Properties

Label 177.5.c.a.58.39
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 58.39
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.2

$q$-expansion

\(f(q)\) \(=\) \(q+7.77798i q^{2} -5.19615 q^{3} -44.4970 q^{4} +28.5836 q^{5} -40.4156i q^{6} +72.7001 q^{7} -221.650i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q+7.77798i q^{2} -5.19615 q^{3} -44.4970 q^{4} +28.5836 q^{5} -40.4156i q^{6} +72.7001 q^{7} -221.650i q^{8} +27.0000 q^{9} +222.323i q^{10} +9.33885i q^{11} +231.213 q^{12} +106.784i q^{13} +565.461i q^{14} -148.525 q^{15} +1012.03 q^{16} +337.515 q^{17} +210.006i q^{18} +546.806 q^{19} -1271.89 q^{20} -377.761 q^{21} -72.6374 q^{22} -39.3036i q^{23} +1151.72i q^{24} +192.023 q^{25} -830.565 q^{26} -140.296 q^{27} -3234.94 q^{28} -444.446 q^{29} -1155.22i q^{30} -1230.69i q^{31} +4325.19i q^{32} -48.5261i q^{33} +2625.19i q^{34} +2078.03 q^{35} -1201.42 q^{36} -1943.27i q^{37} +4253.05i q^{38} -554.866i q^{39} -6335.54i q^{40} -835.576 q^{41} -2938.22i q^{42} +2242.91i q^{43} -415.551i q^{44} +771.758 q^{45} +305.703 q^{46} +3914.09i q^{47} -5258.68 q^{48} +2884.31 q^{49} +1493.55i q^{50} -1753.78 q^{51} -4751.57i q^{52} +3820.28 q^{53} -1091.22i q^{54} +266.938i q^{55} -16113.9i q^{56} -2841.29 q^{57} -3456.89i q^{58} +(-3000.50 - 1764.76i) q^{59} +6608.91 q^{60} +2344.07i q^{61} +9572.29 q^{62} +1962.90 q^{63} -17448.7 q^{64} +3052.27i q^{65} +377.435 q^{66} +3650.67i q^{67} -15018.4 q^{68} +204.228i q^{69} +16162.9i q^{70} -2630.49 q^{71} -5984.54i q^{72} +8924.21i q^{73} +15114.7 q^{74} -997.781 q^{75} -24331.3 q^{76} +678.935i q^{77} +4315.74 q^{78} +1497.53 q^{79} +28927.6 q^{80} +729.000 q^{81} -6499.09i q^{82} +3985.30i q^{83} +16809.2 q^{84} +9647.40 q^{85} -17445.3 q^{86} +2309.41 q^{87} +2069.95 q^{88} +2531.49i q^{89} +6002.72i q^{90} +7763.21i q^{91} +1748.89i q^{92} +6394.85i q^{93} -30443.7 q^{94} +15629.7 q^{95} -22474.3i q^{96} -9210.22i q^{97} +22434.1i q^{98} +252.149i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 7.77798i 1.94450i 0.233953 + 0.972248i \(0.424834\pi\)
−0.233953 + 0.972248i \(0.575166\pi\)
\(3\) −5.19615 −0.577350
\(4\) −44.4970 −2.78106
\(5\) 28.5836 1.14334 0.571672 0.820482i \(-0.306295\pi\)
0.571672 + 0.820482i \(0.306295\pi\)
\(6\) 40.4156i 1.12266i
\(7\) 72.7001 1.48368 0.741838 0.670579i \(-0.233954\pi\)
0.741838 + 0.670579i \(0.233954\pi\)
\(8\) 221.650i 3.46327i
\(9\) 27.0000 0.333333
\(10\) 222.323i 2.22323i
\(11\) 9.33885i 0.0771806i 0.999255 + 0.0385903i \(0.0122867\pi\)
−0.999255 + 0.0385903i \(0.987713\pi\)
\(12\) 231.213 1.60565
\(13\) 106.784i 0.631858i 0.948783 + 0.315929i \(0.102316\pi\)
−0.948783 + 0.315929i \(0.897684\pi\)
\(14\) 565.461i 2.88500i
\(15\) −148.525 −0.660110
\(16\) 1012.03 3.95326
\(17\) 337.515 1.16787 0.583936 0.811800i \(-0.301512\pi\)
0.583936 + 0.811800i \(0.301512\pi\)
\(18\) 210.006i 0.648165i
\(19\) 546.806 1.51470 0.757349 0.653010i \(-0.226494\pi\)
0.757349 + 0.653010i \(0.226494\pi\)
\(20\) −1271.89 −3.17972
\(21\) −377.761 −0.856601
\(22\) −72.6374 −0.150077
\(23\) 39.3036i 0.0742979i −0.999310 0.0371490i \(-0.988172\pi\)
0.999310 0.0371490i \(-0.0118276\pi\)
\(24\) 1151.72i 1.99952i
\(25\) 192.023 0.307237
\(26\) −830.565 −1.22865
\(27\) −140.296 −0.192450
\(28\) −3234.94 −4.12620
\(29\) −444.446 −0.528473 −0.264236 0.964458i \(-0.585120\pi\)
−0.264236 + 0.964458i \(0.585120\pi\)
\(30\) 1155.22i 1.28358i
\(31\) 1230.69i 1.28063i −0.768110 0.640317i \(-0.778803\pi\)
0.768110 0.640317i \(-0.221197\pi\)
\(32\) 4325.19i 4.22382i
\(33\) 48.5261i 0.0445602i
\(34\) 2625.19i 2.27092i
\(35\) 2078.03 1.69635
\(36\) −1201.42 −0.927022
\(37\) 1943.27i 1.41948i −0.704464 0.709740i \(-0.748812\pi\)
0.704464 0.709740i \(-0.251188\pi\)
\(38\) 4253.05i 2.94532i
\(39\) 554.866i 0.364804i
\(40\) 6335.54i 3.95971i
\(41\) −835.576 −0.497071 −0.248535 0.968623i \(-0.579949\pi\)
−0.248535 + 0.968623i \(0.579949\pi\)
\(42\) 2938.22i 1.66566i
\(43\) 2242.91i 1.21304i 0.795069 + 0.606519i \(0.207435\pi\)
−0.795069 + 0.606519i \(0.792565\pi\)
\(44\) 415.551i 0.214644i
\(45\) 771.758 0.381115
\(46\) 305.703 0.144472
\(47\) 3914.09i 1.77188i 0.463797 + 0.885942i \(0.346487\pi\)
