Properties

Label 441.4.e.z.361.3
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 361.3
Root \(-0.272818 - 0.472535i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.4.e.z.226.3

$q$-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 0.639161 0.769073i \(-0.279282\pi\)
−0.985617 + 0.168994i \(0.945948\pi\)
\(3\) 0 0
\(4\) 2.07949 3.60179i 0.259937 0.450224i
\(5\) −5.94483 10.2967i −0.531722 0.920969i −0.999314 0.0370251i \(-0.988212\pi\)
0.467593 0.883944i \(-0.345121\pi\)
\(6\) 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 −0.999999 0.00110512i \(-0.999648\pi\)
0.500957 + 0.865472i \(0.332982\pi\)
\(12\) 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 \(0.413870\pi\)
−0.968163 + 0.250322i \(0.919464\pi\)
\(18\) 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 0.716107 0.697991i \(-0.245922\pi\)
−0.962531 + 0.271171i \(0.912589\pi\)
\(24\) 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 \(-0.236949\pi\)
0.735497 + 0.677528i \(0.236949\pi\)
\(30\) 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 \(-0.795040\pi\)
−0.799760 + 0.600320i \(0.795040\pi\)
\(42\) 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 0.576404 0.817165i \(-0.304455\pi\)
−0.995887 + 0.0905985i \(0.971122\pi\)
\(48\) 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 −0.656221 0.754569i \(-0.727846\pi\)
0.981586 + 0.191019i \(0.0611792\pi\)
\(54\) 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 −0.998397 0.0566051i \(-0.981972\pi\)
0.548220 + 0.836334i \(0.315306\pi\)
\(60\) 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 \(-0.644203\pi\)
−0.437690 + 0.899126i \(0.644203\pi\)
\(72\) 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 \(-0.166903\pi\)
0.865654 + 0.500643i \(0.166903\pi\)
\(84\) 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 0.950952 0.309338i \(-0.100107\pi\)
−0.743371 + 0.668880i \(0.766774\pi\)
\(90\) 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 −0.807225 0.590244i \(-0.799032\pi\)
0.914779 + 0.403955i \(0.132365\pi\)
\(102\) 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 \(0.152287\pi\)
−0.0451586 + 0.998980i \(0.514379\pi\)
\(108\) 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 \(-0.563400\pi\)
−0.197863 + 0.980230i \(0.563400\pi\)
\(114\) 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 \(0.0825603\pi\)
−0.261164 + 0.965294i \(0.584106\pi\)
\(132\) 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 −0.892349 0.451347i \(-0.850944\pi\)
0.837052 + 0.547123i \(0.184277\pi\)
\(138\) 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 0.584978 0.811049i \(-0.301103\pi\)
−0.994878 + 0.101081i \(0.967770\pi\)
\(150\) 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 \(-0.538313\pi\)
−0.120074 + 0.992765i \(0.538313\pi\)
\(168\) 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 0.973480 0.228770i \(-0.0734704\pi\)
−0.684861 + 0.728674i \(0.740137\pi\)
\(174\) 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 \(0.498034\pi\)
−0.869097 + 0.494642i \(0.835299\pi\)
\(180\) 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 \(0.0307513\pi\)
−0.414134 + 0.910216i \(0.635915\pi\)
\(192\) 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 \(-0.735630\pi\)
−0.674476 + 0.738297i \(0.735630\pi\)
\(198\) 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 −0.810229 0.586113i \(-0.800658\pi\)
0.912703 + 0.408623i \(0.133991\pi\)
\(228\) 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 0.840807 0.541335i \(-0.182081\pi\)
−0.889213 + 0.457493i \(0.848748\pi\)
\(234\) 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 \(-0.187508\pi\)
0.831456 + 0.555590i \(0.187508\pi\)
\(240\) 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 \(-0.479155\pi\)
0.0654405 + 0.997856i \(0.479155\pi\)
\(252\) 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 0.999881 0.0154192i \(-0.00490827\pi\)
−0.513294 + 0.858213i \(0.671575\pi\)
\(258\) 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 −0.575678 0.817677i \(-0.695262\pi\)
0.995968 + 0.0897135i \(0.0285951\pi\)
\(264\) 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 \(-0.618697\pi\)
0.988666 0.150133i \(-0.0479700\pi\)
\(270\) 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 \(-0.530307\pi\)
−0.0950692 + 0.995471i \(0.530307\pi\)
\(282\) 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 \(-0.226250\pi\)
0.757850 + 0.652429i \(0.226250\pi\)
\(294\) 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 −0.987132 0.159907i \(-0.948881\pi\)
0.632049 + 0.774928i \(0.282214\pi\)
