Properties

Label 441.2.h.h.214.5
Level $441$
Weight $2$
Character 441.214
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.h (of order \(3\), degree \(2\), not 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 214.5
Character \(\chi\) \(=\) 441.214
Dual form 441.2.h.h.373.5

$q$-expansion

\(f(q)\) \(=\) \(q-1.10281 q^{2} +(-1.22001 + 1.22947i) q^{3} -0.783802 q^{4} +(-0.0527330 + 0.0913363i) q^{5} +(1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(-0.0231690 - 2.99991i) q^{9} +O(q^{10})\) \(q-1.10281 q^{2} +(-1.22001 + 1.22947i) q^{3} -0.783802 q^{4} +(-0.0527330 + 0.0913363i) q^{5} +(1.34544 - 1.35587i) q^{6} +3.07001 q^{8} +(-0.0231690 - 2.99991i) q^{9} +(0.0581547 - 0.100727i) q^{10} +(-1.66866 - 2.89020i) q^{11} +(0.956244 - 0.963657i) q^{12} +(-1.23997 - 2.14770i) q^{13} +(-0.0479602 - 0.176264i) q^{15} -1.81805 q^{16} +(-0.806594 + 1.39706i) q^{17} +(0.0255511 + 3.30834i) q^{18} +(3.84133 + 6.65338i) q^{19} +(0.0413323 - 0.0715896i) q^{20} +(1.84022 + 3.18735i) q^{22} +(0.948593 - 1.64301i) q^{23} +(-3.74544 + 3.77448i) q^{24} +(2.49444 + 4.32049i) q^{25} +(1.36746 + 2.36851i) q^{26} +(3.71655 + 3.63142i) q^{27} +(4.64521 - 8.04574i) q^{29} +(0.0528911 + 0.194387i) q^{30} +9.26162 q^{31} -4.13506 q^{32} +(5.58917 + 1.47451i) q^{33} +(0.889523 - 1.54070i) q^{34} +(0.0181599 + 2.35134i) q^{36} +(0.991268 + 1.71693i) q^{37} +(-4.23627 - 7.33744i) q^{38} +(4.15329 + 1.09570i) q^{39} +(-0.161891 + 0.280404i) q^{40} +(3.74268 + 6.48252i) q^{41} +(-3.77388 + 6.53655i) q^{43} +(1.30790 + 2.26534i) q^{44} +(0.275223 + 0.156078i) q^{45} +(-1.04612 + 1.81194i) q^{46} -3.19560 q^{47} +(2.21803 - 2.23523i) q^{48} +(-2.75090 - 4.76470i) q^{50} +(-0.733589 - 2.69610i) q^{51} +(0.971894 + 1.68337i) q^{52} +(4.98839 - 8.64015i) q^{53} +(-4.09866 - 4.00478i) q^{54} +0.351974 q^{55} +(-12.8665 - 3.39438i) q^{57} +(-5.12280 + 8.87296i) q^{58} +4.45986 q^{59} +(0.0375913 + 0.138156i) q^{60} -5.67100 q^{61} -10.2138 q^{62} +8.19630 q^{64} +0.261550 q^{65} +(-6.16381 - 1.62610i) q^{66} +9.97141 q^{67} +(0.632210 - 1.09502i) q^{68} +(0.862736 + 3.17075i) q^{69} +3.29042 q^{71} +(-0.0711292 - 9.20977i) q^{72} +(2.36189 - 4.09091i) q^{73} +(-1.09318 - 1.89345i) q^{74} +(-8.35513 - 2.20421i) q^{75} +(-3.01084 - 5.21493i) q^{76} +(-4.58031 - 1.20835i) q^{78} +7.69409 q^{79} +(0.0958713 - 0.166054i) q^{80} +(-8.99893 + 0.139010i) q^{81} +(-4.12748 - 7.14901i) q^{82} +(-0.584428 + 1.01226i) q^{83} +(-0.0850683 - 0.147343i) q^{85} +(4.16189 - 7.20860i) q^{86} +(4.22477 + 15.5270i) q^{87} +(-5.12280 - 8.87296i) q^{88} +(-3.01477 - 5.22173i) q^{89} +(-0.303519 - 0.172125i) q^{90} +(-0.743509 + 1.28780i) q^{92} +(-11.2992 + 11.3868i) q^{93} +3.52415 q^{94} -0.810260 q^{95} +(5.04480 - 5.08391i) q^{96} +(-1.90127 + 3.29310i) q^{97} +(-8.63168 + 5.07279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q - 8q^{2} + 24q^{4} - 24q^{8} - 4q^{9} + O(q^{10}) \) \( 24q - 8q^{2} + 24q^{4} - 24q^{8} - 4q^{9} + 20q^{11} + 4q^{15} + 24q^{16} - 32q^{18} + 32q^{23} - 12q^{25} + 16q^{29} - 84q^{30} - 96q^{32} - 4q^{36} - 12q^{37} + 8q^{39} + 56q^{44} + 24q^{46} - 4q^{50} + 64q^{51} + 32q^{53} - 12q^{57} + 32q^{60} + 96q^{64} - 120q^{65} + 24q^{67} - 112q^{71} + 68q^{74} - 60q^{78} - 24q^{79} - 40q^{81} + 12q^{85} + 76q^{86} + 16q^{92} - 32q^{93} - 128q^{95} + 20q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.10281 −0.779807 −0.389903 0.920856i \(-0.627492\pi\)
−0.389903 + 0.920856i \(0.627492\pi\)
\(3\) −1.22001 + 1.22947i −0.704371 + 0.709832i
\(4\) −0.783802 −0.391901
\(5\) −0.0527330 + 0.0913363i −0.0235829 + 0.0408468i −0.877576 0.479438i \(-0.840841\pi\)
0.853993 + 0.520284i \(0.174174\pi\)
\(6\) 1.34544 1.35587i 0.549273 0.553532i
\(7\) 0 0
\(8\) 3.07001 1.08541
\(9\) −0.0231690 2.99991i −0.00772300 0.999970i
\(10\) 0.0581547 0.100727i 0.0183901 0.0318527i
\(11\) −1.66866 2.89020i −0.503119 0.871428i −0.999994 0.00360543i \(-0.998852\pi\)
0.496874 0.867822i \(-0.334481\pi\)
\(12\) 0.956244 0.963657i 0.276044 0.278184i
\(13\) −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
\(16\) −1.81805 −0.454512
\(17\) −0.806594 + 1.39706i −0.195628 + 0.338837i −0.947106 0.320921i \(-0.896008\pi\)
0.751478 + 0.659758i \(0.229341\pi\)
\(18\) 0.0255511 + 3.30834i 0.00602245 + 0.779784i
\(19\) 3.84133 + 6.65338i 0.881262 + 1.52639i 0.849939 + 0.526880i \(0.176638\pi\)
0.0313221 + 0.999509i \(0.490028\pi\)
\(20\) 0.0413323 0.0715896i 0.00924218 0.0160079i
\(21\) 0 0
\(22\) 1.84022 + 3.18735i 0.392336 + 0.679546i
\(23\) 0.948593 1.64301i 0.197795 0.342592i −0.750018 0.661417i \(-0.769955\pi\)
0.947813 + 0.318826i \(0.103289\pi\)
\(24\) −3.74544 + 3.77448i −0.764534 + 0.770462i
\(25\) 2.49444 + 4.32049i 0.498888 + 0.864099i
\(26\) 1.36746 + 2.36851i 0.268181 + 0.464503i
\(27\) 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 \(-0.164495\pi\)