−0.463797 + 0.885942i \(0.653513\pi\)
\(48\) −5258.68 −2.28241
\(49\) 2884.31 1.20130
\(50\) 1493.55i 0.597421i
\(51\) −1753.78 −0.674271
\(52\) 4751.57i 1.75724i
\(53\) 3820.28 1.36001 0.680006 0.733206i \(-0.261977\pi\)
0.680006 + 0.733206i \(0.261977\pi\)
\(54\) 1091.22i 0.374218i
\(55\) 266.938i 0.0882440i
\(56\) 16113.9i 5.13838i
\(57\) −2841.29 −0.874511
\(58\) 3456.89i 1.02761i
\(59\) −3000.50 1764.76i −0.861964 0.506970i
\(60\) 6608.91 1.83581
\(61\) 2344.07i 0.629958i 0.949099 + 0.314979i \(0.101997\pi\)
−0.949099 + 0.314979i \(0.898003\pi\)
\(62\) 9572.29 2.49019
\(63\) 1962.90 0.494559
\(64\) −17448.7 −4.25994
\(65\) 3052.27i 0.722432i
\(66\) 377.435 0.0866472
\(67\) 3650.67i 0.813249i 0.913595 + 0.406624i \(0.133294\pi\)
−0.913595 + 0.406624i \(0.866706\pi\)
\(68\) −15018.4 −3.24793
\(69\) 204.228i 0.0428959i
\(70\) 16162.9i 3.29855i
\(71\) −2630.49 −0.521819 −0.260909 0.965363i \(-0.584022\pi\)
−0.260909 + 0.965363i \(0.584022\pi\)
\(72\) 5984.54i 1.15442i
\(73\) 8924.21i 1.67465i 0.546705 + 0.837325i \(0.315882\pi\)
−0.546705 + 0.837325i \(0.684118\pi\)
\(74\) 15114.7 2.76017
\(75\) −997.781 −0.177383
\(76\) −24331.3 −4.21247
\(77\) 678.935i 0.114511i
\(78\) 4315.74 0.709359
\(79\) 1497.53 0.239951 0.119976 0.992777i \(-0.461718\pi\)
0.119976 + 0.992777i \(0.461718\pi\)
\(80\) 28927.6 4.51993
\(81\) 729.000 0.111111
\(82\) 6499.09i 0.966552i
\(83\) 3985.30i 0.578503i 0.957253 + 0.289251i \(0.0934063\pi\)
−0.957253 + 0.289251i \(0.906594\pi\)
\(84\) 16809.2 2.38226
\(85\) 9647.40 1.33528
\(86\) −17445.3 −2.35875
\(87\) 2309.41 0.305114
\(88\) 2069.95 0.267297
\(89\) 2531.49i 0.319593i 0.987150 + 0.159796i \(0.0510838\pi\)
−0.987150 + 0.159796i \(0.948916\pi\)
\(90\) 6002.72i 0.741076i
\(91\) 7763.21i 0.937473i
\(92\) 1748.89i 0.206627i
\(93\) 6394.85i 0.739375i
\(94\) −30443.7 −3.44542
\(95\) 15629.7 1.73182
\(96\) 22474.3i 2.43862i
\(97\) 9210.22i 0.978874i −0.872039 0.489437i \(-0.837202\pi\)
0.872039 0.489437i \(-0.162798\pi\)
\(98\) 22434.1i 2.33591i
\(99\) 252.149i 0.0257269i
\(100\) −8544.45 −0.854445
\(101\) 13290.3i 1.30284i −0.758717 0.651420i \(-0.774174\pi\)
0.758717 0.651420i \(-0.225826\pi\)
\(102\) 13640.9i 1.31112i
\(103\) 14436.1i 1.36074i −0.732867 0.680372i \(-0.761818\pi\)
0.732867 0.680372i \(-0.238182\pi\)
\(104\) 23668.6 2.18830
\(105\) −10797.8 −0.979390
\(106\) 29714.0i 2.64454i
\(107\) −986.412 −0.0861570 −0.0430785 0.999072i \(-0.513717\pi\)
−0.0430785 + 0.999072i \(0.513717\pi\)
\(108\) 6242.76 0.535216
\(109\) 14934.0i 1.25697i −0.777824 0.628483i \(-0.783676\pi\)
0.777824 0.628483i \(-0.216324\pi\)
\(110\) −2076.24 −0.171590
\(111\) 10097.5i 0.819537i
\(112\) 73575.0 5.86535
\(113\) 19908.8i 1.55915i 0.626308 + 0.779576i \(0.284565\pi\)
−0.626308 + 0.779576i \(0.715435\pi\)
\(114\) 22099.5i 1.70048i
\(115\) 1123.44i 0.0849481i
\(116\) 19776.5 1.46972
\(117\) 2883.17i 0.210619i
\(118\) 13726.3 23337.8i 0.985802 1.67608i
\(119\) 24537.4 1.73274
\(120\) 32920.5i 2.28614i
\(121\) 14553.8 0.994043
\(122\) −18232.2 −1.22495
\(123\) 4341.78 0.286984
\(124\) 54762.1i 3.56153i
\(125\) −12376.0 −0.792067
\(126\) 15267.4i 0.961668i
\(127\) −15531.0 −0.962922 −0.481461 0.876468i \(-0.659894\pi\)
−0.481461 + 0.876468i \(0.659894\pi\)
\(128\) 66512.8i 4.05962i
\(129\) 11654.5i 0.700348i
\(130\) −23740.5 −1.40477
\(131\) 1246.21i 0.0726188i 0.999341 + 0.0363094i \(0.0115602\pi\)
−0.999341 + 0.0363094i \(0.988440\pi\)
\(132\) 2159.27i 0.123925i
\(133\) 39752.9 2.24732
\(134\) −28394.9 −1.58136
\(135\) −4010.17 −0.220037
\(136\) 74810.0i 4.04466i
\(137\) 16792.4 0.894689 0.447344 0.894362i \(-0.352370\pi\)
0.447344 + 0.894362i \(0.352370\pi\)
\(138\) −1588.48 −0.0834110
\(139\) −35922.2 −1.85923 −0.929616 0.368530i \(-0.879861\pi\)
−0.929616 + 0.368530i \(0.879861\pi\)
\(140\) −92466.3 −4.71767
\(141\) 20338.2i 1.02300i
\(142\) 20459.9i 1.01467i
\(143\) −997.240 −0.0487672
\(144\) 27324.9 1.31775
\(145\) −12703.9 −0.604227
\(146\) −69412.4 −3.25635
\(147\) −14987.3 −0.693568
\(148\) 86469.7i 3.94767i
\(149\) 25955.6i 1.16912i 0.811351 + 0.584559i \(0.198732\pi\)
−0.811351 + 0.584559i \(0.801268\pi\)
