Properties

Label 441.2.f.h.295.8
Level $441$
Weight $2$
Character 441.295
Analytic conductor $3.521$
Analytic rank $0$
Dimension $24$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 441.f (of order \(3\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(3.52140272914\)
Analytic rank: \(0\)
Dimension: \(24\)
Relative dimension: \(12\) over \(\Q(\zeta_{3})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 295.8
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.h.148.8

$q$-expansion

\(f(q)\) \(=\) \(q+(0.551407 - 0.955065i) q^{2} +(1.67475 + 0.441824i) q^{3} +(0.391901 + 0.678793i) q^{4} +(-0.0527330 - 0.0913363i) q^{5} +(1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(2.60958 + 1.47989i) q^{9} +O(q^{10})\) \(q+(0.551407 - 0.955065i) q^{2} +(1.67475 + 0.441824i) q^{3} +(0.391901 + 0.678793i) q^{4} +(-0.0527330 - 0.0913363i) q^{5} +(1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(2.60958 + 1.47989i) q^{9} -0.116309 q^{10} +(-1.66866 + 2.89020i) q^{11} +(0.356430 + 1.30996i) q^{12} +(-1.23997 - 2.14770i) q^{13} +(-0.0479602 - 0.176264i) q^{15} +(0.909025 - 1.57448i) q^{16} +1.61319 q^{17} +(2.85233 - 1.67630i) q^{18} -7.68266 q^{19} +(0.0413323 - 0.0715896i) q^{20} +(1.84022 + 3.18735i) q^{22} +(0.948593 + 1.64301i) q^{23} +(5.14151 + 1.35641i) q^{24} +(2.49444 - 4.32049i) q^{25} -2.73492 q^{26} +(3.71655 + 3.63142i) q^{27} +(4.64521 - 8.04574i) q^{29} +(-0.194789 - 0.0513883i) q^{30} +(-4.63081 - 8.02080i) q^{31} +(2.06753 + 3.58107i) q^{32} +(-4.07155 + 4.10311i) q^{33} +(0.889523 - 1.54070i) q^{34} +(0.0181599 + 2.35134i) q^{36} -1.98254 q^{37} +(-4.23627 + 7.33744i) q^{38} +(-1.12774 - 4.14471i) q^{39} +(-0.161891 - 0.280404i) q^{40} +(3.74268 + 6.48252i) q^{41} +(-3.77388 + 6.53655i) q^{43} -2.61579 q^{44} +(-0.00244354 - 0.316389i) q^{45} +2.09224 q^{46} +(1.59780 - 2.76747i) q^{47} +(2.21803 - 2.23523i) q^{48} +(-2.75090 - 4.76470i) q^{50} +(2.70169 + 0.712745i) q^{51} +(0.971894 - 1.68337i) q^{52} -9.97679 q^{53} +(5.51758 - 1.54715i) q^{54} +0.351974 q^{55} +(-12.8665 - 3.39438i) q^{57} +(-5.12280 - 8.87296i) q^{58} +(-2.22993 - 3.86235i) q^{59} +(0.100851 - 0.101633i) q^{60} +(2.83550 - 4.91123i) q^{61} -10.2138 q^{62} +8.19630 q^{64} +(-0.130775 + 0.226509i) q^{65} +(1.67366 + 6.15107i) q^{66} +(-4.98571 - 8.63550i) q^{67} +(0.632210 + 1.09502i) q^{68} +(0.862736 + 3.17075i) q^{69} +3.29042 q^{71} +(8.01146 + 4.54329i) q^{72} -4.72378 q^{73} +(-1.09318 + 1.89345i) q^{74} +(6.08646 - 6.13365i) q^{75} +(-3.01084 - 5.21493i) q^{76} +(-4.58031 - 1.20835i) q^{78} +(-3.84705 + 6.66328i) q^{79} -0.191743 q^{80} +(4.61985 + 7.72379i) q^{81} +8.25496 q^{82} +(-0.584428 + 1.01226i) q^{83} +(-0.0850683 - 0.147343i) q^{85} +(4.16189 + 7.20860i) q^{86} +(11.3344 - 11.4223i) q^{87} +(-5.12280 + 8.87296i) q^{88} +6.02954 q^{89} +(-0.303519 - 0.172125i) q^{90} +(-0.743509 + 1.28780i) q^{92} +(-4.21167 - 15.4788i) q^{93} +(-1.76208 - 3.05201i) q^{94} +(0.405130 + 0.701706i) q^{95} +(1.88040 + 6.91088i) q^{96} +(-1.90127 + 3.29310i) q^{97} +(-8.63168 + 5.07279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} + 8q^{9} + O(q^{10}) \) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} + 8q^{9} + 20q^{11} + 4q^{15} - 12q^{16} + 4q^{18} + 32q^{23} - 12q^{25} + 16q^{29} + 48q^{32} - 4q^{36} + 24q^{37} + 32q^{39} - 112q^{44} - 48q^{46} - 4q^{50} - 56q^{51} - 64q^{53} - 12q^{57} - 88q^{60} + 96q^{64} + 60q^{65} - 12q^{67} - 112q^{71} + 168q^{72} + 68q^{74} - 60q^{78} + 12q^{79} + 80q^{81} + 12q^{85} + 76q^{86} + 16q^{92} - 80q^{93} + 64q^{95} + 20q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

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 −0.602533 0.798094i \(-0.705842\pi\)
0.992436 + 0.122762i \(0.0391750\pi\)
\(3\) 1.67475 + 0.441824i 0.966918 + 0.255087i
\(4\) 0.391901 + 0.678793i 0.195951 + 0.339396i
\(5\) −0.0527330 0.0913363i −0.0235829 0.0408468i 0.853993 0.520284i \(-0.174174\pi\)
−0.877576 + 0.479438i \(0.840841\pi\)
\(6\) 1.34544 1.35587i 0.549273 0.553532i
\(7\) 0 0
\(8\) 3.07001 1.08541
\(9\) 2.60958 + 1.47989i 0.869861 + 0.493297i
\(10\) −0.116309 −0.0367803
\(11\) −1.66866 + 2.89020i −0.503119 + 0.871428i 0.496874 + 0.867822i \(0.334481\pi\)
−0.999994 + 0.00360543i \(0.998852\pi\)
\(12\) 0.356430 + 1.30996i 0.102892 + 0.378153i
\(13\) −1.23997 2.14770i −0.343907 0.595664i 0.641248 0.767334i \(-0.278417\pi\)
−0.985155 + 0.171670i \(0.945084\pi\)
\(14\) 0 0
\(15\) −0.0479602 0.176264i −0.0123833 0.0455113i
\(16\) 0.909025 1.57448i 0.227256 0.393619i
\(17\) 1.61319 0.391255 0.195628 0.980678i \(-0.437326\pi\)
0.195628 + 0.980678i \(0.437326\pi\)
\(18\) 2.85233 1.67630i 0.672301 0.395107i
\(19\) −7.68266 −1.76252 −0.881262 0.472629i \(-0.843305\pi\)
−0.881262 + 0.472629i \(0.843305\pi\)
\(20\) 0.0413323 0.0715896i 0.00924218 0.0160079i
\(21\) 0 0
\(22\) 1.84022 + 3.18735i 0.392336 + 0.679546i
\(23\) 0.948593 + 1.64301i 0.197795 + 0.342592i 0.947813 0.318826i \(-0.103289\pi\)
−0.750018 + 0.661417i \(0.769955\pi\)
\(24\) 5.14151 + 1.35641i 1.04951 + 0.276875i
\(25\) 2.49444 4.32049i 0.498888 0.864099i
\(26\) −2.73492 −0.536362
\(27\) 3.71655 + 3.63142i 0.715251 + 0.698868i
\(28\) 0 0
