Properties

Label 177.5.c.a.58.18
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 58.18
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.23

$q$-expansion

\(f(q)\) \(=\) \(q-1.07792i q^{2} +5.19615 q^{3} +14.8381 q^{4} +26.1400 q^{5} -5.60104i q^{6} +49.1298 q^{7} -33.2410i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-1.07792i q^{2} +5.19615 q^{3} +14.8381 q^{4} +26.1400 q^{5} -5.60104i q^{6} +49.1298 q^{7} -33.2410i q^{8} +27.0000 q^{9} -28.1769i q^{10} -190.415i q^{11} +77.1010 q^{12} +198.277i q^{13} -52.9580i q^{14} +135.828 q^{15} +201.578 q^{16} -81.6050 q^{17} -29.1038i q^{18} -590.362 q^{19} +387.868 q^{20} +255.286 q^{21} -205.252 q^{22} +808.730i q^{23} -172.725i q^{24} +58.3017 q^{25} +213.726 q^{26} +140.296 q^{27} +728.992 q^{28} -714.690 q^{29} -146.411i q^{30} -1370.46i q^{31} -749.141i q^{32} -989.426i q^{33} +87.9637i q^{34} +1284.26 q^{35} +400.628 q^{36} +2106.01i q^{37} +636.363i q^{38} +1030.28i q^{39} -868.921i q^{40} +1132.48 q^{41} -275.178i q^{42} +349.669i q^{43} -2825.40i q^{44} +705.781 q^{45} +871.746 q^{46} -2257.08i q^{47} +1047.43 q^{48} +12.7381 q^{49} -62.8446i q^{50} -424.032 q^{51} +2942.05i q^{52} +4733.28 q^{53} -151.228i q^{54} -4977.46i q^{55} -1633.12i q^{56} -3067.61 q^{57} +770.378i q^{58} +(-3019.48 - 1732.08i) q^{59} +2015.42 q^{60} -1500.86i q^{61} -1477.24 q^{62} +1326.50 q^{63} +2417.74 q^{64} +5182.96i q^{65} -1066.52 q^{66} -233.568i q^{67} -1210.86 q^{68} +4202.28i q^{69} -1384.32i q^{70} +2664.24 q^{71} -897.507i q^{72} +9123.79i q^{73} +2270.11 q^{74} +302.945 q^{75} -8759.85 q^{76} -9355.06i q^{77} +1110.55 q^{78} -8286.52 q^{79} +5269.26 q^{80} +729.000 q^{81} -1220.72i q^{82} +7478.73i q^{83} +3787.96 q^{84} -2133.16 q^{85} +376.915 q^{86} -3713.64 q^{87} -6329.59 q^{88} -10590.0i q^{89} -760.776i q^{90} +9741.29i q^{91} +12000.0i q^{92} -7121.10i q^{93} -2432.95 q^{94} -15432.1 q^{95} -3892.65i q^{96} +15056.8i q^{97} -13.7306i q^{98} -5141.21i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.07792i 0.269480i −0.990881 0.134740i \(-0.956980\pi\)
0.990881 0.134740i \(-0.0430199\pi\)
\(3\) 5.19615 0.577350
\(4\) 14.8381 0.927380
\(5\) 26.1400 1.04560 0.522801 0.852455i \(-0.324887\pi\)
0.522801 + 0.852455i \(0.324887\pi\)
\(6\) 5.60104i 0.155584i
\(7\) 49.1298 1.00265 0.501325 0.865259i \(-0.332846\pi\)
0.501325 + 0.865259i \(0.332846\pi\)
\(8\) 33.2410i 0.519391i
\(9\) 27.0000 0.333333
\(10\) 28.1769i 0.281769i
\(11\) 190.415i 1.57368i −0.617158 0.786839i \(-0.711716\pi\)
0.617158 0.786839i \(-0.288284\pi\)
\(12\) 77.1010 0.535423
\(13\) 198.277i 1.17323i 0.809864 + 0.586617i \(0.199541\pi\)
−0.809864 + 0.586617i \(0.800459\pi\)
\(14\) 52.9580i 0.270194i
\(15\) 135.828 0.603678
\(16\) 201.578 0.787415
\(17\) −81.6050 −0.282370 −0.141185 0.989983i \(-0.545091\pi\)
−0.141185 + 0.989983i \(0.545091\pi\)
\(18\) 29.1038i 0.0898267i
\(19\) −590.362 −1.63535 −0.817676 0.575678i \(-0.804738\pi\)
−0.817676 + 0.575678i \(0.804738\pi\)
\(20\) 387.868 0.969671
\(21\) 255.286 0.578880
\(22\) −205.252 −0.424075
\(23\) 808.730i 1.52879i 0.644748 + 0.764395i \(0.276962\pi\)
−0.644748 + 0.764395i \(0.723038\pi\)
\(24\) 172.725i 0.299870i
\(25\) 58.3017 0.0932828
\(26\) 213.726 0.316163
\(27\) 140.296 0.192450
\(28\) 728.992 0.929837
\(29\) −714.690 −0.849809 −0.424905 0.905238i \(-0.639692\pi\)
−0.424905 + 0.905238i \(0.639692\pi\)
\(30\) 146.411i 0.162679i
\(31\) 1370.46i 1.42607i −0.701126 0.713037i \(-0.747319\pi\)
0.701126 0.713037i \(-0.252681\pi\)
\(32\) 749.141i 0.731583i
\(33\) 989.426i 0.908564i
\(34\) 87.9637i 0.0760932i
\(35\) 1284.26 1.04837
\(36\) 400.628 0.309127
\(37\) 2106.01i 1.53835i 0.639036 + 0.769177i \(0.279334\pi\)
−0.639036 + 0.769177i \(0.720666\pi\)
\(38\) 636.363i 0.440695i
\(39\) 1030.28i 0.677367i
\(40\) 868.921i 0.543076i
\(41\) 1132.48 0.673694 0.336847 0.941559i \(-0.390640\pi\)
0.336847 + 0.941559i \(0.390640\pi\)
\(42\) 275.178i 0.155997i
\(43\) 349.669i 0.189113i 0.995520 + 0.0945563i \(0.0301432\pi\)
−0.995520 + 0.0945563i \(0.969857\pi\)
\(44\) 2825.40i 1.45940i
\(45\) 705.781 0.348534
\(46\) 871.746 0.411978
\(47\) 2257.08i 1.02176i −0.859651 0.510882i \(-0.829319\pi\)
