Properties

Label 177.5.c.a.58.6
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 58.6
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.35

$q$-expansion

\(f(q)\) \(=\) \(q-6.10324i q^{2} -5.19615 q^{3} -21.2495 q^{4} -12.8499 q^{5} +31.7133i q^{6} +4.61608 q^{7} +32.0389i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-6.10324i q^{2} -5.19615 q^{3} -21.2495 q^{4} -12.8499 q^{5} +31.7133i q^{6} +4.61608 q^{7} +32.0389i q^{8} +27.0000 q^{9} +78.4262i q^{10} +159.523i q^{11} +110.416 q^{12} +148.997i q^{13} -28.1731i q^{14} +66.7702 q^{15} -144.451 q^{16} +154.411 q^{17} -164.787i q^{18} +313.342 q^{19} +273.055 q^{20} -23.9859 q^{21} +973.607 q^{22} -420.147i q^{23} -166.479i q^{24} -459.879 q^{25} +909.363 q^{26} -140.296 q^{27} -98.0895 q^{28} +1422.43 q^{29} -407.514i q^{30} -1100.16i q^{31} +1394.24i q^{32} -828.906i q^{33} -942.405i q^{34} -59.3164 q^{35} -573.736 q^{36} -186.690i q^{37} -1912.40i q^{38} -774.211i q^{39} -411.698i q^{40} +435.578 q^{41} +146.391i q^{42} +2365.57i q^{43} -3389.78i q^{44} -346.948 q^{45} -2564.25 q^{46} +2367.77i q^{47} +750.588 q^{48} -2379.69 q^{49} +2806.75i q^{50} -802.342 q^{51} -3166.11i q^{52} +3945.26 q^{53} +856.260i q^{54} -2049.86i q^{55} +147.894i q^{56} -1628.17 q^{57} -8681.45i q^{58} +(2040.07 + 2820.55i) q^{59} -1418.83 q^{60} +1734.71i q^{61} -6714.53 q^{62} +124.634 q^{63} +6198.17 q^{64} -1914.60i q^{65} -5059.01 q^{66} -2714.23i q^{67} -3281.15 q^{68} +2183.15i q^{69} +362.022i q^{70} +5431.15 q^{71} +865.051i q^{72} -2072.73i q^{73} -1139.41 q^{74} +2389.60 q^{75} -6658.35 q^{76} +736.372i q^{77} -4725.19 q^{78} +10773.3 q^{79} +1856.18 q^{80} +729.000 q^{81} -2658.44i q^{82} +10956.5i q^{83} +509.688 q^{84} -1984.17 q^{85} +14437.6 q^{86} -7391.19 q^{87} -5110.95 q^{88} +1731.25i q^{89} +2117.51i q^{90} +687.782i q^{91} +8927.90i q^{92} +5716.59i q^{93} +14451.1 q^{94} -4026.42 q^{95} -7244.69i q^{96} +3594.71i q^{97} +14523.8i q^{98} +4307.12i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.10324i 1.52581i −0.646511 0.762905i \(-0.723773\pi\)
0.646511 0.762905i \(-0.276227\pi\)
\(3\) −5.19615 −0.577350
\(4\) −21.2495 −1.32809
\(5\) −12.8499 −0.513997 −0.256999 0.966412i \(-0.582734\pi\)
−0.256999 + 0.966412i \(0.582734\pi\)
\(6\) 31.7133i 0.880926i
\(7\) 4.61608 0.0942058 0.0471029 0.998890i \(-0.485001\pi\)
0.0471029 + 0.998890i \(0.485001\pi\)
\(8\) 32.0389i 0.500608i
\(9\) 27.0000 0.333333
\(10\) 78.4262i 0.784262i
\(11\) 159.523i 1.31837i 0.751980 + 0.659186i \(0.229099\pi\)
−0.751980 + 0.659186i \(0.770901\pi\)
\(12\) 110.416 0.766775
\(13\) 148.997i 0.881638i 0.897596 + 0.440819i \(0.145312\pi\)
−0.897596 + 0.440819i \(0.854688\pi\)
\(14\) 28.1731i 0.143740i
\(15\) 66.7702 0.296756
\(16\) −144.451 −0.564261
\(17\) 154.411 0.534293 0.267147 0.963656i \(-0.413919\pi\)
0.267147 + 0.963656i \(0.413919\pi\)
\(18\) 164.787i 0.508603i
\(19\) 313.342 0.867982 0.433991 0.900917i \(-0.357105\pi\)
0.433991 + 0.900917i \(0.357105\pi\)
\(20\) 273.055 0.682636
\(21\) −23.9859 −0.0543897
\(22\) 973.607 2.01158
\(23\) 420.147i 0.794228i −0.917769 0.397114i \(-0.870012\pi\)
0.917769 0.397114i \(-0.129988\pi\)
\(24\) 166.479i 0.289026i
\(25\) −459.879 −0.735807
\(26\) 909.363 1.34521
\(27\) −140.296 −0.192450
\(28\) −98.0895 −0.125114
\(29\) 1422.43 1.69136 0.845680 0.533690i \(-0.179195\pi\)
0.845680 + 0.533690i \(0.179195\pi\)
\(30\) 407.514i 0.452794i
\(31\) 1100.16i 1.14481i −0.819972 0.572403i \(-0.806011\pi\)
0.819972 0.572403i \(-0.193989\pi\)
\(32\) 1394.24i 1.36156i
\(33\) 828.906i 0.761163i
\(34\) 942.405i 0.815230i
\(35\) −59.3164 −0.0484215
\(36\) −573.736 −0.442698
\(37\) 186.690i 0.136370i −0.997673 0.0681848i \(-0.978279\pi\)
0.997673 0.0681848i \(-0.0217207\pi\)
\(38\) 1912.40i 1.32437i
\(39\) 774.211i 0.509014i
\(40\) 411.698i 0.257311i
\(41\) 435.578 0.259118 0.129559 0.991572i \(-0.458644\pi\)
0.129559 + 0.991572i \(0.458644\pi\)
\(42\) 146.391i 0.0829884i
\(43\) 2365.57i 1.27938i 0.768634 + 0.639689i \(0.220937\pi\)
−0.768634 + 0.639689i \(0.779063\pi\)
\(44\) 3389.78i 1.75092i
\(45\) −346.948 −0.171332
\(46\) −2564.25 −1.21184
\(47\) 2367.77i 1.07187i 0.844258 + 0.535937i \(0.180042\pi\)