\(29\) 4.64521 8.04574i 0.862594 1.49406i −0.00682200 0.999977i \(-0.502172\pi\)
0.869416 0.494080i \(-0.164495\pi\)
\(30\) −0.194789 0.0513883i −0.0355635 0.00938218i
\(31\) −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
\(33\) −4.07155 + 4.10311i −0.708765 + 0.714260i
\(34\) 0.889523 1.54070i 0.152552 0.264228i
\(35\) 0 0
\(36\) 0.0181599 + 2.35134i 0.00302665 + 0.391889i
\(37\) −1.98254 −0.325927 −0.162963 0.986632i \(-0.552105\pi\)
−0.162963 + 0.986632i \(0.552105\pi\)
\(38\) −4.23627 + 7.33744i −0.687214 + 1.19029i
\(39\) −1.12774 4.14471i −0.180583 0.663684i
\(40\) −0.161891 0.280404i −0.0255973 0.0443357i
\(41\) 3.74268 + 6.48252i 0.584509 + 1.01240i 0.994936 + 0.100506i \(0.0320462\pi\)
−0.410427 + 0.911893i \(0.634621\pi\)
\(42\) 0 0
\(43\) −3.77388 + 6.53655i −0.575512 + 0.996815i 0.420474 + 0.907304i \(0.361864\pi\)
−0.995986 + 0.0895108i \(0.971470\pi\)
\(44\) −2.61579 −0.394346
\(45\) −0.00244354 0.316389i −0.000364262 0.0471645i
\(46\) 2.09224 0.308484
\(47\) 1.59780 2.76747i 0.233063 0.403677i −0.725645 0.688070i \(-0.758458\pi\)
0.958708 + 0.284392i \(0.0917917\pi\)
\(48\) 2.21803 2.23523i 0.320145 0.322627i
\(49\) 0 0
\(50\) −2.75090 4.76470i −0.389036 0.673830i
\(51\) 2.70169 + 0.712745i 0.378312 + 0.0998042i
\(52\) 0.971894 1.68337i 0.134777 0.233441i
\(53\) −9.97679 −1.37042 −0.685209 0.728347i \(-0.740289\pi\)
−0.685209 + 0.728347i \(0.740289\pi\)
\(54\) 5.51758 1.54715i 0.750847 0.210541i
\(55\) 0.351974 0.0474601
\(56\) 0 0
\(57\) −12.8665 3.39438i −1.70422 0.449597i
\(58\) −5.12280 8.87296i −0.672657 1.16508i
\(59\) −2.22993 3.86235i −0.290312 0.502836i 0.683571 0.729884i \(-0.260426\pi\)
−0.973884 + 0.227048i \(0.927093\pi\)
\(60\) 0.100851 0.101633i 0.0130198 0.0131208i
\(61\) 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
\(66\) 1.67366 + 6.15107i 0.206013 + 0.757145i
\(67\) −4.98571 8.63550i −0.609101 1.05499i −0.991389 0.130951i \(-0.958197\pi\)
0.382288 0.924043i \(-0.375136\pi\)
\(68\) 0.632210 + 1.09502i 0.0766667 + 0.132791i
\(69\) 0.862736 + 3.17075i 0.103861 + 0.381713i
\(70\) 0 0
\(71\) 3.29042 0.390502 0.195251 0.980753i \(-0.437448\pi\)
0.195251 + 0.980753i \(0.437448\pi\)
\(72\) 8.01146 + 4.54329i 0.944160 + 0.535431i
\(73\) −4.72378 −0.552877 −0.276438 0.961032i \(-0.589154\pi\)
−0.276438 + 0.961032i \(0.589154\pi\)
\(74\) −1.09318 + 1.89345i −0.127080 + 0.220109i
\(75\) 6.08646 6.13365i 0.702804 0.708253i
\(76\) −3.01084 5.21493i −0.345367 0.598194i
\(77\) 0 0
\(78\) −4.58031 1.20835i −0.518618 0.136819i
\(79\) −3.84705 + 6.66328i −0.432827 + 0.749678i −0.997115 0.0758997i \(-0.975817\pi\)
0.564289 + 0.825577i \(0.309150\pi\)
\(80\) −0.191743 −0.0214375
\(81\) 4.61985 + 7.72379i 0.513317 + 0.858199i
\(82\) 8.25496 0.911608
\(83\) −0.584428 + 1.01226i −0.0641493 + 0.111110i −0.896316 0.443415i \(-0.853767\pi\)
0.832167 + 0.554525i \(0.187100\pi\)
\(84\) 0 0
\(85\) −0.0850683 0.147343i −0.00922695 0.0159815i
\(86\) 4.16189 + 7.20860i 0.448788 + 0.777323i
\(87\) 11.3344 11.4223i 1.21517 1.22459i
\(88\) −5.12280 + 8.87296i −0.546093 + 0.945860i
\(89\) 6.02954 0.639130 0.319565 0.947564i \(-0.396463\pi\)
0.319565 + 0.947564i \(0.396463\pi\)
\(90\) −0.303519 0.172125i −0.0319937 0.0181436i
\(91\) 0 0
\(92\) −0.743509 + 1.28780i −0.0775162 + 0.134262i
\(93\) −4.21167 15.4788i −0.436730 1.60508i
\(94\) −1.76208 3.05201i −0.181744 0.314791i
\(95\) 0.405130 + 0.701706i 0.0415655 + 0.0719935i
\(96\) 1.88040 + 6.91088i 0.191917 + 0.705339i
\(97\) −1.90127 + 3.29310i −0.193045 + 0.334364i −0.946258 0.323413i \(-0.895170\pi\)
0.753213 + 0.657777i \(0.228503\pi\)
\(98\) 0 0
\(99\) −8.63168 + 5.07279i −0.867516 + 0.509834i
\(100\) 3.91029 0.391029
\(101\) −8.73512 + 15.1297i −0.869177 + 1.50546i −0.00633771 + 0.999980i \(0.502017\pi\)
−0.862839 + 0.505479i \(0.831316\pi\)
\(102\) 2.17045 2.18727i 0.214906 0.216572i
\(103\) 4.36602 + 7.56217i 0.430197 + 0.745123i 0.996890 0.0788062i \(-0.0251108\pi\)
−0.566693 + 0.823929i \(0.691777\pi\)
\(104\) −3.80674 6.59346i −0.373281 0.646542i
\(105\) 0 0
\(106\) −5.50127 + 9.52848i −0.534330 + 0.925487i
\(107\) −18.1463 −1.75427 −0.877135 0.480244i \(-0.840548\pi\)
−0.877135 + 0.480244i \(0.840548\pi\)
\(108\) −1.00846 + 3.94593i −0.0970394 + 0.379697i
\(109\) −4.22248 −0.404440 −0.202220 0.979340i \(-0.564816\pi\)
−0.202220 + 0.979340i \(0.564816\pi\)
\(110\) 0.194081 0.336157i 0.0185049 0.0320514i
\(111\) −3.32025 0.875932i −0.315145 0.0831398i
\(112\) 0 0
\(113\) 1.02824 + 1.78096i 0.0967285 + 0.167539i 0.910329 0.413886i \(-0.135829\pi\)
−0.813600 + 0.581425i \(0.802495\pi\)
\(114\) −10.3366 + 10.4167i −0.968107 + 0.975613i
\(115\) 0.100044 0.173282i 0.00932919 0.0161586i
\(116\) 7.28186 0.676103
\(117\) −0.0574579 7.43962i −0.00531198 0.687793i
\(118\) −4.91840 −0.452775
\(119\) 0 0
\(120\) −0.147238 0.541134i −0.0134410 0.0493986i
\(121\) −0.0688352 0.119226i −0.00625774 0.0108387i
\(122\) −3.12703 5.41617i −0.283108 0.490357i
\(123\) 3.40393 + 12.5102i 0.306922 + 1.12801i
\(124\) 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
\(129\) −9.20832 + 9.27971i −0.810747 + 0.817033i
\(130\) 0.144221 + 0.249797i 0.0126490 + 0.0219087i
\(131\) 7.47816 + 12.9525i 0.653370 + 1.13167i 0.982300 + 0.187315i \(0.0599786\pi\)