0.859651 0.510882i \(-0.170681\pi\)
\(48\) 1047.43 0.454614
\(49\) 12.7381 0.00530533
\(50\) 62.8446i 0.0251378i
\(51\) −424.032 −0.163027
\(52\) 2942.05i 1.08803i
\(53\) 4733.28 1.68504 0.842520 0.538665i \(-0.181071\pi\)
0.842520 + 0.538665i \(0.181071\pi\)
\(54\) 151.228i 0.0518615i
\(55\) 4977.46i 1.64544i
\(56\) 1633.12i 0.520767i
\(57\) −3067.61 −0.944171
\(58\) 770.378i 0.229007i
\(59\) −3019.48 1732.08i −0.867417 0.497582i
\(60\) 2015.42 0.559840
\(61\) 1500.86i 0.403349i −0.979453 0.201675i \(-0.935362\pi\)
0.979453 0.201675i \(-0.0646384\pi\)
\(62\) −1477.24 −0.384298
\(63\) 1326.50 0.334216
\(64\) 2417.74 0.590268
\(65\) 5182.96i 1.22674i
\(66\) −1066.52 −0.244840
\(67\) 233.568i 0.0520312i −0.999662 0.0260156i \(-0.991718\pi\)
0.999662 0.0260156i \(-0.00828195\pi\)
\(68\) −1210.86 −0.261865
\(69\) 4202.28i 0.882647i
\(70\) 1384.32i 0.282515i
\(71\) 2664.24 0.528515 0.264258 0.964452i \(-0.414873\pi\)
0.264258 + 0.964452i \(0.414873\pi\)
\(72\) 897.507i 0.173130i
\(73\) 9123.79i 1.71210i 0.516892 + 0.856051i \(0.327089\pi\)
−0.516892 + 0.856051i \(0.672911\pi\)
\(74\) 2270.11 0.414556
\(75\) 302.945 0.0538568
\(76\) −8759.85 −1.51659
\(77\) 9355.06i 1.57785i
\(78\) 1110.55 0.182537
\(79\) −8286.52 −1.32776 −0.663878 0.747841i \(-0.731090\pi\)
−0.663878 + 0.747841i \(0.731090\pi\)
\(80\) 5269.26 0.823323
\(81\) 729.000 0.111111
\(82\) 1220.72i 0.181547i
\(83\) 7478.73i 1.08560i 0.839860 + 0.542802i \(0.182637\pi\)
−0.839860 + 0.542802i \(0.817363\pi\)
\(84\) 3787.96 0.536842
\(85\) −2133.16 −0.295247
\(86\) 376.915 0.0509621
\(87\) −3713.64 −0.490638
\(88\) −6329.59 −0.817354
\(89\) 10590.0i 1.33696i −0.743732 0.668478i \(-0.766946\pi\)
0.743732 0.668478i \(-0.233054\pi\)
\(90\) 760.776i 0.0939229i
\(91\) 9741.29i 1.17634i
\(92\) 12000.0i 1.41777i
\(93\) 7121.10i 0.823344i
\(94\) −2432.95 −0.275345
\(95\) −15432.1 −1.70993
\(96\) 3892.65i 0.422380i
\(97\) 15056.8i 1.60025i 0.599833 + 0.800125i \(0.295234\pi\)
−0.599833 + 0.800125i \(0.704766\pi\)
\(98\) 13.7306i 0.00142968i
\(99\) 5141.21i 0.524559i
\(100\) 865.086 0.0865086
\(101\) 7157.42i 0.701639i 0.936443 + 0.350819i \(0.114097\pi\)
−0.936443 + 0.350819i \(0.885903\pi\)
\(102\) 457.073i 0.0439324i
\(103\) 10141.1i 0.955896i −0.878388 0.477948i \(-0.841381\pi\)
0.878388 0.477948i \(-0.158619\pi\)
\(104\) 6590.91 0.609367
\(105\) 6673.19 0.605278
\(106\) 5102.10i 0.454085i
\(107\) 3578.48 0.312558 0.156279 0.987713i \(-0.450050\pi\)
0.156279 + 0.987713i \(0.450050\pi\)
\(108\) 2081.73 0.178474
\(109\) 2420.34i 0.203716i 0.994799 + 0.101858i \(0.0324787\pi\)
−0.994799 + 0.101858i \(0.967521\pi\)
\(110\) −5365.30 −0.443413
\(111\) 10943.1i 0.888169i
\(112\) 9903.50 0.789501
\(113\) 1468.79i 0.115028i 0.998345 + 0.0575140i \(0.0183174\pi\)
−0.998345 + 0.0575140i \(0.981683\pi\)
\(114\) 3306.64i 0.254435i
\(115\) 21140.2i 1.59851i
\(116\) −10604.6 −0.788097
\(117\) 5353.47i 0.391078i
\(118\) −1867.05 + 3254.76i −0.134089 + 0.233752i
\(119\) −4009.24 −0.283118
\(120\) 4515.05i 0.313545i
\(121\) −21616.9 −1.47646
\(122\) −1617.81 −0.108695
\(123\) 5884.53 0.388957
\(124\) 20335.0i 1.32251i
\(125\) −14813.5 −0.948065
\(126\) 1429.87i 0.0900647i
\(127\) −23012.3 −1.42677 −0.713383 0.700774i \(-0.752838\pi\)
−0.713383 + 0.700774i \(0.752838\pi\)
\(128\) 14592.4i 0.890649i
\(129\) 1816.93i 0.109184i
\(130\) 5586.82 0.330581
\(131\) 16089.2i 0.937543i 0.883319 + 0.468772i \(0.155303\pi\)
−0.883319 + 0.468772i \(0.844697\pi\)
\(132\) 14681.2i 0.842584i
\(133\) −29004.4 −1.63968
\(134\) −251.768 −0.0140214
\(135\) 3667.35 0.201226
\(136\) 2712.63i 0.146661i
\(137\) −4170.90 −0.222223 −0.111111 0.993808i \(-0.535441\pi\)
−0.111111 + 0.993808i \(0.535441\pi\)
\(138\) 4529.73 0.237856
\(139\) 22317.2 1.15508 0.577538 0.816364i \(-0.304014\pi\)
0.577538 + 0.816364i \(0.304014\pi\)
\(140\) 19055.9 0.972239
\(141\) 11728.1i 0.589916i
\(142\) 2871.84i 0.142424i
\(143\) 37754.9 1.84629
\(144\) 5442.61 0.262472
\(145\) −18682.0 −0.888562
\(146\) 9834.72 0.461377
\(147\) 66.1890 0.00306303
\(148\) 31249.1i 1.42664i
\(149\) 20688.1i 0.931853i −0.884823 0.465927i \(-0.845721\pi\)
0.884823 0.465927i \(-0.154279\pi\)
