Properties

Label 177.5.c.a.58.14
Level $177$
Weight $5$
Character 177.58
Analytic conductor $18.296$
Analytic rank $0$
Dimension $40$
CM no
Inner twists $2$

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Newspace parameters

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

Newform invariants

Self dual: no
Analytic conductor: \(18.2964834658\)
Analytic rank: \(0\)
Dimension: \(40\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 58.14
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.27

$q$-expansion

\(f(q)\) \(=\) \(q-2.43119i q^{2} +5.19615 q^{3} +10.0893 q^{4} +25.9319 q^{5} -12.6328i q^{6} -17.4595 q^{7} -63.4281i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-2.43119i q^{2} +5.19615 q^{3} +10.0893 q^{4} +25.9319 q^{5} -12.6328i q^{6} -17.4595 q^{7} -63.4281i q^{8} +27.0000 q^{9} -63.0454i q^{10} -44.7152i q^{11} +52.4255 q^{12} -157.364i q^{13} +42.4475i q^{14} +134.746 q^{15} +7.22282 q^{16} -328.532 q^{17} -65.6422i q^{18} +678.379 q^{19} +261.635 q^{20} -90.7223 q^{21} -108.711 q^{22} +424.331i q^{23} -329.582i q^{24} +47.4624 q^{25} -382.582 q^{26} +140.296 q^{27} -176.154 q^{28} +870.549 q^{29} -327.594i q^{30} +1380.41i q^{31} -1032.41i q^{32} -232.347i q^{33} +798.725i q^{34} -452.758 q^{35} +272.411 q^{36} -2568.09i q^{37} -1649.27i q^{38} -817.687i q^{39} -1644.81i q^{40} +503.324 q^{41} +220.563i q^{42} +2003.40i q^{43} -451.145i q^{44} +700.161 q^{45} +1031.63 q^{46} -2422.01i q^{47} +37.5309 q^{48} -2096.17 q^{49} -115.390i q^{50} -1707.10 q^{51} -1587.69i q^{52} -1526.26 q^{53} -341.087i q^{54} -1159.55i q^{55} +1107.42i q^{56} +3524.96 q^{57} -2116.47i q^{58} +(-1105.23 - 3300.88i) q^{59} +1359.49 q^{60} +5708.35i q^{61} +3356.05 q^{62} -471.407 q^{63} -2394.42 q^{64} -4080.74i q^{65} -564.880 q^{66} +4773.92i q^{67} -3314.66 q^{68} +2204.89i q^{69} +1100.74i q^{70} -2795.15 q^{71} -1712.56i q^{72} +4719.76i q^{73} -6243.53 q^{74} +246.622 q^{75} +6844.37 q^{76} +780.705i q^{77} -1987.96 q^{78} +8669.75 q^{79} +187.301 q^{80} +729.000 q^{81} -1223.68i q^{82} -7458.93i q^{83} -915.325 q^{84} -8519.45 q^{85} +4870.65 q^{86} +4523.51 q^{87} -2836.20 q^{88} +4001.99i q^{89} -1702.23i q^{90} +2747.50i q^{91} +4281.21i q^{92} +7172.83i q^{93} -5888.37 q^{94} +17591.6 q^{95} -5364.56i q^{96} +5912.30i q^{97} +5096.18i q^{98} -1207.31i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.43119i 0.607798i −0.952704 0.303899i \(-0.901711\pi\)
0.952704 0.303899i \(-0.0982886\pi\)
\(3\) 5.19615 0.577350
\(4\) 10.0893 0.630581
\(5\) 25.9319 1.03728 0.518638 0.854994i \(-0.326439\pi\)
0.518638 + 0.854994i \(0.326439\pi\)
\(6\) 12.6328i 0.350912i
\(7\) −17.4595 −0.356317 −0.178158 0.984002i \(-0.557014\pi\)
−0.178158 + 0.984002i \(0.557014\pi\)
\(8\) 63.4281i 0.991064i
\(9\) 27.0000 0.333333
\(10\) 63.0454i 0.630454i
\(11\) 44.7152i 0.369547i −0.982781 0.184773i \(-0.940845\pi\)
0.982781 0.184773i \(-0.0591551\pi\)
\(12\) 52.4255 0.364066
\(13\) 157.364i 0.931148i −0.885009 0.465574i \(-0.845848\pi\)
0.885009 0.465574i \(-0.154152\pi\)
\(14\) 42.4475i 0.216569i
\(15\) 134.746 0.598871
\(16\) 7.22282 0.0282141
\(17\) −328.532 −1.13679 −0.568395 0.822756i \(-0.692435\pi\)
−0.568395 + 0.822756i \(0.692435\pi\)
\(18\) 65.6422i 0.202599i
\(19\) 678.379 1.87917 0.939583 0.342322i \(-0.111213\pi\)
0.939583 + 0.342322i \(0.111213\pi\)
\(20\) 261.635 0.654086
\(21\) −90.7223 −0.205720
\(22\) −108.711 −0.224610
\(23\) 424.331i 0.802139i 0.916048 + 0.401069i \(0.131361\pi\)
−0.916048 + 0.401069i \(0.868639\pi\)
\(24\) 329.582i 0.572191i
\(25\) 47.4624 0.0759398
\(26\) −382.582 −0.565950
\(27\) 140.296 0.192450
\(28\) −176.154 −0.224687
\(29\) 870.549 1.03514 0.517568 0.855642i \(-0.326837\pi\)
0.517568 + 0.855642i \(0.326837\pi\)
\(30\) 327.594i 0.363993i
\(31\) 1380.41i 1.43643i 0.695820 + 0.718216i \(0.255041\pi\)
−0.695820 + 0.718216i \(0.744959\pi\)
\(32\) 1032.41i 1.00821i
\(33\) 232.347i 0.213358i
\(34\) 798.725i 0.690938i
\(35\) −452.758 −0.369599
\(36\) 272.411 0.210194
\(37\) 2568.09i 1.87589i −0.346784 0.937945i \(-0.612726\pi\)
0.346784 0.937945i \(-0.387274\pi\)
\(38\) 1649.27i 1.14215i
\(39\) 817.687i 0.537598i
\(40\) 1644.81i 1.02801i
\(41\) 503.324 0.299419 0.149710 0.988730i \(-0.452166\pi\)
