Properties

Label 405.4.e.r.136.3
Level $405$
Weight $4$
Character 405.136
Analytic conductor $23.896$
Analytic rank $0$
Dimension $6$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 405 = 3^{4} \cdot 5 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 405.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(23.8957735523\)
Analytic rank: \(0\)
Dimension: \(6\)
Relative dimension: \(3\) over \(\Q(\zeta_{3})\)
Coefficient field: 6.0.95327307.1
Defining polynomial: \(x^{6} - 3 x^{5} + 20 x^{4} - 35 x^{3} + 85 x^{2} - 68 x + 16\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 3^{3} \)
Twist minimal: no (minimal twist has level 135)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 136.3
Root \(0.500000 + 2.36807i\) of defining polynomial
Character \(\chi\) \(=\) 405.136
Dual form 405.4.e.r.271.3

$q$-expansion

\(f(q)\) \(=\) \(q+(2.22969 - 3.86194i) q^{2} +(-5.94305 - 10.2937i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-2.54062 + 4.40048i) q^{7} -17.3296 q^{8} +O(q^{10})\) \(q+(2.22969 - 3.86194i) q^{2} +(-5.94305 - 10.2937i) q^{4} +(2.50000 + 4.33013i) q^{5} +(-2.54062 + 4.40048i) q^{7} -17.3296 q^{8} +22.2969 q^{10} +(29.1503 - 50.4899i) q^{11} +(-10.6060 - 18.3701i) q^{13} +(11.3296 + 19.6234i) q^{14} +(8.90475 - 15.4235i) q^{16} +68.8451 q^{17} -40.8133 q^{19} +(29.7152 - 51.4683i) q^{20} +(-129.993 - 225.154i) q^{22} +(-72.1592 - 124.983i) q^{23} +(-12.5000 + 21.6506i) q^{25} -94.5921 q^{26} +60.3960 q^{28} +(-110.029 + 190.576i) q^{29} +(-145.773 - 252.486i) q^{31} +(-109.028 - 188.842i) q^{32} +(153.503 - 265.875i) q^{34} -25.4062 q^{35} +260.637 q^{37} +(-91.0010 + 157.618i) q^{38} +(-43.3240 - 75.0393i) q^{40} +(-84.8832 - 147.022i) q^{41} +(219.298 - 379.835i) q^{43} -692.967 q^{44} -643.571 q^{46} +(-127.740 + 221.253i) q^{47} +(158.591 + 274.687i) q^{49} +(55.7423 + 96.5485i) q^{50} +(-126.063 + 218.348i) q^{52} -214.714 q^{53} +291.503 q^{55} +(44.0278 - 76.2585i) q^{56} +(490.661 + 849.850i) q^{58} +(165.762 + 287.108i) q^{59} +(-27.4823 + 47.6008i) q^{61} -1300.11 q^{62} -829.920 q^{64} +(53.0298 - 91.8503i) q^{65} +(-379.090 - 656.603i) q^{67} +(-409.149 - 708.668i) q^{68} +(-56.6479 + 98.1171i) q^{70} +904.348 q^{71} +866.622 q^{73} +(581.139 - 1006.56i) q^{74} +(242.555 + 420.118i) q^{76} +(148.120 + 256.551i) q^{77} +(-103.480 + 179.233i) q^{79} +89.0475 q^{80} -757.054 q^{82} +(-231.699 + 401.314i) q^{83} +(172.113 + 298.108i) q^{85} +(-977.933 - 1693.83i) q^{86} +(-505.163 + 874.968i) q^{88} -601.736 q^{89} +107.783 q^{91} +(-857.691 + 1485.56i) q^{92} +(569.643 + 986.651i) q^{94} +(-102.033 - 176.727i) q^{95} +(-114.682 + 198.634i) q^{97} +1414.43 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8} + O(q^{10}) \) \( 6 q - q^{2} - 23 q^{4} + 15 q^{5} - 44 q^{7} + 72 q^{8} - 10 q^{10} + 38 q^{11} - 28 q^{13} - 108 q^{14} - 191 q^{16} + 38 q^{17} + 374 q^{19} + 115 q^{20} - 122 q^{22} - 81 q^{23} - 75 q^{25} - 832 q^{26} + 820 q^{28} + 160 q^{29} - 227 q^{31} - 569 q^{32} - 17 q^{34} - 440 q^{35} + 156 q^{37} - 757 q^{38} + 180 q^{40} - 338 q^{41} - 22 q^{43} - 3272 q^{44} - 2850 q^{46} - 472 q^{47} + 197 q^{49} - 25 q^{50} + 1566 q^{52} - 1042 q^{53} + 380 q^{55} - 1254 q^{56} + 2096 q^{58} + 140 q^{59} - 595 q^{61} - 2814 q^{62} - 1836 q^{64} + 140 q^{65} - 878 q^{67} - 3053 q^{68} + 540 q^{70} + 1204 q^{71} + 2588 q^{73} + 2878 q^{74} - 525 q^{76} + 288 q^{77} - 629 q^{79} - 1910 q^{80} - 3364 q^{82} - 1287 q^{83} + 95 q^{85} - 3730 q^{86} + 858 q^{88} - 4308 q^{89} - 880 q^{91} + 1959 q^{92} + 1108 q^{94} + 935 q^{95} - 1392 q^{97} + 5386 q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).

\(n\) \(82\) \(326\)
\(\chi(n)\) \(1\) \(e\left(\frac{2}{3}\right)\)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.22969 3.86194i 0.788315 1.36540i −0.138684 0.990337i \(-0.544287\pi\)
0.926999 0.375065i \(-0.122380\pi\)
\(3\) 0 0
\(4\) −5.94305 10.2937i −0.742881 1.28671i
\(5\) 2.50000 + 4.33013i 0.223607 + 0.387298i
\(6\) 0 0
\(7\) −2.54062 + 4.40048i −0.137180 + 0.237603i −0.926428 0.376471i \(-0.877137\pi\)
0.789248 + 0.614075i \(0.210471\pi\)
\(8\) −17.3296 −0.765867
\(9\) 0 0
\(10\) 22.2969 0.705090
\(11\) 29.1503 50.4899i 0.799014 1.38393i −0.121244 0.992623i \(-0.538688\pi\)
0.920259 0.391311i \(-0.127978\pi\)
\(12\) 0 0
\(13\) −10.6060 18.3701i −0.226274 0.391918i 0.730427 0.682991i \(-0.239321\pi\)
−0.956701 + 0.291073i \(0.905988\pi\)
\(14\) 11.3296 + 19.6234i 0.216283 + 0.374613i
\(15\) 0 0
\(16\) 8.90475 15.4235i 0.139137 0.240992i
\(17\) 68.8451 0.982199 0.491099 0.871104i \(-0.336595\pi\)
0.491099 + 0.871104i \(0.336595\pi\)
\(18\) 0 0
\(19\) −40.8133 −0.492800 −0.246400 0.969168i \(-0.579248\pi\)
−0.246400 + 0.969168i \(0.579248\pi\)
