Properties

Label 441.2.g.h.67.7
Level $441$
Weight $2$
Character 441.67
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.g (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 67.7
Character \(\chi\) \(=\) 441.67
Dual form 441.2.g.h.79.7

$q$-expansion

\(f(q)\) \(=\) \(q+(0.551407 - 0.955065i) q^{2} +(-0.454745 + 1.67129i) q^{3} +(0.391901 + 0.678793i) q^{4} +0.105466 q^{5} +(1.34544 + 1.35587i) q^{6} +3.07001 q^{8} +(-2.58641 - 1.52002i) q^{9} +O(q^{10})\) \(q+(0.551407 - 0.955065i) q^{2} +(-0.454745 + 1.67129i) q^{3} +(0.391901 + 0.678793i) q^{4} +0.105466 q^{5} +(1.34544 + 1.35587i) q^{6} +3.07001 q^{8} +(-2.58641 - 1.52002i) q^{9} +(0.0581547 - 0.100727i) q^{10} +3.33731 q^{11} +(-1.31267 + 0.346303i) q^{12} +(-1.23997 + 2.14770i) q^{13} +(-0.0479602 + 0.176264i) q^{15} +(0.909025 - 1.57448i) q^{16} +(-0.806594 + 1.39706i) q^{17} +(-2.87788 + 1.63204i) q^{18} +(3.84133 + 6.65338i) q^{19} +(0.0413323 + 0.0715896i) q^{20} +(1.84022 - 3.18735i) q^{22} -1.89719 q^{23} +(-1.39607 + 5.13088i) q^{24} -4.98888 q^{25} +(1.36746 + 2.36851i) q^{26} +(3.71655 - 3.63142i) q^{27} +(4.64521 + 8.04574i) q^{29} +(0.141898 + 0.142998i) q^{30} +(-4.63081 - 8.02080i) q^{31} +(2.06753 + 3.58107i) q^{32} +(-1.51763 + 5.57762i) q^{33} +(0.889523 + 1.54070i) q^{34} +(0.0181599 - 2.35134i) q^{36} +(0.991268 + 1.71693i) q^{37} +8.47254 q^{38} +(-3.02555 - 3.04901i) q^{39} +0.323782 q^{40} +(3.74268 - 6.48252i) q^{41} +(-3.77388 - 6.53655i) q^{43} +(1.30790 + 2.26534i) q^{44} +(-0.272779 - 0.160311i) q^{45} +(-1.04612 + 1.81194i) q^{46} +(1.59780 - 2.76747i) q^{47} +(2.21803 + 2.23523i) q^{48} +(-2.75090 + 4.76470i) q^{50} +(-1.96810 - 1.98336i) q^{51} -1.94379 q^{52} +(4.98839 - 8.64015i) q^{53} +(-1.41891 - 5.55194i) q^{54} +0.351974 q^{55} +(-12.8665 + 3.39438i) q^{57} +10.2456 q^{58} +(-2.22993 - 3.86235i) q^{59} +(-0.138443 + 0.0365232i) q^{60} +(2.83550 - 4.91123i) q^{61} -10.2138 q^{62} +8.19630 q^{64} +(-0.130775 + 0.226509i) q^{65} +(4.49016 + 4.52497i) q^{66} +(-4.98571 - 8.63550i) q^{67} -1.26442 q^{68} +(0.862736 - 3.17075i) q^{69} +3.29042 q^{71} +(-7.94033 - 4.66648i) q^{72} +(2.36189 - 4.09091i) q^{73} +2.18637 q^{74} +(2.26867 - 8.33786i) q^{75} +(-3.01084 + 5.21493i) q^{76} +(-4.58031 + 1.20835i) q^{78} +(-3.84705 + 6.66328i) q^{79} +(0.0958713 - 0.166054i) q^{80} +(4.37908 + 7.86280i) q^{81} +(-4.12748 - 7.14901i) q^{82} +(-0.584428 - 1.01226i) q^{83} +(-0.0850683 + 0.147343i) q^{85} -8.32378 q^{86} +(-15.5591 + 4.10473i) q^{87} +10.2456 q^{88} +(-3.01477 - 5.22173i) q^{89} +(-0.303519 + 0.172125i) q^{90} +(-0.743509 - 1.28780i) q^{92} +(15.5109 - 4.09200i) q^{93} +(-1.76208 - 3.05201i) q^{94} +(0.405130 + 0.701706i) q^{95} +(-6.92520 + 1.82697i) q^{96} +(-1.90127 - 3.29310i) q^{97} +(-8.63168 - 5.07279i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} - 4q^{9} + O(q^{10}) \) \( 24q + 4q^{2} - 12q^{4} - 24q^{8} - 4q^{9} - 40q^{11} + 4q^{15} - 12q^{16} + 28q^{18} - 64q^{23} + 24q^{25} + 16q^{29} + 84q^{30} + 48q^{32} - 4q^{36} - 12q^{37} - 40q^{39} + 56q^{44} + 24q^{46} - 4q^{50} - 8q^{51} + 32q^{53} - 12q^{57} + 56q^{60} + 96q^{64} + 60q^{65} - 12q^{67} - 112q^{71} - 168q^{72} - 136q^{74} - 60q^{78} + 12q^{79} - 40q^{81} + 12q^{85} - 152q^{86} + 16q^{92} + 112q^{93} + 64q^{95} + 20q^{99} + O(q^{100}) \)

Character values

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

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

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.551407 0.955065i 0.389903 0.675333i −0.602533 0.798094i \(-0.705842\pi\)
0.992436 + 0.122762i \(0.0391750\pi\)
\(3\) −0.454745 + 1.67129i −0.262547 + 0.964919i
\(4\) 0.391901 + 0.678793i 0.195951 + 0.339396i
\(5\) 0.105466 0.0471659 0.0235829 0.999722i \(-0.492493\pi\)
0.0235829 + 0.999722i \(0.492493\pi\)
\(6\) 1.34544 + 1.35587i 0.549273 + 0.553532i
\(7\) 0 0
\(8\) 3.07001 1.08541
\(9\) −2.58641 1.52002i −0.862138 0.506673i
\(10\) 0.0581547 0.100727i 0.0183901 0.0318527i
\(11\) 3.33731 1.00624 0.503119 0.864217i \(-0.332186\pi\)
0.503119 + 0.864217i \(0.332186\pi\)
\(12\) −1.31267 + 0.346303i −0.378936 + 0.0999689i
\(13\) −1.23997 + 2.14770i −0.343907 + 0.595664i −0.985155 0.171670i \(-0.945084\pi\)
0.641248 + 0.767334i \(0.278417\pi\)
\(14\) 0 0
\(15\) −0.0479602 + 0.176264i −0.0123833 + 0.0455113i
\(16\) 0.909025 1.57448i 0.227256 0.393619i
\(17\) −0.806594 + 1.39706i −0.195628 + 0.338837i −0.947106 0.320921i \(-0.896008\pi\)
0.751478 + 0.659758i \(0.229341\pi\)
\(18\) −2.87788 + 1.63204i −0.678324 + 0.384676i
\(19\) 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
