Properties

Label 1323.2.g.h.361.6
Level $1323$
Weight $2$
Character 1323.361
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.g (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 361.6
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.h.667.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-0.551407 + 0.955065i) q^{2} +(0.391901 + 0.678793i) q^{4} +0.105466 q^{5} -3.07001 q^{8} +O(q^{10})\) \(q+(-0.551407 + 0.955065i) q^{2} +(0.391901 + 0.678793i) q^{4} +0.105466 q^{5} -3.07001 q^{8} +(-0.0581547 + 0.100727i) q^{10} -3.33731 q^{11} +(1.23997 - 2.14770i) q^{13} +(0.909025 - 1.57448i) q^{16} +(-0.806594 + 1.39706i) q^{17} +(-3.84133 - 6.65338i) q^{19} +(0.0413323 + 0.0715896i) q^{20} +(1.84022 - 3.18735i) q^{22} +1.89719 q^{23} -4.98888 q^{25} +(1.36746 + 2.36851i) q^{26} +(-4.64521 - 8.04574i) q^{29} +(4.63081 + 8.02080i) q^{31} +(-2.06753 - 3.58107i) q^{32} +(-0.889523 - 1.54070i) q^{34} +(0.991268 + 1.71693i) q^{37} +8.47254 q^{38} -0.323782 q^{40} +(3.74268 - 6.48252i) q^{41} +(-3.77388 - 6.53655i) q^{43} +(-1.30790 - 2.26534i) q^{44} +(-1.04612 + 1.81194i) q^{46} +(1.59780 - 2.76747i) q^{47} +(2.75090 - 4.76470i) q^{50} +1.94379 q^{52} +(-4.98839 + 8.64015i) q^{53} -0.351974 q^{55} +10.2456 q^{58} +(-2.22993 - 3.86235i) q^{59} +(-2.83550 + 4.91123i) q^{61} -10.2138 q^{62} +8.19630 q^{64} +(0.130775 - 0.226509i) q^{65} +(-4.98571 - 8.63550i) q^{67} -1.26442 q^{68} -3.29042 q^{71} +(-2.36189 + 4.09091i) q^{73} -2.18637 q^{74} +(3.01084 - 5.21493i) q^{76} +(-3.84705 + 6.66328i) q^{79} +(0.0958713 - 0.166054i) q^{80} +(4.12748 + 7.14901i) q^{82} +(-0.584428 - 1.01226i) q^{83} +(-0.0850683 + 0.147343i) q^{85} +8.32378 q^{86} +10.2456 q^{88} +(-3.01477 - 5.22173i) q^{89} +(0.743509 + 1.28780i) q^{92} +(1.76208 + 3.05201i) q^{94} +(-0.405130 - 0.701706i) q^{95} +(1.90127 + 3.29310i) q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 4q^{2} - 12q^{4} + 24q^{8} + O(q^{10}) \) \( 24q - 4q^{2} - 12q^{4} + 24q^{8} + 40q^{11} - 12q^{16} + 64q^{23} + 24q^{25} - 16q^{29} - 48q^{32} - 12q^{37} - 56q^{44} + 24q^{46} + 4q^{50} - 32q^{53} + 96q^{64} - 60q^{65} - 12q^{67} + 112q^{71} + 136q^{74} + 12q^{79} + 12q^{85} + 152q^{86} - 16q^{92} - 64q^{95} + O(q^{100}) \)

Character values

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

\(n\) \(785\) \(1081\)
\(\chi(n)\) \(e\left(\frac{1}{3}\right)\) \(e\left(\frac{2}{3}\right)\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.551407 + 0.955065i −0.389903 + 0.675333i −0.992436 0.122762i \(-0.960825\pi\)
0.602533 + 0.798094i \(0.294158\pi\)
\(3\) 0 0
\(4\) 0.391901 + 0.678793i 0.195951 + 0.339396i
\(5\) 0.105466 0.0471659 0.0235829 0.999722i \(-0.492493\pi\)
0.0235829 + 0.999722i \(0.492493\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −3.07001 −1.08541
\(9\) 0 0
\(10\) −0.0581547 + 0.100727i −0.0183901 + 0.0318527i
\(11\) −3.33731 −1.00624 −0.503119 0.864217i \(-0.667814\pi\)
−0.503119 + 0.864217i \(0.667814\pi\)
\(12\) 0 0
\(13\) 1.23997 2.14770i 0.343907 0.595664i −0.641248 0.767334i \(-0.721583\pi\)
0.985155 + 0.171670i \(0.0549162\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.909025 1.57448i 0.227256 0.393619i
\(17\) −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
\(23\) 1.89719 0.395591 0.197795 0.980243i \(-0.436622\pi\)
0.197795 + 0.980243i \(0.436622\pi\)
\(24\) 0 0
\(25\) −4.98888 −0.997775
\(26\) 1.36746 + 2.36851i 0.268181 + 0.464503i
\(27\) 0 0
\(28\) 0 0
\(29\) −4.64521 8.04574i −0.862594 1.49406i −0.869416 0.494080i \(-0.835505\pi\)
