Properties

Label 177.5.c.a.58.5
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 58.5
Character \(\chi\) \(=\) 177.58
Dual form 177.5.c.a.58.36

$q$-expansion

\(f(q)\) \(=\) \(q-6.70986i q^{2} +5.19615 q^{3} -29.0222 q^{4} -41.0870 q^{5} -34.8655i q^{6} -6.70931 q^{7} +87.3773i q^{8} +27.0000 q^{9} +O(q^{10})\) \(q-6.70986i q^{2} +5.19615 q^{3} -29.0222 q^{4} -41.0870 q^{5} -34.8655i q^{6} -6.70931 q^{7} +87.3773i q^{8} +27.0000 q^{9} +275.688i q^{10} +21.2822i q^{11} -150.804 q^{12} +73.2439i q^{13} +45.0185i q^{14} -213.494 q^{15} +121.934 q^{16} +76.4439 q^{17} -181.166i q^{18} +439.767 q^{19} +1192.43 q^{20} -34.8626 q^{21} +142.801 q^{22} +164.608i q^{23} +454.026i q^{24} +1063.14 q^{25} +491.456 q^{26} +140.296 q^{27} +194.719 q^{28} -788.819 q^{29} +1432.52i q^{30} +754.698i q^{31} +579.878i q^{32} +110.586i q^{33} -512.928i q^{34} +275.665 q^{35} -783.600 q^{36} +1700.99i q^{37} -2950.77i q^{38} +380.586i q^{39} -3590.07i q^{40} +72.3910 q^{41} +233.923i q^{42} +2692.60i q^{43} -617.657i q^{44} -1109.35 q^{45} +1104.50 q^{46} -2903.21i q^{47} +633.587 q^{48} -2355.99 q^{49} -7133.51i q^{50} +397.214 q^{51} -2125.70i q^{52} +1176.18 q^{53} -941.367i q^{54} -874.422i q^{55} -586.241i q^{56} +2285.10 q^{57} +5292.86i q^{58} +(-3479.47 - 103.350i) q^{59} +6196.07 q^{60} +2041.78i q^{61} +5063.92 q^{62} -181.151 q^{63} +5841.84 q^{64} -3009.37i q^{65} +742.014 q^{66} +796.587i q^{67} -2218.57 q^{68} +855.330i q^{69} -1849.67i q^{70} -4861.25 q^{71} +2359.19i q^{72} +1824.82i q^{73} +11413.4 q^{74} +5524.23 q^{75} -12763.0 q^{76} -142.789i q^{77} +2553.68 q^{78} -7086.59 q^{79} -5009.89 q^{80} +729.000 q^{81} -485.734i q^{82} +4425.07i q^{83} +1011.79 q^{84} -3140.85 q^{85} +18067.0 q^{86} -4098.82 q^{87} -1859.58 q^{88} +8041.54i q^{89} +7443.57i q^{90} -491.415i q^{91} -4777.30i q^{92} +3921.52i q^{93} -19480.1 q^{94} -18068.7 q^{95} +3013.13i q^{96} -2354.04i q^{97} +15808.3i q^{98} +574.620i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + O(q^{10}) \) \( 40q - 320q^{4} + 80q^{7} + 1080q^{9} + 360q^{12} + 144q^{15} + 3944q^{16} - 528q^{17} + 444q^{19} + 444q^{20} + 1304q^{22} + 4880q^{25} - 1452q^{26} - 1160q^{28} - 996q^{29} + 10320q^{35} - 8640q^{36} - 5196q^{41} - 10476q^{46} + 576q^{48} + 5104q^{49} + 936q^{51} - 2184q^{53} - 2520q^{57} - 11736q^{59} - 11448q^{60} + 15240q^{62} + 2160q^{63} - 81012q^{64} + 17352q^{66} + 29568q^{68} - 5964q^{71} + 14376q^{74} - 2736q^{75} + 3480q^{76} + 37692q^{78} + 19020q^{79} + 33096q^{80} + 29160q^{81} + 25128q^{84} + 20220q^{85} - 65880q^{86} + 1512q^{87} - 14932q^{88} - 17864q^{94} + 11004q^{95} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 6.70986i 1.67747i −0.544544 0.838733i \(-0.683297\pi\)
0.544544 0.838733i \(-0.316703\pi\)
\(3\) 5.19615 0.577350
\(4\) −29.0222 −1.81389
\(5\) −41.0870 −1.64348 −0.821739 0.569864i \(-0.806996\pi\)
−0.821739 + 0.569864i \(0.806996\pi\)
\(6\) 34.8655i 0.968485i
\(7\) −6.70931 −0.136925 −0.0684623 0.997654i \(-0.521809\pi\)
−0.0684623 + 0.997654i \(0.521809\pi\)
\(8\) 87.3773i 1.36527i
\(9\) 27.0000 0.333333
\(10\) 275.688i 2.75688i
\(11\) 21.2822i 0.175886i 0.996126 + 0.0879430i \(0.0280293\pi\)
−0.996126 + 0.0879430i \(0.971971\pi\)
\(12\) −150.804 −1.04725
\(13\) 73.2439i 0.433396i 0.976239 + 0.216698i \(0.0695286\pi\)
−0.976239 + 0.216698i \(0.930471\pi\)
\(14\) 45.0185i 0.229686i
\(15\) −213.494 −0.948863
\(16\) 121.934 0.476304
\(17\) 76.4439 0.264512 0.132256 0.991216i \(-0.457778\pi\)
0.132256 + 0.991216i \(0.457778\pi\)
\(18\) 181.166i 0.559155i