\(150\) 7760.72i 0.344921i
\(151\) 18565.1i 0.814222i −0.913379 0.407111i \(-0.866536\pi\)
0.913379 0.407111i \(-0.133464\pi\)
\(152\) 121199.i 5.24581i
\(153\) 9112.91 0.389291
\(154\) −5280.75 −0.222666
\(155\) 35177.6i 1.46421i
\(156\) 24689.9i 1.01454i
\(157\) 46527.1i 1.88759i −0.330537 0.943793i \(-0.607230\pi\)
0.330537 0.943793i \(-0.392770\pi\)
\(158\) 11647.8i 0.466584i
\(159\) −19850.7 −0.785204
\(160\) 123630.i 4.82928i
\(161\) 2857.38i 0.110234i
\(162\) 5670.15i 0.216055i
\(163\) −437.670 −0.0164730 −0.00823648 0.999966i \(-0.502622\pi\)
−0.00823648 + 0.999966i \(0.502622\pi\)
\(164\) 37180.6 1.38239
\(165\) 1387.05i 0.0509477i
\(166\) −30997.6 −1.12490
\(167\) 49721.0 1.78282 0.891408 0.453201i \(-0.149718\pi\)
0.891408 + 0.453201i \(0.149718\pi\)
\(168\) 83730.5i 2.96664i
\(169\) 17158.2 0.600755
\(170\) 75037.3i 2.59645i
\(171\) 14763.8 0.504899
\(172\) 99802.8i 3.37354i
\(173\) 30766.7i 1.02799i 0.857793 + 0.513995i \(0.171835\pi\)
−0.857793 + 0.513995i \(0.828165\pi\)
\(174\) 17962.5i 0.593293i
\(175\) 13960.1 0.455840
\(176\) 9451.23i 0.305115i
\(177\) 15591.0 + 9169.98i 0.497655 + 0.292699i
\(178\) −19689.9 −0.621447
\(179\) 20767.6i 0.648156i 0.946030 + 0.324078i \(0.105054\pi\)
−0.946030 + 0.324078i \(0.894946\pi\)
\(180\) −34340.9 −1.05991
\(181\) 27789.6 0.848252 0.424126 0.905603i \(-0.360581\pi\)
0.424126 + 0.905603i \(0.360581\pi\)
\(182\) −60382.2 −1.82291
\(183\) 12180.2i 0.363706i
\(184\) −8711.63 −0.257314
\(185\) 55545.6i 1.62295i
\(186\) −49739.1 −1.43771
\(187\) 3152.00i 0.0901370i
\(188\) 174165.i 4.92772i
\(189\) −10199.5 −0.285534
\(190\) 121568.i 3.36752i
\(191\) 22222.5i 0.609153i 0.952488 + 0.304576i \(0.0985149\pi\)
−0.952488 + 0.304576i \(0.901485\pi\)
\(192\) 90666.2 2.45948
\(193\) 22533.4 0.604941 0.302470 0.953159i \(-0.402189\pi\)
0.302470 + 0.953159i \(0.402189\pi\)
\(194\) 71637.0 1.90342
\(195\) 15860.1i 0.417096i
\(196\) −128343. −3.34088
\(197\) 11138.9 0.287018 0.143509 0.989649i \(-0.454161\pi\)
0.143509 + 0.989649i \(0.454161\pi\)
\(198\) −1961.21 −0.0500258
\(199\) −27923.7 −0.705126 −0.352563 0.935788i \(-0.614690\pi\)
−0.352563 + 0.935788i \(0.614690\pi\)
\(200\) 42561.8i 1.06404i
\(201\) 18969.5i 0.469529i
\(202\) 103372. 2.53337
\(203\) −32311.3 −0.784083
\(204\) 78038.0 1.87519
\(205\) −23883.8 −0.568323
\(206\) 112284. 2.64596
\(207\) 1061.20i 0.0247660i
\(208\) 108069.i 2.49790i
\(209\) 5106.54i 0.116905i
\(210\) 83984.9i 1.90442i
\(211\) 4163.53i 0.0935182i −0.998906 0.0467591i \(-0.985111\pi\)
0.998906 0.0467591i \(-0.0148893\pi\)
\(212\) −169991. −3.78228
\(213\) 13668.4 0.301272
\(214\) 7672.29i 0.167532i
\(215\) 64110.4i 1.38692i
\(216\) 31096.6i 0.666507i
\(217\) 89471.3i 1.90005i
\(218\) 116156. 2.44416
\(219\) 46371.6i 0.966860i
\(220\) 11878.0i 0.245412i
\(221\) 36041.2i 0.737930i
\(222\) −78538.3 −1.59359
\(223\) −77429.7 −1.55703 −0.778517 0.627624i \(-0.784028\pi\)
−0.778517 + 0.627624i \(0.784028\pi\)
\(224\) 314442.i 6.26678i
\(225\) 5184.62 0.102412
\(226\) −154850. −3.03176
\(227\) 6994.10i 0.135731i 0.997694 + 0.0678656i \(0.0216189\pi\)
−0.997694 + 0.0678656i \(0.978381\pi\)
\(228\) 126429. 2.43207
\(229\) 51473.3i 0.981547i −0.871287 0.490773i \(-0.836714\pi\)
0.871287 0.490773i \(-0.163286\pi\)
\(230\) 8738.09 0.165181
\(231\) 3527.85i 0.0661129i
\(232\) 98511.2i 1.83025i
\(233\) 79635.1i 1.46687i −0.679758 0.733437i \(-0.737915\pi\)
0.679758 0.733437i \(-0.262085\pi\)
\(234\) −22425.2 −0.409549
\(235\) 111879.i 2.02587i
\(236\) 133513. + 78526.7i 2.39718 + 1.40992i
\(237\) −7781.42 −0.138536
\(238\) 190851.i 3.36931i
\(239\) −27642.4 −0.483927 −0.241964 0.970285i \(-0.577792\pi\)
−0.241964 + 0.970285i \(0.577792\pi\)
\(240\) −150312. −2.60959
\(241\) 11767.3 0.202602 0.101301 0.994856i \(-0.467700\pi\)
0.101301 + 0.994856i \(0.467700\pi\)
\(242\) 113199.i 1.93291i
\(243\) −3788.00 −0.0641500
\(244\) 104304.i 1.75195i
\(245\) 82444.0 1.37349
\(246\) 33770.3i 0.558039i
\(247\) 58390.2i 0.957075i
\(248\) −272782. −4.43519
\(249\) 20708.2i 0.333999i
\(250\) 96260.7i 1.54017i
\(251\) −98763.5 −1.56765 −0.783825 0.620982i \(-0.786734\pi\)
−0.783825 + 0.620982i \(0.786734\pi\)