0.00682200 0.999977i \(-0.497828\pi\)
\(30\) 0 0
\(31\) 4.63081 + 8.02080i 0.831718 + 1.44058i 0.896675 + 0.442689i \(0.145976\pi\)
−0.0649574 + 0.997888i \(0.520691\pi\)
\(32\) −2.06753 3.58107i −0.365491 0.633049i
\(33\) 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 \(0.781228\pi\)
\(38\) 8.47254 1.37443
\(39\) 0 0
\(40\) −0.323782 −0.0511945
\(41\) 3.74268 6.48252i 0.584509 1.01240i −0.410427 0.911893i \(-0.634621\pi\)
0.994936 0.100506i \(-0.0320462\pi\)
\(42\) 0 0
\(43\) −3.77388 6.53655i −0.575512 0.996815i −0.995986 0.0895108i \(-0.971470\pi\)
0.420474 0.907304i \(-0.361864\pi\)
\(44\) −1.30790 2.26534i −0.197173 0.341514i
\(45\) 0 0
\(46\) −1.04612 + 1.81194i −0.154242 + 0.267155i
\(47\) 1.59780 2.76747i 0.233063 0.403677i −0.725645 0.688070i \(-0.758458\pi\)
0.958708 + 0.284392i \(0.0917917\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 2.75090 4.76470i 0.389036 0.673830i
\(51\) 0 0
\(52\) 1.94379 0.269555
\(53\) −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
\(58\) 10.2456 1.34531
\(59\) −2.22993 3.86235i −0.290312 0.502836i 0.683571 0.729884i \(-0.260426\pi\)
−0.973884 + 0.227048i \(0.927093\pi\)
\(60\) 0 0
\(61\) −2.83550 + 4.91123i −0.363048 + 0.628818i −0.988461 0.151476i \(-0.951597\pi\)
0.625413 + 0.780294i \(0.284931\pi\)
\(62\) −10.2138 −1.29716
\(63\) 0 0
\(64\) 8.19630 1.02454
\(65\) 0.130775 0.226509i 0.0162207 0.0280950i
\(66\) 0 0
\(67\) −4.98571 8.63550i −0.609101 1.05499i −0.991389 0.130951i \(-0.958197\pi\)
0.382288 0.924043i \(-0.375136\pi\)
\(68\) −1.26442 −0.153333
\(69\) 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 \(0.255821\pi\)
\(74\) −2.18637 −0.254160
\(75\) 0 0
\(76\) 3.01084 5.21493i 0.345367 0.598194i
\(77\) 0 0
\(78\) 0 0
\(79\) −3.84705 + 6.66328i −0.432827 + 0.749678i −0.997115 0.0758997i \(-0.975817\pi\)
0.564289 + 0.825577i \(0.309150\pi\)
\(80\) 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 \(-0.187100\pi\)
−0.896316 + 0.443415i \(0.853767\pi\)
\(84\) 0 0
\(85\) −0.0850683 + 0.147343i −0.00922695 + 0.0159815i
\(86\) 8.32378 0.897576
\(87\) 0 0
\(88\) 10.2456 1.09219
\(89\) −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
\(94\) 1.76208 + 3.05201i 0.181744 + 0.314791i
\(95\) −0.405130 0.701706i −0.0415655 0.0719935i
\(96\) 0 0
\(97\) 1.90127 + 3.29310i 0.193045 + 0.334364i 0.946258 0.323413i \(-0.104830\pi\)
−0.753213 + 0.657777i \(0.771497\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.95515 3.38641i −0.195515 0.338641i
\(101\) 17.4702 1.73835 0.869177 0.494501i \(-0.164649\pi\)
0.869177 + 0.494501i \(0.164649\pi\)
\(102\) 0 0
\(103\) 8.73204 0.860394 0.430197 0.902735i \(-0.358444\pi\)
0.430197 + 0.902735i \(0.358444\pi\)
\(104\) −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 \(0.101851\pi\)
\(110\) 0.194081 0.336157i 0.0185049 0.0320514i
\(111\) 0 0
\(112\) 0 0
\(113\) −1.02824 + 1.78096i −0.0967285 + 0.167539i −0.910329 0.413886i \(-0.864171\pi\)
0.813600 + 0.581425i \(0.197505\pi\)
\(114\) 0 0
\(115\) 0.200089 0.0186584
\(116\) 3.64093 6.30627i 0.338052 0.585523i
\(117\) 0 0
\(118\) 4.91840 0.452775
\(119\) 0 0
\(120\) 0 0
\(121\) 0.137670 0.0125155
\(122\) −3.12703 5.41617i −0.283108 0.490357i
\(123\) 0 0
\(124\) −3.62964 + 6.28672i −0.325951 + 0.564564i
\(125\) −1.05349 −0.0942268
\(126\) 0 0
\(127\) 0.317159 0.0281433 0.0140717 0.999901i \(-0.495521\pi\)
0.0140717 + 0.999901i \(0.495521\pi\)
\(128\) −0.384435 + 0.665862i −0.0339796 + 0.0588544i
\(129\) 0 0
