Properties

Label 108.5.d.b.55.5
Level 108
Weight 5
Character 108.55
Analytic conductor 11.164
Analytic rank 0
Dimension 16
CM no
Inner twists 4

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Newspace parameters

Level: \( N \) \(=\) \( 108 = 2^{2} \cdot 3^{3} \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 108.d (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(11.1639560131\)
Analytic rank: \(0\)
Dimension: \(16\)
Coefficient field: \(\mathbb{Q}[x]/(x^{16} + \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2^{32}\cdot 3^{24} \)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 55.5
Root \(1.78073 - 3.08431i\) of \(x^{16} + 38 x^{14} + 1016 x^{12} + 13512 x^{10} + 130640 x^{8} + 569472 x^{6} + 1783808 x^{4} + 352256 x^{2} + 65536\)
Character \(\chi\) \(=\) 108.55
Dual form 108.5.d.b.55.6

$q$-expansion

\(f(q)\) \(=\) \(q+(-2.54696 - 3.08431i) q^{2} +(-3.02598 + 15.7113i) q^{4} +3.58334 q^{5} +16.2605i q^{7} +(56.1655 - 30.6829i) q^{8} +O(q^{10})\) \(q+(-2.54696 - 3.08431i) q^{2} +(-3.02598 + 15.7113i) q^{4} +3.58334 q^{5} +16.2605i q^{7} +(56.1655 - 30.6829i) q^{8} +(-9.12663 - 11.0521i) q^{10} -144.712i q^{11} -223.658 q^{13} +(50.1524 - 41.4148i) q^{14} +(-237.687 - 95.0838i) q^{16} -1.80372 q^{17} -70.1406i q^{19} +(-10.8431 + 56.2988i) q^{20} +(-446.338 + 368.577i) q^{22} -251.394i q^{23} -612.160 q^{25} +(569.647 + 689.830i) q^{26} +(-255.473 - 49.2039i) q^{28} -1641.50 q^{29} +1047.19i q^{31} +(312.111 + 975.276i) q^{32} +(4.59401 + 5.56324i) q^{34} +58.2669i q^{35} -690.791 q^{37} +(-216.336 + 178.645i) q^{38} +(201.260 - 109.947i) q^{40} -993.138 q^{41} -1983.63i q^{43} +(2273.61 + 437.896i) q^{44} +(-775.377 + 640.290i) q^{46} -3199.12i q^{47} +2136.60 q^{49} +(1559.15 + 1888.09i) q^{50} +(676.783 - 3513.94i) q^{52} -2863.25 q^{53} -518.553i q^{55} +(498.919 + 913.278i) q^{56} +(4180.85 + 5062.91i) q^{58} -5577.97i q^{59} +2838.27 q^{61} +(3229.85 - 2667.14i) q^{62} +(2213.12 - 3446.64i) q^{64} -801.442 q^{65} +5289.13i q^{67} +(5.45802 - 28.3387i) q^{68} +(179.713 - 148.403i) q^{70} +1873.59i q^{71} +4523.42 q^{73} +(1759.42 + 2130.62i) q^{74} +(1102.00 + 212.244i) q^{76} +2353.09 q^{77} -7360.48i q^{79} +(-851.713 - 340.718i) q^{80} +(2529.48 + 3063.15i) q^{82} +5006.55i q^{83} -6.46335 q^{85} +(-6118.15 + 5052.24i) q^{86} +(-4440.19 - 8127.83i) q^{88} -11438.5 q^{89} -3636.78i q^{91} +(3949.71 + 760.712i) q^{92} +(-9867.10 + 8148.04i) q^{94} -251.338i q^{95} -9022.44 q^{97} +(-5441.83 - 6589.93i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 16q + 28q^{4} + O(q^{10}) \) \( 16q + 28q^{4} + 176q^{10} + 176q^{13} + 88q^{16} + 384q^{22} + 2736q^{25} + 1812q^{28} + 1520q^{34} + 80q^{37} - 688q^{40} - 1824q^{46} - 7904q^{49} - 5236q^{52} - 11584q^{58} - 1648q^{61} + 5056q^{64} + 26688q^{70} + 80q^{73} - 8388q^{76} - 38464q^{82} - 16832q^{85} - 29520q^{88} - 4512q^{94} + 14864q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/108\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(55\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.54696 3.08431i −0.636740 0.771078i
\(3\) 0 0
\(4\) −3.02598 + 15.7113i −0.189124 + 0.981953i
\(5\) 3.58334 0.143334 0.0716668 0.997429i \(-0.477168\pi\)
0.0716668 + 0.997429i \(0.477168\pi\)
\(6\) 0 0
\(7\) 16.2605i 0.331847i 0.986139 + 0.165923i \(0.0530604\pi\)
−0.986139 + 0.165923i \(0.946940\pi\)
\(8\) 56.1655 30.6829i 0.877586 0.479420i
\(9\) 0 0
\(10\) −9.12663 11.0521i −0.0912663 0.110521i
\(11\) 144.712i 1.19597i −0.801508 0.597985i \(-0.795968\pi\)
0.801508 0.597985i \(-0.204032\pi\)
\(12\) 0 0
\(13\) −223.658 −1.32342 −0.661709 0.749761i \(-0.730169\pi\)
−0.661709 + 0.749761i \(0.730169\pi\)
\(14\) 50.1524 41.4148i 0.255880 0.211300i
\(15\) 0 0
\(16\) −237.687 95.0838i −0.928464 0.371421i
\(17\) −1.80372 −0.00624125 −0.00312062 0.999995i \(-0.500993\pi\)
−0.00312062 + 0.999995i \(0.500993\pi\)
\(18\) 0 0
\(19\) 70.1406i 0.194295i −0.995270 0.0971476i \(-0.969028\pi\)
0.995270 0.0971476i \(-0.0309719\pi\)
\(20\) −10.8431 + 56.2988i −0.0271078 + 0.140747i
\(21\) 0 0
\(22\) −446.338 + 368.577i −0.922186 + 0.761522i
\(23\) 251.394i 0.475225i −0.971360 0.237612i \(-0.923635\pi\)
0.971360 0.237612i \(-0.0763648\pi\)
\(24\) 0 0
\(25\) −612.160 −0.979455
\(26\) 569.647 + 689.830i 0.842674 + 1.02046i
\(27\) 0 0
\(28\) −255.473 49.2039i −0.325858 0.0627601i
\(29\) −1641.50 −1.95185 −0.975924 0.218110i \(-0.930011\pi\)
−0.975924 + 0.218110i \(0.930011\pi\)
\(30\) 0 0
