Properties

Label 483.3.f.a.22.11
Level $483$
Weight $3$
Character 483.22
Analytic conductor $13.161$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 483 = 3 \cdot 7 \cdot 23 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 483.f (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(13.1607967686\)
Analytic rank: \(0\)
Dimension: \(48\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 22.11
Character \(\chi\) \(=\) 483.22
Dual form 483.3.f.a.22.12

$q$-expansion

\(f(q)\) \(=\) \(q-2.49369 q^{2} +1.73205 q^{3} +2.21850 q^{4} +2.66866i q^{5} -4.31920 q^{6} -2.64575i q^{7} +4.44250 q^{8} +3.00000 q^{9} +O(q^{10})\) \(q-2.49369 q^{2} +1.73205 q^{3} +2.21850 q^{4} +2.66866i q^{5} -4.31920 q^{6} -2.64575i q^{7} +4.44250 q^{8} +3.00000 q^{9} -6.65481i q^{10} +5.14993i q^{11} +3.84256 q^{12} +6.24116 q^{13} +6.59769i q^{14} +4.62225i q^{15} -19.9523 q^{16} -11.3967i q^{17} -7.48108 q^{18} -9.41543i q^{19} +5.92043i q^{20} -4.58258i q^{21} -12.8423i q^{22} +(10.8890 + 20.2590i) q^{23} +7.69464 q^{24} +17.8783 q^{25} -15.5635 q^{26} +5.19615 q^{27} -5.86961i q^{28} +27.6168 q^{29} -11.5265i q^{30} -52.6391 q^{31} +31.9848 q^{32} +8.91994i q^{33} +28.4198i q^{34} +7.06060 q^{35} +6.65551 q^{36} +49.4855i q^{37} +23.4792i q^{38} +10.8100 q^{39} +11.8555i q^{40} +15.3168 q^{41} +11.4275i q^{42} -68.2674i q^{43} +11.4251i q^{44} +8.00597i q^{45} +(-27.1539 - 50.5198i) q^{46} +46.0234 q^{47} -34.5583 q^{48} -7.00000 q^{49} -44.5829 q^{50} -19.7396i q^{51} +13.8461 q^{52} +95.2919i q^{53} -12.9576 q^{54} -13.7434 q^{55} -11.7538i q^{56} -16.3080i q^{57} -68.8679 q^{58} +78.9912 q^{59} +10.2545i q^{60} -57.0256i q^{61} +131.266 q^{62} -7.93725i q^{63} +0.0487738 q^{64} +16.6555i q^{65} -22.2436i q^{66} +93.3931i q^{67} -25.2836i q^{68} +(18.8604 + 35.0897i) q^{69} -17.6070 q^{70} +117.690 q^{71} +13.3275 q^{72} +120.277 q^{73} -123.402i q^{74} +30.9661 q^{75} -20.8882i q^{76} +13.6254 q^{77} -26.9569 q^{78} +97.4970i q^{79} -53.2457i q^{80} +9.00000 q^{81} -38.1955 q^{82} +32.6207i q^{83} -10.1665i q^{84} +30.4138 q^{85} +170.238i q^{86} +47.8338 q^{87} +22.8786i q^{88} +140.985i q^{89} -19.9644i q^{90} -16.5126i q^{91} +(24.1574 + 44.9448i) q^{92} -91.1736 q^{93} -114.768 q^{94} +25.1265 q^{95} +55.3993 q^{96} -74.2797i q^{97} +17.4559 q^{98} +15.4498i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + O(q^{10}) \) \( 48q + 4q^{2} + 116q^{4} - 24q^{6} - 4q^{8} + 144q^{9} + 16q^{13} + 324q^{16} + 12q^{18} - 4q^{23} - 24q^{24} - 176q^{25} + 136q^{26} - 128q^{29} - 8q^{31} - 252q^{32} - 56q^{35} + 348q^{36} + 96q^{39} - 24q^{41} - 148q^{46} - 408q^{47} - 96q^{48} - 336q^{49} + 236q^{50} - 32q^{52} - 72q^{54} - 24q^{55} - 56q^{58} + 136q^{59} + 184q^{62} + 716q^{64} - 48q^{69} - 112q^{70} + 48q^{71} - 12q^{72} - 224q^{73} - 48q^{75} + 224q^{77} - 96q^{78} + 432q^{81} + 640q^{82} - 424q^{85} + 312q^{87} + 1060q^{92} + 192q^{93} + 216q^{94} + 624q^{95} + 48q^{96} - 28q^{98} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).

\(n\) \(323\) \(346\) \(442\)
\(\chi(n)\) \(1\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.49369 −1.24685 −0.623423 0.781885i \(-0.714259\pi\)
−0.623423 + 0.781885i \(0.714259\pi\)
\(3\) 1.73205 0.577350
\(4\) 2.21850 0.554626
\(5\) 2.66866i 0.533731i 0.963734 + 0.266866i \(0.0859880\pi\)
−0.963734 + 0.266866i \(0.914012\pi\)
\(6\) −4.31920 −0.719867
\(7\) 2.64575i 0.377964i
\(8\) 4.44250 0.555313
\(9\) 3.00000 0.333333
\(10\) 6.65481i 0.665481i
\(11\) 5.14993i 0.468175i 0.972215 + 0.234088i \(0.0752103\pi\)
−0.972215 + 0.234088i \(0.924790\pi\)
\(12\) 3.84256 0.320214
\(13\) 6.24116 0.480090 0.240045 0.970762i \(-0.422838\pi\)
0.240045 + 0.970762i \(0.422838\pi\)
\(14\) 6.59769i 0.471264i
\(15\) 4.62225i 0.308150i
\(16\) −19.9523 −1.24702
\(17\) 11.3967i 0.670393i −0.942148 0.335197i \(-0.891197\pi\)
0.942148 0.335197i \(-0.108803\pi\)
\(18\) −7.48108 −0.415615
\(19\) 9.41543i 0.495549i −0.968818 0.247774i \(-0.920301\pi\)
0.968818 0.247774i \(-0.0796992\pi\)
\(20\) 5.92043i 0.296021i
\(21\) 4.58258i 0.218218i
\(22\) 12.8423i 0.583743i
\(23\) 10.8890 + 20.2590i 0.473437 + 0.880828i
\(24\) 7.69464 0.320610
\(25\) 17.8783 0.715131
\(26\) −15.5635 −0.598598
\(27\) 5.19615 0.192450
\(28\) 5.86961i 0.209629i
\(29\) 27.6168 0.952305 0.476152 0.879363i \(-0.342031\pi\)
0.476152 + 0.879363i \(0.342031\pi\)
