Properties

Label 441.2.g.h.79.8
Level $441$
Weight $2$
Character 441.79
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 79.8
Character \(\chi\) \(=\) 441.79
Dual form 441.2.g.h.67.8

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.551407 + 0.955065i 0.389903 + 0.675333i 0.992436 0.122762i \(-0.0391750\pi\)
−0.602533 + 0.798094i \(0.705842\pi\)
\(3\) 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 \(-0.507507\pi\)
−0.0235829 + 0.999722i \(0.507507\pi\)
\(6\) −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 \(-0.0549162\pi\)
−0.641248 + 0.767334i \(0.721583\pi\)
\(14\) 0 0
\(15\) −0.0479602 0.176264i −0.0123833 0.0455113i
\(16\) 0.909025 + 1.57448i 0.227256 + 0.393619i
\(17\) 0.806594 + 1.39706i 0.195628 + 0.338837i 0.947106 0.320921i \(-0.103992\pi\)
−0.751478 + 0.659758i \(0.770659\pi\)
\(18\) −2.87788 1.63204i −0.678324 0.384676i
\(19\) −3.84133 + 6.65338i −0.881262 + 1.52639i −0.0313221 + 0.999509i \(0.509972\pi\)
−0.849939 + 0.526880i \(0.823362\pi\)
\(20\) −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 −0.00682200 0.999977i \(-0.502172\pi\)
0.869416 0.494080i \(-0.164495\pi\)
\(30\) 0.141898 0.142998i 0.0259070 0.0261078i
\(31\) 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
\(33\) 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 −0.772967 0.634447i \(-0.781228\pi\)
0.935930 + 0.352186i \(0.114561\pi\)
\(38\) −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 −0.994936 0.100506i \(-0.967954\pi\)
0.410427 0.911893i \(-0.365379\pi\)
\(42\) 0 0
\(43\) −3.77388 + 6.53655i −0.575512 + 0.996815i 0.420474 + 0.907304i \(0.361864\pi\)
−0.995986 + 0.0895108i \(0.971470\pi\)
\(44\) 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 \(-0.241542\pi\)
−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
\(51\) −1.96810 + 1.98336i −0.275589 + 0.277726i
\(52\) 1.94379 0.269555
\(53\) 4.98839 + 8.64015i 0.685209 + 1.18682i 0.973371 + 0.229234i \(0.0736223\pi\)
−0.288163 + 0.957581i \(0.593044\pi\)
\(54\) 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 \(-0.739574\pi\)
0.973884 + 0.227048i \(0.0729075\pi\)
\(60\) −0.138443 0.0365232i −0.0178729 0.00471512i
\(61\) −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
\(66\) −4.49016 + 4.52497i −0.552700 + 0.556985i
\(67\) −4.98571 + 8.63550i −0.609101 + 1.05499i 0.382288 + 0.924043i \(0.375136\pi\)
−0.991389 + 0.130951i \(0.958197\pi\)
\(68\) 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 \(-0.255821\pi\)
−0.970497 + 0.241113i \(0.922488\pi\)
\(74\) 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 0.564289 0.825577i \(-0.309150\pi\)
−0.997115 + 0.0758997i \(0.975817\pi\)
\(80\) −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 \(-0.812900\pi\)
0.896316 + 0.443415i \(0.146233\pi\)
\(84\) 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 \(-0.729797\pi\)
0.980397 + 0.197031i \(0.0631299\pi\)
\(90\) 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 \(-0.771497\pi\)
0.946258 + 0.323413i \(0.104830\pi\)
\(98\) 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 \(-0.835351\pi\)
−0.869177 + 0.494501i \(0.835351\pi\)
\(102\) −2.97946 0.786025i −0.295010 0.0778280i
\(103\) 8.73204 0.860394 0.430197 0.902735i \(-0.358444\pi\)
0.430197 + 0.902735i \(0.358444\pi\)
\(104\) 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 0.0226645 0.999743i \(-0.492785\pi\)