\(19\) 439.767 1.21819 0.609095 0.793097i \(-0.291533\pi\)
0.609095 + 0.793097i \(0.291533\pi\)
\(20\) 1192.43 2.98109
\(21\) −34.8626 −0.0790535
\(22\) 142.801 0.295043
\(23\) 164.608i 0.311169i 0.987823 + 0.155584i \(0.0497260\pi\)
−0.987823 + 0.155584i \(0.950274\pi\)
\(24\) 454.026i 0.788239i
\(25\) 1063.14 1.70102
\(26\) 491.456 0.727006
\(27\) 140.296 0.192450
\(28\) 194.719 0.248366
\(29\) −788.819 −0.937954 −0.468977 0.883211i \(-0.655377\pi\)
−0.468977 + 0.883211i \(0.655377\pi\)
\(30\) 1432.52i 1.59168i
\(31\) 754.698i 0.785325i 0.919683 + 0.392663i \(0.128446\pi\)
−0.919683 + 0.392663i \(0.871554\pi\)
\(32\) 579.878i 0.566287i
\(33\) 110.586i 0.101548i
\(34\) 512.928i 0.443709i
\(35\) 275.665 0.225033
\(36\) −783.600 −0.604630
\(37\) 1700.99i 1.24251i 0.783610 + 0.621253i \(0.213376\pi\)
−0.783610 + 0.621253i \(0.786624\pi\)
\(38\) 2950.77i 2.04347i
\(39\) 380.586i 0.250221i
\(40\) 3590.07i 2.24379i
\(41\) 72.3910 0.0430643 0.0215321 0.999768i \(-0.493146\pi\)
0.0215321 + 0.999768i \(0.493146\pi\)
\(42\) 233.923i 0.132609i
\(43\) 2692.60i 1.45625i 0.685447 + 0.728123i \(0.259607\pi\)
−0.685447 + 0.728123i \(0.740393\pi\)
\(44\) 617.657i 0.319038i
\(45\) −1109.35 −0.547826
\(46\) 1104.50 0.521975
\(47\) 2903.21i 1.31426i −0.753775 0.657132i \(-0.771769\pi\)
0.753775 0.657132i \(-0.228231\pi\)
\(48\) 633.587 0.274994
\(49\) −2355.99 −0.981252
\(50\) 7133.51i 2.85340i
\(51\) 397.214 0.152716
\(52\) 2125.70i 0.786131i
\(53\) 1176.18 0.418719 0.209360 0.977839i \(-0.432862\pi\)
0.209360 + 0.977839i \(0.432862\pi\)
\(54\) 941.367i 0.322828i
\(55\) 874.422i 0.289065i
\(56\) 586.241i 0.186939i
\(57\) 2285.10 0.703323
\(58\) 5292.86i 1.57338i
\(59\) −3479.47 103.350i −0.999559 0.0296897i
\(60\) 6196.07 1.72113
\(61\) 2041.78i 0.548718i 0.961627 + 0.274359i \(0.0884657\pi\)
−0.961627 + 0.274359i \(0.911534\pi\)
\(62\) 5063.92 1.31736
\(63\) −181.151 −0.0456415
\(64\) 5841.84 1.42623
\(65\) 3009.37i 0.712276i
\(66\) 742.014 0.170343
\(67\) 796.587i 0.177453i 0.996056 + 0.0887266i \(0.0282797\pi\)
−0.996056 + 0.0887266i \(0.971720\pi\)
\(68\) −2218.57 −0.479795
\(69\) 855.330i 0.179653i
\(70\) 1849.67i 0.377484i
\(71\) −4861.25 −0.964343 −0.482171 0.876077i \(-0.660152\pi\)
−0.482171 + 0.876077i \(0.660152\pi\)
\(72\) 2359.19i 0.455090i
\(73\) 1824.82i 0.342433i 0.985233 + 0.171216i \(0.0547697\pi\)
−0.985233 + 0.171216i \(0.945230\pi\)
\(74\) 11413.4 2.08426
\(75\) 5524.23 0.982085
\(76\) −12763.0 −2.20966
\(77\) 142.789i 0.0240831i
\(78\) 2553.68 0.419737
\(79\) −7086.59 −1.13549 −0.567745 0.823204i \(-0.692184\pi\)
−0.567745 + 0.823204i \(0.692184\pi\)
\(80\) −5009.89 −0.782795
\(81\) 729.000 0.111111
\(82\) 485.734i 0.0722388i
\(83\) 4425.07i 0.642338i 0.947022 + 0.321169i \(0.104076\pi\)
−0.947022 + 0.321169i \(0.895924\pi\)
\(84\) 1011.79 0.143394
\(85\) −3140.85 −0.434719
\(86\) 18067.0 2.44280
\(87\) −4098.82 −0.541528
\(88\) −1859.58 −0.240132
\(89\) 8041.54i 1.01522i 0.861588 + 0.507609i \(0.169471\pi\)
−0.861588 + 0.507609i \(0.830529\pi\)
\(90\) 7443.57i 0.918959i
\(91\) 491.415i 0.0593425i
\(92\) 4777.30i 0.564425i
\(93\) 3921.52i 0.453408i
\(94\) −19480.1 −2.20463
\(95\) −18068.7 −2.00207
\(96\) 3013.13i 0.326946i
\(97\) 2354.04i 0.250190i −0.992145 0.125095i \(-0.960076\pi\)
0.992145 0.125095i \(-0.0399235\pi\)
\(98\) 15808.3i 1.64602i
\(99\) 574.620i 0.0586287i
\(100\) −30854.6 −3.08546
\(101\) 15071.0i 1.47741i −0.674032 0.738703i \(-0.735439\pi\)
0.674032 0.738703i \(-0.264561\pi\)
\(102\) 2665.25i 0.256176i
\(103\) 13089.2i 1.23378i 0.787048 + 0.616892i \(0.211608\pi\)
−0.787048 + 0.616892i \(0.788392\pi\)