\(20\) 29.7152 51.4683i 0.332226 0.575433i
\(21\) 0 0
\(22\) −129.993 225.154i −1.25975 2.18195i
\(23\) −72.1592 124.983i −0.654184 1.13308i −0.982098 0.188372i \(-0.939679\pi\)
0.327914 0.944708i \(-0.393654\pi\)
\(24\) 0 0
\(25\) −12.5000 + 21.6506i −0.100000 + 0.173205i
\(26\) −94.5921 −0.713501
\(27\) 0 0
\(28\) 60.3960 0.407635
\(29\) −110.029 + 190.576i −0.704547 + 1.22031i 0.262308 + 0.964984i \(0.415516\pi\)
−0.966855 + 0.255327i \(0.917817\pi\)
\(30\) 0 0
\(31\) −145.773 252.486i −0.844566 1.46283i −0.885998 0.463690i \(-0.846525\pi\)
0.0414319 0.999141i \(-0.486808\pi\)
\(32\) −109.028 188.842i −0.602301 1.04322i
\(33\) 0 0
\(34\) 153.503 265.875i 0.774282 1.34110i
\(35\) −25.4062 −0.122698
\(36\) 0 0
\(37\) 260.637 1.15807 0.579033 0.815304i \(-0.303430\pi\)
0.579033 + 0.815304i \(0.303430\pi\)
\(38\) −91.0010 + 157.618i −0.388482 + 0.672870i
\(39\) 0 0
\(40\) −43.3240 75.0393i −0.171253 0.296619i
\(41\) −84.8832 147.022i −0.323330 0.560024i 0.657843 0.753155i \(-0.271469\pi\)
−0.981173 + 0.193131i \(0.938136\pi\)
\(42\) 0 0
\(43\) 219.298 379.835i 0.777735 1.34708i −0.155509 0.987834i \(-0.549702\pi\)
0.933244 0.359242i \(-0.116965\pi\)
\(44\) −692.967 −2.37429
\(45\) 0 0
\(46\) −643.571 −2.06281
\(47\) −127.740 + 221.253i −0.396444 + 0.686661i −0.993284 0.115699i \(-0.963089\pi\)
0.596841 + 0.802360i \(0.296422\pi\)
\(48\) 0 0
\(49\) 158.591 + 274.687i 0.462363 + 0.800836i
\(50\) 55.7423 + 96.5485i 0.157663 + 0.273080i
\(51\) 0 0
\(52\) −126.063 + 218.348i −0.336189 + 0.582297i
\(53\) −214.714 −0.556477 −0.278239 0.960512i \(-0.589751\pi\)
−0.278239 + 0.960512i \(0.589751\pi\)
\(54\) 0 0
\(55\) 291.503 0.714660
\(56\) 44.0278 76.2585i 0.105062 0.181973i
\(57\) 0 0
\(58\) 490.661 + 849.850i 1.11081 + 1.92398i
\(59\) 165.762 + 287.108i 0.365769 + 0.633530i 0.988899 0.148588i \(-0.0474728\pi\)
−0.623131 + 0.782118i \(0.714139\pi\)
\(60\) 0 0
\(61\) −27.4823 + 47.6008i −0.0576845 + 0.0999124i −0.893426 0.449211i \(-0.851705\pi\)
0.835741 + 0.549124i \(0.185038\pi\)
\(62\) −1300.11 −2.66314
\(63\) 0 0
\(64\) −829.920 −1.62094
\(65\) 53.0298 91.8503i 0.101193 0.175271i
\(66\) 0 0
\(67\) −379.090 656.603i −0.691241 1.19727i −0.971431 0.237321i \(-0.923731\pi\)
0.280190 0.959945i \(-0.409603\pi\)
\(68\) −409.149 708.668i −0.729657 1.26380i
\(69\) 0 0
\(70\) −56.6479 + 98.1171i −0.0967246 + 0.167532i
\(71\) 904.348 1.51164 0.755819 0.654780i \(-0.227239\pi\)
0.755819 + 0.654780i \(0.227239\pi\)
\(72\) 0 0
\(73\) 866.622 1.38946 0.694729 0.719271i \(-0.255524\pi\)
0.694729 + 0.719271i \(0.255524\pi\)
\(74\) 581.139 1006.56i 0.912920 1.58122i
\(75\) 0 0
\(76\) 242.555 + 420.118i 0.366092 + 0.634090i
\(77\) 148.120 + 256.551i 0.219218 + 0.379697i
\(78\) 0 0
\(79\) −103.480 + 179.233i −0.147373 + 0.255257i −0.930256 0.366912i \(-0.880415\pi\)
0.782883 + 0.622169i \(0.213748\pi\)
\(80\) 89.0475 0.124448
\(81\) 0 0
\(82\) −757.054 −1.01954
\(83\) −231.699 + 401.314i −0.306412 + 0.530722i −0.977575 0.210589i \(-0.932462\pi\)
0.671162 + 0.741310i \(0.265795\pi\)
\(84\) 0 0
\(85\) 172.113 + 298.108i 0.219626 + 0.380404i
\(86\) −977.933 1693.83i −1.22620 2.12384i
\(87\) 0 0
\(88\) −505.163 + 874.968i −0.611938 + 1.05991i
\(89\) −601.736 −0.716673 −0.358337 0.933592i \(-0.616656\pi\)
−0.358337 + 0.933592i \(0.616656\pi\)
\(90\) 0 0
\(91\) 107.783 0.124162
\(92\) −857.691 + 1485.56i −0.971961 + 1.68349i
\(93\) 0 0
\(94\) 569.643 + 986.651i 0.625045 + 1.08261i
\(95\) −102.033 176.727i −0.110194 0.190861i
\(96\) 0 0
\(97\) −114.682 + 198.634i −0.120043 + 0.207920i −0.919784 0.392424i \(-0.871637\pi\)
0.799741 + 0.600345i \(0.204970\pi\)
\(98\) 1414.43 1.45795
\(99\) 0 0
\(100\) 297.152 0.297152
\(101\) 672.831 1165.38i 0.662863 1.14811i −0.316997 0.948427i \(-0.602674\pi\)
0.979860 0.199686i \(-0.0639923\pi\)
\(102\) 0 0
\(103\) 798.149 + 1382.44i 0.763534 + 1.32248i 0.941018 + 0.338356i \(0.109871\pi\)
−0.177484 + 0.984124i \(0.556796\pi\)
\(104\) 183.797 + 318.345i 0.173296 + 0.300157i
\(105\) 0 0
\(106\) −478.747 + 829.214i −0.438679 + 0.759815i
\(107\) −958.786 −0.866256 −0.433128 0.901333i \(-0.642590\pi\)
−0.433128 + 0.901333i \(0.642590\pi\)
\(108\) 0 0
\(109\) 1690.23 1.48527 0.742635 0.669696i \(-0.233576\pi\)
0.742635 + 0.669696i \(0.233576\pi\)
\(110\) 649.963 1125.77i 0.563377 0.975798i
\(111\) 0 0
\(112\) 45.2471 + 78.3703i 0.0381737 + 0.0661188i
\(113\) −5.81057 10.0642i −0.00483728 0.00837842i 0.863597 0.504183i \(-0.168206\pi\)
−0.868434 + 0.495805i \(0.834873\pi\)
\(114\) 0 0
\(115\) 360.796 624.917i 0.292560 0.506729i
\(116\) 2615.63 2.09358
\(117\) 0 0
\(118\) 1478.39 1.15336
\(119\) −174.909 + 302.951i −0.134738 + 0.233374i
\(120\) 0 0
\(121\) −1033.98 1790.91i −0.776848 1.34554i
\(122\) 122.554 + 212.270i 0.0909471 + 0.157525i