−0.328930 + 0.944354i \(0.606688\pi\)
\(132\) −4.38081 1.15572i −0.381300 0.100593i
\(133\) 0 0
\(134\) −10.9966 −0.949962
\(135\) 0.135696 0.530952i 0.0116788 0.0456971i
\(136\) 4.95251 0.424674
\(137\) 7.62367 13.2046i 0.651334 1.12814i −0.331466 0.943467i \(-0.607543\pi\)
0.982799 0.184676i \(-0.0591235\pi\)
\(138\) 3.50399 + 0.924403i 0.298279 + 0.0786904i
\(139\) −4.05943 7.03114i −0.344316 0.596374i 0.640913 0.767614i \(-0.278556\pi\)
−0.985229 + 0.171240i \(0.945223\pi\)
\(140\) 0 0
\(141\) 3.89866 3.92888i 0.328326 0.330872i
\(142\) 1.81436 3.14257i 0.152258 0.263718i
\(143\) 8.27636 0.692104
\(144\) 4.70223 2.76347i 0.391852 0.230289i
\(145\) −0.979825 −0.0813700
\(146\) −2.60473 + 4.51152i −0.215569 + 0.373376i
\(147\) 0 0
\(148\) −0.776958 1.34573i −0.0638656 0.110618i
\(149\) 5.57430 + 9.65497i 0.456664 + 0.790966i 0.998782 0.0493365i \(-0.0157107\pi\)
−0.542118 + 0.840303i \(0.682377\pi\)
\(150\) −2.50192 9.19510i −0.204281 0.750777i
\(151\) 5.63676 9.76315i 0.458713 0.794514i −0.540180 0.841549i \(-0.681644\pi\)
0.998893 + 0.0470354i \(0.0149774\pi\)
\(152\) −23.5859 −1.91307
\(153\) 4.20975 + 2.38734i 0.340338 + 0.193005i
\(154\) 0 0
\(155\) −0.488393 + 0.845922i −0.0392287 + 0.0679461i
\(156\) 2.37143 2.38982i 0.189867 0.191339i
\(157\) 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
\(159\) −16.7086 4.40798i −1.32508 0.349576i
\(160\) 0.218054 0.377681i 0.0172387 0.0298583i
\(161\) 0 0
\(162\) 9.92414 0.153302i 0.779714 0.0120445i
\(163\) 8.96264 0.702008 0.351004 0.936374i \(-0.385840\pi\)
0.351004 + 0.936374i \(0.385840\pi\)
\(164\) −2.93352 + 5.08101i −0.229070 + 0.396760i
\(165\) 0.589468 + 0.155510i 0.0458900 + 0.0121065i
\(166\) 0.644515 + 1.11633i 0.0500240 + 0.0866442i
\(167\) 8.70833 + 15.0833i 0.673871 + 1.16718i 0.976798 + 0.214165i \(0.0687030\pi\)
−0.302927 + 0.953014i \(0.597964\pi\)
\(168\) 0 0
\(169\) 3.42493 5.93216i 0.263456 0.456320i
\(170\) −0.187629 −0.0143905
\(171\) −20.0485 11.3695i −1.53315 0.869447i
\(172\) −5.91595 −0.451087
\(173\) 1.41466 2.45027i 0.107555 0.186291i −0.807224 0.590245i \(-0.799031\pi\)
0.914779 + 0.403954i \(0.132365\pi\)
\(174\) −4.65914 17.1234i −0.353208 1.29812i
\(175\) 0 0
\(176\) 3.03370 + 5.25453i 0.228674 + 0.396075i
\(177\) −2.02810 7.45372i −0.152441 0.560256i
\(178\) 3.32473 5.75860i 0.249199 0.431625i
\(179\) −10.1627 −0.759595 −0.379798 0.925070i \(-0.624006\pi\)
−0.379798 + 0.925070i \(0.624006\pi\)
\(180\) 0.213805 0.125652i 0.0159361 0.00936553i
\(181\) 17.0870 1.27006 0.635032 0.772486i \(-0.280987\pi\)
0.635032 + 0.772486i \(0.280987\pi\)
\(182\) 0 0
\(183\) 6.91865 6.97229i 0.511441 0.515407i
\(184\) 2.91220 + 5.04407i 0.214690 + 0.371854i
\(185\) 0.104545 + 0.181078i 0.00768631 + 0.0133131i
\(186\) −17.1056 4.51272i −1.25425 0.330888i
\(187\) −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 \(-0.532581\pi\)
0.912582 0.408894i \(-0.134086\pi\)
\(192\) 13.7268 + 3.62132i 0.990644 + 0.261346i
\(193\) 0.128393 + 0.222383i 0.00924194 + 0.0160075i 0.870609 0.491975i \(-0.163725\pi\)
−0.861367 + 0.507982i \(0.830391\pi\)
\(194\) 2.09675 + 3.63168i 0.150538 + 0.260739i
\(195\) −0.319093 + 0.321567i −0.0228507 + 0.0230279i
\(196\) 0 0
\(197\) −0.763370 −0.0543878 −0.0271939 0.999630i \(-0.508657\pi\)
−0.0271939 + 0.999630i \(0.508657\pi\)
\(198\) 0.0852720 + 11.0410i 0.00606002 + 0.784648i
\(199\) 5.03121 0.356653 0.178327 0.983971i \(-0.442932\pi\)
0.178327 + 0.983971i \(0.442932\pi\)
\(200\) 7.65796 13.2640i 0.541500 0.937905i
\(201\) −4.53445 16.6651i −0.319835 1.17547i
\(202\) 9.63321 + 16.6852i 0.677790 + 1.17397i
\(203\) 0 0
\(204\) 0.574988 + 2.11321i 0.0402572 + 0.147954i
\(205\) 0.394726 0.683686i 0.0275689 0.0477507i
\(206\) 9.62981 0.670941
\(207\) 0.0439559 + 5.69139i 0.00305515 + 0.395579i
\(208\) −4.50867 −0.312620
\(209\) 12.8197 22.2044i 0.886759 1.53591i
\(210\) 0 0
\(211\) −3.60537 6.24468i −0.248204 0.429901i 0.714824 0.699305i \(-0.246507\pi\)
−0.963027 + 0.269403i \(0.913174\pi\)
\(212\) −3.90991 6.77217i −0.268534 0.465114i
\(213\) 5.51064 + 1.45379i 0.377583 + 0.0996119i
\(214\) −10.0060 + 17.3309i −0.683996 + 1.18472i
\(215\) 0.796033 0.0542890
\(216\) 11.4099 + 11.1485i 0.776343 + 0.758561i
\(217\) 0 0
\(218\) −2.32831 + 4.03274i −0.157693 + 0.273132i
\(219\) −7.91116 2.08708i −0.534587 0.141032i
\(220\) 0.137939 + 0.238917i 0.00929983 + 0.0161078i
\(221\) −2.00031 3.46464i −0.134555 0.233057i
\(222\) −2.66738 + 2.68806i −0.179023 + 0.180411i
\(223\) −5.59106 + 9.68400i −0.374405 + 0.648488i −0.990238 0.139388i \(-0.955486\pi\)
0.615833 + 0.787877i \(0.288820\pi\)
\(224\) 0 0
\(225\) 12.9033 7.58319i 0.860220 0.505546i
\(226\) 2.26791 0.150859
\(227\) 11.8853 20.5860i 0.788857 1.36634i −0.137811 0.990459i \(-0.544007\pi\)
0.926668 0.375881i \(-0.122660\pi\)
\(228\) −2.73833 10.0640i −0.181350 0.666503i
\(229\) −0.952737 1.65019i −0.0629586 0.109048i 0.832828 0.553532i \(-0.186720\pi\)
−0.895787 + 0.444484i \(0.853387\pi\)
\(230\) −0.110330 0.191098i −0.00727497 0.0126006i
\(231\) 0 0
\(232\) 14.2609 24.7006i 0.936272 1.62167i
\(233\) 6.54184 0.428570 0.214285 0.976771i \(-0.431258\pi\)
0.214285 + 0.976771i \(0.431258\pi\)
\(234\) −7.13700 4.04738i −0.466560 0.264586i
