Properties

Label 441.2.f.h.148.7
Level $441$
Weight $2$
Character 441.148
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 148.7
Character \(\chi\) \(=\) 441.148
Dual form 441.2.f.h.295.7

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

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

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 0.992436 0.122762i \(-0.0391750\pi\)
−0.602533 + 0.798094i \(0.705842\pi\)
\(3\) −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 \(-0.825826\pi\)
0.877576 + 0.479438i \(0.159159\pi\)
\(6\) −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 −0.999994 0.00360543i \(-0.998852\pi\)
0.496874 0.867822i \(-0.334481\pi\)
\(12\) −0.356430 + 1.30996i −0.102892 + 0.378153i
\(13\) 1.23997 2.14770i 0.343907 0.595664i −0.641248 0.767334i \(-0.721583\pi\)
0.985155 + 0.171670i \(0.0549162\pi\)
\(14\) 0 0
\(15\) −0.0479602 + 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 −0.750018 0.661417i \(-0.769955\pi\)
0.947813 + 0.318826i \(0.103289\pi\)
\(24\) −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 0.869416 + 0.494080i \(0.164495\pi\)
−0.00682200 + 0.999977i \(0.502172\pi\)
\(30\) −0.194789 + 0.0513883i −0.0355635 + 0.00938218i
\(31\) 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
\(33\) 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 0.410427 + 0.911893i \(0.365379\pi\)
−0.994936 + 0.100506i \(0.967954\pi\)
\(42\) 0 0
\(43\) −3.77388 6.53655i −0.575512 0.996815i −0.995986 0.0895108i \(-0.971470\pi\)
0.420474 0.907304i \(-0.361864\pi\)
\(44\) −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 \(-0.241542\pi\)
−0.958708 + 0.284392i \(0.908208\pi\)
\(48\) −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 \(-0.739574\pi\)
0.973884 + 0.227048i \(0.0729075\pi\)
\(60\) 0.100851 + 0.101633i 0.0130198 + 0.0131208i
\(61\) −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
\(66\) −1.67366 + 6.15107i −0.206013 + 0.757145i
\(67\) −4.98571 + 8.63550i −0.609101 + 1.05499i 0.382288 + 0.924043i \(0.375136\pi\)
−0.991389 + 0.130951i \(0.958197\pi\)
\(68\) −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 0.564289 0.825577i \(-0.309150\pi\)
−0.997115 + 0.0758997i \(0.975817\pi\)
\(80\) 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 \(-0.146233\pi\)
−0.832167 + 0.554525i \(0.812900\pi\)
\(84\) 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 0.946258 0.323413i \(-0.104830\pi\)
−0.753213 + 0.657777i \(0.771497\pi\)
\(98\) 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 0.862839 + 0.505479i \(0.168684\pi\)
0.00633771 + 0.999980i \(0.497983\pi\)
\(102\) 2.17045 + 2.18727i 0.214906 + 0.216572i
\(103\) −4.36602 + 7.56217i −0.430197 + 0.745123i −0.996890 0.0788062i \(-0.974889\pi\)
0.566693 + 0.823929i \(0.308223\pi\)
\(104\) 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 −0.813600 0.581425i \(-0.802495\pi\)
0.910329 + 0.413886i \(0.135829\pi\)
\(114\) −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 0.328930 + 0.944354i \(0.393312\pi\)
−0.982300 + 0.187315i \(0.940021\pi\)
\(132\) 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 0.982799 + 0.184676i \(0.0591235\pi\)
−0.331466 + 0.943467i \(0.607543\pi\)
\(138\) −3.50399 + 0.924403i −0.298279 + 0.0786904i
\(139\) 4.05943 7.03114i 0.344316 0.596374i −0.640913 0.767614i \(-0.721444\pi\)
0.985229 + 0.171240i \(0.0547774\pi\)
\(140\) 0 0
\(141\) 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 −0.542118 0.840303i \(-0.682377\pi\)
0.998782 + 0.0493365i \(0.0157107\pi\)
\(150\) 2.50192 9.19510i 0.204281 0.750777i
\(151\) 5.63676 + 9.76315i 0.458713 + 0.794514i 0.998893 0.0470354i \(-0.0149774\pi\)
−0.540180 + 0.841549i \(0.681644\pi\)
\(152\) 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 \(-0.995274\pi\)
0.512803 + 0.858506i \(0.328607\pi\)
\(158\) 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 0.302927 + 0.953014i \(0.402036\pi\)
−0.976798 + 0.214165i \(0.931297\pi\)
\(168\) 0 0
\(169\) 3.42493 + 5.93216i 0.263456 + 0.456320i
\(170\) −0.187629 −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 \(-0.200969\pi\)
−0.914779 + 0.403954i \(0.867635\pi\)
\(174\) 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 0.912582 + 0.408894i \(0.134086\pi\)
−0.102178 + 0.994766i \(0.532581\pi\)
\(192\) −13.7268 + 3.62132i −0.990644 + 0.261346i