\(30\) 0.0528911 + 0.194387i 0.00965655 + 0.0354900i
\(31\) 9.26162 1.66344 0.831718 0.555199i \(-0.187358\pi\)
0.831718 + 0.555199i \(0.187358\pi\)
\(32\) −4.13506 −0.730982
\(33\) 5.58917 + 1.47451i 0.972950 + 0.256678i
\(34\) 0.889523 1.54070i 0.152552 0.264228i
\(35\) 0 0
\(36\) 0.0181599 + 2.35134i 0.00302665 + 0.391889i
\(37\) 0.991268 + 1.71693i 0.162963 + 0.282261i 0.935930 0.352186i \(-0.114561\pi\)
−0.772967 + 0.634447i \(0.781228\pi\)
\(38\) −4.23627 7.33744i −0.687214 1.19029i
\(39\) 4.15329 + 1.09570i 0.665059 + 0.175452i
\(40\) −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 \(0.971470\pi\)
\(44\) 1.30790 + 2.26534i 0.197173 + 0.341514i
\(45\) 0.275223 + 0.156078i 0.0410278 + 0.0232668i
\(46\) −1.04612 + 1.81194i −0.154242 + 0.267155i
\(47\) −3.19560 −0.466127 −0.233063 0.972462i \(-0.574875\pi\)
−0.233063 + 0.972462i \(0.574875\pi\)
\(48\) 2.21803 2.23523i 0.320145 0.322627i
\(49\) 0 0
\(50\) −2.75090 4.76470i −0.389036 0.673830i
\(51\) −0.733589 2.69610i −0.102723 0.377530i
\(52\) 0.971894 + 1.68337i 0.134777 + 0.233441i
\(53\) 4.98839 8.64015i 0.685209 1.18682i −0.288163 0.957581i \(-0.593044\pi\)
0.973371 0.229234i \(-0.0736223\pi\)
\(54\) −4.09866 4.00478i −0.557757 0.544982i
\(55\) 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
\(59\) 4.45986 0.580625 0.290312 0.956932i \(-0.406241\pi\)
0.290312 + 0.956932i \(0.406241\pi\)
\(60\) 0.0375913 + 0.138156i 0.00485301 + 0.0178359i
\(61\) −5.67100 −0.726097 −0.363048 0.931770i \(-0.618264\pi\)
−0.363048 + 0.931770i \(0.618264\pi\)
\(62\) −10.2138 −1.29716
\(63\) 0 0
\(64\) 8.19630 1.02454
\(65\) 0.261550 0.0324413
\(66\) −6.16381 1.62610i −0.758713 0.200160i
\(67\) 9.97141 1.21820 0.609101 0.793093i \(-0.291530\pi\)
0.609101 + 0.793093i \(0.291530\pi\)
\(68\) 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 \(0.437448\pi\)
\(72\) −0.0711292 9.20977i −0.00838265 1.08538i
\(73\) 2.36189 4.09091i 0.276438 0.478805i −0.694059 0.719919i \(-0.744179\pi\)
0.970497 + 0.241113i \(0.0775125\pi\)
\(74\) −1.09318 1.89345i −0.127080 0.220109i
\(75\) −8.35513 2.20421i −0.964767 0.254520i
\(76\) −3.01084 5.21493i −0.345367 0.598194i
\(77\) 0 0
\(78\) −4.58031 1.20835i −0.518618 0.136819i
\(79\) 7.69409 0.865653 0.432827 0.901477i \(-0.357516\pi\)
0.432827 + 0.901477i \(0.357516\pi\)
\(80\) 0.0958713 0.166054i 0.0107187 0.0185654i
\(81\) −8.99893 + 0.139010i −0.999881 + 0.0154455i
\(82\) −4.12748 7.14901i −0.455804 0.789476i
\(83\) −0.584428 + 1.01226i −0.0641493 + 0.111110i −0.896316 0.443415i \(-0.853767\pi\)
0.832167 + 0.554525i \(0.187100\pi\)
\(84\) 0 0
\(85\) −0.0850683 0.147343i −0.00922695 0.0159815i
\(86\) 4.16189 7.20860i 0.448788 0.777323i
\(87\) 4.22477 + 15.5270i 0.452943 + 1.66467i
\(88\) −5.12280 8.87296i −0.546093 0.945860i
\(89\) −3.01477 5.22173i −0.319565 0.553503i 0.660832 0.750534i \(-0.270203\pi\)
−0.980397 + 0.197031i \(0.936870\pi\)
\(90\) −0.303519 0.172125i −0.0319937 0.0181436i
\(91\) 0 0
\(92\) −0.743509 + 1.28780i −0.0775162 + 0.134262i
\(93\) −11.2992 + 11.3868i −1.17168 + 1.18076i
\(94\) 3.52415 0.363489
\(95\) −0.810260 −0.0831309
\(96\) 5.04480 5.08391i 0.514883 0.518875i
\(97\) −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
\(100\) −1.95515 3.38641i −0.195515 0.338641i
\(101\) −8.73512 15.1297i −0.869177 1.50546i −0.862839 0.505479i \(-0.831316\pi\)
−0.00633771 0.999980i \(-0.502017\pi\)
\(102\) 0.809012 + 2.97330i 0.0801041 + 0.294400i
\(103\) 4.36602 7.56217i 0.430197 0.745123i −0.566693 0.823929i \(-0.691777\pi\)
0.996890 + 0.0788062i \(0.0251108\pi\)
\(104\) −3.80674 6.59346i −0.373281 0.646542i
\(105\) 0 0
\(106\) −5.50127 + 9.52848i −0.534330 + 0.925487i
\(107\) 9.07316 + 15.7152i 0.877135 + 1.51924i 0.854471 + 0.519500i \(0.173882\pi\)
0.0226645 + 0.999743i \(0.492785\pi\)
\(108\) −2.91304 2.84632i −0.280308 0.273887i
\(109\) 2.11124 3.65678i 0.202220 0.350256i −0.747023 0.664798i \(-0.768518\pi\)
0.949243 + 0.314542i \(0.101851\pi\)
\(110\) −0.388161 −0.0370097
\(111\) −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 \(0.802495\pi\)
\(114\) 14.1894 + 3.74337i 1.32896 + 0.350599i
\(115\) 0.100044 + 0.173282i 0.00932919 + 0.0161586i
\(116\) −3.64093 + 6.30627i −0.338052 + 0.585523i
\(117\) −6.41417 + 3.76957i −0.592990 + 0.348497i
\(118\) −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
\(122\) 6.25405 0.566215
\(123\) −12.5361 3.30721i −1.13034 0.298201i
\(124\) −7.25928 −0.651902
\(125\) −1.05349 −0.0942268
\(126\) 0 0
\(127\) 0.317159 0.0281433 0.0140717 0.999901i \(-0.495521\pi\)
0.0140717 + 0.999901i \(0.495521\pi\)
\(128\) −0.768871 −0.0679592
\(129\) −3.43231 12.6145i −0.302198 1.11064i
\(130\) −0.288441 −0.0252980
\(131\) 7.47816 12.9525i 0.653370 1.13167i −0.328930 0.944354i \(-0.606688\pi\)
0.982300 0.187315i \(-0.0599786\pi\)