\(235\) −0.337028 −0.0219853
\(236\) 1.74782 3.02732i 0.113774 0.197062i
\(237\) −9.38684 + 9.45962i −0.609741 + 0.614468i
\(238\) 0 0
\(239\) 10.6735 + 18.4870i 0.690409 + 1.19582i 0.971704 + 0.236202i \(0.0759028\pi\)
−0.281295 + 0.959621i \(0.590764\pi\)
\(240\) −0.321121 0.0847165i −0.0207283 0.00546842i
\(241\) −10.0331 + 17.3778i −0.646288 + 1.11940i 0.337715 + 0.941248i \(0.390346\pi\)
−0.984003 + 0.178155i \(0.942987\pi\)
\(242\) −0.151825 −0.00975967
\(243\) 4.32454 + 14.9766i 0.277419 + 0.960749i
\(244\) 4.44494 0.284558
\(245\) 0 0
\(246\) 13.8250 + 3.64724i 0.881451 + 0.232540i
\(247\) 9.52629 + 16.5000i 0.606144 + 1.04987i
\(248\) −14.2167 24.6240i −0.902758 1.56362i
\(249\) −1.42601 + 1.43707i −0.0903698 + 0.0910704i
\(250\) −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
\(255\) −0.0773687 0.284347i −0.00484502 0.0178065i
\(256\) 7.77234 + 13.4621i 0.485771 + 0.841380i
\(257\) −7.19415 12.4606i −0.448759 0.777273i 0.549546 0.835463i \(-0.314801\pi\)
−0.998306 + 0.0581897i \(0.981467\pi\)
\(258\) 3.78519 + 13.9114i 0.235656 + 0.866088i
\(259\) 0 0
\(260\) −0.205004 −0.0127138
\(261\) 24.0289 14.1216i 1.48735 0.874107i
\(262\) 16.4940 1.01900
\(263\) 0.769503 1.33282i 0.0474496 0.0821851i −0.841325 0.540529i \(-0.818224\pi\)
0.888775 + 0.458344i \(0.151557\pi\)
\(264\) −12.4997 + 12.5966i −0.769304 + 0.775268i
\(265\) 0.526106 + 0.911243i 0.0323185 + 0.0559772i
\(266\) 0 0
\(267\) 10.0980 + 2.66399i 0.617986 + 0.163034i
\(268\) 3.90781 6.76852i 0.238707 0.413453i
\(269\) 26.2571 1.60092 0.800461 0.599385i \(-0.204588\pi\)
0.800461 + 0.599385i \(0.204588\pi\)
\(270\) −0.432270 0.422369i −0.0263071 0.0257046i
\(271\) −17.9335 −1.08938 −0.544690 0.838637i \(-0.683353\pi\)
−0.544690 + 0.838637i \(0.683353\pi\)
\(272\) 1.46643 2.53993i 0.0889152 0.154006i
\(273\) 0 0
\(274\) −8.40748 14.5622i −0.507915 0.879734i
\(275\) 8.32473 + 14.4188i 0.502000 + 0.869489i
\(276\) −1.81417 + 1.82824i −0.109200 + 0.110047i
\(277\) 9.43563 16.3430i 0.566932 0.981955i −0.429935 0.902860i \(-0.641463\pi\)
0.996867 0.0790954i \(-0.0252032\pi\)
\(278\) −8.95359 −0.537001
\(279\) −0.214582 27.7840i −0.0128467 1.66339i
\(280\) 0 0
\(281\) −2.49578 + 4.32283i −0.148886 + 0.257878i −0.930816 0.365488i \(-0.880902\pi\)
0.781930 + 0.623366i \(0.214235\pi\)
\(282\) −1.60259 5.88988i −0.0954329 0.350737i
\(283\) 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
\(285\) 0.368462 + 1.35418i 0.0218258 + 0.0802146i
\(286\) 4.56364 7.90446i 0.269854 0.467401i
\(287\) 0 0
\(288\) 0.0958052 + 12.4048i 0.00564537 + 0.730960i
\(289\) −14.3976 −0.846919
\(290\) −0.540282 + 0.935796i −0.0317265 + 0.0549518i
\(291\) −4.63913 + 4.67510i −0.271951 + 0.274059i
\(292\) −1.85126 3.20647i −0.108337 0.187644i
\(293\) −12.9013 22.3456i −0.753700 1.30545i −0.946018 0.324114i \(-0.894934\pi\)
0.192318 0.981333i \(-0.438399\pi\)
\(294\) 0 0
\(295\) −0.235182 + 0.407347i −0.0136928 + 0.0237167i
\(296\) −6.08642 −0.353766
\(297\) −16.6972 + 4.68197i −0.968869 + 0.271676i
\(298\) 12.2948 0.712220
\(299\) 2.35246 4.07458i 0.136046 0.235639i
\(300\) 6.54877 + 1.72766i 0.378093 + 0.0997465i
\(301\) 0 0
\(302\) −6.21629 10.7669i −0.357707 0.619567i
\(303\) −21.3138 + 21.4790i −1.22445 + 1.23394i
\(304\) −6.98373 + 12.0962i −0.400544 + 0.693763i
\(305\) −0.598098 −0.0342470
\(306\) 4.60135 2.70418i 0.263042 0.154588i
\(307\) −22.2914 −1.27224 −0.636120 0.771590i \(-0.719462\pi\)
−0.636120 + 0.771590i \(0.719462\pi\)
\(308\) 0 0
\(309\) 3.97085 + 14.5938i 0.225894 + 0.830210i
\(310\) 0.538607 + 0.932894i 0.0305908 + 0.0529848i
\(311\) 0.654931 + 1.13437i 0.0371377 + 0.0643245i 0.883997 0.467493i \(-0.154843\pi\)
−0.846859 + 0.531817i \(0.821509\pi\)
\(312\) −3.46219 12.7243i −0.196008 0.720373i
\(313\) −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 \(-0.588319\pi\)
0.969861 0.243660i \(-0.0783480\pi\)
\(318\) −13.4232 + 13.5272i −0.752734 + 0.758570i
\(319\) 15.5025 + 26.8512i 0.867975 + 1.50338i
\(320\) −0.432216 0.748620i −0.0241616 0.0418491i
\(321\) −30.3906 8.01748i −1.69624 0.447492i
\(322\) 0 0
\(323\) −12.3936 −0.689597
\(324\) −3.43233 + 6.16288i −0.190685 + 0.342382i
\(325\) −12.3722 −0.686283
\(326\) 4.94206 8.55990i 0.273715 0.474089i
\(327\) −7.07161 1.86559i −0.391061 0.103168i
\(328\) 11.4901 + 19.9014i 0.634434 + 1.09887i
\(329\) 0 0
\(330\) 0.473559 0.477231i 0.0260686 0.0262707i
\(331\) −6.92256 + 11.9902i −0.380498 + 0.659042i −0.991133 0.132870i \(-0.957581\pi\)
0.610635 + 0.791912i \(0.290914\pi\)
\(332\) −0.916151 −0.0502803
\(333\) −5.17359 2.93394i −0.283511 0.160779i
\(334\) 19.2073 1.05098
\(335\) −0.525823 + 0.910752i −0.0287288 + 0.0497597i
\(336\) 0 0
\(337\) 1.69444 + 2.93485i 0.0923018 + 0.159871i 0.908479 0.417930i \(-0.137244\pi\)
−0.816178 + 0.577801i \(0.803911\pi\)
\(338\) −3.77706 6.54206i −0.205445 0.355841i
\(339\) 0.935172 + 3.43697i 0.0507916 + 0.186670i
\(340\) 0.0666767 0.115487i 0.00361605 0.00626319i
\(341\) 30.9089 1.67381
\(342\) −21.9135 + 12.8784i −1.18495 + 0.696386i
\(343\) 0 0
\(344\) −11.5859 + 20.0673i −0.624668 + 1.08196i
\(345\) 0.244110 0.246002i 0.0131424 0.0132443i
\(346\) −1.56011 2.70219i −0.0838720 0.145271i
