Properties

Label 177.5.b.a.119.20
Level $177$
Weight $5$
Character 177.119
Analytic conductor $18.296$
Analytic rank $0$
Dimension $78$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 5 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(78\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.20
Character \(\chi\) \(=\) 177.119
Dual form 177.5.b.a.119.59

$q$-expansion

\(f(q)\) \(=\) \(q-4.27932i q^{2} +(-6.98370 - 5.67697i) q^{3} -2.31259 q^{4} -6.15778i q^{5} +(-24.2936 + 29.8855i) q^{6} -22.1503 q^{7} -58.5728i q^{8} +(16.5440 + 79.2925i) q^{9} +O(q^{10})\) \(q-4.27932i q^{2} +(-6.98370 - 5.67697i) q^{3} -2.31259 q^{4} -6.15778i q^{5} +(-24.2936 + 29.8855i) q^{6} -22.1503 q^{7} -58.5728i q^{8} +(16.5440 + 79.2925i) q^{9} -26.3511 q^{10} -60.0378i q^{11} +(16.1504 + 13.1285i) q^{12} -252.105 q^{13} +94.7883i q^{14} +(-34.9575 + 43.0040i) q^{15} -287.653 q^{16} +475.495i q^{17} +(339.318 - 70.7971i) q^{18} -114.066 q^{19} +14.2404i q^{20} +(154.691 + 125.747i) q^{21} -256.921 q^{22} +529.132i q^{23} +(-332.516 + 409.055i) q^{24} +587.082 q^{25} +1078.84i q^{26} +(334.603 - 647.674i) q^{27} +51.2246 q^{28} -1258.45i q^{29} +(184.028 + 149.594i) q^{30} +14.1344 q^{31} +293.796i q^{32} +(-340.833 + 419.286i) q^{33} +2034.79 q^{34} +136.397i q^{35} +(-38.2595 - 183.371i) q^{36} -682.331 q^{37} +488.125i q^{38} +(1760.62 + 1431.19i) q^{39} -360.678 q^{40} +1784.12i q^{41} +(538.110 - 661.972i) q^{42} +1895.39 q^{43} +138.843i q^{44} +(488.265 - 101.874i) q^{45} +2264.33 q^{46} +742.817i q^{47} +(2008.88 + 1633.00i) q^{48} -1910.36 q^{49} -2512.31i q^{50} +(2699.37 - 3320.71i) q^{51} +583.016 q^{52} +3076.72i q^{53} +(-2771.61 - 1431.87i) q^{54} -369.699 q^{55} +1297.41i q^{56} +(796.602 + 647.549i) q^{57} -5385.33 q^{58} +453.188i q^{59} +(80.8424 - 99.4507i) q^{60} +1439.20 q^{61} -60.4856i q^{62} +(-366.455 - 1756.35i) q^{63} -3345.21 q^{64} +1552.41i q^{65} +(1794.26 + 1458.53i) q^{66} +3224.97 q^{67} -1099.62i q^{68} +(3003.87 - 3695.30i) q^{69} +583.685 q^{70} -5483.87i q^{71} +(4644.38 - 969.029i) q^{72} -8856.56 q^{73} +2919.91i q^{74} +(-4100.00 - 3332.85i) q^{75} +263.788 q^{76} +1329.86i q^{77} +(6124.53 - 7534.28i) q^{78} -9349.35 q^{79} +1771.31i q^{80} +(-6013.59 + 2623.63i) q^{81} +7634.84 q^{82} +7555.94i q^{83} +(-357.737 - 290.801i) q^{84} +2927.99 q^{85} -8110.97i q^{86} +(-7144.21 + 8788.66i) q^{87} -3516.58 q^{88} +4863.80i q^{89} +(-435.953 - 2089.44i) q^{90} +5584.20 q^{91} -1223.67i q^{92} +(-98.7102 - 80.2405i) q^{93} +3178.75 q^{94} +702.393i q^{95} +(1667.87 - 2051.78i) q^{96} -12596.8 q^{97} +8175.06i q^{98} +(4760.54 - 993.265i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} + O(q^{10}) \) \( 78q - 612q^{4} + 64q^{6} + 76q^{7} - 100q^{9} - 156q^{10} - 4q^{13} + 13q^{15} + 4948q^{16} + 22q^{18} + 812q^{19} - 173q^{21} - 1644q^{22} - 678q^{24} - 8238q^{25} + 777q^{27} - 3764q^{28} + 1374q^{30} + 4664q^{31} - 1042q^{33} + 3244q^{34} + 3648q^{36} - 3960q^{37} - 7078q^{39} - 1576q^{40} + 4934q^{42} - 1492q^{43} - 2063q^{45} - 2036q^{46} - 2620q^{48} + 24274q^{49} + 7300q^{51} + 8408q^{52} - 14766q^{54} + 9780q^{55} + 6939q^{57} - 3856q^{58} + 4712q^{60} - 212q^{61} - 7438q^{63} - 45760q^{64} + 3048q^{66} - 12972q^{67} + 21672q^{69} + 5828q^{70} - 866q^{72} - 5240q^{73} - 20922q^{75} + 12368q^{76} - 16508q^{78} - 14976q^{79} + 25524q^{81} - 14484q^{82} + 9540q^{84} + 11572q^{85} + 5695q^{87} + 62160q^{88} - 31672q^{90} + 8284q^{91} - 9590q^{93} - 10992q^{94} + 34102q^{96} - 55000q^{97} - 14254q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).

\(n\) \(61\) \(119\)
\(\chi(n)\) \(1\) \(-1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 4.27932i 1.06983i −0.844906 0.534915i \(-0.820344\pi\)
0.844906 0.534915i \(-0.179656\pi\)
\(3\) −6.98370 5.67697i −0.775966 0.630775i
\(4\) −2.31259 −0.144537
\(5\) 6.15778i 0.246311i −0.992387 0.123156i \(-0.960699\pi\)
0.992387 0.123156i \(-0.0393014\pi\)
\(6\) −24.2936 + 29.8855i −0.674822 + 0.830152i
\(7\) −22.1503 −0.452047 −0.226024 0.974122i \(-0.572573\pi\)
−0.226024 + 0.974122i \(0.572573\pi\)
\(8\) 58.5728i 0.915200i
\(9\) 16.5440 + 79.2925i 0.204247 + 0.978919i
\(10\) −26.3511 −0.263511
\(11\) 60.0378i 0.496180i −0.968737 0.248090i \(-0.920197\pi\)
0.968737 0.248090i \(-0.0798029\pi\)
\(12\) 16.1504 + 13.1285i 0.112156 + 0.0911702i
\(13\) −252.105 −1.49175 −0.745873 0.666089i \(-0.767967\pi\)
−0.745873 + 0.666089i \(0.767967\pi\)
\(14\) 94.7883i 0.483614i
\(15\) −34.9575 + 43.0040i −0.155367 + 0.191129i
\(16\) −287.653 −1.12365
\(17\) 475.495i 1.64531i 0.568541 + 0.822655i \(0.307508\pi\)
−0.568541 + 0.822655i \(0.692492\pi\)
\(18\) 339.318 70.7971i 1.04728 0.218510i
\(19\) −114.066 −0.315972 −0.157986 0.987441i \(-0.550500\pi\)
−0.157986 + 0.987441i \(0.550500\pi\)
\(20\) 14.2404i 0.0356010i
\(21\) 154.691 + 125.747i 0.350773 + 0.285140i
\(22\) −256.921 −0.530828
\(23\) 529.132i 1.00025i 0.865953 + 0.500125i \(0.166713\pi\)
−0.865953 + 0.500125i \(0.833287\pi\)
