Properties

Label 882.4.g.bk.361.2
Level $882$
Weight $4$
Character 882.361
Analytic conductor $52.040$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 882 = 2 \cdot 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 882.g (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(52.0396846251\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{2}, \sqrt{-3})\)
Defining polynomial: \(x^{4} + 2 x^{2} + 4\)
Coefficient ring: \(\Z[a_1, \ldots, a_{25}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 294)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(0.707107 - 1.22474i\) of defining polynomial
Character \(\chi\) \(=\) 882.361
Dual form 882.4.g.bk.667.2

$q$-expansion

\(f(q)\) \(=\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.70711 + 6.42090i) q^{5} -8.00000 q^{8} +O(q^{10})\) \(q+(1.00000 + 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(3.70711 + 6.42090i) q^{5} -8.00000 q^{8} +(-7.41421 + 12.8418i) q^{10} +(5.24264 - 9.08052i) q^{11} +2.78680 q^{13} +(-8.00000 - 13.8564i) q^{16} +(25.2218 - 43.6855i) q^{17} +(-62.5269 - 108.300i) q^{19} -29.6569 q^{20} +20.9706 q^{22} +(-91.1249 - 157.833i) q^{23} +(35.0147 - 60.6473i) q^{25} +(2.78680 + 4.82687i) q^{26} -156.132 q^{29} +(-69.8162 + 120.925i) q^{31} +(16.0000 - 27.7128i) q^{32} +100.887 q^{34} +(197.279 + 341.698i) q^{37} +(125.054 - 216.600i) q^{38} +(-29.6569 - 51.3672i) q^{40} -197.605 q^{41} +343.294 q^{43} +(20.9706 + 36.3221i) q^{44} +(182.250 - 315.666i) q^{46} +(-305.002 - 528.279i) q^{47} +140.059 q^{50} +(-5.57359 + 9.65375i) q^{52} +(-68.7645 + 119.104i) q^{53} +77.7401 q^{55} +(-156.132 - 270.429i) q^{58} +(294.718 - 510.466i) q^{59} +(-123.609 - 214.097i) q^{61} -279.265 q^{62} +64.0000 q^{64} +(10.3310 + 17.8937i) q^{65} +(197.823 - 342.640i) q^{67} +(100.887 + 174.742i) q^{68} -285.661 q^{71} +(498.729 - 863.823i) q^{73} +(-394.558 + 683.395i) q^{74} +500.215 q^{76} +(424.132 + 734.618i) q^{79} +(59.3137 - 102.734i) q^{80} +(-197.605 - 342.262i) q^{82} +210.863 q^{83} +374.000 q^{85} +(343.294 + 594.602i) q^{86} +(-41.9411 + 72.6442i) q^{88} +(-276.744 - 479.334i) q^{89} +728.999 q^{92} +(610.004 - 1056.56i) q^{94} +(463.588 - 802.958i) q^{95} -903.910 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q + 4q^{2} - 8q^{4} + 12q^{5} - 32q^{8} + O(q^{10}) \) \( 4q + 4q^{2} - 8q^{4} + 12q^{5} - 32q^{8} - 24q^{10} + 4q^{11} + 96q^{13} - 32q^{16} + 132q^{17} - 120q^{19} - 96q^{20} + 16q^{22} - 76q^{23} + 174q^{25} + 96q^{26} + 224q^{29} - 432q^{31} + 64q^{32} + 528q^{34} + 280q^{37} + 240q^{38} - 96q^{40} - 72q^{41} - 256q^{43} + 16q^{44} + 152q^{46} - 264q^{47} + 696q^{50} - 192q^{52} + 268q^{53} + 96q^{55} + 224q^{58} + 336q^{59} + 504q^{61} - 1728q^{62} + 256q^{64} + 228q^{65} + 384q^{67} + 528q^{68} + 792q^{71} + 312q^{73} - 560q^{74} + 960q^{76} + 848q^{79} + 192q^{80} - 72q^{82} + 1296q^{83} + 1496q^{85} - 256q^{86} - 32q^{88} - 612q^{89} + 608q^{92} + 528q^{94} + 904q^{95} - 4368q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/882\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(785\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 + 1.73205i 0.353553 + 0.612372i
\(3\) 0 0
\(4\) −2.00000 + 3.46410i −0.250000 + 0.433013i
\(5\) 3.70711 + 6.42090i 0.331574 + 0.574303i 0.982821 0.184563i \(-0.0590871\pi\)
−0.651247 + 0.758866i \(0.725754\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −8.00000 −0.353553
\(9\) 0 0
\(10\) −7.41421 + 12.8418i −0.234458 + 0.406093i
\(11\) 5.24264 9.08052i 0.143701 0.248898i −0.785186 0.619260i \(-0.787433\pi\)
0.928888 + 0.370361i \(0.120766\pi\)
\(12\) 0 0
\(13\) 2.78680 0.0594553 0.0297276 0.999558i \(-0.490536\pi\)
0.0297276 + 0.999558i \(0.490536\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) −8.00000 13.8564i −0.125000 0.216506i
\(17\) 25.2218 43.6855i 0.359835 0.623252i −0.628098 0.778134i \(-0.716166\pi\)
0.987933 + 0.154882i \(0.0494997\pi\)
\(18\) 0 0
\(19\) −62.5269 108.300i −0.754982 1.30767i −0.945383 0.325961i \(-0.894312\pi\)
0.190401 0.981706i \(-0.439021\pi\)
\(20\) −29.6569 −0.331574
\(21\) 0 0
\(22\) 20.9706 0.203225
\(23\) −91.1249 157.833i −0.826124 1.43089i −0.901057 0.433700i \(-0.857208\pi\)
0.0749331 0.997189i \(-0.476126\pi\)
\(24\) 0 0
\(25\) 35.0147 60.6473i 0.280118 0.485178i
\(26\) 2.78680 + 4.82687i 0.0210206 + 0.0364088i
\(27\) 0 0
\(28\) 0 0
\(29\) −156.132 −0.999758 −0.499879 0.866095i \(-0.666622\pi\)
−0.499879 + 0.866095i \(0.666622\pi\)
\(30\) 0 0