0.149710 + 0.988730i \(0.452166\pi\)
\(42\) 220.563i 0.125036i
\(43\) 2003.40i 1.08350i 0.840538 + 0.541752i \(0.182239\pi\)
−0.840538 + 0.541752i \(0.817761\pi\)
\(44\) 451.145i 0.233029i
\(45\) 700.161 0.345758
\(46\) 1031.63 0.487538
\(47\) 2422.01i 1.09643i −0.836338 0.548214i \(-0.815308\pi\)
0.836338 0.548214i \(-0.184692\pi\)
\(48\) 37.5309 0.0162894
\(49\) −2096.17 −0.873038
\(50\) 115.390i 0.0461561i
\(51\) −1707.10 −0.656325
\(52\) 1587.69i 0.587164i
\(53\) −1526.26 −0.543347 −0.271674 0.962389i \(-0.587577\pi\)
−0.271674 + 0.962389i \(0.587577\pi\)
\(54\) 341.087i 0.116971i
\(55\) 1159.55i 0.383322i
\(56\) 1107.42i 0.353133i
\(57\) 3524.96 1.08494
\(58\) 2116.47i 0.629154i
\(59\) −1105.23 3300.88i −0.317504 0.948257i
\(60\) 1359.49 0.377637
\(61\) 5708.35i 1.53409i 0.641594 + 0.767045i \(0.278274\pi\)
−0.641594 + 0.767045i \(0.721726\pi\)
\(62\) 3356.05 0.873061
\(63\) −471.407 −0.118772
\(64\) −2394.42 −0.584576
\(65\) 4080.74i 0.965857i
\(66\) −564.880 −0.129679
\(67\) 4773.92i 1.06347i 0.846911 + 0.531735i \(0.178460\pi\)
−0.846911 + 0.531735i \(0.821540\pi\)
\(68\) −3314.66 −0.716838
\(69\) 2204.89i 0.463115i
\(70\) 1100.74i 0.224641i
\(71\) −2795.15 −0.554484 −0.277242 0.960800i \(-0.589420\pi\)
−0.277242 + 0.960800i \(0.589420\pi\)
\(72\) 1712.56i 0.330355i
\(73\) 4719.76i 0.885674i 0.896602 + 0.442837i \(0.146028\pi\)
−0.896602 + 0.442837i \(0.853972\pi\)
\(74\) −6243.53 −1.14016
\(75\) 246.622 0.0438439
\(76\) 6844.37 1.18497
\(77\) 780.705i 0.131676i
\(78\) −1987.96 −0.326751
\(79\) 8669.75 1.38916 0.694580 0.719415i \(-0.255590\pi\)
0.694580 + 0.719415i \(0.255590\pi\)
\(80\) 187.301 0.0292658
\(81\) 729.000 0.111111
\(82\) 1223.68i 0.181987i
\(83\) 7458.93i 1.08273i −0.840787 0.541365i \(-0.817908\pi\)
0.840787 0.541365i \(-0.182092\pi\)
\(84\) −915.325 −0.129723
\(85\) −8519.45 −1.17916
\(86\) 4870.65 0.658552
\(87\) 4523.51 0.597636
\(88\) −2836.20 −0.366245
\(89\) 4001.99i 0.505238i 0.967566 + 0.252619i \(0.0812920\pi\)
−0.967566 + 0.252619i \(0.918708\pi\)
\(90\) 1702.23i 0.210151i
\(91\) 2747.50i 0.331784i
\(92\) 4281.21i 0.505814i
\(93\) 7172.83i 0.829325i
\(94\) −5888.37 −0.666407
\(95\) 17591.6 1.94921
\(96\) 5364.56i 0.582092i
\(97\) 5912.30i 0.628367i 0.949362 + 0.314183i \(0.101731\pi\)
−0.949362 + 0.314183i \(0.898269\pi\)
\(98\) 5096.18i 0.530631i
\(99\) 1207.31i 0.123182i
\(100\) 478.862 0.0478862
\(101\) 14483.7i 1.41983i 0.704286 + 0.709916i \(0.251267\pi\)
−0.704286 + 0.709916i \(0.748733\pi\)
\(102\) 4150.30i 0.398913i
\(103\) 211.537i 0.0199394i −0.999950 0.00996968i \(-0.996826\pi\)
0.999950 0.00996968i \(-0.00317350\pi\)
\(104\) −9981.30 −0.922828
\(105\) −2352.60 −0.213388
\(106\) 3710.64i 0.330246i
\(107\) −12751.0 −1.11373 −0.556863 0.830605i \(-0.687995\pi\)
−0.556863 + 0.830605i \(0.687995\pi\)
\(108\) 1415.49 0.121355
\(109\) 18050.8i 1.51930i 0.650334 + 0.759648i \(0.274629\pi\)
−0.650334 + 0.759648i \(0.725371\pi\)
\(110\) −2819.09 −0.232982
\(111\) 13344.2i 1.08305i
\(112\) −126.107 −0.0100532
\(113\) 9631.35i 0.754276i 0.926157 + 0.377138i \(0.123092\pi\)
−0.926157 + 0.377138i \(0.876908\pi\)
\(114\) 8569.86i 0.659423i
\(115\) 11003.7i 0.832039i
\(116\) 8783.24 0.652737
\(117\) 4248.83i 0.310383i
\(118\) −8025.08 + 2687.03i −0.576349 + 0.192979i
\(119\) 5736.01 0.405057
\(120\) 8546.69i 0.593520i
\(121\) 12641.6 0.863435
\(122\) 13878.1 0.932417
\(123\) 2615.35 0.172870
\(124\) 13927.4i 0.905788i
\(125\) −14976.6 −0.958505
\(126\) 1146.08i 0.0721896i
\(127\) −25023.8 −1.55148 −0.775741 0.631052i \(-0.782624\pi\)
−0.775741 + 0.631052i \(0.782624\pi\)
\(128\) 10697.3i 0.652909i
\(129\) 10410.0i 0.625562i
\(130\) −9921.08 −0.587046
\(131\) 2066.15i 0.120398i −0.998186 0.0601990i \(-0.980826\pi\)
0.998186 0.0601990i \(-0.0191735\pi\)
\(132\) 2344.22i 0.134540i
\(133\) −11844.2 −0.669578
\(134\) 11606.3 0.646375
\(135\) 3638.14 0.199624
\(136\) 20838.2i 1.12663i
\(137\) 8060.06 0.429434 0.214717 0.976676i \(-0.431117\pi\)
0.214717 + 0.976676i \(0.431117\pi\)
\(138\) 5360.51 0.281480
\(139\) −8208.19 −0.424833 −0.212416 0.977179i \(-0.568133\pi\)
−0.212416 + 0.977179i \(0.568133\pi\)
\(140\) −4568.01 −0.233062
\(141\) 12585.1i 0.633023i
