Properties

Label 441.4.e.z.361.6
Level $441$
Weight $4$
Character 441.361
Analytic conductor $26.020$
Analytic rank $0$
Dimension $16$
CM no
Inner twists $8$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(16\)
Relative dimension: \(8\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Defining polynomial: \(x^{16} + 74 x^{14} + 4007 x^{12} + 91050 x^{10} + 1502189 x^{8} + 12598332 x^{6} + 74261084 x^{4} + 22070000 x^{2} + 6250000\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 2^{8}\cdot 7^{4} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.6
Root \(1.68703 + 2.92202i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.4.e.z.226.6

$q$-expansion

\(f(q)\) \(=\) \(q+(0.979925 + 1.69728i) q^{2} +(2.07949 - 3.60179i) q^{4} +(5.94483 + 10.2967i) q^{5} +23.8298 q^{8} +O(q^{10})\) \(q+(0.979925 + 1.69728i) q^{2} +(2.07949 - 3.60179i) q^{4} +(5.94483 + 10.2967i) q^{5} +23.8298 q^{8} +(-11.6510 + 20.1801i) q^{10} +(18.2065 - 31.5346i) q^{11} +0.964525 q^{13} +(6.71545 + 11.6315i) q^{16} +(49.1257 - 85.0882i) q^{17} +(53.0004 + 91.7994i) q^{19} +49.4490 q^{20} +71.3640 q^{22} +(27.1816 + 47.0800i) q^{23} +(-8.18202 + 14.1717i) q^{25} +(0.945162 + 1.63707i) q^{26} -229.725 q^{29} +(-63.8645 + 110.616i) q^{31} +(82.1579 - 142.302i) q^{32} +192.558 q^{34} +(-155.908 - 270.040i) q^{37} +(-103.873 + 179.913i) q^{38} +(141.664 + 245.369i) q^{40} +419.919 q^{41} +523.180 q^{43} +(-75.7207 - 131.152i) q^{44} +(-53.2719 + 92.2697i) q^{46} +(135.164 + 234.111i) q^{47} -32.0711 q^{50} +(2.00572 - 3.47402i) q^{52} +(-125.541 + 217.443i) q^{53} +432.938 q^{55} +(-225.113 - 389.907i) q^{58} +(204.015 - 353.364i) q^{59} +(430.273 + 745.255i) q^{61} -250.329 q^{62} +429.481 q^{64} +(5.73394 + 9.93147i) q^{65} +(-253.180 + 438.520i) q^{67} +(-204.313 - 353.881i) q^{68} +523.702 q^{71} +(-314.982 + 545.565i) q^{73} +(305.556 - 529.239i) q^{74} +440.856 q^{76} +(-159.774 - 276.737i) q^{79} +(-79.8444 + 138.295i) q^{80} +(411.489 + 712.720i) q^{82} -1309.16 q^{83} +1168.18 q^{85} +(512.677 + 887.982i) q^{86} +(433.857 - 751.463i) q^{88} +(-174.290 - 301.880i) q^{89} +226.096 q^{92} +(-264.901 + 458.822i) q^{94} +(-630.157 + 1091.46i) q^{95} -161.996 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q - 68q^{4} + O(q^{10}) \) \( 16q - 68q^{4} - 804q^{16} + 1952q^{22} - 536q^{25} - 64q^{37} + 4320q^{43} + 768q^{46} - 2184q^{58} + 15176q^{64} - 5392q^{79} + 5728q^{85} - 5616q^{88} + O(q^{100}) \)

Character values

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

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

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.979925 + 1.69728i 0.346456 + 0.600079i 0.985617 0.168994i \(-0.0540517\pi\)
−0.639161 + 0.769073i \(0.720718\pi\)
\(3\) 0 0
\(4\) 2.07949 3.60179i 0.259937 0.450224i
\(5\) 5.94483 + 10.2967i 0.531722 + 0.920969i 0.999314 + 0.0370251i \(0.0117881\pi\)
−0.467593 + 0.883944i \(0.654879\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) 23.8298 1.05314
\(9\) 0 0
\(10\) −11.6510 + 20.1801i −0.368436 + 0.638150i
\(11\) 18.2065 31.5346i 0.499043 0.864367i −0.500957 0.865472i \(-0.667018\pi\)
0.999999 + 0.00110512i \(0.000351770\pi\)
\(12\) 0 0
\(13\) 0.964525 0.0205778 0.0102889 0.999947i \(-0.496725\pi\)
0.0102889 + 0.999947i \(0.496725\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 6.71545 + 11.6315i 0.104929 + 0.181742i
\(17\) 49.1257 85.0882i 0.700866 1.21394i −0.267296 0.963614i \(-0.586130\pi\)
0.968163 0.250322i \(-0.0805364\pi\)
\(18\) 0 0
\(19\) 53.0004 + 91.7994i 0.639954 + 1.10843i 0.985442 + 0.170010i \(0.0543801\pi\)
−0.345488 + 0.938423i \(0.612287\pi\)
\(20\) 49.4490 0.552856
\(21\) 0 0
\(22\) 71.3640 0.691585
\(23\) 27.1816 + 47.0800i 0.246424 + 0.426820i 0.962531 0.271171i \(-0.0874110\pi\)
−0.716107 + 0.697991i \(0.754078\pi\)
\(24\) 0 0
\(25\) −8.18202 + 14.1717i −0.0654562 + 0.113373i
\(26\) 0.945162 + 1.63707i 0.00712929 + 0.0123483i
\(27\) 0 0
\(28\) 0 0
\(29\) −229.725 −1.47099 −0.735497 0.677528i \(-0.763051\pi\)
−0.735497 + 0.677528i \(0.763051\pi\)
\(30\) 0 0
\(31\) −63.8645 + 110.616i −0.370013 + 0.640881i −0.989567 0.144073i \(-0.953980\pi\)
0.619554 + 0.784954i \(0.287313\pi\)
\(32\) 82.1579 142.302i 0.453863 0.786113i
\(33\) 0 0
\(34\) 192.558 0.971277
\(35\) 0 0
\(36\) 0 0
\(37\) −155.908 270.040i −0.692732 1.19985i −0.970939 0.239326i \(-0.923073\pi\)
0.278207 0.960521i \(-0.410260\pi\)
\(38\) −103.873 + 179.913i −0.443432 + 0.768046i