\(252\) −87343.4 −1.37540
\(253\) 367.050 0.00573436
\(254\) 120800.i 1.87240i
\(255\) −50129.4 −0.770924
\(256\) 238156. 3.63398
\(257\) 36087.2 0.546370 0.273185 0.961961i \(-0.411923\pi\)
0.273185 + 0.961961i \(0.411923\pi\)
\(258\) 90648.5 1.36182
\(259\) 141276.i 2.10605i
\(260\) 135817.i 2.00913i
\(261\) −12000.0 −0.176158
\(262\) −9693.01 −0.141207
\(263\) −16587.3 −0.239808 −0.119904 0.992786i \(-0.538259\pi\)
−0.119904 + 0.992786i \(0.538259\pi\)
\(264\) −10755.8 −0.154324
\(265\) 109197. 1.55496
\(266\) 309197.i 4.36991i
\(267\) 13154.0i 0.184517i
\(268\) 162444.i 2.26170i
\(269\) 47175.2i 0.651943i −0.945380 0.325971i \(-0.894309\pi\)
0.945380 0.325971i \(-0.105691\pi\)
\(270\) 31191.0i 0.427861i
\(271\) 37006.4 0.503893 0.251946 0.967741i \(-0.418929\pi\)
0.251946 + 0.967741i \(0.418929\pi\)
\(272\) 341577. 4.61690
\(273\) 40338.8i 0.541250i
\(274\) 130611.i 1.73972i
\(275\) 1793.27i 0.0237127i
\(276\) 9087.52i 0.119296i
\(277\) −37499.2 −0.488722 −0.244361 0.969684i \(-0.578578\pi\)
−0.244361 + 0.969684i \(0.578578\pi\)
\(278\) 279402.i 3.61527i
\(279\) 33228.6i 0.426878i
\(280\) 460595.i 5.87494i
\(281\) −8246.03 −0.104432 −0.0522158 0.998636i \(-0.516628\pi\)
−0.0522158 + 0.998636i \(0.516628\pi\)
\(282\) 158190. 1.98921
\(283\) 3380.85i 0.0422137i 0.999777 + 0.0211069i \(0.00671902\pi\)
−0.999777 + 0.0211069i \(0.993281\pi\)
\(284\) 117049. 1.45121
\(285\) −81214.3 −0.999868
\(286\) 7756.52i 0.0948276i
\(287\) −60746.5 −0.737492
\(288\) 116780.i 1.40794i
\(289\) 30395.4 0.363925
\(290\) 98810.4i 1.17492i
\(291\) 47857.7i 0.565153i
\(292\) 397101.i 4.65731i
\(293\) −146875. −1.71085 −0.855427 0.517923i \(-0.826705\pi\)
−0.855427 + 0.517923i \(0.826705\pi\)
\(294\) 116571.i 1.34864i
\(295\) −85765.0 50443.3i −0.985521 0.579642i
\(296\) −430724. −4.91605
\(297\) 1310.20i 0.0148534i
\(298\) −201882. −2.27334
\(299\) 4197.00 0.0469458
\(300\) 44398.3 0.493314
\(301\) 163060.i 1.79976i
\(302\) 144399. 1.58325
\(303\) 69058.3i 0.752195i
\(304\) 553386. 5.98799
\(305\) 67002.1i 0.720259i
\(306\) 70880.0i 0.756974i
\(307\) 92101.3 0.977213 0.488606 0.872504i \(-0.337505\pi\)
0.488606 + 0.872504i \(0.337505\pi\)
\(308\) 30210.6i 0.318462i
\(309\) 75012.4i 0.785626i
\(310\) 273611. 2.84714
\(311\) −32978.0 −0.340960 −0.170480 0.985361i \(-0.554532\pi\)
−0.170480 + 0.985361i \(0.554532\pi\)
\(312\) −122986. −1.26341
\(313\) 40714.0i 0.415581i −0.978173 0.207790i \(-0.933373\pi\)
0.978173 0.207790i \(-0.0666272\pi\)
\(314\) 361887. 3.67040
\(315\) 56106.9 0.565451
\(316\) −66635.9 −0.667320
\(317\) 5097.47 0.0507266 0.0253633 0.999678i \(-0.491926\pi\)
0.0253633 + 0.999678i \(0.491926\pi\)
\(318\) 154399.i 1.52683i
\(319\) 4150.61i 0.0407878i
\(320\) −498748. −4.87058
\(321\) 5125.54 0.0497428
\(322\) 22224.6 0.214350
\(323\) 184555. 1.76897
\(324\) −32438.3 −0.309007
\(325\) 20505.0i 0.194130i
\(326\) 3404.19i 0.0320316i
\(327\) 77599.4i 0.725709i
\(328\) 185205.i 1.72149i
\(329\) 284555.i 2.62890i
\(330\) 10788.5 0.0990676
\(331\) −18523.1 −0.169067 −0.0845334 0.996421i \(-0.526940\pi\)
−0.0845334 + 0.996421i \(0.526940\pi\)
\(332\) 177334.i 1.60885i
\(333\) 52468.2i 0.473160i
\(334\) 386729.i 3.46668i
\(335\) 104349.i 0.929823i
\(336\) −382307. −3.38636
\(337\) 137124.i 1.20741i −0.797209 0.603704i \(-0.793691\pi\)
0.797209 0.603704i \(-0.206309\pi\)
\(338\) 133456.i 1.16817i
\(339\) 103449.i 0.900176i
\(340\) −429281. −3.71350
\(341\) 11493.2 0.0988401
\(342\) 114832.i 0.981775i
\(343\) 35136.7 0.298657
\(344\) 497140. 4.20108
\(345\) 5837.56i 0.0490448i
\(346\) −239303. −1.99892
\(347\) 92388.3i 0.767287i 0.923481 + 0.383643i \(0.125331\pi\)
−0.923481 + 0.383643i \(0.874669\pi\)
\(348\) −102762. −0.848542
\(349\) 192179.i 1.57781i −0.614513 0.788907i \(-0.710648\pi\)
0.614513 0.788907i \(-0.289352\pi\)
\(350\) 108581.i 0.886379i
\(351\) 14981.4i 0.121601i
\(352\) −40392.3 −0.325997
\(353\) 133742.i 1.07329i 0.843808 + 0.536645i \(0.180308\pi\)
−0.843808 + 0.536645i \(0.819692\pi\)
\(354\) −71323.9 + 121267.i −0.569153 + 0.967688i
\(355\) −75188.9 −0.596619
\(356\) 112644.i 0.888808i
\(357\) −127500. −1.00040
\(358\) −161530. −1.26034