\(142\) 6795.56i 0.337014i
\(143\) −7036.56 −0.344103
\(144\) 195.016 0.00940471
\(145\) 22575.0 1.07372
\(146\) 11474.6 0.538311
\(147\) −10892.0 −0.504049
\(148\) 25910.3i 1.18290i
\(149\) 37339.6i 1.68189i −0.541122 0.840944i \(-0.682000\pi\)
0.541122 0.840944i \(-0.318000\pi\)
\(150\) 599.585i 0.0266482i
\(151\) 10313.8i 0.452340i 0.974088 + 0.226170i \(0.0726205\pi\)
−0.974088 + 0.226170i \(0.927379\pi\)
\(152\) 43028.3i 1.86237i
\(153\) −8870.37 −0.378930
\(154\) 1898.04 0.0800323
\(155\) 35796.7i 1.48998i
\(156\) 8249.89i 0.339000i
\(157\) 10989.2i 0.445826i 0.974838 + 0.222913i \(0.0715566\pi\)
−0.974838 + 0.222913i \(0.928443\pi\)
\(158\) 21077.8i 0.844329i
\(159\) −7930.69 −0.313702
\(160\) 26772.3i 1.04579i
\(161\) 7408.62i 0.285815i
\(162\) 1772.34i 0.0675331i
\(163\) 1659.70 0.0624676 0.0312338 0.999512i \(-0.490056\pi\)
0.0312338 + 0.999512i \(0.490056\pi\)
\(164\) 5078.19 0.188808
\(165\) 6025.19i 0.221311i
\(166\) −18134.1 −0.658082
\(167\) −5744.24 −0.205968 −0.102984 0.994683i \(-0.532839\pi\)
−0.102984 + 0.994683i \(0.532839\pi\)
\(168\) 5754.35i 0.203881i
\(169\) 3797.58 0.132964
\(170\) 20712.4i 0.716693i
\(171\) 18316.2 0.626389
\(172\) 20212.9i 0.683238i
\(173\) 48337.4i 1.61507i 0.589821 + 0.807534i \(0.299198\pi\)
−0.589821 + 0.807534i \(0.700802\pi\)
\(174\) 10997.5i 0.363242i
\(175\) −828.671 −0.0270586
\(176\) 322.969i 0.0104264i
\(177\) −5742.96 17151.9i −0.183311 0.547476i
\(178\) 9729.62 0.307083
\(179\) 8489.09i 0.264945i −0.991187 0.132472i \(-0.957708\pi\)
0.991187 0.132472i \(-0.0422916\pi\)
\(180\) 7064.13 0.218029
\(181\) −63579.4 −1.94070 −0.970352 0.241696i \(-0.922296\pi\)
−0.970352 + 0.241696i \(0.922296\pi\)
\(182\) 6679.70 0.201657
\(183\) 29661.4i 0.885707i
\(184\) 26914.5 0.794971
\(185\) 66595.5i 1.94581i
\(186\) 17438.5 0.504062
\(187\) 14690.4i 0.420097i
\(188\) 24436.4i 0.691387i
\(189\) −2449.50 −0.0685732
\(190\) 42768.7i 1.18473i
\(191\) 36006.4i 0.986991i −0.869748 0.493495i \(-0.835719\pi\)
0.869748 0.493495i \(-0.164281\pi\)
\(192\) −12441.8 −0.337505
\(193\) 7371.06 0.197886 0.0989431 0.995093i \(-0.468454\pi\)
0.0989431 + 0.995093i \(0.468454\pi\)
\(194\) 14373.9 0.381920
\(195\) 21204.2i 0.557638i
\(196\) −21148.8 −0.550522
\(197\) 62886.8 1.62042 0.810209 0.586141i \(-0.199353\pi\)
0.810209 + 0.586141i \(0.199353\pi\)
\(198\) −2935.20 −0.0748700
\(199\) 24801.5 0.626285 0.313143 0.949706i \(-0.398618\pi\)
0.313143 + 0.949706i \(0.398618\pi\)
\(200\) 3010.45i 0.0752613i
\(201\) 24806.0i 0.613995i
\(202\) 35212.7 0.862972
\(203\) −15199.4 −0.368836
\(204\) −17223.5 −0.413867
\(205\) 13052.1 0.310580
\(206\) −514.286 −0.0121191
\(207\) 11456.9i 0.267380i
\(208\) 1136.61i 0.0262715i
\(209\) 30333.8i 0.694440i
\(210\) 5719.63i 0.129697i
\(211\) 17502.7i 0.393134i 0.980490 + 0.196567i \(0.0629794\pi\)
−0.980490 + 0.196567i \(0.937021\pi\)
\(212\) −15398.9 −0.342625
\(213\) −14524.0 −0.320131
\(214\) 31000.2i 0.676920i
\(215\) 51951.9i 1.12389i
\(216\) 8898.72i 0.190730i
\(217\) 24101.3i 0.511825i
\(218\) 43884.9 0.923426
\(219\) 24524.6i 0.511344i
\(220\) 11699.0i 0.241716i
\(221\) 51699.1i 1.05852i
\(222\) −32442.3 −0.658273
\(223\) 54042.6 1.08674 0.543371 0.839493i \(-0.317148\pi\)
0.543371 + 0.839493i \(0.317148\pi\)
\(224\) 18025.4i 0.359243i
\(225\) 1281.48 0.0253133
\(226\) 23415.7 0.458448
\(227\) 24892.4i 0.483076i −0.970391 0.241538i \(-0.922348\pi\)
0.970391 0.241538i \(-0.0776518\pi\)
\(228\) 35564.4 0.684141
\(229\) 81045.6i 1.54546i −0.634733 0.772731i \(-0.718890\pi\)
0.634733 0.772731i \(-0.281110\pi\)
\(230\) 26752.1 0.505712
\(231\) 4056.66i 0.0760230i
\(232\) 55217.3i 1.02589i
\(233\) 92463.9i 1.70318i 0.524209 + 0.851589i \(0.324361\pi\)
−0.524209 + 0.851589i \(0.675639\pi\)
\(234\) −10329.7 −0.188650
\(235\) 62807.2i 1.13730i
\(236\) −11151.0 33303.6i −0.200212 0.597953i
\(237\) 45049.3 0.802032
\(238\) 13945.4i 0.246193i
\(239\) −66752.2 −1.16861 −0.584305 0.811534i \(-0.698633\pi\)
−0.584305 + 0.811534i \(0.698633\pi\)
\(240\) 973.246 0.0168966
\(241\) −57886.0 −0.996643 −0.498322 0.866992i \(-0.666050\pi\)
−0.498322 + 0.866992i \(0.666050\pi\)
\(242\) 30734.1i 0.524794i
\(243\) 3788.00 0.0641500
\(244\) 57593.2i 0.967368i
\(245\) −54357.5 −0.905581