\(39\) 0 0
\(40\) 141.664 + 245.369i 0.559976 + 0.969908i
\(41\) 419.919 1.59952 0.799760 0.600320i \(-0.204960\pi\)
0.799760 + 0.600320i \(0.204960\pi\)
\(42\) 0 0
\(43\) 523.180 1.85545 0.927723 0.373270i \(-0.121763\pi\)
0.927723 + 0.373270i \(0.121763\pi\)
\(44\) −75.7207 131.152i −0.259439 0.449362i
\(45\) 0 0
\(46\) −53.2719 + 92.2697i −0.170750 + 0.295748i
\(47\) 135.164 + 234.111i 0.419483 + 0.726566i 0.995887 0.0905985i \(-0.0288780\pi\)
−0.576404 + 0.817165i \(0.695545\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) −32.0711 −0.0907107
\(51\) 0 0
\(52\) 2.00572 3.47402i 0.00534892 0.00926460i
\(53\) −125.541 + 217.443i −0.325366 + 0.563550i −0.981586 0.191019i \(-0.938821\pi\)
0.656221 + 0.754569i \(0.272154\pi\)
\(54\) 0 0
\(55\) 432.938 1.06141
\(56\) 0 0
\(57\) 0 0
\(58\) −225.113 389.907i −0.509634 0.882712i
\(59\) 204.015 353.364i 0.450177 0.779729i −0.548220 0.836334i \(-0.684694\pi\)
0.998397 + 0.0566051i \(0.0180276\pi\)
\(60\) 0 0
\(61\) 430.273 + 745.255i 0.903128 + 1.56426i 0.823411 + 0.567446i \(0.192068\pi\)
0.0797171 + 0.996818i \(0.474598\pi\)
\(62\) −250.329 −0.512772
\(63\) 0 0
\(64\) 429.481 0.838831
\(65\) 5.73394 + 9.93147i 0.0109417 + 0.0189515i
\(66\) 0 0
\(67\) −253.180 + 438.520i −0.461654 + 0.799609i −0.999044 0.0437257i \(-0.986077\pi\)
0.537389 + 0.843334i \(0.319411\pi\)
\(68\) −204.313 353.881i −0.364362 0.631093i
\(69\) 0 0
\(70\) 0 0
\(71\) 523.702 0.875380 0.437690 0.899126i \(-0.355797\pi\)
0.437690 + 0.899126i \(0.355797\pi\)
\(72\) 0 0
\(73\) −314.982 + 545.565i −0.505012 + 0.874706i 0.494972 + 0.868909i \(0.335178\pi\)
−0.999983 + 0.00579655i \(0.998155\pi\)
\(74\) 305.556 529.239i 0.480002 0.831388i
\(75\) 0 0
\(76\) 440.856 0.665391
\(77\) 0 0
\(78\) 0 0
\(79\) −159.774 276.737i −0.227544 0.394118i 0.729535 0.683943i \(-0.239736\pi\)
−0.957080 + 0.289825i \(0.906403\pi\)
\(80\) −79.8444 + 138.295i −0.111586 + 0.193273i
\(81\) 0 0
\(82\) 411.489 + 712.720i 0.554163 + 0.959838i
\(83\) −1309.16 −1.73131 −0.865654 0.500643i \(-0.833097\pi\)
−0.865654 + 0.500643i \(0.833097\pi\)
\(84\) 0 0
\(85\) 1168.18 1.49066
\(86\) 512.677 + 887.982i 0.642830 + 1.11341i
\(87\) 0 0
\(88\) 433.857 751.463i 0.525561 0.910298i
\(89\) −174.290 301.880i −0.207581 0.359542i 0.743371 0.668880i \(-0.233226\pi\)
−0.950952 + 0.309338i \(0.899893\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 226.096 0.256219
\(93\) 0 0
\(94\) −264.901 + 458.822i −0.290665 + 0.503446i
\(95\) −630.157 + 1091.46i −0.680555 + 1.17876i
\(96\) 0 0
\(97\) −161.996 −0.169569 −0.0847844 0.996399i \(-0.527020\pi\)
−0.0847844 + 0.996399i \(0.527020\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 34.0289 + 58.9399i 0.0340289 + 0.0589399i
\(101\) −109.171 + 189.090i −0.107554 + 0.186289i −0.914779 0.403955i \(-0.867635\pi\)
0.807225 + 0.590244i \(0.200968\pi\)
\(102\) 0 0
\(103\) 115.545 + 200.130i 0.110534 + 0.191451i 0.915986 0.401211i \(-0.131411\pi\)
−0.805452 + 0.592661i \(0.798077\pi\)
\(104\) 22.9844 0.0216712
\(105\) 0 0
\(106\) −492.083 −0.450899
\(107\) −932.562 1615.25i −0.842563 1.45936i −0.887721 0.460381i \(-0.847713\pi\)
0.0451586 0.998980i \(-0.485621\pi\)
\(108\) 0 0
\(109\) −300.502 + 520.485i −0.264063 + 0.457371i −0.967318 0.253567i \(-0.918396\pi\)
0.703255 + 0.710938i \(0.251729\pi\)
\(110\) 424.247 + 734.818i 0.367731 + 0.636928i
\(111\) 0 0
\(112\) 0 0
\(113\) 475.349 0.395727 0.197863 0.980230i \(-0.436600\pi\)
0.197863 + 0.980230i \(0.436600\pi\)
\(114\) 0 0
\(115\) −323.180 + 559.765i −0.262058 + 0.453899i
\(116\) −477.711 + 827.420i −0.382365 + 0.662276i
\(117\) 0 0
\(118\) 799.676 0.623865
\(119\) 0 0
\(120\) 0 0
\(121\) 2.54607 + 4.40992i 0.00191290 + 0.00331324i
\(122\) −843.270 + 1460.59i −0.625788 + 1.08390i
\(123\) 0 0
\(124\) 265.612 + 460.053i 0.192360 + 0.333177i
\(125\) 1291.64 0.924226
\(126\) 0 0
\(127\) −29.0876 −0.0203237 −0.0101619 0.999948i \(-0.503235\pi\)
−0.0101619 + 0.999948i \(0.503235\pi\)
\(128\) −236.404 409.463i −0.163245 0.282748i
\(129\) 0 0
\(130\) −11.2377 + 19.4642i −0.00758160 + 0.0131317i
\(131\) −1057.63 1831.87i −0.705387 1.22177i −0.966552 0.256472i \(-0.917440\pi\)
0.261164 0.965294i \(-0.415894\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) −992.389 −0.639771
\(135\) 0 0
\(136\) 1170.65 2027.63i 0.738109 1.27844i
\(137\) 88.6708 153.582i 0.0552968 0.0957768i −0.837052 0.547123i \(-0.815723\pi\)
0.892349 + 0.451347i \(0.149056\pi\)
\(138\) 0 0