−0.844258 + 0.535937i \(0.819958\pi\)
\(48\) 750.588 0.325776
\(49\) −2379.69 −0.991125
\(50\) 2806.75i 1.12270i
\(51\) −802.342 −0.308474
\(52\) 3166.11i 1.17090i
\(53\) 3945.26 1.40451 0.702254 0.711927i \(-0.252177\pi\)
0.702254 + 0.711927i \(0.252177\pi\)
\(54\) 856.260i 0.293642i
\(55\) 2049.86i 0.677640i
\(56\) 147.894i 0.0471602i
\(57\) −1628.17 −0.501130
\(58\) 8681.45i 2.58069i
\(59\) 2040.07 + 2820.55i 0.586057 + 0.810270i
\(60\) −1418.83 −0.394120
\(61\) 1734.71i 0.466194i 0.972453 + 0.233097i \(0.0748860\pi\)
−0.972453 + 0.233097i \(0.925114\pi\)
\(62\) −6714.53 −1.74676
\(63\) 124.634 0.0314019
\(64\) 6198.17 1.51322
\(65\) 1914.60i 0.453160i
\(66\) −5059.01 −1.16139
\(67\) 2714.23i 0.604640i −0.953206 0.302320i \(-0.902239\pi\)
0.953206 0.302320i \(-0.0977611\pi\)
\(68\) −3281.15 −0.709592
\(69\) 2183.15i 0.458548i
\(70\) 362.022i 0.0738820i
\(71\) 5431.15 1.07740 0.538698 0.842499i \(-0.318916\pi\)
0.538698 + 0.842499i \(0.318916\pi\)
\(72\) 865.051i 0.166869i
\(73\) 2072.73i 0.388953i −0.980907 0.194476i \(-0.937699\pi\)
0.980907 0.194476i \(-0.0623008\pi\)
\(74\) −1139.41 −0.208074
\(75\) 2389.60 0.424818
\(76\) −6658.35 −1.15276
\(77\) 736.372i 0.124198i
\(78\) −4725.19 −0.776659
\(79\) 10773.3 1.72622 0.863108 0.505019i \(-0.168515\pi\)
0.863108 + 0.505019i \(0.168515\pi\)
\(80\) 1856.18 0.290029
\(81\) 729.000 0.111111
\(82\) 2658.44i 0.395365i
\(83\) 10956.5i 1.59044i 0.606321 + 0.795220i \(0.292645\pi\)
−0.606321 + 0.795220i \(0.707355\pi\)
\(84\) 509.688 0.0722347
\(85\) −1984.17 −0.274625
\(86\) 14437.6 1.95209
\(87\) −7391.19 −0.976508
\(88\) −5110.95 −0.659988
\(89\) 1731.25i 0.218565i 0.994011 + 0.109283i \(0.0348553\pi\)
−0.994011 + 0.109283i \(0.965145\pi\)
\(90\) 2117.51i 0.261421i
\(91\) 687.782i 0.0830555i
\(92\) 8927.90i 1.05481i
\(93\) 5716.59i 0.660954i
\(94\) 14451.1 1.63547
\(95\) −4026.42 −0.446140
\(96\) 7244.69i 0.786099i
\(97\) 3594.71i 0.382050i 0.981585 + 0.191025i \(0.0611812\pi\)
−0.981585 + 0.191025i \(0.938819\pi\)
\(98\) 14523.8i 1.51227i
\(99\) 4307.12i 0.439457i
\(100\) 9772.20 0.977220
\(101\) 9157.70i 0.897726i 0.893601 + 0.448863i \(0.148171\pi\)
−0.893601 + 0.448863i \(0.851829\pi\)
\(102\) 4896.88i 0.470673i
\(103\) 2682.66i 0.252866i 0.991975 + 0.126433i \(0.0403529\pi\)
−0.991975 + 0.126433i \(0.959647\pi\)
\(104\) −4773.70 −0.441355
\(105\) 308.217 0.0279562
\(106\) 24078.9i 2.14301i
\(107\) −3938.64 −0.344016 −0.172008 0.985096i \(-0.555026\pi\)
−0.172008 + 0.985096i \(0.555026\pi\)
\(108\) 2981.22 0.255592
\(109\) 11260.3i 0.947754i 0.880591 + 0.473877i \(0.157146\pi\)
−0.880591 + 0.473877i \(0.842854\pi\)
\(110\) −12510.8 −1.03395
\(111\) 970.069i 0.0787330i
\(112\) −666.797 −0.0531567
\(113\) 9397.40i 0.735954i 0.929835 + 0.367977i \(0.119950\pi\)
−0.929835 + 0.367977i \(0.880050\pi\)
\(114\) 9937.11i 0.764628i
\(115\) 5398.85i 0.408231i
\(116\) −30226.0 −2.24629
\(117\) 4022.92i 0.293879i
\(118\) 17214.5 12451.0i 1.23632 0.894212i
\(119\) 712.773 0.0503335
\(120\) 2139.25i 0.148559i
\(121\) −10806.6 −0.738105
\(122\) 10587.3 0.711323
\(123\) −2263.33 −0.149602
\(124\) 23377.8i 1.52041i
\(125\) 13940.6 0.892200
\(126\) 760.673i 0.0479134i
\(127\) −9401.70 −0.582906 −0.291453 0.956585i \(-0.594139\pi\)
−0.291453 + 0.956585i \(0.594139\pi\)
\(128\) 15521.0i 0.947328i
\(129\) 12291.9i 0.738649i
\(130\) −11685.3 −0.691435
\(131\) 28050.5i 1.63455i −0.576249 0.817274i \(-0.695484\pi\)
0.576249 0.817274i \(-0.304516\pi\)
\(132\) 17613.8i 1.01090i
\(133\) 1446.41 0.0817690
\(134\) −16565.6 −0.922566
\(135\) 1802.80 0.0989188
\(136\) 4947.16i 0.267472i
\(137\) −10546.1 −0.561888 −0.280944 0.959724i \(-0.590648\pi\)
−0.280944 + 0.959724i \(0.590648\pi\)
\(138\) 13324.3 0.699656
\(139\) 13525.1 0.700020 0.350010 0.936746i \(-0.386178\pi\)
0.350010 + 0.936746i \(0.386178\pi\)
\(140\) 1260.44 0.0643083
\(141\) 12303.3i 0.618847i
\(142\) 33147.6i 1.64390i
\(143\) −23768.4 −1.16233
\(144\) −3900.17 −0.188087
\(145\) −18278.2 −0.869355
\(146\) −12650.4 −0.593468
\(147\) 12365.2 0.572226
\(148\) 3967.07i 0.181112i
\(149\) 4534.58i 0.204251i −0.994772 0.102126i \(-0.967436\pi\)
0.994772 0.102126i \(-0.0325644\pi\)
