Properties

Label 177.5.c.a.58.1
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 58.1
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.40

$q$-expansion

\(f(q)\) \(=\) \(q-7.81880i q^{2} +5.19615 q^{3} -45.1337 q^{4} +21.3172 q^{5} -40.6277i q^{6} -30.7266 q^{7} +227.790i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-7.81880i q^{2} +5.19615 q^{3} -45.1337 q^{4} +21.3172 q^{5} -40.6277i q^{6} -30.7266 q^{7} +227.790i q^{8} +27.0000 q^{9} -166.675i q^{10} +207.480i q^{11} -234.521 q^{12} +206.020i q^{13} +240.245i q^{14} +110.768 q^{15} +1058.91 q^{16} -391.490 q^{17} -211.108i q^{18} -321.627 q^{19} -962.125 q^{20} -159.660 q^{21} +1622.24 q^{22} +287.967i q^{23} +1183.63i q^{24} -170.575 q^{25} +1610.83 q^{26} +140.296 q^{27} +1386.80 q^{28} +1020.53 q^{29} -866.070i q^{30} +560.747i q^{31} -4634.75i q^{32} +1078.10i q^{33} +3060.98i q^{34} -655.006 q^{35} -1218.61 q^{36} -1257.89i q^{37} +2514.74i q^{38} +1070.51i q^{39} +4855.86i q^{40} -1524.79 q^{41} +1248.35i q^{42} -2155.53i q^{43} -9364.31i q^{44} +575.565 q^{45} +2251.55 q^{46} -245.854i q^{47} +5502.25 q^{48} -1456.88 q^{49} +1333.69i q^{50} -2034.24 q^{51} -9298.43i q^{52} -1142.98 q^{53} -1096.95i q^{54} +4422.89i q^{55} -6999.22i q^{56} -1671.22 q^{57} -7979.34i q^{58} +(-3465.52 - 327.946i) q^{59} -4999.35 q^{60} -518.066i q^{61} +4384.37 q^{62} -829.618 q^{63} -19295.6 q^{64} +4391.77i q^{65} +8429.41 q^{66} +2495.71i q^{67} +17669.4 q^{68} +1496.32i q^{69} +5121.36i q^{70} +9311.79 q^{71} +6150.34i q^{72} +8005.70i q^{73} -9835.18 q^{74} -886.336 q^{75} +14516.2 q^{76} -6375.14i q^{77} +8370.11 q^{78} +5130.68 q^{79} +22573.0 q^{80} +729.000 q^{81} +11922.1i q^{82} +13428.1i q^{83} +7206.04 q^{84} -8345.49 q^{85} -16853.7 q^{86} +5302.84 q^{87} -47261.8 q^{88} -3141.70i q^{89} -4500.23i q^{90} -6330.29i q^{91} -12997.0i q^{92} +2913.73i q^{93} -1922.28 q^{94} -6856.20 q^{95} -24082.9i q^{96} +5322.39i q^{97} +11391.0i q^{98} +5601.95i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.81880i 1.95470i −0.211629 0.977350i \(-0.567877\pi\)
0.211629 0.977350i \(-0.432123\pi\)
\(3\) 5.19615 0.577350
\(4\) −45.1337 −2.82085
\(5\) 21.3172 0.852690 0.426345 0.904561i \(-0.359801\pi\)
0.426345 + 0.904561i \(0.359801\pi\)
\(6\) 40.6277i 1.12855i
\(7\) −30.7266 −0.627073 −0.313537 0.949576i \(-0.601514\pi\)
−0.313537 + 0.949576i \(0.601514\pi\)
\(8\) 227.790i 3.55922i
\(9\) 27.0000 0.333333
\(10\) 166.675i 1.66675i
\(11\) 207.480i 1.71471i 0.514728 + 0.857353i \(0.327893\pi\)
−0.514728 + 0.857353i \(0.672107\pi\)
\(12\) −234.521 −1.62862
\(13\) 206.020i 1.21905i 0.792766 + 0.609526i \(0.208640\pi\)
−0.792766 + 0.609526i \(0.791360\pi\)
\(14\) 240.245i 1.22574i
\(15\) 110.768 0.492301
\(16\) 1058.91 4.13636
\(17\) −391.490 −1.35464 −0.677318 0.735690i \(-0.736858\pi\)
−0.677318 + 0.735690i \(0.736858\pi\)
\(18\) 211.108i 0.651567i
\(19\) −321.627 −0.890934 −0.445467 0.895298i \(-0.646962\pi\)
−0.445467 + 0.895298i \(0.646962\pi\)
\(20\) −962.125 −2.40531
\(21\) −159.660 −0.362041
\(22\) 1622.24 3.35174
\(23\) 287.967i 0.544360i 0.962246 + 0.272180i \(0.0877447\pi\)
−0.962246 + 0.272180i \(0.912255\pi\)
\(24\) 1183.63i 2.05492i
\(25\) −170.575 −0.272921
\(26\) 1610.83 2.38288
\(27\) 140.296 0.192450
\(28\) 1386.80 1.76888
\(29\) 1020.53 1.21347 0.606737 0.794902i \(-0.292478\pi\)
0.606737 + 0.794902i \(0.292478\pi\)
\(30\) 866.070i 0.962300i
\(31\) 560.747i 0.583504i 0.956494 + 0.291752i \(0.0942381\pi\)
−0.956494 + 0.291752i \(0.905762\pi\)
\(32\) 4634.75i 4.52612i
\(33\) 1078.10i 0.989987i
\(34\) 3060.98i 2.64791i
\(35\) −655.006 −0.534699
\(36\) −1218.61 −0.940284
\(37\) 1257.89i 0.918838i −0.888220 0.459419i \(-0.848058\pi\)
0.888220 0.459419i \(-0.151942\pi\)
\(38\) 2514.74i 1.74151i
\(39\) 1070.51i 0.703820i
\(40\) 4855.86i 3.03491i
\(41\) −1524.79 −0.907076 −0.453538 0.891237i \(-0.649838\pi\)
−0.453538 + 0.891237i \(0.649838\pi\)
\(42\) 1248.35i 0.707681i
\(43\) 2155.53i 1.16578i −0.812550 0.582892i \(-0.801921\pi\)
0.812550 0.582892i \(-0.198079\pi\)
\(44\) 9364.31i 4.83694i
\(45\) 575.565 0.284230
\(46\) 2251.55 1.06406
\(47\) 245.854i 0.111296i −0.998450 0.0556482i \(-0.982277\pi\)
