Properties

Label 441.4.e.z.361.4
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 361.4
Root \(-1.68703 - 2.92202i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.4.e.z.226.4

$q$-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 \(0.0117881\pi\)
−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 −0.999999 0.00110512i \(-0.999648\pi\)
0.500957 + 0.865472i \(0.332982\pi\)
\(12\) 0 0
\(13\) −0.964525 −0.0205778 −0.0102889 0.999947i \(-0.503275\pi\)
−0.0102889 + 0.999947i \(0.503275\pi\)
\(14\) 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 \(-0.945620\pi\)
0.345488 0.938423i \(-0.387713\pi\)
\(20\) 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 −0.619554 0.784954i \(-0.712687\pi\)
0.989567 + 0.144073i \(0.0460200\pi\)
\(32\) −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 −0.656221 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 −0.548220 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 \(-0.807932\pi\)
−0.0797171 0.996818i \(-0.525402\pi\)
\(62\) −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 \(-0.664822\pi\)
0.999983 0.00579655i \(-0.00184511\pi\)
\(74\) −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 \(-0.472980\pi\)
0.0847844 + 0.996399i \(0.472980\pi\)
\(98\) 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 0.805452 0.592661i \(-0.201923\pi\)
−0.915986 + 0.401211i \(0.868589\pi\)
\(104\) 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 \(-0.917440\pi\)
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 −0.892349 0.451347i \(-0.850944\pi\)
0.837052 + 0.547123i \(0.184277\pi\)
\(138\) 0 0
\(139\) 2369.18 1.44569 0.722846 0.691009i \(-0.242834\pi\)
0.722846 + 0.691009i \(0.242834\pi\)
\(140\) 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 −0.917886 0.396845i \(-0.870105\pi\)
0.802621 + 0.596490i \(0.203438\pi\)
\(158\) −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 \(0.498034\pi\)
−0.869097 + 0.494642i \(0.835299\pi\)
\(180\) 0 0
\(181\) 3714.04 1.52521 0.762603 0.646867i \(-0.223921\pi\)
0.762603 + 0.646867i \(0.223921\pi\)
\(182\) 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 −0.990418 0.138103i \(-0.955900\pi\)
0.614809 + 0.788676i \(0.289233\pi\)
\(200\) 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 \(-0.239628\pi\)
0.729768 + 0.683695i \(0.239628\pi\)
\(224\) 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 \(0.0122755\pi\)
−0.466239 + 0.884659i \(0.654391\pi\)
\(230\) −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 \(-0.562477\pi\)
0.946907 0.321508i \(-0.104190\pi\)
\(242\) 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 −0.575678 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 \(0.381303\pi\)
−0.988666 + 0.150133i \(0.952030\pi\)
\(270\) 0 0
\(271\) 2909.95 + 5040.18i 0.652276 + 1.12977i 0.982569 + 0.185896i \(0.0595189\pi\)
−0.330294 + 0.943878i \(0.607148\pi\)
\(272\) 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 −0.872384 0.488821i \(-0.837427\pi\)
0.859524 + 0.511096i \(0.170760\pi\)
\(284\) −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 \(-0.606700\pi\)
−0.328964 + 0.944342i \(0.606700\pi\)
\(308\) 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 \(-0.879856\pi\)
0.145635 0.989338i \(-0.453478\pi\)
\(314\) 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 \(-0.314250\pi\)
0.550990 + 0.834512i \(0.314250\pi\)
\(350\) 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 0.794795 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 \(-0.612244\pi\)
0.985419 0.170143i \(-0.0544230\pi\)
\(368\) 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 −0.921228 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 0.634415 0.772993i \(-0.281241\pi\)
−0.986639 + 0.162923i \(0.947908\pi\)
\(398\) 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 \(-0.618207\pi\)
0.988434 0.151653i \(-0.0484597\pi\)
\(410\) 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 −0.958347 0.285607i \(-0.907805\pi\)
0.726516 + 0.687149i \(0.241138\pi\)
\(432\) 0 0
\(433\) −1985.64 −0.220378 −0.110189 0.993911i \(-0.535146\pi\)
−0.110189 + 0.993911i \(0.535146\pi\)
\(434\) 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 0.614593 0.788844i \(-0.289320\pi\)
−0.990456 + 0.137831i \(0.955987\pi\)
\(440\) 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 \(-0.252683\pi\)
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 \(-0.691343\pi\)
−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 \(-0.345592\pi\)
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 \(0.208668\pi\)
0.131568 + 0.991307i \(0.457999\pi\)
\(524\) −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 −0.878358 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 \(0.0223158\pi\)
−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 \(0.452528\pi\)
−0.930705 + 0.365771i \(0.880805\pi\)
\(578\) −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 \(-0.546334\pi\)
0.929391 0.369097i \(-0.120333\pi\)
\(600\) 0 0
\(601\) 18027.1 1.22353 0.611764 0.791040i \(-0.290460\pi\)
0.611764 + 0.791040i \(0.290460\pi\)
\(602\) 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 0.985148 0.171707i \(-0.0549281\pi\)
−0.641276 + 0.767310i \(0.721595\pi\)
\(608\) 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 −0.836724 0.547625i \(-0.815532\pi\)
0.892619 + 0.450812i \(0.148866\pi\)
\(620\) 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 \(-0.515012\pi\)
−0.0471456 + 0.998888i \(0.515012\pi\)
\(644\) 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 0.903238 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 −0.715395 0.698720i \(-0.753753\pi\)
0.962807 + 0.270191i \(0.0870867\pi\)
\(662\) −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 −0.510506 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 0.948985 0.315322i \(-0.102113\pi\)
−0.747569 + 0.664184i \(0.768779\pi\)
\(692\) −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 \(-0.996236\pi\)
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 \(-0.802848\pi\)
−0.814243 + 0.580525i \(0.802848\pi\)
\(728\) 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 0.643396 0.765534i \(-0.277525\pi\)
−0.984669 + 0.174430i \(0.944192\pi\)
\(734\) −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 0.999572 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 \(-0.424365\pi\)
0.235385 + 0.971902i \(0.424365\pi\)
\(770\) 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 \(0.488545\pi\)
−0.883454 + 0.468518i \(0.844788\pi\)
\(788\) −7756.28 + 13434.3i −0.350642 + 0.607330i
\(789\) 0 0
\(790\) −7446.10 −0.335342