\(31\) 1047.19i 1.08968i 0.838539 + 0.544842i \(0.183410\pi\)
−0.838539 + 0.544842i \(0.816590\pi\)
\(32\) 312.111 + 975.276i 0.304796 + 0.952418i
\(33\) 0 0
\(34\) 4.59401 + 5.56324i 0.00397405 + 0.00481249i
\(35\) 58.2669i 0.0475648i
\(36\) 0 0
\(37\) −690.791 −0.504596 −0.252298 0.967650i \(-0.581186\pi\)
−0.252298 + 0.967650i \(0.581186\pi\)
\(38\) −216.336 + 178.645i −0.149817 + 0.123716i
\(39\) 0 0
\(40\) 201.260 109.947i 0.125788 0.0687170i
\(41\) −993.138 −0.590802 −0.295401 0.955373i \(-0.595453\pi\)
−0.295401 + 0.955373i \(0.595453\pi\)
\(42\) 0 0
\(43\) 1983.63i 1.07281i −0.843959 0.536407i \(-0.819781\pi\)
0.843959 0.536407i \(-0.180219\pi\)
\(44\) 2273.61 + 437.896i 1.17439 + 0.226186i
\(45\) 0 0
\(46\) −775.377 + 640.290i −0.366435 + 0.302595i
\(47\) 3199.12i 1.44822i −0.689683 0.724111i \(-0.742250\pi\)
0.689683 0.724111i \(-0.257750\pi\)
\(48\) 0 0
\(49\) 2136.60 0.889878
\(50\) 1559.15 + 1888.09i 0.623659 + 0.755237i
\(51\) 0 0
\(52\) 676.783 3513.94i 0.250290 1.29953i
\(53\) −2863.25 −1.01931 −0.509657 0.860378i \(-0.670228\pi\)
−0.509657 + 0.860378i \(0.670228\pi\)
\(54\) 0 0
\(55\) 518.553i 0.171423i
\(56\) 498.919 + 913.278i 0.159094 + 0.291224i
\(57\) 0 0
\(58\) 4180.85 + 5062.91i 1.24282 + 1.50503i
\(59\) 5577.97i 1.60241i −0.598393 0.801203i \(-0.704194\pi\)
0.598393 0.801203i \(-0.295806\pi\)
\(60\) 0 0
\(61\) 2838.27 0.762770 0.381385 0.924416i \(-0.375447\pi\)
0.381385 + 0.924416i \(0.375447\pi\)
\(62\) 3229.85 2667.14i 0.840232 0.693846i
\(63\) 0 0
\(64\) 2213.12 3446.64i 0.540313 0.841464i
\(65\) −801.442 −0.189690
\(66\) 0 0
\(67\) 5289.13i 1.17824i 0.808045 + 0.589121i \(0.200526\pi\)
−0.808045 + 0.589121i \(0.799474\pi\)
\(68\) 5.45802 28.3387i 0.00118037 0.00612861i
\(69\) 0 0
\(70\) 179.713 148.403i 0.0366762 0.0302864i
\(71\) 1873.59i 0.371671i 0.982581 + 0.185835i \(0.0594991\pi\)
−0.982581 + 0.185835i \(0.940501\pi\)
\(72\) 0 0
\(73\) 4523.42 0.848830 0.424415 0.905468i \(-0.360480\pi\)
0.424415 + 0.905468i \(0.360480\pi\)
\(74\) 1759.42 + 2130.62i 0.321296 + 0.389083i
\(75\) 0 0
\(76\) 1102.00 + 212.244i 0.190789 + 0.0367458i
\(77\) 2353.09 0.396879
\(78\) 0 0
\(79\) 7360.48i 1.17937i −0.807632 0.589687i \(-0.799251\pi\)
0.807632 0.589687i \(-0.200749\pi\)
\(80\) −851.713 340.718i −0.133080 0.0532371i
\(81\) 0 0
\(82\) 2529.48 + 3063.15i 0.376187 + 0.455555i
\(83\) 5006.55i 0.726745i 0.931644 + 0.363372i \(0.118375\pi\)
−0.931644 + 0.363372i \(0.881625\pi\)
\(84\) 0 0
\(85\) −6.46335 −0.000894581
\(86\) −6118.15 + 5052.24i −0.827224 + 0.683104i
\(87\) 0 0
\(88\) −4440.19 8127.83i −0.573372 1.04957i
\(89\) −11438.5 −1.44407 −0.722034 0.691858i \(-0.756792\pi\)
−0.722034 + 0.691858i \(0.756792\pi\)
\(90\) 0 0
\(91\) 3636.78i 0.439172i
\(92\) 3949.71 + 760.712i 0.466648 + 0.0898762i
\(93\) 0 0
\(94\) −9867.10 + 8148.04i −1.11669 + 0.922142i
\(95\) 251.338i 0.0278490i
\(96\) 0 0
\(97\) −9022.44 −0.958916 −0.479458 0.877565i \(-0.659167\pi\)
−0.479458 + 0.877565i \(0.659167\pi\)
\(98\) −5441.83 6589.93i −0.566621 0.686165i
\(99\) 0 0
\(100\) 1852.38 9617.80i 0.185238 0.961780i
\(101\) 14876.5 1.45833 0.729167 0.684336i \(-0.239908\pi\)
0.729167 + 0.684336i \(0.239908\pi\)
\(102\) 0 0
\(103\) 12827.6i 1.20912i 0.796558 + 0.604562i \(0.206652\pi\)
−0.796558 + 0.604562i \(0.793348\pi\)
\(104\) −12561.8 + 6862.46i −1.16141 + 0.634473i
\(105\) 0 0
\(106\) 7292.59 + 8831.17i 0.649038 + 0.785971i
\(107\) 18333.9i 1.60136i 0.599095 + 0.800678i \(0.295527\pi\)
−0.599095 + 0.800678i \(0.704473\pi\)
\(108\) 0 0
\(109\) −10407.4 −0.875974 −0.437987 0.898981i \(-0.644308\pi\)
−0.437987 + 0.898981i \(0.644308\pi\)
\(110\) −1599.38 + 1320.74i −0.132180 + 0.109152i
\(111\) 0 0
\(112\) 1546.11 3864.91i 0.123255 0.308108i
\(113\) 21057.9 1.64914 0.824572 0.565758i \(-0.191416\pi\)
0.824572 + 0.565758i \(0.191416\pi\)
\(114\) 0 0
\(115\) 900.829i 0.0681156i
\(116\) 4967.16 25790.1i 0.369141 1.91662i
\(117\) 0 0
\(118\) −17204.2 + 14206.9i −1.23558 + 1.02032i
\(119\) 29.3294i 0.00207114i
\(120\) 0 0
\(121\) −6300.65 −0.430343
\(122\) −7228.95 8754.10i −0.485686 0.588155i
\(123\) 0 0
\(124\) −16452.6 3168.76i −1.07002 0.206085i
\(125\) −4433.16 −0.283723
\(126\) 0 0
\(127\) 8341.04i 0.517145i 0.965992 + 0.258573i \(0.0832521\pi\)
−0.965992 + 0.258573i \(0.916748\pi\)
\(128\) −16267.2 + 1952.49i −0.992874 + 0.119171i
\(129\) 0 0
\(130\) 2041.24 + 2471.90i 0.120783 + 0.146266i
\(131\) 17537.0i 1.02191i −0.859608 0.510955i \(-0.829292\pi\)
0.859608 0.510955i \(-0.170708\pi\)