\(23\) −1.89719 −0.395591 −0.197795 0.980243i \(-0.563378\pi\)
−0.197795 + 0.980243i \(0.563378\pi\)
\(24\) −1.39607 + 5.13088i −0.284972 + 1.04734i
\(25\) −4.98888 −0.997775
\(26\) 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 0.869416 + 0.494080i \(0.164495\pi\)
−0.00682200 + 0.999977i \(0.502172\pi\)
\(30\) 0.141898 + 0.142998i 0.0259070 + 0.0261078i
\(31\) −4.63081 8.02080i −0.831718 1.44058i −0.896675 0.442689i \(-0.854024\pi\)
0.0649574 0.997888i \(-0.479309\pi\)
\(32\) 2.06753 + 3.58107i 0.365491 + 0.633049i
\(33\) −1.51763 + 5.57762i −0.264185 + 0.970939i
\(34\) 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 \(0.781228\pi\)
\(38\) 8.47254 1.37443
\(39\) −3.02555 3.04901i −0.484476 0.488232i
\(40\) 0.323782 0.0511945
\(41\) 3.74268 6.48252i 0.584509 1.01240i −0.410427 0.911893i \(-0.634621\pi\)
0.994936 0.100506i \(-0.0320462\pi\)
\(42\) 0 0
\(43\) −3.77388 6.53655i −0.575512 0.996815i −0.995986 0.0895108i \(-0.971470\pi\)
0.420474 0.907304i \(-0.361864\pi\)
\(44\) 1.30790 + 2.26534i 0.197173 + 0.341514i
\(45\) −0.272779 0.160311i −0.0406635 0.0238977i
\(46\) −1.04612 + 1.81194i −0.154242 + 0.267155i
\(47\) 1.59780 2.76747i 0.233063 0.403677i −0.725645 0.688070i \(-0.758458\pi\)
0.958708 + 0.284392i \(0.0917917\pi\)
\(48\) 2.21803 + 2.23523i 0.320145 + 0.322627i
\(49\) 0 0
\(50\) −2.75090 + 4.76470i −0.389036 + 0.673830i
\(51\) −1.96810 1.98336i −0.275589 0.277726i
\(52\) −1.94379 −0.269555
\(53\) 4.98839 8.64015i 0.685209 1.18682i −0.288163 0.957581i \(-0.593044\pi\)
0.973371 0.229234i \(-0.0736223\pi\)
\(54\) −1.41891 5.55194i −0.193090 0.755523i
\(55\) 0.351974 0.0474601
\(56\) 0 0
\(57\) −12.8665 + 3.39438i −1.70422 + 0.449597i
\(58\) 10.2456 1.34531
\(59\) −2.22993 3.86235i −0.290312 0.502836i 0.683571 0.729884i \(-0.260426\pi\)
−0.973884 + 0.227048i \(0.927093\pi\)
\(60\) −0.138443 + 0.0365232i −0.0178729 + 0.00471512i
\(61\) 2.83550 4.91123i 0.363048 0.628818i −0.625413 0.780294i \(-0.715069\pi\)
0.988461 + 0.151476i \(0.0484027\pi\)
\(62\) −10.2138 −1.29716
\(63\) 0 0
\(64\) 8.19630 1.02454
\(65\) −0.130775 + 0.226509i −0.0162207 + 0.0280950i
\(66\) 4.49016 + 4.52497i 0.552700 + 0.556985i
\(67\) −4.98571 8.63550i −0.609101 1.05499i −0.991389 0.130951i \(-0.958197\pi\)
0.382288 0.924043i \(-0.375136\pi\)
\(68\) −1.26442 −0.153333
\(69\) 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 \(0.437448\pi\)
\(72\) −7.94033 4.66648i −0.935777 0.549950i
\(73\) 2.36189 4.09091i 0.276438 0.478805i −0.694059 0.719919i \(-0.744179\pi\)
0.970497 + 0.241113i \(0.0775125\pi\)
\(74\) 2.18637 0.254160
\(75\) 2.26867 8.33786i 0.261963 0.962773i
\(76\) −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 \(0.309150\pi\)
\(80\) 0.0958713 0.166054i 0.0107187 0.0185654i
\(81\) 4.37908 + 7.86280i 0.486564 + 0.873645i
\(82\) −4.12748 7.14901i −0.455804 0.789476i
\(83\) −0.584428 1.01226i −0.0641493 0.111110i 0.832167 0.554525i \(-0.187100\pi\)
−0.896316 + 0.443415i \(0.853767\pi\)
\(84\) 0 0
\(85\) −0.0850683 + 0.147343i −0.00922695 + 0.0159815i
\(86\) −8.32378 −0.897576
\(87\) −15.5591 + 4.10473i −1.66812 + 0.440073i
\(88\) 10.2456 1.09219
\(89\) −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
\(93\) 15.5109 4.09200i 1.60841 0.424321i
\(94\) −1.76208 3.05201i −0.181744 0.314791i
\(95\) 0.405130 + 0.701706i 0.0415655 + 0.0719935i
\(96\) −6.92520 + 1.82697i −0.706800 + 0.186464i
\(97\) −1.90127 3.29310i −0.193045 0.334364i 0.753213 0.657777i \(-0.228503\pi\)
−0.946258 + 0.323413i \(0.895170\pi\)
\(98\) 0 0
\(99\) −8.63168 5.07279i −0.867516 0.509834i
\(100\) −1.95515 3.38641i −0.195515 0.338641i
\(101\) 17.4702 1.73835 0.869177 0.494501i \(-0.164649\pi\)
0.869177 + 0.494501i \(0.164649\pi\)
\(102\) −2.97946 + 0.786025i −0.295010 + 0.0778280i
\(103\) −8.73204 −0.860394 −0.430197 0.902735i \(-0.641556\pi\)
−0.430197 + 0.902735i \(0.641556\pi\)
\(104\) −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 \(0.492785\pi\)
\(108\) 3.92150 + 1.09961i 0.377347 + 0.105810i
\(109\) 2.11124 3.65678i 0.202220 0.350256i −0.747023 0.664798i \(-0.768518\pi\)
0.949243 + 0.314542i \(0.101851\pi\)
\(110\) 0.194081 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 \(0.135829\pi\)
\(114\) −3.85284 + 14.1601i −0.360852 + 1.32621i
\(115\) −0.200089 −0.0186584
\(116\) −3.64093 + 6.30627i −0.338052 + 0.585523i
\(117\) 6.47163 3.67005i 0.598302 0.339296i
\(118\) −4.91840 −0.452775
\(119\) 0 0
\(120\) −0.147238 + 0.541134i −0.0134410 + 0.0493986i
\(121\) 0.137670 0.0125155
\(122\) −3.12703 5.41617i −0.283108 0.490357i