\(30\) 11.5265i 0.384216i
\(31\) −52.6391 −1.69804 −0.849018 0.528364i \(-0.822806\pi\)
−0.849018 + 0.528364i \(0.822806\pi\)
\(32\) 31.9848 0.999525
\(33\) 8.91994i 0.270301i
\(34\) 28.4198i 0.835878i
\(35\) 7.06060 0.201731
\(36\) 6.65551 0.184875
\(37\) 49.4855i 1.33745i 0.743511 + 0.668723i \(0.233159\pi\)
−0.743511 + 0.668723i \(0.766841\pi\)
\(38\) 23.4792i 0.617873i
\(39\) 10.8100 0.277180
\(40\) 11.8555i 0.296388i
\(41\) 15.3168 0.373581 0.186791 0.982400i \(-0.440191\pi\)
0.186791 + 0.982400i \(0.440191\pi\)
\(42\) 11.4275i 0.272084i
\(43\) 68.2674i 1.58761i −0.608171 0.793806i \(-0.708096\pi\)
0.608171 0.793806i \(-0.291904\pi\)
\(44\) 11.4251i 0.259662i
\(45\) 8.00597i 0.177910i
\(46\) −27.1539 50.5198i −0.590303 1.09826i
\(47\) 46.0234 0.979221 0.489610 0.871941i \(-0.337139\pi\)
0.489610 + 0.871941i \(0.337139\pi\)
\(48\) −34.5583 −0.719965
\(49\) −7.00000 −0.142857
\(50\) −44.5829 −0.891659
\(51\) 19.7396i 0.387052i
\(52\) 13.8461 0.266270
\(53\) 95.2919i 1.79796i 0.437989 + 0.898980i \(0.355691\pi\)
−0.437989 + 0.898980i \(0.644309\pi\)
\(54\) −12.9576 −0.239956
\(55\) −13.7434 −0.249880
\(56\) 11.7538i 0.209889i
\(57\) 16.3080i 0.286105i
\(58\) −68.8679 −1.18738
\(59\) 78.9912 1.33883 0.669417 0.742887i \(-0.266544\pi\)
0.669417 + 0.742887i \(0.266544\pi\)
\(60\) 10.2545i 0.170908i
\(61\) 57.0256i 0.934846i −0.884034 0.467423i \(-0.845183\pi\)
0.884034 0.467423i \(-0.154817\pi\)
\(62\) 131.266 2.11719
\(63\) 7.93725i 0.125988i
\(64\) 0.0487738 0.000762091
\(65\) 16.6555i 0.256239i
\(66\) 22.2436i 0.337024i
\(67\) 93.3931i 1.39393i 0.717107 + 0.696963i \(0.245466\pi\)
−0.717107 + 0.696963i \(0.754534\pi\)
\(68\) 25.2836i 0.371818i
\(69\) 18.8604 + 35.0897i 0.273339 + 0.508546i
\(70\) −17.6070 −0.251528
\(71\) 117.690 1.65761 0.828803 0.559541i \(-0.189022\pi\)
0.828803 + 0.559541i \(0.189022\pi\)
\(72\) 13.3275 0.185104
\(73\) 120.277 1.64763 0.823814 0.566860i \(-0.191842\pi\)
0.823814 + 0.566860i \(0.191842\pi\)
\(74\) 123.402i 1.66759i
\(75\) 30.9661 0.412881
\(76\) 20.8882i 0.274844i
\(77\) 13.6254 0.176954
\(78\) −26.9569 −0.345601
\(79\) 97.4970i 1.23414i 0.786909 + 0.617069i \(0.211680\pi\)
−0.786909 + 0.617069i \(0.788320\pi\)
\(80\) 53.2457i 0.665571i
\(81\) 9.00000 0.111111
\(82\) −38.1955 −0.465799
\(83\) 32.6207i 0.393020i 0.980502 + 0.196510i \(0.0629608\pi\)
−0.980502 + 0.196510i \(0.937039\pi\)
\(84\) 10.1665i 0.121029i
\(85\) 30.4138 0.357810
\(86\) 170.238i 1.97951i
\(87\) 47.8338 0.549813
\(88\) 22.8786i 0.259984i
\(89\) 140.985i 1.58410i 0.610455 + 0.792051i \(0.290987\pi\)
−0.610455 + 0.792051i \(0.709013\pi\)
\(90\) 19.9644i 0.221827i
\(91\) 16.5126i 0.181457i
\(92\) 24.1574 + 44.9448i 0.262580 + 0.488530i
\(93\) −91.1736 −0.980362
\(94\) −114.768 −1.22094
\(95\) 25.1265 0.264490
\(96\) 55.3993 0.577076
\(97\) 74.2797i 0.765770i −0.923796 0.382885i \(-0.874931\pi\)
0.923796 0.382885i \(-0.125069\pi\)
\(98\) 17.4559 0.178121
\(99\) 15.4498i 0.156058i
\(100\) 39.6630 0.396630
\(101\) 69.5857 0.688967 0.344484 0.938792i \(-0.388054\pi\)
0.344484 + 0.938792i \(0.388054\pi\)
\(102\) 49.2246i 0.482594i
\(103\) 90.5965i 0.879577i 0.898101 + 0.439789i \(0.144947\pi\)
−0.898101 + 0.439789i \(0.855053\pi\)
\(104\) 27.7264 0.266600
\(105\) 12.2293 0.116470
\(106\) 237.629i 2.24178i
\(107\) 14.2065i 0.132771i −0.997794 0.0663855i \(-0.978853\pi\)
0.997794 0.0663855i \(-0.0211467\pi\)
\(108\) 11.5277 0.106738
\(109\) 126.930i 1.16450i −0.813010 0.582250i \(-0.802173\pi\)
0.813010 0.582250i \(-0.197827\pi\)
\(110\) 34.2718 0.311562
\(111\) 85.7115i 0.772175i
\(112\) 52.7887i 0.471328i
\(113\) 103.390i 0.914958i −0.889220 0.457479i \(-0.848752\pi\)
0.889220 0.457479i \(-0.151248\pi\)
\(114\) 40.6671i 0.356729i
\(115\) −54.0644 + 29.0591i −0.470125 + 0.252688i
\(116\) 61.2681 0.528173
\(117\) 18.7235 0.160030
\(118\) −196.980 −1.66932
\(119\) −30.1528 −0.253385
\(120\) 20.5343i 0.171120i
\(121\) 94.4782 0.780812
\(122\) 142.204i 1.16561i
\(123\) 26.5295 0.215687
\(124\) −116.780 −0.941775
\(125\) 114.427i 0.915419i
\(126\) 19.7931i 0.157088i
\(127\) 88.5042 0.696884 0.348442 0.937330i \(-0.386711\pi\)
0.348442 + 0.937330i \(0.386711\pi\)
\(128\) −128.061 −1.00047
\(129\) 118.243i 0.916609i
\(130\) 41.5337i 0.319490i
\(131\) −207.393 −1.58315 −0.791574 0.611073i \(-0.790738\pi\)
−0.791574 + 0.611073i \(0.790738\pi\)
\(132\) 19.7889i 0.149916i