\(123\) 0 0
\(124\) −1732.67 + 3001.07i −1.25482 + 2.17342i
\(125\) −125.000 −0.0894427
\(126\) 0 0
\(127\) 309.141 0.215999 0.107999 0.994151i \(-0.465556\pi\)
0.107999 + 0.994151i \(0.465556\pi\)
\(128\) −978.240 + 1694.36i −0.675508 + 1.17001i
\(129\) 0 0
\(130\) −236.480 409.596i −0.159544 0.276338i
\(131\) 1392.51 + 2411.90i 0.928736 + 1.60862i 0.785440 + 0.618938i \(0.212437\pi\)
0.143296 + 0.989680i \(0.454230\pi\)
\(132\) 0 0
\(133\) 103.691 179.598i 0.0676026 0.117091i
\(134\) −3381.01 −2.17966
\(135\) 0 0
\(136\) −1193.06 −0.752233
\(137\) −1244.71 + 2155.89i −0.776222 + 1.34446i 0.157884 + 0.987458i \(0.449533\pi\)
−0.934105 + 0.356998i \(0.883800\pi\)
\(138\) 0 0
\(139\) −893.026 1546.77i −0.544931 0.943849i −0.998611 0.0526839i \(-0.983222\pi\)
0.453680 0.891165i \(-0.350111\pi\)
\(140\) 150.990 + 261.523i 0.0911499 + 0.157876i
\(141\) 0 0
\(142\) 2016.42 3492.54i 1.19165 2.06399i
\(143\) −1236.67 −0.723185
\(144\) 0 0
\(145\) −1100.29 −0.630166
\(146\) 1932.30 3346.84i 1.09533 1.89717i
\(147\) 0 0
\(148\) −1548.98 2682.91i −0.860304 1.49009i
\(149\) 784.416 + 1358.65i 0.431288 + 0.747012i 0.996984 0.0776011i \(-0.0247261\pi\)
−0.565697 + 0.824613i \(0.691393\pi\)
\(150\) 0 0
\(151\) 219.163 379.602i 0.118114 0.204580i −0.800906 0.598790i \(-0.795648\pi\)
0.919020 + 0.394210i \(0.128982\pi\)
\(152\) 707.277 0.377419
\(153\) 0 0
\(154\) 1321.04 0.691252
\(155\) 728.863 1262.43i 0.377701 0.654198i
\(156\) 0 0
\(157\) 22.3739 + 38.7528i 0.0113735 + 0.0196994i 0.871656 0.490118i \(-0.163046\pi\)
−0.860283 + 0.509817i \(0.829713\pi\)
\(158\) 461.458 + 799.270i 0.232352 + 0.402446i
\(159\) 0 0
\(160\) 545.140 944.211i 0.269357 0.466540i
\(161\) 733.315 0.358965
\(162\) 0 0
\(163\) −2611.84 −1.25506 −0.627531 0.778591i \(-0.715935\pi\)
−0.627531 + 0.778591i \(0.715935\pi\)
\(164\) −1008.93 + 1747.52i −0.480391 + 0.832062i
\(165\) 0 0
\(166\) 1033.23 + 1789.61i 0.483099 + 0.836752i
\(167\) −94.4733 163.633i −0.0437758 0.0758220i 0.843307 0.537432i \(-0.180605\pi\)
−0.887083 + 0.461610i \(0.847272\pi\)
\(168\) 0 0
\(169\) 873.527 1512.99i 0.397600 0.688663i
\(170\) 1535.03 0.692539
\(171\) 0 0
\(172\) −5213.19 −2.31106
\(173\) −752.510 + 1303.38i −0.330707 + 0.572801i −0.982651 0.185466i \(-0.940620\pi\)
0.651944 + 0.758267i \(0.273954\pi\)
\(174\) 0 0
\(175\) −63.5154 110.012i −0.0274361 0.0475207i
\(176\) −519.153 899.200i −0.222345 0.385112i
\(177\) 0 0
\(178\) −1341.69 + 2323.87i −0.564964 + 0.978547i
\(179\) 3136.62 1.30973 0.654865 0.755746i \(-0.272725\pi\)
0.654865 + 0.755746i \(0.272725\pi\)
\(180\) 0 0
\(181\) 4512.67 1.85317 0.926586 0.376084i \(-0.122730\pi\)
0.926586 + 0.376084i \(0.122730\pi\)
\(182\) 240.322 416.250i 0.0978784 0.169530i
\(183\) 0 0
\(184\) 1250.49 + 2165.91i 0.501018 + 0.867788i
\(185\) 651.592 + 1128.59i 0.258951 + 0.448517i
\(186\) 0 0
\(187\) 2006.86 3475.98i 0.784791 1.35930i
\(188\) 3036.67 1.17804
\(189\) 0 0
\(190\) −910.010 −0.347469
\(191\) 603.717 1045.67i 0.228709 0.396136i −0.728717 0.684815i \(-0.759883\pi\)
0.957426 + 0.288680i \(0.0932162\pi\)
\(192\) 0 0
\(193\) −461.582 799.483i −0.172152 0.298177i 0.767020 0.641623i \(-0.221739\pi\)
−0.939172 + 0.343447i \(0.888405\pi\)
\(194\) 511.409 + 885.787i 0.189263 + 0.327813i
\(195\) 0 0
\(196\) 1885.02 3264.95i 0.686961 1.18985i
\(197\) 1180.87 0.427075 0.213537 0.976935i \(-0.431501\pi\)
0.213537 + 0.976935i \(0.431501\pi\)
\(198\) 0 0
\(199\) −839.805 −0.299157 −0.149578 0.988750i \(-0.547792\pi\)
−0.149578 + 0.988750i \(0.547792\pi\)
\(200\) 216.620 375.197i 0.0765867 0.132652i
\(201\) 0 0
\(202\) −3000.41 5196.87i −1.04509 1.81015i
\(203\) −559.083 968.360i −0.193300 0.334806i
\(204\) 0 0
\(205\) 424.416 735.110i 0.144598 0.250450i
\(206\) 7118.51 2.40762
\(207\) 0 0
\(208\) −377.774 −0.125932
\(209\) −1189.72 + 2060.66i −0.393755 + 0.682003i
\(210\) 0 0
\(211\) 1294.82 + 2242.70i 0.422461 + 0.731725i 0.996180 0.0873280i \(-0.0278328\pi\)
−0.573718 + 0.819053i \(0.694499\pi\)
\(212\) 1276.06 + 2210.20i 0.413396 + 0.716023i
\(213\) 0 0
\(214\) −2137.80 + 3702.77i −0.682882 + 1.18279i
\(215\) 2192.98 0.695627
\(216\) 0 0
\(217\) 1481.41 0.463432
\(218\) 3768.69 6527.56i 1.17086 2.02799i
\(219\) 0 0
\(220\) −1732.42 3000.64i −0.530907 0.919559i
\(221\) −730.168 1264.69i −0.222246 0.384942i
\(222\) 0 0
\(223\) 2090.38 3620.64i 0.627722 1.08725i −0.360285 0.932842i \(-0.617321\pi\)
0.988008 0.154405i \(-0.0493459\pi\)
\(224\) 1107.99 0.330495
\(225\) 0 0
\(226\) −51.8232 −0.0152532
\(227\) −1301.34 + 2253.98i −0.380497 + 0.659039i −0.991133 0.132872i \(-0.957580\pi\)
0.610637 + 0.791911i \(0.290914\pi\)
\(228\) 0 0
\(229\) 922.676 + 1598.12i 0.266254 + 0.461165i 0.967891 0.251369i \(-0.0808807\pi\)
−0.701638 + 0.712534i \(0.747547\pi\)