\(139\) −2369.18 −1.44569 −0.722846 0.691009i \(-0.757166\pi\)
−0.722846 + 0.691009i \(0.757166\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 513.189 + 888.869i 0.303281 + 0.525297i
\(143\) 17.5606 30.4159i 0.0102692 0.0177868i
\(144\) 0 0
\(145\) −1365.67 2365.42i −0.782159 1.35474i
\(146\) −1234.63 −0.699857
\(147\) 0 0
\(148\) −1296.84 −0.720266
\(149\) 745.517 + 1291.27i 0.409900 + 0.709968i 0.994878 0.101081i \(-0.0322301\pi\)
−0.584978 + 0.811049i \(0.698897\pi\)
\(150\) 0 0
\(151\) −205.230 + 355.469i −0.110605 + 0.191574i −0.916014 0.401145i \(-0.868612\pi\)
0.805409 + 0.592719i \(0.201946\pi\)
\(152\) 1262.99 + 2187.56i 0.673960 + 1.16733i
\(153\) 0 0
\(154\) 0 0
\(155\) −1518.65 −0.786975
\(156\) 0 0
\(157\) 226.750 392.743i 0.115265 0.199645i −0.802621 0.596490i \(-0.796562\pi\)
0.917886 + 0.396845i \(0.129895\pi\)
\(158\) 313.133 542.363i 0.157668 0.273089i
\(159\) 0 0
\(160\) 1953.66 0.965314
\(161\) 0 0
\(162\) 0 0
\(163\) −374.083 647.931i −0.179757 0.311349i 0.762040 0.647530i \(-0.224198\pi\)
−0.941797 + 0.336181i \(0.890865\pi\)
\(164\) 873.219 1512.46i 0.415774 0.720142i
\(165\) 0 0
\(166\) −1282.87 2222.00i −0.599821 1.03892i
\(167\) 518.269 0.240149 0.120074 0.992765i \(-0.461687\pi\)
0.120074 + 0.992765i \(0.461687\pi\)
\(168\) 0 0
\(169\) −2196.07 −0.999577
\(170\) 1144.72 + 1982.72i 0.516449 + 0.894516i
\(171\) 0 0
\(172\) 1087.95 1884.38i 0.482299 0.835366i
\(173\) −656.742 1137.51i −0.288620 0.499904i 0.684861 0.728674i \(-0.259863\pi\)
−0.973480 + 0.228770i \(0.926530\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 489.060 0.209456
\(177\) 0 0
\(178\) 341.583 591.639i 0.143836 0.249131i
\(179\) 2066.57 3579.41i 0.862921 1.49462i −0.00617538 0.999981i \(-0.501966\pi\)
0.869097 0.494642i \(-0.164701\pi\)
\(180\) 0 0
\(181\) −3714.04 −1.52521 −0.762603 0.646867i \(-0.776079\pi\)
−0.762603 + 0.646867i \(0.776079\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 647.733 + 1121.91i 0.259519 + 0.449500i
\(185\) 1853.69 3210.69i 0.736682 1.27597i
\(186\) 0 0
\(187\) −1788.81 3098.32i −0.699524 1.21161i
\(188\) 1124.29 0.436156
\(189\) 0 0
\(190\) −2470.03 −0.943129
\(191\) −1534.19 2657.29i −0.581203 1.00667i −0.995337 0.0964578i \(-0.969249\pi\)
0.414134 0.910216i \(-0.364085\pi\)
\(192\) 0 0
\(193\) −1044.77 + 1809.59i −0.389657 + 0.674906i −0.992403 0.123027i \(-0.960740\pi\)
0.602746 + 0.797933i \(0.294073\pi\)
\(194\) −158.744 274.952i −0.0587481 0.101755i
\(195\) 0 0
\(196\) 0 0
\(197\) 3729.89 1.34895 0.674476 0.738297i \(-0.264370\pi\)
0.674476 + 0.738297i \(0.264370\pi\)
\(198\) 0 0
\(199\) 1054.42 1826.31i 0.375608 0.650573i −0.614809 0.788676i \(-0.710767\pi\)
0.990418 + 0.138103i \(0.0441004\pi\)
\(200\) −194.976 + 337.708i −0.0689344 + 0.119398i
\(201\) 0 0
\(202\) −427.918 −0.149051
\(203\) 0 0
\(204\) 0 0
\(205\) 2496.35 + 4323.80i 0.850499 + 1.47311i
\(206\) −226.451 + 392.225i −0.0765903 + 0.132658i
\(207\) 0 0
\(208\) 6.47722 + 11.2189i 0.00215920 + 0.00373985i
\(209\) 3859.81 1.27746
\(210\) 0 0
\(211\) −1546.53 −0.504584 −0.252292 0.967651i \(-0.581184\pi\)
−0.252292 + 0.967651i \(0.581184\pi\)
\(212\) 522.124 + 904.345i 0.169149 + 0.292975i
\(213\) 0 0
\(214\) 1827.68 3165.64i 0.583821 1.01121i
\(215\) 3110.22 + 5387.05i 0.986581 + 1.70881i
\(216\) 0 0
\(217\) 0 0
\(218\) −1177.88 −0.365945
\(219\) 0 0
\(220\) 900.293 1559.35i 0.275899 0.477871i
\(221\) 47.3829 82.0697i 0.0144223 0.0249801i
\(222\) 0 0
\(223\) −4860.40 −1.45954 −0.729768 0.683695i \(-0.760372\pi\)
−0.729768 + 0.683695i \(0.760372\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 465.807 + 806.801i 0.137102 + 0.237467i
\(227\) −350.471 + 607.034i −0.102474 + 0.177490i −0.912703 0.408623i \(-0.866009\pi\)
0.810229 + 0.586113i \(0.199342\pi\)
\(228\) 0 0
\(229\) −1847.12 3199.30i −0.533018 0.923214i −0.999256 0.0385550i \(-0.987725\pi\)
0.466239 0.884659i \(-0.345609\pi\)
\(230\) −1266.77 −0.363167
\(231\) 0 0
\(232\) −5474.29 −1.54916
\(233\) 172.161 + 298.192i 0.0484062 + 0.0838420i 0.889213 0.457493i \(-0.151252\pi\)
−0.840807 + 0.541335i \(0.817919\pi\)
\(234\) 0 0
\(235\) −1607.06 + 2783.50i −0.446097 + 0.772662i
\(236\) −848.494 1469.64i −0.234035 0.405361i
\(237\) 0 0
\(238\) 0 0
\(239\) −6144.21 −1.66291 −0.831456 0.555590i \(-0.812492\pi\)
−0.831456 + 0.555590i \(0.812492\pi\)
\(240\) 0 0
\(241\) −2813.06 + 4872.36i −0.751888 + 1.30231i 0.195019 + 0.980799i \(0.437523\pi\)