\(150\) 14584.3i 0.648192i
\(151\) 28293.6i 1.24089i 0.784249 + 0.620446i \(0.213048\pi\)
−0.784249 + 0.620446i \(0.786952\pi\)
\(152\) 10039.1i 0.434519i
\(153\) 4169.09 0.178098
\(154\) 4494.25 0.189503
\(155\) 14137.0i 0.588427i
\(156\) 16451.6i 0.676019i
\(157\) 8264.64i 0.335293i −0.985847 0.167647i \(-0.946383\pi\)
0.985847 0.167647i \(-0.0536167\pi\)
\(158\) 65752.1i 2.63388i
\(159\) −20500.2 −0.810893
\(160\) 17915.9i 0.699839i
\(161\) 1939.43i 0.0748209i
\(162\) 4449.26i 0.169534i
\(163\) −22072.4 −0.830759 −0.415379 0.909648i \(-0.636351\pi\)
−0.415379 + 0.909648i \(0.636351\pi\)
\(164\) −9255.81 −0.344133
\(165\) 10651.4i 0.391235i
\(166\) 66870.4 2.42671
\(167\) −13873.2 −0.497445 −0.248723 0.968575i \(-0.580011\pi\)
−0.248723 + 0.968575i \(0.580011\pi\)
\(168\) 768.482i 0.0272280i
\(169\) 6360.93 0.222714
\(170\) 12109.8i 0.419026i
\(171\) 8460.22 0.289327
\(172\) 50267.2i 1.69913i
\(173\) 26589.0i 0.888402i 0.895927 + 0.444201i \(0.146512\pi\)
−0.895927 + 0.444201i \(0.853488\pi\)
\(174\) 45110.2i 1.48996i
\(175\) −2122.84 −0.0693173
\(176\) 23043.2i 0.743906i
\(177\) −10600.5 14656.0i −0.338360 0.467809i
\(178\) 10566.3 0.333489
\(179\) 23765.9i 0.741735i −0.928686 0.370867i \(-0.879060\pi\)
0.928686 0.370867i \(-0.120940\pi\)
\(180\) 7372.47 0.227545
\(181\) −25062.8 −0.765019 −0.382510 0.923951i \(-0.624940\pi\)
−0.382510 + 0.923951i \(0.624940\pi\)
\(182\) 4197.70 0.126727
\(183\) 9013.81i 0.269157i
\(184\) 13461.0 0.397597
\(185\) 2398.95i 0.0700936i
\(186\) 34889.7 1.00849
\(187\) 24632.1i 0.704397i
\(188\) 50313.9i 1.42355i
\(189\) −647.619 −0.0181299
\(190\) 24574.2i 0.680725i
\(191\) 8426.68i 0.230988i −0.993308 0.115494i \(-0.963155\pi\)
0.993308 0.115494i \(-0.0368451\pi\)
\(192\) −32206.6 −0.873660
\(193\) 5162.04 0.138582 0.0692910 0.997596i \(-0.477926\pi\)
0.0692910 + 0.997596i \(0.477926\pi\)
\(194\) 21939.4 0.582936
\(195\) 9948.55i 0.261632i
\(196\) 50567.3 1.31631
\(197\) 13261.3 0.341707 0.170853 0.985296i \(-0.445348\pi\)
0.170853 + 0.985296i \(0.445348\pi\)
\(198\) 26287.4 0.670528
\(199\) −19128.2 −0.483022 −0.241511 0.970398i \(-0.577643\pi\)
−0.241511 + 0.970398i \(0.577643\pi\)
\(200\) 14734.0i 0.368351i
\(201\) 14103.6i 0.349089i
\(202\) 55891.6 1.36976
\(203\) 6566.08 0.159336
\(204\) 17049.4 0.409683
\(205\) −5597.15 −0.133186
\(206\) 16372.9 0.385825
\(207\) 11344.0i 0.264743i
\(208\) 21522.7i 0.497474i
\(209\) 49985.2i 1.14432i
\(210\) 1881.12i 0.0426558i
\(211\) 88561.9i 1.98922i −0.103705 0.994608i \(-0.533070\pi\)
0.103705 0.994608i \(-0.466930\pi\)
\(212\) −83834.9 −1.86532
\(213\) −28221.1 −0.622035
\(214\) 24038.5i 0.524903i
\(215\) 30397.4i 0.657597i
\(216\) 4494.94i 0.0963421i
\(217\) 5078.43i 0.107847i
\(218\) 68724.1 1.44609
\(219\) 10770.2i 0.224562i
\(220\) 43558.5i 0.899969i
\(221\) 23006.7i 0.471053i
\(222\) 5920.56 0.120132
\(223\) 19289.2 0.387885 0.193943 0.981013i \(-0.437872\pi\)
0.193943 + 0.981013i \(0.437872\pi\)
\(224\) 6435.93i 0.128267i
\(225\) −12416.7 −0.245269
\(226\) 57354.6 1.12293
\(227\) 27309.5i 0.529983i 0.964251 + 0.264991i \(0.0853691\pi\)
−0.964251 + 0.264991i \(0.914631\pi\)
\(228\) 34597.8 0.665547
\(229\) 7085.68i 0.135117i −0.997715 0.0675586i \(-0.978479\pi\)
0.997715 0.0675586i \(-0.0215210\pi\)
\(230\) 32950.5 0.622882
\(231\) 3826.30i 0.0717059i
\(232\) 45573.3i 0.846709i
\(233\) 59816.5i 1.10182i 0.834566 + 0.550908i \(0.185719\pi\)
−0.834566 + 0.550908i \(0.814281\pi\)
\(234\) 24552.8 0.448404
\(235\) 30425.7i 0.550940i
\(236\) −43350.4 59935.2i −0.778339 1.07611i
\(237\) −55979.8 −0.996631
\(238\) 4350.22i 0.0767994i
\(239\) 78985.4 1.38277 0.691387 0.722485i \(-0.257000\pi\)
0.691387 + 0.722485i \(0.257000\pi\)
\(240\) −9645.01 −0.167448
\(241\) −50419.4 −0.868088 −0.434044 0.900892i \(-0.642914\pi\)
−0.434044 + 0.900892i \(0.642914\pi\)
\(242\) 65955.2i 1.12621i
\(243\) −3788.00 −0.0641500
\(244\) 36861.7i 0.619149i
\(245\) 30578.9 0.509436
\(246\) 13813.6i 0.228264i
\(247\) 46686.9i 0.765246i
\(248\) 35247.9 0.573099
\(249\) 56931.9i 0.918241i
\(250\) 85082.9i 1.36133i
\(251\) 107267. 1.70262 0.851312 0.524660i \(-0.175807\pi\)
0.851312 + 0.524660i \(0.175807\pi\)