0.854471 0.519500i \(-0.173882\pi\)
\(108\) −3.92150 + 1.09961i −0.377347 + 0.105810i
\(109\) 2.11124 + 3.65678i 0.202220 + 0.350256i 0.949243 0.314542i \(-0.101851\pi\)
−0.747023 + 0.664798i \(0.768518\pi\)
\(110\) −0.194081 0.336157i −0.0185049 0.0320514i
\(111\) 3.32025 + 0.875932i 0.315145 + 0.0831398i
\(112\) 0 0
\(113\) 1.02824 + 1.78096i 0.0967285 + 0.167539i 0.910329 0.413886i \(-0.135829\pi\)
−0.813600 + 0.581425i \(0.802495\pi\)
\(114\) −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 \(-0.273355\pi\)
0.653370 + 0.757039i \(0.273355\pi\)
\(132\) 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 \(-0.0547774\pi\)
−0.640913 + 0.767614i \(0.721444\pi\)
\(140\) 0 0
\(141\) 3.89866 3.92888i 0.328326 0.330872i
\(142\) 1.81436 + 3.14257i 0.152258 + 0.263718i
\(143\) 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 \(-0.995274\pi\)
0.512803 + 0.858506i \(0.328607\pi\)
\(158\) 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 −0.986426 0.164209i \(-0.947493\pi\)
0.635422 + 0.772165i \(0.280826\pi\)
\(164\) −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 −0.976798 0.214165i \(-0.931297\pi\)
0.302927 0.953014i \(-0.402036\pi\)
\(168\) 0 0
\(169\) 3.42493 5.93216i 0.263456 0.456320i
\(170\) 0.0938145 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 \(-0.200969\pi\)
−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
\(177\) 7.46916 + 1.97047i 0.561416 + 0.148110i
\(178\) 6.64946 0.498398
\(179\) 5.08135 + 8.80115i 0.379798 + 0.657829i 0.991033 0.133620i \(-0.0426603\pi\)
−0.611235 + 0.791449i \(0.709327\pi\)
\(180\) −0.00191525 0.247986i −0.000142755 0.0184838i
\(181\) −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
\(184\) −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 0.912582 + 0.408894i \(0.134086\pi\)
−0.102178 + 0.994766i \(0.532581\pi\)
\(192\) 3.72723 + 13.6984i 0.268989 + 0.988596i
\(193\) 0.128393 0.222383i 0.00924194 0.0160075i −0.861367 0.507982i \(-0.830391\pi\)
0.870609 + 0.491975i \(0.163725\pi\)
\(194\) 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 \(-0.109598\pi\)
−0.762981 + 0.646421i \(0.776265\pi\)
\(200\) −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 0.714824 0.699305i \(-0.246507\pi\)
−0.963027 + 0.269403i \(0.913174\pi\)
\(212\) 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 \(-0.711180\pi\)
0.990238 + 0.139388i \(0.0445137\pi\)
\(224\) 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 \(-0.210673\pi\)
0.788857 + 0.614577i \(0.210673\pi\)
\(228\) −7.34649 + 7.40345i −0.486534 + 0.490306i
\(229\) −1.90547 −0.125917 −0.0629586 0.998016i \(-0.520054\pi\)
−0.0629586 + 0.998016i \(0.520054\pi\)
\(230\) 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 −0.953051 0.302809i \(-0.902075\pi\)
0.738766 + 0.673962i \(0.235409\pi\)
\(234\) −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 0.971704 + 0.236202i \(0.0759028\pi\)
−0.281295 + 0.959621i \(0.590764\pi\)
\(240\) 0.233927 0.235741i 0.0150999 0.0152170i
\(241\) −20.0662 −1.29258 −0.646288 0.763094i \(-0.723679\pi\)
−0.646288 + 0.763094i \(0.723679\pi\)
\(242\) 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 \(-0.568998\pi\)
−0.215069 + 0.976599i \(0.568998\pi\)
\(252\) 0 0
\(253\) −6.33151 −0.398059
\(254\) 0.174884 + 0.302907i 0.0109732 + 0.0190061i
\(255\) 0.207568 0.209177i 0.0129984 0.0130992i
\(256\) 7.77234 13.4621i 0.485771 0.841380i