\(132\) −4.38081 1.15572i −0.381300 0.100593i
\(133\) 0 0
\(134\) −10.9966 −0.949962
\(135\) −0.527666 + 0.147960i −0.0454143 + 0.0127344i
\(136\) −2.47625 + 4.28900i −0.212337 + 0.367779i
\(137\) 7.62367 + 13.2046i 0.651334 + 1.12814i 0.982799 + 0.184676i \(0.0591235\pi\)
−0.331466 + 0.943467i \(0.607543\pi\)
\(138\) −0.951437 3.49674i −0.0809917 0.297663i
\(139\) −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
\(142\) −3.62872 −0.304516
\(143\) −4.13818 + 7.16754i −0.346052 + 0.599380i
\(144\) 0.0421224 + 5.45399i 0.00351020 + 0.454499i
\(145\) 0.489912 + 0.848553i 0.0406850 + 0.0704685i
\(146\) −2.60473 + 4.51152i −0.215569 + 0.373376i
\(147\) 0 0
\(148\) −0.776958 1.34573i −0.0638656 0.110618i
\(149\) 5.57430 9.65497i 0.456664 0.790966i −0.542118 0.840303i \(-0.682377\pi\)
0.998782 + 0.0493365i \(0.0157107\pi\)
\(150\) 9.21415 + 2.43083i 0.752332 + 0.198476i
\(151\) 5.63676 + 9.76315i 0.458713 + 0.794514i 0.998893 0.0470354i \(-0.0149774\pi\)
−0.540180 + 0.841549i \(0.681644\pi\)
\(152\) 11.7929 + 20.4260i 0.956534 + 1.65677i
\(153\) 4.20975 + 2.38734i 0.340338 + 0.193005i
\(154\) 0 0
\(155\) −0.488393 + 0.845922i −0.0392287 + 0.0679461i
\(156\) −3.25536 0.858812i −0.260637 0.0687600i
\(157\) −12.2064 −0.974173 −0.487087 0.873354i \(-0.661940\pi\)
−0.487087 + 0.873354i \(0.661940\pi\)
\(158\) −8.48515 −0.675042
\(159\) 4.53689 + 16.6741i 0.359799 + 1.32234i
\(160\) 0.218054 0.377681i 0.0172387 0.0298583i
\(161\) 0 0
\(162\) 9.92414 0.153302i 0.779714 0.0120445i
\(163\) −4.48132 7.76187i −0.351004 0.607957i 0.635422 0.772165i \(-0.280826\pi\)
−0.986426 + 0.164209i \(0.947493\pi\)
\(164\) −2.93352 5.08101i −0.229070 0.396760i
\(165\) −0.429410 + 0.432739i −0.0334295 + 0.0336887i
\(166\) 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
\(170\) 0.0938145 + 0.162491i 0.00719524 + 0.0124625i
\(171\) 19.8705 11.6778i 1.51954 0.893024i
\(172\) 2.95798 5.12337i 0.225544 0.390653i
\(173\) −2.82933 −0.215110 −0.107555 0.994199i \(-0.534302\pi\)
−0.107555 + 0.994199i \(0.534302\pi\)
\(174\) −4.65914 17.1234i −0.353208 1.29812i
\(175\) 0 0
\(176\) 3.03370 + 5.25453i 0.228674 + 0.396075i
\(177\) −5.44106 + 5.48325i −0.408975 + 0.412146i
\(178\) 3.32473 + 5.75860i 0.249199 + 0.431625i
\(179\) 5.08135 8.80115i 0.379798 0.657829i −0.611235 0.791449i \(-0.709327\pi\)
0.991033 + 0.133620i \(0.0426603\pi\)
\(180\) −0.215720 0.122334i −0.0160788 0.00911827i
\(181\) 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
\(185\) −0.209090 −0.0153726
\(186\) 12.4609 12.5576i 0.913681 0.920765i
\(187\) 5.38371 0.393696
\(188\) 2.50472 0.182676
\(189\) 0 0
\(190\) 0.893566 0.0648261
\(191\) −22.4000 −1.62081 −0.810404 0.585872i \(-0.800752\pi\)
−0.810404 + 0.585872i \(0.800752\pi\)
\(192\) −9.99954 + 10.0771i −0.721654 + 0.727249i
\(193\) −0.256786 −0.0184839 −0.00924194 0.999957i \(-0.502942\pi\)
−0.00924194 + 0.999957i \(0.502942\pi\)
\(194\) 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 \(0.508657\pi\)
\(198\) 9.51913 5.59434i 0.676495 0.397572i
\(199\) −2.51561 + 4.35716i −0.178327 + 0.308871i −0.941307 0.337550i \(-0.890402\pi\)
0.762981 + 0.646421i \(0.223735\pi\)
\(200\) 7.65796 + 13.2640i 0.541500 + 0.937905i
\(201\) −12.1652 + 12.2595i −0.858066 + 0.864719i
\(202\) 9.63321 + 16.6852i 0.677790 + 1.17397i
\(203\) 0 0
\(204\) 0.574988 + 2.11321i 0.0402572 + 0.147954i
\(205\) −0.789452 −0.0551377
\(206\) −4.81491 + 8.33966i −0.335470 + 0.581052i
\(207\) −4.95087 2.80763i −0.344109 0.195144i
\(208\) 2.25433 + 3.90462i 0.156310 + 0.270737i
\(209\) 12.8197 22.2044i 0.886759 1.53591i
\(210\) 0 0
\(211\) −3.60537 6.24468i −0.248204 0.429901i 0.714824 0.699305i \(-0.246507\pi\)
−0.963027 + 0.269403i \(0.913174\pi\)
\(212\) −3.90991 + 6.77217i −0.268534 + 0.465114i
\(213\) −4.01434 + 4.04546i −0.275058 + 0.277190i
\(214\) −10.0060 17.3309i −0.683996 1.18472i
\(215\) −0.398017 0.689385i −0.0271445 0.0470157i
\(216\) 11.4099 + 11.1485i 0.776343 + 0.758561i
\(217\) 0 0
\(218\) −2.32831 + 4.03274i −0.157693 + 0.273132i
\(219\) 2.14812 + 7.89480i 0.145156 + 0.533481i
\(220\) −0.275878 −0.0185997
\(221\) 4.00062 0.269111
\(222\) 3.66162 + 0.965990i 0.245752 + 0.0648330i
\(223\) −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
\(226\) −1.13395 1.96407i −0.0754295 0.130648i
\(227\) 11.8853 + 20.5860i 0.788857 + 1.36634i 0.926668 + 0.375881i \(0.122660\pi\)
−0.137811 + 0.990459i \(0.544007\pi\)
\(228\) 10.0848 + 2.66052i 0.667884 + 0.176198i
\(229\) −0.952737 + 1.65019i −0.0629586 + 0.109048i −0.895787 0.444484i \(-0.853387\pi\)
0.832828 + 0.553532i \(0.186720\pi\)
\(230\) −0.110330 0.191098i −0.00727497 0.0126006i
\(231\) 0 0
\(232\) 14.2609 24.7006i 0.936272 1.62167i
\(233\) −3.27092 5.66540i −0.214285 0.371153i 0.738766 0.673962i \(-0.235409\pi\)
−0.953051 + 0.302809i \(0.902075\pi\)