\(132\) 0 0
\(133\) 1140.52 0.0644762
\(134\) 16313.3 13471.2i 0.908516 0.750234i
\(135\) 0 0
\(136\) −101.307 + 55.3434i −0.00547723 + 0.00299218i
\(137\) 15233.4 0.811627 0.405814 0.913956i \(-0.366988\pi\)
0.405814 + 0.913956i \(0.366988\pi\)
\(138\) 0 0
\(139\) 29455.9i 1.52455i −0.647250 0.762277i \(-0.724081\pi\)
0.647250 0.762277i \(-0.275919\pi\)
\(140\) −915.445 176.314i −0.0467064 0.00899563i
\(141\) 0 0
\(142\) 5778.75 4771.97i 0.286587 0.236658i
\(143\) 32366.0i 1.58277i
\(144\) 0 0
\(145\) −5882.07 −0.279766
\(146\) −11521.0 13951.6i −0.540484 0.654515i
\(147\) 0 0
\(148\) 2090.32 10853.2i 0.0954309 0.495489i
\(149\) 25630.4 1.15447 0.577234 0.816579i \(-0.304132\pi\)
0.577234 + 0.816579i \(0.304132\pi\)
\(150\) 0 0
\(151\) 26662.5i 1.16936i 0.811265 + 0.584679i \(0.198780\pi\)
−0.811265 + 0.584679i \(0.801220\pi\)
\(152\) −2152.11 3939.48i −0.0931490 0.170511i
\(153\) 0 0
\(154\) −5993.24 7257.68i −0.252709 0.306024i
\(155\) 3752.43i 0.156188i
\(156\) 0 0
\(157\) 4902.53 0.198894 0.0994468 0.995043i \(-0.468293\pi\)
0.0994468 + 0.995043i \(0.468293\pi\)
\(158\) −22702.0 + 18746.8i −0.909390 + 0.750955i
\(159\) 0 0
\(160\) 1118.40 + 3494.74i 0.0436875 + 0.136513i
\(161\) 4087.79 0.157702
\(162\) 0 0
\(163\) 5606.70i 0.211024i −0.994418 0.105512i \(-0.966352\pi\)
0.994418 0.105512i \(-0.0336481\pi\)
\(164\) 3005.21 15603.4i 0.111735 0.580140i
\(165\) 0 0
\(166\) 15441.8 12751.5i 0.560377 0.462748i
\(167\) 8055.50i 0.288842i −0.989516 0.144421i \(-0.953868\pi\)
0.989516 0.144421i \(-0.0461319\pi\)
\(168\) 0 0
\(169\) 21461.8 0.751436
\(170\) 16.4619 + 19.9350i 0.000569616 + 0.000689792i
\(171\) 0 0
\(172\) 31165.4 + 6002.43i 1.05345 + 0.202894i
\(173\) −37584.7 −1.25580 −0.627898 0.778296i \(-0.716085\pi\)
−0.627898 + 0.778296i \(0.716085\pi\)
\(174\) 0 0
\(175\) 9954.02i 0.325029i
\(176\) −13759.8 + 34396.2i −0.444208 + 1.11042i
\(177\) 0 0
\(178\) 29133.3 + 35279.8i 0.919496 + 1.11349i
\(179\) 34709.7i 1.08329i 0.840608 + 0.541645i \(0.182198\pi\)
−0.840608 + 0.541645i \(0.817802\pi\)
\(180\) 0 0
\(181\) 45374.3 1.38501 0.692504 0.721414i \(-0.256507\pi\)
0.692504 + 0.721414i \(0.256507\pi\)
\(182\) −11217.0 + 9262.75i −0.338636 + 0.279638i
\(183\) 0 0
\(184\) −7713.49 14119.7i −0.227832 0.417050i
\(185\) −2475.34 −0.0723255
\(186\) 0 0
\(187\) 261.021i 0.00746434i
\(188\) 50262.2 + 9680.48i 1.42209 + 0.273893i
\(189\) 0 0
\(190\) −775.204 + 640.147i −0.0214738 + 0.0177326i
\(191\) 24475.4i 0.670907i −0.942057 0.335454i \(-0.891110\pi\)
0.942057 0.335454i \(-0.108890\pi\)
\(192\) 0 0
\(193\) 13113.8 0.352058 0.176029 0.984385i \(-0.443675\pi\)
0.176029 + 0.984385i \(0.443675\pi\)
\(194\) 22979.8 + 27828.0i 0.610581 + 0.739400i
\(195\) 0 0
\(196\) −6465.29 + 33568.6i −0.168297 + 0.873818i
\(197\) −32666.7 −0.841730 −0.420865 0.907123i \(-0.638273\pi\)
−0.420865 + 0.907123i \(0.638273\pi\)
\(198\) 0 0
\(199\) 8800.86i 0.222238i 0.993807 + 0.111119i \(0.0354435\pi\)
−0.993807 + 0.111119i \(0.964556\pi\)
\(200\) −34382.2 + 18782.8i −0.859556 + 0.469571i
\(201\) 0 0
\(202\) −37889.8 45883.7i −0.928580 1.12449i
\(203\) 26691.7i 0.647715i
\(204\) 0 0
\(205\) −3558.75 −0.0846818
\(206\) 39564.3 32671.4i 0.932329 0.769898i
\(207\) 0 0
\(208\) 53160.5 + 21266.2i 1.22875 + 0.491546i
\(209\) −10150.2 −0.232371
\(210\) 0 0
\(211\) 49061.2i 1.10198i −0.834513 0.550989i \(-0.814251\pi\)
0.834513 0.550989i \(-0.185749\pi\)
\(212\) 8664.14 44985.3i 0.192776 1.00092i
\(213\) 0 0
\(214\) 56547.6 46695.8i 1.23477 1.01965i
\(215\) 7108.03i 0.153770i
\(216\) 0 0
\(217\) −17027.8 −0.361608
\(218\) 26507.4 + 32099.8i 0.557768 + 0.675445i
\(219\) 0 0
\(220\) 8147.12 + 1569.13i 0.168329 + 0.0324201i
\(221\) 403.416 0.00825978
\(222\) 0 0
\(223\) 47153.5i 0.948210i 0.880468 + 0.474105i \(0.157228\pi\)
−0.880468 + 0.474105i \(0.842772\pi\)
\(224\) −15858.5 + 5075.08i −0.316057 + 0.101146i
\(225\) 0 0
\(226\) −53633.7 64949.2i −1.05008 1.27162i
\(227\) 61125.3i 1.18623i −0.805117 0.593116i \(-0.797898\pi\)
0.805117 0.593116i \(-0.202102\pi\)
\(228\) 0 0
\(229\) −42983.0 −0.819645 −0.409823 0.912165i \(-0.634409\pi\)
−0.409823 + 0.912165i \(0.634409\pi\)
\(230\) −2778.44 + 2294.38i −0.0525225 + 0.0433720i
\(231\) 0 0
\(232\) −92195.9 + 50366.1i −1.71291 + 0.935755i
\(233\) −63194.6 −1.16404 −0.582020 0.813175i \(-0.697737\pi\)
−0.582020 + 0.813175i \(0.697737\pi\)
\(234\) 0 0
\(235\) 11463.5i 0.207579i
\(236\) 87637.0 + 16878.8i 1.57349 + 0.303053i
\(237\) 0 0