\(24\) −332.516 + 409.055i −0.577285 + 0.710164i
\(25\) 587.082 0.939331
\(26\) 1078.84i 1.59591i
\(27\) 334.603 647.674i 0.458989 0.888442i
\(28\) 51.2246 0.0653375
\(29\) 1258.45i 1.49638i −0.663485 0.748189i \(-0.730923\pi\)
0.663485 0.748189i \(-0.269077\pi\)
\(30\) 184.028 + 149.594i 0.204476 + 0.166216i
\(31\) 14.1344 0.0147080 0.00735400 0.999973i \(-0.497659\pi\)
0.00735400 + 0.999973i \(0.497659\pi\)
\(32\) 293.796i 0.286910i
\(33\) −340.833 + 419.286i −0.312978 + 0.385019i
\(34\) 2034.79 1.76020
\(35\) 136.397i 0.111344i
\(36\) −38.2595 183.371i −0.0295212 0.141490i
\(37\) −682.331 −0.498416 −0.249208 0.968450i \(-0.580170\pi\)
−0.249208 + 0.968450i \(0.580170\pi\)
\(38\) 488.125i 0.338037i
\(39\) 1760.62 + 1431.19i 1.15754 + 0.940955i
\(40\) −360.678 −0.225424
\(41\) 1784.12i 1.06135i 0.847577 + 0.530673i \(0.178061\pi\)
−0.847577 + 0.530673i \(0.821939\pi\)
\(42\) 538.110 661.972i 0.305051 0.375268i
\(43\) 1895.39 1.02509 0.512544 0.858661i \(-0.328703\pi\)
0.512544 + 0.858661i \(0.328703\pi\)
\(44\) 138.843i 0.0717163i
\(45\) 488.265 101.874i 0.241119 0.0503083i
\(46\) 2264.33 1.07010
\(47\) 742.817i 0.336269i 0.985764 + 0.168134i \(0.0537742\pi\)
−0.985764 + 0.168134i \(0.946226\pi\)
\(48\) 2008.88 + 1633.00i 0.871911 + 0.708767i
\(49\) −1910.36 −0.795653
\(50\) 2512.31i 1.00492i
\(51\) 2699.37 3320.71i 1.03782 1.27670i
\(52\) 583.016 0.215612
\(53\) 3076.72i 1.09531i 0.836705 + 0.547654i \(0.184479\pi\)
−0.836705 + 0.547654i \(0.815521\pi\)
\(54\) −2771.61 1431.87i −0.950482 0.491040i
\(55\) −369.699 −0.122215
\(56\) 1297.41i 0.413714i
\(57\) 796.602 + 647.549i 0.245184 + 0.199307i
\(58\) −5385.33 −1.60087
\(59\) 453.188i 0.130189i
\(60\) 80.8424 99.4507i 0.0224562 0.0276252i
\(61\) 1439.20 0.386779 0.193389 0.981122i \(-0.438052\pi\)
0.193389 + 0.981122i \(0.438052\pi\)
\(62\) 60.4856i 0.0157351i
\(63\) −366.455 1756.35i −0.0923292 0.442518i
\(64\) −3345.21 −0.816701
\(65\) 1552.41i 0.367433i
\(66\) 1794.26 + 1458.53i 0.411905 + 0.334833i
\(67\) 3224.97 0.718417 0.359209 0.933257i \(-0.383047\pi\)
0.359209 + 0.933257i \(0.383047\pi\)
\(68\) 1099.62i 0.237808i
\(69\) 3003.87 3695.30i 0.630932 0.776160i
\(70\) 583.685 0.119119
\(71\) 5483.87i 1.08785i −0.839133 0.543927i \(-0.816937\pi\)
0.839133 0.543927i \(-0.183063\pi\)
\(72\) 4644.38 969.029i 0.895907 0.186927i
\(73\) −8856.56 −1.66195 −0.830977 0.556306i \(-0.812218\pi\)
−0.830977 + 0.556306i \(0.812218\pi\)
\(74\) 2919.91i 0.533220i
\(75\) −4100.00 3332.85i −0.728889 0.592506i
\(76\) 263.788 0.0456697
\(77\) 1329.86i 0.224297i
\(78\) 6124.53 7534.28i 1.00666 1.23838i
\(79\) −9349.35 −1.49805 −0.749027 0.662540i \(-0.769479\pi\)
−0.749027 + 0.662540i \(0.769479\pi\)
\(80\) 1771.31i 0.276766i
\(81\) −6013.59 + 2623.63i −0.916566 + 0.399882i
\(82\) 7634.84 1.13546
\(83\) 7555.94i 1.09681i 0.836212 + 0.548406i \(0.184765\pi\)
−0.836212 + 0.548406i \(0.815235\pi\)
\(84\) −357.737 290.801i −0.0506997 0.0412132i
\(85\) 2927.99 0.405258
\(86\) 8110.97i 1.09667i
\(87\) −7144.21 + 8788.66i −0.943878 + 1.16114i
\(88\) −3516.58 −0.454104
\(89\) 4863.80i 0.614038i 0.951703 + 0.307019i \(0.0993316\pi\)
−0.951703 + 0.307019i \(0.900668\pi\)
\(90\) −435.953 2089.44i −0.0538213 0.257956i
\(91\) 5584.20 0.674339
\(92\) 1223.67i 0.144573i
\(93\) −98.7102 80.2405i −0.0114129 0.00927743i
\(94\) 3178.75 0.359750
\(95\) 702.393i 0.0778274i
\(96\) 1667.87 2051.78i 0.180976 0.222633i
\(97\) −12596.8 −1.33880 −0.669400 0.742902i \(-0.733449\pi\)
−0.669400 + 0.742902i \(0.733449\pi\)
\(98\) 8175.06i 0.851214i
\(99\) 4760.54 993.265i 0.485720 0.101343i
\(100\) −1357.68 −0.135768
\(101\) 7786.36i 0.763293i −0.924308 0.381647i \(-0.875357\pi\)
0.924308 0.381647i \(-0.124643\pi\)
\(102\) −14210.4 11551.5i −1.36586 1.11029i
\(103\) −18936.3 −1.78493 −0.892464 0.451118i \(-0.851025\pi\)
−0.892464 + 0.451118i \(0.851025\pi\)
\(104\) 14766.5i 1.36525i
\(105\) 774.320 952.552i 0.0702331 0.0863993i
\(106\) 13166.3 1.17179
\(107\) 11612.8i 1.01431i 0.861856 + 0.507153i \(0.169302\pi\)
−0.861856 + 0.507153i \(0.830698\pi\)
\(108\) −773.800 + 1497.81i −0.0663408 + 0.128413i
\(109\) −20455.6 −1.72171 −0.860854 0.508852i \(-0.830070\pi\)
−0.860854 + 0.508852i \(0.830070\pi\)
\(110\) 1582.06i 0.130749i
\(111\) 4765.19 + 3873.57i 0.386754 + 0.314388i
\(112\) 6371.61 0.507941
\(113\) 16856.6i 1.32012i −0.751215 0.660058i \(-0.770532\pi\)
0.751215 0.660058i \(-0.229468\pi\)
\(114\) 2771.07 3408.92i 0.213225 0.262305i
\(115\) 3258.28 0.246373
\(116\) 2910.29i 0.216282i
\(117\) −4170.82 19990.0i −0.304684 1.46030i
\(118\) 1939.34 0.139280
\(119\) 10532.4i 0.743758i
\(120\) 2518.87 + 2047.56i 0.174921 + 0.142192i
\(121\) 11036.5 0.753805
\(122\) 6158.82i 0.413788i
\(123\) 10128.4 12459.8i 0.669470 0.823569i
\(124\) −32.6871 −0.00212585
\(125\) 7463.73i 0.477679i
\(126\) −7516.00 + 1568.18i −0.473419 + 0.0987766i
\(127\) −13357.8 −0.828186 −0.414093 0.910235i \(-0.635901\pi\)
−0.414093 + 0.910235i \(0.635901\pi\)
\(128\) 19015.9i 1.16064i