\(359\) −63441.2 −0.492246 −0.246123 0.969239i \(-0.579157\pi\)
−0.246123 + 0.969239i \(0.579157\pi\)
\(360\) 171060.i 1.31990i
\(361\) 168676. 1.29431
\(362\) 216147.i 1.64942i
\(363\) −75623.7 −0.573911
\(364\) 345440.i 2.60717i
\(365\) 255086.i 1.91470i
\(366\) 94737.1 0.707225
\(367\) 62757.7i 0.465946i −0.972483 0.232973i \(-0.925155\pi\)
0.972483 0.232973i \(-0.0748453\pi\)
\(368\) 39776.6i 0.293719i
\(369\) −22560.5 −0.165690
\(370\) 432033. 3.15583
\(371\) 277735. 2.01782
\(372\) 284552.i 2.05625i
\(373\) −102419. −0.736148 −0.368074 0.929797i \(-0.619983\pi\)
−0.368074 + 0.929797i \(0.619983\pi\)
\(374\) −24516.2 −0.175271
\(375\) 64307.8 0.457300
\(376\) 867556. 6.13652
\(377\) 47459.7i 0.333920i
\(378\) 79331.9i 0.555219i
\(379\) −115222. −0.802151 −0.401076 0.916045i \(-0.631364\pi\)
−0.401076 + 0.916045i \(0.631364\pi\)
\(380\) −695475. −4.81631
\(381\) 80701.3 0.555943
\(382\) −172846. −1.18450
\(383\) 68700.2 0.468339 0.234170 0.972196i \(-0.424763\pi\)
0.234170 + 0.972196i \(0.424763\pi\)
\(384\) 345611.i 2.34382i
\(385\) 19406.4i 0.130925i
\(386\) 175265.i 1.17631i
\(387\) 60558.5i 0.404346i
\(388\) 409828.i 2.72231i
\(389\) 1971.29 0.0130272 0.00651360 0.999979i \(-0.497927\pi\)
0.00651360 + 0.999979i \(0.497927\pi\)
\(390\) 123359. 0.811042
\(391\) 13265.6i 0.0867705i
\(392\) 639306.i 4.16041i
\(393\) 6475.50i 0.0419265i
\(394\) 86638.0i 0.558105i
\(395\) 42805.0 0.274347
\(396\) 11219.9i 0.0715480i
\(397\) 42440.9i 0.269280i 0.990895 + 0.134640i \(0.0429877\pi\)
−0.990895 + 0.134640i \(0.957012\pi\)
\(398\) 217190.i 1.37111i
\(399\) −206562. −1.29749
\(400\) 194334. 1.21459
\(401\) 103710.i 0.644959i −0.946576 0.322480i \(-0.895484\pi\)
0.946576 0.322480i \(-0.104516\pi\)
\(402\) 147544. 0.912998
\(403\) 131418. 0.809180
\(404\) 591378.i 3.62328i
\(405\) 20837.5 0.127038
\(406\) 251316.i 1.52465i
\(407\) 18147.9 0.109556
\(408\) 388724.i 2.33519i
\(409\) 29250.4i 0.174858i 0.996171 + 0.0874289i \(0.0278651\pi\)
−0.996171 + 0.0874289i \(0.972135\pi\)
\(410\) 185768.i 1.10510i
\(411\) −87255.9 −0.516549
\(412\) 642365.i 3.78432i
\(413\) −218136. 128299.i −1.27887 0.752180i
\(414\) 8253.98 0.0481573
\(415\) 113914.i 0.661428i
\(416\) −461861. −2.66885
\(417\) 186657. 1.07343
\(418\) −39718.6 −0.227322
\(419\) 54737.0i 0.311784i 0.987774 + 0.155892i \(0.0498251\pi\)
−0.987774 + 0.155892i \(0.950175\pi\)
\(420\) 480469. 2.72375
\(421\) 135111.i 0.762303i 0.924513 + 0.381151i \(0.124472\pi\)
−0.924513 + 0.381151i \(0.875528\pi\)
\(422\) 32383.8 0.181846
\(423\) 105680.i 0.590628i
\(424\) 846762.i 4.71010i
\(425\) 64810.6 0.358813
\(426\) 106313.i 0.585823i
\(427\) 170414.i 0.934653i
\(428\) 43892.4 0.239608
\(429\) 5181.81 0.0281557
\(430\) −498650. −2.69686
\(431\) 332324.i 1.78899i −0.447081 0.894493i \(-0.647537\pi\)
0.447081 0.894493i \(-0.352463\pi\)
\(432\) −141984. −0.760805
\(433\) 245001. 1.30675 0.653375 0.757035i \(-0.273353\pi\)
0.653375 + 0.757035i \(0.273353\pi\)
\(434\) 695907. 3.69463
\(435\) 66011.2 0.348850
\(436\) 664519.i 3.49570i
\(437\) 21491.5i 0.112539i
\(438\) 360677. 1.88005
\(439\) −181499. −0.941771 −0.470885 0.882194i \(-0.656066\pi\)
−0.470885 + 0.882194i \(0.656066\pi\)
\(440\) 59166.7 0.305613
\(441\) 77876.4 0.400432
\(442\) −280328. −1.43490
\(443\) 57457.9i 0.292781i 0.989227 + 0.146390i \(0.0467655\pi\)
−0.989227 + 0.146390i \(0.953234\pi\)
\(444\) 449310.i 2.27919i
\(445\) 72359.3i 0.365405i
\(446\) 602247.i 3.02765i
\(447\) 134869.i 0.674990i
\(448\) −1.26852e6 −6.32038
\(449\) 26596.2 0.131925 0.0659624 0.997822i \(-0.478988\pi\)
0.0659624 + 0.997822i \(0.478988\pi\)
\(450\) 40325.9i 0.199140i
\(451\) 7803.31i 0.0383642i
\(452\) 885883.i 4.33610i
\(453\) 96466.9i 0.470091i
\(454\) −54400.0 −0.263929
\(455\) 221901.i 1.07185i
\(456\) 629770.i 3.02867i
\(457\) 300518.i 1.43892i −0.694532 0.719462i \(-0.744388\pi\)
0.694532 0.719462i \(-0.255612\pi\)
\(458\) 400358. 1.90861
\(459\) −47352.0 −0.224757
\(460\) 49989.7i 0.236246i
\(461\) −140059. −0.659038 −0.329519 0.944149i \(-0.606887\pi\)
−0.329519 + 0.944149i \(0.606887\pi\)
\(462\) 27439.6 0.128556