\(252\) −2648.42 −0.0417047
\(253\) 67023.0 1.04709
\(254\) 57380.8i 0.889404i
\(255\) 10310.0 0.158555
\(256\) 4442.15 0.0677818
\(257\) 52186.5 0.790118 0.395059 0.918656i \(-0.370724\pi\)
0.395059 + 0.918656i \(0.370724\pi\)
\(258\) −75020.2 −1.12704
\(259\) 861.776i 0.0128468i
\(260\) 40684.3i 0.601838i
\(261\) 38405.7 0.563787
\(262\) −171199. −2.49401
\(263\) −109997. −1.59026 −0.795132 0.606436i \(-0.792599\pi\)
−0.795132 + 0.606436i \(0.792599\pi\)
\(264\) 26557.3 0.381044
\(265\) −50696.3 −0.721913
\(266\) 8827.79i 0.124764i
\(267\) 8995.86i 0.126189i
\(268\) 57676.0i 0.803019i
\(269\) 60277.7i 0.833014i 0.909133 + 0.416507i \(0.136746\pi\)
−0.909133 + 0.416507i \(0.863254\pi\)
\(270\) 11002.9i 0.150931i
\(271\) −68787.2 −0.936633 −0.468316 0.883561i \(-0.655139\pi\)
−0.468316 + 0.883561i \(0.655139\pi\)
\(272\) −22304.8 −0.301481
\(273\) 3573.82i 0.0479521i
\(274\) 64365.2i 0.857334i
\(275\) 73361.3i 0.970067i
\(276\) 46390.7i 0.608994i
\(277\) −136750. −1.78225 −0.891126 0.453755i \(-0.850084\pi\)
−0.891126 + 0.453755i \(0.850084\pi\)
\(278\) 82546.8i 1.06810i
\(279\) 29704.3i 0.381602i
\(280\) 1900.43i 0.0242402i
\(281\) −128919. −1.63270 −0.816349 0.577559i \(-0.804005\pi\)
−0.816349 + 0.577559i \(0.804005\pi\)
\(282\) −75089.9 −0.944242
\(283\) 35381.9i 0.441782i −0.975298 0.220891i \(-0.929103\pi\)
0.975298 0.220891i \(-0.0708965\pi\)
\(284\) −115409. −1.43088
\(285\) 20921.9 0.257579
\(286\) 145064.i 1.77349i
\(287\) 2010.66 0.0244105
\(288\) 37644.5i 0.453854i
\(289\) −59678.3 −0.714531
\(290\) 111556.i 1.32647i
\(291\) 18678.7i 0.220577i
\(292\) 44044.5i 0.516566i
\(293\) −27782.7 −0.323622 −0.161811 0.986822i \(-0.551734\pi\)
−0.161811 + 0.986822i \(0.551734\pi\)
\(294\) 75468.0i 0.873108i
\(295\) −26214.7 36243.8i −0.301232 0.416476i
\(296\) 5981.34 0.0682677
\(297\) 22380.5i 0.253721i
\(298\) −27675.6 −0.311648
\(299\) 62600.5 0.700222
\(300\) −50777.9 −0.564199
\(301\) 10919.7i 0.120525i
\(302\) 172682. 1.89336
\(303\) 47584.8i 0.518302i
\(304\) −45262.4 −0.489768
\(305\) 22290.9i 0.239622i
\(306\) 25444.9i 0.271743i
\(307\) −87467.0 −0.928042 −0.464021 0.885824i \(-0.653594\pi\)
−0.464021 + 0.885824i \(0.653594\pi\)
\(308\) 15647.5i 0.164947i
\(309\) 13939.5i 0.145992i
\(310\) 86281.2 0.897827
\(311\) 122891. 1.27057 0.635284 0.772279i \(-0.280883\pi\)
0.635284 + 0.772279i \(0.280883\pi\)
\(312\) 24804.9 0.254817
\(313\) 13347.4i 0.136242i 0.997677 + 0.0681208i \(0.0217003\pi\)
−0.997677 + 0.0681208i \(0.978300\pi\)
\(314\) −50441.0 −0.511593
\(315\) −1601.54 −0.0161405
\(316\) −228928. −2.29258
\(317\) −1111.83 −0.0110642 −0.00553210 0.999985i \(-0.501761\pi\)
−0.00553210 + 0.999985i \(0.501761\pi\)
\(318\) 125117.i 1.23727i
\(319\) 226911.i 2.22984i
\(320\) −79646.0 −0.777793
\(321\) 20465.8 0.198618
\(322\) −11836.8 −0.114162
\(323\) 48383.3 0.463757
\(324\) −15490.9 −0.147566
\(325\) 68520.6i 0.648716i
\(326\) 134713.i 1.26758i
\(327\) 58510.1i 0.547186i
\(328\) 13955.5i 0.129717i
\(329\) 10929.8i 0.100977i
\(330\) 65007.9 0.596951
\(331\) 141657. 1.29295 0.646476 0.762935i \(-0.276242\pi\)
0.646476 + 0.762935i \(0.276242\pi\)
\(332\) 232821.i 2.11225i
\(333\) 5040.63i 0.0454565i
\(334\) 84671.7i 0.759006i
\(335\) 34877.7i 0.310783i
\(336\) 3464.78 0.0306900
\(337\) 163985.i 1.44392i 0.691935 + 0.721960i \(0.256758\pi\)
−0.691935 + 0.721960i \(0.743242\pi\)
\(338\) 38822.2i 0.339819i
\(339\) 48830.3i 0.424904i
\(340\) 42162.6 0.364728
\(341\) 175501. 1.50928
\(342\) 51634.7i 0.441458i
\(343\) −22068.1 −0.187576
\(344\) −75790.3 −0.640467
\(345\) 28053.3i 0.235692i
\(346\) 162279. 1.35553
\(347\) 163886.i 1.36108i −0.732710 0.680541i \(-0.761745\pi\)
0.732710 0.680541i \(-0.238255\pi\)
\(348\) 157059. 1.29689
\(349\) 63926.5i 0.524844i 0.964953 + 0.262422i \(0.0845212\pi\)
−0.964953 + 0.262422i \(0.915479\pi\)
\(350\) 12956.2i 0.105765i
\(351\) 20903.7i 0.169671i
\(352\) −222413. −1.79505
\(353\) 87690.5i 0.703725i −0.936052 0.351863i \(-0.885548\pi\)
0.936052 0.351863i \(-0.114452\pi\)
\(354\) −89449.0 + 64697.3i −0.713788 + 0.516273i
\(355\) −69789.9 −0.553779
\(356\) 36788.3i 0.290275i
\(357\) −3703.68 −0.0290601
\(358\) −145049. −1.13175
