Properties

Label 1323.2.g.h.667.6
Level $1323$
Weight $2$
Character 1323.667
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 667.6
Character \(\chi\) \(=\) 1323.667
Dual form 1323.2.g.h.361.6

$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).

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

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.551407 0.955065i −0.389903 0.675333i 0.602533 0.798094i \(-0.294158\pi\)
−0.992436 + 0.122762i \(0.960825\pi\)
\(3\) 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 0.985155 0.171670i \(-0.0549162\pi\)
−0.641248 + 0.767334i \(0.721583\pi\)
\(14\) 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 \(-0.229341\pi\)
−0.947106 + 0.320921i \(0.896008\pi\)
\(18\) 0 0
\(19\) −3.84133 + 6.65338i −0.881262 + 1.52639i −0.0313221 + 0.999509i \(0.509972\pi\)
−0.849939 + 0.526880i \(0.823362\pi\)
\(20\) 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 0.00682200 + 0.999977i \(0.497828\pi\)
−0.869416 + 0.494080i \(0.835505\pi\)
\(30\) 0 0
\(31\) 4.63081 8.02080i 0.831718 1.44058i −0.0649574 0.997888i \(-0.520691\pi\)
0.896675 0.442689i \(-0.145976\pi\)
\(32\) −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 −0.772967 0.634447i \(-0.781228\pi\)
0.935930 + 0.352186i \(0.114561\pi\)
\(38\) 8.47254 1.37443
\(39\) 0 0
\(40\) −0.323782 −0.0511945
\(41\) 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
\(47\) 1.59780 + 2.76747i 0.233063 + 0.403677i 0.958708 0.284392i \(-0.0917917\pi\)
−0.725645 + 0.688070i \(0.758458\pi\)
\(48\) 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 −0.973371 0.229234i \(-0.926378\pi\)
0.288163 0.957581i \(-0.406956\pi\)
\(54\) 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 \(-0.927093\pi\)
0.683571 + 0.729884i \(0.260426\pi\)
\(60\) 0 0
\(61\) −2.83550 4.91123i −0.363048 0.628818i 0.625413 0.780294i \(-0.284931\pi\)
−0.988461 + 0.151476i \(0.951597\pi\)
\(62\) −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 0.382288 + 0.924043i \(0.375136\pi\)
−0.991389 + 0.130951i \(0.958197\pi\)
\(68\) −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 \(-0.255821\pi\)
−0.970497 + 0.241113i \(0.922488\pi\)
\(74\) −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 0.564289 0.825577i \(-0.309150\pi\)
−0.997115 + 0.0758997i \(0.975817\pi\)
\(80\) 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
\(86\) 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 \(-0.936870\pi\)
0.660832 + 0.750534i \(0.270203\pi\)
\(90\) 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 \(-0.771497\pi\)
0.946258 + 0.323413i \(0.104830\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −1.95515 + 3.38641i −0.195515 + 0.338641i
\(101\) 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 −0.0226645 + 0.999743i \(0.507215\pi\)
−0.854471 + 0.519500i \(0.826118\pi\)
\(108\) 0 0
\(109\) 2.11124 + 3.65678i 0.202220 + 0.350256i 0.949243 0.314542i \(-0.101851\pi\)
−0.747023 + 0.664798i \(0.768518\pi\)
\(110\) 0.194081 + 0.336157i 0.0185049 + 0.0320514i
\(111\) 0 0
\(112\) 0 0
\(113\) −1.02824 1.78096i −0.0967285 0.167539i 0.813600 0.581425i \(-0.197505\pi\)
−0.910329 + 0.413886i \(0.864171\pi\)
\(114\) 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 0.985229 0.171240i \(-0.0547774\pi\)
−0.640913 + 0.767614i \(0.721444\pi\)
\(140\) 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 \(-0.995274\pi\)
0.512803 + 0.858506i \(0.328607\pi\)
\(158\) −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 −0.986426 0.164209i \(-0.947493\pi\)
0.635422 + 0.772165i \(0.280826\pi\)
\(164\) 5.86705 0.458139
\(165\) 0 0
\(166\) 1.28903 0.100048
\(167\) 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
\(173\) 1.41466 + 2.45027i 0.107555 + 0.186291i 0.914779 0.403954i \(-0.132365\pi\)
−0.807224 + 0.590245i \(0.799031\pi\)
\(174\) 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 0.611235 0.791449i \(-0.290673\pi\)
−0.991033 + 0.133620i \(0.957340\pi\)
\(180\) 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 −0.912582 0.408894i \(-0.865914\pi\)
0.102178 0.994766i \(-0.467419\pi\)
\(192\) 0 0
\(193\) 0.128393 0.222383i 0.00924194 0.0160075i −0.861367 0.507982i \(-0.830391\pi\)
0.870609 + 0.491975i \(0.163725\pi\)
\(194\) −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 \(-0.109598\pi\)