0.998450 0.0556482i \(-0.0177225\pi\)
\(48\) 5502.25 2.38813
\(49\) −1456.88 −0.606779
\(50\) 1333.69i 0.533478i
\(51\) −2034.24 −0.782100
\(52\) 9298.43i 3.43877i
\(53\) −1142.98 −0.406899 −0.203449 0.979085i \(-0.565215\pi\)
−0.203449 + 0.979085i \(0.565215\pi\)
\(54\) 1096.95i 0.376182i
\(55\) 4422.89i 1.46211i
\(56\) 6999.22i 2.23189i
\(57\) −1671.22 −0.514381
\(58\) 7979.34i 2.37198i
\(59\) −3465.52 327.946i −0.995552 0.0942101i
\(60\) −4999.35 −1.38871
\(61\) 518.066i 0.139228i −0.997574 0.0696138i \(-0.977823\pi\)
0.997574 0.0696138i \(-0.0221767\pi\)
\(62\) 4384.37 1.14057
\(63\) −829.618 −0.209024
\(64\) −19295.6 −4.71085
\(65\) 4391.77i 1.03947i
\(66\) 8429.41 1.93513
\(67\) 2495.71i 0.555961i 0.960587 + 0.277980i \(0.0896650\pi\)
−0.960587 + 0.277980i \(0.910335\pi\)
\(68\) 17669.4 3.82123
\(69\) 1496.32i 0.314287i
\(70\) 5121.36i 1.04518i
\(71\) 9311.79 1.84721 0.923606 0.383344i \(-0.125228\pi\)
0.923606 + 0.383344i \(0.125228\pi\)
\(72\) 6150.34i 1.18641i
\(73\) 8005.70i 1.50229i 0.660138 + 0.751144i \(0.270498\pi\)
−0.660138 + 0.751144i \(0.729502\pi\)
\(74\) −9835.18 −1.79605
\(75\) −886.336 −0.157571
\(76\) 14516.2 2.51319
\(77\) 6375.14i 1.07525i
\(78\) 8370.11 1.37576
\(79\) 5130.68 0.822093 0.411047 0.911614i \(-0.365163\pi\)
0.411047 + 0.911614i \(0.365163\pi\)
\(80\) 22573.0 3.52703
\(81\) 729.000 0.111111
\(82\) 11922.1i 1.77306i
\(83\) 13428.1i 1.94921i 0.223939 + 0.974603i \(0.428108\pi\)
−0.223939 + 0.974603i \(0.571892\pi\)
\(84\) 7206.04 1.02126
\(85\) −8345.49 −1.15508
\(86\) −16853.7 −2.27876
\(87\) 5302.84 0.700600
\(88\) −47261.8 −6.10302
\(89\) 3141.70i 0.396630i −0.980138 0.198315i \(-0.936453\pi\)
0.980138 0.198315i \(-0.0635468\pi\)
\(90\) 4500.23i 0.555584i
\(91\) 6330.29i 0.764435i
\(92\) 12997.0i 1.53556i
\(93\) 2913.73i 0.336886i
\(94\) −1922.28 −0.217551
\(95\) −6856.20 −0.759690
\(96\) 24082.9i 2.61316i
\(97\) 5322.39i 0.565670i 0.959169 + 0.282835i \(0.0912749\pi\)
−0.959169 + 0.282835i \(0.908725\pi\)
\(98\) 11391.0i 1.18607i
\(99\) 5601.95i 0.571569i
\(100\) 7698.69 0.769869
\(101\) 6022.91i 0.590424i −0.955432 0.295212i \(-0.904610\pi\)
0.955432 0.295212i \(-0.0953902\pi\)
\(102\) 15905.3i 1.52877i
\(103\) 3738.09i 0.352350i −0.984359 0.176175i \(-0.943627\pi\)
0.984359 0.176175i \(-0.0563725\pi\)
\(104\) −46929.3 −4.33888
\(105\) −3403.51 −0.308708
\(106\) 8936.72i 0.795365i
\(107\) 10702.1 0.934764 0.467382 0.884056i \(-0.345197\pi\)
0.467382 + 0.884056i \(0.345197\pi\)
\(108\) −6332.08 −0.542873
\(109\) 21298.0i 1.79261i 0.443442 + 0.896303i \(0.353757\pi\)
−0.443442 + 0.896303i \(0.646243\pi\)
\(110\) 34581.7 2.85799
\(111\) 6536.18i 0.530491i
\(112\) −32536.6 −2.59380
\(113\) 16771.3i 1.31344i −0.754135 0.656720i \(-0.771943\pi\)
0.754135 0.656720i \(-0.228057\pi\)
\(114\) 13067.0i 1.00546i
\(115\) 6138.65i 0.464170i
\(116\) −46060.4 −3.42303
\(117\) 5562.54i 0.406351i
\(118\) −2564.14 + 27096.2i −0.184153 + 1.94601i
\(119\) 12029.2 0.849456
\(120\) 25231.8i 1.75221i
\(121\) −28406.8 −1.94022
\(122\) −4050.65 −0.272148
\(123\) −7923.06 −0.523700
\(124\) 25308.6i 1.64598i
\(125\) −16959.5 −1.08541
\(126\) 6486.62i 0.408580i
\(127\) 27235.6 1.68861 0.844305 0.535863i \(-0.180014\pi\)
0.844305 + 0.535863i \(0.180014\pi\)
\(128\) 76712.8i 4.68218i
\(129\) 11200.5i 0.673066i
\(130\) 34338.4 2.03186
\(131\) 1718.72i 0.100153i 0.998745 + 0.0500763i \(0.0159465\pi\)
−0.998745 + 0.0500763i \(0.984054\pi\)
\(132\) 48658.4i 2.79261i
\(133\) 9882.51 0.558681
\(134\) 19513.4 1.08674
\(135\) 2990.73 0.164100
\(136\) 89177.6i 4.82145i
\(137\) 8888.26 0.473560 0.236780 0.971563i \(-0.423908\pi\)
0.236780 + 0.971563i \(0.423908\pi\)
\(138\) 11699.4 0.614336
\(139\) 2771.10 0.143424 0.0717121 0.997425i \(-0.477154\pi\)
0.0717121 + 0.997425i \(0.477154\pi\)
\(140\) 29562.8 1.50831
\(141\) 1277.49i 0.0642570i
\(142\) 72807.1i 3.61074i
\(143\) −42744.9 −2.09032
\(144\) 28590.5 1.37879
\(145\) 21754.9 1.03472
\(146\) 62594.9 2.93652
\(147\) −7570.15 −0.350324
\(148\) 56773.1i 2.59191i
\(149\) 8123.08i 0.365888i 0.983123 + 0.182944i \(0.0585627\pi\)
−0.983123 + 0.182944i \(0.941437\pi\)