\(130\) 0.144221 + 0.249797i 0.0126490 + 0.0219087i
\(131\) −14.9563 −1.30674 −0.653370 0.757039i \(-0.726645\pi\)
−0.653370 + 0.757039i \(0.726645\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 10.9966 0.949962
\(135\) 0 0
\(136\) 2.47625 4.28900i 0.212337 0.367779i
\(137\) 15.2473 1.30267 0.651334 0.758791i \(-0.274210\pi\)
0.651334 + 0.758791i \(0.274210\pi\)
\(138\) 0 0
\(139\) 4.05943 7.03114i 0.344316 0.596374i −0.640913 0.767614i \(-0.721444\pi\)
0.985229 + 0.171240i \(0.0547774\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 1.81436 3.14257i 0.152258 0.263718i
\(143\) −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
\(149\) 11.1486 0.913329 0.456664 0.889639i \(-0.349044\pi\)
0.456664 + 0.889639i \(0.349044\pi\)
\(150\) 0 0
\(151\) −11.2735 −0.917425 −0.458713 0.888585i \(-0.651689\pi\)
−0.458713 + 0.888585i \(0.651689\pi\)
\(152\) 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
\(157\) −6.10318 10.5710i −0.487087 0.843659i 0.512803 0.858506i \(-0.328607\pi\)
−0.999890 + 0.0148476i \(0.995274\pi\)
\(158\) −4.24258 7.34836i −0.337521 0.584604i
\(159\) 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 \(0.947493\pi\)
\(164\) 5.86705 0.458139
\(165\) 0 0
\(166\) 1.28903 0.100048
\(167\) 8.70833 15.0833i 0.673871 1.16718i −0.302927 0.953014i \(-0.597964\pi\)
0.976798 0.214165i \(-0.0687030\pi\)
\(168\) 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
\(173\) 1.41466 2.45027i 0.107555 0.186291i −0.807224 0.590245i \(-0.799031\pi\)
0.914779 + 0.403954i \(0.132365\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −3.03370 + 5.25453i −0.228674 + 0.396075i
\(177\) 0 0
\(178\) 6.64946 0.498398
\(179\) −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
\(184\) −5.82439 −0.429380
\(185\) 0.104545 + 0.181078i 0.00768631 + 0.0133131i
\(186\) 0 0
\(187\) 2.69186 4.66243i 0.196848 0.340951i
\(188\) 2.50472 0.182676
\(189\) 0 0
\(190\) 0.893566 0.0648261
\(191\) −11.2000 + 19.3990i −0.810404 + 1.40366i 0.102178 + 0.994766i \(0.467419\pi\)
−0.912582 + 0.408894i \(0.865914\pi\)
\(192\) 0 0
\(193\) 0.128393 + 0.222383i 0.00924194 + 0.0160075i 0.870609 0.491975i \(-0.163725\pi\)
−0.861367 + 0.507982i \(0.830391\pi\)
\(194\) −4.19350 −0.301076
\(195\) 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 \(0.109598\pi\)
\(200\) 15.3159 1.08300
\(201\) 0 0
\(202\) −9.63321 + 16.6852i −0.677790 + 1.17397i
\(203\) 0 0
\(204\) 0 0
\(205\) 0.394726 0.683686i 0.0275689 0.0477507i
\(206\) −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 −0.963027 0.269403i \(-0.913174\pi\)
0.714824 + 0.699305i \(0.246507\pi\)
\(212\) −7.81983 −0.537068
\(213\) 0 0
\(214\) 20.0120 1.36799
\(215\) −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
\(220\) −0.137939 0.238917i −0.00929983 0.0161078i
\(221\) 2.00031 + 3.46464i 0.134555 + 0.233057i
\(222\) 0 0
\(223\) 5.59106 + 9.68400i 0.374405 + 0.648488i 0.990238 0.139388i \(-0.0445137\pi\)
−0.615833 + 0.787877i \(0.711180\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1.13395 1.96407i −0.0754295 0.130648i
\(227\) −23.7706 −1.57771 −0.788857 0.614577i \(-0.789327\pi\)
−0.788857 + 0.614577i \(0.789327\pi\)
\(228\) 0 0
\(229\) −1.90547 −0.125917 −0.0629586 0.998016i \(-0.520054\pi\)
−0.0629586 + 0.998016i \(0.520054\pi\)
\(230\) −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
\(236\) 1.74782 3.02732i 0.113774 0.197062i
\(237\) 0 0
\(238\) 0 0
\(239\) −10.6735 + 18.4870i −0.690409 + 1.19582i 0.281295 + 0.959621i \(0.409236\pi\)