−0.762981 + 0.646421i \(0.776265\pi\)
\(200\) 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 0.714824 0.699305i \(-0.246507\pi\)
−0.963027 + 0.269403i \(0.913174\pi\)
\(212\) −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 \(-0.711180\pi\)
0.990238 + 0.139388i \(0.0445137\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) −1.13395 + 1.96407i −0.0754295 + 0.130648i
\(227\) −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 −0.738766 0.673962i \(-0.764591\pi\)
0.953051 + 0.302809i \(0.0979245\pi\)
\(234\) 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 −0.971704 0.236202i \(-0.924097\pi\)
0.281295 0.959621i \(-0.409236\pi\)
\(240\) 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 −0.919313 0.393527i \(-0.871255\pi\)
0.118852 0.992912i \(-0.462079\pi\)
\(270\) 0 0
\(271\) −8.96673 + 15.5308i −0.544690 + 0.943431i 0.453936 + 0.891034i \(0.350019\pi\)
−0.998626 + 0.0523969i \(0.983314\pi\)
\(272\) 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 −0.781930 0.623366i \(-0.785765\pi\)
0.930816 + 0.365488i \(0.119098\pi\)
\(282\) 0 0
\(283\) −7.69634 + 13.3304i −0.457500 + 0.792413i −0.998828 0.0483984i \(-0.984588\pi\)
0.541328 + 0.840811i \(0.317922\pi\)
\(284\) −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 −0.946018 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
\(299\) 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 −0.846859 0.531817i \(-0.821509\pi\)
0.883997 + 0.467493i \(0.154843\pi\)
\(312\) 0 0
\(313\) 10.7885 + 18.6862i 0.609802 + 1.05621i 0.991273 + 0.131827i \(0.0420843\pi\)
−0.381471 + 0.924381i \(0.624582\pi\)
\(314\) 13.4613 0.759667
\(315\) 0 0
\(316\) −6.03065 −0.339250
\(317\) −12.3910 21.4618i −0.695946 1.20541i −0.969861 0.243660i \(-0.921652\pi\)
0.273915 0.961754i \(-0.411681\pi\)
\(318\) 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 0.610635 0.791912i \(-0.290914\pi\)
−0.991133 + 0.132870i \(0.957581\pi\)
\(332\) 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 \(0.803911\pi\)
\(338\) −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 −0.992395 0.123091i \(-0.960719\pi\)
0.602798 + 0.797894i \(0.294052\pi\)
\(348\) 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
\(353\) −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 −0.742040 0.670356i \(-0.766141\pi\)
0.951565 + 0.307447i \(0.0994748\pi\)
\(360\) 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 −0.388566 0.921421i \(-0.627029\pi\)
0.992257 0.124203i \(-0.0396373\pi\)
\(398\) 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 0.445636 + 0.895214i \(0.352977\pi\)
−0.998096 + 0.0616748i \(0.980356\pi\)
\(410\) 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 \(-0.120059\pi\)
−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
\(425\) 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 0.531989 0.846751i \(-0.321445\pi\)
−0.999303 + 0.0373401i \(0.988112\pi\)
\(432\) 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 0.995304 0.0967954i \(-0.0308592\pi\)
−0.581479 + 0.813561i \(0.697526\pi\)
\(440\) 1.08056 0.0515139
\(441\) 0 0
\(442\) −4.41194 −0.209854
\(443\) 9.80499 + 16.9827i 0.465849 + 0.806874i 0.999239 0.0389949i \(-0.0124156\pi\)
−0.533390 + 0.845869i \(0.679082\pi\)
\(444\) 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 0.860292 0.509801i \(-0.170281\pi\)
−0.871647 + 0.490135i \(0.836948\pi\)
\(458\) 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 \(0.754987\pi\)
\(464\) −16.8905 −0.784120
\(465\) 0 0
\(466\) −7.21443 −0.334202
\(467\) −10.9489 + 18.9640i −0.506653 + 0.877549i 0.493317 + 0.869849i \(0.335784\pi\)
−0.999970 + 0.00769944i \(0.997549\pi\)
\(468\) 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 0.992841 + 0.119440i \(0.0381100\pi\)
−0.392982 + 0.919546i \(0.628557\pi\)
\(488\) 8.70502 + 15.0775i 0.394058 + 0.682528i
\(489\) 0 0
\(490\) 0 0
\(491\) −14.2149 24.6210i −0.641511 1.11113i −0.985096 0.172008i \(-0.944975\pi\)
0.343584 0.939122i \(-0.388359\pi\)
\(492\) 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 0.952322 + 0.305095i \(0.0986883\pi\)
−0.211941 + 0.977283i \(0.567978\pi\)
\(522\) 0 0
\(523\) 7.18895 12.4516i 0.314351 0.544471i −0.664949 0.746889i \(-0.731547\pi\)