\(463\) 127338.i 0.594014i 0.954875 + 0.297007i \(0.0959885\pi\)
−0.954875 + 0.297007i \(0.904012\pi\)
\(464\) −449794. −2.08919
\(465\) 182788.i 0.845360i
\(466\) 619400. 2.85233
\(467\) 27447.8i 0.125856i −0.998018 0.0629280i \(-0.979956\pi\)
0.998018 0.0629280i \(-0.0200439\pi\)
\(468\) 128292.i 0.585746i
\(469\) 265404.i 1.20660i
\(470\) −870192. −3.93930
\(471\) 241762.i 1.08980i
\(472\) −391159. + 665058.i −1.75578 + 2.98522i
\(473\) −20946.2 −0.0936230
\(474\) 60523.7i 0.269382i
\(475\) 104999. 0.465371
\(476\) −1.09184e6 −4.81887
\(477\) 103147. 0.453338
\(478\) 215002.i 0.940995i
\(479\) −403672. −1.75937 −0.879687 0.475554i \(-0.842248\pi\)
−0.879687 + 0.475554i \(0.842248\pi\)
\(480\) 642398.i 2.78819i
\(481\) 207510. 0.896910
\(482\) 91526.0i 0.393959i
\(483\) 14847.4i 0.0636437i
\(484\) −647600. −2.76450
\(485\) 263261.i 1.11919i
\(486\) 29463.0i 0.124739i
\(487\) 160164. 0.675316 0.337658 0.941269i \(-0.390365\pi\)
0.337658 + 0.941269i \(0.390365\pi\)
\(488\) 519563. 2.18172
\(489\) 2274.20 0.00951067
\(490\) 641248.i 2.67075i
\(491\) −27802.8 −0.115326 −0.0576628 0.998336i \(-0.518365\pi\)
−0.0576628 + 0.998336i \(0.518365\pi\)
\(492\) −193196. −0.798121
\(493\) −150007. −0.617189
\(494\) −454158. −1.86103
\(495\) 7207.33i 0.0294147i
\(496\) 1.24550e6i 5.06268i
\(497\) −191237. −0.774210
\(498\) 161068. 0.649459
\(499\) 136913. 0.549848 0.274924 0.961466i \(-0.411347\pi\)
0.274924 + 0.961466i \(0.411347\pi\)
\(500\) 550697. 2.20279
\(501\) −258358. −1.02931
\(502\) 768181.i 3.04829i
\(503\) 45212.1i 0.178698i 0.996000 + 0.0893489i \(0.0284786\pi\)
−0.996000 + 0.0893489i \(0.971521\pi\)
\(504\) 435077.i 1.71279i
\(505\) 379884.i 1.48960i
\(506\) 2854.91i 0.0111504i
\(507\) −89156.5 −0.346846
\(508\) 691082. 2.67795
\(509\) 420229.i 1.62200i 0.585048 + 0.810999i \(0.301076\pi\)
−0.585048 + 0.810999i \(0.698924\pi\)
\(510\) 389905.i 1.49906i
\(511\) 648791.i 2.48464i
\(512\) 788170.i 3.00663i
\(513\) −76714.8 −0.291504
\(514\) 280686.i 1.06241i
\(515\) 412637.i 1.55580i
\(516\) 518590.i 1.94771i
\(517\) −36553.1 −0.136755
\(518\) 1.09884e6 4.09520
\(519\) 159869.i 0.593510i
\(520\) 676535. 2.50198
\(521\) 176873. 0.651608 0.325804 0.945437i \(-0.394365\pi\)
0.325804 + 0.945437i \(0.394365\pi\)
\(522\) 93336.1i 0.342538i
\(523\) −361972. −1.32334 −0.661670 0.749795i \(-0.730152\pi\)
−0.661670 + 0.749795i \(0.730152\pi\)
\(524\) 55452.7i 0.201958i
\(525\) −72538.8 −0.263179
\(526\) 129015.i 0.466305i
\(527\) 415376.i 1.49562i
\(528\) 49110.0i 0.176158i
\(529\) 278296. 0.994480
\(530\) 849335.i 3.02362i
\(531\) −81013.4 47648.6i −0.287321 0.168990i
\(532\) −1.76889e6 −6.24995
\(533\) 89226.1i 0.314078i
\(534\) 102312. 0.358793
\(535\) −28195.2 −0.0985071
\(536\) 809170. 2.81650
\(537\) 107912.i 0.374213i
\(538\) 366928. 1.26770
\(539\) 26936.1i 0.0927166i
\(540\) 178441. 0.611937
\(541\) 276519.i 0.944779i −0.881390 0.472390i \(-0.843392\pi\)
0.881390 0.472390i \(-0.156608\pi\)
\(542\) 287835.i 0.979818i
\(543\) −144399. −0.489738
\(544\) 1.45982e6i 4.93288i
\(545\) 426868.i 1.43714i
\(546\) 313755. 1.05246
\(547\) −424332. −1.41818 −0.709090 0.705118i \(-0.750894\pi\)
−0.709090 + 0.705118i \(0.750894\pi\)
\(548\) −747213. −2.48819
\(549\) 63290.0i 0.209986i
\(550\) −13948.1 −0.0461093
\(551\) −243026. −0.800477
\(552\) 45266.9 0.148560
\(553\) 108871. 0.356010
\(554\) 291668.i 0.950318i
\(555\) 288624.i 0.937013i
\(556\) 1.59843e6 5.17064
\(557\) −408914. −1.31802 −0.659010 0.752134i \(-0.729024\pi\)
−0.659010 + 0.752134i \(0.729024\pi\)
\(558\) 258452. 0.830063
\(559\) −239507. −0.766468
\(560\) 2.10304e6 6.70612
\(561\) 16378.3i 0.0520406i
\(562\) 64137.5i 0.203067i
\(563\) 165648.i 0.522600i −0.965258 0.261300i \(-0.915849\pi\)
0.965258 0.261300i \(-0.0841512\pi\)
\(564\) 904990.i 2.84502i
\(565\) 569065.i 1.78265i
\(566\) −26296.2 −0.0820844
\(567\) 52998.4 0.164853
\(568\) 583047.i 1.80720i
\(569\) 413247.i 1.27639i −0.769873 0.638197i \(-0.779680\pi\)
0.769873 0.638197i \(-0.220320\pi\)
\(570\) 631683.i 1.94424i
\(571\) 531700.i 1.63078i −0.578914 0.815388i \(-0.696523\pi\)
0.578914 0.815388i \(-0.303477\pi\)
\(572\) 44374.2 0.135625
\(573\) 115472.i 0.351695i