\(123\) 9.13220 + 9.20300i 0.823422 + 0.829806i
\(124\) 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
\(129\) 12.6406 3.33478i 1.11294 0.293611i
\(130\) 0.144221 + 0.249797i 0.0126490 + 0.0219087i
\(131\) −14.9563 −1.30674 −0.653370 0.757039i \(-0.726645\pi\)
−0.653370 + 0.757039i \(0.726645\pi\)
\(132\) −4.38081 + 1.15572i −0.381300 + 0.100593i
\(133\) 0 0
\(134\) −10.9966 −0.949962
\(135\) 0.391970 0.382992i 0.0337354 0.0329627i
\(136\) −2.47625 + 4.28900i −0.212337 + 0.367779i
\(137\) −15.2473 −1.30267 −0.651334 0.758791i \(-0.725790\pi\)
−0.651334 + 0.758791i \(0.725790\pi\)
\(138\) −2.55255 2.57234i −0.217287 0.218972i
\(139\) −4.05943 + 7.03114i −0.344316 + 0.596374i −0.985229 0.171240i \(-0.945223\pi\)
0.640913 + 0.767614i \(0.278556\pi\)
\(140\) 0 0
\(141\) 3.89866 + 3.92888i 0.328326 + 0.330872i
\(142\) 1.81436 3.14257i 0.152258 0.263718i
\(143\) −4.13818 + 7.16754i −0.346052 + 0.599380i
\(144\) −4.74435 + 2.69051i −0.395363 + 0.224210i
\(145\) 0.489912 + 0.848553i 0.0406850 + 0.0704685i
\(146\) −2.60473 4.51152i −0.215569 0.373376i
\(147\) 0 0
\(148\) −0.776958 + 1.34573i −0.0638656 + 0.110618i
\(149\) −11.1486 −0.913329 −0.456664 0.889639i \(-0.650956\pi\)
−0.456664 + 0.889639i \(0.650956\pi\)
\(150\) −6.71223 6.76427i −0.548051 0.552301i
\(151\) −11.2735 −0.917425 −0.458713 0.888585i \(-0.651689\pi\)
−0.458713 + 0.888585i \(0.651689\pi\)
\(152\) 11.7929 + 20.4260i 0.956534 + 1.65677i
\(153\) 4.20975 2.38734i 0.340338 0.193005i
\(154\) 0 0
\(155\) −0.488393 0.845922i −0.0392287 0.0679461i
\(156\) 0.883928 3.24863i 0.0707708 0.260099i
\(157\) 6.10318 + 10.5710i 0.487087 + 0.843659i 0.999890 0.0148476i \(-0.00472630\pi\)
−0.512803 + 0.858506i \(0.671393\pi\)
\(158\) 4.24258 + 7.34836i 0.337521 + 0.584604i
\(159\) 12.1717 + 12.2661i 0.965282 + 0.972766i
\(160\) 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 \(0.947493\pi\)
\(164\) 5.86705 0.458139
\(165\) −0.160058 + 0.588250i −0.0124605 + 0.0457952i
\(166\) −1.28903 −0.100048
\(167\) 8.70833 15.0833i 0.673871 1.16718i −0.302927 0.953014i \(-0.597964\pi\)
0.976798 0.214165i \(-0.0687030\pi\)
\(168\) 0 0
\(169\) 3.42493 + 5.93216i 0.263456 + 0.456320i
\(170\) 0.0938145 + 0.162491i 0.00719524 + 0.0124625i
\(171\) 0.177999 23.0473i 0.0136120 1.76247i
\(172\) 2.95798 5.12337i 0.225544 0.390653i
\(173\) 1.41466 2.45027i 0.107555 0.186291i −0.807224 0.590245i \(-0.799031\pi\)
0.914779 + 0.403954i \(0.132365\pi\)
\(174\) −4.65914 + 17.1234i −0.353208 + 1.29812i
\(175\) 0 0
\(176\) 3.03370 5.25453i 0.228674 0.396075i
\(177\) 7.46916 1.97047i 0.561416 0.148110i
\(178\) −6.64946 −0.498398
\(179\) 5.08135 8.80115i 0.379798 0.657829i −0.611235 0.791449i \(-0.709327\pi\)
0.991033 + 0.133620i \(0.0426603\pi\)
\(180\) 0.00191525 0.247986i 0.000142755 0.0184838i
\(181\) 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
\(184\) −5.82439 −0.429380
\(185\) 0.104545 + 0.181078i 0.00768631 + 0.0133131i
\(186\) 4.64469 17.0703i 0.340565 1.25165i
\(187\) −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 \(-0.134086\pi\)
\(192\) −3.72723 + 13.6984i −0.268989 + 0.988596i
\(193\) 0.128393 + 0.222383i 0.00924194 + 0.0160075i 0.870609 0.491975i \(-0.163725\pi\)
−0.861367 + 0.507982i \(0.830391\pi\)
\(194\) −4.19350 −0.301076
\(195\) −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 \(0.508657\pi\)
\(198\) −9.60440 + 5.44664i −0.682555 + 0.387076i
\(199\) −2.51561 + 4.35716i −0.178327 + 0.308871i −0.941307 0.337550i \(-0.890402\pi\)
0.762981 + 0.646421i \(0.223735\pi\)
\(200\) −15.3159 −1.08300
\(201\) 16.6996 4.40561i 1.17790 0.310748i
\(202\) 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
\(206\) −4.81491 + 8.33966i −0.335470 + 0.581052i
\(207\) 4.90691 + 2.88376i 0.341054 + 0.200435i
\(208\) 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 −0.963027 0.269403i \(-0.913174\pi\)
0.714824 + 0.699305i \(0.246507\pi\)
\(212\) 7.81983 0.537068
\(213\) −1.49630 + 5.49925i −0.102525 + 0.376802i
\(214\) 20.0120 1.36799
\(215\) −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
\(219\) 5.76304 + 5.80772i 0.389430 + 0.392450i
\(220\) 0.137939 + 0.238917i 0.00929983 + 0.0161078i
\(221\) −2.00031 3.46464i −0.134555 0.233057i
\(222\) −0.994239 + 3.65405i −0.0667290 + 0.245244i
\(223\) −5.59106 9.68400i −0.374405 0.648488i 0.615833 0.787877i \(-0.288820\pi\)
−0.990238 + 0.139388i \(0.955486\pi\)
\(224\) 0 0
\(225\) 12.9033 + 7.58319i 0.860220 + 0.505546i
\(226\) −1.13395 1.96407i −0.0754295 0.130648i
\(227\) −23.7706 −1.57771 −0.788857 0.614577i \(-0.789327\pi\)
−0.788857 + 0.614577i \(0.789327\pi\)