0.979299 + 0.202418i \(0.0648799\pi\)
\(524\) −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 −0.457625 0.889145i \(-0.651300\pi\)
0.998835 0.0482577i \(-0.0153669\pi\)
\(542\) 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 −0.830027 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
\(551\) −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 0.996391 0.0848820i \(-0.0270513\pi\)
−0.571705 + 0.820459i \(0.693718\pi\)
\(558\) 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 −0.0522584 0.998634i \(-0.516642\pi\)
0.890971 0.454060i \(-0.150025\pi\)
\(564\) 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 0.973714 0.227776i \(-0.0731454\pi\)
−0.684117 + 0.729373i \(0.739812\pi\)
\(570\) 0 0
\(571\) −5.21935 + 9.04019i −0.218423 + 0.378320i −0.954326 0.298767i \(-0.903425\pi\)
0.735903 + 0.677087i \(0.236758\pi\)
\(572\) −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 0.999361 + 0.0357353i \(0.0113773\pi\)
−0.468733 + 0.883340i \(0.655289\pi\)
\(578\) −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 0.236795 + 0.971560i \(0.423903\pi\)
−0.959793 + 0.280709i \(0.909430\pi\)
\(588\) 0 0
\(589\) 35.5769 + 61.6210i 1.46592 + 2.53905i
\(590\) 0.518724 0.0213555
\(591\) 0 0
\(592\) 3.60435 0.148138
\(593\) 18.0646 31.2888i 0.741824 1.28488i −0.209840 0.977736i \(-0.567294\pi\)
0.951664 0.307141i \(-0.0993724\pi\)
\(594\) 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 0.0562080 + 0.998419i \(0.482099\pi\)
−0.892760 + 0.450532i \(0.851234\pi\)
\(600\) 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
\(605\) 0.0145196 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 0.994459 + 0.105123i \(0.0335235\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(614\) −12.2917 21.2898i −0.496051 0.859185i
\(615\) 0 0
\(616\) 0 0
\(617\) 10.3395 + 17.9085i 0.416252 + 0.720969i 0.995559 0.0941404i \(-0.0300102\pi\)
−0.579307 + 0.815109i \(0.696677\pi\)
\(618\) 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 0.991384 + 0.130987i \(0.0418147\pi\)
−0.382254 + 0.924057i \(0.624852\pi\)
\(644\) 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 \(-0.158533\pi\)
−0.852968 + 0.521964i \(0.825200\pi\)
\(648\) 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 −0.986089 0.166216i \(-0.946845\pi\)
0.636992 + 0.770870i \(0.280178\pi\)
\(660\) 0 0
\(661\) 16.5128 28.6010i 0.642274 1.11245i −0.342649 0.939463i \(-0.611324\pi\)
0.984924 0.172989i \(-0.0553424\pi\)
\(662\) −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 −0.995056 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
\(677\) −4.15084 7.18946i −0.159530 0.276313i 0.775170 0.631753i \(-0.217664\pi\)
−0.934699 + 0.355440i \(0.884331\pi\)
\(678\) 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 0.888902 0.458098i \(-0.151469\pi\)
−0.841176 + 0.540762i \(0.818136\pi\)
\(684\) 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 \(-0.270640\pi\)
−0.980667 + 0.195685i \(0.937307\pi\)
\(692\) 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 0.997995 + 0.0632882i \(0.0201587\pi\)
−0.444188 + 0.895933i \(0.646508\pi\)
\(710\) 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 \(-0.830754\pi\)
0.870049 + 0.492965i \(0.164087\pi\)
\(720\) 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 0.496192 + 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
\(731\) 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 0.963620 0.267278i \(-0.0861241\pi\)
−0.713279 + 0.700880i \(0.752791\pi\)
\(740\) −0.0819427 0.141929i −0.00301227 0.00521741i
\(741\) 0 0
\(742\) 0 0
\(743\) 6.33421 + 10.9712i 0.232380 + 0.402493i 0.958508 0.285066i \(-0.0920155\pi\)
−0.726128 + 0.687559i \(0.758682\pi\)
\(744\) 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 −0.995212 0.0977407i \(-0.968838\pi\)
0.412960 0.910749i \(-0.364495\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −0.100635 0.174305i −0.00362192 0.00627336i
\(773\) 24.2939 + 42.0783i 0.873792 + 1.51345i 0.858044 + 0.513576i \(0.171679\pi\)
0.0157473 + 0.999876i \(0.494987\pi\)
\(774\) 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 0.0131602 0.999913i \(-0.495811\pi\)
0.859370 0.511354i \(-0.170856\pi\)
\(788\) 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
\(797\) 1.44417 +