\(31\) −69.8162 + 120.925i −0.404496 + 0.700607i −0.994263 0.106966i \(-0.965886\pi\)
0.589767 + 0.807573i \(0.299220\pi\)
\(32\) 16.0000 27.7128i 0.0883883 0.153093i
\(33\) 0 0
\(34\) 100.887 0.508883
\(35\) 0 0
\(36\) 0 0
\(37\) 197.279 + 341.698i 0.876554 + 1.51824i 0.855098 + 0.518467i \(0.173497\pi\)
0.0214563 + 0.999770i \(0.493170\pi\)
\(38\) 125.054 216.600i 0.533853 0.924660i
\(39\) 0 0
\(40\) −29.6569 51.3672i −0.117229 0.203047i
\(41\) −197.605 −0.752701 −0.376350 0.926477i \(-0.622821\pi\)
−0.376350 + 0.926477i \(0.622821\pi\)
\(42\) 0 0
\(43\) 343.294 1.21748 0.608741 0.793369i \(-0.291675\pi\)
0.608741 + 0.793369i \(0.291675\pi\)
\(44\) 20.9706 + 36.3221i 0.0718507 + 0.124449i
\(45\) 0 0
\(46\) 182.250 315.666i 0.584158 1.01179i
\(47\) −305.002 528.279i −0.946577 1.63952i −0.752562 0.658521i \(-0.771182\pi\)
−0.194015 0.980999i \(-0.562151\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 140.059 0.396146
\(51\) 0 0
\(52\) −5.57359 + 9.65375i −0.0148638 + 0.0257449i
\(53\) −68.7645 + 119.104i −0.178218 + 0.308682i −0.941270 0.337655i \(-0.890366\pi\)
0.763053 + 0.646336i \(0.223700\pi\)
\(54\) 0 0
\(55\) 77.7401 0.190590
\(56\) 0 0
\(57\) 0 0
\(58\) −156.132 270.429i −0.353468 0.612224i
\(59\) 294.718 510.466i 0.650322 1.12639i −0.332723 0.943025i \(-0.607967\pi\)
0.983045 0.183366i \(-0.0586993\pi\)
\(60\) 0 0
\(61\) −123.609 214.097i −0.259450 0.449381i 0.706644 0.707569i \(-0.250208\pi\)
−0.966095 + 0.258188i \(0.916875\pi\)
\(62\) −279.265 −0.572043
\(63\) 0 0
\(64\) 64.0000 0.125000
\(65\) 10.3310 + 17.8937i 0.0197138 + 0.0341453i
\(66\) 0 0
\(67\) 197.823 342.640i 0.360716 0.624778i −0.627363 0.778727i \(-0.715866\pi\)
0.988079 + 0.153949i \(0.0491990\pi\)
\(68\) 100.887 + 174.742i 0.179917 + 0.311626i
\(69\) 0 0
\(70\) 0 0
\(71\) −285.661 −0.477489 −0.238745 0.971082i \(-0.576736\pi\)
−0.238745 + 0.971082i \(0.576736\pi\)
\(72\) 0 0
\(73\) 498.729 863.823i 0.799613 1.38497i −0.120255 0.992743i \(-0.538371\pi\)
0.919868 0.392228i \(-0.128295\pi\)
\(74\) −394.558 + 683.395i −0.619817 + 1.07356i
\(75\) 0 0
\(76\) 500.215 0.754982
\(77\) 0 0
\(78\) 0 0
\(79\) 424.132 + 734.618i 0.604033 + 1.04622i 0.992204 + 0.124628i \(0.0397737\pi\)
−0.388171 + 0.921587i \(0.626893\pi\)
\(80\) 59.3137 102.734i 0.0828934 0.143576i
\(81\) 0 0
\(82\) −197.605 342.262i −0.266120 0.460933i
\(83\) 210.863 0.278858 0.139429 0.990232i \(-0.455473\pi\)
0.139429 + 0.990232i \(0.455473\pi\)
\(84\) 0 0
\(85\) 374.000 0.477247
\(86\) 343.294 + 594.602i 0.430445 + 0.745553i
\(87\) 0 0
\(88\) −41.9411 + 72.6442i −0.0508061 + 0.0879988i
\(89\) −276.744 479.334i −0.329604 0.570891i 0.652829 0.757505i \(-0.273582\pi\)
−0.982433 + 0.186614i \(0.940249\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 728.999 0.826124
\(93\) 0 0
\(94\) 610.004 1056.56i 0.669331 1.15932i
\(95\) 463.588 802.958i 0.500664 0.867176i
\(96\) 0 0
\(97\) −903.910 −0.946166 −0.473083 0.881018i \(-0.656859\pi\)
−0.473083 + 0.881018i \(0.656859\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 140.059 + 242.589i 0.140059 + 0.242589i
\(101\) −156.806 + 271.595i −0.154482 + 0.267572i −0.932870 0.360212i \(-0.882704\pi\)
0.778388 + 0.627784i \(0.216038\pi\)
\(102\) 0 0
\(103\) −115.487 200.030i −0.110479 0.191355i 0.805485 0.592617i \(-0.201905\pi\)
−0.915963 + 0.401262i \(0.868572\pi\)
\(104\) −22.2944 −0.0210206
\(105\) 0 0
\(106\) −275.058 −0.252038
\(107\) 62.7431 + 108.674i 0.0566879 + 0.0981863i 0.892977 0.450103i \(-0.148613\pi\)
−0.836289 + 0.548289i \(0.815279\pi\)
\(108\) 0 0
\(109\) −372.764 + 645.646i −0.327562 + 0.567354i −0.982028 0.188738i \(-0.939560\pi\)
0.654465 + 0.756092i \(0.272894\pi\)
\(110\) 77.7401 + 134.650i 0.0673839 + 0.116712i
\(111\) 0 0
\(112\) 0 0
\(113\) 1043.76 0.868929 0.434464 0.900689i \(-0.356938\pi\)
0.434464 + 0.900689i \(0.356938\pi\)
\(114\) 0 0
\(115\) 675.619 1170.21i 0.547842 0.948890i
\(116\) 312.264 540.857i 0.249940 0.432908i
\(117\) 0 0
\(118\) 1178.87 0.919694
\(119\) 0 0
\(120\) 0 0
\(121\) 610.529 + 1057.47i 0.458700 + 0.794491i
\(122\) 247.217 428.193i 0.183459 0.317760i
\(123\) 0 0
\(124\) −279.265 483.701i −0.202248 0.350304i
\(125\) 1445.99 1.03467
\(126\) 0 0
\(127\) −2080.17 −1.45343 −0.726715 0.686939i \(-0.758954\pi\)
−0.726715 + 0.686939i \(0.758954\pi\)
\(128\) 64.0000 + 110.851i 0.0441942 + 0.0765466i
\(129\) 0 0
\(130\) −20.6619 + 35.7875i −0.0139398 + 0.0241444i
\(131\) −634.764 1099.44i −0.423355 0.733273i 0.572910 0.819618i \(-0.305814\pi\)