\(228\) −7.34649 7.40345i −0.486534 0.490306i
\(229\) 1.90547 0.125917 0.0629586 0.998016i \(-0.479946\pi\)
0.0629586 + 0.998016i \(0.479946\pi\)
\(230\) −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 \(0.902075\pi\)
\(234\) 0.0633653 8.20451i 0.00414232 0.536346i
\(235\) 0.168514 0.291875i 0.0109926 0.0190398i
\(236\) 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 \(-0.0759028\pi\)
\(240\) 0.233927 + 0.235741i 0.0150999 + 0.0152170i
\(241\) 20.0662 1.29258 0.646288 0.763094i \(-0.276321\pi\)
0.646288 + 0.763094i \(0.276321\pi\)
\(242\) 0.0759124 0.131484i 0.00487983 0.00845212i
\(243\) −15.1324 + 3.74313i −0.970743 + 0.240122i
\(244\) 4.44494 0.284558
\(245\) 0 0
\(246\) 13.8250 3.64724i 0.881451 0.232540i
\(247\) −19.0526 −1.21229
\(248\) −14.2167 24.6240i −0.902758 1.56362i
\(249\) 1.95754 0.516428i 0.124054 0.0327273i
\(250\) −0.580900 + 1.00615i −0.0367394 + 0.0636344i
\(251\) 6.81467 0.430138 0.215069 0.976599i \(-0.431002\pi\)
0.215069 + 0.976599i \(0.431002\pi\)
\(252\) 0 0
\(253\) −6.33151 −0.398059
\(254\) 0.174884 0.302907i 0.0109732 0.0190061i
\(255\) −0.207568 0.209177i −0.0129984 0.0130992i
\(256\) 7.77234 + 13.4621i 0.485771 + 0.841380i
\(257\) 14.3883 0.897518 0.448759 0.893653i \(-0.351866\pi\)
0.448759 + 0.893653i \(0.351866\pi\)
\(258\) 3.78519 13.9114i 0.235656 0.866088i
\(259\) 0 0
\(260\) −0.205004 −0.0127138
\(261\) 0.215250 27.8704i 0.0133236 1.72514i
\(262\) −8.24701 + 14.2842i −0.509502 + 0.882484i
\(263\) −1.53901 −0.0948992 −0.0474496 0.998874i \(-0.515109\pi\)
−0.0474496 + 0.998874i \(0.515109\pi\)
\(264\) −4.65914 + 17.1234i −0.286750 + 1.05387i
\(265\) 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
\(269\) −13.1285 + 22.7393i −0.800461 + 1.38644i 0.118852 + 0.992912i \(0.462079\pi\)
−0.919313 + 0.393527i \(0.871255\pi\)
\(270\) −0.149647 0.585541i −0.00910724 0.0356349i
\(271\) 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
\(275\) −16.6495 −1.00400
\(276\) 2.49039 0.657001i 0.149904 0.0395468i
\(277\) −18.8713 −1.13386 −0.566932 0.823764i \(-0.691870\pi\)
−0.566932 + 0.823764i \(0.691870\pi\)
\(278\) 4.47680 + 7.75404i 0.268500 + 0.465056i
\(279\) −0.214582 + 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 \(0.880902\pi\)
\(282\) 5.90208 1.55706i 0.351464 0.0927213i
\(283\) 7.69634 + 13.3304i 0.457500 + 0.792413i 0.998828 0.0483984i \(-0.0154117\pi\)
−0.541328 + 0.840811i \(0.682078\pi\)
\(284\) 1.28952 + 2.23352i 0.0765190 + 0.132535i
\(285\) −1.35698 + 0.357992i −0.0803808 + 0.0212056i
\(286\) 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
\(290\) 1.08056 0.0634529
\(291\) 6.36832 1.68006i 0.373318 0.0984867i
\(292\) 3.70251 0.216673
\(293\) −12.9013 + 22.3456i −0.753700 + 1.30545i 0.192318 + 0.981333i \(0.438399\pi\)
−0.946018 + 0.324114i \(0.894934\pi\)
\(294\) 0 0
\(295\) −0.235182 0.407347i −0.0136928 0.0237167i
\(296\) 3.04321 + 5.27099i 0.176883 + 0.306370i
\(297\) 12.4033 12.1192i 0.719713 0.703228i
\(298\) −6.14741 + 10.6476i −0.356110 + 0.616801i
\(299\) 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
\(303\) −7.94450 + 29.1978i −0.456400 + 1.67737i
\(304\) 13.9675 0.801089
\(305\) 0.299049 0.517968i 0.0171235 0.0296588i
\(306\) 0.0412187 5.33698i 0.00235632 0.305095i
\(307\) −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
\(310\) −1.07721 −0.0611816
\(311\) 0.654931 + 1.13437i 0.0371377 + 0.0643245i 0.883997 0.467493i \(-0.154843\pi\)
−0.846859 + 0.531817i \(0.821509\pi\)
\(312\) −9.28849 9.36050i −0.525857 0.529934i
\(313\) −10.7885 + 18.6862i −0.609802 + 1.05621i 0.381471 + 0.924381i \(0.375418\pi\)
−0.991273 + 0.131827i \(0.957916\pi\)
\(314\) 13.4613 0.759667
\(315\) 0 0
\(316\) −6.03065 −0.339250
\(317\) 12.3910 21.4618i 0.695946 1.20541i −0.273915 0.961754i \(-0.588319\pi\)
0.969861 0.243660i \(-0.0783480\pi\)
\(318\) 18.4265 4.86118i 1.03331 0.272602i
\(319\) 15.5025 + 26.8512i 0.867975 + 1.50338i
\(320\) 0.864432 0.0483232
\(321\) −30.3906 + 8.01748i −1.69624 + 0.447492i
\(322\) 0 0
\(323\) −12.3936 −0.689597
\(324\) −3.62105 + 6.05393i −0.201169 + 0.336329i
\(325\) 6.18608 10.7146i 0.343142 0.594339i
\(326\) −9.88412 −0.547431
\(327\) 5.15145 + 5.19139i 0.284876 + 0.287085i
\(328\) 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 \(0.290914\pi\)
\(332\) 0.458076 0.793410i 0.0251402 0.0435440i
\(333\) 0.0459334 5.94743i 0.00251713 0.325917i
\(334\) −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 −0.816178 0.577801i \(-0.803911\pi\)
0.908479 + 0.417930i \(0.137244\pi\)
\(338\) 7.55412 0.410890
\(339\) 2.50891 + 2.52837i 0.136265 + 0.137322i