\(150\) 326.550i 0.0145133i
\(151\) 30416.0i 1.33397i 0.745069 + 0.666987i \(0.232417\pi\)
−0.745069 + 0.666987i \(0.767583\pi\)
\(152\) 19624.2i 0.849387i
\(153\) −2203.34 −0.0941235
\(154\) −10084.0 −0.425198
\(155\) 35823.8i 1.49111i
\(156\) 15287.3i 0.628177i
\(157\) 37967.4i 1.54032i −0.637849 0.770162i \(-0.720175\pi\)
0.637849 0.770162i \(-0.279825\pi\)
\(158\) 8932.21i 0.357804i
\(159\) 24594.8 0.972859
\(160\) 19582.6i 0.764945i
\(161\) 39732.7i 1.53284i
\(162\) 785.804i 0.0299422i
\(163\) −25366.6 −0.954745 −0.477372 0.878701i \(-0.658411\pi\)
−0.477372 + 0.878701i \(0.658411\pi\)
\(164\) 16803.8 0.624770
\(165\) 25863.6i 0.949996i
\(166\) 8061.48 0.292549
\(167\) 33472.9 1.20022 0.600110 0.799917i \(-0.295123\pi\)
0.600110 + 0.799917i \(0.295123\pi\)
\(168\) 8485.96i 0.300665i
\(169\) −10752.6 −0.376479
\(170\) 2299.38i 0.0795632i
\(171\) −15939.8 −0.545118
\(172\) 5188.42i 0.175379i
\(173\) 23093.0i 0.771594i −0.922584 0.385797i \(-0.873927\pi\)
0.922584 0.385797i \(-0.126073\pi\)
\(174\) 4003.00i 0.132217i
\(175\) 2864.35 0.0935299
\(176\) 38383.5i 1.23914i
\(177\) −15689.7 9000.17i −0.500803 0.287279i
\(178\) −11415.2 −0.360283
\(179\) 49281.4i 1.53807i −0.639205 0.769036i \(-0.720736\pi\)
0.639205 0.769036i \(-0.279264\pi\)
\(180\) 10472.4 0.323224
\(181\) 52984.7 1.61731 0.808656 0.588282i \(-0.200196\pi\)
0.808656 + 0.588282i \(0.200196\pi\)
\(182\) 10500.3 0.317001
\(183\) 7798.71i 0.232874i
\(184\) 26883.0 0.794039
\(185\) 55051.1i 1.60851i
\(186\) −7675.98 −0.221875
\(187\) 15538.8i 0.444360i
\(188\) 33490.7i 0.947565i
\(189\) 6892.72 0.192960
\(190\) 16634.6i 0.460791i
\(191\) 31600.3i 0.866213i −0.901343 0.433106i \(-0.857417\pi\)
0.901343 0.433106i \(-0.142583\pi\)
\(192\) 12562.9 0.340791
\(193\) −6662.77 −0.178871 −0.0894355 0.995993i \(-0.528506\pi\)
−0.0894355 + 0.995993i \(0.528506\pi\)
\(194\) 16230.0 0.431236
\(195\) 26931.4i 0.708256i
\(196\) 189.009 0.00492006
\(197\) −3249.83 −0.0837391 −0.0418696 0.999123i \(-0.513331\pi\)
−0.0418696 + 0.999123i \(0.513331\pi\)
\(198\) −5541.81 −0.141358
\(199\) −39419.7 −0.995421 −0.497710 0.867343i \(-0.665826\pi\)
−0.497710 + 0.867343i \(0.665826\pi\)
\(200\) 1938.01i 0.0484502i
\(201\) 1213.65i 0.0300402i
\(202\) 7715.12 0.189078
\(203\) −35112.6 −0.852061
\(204\) −6291.83 −0.151188
\(205\) 29603.0 0.704415
\(206\) −10931.3 −0.257595
\(207\) 21835.7i 0.509597i
\(208\) 39968.3i 0.923822i
\(209\) 112414.i 2.57352i
\(210\) 7193.16i 0.163110i
\(211\) 8215.58i 0.184533i 0.995734 + 0.0922663i \(0.0294111\pi\)
−0.995734 + 0.0922663i \(0.970589\pi\)
\(212\) 70232.8 1.56267
\(213\) 13843.8 0.305138
\(214\) 3857.31i 0.0842281i
\(215\) 9140.37i 0.197736i
\(216\) 4663.58i 0.0999568i
\(217\) 67330.3i 1.42985i
\(218\) 2608.94 0.0548973
\(219\) 47408.6i 0.988482i
\(220\) 73856.0i 1.52595i
\(221\) 16180.4i 0.331287i
\(222\) 11795.8 0.239344
\(223\) 24717.2 0.497037 0.248519 0.968627i \(-0.420056\pi\)
0.248519 + 0.968627i \(0.420056\pi\)
\(224\) 36805.2i 0.733521i
\(225\) 1574.15 0.0310943
\(226\) 1583.24 0.0309978
\(227\) 22950.1i 0.445382i 0.974889 + 0.222691i \(0.0714842\pi\)
−0.974889 + 0.222691i \(0.928516\pi\)
\(228\) −45517.5 −0.875606
\(229\) 26740.2i 0.509911i 0.966953 + 0.254955i \(0.0820608\pi\)
−0.966953 + 0.254955i \(0.917939\pi\)
\(230\) 22787.5 0.430765
\(231\) 48610.3i 0.910970i
\(232\) 23757.0i 0.441383i
\(233\) 29499.8i 0.543385i −0.962384 0.271693i \(-0.912417\pi\)
0.962384 0.271693i \(-0.0875834\pi\)
\(234\) 5770.61 0.105388
\(235\) 59000.1i 1.06836i
\(236\) −44803.3 25700.8i −0.804425 0.461448i
\(237\) −43058.0 −0.766580
\(238\) 4321.64i 0.0762948i
\(239\) 37689.9 0.659825 0.329913 0.944011i \(-0.392981\pi\)
0.329913 + 0.944011i \(0.392981\pi\)
\(240\) 27379.9 0.475345
\(241\) 49193.4 0.846979 0.423489 0.905901i \(-0.360805\pi\)
0.423489 + 0.905901i \(0.360805\pi\)
\(242\) 23301.3i 0.397877i
\(243\) 3788.00 0.0641500
\(244\) 22269.9i 0.374058i
\(245\) 332.974 0.00554726
\(246\) 6343.06i 0.104816i
\(247\) 117055.i 1.91865i
\(248\) −45555.4 −0.740689
\(249\) 38860.6i 0.626774i
\(250\) 15967.8i 0.255485i
\(251\) −67494.9 −1.07133 −0.535666 0.844430i \(-0.679939\pi\)