\(246\) 6358.42i 0.105070i
\(247\) 106752.i 1.74978i
\(248\) 87556.9 1.42360
\(249\) 38757.8i 0.625115i
\(250\) 36411.1i 0.582577i
\(251\) −1482.64 −0.0235336 −0.0117668 0.999931i \(-0.503746\pi\)
−0.0117668 + 0.999931i \(0.503746\pi\)
\(252\) −4756.17 −0.0748956
\(253\) 18974.0 0.296428
\(254\) 60837.8i 0.942988i
\(255\) −44268.4 −0.680790
\(256\) −64317.9 −0.981413
\(257\) −63595.3 −0.962850 −0.481425 0.876487i \(-0.659881\pi\)
−0.481425 + 0.876487i \(0.659881\pi\)
\(258\) 25308.6 0.380215
\(259\) 44837.7i 0.668411i
\(260\) 41171.9i 0.609051i
\(261\) 23504.8 0.345045
\(262\) −5023.21 −0.0731777
\(263\) −79407.3 −1.14802 −0.574010 0.818849i \(-0.694613\pi\)
−0.574010 + 0.818849i \(0.694613\pi\)
\(264\) −14737.3 −0.211451
\(265\) −39578.9 −0.563601
\(266\) 28795.5i 0.406968i
\(267\) 20795.0i 0.291699i
\(268\) 48165.5i 0.670605i
\(269\) 103489.i 1.43018i 0.699031 + 0.715091i \(0.253615\pi\)
−0.699031 + 0.715091i \(0.746385\pi\)
\(270\) 8845.02i 0.121331i
\(271\) 144360. 1.96566 0.982830 0.184513i \(-0.0590709\pi\)
0.982830 + 0.184513i \(0.0590709\pi\)
\(272\) −2372.93 −0.0320735
\(273\) 14276.4i 0.191555i
\(274\) 19595.5i 0.261010i
\(275\) 2122.29i 0.0280633i
\(276\) 22245.8i 0.292032i
\(277\) 47254.9 0.615867 0.307934 0.951408i \(-0.400363\pi\)
0.307934 + 0.951408i \(0.400363\pi\)
\(278\) 19955.7i 0.258213i
\(279\) 37271.1i 0.478811i
\(280\) 28717.6i 0.366296i
\(281\) −31731.5 −0.401863 −0.200931 0.979605i \(-0.564397\pi\)
−0.200931 + 0.979605i \(0.564397\pi\)
\(282\) −30596.9 −0.384750
\(283\) 12999.5i 0.162313i 0.996701 + 0.0811563i \(0.0258613\pi\)
−0.996701 + 0.0811563i \(0.974139\pi\)
\(284\) −28201.1 −0.349647
\(285\) 91408.8 1.12538
\(286\) 17107.2i 0.209145i
\(287\) −8787.80 −0.106688
\(288\) 27875.1i 0.336071i
\(289\) 24412.3 0.292289
\(290\) 54884.1i 0.652606i
\(291\) 30721.2i 0.362788i
\(292\) 47619.0i 0.558489i
\(293\) −27627.7 −0.321817 −0.160909 0.986969i \(-0.551442\pi\)
−0.160909 + 0.986969i \(0.551442\pi\)
\(294\) 26480.5i 0.306360i
\(295\) −28660.8 85598.1i −0.329339 0.983603i
\(296\) −162889. −1.85913
\(297\) 6273.36i 0.0711193i
\(298\) −90779.8 −1.02225
\(299\) 66774.5 0.746910
\(300\) 2488.24 0.0276471
\(301\) 34978.4i 0.386071i
\(302\) 25074.9 0.274932
\(303\) 75259.6i 0.819741i
\(304\) 4899.81 0.0530190
\(305\) 148028.i 1.59127i
\(306\) 21565.6i 0.230313i
\(307\) −25754.0 −0.273255 −0.136627 0.990623i \(-0.543626\pi\)
−0.136627 + 0.990623i \(0.543626\pi\)
\(308\) 7876.77i 0.0830322i
\(309\) 1099.18i 0.0115120i
\(310\) 87028.6 0.905605
\(311\) 123728. 1.27923 0.639613 0.768697i \(-0.279095\pi\)
0.639613 + 0.768697i \(0.279095\pi\)
\(312\) −51864.4 −0.532795
\(313\) 12824.2i 0.130900i 0.997856 + 0.0654502i \(0.0208484\pi\)
−0.997856 + 0.0654502i \(0.979152\pi\)
\(314\) 26716.8 0.270972
\(315\) −12224.5 −0.123200
\(316\) 87471.7 0.875978
\(317\) −136329. −1.35666 −0.678329 0.734759i \(-0.737295\pi\)
−0.678329 + 0.734759i \(0.737295\pi\)
\(318\) 19281.0i 0.190667i
\(319\) 38926.8i 0.382531i
\(320\) −62091.9 −0.606366
\(321\) −66256.4 −0.643010
\(322\) −18011.8 −0.173718
\(323\) −222869. −2.13622
\(324\) 7355.10 0.0700646
\(325\) 7468.87i 0.0707112i
\(326\) 4035.05i 0.0379677i
\(327\) 93794.5i 0.877166i
\(328\) 31924.9i 0.296744i
\(329\) 42287.1i 0.390676i
\(330\) −14648.4 −0.134512
\(331\) −153145. −1.39781 −0.698904 0.715216i \(-0.746328\pi\)
−0.698904 + 0.715216i \(0.746328\pi\)
\(332\) 75255.4i 0.682750i
\(333\) 69338.5i 0.625297i
\(334\) 13965.4i 0.125187i
\(335\) 123797.i 1.10311i
\(336\) −655.271 −0.00580420
\(337\) 60949.0i 0.536669i 0.963326 + 0.268335i \(0.0864733\pi\)
−0.963326 + 0.268335i \(0.913527\pi\)
\(338\) 9232.64i 0.0808151i
\(339\) 50046.0i 0.435482i
\(340\) −85955.3 −0.743558
\(341\) 61725.3 0.530829
\(342\) 44530.3i 0.380718i
\(343\) 78518.3 0.667395
\(344\) 127072. 1.07382
\(345\) 57177.0i 0.480378i
\(346\) 117517. 0.981635
\(347\) 150274.i 1.24803i −0.781412 0.624015i \(-0.785500\pi\)
0.781412 0.624015i \(-0.214500\pi\)
\(348\) 45639.0 0.376858
\(349\) 4128.34i 0.0338942i −0.999856 0.0169471i \(-0.994605\pi\)
0.999856 0.0169471i \(-0.00539468\pi\)
\(350\) 2014.66i 0.0164462i
\(351\) 22077.6i 0.179199i
\(352\) −46164.4 −0.372582
\(353\) 126346.i 1.01394i −0.861964 0.506969i \(-0.830766\pi\)