\(234\) 7.07363 4.15713i 0.462418 0.271760i
\(235\) 0.168514 0.291875i 0.0109926 0.0190398i
\(236\) −3.49565 −0.227547
\(237\) −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 \(0.590764\pi\)
\(240\) 0.0871940 + 0.320457i 0.00562835 + 0.0206854i
\(241\) −10.0331 17.3778i −0.646288 1.11940i −0.984003 0.178155i \(-0.942987\pi\)
0.337715 0.941248i \(-0.390346\pi\)
\(242\) 0.0759124 0.131484i 0.00487983 0.00845212i
\(243\) 10.8078 11.2335i 0.693323 0.720627i
\(244\) 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
\(248\) 28.4333 1.80552
\(249\) −0.531531 1.95349i −0.0336844 0.123798i
\(250\) 1.16180 0.0734787
\(251\) 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
\(254\) −0.349767 −0.0219464
\(255\) 0.284936 + 0.0751704i 0.0178434 + 0.00470735i
\(256\) −15.5447 −0.971542
\(257\) −7.19415 + 12.4606i −0.448759 + 0.777273i −0.998306 0.0581897i \(-0.981467\pi\)
0.549546 + 0.835463i \(0.314801\pi\)
\(258\) 3.78519 + 13.9114i 0.235656 + 0.866088i
\(259\) 0 0
\(260\) −0.205004 −0.0127138
\(261\) −24.2441 13.7488i −1.50067 0.851030i
\(262\) −8.24701 + 14.2842i −0.509502 + 0.882484i
\(263\) 0.769503 + 1.33282i 0.0474496 + 0.0821851i 0.888775 0.458344i \(-0.151557\pi\)
−0.841325 + 0.540529i \(0.818224\pi\)
\(264\) 17.1588 + 4.52675i 1.05605 + 0.278602i
\(265\) 0.526106 + 0.911243i 0.0323185 + 0.0559772i
\(266\) 0 0
\(267\) 10.0980 + 2.66399i 0.617986 + 0.163034i
\(268\) −7.81562 −0.477415
\(269\) −13.1285 + 22.7393i −0.800461 + 1.38644i 0.118852 + 0.992912i \(0.462079\pi\)
−0.919313 + 0.393527i \(0.871255\pi\)
\(270\) 0.581917 0.163172i 0.0354144 0.00993035i
\(271\) 8.96673 + 15.5308i 0.544690 + 0.943431i 0.998626 + 0.0523969i \(0.0166861\pi\)
−0.453936 + 0.891034i \(0.649981\pi\)
\(272\) 1.46643 2.53993i 0.0889152 0.154006i
\(273\) 0 0
\(274\) −8.40748 14.5622i −0.507915 0.879734i
\(275\) 8.32473 14.4188i 0.502000 0.869489i
\(276\) −0.676214 2.48524i −0.0407033 0.149594i
\(277\) 9.43563 + 16.3430i 0.566932 + 0.981955i 0.996867 + 0.0790954i \(0.0252032\pi\)
−0.429935 + 0.902860i \(0.641463\pi\)
\(278\) 4.47680 + 7.75404i 0.268500 + 0.465056i
\(279\) −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 \(0.214235\pi\)
\(282\) −4.29949 + 4.33282i −0.256031 + 0.258016i
\(283\) −15.3927 −0.915000 −0.457500 0.889210i \(-0.651255\pi\)
−0.457500 + 0.889210i \(0.651255\pi\)
\(284\) −2.57904 −0.153038
\(285\) 0.988522 0.996187i 0.0585550 0.0590090i
\(286\) 4.56364 7.90446i 0.269854 0.467401i
\(287\) 0 0
\(288\) 0.0958052 + 12.4048i 0.00564537 + 0.730960i
\(289\) 7.19881 + 12.4687i 0.423460 + 0.733454i
\(290\) −0.540282 0.935796i −0.0317265 0.0549518i
\(291\) −1.72919 6.35516i −0.101367 0.372546i
\(292\) −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
\(296\) 3.04321 + 5.27099i 0.176883 + 0.306370i
\(297\) 4.29389 16.8012i 0.249157 0.974903i
\(298\) −6.14741 + 10.6476i −0.356110 + 0.616801i
\(299\) −4.70492 −0.272093
\(300\) 6.54877 + 1.72766i 0.378093 + 0.0997465i
\(301\) 0 0
\(302\) −6.21629 10.7669i −0.357707 0.619567i
\(303\) 29.2583 + 7.71877i 1.68085 + 0.443432i
\(304\) −6.98373 12.0962i −0.400544 0.693763i
\(305\) 0.299049 0.517968i 0.0171235 0.0296588i
\(306\) −4.64257 2.63279i −0.265398 0.150507i
\(307\) −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
\(311\) −1.30986 −0.0742755 −0.0371377 0.999310i \(-0.511824\pi\)
−0.0371377 + 0.999310i \(0.511824\pi\)
\(312\) 12.7507 + 3.36382i 0.721865 + 0.190439i
\(313\) 21.5770 1.21960 0.609802 0.792554i \(-0.291249\pi\)
0.609802 + 0.792554i \(0.291249\pi\)
\(314\) 13.4613 0.759667
\(315\) 0 0
\(316\) −6.03065 −0.339250
\(317\) −24.7819 −1.39189 −0.695946 0.718094i \(-0.745015\pi\)
−0.695946 + 0.718094i \(0.745015\pi\)
\(318\) −5.00335 18.3884i −0.280574 1.03117i
\(319\) −31.0051 −1.73595
\(320\) −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
\(324\) 7.05338 0.108956i 0.391854 0.00605312i
\(325\) 6.18608 10.7146i 0.343142 0.594339i
\(326\) 4.94206 + 8.55990i 0.273715 + 0.474089i
\(327\) 1.92015 + 7.05699i 0.106185 + 0.390252i
\(328\) 11.4901 + 19.9014i 0.634434 + 1.09887i
\(329\) 0 0
\(330\) 0.473559 0.477231i 0.0260686 0.0262707i
\(331\) 13.8451 0.760996 0.380498 0.924782i \(-0.375753\pi\)
0.380498 + 0.924782i \(0.375753\pi\)
\(332\) 0.458076 0.793410i 0.0251402 0.0435440i
\(333\) 5.12766 3.01349i 0.280994 0.165139i
\(334\) −9.60367 16.6340i −0.525489 0.910174i
\(335\) −0.525823 + 0.910752i −0.0287288 + 0.0497597i
\(336\) 0 0
\(337\) 1.69444 + 2.93485i 0.0923018 + 0.159871i 0.908479 0.417930i \(-0.137244\pi\)
−0.816178 + 0.577801i \(0.803911\pi\)
\(338\) −3.77706 + 6.54206i −0.205445 + 0.355841i
\(339\) −3.44408 0.908600i −0.187057 0.0493484i
\(340\) 0.0666767 + 0.115487i 0.00361605 + 0.00626319i
\(341\) −15.4545 26.7679i −0.836906 1.44956i
\(342\) −21.9135 + 12.8784i −1.18495 + 0.696386i
\(343\) 0 0