−0.535666 + 0.844430i \(0.679939\pi\)
\(252\) 19682.8 0.309946
\(253\) 153994. 2.40582
\(254\) 24805.4i 0.384485i
\(255\) −11084.2 −0.170461
\(256\) 22954.4 0.350256
\(257\) −94378.9 −1.42892 −0.714461 0.699675i \(-0.753328\pi\)
−0.714461 + 0.699675i \(0.753328\pi\)
\(258\) 1958.51 0.0294230
\(259\) 103468.i 1.54243i
\(260\) 76905.2i 1.13765i
\(261\) −19296.6 −0.283270
\(262\) 17342.8 0.252649
\(263\) −96817.8 −1.39973 −0.699864 0.714276i \(-0.746756\pi\)
−0.699864 + 0.714276i \(0.746756\pi\)
\(264\) −32889.5 −0.471899
\(265\) 123728. 1.76188
\(266\) 31264.4i 0.441862i
\(267\) 55027.4i 0.771892i
\(268\) 3465.70i 0.0482527i
\(269\) 56566.9i 0.781732i 0.920448 + 0.390866i \(0.127824\pi\)
−0.920448 + 0.390866i \(0.872176\pi\)
\(270\) 3953.11i 0.0542264i
\(271\) −17865.0 −0.243257 −0.121628 0.992576i \(-0.538812\pi\)
−0.121628 + 0.992576i \(0.538812\pi\)
\(272\) −16449.8 −0.222343
\(273\) 50617.2i 0.679162i
\(274\) 4495.90i 0.0598846i
\(275\) 11101.5i 0.146797i
\(276\) 62353.9i 0.818550i
\(277\) −86629.0 −1.12902 −0.564512 0.825425i \(-0.690936\pi\)
−0.564512 + 0.825425i \(0.690936\pi\)
\(278\) 24056.2i 0.311270i
\(279\) 37002.3i 0.475358i
\(280\) 42689.9i 0.544514i
\(281\) −84063.8 −1.06462 −0.532312 0.846548i \(-0.678677\pi\)
−0.532312 + 0.846548i \(0.678677\pi\)
\(282\) −12642.0 −0.158971
\(283\) 10026.8i 0.125195i −0.998039 0.0625977i \(-0.980062\pi\)
0.998039 0.0625977i \(-0.0199385\pi\)
\(284\) 39532.3 0.490135
\(285\) −80187.5 −0.987227
\(286\) 40696.7i 0.497539i
\(287\) 55638.5 0.675478
\(288\) 20226.8i 0.243861i
\(289\) −76861.6 −0.920267
\(290\) 20137.7i 0.239450i
\(291\) 78237.2i 0.923905i
\(292\) 135380.i 1.58777i
\(293\) −68620.8 −0.799319 −0.399660 0.916664i \(-0.630872\pi\)
−0.399660 + 0.916664i \(0.630872\pi\)
\(294\) 71.3465i 0.000825426i
\(295\) −78929.3 45276.8i −0.906972 0.520273i
\(296\) 70005.8 0.799007
\(297\) 26714.5i 0.302855i
\(298\) −22300.1 −0.251116
\(299\) −160352. −1.79363
\(300\) 4495.12 0.0499458
\(301\) 17179.2i 0.189614i
\(302\) 32786.0 0.359480
\(303\) 37191.0i 0.405091i
\(304\) −119004. −1.28770
\(305\) 39232.6i 0.421743i
\(306\) 2375.02i 0.0253644i
\(307\) 158352. 1.68014 0.840072 0.542475i \(-0.182513\pi\)
0.840072 + 0.542475i \(0.182513\pi\)
\(308\) 138811.i 1.46326i
\(309\) 52694.7i 0.551887i
\(310\) −38615.2 −0.401823
\(311\) 58229.0 0.602030 0.301015 0.953619i \(-0.402675\pi\)
0.301015 + 0.953619i \(0.402675\pi\)
\(312\) 34247.4 0.351818
\(313\) 38385.1i 0.391808i 0.980623 + 0.195904i \(0.0627642\pi\)
−0.980623 + 0.195904i \(0.937236\pi\)
\(314\) −40925.9 −0.415086
\(315\) 34674.9 0.349457
\(316\) −122956. −1.23133
\(317\) 25846.8 0.257210 0.128605 0.991696i \(-0.458950\pi\)
0.128605 + 0.991696i \(0.458950\pi\)
\(318\) 26511.3i 0.262166i
\(319\) 136088.i 1.33733i
\(320\) 63199.8 0.617185
\(321\) 18594.3 0.180455
\(322\) 42828.7 0.413070
\(323\) 48176.5 0.461775
\(324\) 10817.0 0.103042
\(325\) 11559.9i 0.109443i
\(326\) 27343.2i 0.257285i
\(327\) 12576.5i 0.117615i
\(328\) 37644.7i 0.349910i
\(329\) 110890.i 1.02447i
\(330\) −27878.9 −0.256005
\(331\) 127603. 1.16467 0.582337 0.812947i \(-0.302138\pi\)
0.582337 + 0.812947i \(0.302138\pi\)
\(332\) 110970.i 1.00677i
\(333\) 56862.2i 0.512785i
\(334\) 36081.2i 0.323435i
\(335\) 6105.48i 0.0544039i
\(336\) 51460.1 0.455819
\(337\) 55504.5i 0.488730i −0.969683 0.244365i \(-0.921421\pi\)
0.969683 0.244365i \(-0.0785794\pi\)
\(338\) 11590.5i 0.101454i
\(339\) 7632.07i 0.0664115i
\(340\) −31652.0 −0.273806
\(341\) −260956. −2.24418
\(342\) 17181.8i 0.146898i
\(343\) −117335. −0.997330
\(344\) 11623.4 0.0982233
\(345\) 109848.i 0.922897i
\(346\) −24892.5 −0.207929
\(347\) 84690.6i 0.703358i −0.936121 0.351679i \(-0.885611\pi\)
0.936121 0.351679i \(-0.114389\pi\)
\(348\) −55103.3 −0.455008
\(349\) 74255.3i 0.609645i −0.952409 0.304822i \(-0.901403\pi\)
0.952409 0.304822i \(-0.0985971\pi\)
\(350\) 3087.54i 0.0252044i
\(351\) 27817.4i 0.225789i
\(352\) −142648. −1.15128
\(353\) 221926.i 1.78098i 0.455001 + 0.890491i \(0.349639\pi\)
−0.455001 + 0.890491i \(0.650361\pi\)
\(354\) −9701.47 + 16912.2i −0.0774160 + 0.134956i
\(355\) 69643.5 0.552616
\(356\) 157136.i 1.23987i
\(357\) −20832.6 −0.163459