\(193\) 0.128393 0.222383i 0.00924194 0.0160075i −0.861367 0.507982i \(-0.830391\pi\)
0.870609 + 0.491975i \(0.163725\pi\)
\(194\) −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 −0.963027 0.269403i \(-0.913174\pi\)
0.714824 + 0.699305i \(0.246507\pi\)
\(212\) −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 \(-0.0445137\pi\)
−0.615833 + 0.787877i \(0.711180\pi\)
\(224\) 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 −0.926668 0.375881i \(-0.877340\pi\)
0.137811 0.990459i \(-0.455993\pi\)
\(228\) −2.73833 + 10.0640i −0.181350 + 0.666503i
\(229\) 0.952737 1.65019i 0.0629586 0.109048i −0.832828 0.553532i \(-0.813280\pi\)
0.895787 + 0.444484i \(0.146613\pi\)
\(230\) 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 −0.281295 0.959621i \(-0.590764\pi\)
0.971704 0.236202i \(-0.0759028\pi\)
\(240\) −0.321121 + 0.0847165i −0.0207283 + 0.00546842i
\(241\) 10.0331 + 17.3778i 0.646288 + 1.11940i 0.984003 + 0.178155i \(0.0570127\pi\)
−0.337715 + 0.941248i \(0.609654\pi\)
\(242\) −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 −0.549546 0.835463i \(-0.685199\pi\)
0.998306 + 0.0581897i \(0.0185328\pi\)
\(258\) −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 0.888775 0.458344i \(-0.151557\pi\)
−0.841325 + 0.540529i \(0.818224\pi\)
\(264\) 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 0.996867 + 0.0790954i \(0.0252032\pi\)
−0.429935 + 0.902860i \(0.641463\pi\)
\(278\) 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 0.781930 0.623366i \(-0.214235\pi\)
−0.930816 + 0.365488i \(0.880902\pi\)
\(282\) −1.60259 + 5.88988i −0.0954329 + 0.350737i
\(283\) −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
\(285\) −0.368462 + 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 −0.192318 0.981333i \(-0.561601\pi\)
0.946018 0.324114i \(-0.105066\pi\)
\(294\) 0 0
\(295\) −0.235182 0.407347i −0.0136928 0.0237167i
\(296\) −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 −0.883997 0.467493i \(-0.845157\pi\)
0.846859 + 0.531817i \(0.178491\pi\)
\(312\) −3.46219 + 12.7243i −0.196008 + 0.720373i
\(313\) 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 \(0.0783480\pi\)
−0.273915 + 0.961754i \(0.588319\pi\)
\(318\) 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 0.610635 0.791912i \(-0.290914\pi\)
−0.991133 + 0.132870i \(0.957581\pi\)
\(332\) 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 −0.816178 0.577801i \(-0.803911\pi\)
0.908479 + 0.417930i \(0.137244\pi\)
\(338\) −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 −0.602798 0.797894i \(-0.705948\pi\)
0.992395 + 0.123091i \(0.0392809\pi\)
\(348\) −12.1953 + 3.21730i −0.653736 + 0.172465i
\(349\) −7.86412 13.6211i −0.420957 0.729119i 0.575076 0.818100i \(-0.304972\pi\)
−0.996033 + 0.0889810i \(0.971639\pi\)
\(350\) 0 0
\(351\) 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 \(-0.201844\pi\)
−0.915886 + 0.401438i \(0.868510\pi\)
\(354\) −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 \(-0.278174\pi\)
−0.985023 + 0.172423i \(0.944840\pi\)
\(368\) 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 −0.949242 0.314547i \(-0.898147\pi\)
0.747026 + 0.664794i \(0.231481\pi\)
\(374\) −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 \(-0.921742\pi\)
0.695743 + 0.718291i \(0.255075\pi\)
\(384\) −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 −0.990878 0.134763i \(-0.956973\pi\)
0.378731 0.925507i \(-0.376361\pi\)
\(390\) −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 −0.845862 0.533402i \(-0.820913\pi\)
0.884871 + 0.465836i \(0.154247\pi\)
\(402\) 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 0.445636 + 0.895214i \(0.352977\pi\)
−0.998096 + 0.0616748i \(0.980356\pi\)
\(410\) −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 \(-0.879941\pi\)
0.783809 + 0.621002i \(0.213274\pi\)
\(420\) 0 0
\(421\) 7.31594 + 12.6716i 0.356557 + 0.617575i 0.987383 0.158349i \(-0.0506172\pi\)
−0.630826 + 0.775924i \(0.717284\pi\)
\(422\) −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 0.995304 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 0.533390 0.845869i \(-0.320918\pi\)
−0.999239 + 0.0389949i \(0.987584\pi\)
\(444\) 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 0.860292 0.509801i \(-0.170281\pi\)
−0.871647 + 0.490135i \(0.836948\pi\)
\(458\) 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 \(-0.226269\pi\)