\(257\) −14.3883 −0.897518 −0.448759 0.893653i \(-0.648134\pi\)
−0.448759 + 0.893653i \(0.648134\pi\)
\(258\) −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 0.919313 + 0.393527i \(0.128745\pi\)
−0.118852 + 0.992912i \(0.537921\pi\)
\(270\) −0.149647 + 0.585541i −0.00910724 + 0.0356349i
\(271\) −8.96673 + 15.5308i −0.544690 + 0.943431i 0.453936 + 0.891034i \(0.350019\pi\)
−0.998626 + 0.0523969i \(0.983314\pi\)
\(272\) −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 −0.930816 0.365488i \(-0.880902\pi\)
0.781930 + 0.623366i \(0.214235\pi\)
\(282\) 5.90208 + 1.55706i 0.351464 + 0.0927213i
\(283\) −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
\(285\) 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 0.946018 + 0.324114i \(0.105066\pi\)
−0.192318 + 0.981333i \(0.561601\pi\)
\(294\) 0 0
\(295\) −0.235182 + 0.407347i −0.0136928 + 0.0237167i
\(296\) 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 \(-0.280538\pi\)
0.636120 + 0.771590i \(0.280538\pi\)
\(308\) 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 \(-0.845157\pi\)
0.846859 + 0.531817i \(0.178491\pi\)
\(312\) −9.28849 + 9.36050i −0.525857 + 0.529934i
\(313\) 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 \(0.588319\pi\)
\(318\) −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 0.610635 0.791912i \(-0.290914\pi\)
−0.991133 + 0.132870i \(0.957581\pi\)
\(332\) −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 0.908479 0.417930i \(-0.137244\pi\)
−0.816178 + 0.577801i \(0.803911\pi\)
\(338\) 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 −0.602798 0.797894i \(-0.705948\pi\)
0.992395 + 0.123091i \(0.0392809\pi\)
\(348\) 8.88391 8.95279i 0.476228 0.479920i
\(349\) −7.86412 + 13.6211i −0.420957 + 0.729119i −0.996033 0.0889810i \(-0.971639\pi\)
0.575076 + 0.818100i \(0.304972\pi\)
\(350\) 0 0
\(351\) 3.19077 12.4849i 0.170311 0.666395i
\(352\) 6.90000 11.9511i 0.367771 0.636998i
\(353\) 4.14423 0.220575 0.110287 0.993900i \(-0.464823\pi\)
0.110287 + 0.993900i \(0.464823\pi\)
\(354\) 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 −0.951565 0.307447i \(-0.900525\pi\)
0.742040 + 0.670356i \(0.233859\pi\)
\(360\) 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 \(-0.388493\pi\)
0.343189 + 0.939266i \(0.388493\pi\)
\(368\) −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 \(-0.411592\pi\)
0.274186 + 0.961677i \(0.411592\pi\)
\(384\) −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 −0.388566 0.921421i \(-0.627029\pi\)
0.992257 0.124203i \(-0.0396373\pi\)
\(398\) −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 0.445636 + 0.895214i \(0.352977\pi\)
−0.998096 + 0.0616748i \(0.980356\pi\)
\(410\) −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 \(-0.213274\pi\)
−0.929708 + 0.368298i \(0.879941\pi\)
\(420\) 0 0
\(421\) 7.31594 12.6716i 0.356557 0.617575i −0.630826 0.775924i \(-0.717284\pi\)
0.987383 + 0.158349i \(0.0506172\pi\)
\(422\) 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 0.999303 0.0373401i \(-0.0118885\pi\)
−0.531989 + 0.846751i \(0.678555\pi\)
\(432\) 2.33916 9.15268i 0.112543 0.440359i
\(433\) −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
\(436\) 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 \(-0.0308592\pi\)
−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 \(0.987584\pi\)