\(150\) 6930.08i 0.308004i
\(151\) 2438.11i 0.106930i −0.998570 0.0534651i \(-0.982973\pi\)
0.998570 0.0534651i \(-0.0170266\pi\)
\(152\) 73263.5i 3.17103i
\(153\) −10570.2 −0.451546
\(154\) −49845.9 −2.10179
\(155\) 11953.6i 0.497547i
\(156\) 48316.1i 1.98537i
\(157\) 13811.6i 0.560332i 0.959952 + 0.280166i \(0.0903895\pi\)
−0.959952 + 0.280166i \(0.909611\pi\)
\(158\) 40115.8i 1.60695i
\(159\) −5939.09 −0.234923
\(160\) 98800.0i 3.85938i
\(161\) 8848.23i 0.341354i
\(162\) 5699.91i 0.217189i
\(163\) −14070.7 −0.529593 −0.264796 0.964304i \(-0.585305\pi\)
−0.264796 + 0.964304i \(0.585305\pi\)
\(164\) 68819.5 2.55873
\(165\) 22982.0i 0.844151i
\(166\) 104991. 3.81011
\(167\) −37863.4 −1.35765 −0.678823 0.734302i \(-0.737510\pi\)
−0.678823 + 0.734302i \(0.737510\pi\)
\(168\) 36369.0i 1.28858i
\(169\) −13883.2 −0.486089
\(170\) 65251.7i 2.25784i
\(171\) −8683.93 −0.296978
\(172\) 97287.2i 3.28851i
\(173\) 13221.6i 0.441765i 0.975300 + 0.220883i \(0.0708938\pi\)
−0.975300 + 0.220883i \(0.929106\pi\)
\(174\) 41461.9i 1.36946i
\(175\) 5241.20 0.171141
\(176\) 219702.i 7.09264i
\(177\) −18007.4 1704.05i −0.574782 0.0543923i
\(178\) −24564.3 −0.775292
\(179\) 398.257i 0.0124296i −0.999981 0.00621480i \(-0.998022\pi\)
0.999981 0.00621480i \(-0.00197825\pi\)
\(180\) −25977.4 −0.801771
\(181\) 46013.5 1.40452 0.702260 0.711920i \(-0.252174\pi\)
0.702260 + 0.711920i \(0.252174\pi\)
\(182\) −49495.3 −1.49424
\(183\) 2691.95i 0.0803831i
\(184\) −65596.0 −1.93750
\(185\) 26814.7i 0.783483i
\(186\) 22781.8 0.658511
\(187\) 81226.2i 2.32281i
\(188\) 11096.3i 0.313951i
\(189\) −4310.82 −0.120680
\(190\) 53607.3i 1.48497i
\(191\) 60179.4i 1.64961i −0.565418 0.824804i \(-0.691285\pi\)
0.565418 0.824804i \(-0.308715\pi\)
\(192\) −100263. −2.71981
\(193\) −31955.1 −0.857879 −0.428939 0.903333i \(-0.641113\pi\)
−0.428939 + 0.903333i \(0.641113\pi\)
\(194\) 41614.7 1.10572
\(195\) 22820.3i 0.600140i
\(196\) 65754.2 1.71163
\(197\) −34993.6 −0.901689 −0.450844 0.892603i \(-0.648877\pi\)
−0.450844 + 0.892603i \(0.648877\pi\)
\(198\) 43800.5 1.11725
\(199\) 3731.67 0.0942317 0.0471159 0.998889i \(-0.484997\pi\)
0.0471159 + 0.998889i \(0.484997\pi\)
\(200\) 38855.4i 0.971385i
\(201\) 12968.1i 0.320984i
\(202\) −47092.0 −1.15410
\(203\) −31357.5 −0.760938
\(204\) 91812.8 2.20619
\(205\) −32504.4 −0.773454
\(206\) −29227.4 −0.688740
\(207\) 7775.10i 0.181453i
\(208\) 218156.i 5.04244i
\(209\) 66731.1i 1.52769i
\(210\) 26611.4i 0.603433i
\(211\) 13733.7i 0.308476i 0.988034 + 0.154238i \(0.0492923\pi\)
−0.988034 + 0.154238i \(0.950708\pi\)
\(212\) 51586.8 1.14780
\(213\) 48385.5 1.06649
\(214\) 83677.7i 1.82718i
\(215\) 45950.0i 0.994052i
\(216\) 31958.1i 0.684973i
\(217\) 17229.8i 0.365899i
\(218\) 166524. 3.50401
\(219\) 41598.8i 0.867347i
\(220\) 199621.i 4.12441i
\(221\) 80654.7i 1.65137i
\(222\) −51105.1 −1.03695
\(223\) −62492.9 −1.25667 −0.628335 0.777943i \(-0.716263\pi\)
−0.628335 + 0.777943i \(0.716263\pi\)
\(224\) 142410.i 2.83821i
\(225\) −4605.54 −0.0909735
\(226\) −131132. −2.56738
\(227\) 15746.2i 0.305579i 0.988259 + 0.152790i \(0.0488257\pi\)
−0.988259 + 0.152790i \(0.951174\pi\)
\(228\) 75428.4 1.45099
\(229\) 50347.4i 0.960078i 0.877247 + 0.480039i \(0.159377\pi\)
−0.877247 + 0.480039i \(0.840623\pi\)
\(230\) 47996.9 0.907314
\(231\) 33126.2i 0.620794i
\(232\) 232467.i 4.31903i
\(233\) 54304.7i 1.00029i −0.865942 0.500144i \(-0.833280\pi\)
0.865942 0.500144i \(-0.166720\pi\)
\(234\) 43492.4 0.794294
\(235\) 5240.92i 0.0949012i
\(236\) 156411. + 14801.4i 2.80831 + 0.265753i
\(237\) 26659.8 0.474636
\(238\) 94053.6i 1.66043i
\(239\) 44247.5 0.774628 0.387314 0.921948i \(-0.373403\pi\)
0.387314 + 0.921948i \(0.373403\pi\)
\(240\) 117293. 2.03633
\(241\) 93615.1 1.61180 0.805902 0.592050i \(-0.201681\pi\)
0.805902 + 0.592050i \(0.201681\pi\)
\(242\) 222107.i 3.79255i
\(243\) 3788.00 0.0641500
\(244\) 23382.2i 0.392741i
\(245\) −31056.6 −0.517394
\(246\) 61948.8i 1.02368i
\(247\) 66261.6i 1.08610i
\(248\) −127733. −2.07682
\(249\) 69774.4i 1.12537i
\(250\) 132603.i 2.12164i
\(251\) −31025.2 −0.492455 −0.246228 0.969212i \(-0.579191\pi\)
−0.246228 + 0.969212i \(0.579191\pi\)