\(340\) −0.133353 −0.00723210
\(341\) −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
\(345\) 0.0909894 0.334406i 0.00489870 0.0180038i
\(346\) −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 \(0.705948\pi\)
\(348\) −8.88391 8.95279i −0.476228 0.479920i
\(349\) 7.86412 + 13.6211i 0.420957 + 0.729119i 0.996033 0.0889810i \(-0.0283610\pi\)
−0.575076 + 0.818100i \(0.695028\pi\)
\(350\) 0 0
\(351\) 3.19077 + 12.4849i 0.170311 + 0.666395i
\(352\) 6.90000 + 11.9511i 0.367771 + 0.636998i
\(353\) −4.14423 −0.220575 −0.110287 0.993900i \(-0.535177\pi\)
−0.110287 + 0.993900i \(0.535177\pi\)
\(354\) 2.23662 8.22006i 0.118875 0.436891i
\(355\) 0.347028 0.0184183
\(356\) 2.36298 4.09281i 0.125238 0.216918i
\(357\) 0 0
\(358\) −5.60378 9.70603i −0.296169 0.512979i
\(359\) −3.96994 6.87614i −0.209525 0.362909i 0.742040 0.670356i \(-0.233859\pi\)
−0.951565 + 0.307447i \(0.900525\pi\)
\(360\) −0.837436 0.492156i −0.0441367 0.0259389i
\(361\) −20.0116 + 34.6612i −1.05324 + 1.82427i
\(362\) 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
\(366\) 10.4740 2.76319i 0.547484 0.144434i
\(367\) −13.1491 −0.686377 −0.343189 0.939266i \(-0.611507\pi\)
−0.343189 + 0.939266i \(0.611507\pi\)
\(368\) −1.72459 + 2.98708i −0.0899004 + 0.155712i
\(369\) −19.5337 + 11.0775i −1.01688 + 0.576673i
\(370\) 0.230588 0.0119877
\(371\) 0 0
\(372\) 8.85636 + 8.92503i 0.459181 + 0.462741i
\(373\) 7.81086 0.404431 0.202216 0.979341i \(-0.435186\pi\)
0.202216 + 0.979341i \(0.435186\pi\)
\(374\) 2.96862 + 5.14180i 0.153504 + 0.265876i
\(375\) 0.479068 1.76068i 0.0247390 0.0909213i
\(376\) 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
\(381\) −0.144226 + 0.530064i −0.00738894 + 0.0271560i
\(382\) −12.3515 21.3934i −0.631958 1.09458i
\(383\) −10.7319 −0.548373 −0.274186 0.961677i \(-0.588408\pi\)
−0.274186 + 0.961677i \(0.588408\pi\)
\(384\) 0.938027 + 0.945300i 0.0478685 + 0.0482396i
\(385\) 0 0
\(386\) 0.283187 0.0144139
\(387\) −0.174874 + 22.6426i −0.00888935 + 1.15099i
\(388\) 1.49022 2.58114i 0.0756546 0.131038i
\(389\) 24.1468 1.22429 0.612147 0.790744i \(-0.290306\pi\)
0.612147 + 0.790744i \(0.290306\pi\)
\(390\) −0.483067 + 0.127440i −0.0244611 + 0.00645319i
\(391\) 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
\(395\) −0.405733 + 0.702750i −0.0204146 + 0.0353592i
\(396\) 0.0606053 7.84715i 0.00304553 0.394334i
\(397\) −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
\(401\) −1.56232 −0.0780183 −0.0390092 0.999239i \(-0.512420\pi\)
−0.0390092 + 0.999239i \(0.512420\pi\)
\(402\) 5.00065 18.3785i 0.249410 0.916637i
\(403\) 22.9683 1.14413
\(404\) 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
\(408\) −6.04209 6.08894i −0.299128 0.301447i
\(409\) 11.1728 + 19.3519i 0.552460 + 0.956889i 0.998096 + 0.0616748i \(0.0196442\pi\)
−0.445636 + 0.895214i \(0.647023\pi\)
\(410\) −0.435309 0.753978i −0.0214984 0.0372363i
\(411\) 6.93365 25.4827i 0.342012 1.25697i
\(412\) −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
\(416\) −10.2547 −0.502779
\(417\) −9.90506 9.98186i −0.485053 0.488814i
\(418\) 28.2755 1.38300
\(419\) 2.98648 5.17273i 0.145899 0.252704i −0.783809 0.621002i \(-0.786726\pi\)
0.929708 + 0.368298i \(0.120059\pi\)
\(420\) 0 0
\(421\) 7.31594 + 12.6716i 0.356557 + 0.617575i 0.987383 0.158349i \(-0.0506172\pi\)
−0.630826 + 0.775924i \(0.717284\pi\)
\(422\) 3.97605 + 6.88672i 0.193551 + 0.335240i
\(423\) −8.33919 + 4.72914i −0.405465 + 0.229939i
\(424\) 15.3144 26.5254i 0.743735 1.28819i
\(425\) 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
\(429\) −10.0972 10.1755i −0.487498 0.491278i
\(430\) −0.877876 −0.0423349
\(431\) 9.70169 16.8038i 0.467314 0.809411i −0.531989 0.846751i \(-0.678555\pi\)
0.999303 + 0.0373401i \(0.0118885\pi\)
\(432\) −2.33916 9.15268i −0.112543 0.440359i
\(433\) 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
\(436\) 3.30959 0.158501
\(437\) −7.28772 12.6227i −0.348619 0.603826i
\(438\) 8.72453 2.30166i 0.416874 0.109978i
\(439\) −8.67059 + 15.0179i −0.413825 + 0.716766i −0.995304 0.0967954i \(-0.969141\pi\)
0.581479 + 0.813561i \(0.302474\pi\)
\(440\) 1.08056 0.0515139
\(441\) 0 0
\(442\) −4.41194 −0.209854
\(443\) −9.80499 + 16.9827i −0.465849 + 0.806874i −0.999239 0.0389949i \(-0.987584\pi\)
0.533390 + 0.845869i \(0.320918\pi\)
\(444\) −1.89579 1.91049i −0.0899701 0.0906676i
\(445\) −0.317956 0.550716i −0.0150726 0.0261064i
\(446\) −12.3318 −0.583927
\(447\) 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 \(0.637434\pi\)
\(450\) 14.3574 8.14206i 0.676815 0.383821i
\(451\) 12.4905 21.6342i 0.588155 1.01871i