\(444\) 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 0.860292 0.509801i \(-0.170281\pi\)
−0.871647 + 0.490135i \(0.836948\pi\)
\(458\) −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 \(-0.892935\pi\)
0.757811 + 0.652474i \(0.226269\pi\)
\(462\) 0 0
\(463\) 5.24280 + 9.08080i 0.243654 + 0.422021i 0.961752 0.273921i \(-0.0883206\pi\)
−0.718098 + 0.695942i \(0.754987\pi\)
\(464\) 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 −0.493317 0.869849i \(-0.664216\pi\)
0.999970 0.00769944i \(-0.00245083\pi\)
\(468\) −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 \(-0.529141\pi\)
−0.0914210 + 0.995812i \(0.529141\pi\)
\(480\) −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 0.992841 + 0.119440i \(0.0381100\pi\)
−0.392982 + 0.919546i \(0.628557\pi\)
\(488\) −8.70502 15.0775i −0.394058 0.682528i
\(489\) −15.0102 3.95991i −0.678784 0.179073i
\(490\) 0 0
\(491\) 14.2149 + 24.6210i 0.641511 + 1.11113i 0.985096 + 0.172008i \(0.0550255\pi\)
−0.343584 + 0.939122i \(0.611641\pi\)
\(492\) −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 \(-0.427262\pi\)
0.226529 + 0.974004i \(0.427262\pi\)
\(504\) 0 0
\(505\) 1.84252 0.0819910
\(506\) −3.49124 6.04700i −0.155204 0.268822i
\(507\) 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 \(-0.721325\pi\)
−0.640625 + 0.767854i \(0.721325\pi\)
\(510\) 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 −0.952322 0.305095i \(-0.901312\pi\)
0.211941 0.977283i \(-0.432022\pi\)
\(522\) −26.4994 + 15.5735i −1.15985 + 0.681635i
\(523\) 7.18895 12.4516i 0.314351 0.544471i −0.664949 0.746889i \(-0.731547\pi\)
0.979299 + 0.202418i \(0.0648799\pi\)
\(524\) 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 −0.457625 0.889145i \(-0.651300\pi\)
0.998835 0.0482577i \(-0.0153669\pi\)
\(542\) −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 −0.830027 0.557723i \(-0.811675\pi\)
0.898016 + 0.439963i \(0.145009\pi\)
\(548\) −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 0.571705 0.820459i \(-0.306282\pi\)
−0.996391 + 0.0848820i \(0.972949\pi\)
\(558\) −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 0.0522584 + 0.998634i \(0.483358\pi\)
−0.890971 + 0.454060i \(0.849975\pi\)
\(564\) −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 0.684117 0.729373i \(-0.260188\pi\)
−0.973714 + 0.227776i \(0.926855\pi\)
\(570\) 0.406344 + 1.49341i 0.0170199 + 0.0625519i
\(571\) −5.21935 + 9.04019i −0.218423 + 0.378320i −0.954326 0.298767i \(-0.903425\pi\)
0.735903 + 0.677087i \(0.236758\pi\)
\(572\) 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 0.999361 + 0.0357353i \(0.0113773\pi\)
−0.468733 + 0.883340i \(0.655289\pi\)
\(578\) 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 −0.236795 0.971560i \(-0.576097\pi\)
0.959793 0.280709i \(-0.0905697\pi\)
\(588\) 0 0
\(589\) 35.5769 + 61.6210i 1.46592 + 2.53905i
\(590\) −0.518724 −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 0.209840 + 0.977736i \(0.432706\pi\)
−0.951664 + 0.307141i \(0.900628\pi\)
\(594\) 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 −0.0562080 0.998419i \(-0.517901\pi\)
0.892760 0.450532i \(-0.148766\pi\)
\(600\) −6.96484 25.5973i −0.284338 1.04501i
\(601\) −12.8547 + 22.2650i −0.524354 + 0.908207i 0.475244 + 0.879854i \(0.342360\pi\)
−0.999598 + 0.0283533i \(0.990974\pi\)
\(602\) 0 0
\(603\) −0.231028 29.9133i −0.00940817 1.21817i