\(252\) 37443.7 0.589627
\(253\) −59747.2 −0.933419
\(254\) 212950.i 3.30073i
\(255\) −43364.4 −0.666888
\(256\) 291072. 4.44141
\(257\) −51107.2 −0.773777 −0.386889 0.922126i \(-0.626450\pi\)
−0.386889 + 0.922126i \(0.626450\pi\)
\(258\) −87574.4 −1.31564
\(259\) 38650.6i 0.576179i
\(260\) 198217.i 2.93220i
\(261\) 27554.4 0.404492
\(262\) 13438.3 0.195768
\(263\) 83386.8 1.20555 0.602776 0.797911i \(-0.294061\pi\)
0.602776 + 0.797911i \(0.294061\pi\)
\(264\) −245580. −3.52358
\(265\) −24365.1 −0.346958
\(266\) 77269.3i 1.09205i
\(267\) 16324.8i 0.228994i
\(268\) 112640.i 1.56828i
\(269\) 55398.4i 0.765584i 0.923835 + 0.382792i \(0.125037\pi\)
−0.923835 + 0.382792i \(0.874963\pi\)
\(270\) 23383.9i 0.320767i
\(271\) 33799.6 0.460228 0.230114 0.973164i \(-0.426090\pi\)
0.230114 + 0.973164i \(0.426090\pi\)
\(272\) −414552. −5.60326
\(273\) 32893.1i 0.441347i
\(274\) 69495.5i 0.925669i
\(275\) 35390.9i 0.467979i
\(276\) 67534.3i 0.886557i
\(277\) 71567.4 0.932730 0.466365 0.884592i \(-0.345563\pi\)
0.466365 + 0.884592i \(0.345563\pi\)
\(278\) 21666.7i 0.280351i
\(279\) 15140.2i 0.194501i
\(280\) 149204.i 1.90311i
\(281\) 121564. 1.53955 0.769774 0.638316i \(-0.220369\pi\)
0.769774 + 0.638316i \(0.220369\pi\)
\(282\) −9988.46 −0.125603
\(283\) 142151.i 1.77491i 0.460890 + 0.887457i \(0.347530\pi\)
−0.460890 + 0.887457i \(0.652470\pi\)
\(284\) −420275. −5.21071
\(285\) −35625.9 −0.438607
\(286\) 334214.i 4.08594i
\(287\) 46851.7 0.568803
\(288\) 125138.i 1.50871i
\(289\) 69743.4 0.835041
\(290\) 170097.i 2.02256i
\(291\) 27655.9i 0.326590i
\(292\) 361326.i 4.23774i
\(293\) −96135.1 −1.11982 −0.559908 0.828555i \(-0.689164\pi\)
−0.559908 + 0.828555i \(0.689164\pi\)
\(294\) 59189.5i 0.684779i
\(295\) −73875.3 6990.89i −0.848897 0.0803320i
\(296\) 286535. 3.27035
\(297\) 29108.6i 0.329996i
\(298\) 63512.8 0.715202
\(299\) −59326.9 −0.663604
\(300\) 40003.6 0.444484
\(301\) 66232.2i 0.731032i
\(302\) −19063.1 −0.209016
\(303\) 31296.0i 0.340881i
\(304\) −340574. −3.68522
\(305\) 11043.7i 0.118718i
\(306\) 82646.5i 0.882636i
\(307\) 35837.3 0.380240 0.190120 0.981761i \(-0.439112\pi\)
0.190120 + 0.981761i \(0.439112\pi\)
\(308\) 287733.i 3.03311i
\(309\) 19423.7i 0.203430i
\(310\) 93462.6 0.972556
\(311\) −55265.8 −0.571394 −0.285697 0.958320i \(-0.592225\pi\)
−0.285697 + 0.958320i \(0.592225\pi\)
\(312\) −243852. −2.50505
\(313\) 96714.2i 0.987192i −0.869691 0.493596i \(-0.835682\pi\)
0.869691 0.493596i \(-0.164318\pi\)
\(314\) 107990. 1.09528
\(315\) −17685.2 −0.178233
\(316\) −231566. −2.31900
\(317\) −132005. −1.31363 −0.656813 0.754053i \(-0.728096\pi\)
−0.656813 + 0.754053i \(0.728096\pi\)
\(318\) 46436.5i 0.459204i
\(319\) 211740.i 2.08075i
\(320\) −411330. −4.01689
\(321\) 55609.8 0.539686
\(322\) −69182.6 −0.667245
\(323\) 125914. 1.20689
\(324\) −32902.4 −0.313428
\(325\) 35141.9i 0.332705i
\(326\) 110016.i 1.03519i
\(327\) 110667.i 1.03496i
\(328\) 347333.i 3.22848i
\(329\) 7554.24i 0.0697909i
\(330\) 179692. 1.65006
\(331\) 53983.3 0.492724 0.246362 0.969178i \(-0.420765\pi\)
0.246362 + 0.969178i \(0.420765\pi\)
\(332\) 606058.i 5.49842i
\(333\) 33963.0i 0.306279i
\(334\) 296046.i 2.65379i
\(335\) 53201.6i 0.474062i
\(336\) −169065. −1.49753
\(337\) 87020.3i 0.766233i −0.923700 0.383116i \(-0.874851\pi\)
0.923700 0.383116i \(-0.125149\pi\)
\(338\) 108550.i 0.950158i
\(339\) 87146.3i 0.758315i
\(340\) 376662. 3.25832
\(341\) −116344. −1.00054
\(342\) 67897.9i 0.580503i
\(343\) 118539. 1.00757
\(344\) 491010. 4.14928
\(345\) 31897.4i 0.267989i
\(346\) 103377. 0.863519
\(347\) 74094.0i 0.615353i −0.951491 0.307677i \(-0.900449\pi\)
0.951491 0.307677i \(-0.0995515\pi\)
\(348\) −239337. −1.97629
\(349\) 27934.6i 0.229347i −0.993403 0.114673i \(-0.963418\pi\)
0.993403 0.114673i \(-0.0365821\pi\)
\(350\) 40979.9i 0.334530i
\(351\) 28903.8i 0.234607i
\(352\) 961615. 7.76097
\(353\) 140969.i 1.13129i −0.824648 0.565647i \(-0.808627\pi\)
0.824648 0.565647i \(-0.191373\pi\)
\(354\) −13323.7 + 140796.i −0.106321 + 1.12353i
\(355\) 198502. 1.57510
\(356\) 141797.i 1.11883i
\(357\) 62505.3 0.490434
\(358\) −3113.89 −0.0242961