−0.996265 + 0.0863453i \(0.972481\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 791.294 0.510129
\(135\) 0 0
\(136\) −201.775 + 349.484i −0.127221 + 0.220353i
\(137\) 1536.59 2661.46i 0.958249 1.65974i 0.231497 0.972836i \(-0.425638\pi\)
0.726752 0.686900i \(-0.241029\pi\)
\(138\) 0 0
\(139\) 1013.60 0.618504 0.309252 0.950980i \(-0.399921\pi\)
0.309252 + 0.950980i \(0.399921\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −285.661 494.779i −0.168818 0.292401i
\(143\) 14.6102 25.3056i 0.00854380 0.0147983i
\(144\) 0 0
\(145\) −578.798 1002.51i −0.331494 0.574164i
\(146\) 1994.91 1.13082
\(147\) 0 0
\(148\) −1578.23 −0.876554
\(149\) 615.735 + 1066.48i 0.338544 + 0.586375i 0.984159 0.177288i \(-0.0567324\pi\)
−0.645615 + 0.763663i \(0.723399\pi\)
\(150\) 0 0
\(151\) 1122.37 1944.00i 0.604881 1.04768i −0.387190 0.922000i \(-0.626554\pi\)
0.992070 0.125684i \(-0.0401125\pi\)
\(152\) 500.215 + 866.398i 0.266926 + 0.462330i
\(153\) 0 0
\(154\) 0 0
\(155\) −1035.26 −0.536481
\(156\) 0 0
\(157\) 1893.58 3279.77i 0.962573 1.66723i 0.246575 0.969124i \(-0.420695\pi\)
0.715998 0.698102i \(-0.245972\pi\)
\(158\) −848.264 + 1469.24i −0.427116 + 0.739786i
\(159\) 0 0
\(160\) 237.255 0.117229
\(161\) 0 0
\(162\) 0 0
\(163\) 1054.28 + 1826.07i 0.506611 + 0.877476i 0.999971 + 0.00765060i \(0.00243528\pi\)
−0.493360 + 0.869825i \(0.664231\pi\)
\(164\) 395.210 684.524i 0.188175 0.325929i
\(165\) 0 0
\(166\) 210.863 + 365.225i 0.0985912 + 0.170765i
\(167\) −1502.41 −0.696170 −0.348085 0.937463i \(-0.613168\pi\)
−0.348085 + 0.937463i \(0.613168\pi\)
\(168\) 0 0
\(169\) −2189.23 −0.996465
\(170\) 374.000 + 647.787i 0.168732 + 0.292253i
\(171\) 0 0
\(172\) −686.587 + 1189.20i −0.304371 + 0.527186i
\(173\) 235.628 + 408.120i 0.103552 + 0.179357i 0.913146 0.407634i \(-0.133646\pi\)
−0.809594 + 0.586991i \(0.800313\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −167.765 −0.0718507
\(177\) 0 0
\(178\) 553.487 958.668i 0.233065 0.403681i
\(179\) 666.244 1153.97i 0.278198 0.481852i −0.692739 0.721188i \(-0.743596\pi\)
0.970937 + 0.239336i \(0.0769296\pi\)
\(180\) 0 0
\(181\) −997.727 −0.409726 −0.204863 0.978791i \(-0.565675\pi\)
−0.204863 + 0.978791i \(0.565675\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 728.999 + 1262.66i 0.292079 + 0.505896i
\(185\) −1462.67 + 2533.42i −0.581285 + 1.00681i
\(186\) 0 0
\(187\) −264.458 458.055i −0.103418 0.179124i
\(188\) 2440.02 0.946577
\(189\) 0 0
\(190\) 1854.35 0.708046
\(191\) 613.360 + 1062.37i 0.232362 + 0.402463i 0.958503 0.285083i \(-0.0920212\pi\)
−0.726141 + 0.687546i \(0.758688\pi\)
\(192\) 0 0
\(193\) 1739.65 3013.16i 0.648821 1.12379i −0.334584 0.942366i \(-0.608596\pi\)
0.983405 0.181425i \(-0.0580709\pi\)
\(194\) −903.910 1565.62i −0.334520 0.579406i
\(195\) 0 0
\(196\) 0 0
\(197\) −3193.47 −1.15495 −0.577476 0.816408i \(-0.695962\pi\)
−0.577476 + 0.816408i \(0.695962\pi\)
\(198\) 0 0
\(199\) −532.574 + 922.446i −0.189715 + 0.328595i −0.945155 0.326622i \(-0.894090\pi\)
0.755440 + 0.655217i \(0.227423\pi\)
\(200\) −280.118 + 485.178i −0.0990366 + 0.171536i
\(201\) 0 0
\(202\) −627.222 −0.218471
\(203\) 0 0
\(204\) 0 0
\(205\) −732.543 1268.80i −0.249576 0.432278i
\(206\) 230.975 400.060i 0.0781203 0.135308i
\(207\) 0 0
\(208\) −22.2944 38.6150i −0.00743191 0.0128724i
\(209\) −1311.22 −0.433968
\(210\) 0 0
\(211\) 2057.50 0.671298 0.335649 0.941987i \(-0.391044\pi\)
0.335649 + 0.941987i \(0.391044\pi\)
\(212\) −275.058 476.414i −0.0891088 0.154341i
\(213\) 0 0
\(214\) −125.486 + 217.348i −0.0400844 + 0.0694282i
\(215\) 1272.63 + 2204.25i 0.403685 + 0.699204i
\(216\) 0 0
\(217\) 0 0
\(218\) −1491.05 −0.463243
\(219\) 0 0
\(220\) −155.480 + 269.300i −0.0476476 + 0.0825281i
\(221\) 70.2881 121.743i 0.0213941 0.0370556i
\(222\) 0 0
\(223\) 2028.27 0.609071 0.304536 0.952501i \(-0.401499\pi\)
0.304536 + 0.952501i \(0.401499\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1043.76 + 1807.85i 0.307213 + 0.532108i
\(227\) 1211.98 2099.21i 0.354369 0.613786i −0.632640 0.774446i \(-0.718029\pi\)
0.987010 + 0.160660i \(0.0513622\pi\)
\(228\) 0 0
\(229\) 983.584 + 1703.62i 0.283830 + 0.491608i 0.972325 0.233633i \(-0.0750615\pi\)
−0.688495 + 0.725241i \(0.741728\pi\)
\(230\) 2702.48 0.774766
\(231\) 0 0
\(232\) 1249.06 0.353468
\(233\) 2239.17 + 3878.35i 0.629582 + 1.09047i 0.987636 + 0.156767i \(0.0501073\pi\)
−0.358053 + 0.933701i \(0.616559\pi\)
\(234\) 0 0
\(235\) 2261.35 3916.77i 0.627720 1.08724i
\(236\) 1178.87 + 2041.86i 0.325161 + 0.563195i
\(237\) 0 0
\(238\) 0 0