\(344\) −11.5859 + 20.0673i −0.624668 + 1.08196i
\(345\) −0.335099 0.0884040i −0.0180411 0.00475951i
\(346\) 3.12022 0.167744
\(347\) −14.5148 −0.779195 −0.389597 0.920985i \(-0.627386\pi\)
−0.389597 + 0.920985i \(0.627386\pi\)
\(348\) −3.31139 12.1701i −0.177509 0.652385i
\(349\) 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
\(352\) 6.90000 + 11.9511i 0.367771 + 0.636998i
\(353\) 2.07211 + 3.58900i 0.110287 + 0.191023i 0.915886 0.401438i \(-0.131490\pi\)
−0.805599 + 0.592462i \(0.798156\pi\)
\(354\) 6.00048 6.04700i 0.318922 0.321394i
\(355\) −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
\(359\) −3.96994 6.87614i −0.209525 0.362909i 0.742040 0.670356i \(-0.233859\pi\)
−0.951565 + 0.307447i \(0.900525\pi\)
\(360\) 0.844937 + 0.479163i 0.0445321 + 0.0252541i
\(361\) −20.0116 + 34.6612i −1.05324 + 1.82427i
\(362\) −18.8437 −0.990405
\(363\) −0.0626049 0.230087i −0.00328590 0.0120764i
\(364\) 0 0
\(365\) 0.249099 + 0.431453i 0.0130385 + 0.0225833i
\(366\) −7.62998 + 7.68914i −0.398826 + 0.401918i
\(367\) 6.57455 + 11.3875i 0.343189 + 0.594420i 0.985023 0.172423i \(-0.0551596\pi\)
−0.641834 + 0.766843i \(0.721826\pi\)
\(368\) −1.72459 + 2.98708i −0.0899004 + 0.155712i
\(369\) 19.3603 11.3779i 1.00785 0.592310i
\(370\) 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 \(0.231481\pi\)
\(374\) −5.93723 −0.307007
\(375\) 1.28526 1.29523i 0.0663706 0.0668852i
\(376\) −9.81055 −0.505940
\(377\) −23.0398 −1.18661
\(378\) 0 0
\(379\) −31.6147 −1.62394 −0.811968 0.583702i \(-0.801604\pi\)
−0.811968 + 0.583702i \(0.801604\pi\)
\(380\) 0.635084 0.0325791
\(381\) −0.386936 + 0.389936i −0.0198233 + 0.0199770i
\(382\) 24.7030 1.26392
\(383\) 5.36593 9.29407i 0.274186 0.474905i −0.695743 0.718291i \(-0.744925\pi\)
0.969930 + 0.243386i \(0.0782582\pi\)
\(384\) 0.938027 0.945300i 0.0478685 0.0482396i
\(385\) 0 0
\(386\) 0.283187 0.0144139
\(387\) 19.6965 + 11.1699i 1.00123 + 0.567796i
\(388\) 1.49022 2.58114i 0.0756546 0.131038i
\(389\) −12.0734 20.9118i −0.612147 1.06027i −0.990878 0.134763i \(-0.956973\pi\)
0.378731 0.925507i \(-0.376361\pi\)
\(390\) 0.351900 0.354628i 0.0178192 0.0179573i
\(391\) 1.53026 + 2.65049i 0.0773885 + 0.134041i
\(392\) 0 0
\(393\) 6.80131 + 24.9963i 0.343081 + 1.26090i
\(394\) 0.841854 0.0424120
\(395\) −0.405733 + 0.702750i −0.0204146 + 0.0353592i
\(396\) 6.76553 3.97606i 0.339981 0.199805i
\(397\) −12.0285 20.8339i −0.603691 1.04562i −0.992257 0.124203i \(-0.960363\pi\)
0.388566 0.921421i \(-0.372971\pi\)
\(398\) 2.77424 4.80513i 0.139060 0.240860i
\(399\) 0 0
\(400\) −4.53501 7.85487i −0.226751 0.392744i
\(401\) 0.781158 1.35301i 0.0390092 0.0675659i −0.845862 0.533402i \(-0.820913\pi\)
0.884871 + 0.465836i \(0.154247\pi\)
\(402\) 13.4159 13.5199i 0.669126 0.674314i
\(403\) −11.4842 19.8911i −0.572067 0.990849i
\(404\) 6.84661 + 11.8587i 0.340631 + 0.589991i
\(405\) 0.461844 0.829259i 0.0229492 0.0412062i
\(406\) 0 0
\(407\) 3.30817 5.72992i 0.163980 0.284022i
\(408\) −2.25213 8.27708i −0.111497 0.409776i
\(409\) −22.3456 −1.10492 −0.552460 0.833539i \(-0.686311\pi\)
−0.552460 + 0.833539i \(0.686311\pi\)
\(410\) 0.870619 0.0429968
\(411\) −25.5355 6.73664i −1.25957 0.332294i
\(412\) −3.42210 + 5.92725i −0.168595 + 0.292014i
\(413\) 0 0
\(414\) 5.45988 + 3.09629i 0.268339 + 0.152174i
\(415\) −0.0616373 0.106759i −0.00302566 0.00524059i
\(416\) 5.12736 + 8.88086i 0.251390 + 0.435420i
\(417\) 13.5971 + 3.58711i 0.665852 + 0.175661i
\(418\) −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 \(0.0506172\pi\)
\(422\) 3.97605 + 6.88672i 0.193551 + 0.335240i
\(423\) 0.0740389 + 9.58652i 0.00359989 + 0.466113i
\(424\) 15.3144 26.5254i 0.743735 1.28819i
\(425\) −8.04799 −0.390385
\(426\) 4.42707 4.46139i 0.214492 0.216155i
\(427\) 0 0
\(428\) −7.11156 12.3176i −0.343750 0.595393i
\(429\) −3.76363 13.8322i −0.181710 0.667825i
\(430\) 0.438938 + 0.760263i 0.0211675 + 0.0366631i
\(431\) 9.70169 16.8038i 0.467314 0.809411i −0.531989 0.846751i \(-0.678555\pi\)
0.999303 + 0.0373401i \(0.0118885\pi\)
\(432\) −6.75688 6.60211i −0.325090 0.317644i
\(433\) 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
\(437\) 14.5754 0.697238
\(438\) −2.36897 8.70650i −0.113194 0.416013i
\(439\) 17.3412 0.827650 0.413825 0.910356i \(-0.364193\pi\)
0.413825 + 0.910356i \(0.364193\pi\)
\(440\) 1.08056 0.0515139
\(441\) 0 0
\(442\) −4.41194 −0.209854
\(443\) 19.6100 0.931698 0.465849 0.884864i \(-0.345749\pi\)
0.465849 + 0.884864i \(0.345749\pi\)
\(444\) 2.60242 + 0.686557i 0.123506 + 0.0325826i
\(445\) 0.635912 0.0301451
\(446\) 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 \(0.637434\pi\)
\(450\) −14.2299 + 8.36285i −0.670806 + 0.394228i
\(451\) 12.4905 21.6342i 0.588155 1.01871i
\(452\) −0.805935 1.39592i −0.0379080 0.0656586i
\(453\) −18.8803 4.98091i −0.887075 0.234023i