−0.971704 + 0.236202i \(0.924097\pi\)
\(240\) 0 0
\(241\) −20.0662 −1.29258 −0.646288 0.763094i \(-0.723679\pi\)
−0.646288 + 0.763094i \(0.723679\pi\)
\(242\) −0.0759124 + 0.131484i −0.00487983 + 0.00845212i
\(243\) 0 0
\(244\) −4.44494 −0.284558
\(245\) 0 0
\(246\) 0 0
\(247\) −19.0526 −1.21229
\(248\) −14.2167 24.6240i −0.902758 1.56362i
\(249\) 0 0
\(250\) 0.580900 1.00615i 0.0367394 0.0636344i
\(251\) 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
\(254\) −0.174884 + 0.302907i −0.0109732 + 0.0190061i
\(255\) 0 0
\(256\) 7.77234 + 13.4621i 0.485771 + 0.841380i
\(257\) 14.3883 0.897518 0.448759 0.893653i \(-0.351866\pi\)
0.448759 + 0.893653i \(0.351866\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 0.205004 0.0127138
\(261\) 0 0
\(262\) 8.24701 14.2842i 0.509502 0.882484i
\(263\) 1.53901 0.0948992 0.0474496 0.998874i \(-0.484891\pi\)
0.0474496 + 0.998874i \(0.484891\pi\)
\(264\) 0 0
\(265\) −0.526106 + 0.911243i −0.0323185 + 0.0559772i
\(266\) 0 0
\(267\) 0 0
\(268\) 3.90781 6.76852i 0.238707 0.413453i
\(269\) −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
\(275\) 16.6495 1.00400
\(276\) 0 0
\(277\) −18.8713 −1.13386 −0.566932 0.823764i \(-0.691870\pi\)
−0.566932 + 0.823764i \(0.691870\pi\)
\(278\) 4.47680 + 7.75404i 0.268500 + 0.465056i
\(279\) 0 0
\(280\) 0 0
\(281\) 2.49578 + 4.32283i 0.148886 + 0.257878i 0.930816 0.365488i \(-0.119098\pi\)
−0.781930 + 0.623366i \(0.785765\pi\)
\(282\) 0 0
\(283\) −7.69634 13.3304i −0.457500 0.792413i 0.541328 0.840811i \(-0.317922\pi\)
−0.998828 + 0.0483984i \(0.984588\pi\)
\(284\) −1.28952 2.23352i −0.0765190 0.132535i
\(285\) 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
\(290\) 1.08056 0.0634529
\(291\) 0 0
\(292\) −3.70251 −0.216673
\(293\) −12.9013 + 22.3456i −0.753700 + 1.30545i 0.192318 + 0.981333i \(0.438399\pi\)
−0.946018 + 0.324114i \(0.894934\pi\)
\(294\) 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
\(299\) 2.35246 4.07458i 0.136046 0.235639i
\(300\) 0 0
\(301\) 0 0
\(302\) 6.21629 10.7669i 0.357707 0.619567i
\(303\) 0 0
\(304\) −13.9675 −0.801089
\(305\) −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
\(310\) −1.07721 −0.0611816
\(311\) 0.654931 + 1.13437i 0.0371377 + 0.0643245i 0.883997 0.467493i \(-0.154843\pi\)
−0.846859 + 0.531817i \(0.821509\pi\)
\(312\) 0 0
\(313\) 10.7885 18.6862i 0.609802 1.05621i −0.381471 0.924381i \(-0.624582\pi\)
0.991273 0.131827i \(-0.0420843\pi\)
\(314\) 13.4613 0.759667
\(315\) 0 0
\(316\) −6.03065 −0.339250
\(317\) −12.3910 + 21.4618i −0.695946 + 1.20541i 0.273915 + 0.961754i \(0.411681\pi\)
−0.969861 + 0.243660i \(0.921652\pi\)
\(318\) 0 0
\(319\) 15.5025 + 26.8512i 0.867975 + 1.50338i
\(320\) 0.864432 0.0483232
\(321\) 0 0
\(322\) 0 0
\(323\) 12.3936 0.689597
\(324\) 0 0
\(325\) −6.18608 + 10.7146i −0.343142 + 0.594339i
\(326\) 9.88412 0.547431
\(327\) 0 0
\(328\) −11.4901 + 19.9014i −0.634434 + 1.09887i
\(329\) 0 0
\(330\) 0 0
\(331\) −6.92256 + 11.9902i −0.380498 + 0.659042i −0.991133 0.132870i \(-0.957581\pi\)
0.610635 + 0.791912i \(0.290914\pi\)
\(332\) 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 −0.816178 0.577801i \(-0.803911\pi\)
0.908479 + 0.417930i \(0.137244\pi\)
\(338\) −7.55412 −0.410890
\(339\) 0 0
\(340\) −0.133353 −0.00723210
\(341\) −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
\(346\) 1.56011 + 2.70219i 0.0838720 + 0.145271i
\(347\) −7.25739 12.5702i −0.389597 0.674802i 0.602798 0.797894i \(-0.294052\pi\)
−0.992395 + 0.123091i \(0.960719\pi\)