\(239\) −6116.92 −1.65553 −0.827763 0.561078i \(-0.810387\pi\)
−0.827763 + 0.561078i \(0.810387\pi\)
\(240\) 0 0
\(241\) −3114.19 + 5393.94i −0.832376 + 1.44172i 0.0637726 + 0.997964i \(0.479687\pi\)
−0.896149 + 0.443754i \(0.853647\pi\)
\(242\) −1221.06 + 2114.94i −0.324350 + 0.561790i
\(243\) 0 0
\(244\) 988.870 0.259450
\(245\) 0 0
\(246\) 0 0
\(247\) −174.250 301.809i −0.0448876 0.0777477i
\(248\) 558.530 967.402i 0.143011 0.247702i
\(249\) 0 0
\(250\) 1445.99 + 2504.53i 0.365810 + 0.633601i
\(251\) −5904.42 −1.48479 −0.742397 0.669960i \(-0.766311\pi\)
−0.742397 + 0.669960i \(0.766311\pi\)
\(252\) 0 0
\(253\) −1910.94 −0.474861
\(254\) −2080.17 3602.97i −0.513865 0.890041i
\(255\) 0 0
\(256\) −128.000 + 221.703i −0.0312500 + 0.0541266i
\(257\) −204.112 353.532i −0.0495414 0.0858082i 0.840191 0.542290i \(-0.182443\pi\)
−0.889733 + 0.456482i \(0.849109\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −82.6476 −0.0197138
\(261\) 0 0
\(262\) 1269.53 2198.89i 0.299357 0.518502i
\(263\) −2313.00 + 4006.24i −0.542304 + 0.939298i 0.456467 + 0.889740i \(0.349115\pi\)
−0.998771 + 0.0495577i \(0.984219\pi\)
\(264\) 0 0
\(265\) −1019.67 −0.236369
\(266\) 0 0
\(267\) 0 0
\(268\) 791.294 + 1370.56i 0.180358 + 0.312389i
\(269\) −435.646 + 754.562i −0.0987429 + 0.171028i −0.911165 0.412043i \(-0.864815\pi\)
0.812422 + 0.583070i \(0.198149\pi\)
\(270\) 0 0
\(271\) −3236.17 5605.22i −0.725401 1.25643i −0.958809 0.284052i \(-0.908321\pi\)
0.233408 0.972379i \(-0.425012\pi\)
\(272\) −807.098 −0.179917
\(273\) 0 0
\(274\) 6146.38 1.35517
\(275\) −367.139 635.904i −0.0805066 0.139442i
\(276\) 0 0
\(277\) −2355.94 + 4080.61i −0.511028 + 0.885126i 0.488890 + 0.872345i \(0.337402\pi\)
−0.999918 + 0.0127811i \(0.995932\pi\)
\(278\) 1013.60 + 1755.60i 0.218674 + 0.378755i
\(279\) 0 0
\(280\) 0 0
\(281\) 7165.66 1.52124 0.760618 0.649200i \(-0.224896\pi\)
0.760618 + 0.649200i \(0.224896\pi\)
\(282\) 0 0
\(283\) −3173.50 + 5496.67i −0.666590 + 1.15457i 0.312261 + 0.949996i \(0.398914\pi\)
−0.978851 + 0.204572i \(0.934420\pi\)
\(284\) 571.322 989.559i 0.119372 0.206759i
\(285\) 0 0
\(286\) 58.4407 0.0120828
\(287\) 0 0
\(288\) 0 0
\(289\) 1184.22 + 2051.13i 0.241038 + 0.417490i
\(290\) 1157.60 2005.02i 0.234401 0.405995i
\(291\) 0 0
\(292\) 1994.91 + 3455.29i 0.399807 + 0.692485i
\(293\) −9233.78 −1.84110 −0.920552 0.390621i \(-0.872260\pi\)
−0.920552 + 0.390621i \(0.872260\pi\)
\(294\) 0 0
\(295\) 4370.20 0.862519
\(296\) −1578.23 2733.58i −0.309909 0.536778i
\(297\) 0 0
\(298\) −1231.47 + 2132.97i −0.239386 + 0.414629i
\(299\) −253.947 439.848i −0.0491174 0.0850739i
\(300\) 0 0
\(301\) 0 0
\(302\) 4489.47 0.855430
\(303\) 0 0
\(304\) −1000.43 + 1732.80i −0.188745 + 0.326917i
\(305\) 916.461 1587.36i 0.172054 0.298006i
\(306\) 0 0
\(307\) 6786.53 1.26165 0.630827 0.775923i \(-0.282716\pi\)
0.630827 + 0.775923i \(0.282716\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −1035.26 1793.13i −0.189675 0.328526i
\(311\) 2568.38 4448.57i 0.468295 0.811111i −0.531048 0.847341i \(-0.678202\pi\)
0.999343 + 0.0362307i \(0.0115351\pi\)
\(312\) 0 0
\(313\) 1881.78 + 3259.34i 0.339822 + 0.588590i 0.984399 0.175950i \(-0.0562997\pi\)
−0.644577 + 0.764540i \(0.722966\pi\)
\(314\) 7574.31 1.36128
\(315\) 0 0
\(316\) −3393.06 −0.604033
\(317\) −517.473 896.289i −0.0916851 0.158803i 0.816535 0.577296i \(-0.195892\pi\)
−0.908220 + 0.418492i \(0.862559\pi\)
\(318\) 0 0
\(319\) −818.544 + 1417.76i −0.143667 + 0.248838i
\(320\) 237.255 + 410.937i 0.0414467 + 0.0717878i
\(321\) 0 0
\(322\) 0 0
\(323\) −6308.17 −1.08668
\(324\) 0 0
\(325\) 97.5789 169.012i 0.0166545 0.0288464i
\(326\) −2108.56 + 3652.13i −0.358228 + 0.620469i
\(327\) 0 0
\(328\) 1580.84 0.266120
\(329\) 0 0
\(330\) 0 0
\(331\) −4400.03 7621.08i −0.730657 1.26554i −0.956603 0.291395i \(-0.905880\pi\)
0.225945 0.974140i \(-0.427453\pi\)
\(332\) −421.726 + 730.451i −0.0697145 + 0.120749i
\(333\) 0 0
\(334\) −1502.41 2602.26i −0.246133 0.426315i
\(335\) 2933.41 0.478416
\(336\) 0 0
\(337\) −5859.78 −0.947189 −0.473595 0.880743i \(-0.657044\pi\)
−0.473595 + 0.880743i \(0.657044\pi\)
\(338\) −2189.23 3791.86i −0.352304 0.610208i
\(339\) 0 0
\(340\) −748.000 + 1295.57i −0.119312 + 0.206654i
\(341\) 732.043 + 1267.94i 0.116253 + 0.201356i
\(342\) 0 0
\(343\) 0 0
\(344\) −2746.35 −0.430445
\(345\) 0 0
\(346\) −471.256 + 816.239i −0.0732222 + 0.126825i
\(347\) 3969.27 6874.98i 0.614068 1.06360i −0.376479 0.926425i \(-0.622865\pi\)
0.990547 0.137172i \(-0.0438013\pi\)