\(454\) −13.1073 22.7025i −0.615156 1.06548i
\(455\) 0 0
\(456\) −39.5005 10.4208i −1.84978 0.487999i
\(457\) 0.485451 0.0227084 0.0113542 0.999936i \(-0.496386\pi\)
0.0113542 + 0.999936i \(0.496386\pi\)
\(458\) 1.05069 1.81985i 0.0490956 0.0850361i
\(459\) −8.07107 + 2.26317i −0.376725 + 0.105636i
\(460\) −0.0784150 0.135819i −0.00365612 0.00633259i
\(461\) 3.99687 6.92279i 0.186153 0.322426i −0.757811 0.652474i \(-0.773731\pi\)
0.943964 + 0.330047i \(0.107065\pi\)
\(462\) 0 0
\(463\) 5.24280 + 9.08080i 0.243654 + 0.422021i 0.961752 0.273921i \(-0.0883206\pi\)
−0.718098 + 0.695942i \(0.754987\pi\)
\(464\) −8.44523 + 14.6276i −0.392060 + 0.679068i
\(465\) −0.444189 1.63249i −0.0205988 0.0757050i
\(466\) 3.60721 + 6.24788i 0.167101 + 0.289427i
\(467\) −10.9489 18.9640i −0.506653 0.877549i −0.999970 0.00769944i \(-0.997549\pi\)
0.493317 0.869849i \(-0.335784\pi\)
\(468\) 5.02744 2.95460i 0.232394 0.136576i
\(469\) 0 0
\(470\) −0.185839 + 0.321883i −0.00857213 + 0.0148474i
\(471\) 14.8918 15.0073i 0.686179 0.691499i
\(472\) 13.6918 0.630218
\(473\) 25.1893 1.15820
\(474\) 10.3519 10.4322i 0.475480 0.479167i
\(475\) −19.1639 + 33.1929i −0.879301 + 1.52299i
\(476\) 0 0
\(477\) −26.0353 14.7645i −1.19207 0.676022i
\(478\) −11.7708 20.3877i −0.538386 0.932512i
\(479\) −2.00085 3.46557i −0.0914210 0.158346i 0.816688 0.577079i \(-0.195808\pi\)
−0.908109 + 0.418733i \(0.862474\pi\)
\(480\) 0.198318 + 0.728864i 0.00905194 + 0.0332679i
\(481\) 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
\(485\) −0.200520 0.347311i −0.00910514 0.0157706i
\(486\) −11.9190 + 12.3884i −0.540658 + 0.561950i
\(487\) 13.2377 22.9284i 0.599859 1.03899i −0.392982 0.919546i \(-0.628557\pi\)
0.992841 0.119440i \(-0.0381100\pi\)
\(488\) −17.4100 −0.788116
\(489\) 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 \(0.611641\pi\)
\(492\) 9.82584 + 2.59220i 0.442983 + 0.116865i
\(493\) 7.49360 + 12.9793i 0.337495 + 0.584558i
\(494\) −10.5057 + 18.1965i −0.472675 + 0.818697i
\(495\) −0.00815487 1.05589i −0.000366534 0.0474587i
\(496\) −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 \(0.113474\pi\)
\(500\) 0.825726 0.0369276
\(501\) −29.1686 7.69510i −1.30316 0.343792i
\(502\) −7.51531 −0.335425
\(503\) −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
\(506\) 6.98247 0.310409
\(507\) 3.11494 + 11.4481i 0.138339 + 0.508428i
\(508\) −0.248590 −0.0110294
\(509\) −14.4532 + 25.0336i −0.640625 + 1.10960i 0.344668 + 0.938725i \(0.387991\pi\)
−0.985293 + 0.170871i \(0.945342\pi\)
\(510\) −0.314232 0.0828990i −0.0139144 0.00367083i
\(511\) 0 0
\(512\) 18.6806 0.825575
\(513\) −9.88474 + 38.6771i −0.436422 + 1.70764i
\(514\) 7.93381 13.7418i 0.349945 0.606123i
\(515\) 0.460467 + 0.797553i 0.0202906 + 0.0351444i
\(516\) 2.69025 + 9.88727i 0.118432 + 0.435263i
\(517\) 5.33237 + 9.23593i 0.234517 + 0.406196i
\(518\) 0 0
\(519\) 3.45180 3.47856i 0.151517 0.152692i
\(520\) 0.802963 0.0352123
\(521\) 16.8995 29.2708i 0.740381 1.28238i −0.211941 0.977283i \(-0.567978\pi\)
0.952322 0.305095i \(-0.0986883\pi\)
\(522\) 26.7368 + 15.1624i 1.17024 + 0.663639i
\(523\) −7.18895 12.4516i −0.314351 0.544471i 0.664949 0.746889i \(-0.268453\pi\)
−0.979299 + 0.202418i \(0.935120\pi\)
\(524\) −5.86140 + 10.1522i −0.256056 + 0.443502i
\(525\) 0 0
\(526\) −0.848618 1.46985i −0.0370015 0.0640885i
\(527\) −7.47036 + 12.9390i −0.325414 + 0.563634i
\(528\) −10.1614 2.68072i −0.442218 0.116664i
\(529\) 9.70034 + 16.8015i 0.421754 + 0.730499i
\(530\) −0.580197 1.00493i −0.0252022 0.0436514i
\(531\) −0.103331 13.3792i −0.00448416 0.580607i
\(532\) 0 0
\(533\) 9.28166 16.0763i 0.402033 0.696342i
\(534\) −11.1362 2.93789i −0.481910 0.127135i
\(535\) −1.91382 −0.0827417
\(536\) 30.6124 1.32225
\(537\) 4.62143 + 16.9848i 0.199429 + 0.732948i
\(538\) 14.4783 25.0772i 0.624205 1.08116i
\(539\) 0 0
\(540\) 0.413586 0.115971i 0.0177979 0.00499062i
\(541\) 12.5882 + 21.8034i 0.541210 + 0.937403i 0.998835 + 0.0482577i \(0.0153669\pi\)
−0.457625 + 0.889145i \(0.651300\pi\)
\(542\) −9.88863 17.1276i −0.424753 0.735694i
\(543\) −20.8462 + 21.0078i −0.894596 + 0.901532i
\(544\) 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 \(0.145009\pi\)
\(548\) −5.97545 10.3498i −0.255258 0.442121i
\(549\) 0.131391 + 17.0125i 0.00560764 + 0.726075i
\(550\) −9.18062 + 15.9013i −0.391463 + 0.678034i
\(551\) 71.3752 3.04068
\(552\) 2.64861 + 9.73424i 0.112732 + 0.414317i
\(553\) 0 0
\(554\) −10.4057 18.0233i −0.442098 0.765736i
\(555\) 0.255092 0.257069i 0.0108280 0.0109120i
\(556\) 3.18179 + 5.51102i 0.134938 + 0.233719i
\(557\) −10.0229 + 17.3602i −0.424686 + 0.735577i −0.996391 0.0848820i \(-0.972949\pi\)
0.571705 + 0.820459i \(0.306282\pi\)
\(558\) 0.236644 + 30.6406i 0.0100180 + 1.29712i
\(559\) 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