\(230\) −1608.93 2786.74i −0.461259 0.798923i
\(231\) 0 0
\(232\) 1906.76 3302.60i 0.539589 0.934596i
\(233\) −240.637 −0.0676594 −0.0338297 0.999428i \(-0.510770\pi\)
−0.0338297 + 0.999428i \(0.510770\pi\)
\(234\) 0 0
\(235\) −1277.40 −0.354590
\(236\) 1970.26 3412.59i 0.543445 0.941275i
\(237\) 0 0
\(238\) 779.986 + 1350.98i 0.212433 + 0.367944i
\(239\) 1283.82 + 2223.64i 0.347462 + 0.601822i 0.985798 0.167936i \(-0.0537102\pi\)
−0.638336 + 0.769758i \(0.720377\pi\)
\(240\) 0 0
\(241\) −1994.00 + 3453.70i −0.532965 + 0.923122i 0.466294 + 0.884630i \(0.345589\pi\)
−0.999259 + 0.0384925i \(0.987744\pi\)
\(242\) −9221.86 −2.44960
\(243\) 0 0
\(244\) 653.315 0.171411
\(245\) −792.953 + 1373.43i −0.206775 + 0.358145i
\(246\) 0 0
\(247\) 432.864 + 749.742i 0.111508 + 0.193137i
\(248\) 2526.18 + 4375.47i 0.646825 + 1.12033i
\(249\) 0 0
\(250\) −278.711 + 482.742i −0.0705090 + 0.122125i
\(251\) −967.393 −0.243272 −0.121636 0.992575i \(-0.538814\pi\)
−0.121636 + 0.992575i \(0.538814\pi\)
\(252\) 0 0
\(253\) −8413.86 −2.09081
\(254\) 689.289 1193.88i 0.170275 0.294925i
\(255\) 0 0
\(256\) 1042.67 + 1805.96i 0.254558 + 0.440907i
\(257\) 1871.52 + 3241.56i 0.454249 + 0.786783i 0.998645 0.0520460i \(-0.0165742\pi\)
−0.544396 + 0.838829i \(0.683241\pi\)
\(258\) 0 0
\(259\) −662.178 + 1146.93i −0.158864 + 0.275160i
\(260\) −1260.63 −0.300697
\(261\) 0 0
\(262\) 12419.5 2.92855
\(263\) −1248.74 + 2162.88i −0.292777 + 0.507105i −0.974465 0.224538i \(-0.927913\pi\)
0.681688 + 0.731643i \(0.261246\pi\)
\(264\) 0 0
\(265\) −536.786 929.741i −0.124432 0.215523i
\(266\) −462.397 800.896i −0.106584 0.184609i
\(267\) 0 0
\(268\) −4505.90 + 7804.44i −1.02702 + 1.77885i
\(269\) 2142.91 0.485709 0.242855 0.970063i \(-0.421916\pi\)
0.242855 + 0.970063i \(0.421916\pi\)
\(270\) 0 0
\(271\) 1540.64 0.345341 0.172671 0.984980i \(-0.444760\pi\)
0.172671 + 0.984980i \(0.444760\pi\)
\(272\) 613.048 1061.83i 0.136660 0.236702i
\(273\) 0 0
\(274\) 5550.62 + 9613.95i 1.22381 + 2.11971i
\(275\) 728.758 + 1262.25i 0.159803 + 0.276787i
\(276\) 0 0
\(277\) −3388.90 + 5869.75i −0.735088 + 1.27321i 0.219597 + 0.975591i \(0.429526\pi\)
−0.954685 + 0.297619i \(0.903808\pi\)
\(278\) −7964.69 −1.71831
\(279\) 0 0
\(280\) 440.278 0.0939702
\(281\) 413.827 716.769i 0.0878535 0.152167i −0.818750 0.574150i \(-0.805333\pi\)
0.906604 + 0.421983i \(0.138666\pi\)
\(282\) 0 0
\(283\) 1585.99 + 2747.01i 0.333135 + 0.577007i 0.983125 0.182936i \(-0.0585602\pi\)
−0.649990 + 0.759943i \(0.725227\pi\)
\(284\) −5374.58 9309.05i −1.12297 1.94504i
\(285\) 0 0
\(286\) −2757.39 + 4775.94i −0.570098 + 0.987438i
\(287\) 862.623 0.177418
\(288\) 0 0
\(289\) −173.358 −0.0352856
\(290\) −2453.31 + 4249.25i −0.496769 + 0.860430i
\(291\) 0 0
\(292\) −5150.38 8920.71i −1.03220 1.78783i
\(293\) 688.012 + 1191.67i 0.137181 + 0.237605i 0.926429 0.376471i \(-0.122862\pi\)
−0.789247 + 0.614075i \(0.789529\pi\)
\(294\) 0 0
\(295\) −828.809 + 1435.54i −0.163577 + 0.283323i
\(296\) −4516.73 −0.886923
\(297\) 0 0
\(298\) 6996.02 1.35996
\(299\) −1530.63 + 2651.14i −0.296050 + 0.512773i
\(300\) 0 0
\(301\) 1114.30 + 1930.03i 0.213380 + 0.369585i
\(302\) −977.333 1692.79i −0.186223 0.322547i
\(303\) 0 0
\(304\) −363.432 + 629.483i −0.0685666 + 0.118761i
\(305\) −274.823 −0.0515946
\(306\) 0 0
\(307\) −119.504 −0.0222165 −0.0111083 0.999938i \(-0.503536\pi\)
−0.0111083 + 0.999938i \(0.503536\pi\)
\(308\) 1760.56 3049.39i 0.325706 0.564140i
\(309\) 0 0
\(310\) −3250.28 5629.65i −0.595495 1.03143i
\(311\) 1069.68 + 1852.73i 0.195035 + 0.337810i 0.946912 0.321493i \(-0.104185\pi\)
−0.751877 + 0.659303i \(0.770851\pi\)
\(312\) 0 0
\(313\) −2581.75 + 4471.72i −0.466227 + 0.807529i −0.999256 0.0385677i \(-0.987720\pi\)
0.533029 + 0.846097i \(0.321054\pi\)
\(314\) 199.548 0.0358635
\(315\) 0 0
\(316\) 2459.95 0.437922
\(317\) −4315.85 + 7475.26i −0.764675 + 1.32446i 0.175743 + 0.984436i \(0.443767\pi\)
−0.940418 + 0.340020i \(0.889566\pi\)
\(318\) 0 0
\(319\) 6414.76 + 11110.7i 1.12589 + 1.95009i
\(320\) −2074.80 3593.66i −0.362452 0.627786i
\(321\) 0 0
\(322\) 1635.07 2832.02i 0.282977 0.490131i
\(323\) −2809.79 −0.484028
\(324\) 0 0
\(325\) 530.298 0.0905097
\(326\) −5823.60 + 10086.8i −0.989385 + 1.71366i
\(327\) 0 0
\(328\) 1470.99 + 2547.83i 0.247628 + 0.428904i
\(329\) −649.079 1124.24i −0.108769 0.188393i
\(330\) 0 0
\(331\) 1471.17 2548.14i 0.244298 0.423137i −0.717636 0.696419i \(-0.754776\pi\)
0.961934 + 0.273281i \(0.0881090\pi\)
\(332\) 5507.98 0.910512
\(333\) 0 0
\(334\) −842.585 −0.138037
\(335\) 1895.45 3283.01i 0.309133 0.535433i
\(336\) 0 0
\(337\) −4948.73 8571.45i −0.799924 1.38551i −0.919665 0.392704i \(-0.871540\pi\)
0.119740 0.992805i \(-0.461794\pi\)
\(338\) −3895.39 6747.02i −0.626868 1.08577i