\(359\) 119280. 0.925504 0.462752 0.886488i \(-0.346862\pi\)
0.462752 + 0.886488i \(0.346862\pi\)
\(360\) 11115.8i 0.0857704i
\(361\) −32138.1 −0.246607
\(362\) 152964.i 1.16727i
\(363\) 56152.7 0.426145
\(364\) 14615.0i 0.110305i
\(365\) 26634.4i 0.199921i
\(366\) −55013.4 −0.410683
\(367\) 56563.1i 0.419953i −0.977706 0.209977i \(-0.932661\pi\)
0.977706 0.209977i \(-0.0673388\pi\)
\(368\) 60690.5i 0.448152i
\(369\) 11760.6 0.0863728
\(370\) 14641.4 0.106949
\(371\) 18211.7 0.132313
\(372\) 121475.i 0.877809i
\(373\) 123782. 0.889691 0.444846 0.895607i \(-0.353259\pi\)
0.444846 + 0.895607i \(0.353259\pi\)
\(374\) 150335. 1.07478
\(375\) −72437.6 −0.515112
\(376\) −75860.8 −0.536589
\(377\) 211938.i 1.49117i
\(378\) 3952.57i 0.0276628i
\(379\) 237594. 1.65408 0.827042 0.562140i \(-0.190022\pi\)
0.827042 + 0.562140i \(0.190022\pi\)
\(380\) 85559.3 0.592516
\(381\) 48852.6 0.336541
\(382\) −51430.0 −0.352444
\(383\) 271890. 1.85351 0.926757 0.375661i \(-0.122584\pi\)
0.926757 + 0.375661i \(0.122584\pi\)
\(384\) 80649.6i 0.546940i
\(385\) 9462.33i 0.0638376i
\(386\) 31505.2i 0.211450i
\(387\) 63870.4i 0.426459i
\(388\) 76385.8i 0.507398i
\(389\) −76616.7 −0.506319 −0.253160 0.967425i \(-0.581470\pi\)
−0.253160 + 0.967425i \(0.581470\pi\)
\(390\) 60718.4 0.399200
\(391\) 64875.1i 0.424351i
\(392\) 76242.8i 0.496166i
\(393\) 145755.i 0.943707i
\(394\) 80936.8i 0.521379i
\(395\) −138436. −0.887270
\(396\) 91524.2i 0.583641i
\(397\) 2682.43i 0.0170195i −0.999964 0.00850977i \(-0.997291\pi\)
0.999964 0.00850977i \(-0.00270878\pi\)
\(398\) 116744.i 0.737000i
\(399\) −7515.77 −0.0472093
\(400\) 66429.9 0.415187
\(401\) 208279.i 1.29526i −0.761955 0.647630i \(-0.775760\pi\)
0.761955 0.647630i \(-0.224240\pi\)
\(402\) 86077.3 0.532643
\(403\) 163920. 1.00931
\(404\) 194597.i 1.19226i
\(405\) −9367.60 −0.0571108
\(406\) 40074.3i 0.243116i
\(407\) 29781.3 0.179786
\(408\) 25706.2i 0.154425i
\(409\) 306294.i 1.83102i 0.402299 + 0.915508i \(0.368211\pi\)
−0.402299 + 0.915508i \(0.631789\pi\)
\(410\) 34160.7i 0.203217i
\(411\) 54799.0 0.324406
\(412\) 57005.1i 0.335830i
\(413\) 9417.11 + 13019.9i 0.0552100 + 0.0763321i
\(414\) −69234.8 −0.403947
\(415\) 140791.i 0.817482i
\(416\) −207737. −1.20041
\(417\) −70278.4 −0.404157
\(418\) 305071. 1.74602
\(419\) 214239.i 1.22031i 0.792282 + 0.610155i \(0.208893\pi\)
−0.792282 + 0.610155i \(0.791107\pi\)
\(420\) −6549.45 −0.0371284
\(421\) 211231.i 1.19177i 0.803069 + 0.595886i \(0.203199\pi\)
−0.803069 + 0.595886i \(0.796801\pi\)
\(422\) −540514. −3.03516
\(423\) 63929.8i 0.357291i
\(424\) 126402.i 0.703108i
\(425\) −71010.3 −0.393137
\(426\) 172240.i 0.949107i
\(427\) 8007.56i 0.0439182i
\(428\) 83694.2 0.456886
\(429\) 123504. 0.671070
\(430\) −185523. −1.00337
\(431\) 77388.2i 0.416601i −0.978065 0.208300i \(-0.933207\pi\)
0.978065 0.208300i \(-0.0667932\pi\)
\(432\) 20265.9 0.108592
\(433\) 246940. 1.31709 0.658546 0.752541i \(-0.271172\pi\)
0.658546 + 0.752541i \(0.271172\pi\)
\(434\) −30994.8 −0.164555
\(435\) 94976.2 0.501922
\(436\) 239275.i 1.25871i
\(437\) 131649.i 0.689375i
\(438\) 65733.2 0.342639
\(439\) −43951.4 −0.228057 −0.114028 0.993477i \(-0.536376\pi\)
−0.114028 + 0.993477i \(0.536376\pi\)
\(440\) 65675.3 0.339232
\(441\) −64251.7 −0.330375
\(442\) 140415. 0.718738
\(443\) 204422.i 1.04165i −0.853665 0.520823i \(-0.825625\pi\)
0.853665 0.520823i \(-0.174375\pi\)
\(444\) 20613.5i 0.104565i
\(445\) 22246.5i 0.112342i
\(446\) 117726.i 0.591839i
\(447\) 23562.4i 0.117925i
\(448\) 28611.3 0.142554
\(449\) 37083.0 0.183943 0.0919713 0.995762i \(-0.470683\pi\)
0.0919713 + 0.995762i \(0.470683\pi\)
\(450\) 75782.3i 0.374234i
\(451\) 69484.7i 0.341614i
\(452\) 199690.i 0.977416i
\(453\) 147018.i 0.716429i
\(454\) 166676. 0.808653
\(455\) 8837.95i 0.0426903i
\(456\) 52164.8i 0.250870i
\(457\) 29076.9i 0.139225i 0.997574 + 0.0696123i \(0.0221762\pi\)
−0.997574 + 0.0696123i \(0.977824\pi\)
\(458\) −43245.6 −0.206163
\(459\) −21663.2 −0.102825
\(460\) 114723.i 0.542169i
\(461\) −254103. −1.19566 −0.597831 0.801622i \(-0.703971\pi\)
−0.597831 + 0.801622i \(0.703971\pi\)
\(462\) −23352.8 −0.109410
\(463\) 386615.i 1.80350i −0.432256 0.901751i \(-0.642282\pi\)