\(359\) −29736.8 −0.230731 −0.115365 0.993323i \(-0.536804\pi\)
−0.115365 + 0.993323i \(0.536804\pi\)
\(360\) 131108.i 1.01164i
\(361\) −26877.0 −0.206237
\(362\) 359770.i 2.74542i
\(363\) −147606. −1.12019
\(364\) 285709.i 2.15636i
\(365\) 170659.i 1.28099i
\(366\) −21047.8 −0.157125
\(367\) 52026.5i 0.386272i 0.981172 + 0.193136i \(0.0618658\pi\)
−0.981172 + 0.193136i \(0.938134\pi\)
\(368\) 304930.i 2.25167i
\(369\) −41169.4 −0.302359
\(370\) −209659. −1.53148
\(371\) 35119.8 0.255155
\(372\) 131507.i 0.950306i
\(373\) 70424.5 0.506181 0.253091 0.967443i \(-0.418553\pi\)
0.253091 + 0.967443i \(0.418553\pi\)
\(374\) −635091. −4.54039
\(375\) −88124.0 −0.626659
\(376\) 56003.0 0.396128
\(377\) 210250.i 1.47929i
\(378\) 33705.5i 0.235894i
\(379\) −39937.6 −0.278038 −0.139019 0.990290i \(-0.544395\pi\)
−0.139019 + 0.990290i \(0.544395\pi\)
\(380\) 309445. 2.14297
\(381\) 141520. 0.974919
\(382\) −470531. −3.22449
\(383\) 155977. 1.06332 0.531659 0.846959i \(-0.321569\pi\)
0.531659 + 0.846959i \(0.321569\pi\)
\(384\) 398612.i 2.70326i
\(385\) 135900.i 0.916852i
\(386\) 249851.i 1.67690i
\(387\) 58199.4i 0.388595i
\(388\) 240219.i 1.59567i
\(389\) −184572. −1.21974 −0.609870 0.792501i \(-0.708778\pi\)
−0.609870 + 0.792501i \(0.708778\pi\)
\(390\) 178428. 1.17309
\(391\) 112736.i 0.737411i
\(392\) 331862.i 2.15966i
\(393\) 8930.73i 0.0578232i
\(394\) 273608.i 1.76253i
\(395\) 109372. 0.700990
\(396\) 252836.i 1.61231i
\(397\) 216054.i 1.37082i 0.728155 + 0.685412i \(0.240378\pi\)
−0.728155 + 0.685412i \(0.759622\pi\)
\(398\) 29177.2i 0.184195i
\(399\) 51351.0 0.322555
\(400\) −180624. −1.12890
\(401\) 186079.i 1.15720i 0.815611 + 0.578601i \(0.196401\pi\)
−0.815611 + 0.578601i \(0.803599\pi\)
\(402\) 101395. 0.627428
\(403\) −115525. −0.711321
\(404\) 271836.i 1.66550i
\(405\) 15540.3 0.0947433
\(406\) 245178.i 1.48741i
\(407\) 260986. 1.57554
\(408\) 463380.i 2.78367i
\(409\) 142032.i 0.849064i 0.905413 + 0.424532i \(0.139561\pi\)
−0.905413 + 0.424532i \(0.860439\pi\)
\(410\) 254145.i 1.51187i
\(411\) 46184.7 0.273410
\(412\) 168713.i 0.993929i
\(413\) 106484. + 10076.6i 0.624284 + 0.0590767i
\(414\) 60792.0 0.354687
\(415\) 286250.i 1.66207i
\(416\) 954850. 5.51758
\(417\) 14399.0 0.0828060
\(418\) −521757. −2.98618
\(419\) 305281.i 1.73889i −0.494032 0.869444i \(-0.664477\pi\)
0.494032 0.869444i \(-0.335523\pi\)
\(420\) 153613. 0.870821
\(421\) 40020.9i 0.225799i 0.993606 + 0.112900i \(0.0360139\pi\)
−0.993606 + 0.112900i \(0.963986\pi\)
\(422\) 107381. 0.602978
\(423\) 6638.05i 0.0370988i
\(424\) 260359.i 1.44824i
\(425\) 66778.6 0.369708
\(426\) 378317.i 2.08466i
\(427\) 15918.4i 0.0873059i
\(428\) −483025. −2.63683
\(429\) −222109. −1.20685
\(430\) −359274. −1.94307
\(431\) 199954.i 1.07641i −0.842815 0.538203i \(-0.819103\pi\)
0.842815 0.538203i \(-0.180897\pi\)
\(432\) 148561. 0.796043
\(433\) −173422. −0.924972 −0.462486 0.886627i \(-0.653042\pi\)
−0.462486 + 0.886627i \(0.653042\pi\)
\(434\) −134717. −0.715224
\(435\) 113042. 0.597394
\(436\) 961254.i 5.05668i
\(437\) 92617.9i 0.484989i
\(438\) 325253. 1.69540
\(439\) 236050. 1.22483 0.612415 0.790536i \(-0.290198\pi\)
0.612415 + 0.790536i \(0.290198\pi\)
\(440\) −1.00749e6 −5.20398
\(441\) −39335.7 −0.202260
\(442\) −630623. −3.22794
\(443\) 390579.i 1.99022i 0.0987629 + 0.995111i \(0.468511\pi\)
−0.0987629 + 0.995111i \(0.531489\pi\)
\(444\) 295002.i 1.49644i
\(445\) 66972.4i 0.338202i
\(446\) 488620.i 2.45641i
\(447\) 42208.8i 0.211246i
\(448\) 592889. 2.95405
\(449\) 297658. 1.47647 0.738236 0.674543i \(-0.235659\pi\)
0.738236 + 0.674543i \(0.235659\pi\)
\(450\) 36009.8i 0.177826i
\(451\) 316364.i 1.55537i
\(452\) 756951.i 3.70502i
\(453\) 12668.8i 0.0617361i
\(454\) 123116. 0.597316
\(455\) 134944.i 0.651826i
\(456\) 380688.i 1.83080i
\(457\) 138561.i 0.663449i 0.943376 + 0.331725i \(0.107630\pi\)
−0.943376 + 0.331725i \(0.892370\pi\)
\(458\) 393657. 1.87666
\(459\) −54924.5 −0.260700
\(460\) 277060.i 1.30936i
\(461\) −249929. −1.17602 −0.588010 0.808853i \(-0.700089\pi\)
−0.588010 + 0.808853i \(0.700089\pi\)
\(462\) −259007. −1.21347
\(463\) 101021.i 0.471248i −0.971844 0.235624i \(-0.924287\pi\)