0.861964 0.506969i \(-0.169234\pi\)
\(354\) −41699.5 + 13962.2i −0.332755 + 0.111416i
\(355\) −72483.6 −0.575152
\(356\) 40377.3i 0.318594i
\(357\) 29805.2 0.233860
\(358\) −20638.6 −0.161033
\(359\) 182628. 1.41703 0.708514 0.705697i \(-0.249366\pi\)
0.708514 + 0.705697i \(0.249366\pi\)
\(360\) 44409.9i 0.342669i
\(361\) 329877. 2.53126
\(362\) 154574.i 1.17956i
\(363\) 65687.4 0.498505
\(364\) 27720.4i 0.209217i
\(365\) 122392.i 0.918688i
\(366\) 72112.7 0.538331
\(367\) 8500.43i 0.0631116i −0.999502 0.0315558i \(-0.989954\pi\)
0.999502 0.0315558i \(-0.0100462\pi\)
\(368\) 3064.87i 0.0226316i
\(369\) 13589.7 0.0998065
\(370\) −161907. −1.18266
\(371\) 26647.8 0.193604
\(372\) 72368.8i 0.522957i
\(373\) 82283.7 0.591420 0.295710 0.955278i \(-0.404444\pi\)
0.295710 + 0.955278i \(0.404444\pi\)
\(374\) 35715.1 0.255334
\(375\) −77820.9 −0.553393
\(376\) −153623. −1.08663
\(377\) 136993.i 0.963865i
\(378\) 5955.21i 0.0416787i
\(379\) 2637.31 0.0183604 0.00918022 0.999958i \(-0.497078\pi\)
0.00918022 + 0.999958i \(0.497078\pi\)
\(380\) 177487. 1.22914
\(381\) −130028. −0.895748
\(382\) −87538.5 −0.599891
\(383\) 45438.5 0.309761 0.154880 0.987933i \(-0.450501\pi\)
0.154880 + 0.987933i \(0.450501\pi\)
\(384\) 55584.6i 0.376957i
\(385\) 20245.2i 0.136584i
\(386\) 17920.5i 0.120275i
\(387\) 54091.8i 0.361168i
\(388\) 59651.0i 0.396236i
\(389\) −36809.8 −0.243257 −0.121628 0.992576i \(-0.538812\pi\)
−0.121628 + 0.992576i \(0.538812\pi\)
\(390\) −51551.4 −0.338931
\(391\) 139406.i 0.911862i
\(392\) 132956.i 0.865237i
\(393\) 10736.0i 0.0695118i
\(394\) 152890.i 0.984888i
\(395\) 224823. 1.44094
\(396\) 12180.9i 0.0776764i
\(397\) 184237.i 1.16895i −0.811412 0.584475i \(-0.801300\pi\)
0.811412 0.584475i \(-0.198700\pi\)
\(398\) 60297.3i 0.380655i
\(399\) −61544.1 −0.386581
\(400\) 342.812 0.00214258
\(401\) 243995.i 1.51738i −0.651455 0.758688i \(-0.725841\pi\)
0.651455 0.758688i \(-0.274159\pi\)
\(402\) 60308.2 0.373185
\(403\) 217227. 1.33753
\(404\) 146131.i 0.895320i
\(405\) 18904.3 0.115253
\(406\) 36952.6i 0.224178i
\(407\) −114833. −0.693229
\(408\) 108278.i 0.650461i
\(409\) 39142.7i 0.233994i −0.993132 0.116997i \(-0.962673\pi\)
0.993132 0.116997i \(-0.0373268\pi\)
\(410\) 31732.3i 0.188770i
\(411\) 41881.3 0.247934
\(412\) 2134.26i 0.0125734i
\(413\) 19296.8 + 57631.8i 0.113132 + 0.337880i
\(414\) 27854.0 0.162513
\(415\) 193424.i 1.12309i
\(416\) −162464. −0.938795
\(417\) −42651.0 −0.245277
\(418\) −73747.4 −0.422079
\(419\) 148939.i 0.848362i −0.905577 0.424181i \(-0.860562\pi\)
0.905577 0.424181i \(-0.139438\pi\)
\(420\) −23736.1 −0.134558
\(421\) 258237.i 1.45698i −0.685055 0.728492i \(-0.740222\pi\)
0.685055 0.728492i \(-0.259778\pi\)
\(422\) 42552.5 0.238946
\(423\) 65394.2i 0.365476i
\(424\) 96808.0i 0.538492i
\(425\) −15592.9 −0.0863276
\(426\) 35310.8i 0.194575i
\(427\) 99665.0i 0.546622i
\(428\) −128649. −0.702295
\(429\) −36563.0 −0.198668
\(430\) 126305. 0.683100
\(431\) 260135.i 1.40037i −0.713960 0.700187i \(-0.753100\pi\)
0.713960 0.700187i \(-0.246900\pi\)
\(432\) 1013.33 0.00542981
\(433\) 281301. 1.50036 0.750181 0.661232i \(-0.229966\pi\)
0.750181 + 0.661232i \(0.229966\pi\)
\(434\) −58595.0 −0.311086
\(435\) 117303. 0.619913
\(436\) 182120.i 0.958040i
\(437\) 287857.i 1.50735i
\(438\) 59624.0 0.310794
\(439\) −226376. −1.17463 −0.587316 0.809357i \(-0.699816\pi\)
−0.587316 + 0.809357i \(0.699816\pi\)
\(440\) −73548.0 −0.379897
\(441\) −56596.5 −0.291013
\(442\) 125691. 0.643366
\(443\) 191214.i 0.974346i −0.873305 0.487173i \(-0.838028\pi\)
0.873305 0.487173i \(-0.161972\pi\)
\(444\) 134634.i 0.682948i
\(445\) 103779.i 0.524071i
\(446\) 131388.i 0.660519i
\(447\) 194022.i 0.971039i
\(448\) 41805.5 0.208294
\(449\) 205380. 1.01874 0.509372 0.860546i \(-0.329878\pi\)
0.509372 + 0.860546i \(0.329878\pi\)
\(450\) 3115.54i 0.0153854i
\(451\) 22506.2i 0.110649i
\(452\) 97173.6i 0.475633i
\(453\) 53592.1i 0.261159i
\(454\) −60518.3 −0.293613
\(455\) 71247.8i 0.344151i
\(456\) 223582.i 1.07524i
\(457\) 145715.i 0.697703i −0.937178 0.348852i \(-0.886572\pi\)
0.937178 0.348852i \(-0.113428\pi\)
\(458\) −197038. −0.939329
\(459\) −46091.8 −0.218775
\(460\) 111020.i 0.524668i