\(104\) −6399.85 −0.591702
\(105\) 1432.40 0.129923
\(106\) 7892.02i 0.702387i
\(107\) −264.977 −0.0231441 −0.0115721 0.999933i \(-0.503684\pi\)
−0.0115721 + 0.999933i \(0.503684\pi\)
\(108\) −4071.70 −0.349083
\(109\) 13760.9i 1.15823i 0.815247 + 0.579113i \(0.196601\pi\)
−0.815247 + 0.579113i \(0.803399\pi\)
\(110\) −5867.25 −0.484896
\(111\) 8838.61i 0.717361i
\(112\) −818.091 −0.0652177
\(113\) 8838.66i 0.692197i 0.938198 + 0.346098i \(0.112494\pi\)
−0.938198 + 0.346098i \(0.887506\pi\)
\(114\) 15332.7i 1.17980i
\(115\) 6763.25i 0.511399i
\(116\) 22893.3 1.70134
\(117\) 1977.58i 0.144465i
\(118\) −693.464 + 23346.7i −0.0498035 + 1.67673i
\(119\) −512.886 −0.0362182
\(120\) 18654.5i 1.29545i
\(121\) 14188.1 0.969064
\(122\) 13700.1 0.920456
\(123\) 376.155 0.0248632
\(124\) 21903.0i 1.42449i
\(125\) −18001.8 −1.15211
\(126\) 1215.50i 0.0765621i
\(127\) −12508.4 −0.775524 −0.387762 0.921759i \(-0.626752\pi\)
−0.387762 + 0.921759i \(0.626752\pi\)
\(128\) 29919.9i 1.82616i
\(129\) 13991.2i 0.840764i
\(130\) −20192.4 −1.19482
\(131\) 30033.4i 1.75010i 0.484036 + 0.875048i \(0.339170\pi\)
−0.484036 + 0.875048i \(0.660830\pi\)
\(132\) 3209.44i 0.184197i
\(133\) −2950.53 −0.166800
\(134\) 5344.99 0.297672
\(135\) −5764.34 −0.316288
\(136\) 6679.46i 0.361130i
\(137\) 30546.6 1.62750 0.813751 0.581213i \(-0.197422\pi\)
0.813751 + 0.581213i \(0.197422\pi\)
\(138\) 5739.14 0.301362
\(139\) 13641.7 0.706056 0.353028 0.935613i \(-0.385152\pi\)
0.353028 + 0.935613i \(0.385152\pi\)
\(140\) −8000.41 −0.408184
\(141\) 15085.5i 0.758791i
\(142\) 32618.3i 1.61765i
\(143\) −1558.79 −0.0762283
\(144\) 3292.21 0.158768
\(145\) 32410.2 1.54151
\(146\) 12244.3 0.574419
\(147\) −12242.1 −0.566526
\(148\) 49366.5i 2.25377i
\(149\) 18026.1i 0.811949i −0.913884 0.405975i \(-0.866932\pi\)
0.913884 0.405975i \(-0.133068\pi\)
\(150\) 37066.8i 1.64741i
\(151\) 39094.7i 1.71460i −0.514814 0.857302i \(-0.672139\pi\)
0.514814 0.857302i \(-0.327861\pi\)
\(152\) 38425.6i 1.66316i
\(153\) 2063.99 0.0881706
\(154\) −958.094 −0.0403986
\(155\) 31008.2i 1.29067i
\(156\) 11045.5i 0.453873i
\(157\) 27675.1i 1.12277i −0.827556 0.561383i \(-0.810269\pi\)
0.827556 0.561383i \(-0.189731\pi\)
\(158\) 47550.1i 1.90475i
\(159\) 6111.62 0.241748
\(160\) 23825.4i 0.930680i
\(161\) 1104.41i 0.0426067i
\(162\) 4891.49i 0.186385i
\(163\) −28910.4 −1.08813 −0.544063 0.839044i \(-0.683115\pi\)
−0.544063 + 0.839044i \(0.683115\pi\)
\(164\) −2100.95 −0.0781138
\(165\) 4543.63i 0.166892i
\(166\) 29691.6 1.07750
\(167\) −44721.0 −1.60354 −0.801768 0.597635i \(-0.796107\pi\)
−0.801768 + 0.597635i \(0.796107\pi\)
\(168\) 3046.20i 0.107929i
\(169\) 23196.3 0.812168
\(170\) 21074.6i 0.729227i
\(171\) 11873.7 0.406064
\(172\) 78145.2i 2.64147i
\(173\) 37239.4i 1.24426i 0.782914 + 0.622129i \(0.213732\pi\)
−0.782914 + 0.622129i \(0.786268\pi\)
\(174\) 27502.5i 0.908394i
\(175\) −7132.92 −0.232912
\(176\) 2595.02i 0.0837752i
\(177\) −18079.8 537.022i −0.577096 0.0171414i
\(178\) 53957.6 1.70299
\(179\) 23586.9i 0.736147i −0.929797 0.368073i \(-0.880017\pi\)
0.929797 0.368073i \(-0.119983\pi\)
\(180\) 32195.7 0.993696
\(181\) −1350.22 −0.0412144 −0.0206072 0.999788i \(-0.506560\pi\)
−0.0206072 + 0.999788i \(0.506560\pi\)
\(182\) −3297.33 −0.0995450
\(183\) 10609.4i 0.316803i
\(184\) −14383.0 −0.424829
\(185\) 69888.5i 2.04203i
\(186\) 26312.9 0.760576
\(187\) 1626.90i 0.0465239i
\(188\) 84257.6i 2.38393i
\(189\) −941.290 −0.0263512
\(190\) 121238.i 3.35840i
\(191\) 34964.8i 0.958438i 0.877695 + 0.479219i \(0.159080\pi\)