\(347\) 7.25739 + 12.5702i 0.389597 + 0.674802i 0.992395 0.123091i \(-0.0392809\pi\)
−0.602798 + 0.797894i \(0.705948\pi\)
\(348\) 12.1953 + 3.21730i 0.653736 + 0.172465i
\(349\) 7.86412 13.6211i 0.420957 0.729119i −0.575076 0.818100i \(-0.695028\pi\)
0.996033 + 0.0889810i \(0.0283610\pi\)
\(350\) 0 0
\(351\) 3.19077 12.4849i 0.170311 0.666395i
\(352\) −13.8000 −0.735542
\(353\) 2.07211 3.58900i 0.110287 0.191023i −0.805599 0.592462i \(-0.798156\pi\)
0.915886 + 0.401438i \(0.131490\pi\)
\(354\) −8.23709 2.17307i −0.437796 0.115497i
\(355\) −0.173514 0.300535i −0.00920917 0.0159508i
\(356\) 2.36298 + 4.09281i 0.125238 + 0.216918i
\(357\) 0 0
\(358\) −5.60378 + 9.70603i −0.296169 + 0.512979i
\(359\) 7.93988 0.419051 0.209525 0.977803i \(-0.432808\pi\)
0.209525 + 0.977803i \(0.432808\pi\)
\(360\) −0.00750171 0.971318i −0.000395375 0.0511930i
\(361\) 40.0233 2.10649
\(362\) 9.42187 16.3192i 0.495202 0.857716i
\(363\) −0.0626049 0.230087i −0.00328590 0.0120764i
\(364\) 0 0
\(365\) 0.249099 + 0.431453i 0.0130385 + 0.0225833i
\(366\) −2.84400 10.4523i −0.148658 0.546352i
\(367\) 6.57455 11.3875i 0.343189 0.594420i −0.641834 0.766843i \(-0.721826\pi\)
0.985023 + 0.172423i \(0.0551596\pi\)
\(368\) 3.44918 0.179801
\(369\) 0.173428 + 22.4554i 0.00902832 + 1.16898i
\(370\) 0.230588 0.0119877
\(371\) 0 0
\(372\) 8.85636 8.92503i 0.459181 0.462741i
\(373\) −3.90543 6.76441i −0.202216 0.350248i 0.747026 0.664794i \(-0.231481\pi\)
−0.949242 + 0.314547i \(0.898147\pi\)
\(374\) 2.96862 + 5.14180i 0.153504 + 0.265876i
\(375\) −1.76433 0.465456i −0.0911096 0.0240361i
\(376\) 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
\(381\) 0.531163 + 0.140128i 0.0272123 + 0.00717900i
\(382\) −12.3515 21.3934i −0.631958 1.09458i
\(383\) 5.36593 + 9.29407i 0.274186 + 0.474905i 0.969930 0.243386i \(-0.0782582\pi\)
−0.695743 + 0.718291i \(0.744925\pi\)
\(384\) 0.938027 0.945300i 0.0478685 0.0482396i
\(385\) 0 0
\(386\) 0.283187 0.0144139
\(387\) −19.5216 + 11.4728i −0.992341 + 0.583193i
\(388\) −2.98045 −0.151309
\(389\) −12.0734 + 20.9118i −0.612147 + 1.06027i 0.378731 + 0.925507i \(0.376361\pi\)
−0.990878 + 0.134763i \(0.956973\pi\)
\(390\) 0.131167 + 0.482069i 0.00664191 + 0.0244105i
\(391\) 1.53026 + 2.65049i 0.0773885 + 0.134041i
\(392\) 0 0
\(393\) 6.80131 + 24.9963i 0.343081 + 1.26090i
\(394\) −0.420927 + 0.729067i −0.0212060 + 0.0367299i
\(395\) 0.811466 0.0408293
\(396\) −6.82613 3.87109i −0.343026 0.194530i
\(397\) 24.0569 1.20738 0.603691 0.797218i \(-0.293696\pi\)
0.603691 + 0.797218i \(0.293696\pi\)
\(398\) 2.77424 4.80513i 0.139060 0.240860i
\(399\) 0 0
\(400\) −4.53501 7.85487i −0.226751 0.392744i
\(401\) 0.781158 + 1.35301i 0.0390092 + 0.0675659i 0.884871 0.465836i \(-0.154247\pi\)
−0.845862 + 0.533402i \(0.820913\pi\)
\(402\) −18.4166 4.85857i −0.918536 0.242323i
\(403\) −11.4842 + 19.8911i −0.572067 + 0.990849i
\(404\) −13.6932 −0.681263
\(405\) 0.461844 0.829259i 0.0229492 0.0412062i
\(406\) 0 0
\(407\) 3.30817 5.72992i 0.163980 0.284022i
\(408\) 8.29422 + 2.18814i 0.410625 + 0.108329i
\(409\) 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
\(411\) 18.6018 18.7461i 0.917561 0.924675i
\(412\) −3.42210 + 5.92725i −0.168595 + 0.292014i
\(413\) 0 0
\(414\) 5.45988 + 3.09629i 0.268339 + 0.152174i
\(415\) 0.123275 0.00605131
\(416\) 5.12736 8.88086i 0.251390 0.435420i
\(417\) −3.69201 13.5690i −0.180799 0.664475i
\(418\) −14.1378 24.4873i −0.691501 1.19771i
\(419\) 2.98648 + 5.17273i 0.145899 + 0.252704i 0.929708 0.368298i \(-0.120059\pi\)
−0.783809 + 0.621002i \(0.786726\pi\)
\(420\) 0 0
\(421\) 7.31594 12.6716i 0.356557 0.617575i −0.630826 0.775924i \(-0.717284\pi\)
0.987383 + 0.158349i \(0.0506172\pi\)
\(422\) −7.95210 −0.387102
\(423\) 8.26515 4.85738i 0.401865 0.236174i
\(424\) −30.6289 −1.48747
\(425\) 4.02400 6.96977i 0.195193 0.338083i
\(426\) 4.42707 4.46139i 0.214492 0.216155i
\(427\) 0 0
\(428\) −7.11156 12.3176i −0.343750 0.595393i
\(429\) 13.8609 + 3.65670i 0.669208 + 0.176547i
\(430\) 0.438938 0.760263i 0.0211675 0.0366631i
\(431\) −19.4034 −0.934628 −0.467314 0.884091i \(-0.654778\pi\)
−0.467314 + 0.884091i \(0.654778\pi\)
\(432\) 9.09603 2.55057i 0.437633 0.122714i
\(433\) 1.35217 0.0649810 0.0324905 0.999472i \(-0.489656\pi\)
0.0324905 + 0.999472i \(0.489656\pi\)
\(434\) 0 0
\(435\) −1.64096 0.432910i −0.0786781 0.0207564i
\(436\) −1.65480 2.86619i −0.0792503 0.137266i
\(437\) −7.28772 12.6227i −0.348619 0.603826i
\(438\) −6.35556 + 6.40484i −0.303681 + 0.306035i
\(439\) −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 −0.999239 0.0389949i \(-0.987584\pi\)
0.533390 + 0.845869i \(0.320918\pi\)
\(444\) −0.706635 2.59704i −0.0335354 0.123250i
\(445\) −0.317956 0.550716i −0.0150726 0.0261064i
\(446\) 6.16590 + 10.6796i 0.291964 + 0.505696i
\(447\) 5.06977 + 18.6325i 0.239792 + 0.881289i
\(448\) 0 0
\(449\) −17.7345 −0.836942 −0.418471 0.908230i \(-0.637434\pi\)
−0.418471 + 0.908230i \(0.637434\pi\)
\(450\) −0.127471 16.5049i −0.00600905 0.778049i
\(451\) −24.9810 −1.17631
\(452\) −0.805935 + 1.39592i −0.0379080 + 0.0656586i
\(453\) 13.7538 13.8604i 0.646208 0.651218i
\(454\) −13.1073 22.7025i −0.615156 1.06548i
\(455\) 0 0
\(456\) −39.5005 10.4208i −1.84978 0.487999i