\(348\) 0 0
\(349\) −7.86412 13.6211i −0.420957 0.729119i 0.575076 0.818100i \(-0.304972\pi\)
−0.996033 + 0.0889810i \(0.971639\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 6.90000 + 11.9511i 0.367771 + 0.636998i
\(353\) −4.14423 −0.220575 −0.110287 0.993900i \(-0.535177\pi\)
−0.110287 + 0.993900i \(0.535177\pi\)
\(354\) 0 0
\(355\) −0.347028 −0.0184183
\(356\) 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
\(362\) 9.42187 16.3192i 0.495202 0.857716i
\(363\) 0 0
\(364\) 0 0
\(365\) −0.249099 + 0.431453i −0.0130385 + 0.0225833i
\(366\) 0 0
\(367\) 13.1491 0.686377 0.343189 0.939266i \(-0.388493\pi\)
0.343189 + 0.939266i \(0.388493\pi\)
\(368\) 1.72459 2.98708i 0.0899004 0.155712i
\(369\) 0 0
\(370\) −0.230588 −0.0119877
\(371\) 0 0
\(372\) 0 0
\(373\) 7.81086 0.404431 0.202216 0.979341i \(-0.435186\pi\)
0.202216 + 0.979341i \(0.435186\pi\)
\(374\) 2.96862 + 5.14180i 0.153504 + 0.265876i
\(375\) 0 0
\(376\) −4.90527 + 8.49618i −0.252970 + 0.438157i
\(377\) −23.0398 −1.18661
\(378\) 0 0
\(379\) −31.6147 −1.62394 −0.811968 0.583702i \(-0.801604\pi\)
−0.811968 + 0.583702i \(0.801604\pi\)
\(380\) 0.317542 0.549999i 0.0162896 0.0282143i
\(381\) 0 0
\(382\) −12.3515 21.3934i −0.631958 1.09458i
\(383\) −10.7319 −0.548373 −0.274186 0.961677i \(-0.588408\pi\)
−0.274186 + 0.961677i \(0.588408\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −0.283187 −0.0144139
\(387\) 0 0
\(388\) −1.49022 + 2.58114i −0.0756546 + 0.131038i
\(389\) −24.1468 −1.22429 −0.612147 0.790744i \(-0.709694\pi\)
−0.612147 + 0.790744i \(0.709694\pi\)
\(390\) 0 0
\(391\) −1.53026 + 2.65049i −0.0773885 + 0.134041i
\(392\) 0 0
\(393\) 0 0
\(394\) −0.420927 + 0.729067i −0.0212060 + 0.0367299i
\(395\) −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
\(401\) 1.56232 0.0780183 0.0390092 0.999239i \(-0.487580\pi\)
0.0390092 + 0.999239i \(0.487580\pi\)
\(402\) 0 0
\(403\) 22.9683 1.14413
\(404\) 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
\(409\) −11.1728 19.3519i −0.552460 0.956889i −0.998096 0.0616748i \(-0.980356\pi\)
0.445636 0.895214i \(-0.352977\pi\)
\(410\) 0.435309 + 0.753978i 0.0214984 + 0.0372363i
\(411\) 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
\(416\) −10.2547 −0.502779
\(417\) 0 0
\(418\) −28.2755 −1.38300
\(419\) 2.98648 5.17273i 0.145899 0.252704i −0.783809 0.621002i \(-0.786726\pi\)
0.929708 + 0.368298i \(0.120059\pi\)
\(420\) 0 0
\(421\) 7.31594 + 12.6716i 0.356557 + 0.617575i 0.987383 0.158349i \(-0.0506172\pi\)
−0.630826 + 0.775924i \(0.717284\pi\)
\(422\) −3.97605 6.88672i −0.193551 0.335240i
\(423\) 0 0
\(424\) 15.3144 26.5254i 0.743735 1.28819i
\(425\) 4.02400 6.96977i 0.195193 0.338083i
\(426\) 0 0
\(427\) 0 0
\(428\) 7.11156 12.3176i 0.343750 0.595393i
\(429\) 0 0
\(430\) 0.877876 0.0423349
\(431\) −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
\(436\) 3.30959 0.158501
\(437\) −7.28772 12.6227i −0.348619 0.603826i
\(438\) 0 0
\(439\) 8.67059 15.0179i 0.413825 0.716766i −0.581479 0.813561i \(-0.697526\pi\)
0.995304 + 0.0967954i \(0.0308592\pi\)
\(440\) 1.08056 0.0515139
\(441\) 0 0
\(442\) −4.41194 −0.209854
\(443\) 9.80499 16.9827i 0.465849 0.806874i −0.533390 0.845869i \(-0.679082\pi\)
0.999239 + 0.0389949i \(0.0124156\pi\)
\(444\) 0 0
\(445\) −0.317956 0.550716i −0.0150726 0.0261064i
\(446\) −12.3318 −0.583927
\(447\) 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
\(452\) −1.61187 −0.0758160
\(453\) 0 0
\(454\) 13.1073 22.7025i 0.615156 1.06548i
\(455\) 0 0