−0.877695 + 0.479219i \(0.840920\pi\)
\(192\) 30355.1 0.823435
\(193\) −28062.0 −0.753362 −0.376681 0.926343i \(-0.622935\pi\)
−0.376681 + 0.926343i \(0.622935\pi\)
\(194\) −15795.3 −0.419685
\(195\) 15637.1i 0.411233i
\(196\) 68375.9 1.77988
\(197\) −8658.99 −0.223118 −0.111559 0.993758i \(-0.535584\pi\)
−0.111559 + 0.993758i \(0.535584\pi\)
\(198\) 3855.62 0.0983476
\(199\) −31291.6 −0.790173 −0.395087 0.918644i \(-0.629285\pi\)
−0.395087 + 0.918644i \(0.629285\pi\)
\(200\) 92894.1i 2.32235i
\(201\) 4139.19i 0.102453i
\(202\) −101124. −2.47830
\(203\) 5292.43 0.128429
\(204\) −11528.0 −0.277010
\(205\) −2974.33 −0.0707752
\(206\) 87826.8 2.06963
\(207\) 4444.42i 0.103723i
\(208\) 8930.90i 0.206428i
\(209\) 9359.21i 0.214263i
\(210\) 9611.19i 0.217941i
\(211\) 1277.25i 0.0286888i 0.999897 + 0.0143444i \(0.00456612\pi\)
−0.999897 + 0.0143444i \(0.995434\pi\)
\(212\) −34135.4 −0.759510
\(213\) −25259.8 −0.556764
\(214\) 1777.96i 0.0388235i
\(215\) 110631.i 2.39331i
\(216\) 12258.7i 0.262746i
\(217\) 5063.50i 0.107530i
\(218\) 92333.7 1.94288
\(219\) 9482.07i 0.197704i
\(220\) 25377.7i 0.524332i
\(221\) 5599.05i 0.114638i
\(222\) 59305.8 1.20335
\(223\) 18556.2 0.373146 0.186573 0.982441i \(-0.440262\pi\)
0.186573 + 0.982441i \(0.440262\pi\)
\(224\) 3890.58i 0.0775386i
\(225\) 28704.7 0.567007
\(226\) 59306.2 1.16114
\(227\) 61320.0i 1.19001i −0.803722 0.595005i \(-0.797150\pi\)
0.803722 0.595005i \(-0.202850\pi\)
\(228\) −66318.6 −1.27575
\(229\) 86222.5i 1.64418i 0.569356 + 0.822091i \(0.307193\pi\)
−0.569356 + 0.822091i \(0.692807\pi\)
\(230\) −45380.5 −0.857854
\(231\) 741.953i 0.0139044i
\(232\) 68924.9i 1.28056i
\(233\) 40899.5i 0.753367i −0.926342 0.376683i \(-0.877064\pi\)
0.926342 0.376683i \(-0.122936\pi\)
\(234\) 13269.3 0.242335
\(235\) 119284.i 2.15997i
\(236\) 100982. + 2999.45i 1.81309 + 0.0538539i
\(237\) −36823.0 −0.655576
\(238\) 3441.39i 0.0607547i
\(239\) 4438.81 0.0777089 0.0388544 0.999245i \(-0.487629\pi\)
0.0388544 + 0.999245i \(0.487629\pi\)
\(240\) −26032.1 −0.451947
\(241\) −65511.7 −1.12794 −0.563968 0.825797i \(-0.690726\pi\)
−0.563968 + 0.825797i \(0.690726\pi\)
\(242\) 95199.9i 1.62557i
\(243\) 3788.00 0.0641500
\(244\) 59257.0i 0.995314i
\(245\) 96800.3 1.61267
\(246\) 2523.95i 0.0417071i
\(247\) 32210.2i 0.527959i
\(248\) −65943.4 −1.07218
\(249\) 22993.3i 0.370854i
\(250\) 120789.i 1.93263i
\(251\) −26481.1 −0.420328 −0.210164 0.977666i \(-0.567400\pi\)
−0.210164 + 0.977666i \(0.567400\pi\)
\(252\) 5257.41 0.0827887
\(253\) −3503.23 −0.0547302
\(254\) 83929.8i 1.30091i
\(255\) −16320.3 −0.250985
\(256\) −107289. −1.63710
\(257\) −73530.4 −1.11327 −0.556635 0.830757i \(-0.687908\pi\)
−0.556635 + 0.830757i \(0.687908\pi\)
\(258\) 93878.7 1.41035
\(259\) 11412.5i 0.170130i
\(260\) 87338.5i 1.29199i
\(261\) −21298.1 −0.312651
\(262\) 201520. 2.93573
\(263\) −58037.1 −0.839062 −0.419531 0.907741i \(-0.637806\pi\)
−0.419531 + 0.907741i \(0.637806\pi\)
\(264\) −9662.67 −0.138640
\(265\) −48325.8 −0.688156
\(266\) 19797.6i 0.279802i
\(267\) 41785.1i 0.586136i
\(268\) 23118.7i 0.321880i
\(269\) 119064.i 1.64542i −0.568464 0.822708i \(-0.692462\pi\)
0.568464 0.822708i \(-0.307538\pi\)
\(270\) 38677.9i 0.530561i
\(271\) 95279.2 1.29736 0.648679 0.761062i \(-0.275322\pi\)
0.648679 + 0.761062i \(0.275322\pi\)
\(272\) 9321.10 0.125988
\(273\) 2553.47i 0.0342614i
\(274\) 204963.i 2.73008i
\(275\) 22625.9i 0.299186i
\(276\) 24823.6i 0.325871i
\(277\) −70994.3 −0.925260 −0.462630 0.886551i \(-0.653094\pi\)
−0.462630 + 0.886551i \(0.653094\pi\)
\(278\) 91534.0i 1.18438i
\(279\) 20376.8i 0.261775i