\(574\) 472485.i 1.43405i
\(575\) 7547.20i 0.0228271i
\(576\) −471116. −1.41998
\(577\) −94373.0 −0.283463 −0.141731 0.989905i \(-0.545267\pi\)
−0.141731 + 0.989905i \(0.545267\pi\)
\(578\) 236415.i 0.707651i
\(579\) −117087. −0.349263
\(580\) 565284. 1.68039
\(581\) 289732.i 0.858310i
\(582\) −372237. −1.09894
\(583\) 35677.0i 0.104967i
\(584\) 1.97805e6 5.79977
\(585\) 82411.4i 0.240811i
\(586\) 1.14239e6i 3.32675i
\(587\) 16716.5i 0.0485142i −0.999706 0.0242571i \(-0.992278\pi\)
0.999706 0.0242571i \(-0.00772203\pi\)
\(588\) 666891. 1.92886
\(589\) 672949.i 1.93978i
\(590\) 392347. 667079.i 1.12711 1.91634i
\(591\) −57879.3 −0.165710
\(592\) 1.96665e6i 5.61157i
\(593\) −406858. −1.15700 −0.578500 0.815683i \(-0.696362\pi\)
−0.578500 + 0.815683i \(0.696362\pi\)
\(594\) 10190.7 0.0288824
\(595\) 701367. 1.98112
\(596\) 1.15495e6i 3.25139i
\(597\) 145096. 0.407105
\(598\) 32644.2i 0.0912858i
\(599\) −216469. −0.603313 −0.301656 0.953417i \(-0.597540\pi\)
−0.301656 + 0.953417i \(0.597540\pi\)
\(600\) 221158.i 0.614327i
\(601\) 114850.i 0.317966i 0.987281 + 0.158983i \(0.0508214\pi\)
−0.987281 + 0.158983i \(0.949179\pi\)
\(602\) −1.26828e6 −3.49962
\(603\) 98568.2i 0.271083i
\(604\) 826091.i 2.26440i
\(605\) 416000. 1.13653
\(606\) −537134. −1.46264
\(607\) 460090. 1.24872 0.624360 0.781136i \(-0.285360\pi\)
0.624360 + 0.781136i \(0.285360\pi\)
\(608\) 2.36504e6i 6.39781i
\(609\) 167894. 0.452690
\(610\) −521141. −1.40054
\(611\) −417962. −1.11958
\(612\) −405497. −1.08264
\(613\) 54204.8i 0.144250i 0.997396 + 0.0721252i \(0.0229781\pi\)
−0.997396 + 0.0721252i \(0.977022\pi\)
\(614\) 716363.i 1.90019i
\(615\) 124104. 0.328121
\(616\) 150486. 0.396583
\(617\) −446671. −1.17332 −0.586662 0.809832i \(-0.699558\pi\)
−0.586662 + 0.809832i \(0.699558\pi\)
\(618\) −583445. −1.52765
\(619\) 608019. 1.58685 0.793425 0.608668i \(-0.208296\pi\)
0.793425 + 0.608668i \(0.208296\pi\)
\(620\) 1.56530e6i 4.07205i
\(621\) 5514.14i 0.0142986i
\(622\) 256503.i 0.662996i
\(623\) 184040.i 0.474172i
\(624\) 561543.i 1.44216i
\(625\) −473767. −1.21284
\(626\) 316673. 0.808095
\(627\) 26534.4i 0.0674953i
\(628\) 2.07032e6i 5.24950i
\(629\) 655882.i 1.65777i
\(630\) 436398.i 1.09952i
\(631\) −89180.6 −0.223981 −0.111991 0.993709i \(-0.535723\pi\)
−0.111991 + 0.993709i \(0.535723\pi\)
\(632\) 331928.i 0.831016i
\(633\) 21634.3i 0.0539928i
\(634\) 39648.0i 0.0986377i
\(635\) −443931. −1.10095
\(636\) 883299. 2.18370
\(637\) 307998.i 0.759048i
\(638\) 32283.4 0.0793118
\(639\) −71023.2 −0.173940
\(640\) 1.90118e6i 4.64155i
\(641\) 496660. 1.20877 0.604384 0.796693i \(-0.293419\pi\)
0.604384 + 0.796693i \(0.293419\pi\)
\(642\) 39866.4i 0.0967246i
\(643\) −477619. −1.15521 −0.577603 0.816318i \(-0.696012\pi\)
−0.577603 + 0.816318i \(0.696012\pi\)
\(644\) 127145.i 0.306568i
\(645\) 333128.i 0.800739i
\(646\) 1.43547e6i 3.43976i
\(647\) 255266. 0.609796 0.304898 0.952385i \(-0.401378\pi\)
0.304898 + 0.952385i \(0.401378\pi\)
\(648\) 161582.i 0.384808i
\(649\) 16480.9 28021.2i 0.0391282 0.0665268i
\(650\) −159487. −0.377485
\(651\) 464907.i 1.09699i
\(652\) 19475.0 0.0458124
\(653\) 12720.0 0.0298305 0.0149152 0.999889i \(-0.495252\pi\)
0.0149152 + 0.999889i \(0.495252\pi\)
\(654\) −603567. −1.41114
\(655\) 35621.2i 0.0830283i
\(656\) −845631. −1.96505
\(657\) 240954.i 0.558217i
\(658\) −2.21326e6 −5.11189
\(659\) 732103.i 1.68578i 0.538084 + 0.842891i \(0.319148\pi\)
−0.538084 + 0.842891i \(0.680852\pi\)
\(660\) 61719.6i 0.141689i
\(661\) 601813. 1.37740 0.688698 0.725049i \(-0.258183\pi\)
0.688698 + 0.725049i \(0.258183\pi\)
\(662\) 144073.i 0.328750i
\(663\) 187276.i 0.426044i
\(664\) 883341. 2.00351
\(665\) 1.13628e6 2.56946
\(666\) 408097. 0.920058
\(667\) 17468.3i 0.0392644i
\(668\) −2.21244e6 −4.95813
\(669\) 402337. 0.898954
\(670\) −811628. −1.80804
\(671\) −21890.9 −0.0486205
\(672\) 1.63389e6i 3.61813i
\(673\) 177803.i 0.392563i −0.980548 0.196282i \(-0.937113\pi\)
0.980548 0.196282i \(-0.0628867\pi\)
\(674\) 1.06655e6 2.34780
\(675\) −26940.1 −0.0591277
\(676\) −763488. −1.67074
\(677\) 238228. 0.519774 0.259887 0.965639i \(-0.416315\pi\)
0.259887 + 0.965639i \(0.416315\pi\)