\(456\) 0 0
\(457\) −0.242725 + 0.420413i −0.0113542 + 0.0196661i −0.871647 0.490135i \(-0.836948\pi\)
0.860292 + 0.509801i \(0.170281\pi\)
\(458\) 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 \(-0.107065\pi\)
−0.757811 + 0.652474i \(0.773731\pi\)
\(462\) 0 0
\(463\) 5.24280 9.08080i 0.243654 0.422021i −0.718098 0.695942i \(-0.754987\pi\)
0.961752 + 0.273921i \(0.0883206\pi\)
\(464\) −16.8905 −0.784120
\(465\) 0 0
\(466\) −7.21443 −0.334202
\(467\) −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
\(472\) 6.84592 + 11.8575i 0.315109 + 0.545785i
\(473\) 12.5946 + 21.8145i 0.579102 + 1.00303i
\(474\) 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
\(479\) 4.00169 0.182842 0.0914210 0.995812i \(-0.470859\pi\)
0.0914210 + 0.995812i \(0.470859\pi\)
\(480\) 0 0
\(481\) 4.91658 0.224177
\(482\) 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 \(-0.0381100\pi\)
\(488\) 8.70502 15.0775i 0.394058 0.682528i
\(489\) 0 0
\(490\) 0 0
\(491\) −14.2149 + 24.6210i −0.641511 + 1.11113i 0.343584 + 0.939122i \(0.388359\pi\)
−0.985096 + 0.172008i \(0.944975\pi\)
\(492\) 0 0
\(493\) 14.9872 0.674989
\(494\) 10.5057 18.1965i 0.472675 0.818697i
\(495\) 0 0
\(496\) 16.8381 0.756052
\(497\) 0 0
\(498\) 0 0
\(499\) −7.43118 −0.332665 −0.166333 0.986070i \(-0.553193\pi\)
−0.166333 + 0.986070i \(0.553193\pi\)
\(500\) −0.412863 0.715100i −0.0184638 0.0319802i
\(501\) 0 0
\(502\) −3.75765 + 6.50845i −0.167712 + 0.290486i
\(503\) −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
\(506\) 3.49124 6.04700i 0.155204 0.268822i
\(507\) 0 0
\(508\) 0.124295 + 0.215285i 0.00551470 + 0.00955174i
\(509\) 28.9063 1.28125 0.640625 0.767854i \(-0.278675\pi\)
0.640625 + 0.767854i \(0.278675\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −18.6806 −0.825575
\(513\) 0 0
\(514\) −7.93381 + 13.7418i −0.349945 + 0.606123i
\(515\) 0.920934 0.0405812
\(516\) 0 0
\(517\) −5.33237 + 9.23593i −0.234517 + 0.406196i
\(518\) 0 0
\(519\) 0 0
\(520\) −0.401482 + 0.695387i −0.0176061 + 0.0304947i
\(521\) 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
\(527\) −14.9407 −0.650828
\(528\) 0 0
\(529\) −19.4007 −0.843508
\(530\) −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
\(535\) −0.956910 1.65742i −0.0413708 0.0716564i
\(536\) 15.3062 + 26.5111i 0.661127 + 1.14511i
\(537\) 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 \(0.651300\pi\)
\(542\) 19.7773 0.849506
\(543\) 0 0
\(544\) 6.67063 0.286001
\(545\) 0.222664 0.385666i 0.00953789 0.0165201i
\(546\) 0 0
\(547\) 1.59011 + 2.75416i 0.0679883 + 0.117759i 0.898016 0.439963i \(-0.145009\pi\)
−0.830027 + 0.557723i \(0.811675\pi\)
\(548\) 5.97545 + 10.3498i 0.255258 + 0.442121i
\(549\) 0 0
\(550\) −9.18062 + 15.9013i −0.391463 + 0.678034i
\(551\) −35.6876 + 61.8127i −1.52034 + 2.63331i
\(552\) 0 0
\(553\) 0 0
\(554\) 10.4057 18.0233i 0.442098 0.765736i
\(555\) 0 0
\(556\) 6.36358 0.269876
\(557\) 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
\(562\) −5.50477 −0.232205
\(563\) 19.9007 + 34.4690i 0.838713 + 1.45269i 0.890971 + 0.454060i \(0.150025\pi\)
−0.0522584 + 0.998634i \(0.516642\pi\)
\(564\) 0 0
\(565\) −0.108444 + 0.187831i −0.00456228 + 0.00790211i
\(566\) 16.9753 0.713523
\(567\) 0 0
\(568\) 10.1017 0.423856
\(569\) 6.90797 11.9649i 0.289597 0.501597i −0.684117 0.729373i \(-0.739812\pi\)
0.973714 + 0.227776i \(0.0731454\pi\)
\(570\) 0 0
\(571\) −5.21935 9.04019i −0.218423 0.378320i 0.735903 0.677087i \(-0.236758\pi\)
−0.954326 + 0.298767i \(0.903425\pi\)