\(280\) 24086.9i 0.307230i
\(281\) 89157.2 1.12913 0.564565 0.825389i \(-0.309044\pi\)
0.564565 + 0.825389i \(0.309044\pi\)
\(282\) −101222. −1.27285
\(283\) 121771.i 1.52044i −0.649664 0.760222i \(-0.725090\pi\)
0.649664 0.760222i \(-0.274910\pi\)
\(284\) 141084. 1.74921
\(285\) −93887.6 −1.15590
\(286\) 10459.3i 0.127870i
\(287\) −485.693 −0.00589656
\(288\) 15656.7i 0.188762i
\(289\) −77677.3 −0.930034
\(290\) 217468.i 2.58582i
\(291\) 12231.9i 0.144447i
\(292\) 52960.5i 0.621135i
\(293\) −14072.9 −0.163927 −0.0819633 0.996635i \(-0.526119\pi\)
−0.0819633 + 0.996635i \(0.526119\pi\)
\(294\) 82142.5i 0.950327i
\(295\) 142961. + 4246.34i 1.64275 + 0.0487944i
\(296\) −148628. −1.69636
\(297\) 2985.81i 0.0338493i
\(298\) −120953. −1.36202
\(299\) −12056.5 −0.134859
\(300\) −160325. −1.78139
\(301\) 18065.5i 0.199396i
\(302\) −262320. −2.87619
\(303\) 78311.3i 0.852980i
\(304\) 53622.4 0.580229
\(305\) 83890.6i 0.901807i
\(306\) 13849.1i 0.147903i
\(307\) 84061.4 0.891908 0.445954 0.895056i \(-0.352865\pi\)
0.445954 + 0.895056i \(0.352865\pi\)
\(308\) 4144.05i 0.0436841i
\(309\) 68013.5i 0.712325i
\(310\) −208061. −2.16505
\(311\) −27808.7 −0.287514 −0.143757 0.989613i \(-0.545918\pi\)
−0.143757 + 0.989613i \(0.545918\pi\)
\(312\) −33254.6 −0.341619
\(313\) 3675.80i 0.0375200i −0.999824 0.0187600i \(-0.994028\pi\)
0.999824 0.0187600i \(-0.00597184\pi\)
\(314\) −185696. −1.88340
\(315\) 7442.96 0.0750109
\(316\) 205669. 2.05965
\(317\) 30461.2 0.303129 0.151565 0.988447i \(-0.451569\pi\)
0.151565 + 0.988447i \(0.451569\pi\)
\(318\) 41008.1i 0.405523i
\(319\) 16787.8i 0.164973i
\(320\) −240023. −2.34398
\(321\) −1376.86 −0.0133623
\(322\) −7410.42 −0.0714712
\(323\) 33617.5 0.322226
\(324\) −21157.2 −0.201543
\(325\) 77868.4i 0.737215i
\(326\) 193985.i 1.82529i
\(327\) 71503.7i 0.668703i
\(328\) 6325.33i 0.0587943i
\(329\) 19478.5i 0.179955i
\(330\) −30487.1 −0.279955
\(331\) 206607. 1.88577 0.942884 0.333120i \(-0.108102\pi\)
0.942884 + 0.333120i \(0.108102\pi\)
\(332\) 128425.i 1.16513i
\(333\) 45926.7i 0.414169i
\(334\) 300072.i 2.68988i
\(335\) 32729.4i 0.291641i
\(336\) −4250.93 −0.0376535
\(337\) 145823.i 1.28401i −0.766702 0.642004i \(-0.778103\pi\)
0.766702 0.642004i \(-0.221897\pi\)
\(338\) 155644.i 1.36238i
\(339\) 45927.0i 0.399640i
\(340\) 91154.4 0.788533
\(341\) −16061.6 −0.138128
\(342\) 79670.9i 0.681158i
\(343\) 31916.1 0.271282
\(344\) −235272. −1.98817
\(345\) 35142.9i 0.295256i
\(346\) 249871. 2.08720
\(347\) 32401.9i 0.269098i 0.990907 + 0.134549i \(0.0429586\pi\)
−0.990907 + 0.134549i \(0.957041\pi\)
\(348\) 118957. 0.982271
\(349\) 165183.i 1.35617i 0.734982 + 0.678086i \(0.237191\pi\)
−0.734982 + 0.678086i \(0.762809\pi\)
\(350\) 47860.9i 0.390701i
\(351\) 10275.8i 0.0834070i
\(352\) −12341.1 −0.0996020
\(353\) 193446.i 1.55242i 0.630472 + 0.776212i \(0.282861\pi\)
−0.630472 + 0.776212i \(0.717139\pi\)
\(354\) −3603.34 + 121313.i −0.0287541 + 0.968058i
\(355\) 199734. 1.58488
\(356\) 233383.i 1.84149i
\(357\) −2665.03 −0.0209106
\(358\) −158265. −1.23486
\(359\) −94638.7 −0.734311 −0.367155 0.930160i \(-0.619668\pi\)
−0.367155 + 0.930160i \(0.619668\pi\)
\(360\) 96931.8i 0.747931i
\(361\) 63073.9 0.483989
\(362\) 9059.82i 0.0691357i
\(363\) 73723.4 0.559489
\(364\) 14262.0i 0.107641i
\(365\) 74976.5i 0.562781i
\(366\) 71187.6 0.531425
\(367\) 250626.i 1.86078i 0.366576 + 0.930388i \(0.380530\pi\)
−0.366576 + 0.930388i \(0.619470\pi\)
\(368\) 20071.3i 0.148211i
\(369\) 1954.56 0.0143548
\(370\) −468942. −3.42544
\(371\) −7891.37 −0.0573330
\(372\) 113811.i 0.822431i