0.971844 0.235624i \(-0.0757134\pi\)
\(464\) 1.08065e6 5.01937
\(465\) 62112.6i 0.287259i
\(466\) −424597. −1.95526
\(467\) 290164.i 1.33048i 0.746628 + 0.665242i \(0.231672\pi\)
−0.746628 + 0.665242i \(0.768328\pi\)
\(468\) 251058.i 1.14626i
\(469\) 76684.6i 0.348628i
\(470\) −40977.7 −0.185503
\(471\) 71767.3i 0.323508i
\(472\) 74702.8 789411.i 0.335315 3.54339i
\(473\) 447229. 1.99898
\(474\) 208448.i 0.927771i
\(475\) 54861.7 0.243154
\(476\) −542920. −2.39619
\(477\) −30860.4 −0.135633
\(478\) 345963.i 1.51417i
\(479\) −90383.7 −0.393930 −0.196965 0.980411i \(-0.563109\pi\)
−0.196965 + 0.980411i \(0.563109\pi\)
\(480\) 513380.i 2.22821i
\(481\) 259150. 1.12011
\(482\) 731958.i 3.15059i
\(483\) 45976.8i 0.197081i
\(484\) 1.28210e6 5.47308
\(485\) 113459.i 0.482341i
\(486\) 29617.6i 0.125394i
\(487\) 151820. 0.640132 0.320066 0.947395i \(-0.396295\pi\)
0.320066 + 0.947395i \(0.396295\pi\)
\(488\) 118010. 0.495542
\(489\) −73113.7 −0.305760
\(490\) 242825.i 1.01135i
\(491\) −103785. −0.430497 −0.215249 0.976559i \(-0.569056\pi\)
−0.215249 + 0.976559i \(0.569056\pi\)
\(492\) 357597. 1.47728
\(493\) −399528. −1.64382
\(494\) −518086. −2.12299
\(495\) 119418.i 0.487371i
\(496\) 593779.i 2.41358i
\(497\) −286120. −1.15834
\(498\) 545552. 2.19977
\(499\) 469746. 1.88652 0.943262 0.332049i \(-0.107740\pi\)
0.943262 + 0.332049i \(0.107740\pi\)
\(500\) 765443. 3.06177
\(501\) −196744. −0.783837
\(502\) 242580.i 0.962602i
\(503\) 138093.i 0.545801i 0.962042 + 0.272901i \(0.0879831\pi\)
−0.962042 + 0.272901i \(0.912017\pi\)
\(504\) 188979.i 0.743964i
\(505\) 128392.i 0.503448i
\(506\) 467151.i 1.82455i
\(507\) −72139.2 −0.280644
\(508\) −1.22924e6 −4.76332
\(509\) 123336.i 0.476051i 0.971259 + 0.238026i \(0.0765002\pi\)
−0.971259 + 0.238026i \(0.923500\pi\)
\(510\) 339058.i 1.30357i
\(511\) 245988.i 0.942045i
\(512\) 1.04843e6i 3.99944i
\(513\) −45123.0 −0.171460
\(514\) 399597.i 1.51250i
\(515\) 79685.7i 0.300446i
\(516\) 505519.i 1.89862i
\(517\) 51009.6 0.190841
\(518\) 302202. 1.12626
\(519\) 68701.4i 0.255053i
\(520\) −1.00040e6 −3.69972
\(521\) −68858.9 −0.253679 −0.126840 0.991923i \(-0.540483\pi\)
−0.126840 + 0.991923i \(0.540483\pi\)
\(522\) 215442.i 0.790660i
\(523\) 269285. 0.984482 0.492241 0.870459i \(-0.336178\pi\)
0.492241 + 0.870459i \(0.336178\pi\)
\(524\) 77572.1i 0.282516i
\(525\) 27234.1 0.0988084
\(526\) 651985.i 2.35649i
\(527\) 219527.i 0.790435i
\(528\) 1.14160e6i 4.09494i
\(529\) 196916. 0.703672
\(530\) 190506.i 0.678199i
\(531\) −93569.0 8854.53i −0.331851 0.0314034i
\(532\) −446034. −1.57596
\(533\) 314138.i 1.10577i
\(534\) −127640. −0.447615
\(535\) 228139. 0.797063
\(536\) −568498. −1.97879
\(537\) 2069.40i 0.00717623i
\(538\) 433149. 1.49649
\(539\) 302272.i 1.04045i
\(540\) −134982. −0.462902
\(541\) 110046.i 0.375993i 0.982170 + 0.187997i \(0.0601994\pi\)
−0.982170 + 0.187997i \(0.939801\pi\)
\(542\) 264272.i 0.899607i
\(543\) 239093. 0.810900
\(544\) 1.81446e6i 6.13125i
\(545\) 454014.i 1.52854i
\(546\) −257185. −0.862701
\(547\) 163036. 0.544889 0.272444 0.962172i \(-0.412168\pi\)
0.272444 + 0.962172i \(0.412168\pi\)
\(548\) −401159. −1.33584
\(549\) 13987.8i 0.0464092i
\(550\) −276714. −0.914758
\(551\) −328231. −1.08113
\(552\) −340847. −1.11862
\(553\) −157648. −0.515513
\(554\) 559572.i 1.82321i
\(555\) 139333.i 0.452344i
\(556\) −125070. −0.404578
\(557\) −447290. −1.44171 −0.720857 0.693084i \(-0.756251\pi\)
−0.720857 + 0.693084i \(0.756251\pi\)
\(558\) 118378. 0.380192
\(559\) 444083. 1.42115
\(560\) −693591. −2.21171
\(561\) 422064.i 1.34107i
\(562\) 950487.i 3.00936i
\(563\) 50595.3i 0.159622i 0.996810 + 0.0798111i \(0.0254317\pi\)
−0.996810 + 0.0798111i \(0.974568\pi\)
\(564\) 57657.9i 0.181259i
\(565\) 357518.i 1.11996i
\(566\) 1.11145e6 3.46943
\(567\) −22399.7 −0.0696748
\(568\) 2.12114e6i 6.57464i
\(569\) 596739.i 1.84315i 0.388204 + 0.921573i \(0.373096\pi\)
−0.388204 + 0.921573i \(0.626904\pi\)
\(570\) 278552.i 0.857346i
\(571\) 2297.80i 0.00704759i −0.999994 0.00352379i \(-0.998878\pi\)
0.999994 0.00352379i \(-0.00112166\pi\)
\(572\) 1.92923e6 5.89648
\(573\) 312701.i 0.952402i
\(574\) 366324.i 1.11184i