−0.946907 + 0.321508i \(0.895810\pi\)
\(242\) −4.98991 + 8.64277i −0.00132547 + 0.00229578i
\(243\) 0 0
\(244\) 3579.00 0.939025
\(245\) 0 0
\(246\) 0 0
\(247\) 51.1202 + 88.5429i 0.0131688 + 0.0228091i
\(248\) −1521.88 + 2635.97i −0.389674 + 0.674936i
\(249\) 0 0
\(250\) 1265.71 + 2192.28i 0.320203 + 0.554608i
\(251\) −520.460 −0.130881 −0.0654405 0.997856i \(-0.520845\pi\)
−0.0654405 + 0.997856i \(0.520845\pi\)
\(252\) 0 0
\(253\) 1979.53 0.491905
\(254\) −28.5037 49.3699i −0.00704127 0.0121958i
\(255\) 0 0
\(256\) 2181.24 3778.02i 0.532530 0.922368i
\(257\) −2004.75 3472.33i −0.486587 0.842794i 0.513294 0.858213i \(-0.328425\pi\)
−0.999881 + 0.0154192i \(0.995092\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) 47.6948 0.0113766
\(261\) 0 0
\(262\) 2072.80 3590.20i 0.488771 0.846576i
\(263\) −1792.60 + 3104.87i −0.420290 + 0.727963i −0.995968 0.0897135i \(-0.971405\pi\)
0.575678 + 0.817677i \(0.304738\pi\)
\(264\) 0 0
\(265\) −2985.28 −0.692016
\(266\) 0 0
\(267\) 0 0
\(268\) 1052.97 + 1823.80i 0.240002 + 0.415695i
\(269\) −2754.59 + 4771.10i −0.624352 + 1.08141i 0.364314 + 0.931276i \(0.381303\pi\)
−0.988666 + 0.150133i \(0.952030\pi\)
\(270\) 0 0
\(271\) −2909.95 5040.18i −0.652276 1.12977i −0.982569 0.185896i \(-0.940481\pi\)
0.330294 0.943878i \(-0.392852\pi\)
\(272\) 1319.60 0.294165
\(273\) 0 0
\(274\) 347.563 0.0766316
\(275\) 297.932 + 516.034i 0.0653308 + 0.113156i
\(276\) 0 0
\(277\) 575.226 996.320i 0.124772 0.216112i −0.796872 0.604149i \(-0.793513\pi\)
0.921644 + 0.388037i \(0.126847\pi\)
\(278\) −2321.62 4021.16i −0.500868 0.867529i
\(279\) 0 0
\(280\) 0 0
\(281\) 895.631 0.190138 0.0950692 0.995471i \(-0.469693\pi\)
0.0950692 + 0.995471i \(0.469693\pi\)
\(282\) 0 0
\(283\) 61.2251 106.045i 0.0128603 0.0222746i −0.859524 0.511096i \(-0.829240\pi\)
0.872384 + 0.488821i \(0.162573\pi\)
\(284\) 1089.04 1886.27i 0.227544 0.394117i
\(285\) 0 0
\(286\) 68.8324 0.0142313
\(287\) 0 0
\(288\) 0 0
\(289\) −2370.16 4105.24i −0.482427 0.835588i
\(290\) 2676.52 4635.86i 0.541967 0.938715i
\(291\) 0 0
\(292\) 1310.01 + 2269.00i 0.262542 + 0.454736i
\(293\) −7601.77 −1.51570 −0.757850 0.652429i \(-0.773750\pi\)
−0.757850 + 0.652429i \(0.773750\pi\)
\(294\) 0 0
\(295\) 4851.33 0.957475
\(296\) −3715.25 6435.01i −0.729543 1.26360i
\(297\) 0 0
\(298\) −1461.10 + 2530.70i −0.284025 + 0.491945i
\(299\) 26.2174 + 45.4098i 0.00507087 + 0.00878300i
\(300\) 0 0
\(301\) 0 0
\(302\) −804.441 −0.153279
\(303\) 0 0
\(304\) −711.844 + 1232.95i −0.134299 + 0.232613i
\(305\) −5115.80 + 8860.82i −0.960426 + 1.66351i
\(306\) 0 0
\(307\) 3539.05 0.657929 0.328964 0.944342i \(-0.393300\pi\)
0.328964 + 0.944342i \(0.393300\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1488.17 2577.58i −0.272652 0.472247i
\(311\) 1947.47 3373.11i 0.355083 0.615021i −0.632049 0.774928i \(-0.717786\pi\)
0.987132 + 0.159907i \(0.0511194\pi\)
\(312\) 0 0
\(313\) 4341.29 + 7519.33i 0.783975 + 1.35788i 0.929610 + 0.368546i \(0.120144\pi\)
−0.145635 + 0.989338i \(0.546522\pi\)
\(314\) 888.792 0.159737
\(315\) 0 0
\(316\) −1329.00 −0.236589
\(317\) 4247.76 + 7357.34i 0.752612 + 1.30356i 0.946553 + 0.322549i \(0.104540\pi\)
−0.193941 + 0.981013i \(0.562127\pi\)
\(318\) 0 0
\(319\) −4182.48 + 7244.28i −0.734088 + 1.27148i
\(320\) 2553.19 + 4422.26i 0.446025 + 0.772537i
\(321\) 0 0
\(322\) 0 0
\(323\) 10414.7 1.79409
\(324\) 0 0
\(325\) −7.89177 + 13.6689i −0.00134694 + 0.00233297i
\(326\) 733.147 1269.85i 0.124556 0.215737i
\(327\) 0 0
\(328\) 10006.6 1.68451
\(329\) 0 0
\(330\) 0 0
\(331\) −635.355 1100.47i −0.105505 0.182741i 0.808439 0.588580i \(-0.200313\pi\)
−0.913945 + 0.405839i \(0.866979\pi\)
\(332\) −2722.38 + 4715.30i −0.450031 + 0.779476i
\(333\) 0 0
\(334\) 507.865 + 879.647i 0.0832010 + 0.144108i
\(335\) −6020.44 −0.981886
\(336\) 0 0
\(337\) 4695.47 0.758986 0.379493 0.925195i \(-0.376098\pi\)
0.379493 + 0.925195i \(0.376098\pi\)
\(338\) −2151.98 3727.34i −0.346309 0.599825i
\(339\) 0 0
\(340\) 2429.21 4207.52i 0.387478 0.671132i
\(341\) 2325.50 + 4027.88i 0.369304 + 0.639654i
\(342\) 0 0
\(343\) 0 0
\(344\) 12467.3 1.95404
\(345\) 0 0
\(346\) 1287.12 2229.35i 0.199988 0.346389i
\(347\) 3256.98 5641.26i 0.503874 0.872735i −0.496116 0.868256i \(-0.665241\pi\)
0.999990 0.00447854i \(-0.00142557\pi\)
\(348\) 0 0
\(349\) −7184.75 −1.10198 −0.550990 0.834512i \(-0.685750\pi\)
−0.550990 + 0.834512i \(0.685750\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2991.62 5181.63i −0.452994 0.784608i