\(373\) 65456.3 0.470472 0.235236 0.971938i \(-0.424414\pi\)
0.235236 + 0.971938i \(0.424414\pi\)
\(374\) 10916.2 0.0780423
\(375\) −93540.0 −0.665173
\(376\) 253675. 1.79433
\(377\) 57776.1i 0.406505i
\(378\) 6315.92i 0.0442031i
\(379\) 60322.5 0.419953 0.209977 0.977706i \(-0.432661\pi\)
0.209977 + 0.977706i \(0.432661\pi\)
\(380\) 524393. 3.63153
\(381\) −64995.7 −0.447749
\(382\) 234609. 1.60775
\(383\) −53450.5 −0.364380 −0.182190 0.983263i \(-0.558319\pi\)
−0.182190 + 0.983263i \(0.558319\pi\)
\(384\) 155468.i 1.05434i
\(385\) 5866.76i 0.0395801i
\(386\) 188292.i 1.26374i
\(387\) 72700.2i 0.485415i
\(388\) 68319.4i 0.453817i
\(389\) 49209.3 0.325198 0.162599 0.986692i \(-0.448012\pi\)
0.162599 + 0.986692i \(0.448012\pi\)
\(390\) −104923. −0.689829
\(391\) 12583.3i 0.0823078i
\(392\) 205860.i 1.33967i
\(393\) 156058.i 1.01042i
\(394\) 58100.6i 0.374273i
\(395\) 291167. 1.86615
\(396\) 16676.7i 0.106346i
\(397\) 75598.4i 0.479658i −0.970815 0.239829i \(-0.922909\pi\)
0.970815 0.239829i \(-0.0770914\pi\)
\(398\) 209963.i 1.32549i
\(399\) −15331.4 −0.0963022
\(400\) 129633. 0.810203
\(401\) 289441.i 1.80000i 0.435893 + 0.899999i \(0.356433\pi\)
−0.435893 + 0.899999i \(0.643567\pi\)
\(402\) 27773.4 0.171861
\(403\) −55277.0 −0.340357
\(404\) 437394.i 2.67985i
\(405\) −29952.4 −0.182609
\(406\) 35511.4i 0.215435i
\(407\) −36200.9 −0.218540
\(408\) 34707.5i 0.208498i
\(409\) 157956.i 0.944256i 0.881530 + 0.472128i \(0.156514\pi\)
−0.881530 + 0.472128i \(0.843486\pi\)
\(410\) 19957.3i 0.118723i
\(411\) 158725. 0.939639
\(412\) 379878.i 2.23795i
\(413\) 23344.8 + 693.407i 0.136864 + 0.00406526i
\(414\) 29821.5 0.173992
\(415\) 181813.i 1.05567i
\(416\) −42472.5 −0.245426
\(417\) 70884.4 0.407642
\(418\) 62799.0 0.359418
\(419\) 280260.i 1.59637i 0.602412 + 0.798185i \(0.294206\pi\)
−0.602412 + 0.798185i \(0.705794\pi\)
\(420\) −41571.4 −0.235665
\(421\) 123028.i 0.694126i −0.937842 0.347063i \(-0.887179\pi\)
0.937842 0.347063i \(-0.112821\pi\)
\(422\) 8570.20 0.0481245
\(423\) 78386.7i 0.438088i
\(424\) 102772.i 0.571665i
\(425\) 81270.4 0.449940
\(426\) 169490.i 0.933951i
\(427\) 13698.9i 0.0751331i
\(428\) 7690.23 0.0419809
\(429\) −8099.72 −0.0440104
\(430\) −742317. −4.01469
\(431\) 118678.i 0.638877i 0.947607 + 0.319438i \(0.103494\pi\)
−0.947607 + 0.319438i \(0.896506\pi\)
\(432\) 17106.8 0.0916647
\(433\) −336890. −1.79685 −0.898425 0.439127i \(-0.855288\pi\)
−0.898425 + 0.439127i \(0.855288\pi\)
\(434\) −33975.4 −0.180378
\(435\) 168408. 0.889989
\(436\) 399372.i 2.10089i
\(437\) 72389.3i 0.379063i
\(438\) 63623.3 0.331641
\(439\) 333202. 1.72893 0.864466 0.502691i \(-0.167657\pi\)
0.864466 + 0.502691i \(0.167657\pi\)
\(440\) 76404.6 0.394652
\(441\) −63611.6 −0.327084
\(442\) 37568.8 0.192302
\(443\) 79729.2i 0.406265i 0.979151 + 0.203133i \(0.0651123\pi\)
−0.979151 + 0.203133i \(0.934888\pi\)
\(444\) 256516.i 1.30121i
\(445\) 330403.i 1.66849i
\(446\) 124509.i 0.625940i
\(447\) 93666.3i 0.468779i
\(448\) −39194.7 −0.195286
\(449\) −278079. −1.37935 −0.689676 0.724118i \(-0.742247\pi\)
−0.689676 + 0.724118i \(0.742247\pi\)
\(450\) 192605.i 0.951135i
\(451\) 1540.64i 0.00757440i
\(452\) 256518.i 1.25557i
\(453\) 203142.i 0.989927i
\(454\) −411449. −1.99620
\(455\) 20190.8i 0.0975282i
\(456\) 199665.i 0.960226i
\(457\) 175865.i 0.842067i −0.907045 0.421033i \(-0.861668\pi\)
0.907045 0.421033i \(-0.138332\pi\)
\(458\) 578541. 2.75806
\(459\) 10724.8 0.0509053
\(460\) 196285.i 0.927621i
\(461\) −158569. −0.746134 −0.373067 0.927804i \(-0.621694\pi\)
−0.373067 + 0.927804i \(0.621694\pi\)