\(678\) 804626. 1.75039
\(679\) 669585.i 1.45233i
\(680\) 2.13834e6i 4.62444i
\(681\) 36342.4i 0.0783645i
\(682\) 89394.1i 0.192194i
\(683\) 660787.i 1.41651i 0.705956 + 0.708256i \(0.250518\pi\)
−0.705956 + 0.708256i \(0.749482\pi\)
\(684\) −656944. −1.40416
\(685\) 479988. 1.02294
\(686\) 273293.i 0.580737i
\(687\) 267463.i 0.566696i
\(688\) 2.26990e6i 4.79545i
\(689\) 407945.i 0.859335i
\(690\) −45404.5 −0.0953675
\(691\) 252072.i 0.527919i 0.964534 + 0.263960i \(0.0850286\pi\)
−0.964534 + 0.263960i \(0.914971\pi\)
\(692\) 1.36903e6i 2.85891i
\(693\) 18331.3i 0.0381703i
\(694\) −718594. −1.49199
\(695\) −1.02679e6 −2.12574
\(696\) 511879.i 1.05669i
\(697\) −282019. −0.580515
\(698\) 1.49477e6 3.06805
\(699\) 413796.i 0.846900i
\(700\) −621183. −1.26772
\(701\) 601181.i 1.22340i −0.791089 0.611701i \(-0.790486\pi\)
0.791089 0.611701i \(-0.209514\pi\)
\(702\) 116525. 0.236453
\(703\) 1.06259e6i 2.15008i
\(704\) 162951.i 0.328785i
\(705\) 581340.i 1.16964i
\(706\) −1.04024e6 −2.08701
\(707\) 966205.i 1.93299i
\(708\) −693755. 408037.i −1.38401 0.814016i
\(709\) 769466. 1.53072 0.765362 0.643600i \(-0.222560\pi\)
0.765362 + 0.643600i \(0.222560\pi\)
\(710\) 584818.i 1.16012i
\(711\) 40433.4 0.0799837
\(712\) 561105. 1.10684
\(713\) −48370.6 −0.0951485
\(714\) 991693.i 1.94527i
\(715\) −28504.7 −0.0557577
\(716\) 924096.i 1.80256i
\(717\) 143634. 0.279396
\(718\) 493444.i 0.957171i
\(719\) 412760.i 0.798435i 0.916856 + 0.399218i \(0.130718\pi\)
−0.916856 + 0.399218i \(0.869282\pi\)
\(720\) 781045. 1.50664
\(721\) 1.04951e6i 2.01890i
\(722\) 1.31196e6i 2.51678i
\(723\) −61144.8 −0.116972
\(724\) −1.23655e6 −2.35904
\(725\) −85343.8 −0.162366
\(726\) 588200.i 1.11597i
\(727\) −352870. −0.667645 −0.333822 0.942636i \(-0.608339\pi\)
−0.333822 + 0.942636i \(0.608339\pi\)
\(728\) 1.72071e6 3.24673
\(729\) 19683.0 0.0370370
\(730\) −1.98406e6 −3.72313
\(731\) 757015.i 1.41667i
\(732\) 541981.i 1.01149i
\(733\) 566886. 1.05509 0.527543 0.849528i \(-0.323113\pi\)
0.527543 + 0.849528i \(0.323113\pi\)
\(734\) 488129. 0.906029
\(735\) −428392. −0.792987
\(736\) 169996. 0.313821
\(737\) −34093.1 −0.0627670
\(738\) 175476.i 0.322184i
\(739\) 110960.i 0.203179i −0.994826 0.101589i \(-0.967607\pi\)
0.994826 0.101589i \(-0.0323928\pi\)
\(740\) 2.47162e6i 4.51354i
\(741\) 303404.i 0.552567i
\(742\) 2.16022e6i 3.92364i
\(743\) −565178. −1.02378 −0.511891 0.859050i \(-0.671055\pi\)
−0.511891 + 0.859050i \(0.671055\pi\)
\(744\) 1.41742e6 2.56066
\(745\) 741904.i 1.33670i
\(746\) 796617.i 1.43144i
\(747\) 107603.i 0.192834i
\(748\) 140255.i 0.250677i
\(749\) −71712.3 −0.127829
\(750\) 500185.i 0.889218i
\(751\) 217676.i 0.385950i −0.981204 0.192975i \(-0.938186\pi\)
0.981204 0.192975i \(-0.0618136\pi\)
\(752\) 3.96119e6i 7.00471i
\(753\) 513190. 0.905083
\(754\) 369141. 0.649306
\(755\) 530657.i 0.930936i
\(756\) 453850. 0.794088
\(757\) 169980. 0.296623 0.148312 0.988941i \(-0.452616\pi\)
0.148312 + 0.988941i \(0.452616\pi\)
\(758\) 896194.i 1.55978i
\(759\) −1907.25 −0.00331073
\(760\) 3.46431e6i 5.99777i
\(761\) 880285. 1.52004 0.760019 0.649901i \(-0.225190\pi\)
0.760019 + 0.649901i \(0.225190\pi\)
\(762\) 627693.i 1.08103i
\(763\) 1.08570e6i 1.86493i
\(764\) 988836.i 1.69409i
\(765\) 260480. 0.445093
\(766\) 534349.i 0.910684i
\(767\) 188449. 320405.i 0.320333 0.544639i
\(768\) −1.23750e6 −2.09808
\(769\) 619749.i 1.04801i 0.851717 + 0.524003i \(0.175562\pi\)
−0.851717 + 0.524003i \(0.824438\pi\)
\(770\) −150943. −0.254584
\(771\) −187515. −0.315447
\(772\) −1.00267e6 −1.68238
\(773\) 1.11076e6i 1.85892i −0.368917 0.929462i \(-0.620271\pi\)
0.368917 0.929462i \(-0.379729\pi\)
\(774\) −471023. −0.786250
\(775\) 236321.i 0.393458i
\(776\) −2.04144e6 −3.39011
\(777\) 734091.i 1.21593i
\(778\) 15332.7i 0.0253313i
\(779\) −456898. −0.752912
\(780\) 705727.i 1.15997i
\(781\) 24565.7i 0.0402743i
\(782\) 103179. 0.168725
\(783\) 62354.0 0.101705
\(784\) 2.91902e6 4.74903
\(785\) 1.32991e6i 2.15816i
\(786\) 50366.4 0.0815259
\(787\) 243033. 0.392389 0.196194 0.980565i \(-0.437142\pi\)
0.196194 + 0.980565i \(0.437142\pi\)
\(788\) −495647. −0.798216
\(789\) 86190.0