\(348\) 0 0
\(349\) −9927.75 −1.52269 −0.761347 0.648344i \(-0.775462\pi\)
−0.761347 + 0.648344i \(0.775462\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −167.765 290.577i −0.0254031 0.0439994i
\(353\) −5051.52 + 8749.49i −0.761658 + 1.31923i 0.180338 + 0.983605i \(0.442281\pi\)
−0.941996 + 0.335625i \(0.891052\pi\)
\(354\) 0 0
\(355\) −1058.98 1834.20i −0.158323 0.274223i
\(356\) 2213.95 0.329604
\(357\) 0 0
\(358\) 2664.97 0.393431
\(359\) −2412.64 4178.81i −0.354691 0.614343i 0.632374 0.774663i \(-0.282081\pi\)
−0.987065 + 0.160320i \(0.948747\pi\)
\(360\) 0 0
\(361\) −4389.73 + 7603.23i −0.639996 + 1.10850i
\(362\) −997.727 1728.11i −0.144860 0.250905i
\(363\) 0 0
\(364\) 0 0
\(365\) 7395.36 1.06052
\(366\) 0 0
\(367\) −3467.65 + 6006.15i −0.493215 + 0.854274i −0.999969 0.00781688i \(-0.997512\pi\)
0.506754 + 0.862091i \(0.330845\pi\)
\(368\) −1458.00 + 2525.33i −0.206531 + 0.357722i
\(369\) 0 0
\(370\) −5850.68 −0.822061
\(371\) 0 0
\(372\) 0 0
\(373\) −7046.55 12205.0i −0.978168 1.69424i −0.669058 0.743210i \(-0.733302\pi\)
−0.309110 0.951026i \(-0.600031\pi\)
\(374\) 528.916 916.109i 0.0731272 0.126660i
\(375\) 0 0
\(376\) 2440.02 + 4226.23i 0.334666 + 0.579658i
\(377\) −435.108 −0.0594409
\(378\) 0 0
\(379\) 5354.17 0.725661 0.362830 0.931855i \(-0.381810\pi\)
0.362830 + 0.931855i \(0.381810\pi\)
\(380\) 1854.35 + 3211.83i 0.250332 + 0.433588i
\(381\) 0 0
\(382\) −1226.72 + 2124.74i −0.164305 + 0.284585i
\(383\) −4485.24 7768.66i −0.598394 1.03645i −0.993058 0.117623i \(-0.962472\pi\)
0.394664 0.918825i \(-0.370861\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 6958.58 0.917571
\(387\) 0 0
\(388\) 1807.82 3131.23i 0.236542 0.409702i
\(389\) −1851.29 + 3206.53i −0.241296 + 0.417937i −0.961084 0.276257i \(-0.910906\pi\)
0.719788 + 0.694194i \(0.244239\pi\)
\(390\) 0 0
\(391\) −9193.34 −1.18907
\(392\) 0 0
\(393\) 0 0
\(394\) −3193.47 5531.26i −0.408337 0.707260i
\(395\) −3144.61 + 5446.62i −0.400563 + 0.693795i
\(396\) 0 0
\(397\) 1041.62 + 1804.13i 0.131681 + 0.228078i 0.924325 0.381607i \(-0.124629\pi\)
−0.792644 + 0.609685i \(0.791296\pi\)
\(398\) −2130.30 −0.268297
\(399\) 0 0
\(400\) −1120.47 −0.140059
\(401\) −5317.01 9209.33i −0.662141 1.14686i −0.980052 0.198742i \(-0.936314\pi\)
0.317910 0.948121i \(-0.397019\pi\)
\(402\) 0 0
\(403\) −194.564 + 336.994i −0.0240494 + 0.0416548i
\(404\) −627.222 1086.38i −0.0772412 0.133786i
\(405\) 0 0
\(406\) 0 0
\(407\) 4137.06 0.503848
\(408\) 0 0
\(409\) 3258.18 5643.34i 0.393904 0.682262i −0.599056 0.800707i \(-0.704458\pi\)
0.992961 + 0.118445i \(0.0377908\pi\)
\(410\) 1465.09 2537.60i 0.176477 0.305667i
\(411\) 0 0
\(412\) 923.899 0.110479
\(413\) 0 0
\(414\) 0 0
\(415\) 781.691 + 1353.93i 0.0924620 + 0.160149i
\(416\) 44.5887 77.2300i 0.00525515 0.00910219i
\(417\) 0 0
\(418\) −1311.22 2271.11i −0.153431 0.265750i
\(419\) −6079.92 −0.708887 −0.354443 0.935077i \(-0.615330\pi\)
−0.354443 + 0.935077i \(0.615330\pi\)
\(420\) 0 0
\(421\) −5631.58 −0.651939 −0.325969 0.945380i \(-0.605691\pi\)
−0.325969 + 0.945380i \(0.605691\pi\)
\(422\) 2057.50 + 3563.69i 0.237340 + 0.411084i
\(423\) 0 0
\(424\) 550.116 952.829i 0.0630094 0.109136i
\(425\) −1766.27 3059.27i −0.201592 0.349168i
\(426\) 0 0
\(427\) 0 0
\(428\) −501.945 −0.0566879
\(429\) 0 0
\(430\) −2545.25 + 4408.50i −0.285449 + 0.494412i
\(431\) −1868.45 + 3236.25i −0.208817 + 0.361681i −0.951342 0.308137i \(-0.900295\pi\)
0.742525 + 0.669818i \(0.233628\pi\)
\(432\) 0 0
\(433\) −5757.46 −0.638998 −0.319499 0.947587i \(-0.603515\pi\)
−0.319499 + 0.947587i \(0.603515\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −1491.05 2582.58i −0.163781 0.283677i
\(437\) −11395.5 + 19737.6i −1.24742 + 2.16059i
\(438\) 0 0
\(439\) 4906.38 + 8498.10i 0.533414 + 0.923900i 0.999238 + 0.0390229i \(0.0124245\pi\)
−0.465824 + 0.884877i \(0.654242\pi\)
\(440\) −621.921 −0.0673839
\(441\) 0 0
\(442\) 281.152 0.0302558
\(443\) 2915.15 + 5049.19i 0.312648 + 0.541522i 0.978935 0.204174i \(-0.0654507\pi\)
−0.666287 + 0.745695i \(0.732117\pi\)
\(444\) 0 0
\(445\) 2051.84 3553.89i 0.218576 0.378585i
\(446\) 2028.27 + 3513.06i 0.215339 + 0.372978i
\(447\) 0 0
\(448\) 0 0
\(449\) 8674.94 0.911794 0.455897 0.890033i \(-0.349319\pi\)
0.455897 + 0.890033i \(0.349319\pi\)
\(450\) 0 0
\(451\) −1035.97 + 1794.36i −0.108164 + 0.187346i
\(452\) −2087.53 + 3615.70i −0.217232 + 0.376257i
\(453\) 0 0
\(454\) 4847.91 0.501154
\(455\) 0 0
\(456\) 0 0