\(358\) −53121.4 −0.414480
\(359\) 55048.5 0.427127 0.213563 0.976929i \(-0.431493\pi\)
0.213563 + 0.976929i \(0.431493\pi\)
\(360\) 23460.9i 0.181025i
\(361\) 218207. 1.67438
\(362\) 57113.3i 0.435833i
\(363\) −112325. −0.852436
\(364\) 144542.i 1.09092i
\(365\) 238496.i 1.79018i
\(366\) −8406.39 −0.0627549
\(367\) 146662.i 1.08889i −0.838796 0.544446i \(-0.816740\pi\)
0.838796 0.544446i \(-0.183260\pi\)
\(368\) 163022.i 1.20379i
\(369\) 30576.9 0.224565
\(370\) 59340.7 0.433460
\(371\) 232545. 1.68950
\(372\) 105664.i 0.763553i
\(373\) 166279. 1.19515 0.597573 0.801815i \(-0.296132\pi\)
0.597573 + 0.801815i \(0.296132\pi\)
\(374\) 16749.6 0.119746
\(375\) −76973.3 −0.547366
\(376\) −75027.5 −0.530695
\(377\) 141706.i 0.997025i
\(378\) 7429.80i 0.0519989i
\(379\) 60758.9 0.422991 0.211496 0.977379i \(-0.432167\pi\)
0.211496 + 0.977379i \(0.432167\pi\)
\(380\) −228983. −1.58575
\(381\) −119575. −0.823744
\(382\) −34062.6 −0.233427
\(383\) 120080. 0.818601 0.409300 0.912400i \(-0.365773\pi\)
0.409300 + 0.912400i \(0.365773\pi\)
\(384\) 75824.3i 0.514216i
\(385\) 244542.i 1.64980i
\(386\) 7181.93i 0.0482022i
\(387\) 9441.07i 0.0630375i
\(388\) 223413.i 1.48404i
\(389\) 184834. 1.22147 0.610735 0.791835i \(-0.290874\pi\)
0.610735 + 0.791835i \(0.290874\pi\)
\(390\) 29029.9 0.190861
\(391\) 65996.4i 0.431685i
\(392\) 423.427i 0.00275554i
\(393\) 83601.8i 0.541291i
\(394\) 3503.06i 0.0225660i
\(395\) −216610. −1.38830
\(396\) 76285.7i 0.486466i
\(397\) 170314.i 1.08061i 0.841469 + 0.540306i \(0.181692\pi\)
−0.841469 + 0.540306i \(0.818308\pi\)
\(398\) 42491.2i 0.268246i
\(399\) −150711. −0.946672
\(400\) 11752.4 0.0734523
\(401\) 32629.9i 0.202921i −0.994840 0.101461i \(-0.967648\pi\)
0.994840 0.101461i \(-0.0323516\pi\)
\(402\) −1308.22 −0.00809524
\(403\) 271730. 1.67312
\(404\) 106202.i 0.650686i
\(405\) 19056.1 0.116178
\(406\) 37848.5i 0.229613i
\(407\) 401015. 2.42087
\(408\) 14095.3i 0.0846745i
\(409\) 278424.i 1.66441i −0.554468 0.832205i \(-0.687078\pi\)
0.554468 0.832205i \(-0.312922\pi\)
\(410\) 31909.7i 0.189826i
\(411\) −21672.6 −0.128300
\(412\) 150475.i 0.886480i
\(413\) −148346. 85097.0i −0.869715 0.498901i
\(414\) 23537.2 0.137326
\(415\) 195494.i 1.13511i
\(416\) 148537. 0.858319
\(417\) 115964. 0.666883
\(418\) 121173. 0.693512
\(419\) 99149.5i 0.564758i 0.959303 + 0.282379i \(0.0911236\pi\)
−0.959303 + 0.282379i \(0.908876\pi\)
\(420\) 99017.3 0.561323
\(421\) 124249.i 0.701015i −0.936560 0.350508i \(-0.886009\pi\)
0.936560 0.350508i \(-0.113991\pi\)
\(422\) 8855.74 0.0497279
\(423\) 60941.1i 0.340588i
\(424\) 157339.i 0.875194i
\(425\) −4757.72 −0.0263403
\(426\) 14922.5i 0.0822287i
\(427\) 73737.1i 0.404418i
\(428\) 53097.7 0.289860
\(429\) 196180. 1.06596
\(430\) 9852.59 0.0532860
\(431\) 80751.0i 0.434704i 0.976093 + 0.217352i \(0.0697419\pi\)
−0.976093 + 0.217352i \(0.930258\pi\)
\(432\) 28280.6 0.151538
\(433\) 267478. 1.42663 0.713317 0.700841i \(-0.247192\pi\)
0.713317 + 0.700841i \(0.247192\pi\)
\(434\) −72576.7 −0.385317
\(435\) −97074.6 −0.513011
\(436\) 35913.3i 0.188922i
\(437\) 477444.i 2.50011i
\(438\) 51102.7 0.266376
\(439\) 244540. 1.26888 0.634441 0.772971i \(-0.281230\pi\)
0.634441 + 0.772971i \(0.281230\pi\)
\(440\) −165456. −0.854626
\(441\) 343.928 0.00176844
\(442\) −17441.1 −0.0892751
\(443\) 303375.i 1.54587i −0.634487 0.772933i \(-0.718789\pi\)
0.634487 0.772933i \(-0.281211\pi\)
\(444\) 162375.i 0.823671i
\(445\) 276824.i 1.39792i
\(446\) 26643.1i 0.133942i
\(447\) 107498.i 0.538006i
\(448\) 118783. 0.591832
\(449\) −265110. −1.31503 −0.657513 0.753444i \(-0.728391\pi\)
−0.657513 + 0.753444i \(0.728391\pi\)
\(450\) 1696.80i 0.00837928i
\(451\) 215641.i 1.06018i
\(452\) 21794.1i 0.106675i
\(453\) 158046.i 0.770171i
\(454\) 24738.4 0.120022
\(455\) 254638.i 1.22999i
\(456\) 101970.i 0.490394i
\(457\) 351393.i 1.68252i 0.540628 + 0.841262i \(0.318187\pi\)
−0.540628 + 0.841262i \(0.681813\pi\)
\(458\) 28823.8 0.137411
\(459\) −11448.9 −0.0543422
\(460\) 313681.i 1.48242i
\(461\) 96578.1 0.454440 0.227220 0.973843i \(-0.427036\pi\)
0.227220 + 0.973843i \(0.427036\pi\)
\(462\) −52398.0 −0.245488
