Properties

Label 441.2.f.h.295.7
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 295.7
Character \(\chi\) \(=\) 441.295
Dual form 441.2.f.h.148.7

$q$-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 0.877576 0.479438i \(-0.159159\pi\)
−0.853993 + 0.520284i \(0.825826\pi\)
\(6\) −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 0.985155 0.171670i \(-0.0549162\pi\)
−0.641248 + 0.767334i \(0.721583\pi\)
\(14\) 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 \(-0.562674\pi\)
−0.195628 + 0.980678i \(0.562674\pi\)
\(18\) 2.85233 1.67630i 0.672301 0.395107i
\(19\) 7.68266 1.76252 0.881262 0.472629i \(-0.156695\pi\)
0.881262 + 0.472629i \(0.156695\pi\)
\(20\) −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 \(0.145976\pi\)
−0.0649574 + 0.997888i \(0.520691\pi\)
\(32\) 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 \(-0.967954\pi\)
0.410427 0.911893i \(-0.365379\pi\)
\(42\) 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 −0.958708 0.284392i \(-0.908208\pi\)
0.725645 + 0.688070i \(0.241542\pi\)
\(48\) −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 0.973884 0.227048i \(-0.0729075\pi\)
−0.683571 + 0.729884i \(0.739574\pi\)
\(60\) 0.100851 0.101633i 0.0130198 0.0131208i
\(61\) −2.83550 + 4.91123i −0.363048 + 0.628818i −0.988461 0.151476i \(-0.951597\pi\)
0.625413 + 0.780294i \(0.284931\pi\)
\(62\) 10.2138 1.29716
\(63\) 0 0
\(64\) 8.19630 1.02454
\(65\) −0.130775 + 0.226509i −0.0162207 + 0.0280950i
\(66\) −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 \(-0.410846\pi\)
0.276438 + 0.961032i \(0.410846\pi\)
\(74\) −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 −0.832167 0.554525i \(-0.812900\pi\)
0.896316 + 0.443415i \(0.146233\pi\)
\(84\) 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 \(-0.603537\pi\)
−0.319565 + 0.947564i \(0.603537\pi\)
\(90\) 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 −0.753213 0.657777i \(-0.771497\pi\)
0.946258 + 0.323413i \(0.104830\pi\)
\(98\) 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 \(-0.497983\pi\)
0.862839 0.505479i \(-0.168684\pi\)
\(102\) 2.17045 2.18727i 0.214906 0.216572i
\(103\) −4.36602 7.56217i −0.430197 0.745123i 0.566693 0.823929i \(-0.308223\pi\)
−0.996890 + 0.0788062i \(0.974889\pi\)
\(104\) 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 \(-0.940021\pi\)
0.328930 0.944354i \(-0.393312\pi\)
\(132\) 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 0.985229 0.171240i \(-0.0547774\pi\)
−0.640913 + 0.767614i \(0.721444\pi\)
\(140\) 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 0.512803 0.858506i \(-0.328607\pi\)
−0.999890 + 0.0148476i \(0.995274\pi\)
\(158\) 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 \(-0.931297\pi\)
0.302927 0.953014i \(-0.402036\pi\)
\(168\) 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 −0.914779 0.403954i \(-0.867635\pi\)
0.807224 + 0.590245i \(0.200969\pi\)
\(174\) 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 \(-0.719013\pi\)
−0.635032 + 0.772486i \(0.719013\pi\)
\(182\) 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 \(-0.557068\pi\)
−0.178327 + 0.983971i \(0.557068\pi\)
\(200\) 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 −0.615833 0.787877i \(-0.711180\pi\)
0.990238 + 0.139388i \(0.0445137\pi\)
\(224\) 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 \(0.455993\pi\)
−0.926668 + 0.375881i \(0.877340\pi\)
\(228\) −2.73833 10.0640i −0.181350 0.666503i
\(229\) 0.952737 + 1.65019i 0.0629586 + 0.109048i 0.895787 0.444484i \(-0.146613\pi\)
−0.832828 + 0.553532i \(0.813280\pi\)
\(230\) 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 \(-0.609654\pi\)
0.984003 0.178155i \(-0.0570127\pi\)
\(242\) −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 \(-0.568998\pi\)
−0.215069 + 0.976599i \(0.568998\pi\)
\(252\) 0 0
\(253\) −6.33151 −0.398059
\(254\) 0.174884 0.302907i 0.0109732 0.0190061i
\(255\) 0.0773687 + 0.284347i 0.00484502 + 0.0178065i
\(256\) 7.77234 + 13.4621i 0.485771 + 0.841380i
\(257\) 7.19415 + 12.4606i 0.448759 + 0.777273i 0.998306 0.0581897i \(-0.0185328\pi\)
−0.549546 + 0.835463i \(0.685199\pi\)
\(258\) −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 \(-0.795412\pi\)
−0.800461 + 0.599385i \(0.795412\pi\)
\(270\) −0.432270 0.422369i −0.0263071 0.0257046i
\(271\) 17.9335 1.08938 0.544690 0.838637i \(-0.316647\pi\)
0.544690 + 0.838637i \(0.316647\pi\)
\(272\) −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 0.541328 0.840811i \(-0.317922\pi\)
−0.998828 + 0.0483984i \(0.984588\pi\)
\(284\) 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 \(0.105066\pi\)
−0.192318 + 0.981333i \(0.561601\pi\)
\(294\) 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 \(-0.280538\pi\)
0.636120 + 0.771590i \(0.280538\pi\)
\(308\) 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 0.846859 0.531817i \(-0.178491\pi\)
−0.883997 + 0.467493i \(0.845157\pi\)
\(312\) −3.46219 12.7243i −0.196008 0.720373i