\(339\) 0 0
\(340\) 2045.75 3543.34i 0.326312 0.565190i
\(341\) −16997.3 −2.69928
\(342\) 0 0
\(343\) −3354.53 −0.528070
\(344\) −3800.34 + 6582.38i −0.595641 + 1.03168i
\(345\) 0 0
\(346\) 3355.73 + 5812.29i 0.521402 + 0.903095i
\(347\) −6007.87 10405.9i −0.929451 1.60986i −0.784242 0.620454i \(-0.786948\pi\)
−0.145208 0.989401i \(-0.546385\pi\)
\(348\) 0 0
\(349\) −3947.31 + 6836.94i −0.605428 + 1.04863i 0.386555 + 0.922266i \(0.373665\pi\)
−0.991984 + 0.126367i \(0.959668\pi\)
\(350\) −566.479 −0.0865131
\(351\) 0 0
\(352\) −12712.8 −1.92499
\(353\) 370.577 641.858i 0.0558748 0.0967781i −0.836735 0.547608i \(-0.815539\pi\)
0.892610 + 0.450830i \(0.148872\pi\)
\(354\) 0 0
\(355\) 2260.87 + 3915.94i 0.338013 + 0.585455i
\(356\) 3576.15 + 6194.07i 0.532403 + 0.922149i
\(357\) 0 0
\(358\) 6993.68 12113.4i 1.03248 1.78831i
\(359\) 11564.4 1.70012 0.850060 0.526685i \(-0.176565\pi\)
0.850060 + 0.526685i \(0.176565\pi\)
\(360\) 0 0
\(361\) −5193.28 −0.757148
\(362\) 10061.9 17427.6i 1.46088 2.53032i
\(363\) 0 0
\(364\) −640.558 1109.48i −0.0922372 0.159760i
\(365\) 2166.56 + 3752.58i 0.310692 + 0.538135i
\(366\) 0 0
\(367\) 574.284 994.690i 0.0816823 0.141478i −0.822290 0.569068i \(-0.807304\pi\)
0.903973 + 0.427590i \(0.140637\pi\)
\(368\) −2570.24 −0.364084
\(369\) 0 0
\(370\) 5811.39 0.816540
\(371\) 545.507 944.846i 0.0763378 0.132221i
\(372\) 0 0
\(373\) 2301.49 + 3986.29i 0.319481 + 0.553358i 0.980380 0.197117i \(-0.0631580\pi\)
−0.660899 + 0.750475i \(0.729825\pi\)
\(374\) −8949.34 15500.7i −1.23732 2.14311i
\(375\) 0 0
\(376\) 2213.69 3834.22i 0.303623 0.525890i
\(377\) 4667.85 0.637683
\(378\) 0 0
\(379\) −3988.46 −0.540563 −0.270282 0.962781i \(-0.587117\pi\)
−0.270282 + 0.962781i \(0.587117\pi\)
\(380\) −1212.78 + 2100.59i −0.163721 + 0.283574i
\(381\) 0 0
\(382\) −2692.21 4663.04i −0.360590 0.624559i
\(383\) 3894.10 + 6744.78i 0.519528 + 0.899849i 0.999742 + 0.0226975i \(0.00722546\pi\)
−0.480215 + 0.877151i \(0.659441\pi\)
\(384\) 0 0
\(385\) −740.599 + 1282.75i −0.0980374 + 0.169806i
\(386\) −4116.74 −0.542841
\(387\) 0 0
\(388\) 2726.23 0.356710
\(389\) 4262.43 7382.75i 0.555563 0.962263i −0.442297 0.896869i \(-0.645836\pi\)
0.997859 0.0653944i \(-0.0208305\pi\)
\(390\) 0 0
\(391\) −4967.80 8604.49i −0.642538 1.11291i
\(392\) −2748.31 4760.21i −0.354108 0.613334i
\(393\) 0 0
\(394\) 2632.98 4560.46i 0.336669 0.583129i
\(395\) −1034.80 −0.131814
\(396\) 0 0
\(397\) −155.729 −0.0196872 −0.00984361 0.999952i \(-0.503133\pi\)
−0.00984361 + 0.999952i \(0.503133\pi\)
\(398\) −1872.51 + 3243.27i −0.235830 + 0.408469i
\(399\) 0 0
\(400\) 222.619 + 385.587i 0.0278274 + 0.0481984i
\(401\) 2966.98 + 5138.96i 0.369486 + 0.639968i 0.989485 0.144634i \(-0.0462005\pi\)
−0.619999 + 0.784602i \(0.712867\pi\)
\(402\) 0 0
\(403\) −3092.12 + 5355.70i −0.382207 + 0.662002i
\(404\) −15994.7 −1.96971
\(405\) 0 0
\(406\) −4986.33 −0.609526
\(407\) 7597.65 13159.5i 0.925311 1.60268i
\(408\) 0 0
\(409\) −7080.71 12264.1i −0.856035 1.48270i −0.875681 0.482890i \(-0.839587\pi\)
0.0196459 0.999807i \(-0.493746\pi\)
\(410\) −1892.63 3278.14i −0.227977 0.394868i
\(411\) 0 0
\(412\) 9486.88 16431.8i 1.13443 1.96489i
\(413\) −1684.55 −0.200705
\(414\) 0 0
\(415\) −2316.99 −0.274064
\(416\) −2312.69 + 4005.70i −0.272570 + 0.472105i
\(417\) 0 0
\(418\) 5305.42 + 9189.26i 0.620805 + 1.07527i
\(419\) 4812.12 + 8334.84i 0.561068 + 0.971798i 0.997404 + 0.0720142i \(0.0229427\pi\)
−0.436336 + 0.899784i \(0.643724\pi\)
\(420\) 0 0
\(421\) 768.128 1330.44i 0.0889223 0.154018i −0.818134 0.575028i \(-0.804991\pi\)
0.907056 + 0.421010i \(0.138324\pi\)
\(422\) 11548.2 1.33213
\(423\) 0 0
\(424\) 3720.91 0.426187
\(425\) −860.563 + 1490.54i −0.0982199 + 0.170122i
\(426\) 0 0
\(427\) −139.644 241.871i −0.0158264 0.0274121i
\(428\) 5698.11 + 9869.42i 0.643525 + 1.11462i
\(429\) 0 0
\(430\) 4889.67 8469.15i 0.548373 0.949811i
\(431\) −11582.2 −1.29441 −0.647207 0.762314i \(-0.724063\pi\)
−0.647207 + 0.762314i \(0.724063\pi\)
\(432\) 0 0
\(433\) 14892.6 1.65287 0.826437 0.563029i \(-0.190364\pi\)
0.826437 + 0.563029i \(0.190364\pi\)
\(434\) 3303.09 5721.11i 0.365330 0.632770i
\(435\) 0 0
\(436\) −10045.1 17398.6i −1.10338 1.91111i
\(437\) 2945.05 + 5100.98i 0.322382 + 0.558382i
\(438\) 0 0
\(439\) 821.253 1422.45i 0.0892853 0.154647i −0.817924 0.575326i \(-0.804875\pi\)
0.907209 + 0.420680i \(0.138208\pi\)
\(440\) −5051.63 −0.547334
\(441\) 0 0
\(442\) −6512.20 −0.700800
\(443\) 1958.15 3391.62i 0.210011 0.363749i −0.741707 0.670724i \(-0.765983\pi\)
0.951718 + 0.306975i \(0.0993168\pi\)
\(444\) 0 0
\(445\) −1504.34 2605.59i −0.160253 0.277566i
\(446\) −9321.79 16145.8i −0.989686 1.71419i
\(447\) 0 0
\(448\) 2108.51 3652.04i 0.222361 0.385140i