\(463\) 247348.i 1.15384i −0.816800 0.576922i \(-0.804254\pi\)
0.816800 0.576922i \(-0.195746\pi\)
\(464\) −144066. −0.669153
\(465\) 186146.i 0.860890i
\(466\) −31798.5 −0.146432
\(467\) 233363.i 1.07004i 0.844841 + 0.535018i \(0.179695\pi\)
−0.844841 + 0.535018i \(0.820305\pi\)
\(468\) 79435.2i 0.362678i
\(469\) 11475.1i 0.0521690i
\(470\) −63597.4 −0.287901
\(471\) 197285.i 0.889306i
\(472\) −57576.2 + 100370.i −0.258440 + 0.450528i
\(473\) 66582.3 0.297602
\(474\) 46413.1i 0.206578i
\(475\) −34419.1 −0.152550
\(476\) −59489.5 −0.262559
\(477\) 127799. 0.561680
\(478\) 40626.7i 0.177810i
\(479\) 254275. 1.10824 0.554119 0.832438i \(-0.313055\pi\)
0.554119 + 0.832438i \(0.313055\pi\)
\(480\) 101754.i 0.441641i
\(481\) −417572. −1.80485
\(482\) 53026.5i 0.228244i
\(483\) 206457.i 0.884986i
\(484\) −320753. −1.36924
\(485\) 393584.i 1.67322i
\(486\) 4083.16i 0.0172872i
\(487\) 221313. 0.933146 0.466573 0.884483i \(-0.345488\pi\)
0.466573 + 0.884483i \(0.345488\pi\)
\(488\) −49890.2 −0.209496
\(489\) −131809. −0.551222
\(490\) 358.920i 0.00149488i
\(491\) 20143.2 0.0835537 0.0417769 0.999127i \(-0.486698\pi\)
0.0417769 + 0.999127i \(0.486698\pi\)
\(492\) 87315.2 0.360711
\(493\) 58322.3 0.239961
\(494\) −126176. −0.517038
\(495\) 134391.i 0.548480i
\(496\) 276254.i 1.12291i
\(497\) 130894. 0.529915
\(498\) 41888.7 0.168903
\(499\) −142382. −0.571813 −0.285907 0.958258i \(-0.592295\pi\)
−0.285907 + 0.958258i \(0.592295\pi\)
\(500\) −219804. −0.879217
\(501\) 173930. 0.692947
\(502\) 72754.1i 0.288702i
\(503\) 61029.3i 0.241214i 0.992700 + 0.120607i \(0.0384841\pi\)
−0.992700 + 0.120607i \(0.961516\pi\)
\(504\) 44094.3i 0.173589i
\(505\) 187095.i 0.733635i
\(506\) 165994.i 0.648321i
\(507\) −55872.2 −0.217360
\(508\) −341459. −1.32315
\(509\) 119724.i 0.462111i −0.972941 0.231056i \(-0.925782\pi\)
0.972941 0.231056i \(-0.0742179\pi\)
\(510\) 11947.9i 0.0459358i
\(511\) 448250.i 1.71664i
\(512\) 258221.i 0.985036i
\(513\) −82825.5 −0.314724
\(514\) 101733.i 0.385066i
\(515\) 265089.i 0.999487i
\(516\) 26959.8i 0.101255i
\(517\) −429782. −1.60793
\(518\) 111530. 0.415654
\(519\) 119995.i 0.445480i
\(520\) 172287. 0.637155
\(521\) 526245. 1.93871 0.969355 0.245663i \(-0.0790058\pi\)
0.969355 + 0.245663i \(0.0790058\pi\)
\(522\) 20800.2i 0.0763356i
\(523\) 43580.1 0.159325 0.0796626 0.996822i \(-0.474616\pi\)
0.0796626 + 0.996822i \(0.474616\pi\)
\(524\) 238733.i 0.869459i
\(525\) 14883.6 0.0539995
\(526\) 104362.i 0.377199i
\(527\) 111836.i 0.402681i
\(528\) 199447.i 0.715417i
\(529\) −374203. −1.33720
\(530\) 133369.i 0.474792i
\(531\) −81525.9 46766.3i −0.289139 0.165861i
\(532\) −430370. −1.52061
\(533\) 224544.i 0.790400i
\(534\) −59315.1 −0.208009
\(535\) 93541.5 0.326811
\(536\) −7764.03 −0.0270245
\(537\) 256074.i 0.888007i
\(538\) 60974.6 0.210661
\(539\) 2425.52i 0.00834888i
\(540\) 54416.4 0.186613
\(541\) 318207.i 1.08721i 0.839340 + 0.543606i \(0.182942\pi\)
−0.839340 + 0.543606i \(0.817058\pi\)
\(542\) 19257.1i 0.0655529i
\(543\) 275317. 0.933755
\(544\) 61133.7i 0.206577i
\(545\) 63267.9i 0.213005i
\(546\) 54561.3 0.183021
\(547\) −151057. −0.504856 −0.252428 0.967616i \(-0.581229\pi\)
−0.252428 + 0.967616i \(0.581229\pi\)
\(548\) −61888.2 −0.206085
\(549\) 40523.3i 0.134450i
\(550\) −11966.6 −0.0395589
\(551\) 421926. 1.38974
\(552\) 139688. 0.458439
\(553\) −407115. −1.33127
\(554\) 93379.1i 0.304250i
\(555\) 286054.i 0.928671i
\(556\) 331145. 1.07119
\(557\) −439612. −1.41697 −0.708483 0.705728i \(-0.750620\pi\)
−0.708483 + 0.705728i \(0.750620\pi\)
\(558\) −39885.6 −0.128099
\(559\) −69331.2 −0.221873
\(560\) 258878. 0.825504
\(561\) 80742.1i 0.256551i
\(562\) 90614.0i 0.286895i
\(563\) 468132.i 1.47690i −0.674308 0.738450i \(-0.735558\pi\)
0.674308 0.738450i \(-0.264442\pi\)
\(564\) 174023.i 0.547077i
\(565\) 38394.3i 0.120274i
\(566\) −10808.1 −0.0337376
\(567\) 35815.6 0.111405
\(568\) 88562.2i 0.274506i
\(569\) 156283.i 0.482711i −0.970437 0.241356i \(-0.922408\pi\)
0.970437 0.241356i \(-0.0775920\pi\)
\(570\) 86435.7i 0.266038i
\(571\) 214333.i 0.657379i −0.944438 0.328690i \(-0.893393\pi\)
0.944438 0.328690i \(-0.106607\pi\)
\(572\) 560210. 1.71222
\(573\) 164200.i 0.500108i