0.432256 0.901751i \(-0.357718\pi\)
\(464\) −205472. −0.954369
\(465\) 73457.8i 0.339729i
\(466\) 365074. 1.68116
\(467\) 344576.i 1.57998i −0.613122 0.789988i \(-0.710087\pi\)
0.613122 0.789988i \(-0.289913\pi\)
\(468\) 85484.9i 0.390299i
\(469\) 12529.1i 0.0569606i
\(470\) −185695. −0.840629
\(471\) 42944.3i 0.193582i
\(472\) −90367.4 + 65361.5i −0.405628 + 0.293385i
\(473\) −377363. −1.68670
\(474\) 341658.i 1.52067i
\(475\) −144099. −0.638667
\(476\) −15146.1 −0.0668476
\(477\) 106522. 0.468169
\(478\) 482067.i 2.10985i
\(479\) 304897. 1.32887 0.664435 0.747346i \(-0.268672\pi\)
0.664435 + 0.747346i \(0.268672\pi\)
\(480\) 93093.7i 0.404052i
\(481\) 27816.2 0.120229
\(482\) 307722.i 1.32454i
\(483\) 10077.6i 0.0431979i
\(484\) 229635. 0.980273
\(485\) 46191.8i 0.196373i
\(486\) 23119.0i 0.0978807i
\(487\) −327375. −1.38034 −0.690171 0.723646i \(-0.742465\pi\)
−0.690171 + 0.723646i \(0.742465\pi\)
\(488\) −55578.2 −0.233381
\(489\) 114692. 0.479639
\(490\) 186630.i 0.777301i
\(491\) −330527. −1.37102 −0.685511 0.728063i \(-0.740421\pi\)
−0.685511 + 0.728063i \(0.740421\pi\)
\(492\) 48094.6 0.198686
\(493\) 219639. 0.903683
\(494\) 284941. 1.16762
\(495\) 55346.2i 0.225880i
\(496\) 158919.i 0.645969i
\(497\) 25070.7 0.101497
\(498\) −347469. −1.40106
\(499\) −207100. −0.831724 −0.415862 0.909428i \(-0.636520\pi\)
−0.415862 + 0.909428i \(0.636520\pi\)
\(500\) −296231. −1.18492
\(501\) 72087.5 0.287200
\(502\) 654676.i 2.59788i
\(503\) 187431.i 0.740807i 0.928871 + 0.370403i \(0.120781\pi\)
−0.928871 + 0.370403i \(0.879219\pi\)
\(504\) 3993.15i 0.0157201i
\(505\) 117676.i 0.461429i
\(506\) 409058.i 1.59766i
\(507\) −33052.3 −0.128584
\(508\) 199781. 0.774154
\(509\) 27177.2i 0.104899i 0.998624 + 0.0524493i \(0.0167028\pi\)
−0.998624 + 0.0524493i \(0.983297\pi\)
\(510\) 62924.6i 0.241925i
\(511\) 9567.90i 0.0366416i
\(512\) 275448.i 1.05075i
\(513\) −43960.6 −0.167043
\(514\) 318507.i 1.20557i
\(515\) 34471.9i 0.129972i
\(516\) 261196.i 0.980995i
\(517\) −377714. −1.41313
\(518\) −5259.63 −0.0196018
\(519\) 138160.i 0.512919i
\(520\) 61341.7 0.226855
\(521\) 492814. 1.81555 0.907774 0.419460i \(-0.137781\pi\)
0.907774 + 0.419460i \(0.137781\pi\)
\(522\) 234399.i 0.860231i
\(523\) −154182. −0.563678 −0.281839 0.959462i \(-0.590944\pi\)
−0.281839 + 0.959462i \(0.590944\pi\)
\(524\) 596059.i 2.17083i
\(525\) 11030.6 0.0400204
\(526\) 671338.i 2.42644i
\(527\) 169876.i 0.611662i
\(528\) 119736.i 0.429494i
\(529\) 103318. 0.369202
\(530\) 309412.i 1.10150i
\(531\) 55081.8 + 76154.8i 0.195352 + 0.270090i
\(532\) −30735.5 −0.108597
\(533\) 64899.8i 0.228449i
\(534\) −54903.9 −0.192540
\(535\) 50611.3 0.176823
\(536\) 86961.0 0.302688
\(537\) 123491.i 0.428241i
\(538\) 367889. 1.27102
\(539\) 379616.i 1.30667i
\(540\) −38308.5 −0.131373
\(541\) 175670.i 0.600210i 0.953906 + 0.300105i \(0.0970217\pi\)
−0.953906 + 0.300105i \(0.902978\pi\)
\(542\) 419825.i 1.42912i
\(543\) 130230. 0.441684
\(544\) 215286.i 0.727474i
\(545\) 144694.i 0.487143i
\(546\) −21811.9 −0.0731657
\(547\) 22187.9 0.0741552 0.0370776 0.999312i \(-0.488195\pi\)
0.0370776 + 0.999312i \(0.488195\pi\)
\(548\) 224099. 0.746240
\(549\) 46837.1i 0.155398i
\(550\) −447742. −1.48014
\(551\) 445708. 1.46807
\(552\) −69945.6 −0.229553
\(553\) 49730.5 0.162620
\(554\) 834620.i 2.71938i
\(555\) 12465.3i 0.0404685i
\(556\) −287401. −0.929692
\(557\) −475276. −1.53192 −0.765959 0.642890i \(-0.777735\pi\)
−0.765959 + 0.642890i \(0.777735\pi\)
\(558\) −181292. −0.582252
\(559\) −352463. −1.12795
\(560\) 8568.30 0.0273224
\(561\) 127992.i 0.406684i
\(562\) 786826.i 2.49118i
\(563\) 28507.6i 0.0899382i −0.998988 0.0449691i \(-0.985681\pi\)
0.998988 0.0449691i \(-0.0143189\pi\)
\(564\) 261439.i 0.821886i
\(565\) 120756.i 0.378278i
\(566\) −215944. −0.674075
\(567\) 3365.13 0.0104673
\(568\) 174008.i 0.539353i
\(569\) 112438.i 0.347287i −0.984809 0.173644i \(-0.944446\pi\)
0.984809 0.173644i \(-0.0555541\pi\)
\(570\) 127691.i 0.393017i
\(571\) 428720.i 1.31493i 0.753486 + 0.657464i \(0.228371\pi\)
−0.753486 + 0.657464i \(0.771629\pi\)
\(572\) 505067. 1.54368
\(573\) 43786.3i 0.133361i
\(574\) 12271.6i 0.0372457i