\(129\) −13236.8 10760.1i −0.795433 0.646599i
\(130\) 6643.24 0.393091
\(131\) 2111.19i 0.123022i −0.998106 0.0615112i \(-0.980408\pi\)
0.998106 0.0615112i \(-0.0195920\pi\)
\(132\) 788.207 969.636i 0.0452368 0.0556495i
\(133\) 2526.60 0.142834
\(134\) 13800.7i 0.768584i
\(135\) −3988.23 2060.41i −0.218833 0.113054i
\(136\) 27851.1 1.50579
\(137\) 8167.28i 0.435148i −0.976044 0.217574i \(-0.930186\pi\)
0.976044 0.217574i \(-0.0698143\pi\)
\(138\) −15813.4 12854.5i −0.830360 0.674991i
\(139\) 29247.4 1.51376 0.756880 0.653554i \(-0.226723\pi\)
0.756880 + 0.653554i \(0.226723\pi\)
\(140\) 315.430i 0.0160933i
\(141\) 4216.95 5187.61i 0.212110 0.260933i
\(142\) −23467.2 −1.16382
\(143\) 15135.8i 0.740174i
\(144\) −4758.94 22808.7i −0.229501 1.09996i
\(145\) −7749.28 −0.368575
\(146\) 37900.0i 1.77801i
\(147\) 13341.4 + 10845.1i 0.617400 + 0.501878i
\(148\) 1577.95 0.0720395
\(149\) 7551.99i 0.340164i −0.985430 0.170082i \(-0.945597\pi\)
0.985430 0.170082i \(-0.0544033\pi\)
\(150\) −14262.3 + 17545.2i −0.633881 + 0.779788i
\(151\) 855.883 0.0375371 0.0187685 0.999824i \(-0.494025\pi\)
0.0187685 + 0.999824i \(0.494025\pi\)
\(152\) 6681.16i 0.289178i
\(153\) −37703.1 + 7866.58i −1.61063 + 0.336049i
\(154\) 5690.88 0.239959
\(155\) 87.0364i 0.00362274i
\(156\) −4071.60 3309.76i −0.167308 0.136003i
\(157\) −283.730 −0.0115108 −0.00575540 0.999983i \(-0.501832\pi\)
−0.00575540 + 0.999983i \(0.501832\pi\)
\(158\) 40008.9i 1.60266i
\(159\) 17466.4 21486.9i 0.690892 0.849921i
\(160\) 1809.13 0.0706692
\(161\) 11720.4i 0.452160i
\(162\) 11227.4 + 25734.1i 0.427806 + 0.980571i
\(163\) −24701.2 −0.929699 −0.464850 0.885390i \(-0.653892\pi\)
−0.464850 + 0.885390i \(0.653892\pi\)
\(164\) 4125.95i 0.153404i
\(165\) 2581.87 + 2098.77i 0.0948344 + 0.0770899i
\(166\) 32334.3 1.17340
\(167\) 18044.7i 0.647019i 0.946225 + 0.323509i \(0.104863\pi\)
−0.946225 + 0.323509i \(0.895137\pi\)
\(168\) 7365.34 9060.69i 0.260960 0.321028i
\(169\) 34995.9 1.22530
\(170\) 12529.8i 0.433557i
\(171\) −1887.11 9044.57i −0.0645363 0.309311i
\(172\) −4383.26 −0.148163
\(173\) 34014.6i 1.13651i −0.822853 0.568254i \(-0.807619\pi\)
0.822853 0.568254i \(-0.192381\pi\)
\(174\) 37609.5 + 30572.4i 1.24222 + 1.00979i
\(175\) −13004.0 −0.424622
\(176\) 17270.1i 0.557531i
\(177\) 2572.73 3164.92i 0.0821199 0.101022i
\(178\) 20813.8 0.656917
\(179\) 43081.0i 1.34456i −0.740298 0.672279i \(-0.765316\pi\)
0.740298 0.672279i \(-0.234684\pi\)
\(180\) −1129.16 + 235.593i −0.0348506 + 0.00727140i
\(181\) −13197.5 −0.402840 −0.201420 0.979505i \(-0.564556\pi\)
−0.201420 + 0.979505i \(0.564556\pi\)
\(182\) 23896.6i 0.721428i
\(183\) −10051.0 8170.32i −0.300127 0.243970i
\(184\) 30992.8 0.915429
\(185\) 4201.64i 0.122765i
\(186\) −343.375 + 422.413i −0.00992528 + 0.0122099i
\(187\) 28547.6 0.816370
\(188\) 1717.83i 0.0486032i
\(189\) −7411.55 + 14346.2i −0.207485 + 0.401618i
\(190\) 3005.76 0.0832621
\(191\) 31696.9i 0.868860i 0.900706 + 0.434430i \(0.143050\pi\)
−0.900706 + 0.434430i \(0.856950\pi\)
\(192\) 23361.9 + 18990.6i 0.633732 + 0.515154i
\(193\) 9475.70 0.254388 0.127194 0.991878i \(-0.459403\pi\)
0.127194 + 0.991878i \(0.459403\pi\)
\(194\) 53905.7i 1.43229i
\(195\) 8812.96 10841.5i 0.231768 0.285116i
\(196\) 4417.89 0.115001
\(197\) 60627.6i 1.56221i 0.624402 + 0.781103i \(0.285343\pi\)
−0.624402 + 0.781103i \(0.714657\pi\)
\(198\) −4250.50 20371.9i −0.108420 0.519638i
\(199\) 48045.0 1.21323 0.606614 0.794996i \(-0.292527\pi\)
0.606614 + 0.794996i \(0.292527\pi\)
\(200\) 34387.0i 0.859676i
\(201\) −22522.2 18308.1i −0.557467 0.453159i
\(202\) −33320.3 −0.816594
\(203\) 27875.2i 0.676434i
\(204\) −6242.54 + 7679.44i −0.150003 + 0.184531i
\(205\) 10986.2 0.261421
\(206\) 81034.5i 1.90957i
\(207\) −41956.2 + 8753.97i −0.979164 + 0.204298i
\(208\) 72518.8 1.67619
\(209\) 6848.27i 0.156779i
\(210\) −4076.28 3313.56i −0.0924326 0.0751375i
\(211\) −44652.8 −1.00296 −0.501480 0.865169i \(-0.667211\pi\)
−0.501480 + 0.865169i \(0.667211\pi\)
\(212\) 7115.19i 0.158312i
\(213\) −31131.8 + 38297.7i −0.686191 + 0.844138i
\(214\) 49694.8 1.08514
\(215\) 11671.4i 0.252490i
\(216\) −37936.1 19598.6i −0.813102 0.420067i
\(217\) −313.081 −0.00664871
\(218\) 87536.2i 1.84194i
\(219\) 61851.5 + 50278.4i 1.28962 + 1.04832i
\(220\) 854.963 0.0176645
\(221\) 119875.i 2.45438i
\(222\) 16576.3 20391.8i 0.336342 0.413761i
\(223\) −21774.9 −0.437872 −0.218936 0.975739i \(-0.570259\pi\)
−0.218936 + 0.975739i \(0.570259\pi\)
\(224\) 6507.67i 0.129697i
\(225\) 9712.68 + 46551.2i 0.191855 + 0.919529i
\(226\) −72134.6 −1.41230
\(227\) 37951.3i 0.736504i 0.929726 + 0.368252i \(0.120044\pi\)
−0.929726 + 0.368252i \(0.879956\pi\)
\(228\) −1842.21 1497.52i −0.0354381 0.0288073i
\(229\) −67237.0 −1.28215 −0.641073 0.767480i \(-0.721510\pi\)
−0.641073 + 0.767480i \(0.721510\pi\)
\(230\) 13943.2i 0.263577i
\(231\) 7549.55 9287.30i 0.141481 0.174047i
\(232\) −73711.2 −1.36949
\(233\) 20931.8i 0.385562i 0.981242 + 0.192781i \(0.0617507\pi\)
−0.981242 + 0.192781i \(0.938249\pi\)