\(449\) 3985.25 0.418876 0.209438 0.977822i \(-0.432837\pi\)
0.209438 + 0.977822i \(0.432837\pi\)
\(450\) 0 0
\(451\) −9897.50 −1.03338
\(452\) −69.0650 + 119.624i −0.00718705 + 0.0124483i
\(453\) 0 0
\(454\) 5803.16 + 10051.4i 0.599902 + 1.03906i
\(455\) 269.457 + 466.713i 0.0277634 + 0.0480876i
\(456\) 0 0
\(457\) 7088.89 12278.3i 0.725611 1.25680i −0.233111 0.972450i \(-0.574890\pi\)
0.958722 0.284345i \(-0.0917763\pi\)
\(458\) 8229.13 0.839567
\(459\) 0 0
\(460\) −8576.91 −0.869349
\(461\) −8197.14 + 14197.9i −0.828154 + 1.43441i 0.0713305 + 0.997453i \(0.477275\pi\)
−0.899485 + 0.436952i \(0.856058\pi\)
\(462\) 0 0
\(463\) −1659.80 2874.86i −0.166603 0.288566i 0.770620 0.637295i \(-0.219947\pi\)
−0.937224 + 0.348729i \(0.886613\pi\)
\(464\) 1959.56 + 3394.06i 0.196057 + 0.339580i
\(465\) 0 0
\(466\) −536.546 + 929.324i −0.0533369 + 0.0923822i
\(467\) 2529.79 0.250674 0.125337 0.992114i \(-0.459999\pi\)
0.125337 + 0.992114i \(0.459999\pi\)
\(468\) 0 0
\(469\) 3852.49 0.379299
\(470\) −2848.22 + 4933.26i −0.279529 + 0.484158i
\(471\) 0 0
\(472\) −2872.58 4975.46i −0.280130 0.485199i
\(473\) −12785.2 22144.6i −1.24284 2.15267i
\(474\) 0 0
\(475\) 510.166 883.633i 0.0492800 0.0853555i
\(476\) 4157.97 0.400379
\(477\) 0 0
\(478\) 11450.1 1.09564
\(479\) −4323.38 + 7488.31i −0.412401 + 0.714300i −0.995152 0.0983514i \(-0.968643\pi\)
0.582751 + 0.812651i \(0.301976\pi\)
\(480\) 0 0
\(481\) −2764.30 4787.91i −0.262040 0.453867i
\(482\) 8891.99 + 15401.4i 0.840288 + 1.45542i
\(483\) 0 0
\(484\) −12290.0 + 21287.0i −1.15421 + 1.99915i
\(485\) −1146.82 −0.107370
\(486\) 0 0
\(487\) −15251.7 −1.41914 −0.709569 0.704636i \(-0.751110\pi\)
−0.709569 + 0.704636i \(0.751110\pi\)
\(488\) 476.257 824.902i 0.0441786 0.0765196i
\(489\) 0 0
\(490\) 3536.08 + 6124.67i 0.326008 + 0.564662i
\(491\) −883.434 1530.15i −0.0811992 0.140641i 0.822566 0.568670i \(-0.192542\pi\)
−0.903765 + 0.428028i \(0.859208\pi\)
\(492\) 0 0
\(493\) −7574.95 + 13120.2i −0.692005 + 1.19859i
\(494\) 3860.61 0.351614
\(495\) 0 0
\(496\) −5192.28 −0.470041
\(497\) −2297.60 + 3979.56i −0.207367 + 0.359171i
\(498\) 0 0
\(499\) −5866.92 10161.8i −0.526332 0.911633i −0.999529 0.0306768i \(-0.990234\pi\)
0.473198 0.880956i \(-0.343100\pi\)
\(500\) 742.881 + 1286.71i 0.0664453 + 0.115087i
\(501\) 0 0
\(502\) −2156.99 + 3736.01i −0.191775 + 0.332164i
\(503\) 977.608 0.0866589 0.0433294 0.999061i \(-0.486203\pi\)
0.0433294 + 0.999061i \(0.486203\pi\)
\(504\) 0 0
\(505\) 6728.31 0.592883
\(506\) −18760.3 + 32493.8i −1.64822 + 2.85479i
\(507\) 0 0
\(508\) −1837.24 3182.19i −0.160461 0.277927i
\(509\) 4837.36 + 8378.55i 0.421242 + 0.729613i 0.996061 0.0886678i \(-0.0282609\pi\)
−0.574819 + 0.818280i \(0.694928\pi\)
\(510\) 0 0
\(511\) −2201.76 + 3813.55i −0.190607 + 0.330140i
\(512\) −6352.52 −0.548329
\(513\) 0 0
\(514\) 16691.6 1.43237
\(515\) −3990.75 + 6912.18i −0.341463 + 0.591431i
\(516\) 0 0
\(517\) 7447.35 + 12899.2i 0.633528 + 1.09730i
\(518\) 2952.91 + 5114.58i 0.250470 + 0.433826i
\(519\) 0 0
\(520\) −918.984 + 1591.73i −0.0775002 + 0.134234i
\(521\) −5178.95 −0.435497 −0.217748 0.976005i \(-0.569871\pi\)
−0.217748 + 0.976005i \(0.569871\pi\)
\(522\) 0 0
\(523\) 14280.7 1.19398 0.596992 0.802248i \(-0.296363\pi\)
0.596992 + 0.802248i \(0.296363\pi\)
\(524\) 16551.5 28668.1i 1.37988 2.39002i
\(525\) 0 0
\(526\) 5568.60 + 9645.09i 0.461601 + 0.799517i
\(527\) −10035.7 17382.4i −0.829532 1.43679i
\(528\) 0 0
\(529\) −4330.39 + 7500.46i −0.355913 + 0.616459i
\(530\) −4787.47 −0.392367
\(531\) 0 0
\(532\) −2464.96 −0.200883
\(533\) −1800.54 + 3118.62i −0.146322 + 0.253438i
\(534\) 0 0
\(535\) −2396.97 4151.67i −0.193701 0.335499i
\(536\) 6569.47 + 11378.7i 0.529399 + 0.916946i
\(537\) 0 0
\(538\) 4778.04 8275.80i 0.382892 0.663188i
\(539\) 18491.9 1.47774
\(540\) 0 0
\(541\) 12923.8 1.02706 0.513529 0.858072i \(-0.328338\pi\)
0.513529 + 0.858072i \(0.328338\pi\)
\(542\) 3435.16 5949.87i 0.272238 0.471529i
\(543\) 0 0
\(544\) −7506.04 13000.8i −0.591579 1.02464i
\(545\) 4225.57 + 7318.90i 0.332117 + 0.575243i
\(546\) 0 0
\(547\) −6826.66 + 11824.1i −0.533614 + 0.924246i 0.465615 + 0.884987i \(0.345833\pi\)
−0.999229 + 0.0392591i \(0.987500\pi\)
\(548\) 29589.4 2.30656
\(549\) 0 0
\(550\) 6499.63 0.503900
\(551\) 4490.64 7778.02i 0.347201 0.601370i
\(552\) 0 0
\(553\) −525.808 910.726i −0.0404333 0.0700326i
\(554\) 15112.4 + 26175.5i 1.15896 + 2.00738i
\(555\) 0 0
\(556\) −10614.6 + 18385.0i −0.809638 + 1.40233i
\(557\) 9313.63 0.708494 0.354247 0.935152i \(-0.384737\pi\)
0.354247 + 0.935152i \(0.384737\pi\)
\(558\) 0 0
\(559\) −9303.46 −0.703925
\(560\) −226.236 + 391.852i −0.0170718 + 0.0295692i
\(561\) 0 0
\(562\) −1845.41 3196.35i −0.138512 0.239911i