\(353\) −3034.27 + 5255.52i −0.457502 + 0.792416i −0.998828 0.0483961i \(-0.984589\pi\)
0.541326 + 0.840813i \(0.317922\pi\)
\(354\) 0 0
\(355\) 3113.32 + 5392.43i 0.465459 + 0.806198i
\(356\) −1449.74 −0.215832
\(357\) 0 0
\(358\) 8100.34 1.19586
\(359\) 871.857 + 1510.10i 0.128175 + 0.222006i 0.922970 0.384873i \(-0.125755\pi\)
−0.794795 + 0.606879i \(0.792421\pi\)
\(360\) 0 0
\(361\) −2188.59 + 3790.75i −0.319083 + 0.552668i
\(362\) −3639.48 6303.76i −0.528416 0.915244i
\(363\) 0 0
\(364\) 0 0
\(365\) −7490.06 −1.07410
\(366\) 0 0
\(367\) −4500.06 + 7794.33i −0.640058 + 1.10861i 0.345361 + 0.938470i \(0.387756\pi\)
−0.985419 + 0.170143i \(0.945577\pi\)
\(368\) −365.074 + 632.326i −0.0517141 + 0.0895714i
\(369\) 0 0
\(370\) 7265.91 1.02091
\(371\) 0 0
\(372\) 0 0
\(373\) −2635.88 4565.47i −0.365899 0.633757i 0.623021 0.782205i \(-0.285905\pi\)
−0.988920 + 0.148449i \(0.952572\pi\)
\(374\) 3505.81 6072.24i 0.484708 0.839540i
\(375\) 0 0
\(376\) 3220.93 + 5578.82i 0.441774 + 0.765174i
\(377\) −221.575 −0.0302698
\(378\) 0 0
\(379\) 10480.0 1.42037 0.710185 0.704015i \(-0.248611\pi\)
0.710185 + 0.704015i \(0.248611\pi\)
\(380\) 2620.82 + 4539.39i 0.353803 + 0.612804i
\(381\) 0 0
\(382\) 3006.78 5207.89i 0.402723 0.697536i
\(383\) −687.014 1189.94i −0.0916574 0.158755i 0.816551 0.577273i \(-0.195883\pi\)
−0.908209 + 0.418518i \(0.862550\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −4095.17 −0.539996
\(387\) 0 0
\(388\) −336.869 + 583.475i −0.0440772 + 0.0763439i
\(389\) 949.135 1643.95i 0.123710 0.214271i −0.797518 0.603295i \(-0.793854\pi\)
0.921228 + 0.389024i \(0.127188\pi\)
\(390\) 0 0
\(391\) 5341.26 0.690842
\(392\) 0 0
\(393\) 0 0
\(394\) 3655.01 + 6330.66i 0.467352 + 0.809478i
\(395\) 1899.66 3290.31i 0.241980 0.419123i
\(396\) 0 0
\(397\) 2786.15 + 4825.75i 0.352224 + 0.610070i 0.986639 0.162923i \(-0.0520922\pi\)
−0.634415 + 0.772993i \(0.718759\pi\)
\(398\) 4133.02 0.520527
\(399\) 0 0
\(400\) −219.784 −0.0274730
\(401\) −2858.19 4950.53i −0.355938 0.616503i 0.631340 0.775506i \(-0.282505\pi\)
−0.987278 + 0.159003i \(0.949172\pi\)
\(402\) 0 0
\(403\) −61.5989 + 106.692i −0.00761404 + 0.0131879i
\(404\) 454.042 + 786.423i 0.0559144 + 0.0968466i
\(405\) 0 0
\(406\) 0 0
\(407\) −11354.2 −1.38281
\(408\) 0 0
\(409\) −5174.27 + 8962.09i −0.625553 + 1.08349i 0.362881 + 0.931835i \(0.381793\pi\)
−0.988434 + 0.151653i \(0.951540\pi\)
\(410\) −4892.46 + 8474.00i −0.589321 + 1.02073i
\(411\) 0 0
\(412\) 961.103 0.114927
\(413\) 0 0
\(414\) 0 0
\(415\) −7782.71 13480.0i −0.920574 1.59448i
\(416\) 79.2433 137.253i 0.00933948 0.0161765i
\(417\) 0 0
\(418\) 3782.33 + 6551.18i 0.442583 + 0.766576i
\(419\) 3251.80 0.379142 0.189571 0.981867i \(-0.439290\pi\)
0.189571 + 0.981867i \(0.439290\pi\)
\(420\) 0 0
\(421\) 3708.63 0.429329 0.214664 0.976688i \(-0.431134\pi\)
0.214664 + 0.976688i \(0.431134\pi\)
\(422\) −1515.48 2624.89i −0.174816 0.302790i
\(423\) 0 0
\(424\) −2991.62 + 5181.63i −0.342655 + 0.593496i
\(425\) 803.895 + 1392.39i 0.0917521 + 0.158919i
\(426\) 0 0
\(427\) 0 0
\(428\) −7757.03 −0.876052
\(429\) 0 0
\(430\) −6095.55 + 10557.8i −0.683613 + 1.18405i
\(431\) 2074.37 3592.92i 0.231831 0.401542i −0.726516 0.687149i \(-0.758862\pi\)
0.958347 + 0.285607i \(0.0921952\pi\)
\(432\) 0 0
\(433\) 1985.64 0.220378 0.110189 0.993911i \(-0.464854\pi\)
0.110189 + 0.993911i \(0.464854\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1249.79 + 2164.69i 0.137280 + 0.237775i
\(437\) −2881.28 + 4990.52i −0.315401 + 0.546290i
\(438\) 0 0
\(439\) 3457.21 + 5988.07i 0.375863 + 0.651013i 0.990456 0.137831i \(-0.0440131\pi\)
−0.614593 + 0.788844i \(0.710680\pi\)
\(440\) 10316.8 1.11781
\(441\) 0 0
\(442\) 185.727 0.0199867
\(443\) 2118.73 + 3669.76i 0.227233 + 0.393579i 0.956987 0.290131i \(-0.0936989\pi\)
−0.729754 + 0.683710i \(0.760366\pi\)
\(444\) 0 0
\(445\) 2072.25 3589.25i 0.220751 0.382352i
\(446\) −4762.82 8249.45i −0.505664 0.875836i
\(447\) 0 0
\(448\) 0 0
\(449\) 2097.02 0.220411 0.110206 0.993909i \(-0.464849\pi\)
0.110206 + 0.993909i \(0.464849\pi\)
\(450\) 0 0
\(451\) 7645.26 13242.0i 0.798228 1.38257i
\(452\) 988.487 1712.11i 0.102864 0.178166i
\(453\) 0 0
\(454\) −1373.74 −0.142011
\(455\) 0 0
\(456\) 0 0
\(457\) 9338.14 + 16174.1i 0.955842 + 1.65557i 0.732429 + 0.680844i \(0.238387\pi\)
0.223414 + 0.974724i \(0.428280\pi\)
\(458\) 3620.08 6270.16i 0.369334 0.639706i
\(459\) 0 0