\(234\) −85543.7 + 17848.3i −1.56227 + 0.325960i
\(235\) 4574.10 0.0828267
\(236\) 1048.04i 0.0188171i
\(237\) 65293.0 + 53076.0i 1.16244 + 0.944934i
\(238\) −45071.3 −0.795694
\(239\) 98619.7i 1.72651i −0.504772 0.863253i \(-0.668423\pi\)
0.504772 0.863253i \(-0.331577\pi\)
\(240\) 10055.6 12370.3i 0.174577 0.214761i
\(241\) −12396.0 −0.213426 −0.106713 0.994290i \(-0.534033\pi\)
−0.106713 + 0.994290i \(0.534033\pi\)
\(242\) 47228.6i 0.806444i
\(243\) 56891.4 + 15816.4i 0.963460 + 0.267852i
\(244\) −3328.29 −0.0559039
\(245\) 11763.6i 0.195978i
\(246\) −53319.4 43342.8i −0.881079 0.716220i
\(247\) 28756.6 0.471350
\(248\) 827.891i 0.0134608i
\(249\) 42894.8 52768.3i 0.691841 0.851089i
\(250\) −31939.7 −0.511035
\(251\) 14187.1i 0.225189i 0.993641 + 0.112594i \(0.0359160\pi\)
−0.993641 + 0.112594i \(0.964084\pi\)
\(252\) 847.460 + 4061.73i 0.0133450 + 0.0639601i
\(253\) 31767.9 0.496304
\(254\) 57162.3i 0.886018i
\(255\) −20448.2 16622.1i −0.314466 0.255626i
\(256\) 27852.1 0.424989
\(257\) 80227.0i 1.21466i 0.794450 + 0.607330i \(0.207759\pi\)
−0.794450 + 0.607330i \(0.792241\pi\)
\(258\) −46045.8 + 56644.6i −0.691752 + 0.850979i
\(259\) 15113.8 0.225307
\(260\) 3590.08i 0.0531077i
\(261\) 99786.0 20819.9i 1.46483 0.305631i
\(262\) −9034.45 −0.131613
\(263\) 9763.42i 0.141153i 0.997506 + 0.0705766i \(0.0224839\pi\)
−0.997506 + 0.0705766i \(0.977516\pi\)
\(264\) 24558.7 + 19963.5i 0.352369 + 0.286437i
\(265\) 18945.7 0.269786
\(266\) 10812.1i 0.152808i
\(267\) 27611.6 33967.3i 0.387320 0.476473i
\(268\) −7458.05 −0.103838
\(269\) 80885.6i 1.11781i −0.829233 0.558903i \(-0.811222\pi\)
0.829233 0.558903i \(-0.188778\pi\)
\(270\) −8817.15 + 17066.9i −0.120949 + 0.234114i
\(271\) 6394.26 0.0870667 0.0435333 0.999052i \(-0.486139\pi\)
0.0435333 + 0.999052i \(0.486139\pi\)
\(272\) 136778.i 1.84875i
\(273\) −38998.4 31701.3i −0.523264 0.425356i
\(274\) −34950.4 −0.465534
\(275\) 35247.1i 0.466077i
\(276\) −6946.72 + 8545.72i −0.0911931 + 0.112184i
\(277\) −106955. −1.39393 −0.696966 0.717104i \(-0.745467\pi\)
−0.696966 + 0.717104i \(0.745467\pi\)
\(278\) 125159.i 1.61947i
\(279\) 233.839 + 1120.75i 0.00300406 + 0.0143979i
\(280\) 7989.13 0.101902
\(281\) 63996.3i 0.810480i −0.914210 0.405240i \(-0.867188\pi\)
0.914210 0.405240i \(-0.132812\pi\)
\(282\) −22199.5 18045.7i −0.279154 0.226921i
\(283\) −73114.9 −0.912921 −0.456461 0.889744i \(-0.650883\pi\)
−0.456461 + 0.889744i \(0.650883\pi\)
\(284\) 12682.0i 0.157235i
\(285\) 3987.46 4905.30i 0.0490916 0.0603915i
\(286\) 64771.0 0.791861
\(287\) 39518.9i 0.479779i
\(288\) −23295.8 + 4860.56i −0.280862 + 0.0586005i
\(289\) −142574. −1.70704
\(290\) 33161.7i 0.394312i
\(291\) 87972.1 + 71511.5i 1.03886 + 0.844482i
\(292\) 20481.6 0.240214
\(293\) 135587.i 1.57937i −0.613511 0.789686i \(-0.710244\pi\)
0.613511 0.789686i \(-0.289756\pi\)
\(294\) 46409.6 57092.1i 0.536924 0.660513i
\(295\) 2790.63 0.0320670
\(296\) 39966.1i 0.456150i
\(297\) −38884.9 20088.8i −0.440827 0.227741i
\(298\) −32317.4 −0.363918
\(299\) 133397.i 1.49212i
\(300\) 9481.62 + 7707.51i 0.105351 + 0.0856390i
\(301\) −41983.4 −0.463388
\(302\) 3662.60i 0.0401583i
\(303\) −44202.9 + 54377.5i −0.481466 + 0.592290i
\(304\) 32811.5 0.355041
\(305\) 8862.30i 0.0952679i
\(306\) 33663.6 + 161344.i 0.359516 + 1.72310i
\(307\) 76474.3 0.811407 0.405703 0.914005i \(-0.367027\pi\)
0.405703 + 0.914005i \(0.367027\pi\)
\(308\) 3075.41i 0.0324192i
\(309\) 132245. + 107501.i 1.38504 + 1.12589i
\(310\) −372.457 −0.00387572
\(311\) 2253.38i 0.0232977i −0.999932 0.0116489i \(-0.996292\pi\)
0.999932 0.0116489i \(-0.00370803\pi\)
\(312\) 83829.0 103125.i 0.861162 1.05938i
\(313\) 108428. 1.10676 0.553380 0.832929i \(-0.313338\pi\)
0.553380 + 0.832929i \(0.313338\pi\)
\(314\) 1214.17i 0.0123146i
\(315\) −10815.2 + 2256.55i −0.108997 + 0.0227417i
\(316\) 21621.2 0.216524
\(317\) 25903.9i 0.257778i −0.991659 0.128889i \(-0.958859\pi\)
0.991659 0.128889i \(-0.0411412\pi\)
\(318\) −91949.2 74744.5i −0.909271 0.739137i
\(319\) −75554.8 −0.742473
\(320\) 20599.0i 0.201162i
\(321\) 65925.5 81100.2i 0.639798 0.787067i
\(322\) −50155.6 −0.483735
\(323\) 54237.7i 0.519872i
\(324\) 13907.0 6067.38i 0.132478 0.0577978i
\(325\) −148006. −1.40124
\(326\) 105704.i 0.994621i
\(327\) 142856. + 116126.i 1.33599 + 1.08601i
\(328\) 104501. 0.971345
\(329\) 16453.6i 0.152009i
\(330\) 8981.32 11048.6i 0.0824731 0.101457i
\(331\) 197638. 1.80391 0.901956 0.431828i \(-0.142131\pi\)
0.901956 + 0.431828i \(0.142131\pi\)
\(332\) 17473.8i 0.158530i
\(333\) −11288.5 54103.7i −0.101800 0.487909i
\(334\) 77219.1 0.692200
\(335\) 19858.7i 0.176954i
\(336\) −44497.4 36171.4i −0.394145 0.320396i
\(337\) −104229. −0.917756 −0.458878 0.888499i \(-0.651749\pi\)
−0.458878 + 0.888499i \(0.651749\pi\)
\(338\) 149759.i 1.31087i
\(339\) −95694.2 + 117721.i −0.832695 + 1.02436i
\(340\) −6771.24 −0.0585748
\(341\) 848.597i 0.00729781i
\(342\) −38704.6 + 8075.54i −0.330911 + 0.0690429i
\(343\) 95498.0 0.811720