\(238\) −90.4610 + 74.7008i −0.00159701 + 0.00131878i
\(239\) 67281.6i 1.17788i −0.808177 0.588940i \(-0.799546\pi\)
0.808177 0.588940i \(-0.200454\pi\)
\(240\) 0 0
\(241\) 14307.7 0.246341 0.123171 0.992386i \(-0.460694\pi\)
0.123171 + 0.992386i \(0.460694\pi\)
\(242\) 16047.5 + 19433.2i 0.274016 + 0.331828i
\(243\) 0 0
\(244\) −8588.53 + 44592.7i −0.144258 + 0.749004i
\(245\) 7656.15 0.127549
\(246\) 0 0
\(247\) 15687.5i 0.257134i
\(248\) 32130.7 + 58815.8i 0.522417 + 0.956291i
\(249\) 0 0
\(250\) 11291.1 + 13673.3i 0.180658 + 0.218772i
\(251\) 92024.1i 1.46068i −0.683085 0.730339i \(-0.739362\pi\)
0.683085 0.730339i \(-0.260638\pi\)
\(252\) 0 0
\(253\) −36379.8 −0.568354
\(254\) 25726.4 21244.3i 0.398760 0.329287i
\(255\) 0 0
\(256\) 47454.1 + 45200.4i 0.724093 + 0.689703i
\(257\) −47095.9 −0.713045 −0.356523 0.934287i \(-0.616038\pi\)
−0.356523 + 0.934287i \(0.616038\pi\)
\(258\) 0 0
\(259\) 11232.6i 0.167448i
\(260\) 2425.14 12591.7i 0.0358749 0.186267i
\(261\) 0 0
\(262\) −54089.5 + 44666.0i −0.787972 + 0.650691i
\(263\) 64791.0i 0.936706i 0.883542 + 0.468353i \(0.155152\pi\)
−0.883542 + 0.468353i \(0.844848\pi\)
\(264\) 0 0
\(265\) −10260.0 −0.146102
\(266\) −2904.86 3517.72i −0.0410546 0.0497162i
\(267\) 0 0
\(268\) −83098.8 16004.8i −1.15698 0.222833i
\(269\) 13020.2 0.179934 0.0899669 0.995945i \(-0.471324\pi\)
0.0899669 + 0.995945i \(0.471324\pi\)
\(270\) 0 0
\(271\) 86544.0i 1.17842i 0.807981 + 0.589208i \(0.200560\pi\)
−0.807981 + 0.589208i \(0.799440\pi\)
\(272\) 428.721 + 171.505i 0.00579478 + 0.00231813i
\(273\) 0 0
\(274\) −38799.0 46984.7i −0.516796 0.625828i
\(275\) 88587.0i 1.17140i
\(276\) 0 0
\(277\) −71659.6 −0.933931 −0.466966 0.884275i \(-0.654653\pi\)
−0.466966 + 0.884275i \(0.654653\pi\)
\(278\) −90851.3 + 75023.1i −1.17555 + 0.970745i
\(279\) 0 0
\(280\) 1787.80 + 3272.59i 0.0228035 + 0.0417422i
\(281\) −15636.0 −0.198022 −0.0990110 0.995086i \(-0.531568\pi\)
−0.0990110 + 0.995086i \(0.531568\pi\)
\(282\) 0 0
\(283\) 34109.5i 0.425895i −0.977064 0.212947i \(-0.931694\pi\)
0.977064 0.212947i \(-0.0683063\pi\)
\(284\) −29436.5 5669.45i −0.364964 0.0702918i
\(285\) 0 0
\(286\) 99826.9 82435.0i 1.22044 1.00781i
\(287\) 16148.9i 0.196056i
\(288\) 0 0
\(289\) −83517.7 −0.999961
\(290\) 14981.4 + 18142.1i 0.178138 + 0.215721i
\(291\) 0 0
\(292\) −13687.8 + 71068.5i −0.160534 + 0.833512i
\(293\) −82967.5 −0.966436 −0.483218 0.875500i \(-0.660532\pi\)
−0.483218 + 0.875500i \(0.660532\pi\)
\(294\) 0 0
\(295\) 19987.8i 0.229679i
\(296\) −38798.6 + 21195.5i −0.442826 + 0.241913i
\(297\) 0 0
\(298\) −65279.5 79052.1i −0.735097 0.890186i
\(299\) 56226.1i 0.628921i
\(300\) 0 0
\(301\) 32254.8 0.356010
\(302\) 82235.6 67908.4i 0.901667 0.744577i
\(303\) 0 0
\(304\) −6669.23 + 16671.5i −0.0721654 + 0.180396i
\(305\) 10170.5 0.109331
\(306\) 0 0
\(307\) 156067.i 1.65590i −0.560802 0.827950i \(-0.689507\pi\)
0.560802 0.827950i \(-0.310493\pi\)
\(308\) −7120.41 + 36970.0i −0.0750591 + 0.389716i
\(309\) 0 0
\(310\) 11573.7 9557.29i 0.120434 0.0994515i
\(311\) 23137.2i 0.239216i 0.992821 + 0.119608i \(0.0381638\pi\)
−0.992821 + 0.119608i \(0.961836\pi\)
\(312\) 0 0
\(313\) 21035.4 0.214715 0.107358 0.994220i \(-0.465761\pi\)
0.107358 + 0.994220i \(0.465761\pi\)
\(314\) −12486.5 15120.9i −0.126644 0.153363i
\(315\) 0 0
\(316\) 115642. + 22272.6i 1.15809 + 0.223048i
\(317\) 106440. 1.05922 0.529611 0.848240i \(-0.322338\pi\)
0.529611 + 0.848240i \(0.322338\pi\)
\(318\) 0 0
\(319\) 237546.i 2.33435i
\(320\) 7930.37 12350.5i 0.0774450 0.120610i
\(321\) 0 0
\(322\) −10411.4 12608.0i −0.100415 0.121600i
\(323\) 126.514i 0.00121264i
\(324\) 0 0
\(325\) 136914. 1.29623
\(326\) −17292.8 + 14280.0i −0.162716 + 0.134367i
\(327\) 0 0
\(328\) −55780.1 + 30472.3i −0.518479 + 0.283242i
\(329\) 52019.3 0.480588
\(330\) 0 0
\(331\) 194535.i 1.77559i −0.460239 0.887795i \(-0.652236\pi\)
0.460239 0.887795i \(-0.347764\pi\)
\(332\) −78659.1 15149.7i −0.713630 0.137445i
\(333\) 0 0
\(334\) −24845.7 + 20517.1i −0.222720 + 0.183917i
\(335\) 18952.7i 0.168882i
\(336\) 0 0
\(337\) 81272.1 0.715618 0.357809 0.933795i \(-0.383524\pi\)
0.357809 + 0.933795i \(0.383524\pi\)
\(338\) −54662.2 66194.8i −0.478469 0.579416i
\(339\) 0 0
\(340\) 19.5579 101.547i 0.000169186 0.000878436i
\(341\) 151541. 1.30323
\(342\) 0 0
\(343\) 73783.5i 0.627150i
\(344\) −60863.6 111412.i −0.514328 0.941486i
\(345\) 0 0
\(346\) 95726.8 + 115923.i 0.799616 + 0.968317i
\(347\) 113947.i 0.946331i 0.880974 + 0.473165i \(0.156889\pi\)