\(457\) −0.242725 + 0.420413i −0.0113542 + 0.0196661i −0.871647 0.490135i \(-0.836948\pi\)
0.860292 + 0.509801i \(0.170281\pi\)
\(458\) −2.10138 −0.0981912
\(459\) 5.99549 + 5.85817i 0.279846 + 0.273436i
\(460\) 0.156830 0.00731224
\(461\) 3.99687 6.92279i 0.186153 0.322426i −0.757811 0.652474i \(-0.773731\pi\)
0.943964 + 0.330047i \(0.107065\pi\)
\(462\) 0 0
\(463\) 5.24280 + 9.08080i 0.243654 + 0.422021i 0.961752 0.273921i \(-0.0883206\pi\)
−0.718098 + 0.695942i \(0.754987\pi\)
\(464\) −8.44523 14.6276i −0.392060 0.679068i
\(465\) −1.19169 + 1.20092i −0.0552631 + 0.0556916i
\(466\) 3.60721 6.24788i 0.167101 0.289427i
\(467\) 21.8977 1.01331 0.506653 0.862150i \(-0.330883\pi\)
0.506653 + 0.862150i \(0.330883\pi\)
\(468\) 5.02744 2.95460i 0.232394 0.136576i
\(469\) 0 0
\(470\) −0.185839 + 0.321883i −0.00857213 + 0.0148474i
\(471\) 5.55078 + 20.4003i 0.255766 + 0.939998i
\(472\) −6.84592 11.8575i −0.315109 0.545785i
\(473\) −12.5946 21.8145i −0.579102 1.00303i
\(474\) 3.85858 + 14.1811i 0.177230 + 0.651361i
\(475\) −19.1639 + 33.1929i −0.879301 + 1.52299i
\(476\) 0 0
\(477\) −26.0353 14.7645i −1.19207 0.676022i
\(478\) 23.5417 1.07677
\(479\) −2.00085 + 3.46557i −0.0914210 + 0.158346i −0.908109 0.418733i \(-0.862474\pi\)
0.816688 + 0.577079i \(0.195808\pi\)
\(480\) 0.532055 0.536180i 0.0242849 0.0244732i
\(481\) 2.45829 + 4.25789i 0.112088 + 0.194143i
\(482\) 11.0646 + 19.1645i 0.503980 + 0.872918i
\(483\) 0 0
\(484\) 0.0539532 0.0934496i 0.00245242 0.00424771i
\(485\) 0.401040 0.0182103
\(486\) 16.6882 + 4.12798i 0.756992 + 0.187249i
\(487\) −26.4755 −1.19972 −0.599859 0.800106i \(-0.704777\pi\)
−0.599859 + 0.800106i \(0.704777\pi\)
\(488\) 8.70502 15.0775i 0.394058 0.682528i
\(489\) 15.0102 + 3.95991i 0.678784 + 0.179073i
\(490\) 0 0
\(491\) 14.2149 + 24.6210i 0.641511 + 1.11113i 0.985096 + 0.172008i \(0.0550255\pi\)
−0.343584 + 0.939122i \(0.611641\pi\)
\(492\) −7.15783 + 7.21333i −0.322700 + 0.325202i
\(493\) 7.49360 12.9793i 0.337495 0.584558i
\(494\) 21.0115 0.945350
\(495\) 0.918504 + 0.520882i 0.0412837 + 0.0234119i
\(496\) −16.8381 −0.756052
\(497\) 0 0
\(498\) 0.586179 + 2.15434i 0.0262673 + 0.0965383i
\(499\) 3.71559 + 6.43559i 0.166333 + 0.288097i 0.937128 0.348986i \(-0.113474\pi\)
−0.770795 + 0.637083i \(0.780141\pi\)
\(500\) −0.412863 0.715100i −0.0184638 0.0319802i
\(501\) 7.92014 + 29.1083i 0.353846 + 1.30046i
\(502\) 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
\(507\) 8.35688 8.42167i 0.371142 0.374019i
\(508\) 0.124295 + 0.215285i 0.00551470 + 0.00955174i
\(509\) −14.4532 25.0336i −0.640625 1.10960i −0.985293 0.170871i \(-0.945342\pi\)
0.344668 0.938725i \(-0.387991\pi\)
\(510\) −0.314232 0.0828990i −0.0139144 0.00367083i
\(511\) 0 0
\(512\) 18.6806 0.825575
\(513\) −28.5530 27.8990i −1.26065 1.23177i
\(514\) −15.8676 −0.699891
\(515\) 0.460467 0.797553i 0.0202906 0.0351444i
\(516\) −9.90775 2.61381i −0.436164 0.115067i
\(517\) 5.33237 + 9.23593i 0.234517 + 0.406196i
\(518\) 0 0
\(519\) 3.45180 3.47856i 0.151517 0.152692i
\(520\) −0.401482 + 0.695387i −0.0176061 + 0.0304947i
\(521\) −33.7990 −1.48076 −0.740381 0.672187i \(-0.765355\pi\)
−0.740381 + 0.672187i \(0.765355\pi\)
\(522\) −0.237380 30.7359i −0.0103899 1.34527i
\(523\) 14.3779 0.628701 0.314351 0.949307i \(-0.398213\pi\)
0.314351 + 0.949307i \(0.398213\pi\)
\(524\) −5.86140 + 10.1522i −0.256056 + 0.443502i
\(525\) 0 0
\(526\) −0.848618 1.46985i −0.0370015 0.0640885i
\(527\) −7.47036 12.9390i −0.325414 0.563634i
\(528\) 2.75912 + 10.1404i 0.120075 + 0.441304i
\(529\) 9.70034 16.8015i 0.421754 0.730499i
\(530\) 1.16039 0.0504043
\(531\) −0.103331 13.3792i −0.00448416 0.580607i
\(532\) 0 0
\(533\) 9.28166 16.0763i 0.402033 0.696342i
\(534\) 8.11238 8.17528i 0.351057 0.353779i
\(535\) 0.956910 + 1.65742i 0.0413708 + 0.0716564i
\(536\) −15.3062 26.5111i −0.661127 1.14511i
\(537\) −17.0200 4.49012i −0.734466 0.193763i
\(538\) 14.4783 25.0772i 0.624205 1.08116i
\(539\) 0 0
\(540\) 0.413586 0.115971i 0.0177979 0.00499062i
\(541\) −25.1764 −1.08242 −0.541210 0.840888i \(-0.682034\pi\)
−0.541210 + 0.840888i \(0.682034\pi\)
\(542\) −9.88863 + 17.1276i −0.424753 + 0.735694i
\(543\) 28.6164 + 7.54943i 1.22805 + 0.323977i
\(544\) 3.33531 + 5.77693i 0.143000 + 0.247684i
\(545\) 0.222664 + 0.385666i 0.00953789 + 0.0165201i
\(546\) 0 0
\(547\) 1.59011 2.75416i 0.0679883 0.117759i −0.830027 0.557723i \(-0.811675\pi\)
0.898016 + 0.439963i \(0.145009\pi\)
\(548\) 11.9509 0.510517
\(549\) 14.6675 8.62003i 0.625996 0.367894i
\(550\) 18.3612 0.782926
\(551\) −35.6876 + 61.8127i −1.52034 + 2.63331i
\(552\) 2.64861 + 9.73424i 0.112732 + 0.414317i
\(553\) 0 0
\(554\) −10.4057 18.0233i −0.442098 0.765736i
\(555\) 0.0950828 + 0.349450i 0.00403604 + 0.0148333i
\(556\) 3.18179 5.51102i 0.134938 0.233719i
\(557\) 20.0459 0.849371 0.424686 0.905341i \(-0.360385\pi\)
0.424686 + 0.905341i \(0.360385\pi\)
\(558\) −26.6539 15.1154i −1.12835 0.639884i
\(559\) 18.7181 0.791689
\(560\) 0 0
\(561\) −6.56817 + 6.61909i −0.277308 + 0.279458i
\(562\) 2.75238 + 4.76727i 0.116102 + 0.201095i
\(563\) 19.9007 + 34.4690i 0.838713 + 1.45269i 0.890971 + 0.454060i \(0.150025\pi\)
−0.0522584 + 0.998634i \(0.516642\pi\)