\(457\) −4553.41 7886.74i −0.466082 0.807278i 0.533167 0.846010i \(-0.321002\pi\)
−0.999250 + 0.0387315i \(0.987668\pi\)
\(458\) −1967.17 + 3407.24i −0.200698 + 0.347619i
\(459\) 0 0
\(460\) 2702.48 + 4680.83i 0.273921 + 0.474445i
\(461\) 8729.69 0.881957 0.440979 0.897518i \(-0.354631\pi\)
0.440979 + 0.897518i \(0.354631\pi\)
\(462\) 0 0
\(463\) −1795.62 −0.180237 −0.0901184 0.995931i \(-0.528725\pi\)
−0.0901184 + 0.995931i \(0.528725\pi\)
\(464\) 1249.06 + 2163.43i 0.124970 + 0.216454i
\(465\) 0 0
\(466\) −4478.33 + 7756.70i −0.445182 + 0.771078i
\(467\) 65.2797 + 113.068i 0.00646849 + 0.0112038i 0.869242 0.494388i \(-0.164608\pi\)
−0.862773 + 0.505591i \(0.831274\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 9045.40 0.887730
\(471\) 0 0
\(472\) −2357.74 + 4083.73i −0.229924 + 0.398239i
\(473\) 1799.76 3117.28i 0.174954 0.303029i
\(474\) 0 0
\(475\) −8757.45 −0.845935
\(476\) 0 0
\(477\) 0 0
\(478\) −6116.92 10594.8i −0.585317 1.01380i
\(479\) 5922.90 10258.8i 0.564978 0.978570i −0.432074 0.901838i \(-0.642218\pi\)
0.997052 0.0767319i \(-0.0244485\pi\)
\(480\) 0 0
\(481\) 549.777 + 952.242i 0.0521158 + 0.0902671i
\(482\) −12456.8 −1.17716
\(483\) 0 0
\(484\) −4884.24 −0.458700
\(485\) −3350.89 5803.91i −0.313724 0.543386i
\(486\) 0 0
\(487\) 2403.61 4163.17i 0.223650 0.387374i −0.732263 0.681022i \(-0.761536\pi\)
0.955914 + 0.293648i \(0.0948693\pi\)
\(488\) 988.870 + 1712.77i 0.0917296 + 0.158880i
\(489\) 0 0
\(490\) 0 0
\(491\) −6068.04 −0.557733 −0.278866 0.960330i \(-0.589959\pi\)
−0.278866 + 0.960330i \(0.589959\pi\)
\(492\) 0 0
\(493\) −3937.93 + 6820.70i −0.359748 + 0.623101i
\(494\) 348.500 603.619i 0.0317404 0.0549759i
\(495\) 0 0
\(496\) 2234.12 0.202248
\(497\) 0 0
\(498\) 0 0
\(499\) 7753.21 + 13429.0i 0.695554 + 1.20473i 0.969994 + 0.243130i \(0.0781742\pi\)
−0.274440 + 0.961604i \(0.588492\pi\)
\(500\) −2891.98 + 5009.06i −0.258667 + 0.448024i
\(501\) 0 0
\(502\) −5904.42 10226.7i −0.524954 0.909247i
\(503\) 1496.79 0.132681 0.0663405 0.997797i \(-0.478868\pi\)
0.0663405 + 0.997797i \(0.478868\pi\)
\(504\) 0 0
\(505\) −2325.18 −0.204889
\(506\) −1910.94 3309.85i −0.167889 0.290792i
\(507\) 0 0
\(508\) 4160.35 7205.94i 0.363358 0.629354i
\(509\) −2526.87 4376.66i −0.220042 0.381124i 0.734778 0.678307i \(-0.237286\pi\)
−0.954821 + 0.297183i \(0.903953\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −512.000 −0.0441942
\(513\) 0 0
\(514\) 408.223 707.063i 0.0350310 0.0606755i
\(515\) 856.248 1483.07i 0.0732637 0.126896i
\(516\) 0 0
\(517\) −6396.07 −0.544098
\(518\) 0 0
\(519\) 0 0
\(520\) −82.6476 143.150i −0.00696988 0.0120722i
\(521\) 4868.36 8432.25i 0.409380 0.709067i −0.585441 0.810715i \(-0.699078\pi\)
0.994820 + 0.101649i \(0.0324118\pi\)
\(522\) 0 0
\(523\) 5898.34 + 10216.2i 0.493148 + 0.854157i 0.999969 0.00789446i \(-0.00251291\pi\)
−0.506821 + 0.862051i \(0.669180\pi\)
\(524\) 5078.11 0.423355
\(525\) 0 0
\(526\) −9252.01 −0.766933
\(527\) 3521.79 + 6099.91i 0.291103 + 0.504206i
\(528\) 0 0
\(529\) −10524.0 + 18228.1i −0.864962 + 1.49816i
\(530\) −1019.67 1766.12i −0.0835691 0.144746i
\(531\) 0 0
\(532\) 0 0
\(533\) −550.685 −0.0447520
\(534\) 0 0
\(535\) −465.191 + 805.734i −0.0375924 + 0.0651120i
\(536\) −1582.59 + 2741.12i −0.127532 + 0.220893i
\(537\) 0 0
\(538\) −1742.59 −0.139644
\(539\) 0 0
\(540\) 0 0
\(541\) 2155.41 + 3733.28i 0.171291 + 0.296684i 0.938871 0.344268i \(-0.111873\pi\)
−0.767581 + 0.640952i \(0.778540\pi\)
\(542\) 6472.35 11210.4i 0.512936 0.888431i
\(543\) 0 0
\(544\) −807.098 1397.94i −0.0636104 0.110176i
\(545\) −5527.50 −0.434444
\(546\) 0 0
\(547\) 17015.9 1.33007 0.665034 0.746813i \(-0.268417\pi\)
0.665034 + 0.746813i \(0.268417\pi\)
\(548\) 6146.38 + 10645.8i 0.479124 + 0.829868i
\(549\) 0 0
\(550\) 734.278 1271.81i 0.0569268 0.0986001i
\(551\) 9762.45 + 16909.1i 0.754799 + 1.30735i
\(552\) 0 0
\(553\) 0 0
\(554\) −9423.76 −0.722703
\(555\) 0 0
\(556\) −2027.19 + 3511.20i −0.154626 + 0.267820i
\(557\) 870.588 1507.90i 0.0662262 0.114707i −0.831011 0.556256i \(-0.812237\pi\)
0.897237 + 0.441549i \(0.145571\pi\)
\(558\) 0 0
\(559\) 956.689 0.0723858
\(560\) 0 0
\(561\) 0 0
\(562\) 7165.66 + 12411.3i 0.537838 + 0.931563i
\(563\) 5673.42 9826.66i 0.424700 0.735602i −0.571692 0.820468i \(-0.693713\pi\)
0.996392 + 0.0848658i \(0.0270461\pi\)
\(564\) 0 0
\(565\) 3869.34 + 6701.89i 0.288114 + 0.499028i
\(566\) −12694.0 −0.942701
\(567\) 0 0
\(568\) 2285.29 0.168818
\(569\) −9208.72 15950.0i −0.678470 1.17514i −0.975442 0.220258i \(-0.929310\pi\)