−0.880974 + 0.473165i \(0.843111\pi\)
\(348\) 0 0
\(349\) 25419.8 0.208700 0.104350 0.994541i \(-0.466724\pi\)
0.104350 + 0.994541i \(0.466724\pi\)
\(350\) −30701.3 + 25352.5i −0.250623 + 0.206959i
\(351\) 0 0
\(352\) 141134. 45166.3i 1.13906 0.364527i
\(353\) 39576.0 0.317601 0.158801 0.987311i \(-0.449237\pi\)
0.158801 + 0.987311i \(0.449237\pi\)
\(354\) 0 0
\(355\) 6713.72i 0.0532729i
\(356\) 34612.5 179712.i 0.273107 1.41801i
\(357\) 0 0
\(358\) 107056. 88404.2i 0.835301 0.689774i
\(359\) 120831.i 0.937541i −0.883320 0.468771i \(-0.844697\pi\)
0.883320 0.468771i \(-0.155303\pi\)
\(360\) 0 0
\(361\) 125401. 0.962249
\(362\) −115566. 139948.i −0.881891 1.06795i
\(363\) 0 0
\(364\) 57138.4 + 11004.8i 0.431246 + 0.0830578i
\(365\) 16208.9 0.121666
\(366\) 0 0
\(367\) 113429.i 0.842156i 0.907024 + 0.421078i \(0.138348\pi\)
−0.907024 + 0.421078i \(0.861652\pi\)
\(368\) −23903.5 + 59753.0i −0.176508 + 0.441229i
\(369\) 0 0
\(370\) 6304.60 + 7634.73i 0.0460526 + 0.0557686i
\(371\) 46557.9i 0.338256i
\(372\) 0 0
\(373\) −23277.7 −0.167310 −0.0836551 0.996495i \(-0.526659\pi\)
−0.0836551 + 0.996495i \(0.526659\pi\)
\(374\) 805.069 664.809i 0.00575559 0.00475285i
\(375\) 0 0
\(376\) −98158.3 179680.i −0.694307 1.27094i
\(377\) 367135. 2.58311
\(378\) 0 0
\(379\) 89977.3i 0.626404i −0.949686 0.313202i \(-0.898598\pi\)
0.949686 0.313202i \(-0.101402\pi\)
\(380\) 3948.83 + 760.542i 0.0273465 + 0.00526691i
\(381\) 0 0
\(382\) −75489.7 + 62337.8i −0.517322 + 0.427194i
\(383\) 242067.i 1.65020i 0.564984 + 0.825102i \(0.308882\pi\)
−0.564984 + 0.825102i \(0.691118\pi\)
\(384\) 0 0
\(385\) 8431.93 0.0568860
\(386\) −33400.3 40447.1i −0.224169 0.271464i
\(387\) 0 0
\(388\) 27301.7 141754.i 0.181354 0.941611i
\(389\) −229775. −1.51846 −0.759230 0.650823i \(-0.774424\pi\)
−0.759230 + 0.650823i \(0.774424\pi\)
\(390\) 0 0
\(391\) 453.444i 0.00296599i
\(392\) 120003. 65556.9i 0.780944 0.426625i
\(393\) 0 0
\(394\) 83200.8 + 100754.i 0.535963 + 0.649040i
\(395\) 26375.1i 0.169044i
\(396\) 0 0
\(397\) −78709.5 −0.499397 −0.249699 0.968324i \(-0.580332\pi\)
−0.249699 + 0.968324i \(0.580332\pi\)
\(398\) 27144.6 22415.4i 0.171363 0.141508i
\(399\) 0 0
\(400\) 145502. + 58206.5i 0.909390 + 0.363791i
\(401\) −42894.9 −0.266757 −0.133379 0.991065i \(-0.542583\pi\)
−0.133379 + 0.991065i \(0.542583\pi\)
\(402\) 0 0
\(403\) 234211.i 1.44211i
\(404\) −45015.9 + 233728.i −0.275805 + 1.43202i
\(405\) 0 0
\(406\) −82325.5 + 67982.6i −0.499439 + 0.412426i
\(407\) 99966.0i 0.603481i
\(408\) 0 0
\(409\) −7021.98 −0.0419771 −0.0209886 0.999780i \(-0.506681\pi\)
−0.0209886 + 0.999780i \(0.506681\pi\)
\(410\) 9064.00 + 10976.3i 0.0539203 + 0.0652963i
\(411\) 0 0
\(412\) −201538. 38816.0i −1.18730 0.228674i
\(413\) 90700.6 0.531753
\(414\) 0 0
\(415\) 17940.2i 0.104167i
\(416\) −69806.0 218128.i −0.403372 1.26045i
\(417\) 0 0
\(418\) 25852.2 + 31306.4i 0.147960 + 0.179176i
\(419\) 93841.8i 0.534525i 0.963624 + 0.267263i \(0.0861191\pi\)
−0.963624 + 0.267263i \(0.913881\pi\)
\(420\) 0 0
\(421\) 131807. 0.743662 0.371831 0.928300i \(-0.378730\pi\)
0.371831 + 0.928300i \(0.378730\pi\)
\(422\) −151320. + 124957.i −0.849711 + 0.701674i
\(423\) 0 0
\(424\) −160816. + 87852.8i −0.894535 + 0.488679i
\(425\) 1104.17 0.00611302
\(426\) 0 0
\(427\) 46151.6i 0.253123i
\(428\) −288049. 55478.1i −1.57246 0.302854i
\(429\) 0 0
\(430\) −21923.4 + 18103.9i −0.118569 + 0.0979117i
\(431\) 14141.6i 0.0761279i −0.999275 0.0380640i \(-0.987881\pi\)
0.999275 0.0380640i \(-0.0121191\pi\)
\(432\) 0 0
\(433\) −224082. −1.19517 −0.597586 0.801805i \(-0.703873\pi\)
−0.597586 + 0.801805i \(0.703873\pi\)
\(434\) 43369.1 + 52519.0i 0.230251 + 0.278828i
\(435\) 0 0
\(436\) 31492.7 163514.i 0.165667 0.860166i
\(437\) −17632.9 −0.0923338
\(438\) 0 0
\(439\) 168793.i 0.875842i 0.899013 + 0.437921i \(0.144285\pi\)
−0.899013 + 0.437921i \(0.855715\pi\)
\(440\) −15910.7 29124.8i −0.0821834 0.150438i
\(441\) 0 0
\(442\) −1027.48 1244.26i −0.00525934 0.00636894i
\(443\) 129808.i 0.661446i 0.943728 + 0.330723i \(0.107293\pi\)
−0.943728 + 0.330723i \(0.892707\pi\)
\(444\) 0 0
\(445\) −40987.9 −0.206983
\(446\) 145436. 120098.i 0.731144 0.603764i
\(447\) 0 0
\(448\) 56044.0 + 35986.4i 0.279237 + 0.179301i
\(449\) −107176. −0.531623 −0.265811 0.964025i \(-0.585640\pi\)
−0.265811 + 0.964025i \(0.585640\pi\)
\(450\) 0 0
\(451\) 143719.i 0.706581i
\(452\) −63720.8 + 330846.i −0.311892 + 1.61938i
\(453\) 0 0