\(344\) 111018.i 0.938161i
\(345\) −22754.8 18497.2i −0.191177 0.155406i
\(346\) −145559. −1.21587
\(347\) 14398.4i 0.119579i 0.998211 + 0.0597895i \(0.0190429\pi\)
−0.998211 + 0.0597895i \(0.980957\pi\)
\(348\) 16521.6 20324.6i 0.136425 0.167828i
\(349\) −97324.6 −0.799046 −0.399523 0.916723i \(-0.630824\pi\)
−0.399523 + 0.916723i \(0.630824\pi\)
\(350\) 55648.5i 0.454273i
\(351\) −84355.0 + 163282.i −0.684694 + 1.32533i
\(352\) 17638.9 0.142359
\(353\) 72467.5i 0.581559i 0.956790 + 0.290780i \(0.0939146\pi\)
−0.956790 + 0.290780i \(0.906085\pi\)
\(354\) −13543.7 11009.6i −0.108077 0.0878543i
\(355\) −33768.5 −0.267950
\(356\) 11248.0i 0.0887512i
\(357\) −59791.8 + 73554.7i −0.469143 + 0.577131i
\(358\) −184357. −1.43845
\(359\) 160864.i 1.24816i 0.781361 + 0.624080i \(0.214526\pi\)
−0.781361 + 0.624080i \(0.785474\pi\)
\(360\) −5967.06 28599.1i −0.0460421 0.220672i
\(361\) −117310. −0.900162
\(362\) 56476.2i 0.430971i
\(363\) −77075.3 62653.7i −0.584927 0.475481i
\(364\) −12914.0 −0.0974669
\(365\) 54536.7i 0.409358i
\(366\) −34963.4 + 43011.3i −0.261007 + 0.321085i
\(367\) 243423. 1.80729 0.903647 0.428277i \(-0.140879\pi\)
0.903647 + 0.428277i \(0.140879\pi\)
\(368\) 152207.i 1.12393i
\(369\) −141468. + 29516.5i −1.03897 + 0.216777i
\(370\) 17980.2 0.131338
\(371\) 68150.2i 0.495130i
\(372\) 228.276 + 185.563i 0.00164959 + 0.00134093i
\(373\) −167437. −1.20346 −0.601732 0.798698i \(-0.705523\pi\)
−0.601732 + 0.798698i \(0.705523\pi\)
\(374\) 122165.i 0.873377i
\(375\) −42371.4 + 52124.4i −0.301308 + 0.370662i
\(376\) 43508.9 0.307753
\(377\) 317263.i 2.23222i
\(378\) 61391.9 + 31716.4i 0.429663 + 0.221973i
\(379\) 184407. 1.28380 0.641902 0.766786i \(-0.278145\pi\)
0.641902 + 0.766786i \(0.278145\pi\)
\(380\) 1624.35i 0.0112489i
\(381\) 93286.9 + 75831.9i 0.642644 + 0.522398i
\(382\) 135641. 0.929532
\(383\) 83917.5i 0.572077i −0.958218 0.286039i \(-0.907661\pi\)
0.958218 0.286039i \(-0.0923386\pi\)
\(384\) 107953. 132802.i 0.732103 0.900618i
\(385\) 8188.95 0.0552468
\(386\) 40549.5i 0.272152i
\(387\) 31357.3 + 150290.i 0.209371 + 1.00348i
\(388\) 29131.2 0.193506
\(389\) 110053.i 0.727280i 0.931540 + 0.363640i \(0.118466\pi\)
−0.931540 + 0.363640i \(0.881534\pi\)
\(390\) −46394.4 37713.5i −0.305026 0.247952i
\(391\) −251600. −1.64572
\(392\) 111895.i 0.728182i
\(393\) −11985.1 + 14743.9i −0.0775994 + 0.0954612i
\(394\) 259445. 1.67130
\(395\) 57571.2i 0.368987i
\(396\) −11009.2 + 2297.02i −0.0702045 + 0.0146478i
\(397\) −136778. −0.867831 −0.433916 0.900953i \(-0.642868\pi\)
−0.433916 + 0.900953i \(0.642868\pi\)
\(398\) 205600.i 1.29795i
\(399\) −17645.0 14343.4i −0.110835 0.0900962i
\(400\) −168876. −1.05548
\(401\) 294178.i 1.82945i −0.404075 0.914726i \(-0.632406\pi\)
0.404075 0.914726i \(-0.367594\pi\)
\(402\) −78346.2 + 96379.9i −0.484803 + 0.596395i
\(403\) −3563.35 −0.0219406
\(404\) 18006.7i 0.110324i
\(405\) 16155.7 + 37030.4i 0.0984955 + 0.225760i
\(406\) 119287. 0.723669
\(407\) 40965.6i 0.247304i
\(408\) −194503. 158110.i −1.16844 0.949813i
\(409\) −25699.3 −0.153629 −0.0768146 0.997045i \(-0.524475\pi\)
−0.0768146 + 0.997045i \(0.524475\pi\)
\(410\) 47013.6i 0.279676i
\(411\) −46365.4 + 57037.8i −0.274480 + 0.337660i
\(412\) 43791.9 0.257988
\(413\) 10038.2i 0.0588515i
\(414\) 37461.0 + 179544.i 0.218564 + 1.04754i
\(415\) 46527.8 0.270157
\(416\) 74067.4i 0.427997i
\(417\) −204255. 166036.i −1.17463 0.954841i
\(418\) 29305.9 0.167727
\(419\) 285438.i 1.62586i 0.582362 + 0.812930i \(0.302129\pi\)
−0.582362 + 0.812930i \(0.697871\pi\)
\(420\) −1790.68 + 2202.86i −0.0101513 + 0.0124879i
\(421\) 232861. 1.31381 0.656906 0.753973i \(-0.271865\pi\)
0.656906 + 0.753973i \(0.271865\pi\)
\(422\) 191084.i 1.07300i
\(423\) −58899.8 + 12289.2i −0.329180 + 0.0686818i
\(424\) 180212. 1.00243
\(425\) 279154.i 1.54549i
\(426\) 163888. + 133223.i 0.903084 + 0.734108i
\(427\) −31878.8 −0.174842
\(428\) 26855.6i 0.146605i
\(429\) 85925.6 105704.i 0.466883 0.574350i
\(430\) −49945.5 −0.270122
\(431\) 173860.i 0.935934i 0.883746 + 0.467967i \(0.155013\pi\)
−0.883746 + 0.467967i \(0.844987\pi\)
\(432\) −96249.6 + 186306.i −0.515741 + 0.998294i
\(433\) 41757.2 0.222718 0.111359 0.993780i \(-0.464480\pi\)
0.111359 + 0.993780i \(0.464480\pi\)
\(434\) 1339.77i 0.00711299i
\(435\) 54118.6 + 43992.4i 0.286001 + 0.232487i
\(436\) 47305.5 0.248850
\(437\) 60356.0i 0.316051i
\(438\) 215157. 264682.i 1.12152 1.37968i
\(439\) 130301. 0.676112 0.338056 0.941126i \(-0.390231\pi\)
0.338056 + 0.941126i \(0.390231\pi\)
\(440\) 21654.3i 0.111851i
\(441\) −31605.1 151477.i −0.162510 0.778881i
\(442\) −512982. −2.62577
\(443\) 141019.i 0.718571i −0.933228 0.359286i \(-0.883020\pi\)
0.933228 0.359286i \(-0.116980\pi\)
\(444\) −11019.9 8957.99i −0.0559002 0.0454407i
\(445\) 29950.2 0.151244
\(446\) 93181.9i 0.468449i
\(447\) −42872.4 + 52740.8i −0.214567 + 0.263956i
\(448\) 74097.3 0.369187
\(449\) 147657.i 0.732422i −0.930532 0.366211i \(-0.880655\pi\)
0.930532 0.366211i \(-0.119345\pi\)