\(563\) −39.8013 −1.67743 −0.838713 0.544574i \(-0.816691\pi\)
−0.838713 + 0.544574i \(0.816691\pi\)
\(564\) −3.05578 + 3.07947i −0.128671 + 0.129669i
\(565\) −0.216888 −0.00912457
\(566\) 16.9753 0.713523
\(567\) 0 0
\(568\) 10.1017 0.423856
\(569\) 13.8159 0.579194 0.289597 0.957149i \(-0.406479\pi\)
0.289597 + 0.957149i \(0.406479\pi\)
\(570\) −1.09016 + 1.09861i −0.0456616 + 0.0460156i
\(571\) 10.4387 0.436846 0.218423 0.975854i \(-0.429909\pi\)
0.218423 + 0.975854i \(0.429909\pi\)
\(572\) 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
\(576\) −0.189900 24.5882i −0.00791250 1.02451i
\(577\) −12.7461 + 22.0769i −0.530628 + 0.919075i 0.468733 + 0.883340i \(0.344711\pi\)
−0.999361 + 0.0357353i \(0.988623\pi\)
\(578\) −7.93895 13.7507i −0.330217 0.571952i
\(579\) 0.313281 0.315710i 0.0130195 0.0131204i
\(580\) −0.383994 0.665098i −0.0159445 0.0276167i
\(581\) 0 0
\(582\) 1.90697 + 7.00855i 0.0790466 + 0.290514i
\(583\) −33.2957 −1.37897
\(584\) 7.25104 12.5592i 0.300050 0.519702i
\(585\) −0.00605986 0.784628i −0.000250544 0.0324404i
\(586\) 14.2277 + 24.6431i 0.587740 + 1.01800i
\(587\) −17.5168 + 30.3401i −0.722998 + 1.25227i 0.236795 + 0.971560i \(0.423903\pi\)
−0.959793 + 0.280709i \(0.909430\pi\)
\(588\) 0 0
\(589\) 35.5769 + 61.6210i 1.46592 + 2.53905i
\(590\) 0.259362 0.449228i 0.0106778 0.0184944i
\(591\) 0.931316 0.938536i 0.0383092 0.0386062i
\(592\) −1.80217 3.12146i −0.0740689 0.128291i
\(593\) 18.0646 + 31.2888i 0.741824 + 1.28488i 0.951664 + 0.307141i \(0.0993724\pi\)
−0.209840 + 0.977736i \(0.567294\pi\)
\(594\) −4.73536 + 18.5286i −0.194294 + 0.760236i
\(595\) 0 0
\(596\) −4.36915 + 7.56759i −0.178967 + 0.309980i
\(597\) −2.28792 8.40861i −0.0936383 0.344142i
\(598\) 5.18865 0.212180
\(599\) −40.9484 −1.67310 −0.836552 0.547887i \(-0.815432\pi\)
−0.836552 + 0.547887i \(0.815432\pi\)
\(600\) −25.6504 6.76694i −1.04717 0.276259i
\(601\) 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
\(604\) −4.41810 7.65238i −0.179770 0.311371i
\(605\) −0.00725978 0.0125743i −0.000295152 0.000511218i
\(606\) −32.2665 8.51236i −1.31074 0.345791i
\(607\) −3.42258 + 5.92808i −0.138918 + 0.240613i −0.927087 0.374845i \(-0.877696\pi\)
0.788169 + 0.615459i \(0.211029\pi\)
\(608\) −15.8841 27.5121i −0.644187 1.11576i
\(609\) 0 0
\(610\) −0.329795 + 0.571222i −0.0133530 + 0.0231281i
\(611\) 3.96246 + 6.86319i 0.160304 + 0.277655i
\(612\) −3.29961 1.87120i −0.133379 0.0756389i
\(613\) 14.5648 25.2271i 0.588269 1.01891i −0.406191 0.913788i \(-0.633143\pi\)
0.994459 0.105123i \(-0.0335235\pi\)
\(614\) 24.5833 0.992101
\(615\) 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 \(0.969990\pi\)
\(618\) −4.37911 16.0942i −0.176154 0.647404i
\(619\) 4.43178 + 7.67606i 0.178128 + 0.308527i 0.941239 0.337740i \(-0.109663\pi\)
−0.763111 + 0.646267i \(0.776329\pi\)
\(620\) 0.382804 0.663035i 0.0153738 0.0266281i
\(621\) 9.49197 2.66159i 0.380900 0.106806i
\(622\) 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
\(626\) −23.7954 −0.951055
\(627\) 11.6594 + 42.8509i 0.465632 + 1.71130i
\(628\) 9.56737 0.381779
\(629\) −3.19820 −0.127521
\(630\) 0 0
\(631\) 26.4661 1.05360 0.526799 0.849990i \(-0.323392\pi\)
0.526799 + 0.849990i \(0.323392\pi\)
\(632\) 23.6210 0.939592
\(633\) 12.0762 + 3.18588i 0.479985 + 0.126627i
\(634\) 27.3299 1.08541
\(635\) −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
\(639\) −0.0762358 9.87098i −0.00301584 0.390490i
\(640\) 0.0405449 0.0702258i 0.00160268 0.00277592i
\(641\) 8.26595 + 14.3171i 0.326486 + 0.565489i 0.981812 0.189856i \(-0.0608022\pi\)
−0.655326 + 0.755346i \(0.727469\pi\)
\(642\) 33.5151 + 8.84178i 1.32274 + 0.348957i
\(643\) −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
\(646\) 13.6678 0.537752
\(647\) 0.649903 1.12567i 0.0255503 0.0442545i −0.852968 0.521964i \(-0.825200\pi\)
0.878518 + 0.477710i \(0.158533\pi\)
\(648\) −27.6268 + 0.426762i −1.08528 + 0.0167648i
\(649\) −7.44198 12.8899i −0.292123 0.505972i
\(650\) −6.82209 + 11.8162i −0.267584 + 0.463470i
\(651\) 0 0
\(652\) 3.51247 + 6.08377i 0.137559 + 0.238259i
\(653\) 22.4435 38.8733i 0.878281 1.52123i 0.0250558 0.999686i \(-0.492024\pi\)
0.853226 0.521542i \(-0.174643\pi\)
\(654\) −2.11757 7.78254i −0.0828035 0.304321i
\(655\) 0.788692 + 1.36605i 0.0308167 + 0.0533762i
\(656\) −6.80438 11.7855i −0.265667 0.460148i
\(657\) −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 \(0.0531549\pi\)
\(660\) 0.336572 0.339182i 0.0131011 0.0132026i
\(661\) 33.0256 1.28455 0.642274 0.766475i \(-0.277991\pi\)
0.642274 + 0.766475i \(0.277991\pi\)
\(662\) −15.2686 −0.593430
\(663\) −4.88078 + 4.91862i −0.189554 + 0.191023i
\(664\) −1.79420 + 3.10765i −0.0696285 + 0.120600i
\(665\) 0 0
\(666\) −5.65485 + 3.32332i −0.219121 + 0.128776i
\(667\) −8.81283 15.2643i −0.341234 0.591035i