\(454\) −188530. + 155684.i −0.914677 + 0.755321i
\(455\) 13031.8i 0.0629481i
\(456\) 0 0
\(457\) −345116. −1.65247 −0.826234 0.563327i \(-0.809521\pi\)
−0.826234 + 0.563327i \(0.809521\pi\)
\(458\) 109476. + 132573.i 0.521901 + 0.632011i
\(459\) 0 0
\(460\) 14153.2 + 2725.89i 0.0668864 + 0.0128823i
\(461\) 26097.1 0.122798 0.0613988 0.998113i \(-0.480444\pi\)
0.0613988 + 0.998113i \(0.480444\pi\)
\(462\) 0 0
\(463\) 6582.77i 0.0307077i 0.999882 + 0.0153538i \(0.00488747\pi\)
−0.999882 + 0.0153538i \(0.995113\pi\)
\(464\) 390164. + 156081.i 1.81222 + 0.724958i
\(465\) 0 0
\(466\) 160954. + 194912.i 0.741191 + 0.897566i
\(467\) 107337.i 0.492171i −0.969248 0.246085i \(-0.920856\pi\)
0.969248 0.246085i \(-0.0791443\pi\)
\(468\) 0 0
\(469\) −86003.8 −0.390996
\(470\) −35357.2 + 29197.2i −0.160060 + 0.132174i
\(471\) 0 0
\(472\) −171148. 313290.i −0.768225 1.40625i
\(473\) −287056. −1.28305
\(474\) 0 0
\(475\) 42937.2i 0.190304i
\(476\) 460.801 + 88.7501i 0.00203376 + 0.000391701i
\(477\) 0 0
\(478\) −207518. + 171364.i −0.908237 + 0.750003i
\(479\) 348828.i 1.52034i −0.649724 0.760170i \(-0.725116\pi\)
0.649724 0.760170i \(-0.274884\pi\)
\(480\) 0 0
\(481\) 154501. 0.667791
\(482\) −36441.3 44129.6i −0.156855 0.189948i
\(483\) 0 0
\(484\) 19065.6 98991.0i 0.0813880 0.422576i
\(485\) −32330.5 −0.137445
\(486\) 0 0
\(487\) 104528.i 0.440732i 0.975417 + 0.220366i \(0.0707251\pi\)
−0.975417 + 0.220366i \(0.929275\pi\)
\(488\) 159413. 87086.2i 0.669396 0.365687i
\(489\) 0 0
\(490\) −19499.9 23614.0i −0.0812158 0.0983506i
\(491\) 181720.i 0.753770i −0.926260 0.376885i \(-0.876995\pi\)
0.926260 0.376885i \(-0.123005\pi\)
\(492\) 0 0
\(493\) 2960.82 0.0121820
\(494\) 48385.1 39955.4i 0.198270 0.163727i
\(495\) 0 0
\(496\) 99570.5 248903.i 0.404732 1.01173i
\(497\) −30465.5 −0.123338
\(498\) 0 0
\(499\) 329701.i 1.32409i −0.749462 0.662047i \(-0.769688\pi\)
0.749462 0.662047i \(-0.230312\pi\)
\(500\) 13414.7 69650.6i 0.0536586 0.278602i
\(501\) 0 0
\(502\) −283831. + 234382.i −1.12630 + 0.930072i
\(503\) 225559.i 0.891507i −0.895156 0.445753i \(-0.852936\pi\)
0.895156 0.445753i \(-0.147064\pi\)
\(504\) 0 0
\(505\) 53307.4 0.209028
\(506\) 92657.9 + 112207.i 0.361894 + 0.438245i
\(507\) 0 0
\(508\) −131048. 25239.8i −0.507813 0.0978044i
\(509\) −71361.2 −0.275440 −0.137720 0.990471i \(-0.543977\pi\)
−0.137720 + 0.990471i \(0.543977\pi\)
\(510\) 0 0
\(511\) 73553.0i 0.281682i
\(512\) 18548.2 261487.i 0.0707559 0.997494i
\(513\) 0 0
\(514\) 119952. + 145259.i 0.454025 + 0.549814i
\(515\) 45965.6i 0.173308i
\(516\) 0 0
\(517\) −462952. −1.73203
\(518\) −34644.9 + 28609.0i −0.129116 + 0.106621i
\(519\) 0 0
\(520\) −45013.3 + 24590.5i −0.166469 + 0.0909413i
\(521\) −254162. −0.936344 −0.468172 0.883637i \(-0.655087\pi\)
−0.468172 + 0.883637i \(0.655087\pi\)
\(522\) 0 0
\(523\) 449711.i 1.64411i −0.569410 0.822054i \(-0.692828\pi\)
0.569410 0.822054i \(-0.307172\pi\)
\(524\) 275528. + 53066.5i 1.00347 + 0.193267i
\(525\) 0 0
\(526\) 199836. 165020.i 0.722273 0.596438i
\(527\) 1888.83i 0.00680099i
\(528\) 0 0
\(529\) 216642. 0.774162
\(530\) 26131.8 + 31645.1i 0.0930290 + 0.112656i
\(531\) 0 0
\(532\) −3451.19 + 17919.0i −0.0121940 + 0.0633126i
\(533\) 222123. 0.781878
\(534\) 0 0
\(535\) 65696.7i 0.229528i
\(536\) 162286. + 297066.i 0.564873 + 1.03401i
\(537\) 0 0
\(538\) −33161.9 40158.4i −0.114571 0.138743i
\(539\) 309192.i 1.06427i
\(540\) 0 0
\(541\) 479811. 1.63936 0.819682 0.572819i \(-0.194150\pi\)
0.819682 + 0.572819i \(0.194150\pi\)
\(542\) 266929. 220424.i 0.908651 0.750345i
\(543\) 0 0
\(544\) −562.961 1759.13i −0.00190231 0.00594428i
\(545\) −37293.4 −0.125557
\(546\) 0 0
\(547\) 352931.i 1.17955i 0.807569 + 0.589773i \(0.200783\pi\)
−0.807569 + 0.589773i \(0.799217\pi\)
\(548\) −46096.0 + 239336.i −0.153498 + 0.796980i
\(549\) 0 0
\(550\) 273230. 225628.i 0.903240 0.745877i
\(551\) 115136.i 0.379235i
\(552\) 0 0
\(553\) 119685. 0.391372
\(554\) 182514. + 221021.i 0.594672 + 0.720134i
\(555\) 0 0
\(556\) 462789. + 89133.0i 1.49704 + 0.288329i
\(557\) −360746. −1.16276 −0.581382 0.813631i \(-0.697488\pi\)
−0.581382 + 0.813631i \(0.697488\pi\)
\(558\) 0 0
\(559\) 443655.i 1.41978i
\(560\) 5540.24 13849.3i 0.0176666 0.0441622i
\(561\) 0 0
\(562\) 39824.3 + 48226.4i 0.126089 + 0.152691i
\(563\) 466715.i 1.47243i −0.676747 0.736216i \(-0.736611\pi\)
0.676747 0.736216i \(-0.263389\pi\)
\(564\) 0 0
\(565\) 75457.6 0.236378
\(566\) −105204. + 86875.6i −0.328398 + 0.271184i
\(567\) 0 0