\(574\) 59973.8i 0.182028i
\(575\) 47150.4i 0.142610i
\(576\) 65278.9 0.196756
\(577\) −83530.0 −0.250894 −0.125447 0.992100i \(-0.540037\pi\)
−0.125447 + 0.992100i \(0.540037\pi\)
\(578\) 82850.7i 0.247994i
\(579\) −34620.8 −0.103271
\(580\) −277205. −0.824035
\(581\) 367429.i 1.08848i
\(582\) 84333.5 0.248974
\(583\) 901288.i 2.65171i
\(584\) 303284. 0.889249
\(585\) 139940.i 0.408912i
\(586\) 73967.7i 0.215401i
\(587\) 65804.0i 0.190975i −0.995431 0.0954873i \(-0.969559\pi\)
0.995431 0.0954873i \(-0.0304409\pi\)
\(588\) 982.119 0.00284060
\(589\) 809066.i 2.33213i
\(590\) −48804.7 + 85079.5i −0.140203 + 0.244411i
\(591\) −16886.6 −0.0483468
\(592\) 424525.i 1.21132i
\(593\) −180576. −0.513511 −0.256756 0.966476i \(-0.582654\pi\)
−0.256756 + 0.966476i \(0.582654\pi\)
\(594\) −28796.1 −0.0816133
\(595\) −104802. −0.296029
\(596\) 306971.i 0.864183i
\(597\) −204831. −0.574706
\(598\) 172847.i 0.483347i
\(599\) −121500. −0.338629 −0.169314 0.985562i \(-0.554155\pi\)
−0.169314 + 0.985562i \(0.554155\pi\)
\(600\) 10070.2i 0.0279727i
\(601\) 246152.i 0.681483i 0.940157 + 0.340742i \(0.110678\pi\)
−0.940157 + 0.340742i \(0.889322\pi\)
\(602\) 18517.8 0.0510971
\(603\) 6306.33i 0.0173437i
\(604\) 451315.i 1.23710i
\(605\) −565067. −1.54379
\(606\) 40089.0 0.109164
\(607\) 91016.6 0.247026 0.123513 0.992343i \(-0.460584\pi\)
0.123513 + 0.992343i \(0.460584\pi\)
\(608\) 442265.i 1.19640i
\(609\) −182450. −0.491937
\(610\) −42289.6 −0.113651
\(611\) 447526. 1.19877
\(612\) −32693.3 −0.0872883
\(613\) 165519.i 0.440481i 0.975446 + 0.220240i \(0.0706842\pi\)
−0.975446 + 0.220240i \(0.929316\pi\)
\(614\) 170691.i 0.452765i
\(615\) 153822. 0.406694
\(616\) −310971. −0.819519
\(617\) −337650. −0.886945 −0.443472 0.896288i \(-0.646254\pi\)
−0.443472 + 0.896288i \(0.646254\pi\)
\(618\) −56800.7 −0.148723
\(619\) −158426. −0.413470 −0.206735 0.978397i \(-0.566284\pi\)
−0.206735 + 0.978397i \(0.566284\pi\)
\(620\) 531557.i 1.38282i
\(621\) 113462.i 0.294216i
\(622\) 62766.2i 0.162235i
\(623\) 520286.i 1.34050i
\(624\) 207681.i 0.533369i
\(625\) −423664. −1.08458
\(626\) 41376.1 0.105585
\(627\) 584120.i 1.48582i
\(628\) 563364.i 1.42847i
\(629\) 171861.i 0.434386i
\(630\) 37376.8i 0.0941717i
\(631\) 563902. 1.41627 0.708133 0.706080i \(-0.249538\pi\)
0.708133 + 0.706080i \(0.249538\pi\)
\(632\) 275452.i 0.689624i
\(633\) 42689.4i 0.106540i
\(634\) 27860.7i 0.0693129i
\(635\) −601543. −1.49183
\(636\) 364940. 0.902210
\(637\) 2525.66i 0.00622439i
\(638\) 146692. 0.360383
\(639\) 71934.6 0.176172
\(640\) 381446.i 0.931264i
\(641\) −46995.0 −0.114376 −0.0571881 0.998363i \(-0.518213\pi\)
−0.0571881 + 0.998363i \(0.518213\pi\)
\(642\) 20043.2i 0.0486291i
\(643\) 357241. 0.864050 0.432025 0.901862i \(-0.357799\pi\)
0.432025 + 0.901862i \(0.357799\pi\)
\(644\) 589558.i 1.42153i
\(645\) 47494.7i 0.114163i
\(646\) 51930.5i 0.124439i
\(647\) −146425. −0.349790 −0.174895 0.984587i \(-0.555959\pi\)
−0.174895 + 0.984587i \(0.555959\pi\)
\(648\) 24232.7i 0.0577101i
\(649\) −329815. + 574954.i −0.783035 + 1.36503i
\(650\) 12460.6 0.0294926
\(651\) 349858.i 0.825525i
\(652\) −376392. −0.885412
\(653\) −149895. −0.351529 −0.175764 0.984432i \(-0.556240\pi\)
−0.175764 + 0.984432i \(0.556240\pi\)
\(654\) 13556.4 0.0316950
\(655\) 420572.i 0.980297i
\(656\) 228283. 0.530477
\(657\) 246342.i 0.570700i
\(658\) −119530. −0.276075
\(659\) 561285.i 1.29245i −0.763148 0.646223i \(-0.776347\pi\)
0.763148 0.646223i \(-0.223653\pi\)
\(660\) 383767.i 0.881007i
\(661\) −158811. −0.363478 −0.181739 0.983347i \(-0.558173\pi\)
−0.181739 + 0.983347i \(0.558173\pi\)
\(662\) 137546.i 0.313856i
\(663\) 84075.7i 0.191268i
\(664\) 248600. 0.563853
\(665\) −758176. −1.71446
\(666\) 61292.9 0.138185
\(667\) 577991.i 1.29918i
\(668\) 496674. 1.11306
\(669\) 128434. 0.286964
\(670\) −6581.22 −0.0146608
\(671\) −285787. −0.634742
\(672\) 191245.i 0.423499i
\(673\) 468994.i 1.03547i 0.855541 + 0.517735i \(0.173225\pi\)
−0.855541 + 0.517735i \(0.826775\pi\)
\(674\) −59829.5 −0.131703
\(675\) 8179.51 0.0179523
\(676\) −159548. −0.349139
\(677\) −560613. −1.22317 −0.611584 0.791180i \(-0.709467\pi\)