\(133\) −24.9109 −0.187300
\(134\) 232.894i 1.73801i
\(135\) 13.8667i 0.102717i
\(136\) 50.6298i 0.372278i
\(137\) 157.449i 1.14926i −0.818413 0.574630i \(-0.805146\pi\)
0.818413 0.574630i \(-0.194854\pi\)
\(138\) −47.0320 87.5029i −0.340812 0.634079i
\(139\) 115.205 0.828812 0.414406 0.910092i \(-0.363989\pi\)
0.414406 + 0.910092i \(0.363989\pi\)
\(140\) 15.6640 0.111886
\(141\) 79.7148 0.565353
\(142\) −293.483 −2.06678
\(143\) 32.1416i 0.224766i
\(144\) −59.8568 −0.415672
\(145\) 73.6998i 0.508275i
\(146\) −299.934 −2.05434
\(147\) −12.1244 −0.0824786
\(148\) 109.784i 0.741783i
\(149\) 4.64544i 0.0311775i 0.999878 + 0.0155887i \(0.00496225\pi\)
−0.999878 + 0.0155887i \(0.995038\pi\)
\(150\) −77.2199 −0.514799
\(151\) −221.430 −1.46643 −0.733214 0.679998i \(-0.761980\pi\)
−0.733214 + 0.679998i \(0.761980\pi\)
\(152\) 41.8281i 0.275185i
\(153\) 34.1901i 0.223464i
\(154\) −33.9777 −0.220634
\(155\) 140.476i 0.906295i
\(156\) 23.9821 0.153731
\(157\) 208.739i 1.32955i −0.747044 0.664775i \(-0.768528\pi\)
0.747044 0.664775i \(-0.231472\pi\)
\(158\) 243.127i 1.53878i
\(159\) 165.050i 1.03805i
\(160\) 85.3564i 0.533477i
\(161\) 53.6004 28.8097i 0.332922 0.178942i
\(162\) −22.4432 −0.138538
\(163\) −101.699 −0.623923 −0.311961 0.950095i \(-0.600986\pi\)
−0.311961 + 0.950095i \(0.600986\pi\)
\(164\) 33.9805 0.207198
\(165\) −23.8043 −0.144268
\(166\) 81.3459i 0.490036i
\(167\) −212.169 −1.27047 −0.635236 0.772318i \(-0.719097\pi\)
−0.635236 + 0.772318i \(0.719097\pi\)
\(168\) 20.3581i 0.121179i
\(169\) −130.048 −0.769514
\(170\) −75.8428 −0.446134
\(171\) 28.2463i 0.165183i
\(172\) 151.451i 0.880532i
\(173\) −198.776 −1.14900 −0.574498 0.818506i \(-0.694803\pi\)
−0.574498 + 0.818506i \(0.694803\pi\)
\(174\) −119.283 −0.685533
\(175\) 47.3015i 0.270294i
\(176\) 102.753i 0.583822i
\(177\) 136.817 0.772976
\(178\) 351.573i 1.97513i
\(179\) −40.3609 −0.225480 −0.112740 0.993625i \(-0.535963\pi\)
−0.112740 + 0.993625i \(0.535963\pi\)
\(180\) 17.7613i 0.0986738i
\(181\) 268.080i 1.48111i 0.671998 + 0.740553i \(0.265437\pi\)
−0.671998 + 0.740553i \(0.734563\pi\)
\(182\) 41.1773i 0.226249i
\(183\) 98.7713i 0.539734i
\(184\) 48.3746 + 90.0008i 0.262906 + 0.489135i
\(185\) −132.060 −0.713837
\(186\) 227.359 1.22236
\(187\) 58.6921 0.313862
\(188\) 102.103 0.543101
\(189\) 13.7477i 0.0727393i
\(190\) −62.6579 −0.329778
\(191\) 146.577i 0.767420i 0.923454 + 0.383710i \(0.125354\pi\)
−0.923454 + 0.383710i \(0.874646\pi\)
\(192\) 0.0844787 0.000439993
\(193\) 87.5334 0.453541 0.226771 0.973948i \(-0.427183\pi\)
0.226771 + 0.973948i \(0.427183\pi\)
\(194\) 185.231i 0.954797i
\(195\) 28.8482i 0.147939i
\(196\) −15.5295 −0.0792323
\(197\) 59.4002 0.301524 0.150762 0.988570i \(-0.451827\pi\)
0.150762 + 0.988570i \(0.451827\pi\)
\(198\) 38.5270i 0.194581i
\(199\) 393.816i 1.97897i −0.144624 0.989487i \(-0.546197\pi\)
0.144624 0.989487i \(-0.453803\pi\)
\(200\) 79.4243 0.397121
\(201\) 161.762i 0.804784i
\(202\) −173.525 −0.859036
\(203\) 73.0673i 0.359937i
\(204\) 43.7925i 0.214669i
\(205\) 40.8754i 0.199392i
\(206\) 225.920i 1.09670i
\(207\) 32.6671 + 60.7771i 0.157812 + 0.293609i
\(208\) −124.525 −0.598679
\(209\) 48.4888 0.232004
\(210\) −30.4962 −0.145220
\(211\) −138.956 −0.658560 −0.329280 0.944232i \(-0.606806\pi\)
−0.329280 + 0.944232i \(0.606806\pi\)
\(212\) 211.406i 0.997196i
\(213\) 203.845 0.957019
\(214\) 35.4266i 0.165545i
\(215\) 182.182 0.847358
\(216\) 23.0839 0.106870
\(217\) 139.270i 0.641797i
\(218\) 316.526i 1.45195i
\(219\) 208.326 0.951259
\(220\) −30.4898 −0.138590
\(221\) 71.1286i 0.321849i
\(222\) 213.738i 0.962784i
\(223\) −72.6245 −0.325671 −0.162835 0.986653i \(-0.552064\pi\)
−0.162835 + 0.986653i \(0.552064\pi\)
\(224\) 84.6238i 0.377785i
\(225\) 53.6348 0.238377
\(226\) 257.824i 1.14081i
\(227\) 295.613i 1.30226i 0.758967 + 0.651130i \(0.225705\pi\)
−0.758967 + 0.651130i \(0.774295\pi\)
\(228\) 36.1794i 0.158681i
\(229\) 244.457i 1.06750i −0.845642 0.533750i \(-0.820782\pi\)
0.845642 0.533750i \(-0.179218\pi\)
\(230\) 134.820 72.4645i 0.586174 0.315063i
\(231\) 23.5999 0.102164
\(232\) 122.688 0.528827
\(233\) −374.035 −1.60530 −0.802650 0.596451i \(-0.796577\pi\)
−0.802650 + 0.596451i \(0.796577\pi\)
\(234\) −46.6906 −0.199533
\(235\) 122.821i 0.522640i
\(236\) 175.242 0.742553
\(237\) 168.870i 0.712530i
\(238\) 75.1918 0.315932