−0.943964 + 0.330047i \(0.892935\pi\)
\(462\) 0 0
\(463\) 5.24280 9.08080i 0.243654 0.422021i −0.718098 0.695942i \(-0.754987\pi\)
0.961752 + 0.273921i \(0.0883206\pi\)
\(464\) −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 0.908109 0.418733i \(-0.137526\pi\)
−0.816688 + 0.577079i \(0.804192\pi\)
\(480\) 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 −0.343584 0.939122i \(-0.611641\pi\)
0.985096 0.172008i \(-0.0550255\pi\)
\(492\) −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 −0.770795 0.637083i \(-0.780141\pi\)
0.937128 + 0.348986i \(0.113474\pi\)
\(500\) 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 −0.344668 0.938725i \(-0.612009\pi\)
0.985293 0.170871i \(-0.0546581\pi\)
\(510\) 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 0.898016 0.439963i \(-0.145009\pi\)
−0.830027 + 0.557723i \(0.811675\pi\)
\(548\) 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 0.0522584 + 0.998634i \(0.483358\pi\)
−0.890971 + 0.454060i \(0.849975\pi\)
\(564\) 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 0.684117 0.729373i \(-0.260188\pi\)
−0.973714 + 0.227776i \(0.926855\pi\)
\(570\) −1.49650 + 0.394799i −0.0626815 + 0.0165363i
\(571\) −5.21935 + 9.04019i −0.218423 + 0.378320i −0.954326 0.298767i \(-0.903425\pi\)
0.735903 + 0.677087i \(0.236758\pi\)
\(572\) −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 0.959793 + 0.280709i \(0.0905697\pi\)
−0.236795 + 0.971560i \(0.576097\pi\)
\(588\) 0 0
\(589\) 35.5769 61.6210i 1.46592 2.53905i
\(590\) 0.259362 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 −0.0562080 0.998419i \(-0.517901\pi\)
0.892760 0.450532i \(-0.148766\pi\)
\(600\) −18.6855 18.8304i −0.762833 0.768748i
\(601\) −12.8547 22.2650i −0.524354 0.908207i −0.999598 0.0283533i \(-0.990974\pi\)
0.475244 0.879854i \(-0.342360\pi\)
\(602\) 0 0
\(603\) −0.231028 + 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 \(-0.788971\pi\)
0.927087 + 0.374845i \(0.122304\pi\)
\(608\) 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 −0.995559 0.0941404i \(-0.969990\pi\)
0.579307 + 0.815109i \(0.303323\pi\)
\(618\) 16.1275 4.25468i 0.648745 0.171148i
\(619\) −4.43178 7.67606i −0.178128 0.308527i 0.763111 0.646267i \(-0.223671\pi\)
−0.941239 + 0.337740i \(0.890337\pi\)
\(620\) −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 0.981812 0.189856i \(-0.0608022\pi\)
−0.655326 + 0.755346i \(0.727469\pi\)
\(642\) 24.4148 + 24.6041i 0.963574 + 0.971045i
\(643\) 15.4460 26.7532i 0.609130 1.05504i −0.382254 0.924057i \(-0.624852\pi\)
0.991384 0.130987i \(-0.0418147\pi\)
\(644\) 0 0
\(645\) 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 0.0250558 0.999686i \(-0.492024\pi\)
0.853226 0.521542i \(-0.174643\pi\)
\(654\) 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 0.986089 0.166216i \(-0.0531549\pi\)
−0.636992 + 0.770870i \(0.719822\pi\)
\(660\) 0.125454 0.461071i 0.00488329 0.0179472i
\(661\) 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
\(663\) 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 0.583536 0.812087i \(-0.301669\pi\)
−0.995056 + 0.0993135i \(0.968335\pi\)
\(674\) 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 \(-0.115669\pi\)
−0.775170 + 0.631753i \(0.782336\pi\)
\(678\) −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 \(-0.270640\pi\)
−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
\(696\) −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 0.997995 + 0.0632882i \(0.0201587\pi\)
−0.444188 + 0.895933i \(0.646508\pi\)
\(710\) 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 −0.999990 0.00439187i \(-0.998602\pi\)
0.496192 0.868213i \(-0.334731\pi\)
\(728\) 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 \(-0.866703\pi\)
0.808950 + 0.587878i \(0.200036\pi\)
\(734\) 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 −0.958508 0.285066i \(-0.907985\pi\)
0.726128 + 0.687559i \(0.241318\pi\)
\(744\) −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 −0.793450 0.608636i \(-0.791717\pi\)
0.923819 + 0.382830i \(0.125050\pi\)
\(752\) 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 \(-0.775042\pi\)
0.942597 + 0.333933i \(0.108376\pi\)
\(762\) −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 0.412960 + 0.910749i \(0.364495\pi\)
−0.995212 + 0.0977407i \(0.968838\pi\)
\(770\) 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