\(460\) 1344.10 + 2328.06i 0.136237 + 0.235970i
\(461\) 13879.5 1.40224 0.701121 0.713043i \(-0.252683\pi\)
0.701121 + 0.713043i \(0.252683\pi\)
\(462\) 0 0
\(463\) 4780.89 0.479885 0.239942 0.970787i \(-0.422871\pi\)
0.239942 + 0.970787i \(0.422871\pi\)
\(464\) −1542.70 2672.04i −0.154350 0.267342i
\(465\) 0 0
\(466\) −337.410 + 584.411i −0.0335412 + 0.0580951i
\(467\) 4188.09 + 7253.99i 0.414993 + 0.718789i 0.995428 0.0955176i \(-0.0304506\pi\)
−0.580435 + 0.814307i \(0.697117\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −6299.17 −0.618211
\(471\) 0 0
\(472\) 4861.62 8420.58i 0.474098 0.821162i
\(473\) 9525.28 16498.3i 0.925947 1.60379i
\(474\) 0 0
\(475\) −1734.60 −0.167556
\(476\) 0 0
\(477\) 0 0
\(478\) −6020.87 10428.4i −0.576126 0.997879i
\(479\) −8505.68 + 14732.3i −0.811346 + 1.40529i 0.100577 + 0.994929i \(0.467931\pi\)
−0.911922 + 0.410363i \(0.865402\pi\)
\(480\) 0 0
\(481\) −150.377 260.461i −0.0142549 0.0246902i
\(482\) −11026.3 −1.04198
\(483\) 0 0
\(484\) 21.1781 0.00198893
\(485\) −963.037 1668.03i −0.0901635 0.156168i
\(486\) 0 0
\(487\) −3008.83 + 5211.44i −0.279965 + 0.484913i −0.971376 0.237548i \(-0.923656\pi\)
0.691411 + 0.722462i \(0.256990\pi\)
\(488\) 10253.3 + 17759.3i 0.951118 + 1.64739i
\(489\) 0 0
\(490\) 0 0
\(491\) 12306.6 1.13113 0.565567 0.824702i \(-0.308657\pi\)
0.565567 + 0.824702i \(0.308657\pi\)
\(492\) 0 0
\(493\) −11285.4 + 19546.9i −1.03097 + 1.78569i
\(494\) −100.188 + 173.531i −0.00912484 + 0.0158047i
\(495\) 0 0
\(496\) −1715.51 −0.155300
\(497\) 0 0
\(498\) 0 0
\(499\) −4282.96 7418.31i −0.384232 0.665509i 0.607430 0.794373i \(-0.292200\pi\)
−0.991662 + 0.128864i \(0.958867\pi\)
\(500\) 2685.97 4652.23i 0.240240 0.416108i
\(501\) 0 0
\(502\) −510.012 883.366i −0.0453445 0.0785390i
\(503\) 10520.4 0.932568 0.466284 0.884635i \(-0.345592\pi\)
0.466284 + 0.884635i \(0.345592\pi\)
\(504\) 0 0
\(505\) −2596.02 −0.228755
\(506\) 1939.79 + 3359.82i 0.170423 + 0.295182i
\(507\) 0 0
\(508\) −60.4876 + 104.768i −0.00528288 + 0.00915022i
\(509\) 2722.71 + 4715.86i 0.237096 + 0.410662i 0.959880 0.280412i \(-0.0904711\pi\)
−0.722784 + 0.691074i \(0.757138\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) 4767.35 0.411502
\(513\) 0 0
\(514\) 3929.01 6805.24i 0.337162 0.583981i
\(515\) −1373.79 + 2379.48i −0.117547 + 0.203597i
\(516\) 0 0
\(517\) 9843.46 0.837360
\(518\) 0 0
\(519\) 0 0
\(520\) 136.639 + 236.665i 0.0115231 + 0.0199585i
\(521\) 11108.9 19241.3i 0.934149 1.61799i 0.158005 0.987438i \(-0.449494\pi\)
0.776144 0.630555i \(-0.217173\pi\)
\(522\) 0 0
\(523\) −11054.9 19147.7i −0.924281 1.60090i −0.792713 0.609595i \(-0.791332\pi\)
−0.131568 0.991307i \(-0.542001\pi\)
\(524\) −8797.36 −0.733425
\(525\) 0 0
\(526\) −7026.44 −0.582447
\(527\) 6274.77 + 10868.2i 0.518659 + 0.898344i
\(528\) 0 0
\(529\) 4605.82 7977.51i 0.378550 0.655668i
\(530\) −2925.35 5066.86i −0.239753 0.415265i
\(531\) 0 0
\(532\) 0 0
\(533\) 405.022 0.0329146
\(534\) 0 0
\(535\) 11087.8 19204.7i 0.896018 1.55195i
\(536\) −6033.22 + 10449.8i −0.486186 + 0.842098i
\(537\) 0 0
\(538\) −10797.2 −0.865241
\(539\) 0 0
\(540\) 0 0
\(541\) 4315.67 + 7474.96i 0.342967 + 0.594036i 0.984982 0.172656i \(-0.0552348\pi\)
−0.642015 + 0.766692i \(0.721901\pi\)
\(542\) 5703.06 9877.99i 0.451969 0.782834i
\(543\) 0 0
\(544\) −8072.12 13981.3i −0.636194 1.10192i
\(545\) −7145.74 −0.561633
\(546\) 0 0
\(547\) −17846.7 −1.39501 −0.697505 0.716580i \(-0.745707\pi\)
−0.697505 + 0.716580i \(0.745707\pi\)
\(548\) −368.781 638.747i −0.0287473 0.0497918i
\(549\) 0 0
\(550\) −583.902 + 1011.35i −0.0452685 + 0.0784073i
\(551\) −12175.5 21088.6i −0.941369 1.63050i
\(552\) 0 0
\(553\) 0 0
\(554\) 2254.71 0.172913
\(555\) 0 0
\(556\) −4926.70 + 8533.29i −0.375789 + 0.650885i
\(557\) 7851.64 13599.4i 0.597279 1.03452i −0.395942 0.918276i \(-0.629582\pi\)
0.993221 0.116242i \(-0.0370849\pi\)
\(558\) 0 0
\(559\) 504.620 0.0381810
\(560\) 0 0
\(561\) 0 0
\(562\) 877.651 + 1520.14i 0.0658745 + 0.114098i
\(563\) −336.839 + 583.423i −0.0252151 + 0.0436738i −0.878358 0.478004i \(-0.841360\pi\)
0.853143 + 0.521678i \(0.174694\pi\)
\(564\) 0 0
\(565\) 2825.87 + 4894.55i 0.210417 + 0.364452i
\(566\) 239.984 0.0178221
\(567\) 0 0
\(568\) 12479.7 0.921896
\(569\) −7593.10 13151.6i −0.559436 0.968972i −0.997544 0.0700496i \(-0.977684\pi\)
0.438107 0.898923i \(-0.355649\pi\)
\(570\) 0 0
\(571\) −1263.33 + 2188.15i −0.0925898 + 0.160370i −0.908600 0.417667i \(-0.862848\pi\)