\(461\) −91731.3 −0.431634 −0.215817 0.976434i \(-0.569241\pi\)
−0.215817 + 0.976434i \(0.569241\pi\)
\(462\) 9862.53 0.0462066
\(463\) 363576.i 1.69603i −0.529974 0.848014i \(-0.677798\pi\)
0.529974 0.848014i \(-0.322202\pi\)
\(464\) 6287.82 0.0292055
\(465\) 186005.i 0.860238i
\(466\) 224797. 1.03519
\(467\) 107740.i 0.494019i 0.969013 + 0.247009i \(0.0794478\pi\)
−0.969013 + 0.247009i \(0.920552\pi\)
\(468\) 42867.7i 0.195721i
\(469\) 83350.3i 0.378932i
\(470\) −152697. −0.691247
\(471\) 57101.4i 0.257398i
\(472\) −209369. + 70102.9i −0.939784 + 0.314667i
\(473\) 89582.3 0.400406
\(474\) 109524.i 0.487474i
\(475\) 32197.5 0.142704
\(476\) 57872.4 0.255421
\(477\) −41209.1 −0.181116
\(478\) 162288.i 0.710280i
\(479\) 148486. 0.647165 0.323582 0.946200i \(-0.395113\pi\)
0.323582 + 0.946200i \(0.395113\pi\)
\(480\) 139113.i 0.603790i
\(481\) −404125. −1.74673
\(482\) 140732.i 0.605758i
\(483\) 38496.3i 0.165016i
\(484\) 127544. 0.544466
\(485\) 153317.i 0.651789i
\(486\) 9209.35i 0.0389903i
\(487\) −3404.16 −0.0143533 −0.00717666 0.999974i \(-0.502284\pi\)
−0.00717666 + 0.999974i \(0.502284\pi\)
\(488\) 362070. 1.52038
\(489\) 8624.06 0.0360657
\(490\) 132154.i 0.550411i
\(491\) 326718. 1.35522 0.677611 0.735420i \(-0.263015\pi\)
0.677611 + 0.735420i \(0.263015\pi\)
\(492\) 26387.0 0.109009
\(493\) −286003. −1.17673
\(494\) −259536. −1.06351
\(495\) 31307.8i 0.127774i
\(496\) 9970.46i 0.0405277i
\(497\) 48802.0 0.197572
\(498\) −94227.6 −0.379944
\(499\) 170255. 0.683754 0.341877 0.939745i \(-0.388937\pi\)
0.341877 + 0.939745i \(0.388937\pi\)
\(500\) −151104. −0.604415
\(501\) −29847.9 −0.118916
\(502\) 3604.58i 0.0143037i
\(503\) 198224.i 0.783466i −0.920079 0.391733i \(-0.871876\pi\)
0.920079 0.391733i \(-0.128124\pi\)
\(504\) 29900.5i 0.117711i
\(505\) 375590.i 1.47276i
\(506\) 46129.6i 0.180168i
\(507\) 19732.8 0.0767666
\(508\) −252473. −0.978335
\(509\) 252370.i 0.974099i 0.873374 + 0.487049i \(0.161927\pi\)
−0.873374 + 0.487049i \(0.838073\pi\)
\(510\) 107625.i 0.413783i
\(511\) 82404.7i 0.315580i
\(512\) 14787.0i 0.0564079i
\(513\) 95173.9 0.361646
\(514\) 154612.i 0.585219i
\(515\) 5485.54i 0.0206826i
\(516\) 105029.i 0.394467i
\(517\) −108301. −0.405181
\(518\) 109009. 0.406259
\(519\) 251168.i 0.932460i
\(520\) −258834. −0.957226
\(521\) −372104. −1.37085 −0.685424 0.728144i \(-0.740383\pi\)
−0.685424 + 0.728144i \(0.740383\pi\)
\(522\) 57144.8i 0.209718i
\(523\) −68686.7 −0.251113 −0.125557 0.992086i \(-0.540072\pi\)
−0.125557 + 0.992086i \(0.540072\pi\)
\(524\) 20846.0i 0.0759207i
\(525\) −4305.90 −0.0156223
\(526\) 193055.i 0.697764i
\(527\) 453510.i 1.63292i
\(528\) 1678.20i 0.00601971i
\(529\) 99783.9 0.356574
\(530\) 96223.8i 0.342556i
\(531\) −29841.3 89123.8i −0.105835 0.316086i
\(532\) −119499. −0.422223
\(533\) 79205.1i 0.278804i
\(534\) 50556.6 0.177294
\(535\) −330659. −1.15524
\(536\) 302801. 1.05397
\(537\) 44110.6i 0.152966i
\(538\) 251603. 0.869262
\(539\) 93730.4i 0.322629i
\(540\) 36706.3 0.125879
\(541\) 51022.3i 0.174327i 0.996194 + 0.0871637i \(0.0277803\pi\)
−0.996194 + 0.0871637i \(0.972220\pi\)
\(542\) 350967.i 1.19472i
\(543\) −330368. −1.12047
\(544\) 339180.i 1.14613i
\(545\) 468090.i 1.57593i
\(546\) 34708.7 0.116427
\(547\) 116201. 0.388362 0.194181 0.980966i \(-0.437795\pi\)
0.194181 + 0.980966i \(0.437795\pi\)
\(548\) 81320.3 0.270793
\(549\) 154125.i 0.511363i
\(550\) −5159.69 −0.0170568
\(551\) 590562. 1.94519
\(552\) 139852. 0.458977
\(553\) −151370. −0.494981
\(554\) 114886.i 0.374323i
\(555\) 346040.i 1.12342i
\(556\) −82814.9 −0.267892
\(557\) −428570. −1.38137 −0.690687 0.723154i \(-0.742692\pi\)
−0.690687 + 0.723154i \(0.742692\pi\)
\(558\) 90613.3 0.291020
\(559\) 315263. 1.00890
\(560\) −3270.19 −0.0104279
\(561\) 76333.4i 0.242543i
\(562\) 77145.4i 0.244251i
\(563\) 131577.i 0.415110i 0.978223 + 0.207555i \(0.0665506\pi\)
−0.978223 + 0.207555i \(0.933449\pi\)
\(564\) 126975.i 0.399172i
\(565\) 249759.i 0.782392i
\(566\) 31604.2 0.0986533
\(567\) −12728.0 −0.0395907
\(568\) 177291.i 0.549529i
\(569\) 399439.i 1.23375i −0.787063 0.616873i \(-0.788399\pi\)
0.787063 0.616873i \(-0.211601\pi\)
\(570\) 222233.i 0.684003i
\(571\) 131744.i 0.404072i 0.979378 + 0.202036i \(0.0647558\pi\)
