Properties

Label 1323.2.g.h.361.5
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 361.5
Character \(\chi\) \(=\) 1323.361
Dual form 1323.2.g.h.667.5

$q$-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 \(-0.507507\pi\)
−0.0235829 + 0.999722i \(0.507507\pi\)
\(6\) 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 −0.985155 0.171670i \(-0.945084\pi\)
0.641248 + 0.767334i \(0.278417\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 0.909025 1.57448i 0.227256 0.393619i
\(17\) 0.806594 1.39706i 0.195628 0.338837i −0.751478 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
\(23\) 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 \(-0.854024\pi\)
0.0649574 0.997888i \(-0.479309\pi\)
\(32\) −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 \(0.365379\pi\)
−0.994936 + 0.100506i \(0.967954\pi\)
\(42\) 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 −0.958708 0.284392i \(-0.908208\pi\)
0.725645 + 0.688070i \(0.241542\pi\)
\(48\) 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 0.973884 0.227048i \(-0.0729075\pi\)
−0.683571 + 0.729884i \(0.739574\pi\)
\(60\) 0 0
\(61\) 2.83550 4.91123i 0.363048 0.628818i −0.625413 0.780294i \(-0.715069\pi\)
0.988461 + 0.151476i \(0.0484027\pi\)
\(62\) 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 −0.694059 0.719919i \(-0.744179\pi\)
0.970497 + 0.241113i \(0.0775125\pi\)
\(74\) −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 0.896316 0.443415i \(-0.146233\pi\)
−0.832167 + 0.554525i \(0.812900\pi\)
\(84\) 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 0.980397 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
\(94\) −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 0.753213 0.657777i \(-0.228503\pi\)
−0.946258 + 0.323413i \(0.895170\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.95515 3.38641i −0.195515 0.338641i
\(101\) −17.4702 −1.73835 −0.869177 0.494501i \(-0.835351\pi\)
−0.869177 + 0.494501i \(0.835351\pi\)
\(102\) 0 0
\(103\) −8.73204 −0.860394 −0.430197 0.902735i \(-0.641556\pi\)
−0.430197 + 0.902735i \(0.641556\pi\)
\(104\) 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 \(-0.273355\pi\)
0.653370 + 0.757039i \(0.273355\pi\)
\(132\) 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 −0.985229 0.171240i \(-0.945223\pi\)
0.640913 + 0.767614i \(0.278556\pi\)
\(140\) 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 0.999890 0.0148476i \(-0.00472630\pi\)
−0.512803 + 0.858506i \(0.671393\pi\)
\(158\) −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 \(0.402036\pi\)
−0.976798 + 0.214165i \(0.931297\pi\)
\(168\) 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 −0.914779 0.403954i \(-0.867635\pi\)
0.807224 + 0.590245i \(0.200969\pi\)
\(174\) 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 \(-0.280987\pi\)
0.635032 + 0.772486i \(0.280987\pi\)
\(182\) 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 −0.941307 0.337550i \(-0.890402\pi\)
0.762981 + 0.646421i \(0.223735\pi\)
\(200\) 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 0.615833 0.787877i \(-0.288820\pi\)
−0.990238 + 0.139388i \(0.955486\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1.13395 1.96407i −0.0754295 0.130648i
\(227\) 23.7706 1.57771 0.788857 0.614577i \(-0.210673\pi\)
0.788857 + 0.614577i \(0.210673\pi\)
\(228\) 0 0
\(229\) 1.90547 0.125917 0.0629586 0.998016i \(-0.479946\pi\)
0.0629586 + 0.998016i \(0.479946\pi\)
\(230\) 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 \(-0.276321\pi\)
0.646288 + 0.763094i \(0.276321\pi\)
\(242\) −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 \(-0.568998\pi\)
−0.215069 + 0.976599i \(0.568998\pi\)
\(252\) 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 \(-0.648134\pi\)
−0.448759 + 0.893653i \(0.648134\pi\)
\(258\) 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 \(-0.537921\pi\)
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
\(275\) 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 0.998828 0.0483984i \(-0.0154117\pi\)
−0.541328 + 0.840811i \(0.682078\pi\)
\(284\) −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 \(-0.561601\pi\)
0.946018 0.324114i \(-0.105066\pi\)
\(294\) 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 \(-0.719462\pi\)
−0.636120 + 0.771590i \(0.719462\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1.07721 −0.0611816
\(311\) −0.654931 1.13437i −0.0371377 0.0643245i 0.846859 0.531817i \(-0.178491\pi\)
−0.883997 + 0.467493i \(0.845157\pi\)
\(312\) 0 0
\(313\) −10.7885 + 18.6862i −0.609802 + 1.05621i 0.381471 + 0.924381i \(0.375418\pi\)