−0.611584 + 0.791180i \(0.709467\pi\)
\(678\) 8226.77 0.0178966
\(679\) 739736.i 1.60449i
\(680\) 70908.3i 0.153348i
\(681\) 119252.i 0.257142i
\(682\) 281289.i 0.604762i
\(683\) 39053.9i 0.0837188i 0.999124 + 0.0418594i \(0.0133282\pi\)
−0.999124 + 0.0418594i \(0.986672\pi\)
\(684\) −236516. −0.505531
\(685\) −109027. −0.232356
\(686\) 126478.i 0.268760i
\(687\) 138946.i 0.294397i
\(688\) 70485.7i 0.148910i
\(689\) 938499.i 1.97695i
\(690\) 118407. 0.248702
\(691\) 138810.i 0.290714i −0.989379 0.145357i \(-0.953567\pi\)
0.989379 0.145357i \(-0.0464330\pi\)
\(692\) 342657.i 0.715561i
\(693\) 252587.i 0.525949i
\(694\) −91289.7 −0.189541
\(695\) 583373. 1.20775
\(696\) 123445.i 0.254833i
\(697\) −92416.0 −0.190231
\(698\) −80041.3 −0.164287
\(699\) 153286.i 0.313724i
\(700\) 42501.5 0.0867378
\(701\) 399850.i 0.813695i 0.913496 + 0.406847i \(0.133372\pi\)
−0.913496 + 0.406847i \(0.866628\pi\)
\(702\) 29985.0 0.0608456
\(703\) 1.24331e6i 2.51575i
\(704\) 460374.i 0.928892i
\(705\) 306574.i 0.616817i
\(706\) 239219. 0.479939
\(707\) 351642.i 0.703497i
\(708\) −232805. 133545.i −0.464435 0.266417i
\(709\) −572973. −1.13983 −0.569917 0.821702i \(-0.693025\pi\)
−0.569917 + 0.821702i \(0.693025\pi\)
\(710\) 75070.1i 0.148919i
\(711\) −223736. −0.442585
\(712\) −352023. −0.694402
\(713\) 1.10833e6 2.18017
\(714\) 22455.9i 0.0440488i
\(715\) 986913. 1.93049
\(716\) 731242.i 1.42638i
\(717\) 195842. 0.380950
\(718\) 59337.9i 0.115102i
\(719\) 655458.i 1.26791i 0.773372 + 0.633953i \(0.218569\pi\)
−0.773372 + 0.633953i \(0.781431\pi\)
\(720\) 142270. 0.274441
\(721\) 498231.i 0.958429i
\(722\) 235209.i 0.451211i
\(723\) 255616. 0.489003
\(724\) 786192. 1.49986
\(725\) −41667.6 −0.0792726
\(726\) 121077.i 0.229715i
\(727\) 438565. 0.829785 0.414892 0.909870i \(-0.363819\pi\)
0.414892 + 0.909870i \(0.363819\pi\)
\(728\) 323810. 0.610981
\(729\) 19683.0 0.0370370
\(730\) 257080. 0.482417
\(731\) 28534.8i 0.0533998i
\(732\) 115718.i 0.215963i
\(733\) 524612. 0.976406 0.488203 0.872730i \(-0.337653\pi\)
0.488203 + 0.872730i \(0.337653\pi\)
\(734\) −158090. −0.293435
\(735\) 1730.18 0.00320271
\(736\) 605853. 1.11844
\(737\) −44474.9 −0.0818803
\(738\) 32959.5i 0.0605157i
\(739\) 354679.i 0.649451i −0.945808 0.324725i \(-0.894728\pi\)
0.945808 0.324725i \(-0.105272\pi\)
\(740\) 816853.i 1.49170i
\(741\) 608236.i 1.10773i
\(742\) 250665.i 0.455288i
\(743\) −9241.58 −0.0167405 −0.00837025 0.999965i \(-0.502664\pi\)
−0.00837025 + 0.999965i \(0.502664\pi\)
\(744\) −236713. −0.427637
\(745\) 540787.i 0.974347i
\(746\) 179236.i 0.322068i
\(747\) 201926.i 0.361868i
\(748\) 230567.i 0.412091i
\(749\) 175810. 0.313386
\(750\) 82971.1i 0.147504i
\(751\) 1.07245e6i 1.90150i −0.309962 0.950749i \(-0.600316\pi\)
0.309962 0.950749i \(-0.399684\pi\)
\(752\) 454978.i 0.804553i
\(753\) −350714. −0.618533
\(754\) −152748. −0.268678
\(755\) 795074.i 1.39481i
\(756\) 102275. 0.178947
\(757\) 513889. 0.896762 0.448381 0.893842i \(-0.352001\pi\)
0.448381 + 0.893842i \(0.352001\pi\)
\(758\) 65493.2i 0.113988i
\(759\) 800178. 1.38900
\(760\) 512978.i 0.888120i
\(761\) 300411. 0.518736 0.259368 0.965779i \(-0.416486\pi\)
0.259368 + 0.965779i \(0.416486\pi\)
\(762\) 128893.i 0.221983i
\(763\) 118911.i 0.204255i
\(764\) 468888.i 0.803309i
\(765\) −57595.3 −0.0984156
\(766\) 129436.i 0.220597i
\(767\) 343432. 598692.i 0.583781 1.01768i
\(768\) 119274. 0.202220
\(769\) 690998.i 1.16849i −0.811579 0.584243i \(-0.801391\pi\)
0.811579 0.584243i \(-0.198609\pi\)
\(770\) −263596. −0.444588
\(771\) −490407. −0.824988
\(772\) −98862.7 −0.165882
\(773\) 312549.i 0.523069i −0.965194 0.261534i \(-0.915771\pi\)
0.965194 0.261534i \(-0.0842285\pi\)
\(774\) 10176.7 0.0169874
\(775\) 79900.0i 0.133028i
\(776\) 500502. 0.831155
\(777\) 537634.i 0.890522i
\(778\) 199236.i 0.329162i
\(779\) −668573. −1.10173
\(780\) 399611.i 0.656823i
\(781\) 507312.i 0.831713i
\(782\) −71138.9 −0.116331
\(783\) −100268. −0.163546
\(784\) 2567.72 0.00417749
\(785\) 992470.i 1.61056i
\(786\) 90116.1 0.145867
\(787\) 858686. 1.38639 0.693194 0.720751i \(-0.256203\pi\)
0.693194 + 0.720751i \(0.256203\pi\)
\(788\) −48221.3 −0.0776580
\(789\) −503080. −0.808134