−0.979378 + 0.202036i \(0.935244\pi\)
\(572\) −70993.9 −0.216985
\(573\) 187095.i 0.569839i
\(574\) 21364.8i 0.0648449i
\(575\) 20139.8i 0.0609143i
\(576\) −64649.4 −0.194859
\(577\) −160918. −0.483339 −0.241670 0.970359i \(-0.577695\pi\)
−0.241670 + 0.970359i \(0.577695\pi\)
\(578\) 59351.0i 0.177653i
\(579\) 38301.2 0.114250
\(580\) 227766. 0.677068
\(581\) 130229.i 0.385795i
\(582\) 74689.2 0.220502
\(583\) 68247.1i 0.200792i
\(584\) 299365. 0.877760
\(585\) 110180.i 0.321952i
\(586\) 67168.2i 0.195600i
\(587\) 171759.i 0.498474i −0.968443 0.249237i \(-0.919820\pi\)
0.968443 0.249237i \(-0.0801798\pi\)
\(588\) −109893. −0.317844
\(589\) 936442.i 2.69929i
\(590\) −208105. + 69679.9i −0.597832 + 0.200172i
\(591\) 326770. 0.935549
\(592\) 18548.9i 0.0529266i
\(593\) 457675. 1.30151 0.650755 0.759288i \(-0.274453\pi\)
0.650755 + 0.759288i \(0.274453\pi\)
\(594\) −15251.8 −0.0432262
\(595\) 148746. 0.420156
\(596\) 376731.i 1.06057i
\(597\) 128872. 0.361586
\(598\) 162342.i 0.453970i
\(599\) −450231. −1.25482 −0.627410 0.778689i \(-0.715885\pi\)
−0.627410 + 0.778689i \(0.715885\pi\)
\(600\) 15642.8i 0.0434521i
\(601\) 188572.i 0.522071i 0.965329 + 0.261035i \(0.0840639\pi\)
−0.965329 + 0.261035i \(0.915936\pi\)
\(602\) −85039.2 −0.234653
\(603\) 128896.i 0.354490i
\(604\) 104059.i 0.285237i
\(605\) 327819. 0.895620
\(606\) 182971. 0.498237
\(607\) 266272. 0.722682 0.361341 0.932434i \(-0.382319\pi\)
0.361341 + 0.932434i \(0.382319\pi\)
\(608\) 700365.i 1.89460i
\(609\) −78978.3 −0.212948
\(610\) 359885. 0.967173
\(611\) −381137. −1.02094
\(612\) −89495.8 −0.238946
\(613\) 331432.i 0.882010i 0.897505 + 0.441005i \(0.145378\pi\)
−0.897505 + 0.441005i \(0.854622\pi\)
\(614\) 62612.9i 0.166084i
\(615\) 67820.9 0.179314
\(616\) 49518.7 0.130499
\(617\) −341099. −0.896005 −0.448002 0.894032i \(-0.647864\pi\)
−0.448002 + 0.894032i \(0.647864\pi\)
\(618\) −2672.31 −0.00699697
\(619\) −101548. −0.265027 −0.132513 0.991181i \(-0.542305\pi\)
−0.132513 + 0.991181i \(0.542305\pi\)
\(620\) 361163.i 0.939551i
\(621\) 59532.0i 0.154372i
\(622\) 300807.i 0.777511i
\(623\) 69872.9i 0.180025i
\(624\) 5906.01i 0.0151679i
\(625\) −418036. −1.07017
\(626\) 31178.1 0.0795611
\(627\) 157619.i 0.400935i
\(628\) 110873.i 0.281130i
\(629\) 843701.i 2.13249i
\(630\) 29720.0i 0.0748804i
\(631\) −278409. −0.699238 −0.349619 0.936892i \(-0.613689\pi\)
−0.349619 + 0.936892i \(0.613689\pi\)
\(632\) 549906.i 1.37675i
\(633\) 90946.9i 0.226976i
\(634\) 331442.i 0.824574i
\(635\) −648915. −1.60931
\(636\) −80015.2 −0.197814
\(637\) 329861.i 0.812928i
\(638\) −94638.5 −0.232502
\(639\) −75469.1 −0.184828
\(640\) 277400.i 0.677246i
\(641\) 267843. 0.651874 0.325937 0.945391i \(-0.394320\pi\)
0.325937 + 0.945391i \(0.394320\pi\)
\(642\) 161082.i 0.390820i
\(643\) 247371. 0.598311 0.299155 0.954204i \(-0.403295\pi\)
0.299155 + 0.954204i \(0.403295\pi\)
\(644\) 74747.8i 0.180230i
\(645\) 269950.i 0.648880i
\(646\) 541838.i 1.29839i
\(647\) −66763.5 −0.159489 −0.0797445 0.996815i \(-0.525410\pi\)
−0.0797445 + 0.996815i \(0.525410\pi\)
\(648\) 46239.1i 0.110118i
\(649\) −147599. + 49420.7i −0.350425 + 0.117333i
\(650\) −18158.3 −0.0429781
\(651\) 125234.i 0.295502i
\(652\) 16745.2 0.0393909
\(653\) −585647. −1.37344 −0.686719 0.726923i \(-0.740950\pi\)
−0.686719 + 0.726923i \(0.740950\pi\)
\(654\) 228033. 0.533140
\(655\) 53579.2i 0.124886i
\(656\) 3635.42 0.00844786
\(657\) 127433.i 0.295225i
\(658\) 102808. 0.237452
\(659\) 34391.7i 0.0791922i −0.999216 0.0395961i \(-0.987393\pi\)
0.999216 0.0395961i \(-0.0126071\pi\)
\(660\) 60789.9i 0.139555i
\(661\) −151480. −0.346698 −0.173349 0.984860i \(-0.555459\pi\)
−0.173349 + 0.984860i \(0.555459\pi\)
\(662\) 372325.i 0.849585i
\(663\) 268636.i 0.611136i
\(664\) −473106. −1.07306
\(665\) −307142. −0.694537
\(666\) −168575. −0.380054
\(667\) 369401.i 0.830323i
\(668\) −57955.4 −0.129880
\(669\) 280813. 0.627430
\(670\) 300974. 0.670469
\(671\) 255250. 0.566918
\(672\) 93662.6i 0.207409i
\(673\) 355378.i 0.784622i −0.919833 0.392311i \(-0.871676\pi\)
0.919833 0.392311i \(-0.128324\pi\)
\(674\) 148179. 0.326187
\(675\) 6658.79 0.0146146
\(676\) 38314.9 0.0838444
\(677\) 670210. 1.46229 0.731145 0.682222i \(-0.238986\pi\)