\(239\) 45.5079 0.190409 0.0952047 0.995458i \(-0.469649\pi\)
0.0952047 + 0.995458i \(0.469649\pi\)
\(240\) 92.2243i 0.384268i
\(241\) 266.574i 1.10612i 0.833143 + 0.553058i \(0.186539\pi\)
−0.833143 + 0.553058i \(0.813461\pi\)
\(242\) −235.600 −0.973552
\(243\) 15.5885 0.0641500
\(244\) 126.512i 0.518490i
\(245\) 18.6806i 0.0762473i
\(246\) −66.1565 −0.268929
\(247\) 58.7632i 0.237908i
\(248\) −233.849 −0.942941
\(249\) 56.5007i 0.226910i
\(250\) 285.347i 1.14139i
\(251\) 6.34778i 0.0252899i −0.999920 0.0126450i \(-0.995975\pi\)
0.999920 0.0126450i \(-0.00402513\pi\)
\(252\) 17.6088i 0.0698763i
\(253\) −104.333 + 56.0778i −0.412382 + 0.221652i
\(254\) −220.702 −0.868907
\(255\) 52.6783 0.206582
\(256\) 319.149 1.24668
\(257\) 125.676 0.489013 0.244506 0.969648i \(-0.421374\pi\)
0.244506 + 0.969648i \(0.421374\pi\)
\(258\) 294.861i 1.14287i
\(259\) 130.926 0.505507
\(260\) 36.9503i 0.142117i
\(261\) 82.8505 0.317435
\(262\) 517.173 1.97394
\(263\) 344.866i 1.31128i −0.755074 0.655639i \(-0.772399\pi\)
0.755074 0.655639i \(-0.227601\pi\)
\(264\) 39.6269i 0.150102i
\(265\) −254.301 −0.959627
\(266\) 62.1201 0.233534
\(267\) 244.193i 0.914581i
\(268\) 207.193i 0.773108i
\(269\) 135.450 0.503533 0.251766 0.967788i \(-0.418989\pi\)
0.251766 + 0.967788i \(0.418989\pi\)
\(270\) 34.5794i 0.128072i
\(271\) 361.853 1.33525 0.667626 0.744497i \(-0.267311\pi\)
0.667626 + 0.744497i \(0.267311\pi\)
\(272\) 227.390i 0.835991i
\(273\) 28.6006i 0.104764i
\(274\) 392.629i 1.43295i
\(275\) 92.0719i 0.334807i
\(276\) 41.8419 + 77.8466i 0.151601 + 0.282053i
\(277\) 86.5619 0.312498 0.156249 0.987718i \(-0.450060\pi\)
0.156249 + 0.987718i \(0.450060\pi\)
\(278\) −287.286 −1.03340
\(279\) −157.917 −0.566012
\(280\) 31.3667 0.112024
\(281\) 281.370i 1.00132i −0.865645 0.500658i \(-0.833091\pi\)
0.865645 0.500658i \(-0.166909\pi\)
\(282\) −198.784 −0.704909
\(283\) 68.6536i 0.242592i −0.992616 0.121296i \(-0.961295\pi\)
0.992616 0.121296i \(-0.0387050\pi\)
\(284\) 261.096 0.919352
\(285\) 43.5204 0.152703
\(286\) 80.1512i 0.280249i
\(287\) 40.5245i 0.141201i
\(288\) 95.9544 0.333175
\(289\) 159.116 0.550573
\(290\) 183.785i 0.633741i
\(291\) 128.656i 0.442117i
\(292\) 266.835 0.913818
\(293\) 340.957i 1.16368i −0.813305 0.581838i \(-0.802334\pi\)
0.813305 0.581838i \(-0.197666\pi\)
\(294\) 30.2344 0.102838
\(295\) 210.800i 0.714578i
\(296\) 219.840i 0.742701i
\(297\) 26.7598i 0.0901004i
\(298\) 11.5843i 0.0388735i
\(299\) 67.9603 + 126.440i 0.227292 + 0.422876i
\(300\) 68.6984 0.228995
\(301\) −180.618 −0.600061
\(302\) 552.180 1.82841
\(303\) 120.526 0.397775
\(304\) 187.859i 0.617957i
\(305\) 152.182 0.498956
\(306\) 85.2595i 0.278626i
\(307\) 270.059 0.879671 0.439836 0.898078i \(-0.355037\pi\)
0.439836 + 0.898078i \(0.355037\pi\)
\(308\) 30.2281 0.0981432
\(309\) 156.918i 0.507824i
\(310\) 350.303i 1.13001i
\(311\) 210.711 0.677527 0.338763 0.940872i \(-0.389991\pi\)
0.338763 + 0.940872i \(0.389991\pi\)
\(312\) 48.0235 0.153921
\(313\) 301.021i 0.961727i −0.876795 0.480864i \(-0.840323\pi\)
0.876795 0.480864i \(-0.159677\pi\)
\(314\) 520.532i 1.65774i
\(315\) 21.1818 0.0672438
\(316\) 216.297i 0.684486i
\(317\) 205.023 0.646759 0.323380 0.946269i \(-0.395181\pi\)
0.323380 + 0.946269i \(0.395181\pi\)
\(318\) 411.585i 1.29429i
\(319\) 142.225i 0.445846i
\(320\) 0.130161i 0.000406752i
\(321\) 24.6064i 0.0766554i
\(322\) −133.663 + 71.8426i −0.415102 + 0.223114i
\(323\) −107.305 −0.332213
\(324\) 19.9665 0.0616251
\(325\) 111.581 0.343327
\(326\) 253.607 0.777936
\(327\) 219.850i 0.672324i
\(328\) 68.0451 0.207455
\(329\) 121.766i 0.370111i
\(330\) 59.3605 0.179880
\(331\) −482.620 −1.45807 −0.729033 0.684478i \(-0.760030\pi\)
−0.729033 + 0.684478i \(0.760030\pi\)
\(332\) 72.3691i 0.217979i
\(333\) 148.457i 0.445816i
\(334\) 529.084 1.58408
\(335\) −249.234 −0.743982
\(336\) 91.4327i 0.272121i
\(337\) 72.6179i 0.215483i −0.994179 0.107742i \(-0.965638\pi\)
0.994179 0.107742i \(-0.0343620\pi\)
\(338\) 324.299 0.959466
\(339\) 179.077i 0.528251i
\(340\) 67.4732 0.198451
\(341\) 271.088i 0.794979i
\(342\) 70.4376i 0.205958i
\(343\) 18.5203i 0.0539949i
\(344\) 303.278i 0.881622i
\(345\) −93.6423 + 50.3319i −0.271427 + 0.145889i
\(346\) 495.688 1.43262
\(347\) −392.651 −1.13156 −0.565779 0.824557i \(-0.691425\pi\)
−0.565779 + 0.824557i \(0.691425\pi\)