\(312\) 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 \(-0.895460\pi\)
0.193941 0.981013i \(-0.437873\pi\)
\(318\) 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 \(0.334759\pi\)
−0.999990 + 0.00447854i \(0.998574\pi\)
\(348\) 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 −0.541326 0.840813i \(-0.682078\pi\)
0.998828 + 0.0483961i \(0.0154110\pi\)
\(354\) 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 0.794795 0.606879i \(-0.207579\pi\)
−0.922970 + 0.384873i \(0.874245\pi\)
\(360\) 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 0.908209 0.418518i \(-0.137450\pi\)
−0.816551 + 0.577273i \(0.804117\pi\)
\(384\) 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 −0.921228 0.389024i \(-0.872812\pi\)
0.797518 + 0.603295i \(0.206146\pi\)
\(390\) 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 0.987278 0.159003i \(-0.0508280\pi\)
−0.631340 + 0.775506i \(0.717495\pi\)
\(402\) 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 \(-0.560710\pi\)
−0.189571 + 0.981867i \(0.560710\pi\)
\(420\) 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 −0.958347 0.285607i \(-0.907805\pi\)
0.726516 + 0.687149i \(0.241138\pi\)
\(432\) 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 0.729754 0.683710i \(-0.239634\pi\)
−0.956987 + 0.290131i \(0.906301\pi\)
\(444\) 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 \(-0.535151\pi\)
−0.110206 + 0.993909i \(0.535151\pi\)
\(450\) 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 \(-0.747317\pi\)
−0.701121 + 0.713043i \(0.747317\pi\)
\(462\) 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 0.580435 0.814307i \(-0.302883\pi\)
−0.995428 + 0.0955176i \(0.969549\pi\)
\(468\) 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 \(-0.532069\pi\)
0.911922 0.410363i \(-0.134598\pi\)
\(480\) 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 \(-0.691343\pi\)
−0.565567 + 0.824702i \(0.691343\pi\)
\(492\) 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 \(-0.654408\pi\)
−0.466284 + 0.884635i \(0.654408\pi\)
\(504\) 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 0.722784 0.691074i \(-0.242862\pi\)
−0.959880 + 0.280412i \(0.909529\pi\)
\(510\) 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 \(0.550506\pi\)
−0.776144 + 0.630555i \(0.782827\pi\)
\(522\) 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 \(0.370418\pi\)
−0.993221 + 0.116242i \(0.962915\pi\)
\(558\) 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 −0.853143 0.521678i \(-0.825306\pi\)
0.878358 + 0.478004i \(0.158640\pi\)
\(564\) 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 \(0.0223158\pi\)
−0.438107 + 0.898923i \(0.644351\pi\)
\(570\) 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 \(-0.289650\pi\)
0.613776 + 0.789481i \(0.289650\pi\)
\(588\) 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 0.945245 0.326360i \(-0.105822\pi\)
−0.755259 + 0.655427i \(0.772489\pi\)
\(594\) 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 \(-0.546334\pi\)
0.929391 0.369097i \(-0.120333\pi\)
\(600\) 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 \(-0.438867\pi\)
0.190877 + 0.981614i \(0.438867\pi\)
\(618\) 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 \(-0.575680\pi\)
0.959424 0.281967i \(-0.0909870\pi\)
\(642\) 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 \(-0.504429\pi\)
0.872898 0.487903i \(-0.162238\pi\)
\(648\) 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 0.903238 0.429140i \(-0.141183\pi\)
−0.823265 + 0.567657i \(0.807850\pi\)
\(654\) 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 \(-0.560036\pi\)
−0.187494 + 0.982266i \(0.560036\pi\)
\(660\) 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 0.620128 0.784500i \(-0.287081\pi\)
−0.989461 + 0.144797i \(0.953747\pi\)
\(678\) 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 −0.510506 0.859874i \(-0.670542\pi\)
0.999926 + 0.0121740i \(0.00387519\pi\)
\(684\) 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 \(-0.431956\pi\)
0.212141 + 0.977239i \(0.431956\pi\)
\(702\) 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 \(0.00376448\pi\)
−0.489723 + 0.871878i \(0.662902\pi\)
\(720\) 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 \(-0.588742\pi\)
−0.275195 + 0.961388i \(0.588742\pi\)
\(744\) 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 0.525132 0.851021i \(-0.324016\pi\)
−0.999572 + 0.0292668i \(0.990683\pi\)
\(762\) 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 −0.999996 0.00285350i \(-0.999092\pi\)
0.502469 + 0.864595i \(0.332425\pi\)
\(774\) 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
\(791\)