\(313\) 10.7885 18.6862i 0.609802 1.05621i −0.381471 0.924381i \(-0.624582\pi\)
0.991273 0.131827i \(-0.0420843\pi\)
\(314\) −13.4613 −0.759667
\(315\) 0 0
\(316\) −6.03065 −0.339250
\(317\) 12.3910 21.4618i 0.695946 1.20541i −0.273915 0.961754i \(-0.588319\pi\)
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 −0.996033 0.0889810i \(-0.971639\pi\)
0.575076 + 0.818100i \(0.304972\pi\)
\(350\) 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 −0.915886 0.401438i \(-0.868510\pi\)
0.805599 + 0.592462i \(0.201844\pi\)
\(354\) −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 −0.985023 0.172423i \(-0.944840\pi\)
0.641834 + 0.766843i \(0.278174\pi\)
\(368\) 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 0.695743 0.718291i \(-0.255075\pi\)
−0.969930 + 0.243386i \(0.921742\pi\)
\(384\) −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 \(-0.706304\pi\)
−0.603691 + 0.797218i \(0.706304\pi\)
\(398\) −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 \(-0.980356\pi\)
0.445636 0.895214i \(-0.352977\pi\)
\(410\) −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 0.783809 0.621002i \(-0.213274\pi\)
−0.929708 + 0.368298i \(0.879941\pi\)
\(420\) 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 \(-0.510344\pi\)
−0.0324905 + 0.999472i \(0.510344\pi\)
\(434\) 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 −0.581479 0.813561i \(-0.697526\pi\)
0.995304 + 0.0967954i \(0.0308592\pi\)
\(440\) −1.08056 −0.0515139
\(441\) 0 0
\(442\) −4.41194 −0.209854
\(443\) −9.80499 + 16.9827i −0.465849 + 0.806874i −0.999239 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 −0.943964 0.330047i \(-0.892935\pi\)
0.757811 + 0.652474i \(0.226269\pi\)
\(462\) 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 \(-0.669117\pi\)
−0.506653 + 0.862150i \(0.669117\pi\)
\(468\) −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 −0.816688 0.577079i \(-0.804192\pi\)
0.908109 + 0.418733i \(0.137526\pi\)
\(480\) 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 \(-0.427262\pi\)
0.226529 + 0.974004i \(0.427262\pi\)
\(504\) 0 0
\(505\) 1.84252 0.0819910
\(506\) −3.49124 + 6.04700i −0.155204 + 0.268822i
\(507\) −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 \(0.0546581\pi\)
−0.344668 + 0.938725i \(0.612009\pi\)
\(510\) 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 \(-0.234645\pi\)
0.740381 + 0.672187i \(0.234645\pi\)
\(522\) −0.237380 30.7359i −0.0103899 1.34527i
\(523\) −14.3779 −0.628701 −0.314351 0.949307i \(-0.601787\pi\)
−0.314351 + 0.949307i \(0.601787\pi\)
\(524\) 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 \(-0.849975\pi\)
0.0522584 0.998634i \(-0.483358\pi\)
\(564\) 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 \(-0.678044\pi\)
−0.530628 + 0.847605i \(0.678044\pi\)
\(578\) −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 \(-0.576097\pi\)
0.959793 0.280709i \(-0.0905697\pi\)
\(588\) 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 \(-0.233961\pi\)
0.741824 + 0.670594i \(0.233961\pi\)
\(594\) 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 \(0.342360\pi\)
−0.999598 + 0.0283533i \(0.990974\pi\)
\(602\) 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 0.927087 0.374845i \(-0.122304\pi\)
−0.788169 + 0.615459i \(0.788971\pi\)
\(608\) 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 −0.941239 0.337740i \(-0.890337\pi\)
0.763111 + 0.646267i \(0.223671\pi\)
\(620\) −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 \(0.0418147\pi\)
−0.382254 + 0.924057i \(0.624852\pi\)
\(644\) 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 \(-0.491866\pi\)
0.0255503 + 0.999674i \(0.491866\pi\)
\(648\) 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 \(0.0553424\pi\)
−0.342649 + 0.939463i \(0.611324\pi\)
\(662\) 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 −0.775170 0.631753i \(-0.782336\pi\)
0.934699 + 0.355440i \(0.115669\pi\)
\(678\) −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 −0.980667 0.195685i \(-0.937307\pi\)
0.659801 + 0.751440i \(0.270640\pi\)
\(692\) −2.21763 −0.0843017
\(693\) 0 0
\(694\) 16.0071 0.607621
\(695\) −0.428132 + 0.741547i −0.0162400 + 0.0281285i
\(696\) −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 \(-0.497420\pi\)
0.00810433 + 0.999967i \(0.497420\pi\)
\(720\) 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 \(0.334731\pi\)
−0.999990 + 0.00439187i \(0.998602\pi\)
\(728\) 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 0.808950 0.587878i \(-0.200036\pi\)
−0.913592 + 0.406632i \(0.866703\pi\)
\(734\) 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 0.942597 0.333933i \(-0.108376\pi\)
−0.760493 + 0.649347i \(0.775042\pi\)
\(762\) −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 \(-0.968838\pi\)
0.412960 0.910749i \(-0.364495\pi\)
\(770\) 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 \(-0.161654\pi\)
0.873792 + 0.486300i \(0.161654\pi\)
\(774\) 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