\(452\) 1.61187 0.0758160
\(453\) 5.12657 18.8413i 0.240867 0.885241i
\(454\) −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 \(0.170281\pi\)
\(458\) 1.05069 1.81985i 0.0490956 0.0850361i
\(459\) 2.07558 + 8.12134i 0.0968796 + 0.379071i
\(460\) −0.0784150 0.135819i −0.00365612 0.00633259i
\(461\) 3.99687 + 6.92279i 0.186153 + 0.322426i 0.943964 0.330047i \(-0.107065\pi\)
−0.757811 + 0.652474i \(0.773731\pi\)
\(462\) 0 0
\(463\) 5.24280 9.08080i 0.243654 0.422021i −0.718098 0.695942i \(-0.754987\pi\)
0.961752 + 0.273921i \(0.0883206\pi\)
\(464\) 16.8905 0.784120
\(465\) 1.63587 0.431568i 0.0758619 0.0200135i
\(466\) −7.21443 −0.334202
\(467\) −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
\(471\) −20.4426 + 5.39306i −0.941945 + 0.248499i
\(472\) −6.84592 11.8575i −0.315109 0.545785i
\(473\) −12.5946 21.8145i −0.579102 1.00303i
\(474\) −14.2105 + 3.74894i −0.652711 + 0.172195i
\(475\) −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
\(479\) 4.00169 0.182842 0.0914210 0.995812i \(-0.470859\pi\)
0.0914210 + 0.995812i \(0.470859\pi\)
\(480\) −0.730373 + 0.192683i −0.0333368 + 0.00879474i
\(481\) −4.91658 −0.224177
\(482\) 11.0646 19.1645i 0.503980 0.872918i
\(483\) 0 0
\(484\) 0.0539532 + 0.0934496i 0.00245242 + 0.00424771i
\(485\) −0.200520 0.347311i −0.00910514 0.0157706i
\(486\) −4.76916 + 16.5164i −0.216334 + 0.749199i
\(487\) 13.2377 22.9284i 0.599859 1.03899i −0.392982 0.919546i \(-0.628557\pi\)
0.992841 0.119440i \(-0.0381100\pi\)
\(488\) 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 \(-0.0550255\pi\)
\(492\) −2.66801 + 9.80553i −0.120283 + 0.442068i
\(493\) −14.9872 −0.674989
\(494\) −10.5057 + 18.1965i −0.472675 + 0.818697i
\(495\) −0.910349 0.535007i −0.0409172 0.0240468i
\(496\) −16.8381 −0.756052
\(497\) 0 0
\(498\) 0.586179 2.15434i 0.0262673 0.0965383i
\(499\) −7.43118 −0.332665 −0.166333 0.986070i \(-0.553193\pi\)
−0.166333 + 0.986070i \(0.553193\pi\)
\(500\) −0.412863 0.715100i −0.0184638 0.0319802i
\(501\) 21.2484 + 21.4132i 0.949310 + 0.956670i
\(502\) 3.75765 6.50845i 0.167712 0.290486i
\(503\) −10.1610 −0.453057 −0.226529 0.974004i \(-0.572738\pi\)
−0.226529 + 0.974004i \(0.572738\pi\)
\(504\) 0 0
\(505\) 1.84252 0.0819910
\(506\) −3.49124 + 6.04700i −0.155204 + 0.268822i
\(507\) −11.4718 + 3.02643i −0.509481 + 0.134409i
\(508\) 0.124295 + 0.215285i 0.00551470 + 0.00955174i
\(509\) 28.9063 1.28125 0.640625 0.767854i \(-0.278675\pi\)
0.640625 + 0.767854i \(0.278675\pi\)
\(510\) −0.314232 + 0.0828990i −0.0139144 + 0.00367083i
\(511\) 0 0
\(512\) 18.6806 0.825575
\(513\) 38.4377 + 10.7781i 1.69707 + 0.475866i
\(514\) 7.93381 13.7418i 0.349945 0.606123i
\(515\) −0.920934 −0.0405812
\(516\) 7.21750 + 7.27346i 0.317733 + 0.320196i
\(517\) 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
\(521\) 16.8995 29.2708i 0.740381 1.28238i −0.211941 0.977283i \(-0.567978\pi\)
0.952322 0.305095i \(-0.0986883\pi\)
\(522\) −26.4994 15.5735i −1.15985 0.681635i
\(523\) −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
\(527\) 14.9407 0.650828
\(528\) 7.40227 + 7.45966i 0.322143 + 0.324640i
\(529\) −19.4007 −0.843508
\(530\) −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
\(534\) 3.02381 11.1132i 0.130853 0.480914i
\(535\) 0.956910 + 1.65742i 0.0413708 + 0.0716564i
\(536\) −15.3062 26.5111i −0.661127 1.14511i
\(537\) 12.3985 + 12.4947i 0.535037 + 0.539185i
\(538\) 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 \(0.651300\pi\)
\(542\) 19.7773 0.849506
\(543\) −7.77021 + 28.5573i −0.333452 + 1.22551i
\(544\) −6.67063 −0.286001
\(545\) 0.222664 0.385666i 0.00953789 0.0165201i
\(546\) 0 0
\(547\) 1.59011 + 2.75416i 0.0679883 + 0.117759i 0.898016 0.439963i \(-0.145009\pi\)
−0.830027 + 0.557723i \(0.811675\pi\)
\(548\) −5.97545 10.3498i −0.255258 0.442121i
\(549\) −14.7989 + 8.39245i −0.631603 + 0.358181i
\(550\) −9.18062 + 15.9013i −0.391463 + 0.678034i
\(551\) −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
\(555\) −0.350174 + 0.0923811i −0.0148641 + 0.00392136i
\(556\) −6.36358 −0.269876
\(557\) −10.0229 + 17.3602i −0.424686 + 0.735577i −0.996391 0.0848820i \(-0.972949\pi\)
0.571705 + 0.820459i \(0.306282\pi\)
\(558\) 26.4172 + 15.5252i 1.11833 + 0.657236i
\(559\) 18.7181 0.791689
\(560\) 0 0
\(561\) −6.56817 6.61909i −0.277308 0.279458i
\(562\) −5.50477 −0.232205
\(563\) 19.9007 + 34.4690i 0.838713 + 1.45269i 0.890971 + 0.454060i \(0.150025\pi\)
−0.0522584 + 0.998634i \(0.516642\pi\)
\(564\) −1.13901 + 4.18611i −0.0479609 + 0.176267i
\(565\) 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 \(0.260188\pi\)