\(564\) 4.19478 + 1.10665i 0.176632 + 0.0465982i
\(565\) 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 \(-0.926855\pi\)
0.684117 + 0.729373i \(0.260188\pi\)
\(570\) 1.49650 + 0.394799i 0.0626815 + 0.0165363i
\(571\) −5.21935 9.04019i −0.218423 0.378320i 0.735903 0.677087i \(-0.236758\pi\)
−0.954326 + 0.298767i \(0.903425\pi\)
\(572\) 3.24352 + 5.61793i 0.135618 + 0.234898i
\(573\) 27.3281 27.5400i 1.14165 1.15050i
\(574\) 0 0
\(575\) 9.46483 0.394711
\(576\) 21.3889 + 12.1296i 0.891205 + 0.505401i
\(577\) 25.4923 1.06126 0.530628 0.847605i \(-0.321956\pi\)
0.530628 + 0.847605i \(0.321956\pi\)
\(578\) −7.93895 + 13.7507i −0.330217 + 0.571952i
\(579\) 0.116772 + 0.429164i 0.00485289 + 0.0178354i
\(580\) −0.383994 0.665098i −0.0159445 0.0276167i
\(581\) 0 0
\(582\) 1.90697 + 7.00855i 0.0790466 + 0.290514i
\(583\) 16.6478 28.8349i 0.689483 1.19422i
\(584\) −14.5021 −0.600100
\(585\) −0.676477 + 0.397562i −0.0279689 + 0.0164372i
\(586\) −28.4554 −1.17548
\(587\) −17.5168 + 30.3401i −0.722998 + 1.25227i 0.236795 + 0.971560i \(0.423903\pi\)
−0.959793 + 0.280709i \(0.909430\pi\)
\(588\) 0 0
\(589\) 35.5769 + 61.6210i 1.46592 + 2.53905i
\(590\) 0.259362 + 0.449228i 0.0106778 + 0.0184944i
\(591\) −1.27845 0.337275i −0.0525886 0.0138736i
\(592\) −1.80217 + 3.12146i −0.0740689 + 0.128291i
\(593\) −36.1292 −1.48365 −0.741824 0.670594i \(-0.766039\pi\)
−0.741824 + 0.670594i \(0.766039\pi\)
\(594\) −4.73536 + 18.5286i −0.194294 + 0.760236i
\(595\) 0 0
\(596\) −4.36915 + 7.56759i −0.178967 + 0.309980i
\(597\) 8.42603 + 2.22291i 0.344854 + 0.0909777i
\(598\) −2.59433 4.49350i −0.106090 0.183753i
\(599\) 20.4742 + 35.4623i 0.836552 + 1.44895i 0.892760 + 0.450532i \(0.148766\pi\)
−0.0562080 + 0.998419i \(0.517901\pi\)
\(600\) 18.6855 18.8304i 0.762833 0.768748i
\(601\) 12.8547 22.2650i 0.524354 0.908207i −0.475244 0.879854i \(-0.657640\pi\)
0.999598 0.0283533i \(-0.00902635\pi\)
\(602\) 0 0
\(603\) −0.231028 29.9133i −0.00940817 1.21817i
\(604\) 8.83620 0.359540
\(605\) −0.00725978 + 0.0125743i −0.000295152 + 0.000511218i
\(606\) 8.76130 + 32.1998i 0.355904 + 1.30803i
\(607\) −3.42258 5.92808i −0.138918 0.240613i 0.788169 0.615459i \(-0.211029\pi\)
−0.927087 + 0.374845i \(0.877696\pi\)
\(608\) −15.8841 27.5121i −0.644187 1.11576i
\(609\) 0 0
\(610\) −0.329795 + 0.571222i −0.0133530 + 0.0231281i
\(611\) −7.92493 −0.320608
\(612\) 0.0292953 + 3.79315i 0.00118419 + 0.153329i
\(613\) −29.1297 −1.17654 −0.588269 0.808666i \(-0.700190\pi\)
−0.588269 + 0.808666i \(0.700190\pi\)
\(614\) −12.2917 + 21.2898i −0.496051 + 0.859185i
\(615\) 0.963137 0.970604i 0.0388374 0.0391385i
\(616\) 0 0
\(617\) −10.3395 17.9085i −0.416252 0.720969i 0.579307 0.815109i \(-0.303323\pi\)
−0.995559 + 0.0941404i \(0.969990\pi\)
\(618\) 16.1275 + 4.25468i 0.648745 + 0.171148i
\(619\) 4.43178 7.67606i 0.178128 0.308527i −0.763111 0.646267i \(-0.776329\pi\)
0.941239 + 0.337740i \(0.109663\pi\)
\(620\) −0.765607 −0.0307475
\(621\) −2.44098 + 9.55108i −0.0979530 + 0.383272i
\(622\) 1.44453 0.0579205
\(623\) 0 0
\(624\) −7.55090 1.99204i −0.302278 0.0797453i
\(625\) −12.4166 21.5062i −0.496666 0.860250i
\(626\) 11.8977 + 20.6074i 0.475528 + 0.823638i
\(627\) 31.2803 31.5228i 1.24921 1.25890i
\(628\) −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
\(633\) −3.27904 12.0512i −0.130330 0.478993i
\(634\) −13.6649 23.6683i −0.542704 0.939990i
\(635\) −0.0167248 0.0289681i −0.000663702 0.00114957i
\(636\) −3.55603 13.0692i −0.141006 0.518227i
\(637\) 0 0
\(638\) 34.1928 1.35371
\(639\) 8.58664 + 4.86947i 0.339682 + 0.192633i
\(640\) −0.0810898 −0.00320536
\(641\) 8.26595 14.3171i 0.326486 0.565489i −0.655326 0.755346i \(-0.727469\pi\)
0.981812 + 0.189856i \(0.0608022\pi\)
\(642\) −24.4148 + 24.6041i −0.963574 + 0.971045i
\(643\) −15.4460 26.7532i −0.609130 1.05504i −0.991384 0.130987i \(-0.958185\pi\)
0.382254 0.924057i \(-0.375148\pi\)
\(644\) 0 0
\(645\) 1.33316 + 0.351706i 0.0524930 + 0.0138484i
\(646\) −6.83390 + 11.8367i −0.268876 + 0.465707i
\(647\) −1.29981 −0.0511007 −0.0255503 0.999674i \(-0.508134\pi\)
−0.0255503 + 0.999674i \(0.508134\pi\)
\(648\) 14.1830 + 23.7122i 0.557161 + 0.931502i
\(649\) 14.8840 0.584247
\(650\) −6.82209 + 11.8162i −0.267584 + 0.463470i
\(651\) 0 0
\(652\) 3.51247 + 6.08377i 0.137559 + 0.238259i
\(653\) 22.4435 + 38.8733i 0.878281 + 1.52123i 0.853226 + 0.521542i \(0.174643\pi\)
0.0250558 + 0.999686i \(0.492024\pi\)
\(654\) −5.68109 + 5.72514i −0.222148 + 0.223871i
\(655\) 0.788692 1.36605i 0.0308167 0.0533762i
\(656\) 13.6088 0.531333
\(657\) −12.3271 6.99068i −0.480926 0.272732i
\(658\) 0 0
\(659\) 8.96167 15.5221i 0.349097 0.604654i −0.636992 0.770870i \(-0.719822\pi\)
0.986089 + 0.166216i \(0.0531549\pi\)
\(660\) 0.125454 + 0.461071i 0.00488329 + 0.0179472i
\(661\) −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
\(663\) −1.81926 6.68619i −0.0706542 0.259670i
\(664\) −1.79420 + 3.10765i −0.0696285 + 0.120600i
\(665\) 0 0
\(666\) −5.65485 + 3.32332i −0.219121 + 0.128776i
\(667\) 17.6257 0.682469
\(668\) −6.82561 + 11.8223i −0.264091 + 0.457419i
\(669\) −13.6423 + 13.7480i −0.527440 + 0.531529i
\(670\) 0.579885 + 1.00439i 0.0224029 + 0.0388030i
\(671\) 9.46295 + 16.3903i 0.365313 + 0.632741i