0.816010 + 0.578037i \(0.196181\pi\)
\(572\) −73.0345 126.499i −0.00533868 0.00924687i
\(573\) 0 0
\(574\) 0 0
\(575\) −889.603 −0.0645200
\(576\) 0 0
\(577\) 10840.2 18775.8i 0.782119 1.35467i −0.148586 0.988900i \(-0.547472\pi\)
0.930705 0.365771i \(-0.119195\pi\)
\(578\) 4645.17 8045.66i 0.334279 0.578989i
\(579\) 0 0
\(580\) −11359.6 −0.813248
\(581\) 0 0
\(582\) 0 0
\(583\) 4571.33 + 7917.77i 0.324743 + 0.562471i
\(584\) −7505.95 + 13000.7i −0.531847 + 0.921186i
\(585\) 0 0
\(586\) −7449.16 12902.3i −0.525123 0.909540i
\(587\) −17458.1 −1.22755 −0.613776 0.789481i \(-0.710350\pi\)
−0.613776 + 0.789481i \(0.710350\pi\)
\(588\) 0 0
\(589\) −13539.4 −0.947165
\(590\) 4753.94 + 8234.06i 0.331723 + 0.574561i
\(591\) 0 0
\(592\) 2093.98 3626.88i 0.145375 0.251797i
\(593\) −2743.50 4751.88i −0.189987 0.329066i 0.755259 0.655427i \(-0.227511\pi\)
−0.945245 + 0.326360i \(0.894178\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 6201.20 0.426193
\(597\) 0 0
\(598\) −51.3821 + 88.9964i −0.00351366 + 0.00608584i
\(599\) −11498.6 + 19916.2i −0.784343 + 1.35852i 0.145048 + 0.989425i \(0.453666\pi\)
−0.929391 + 0.369097i \(0.879667\pi\)
\(600\) 0 0
\(601\) −18027.1 −1.22353 −0.611764 0.791040i \(-0.709540\pi\)
−0.611764 + 0.791040i \(0.709540\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 853.551 + 1478.39i 0.0575008 + 0.0995943i
\(605\) −30.2719 + 52.4324i −0.00203426 + 0.00352344i
\(606\) 0 0
\(607\) −5142.56 8907.18i −0.343872 0.595604i 0.641276 0.767310i \(-0.278405\pi\)
−0.985148 + 0.171707i \(0.945072\pi\)
\(608\) 17417.6 1.16181
\(609\) 0 0
\(610\) −20052.4 −1.33098
\(611\) 130.369 + 225.806i 0.00863203 + 0.0149511i
\(612\) 0 0
\(613\) 798.464 1382.98i 0.0526096 0.0911224i −0.838521 0.544869i \(-0.816579\pi\)
0.891131 + 0.453746i \(0.149913\pi\)
\(614\) 3468.00 + 6006.75i 0.227943 + 0.394809i
\(615\) 0 0
\(616\) 0 0
\(617\) −5850.74 −0.381753 −0.190877 0.981614i \(-0.561133\pi\)
−0.190877 + 0.981614i \(0.561133\pi\)
\(618\) 0 0
\(619\) −860.808 + 1490.96i −0.0558947 + 0.0968124i −0.892619 0.450812i \(-0.851134\pi\)
0.836724 + 0.547625i \(0.184468\pi\)
\(620\) −3158.03 + 5469.87i −0.204564 + 0.354315i
\(621\) 0 0
\(622\) 7633.48 0.492082
\(623\) 0 0
\(624\) 0 0
\(625\) 8701.36 + 15071.2i 0.556887 + 0.964557i
\(626\) −8508.27 + 14736.8i −0.543225 + 0.940894i
\(627\) 0 0
\(628\) −943.051 1633.41i −0.0599233 0.103790i
\(629\) −30636.3 −1.94205
\(630\) 0 0
\(631\) −19533.5 −1.23235 −0.616177 0.787608i \(-0.711319\pi\)
−0.616177 + 0.787608i \(0.711319\pi\)
\(632\) −3807.38 6594.58i −0.239636 0.415061i
\(633\) 0 0
\(634\) −8324.97 + 14419.3i −0.521493 + 0.903253i
\(635\) −172.921 299.508i −0.0108066 0.0187175i
\(636\) 0 0
\(637\) 0 0
\(638\) −16394.1 −1.01732
\(639\) 0 0
\(640\) 2810.76 4868.38i 0.173602 0.300687i
\(641\) −11748.1 + 20348.3i −0.723903 + 1.25384i 0.235521 + 0.971869i \(0.424320\pi\)
−0.959424 + 0.281967i \(0.909013\pi\)
\(642\) 0 0
\(643\) 1537.40 0.0942913 0.0471456 0.998888i \(-0.484988\pi\)
0.0471456 + 0.998888i \(0.484988\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) 10205.7 + 17676.7i 0.621573 + 1.07660i
\(647\) −14136.5 + 24485.1i −0.858985 + 1.48781i 0.0139128 + 0.999903i \(0.495571\pi\)
−0.872898 + 0.487903i \(0.837762\pi\)
\(648\) 0 0
\(649\) −7428.79 12867.0i −0.449315 0.778236i
\(650\) −30.9333 −0.00186662
\(651\) 0 0
\(652\) −3111.62 −0.186902
\(653\) −1334.48 2311.39i −0.0799730 0.138517i 0.823265 0.567657i \(-0.192150\pi\)
−0.903238 + 0.429140i \(0.858817\pi\)
\(654\) 0 0
\(655\) 12574.9 21780.3i 0.750140 1.29928i
\(656\) 2819.94 + 4884.29i 0.167836 + 0.290700i
\(657\) 0 0
\(658\) 0 0
\(659\) 6343.74 0.374988 0.187494 0.982266i \(-0.439964\pi\)
0.187494 + 0.982266i \(0.439964\pi\)
\(660\) 0 0
\(661\) −4204.58 + 7282.54i −0.247412 + 0.428529i −0.962807 0.270191i \(-0.912913\pi\)
0.715395 + 0.698720i \(0.246247\pi\)
\(662\) 1245.20 2156.75i 0.0731059 0.126623i
\(663\) 0 0
\(664\) −31196.9 −1.82331
\(665\) 0 0
\(666\) 0 0
\(667\) −6244.29 10815.4i −0.362489 0.627849i
\(668\) 1077.74 1866.70i 0.0624235 0.108121i
\(669\) 0 0
\(670\) −5899.58 10218.4i −0.340180 0.589209i
\(671\) 31335.1 1.80280
\(672\) 0 0
\(673\) −15326.7 −0.877862 −0.438931 0.898521i \(-0.644643\pi\)
−0.438931 + 0.898521i \(0.644643\pi\)
\(674\) 4601.20 + 7969.52i 0.262955 + 0.455452i
\(675\) 0 0
\(676\) −4566.71 + 7909.78i −0.259827 + 0.450033i
\(677\) 6505.81 + 11268.4i 0.369333 + 0.639704i 0.989461 0.144797i \(-0.0462528\pi\)