\(348\) 106.119 0.304941
\(349\) −4.12922 −0.0118316 −0.00591579 0.999983i \(-0.501883\pi\)
−0.00591579 + 0.999983i \(0.501883\pi\)
\(350\) 117.955i 0.337015i
\(351\) 32.4300 0.0923933
\(352\) 164.719i 0.467953i
\(353\) −462.131 −1.30915 −0.654577 0.755996i \(-0.727153\pi\)
−0.654577 + 0.755996i \(0.727153\pi\)
\(354\) −341.179 −0.963783
\(355\) 314.074i 0.884716i
\(356\) 312.776i 0.878584i
\(357\) −52.2262 −0.146292
\(358\) 100.648 0.281139
\(359\) 160.266i 0.446424i −0.974770 0.223212i \(-0.928346\pi\)
0.974770 0.223212i \(-0.0716542\pi\)
\(360\) 35.5665i 0.0987959i
\(361\) 272.350 0.754431
\(362\) 668.510i 1.84671i
\(363\) 163.641 0.450802
\(364\) 36.6332i 0.100641i
\(365\) 320.978i 0.879390i
\(366\) 246.305i 0.672965i
\(367\) 360.101i 0.981203i −0.871384 0.490601i \(-0.836777\pi\)
0.871384 0.490601i \(-0.163223\pi\)
\(368\) −217.261 404.214i −0.590383 1.09841i
\(369\) 45.9505 0.124527
\(370\) 329.317 0.890045
\(371\) 252.119 0.679565
\(372\) −202.269 −0.543734
\(373\) 375.533i 1.00679i 0.864057 + 0.503395i \(0.167916\pi\)
−0.864057 + 0.503395i \(0.832084\pi\)
\(374\) −146.360 −0.391337
\(375\) 198.194i 0.528517i
\(376\) 204.459 0.543774
\(377\) 172.361 0.457192
\(378\) 34.2826i 0.0906947i
\(379\) 139.156i 0.367167i −0.983004 0.183583i \(-0.941230\pi\)
0.983004 0.183583i \(-0.0587697\pi\)
\(380\) 55.7433 0.146693
\(381\) 153.294 0.402346
\(382\) 365.519i 0.956855i
\(383\) 160.388i 0.418767i −0.977834 0.209383i \(-0.932854\pi\)
0.977834 0.209383i \(-0.0671457\pi\)
\(384\) −221.808 −0.577624
\(385\) 36.3616i 0.0944457i
\(386\) −218.281 −0.565496
\(387\) 204.802i 0.529204i
\(388\) 164.790i 0.424716i
\(389\) 670.351i 1.72327i 0.507532 + 0.861633i \(0.330558\pi\)
−0.507532 + 0.861633i \(0.669442\pi\)
\(390\) 71.9386i 0.184458i
\(391\) 230.886 124.099i 0.590501 0.317389i
\(392\) −31.0975 −0.0793304
\(393\) −359.214 −0.914031
\(394\) −148.126 −0.375954
\(395\) −260.186 −0.658698
\(396\) 34.2754i 0.0865541i
\(397\) −256.252 −0.645472 −0.322736 0.946489i \(-0.604603\pi\)
−0.322736 + 0.946489i \(0.604603\pi\)
\(398\) 982.055i 2.46748i
\(399\) −43.1469 −0.108138
\(400\) −356.712 −0.891780
\(401\) 509.697i 1.27106i 0.772075 + 0.635532i \(0.219219\pi\)
−0.772075 + 0.635532i \(0.780781\pi\)
\(402\) 403.384i 1.00344i
\(403\) −328.529 −0.815209
\(404\) 154.376 0.382119
\(405\) 24.0179i 0.0593035i
\(406\) 182.207i 0.448787i
\(407\) −254.847 −0.626160
\(408\) 87.6934i 0.214935i
\(409\) 409.626 1.00153 0.500766 0.865583i \(-0.333052\pi\)
0.500766 + 0.865583i \(0.333052\pi\)
\(410\) 101.931i 0.248611i
\(411\) 272.709i 0.663526i
\(412\) 200.989i 0.487837i
\(413\) 208.991i 0.506032i
\(414\) −81.4618 151.559i −0.196768 0.366086i
\(415\) −87.0533 −0.209767
\(416\) 199.622 0.479861
\(417\) 199.541 0.478515
\(418\) −120.916 −0.289273
\(419\) 256.628i 0.612476i −0.951955 0.306238i \(-0.900930\pi\)
0.951955 0.306238i \(-0.0990704\pi\)
\(420\) 27.1308 0.0645971
\(421\) 481.447i 1.14358i 0.820400 + 0.571790i \(0.193751\pi\)
−0.820400 + 0.571790i \(0.806249\pi\)
\(422\) 346.514 0.821124
\(423\) 138.070 0.326407
\(424\) 423.334i 0.998430i
\(425\) 203.753i 0.479419i
\(426\) −508.327 −1.19326
\(427\) −150.876 −0.353339
\(428\) 31.5172i 0.0736383i
\(429\) 55.6708i 0.129769i
\(430\) −454.306 −1.05653
\(431\) 412.625i 0.957367i −0.877988 0.478684i \(-0.841114\pi\)
0.877988 0.478684i \(-0.158886\pi\)
\(432\) −103.675 −0.239988
\(433\) 291.701i 0.673674i −0.941563 0.336837i \(-0.890643\pi\)
0.941563 0.336837i \(-0.109357\pi\)
\(434\) 347.297i 0.800223i
\(435\) 127.652i 0.293453i
\(436\) 281.596i 0.645862i
\(437\) 190.748 102.525i 0.436493 0.234611i
\(438\) −519.500 −1.18607
\(439\) −408.934 −0.931513 −0.465757 0.884913i \(-0.654218\pi\)
−0.465757 + 0.884913i \(0.654218\pi\)
\(440\) −61.0550 −0.138761
\(441\) −21.0000 −0.0476190
\(442\) 177.373i 0.401296i
\(443\) −608.745 −1.37414 −0.687071 0.726591i \(-0.741104\pi\)
−0.687071 + 0.726591i \(0.741104\pi\)
\(444\) 190.151i 0.428269i
\(445\) −376.240 −0.845484
\(446\) 181.103 0.406061
\(447\) 8.04614i 0.0180003i
\(448\) 0.129043i 0.000288043i
\(449\) 104.386 0.232486 0.116243 0.993221i \(-0.462915\pi\)
0.116243 + 0.993221i \(0.462915\pi\)
\(450\) −133.749 −0.297220
\(451\) 78.8807i 0.174902i
\(452\) 229.372i 0.507460i
\(453\) −383.529 −0.846642
\(454\) 737.168i 1.62372i
\(455\) 44.0664 0.0968491
\(456\) 72.4483i 0.158878i