\(450\) 199207. 41563.7i 0.983740 0.205253i
\(451\) 107115. 0.526619
\(452\) 38982.3i 0.190805i
\(453\) −5977.23 4858.82i −0.0291275 0.0236774i
\(454\) 162406. 0.787934
\(455\) 34386.3i 0.166097i
\(456\) 37928.8 46659.2i 0.182406 0.224392i
\(457\) 321911. 1.54136 0.770679 0.637224i \(-0.219917\pi\)
0.770679 + 0.637224i \(0.219917\pi\)
\(458\) 287729.i 1.37168i
\(459\) 307966. + 159102.i 1.46176 + 0.755179i
\(460\) −7535.07 −0.0356100
\(461\) 11046.7i 0.0519794i 0.999662 + 0.0259897i \(0.00827372\pi\)
−0.999662 + 0.0259897i \(0.991726\pi\)
\(462\) −39743.4 32306.9i −0.186200 0.151360i
\(463\) 26678.1 0.124450 0.0622248 0.998062i \(-0.480180\pi\)
0.0622248 + 0.998062i \(0.480180\pi\)
\(464\) 361999.i 1.68140i
\(465\) −494.103 + 607.836i −0.00228513 + 0.00281112i
\(466\) 89573.8 0.412486
\(467\) 115761.i 0.530796i 0.964139 + 0.265398i \(0.0855034\pi\)
−0.964139 + 0.265398i \(0.914497\pi\)
\(468\) 9645.41 + 46228.7i 0.0440381 + 0.211067i
\(469\) −71434.2 −0.324758
\(470\) 19574.1i 0.0886105i
\(471\) 1981.48 + 1610.72i 0.00893199 + 0.00726072i
\(472\) 26544.5 0.119149
\(473\) 113795.i 0.508628i
\(474\) 227129. 279410.i 1.01092 1.24361i
\(475\) −66966.0 −0.296802
\(476\) 24357.0i 0.107500i
\(477\) −243961. + 50901.2i −1.07222 + 0.223713i
\(478\) −422025. −1.84707
\(479\) 65690.2i 0.286306i −0.989701 0.143153i \(-0.954276\pi\)
0.989701 0.143153i \(-0.0457240\pi\)
\(480\) −12634.4 10270.4i −0.0548369 0.0445763i
\(481\) 172019. 0.743509
\(482\) 53046.4i 0.228330i
\(483\) −66536.6 + 81852.0i −0.285211 + 0.350861i
\(484\) −25522.8 −0.108953
\(485\) 77568.1i 0.329761i
\(486\) 67683.3 243456.i 0.286556 1.03074i
\(487\) 228454. 0.963255 0.481628 0.876376i \(-0.340046\pi\)
0.481628 + 0.876376i \(0.340046\pi\)
\(488\) 84298.3i 0.353980i
\(489\) 172506. + 140228.i 0.721415 + 0.586431i
\(490\) 50340.2 0.209663
\(491\) 257752.i 1.06915i −0.845121 0.534575i \(-0.820472\pi\)
0.845121 0.534575i \(-0.179528\pi\)
\(492\) −23422.9 + 28814.4i −0.0967632 + 0.119036i
\(493\) 598388. 2.46201
\(494\) 123059.i 0.504264i
\(495\) −6116.30 29314.4i −0.0249620 0.119638i
\(496\) −4065.80 −0.0165266
\(497\) 121469.i 0.491761i
\(498\) −225813. 183561.i −0.910520 0.740152i
\(499\) 89231.0 0.358356 0.179178 0.983817i \(-0.442656\pi\)
0.179178 + 0.983817i \(0.442656\pi\)
\(500\) 17260.6i 0.0690422i
\(501\) 102439. 126019.i 0.408123 0.502065i
\(502\) 60711.2 0.240914
\(503\) 83970.8i 0.331889i −0.986135 0.165944i \(-0.946933\pi\)
0.986135 0.165944i \(-0.0530672\pi\)
\(504\) −102875. + 21464.3i −0.404992 + 0.0844997i
\(505\) −47946.6 −0.188008
\(506\) 135945.i 0.530961i
\(507\) −244401. 198671.i −0.950794 0.772890i
\(508\) 30891.1 0.119703
\(509\) 181429.i 0.700279i −0.936697 0.350140i \(-0.886134\pi\)
0.936697 0.350140i \(-0.113866\pi\)
\(510\) −71131.3 + 87504.3i −0.273477 + 0.336426i
\(511\) 196175. 0.751282
\(512\) 185067.i 0.705976i
\(513\) −38166.8 + 73877.6i −0.145028 + 0.280723i
\(514\) 343317. 1.29948
\(515\) 116606.i 0.439648i
\(516\) 30611.3 + 24883.6i 0.114970 + 0.0934575i
\(517\) 44597.1 0.166850
\(518\) 64677.0i 0.241041i
\(519\) −193100. + 237547.i −0.716881 + 0.881892i
\(520\) 90928.8 0.336275
\(521\) 196948.i 0.725565i −0.931874 0.362782i \(-0.881827\pi\)
0.931874 0.362782i \(-0.118173\pi\)
\(522\) −89094.9 427016.i −0.326973 1.56712i
\(523\) −254761. −0.931386 −0.465693 0.884946i \(-0.654195\pi\)
−0.465693 + 0.884946i \(0.654195\pi\)
\(524\) 4882.31i 0.0177813i
\(525\) 90816.3 + 73823.6i 0.329492 + 0.267841i
\(526\) 41780.8 0.151010
\(527\) 6720.82i 0.0241992i
\(528\) 98041.7 120609.i 0.351676 0.432625i
\(529\) −140.123 −0.000500723
\(530\) 81074.9i 0.288625i
\(531\) −35934.4 + 7497.53i −0.127444 + 0.0265907i
\(532\) −5842.98 −0.0206448
\(533\) 449786.i 1.58326i
\(534\) −145357. 118159.i −0.509745 0.414366i
\(535\) 71508.9 0.249835
\(536\) 188896.i 0.657496i
\(537\) −244569. + 300864.i −0.848113 + 1.04333i
\(538\) −346136. −1.19586
\(539\) 114694.i 0.394787i
\(540\) 9223.15 + 4764.88i 0.0316295 + 0.0163405i
\(541\) 262863. 0.898123 0.449061 0.893501i \(-0.351758\pi\)
0.449061 + 0.893501i \(0.351758\pi\)
\(542\) 27363.1i 0.0931466i
\(543\) 92167.0 + 74921.6i 0.312591 + 0.254102i
\(544\) −139698. −0.472056
\(545\) 125961.i 0.424076i
\(546\) −135660. + 166887.i −0.455059 + 0.559804i
\(547\) −578584. −1.93371 −0.966856 0.255324i \(-0.917818\pi\)
−0.966856 + 0.255324i \(0.917818\pi\)
\(548\) 18887.6i 0.0628949i
\(549\) 23810.2 + 114118.i 0.0789984 + 0.378625i
\(550\) −150834. −0.498623
\(551\) 143547.i 0.472814i
\(552\) −216444. 175945.i −0.710342 0.577430i
\(553\) 207091. 0.677191
\(554\) 457695.i 1.49127i
\(555\) 23852.6 29343.0i 0.0774372 0.0952617i
\(556\) −67637.2 −0.218794
\(557\) 306771.i 0.988789i −0.869238 0.494395i \(-0.835390\pi\)
0.869238 0.494395i \(-0.164610\pi\)
\(558\) 4796.05 1000.67i 0.0154034 0.00321384i
\(559\) −477836. −1.52917
\(560\) 39234.9i 0.125111i
\(561\) −199368. 162064.i −0.633475 0.514945i
\(562\) −273861. −0.867076
\(563\) 140141.i 0.442127i 0.975259 + 0.221063i \(0.0709528\pi\)