0.296972 0.954886i \(-0.404023\pi\)
\(570\) 0 0
\(571\) −4999.25 + 8658.95i −0.366396 + 0.634616i −0.988999 0.147922i \(-0.952742\pi\)
0.622603 + 0.782538i \(0.286075\pi\)
\(572\) 58.4407 + 101.222i 0.00427190 + 0.00739915i
\(573\) 0 0
\(574\) 0 0
\(575\) −12762.8 −0.925648
\(576\) 0 0
\(577\) 700.855 1213.92i 0.0505667 0.0875840i −0.839634 0.543152i \(-0.817231\pi\)
0.890201 + 0.455568i \(0.150564\pi\)
\(578\) −2368.44 + 4102.26i −0.170440 + 0.295210i
\(579\) 0 0
\(580\) 4630.38 0.331494
\(581\) 0 0
\(582\) 0 0
\(583\) 721.015 + 1248.83i 0.0512202 + 0.0887160i
\(584\) −3989.83 + 6910.59i −0.282706 + 0.489661i
\(585\) 0 0
\(586\) −9233.78 15993.4i −0.650928 1.12744i
\(587\) 10851.3 0.763001 0.381500 0.924369i \(-0.375407\pi\)
0.381500 + 0.924369i \(0.375407\pi\)
\(588\) 0 0
\(589\) 17461.6 1.22155
\(590\) 4370.20 + 7569.41i 0.304946 + 0.528183i
\(591\) 0 0
\(592\) 3156.47 5467.16i 0.219139 0.379559i
\(593\) 10231.0 + 17720.6i 0.708493 + 1.22715i 0.965416 + 0.260715i \(0.0839581\pi\)
−0.256923 + 0.966432i \(0.582709\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −4925.88 −0.338544
\(597\) 0 0
\(598\) 507.893 879.697i 0.0347313 0.0601563i
\(599\) 4995.21 8651.96i 0.340733 0.590166i −0.643836 0.765163i \(-0.722658\pi\)
0.984569 + 0.174997i \(0.0559916\pi\)
\(600\) 0 0
\(601\) 17435.9 1.18341 0.591703 0.806156i \(-0.298456\pi\)
0.591703 + 0.806156i \(0.298456\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 4489.47 + 7775.99i 0.302440 + 0.523842i
\(605\) −4526.60 + 7840.29i −0.304186 + 0.526865i
\(606\) 0 0
\(607\) −8350.16 14462.9i −0.558356 0.967102i −0.997634 0.0687503i \(-0.978099\pi\)
0.439277 0.898351i \(-0.355234\pi\)
\(608\) −4001.72 −0.266926
\(609\) 0 0
\(610\) 3665.85 0.243321
\(611\) −849.979 1472.21i −0.0562790 0.0974781i
\(612\) 0 0
\(613\) 13351.5 23125.4i 0.879707 1.52370i 0.0280452 0.999607i \(-0.491072\pi\)
0.851662 0.524091i \(-0.175595\pi\)
\(614\) 6786.53 + 11754.6i 0.446062 + 0.772602i
\(615\) 0 0
\(616\) 0 0
\(617\) −27790.4 −1.81329 −0.906645 0.421894i \(-0.861365\pi\)
−0.906645 + 0.421894i \(0.861365\pi\)
\(618\) 0 0
\(619\) −868.040 + 1503.49i −0.0563642 + 0.0976257i −0.892831 0.450392i \(-0.851284\pi\)
0.836467 + 0.548018i \(0.184617\pi\)
\(620\) 2070.53 3586.26i 0.134120 0.232303i
\(621\) 0 0
\(622\) 10273.5 0.662269
\(623\) 0 0
\(624\) 0 0
\(625\) 983.599 + 1703.64i 0.0629503 + 0.109033i
\(626\) −3763.56 + 6518.67i −0.240291 + 0.416196i
\(627\) 0 0
\(628\) 7574.31 + 13119.1i 0.481287 + 0.833613i
\(629\) 19903.0 1.26166
\(630\) 0 0
\(631\) −8990.27 −0.567190 −0.283595 0.958944i \(-0.591527\pi\)
−0.283595 + 0.958944i \(0.591527\pi\)
\(632\) −3393.06 5876.95i −0.213558 0.369893i
\(633\) 0 0
\(634\) 1034.95 1792.58i 0.0648311 0.112291i
\(635\) −7711.43 13356.6i −0.481919 0.834709i
\(636\) 0 0
\(637\) 0 0
\(638\) −3274.18 −0.203175
\(639\) 0 0
\(640\) −474.510 + 821.875i −0.0293073 + 0.0507617i
\(641\) −6884.81 + 11924.8i −0.424233 + 0.734794i −0.996348 0.0853796i \(-0.972790\pi\)
0.572115 + 0.820173i \(0.306123\pi\)
\(642\) 0 0
\(643\) 26969.9 1.65411 0.827053 0.562124i \(-0.190015\pi\)
0.827053 + 0.562124i \(0.190015\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −6308.17 10926.1i −0.384198 0.665450i
\(647\) 12200.9 21132.5i 0.741368 1.28409i −0.210504 0.977593i \(-0.567510\pi\)
0.951872 0.306495i \(-0.0991562\pi\)
\(648\) 0 0
\(649\) −3090.20 5352.38i −0.186904 0.323728i
\(650\) 390.316 0.0235530
\(651\) 0 0
\(652\) −8434.24 −0.506611
\(653\) 7984.79 + 13830.1i 0.478513 + 0.828809i 0.999696 0.0246357i \(-0.00784257\pi\)
−0.521183 + 0.853445i \(0.674509\pi\)
\(654\) 0 0
\(655\) 4706.27 8151.50i 0.280747 0.486268i
\(656\) 1580.84 + 2738.10i 0.0940876 + 0.162965i
\(657\) 0 0
\(658\) 0 0
\(659\) 11596.2 0.685467 0.342733 0.939433i \(-0.388647\pi\)
0.342733 + 0.939433i \(0.388647\pi\)
\(660\) 0 0
\(661\) −6301.11 + 10913.8i −0.370779 + 0.642208i −0.989686 0.143257i \(-0.954243\pi\)
0.618907 + 0.785464i \(0.287576\pi\)
\(662\) 8800.06 15242.2i 0.516653 0.894869i
\(663\) 0 0
\(664\) −1686.90 −0.0985912
\(665\) 0 0
\(666\) 0 0
\(667\) 14227.5 + 24642.8i 0.825924 + 1.43054i
\(668\) 3004.83 5204.52i 0.174042 0.301450i
\(669\) 0 0
\(670\) 2933.41 + 5080.81i 0.169146 + 0.292969i
\(671\) −2592.14 −0.149134
\(672\) 0 0
\(673\) 2126.29 0.121787 0.0608934 0.998144i \(-0.480605\pi\)
0.0608934 + 0.998144i \(0.480605\pi\)
\(674\) −5859.78 10149.4i −0.334882 0.580032i
\(675\) 0 0
\(676\) 4378.47 7583.73i 0.249116 0.431482i