\(457\) 329.999i 0.722098i −0.932547 0.361049i \(-0.882419\pi\)
0.932547 0.361049i \(-0.117581\pi\)
\(458\) 609.602i 1.33101i
\(459\) 59.2189i 0.129017i
\(460\) −119.942 + 64.4678i −0.260744 + 0.140147i
\(461\) −96.9709 −0.210349 −0.105175 0.994454i \(-0.533540\pi\)
−0.105175 + 0.994454i \(0.533540\pi\)
\(462\) −58.8510 −0.127383
\(463\) −445.155 −0.961459 −0.480729 0.876869i \(-0.659628\pi\)
−0.480729 + 0.876869i \(0.659628\pi\)
\(464\) −551.018 −1.18754
\(465\) 243.311i 0.523250i
\(466\) 932.728 2.00156
\(467\) 494.092i 1.05801i 0.848618 + 0.529006i \(0.177435\pi\)
−0.848618 + 0.529006i \(0.822565\pi\)
\(468\) 41.5382 0.0887567
\(469\) 247.095 0.526855
\(470\) 306.277i 0.651652i
\(471\) 361.547i 0.767616i
\(472\) 350.919 0.743472
\(473\) 351.572 0.743281
\(474\) 421.109i 0.888416i
\(475\) 168.332i 0.354382i
\(476\) −66.8941 −0.140534
\(477\) 285.876i 0.599320i
\(478\) −113.483 −0.237411
\(479\) 362.166i 0.756088i 0.925788 + 0.378044i \(0.123403\pi\)
−0.925788 + 0.378044i \(0.876597\pi\)
\(480\) 147.842i 0.308003i
\(481\) 308.847i 0.642094i
\(482\) 664.754i 1.37916i
\(483\) 92.8386 49.8999i 0.192212 0.103312i
\(484\) 209.600 0.433059
\(485\) 198.227 0.408715
\(486\) −38.8728 −0.0799852
\(487\) −121.978 −0.250468 −0.125234 0.992127i \(-0.539968\pi\)
−0.125234 + 0.992127i \(0.539968\pi\)
\(488\) 253.336i 0.519132i
\(489\) −176.149 −0.360222
\(490\) 46.5837i 0.0950687i
\(491\) 54.4849 0.110967 0.0554836 0.998460i \(-0.482330\pi\)
0.0554836 + 0.998460i \(0.482330\pi\)
\(492\) 58.8559 0.119626
\(493\) 314.741i 0.638419i
\(494\) 146.537i 0.296635i
\(495\) −41.2302 −0.0832933
\(496\) 1050.27 2.11748
\(497\) 311.379i 0.626516i
\(498\) 140.895i 0.282922i
\(499\) −146.517 −0.293621 −0.146811 0.989165i \(-0.546901\pi\)
−0.146811 + 0.989165i \(0.546901\pi\)
\(500\) 253.858i 0.507715i
\(501\) −367.487 −0.733507
\(502\) 15.8294i 0.0315327i
\(503\) 655.135i 1.30246i −0.758882 0.651228i \(-0.774254\pi\)
0.758882 0.651228i \(-0.225746\pi\)
\(504\) 35.2613i 0.0699628i
\(505\) 185.700i 0.367723i
\(506\) 260.174 139.841i 0.514177 0.276365i
\(507\) −225.250 −0.444279
\(508\) 196.347 0.386510
\(509\) 5.65935 0.0111186 0.00555928 0.999985i \(-0.498230\pi\)
0.00555928 + 0.999985i \(0.498230\pi\)
\(510\) −131.364 −0.257576
\(511\) 318.223i 0.622745i
\(512\) −283.617 −0.553939
\(513\) 48.9240i 0.0953684i
\(514\) −313.398 −0.609724
\(515\) −241.771 −0.469458
\(516\) 262.322i 0.508375i
\(517\) 237.017i 0.458447i
\(518\) −326.490 −0.630290
\(519\) −344.291 −0.663374
\(520\) 73.9922i 0.142293i
\(521\) 722.523i 1.38680i 0.720553 + 0.693400i \(0.243888\pi\)
−0.720553 + 0.693400i \(0.756112\pi\)
\(522\) −206.604 −0.395793
\(523\) 718.409i 1.37363i −0.726832 0.686815i \(-0.759008\pi\)
0.726832 0.686815i \(-0.240992\pi\)
\(524\) −460.101 −0.878056
\(525\) 81.9286i 0.156054i
\(526\) 859.990i 1.63496i
\(527\) 599.912i 1.13835i
\(528\) 177.973i 0.337070i
\(529\) −291.857 + 441.203i −0.551715 + 0.834033i
\(530\) 634.149 1.19651
\(531\) 236.974 0.446278
\(532\) −55.2649 −0.103881
\(533\) 95.5949 0.179353
\(534\) 608.943i 1.14034i
\(535\) 37.9122 0.0708640
\(536\) 414.899i 0.774065i
\(537\) −69.9071 −0.130181
\(538\) −337.772 −0.627828
\(539\) 36.0495i 0.0668822i
\(540\) 30.7634i 0.0569693i
\(541\) 894.865 1.65410 0.827048 0.562132i \(-0.190019\pi\)
0.827048 + 0.562132i \(0.190019\pi\)
\(542\) −902.351 −1.66485
\(543\) 464.329i 0.855117i
\(544\) 364.521i 0.670075i
\(545\) 338.734 0.621530
\(546\) 71.3211i 0.130625i
\(547\) −828.170 −1.51402 −0.757011 0.653402i \(-0.773341\pi\)
−0.757011 + 0.653402i \(0.773341\pi\)
\(548\) 349.301i 0.637410i
\(549\) 171.077i 0.311615i
\(550\) 229.599i 0.417453i
\(551\) 260.024i 0.471914i
\(552\) 83.7873 + 155.886i 0.151789 + 0.282402i
\(553\) 257.953 0.466461
\(554\) −215.859 −0.389637
\(555\) −228.734 −0.412134
\(556\) 255.583 0.459681
\(557\) 1087.71i 1.95279i 0.215988 + 0.976396i \(0.430703\pi\)
−0.215988 + 0.976396i \(0.569297\pi\)
\(558\) 393.797 0.705730
\(559\) 426.068i 0.762196i
\(560\) −140.875 −0.251562
\(561\) 101.658 0.181208
\(562\) 701.650i 1.24849i
\(563\) 188.523i 0.334855i −0.985884 0.167428i \(-0.946454\pi\)
0.985884 0.167428i \(-0.0535460\pi\)
\(564\) 176.848 0.313560
\(565\) 275.913 0.488342
\(566\) 171.201i 0.302475i
\(567\) 23.8118i 0.0419961i
\(568\) 522.838 0.920490
\(569\) 765.885i 1.34602i −0.739634 0.673010i \(-0.765001\pi\)