\(568\) 57487.2 + 105231.i 0.178187 + 0.326173i
\(569\) −264863. −0.818083 −0.409041 0.912516i \(-0.634137\pi\)
−0.409041 + 0.912516i \(0.634137\pi\)
\(570\) 0 0
\(571\) 605767.i 1.85795i −0.370146 0.928974i \(-0.620692\pi\)
0.370146 0.928974i \(-0.379308\pi\)
\(572\) −508511. 97938.9i −1.55420 0.299339i
\(573\) 0 0
\(574\) −49808.3 + 41130.7i −0.151174 + 0.124837i
\(575\) 153893.i 0.465461i
\(576\) 0 0
\(577\) −160301. −0.481488 −0.240744 0.970589i \(-0.577391\pi\)
−0.240744 + 0.970589i \(0.577391\pi\)
\(578\) 212716. + 257595.i 0.636715 + 0.771048i
\(579\) 0 0
\(580\) 17799.0 92414.7i 0.0529103 0.274717i
\(581\) −81408.9 −0.241168
\(582\) 0 0
\(583\) 414348.i 1.21907i
\(584\) 254060. 138791.i 0.744921 0.406946i
\(585\) 0 0
\(586\) 211315. + 255898.i 0.615369 + 0.745198i
\(587\) 64997.1i 0.188633i 0.995542 + 0.0943165i \(0.0300665\pi\)
−0.995542 + 0.0943165i \(0.969933\pi\)
\(588\) 0 0
\(589\) 73450.3 0.211721
\(590\) −61648.6 + 50908.1i −0.177100 + 0.146246i
\(591\) 0 0
\(592\) 164192. + 65683.1i 0.468499 + 0.187417i
\(593\) −150269. −0.427326 −0.213663 0.976907i \(-0.568539\pi\)
−0.213663 + 0.976907i \(0.568539\pi\)
\(594\) 0 0
\(595\) 105.097i 0.000296864i
\(596\) −77556.9 + 402685.i −0.218337 + 1.13363i
\(597\) 0 0
\(598\) 173419. 143206.i 0.484947 0.400459i
\(599\) 133110.i 0.370985i 0.982646 + 0.185492i \(0.0593880\pi\)
−0.982646 + 0.185492i \(0.940612\pi\)
\(600\) 0 0
\(601\) 462021. 1.27913 0.639563 0.768739i \(-0.279115\pi\)
0.639563 + 0.768739i \(0.279115\pi\)
\(602\) −82151.8 99484.0i −0.226686 0.274511i
\(603\) 0 0
\(604\) −418902. 80680.3i −1.14826 0.221153i
\(605\) −22577.4 −0.0616826
\(606\) 0 0
\(607\) 223633.i 0.606959i −0.952838 0.303479i \(-0.901852\pi\)
0.952838 0.303479i \(-0.0981484\pi\)
\(608\) 68406.4 21891.6i 0.185050 0.0592204i
\(609\) 0 0
\(610\) −25903.8 31368.9i −0.0696152 0.0843024i
\(611\) 715508.i 1.91660i
\(612\) 0 0
\(613\) 383985. 1.02187 0.510933 0.859621i \(-0.329300\pi\)
0.510933 + 0.859621i \(0.329300\pi\)
\(614\) −481359. + 397496.i −1.27683 + 1.05438i
\(615\) 0 0
\(616\) 132163. 72199.7i 0.348295 0.190272i
\(617\) 608003. 1.59711 0.798555 0.601921i \(-0.205598\pi\)
0.798555 + 0.601921i \(0.205598\pi\)
\(618\) 0 0
\(619\) 573813.i 1.49758i −0.662810 0.748788i \(-0.730636\pi\)
0.662810 0.748788i \(-0.269364\pi\)
\(620\) −58955.3 11354.8i −0.153370 0.0295389i
\(621\) 0 0
\(622\) 71362.5 58929.6i 0.184454 0.152319i
\(623\) 185995.i 0.479209i
\(624\) 0 0
\(625\) 366714. 0.938789
\(626\) −53576.5 64879.9i −0.136718 0.165562i
\(627\) 0 0
\(628\) −14834.9 + 77024.8i −0.0376155 + 0.195304i
\(629\) 1245.99 0.00314931
\(630\) 0 0
\(631\) 367125.i 0.922053i −0.887386 0.461026i \(-0.847481\pi\)
0.887386 0.461026i \(-0.152519\pi\)
\(632\) −225841. 413405.i −0.565416 1.03500i
\(633\) 0 0
\(634\) −271099. 328295.i −0.674450 0.816744i
\(635\) 29888.8i 0.0741243i
\(636\) 0 0
\(637\) −477866. −1.17768
\(638\) 732666. 605020.i 1.79997 1.48638i
\(639\) 0 0
\(640\) −58291.1 + 6996.44i −0.142312 + 0.0170812i
\(641\) 161096. 0.392075 0.196037 0.980596i \(-0.437193\pi\)
0.196037 + 0.980596i \(0.437193\pi\)
\(642\) 0 0
\(643\) 658474.i 1.59264i 0.604878 + 0.796318i \(0.293222\pi\)
−0.604878 + 0.796318i \(0.706778\pi\)
\(644\) −12369.6 + 64224.2i −0.0298251 + 0.154856i
\(645\) 0 0
\(646\) 390.209 322.226i 0.000935044 0.000772140i
\(647\) 410472.i 0.980563i 0.871564 + 0.490281i \(0.163106\pi\)
−0.871564 + 0.490281i \(0.836894\pi\)
\(648\) 0 0
\(649\) −807201. −1.91643
\(650\) −348715. 422286.i −0.825361 0.999494i
\(651\) 0 0
\(652\) 88088.2 + 16965.7i 0.207216 + 0.0399096i
\(653\) −23202.5 −0.0544136 −0.0272068 0.999630i \(-0.508661\pi\)
−0.0272068 + 0.999630i \(0.508661\pi\)
\(654\) 0 0
\(655\) 62841.0i 0.146474i
\(656\) 236056. + 94431.4i 0.548539 + 0.219436i
\(657\) 0 0
\(658\) −132491. 160444.i −0.306010 0.370571i
\(659\) 210220.i 0.484064i −0.970268 0.242032i \(-0.922186\pi\)
0.970268 0.242032i \(-0.0778139\pi\)
\(660\) 0 0
\(661\) −21515.2 −0.0492428 −0.0246214 0.999697i \(-0.507838\pi\)
−0.0246214 + 0.999697i \(0.507838\pi\)
\(662\) −600008. + 495474.i −1.36912 + 1.13059i
\(663\) 0 0
\(664\) 153615. + 281195.i 0.348416 + 0.637781i
\(665\) 4086.87 0.00924161
\(666\) 0 0
\(667\) 412664.i 0.927566i
\(668\) 126562. + 24375.8i 0.283629 + 0.0546268i
\(669\) 0 0
\(670\) 58456.2 48271.9i 0.130221 0.107534i
\(671\) 410732.i 0.912249i
\(672\) 0 0
\(673\) 79154.4 0.174761 0.0873806 0.996175i \(-0.472150\pi\)
0.0873806 + 0.996175i \(0.472150\pi\)