\(563\) −5312.70 9201.86i −0.397697 0.688831i 0.595744 0.803174i \(-0.296857\pi\)
−0.993441 + 0.114343i \(0.963524\pi\)
\(564\) 0 0
\(565\) 29.0529 50.3211i 0.00216330 0.00374694i
\(566\) 14145.1 1.05046
\(567\) 0 0
\(568\) −15672.0 −1.15771
\(569\) 4530.25 7846.62i 0.333775 0.578115i −0.649474 0.760384i \(-0.725011\pi\)
0.983249 + 0.182269i \(0.0583441\pi\)
\(570\) 0 0
\(571\) 10689.6 + 18514.9i 0.783440 + 1.35696i 0.929926 + 0.367746i \(0.119870\pi\)
−0.146486 + 0.989213i \(0.546796\pi\)
\(572\) 7349.58 + 12729.9i 0.537240 + 0.930528i
\(573\) 0 0
\(574\) 1923.38 3331.40i 0.139861 0.242247i
\(575\) 3607.96 0.261674
\(576\) 0 0
\(577\) 6347.76 0.457991 0.228996 0.973427i \(-0.426456\pi\)
0.228996 + 0.973427i \(0.426456\pi\)
\(578\) −386.535 + 669.499i −0.0278162 + 0.0481791i
\(579\) 0 0
\(580\) 6539.07 + 11326.0i 0.468138 + 0.810839i
\(581\) −1177.32 2039.17i −0.0840676 0.145609i
\(582\) 0 0
\(583\) −6259.00 + 10840.9i −0.444633 + 0.770127i
\(584\) −15018.2 −1.06414
\(585\) 0 0
\(586\) 6136.22 0.432568
\(587\) 7386.86 12794.4i 0.519401 0.899628i −0.480345 0.877080i \(-0.659489\pi\)
0.999746 0.0225488i \(-0.00717811\pi\)
\(588\) 0 0
\(589\) 5949.46 + 10304.8i 0.416202 + 0.720884i
\(590\) 3695.98 + 6401.62i 0.257900 + 0.446696i
\(591\) 0 0
\(592\) 2320.91 4019.93i 0.161129 0.279084i
\(593\) −26868.1 −1.86061 −0.930304 0.366790i \(-0.880457\pi\)
−0.930304 + 0.366790i \(0.880457\pi\)
\(594\) 0 0
\(595\) −1749.09 −0.120514
\(596\) 9323.64 16149.0i 0.640791 1.10988i
\(597\) 0 0
\(598\) 6825.68 + 11822.4i 0.466761 + 0.808454i
\(599\) −874.913 1515.39i −0.0596794 0.103368i 0.834642 0.550793i \(-0.185675\pi\)
−0.894322 + 0.447425i \(0.852341\pi\)
\(600\) 0 0
\(601\) 8981.99 15557.3i 0.609622 1.05590i −0.381680 0.924294i \(-0.624654\pi\)
0.991303 0.131602i \(-0.0420122\pi\)
\(602\) 9938.21 0.672843
\(603\) 0 0
\(604\) −5209.99 −0.350979
\(605\) 5169.92 8954.57i 0.347417 0.601744i
\(606\) 0 0
\(607\) 2209.11 + 3826.29i 0.147718 + 0.255856i 0.930384 0.366587i \(-0.119474\pi\)
−0.782666 + 0.622443i \(0.786140\pi\)
\(608\) 4449.79 + 7707.26i 0.296814 + 0.514097i
\(609\) 0 0
\(610\) −612.771 + 1061.35i −0.0406728 + 0.0704473i
\(611\) 5419.24 0.358820
\(612\) 0 0
\(613\) −20179.7 −1.32961 −0.664804 0.747018i \(-0.731485\pi\)
−0.664804 + 0.747018i \(0.731485\pi\)
\(614\) −266.458 + 461.518i −0.0175136 + 0.0303345i
\(615\) 0 0
\(616\) −2566.85 4445.92i −0.167892 0.290797i
\(617\) −2336.51 4046.95i −0.152454 0.264058i 0.779675 0.626184i \(-0.215384\pi\)
−0.932129 + 0.362126i \(0.882051\pi\)
\(618\) 0 0
\(619\) 9988.40 17300.4i 0.648574 1.12336i −0.334889 0.942258i \(-0.608699\pi\)
0.983464 0.181106i \(-0.0579678\pi\)
\(620\) −17326.7 −1.12235
\(621\) 0 0
\(622\) 9540.19 0.614994
\(623\) 1528.78 2647.93i 0.0983136 0.170284i
\(624\) 0 0
\(625\) −312.500 541.266i −0.0200000 0.0346410i
\(626\) 11513.0 + 19941.1i 0.735068 + 1.27318i
\(627\) 0 0
\(628\) 265.939 460.619i 0.0168983 0.0292686i
\(629\) 17943.5 1.13745
\(630\) 0 0
\(631\) 10457.5 0.659757 0.329879 0.944023i \(-0.392992\pi\)
0.329879 + 0.944023i \(0.392992\pi\)
\(632\) 1793.27 3106.04i 0.112868 0.195493i
\(633\) 0 0
\(634\) 19246.0 + 33335.1i 1.20561 + 2.08818i
\(635\) 772.852 + 1338.62i 0.0482988 + 0.0836559i
\(636\) 0 0
\(637\) 3364.01 5826.63i 0.209242 0.362417i
\(638\) 57211.8 3.55021
\(639\) 0 0
\(640\) −9782.40 −0.604193
\(641\) 2197.93 3806.92i 0.135434 0.234578i −0.790329 0.612682i \(-0.790091\pi\)
0.925763 + 0.378104i \(0.123424\pi\)
\(642\) 0 0
\(643\) −2893.18 5011.13i −0.177443 0.307340i 0.763561 0.645736i \(-0.223449\pi\)
−0.941004 + 0.338395i \(0.890116\pi\)
\(644\) −4358.13 7548.50i −0.266668 0.461883i
\(645\) 0 0
\(646\) −6264.97 + 10851.2i −0.381566 + 0.660892i
\(647\) 25367.7 1.54143 0.770717 0.637178i \(-0.219898\pi\)
0.770717 + 0.637178i \(0.219898\pi\)
\(648\) 0 0
\(649\) 19328.1 1.16902
\(650\) 1182.40 2047.98i 0.0713501 0.123582i
\(651\) 0 0
\(652\) 15522.3 + 26885.4i 0.932362 + 1.61490i
\(653\) −10816.6 18734.9i −0.648218 1.12275i −0.983548 0.180646i \(-0.942181\pi\)
0.335330 0.942101i \(-0.391152\pi\)
\(654\) 0 0
\(655\) −6962.56 + 12059.5i −0.415343 + 0.719396i
\(656\) −3023.46 −0.179948
\(657\) 0 0
\(658\) −5788.98 −0.342976
\(659\) 9156.22 15859.0i 0.541238 0.937451i −0.457596 0.889160i \(-0.651289\pi\)
0.998833 0.0482907i \(-0.0153774\pi\)
\(660\) 0 0
\(661\) 2763.04 + 4785.73i 0.162587 + 0.281609i 0.935796 0.352543i \(-0.114683\pi\)
−0.773209 + 0.634151i \(0.781350\pi\)
\(662\) −6560.51 11363.1i −0.385168 0.667131i
\(663\) 0 0
\(664\) 4015.24 6954.60i 0.234671 0.406462i
\(665\) 1036.91 0.0604656
\(666\) 0 0
\(667\) 31758.4 1.84361
\(668\) −1122.92 + 1944.95i −0.0650404 + 0.112653i
\(669\) 0 0
\(670\) −8452.53 14640.2i −0.487388 0.844180i