\(575\) 193217.i 0.584398i
\(576\) 167350. 0.504408
\(577\) −75213.5 −0.225915 −0.112957 0.993600i \(-0.536032\pi\)
−0.112957 + 0.993600i \(0.536032\pi\)
\(578\) 364231.i 1.09024i
\(579\) −26822.8 −0.0800104
\(580\) 388402. 1.15458
\(581\) 50576.3i 0.149829i
\(582\) −114000. −0.336558
\(583\) 629360.i 1.85166i
\(584\) 66408.0 0.194713
\(585\) 51694.2i 0.151053i
\(586\) 169564.i 0.493786i
\(587\) 134395.i 0.390039i −0.980799 0.195019i \(-0.937523\pi\)
0.980799 0.195019i \(-0.0624770\pi\)
\(588\) −262755. −0.759970
\(589\) 344725.i 0.993671i
\(590\) −221205. + 159994.i −0.635463 + 0.459622i
\(591\) −68907.7 −0.197284
\(592\) 26967.5i 0.0769480i
\(593\) −351119. −0.998493 −0.499247 0.866460i \(-0.666390\pi\)
−0.499247 + 0.866460i \(0.666390\pi\)
\(594\) −136593. −0.387130
\(595\) −9159.08 −0.0258713
\(596\) 96357.6i 0.271265i
\(597\) 99392.9 0.278873
\(598\) 382066.i 1.06840i
\(599\) 31310.5 0.0872641 0.0436321 0.999048i \(-0.486107\pi\)
0.0436321 + 0.999048i \(0.486107\pi\)
\(600\) 76560.3i 0.212668i
\(601\) 583406.i 1.61518i 0.589742 + 0.807592i \(0.299229\pi\)
−0.589742 + 0.807592i \(0.700771\pi\)
\(602\) 66645.3 0.183898
\(603\) 73284.2i 0.201547i
\(604\) 601224.i 1.64802i
\(605\) 138864. 0.379384
\(606\) −290421. −0.790830
\(607\) 470041. 1.27573 0.637864 0.770149i \(-0.279818\pi\)
0.637864 + 0.770149i \(0.279818\pi\)
\(608\) 436873.i 1.18181i
\(609\) −34118.3 −0.0919927
\(610\) −136046. −0.365618
\(611\) −352790. −0.945005
\(612\) −88591.1 −0.236531
\(613\) 463701.i 1.23400i −0.786961 0.617002i \(-0.788347\pi\)
0.786961 0.617002i \(-0.211653\pi\)
\(614\) 533832.i 1.41602i
\(615\) 29083.6 0.0768950
\(616\) −23592.6 −0.0621747
\(617\) 23997.3 0.0630365 0.0315183 0.999503i \(-0.489966\pi\)
0.0315183 + 0.999503i \(0.489966\pi\)
\(618\) −85076.0 −0.222756
\(619\) 479797. 1.25221 0.626104 0.779739i \(-0.284648\pi\)
0.626104 + 0.779739i \(0.284648\pi\)
\(620\) 300403.i 0.781486i
\(621\) 58944.9i 0.152849i
\(622\) 750031.i 1.93864i
\(623\) 7991.61i 0.0205901i
\(624\) 111835.i 0.287217i
\(625\) 108289. 0.277219
\(626\) 81462.6 0.207879
\(627\) 259731.i 0.660675i
\(628\) 175619.i 0.445301i
\(629\) 28826.9i 0.0728613i
\(630\) 9774.59i 0.0246273i
\(631\) −359273. −0.902331 −0.451166 0.892440i \(-0.648992\pi\)
−0.451166 + 0.892440i \(0.648992\pi\)
\(632\) 345166.i 0.864158i
\(633\) 460181.i 1.14847i
\(634\) 6785.76i 0.0168818i
\(635\) 120811. 0.299612
\(636\) 435619. 1.07694
\(637\) 354567.i 0.873814i
\(638\) 1.38489e6 3.40232
\(639\) 146641. 0.359132
\(640\) 199444.i 0.486924i
\(641\) −107842. −0.262465 −0.131232 0.991352i \(-0.541893\pi\)
−0.131232 + 0.991352i \(0.541893\pi\)
\(642\) 124908.i 0.303053i
\(643\) 727011. 1.75840 0.879202 0.476448i \(-0.158076\pi\)
0.879202 + 0.476448i \(0.158076\pi\)
\(644\) 41212.0i 0.0993691i
\(645\) 157950.i 0.379664i
\(646\) 295295.i 0.707605i
\(647\) −413352. −0.987443 −0.493721 0.869620i \(-0.664364\pi\)
−0.493721 + 0.869620i \(0.664364\pi\)
\(648\) 23356.4i 0.0556231i
\(649\) −449942. + 325437.i −1.06824 + 0.772642i
\(650\) −418197. −0.989816
\(651\) 26388.3i 0.0622657i
\(652\) 469028. 1.10333
\(653\) −189327. −0.444002 −0.222001 0.975046i \(-0.571259\pi\)
−0.222001 + 0.975046i \(0.571259\pi\)
\(654\) −357101. −0.834901
\(655\) 360447.i 0.840153i
\(656\) −62919.6 −0.146210
\(657\) 55963.7i 0.129651i
\(658\) 66707.3 0.154071
\(659\) 496507.i 1.14328i −0.820503 0.571642i \(-0.806307\pi\)
0.820503 0.571642i \(-0.193693\pi\)
\(660\) 226337.i 0.519597i
\(661\) −542654. −1.24199 −0.620997 0.783813i \(-0.713272\pi\)
−0.620997 + 0.783813i \(0.713272\pi\)
\(662\) 864566.i 1.97280i
\(663\) 119546.i 0.271963i
\(664\) −351036. −0.796188
\(665\) −18586.3 −0.0420290
\(666\) −30764.1 −0.0693580
\(667\) 597631.i 1.34333i
\(668\) 294799. 0.660654
\(669\) −100229. −0.223946
\(670\) 212867. 0.474196
\(671\) −276726. −0.614617
\(672\) 33442.1i 0.0740551i
\(673\) 243660.i 0.537964i −0.963145 0.268982i \(-0.913313\pi\)
0.963145 0.268982i \(-0.0866873\pi\)
\(674\) 1.00084e6 2.20315
\(675\) 64519.3 0.141606
\(676\) −135166. −0.295785
\(677\) 430256. 0.938750 0.469375 0.882999i \(-0.344479\pi\)
0.469375 + 0.882999i \(0.344479\pi\)
\(678\) −298023. −0.648322