\(570\) −0.406344 + 1.49341i −0.0170199 + 0.0625519i
\(571\) −5.21935 9.04019i −0.218423 0.378320i 0.735903 0.677087i \(-0.236758\pi\)
−0.954326 + 0.298767i \(0.903425\pi\)
\(572\) −6.48703 −0.271236
\(573\) 27.3281 + 27.5400i 1.14165 + 1.15050i
\(574\) 0 0
\(575\) 9.46483 0.394711
\(576\) −21.1990 12.4585i −0.883293 0.519106i
\(577\) −12.7461 + 22.0769i −0.530628 + 0.919075i 0.468733 + 0.883340i \(0.344711\pi\)
−0.999361 + 0.0357353i \(0.988623\pi\)
\(578\) 15.8779 0.660433
\(579\) −0.430053 + 0.113454i −0.0178724 + 0.00471500i
\(580\) −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
\(584\) 7.25104 12.5592i 0.300050 0.519702i
\(585\) 0.682537 0.387066i 0.0282194 0.0160032i
\(586\) 14.2277 + 24.6431i 0.587740 + 1.01800i
\(587\) −17.5168 30.3401i −0.722998 1.25227i −0.959793 0.280709i \(-0.909430\pi\)
0.236795 0.971560i \(-0.423903\pi\)
\(588\) 0 0
\(589\) 35.5769 61.6210i 1.46592 2.53905i
\(590\) −0.518724 −0.0213555
\(591\) 0.347138 1.27581i 0.0142794 0.0524799i
\(592\) 3.60435 0.148138
\(593\) 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
\(597\) −6.13811 6.18570i −0.251216 0.253164i
\(598\) −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 \(0.517901\pi\)
\(600\) 6.96484 25.5973i 0.284338 1.04501i
\(601\) 12.8547 + 22.2650i 0.524354 + 0.908207i 0.999598 + 0.0283533i \(0.00902635\pi\)
−0.475244 + 0.879854i \(0.657640\pi\)
\(602\) 0 0
\(603\) −0.231028 + 29.9133i −0.00940817 + 1.21817i
\(604\) −4.41810 7.65238i −0.179770 0.311371i
\(605\) 0.0145196 0.000590304
\(606\) 23.5052 + 23.6874i 0.954831 + 0.962234i
\(607\) 6.84516 0.277836 0.138918 0.990304i \(-0.455638\pi\)
0.138918 + 0.990304i \(0.455638\pi\)
\(608\) −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
\(612\) 3.27031 + 1.92194i 0.132195 + 0.0776900i
\(613\) 14.5648 25.2271i 0.588269 1.01891i −0.406191 0.913788i \(-0.633143\pi\)
0.994459 0.105123i \(-0.0335235\pi\)
\(614\) −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 \(0.303323\pi\)
\(618\) −11.7484 11.8395i −0.472591 0.476255i
\(619\) −8.86355 −0.356256 −0.178128 0.984007i \(-0.557004\pi\)
−0.178128 + 0.984007i \(0.557004\pi\)
\(620\) 0.382804 0.663035i 0.0153738 0.0266281i
\(621\) −7.05099 + 6.88949i −0.282947 + 0.276466i
\(622\) 1.44453 0.0579205
\(623\) 0 0
\(624\) −7.55090 + 1.99204i −0.302278 + 0.0797453i
\(625\) 24.8333 0.993331
\(626\) 11.8977 + 20.6074i 0.475528 + 0.823638i
\(627\) −42.9397 + 11.3281i −1.71485 + 0.452402i
\(628\) −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
\(633\) −8.79714 8.86535i −0.349655 0.352366i
\(634\) −13.6649 23.6683i −0.542704 0.939990i
\(635\) 0.0334495 0.00132740
\(636\) −3.55603 + 13.0692i −0.141006 + 0.518227i
\(637\) 0 0
\(638\) 34.1928 1.35371
\(639\) −8.51040 5.00151i −0.336666 0.197857i
\(640\) 0.0405449 0.0702258i 0.00160268 0.00277592i
\(641\) −16.5319 −0.652971 −0.326486 0.945202i \(-0.605864\pi\)
−0.326486 + 0.945202i \(0.605864\pi\)
\(642\) −9.10035 + 33.4458i −0.359162 + 1.32000i
\(643\) −15.4460 + 26.7532i −0.609130 + 1.05504i 0.382254 + 0.924057i \(0.375148\pi\)
−0.991384 + 0.130987i \(0.958185\pi\)
\(644\) 0 0
\(645\) 1.33316 0.351706i 0.0524930 0.0138484i
\(646\) −6.83390 + 11.8367i −0.268876 + 0.465707i
\(647\) 0.649903 1.12567i 0.0255503 0.0442545i −0.852968 0.521964i \(-0.825200\pi\)
0.878518 + 0.477710i \(0.158533\pi\)
\(648\) 13.4438 + 24.1389i 0.528124 + 0.948267i
\(649\) −7.44198 12.8899i −0.292123 0.505972i
\(650\) −6.82209 11.8162i −0.267584 0.463470i
\(651\) 0 0
\(652\) 3.51247 6.08377i 0.137559 0.238259i
\(653\) −44.8870 −1.75656 −0.878281 0.478144i \(-0.841310\pi\)
−0.878281 + 0.478144i \(0.841310\pi\)
\(654\) 7.79866 2.05740i 0.304952 0.0804508i
\(655\) −1.57738 −0.0616335
\(656\) −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 0.986089 0.166216i \(-0.0531549\pi\)
−0.636992 + 0.770870i \(0.719822\pi\)
\(660\) −0.462026 + 0.121889i −0.0179844 + 0.00474454i
\(661\) −16.5128 28.6010i −0.642274 1.11245i −0.984924 0.172989i \(-0.944658\pi\)
0.342649 0.939463i \(-0.388676\pi\)
\(662\) 7.63429 + 13.2230i 0.296715 + 0.513925i
\(663\) 6.70004 1.76757i 0.260208 0.0686467i
\(664\) −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
\(668\) 13.6512 0.528182
\(669\) 18.7273 4.94053i 0.724038 0.191012i
\(670\) −1.15977 −0.0448058
\(671\) 9.46295 16.3903i 0.365313 0.632741i
\(672\) 0 0
\(673\) −10.6758 18.4909i −0.411520 0.712774i 0.583536 0.812087i \(-0.301669\pi\)
−0.995056 + 0.0993135i \(0.968335\pi\)
\(674\) −1.86865 3.23659i −0.0719776 0.124669i
\(675\) −18.5414 + 18.1167i −0.713660 + 0.697313i