−0.975259 + 0.221063i \(0.929047\pi\)
\(564\) −9752.09 + 11996.8i −0.0306577 + 0.0377145i
\(565\) −103799. −0.325159
\(566\) 312882.i 0.976671i
\(567\) 133203. 58114.2i 0.414331 0.180766i
\(568\) −321206. −0.995604
\(569\) 138389.i 0.427440i 0.976895 + 0.213720i \(0.0685581\pi\)
−0.976895 + 0.213720i \(0.931442\pi\)
\(570\) −20991.3 17063.6i −0.0646086 0.0525196i
\(571\) −456870. −1.40127 −0.700633 0.713522i \(-0.747099\pi\)
−0.700633 + 0.713522i \(0.747099\pi\)
\(572\) 35003.0i 0.106982i
\(573\) 179942. 221361.i 0.548055 0.674206i
\(574\) −169114. −0.513282
\(575\) 310644.i 0.939566i
\(576\) −55343.1 265250.i −0.166809 0.799484i
\(577\) −78115.9 −0.234632 −0.117316 0.993095i \(-0.537429\pi\)
−0.117316 + 0.993095i \(0.537429\pi\)
\(578\) 610120.i 1.82625i
\(579\) −66175.4 53793.2i −0.197396 0.160461i
\(580\) 17920.9 0.0532726
\(581\) 167366.i 0.495810i
\(582\) 306021. 376461.i 0.903452 1.11141i
\(583\) 184719. 0.543469
\(584\) 518753.i 1.52102i
\(585\) −123094. + 25683.0i −0.359688 + 0.0750471i
\(586\) −580222. −1.68966
\(587\) 72130.4i 0.209335i −0.994507 0.104668i \(-0.966622\pi\)
0.994507 0.104668i \(-0.0333778\pi\)
\(588\) −30853.2 25080.2i −0.0892371 0.0725399i
\(589\) −1612.25 −0.00464732
\(590\) 11942.0i 0.0343062i
\(591\) 344181. 423405.i 0.985400 1.21222i
\(592\) 196275. 0.560043
\(593\) 553039.i 1.57270i −0.617781 0.786350i \(-0.711968\pi\)
0.617781 0.786350i \(-0.288032\pi\)
\(594\) −85966.5 + 166401.i −0.243644 + 0.471610i
\(595\) −64855.9 −0.183196
\(596\) 17464.7i 0.0491663i
\(597\) −335532. 272750.i −0.941424 0.765273i
\(598\) −570848. −1.59631
\(599\) 119830.i 0.333973i 0.985959 + 0.166987i \(0.0534037\pi\)
−0.985959 + 0.166987i \(0.946596\pi\)
\(600\) −195214. + 240149.i −0.542262 + 0.667079i
\(601\) −502379. −1.39086 −0.695428 0.718595i \(-0.744785\pi\)
−0.695428 + 0.718595i \(0.744785\pi\)
\(602\) 179661.i 0.495746i
\(603\) 53354.0 + 255716.i 0.146734 + 0.703272i
\(604\) −1979.31 −0.00542550
\(605\) 67960.1i 0.185671i
\(606\) 232699. + 189158.i 0.633650 + 0.515087i
\(607\) −58904.7 −0.159872 −0.0799361 0.996800i \(-0.525472\pi\)
−0.0799361 + 0.996800i \(0.525472\pi\)
\(608\) 33512.1i 0.0906557i
\(609\) 158246. 194672.i 0.426677 0.524890i
\(610\) −37924.6 −0.101921
\(611\) 187268.i 0.501627i
\(612\) 87191.9 18192.2i 0.232795 0.0485716i
\(613\) 105673. 0.281219 0.140609 0.990065i \(-0.455094\pi\)
0.140609 + 0.990065i \(0.455094\pi\)
\(614\) 327258.i 0.868067i
\(615\) −76724.5 62368.5i −0.202854 0.164898i
\(616\) 77893.4 0.205276
\(617\) 98537.6i 0.258840i −0.991590 0.129420i \(-0.958688\pi\)
0.991590 0.129420i \(-0.0413116\pi\)
\(618\) 460031. 565920.i 1.20451 1.48176i
\(619\) 544530. 1.42115 0.710576 0.703620i \(-0.248434\pi\)
0.710576 + 0.703620i \(0.248434\pi\)
\(620\) 201.280i 0.000523620i
\(621\) 342705. + 177049.i 0.888664 + 0.459104i
\(622\) −9642.94 −0.0249246
\(623\) 107735.i 0.277574i
\(624\) −506449. 411687.i −1.30067 1.05730i
\(625\) 320966. 0.821673
\(626\) 463999.i 1.18405i
\(627\) 38877.4 47826.2i 0.0988922 0.121655i
\(628\) 656.151 0.00166374
\(629\) 324445.i 0.820048i
\(630\) 9656.48 + 46281.8i 0.0243298 + 0.116608i
\(631\) −174511. −0.438293 −0.219146 0.975692i \(-0.570327\pi\)
−0.219146 + 0.975692i \(0.570327\pi\)
\(632\) 547618.i 1.37102i
\(633\) 311842. + 253493.i 0.778263 + 0.632642i
\(634\) −110851. −0.275779
\(635\) 82254.4i 0.203991i
\(636\) −40392.7 + 49690.3i −0.0998594 + 0.122845i
\(637\) 481612. 1.18691
\(638\) 323323.i 0.794320i
\(639\) 434830. 90725.2i 1.06492 0.222191i
\(640\) 117096. 0.285879
\(641\) 336179.i 0.818192i 0.912491 + 0.409096i \(0.134156\pi\)
−0.912491 + 0.409096i \(0.865844\pi\)
\(642\) −347054. 282116.i −0.842028 0.684476i
\(643\) 148628. 0.359484 0.179742 0.983714i \(-0.442474\pi\)
0.179742 + 0.983714i \(0.442474\pi\)
\(644\) 27104.6i 0.0653539i
\(645\) −66258.0 + 81509.3i −0.159265 + 0.195924i
\(646\) −232101. −0.556175
\(647\) 222352.i 0.531168i −0.964088 0.265584i \(-0.914435\pi\)
0.964088 0.265584i \(-0.0855648\pi\)
\(648\) 153673. + 352233.i 0.365973 + 0.838842i
\(649\) 27208.4 0.0645971
\(650\) 633366.i 1.49909i
\(651\) 2186.46 + 1777.35i 0.00515917 + 0.00419383i
\(652\) 57123.7 0.134376
\(653\) 712522.i 1.67098i 0.549504 + 0.835491i \(0.314817\pi\)
−0.549504 + 0.835491i \(0.685183\pi\)
\(654\) 496940. 611326.i 1.16185 1.42928i
\(655\) −13000.2 −0.0303018
\(656\) 513209.i 1.19258i
\(657\) −146523. 702258.i −0.339449 1.62692i
\(658\) −70410.4 −0.162624
\(659\) 294531.i 0.678205i 0.940749 + 0.339102i \(0.110123\pi\)
−0.940749 + 0.339102i \(0.889877\pi\)
\(660\) −5970.80 4853.60i −0.0137071 0.0111423i
\(661\) −217428. −0.497638 −0.248819 0.968550i \(-0.580042\pi\)
−0.248819 + 0.968550i \(0.580042\pi\)
\(662\) 845758.i 1.92988i
\(663\) −680524. + 837167.i −1.54816 + 1.90452i
\(664\) 442572. 1.00380
\(665\) 15558.2i 0.0351817i
\(666\) −231527. + 48307.0i −0.521980 + 0.108909i
\(667\) 665889. 1.49675
\(668\) 41730.0i 0.0935181i
\(669\) 152069. + 123616.i 0.339774 + 0.276198i