−0.991273 + 0.131827i \(0.957916\pi\)
\(314\) −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 0.996033 0.0889810i \(-0.0283610\pi\)
−0.575076 + 0.818100i \(0.695028\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 6.90000 + 11.9511i 0.367771 + 0.636998i
\(353\) 4.14423 0.220575 0.110287 0.993900i \(-0.464823\pi\)
0.110287 + 0.993900i \(0.464823\pi\)
\(354\) 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 \(-0.611507\pi\)
−0.343189 + 0.939266i \(0.611507\pi\)
\(368\) 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 \(-0.411592\pi\)
0.274186 + 0.961677i \(0.411592\pi\)
\(384\) 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 \(-0.960363\pi\)
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
\(401\) 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 \(0.0196442\pi\)
−0.445636 + 0.895214i \(0.647023\pi\)
\(410\) 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 −0.929708 0.368298i \(-0.879941\pi\)
0.783809 + 0.621002i \(0.213274\pi\)
\(420\) 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 \(-0.489656\pi\)
0.0324905 + 0.999472i \(0.489656\pi\)
\(434\) 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 −0.995304 0.0967954i \(-0.969141\pi\)
0.581479 + 0.813561i \(0.302474\pi\)
\(440\) −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 0.757811 0.652474i \(-0.226269\pi\)
−0.943964 + 0.330047i \(0.892935\pi\)
\(462\) 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 \(0.00245083\pi\)
−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
\(472\) −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 \(-0.529141\pi\)
−0.0914210 + 0.995812i \(0.529141\pi\)
\(480\) 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 \(-0.427262\pi\)
0.226529 + 0.974004i \(0.427262\pi\)
\(504\) 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 \(-0.721325\pi\)
−0.640625 + 0.767854i \(0.721325\pi\)
\(510\) 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 \(0.432022\pi\)
−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
\(527\) −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 \(-0.849975\pi\)
0.0522584 0.998634i \(-0.483358\pi\)
\(564\) 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 \(0.344711\pi\)
−0.999361 + 0.0357353i \(0.988623\pi\)
\(578\) −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 \(0.0905697\pi\)
−0.236795 + 0.971560i \(0.576097\pi\)
\(588\) 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 \(-0.900628\pi\)
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
\(598\) −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 \(0.00902635\pi\)
−0.475244 + 0.879854i \(0.657640\pi\)
\(602\) 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 \(-0.455638\pi\)
0.138918 + 0.990304i \(0.455638\pi\)
\(608\) 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 \(-0.557004\pi\)
−0.178128 + 0.984007i \(0.557004\pi\)
\(620\) −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 \(0.375148\pi\)
−0.991384 + 0.130987i \(0.958185\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6.83390 + 11.8367i −0.268876 + 0.465707i
\(647\) −0.649903 + 1.12567i −0.0255503 + 0.0442545i −0.878518 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
\(653\) 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 \(-0.944658\pi\)
0.342649 0.939463i \(-0.388676\pi\)
\(662\) −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 −0.775170 0.631753i \(-0.782336\pi\)
0.934699 + 0.355440i \(0.115669\pi\)
\(678\) 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 −0.659801 0.751440i \(-0.729360\pi\)
0.980667 + 0.195685i \(0.0626930\pi\)
\(692\) −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 0.861945 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
\(724\) 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 \(0.00139798\pi\)
−0.496192 + 0.868213i \(0.665269\pi\)
\(728\) 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 \(-0.533370\pi\)
−0.104642 + 0.994510i \(0.533370\pi\)
\(734\) 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 \(-0.558291\pi\)
−0.182104 + 0.983279i \(0.558291\pi\)
\(762\) 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 \(-0.635505\pi\)
0.995212 0.0977407i \(-0.0311616\pi\)
\(770\) 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 \(0.505013\pi\)
−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
\(779\) −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 \(-0.829144\pi\)
−0.0131602 0.999913i \(-0.504189\pi\)
\(788\) 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