0.731145 + 0.682222i \(0.238986\pi\)
\(678\) 121671. 0.264685
\(679\) 103226.i 0.223898i
\(680\) 540373.i 1.16863i
\(681\) 129345.i 0.278904i
\(682\) 150066.i 0.322637i
\(683\) 237295.i 0.508683i 0.967114 + 0.254341i \(0.0818587\pi\)
−0.967114 + 0.254341i \(0.918141\pi\)
\(684\) 184798. 0.394989
\(685\) 209012. 0.445442
\(686\) 190893.i 0.405641i
\(687\) 421125.i 0.892273i
\(688\) 14470.2i 0.0305701i
\(689\) 240179.i 0.505937i
\(690\) 139008. 0.291973
\(691\) 40265.6i 0.0843293i −0.999111 0.0421646i \(-0.986575\pi\)
0.999111 0.0421646i \(-0.0134254\pi\)
\(692\) 487690.i 1.01843i
\(693\) 21079.0i 0.0438919i
\(694\) −365345. −0.758551
\(695\) −212854. −0.440668
\(696\) 286918.i 0.592296i
\(697\) −165358. −0.340377
\(698\) −10036.8 −0.0206008
\(699\) 480456.i 0.983331i
\(700\) −8360.71 −0.0170627
\(701\) 55287.6i 0.112510i −0.998416 0.0562551i \(-0.982084\pi\)
0.998416 0.0562551i \(-0.0179160\pi\)
\(702\) −53674.8 −0.108917
\(703\) 1.74214e6i 3.52511i
\(704\) 107067.i 0.216028i
\(705\) 326356.i 0.656619i
\(706\) −307171. −0.616270
\(707\) 252879.i 0.505910i
\(708\) −57942.4 173051.i −0.115593 0.345228i
\(709\) 91346.8 0.181719 0.0908596 0.995864i \(-0.471039\pi\)
0.0908596 + 0.995864i \(0.471039\pi\)
\(710\) 176222.i 0.349577i
\(711\) 234083. 0.463053
\(712\) 253839. 0.500724
\(713\) −585752. −1.15222
\(714\) 72462.2i 0.142140i
\(715\) −182471. −0.356929
\(716\) 85649.0i 0.167069i
\(717\) −346855. −0.674698
\(718\) 444004.i 0.861267i
\(719\) 25854.5i 0.0500124i 0.999687 + 0.0250062i \(0.00796055\pi\)
−0.999687 + 0.0250062i \(0.992039\pi\)
\(720\) 5057.13 0.00975527
\(721\) 3693.33i 0.00710473i
\(722\) 801994.i 1.53850i
\(723\) −300785. −0.575412
\(724\) −641472. −1.22377
\(725\) 41318.4 0.0786081
\(726\) 159699.i 0.302990i
\(727\) 441000. 0.834391 0.417196 0.908817i \(-0.363013\pi\)
0.417196 + 0.908817i \(0.363013\pi\)
\(728\) 174269. 0.328819
\(729\) 19683.0 0.0370370
\(730\) 297559. 0.558377
\(731\) 658181.i 1.23172i
\(732\) 299263.i 0.558510i
\(733\) 426201. 0.793244 0.396622 0.917982i \(-0.370182\pi\)
0.396622 + 0.917982i \(0.370182\pi\)
\(734\) −20666.2 −0.0383591
\(735\) −282450. −0.522837
\(736\) 438084. 0.808727
\(737\) 213467. 0.393002
\(738\) 33039.3i 0.0606622i
\(739\) 91383.8i 0.167333i 0.996494 + 0.0836663i \(0.0266630\pi\)
−0.996494 + 0.0836663i \(0.973337\pi\)
\(740\) 671902.i 1.22699i
\(741\) 554702.i 1.01024i
\(742\) 64786.0i 0.117672i
\(743\) 309686. 0.560975 0.280488 0.959858i \(-0.409504\pi\)
0.280488 + 0.959858i \(0.409504\pi\)
\(744\) 454959. 0.821914
\(745\) 968286.i 1.74458i
\(746\) 200048.i 0.359464i
\(747\) 201391.i 0.360910i
\(748\) 148215.i 0.264905i
\(749\) 222627. 0.396839
\(750\) 189198.i 0.336351i
\(751\) 218166.i 0.386819i −0.981118 0.193409i \(-0.938045\pi\)
0.981118 0.193409i \(-0.0619545\pi\)
\(752\) 17493.7i 0.0309348i
\(753\) −7704.02 −0.0135871
\(754\) −333057. −0.585835
\(755\) 267457.i 0.469201i
\(756\) −24713.8 −0.0432410
\(757\) 48000.1 0.0837627 0.0418813 0.999123i \(-0.486665\pi\)
0.0418813 + 0.999123i \(0.486665\pi\)
\(758\) 6411.81i 0.0111594i
\(759\) 98592.0 0.171143
\(760\) 1.11580e6i 1.93179i
\(761\) 236294. 0.408021 0.204011 0.978969i \(-0.434602\pi\)
0.204011 + 0.978969i \(0.434602\pi\)
\(762\) 316122.i 0.544434i
\(763\) 315158.i 0.541351i
\(764\) 363279.i 0.622378i
\(765\) −230025. −0.393054
\(766\) 110470.i 0.188272i
\(767\) −519440. + 173924.i −0.882967 + 0.295644i
\(768\) −334205. −0.566619
\(769\) 110994.i 0.187692i 0.995587 + 0.0938459i \(0.0299161\pi\)
−0.995587 + 0.0938459i \(0.970084\pi\)
\(770\) 49219.9 0.0830155
\(771\) −330451. −0.555902
\(772\) 74368.9 0.124783
\(773\) 164246.i 0.274875i −0.990510 0.137437i \(-0.956113\pi\)
0.990510 0.137437i \(-0.0438866\pi\)
\(774\) 131508. 0.219517
\(775\) 65517.7i 0.109082i
\(776\) 375006. 0.622752
\(777\) 232983.i 0.385907i
\(778\) 89491.8i 0.147851i
\(779\) 341444. 0.562659
\(780\) 213935.i 0.351636i
\(781\) 124986.i 0.204908i
\(782\) −338924. −0.554228
\(783\) 122135. 0.199212
\(784\) −15140.2 −0.0246320
\(785\) 284970.i 0.462445i
\(786\) −26101.4 −0.0422492
\(787\) 909477. 1.46839 0.734196 0.678937i \(-0.237559\pi\)
0.734196 + 0.678937i \(0.237559\pi\)
\(788\) 634484. 1.02181
\(789\) −412613.