\(670\) −84981.6 −0.189311
\(671\) 86406.6i 0.191912i
\(672\) −36943.9 + 45447.6i −0.0818095 + 0.100640i
\(673\) −793047. −1.75093 −0.875465 0.483282i \(-0.839445\pi\)
−0.875465 + 0.483282i \(0.839445\pi\)
\(674\) 446028.i 0.981844i
\(675\) 196439. 380238.i 0.431142 0.834541i
\(676\) −80931.2 −0.177102
\(677\) 866103.i 1.88970i 0.327509 + 0.944848i \(0.393791\pi\)
−0.327509 + 0.944848i \(0.606209\pi\)
\(678\) 503766. + 409506.i 1.09590 + 0.890842i
\(679\) 279022. 0.605201
\(680\) 171501.i 0.370892i
\(681\) 215449. 265040.i 0.464568 0.571502i
\(682\) −3631.42 −0.00780742
\(683\) 837102.i 1.79447i −0.441551 0.897236i \(-0.645571\pi\)
0.441551 0.897236i \(-0.354429\pi\)
\(684\) 4364.11 + 20916.4i 0.00932788 + 0.0447069i
\(685\) −50292.3 −0.107182
\(686\) 408667.i 0.868403i
\(687\) 469563. + 381702.i 0.994901 + 0.808745i
\(688\) −545215. −1.15184
\(689\) 775656.i 1.63392i
\(690\) −79155.3 + 97375.2i −0.166258 + 0.204527i
\(691\) −354204. −0.741817 −0.370909 0.928669i \(-0.620954\pi\)
−0.370909 + 0.928669i \(0.620954\pi\)
\(692\) 78661.8i 0.164268i
\(693\) −105448. + 22001.1i −0.219568 + 0.0458119i
\(694\) 61615.3 0.127929
\(695\) 180099.i 0.372856i
\(696\) 514777. + 418457.i 1.06267 + 0.863837i
\(697\) −848341. −1.74624
\(698\) 416483.i 0.854843i
\(699\) 118829. 146181.i 0.243203 0.299183i
\(700\) 30073.0 0.0613735
\(701\) 95502.1i 0.194347i 0.995267 + 0.0971733i \(0.0309801\pi\)
−0.995267 + 0.0971733i \(0.969020\pi\)
\(702\) 698736. + 360982.i 1.41788 + 0.732507i
\(703\) 77830.7 0.157485
\(704\) 200839.i 0.405231i
\(705\) −31944.1 25967.0i −0.0642707 0.0522450i
\(706\) 310112. 0.622170
\(707\) 172470.i 0.345045i
\(708\) −5949.68 + 7319.18i −0.0118694 + 0.0146014i
\(709\) 512215. 1.01897 0.509483 0.860481i \(-0.329837\pi\)
0.509483 + 0.860481i \(0.329837\pi\)
\(710\) 144506.i 0.286661i
\(711\) −154676. 741333.i −0.305973 1.46647i
\(712\) 284886. 0.561968
\(713\) 7478.96i 0.0147117i
\(714\) 314764. + 255869.i 0.617432 + 0.501904i
\(715\) 93203.0 0.182313
\(716\) 99628.7i 0.194338i
\(717\) −559861. + 688730.i −1.08904 + 1.33971i
\(718\) 688389. 1.33532
\(719\) 684555.i 1.32419i 0.749420 + 0.662095i \(0.230333\pi\)
−0.749420 + 0.662095i \(0.769667\pi\)
\(720\) −140451. + 29304.5i −0.270932 + 0.0565287i
\(721\) 419445. 0.806872
\(722\) 502007.i 0.963020i
\(723\) 86569.8 + 70371.7i 0.165611 + 0.134624i
\(724\) 30520.3 0.0582253
\(725\) 738816.i 1.40559i
\(726\) −268115. + 329830.i −0.508684 + 0.625773i
\(727\) 327581. 0.619798 0.309899 0.950769i \(-0.399705\pi\)
0.309899 + 0.950769i \(0.399705\pi\)
\(728\) 327082.i 0.617155i
\(729\) −307523. 433427.i −0.578659 0.815570i
\(730\) 233380. 0.437943
\(731\) 901246.i 1.68659i
\(732\) 23243.8 + 18894.6i 0.0433795 + 0.0352627i
\(733\) 47153.8 0.0877624 0.0438812 0.999037i \(-0.486028\pi\)
0.0438812 + 0.999037i \(0.486028\pi\)
\(734\) 1.04168e6i 1.93350i
\(735\) 66781.6 82153.4i 0.123618 0.152072i
\(736\) −155457. −0.286982
\(737\) 193620.i 0.356464i
\(738\) 126311. + 605385.i 0.231914 + 1.11152i
\(739\) −61.3175 −0.000112278 −5.61392e−5 1.00000i \(-0.500018\pi\)
−5.61392e−5 1.00000i \(0.500018\pi\)
\(740\) 9716.68i 0.0177441i
\(741\) −200827. 163250.i −0.365752 0.297316i
\(742\) −291637. −0.529705
\(743\) 272594.i 0.493785i −0.969043 0.246893i \(-0.920591\pi\)
0.969043 0.246893i \(-0.0794095\pi\)
\(744\) −4699.91 + 5781.74i −0.00849071 + 0.0104451i
\(745\) −46503.4 −0.0837862
\(746\) 716516.i 1.28750i
\(747\) −599129. + 125005.i −1.07369 + 0.224020i
\(748\) −66019.0 −0.117996
\(749\) 257227.i 0.458514i
\(750\) 223057. + 181321.i 0.396546 + 0.322348i
\(751\) 576871. 1.02282 0.511409 0.859337i \(-0.329124\pi\)
0.511409 + 0.859337i \(0.329124\pi\)
\(752\) 213674.i 0.377847i
\(753\) 80539.8 99078.4i 0.142043 0.174739i
\(754\) 1.35767e6 2.38809
\(755\) 5270.34i 0.00924580i
\(756\) 17139.9 33176.9i 0.0299892 0.0580486i
\(757\) −959951. −1.67516 −0.837582 0.546311i \(-0.816032\pi\)
−0.837582 + 0.546311i \(0.816032\pi\)
\(758\) 789137.i 1.37345i
\(759\) −221858. 180346.i −0.385115 0.313056i
\(760\) 41141.1 0.0712277
\(761\) 7881.85i 0.0136100i 0.999977 + 0.00680502i \(0.00216612\pi\)
−0.999977 + 0.00680502i \(0.997834\pi\)
\(762\) 324509. 399204.i 0.558878 0.687520i
\(763\) 453098. 0.778293
\(764\) 73301.9i 0.125582i
\(765\) 48440.6 + 232167.i 0.0827727 + 0.396715i
\(766\) −359110. −0.612026
\(767\) 114251.i 0.194209i
\(768\) −194510. 158115.i −0.329777 0.268072i
\(769\) −561017. −0.948688 −0.474344 0.880339i \(-0.657315\pi\)
−0.474344 + 0.880339i \(0.657315\pi\)
\(770\) 35043.1i 0.0591047i
\(771\) 455447. 560281.i 0.766176 0.942535i
\(772\) −21913.4 −0.0367685
\(773\) 168175.i 0.281450i −0.990049 0.140725i \(-0.955057\pi\)
0.990049 0.140725i \(-0.0449434\pi\)
\(774\) 643139. 134188.i 1.07355 0.223991i
\(775\) 8298.04 0.0138157
\(776\) 737829.i 1.22527i
\(777\) −105550. 85800.8i −0.174831 0.142118i
\(778\) 470951. 0.778066
\(779\) 203508.i 0.335356i
\(780\) −20380.8 + 25072.0i −0.0334990 + 0.0412098i
\(781\) −329239. −0.539771
\(782\) 1.07668e6i