\(462\) −4978.40 −0.0233242
\(463\) 77926.4i 0.363515i 0.983343 + 0.181758i \(0.0581786\pi\)
−0.983343 + 0.181758i \(0.941821\pi\)
\(464\) −96183.7 −0.446751
\(465\) 161124.i 0.745166i
\(466\) −274430. −1.26375
\(467\) 408542.i 1.87328i −0.350291 0.936641i \(-0.613917\pi\)
0.350291 0.936641i \(-0.386083\pi\)
\(468\) 57393.9i 0.262044i
\(469\) 5344.55i 0.0242977i
\(470\) 800380. 3.62327
\(471\) 143804.i 0.648230i
\(472\) 9030.44 304026.i 0.0405345 1.36467i
\(473\) −57304.5 −0.256133
\(474\) 247077.i 1.09971i
\(475\) 467533. 2.07217
\(476\) 14885.1 0.0656957
\(477\) 31756.9 0.139573
\(478\) 29783.8i 0.130354i
\(479\) −161846. −0.705393 −0.352697 0.935738i \(-0.614735\pi\)
−0.352697 + 0.935738i \(0.614735\pi\)
\(480\) 123801.i 0.537329i
\(481\) −124587. −0.538497
\(482\) 439574.i 1.89207i
\(483\) 5738.67i 0.0245990i
\(484\) −411769. −1.75777
\(485\) 96720.2i 0.411182i
\(486\) 25416.9i 0.107609i
\(487\) −156630. −0.660414 −0.330207 0.943909i \(-0.607119\pi\)
−0.330207 + 0.943909i \(0.607119\pi\)
\(488\) −178405. −0.749149
\(489\) −150223. −0.628230
\(490\) 649516.i 2.70519i
\(491\) 289340. 1.20018 0.600089 0.799933i \(-0.295132\pi\)
0.600089 + 0.799933i \(0.295132\pi\)
\(492\) −10916.8 −0.0450990
\(493\) −60300.4 −0.248100
\(494\) 216126. 0.885632
\(495\) 23609.4i 0.0963550i
\(496\) 92023.2i 0.374054i
\(497\) 32615.6 0.132042
\(498\) 154282. 0.622095
\(499\) 366469. 1.47176 0.735878 0.677114i \(-0.236769\pi\)
0.735878 + 0.677114i \(0.236769\pi\)
\(500\) 522452. 2.08981
\(501\) −232377. −0.925802
\(502\) 177684.i 0.705085i
\(503\) 160477.i 0.634274i 0.948380 + 0.317137i \(0.102722\pi\)
−0.948380 + 0.317137i \(0.897278\pi\)
\(504\) 15828.5i 0.0623130i
\(505\) 619222.i 2.42808i
\(506\) 23506.2i 0.0918081i
\(507\) 120532. 0.468906
\(508\) 363022. 1.40671
\(509\) 244953.i 0.945468i 0.881205 + 0.472734i \(0.156733\pi\)
−0.881205 + 0.472734i \(0.843267\pi\)
\(510\) 109507.i 0.421019i
\(511\) 12243.3i 0.0468875i
\(512\) 241175.i 0.920008i
\(513\) 61697.6 0.234441
\(514\) 493379.i 1.86747i
\(515\) 537796.i 2.02770i
\(516\) 406054.i 1.52505i
\(517\) 61786.8 0.231161
\(518\) −76576.1 −0.285387
\(519\) 193502.i 0.718373i
\(520\) 262950. 0.972450
\(521\) −366691. −1.35090 −0.675452 0.737404i \(-0.736052\pi\)
−0.675452 + 0.737404i \(0.736052\pi\)
\(522\) 142907.i 0.524461i
\(523\) 97476.4 0.356366 0.178183 0.983997i \(-0.442978\pi\)
0.178183 + 0.983997i \(0.442978\pi\)
\(524\) 871636.i 3.17448i
\(525\) −37063.7 −0.134472
\(526\) 389421.i 1.40750i
\(527\) 57692.0i 0.207728i
\(528\) 13484.1i 0.0483677i
\(529\) 252745. 0.903174
\(530\) 324259.i 1.15436i
\(531\) −93945.6 2790.45i −0.333186 0.00989658i
\(532\) 85631.0 0.302557
\(533\) 5302.20i 0.0186639i
\(534\) 280372. 0.983223
\(535\) 10887.1 0.0380369
\(536\) −69603.6 −0.242272
\(537\) 122561.i 0.425015i
\(538\) −798903. −2.76013
\(539\) 50140.6i 0.172589i
\(540\) 167294. 0.573711
\(541\) 321027.i 1.09685i 0.836199 + 0.548425i \(0.184773\pi\)
−0.836199 + 0.548425i \(0.815227\pi\)
\(542\) 639310.i 2.17627i
\(543\) −7015.97 −0.0237951
\(544\) 44328.1i 0.149790i
\(545\) 565393.i 1.90352i
\(546\) −17133.4 −0.0574723
\(547\) −82148.9 −0.274554 −0.137277 0.990533i \(-0.543835\pi\)
−0.137277 + 0.990533i \(0.543835\pi\)
\(548\) −886530. −2.95211
\(549\) 55128.1i 0.182906i
\(550\) 151817. 0.501874
\(551\) −346896. −1.14261
\(552\) −74736.4 −0.245275
\(553\) 47546.1 0.155477
\(554\) 476362.i 1.55209i
\(555\) 363151.i 1.17897i
\(556\) −395913. −1.28071
\(557\) −92439.5 −0.297953 −0.148976 0.988841i \(-0.547598\pi\)
−0.148976 + 0.988841i \(0.547598\pi\)