−0.620128 + 0.784500i \(0.712919\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 27837.4 1.56987
\(681\) 0 0
\(682\) −4557.63 + 7894.04i −0.255895 + 0.443223i
\(683\) −8736.00 + 15131.2i −0.489420 + 0.847700i −0.999926 0.0121740i \(-0.996125\pi\)
0.510506 + 0.859874i \(0.329458\pi\)
\(684\) 0 0
\(685\) 2108.53 0.117610
\(686\) 0 0
\(687\) 0 0
\(688\) 3513.39 + 6085.37i 0.194690 + 0.337213i
\(689\) −121.087 + 209.730i −0.00669531 + 0.0115966i
\(690\) 0 0
\(691\) −3658.55 6336.80i −0.201415 0.348861i 0.747569 0.664184i \(-0.231221\pi\)
−0.948985 + 0.315322i \(0.897887\pi\)
\(692\) −5462.77 −0.300091
\(693\) 0 0
\(694\) 12766.4 0.698280
\(695\) −14084.4 24394.8i −0.768706 1.33144i
\(696\) 0 0
\(697\) 20628.8 35730.1i 1.12105 1.94171i
\(698\) −7040.52 12194.5i −0.381787 0.661275i
\(699\) 0 0
\(700\) 0 0
\(701\) −7874.65 −0.424282 −0.212141 0.977239i \(-0.568044\pi\)
−0.212141 + 0.977239i \(0.568044\pi\)
\(702\) 0 0
\(703\) 16526.4 28624.5i 0.886634 1.53570i
\(704\) 7819.36 13543.5i 0.418612 0.725058i
\(705\) 0 0
\(706\) −11893.4 −0.634017
\(707\) 0 0
\(708\) 0 0
\(709\) 12618.4 + 21855.7i 0.668398 + 1.15770i 0.978352 + 0.206948i \(0.0663531\pi\)
−0.309954 + 0.950752i \(0.600314\pi\)
\(710\) −6101.64 + 10568.4i −0.322522 + 0.558624i
\(711\) 0 0
\(712\) −4153.30 7193.73i −0.218612 0.378647i
\(713\) −6943.76 −0.364721
\(714\) 0 0
\(715\) 417.580 0.0218414
\(716\) −8594.85 14886.7i −0.448610 0.777015i
\(717\) 0 0
\(718\) −1708.71 + 2959.57i −0.0888139 + 0.153830i
\(719\) −9836.48 17037.3i −0.510207 0.883704i −0.999930 0.0118262i \(-0.996236\pi\)
0.489723 0.871878i \(-0.337098\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −8578.62 −0.442193
\(723\) 0 0
\(724\) −7723.32 + 13377.2i −0.396457 + 0.686684i
\(725\) 1879.61 3255.58i 0.0962856 0.166772i
\(726\) 0 0
\(727\) 31921.7 1.62849 0.814243 0.580525i \(-0.197152\pi\)
0.814243 + 0.580525i \(0.197152\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −7339.69 12712.7i −0.372129 0.644546i
\(731\) 25701.6 44516.4i 1.30042 2.25239i
\(732\) 0 0
\(733\) 6772.65 + 11730.6i 0.341274 + 0.591103i 0.984669 0.174430i \(-0.0558084\pi\)
−0.643396 + 0.765534i \(0.722475\pi\)
\(734\) −17638.9 −0.887007
\(735\) 0 0
\(736\) 8932.74 0.447371
\(737\) 9219.04 + 15967.8i 0.460770 + 0.798078i
\(738\) 0 0
\(739\) −12748.8 + 22081.6i −0.634604 + 1.09917i 0.351995 + 0.936002i \(0.385503\pi\)
−0.986599 + 0.163164i \(0.947830\pi\)
\(740\) −7709.48 13353.2i −0.382981 0.663343i
\(741\) 0 0
\(742\) 0 0
\(743\) 11146.9 0.550390 0.275195 0.961388i \(-0.411258\pi\)
0.275195 + 0.961388i \(0.411258\pi\)
\(744\) 0 0
\(745\) −8863.95 + 15352.8i −0.435906 + 0.755011i
\(746\) 5165.92 8947.64i 0.253536 0.439137i
\(747\) 0 0
\(748\) −14879.3 −0.727328
\(749\) 0 0
\(750\) 0 0
\(751\) −10706.2 18543.8i −0.520208 0.901027i −0.999724 0.0234936i \(-0.992521\pi\)
0.479516 0.877533i \(-0.340812\pi\)
\(752\) −1815.38 + 3144.32i −0.0880318 + 0.152476i
\(753\) 0 0
\(754\) −217.127 376.075i −0.0104871 0.0181643i
\(755\) −4880.24 −0.235245
\(756\) 0 0
\(757\) −33963.9 −1.63070 −0.815350 0.578968i \(-0.803456\pi\)
−0.815350 + 0.578968i \(0.803456\pi\)
\(758\) 10269.6 + 17787.5i 0.492096 + 0.852335i
\(759\) 0 0
\(760\) −15016.5 + 26009.4i −0.716719 + 1.24139i
\(761\) 9959.98 + 17251.2i 0.474440 + 0.821754i 0.999572 0.0292668i \(-0.00931725\pi\)
−0.525132 + 0.851021i \(0.675984\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −12761.3 −0.604305
\(765\) 0 0
\(766\) 1346.44 2332.11i 0.0635105 0.110003i
\(767\) 196.777 340.828i 0.00926364 0.0160451i
\(768\) 0 0
\(769\) −10039.2 −0.470769 −0.235385 0.971902i \(-0.575635\pi\)
−0.235385 + 0.971902i \(0.575635\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 4345.17 + 7526.05i 0.202573 + 0.350866i
\(773\) 10692.7 18520.2i 0.497527 0.861742i −0.502469 0.864595i \(-0.667575\pi\)
0.999996 + 0.00285350i \(0.000908298\pi\)
\(774\) 0 0
\(775\) −1045.08 1810.13i −0.0484392 0.0838992i
\(776\) −3860.33 −0.178579
\(777\) 0 0
\(778\) 3720.32 0.171440
\(779\) 22255.9 + 38548.3i 1.02362 + 1.77296i
\(780\) 0 0
\(781\) 9534.79 16514.7i 0.436852 0.756650i
\(782\) 5234.04 + 9065.62i 0.239346 + 0.414560i
\(783\) 0 0
\(784\) 0 0
\(785\) 5391.96 0.245156
\(786\) 0 0
\(787\) 18710.7 32407.8i 0.847475 1.46787i −0.0359790 0.999353i \(-0.511455\pi\)
0.883454 0.468518i \(-0.155212\pi\)
\(788\) 7756.28 13434.3i 0.350642 0.607330i
\(789\) 0 0
\(790\) 7446.10 0.335342
\(791\) 0