\(575\) 49120.0i 0.148567i
\(576\) −520982. −1.57028
\(577\) −635182. −1.90786 −0.953931 0.300027i \(-0.903004\pi\)
−0.953931 + 0.300027i \(0.903004\pi\)
\(578\) 545310.i 1.63225i
\(579\) −166044. −0.495296
\(580\) −981880. −2.91879
\(581\) 412599.i 1.22229i
\(582\) 216236. 0.638385
\(583\) 237145.i 0.697712i
\(584\) −1.82362e6 −5.34698
\(585\) 118578.i 0.346491i
\(586\) 751661.i 2.18891i
\(587\) 46453.2i 0.134815i −0.997726 0.0674077i \(-0.978527\pi\)
0.997726 0.0674077i \(-0.0214728\pi\)
\(588\) 341669. 0.988213
\(589\) 180351.i 0.519863i
\(590\) −54660.4 + 577616.i −0.157025 + 1.65934i
\(591\) −181832. −0.520590
\(592\) 1.33199e6i 3.80064i
\(593\) −292298. −0.831221 −0.415611 0.909543i \(-0.636432\pi\)
−0.415611 + 0.909543i \(0.636432\pi\)
\(594\) 227594. 0.645042
\(595\) 256428. 0.724323
\(596\) 366624.i 1.03212i
\(597\) 19390.3 0.0544047
\(598\) 463865.i 1.29715i
\(599\) 239592. 0.667758 0.333879 0.942616i \(-0.391642\pi\)
0.333879 + 0.942616i \(0.391642\pi\)
\(600\) 201899.i 0.560829i
\(601\) 235688.i 0.652512i −0.945281 0.326256i \(-0.894213\pi\)
0.945281 0.326256i \(-0.105787\pi\)
\(602\) 517857. 1.42895
\(603\) 67384.1i 0.185320i
\(604\) 110041.i 0.301634i
\(605\) −605554. −1.65441
\(606\) −244697. −0.666321
\(607\) 423021. 1.14811 0.574056 0.818816i \(-0.305369\pi\)
0.574056 + 0.818816i \(0.305369\pi\)
\(608\) 1.49066e6i 4.03247i
\(609\) −162938. −0.439328
\(610\) −86348.7 −0.232058
\(611\) 50650.7 0.135676
\(612\) 477073. 1.27374
\(613\) 210522.i 0.560243i 0.959965 + 0.280122i \(0.0903748\pi\)
−0.959965 + 0.280122i \(0.909625\pi\)
\(614\) 280205.i 0.743256i
\(615\) −168898. −0.446554
\(616\) 1.45219e6 3.82704
\(617\) −342587. −0.899914 −0.449957 0.893050i \(-0.648561\pi\)
−0.449957 + 0.893050i \(0.648561\pi\)
\(618\) −151870. −0.397644
\(619\) −202870. −0.529463 −0.264732 0.964322i \(-0.585283\pi\)
−0.264732 + 0.964322i \(0.585283\pi\)
\(620\) 539508.i 1.40351i
\(621\) 40400.6i 0.104762i
\(622\) 432112.i 1.11690i
\(623\) 96533.8i 0.248716i
\(624\) 1.13357e6i 2.91125i
\(625\) −254919. −0.652594
\(626\) −756189. −1.92966
\(627\) 346745.i 0.882013i
\(628\) 623369.i 1.58061i
\(629\) 492451.i 1.24469i
\(630\) 138277.i 0.348392i
\(631\) −41966.6 −0.105401 −0.0527006 0.998610i \(-0.516783\pi\)
−0.0527006 + 0.998610i \(0.516783\pi\)
\(632\) 1.16872e6i 2.92601i
\(633\) 71362.2i 0.178099i
\(634\) 1.03212e6i 2.56775i
\(635\) 580587. 1.43986
\(636\) 268053. 0.662683
\(637\) 300146.i 0.739696i
\(638\) 1.65555e6 4.06725
\(639\) 251418. 0.615737
\(640\) 1.63531e6i 3.99245i
\(641\) −336370. −0.818656 −0.409328 0.912387i \(-0.634237\pi\)
−0.409328 + 0.912387i \(0.634237\pi\)
\(642\) 434802.i 1.05492i
\(643\) −387046. −0.936140 −0.468070 0.883691i \(-0.655051\pi\)
−0.468070 + 0.883691i \(0.655051\pi\)
\(644\) 399353.i 0.962909i
\(645\) 238763.i 0.573916i
\(646\) 984495.i 2.35911i
\(647\) 640773. 1.53072 0.765360 0.643602i \(-0.222561\pi\)
0.765360 + 0.643602i \(0.222561\pi\)
\(648\) 166059.i 0.395469i
\(649\) 68042.0 719024.i 0.161543 1.70708i
\(650\) −274768. −0.650338
\(651\) 89528.9i 0.211252i
\(652\) 635064. 1.49390
\(653\) 59695.3 0.139995 0.0699977 0.997547i \(-0.477701\pi\)
0.0699977 + 0.997547i \(0.477701\pi\)
\(654\) 865287. 2.02304
\(655\) 36638.4i 0.0853991i
\(656\) −1.61462e6 −3.75199
\(657\) 216154.i 0.500763i
\(658\) 59065.1 0.136420
\(659\) 277090.i 0.638043i 0.947747 + 0.319022i \(0.103354\pi\)
−0.947747 + 0.319022i \(0.896646\pi\)
\(660\) 1.03726e6i 2.38123i
\(661\) −170596. −0.390450 −0.195225 0.980758i \(-0.562544\pi\)
−0.195225 + 0.980758i \(0.562544\pi\)
\(662\) 422085.i 0.963128i
\(663\) 419094.i 0.953421i
\(664\) −3.05879e6 −6.93766
\(665\) 210668. 0.476381
\(666\) −265550. −0.598684
\(667\) 293879.i 0.660568i
\(668\) 1.70891e6 3.82972
\(669\) −324723. −0.725539
\(670\) 415973. 0.926649
\(671\) 107488. 0.238734
\(672\) 739984.i 1.63864i
\(673\) 124494.i 0.274864i −0.990511 0.137432i \(-0.956115\pi\)
0.990511 0.137432i \(-0.0438848\pi\)
\(674\) −680394. −1.49775
\(675\) −23931.1 −0.0525236
\(676\) 626599. 1.37119
\(677\) 470982. 1.02761 0.513804 0.857908i \(-0.328236\pi\)
0.513804 + 0.857908i \(0.328236\pi\)
\(678\) −681380. −1.48228