\(572\) −6.48703 −0.271236
\(573\) 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 \(-0.0113773\pi\)
\(578\) −15.8779 −0.660433
\(579\) 0 0
\(580\) 0.383994 0.665098i 0.0159445 0.0276167i
\(581\) 0 0
\(582\) 0 0
\(583\) 16.6478 28.8349i 0.689483 1.19422i
\(584\) 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 −0.959793 0.280709i \(-0.909430\pi\)
0.236795 0.971560i \(-0.423903\pi\)
\(588\) 0 0
\(589\) 35.5769 61.6210i 1.46592 2.53905i
\(590\) 0.518724 0.0213555
\(591\) 0 0
\(592\) 3.60435 0.148138
\(593\) 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
\(598\) 2.59433 + 4.49350i 0.106090 + 0.183753i
\(599\) −20.4742 35.4623i −0.836552 1.44895i −0.892760 0.450532i \(-0.851234\pi\)
0.0562080 0.998419i \(-0.482099\pi\)
\(600\) 0 0
\(601\) −12.8547 22.2650i −0.524354 0.908207i −0.999598 0.0283533i \(-0.990974\pi\)
0.475244 0.879854i \(-0.342360\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) −4.41810 7.65238i −0.179770 0.311371i
\(605\) 0.0145196 0.000590304
\(606\) 0 0
\(607\) −6.84516 −0.277836 −0.138918 0.990304i \(-0.544362\pi\)
−0.138918 + 0.990304i \(0.544362\pi\)
\(608\) −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 \(-0.0335235\pi\)
\(614\) −12.2917 + 21.2898i −0.496051 + 0.859185i
\(615\) 0 0
\(616\) 0 0
\(617\) 10.3395 17.9085i 0.416252 0.720969i −0.579307 0.815109i \(-0.696677\pi\)
0.995559 + 0.0941404i \(0.0300102\pi\)
\(618\) 0 0
\(619\) 8.86355 0.356256 0.178128 0.984007i \(-0.442996\pi\)
0.178128 + 0.984007i \(0.442996\pi\)
\(620\) −0.382804 + 0.663035i −0.0153738 + 0.0266281i
\(621\) 0 0
\(622\) −1.44453 −0.0579205
\(623\) 0 0
\(624\) 0 0
\(625\) 24.8333 0.993331
\(626\) 11.8977 + 20.6074i 0.475528 + 0.823638i
\(627\) 0 0
\(628\) 4.78368 8.28558i 0.190890 0.330631i
\(629\) −3.19820 −0.127521
\(630\) 0 0
\(631\) 26.4661 1.05360 0.526799 0.849990i \(-0.323392\pi\)
0.526799 + 0.849990i \(0.323392\pi\)
\(632\) 11.8105 20.4564i 0.469796 0.813711i
\(633\) 0 0
\(634\) −13.6649 23.6683i −0.542704 0.939990i
\(635\) 0.0334495 0.00132740
\(636\) 0 0
\(637\) 0 0
\(638\) −34.1928 −1.35371
\(639\) 0 0
\(640\) −0.0405449 + 0.0702258i −0.00160268 + 0.00277592i
\(641\) 16.5319 0.652971 0.326486 0.945202i \(-0.394136\pi\)
0.326486 + 0.945202i \(0.394136\pi\)
\(642\) 0 0
\(643\) 15.4460 26.7532i 0.609130 1.05504i −0.382254 0.924057i \(-0.624852\pi\)
0.991384 0.130987i \(-0.0418147\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.83390 + 11.8367i −0.268876 + 0.465707i
\(647\) 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
\(653\) 44.8870 1.75656 0.878281 0.478144i \(-0.158690\pi\)
0.878281 + 0.478144i \(0.158690\pi\)
\(654\) 0 0
\(655\) −1.57738 −0.0616335
\(656\) −6.80438 11.7855i −0.265667 0.460148i
\(657\) 0 0
\(658\) 0 0
\(659\) −8.96167 15.5221i −0.349097 0.604654i 0.636992 0.770870i \(-0.280178\pi\)
−0.986089 + 0.166216i \(0.946845\pi\)
\(660\) 0 0
\(661\) 16.5128 + 28.6010i 0.642274 + 1.11245i 0.984924 + 0.172989i \(0.0553424\pi\)
−0.342649 + 0.939463i \(0.611324\pi\)
\(662\) −7.63429 13.2230i −0.296715 0.513925i
\(663\) 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
\(668\) 13.6512 0.528182
\(669\) 0 0
\(670\) 1.15977 0.0448058
\(671\) 9.46295 16.3903i 0.365313 0.632741i
\(672\) 0 0
\(673\) −10.6758 18.4909i −0.411520 0.712774i 0.583536 0.812087i \(-0.301669\pi\)
−0.995056 + 0.0993135i \(0.968335\pi\)
\(674\) 1.86865 + 3.23659i 0.0719776 + 0.124669i
\(675\) 0 0
\(676\) −2.68447 + 4.64964i −0.103249 + 0.178832i