0.739634 0.673010i \(-0.234999\pi\)
\(570\) −108.527 −0.190398
\(571\) 206.350i 0.361384i −0.983540 0.180692i \(-0.942166\pi\)
0.983540 0.180692i \(-0.0578338\pi\)
\(572\) 71.3062i 0.124661i
\(573\) 253.879i 0.443070i
\(574\) 101.056i 0.176055i
\(575\) 194.677 + 362.197i 0.338569 + 0.629907i
\(576\) 0.146321 0.000254030
\(577\) −269.172 −0.466503 −0.233251 0.972416i \(-0.574936\pi\)
−0.233251 + 0.972416i \(0.574936\pi\)
\(578\) −396.785 −0.686480
\(579\) 151.612 0.261852
\(580\) 163.503i 0.281902i
\(581\) 86.3062 0.148548
\(582\) 320.829i 0.551253i
\(583\) −490.747 −0.841761
\(584\) 534.330 0.914949
\(585\) 49.9666i 0.0854129i
\(586\) 850.243i 1.45093i
\(587\) 239.644 0.408251 0.204126 0.978945i \(-0.434565\pi\)
0.204126 + 0.978945i \(0.434565\pi\)
\(588\) −26.8979 −0.0457448
\(589\) 495.620i 0.841460i
\(590\) 525.671i 0.890969i
\(591\) 102.884 0.174085
\(592\) 987.348i 1.66782i
\(593\) −3.82945 −0.00645775 −0.00322887 0.999995i \(-0.501028\pi\)
−0.00322887 + 0.999995i \(0.501028\pi\)
\(594\) 66.7308i 0.112341i
\(595\) 80.4674i 0.135239i
\(596\) 10.3059i 0.0172918i
\(597\) 682.109i 1.14256i
\(598\) −169.472 315.302i −0.283398 0.527262i
\(599\) 737.444 1.23112 0.615562 0.788088i \(-0.288929\pi\)
0.615562 + 0.788088i \(0.288929\pi\)
\(600\) 137.567 0.229278
\(601\) 41.7430 0.0694558 0.0347279 0.999397i \(-0.488944\pi\)
0.0347279 + 0.999397i \(0.488944\pi\)
\(602\) 450.407 0.748184
\(603\) 280.179i 0.464642i
\(604\) −491.245 −0.813319
\(605\) 252.130i 0.416744i
\(606\) −300.555 −0.495965
\(607\) 226.628 0.373357 0.186679 0.982421i \(-0.440228\pi\)
0.186679 + 0.982421i \(0.440228\pi\)
\(608\) 301.151i 0.495313i
\(609\) 126.556i 0.207810i
\(610\) −379.494 −0.622122
\(611\) 287.239 0.470114
\(612\) 75.8508i 0.123939i
\(613\) 412.370i 0.672708i 0.941736 + 0.336354i \(0.109194\pi\)
−0.941736 + 0.336354i \(0.890806\pi\)
\(614\) −673.445 −1.09682
\(615\) 70.7982i 0.115119i
\(616\) 60.5310 0.0982647
\(617\) 215.207i 0.348797i −0.984675 0.174398i \(-0.944202\pi\)
0.984675 0.174398i \(-0.0557980\pi\)
\(618\) 391.305i 0.633179i
\(619\) 605.499i 0.978189i −0.872231 0.489095i \(-0.837327\pi\)
0.872231 0.489095i \(-0.162673\pi\)
\(620\) 311.646i 0.502655i
\(621\) 56.5812 + 105.269i 0.0911130 + 0.169515i
\(622\) −525.448 −0.844772
\(623\) 373.011 0.598734
\(624\) −215.684 −0.345648
\(625\) 141.590 0.226544
\(626\) 750.653i 1.19913i
\(627\) 83.9851 0.133947
\(628\) 463.089i 0.737403i
\(629\) 563.971 0.896615
\(630\) −52.8209 −0.0838427
\(631\) 1029.64i 1.63176i 0.578224 + 0.815878i \(0.303746\pi\)
−0.578224 + 0.815878i \(0.696254\pi\)
\(632\) 433.130i 0.685333i
\(633\) −240.679 −0.380220
\(634\) −511.264 −0.806409
\(635\) 236.187i 0.371949i
\(636\) 366.165i 0.575731i
\(637\) −43.6881 −0.0685842
\(638\) 354.665i 0.555901i
\(639\) 353.070 0.552535
\(640\) 341.750i 0.533985i
\(641\) 140.851i 0.219737i 0.993946 + 0.109868i \(0.0350430\pi\)
−0.993946 + 0.109868i \(0.964957\pi\)
\(642\) 61.3607i 0.0955775i
\(643\) 847.482i 1.31801i −0.752138 0.659006i \(-0.770977\pi\)
0.752138 0.659006i \(-0.229023\pi\)
\(644\) 118.913 63.9145i 0.184647 0.0992461i
\(645\) 315.549 0.489223
\(646\) 267.585 0.414218
\(647\) −468.639 −0.724325 −0.362163 0.932115i \(-0.617962\pi\)
−0.362163 + 0.932115i \(0.617962\pi\)
\(648\) 39.9825 0.0617014
\(649\) 406.799i 0.626809i
\(650\) −278.249 −0.428076
\(651\) 241.223i 0.370542i
\(652\) −225.621 −0.346044
\(653\) −82.0353 −0.125628 −0.0628142 0.998025i \(-0.520008\pi\)
−0.0628142 + 0.998025i \(0.520008\pi\)
\(654\) 548.238i 0.838285i
\(655\) 553.459i 0.844976i
\(656\) −305.605 −0.465862
\(657\) 360.831 0.549209
\(658\) 303.648i 0.461471i
\(659\) 217.649i 0.330272i −0.986271 0.165136i \(-0.947194\pi\)
0.986271 0.165136i \(-0.0528063\pi\)
\(660\) −52.8098 −0.0800149
\(661\) 957.496i 1.44856i −0.689508 0.724278i \(-0.742173\pi\)
0.689508 0.724278i \(-0.257827\pi\)
\(662\) 1203.51 1.81799
\(663\) 123.198i 0.185820i
\(664\) 144.917i 0.218249i
\(665\) 66.4786i 0.0999678i
\(666\) 370.205i 0.555864i
\(667\) 300.721 + 559.491i 0.450856 + 0.838817i
\(668\) −470.697 −0.704637
\(669\) −125.789 −0.188026
\(670\) 621.513 0.927632
\(671\) 293.678 0.437672
\(672\) 146.573i 0.218114i
\(673\) −722.505 −1.07356 −0.536780 0.843722i \(-0.680359\pi\)
−0.536780 + 0.843722i \(0.680359\pi\)
\(674\) 181.087i 0.268675i
\(675\) 92.8983 0.137627
\(676\) −288.512 −0.426793