\(679\) 163539.i 0.354716i
\(680\) 1.90102e6i 4.11120i
\(681\) 81819.6i 0.176426i
\(682\) 909667.i 1.95575i
\(683\) 543532.i 1.16516i 0.812775 + 0.582578i \(0.197956\pi\)
−0.812775 + 0.582578i \(0.802044\pi\)
\(684\) 391938. 0.837731
\(685\) 189473. 0.403800
\(686\) 926836.i 1.96949i
\(687\) 261613.i 0.554301i
\(688\) 2.28251e6i 4.82210i
\(689\) 235476.i 0.496031i
\(690\) 249399. 0.523838
\(691\) 466845.i 0.977725i −0.872361 0.488862i \(-0.837412\pi\)
0.872361 0.488862i \(-0.162588\pi\)
\(692\) 596739.i 1.24615i
\(693\) 172129.i 0.358416i
\(694\) −579327. −1.20283
\(695\) 59072.1 0.122296
\(696\) 1.20794e6i 2.49359i
\(697\) 596942. 1.22876
\(698\) −218415. −0.448304
\(699\) 282175.i 0.577517i
\(700\) −236554. −0.482764
\(701\) 661106.i 1.34535i −0.739939 0.672674i \(-0.765145\pi\)
0.739939 0.672674i \(-0.234855\pi\)
\(702\) 225993. 0.458586
\(703\) 404571.i 0.818624i
\(704\) 4.00345e6i 8.07773i
\(705\) 27232.6i 0.0547912i
\(706\) −1.10221e6 −2.21134
\(707\) 185064.i 0.370239i
\(708\) 812738. + 76910.2i 1.62138 + 0.153433i
\(709\) −64729.8 −0.128769 −0.0643845 0.997925i \(-0.520508\pi\)
−0.0643845 + 0.997925i \(0.520508\pi\)
\(710\) 1.55205e6i 3.07884i
\(711\) 138528. 0.274031
\(712\) 715649. 1.41169
\(713\) −161476. −0.317636
\(714\) 488717.i 0.958651i
\(715\) −911203. −1.78239
\(716\) 17974.8i 0.0350621i
\(717\) 229917. 0.447232
\(718\) 232506.i 0.451009i
\(719\) 648569.i 1.25458i 0.778786 + 0.627290i \(0.215836\pi\)
−0.778786 + 0.627290i \(0.784164\pi\)
\(720\) 609471. 1.17568
\(721\) 114859.i 0.220950i
\(722\) 210146.i 0.403131i
\(723\) 486439. 0.930575
\(724\) −2.07676e6 −3.96195
\(725\) −174078. −0.331182
\(726\) 1.15410e6i 2.18963i
\(727\) 201809. 0.381831 0.190916 0.981606i \(-0.438854\pi\)
0.190916 + 0.981606i \(0.438854\pi\)
\(728\) 1.44198e6 2.72079
\(729\) 19683.0 0.0370370
\(730\) 1.33435e6 2.50394
\(731\) 843870.i 1.57921i
\(732\) 121497.i 0.226749i
\(733\) −517718. −0.963575 −0.481787 0.876288i \(-0.660012\pi\)
−0.481787 + 0.876288i \(0.660012\pi\)
\(734\) 406785. 0.755045
\(735\) −161375. −0.298718
\(736\) 1.33465e6 2.46384
\(737\) −517808. −0.953310
\(738\) 321896.i 0.591020i
\(739\) 1.01019e6i 1.84976i −0.380263 0.924879i \(-0.624166\pi\)
0.380263 0.924879i \(-0.375834\pi\)
\(740\) 1.21025e6i 2.21009i
\(741\) 344305.i 0.627057i
\(742\) 274595.i 0.498752i
\(743\) −521556. −0.944765 −0.472382 0.881394i \(-0.656606\pi\)
−0.472382 + 0.881394i \(0.656606\pi\)
\(744\) −663718. −1.19905
\(745\) 173162.i 0.311989i
\(746\) 550635.i 0.989432i
\(747\) 362558.i 0.649735i
\(748\) 3.66603e6i 6.55229i
\(749\) −328839. −0.586165
\(750\) 689024.i 1.22493i
\(751\) 879845.i 1.56001i 0.625776 + 0.780003i \(0.284783\pi\)
−0.625776 + 0.780003i \(0.715217\pi\)
\(752\) 260336.i 0.460362i
\(753\) −161212. −0.284319
\(754\) 1.64390e6 2.89157
\(755\) 51973.9i 0.0911782i
\(756\) 194563. 0.340421
\(757\) −1.05871e6 −1.84750 −0.923748 0.383000i \(-0.874891\pi\)
−0.923748 + 0.383000i \(0.874891\pi\)
\(758\) 312264.i 0.543481i
\(759\) −310456. −0.538910
\(760\) 1.56178e6i 2.70391i
\(761\) −319446. −0.551604 −0.275802 0.961214i \(-0.588943\pi\)
−0.275802 + 0.961214i \(0.588943\pi\)
\(762\) 1.10652e6i 1.90567i
\(763\) 654414.i 1.12410i
\(764\) 2.71612e6i 4.65330i
\(765\) −225328. −0.385028
\(766\) 1.21955e6i 2.07847i
\(767\) 67563.3 713966.i 0.114847 1.21363i
\(768\) 1.51245e6 2.56425
\(769\) 547254.i 0.925414i 0.886511 + 0.462707i \(0.153122\pi\)
−0.886511 + 0.462707i \(0.846878\pi\)
\(770\) −1.06258e6 −1.79217
\(771\) −265561. −0.446741
\(772\) 1.44225e6 2.41995
\(773\) 385413.i 0.645011i −0.946568 0.322505i \(-0.895475\pi\)
0.946568 0.322505i \(-0.104525\pi\)
\(774\) −455050. −0.759586
\(775\) 95649.6i 0.159250i
\(776\) −1.21239e6 −2.01335
\(777\) 200835.i 0.332657i
\(778\) 1.44313e6i 2.38423i
\(779\) 490415. 0.808144
\(780\) 1.02996e6i 1.69291i
\(781\) 1.93201e6i 3.16743i
\(782\) −881461. −1.44142
\(783\) 143177. 0.233533
\(784\) −1.54270e6 −2.50986
\(785\) 294426.i 0.477789i
\(786\) 69827.6 0.113027
\(787\) 1.03990e6 1.67896 0.839481 0.543389i \(-0.182859\pi\)
0.839481 + 0.543389i \(0.182859\pi\)
\(788\) 1.57939e6 2.54353
\(789\) 433290. 0.696025