\(674\) −206997. 250668.i −0.455663 0.551798i
\(675\) 0 0
\(676\) −64942.8 + 337191.i −0.142114 + 0.737875i
\(677\) 94999.9 0.207274 0.103637 0.994615i \(-0.466952\pi\)
0.103637 + 0.994615i \(0.466952\pi\)
\(678\) 0 0
\(679\) 146709.i 0.318213i
\(680\) −363.017 + 198.314i −0.000785071 + 0.000428880i
\(681\) 0 0
\(682\) −385969. 467399.i −0.829819 1.00489i
\(683\) 265559.i 0.569272i 0.958636 + 0.284636i \(0.0918727\pi\)
−0.958636 + 0.284636i \(0.908127\pi\)
\(684\) 0 0
\(685\) 54586.6 0.116333
\(686\) 227572. 187924.i 0.483582 0.399332i
\(687\) 0 0
\(688\) −188611. + 471484.i −0.398466 + 0.996070i
\(689\) 640388. 1.34898
\(690\) 0 0
\(691\) 497888.i 1.04274i 0.853331 + 0.521369i \(0.174579\pi\)
−0.853331 + 0.521369i \(0.825421\pi\)
\(692\) 113731. 590503.i 0.237501 1.23313i
\(693\) 0 0
\(694\) 351448. 290218.i 0.729695 0.602567i
\(695\) 105551.i 0.218520i
\(696\) 0 0
\(697\) 1791.34 0.00368734
\(698\) −64743.3 78402.8i −0.132888 0.160924i
\(699\) 0 0
\(700\) 156390. + 30120.6i 0.319163 + 0.0614707i
\(701\) 102403. 0.208389 0.104195 0.994557i \(-0.466774\pi\)
0.104195 + 0.994557i \(0.466774\pi\)
\(702\) 0 0
\(703\) 48452.5i 0.0980405i
\(704\) −498771. 320266.i −1.00637 0.646198i
\(705\) 0 0
\(706\) −100798. 122065.i −0.202230 0.244896i
\(707\) 241899.i 0.483943i
\(708\) 0 0
\(709\) −557443. −1.10894 −0.554470 0.832204i \(-0.687079\pi\)
−0.554470 + 0.832204i \(0.687079\pi\)
\(710\) 20707.2 17099.6i 0.0410776 0.0339210i
\(711\) 0 0
\(712\) −642446. + 350965.i −1.26729 + 0.692315i
\(713\) 263256. 0.517845
\(714\) 0 0
\(715\) 115978.i 0.226864i
\(716\) −545332. 105031.i −1.06374 0.204876i
\(717\) 0 0
\(718\) −372682. + 307753.i −0.722918 + 0.596970i
\(719\) 665001.i 1.28637i 0.765713 + 0.643183i \(0.222386\pi\)
−0.765713 + 0.643183i \(0.777614\pi\)
\(720\) 0 0
\(721\) −208583. −0.401244
\(722\) −319392. 386777.i −0.612703 0.741970i
\(723\) 0 0
\(724\) −137302. + 712887.i −0.261938 + 1.36001i
\(725\) 1.00486e6 1.91175
\(726\) 0 0
\(727\) 903006.i 1.70853i −0.519841 0.854263i \(-0.674009\pi\)
0.519841 0.854263i \(-0.325991\pi\)
\(728\) −111587. 204262.i −0.210548 0.385411i
\(729\) 0 0
\(730\) −41283.5 49993.5i −0.0774696 0.0938140i
\(731\) 3577.92i 0.00669570i
\(732\) 0 0
\(733\) −633281. −1.17866 −0.589330 0.807893i \(-0.700608\pi\)
−0.589330 + 0.807893i \(0.700608\pi\)
\(734\) 349851. 288900.i 0.649368 0.536235i
\(735\) 0 0
\(736\) 245178. 78462.8i 0.452612 0.144846i
\(737\) 765401. 1.40914
\(738\) 0 0
\(739\) 72439.1i 0.132643i −0.997798 0.0663215i \(-0.978874\pi\)
0.997798 0.0663215i \(-0.0211263\pi\)
\(740\) 7490.33 38890.7i 0.0136785 0.0710203i
\(741\) 0 0
\(742\) −143599. + 118581.i −0.260822 + 0.215381i
\(743\) 600017.i 1.08689i −0.839444 0.543446i \(-0.817119\pi\)
0.839444 0.543446i \(-0.182881\pi\)
\(744\) 0 0
\(745\) 91842.3 0.165474
\(746\) 59287.4 + 71795.7i 0.106533 + 0.129009i
\(747\) 0 0
\(748\) −4100.96 789.843i −0.00732963 0.00141168i
\(749\) −298119. −0.531405
\(750\) 0 0
\(751\) 710454.i 1.25967i 0.776730 + 0.629834i \(0.216877\pi\)
−0.776730 + 0.629834i \(0.783123\pi\)
\(752\) −304185. + 760390.i −0.537900 + 1.34462i
\(753\) 0 0
\(754\) −935079. 1.13236e6i −1.64477 1.99178i
\(755\) 95540.9i 0.167608i
\(756\) 0 0
\(757\) 577805. 1.00830 0.504150 0.863616i \(-0.331806\pi\)
0.504150 + 0.863616i \(0.331806\pi\)
\(758\) −277518. + 229169.i −0.483007 + 0.398857i
\(759\) 0 0
\(760\) −7711.76 14116.5i −0.0133514 0.0244399i
\(761\) −751658. −1.29793 −0.648965 0.760818i \(-0.724798\pi\)
−0.648965 + 0.760818i \(0.724798\pi\)
\(762\) 0 0
\(763\) 169230.i 0.290689i
\(764\) 384539. + 74061.9i 0.658800 + 0.126884i
\(765\) 0 0
\(766\) 746610. 616535.i 1.27244 1.05075i
\(767\) 1.24756e6i 2.12065i
\(768\) 0 0
\(769\) −416567. −0.704421 −0.352211 0.935921i \(-0.614570\pi\)
−0.352211 + 0.935921i \(0.614570\pi\)
\(770\) −21475.8 26006.7i −0.0362216 0.0438636i
\(771\) 0 0
\(772\) −39682.1 + 206034.i −0.0665824 + 0.345704i
\(773\) −611604. −1.02356 −0.511778 0.859118i \(-0.671013\pi\)
−0.511778 + 0.859118i \(0.671013\pi\)
\(774\) 0 0
\(775\) 641046.i 1.06730i
\(776\) −506750. + 276835.i −0.841531 + 0.459724i
\(777\) 0 0
\(778\) 585228. + 708698.i 0.966864 + 1.17085i
\(779\) 69659.3i 0.114790i
\(780\) 0 0
\(781\) 271132. 0.444507
\(782\) 1398.56 1154.90i 0.00228701 0.00188857i
\(783\) 0 0
\(784\) −507841. 203156.i −0.826220 0.330519i
\(785\) 17567.4 0.0285081
\(786\) 0 0
\(787\) 462322.i 0.746440i 0.927743 + 0.373220i \(0.121746\pi\)
−0.927743 + 0.373220i \(0.878254\pi\)