\(668\) −6.82561 11.8223i −0.264091 0.457419i
\(669\) −5.08501 18.6885i −0.196598 0.722541i
\(670\) 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 \(0.301669\pi\)
\(674\) −1.86865 3.23659i −0.0719776 0.124669i
\(675\) −6.41884 + 25.1157i −0.247061 + 0.966704i
\(676\) −2.68447 + 4.64964i −0.103249 + 0.178832i
\(677\) 8.30167 0.319059 0.159530 0.987193i \(-0.449002\pi\)
0.159530 + 0.987193i \(0.449002\pi\)
\(678\) 3.79818 + 1.00202i 0.145868 + 0.0384822i
\(679\) 0 0
\(680\) −0.261161 0.452344i −0.0100151 0.0173466i
\(681\) −39.8099 10.5024i −1.52552 0.402454i
\(682\) 17.0434 + 29.5200i 0.652625 + 1.13038i
\(683\) −1.24728 + 2.16036i −0.0477259 + 0.0826637i −0.888902 0.458098i \(-0.848531\pi\)
0.841176 + 0.540762i \(0.181864\pi\)
\(684\) −15.5746 + 9.15308i −0.595509 + 0.349977i
\(685\) −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
\(689\) −24.7419 −0.942591
\(690\) 0.369552 + 0.0974932i 0.0140686 + 0.00371150i
\(691\) −16.8691 −0.641731 −0.320865 0.947125i \(-0.603974\pi\)
−0.320865 + 0.947125i \(0.603974\pi\)
\(692\) 2.21763 0.0843017
\(693\) 0 0
\(694\) 16.0071 0.607621
\(695\) 0.856265 0.0324800
\(696\) 12.9701 + 47.6681i 0.491631 + 1.80685i
\(697\) −12.0753 −0.457385
\(698\) −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 \(0.399258\pi\)
\(702\) −3.51883 + 13.7685i −0.132810 + 0.519659i
\(703\) −7.61558 + 13.1906i −0.287227 + 0.497492i
\(704\) −13.6768 23.6889i −0.515464 0.892811i
\(705\) 0.153262 + 0.563271i 0.00577217 + 0.0212140i
\(706\) −2.28515 3.95800i −0.0860029 0.148961i
\(707\) 0 0
\(708\) 4.26472 4.29778i 0.160278 0.161520i
\(709\) −29.4925 −1.10761 −0.553807 0.832645i \(-0.686825\pi\)
−0.553807 + 0.832645i \(0.686825\pi\)
\(710\) 0.191354 0.331434i 0.00718138 0.0124385i
\(711\) −0.178264 23.0816i −0.00668544 0.865627i
\(712\) −9.25539 16.0308i −0.346860 0.600780i
\(713\) 8.78551 15.2169i 0.329020 0.569879i
\(714\) 0 0
\(715\) −0.436438 0.755933i −0.0163219 0.0282703i
\(716\) −3.98277 + 6.89836i −0.148843 + 0.257804i
\(717\) −35.7508 9.43158i −1.33514 0.352229i
\(718\) 4.37810 + 7.58310i 0.163389 + 0.282999i
\(719\) 0.217311 + 0.376394i 0.00810433 + 0.0140371i 0.870049 0.492965i \(-0.164087\pi\)
−0.861945 + 0.507002i \(0.830754\pi\)
\(720\) −0.500368 0.283758i −0.0186476 0.0105750i
\(721\) 0 0
\(722\) 22.0691 38.2248i 0.821327 1.42258i
\(723\) 33.6058 + 8.86571i 1.24981 + 0.329719i
\(724\) −13.3928 −0.497740
\(725\) 46.3488 1.72135
\(726\) 0.0690415 + 0.253743i 0.00256237 + 0.00941729i
\(727\) 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
\(730\) −0.274710 0.475812i −0.0101675 0.0176106i
\(731\) −6.08798 10.5447i −0.225172 0.390009i
\(732\) −5.42285 + 5.46490i −0.200434 + 0.201988i
\(733\) 2.83307 4.90702i 0.104642 0.181245i −0.808950 0.587878i \(-0.799964\pi\)
0.913592 + 0.406632i \(0.133297\pi\)
\(734\) −7.25050 12.5582i −0.267621 0.463533i
\(735\) 0 0
\(736\) −3.92249 + 6.79395i −0.144585 + 0.250428i
\(737\) −16.6389 28.8194i −0.612901 1.06158i
\(738\) −21.3508 + 12.5477i −0.785932 + 0.461888i
\(739\) 6.80540 11.7873i 0.250341 0.433603i −0.713279 0.700880i \(-0.752791\pi\)
0.963620 + 0.267278i \(0.0861241\pi\)
\(740\) 0.163885 0.00602455
\(741\) 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 \(0.907985\pi\)
\(744\) −34.6888 + 34.9578i −1.27175 + 1.28161i
\(745\) 0.587900 + 1.01827i 0.0215390 + 0.0373066i
\(746\) 4.30696 7.45988i 0.157689 0.273126i
\(747\) 3.05022 + 1.72978i 0.111602 + 0.0632892i
\(748\) −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 \(0.125050\pi\)
\(752\) 5.80977 0.211860
\(753\) −8.31394 + 8.37840i −0.302977 + 0.305326i
\(754\) 25.4086 0.925325
\(755\) −1.18897 −0.0432712
\(756\) 0 0
\(757\) 37.6446 1.36822 0.684108 0.729381i \(-0.260192\pi\)
0.684108 + 0.729381i \(0.260192\pi\)
\(758\) 34.8651 1.26636
\(759\) 7.72448 7.78437i 0.280381 0.282555i
\(760\) −2.48751 −0.0902315
\(761\) −5.02358 + 8.70109i −0.182104 + 0.315414i −0.942597 0.333933i \(-0.891624\pi\)
0.760493 + 0.649347i \(0.224958\pi\)
\(762\) 0.426718 0.430027i 0.0154584 0.0155782i
\(763\) 0 0
\(764\) 17.5572 0.635196
\(765\) −0.440044 + 0.258611i −0.0159098 + 0.00935010i
\(766\) −5.91762 + 10.2496i −0.213812 + 0.370334i
\(767\) −5.53011 9.57843i −0.199681 0.345857i
\(768\) 18.9646 19.1116i 0.684326 0.689632i
\(769\) 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
\(772\) 0.201270 0.00724385
\(773\) 24.2939 42.0783i 0.873792 1.51345i 0.0157473 0.999876i \(-0.494987\pi\)
0.858044 0.513576i \(-0.171679\pi\)
\(774\) −21.7216 12.3183i −0.780766 0.442771i
\(775\) 23.1025 + 40.0148i 0.829867 + 1.43737i
\(776\) −5.83694 + 10.1099i −0.209534 + 0.362923i
\(777\) 0 0
\(778\) 13.3147 + 23.0618i 0.477356 + 0.826806i
\(779\) −28.7538 + 49.8030i −1.03021 + 1.78438i
\(780\) 0.250106 0.252045i 0.00895522 0.00902466i
\(781\) −5.49059 9.50998i −0.196469 0.340294i
\(782\) −1.68759