\(677\) 1309.69 + 2268.45i 0.0743508 + 0.128779i 0.900804 0.434226i \(-0.142978\pi\)
−0.826453 + 0.563006i \(0.809645\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) −2992.00 −0.168732
\(681\) 0 0
\(682\) −1464.09 + 2535.87i −0.0822034 + 0.142381i
\(683\) −14964.9 + 25919.9i −0.838383 + 1.45212i 0.0528633 + 0.998602i \(0.483165\pi\)
−0.891246 + 0.453520i \(0.850168\pi\)
\(684\) 0 0
\(685\) 22785.3 1.27092
\(686\) 0 0
\(687\) 0 0
\(688\) −2746.35 4756.81i −0.152185 0.263593i
\(689\) −191.633 + 331.918i −0.0105960 + 0.0183528i
\(690\) 0 0
\(691\) −3380.45 5855.11i −0.186105 0.322343i 0.757844 0.652436i \(-0.226253\pi\)
−0.943948 + 0.330094i \(0.892920\pi\)
\(692\) −1885.02 −0.103552
\(693\) 0 0
\(694\) 15877.1 0.868423
\(695\) 3757.51 + 6508.20i 0.205080 + 0.355209i
\(696\) 0 0
\(697\) −4983.96 + 8632.48i −0.270848 + 0.469122i
\(698\) −9927.75 17195.4i −0.538354 0.932456i
\(699\) 0 0
\(700\) 0 0
\(701\) −467.205 −0.0251727 −0.0125864 0.999921i \(-0.504006\pi\)
−0.0125864 + 0.999921i \(0.504006\pi\)
\(702\) 0 0
\(703\) 24670.5 42730.6i 1.32357 2.29248i
\(704\) 335.529 581.153i 0.0179627 0.0311123i
\(705\) 0 0
\(706\) −20206.1 −1.07715
\(707\) 0 0
\(708\) 0 0
\(709\) −4412.32 7642.36i −0.233721 0.404816i 0.725179 0.688560i \(-0.241757\pi\)
−0.958900 + 0.283744i \(0.908424\pi\)
\(710\) 2117.95 3668.40i 0.111951 0.193905i
\(711\) 0 0
\(712\) 2213.95 + 3834.67i 0.116533 + 0.201841i
\(713\) 25448.0 1.33665
\(714\) 0 0
\(715\) 216.646 0.0113316
\(716\) 2664.97 + 4615.87i 0.139099 + 0.240926i
\(717\) 0 0
\(718\) 4825.27 8357.62i 0.250804 0.434406i
\(719\) −10549.4 18272.2i −0.547188 0.947757i −0.998466 0.0553733i \(-0.982365\pi\)
0.451278 0.892383i \(-0.350968\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) −17558.9 −0.905090
\(723\) 0 0
\(724\) 1995.45 3456.23i 0.102432 0.177417i
\(725\) −5466.92 + 9468.98i −0.280050 + 0.485061i
\(726\) 0 0
\(727\) −4616.48 −0.235510 −0.117755 0.993043i \(-0.537570\pi\)
−0.117755 + 0.993043i \(0.537570\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 7395.36 + 12809.1i 0.374951 + 0.649435i
\(731\) 8658.49 14996.9i 0.438093 0.758799i
\(732\) 0 0
\(733\) 5344.03 + 9256.13i 0.269285 + 0.466416i 0.968678 0.248322i \(-0.0798791\pi\)
−0.699392 + 0.714738i \(0.746546\pi\)
\(734\) −13870.6 −0.697511
\(735\) 0 0
\(736\) −5831.99 −0.292079
\(737\) −2074.23 3592.68i −0.103671 0.179563i
\(738\) 0 0
\(739\) 7683.78 13308.7i 0.382480 0.662474i −0.608936 0.793219i \(-0.708404\pi\)
0.991416 + 0.130745i \(0.0417369\pi\)
\(740\) −5850.68 10133.7i −0.290642 0.503407i
\(741\) 0 0
\(742\) 0 0
\(743\) −6502.58 −0.321072 −0.160536 0.987030i \(-0.551322\pi\)
−0.160536 + 0.987030i \(0.551322\pi\)
\(744\) 0 0
\(745\) −4565.19 + 7907.14i −0.224504 + 0.388853i
\(746\) 14093.1 24410.0i 0.691669 1.19801i
\(747\) 0 0
\(748\) 2115.66 0.103418
\(749\) 0 0
\(750\) 0 0
\(751\) 9937.07 + 17211.5i 0.482835 + 0.836295i 0.999806 0.0197085i \(-0.00627380\pi\)
−0.516971 + 0.856003i \(0.672940\pi\)
\(752\) −4880.03 + 8452.47i −0.236644 + 0.409880i
\(753\) 0 0
\(754\) −435.108 753.630i −0.0210155 0.0364000i
\(755\) 16642.9 0.802250
\(756\) 0 0
\(757\) −15157.8 −0.727765 −0.363883 0.931445i \(-0.618549\pi\)
−0.363883 + 0.931445i \(0.618549\pi\)
\(758\) 5354.17 + 9273.70i 0.256560 + 0.444375i
\(759\) 0 0
\(760\) −3708.70 + 6423.66i −0.177012 + 0.306593i
\(761\) 17609.9 + 30501.3i 0.838842 + 1.45292i 0.890863 + 0.454271i \(0.150100\pi\)
−0.0520212 + 0.998646i \(0.516566\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −4906.88 −0.232362
\(765\) 0 0
\(766\) 8970.47 15537.3i 0.423128 0.732880i
\(767\) 821.319 1422.57i 0.0386651 0.0669698i
\(768\) 0 0
\(769\) −2264.35 −0.106183 −0.0530915 0.998590i \(-0.516907\pi\)
−0.0530915 + 0.998590i \(0.516907\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 6958.58 + 12052.6i 0.324410 + 0.561895i
\(773\) −4766.39 + 8255.64i −0.221779 + 0.384133i −0.955348 0.295482i \(-0.904520\pi\)
0.733569 + 0.679615i \(0.237853\pi\)
\(774\) 0 0
\(775\) 4889.19 + 8468.33i 0.226613 + 0.392505i
\(776\) 7231.28 0.334520
\(777\) 0 0
\(778\) −7405.16 −0.341244
\(779\) 12355.6 + 21400.6i 0.568276 + 0.984282i
\(780\) 0 0
\(781\) −1497.62 + 2593.95i −0.0686159 + 0.118846i
\(782\) −9193.34 15923.3i −0.420401 0.728155i
\(783\) 0 0
\(784\) 0 0
\(785\) 28078.8 1.27666
\(786\) 0 0
\(787\) 16606.5 28763.3i 0.752170 1.30280i −0.194599 0.980883i \(-0.562341\pi\)
0.946769 0.321913i \(-0.104326\pi\)
\(788\) 6386.94 11062.5i 0.288738 0.500109i
\(789\) 0 0
\(790\) −12578.4 −0.566481
\(791\) 0