\(676\) −2.68447 + 4.64964i −0.103249 + 0.178832i
\(677\) −4.15084 + 7.18946i −0.159530 + 0.276313i −0.934699 0.355440i \(-0.884331\pi\)
0.775170 + 0.631753i \(0.217664\pi\)
\(678\) 3.79818 1.00202i 0.145868 0.0384822i
\(679\) 0 0
\(680\) −0.261161 + 0.452344i −0.0100151 + 0.0173466i
\(681\) 10.8096 39.7276i 0.414224 1.52237i
\(682\) −34.0868 −1.30525
\(683\) −1.24728 + 2.16036i −0.0477259 + 0.0826637i −0.888902 0.458098i \(-0.848531\pi\)
0.841176 + 0.540762i \(0.181864\pi\)
\(684\) 15.7141 8.91143i 0.600843 0.340737i
\(685\) −1.60808 −0.0614414
\(686\) 0 0
\(687\) −0.866505 + 3.18460i −0.0330592 + 0.121500i
\(688\) −13.7222 −0.523154
\(689\) 12.3710 + 21.4271i 0.471296 + 0.816308i
\(690\) −0.269207 0.271295i −0.0102486 0.0103280i
\(691\) 8.43455 14.6091i 0.320865 0.555755i −0.659801 0.751440i \(-0.729360\pi\)
0.980667 + 0.195685i \(0.0626930\pi\)
\(692\) 2.21763 0.0843017
\(693\) 0 0
\(694\) 16.0071 0.607621
\(695\) −0.428132 + 0.741547i −0.0162400 + 0.0281285i
\(696\) −47.7668 + 12.6016i −1.81060 + 0.477662i
\(697\) 6.03765 + 10.4575i 0.228692 + 0.396107i
\(698\) 17.3453 0.656530
\(699\) 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 \(0.399258\pi\)
\(702\) 13.6833 + 3.83686i 0.516443 + 0.144813i
\(703\) −7.61558 + 13.1906i −0.287227 + 0.497492i
\(704\) 27.3536 1.03093
\(705\) 0.411176 + 0.414364i 0.0154858 + 0.0156058i
\(706\) −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 \(-0.0201587\pi\)
\(710\) 0.191354 0.331434i 0.00718138 0.0124385i
\(711\) 20.0784 11.3864i 0.752998 0.427024i
\(712\) −9.25539 16.0308i −0.346860 0.600780i
\(713\) 8.78551 + 15.2169i 0.329020 + 0.569879i
\(714\) 0 0
\(715\) −0.436438 + 0.755933i −0.0163219 + 0.0282703i
\(716\) 7.96554 0.297686
\(717\) 26.0434 + 26.2453i 0.972608 + 0.980149i
\(718\) −8.75620 −0.326779
\(719\) 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
\(723\) −9.12499 + 33.5364i −0.339362 + 1.24723i
\(724\) 6.69640 + 11.5985i 0.248870 + 0.431055i
\(725\) −23.1744 40.1392i −0.860675 1.49073i
\(726\) 0.185227 + 0.186663i 0.00687443 + 0.00692772i
\(727\) 13.5839 + 23.5280i 0.503799 + 0.872605i 0.999990 + 0.00439187i \(0.00139798\pi\)
−0.496192 + 0.868213i \(0.665269\pi\)
\(728\) 0 0
\(729\) 0.625513 26.9928i 0.0231672 0.999732i
\(730\) −0.274710 0.475812i −0.0101675 0.0176106i
\(731\) 12.1760 0.450344
\(732\) −2.02131 + 7.42878i −0.0747099 + 0.274576i
\(733\) −5.66614 −0.209284 −0.104642 0.994510i \(-0.533370\pi\)
−0.104642 + 0.994510i \(0.533370\pi\)
\(734\) −7.25050 + 12.5582i −0.267621 + 0.463533i
\(735\) 0 0
\(736\) −3.92249 6.79395i −0.144585 0.250428i
\(737\) −16.6389 28.8194i −0.612901 1.06158i
\(738\) −0.191259 + 24.7642i −0.00704035 + 0.911581i
\(739\) 6.80540 11.7873i 0.250341 0.433603i −0.713279 0.700880i \(-0.752791\pi\)
0.963620 + 0.267278i \(0.0861241\pi\)
\(740\) −0.0819427 + 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 \(0.241318\pi\)
\(744\) 47.6187 12.5625i 1.74579 0.460564i
\(745\) −1.17580 −0.0430779
\(746\) 4.30696 7.45988i 0.157689 0.273126i
\(747\) −0.0270812 + 3.50646i −0.000990849 + 0.128295i
\(748\) −4.21977 −0.154290
\(749\) 0 0
\(750\) −1.41740 1.42839i −0.0517563 0.0521576i
\(751\) −7.14538 −0.260739 −0.130369 0.991465i \(-0.541616\pi\)
−0.130369 + 0.991465i \(0.541616\pi\)
\(752\) −2.90488 5.03140i −0.105930 0.183476i
\(753\) −3.09894 + 11.3893i −0.112931 + 0.415048i
\(754\) −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
\(759\) 2.87922 10.5818i 0.104509 0.384094i
\(760\) 1.24376 + 2.15425i 0.0451157 + 0.0781428i
\(761\) 10.0472 0.364209 0.182104 0.983279i \(-0.441709\pi\)
0.182104 + 0.983279i \(0.441709\pi\)
\(762\) 0.426718 + 0.430027i 0.0154584 + 0.0155782i
\(763\) 0 0
\(764\) 17.5572 0.635196
\(765\) 0.443986 0.251783i 0.0160523 0.00910325i
\(766\) −5.91762 + 10.2496i −0.213812 + 0.370334i
\(767\) 11.0602 0.399361
\(768\) −26.0335 + 6.86801i −0.939402 + 0.247828i
\(769\) 16.1463 27.9663i 0.582252 1.00849i −0.412960 0.910749i \(-0.635505\pi\)
0.995212 0.0977407i \(-0.0311616\pi\)
\(770\) 0 0
\(771\) −6.54301 + 24.0470i −0.235641 + 0.866032i
\(772\) −0.100635 + 0.174305i −0.00362192 + 0.00627336i
\(773\) 24.2939 42.0783i 0.873792 1.51345i 0.0157473 0.999876i \(-0.494987\pi\)
0.858044 0.513576i \(-0.171679\pi\)
\(774\) 21.5287 + 12.6523i 0.773834 + 0.454778i
\(775\) 23.1025 + 40.0148i 0.829867 + 1.43737i
\(776\) −5.83694 10.1099i −0.209534 0.362923i
\(777\) 0 0
\(778\) 13.3147 23.0618i 0.477356 0.826806i
\(779\) 57.5075 2.06042
\(780\) 0.0932244 0.342620i 0.00333797 0.0122678i
\(781\) 10.9812 0.392938
\(782\) −1.68759 2.92299i −0.0603481 0.104526i