.895787 + 0.444484i \(0.146613\pi\)
\(230\) −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 \(0.0570127\pi\)
−0.337715 + 0.941248i \(0.609654\pi\)
\(242\) −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 \(-0.431002\pi\)
0.215069 + 0.976599i \(0.431002\pi\)
\(252\) 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 −0.998306 0.0581897i \(-0.981467\pi\)
0.549546 + 0.835463i \(0.314801\pi\)
\(258\) 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 \(0.462079\pi\)
−0.919313 + 0.393527i \(0.871255\pi\)
\(270\) 0 0
\(271\) −8.96673 15.5308i −0.544690 0.943431i −0.998626 0.0523969i \(-0.983314\pi\)
0.453936 0.891034i \(-0.350019\pi\)
\(272\) 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 \(-0.348745\pi\)
0.457500 + 0.889210i \(0.348745\pi\)
\(284\) 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 \(-0.894934\pi\)
0.192318 0.981333i \(-0.438399\pi\)
\(294\) 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 \(-0.280538\pi\)
0.636120 + 0.771590i \(0.280538\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 0.538607 0.932894i 0.0305908 0.0529848i
\(311\) −1.30986 −0.0742755 −0.0371377 0.999310i \(-0.511824\pi\)
−0.0371377 + 0.999310i \(0.511824\pi\)
\(312\) 0 0
\(313\) −21.5770 −1.21960 −0.609802 0.792554i \(-0.708751\pi\)
−0.609802 + 0.792554i \(0.708751\pi\)
\(314\) 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 −0.996033 0.0889810i \(-0.971639\pi\)
0.575076 + 0.818100i \(0.304972\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 6.90000 + 11.9511i 0.367771 + 0.636998i
\(353\) 2.07211 + 3.58900i 0.110287 + 0.191023i 0.915886 0.401438i \(-0.131490\pi\)
−0.805599 + 0.592462i \(0.798156\pi\)
\(354\) 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 0.641834 0.766843i \(-0.278174\pi\)
−0.985023 + 0.172423i \(0.944840\pi\)
\(368\) 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 −0.695743 0.718291i \(-0.744925\pi\)
0.969930 + 0.243386i \(0.0782582\pi\)
\(384\) 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 \(0.0396373\pi\)
−0.388566 + 0.921421i \(0.627029\pi\)
\(398\) 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 \(-0.313689\pi\)
0.552460 + 0.833539i \(0.313689\pi\)
\(410\) −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 0.929708 0.368298i \(-0.120059\pi\)
−0.783809 + 0.621002i \(0.786726\pi\)
\(420\) 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 \(-0.510344\pi\)
−0.0324905 + 0.999472i \(0.510344\pi\)
\(434\) 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 \(-0.635807\pi\)
−0.413825 + 0.910356i \(0.635807\pi\)
\(440\) 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 −0.757811 0.652474i \(-0.773731\pi\)
0.943964 + 0.330047i \(0.107065\pi\)
\(462\) 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 \(-0.997549\pi\)
0.493317 0.869849i \(-0.335784\pi\)
\(468\) 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 0.816688 0.577079i \(-0.195808\pi\)
−0.908109 + 0.418733i \(0.862474\pi\)
\(480\) 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 \(-0.572738\pi\)
−0.226529 + 0.974004i \(0.572738\pi\)
\(504\) 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 \(0.387991\pi\)
−0.985293 + 0.170871i \(0.945342\pi\)
\(510\) 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 \(-0.567978\pi\)
0.952322 0.305095i \(-0.0986883\pi\)
\(522\) 0 0
\(523\) 7.18895 + 12.4516i 0.314351 + 0.544471i 0.979299 0.202418i \(-0.0648799\pi\)
−0.664949 + 0.746889i \(0.731547\pi\)
\(524\) −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 \(-0.816691\pi\)
−0.838713 + 0.544574i \(0.816691\pi\)
\(564\) 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 \(-0.655289\pi\)
0.999361 0.0357353i \(-0.0113773\pi\)
\(578\) 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 \(0.423903\pi\)
−0.959793 + 0.280709i \(0.909430\pi\)
\(588\) 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 \(0.0993724\pi\)
−0.209840 + 0.977736i \(0.567294\pi\)
\(594\) 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 \(0.342360\pi\)
−0.999598 + 0.0283533i \(0.990974\pi\)
\(602\) 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 −0.788169 0.615459i \(-0.788971\pi\)
0.927087 + 0.374845i \(0.122304\pi\)
\(608\) −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 0.763111 0.646267i \(-0.223671\pi\)
−0.941239 + 0.337740i \(0.890337\pi\)
\(620\) −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 \(0.0418147\pi\)
−0.382254 + 0.924057i \(0.624852\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 13.6678 0.537752
\(647\) 0.649903 1.12567i 0.0255503 0.0442545i −0.852968 0.521964i \(-0.825200\pi\)
0.878518 + 0.477710i \(0.158533\pi\)
\(648\) 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 \(-0.722009\pi\)
−0.642274 + 0.766475i \(0.722009\pi\)
\(662\) 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 \(-0.449002\pi\)
0.159530 + 0.987193i \(0.449002\pi\)
\(678\) 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 \(-0.396026\pi\)
0.320865 + 0.947125i \(0.396026\pi\)
\(692\) 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 0.870049 0.492965i \(-0.164087\pi\)
−0.861945 + 0.507002i \(0.830754\pi\)
\(720\) 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 \(0.334731\pi\)
−0.999990 + 0.00439187i \(0.998602\pi\)
\(728\) 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 −0.913592 0.406632i \(-0.866703\pi\)
0.808950 + 0.587878i \(0.200036\pi\)
\(734\) −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 −0.942597 0.333933i \(-0.891624\pi\)
0.760493 + 0.649347i \(0.224958\pi\)
\(762\) 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 \(-0.968838\pi\)
0.412960 0.910749i \(-0.364495\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 0.201270 0.00724385
\(773\) 24.2939 42.0783i 0.873792 1.51345i 0.0157473 0.999876i \(-0.494987\pi\)
0.858044 0.513576i \(-0.171679\pi\)
\(774\) 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 \(-0.837522\pi\)
−0.872531 + 0.488560i \(0.837522\pi\)
\(788\) −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