\(672\) 0 0
\(673\) −10.6758 + 18.4909i −0.411520 + 0.712774i −0.995056 0.0993135i \(-0.968335\pi\)
0.583536 + 0.812087i \(0.301669\pi\)
\(674\) 3.73729 0.143955
\(675\) 24.9603 6.99898i 0.960721 0.269391i
\(676\) 5.36894 0.206498
\(677\) −4.15084 + 7.18946i −0.159530 + 0.276313i −0.934699 0.355440i \(-0.884331\pi\)
0.775170 + 0.631753i \(0.217664\pi\)
\(678\) 3.79818 + 1.00202i 0.145868 + 0.0384822i
\(679\) 0 0
\(680\) −0.261161 0.452344i −0.0100151 0.0173466i
\(681\) 29.0003 29.2252i 1.11130 1.11991i
\(682\) 17.0434 29.5200i 0.652625 1.13038i
\(683\) 2.49456 0.0954518 0.0477259 0.998860i \(-0.484803\pi\)
0.0477259 + 0.998860i \(0.484803\pi\)
\(684\) −0.139516 18.0645i −0.00533454 0.690714i
\(685\) −1.60808 −0.0614414
\(686\) 0 0
\(687\) −0.866505 3.18460i −0.0330592 0.121500i
\(688\) 6.86110 + 11.8838i 0.261577 + 0.453065i
\(689\) 12.3710 + 21.4271i 0.471296 + 0.816308i
\(690\) −0.100344 0.368788i −0.00382004 0.0140395i
\(691\) 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
\(696\) 34.7967 35.0665i 1.31897 1.32919i
\(697\) 6.03765 + 10.4575i 0.228692 + 0.396107i
\(698\) −8.67266 15.0215i −0.328265 0.568572i
\(699\) 10.9559 + 2.89034i 0.414392 + 0.109323i
\(700\) 0 0
\(701\) 16.4806 0.622465 0.311232 0.950334i \(-0.399258\pi\)
0.311232 + 0.950334i \(0.399258\pi\)
\(702\) −10.1645 9.93165i −0.383633 0.374846i
\(703\) 15.2312 0.574454
\(704\) −13.6768 + 23.6889i −0.515464 + 0.892811i
\(705\) −0.564438 0.148907i −0.0212580 0.00560816i
\(706\) −2.28515 3.95800i −0.0860029 0.148961i
\(707\) 0 0
\(708\) 4.26472 4.29778i 0.160278 0.161520i
\(709\) 14.7462 25.5412i 0.553807 0.959222i −0.444188 0.895933i \(-0.646508\pi\)
0.997995 0.0632882i \(-0.0201587\pi\)
\(710\) −0.382707 −0.0143628
\(711\) −19.9001 + 11.6952i −0.746313 + 0.438604i
\(712\) 18.5108 0.693721
\(713\) 8.78551 15.2169i 0.329020 0.569879i
\(714\) 0 0
\(715\) −0.436438 0.755933i −0.0163219 0.0282703i
\(716\) −3.98277 6.89836i −0.148843 0.257804i
\(717\) 9.70741 + 35.6769i 0.362530 + 1.33238i
\(718\) 4.37810 7.58310i 0.163389 0.282999i
\(719\) −0.434622 −0.0162087 −0.00810433 0.999967i \(-0.502580\pi\)
−0.00810433 + 0.999967i \(0.502580\pi\)
\(720\) −0.500368 0.283758i −0.0186476 0.0105750i
\(721\) 0 0
\(722\) 22.0691 38.2248i 0.821327 1.42258i
\(723\) −24.4808 + 24.6707i −0.910453 + 0.917511i
\(724\) 6.69640 + 11.5985i 0.248870 + 0.431055i
\(725\) −23.1744 40.1392i −0.860675 1.49073i
\(726\) −0.254269 0.0670798i −0.00943680 0.00248957i
\(727\) 13.5839 23.5280i 0.503799 0.872605i −0.496192 0.868213i \(-0.665269\pi\)
0.999990 0.00439187i \(-0.00139798\pi\)
\(728\) 0 0
\(729\) 0.625513 + 26.9928i 0.0231672 + 0.999732i
\(730\) 0.549420 0.0203350
\(731\) −6.08798 + 10.5447i −0.225172 + 0.390009i
\(732\) 7.44417 + 1.96388i 0.275144 + 0.0725871i
\(733\) 2.83307 + 4.90702i 0.104642 + 0.181245i 0.913592 0.406632i \(-0.133297\pi\)
−0.808950 + 0.587878i \(0.799964\pi\)
\(734\) −7.25050 12.5582i −0.267621 0.463533i
\(735\) 0 0
\(736\) −3.92249 + 6.79395i −0.144585 + 0.250428i
\(737\) 33.2777 1.22580
\(738\) 21.5420 + 12.2164i 0.792973 + 0.449693i
\(739\) −13.6108 −0.500681 −0.250341 0.968158i \(-0.580543\pi\)
−0.250341 + 0.968158i \(0.580543\pi\)
\(740\) −0.0819427 + 0.141929i −0.00301227 + 0.00521741i
\(741\) 8.66407 + 31.8424i 0.318282 + 1.16976i
\(742\) 0 0
\(743\) −6.33421 10.9712i −0.232380 0.402493i 0.726128 0.687559i \(-0.241318\pi\)
−0.958508 + 0.285066i \(0.907985\pi\)
\(744\) −12.9299 47.5203i −0.474033 1.74218i
\(745\) 0.587900 1.01827i 0.0215390 0.0373066i
\(746\) −8.61393 −0.315378
\(747\) −3.02314 + 1.77668i −0.110611 + 0.0650055i
\(748\) −4.21977 −0.154290
\(749\) 0 0
\(750\) −1.41740 + 1.42839i −0.0517563 + 0.0521576i
\(751\) 3.57269 + 6.18808i 0.130369 + 0.225806i 0.923819 0.382830i \(-0.125050\pi\)
−0.793450 + 0.608636i \(0.791717\pi\)
\(752\) −2.90488 5.03140i −0.105930 0.183476i
\(753\) 11.4129 + 3.01088i 0.415908 + 0.109723i
\(754\) −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
\(759\) −10.6037 2.79741i −0.384890 0.101540i
\(760\) 1.24376 + 2.15425i 0.0451157 + 0.0781428i
\(761\) −5.02358 8.70109i −0.182104 0.315414i 0.760493 0.649347i \(-0.224958\pi\)
−0.942597 + 0.333933i \(0.891624\pi\)
\(762\) 0.426718 0.430027i 0.0154584 0.0155782i
\(763\) 0 0
\(764\) 17.5572 0.635196
\(765\) −0.00394189 0.510395i −0.000142519 0.0184534i
\(766\) 11.8352 0.427625
\(767\) −5.53011 + 9.57843i −0.199681 + 0.345857i
\(768\) 7.06886 + 25.9797i 0.255076 + 0.937460i
\(769\) 16.1463 + 27.9663i 0.582252 + 1.00849i 0.995212 + 0.0977407i \(0.0311616\pi\)
−0.412960 + 0.910749i \(0.635505\pi\)
\(770\) 0 0
\(771\) −6.54301 24.0470i −0.235641 0.866032i
\(772\) −0.100635 + 0.174305i −0.00362192 + 0.00627336i
\(773\) −48.5878 −1.74758 −0.873792 0.486300i \(-0.838346\pi\)
−0.873792 + 0.486300i \(0.838346\pi\)
\(774\) 0.192853 + 24.9706i 0.00693198 + 0.897549i
\(775\) −46.2051 −1.65973
\(776\) −5.83694 + 10.1099i −0.209534 + 0.362923i
\(777\) 0 0
\(778\) 13.3147 + 23.0618i 0.477356 + 0.826806i
\(779\) −28.7538 49.8030i −1.03021 1.78438i
\(780\) −0.343330 0.0905755i −0.0122932 0.00324312i
\(781\) −5.49059 + 9.50998i −0.196469 + 0.340294i
\(782\) 3.37518 0.120696
\(783\) 46.4817 13.0337i 1.66112