\(671\) 1602.24 + 2775.16i 0.0921814 + 0.159663i
\(672\) 0 0
\(673\) −718.621 + 1244.69i −0.0411602 + 0.0712916i −0.885872 0.463931i \(-0.846439\pi\)
0.844711 + 0.535222i \(0.179772\pi\)
\(674\) −44136.6 −2.52237
\(675\) 0 0
\(676\) −20765.7 −1.18148
\(677\) −11702.9 + 20270.1i −0.664373 + 1.15073i 0.315082 + 0.949064i \(0.397968\pi\)
−0.979455 + 0.201663i \(0.935365\pi\)
\(678\) 0 0
\(679\) −582.724 1009.31i −0.0329351 0.0570452i
\(680\) −2982.64 5166.08i −0.168204 0.291339i
\(681\) 0 0
\(682\) −37898.7 + 65642.5i −2.12788 + 3.68560i
\(683\) −19227.4 −1.07719 −0.538593 0.842566i \(-0.681044\pi\)
−0.538593 + 0.842566i \(0.681044\pi\)
\(684\) 0 0
\(685\) −12447.1 −0.694274
\(686\) −7479.58 + 12955.0i −0.416285 + 0.721027i
\(687\) 0 0
\(688\) −3905.59 6764.67i −0.216423 0.374856i
\(689\) 2277.25 + 3944.32i 0.125916 + 0.218094i
\(690\) 0 0
\(691\) 17642.4 30557.5i 0.971271 1.68229i 0.279544 0.960133i \(-0.409817\pi\)
0.691728 0.722158i \(-0.256850\pi\)
\(692\) 17888.8 0.982703
\(693\) 0 0
\(694\) −53582.8 −2.93080
\(695\) 4465.13 7733.83i 0.243701 0.422102i
\(696\) 0 0
\(697\) −5843.79 10121.7i −0.317574 0.550055i
\(698\) 17602.6 + 30488.5i 0.954537 + 1.65331i
\(699\) 0 0
\(700\) −754.950 + 1307.61i −0.0407635 + 0.0706044i
\(701\) −9173.00 −0.494236 −0.247118 0.968985i \(-0.579484\pi\)
−0.247118 + 0.968985i \(0.579484\pi\)
\(702\) 0 0
\(703\) −10637.4 −0.570695
\(704\) −24192.4 + 41902.5i −1.29515 + 2.24327i
\(705\) 0 0
\(706\) −1652.54 2862.29i −0.0880940 0.152583i
\(707\) 3418.81 + 5921.56i 0.181864 + 0.314997i
\(708\) 0 0
\(709\) 16975.8 29403.0i 0.899210 1.55748i 0.0707045 0.997497i \(-0.477475\pi\)
0.828506 0.559981i \(-0.189191\pi\)
\(710\) 20164.2 1.06584
\(711\) 0 0
\(712\) 10427.8 0.548876
\(713\) −21037.7 + 36438.3i −1.10500 + 1.91392i
\(714\) 0 0
\(715\) −3091.67 5354.93i −0.161709 0.280088i
\(716\) −18641.1 32287.3i −0.972973 1.68524i
\(717\) 0 0
\(718\) 25784.9 44660.8i 1.34023 2.32135i
\(719\) 6727.90 0.348968 0.174484 0.984660i \(-0.444174\pi\)
0.174484 + 0.984660i \(0.444174\pi\)
\(720\) 0 0
\(721\) −8111.17 −0.418968
\(722\) −11579.4 + 20056.1i −0.596871 + 1.03381i
\(723\) 0 0
\(724\) −26819.0 46451.9i −1.37669 2.38449i
\(725\) −2750.72 4764.39i −0.140909 0.244062i
\(726\) 0 0
\(727\) 18363.1 31805.8i 0.936793 1.62257i 0.165387 0.986229i \(-0.447113\pi\)
0.771406 0.636344i \(-0.219554\pi\)
\(728\) −1867.83 −0.0950912
\(729\) 0 0
\(730\) 19323.0 0.979694
\(731\) 15097.6 26149.8i 0.763890 1.32310i
\(732\) 0 0
\(733\) −13345.7 23115.4i −0.672489 1.16478i −0.977196 0.212338i \(-0.931892\pi\)
0.304708 0.952446i \(-0.401441\pi\)
\(734\) −2560.95 4435.70i −0.128783 0.223058i
\(735\) 0 0
\(736\) −15734.7 + 27253.4i −0.788030 + 1.36491i
\(737\) −44202.4 −2.20925
\(738\) 0 0
\(739\) 12207.0 0.607634 0.303817 0.952730i \(-0.401739\pi\)
0.303817 + 0.952730i \(0.401739\pi\)
\(740\) 7744.88 13414.5i 0.384740 0.666389i
\(741\) 0 0
\(742\) −2432.62 4213.43i −0.120356 0.208463i
\(743\) −6236.64 10802.2i −0.307941 0.533370i 0.669971 0.742388i \(-0.266307\pi\)
−0.977912 + 0.209018i \(0.932973\pi\)
\(744\) 0 0
\(745\) −3922.08 + 6793.24i −0.192878 + 0.334074i
\(746\) 20526.4 1.00741
\(747\) 0 0
\(748\) −47707.4 −2.33202
\(749\) 2435.91 4219.12i 0.118833 0.205825i
\(750\) 0 0
\(751\) 7551.32 + 13079.3i 0.366913 + 0.635511i 0.989081 0.147372i \(-0.0470814\pi\)
−0.622168 + 0.782883i \(0.713748\pi\)
\(752\) 2274.99 + 3940.40i 0.110320 + 0.191079i
\(753\) 0 0
\(754\) 10407.9 18027.0i 0.502695 0.870693i
\(755\) 2191.63 0.105645
\(756\) 0 0
\(757\) −3418.34 −0.164124 −0.0820618 0.996627i \(-0.526150\pi\)
−0.0820618 + 0.996627i \(0.526150\pi\)
\(758\) −8893.04 + 15403.2i −0.426134 + 0.738086i
\(759\) 0 0
\(760\) 1768.19 + 3062.60i 0.0843935 + 0.146174i
\(761\) −6342.27 10985.1i −0.302112 0.523273i 0.674502 0.738273i \(-0.264358\pi\)
−0.976614 + 0.215000i \(0.931025\pi\)
\(762\) 0 0
\(763\) −4294.22 + 7437.81i −0.203750 + 0.352906i
\(764\) −14351.7 −0.679614
\(765\) 0 0
\(766\) 34730.6 1.63821
\(767\) 3516.13 6090.11i 0.165528 0.286703i
\(768\) 0 0
\(769\) 13790.1 + 23885.2i 0.646663 + 1.12005i 0.983915 + 0.178639i \(0.0571693\pi\)
−0.337252 + 0.941415i \(0.609497\pi\)
\(770\) 3302.61 + 5720.29i 0.154569 + 0.267721i
\(771\) 0 0
\(772\) −5486.41 + 9502.74i −0.255777 + 0.443019i
\(773\) −17386.0 −0.808966 −0.404483 0.914546i \(-0.632548\pi\)
−0.404483 + 0.914546i \(0.632548\pi\)
\(774\) 0 0
\(775\) 7288.63 0.337826
\(776\) 1987.39 3442.25i 0.0919368 0.159239i
\(777\) 0 0
\(778\) −19007.8 32922.5i −0.875917 1.51713i
\(779\) 3464.36 + 6000.45i 0.159337 + 0.275980i
\(780\) 0 0
\(781\) 26362.0 45660.4i 1.20782 2.09201i
\(782\) −44306.7 −2.02609
\(783\) 0 0
\(784\) 5648.84 0.257327
\(785\) −111.870 + 193.764i −0.00508637 + 0.00880985i
\(786\) 0 0
\(787\) −2340.15