\(677\) −4.15084 + 7.18946i −0.159530 + 0.276313i −0.934699 0.355440i \(-0.884331\pi\)
0.775170 + 0.631753i \(0.217664\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 0.261161 0.452344i 0.0100151 0.0173466i
\(681\) 0 0
\(682\) 34.0868 1.30525
\(683\) 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
\(688\) −13.7222 −0.523154
\(689\) 12.3710 + 21.4271i 0.471296 + 0.816308i
\(690\) 0 0
\(691\) −8.43455 + 14.6091i −0.320865 + 0.555755i −0.980667 0.195685i \(-0.937307\pi\)
0.659801 + 0.751440i \(0.270640\pi\)
\(692\) 2.21763 0.0843017
\(693\) 0 0
\(694\) 16.0071 0.607621
\(695\) 0.428132 0.741547i 0.0162400 0.0281285i
\(696\) 0 0
\(697\) 6.03765 + 10.4575i 0.228692 + 0.396107i
\(698\) 17.3453 0.656530
\(699\) 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
\(704\) −27.3536 −1.03093
\(705\) 0 0
\(706\) 2.28515 3.95800i 0.0860029 0.148961i
\(707\) 0 0
\(708\) 0 0
\(709\) 14.7462 25.5412i 0.553807 0.959222i −0.444188 0.895933i \(-0.646508\pi\)
0.997995 0.0632882i \(-0.0201587\pi\)
\(710\) 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
\(716\) −7.96554 −0.297686
\(717\) 0 0
\(718\) −8.75620 −0.326779
\(719\) 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
\(724\) −6.69640 11.5985i −0.248870 0.431055i
\(725\) 23.1744 + 40.1392i 0.860675 + 1.49073i
\(726\) 0 0
\(727\) −13.5839 23.5280i −0.503799 0.872605i −0.999990 0.00439187i \(-0.998602\pi\)
0.496192 0.868213i \(-0.334731\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −0.274710 0.475812i −0.0101675 0.0176106i
\(731\) 12.1760 0.450344
\(732\) 0 0
\(733\) 5.66614 0.209284 0.104642 0.994510i \(-0.466630\pi\)
0.104642 + 0.994510i \(0.466630\pi\)
\(734\) −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 \(0.0861241\pi\)
\(740\) −0.0819427 + 0.141929i −0.00301227 + 0.00521741i
\(741\) 0 0
\(742\) 0 0
\(743\) 6.33421 10.9712i 0.232380 0.402493i −0.726128 0.687559i \(-0.758682\pi\)
0.958508 + 0.285066i \(0.0920155\pi\)
\(744\) 0 0
\(745\) 1.17580 0.0430779
\(746\) −4.30696 + 7.45988i −0.157689 + 0.273126i
\(747\) 0 0
\(748\) 4.21977 0.154290
\(749\) 0 0
\(750\) 0 0
\(751\) −7.14538 −0.260739 −0.130369 0.991465i \(-0.541616\pi\)
−0.130369 + 0.991465i \(0.541616\pi\)
\(752\) −2.90488 5.03140i −0.105930 0.183476i
\(753\) 0 0
\(754\) 12.7043 22.0045i 0.462663 0.801355i
\(755\) −1.18897 −0.0432712
\(756\) 0 0
\(757\) 37.6446 1.36822 0.684108 0.729381i \(-0.260192\pi\)
0.684108 + 0.729381i \(0.260192\pi\)
\(758\) 17.4325 30.1940i 0.633178 1.09670i
\(759\) 0 0
\(760\) 1.24376 + 2.15425i 0.0451157 + 0.0781428i
\(761\) 10.0472 0.364209 0.182104 0.983279i \(-0.441709\pi\)
0.182104 + 0.983279i \(0.441709\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −17.5572 −0.635196
\(765\) 0 0
\(766\) 5.91762 10.2496i 0.213812 0.370334i
\(767\) −11.0602 −0.399361
\(768\) 0 0
\(769\) −16.1463 + 27.9663i −0.582252 + 1.00849i 0.412960 + 0.910749i \(0.364495\pi\)
−0.995212 + 0.0977407i \(0.968838\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.100635 + 0.174305i −0.00362192 + 0.00627336i
\(773\) 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
\(779\) −57.5075 −2.06042
\(780\) 0 0
\(781\) 10.9812 0.392938
\(782\) −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
\(787\) 24.4776 + 42.3964i 0.872531 + 1.51127i 0.859370 + 0.511354i \(0.170856\pi\)
0.0131602 + 0.999913i \(0.495811\pi\)
\(788\) 0.299165 + 0.518170i 0.0106573 + 0.0184590i
\(789\) 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
\(794\) −26.5303 −0.941525
\(795\) 0 0
\(796\) 3.94348 0.139773