\(604\) −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 \(-0.544362\pi\)
−0.138918 + 0.990304i \(0.544362\pi\)
\(608\) 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 0.994459 + 0.105123i \(0.0335235\pi\)
−0.406191 + 0.913788i \(0.633143\pi\)
\(614\) 12.2917 + 21.2898i 0.496051 + 0.859185i
\(615\) −0.963137 + 0.970604i −0.0388374 + 0.0391385i
\(616\) 0 0
\(617\) −10.3395 17.9085i −0.416252 0.720969i 0.579307 0.815109i \(-0.303323\pi\)
−0.995559 + 0.0941404i \(0.969990\pi\)
\(618\) −11.7484 + 11.8395i −0.472591 + 0.476255i
\(619\) 8.86355 0.356256 0.178128 0.984007i \(-0.442996\pi\)
0.178128 + 0.984007i \(0.442996\pi\)
\(620\) 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 0.991384 + 0.130987i \(0.0418147\pi\)
−0.382254 + 0.924057i \(0.624852\pi\)
\(644\) 0 0
\(645\) 1.33316 + 0.351706i 0.0524930 + 0.0138484i
\(646\) −6.83390 11.8367i −0.268876 0.465707i
\(647\) −0.649903 1.12567i −0.0255503 0.0442545i 0.852968 0.521964i \(-0.174800\pi\)
−0.878518 + 0.477710i \(0.841467\pi\)
\(648\) 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 −0.636992 0.770870i \(-0.719822\pi\)
0.986089 + 0.166216i \(0.0531549\pi\)
\(660\) −0.462026 0.121889i −0.0179844 0.00474454i
\(661\) 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
\(663\) −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 −0.995056 0.0993135i \(-0.968335\pi\)
0.583536 + 0.812087i \(0.301669\pi\)
\(674\) −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 \(-0.115669\pi\)
−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
\(681\) 10.8096 + 39.7276i 0.414224 + 1.52237i
\(682\) 34.0868 1.30525
\(683\) −1.24728 2.16036i −0.0477259 0.0826637i 0.841176 0.540762i \(-0.181864\pi\)
−0.888902 + 0.458098i \(0.848531\pi\)
\(684\) −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 \(-0.270640\pi\)
−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
\(696\) 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 0.997995 + 0.0632882i \(0.0201587\pi\)
−0.444188 + 0.895933i \(0.646508\pi\)
\(710\) −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 \(-0.835913\pi\)
0.861945 + 0.507002i \(0.169246\pi\)
\(720\) 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 0.496192 + 0.868213i \(0.334731\pi\)
−0.999990 + 0.00439187i \(0.998602\pi\)
\(728\) 0 0
\(729\) 0.625513 + 26.9928i 0.0231672 + 0.999732i
\(730\) −0.274710 + 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 \(-0.466630\pi\)
0.104642 + 0.994510i \(0.466630\pi\)
\(734\) 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 0.963620 0.267278i \(-0.0861241\pi\)
−0.713279 + 0.700880i \(0.752791\pi\)
\(740\) 0.0819427 + 0.141929i 0.00301227 + 0.00521741i
\(741\) −8.66407 31.8424i −0.318282 1.16976i
\(742\) 0 0
\(743\) −6.33421 10.9712i −0.232380 0.402493i 0.726128 0.687559i \(-0.241318\pi\)
−0.958508 + 0.285066i \(0.907985\pi\)
\(744\) 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 \(-0.558291\pi\)
−0.182104 + 0.983279i \(0.558291\pi\)
\(762\) −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 −0.995212 0.0977407i \(-0.968838\pi\)
0.412960 0.910749i \(-0.364495\pi\)
\(770\) 0 0
\(771\) −6.54301 24.0470i −0.235641 0.866032i
\(772\) −0.100635 0.174305i −0.00362192 0.00627336i
\(773\) −24.2939 42.0783i −0.873792 1.51345i −0.858044 0.513576i \(-0.828321\pi\)
−0.0157473 0.999876i \(-0.505013\pi\)
\(774\) 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