\(677\) 695.664i 1.02757i −0.857919 0.513784i \(-0.828243\pi\)
0.857919 0.513784i \(-0.171757\pi\)
\(678\) 446.564i 0.658648i
\(679\) −196.526 −0.289434
\(680\) 135.114 0.198696
\(681\) 512.017i 0.751860i
\(682\) 676.010i 0.991217i
\(683\) −610.279 −0.893527 −0.446763 0.894652i \(-0.647423\pi\)
−0.446763 + 0.894652i \(0.647423\pi\)
\(684\) 62.6645i 0.0916148i
\(685\) 420.176 0.613396
\(686\) 46.1838i 0.0673234i
\(687\) 423.413i 0.616321i
\(688\) 1362.09i 1.97978i
\(689\) 594.732i 0.863182i
\(690\) 233.515 125.512i 0.338428 0.181902i
\(691\) −951.249 −1.37663 −0.688313 0.725413i \(-0.741649\pi\)
−0.688313 + 0.725413i \(0.741649\pi\)
\(692\) −440.987 −0.637264
\(693\) 40.8763 0.0589846
\(694\) 979.150 1.41088
\(695\) 307.442i 0.442363i
\(696\) 212.502 0.305318
\(697\) 174.561i 0.250447i
\(698\) 10.2970 0.0147522
\(699\) −647.847 −0.926820
\(700\) 104.939i 0.149912i
\(701\) 757.495i 1.08059i −0.841475 0.540296i \(-0.818312\pi\)
0.841475 0.540296i \(-0.181688\pi\)
\(702\) −80.8706 −0.115200
\(703\) 465.927 0.662770
\(704\) 0.251182i 0.000356792i
\(705\) 212.731i 0.301747i
\(706\) 1152.41 1.63231
\(707\) 184.106i 0.260405i
\(708\) 303.529 0.428713
\(709\) 1172.53i 1.65379i −0.562359 0.826893i \(-0.690106\pi\)
0.562359 0.826893i \(-0.309894\pi\)
\(710\) 783.204i 1.10310i
\(711\) 292.491i 0.411380i
\(712\) 626.326i 0.879672i
\(713\) −573.190 1066.42i −0.803913 1.49568i
\(714\) 130.236 0.182403
\(715\) −85.7748 −0.119965
\(716\) −89.5408 −0.125057
\(717\) 78.8219 0.109933
\(718\) 399.654i 0.556622i
\(719\) −181.032 −0.251784 −0.125892 0.992044i \(-0.540179\pi\)
−0.125892 + 0.992044i \(0.540179\pi\)
\(720\) 159.737i 0.221857i
\(721\) 239.696 0.332449
\(722\) −679.157 −0.940660
\(723\) 461.720i 0.638616i
\(724\) 594.737i 0.821461i
\(725\) 493.742 0.681023
\(726\) −408.071 −0.562081
\(727\) 835.202i 1.14883i −0.818563 0.574417i \(-0.805229\pi\)
0.818563 0.574417i \(-0.194771\pi\)
\(728\) 73.3571i 0.100765i
\(729\) 27.0000 0.0370370
\(730\) 800.419i 1.09646i
\(731\) −778.022 −1.06433
\(732\) 219.124i 0.299350i
\(733\) 777.897i 1.06125i 0.847606 + 0.530625i \(0.178043\pi\)
−0.847606 + 0.530625i \(0.821957\pi\)
\(734\) 897.982i 1.22341i
\(735\) 32.3557i 0.0440214i
\(736\) 348.284 + 647.981i 0.473212 + 0.880409i
\(737\) −480.968 −0.652602
\(738\) −114.586 −0.155266
\(739\) −44.8546 −0.0606963 −0.0303482 0.999539i \(-0.509662\pi\)
−0.0303482 + 0.999539i \(0.509662\pi\)
\(740\) −292.975 −0.395913
\(741\) 101.781i 0.137356i
\(742\) −628.706 −0.847313
\(743\) 896.506i 1.20660i 0.797513 + 0.603301i \(0.206148\pi\)
−0.797513 + 0.603301i \(0.793852\pi\)
\(744\) −405.039 −0.544407
\(745\) −12.3971 −0.0166404
\(746\) 936.463i 1.25531i
\(747\) 97.8620i 0.131007i
\(748\) 130.209 0.174076
\(749\) −37.5869 −0.0501827
\(750\) 494.235i 0.658980i
\(751\) 484.548i 0.645204i −0.946535 0.322602i \(-0.895443\pi\)
0.946535 0.322602i \(-0.104557\pi\)
\(752\) −918.270 −1.22110
\(753\) 10.9947i 0.0146012i
\(754\) −429.816 −0.570048
\(755\) 590.922i 0.782678i
\(756\) 30.4994i 0.0403431i
\(757\) 1187.18i 1.56827i 0.620588 + 0.784137i \(0.286894\pi\)
−0.620588 + 0.784137i \(0.713106\pi\)
\(758\) 347.013i 0.457800i
\(759\) −180.709 + 97.1297i −0.238089 + 0.127971i
\(760\) 111.625 0.146875
\(761\) 1485.05 1.95144 0.975720 0.219023i \(-0.0702871\pi\)
0.975720 + 0.219023i \(0.0702871\pi\)
\(762\) −382.268 −0.501664
\(763\) −335.826 −0.440139
\(764\) 325.182i 0.425631i
\(765\) 91.2415 0.119270
\(766\) 399.958i 0.522138i
\(767\) 492.997 0.642760
\(768\) 552.783 0.719769
\(769\) 523.256i 0.680437i −0.940346 0.340219i \(-0.889499\pi\)
0.940346 0.340219i \(-0.110501\pi\)
\(770\) 90.6747i 0.117759i
\(771\) 217.678 0.282332
\(772\) 194.193 0.251546
\(773\) 1040.51i 1.34607i 0.739611 + 0.673035i \(0.235010\pi\)
−0.739611 + 0.673035i \(0.764990\pi\)
\(774\) 510.713i 0.659836i
\(775\) −941.097 −1.21432
\(776\) 329.988i 0.425242i
\(777\) 226.771 0.291855
\(778\) 1671.65i 2.14865i
\(779\) 144.215i 0.185128i
\(780\) 63.9999i 0.0820511i
\(781\) 606.095i 0.776050i
\(782\) −575.759 + 309.465i −0.736264 + 0.395735i
\(783\) 143.501 0.183271
\(784\) 139.666 0.178145
\(785\) 557.053 0.709622
\(786\) 895.770 1.13966
\(787\) 234.535i 0.298011i −0.988836 0.149006i \(-0.952393\pi\)
0.988836 0.149006i \(-0.0476072\pi\)
\(788\) 131.780 0.167233
\(789\) 597.326i 0.757067i
\(790\) 648.824 0.821296
\(791\) −273.545 −0.345822