\(679\) 16593.5i 0.0359913i
\(680\) 63570.6i 0.137480i
\(681\) 141904.i 0.305986i
\(682\) 1.07112e6i 2.30287i
\(683\) 163345.i 0.350158i −0.984554 0.175079i \(-0.943982\pi\)
0.984554 0.175079i \(-0.0560181\pi\)
\(684\) −179775. −0.384254
\(685\) 135516. 0.288809
\(686\) 134687.i 0.286205i
\(687\) 36818.3i 0.0780100i
\(688\) 341709.i 0.721903i
\(689\) 587832.i 1.23827i
\(690\) −171216. −0.359621
\(691\) 529874.i 1.10973i −0.831941 0.554864i \(-0.812770\pi\)
0.831941 0.554864i \(-0.187230\pi\)
\(692\) 565002.i 1.17988i
\(693\) 19882.0i 0.0413994i
\(694\) −1.00024e6 −2.07675
\(695\) −173796. −0.359808
\(696\) 236806.i 0.488848i
\(697\) 67257.9 0.138445
\(698\) 390159. 0.800812
\(699\) 310816.i 0.636134i
\(700\) 45109.3 0.0920598
\(701\) 182341.i 0.371064i 0.982638 + 0.185532i \(0.0594008\pi\)
−0.982638 + 0.185532i \(0.940599\pi\)
\(702\) −127580. −0.258886
\(703\) 58497.7i 0.118366i
\(704\) 988750.i 1.99499i
\(705\) 158096.i 0.318085i
\(706\) −535196. −1.07375
\(707\) 42272.7i 0.0845710i
\(708\) 225255. + 311433.i 0.449374 + 0.621295i
\(709\) −860411. −1.71164 −0.855822 0.517271i \(-0.826948\pi\)
−0.855822 + 0.517271i \(0.826948\pi\)
\(710\) 425945.i 0.844960i
\(711\) 290880. 0.575405
\(712\) −55467.5 −0.109415
\(713\) −462228. −0.909237
\(714\) 22604.4i 0.0443401i
\(715\) 305423. 0.597433
\(716\) 505014.i 0.985093i
\(717\) −410420. −0.798345
\(718\) 727993.i 1.41214i
\(719\) 198523.i 0.384019i 0.981393 + 0.192010i \(0.0615005\pi\)
−0.981393 + 0.192010i \(0.938499\pi\)
\(720\) 50116.9 0.0966762
\(721\) 12383.4i 0.0238215i
\(722\) 196146.i 0.376275i
\(723\) 261987. 0.501191
\(724\) 532572. 1.01602
\(725\) −654148. −1.24452
\(726\) 342713.i 0.650216i
\(727\) −649.946 −0.00122973 −0.000614863 1.00000i \(-0.500196\pi\)
−0.000614863 1.00000i \(0.500196\pi\)
\(728\) −22035.8 −0.0415783
\(729\) 19683.0 0.0370370
\(730\) 162556. 0.305041
\(731\) 365269.i 0.683563i
\(732\) 191539.i 0.357466i
\(733\) 27948.5 0.0520176 0.0260088 0.999662i \(-0.491720\pi\)
0.0260088 + 0.999662i \(0.491720\pi\)
\(734\) −345218. −0.640769
\(735\) −158892. −0.294123
\(736\) 585785. 1.08139
\(737\) 432982. 0.797141
\(738\) 71777.8i 0.131788i
\(739\) 406137.i 0.743675i 0.928298 + 0.371838i \(0.121272\pi\)
−0.928298 + 0.371838i \(0.878728\pi\)
\(740\) 50976.5i 0.0930908i
\(741\) 242592.i 0.441815i
\(742\) 111150.i 0.201884i
\(743\) −426473. −0.772528 −0.386264 0.922388i \(-0.626235\pi\)
−0.386264 + 0.922388i \(0.626235\pi\)
\(744\) −183153. −0.330879
\(745\) 58269.1i 0.104985i
\(746\) 755470.i 1.35750i
\(747\) 295827.i 0.530147i
\(748\) 523419.i 0.935506i
\(749\) −18181.1 −0.0324083
\(750\) 442104.i 0.785962i
\(751\) 625542.i 1.10911i 0.832146 + 0.554557i \(0.187112\pi\)
−0.832146 + 0.554557i \(0.812888\pi\)
\(752\) 342026.i 0.604816i
\(753\) −557376. −0.983010
\(754\) 1.29351e6 2.27524
\(755\) 363570.i 0.637815i
\(756\) 13761.6 0.0240782
\(757\) −42832.4 −0.0747448 −0.0373724 0.999301i \(-0.511899\pi\)
−0.0373724 + 0.999301i \(0.511899\pi\)
\(758\) 1.45009e6i 2.52382i
\(759\) −348262. −0.604536
\(760\) 129002.i 0.223342i
\(761\) 297397. 0.513532 0.256766 0.966474i \(-0.417343\pi\)
0.256766 + 0.966474i \(0.417343\pi\)
\(762\) 298159.i 0.513497i
\(763\) 51978.3i 0.0892839i
\(764\) 179063.i 0.306774i
\(765\) −53572.5 −0.0915417
\(766\) 1.65941e6i 2.82811i
\(767\) −420253. + 303963.i −0.714365 + 0.516691i
\(768\) −23082.1 −0.0391338
\(769\) 211683.i 0.357960i 0.983853 + 0.178980i \(0.0572797\pi\)
−0.983853 + 0.178980i \(0.942720\pi\)
\(770\) −57750.8 −0.0974040
\(771\) −271169. −0.456175
\(772\) −109691. −0.184050
\(773\) 869866.i 1.45577i 0.685698 + 0.727886i \(0.259497\pi\)
−0.685698 + 0.727886i \(0.740503\pi\)
\(774\) 389816. 0.650696
\(775\) 505940.i 0.842356i
\(776\) −115171. −0.191257
\(777\) 4477.92i 0.00741711i
\(778\) 467610.i 0.772546i
\(779\) 136485. 0.224910
\(780\) 211402.i 0.347472i
\(781\) 866394.i 1.42041i
\(782\) −395948. −0.647478
\(783\) −199562. −0.325503
\(784\) 343748. 0.559253
\(785\) 106200.i 0.172340i
\(786\) 889575. 1.43992
\(787\) −281012. −0.453707 −0.226853 0.973929i \(-0.572844\pi\)
−0.226853 + 0.973929i \(0.572844\pi\)
\(788\) −281796. −0.453818
\(789\) 571561. 0.918140