\(558\) 136726. 0.439119
\(559\) −197216. −0.631131
\(560\) 33612.9 0.107184
\(561\) 8453.60i 0.0268606i
\(562\) 598232.i 1.89408i
\(563\) 332807.i 1.04997i 0.851112 + 0.524984i \(0.175929\pi\)
−0.851112 + 0.524984i \(0.824071\pi\)
\(564\) 437815.i 1.37636i
\(565\) 363154.i 1.13761i
\(566\) −817065. −2.55049
\(567\) −4891.08 −0.0152138
\(568\) 424763.i 1.31659i
\(569\) 71655.2i 0.221321i 0.993858 + 0.110661i \(0.0352966\pi\)
−0.993858 + 0.110661i \(0.964703\pi\)
\(570\) 629973.i 1.93897i
\(571\) 235330.i 0.721780i −0.932608 0.360890i \(-0.882473\pi\)
0.932608 0.360890i \(-0.117527\pi\)
\(572\) 45239.6 0.138270
\(573\) 181682.i 0.553354i
\(574\) 3258.94i 0.00989127i
\(575\) 175001.i 0.529305i
\(576\) 157730. 0.475410
\(577\) 582269. 1.74893 0.874465 0.485089i \(-0.161213\pi\)
0.874465 + 0.485089i \(0.161213\pi\)
\(578\) 521204.i 1.56010i
\(579\) −145814. −0.434954
\(580\) −940615. −2.79612
\(581\) 29689.1i 0.0879519i
\(582\) −82074.6 −0.242305
\(583\) 25031.8i 0.0736469i
\(584\) −159448. −0.467513
\(585\) 81252.9i 0.237425i
\(586\) 94427.4i 0.274981i
\(587\) 535088.i 1.55292i 0.630166 + 0.776460i \(0.282987\pi\)
−0.630166 + 0.776460i \(0.717013\pi\)
\(588\) 355292. 1.02762
\(589\) 331891.i 0.956676i
\(590\) 28492.3 959246.i 0.0818510 2.75566i
\(591\) −44993.4 −0.128817
\(592\) 207408.i 0.591810i
\(593\) 439880. 1.25091 0.625453 0.780262i \(-0.284914\pi\)
0.625453 + 0.780262i \(0.284914\pi\)
\(594\) 20034.4 0.0567810
\(595\) 21072.9 0.0595238
\(596\) 523157.i 1.47279i
\(597\) −162596. −0.456207
\(598\) 80897.7i 0.226222i
\(599\) −177415. −0.494465 −0.247233 0.968956i \(-0.579521\pi\)
−0.247233 + 0.968956i \(0.579521\pi\)
\(600\) 482692.i 1.34081i
\(601\) 602513.i 1.66808i −0.551703 0.834041i \(-0.686022\pi\)
0.551703 0.834041i \(-0.313978\pi\)
\(602\) −121217. −0.334480
\(603\) 21507.9i 0.0591511i
\(604\) 1.13461e6i 3.11010i
\(605\) −582945. −1.59264
\(606\) −525458. −1.43084
\(607\) −235674. −0.639639 −0.319820 0.947478i \(-0.603622\pi\)
−0.319820 + 0.947478i \(0.603622\pi\)
\(608\) 255011.i 0.689846i
\(609\) 27500.3 0.0741485
\(610\) −562894. −1.51275
\(611\) 212642. 0.569597
\(612\) −59901.4 −0.159932
\(613\) 3306.79i 0.00880006i −0.999990 0.00440003i \(-0.998599\pi\)
0.999990 0.00440003i \(-0.00140058\pi\)
\(614\) 564040.i 1.49614i
\(615\) −15455.1 −0.0408621
\(616\) 12476.5 0.0328800
\(617\) 194814. 0.511740 0.255870 0.966711i \(-0.417638\pi\)
0.255870 + 0.966711i \(0.417638\pi\)
\(618\) 456361. 1.19490
\(619\) −346456. −0.904206 −0.452103 0.891966i \(-0.649326\pi\)
−0.452103 + 0.891966i \(0.649326\pi\)
\(620\) 899928.i 2.34112i
\(621\) 23093.9i 0.0598844i
\(622\) 186592.i 0.482295i
\(623\) 53953.2i 0.139008i
\(624\) 46406.3i 0.119181i
\(625\) 75176.8 0.192453
\(626\) −24664.1 −0.0629385
\(627\) 48631.9i 0.123705i
\(628\) 803192.i 2.03657i
\(629\) 130030.i 0.328657i
\(630\) 49941.2i 0.125828i
\(631\) 694008. 1.74303 0.871517 0.490365i \(-0.163136\pi\)
0.871517 + 0.490365i \(0.163136\pi\)
\(632\) 619207.i 1.55025i
\(633\) 6636.81i 0.0165635i
\(634\) 204390.i 0.508489i
\(635\) 513933. 1.27456
\(636\) −177373. −0.438503
\(637\) 172561.i 0.425270i
\(638\) −112644. −0.276736
\(639\) −131254. −0.321448
\(640\) 1.22932e6i 3.00126i
\(641\) −97669.8 −0.237708 −0.118854 0.992912i \(-0.537922\pi\)
−0.118854 + 0.992912i \(0.537922\pi\)
\(642\) 9238.55i 0.0224147i
\(643\) −128561. −0.310947 −0.155474 0.987840i \(-0.549690\pi\)
−0.155474 + 0.987840i \(0.549690\pi\)
\(644\) 32052.3i 0.0772837i
\(645\) 574854.i 1.38178i
\(646\) 225569.i 0.540523i
\(647\) −280631. −0.670390 −0.335195 0.942149i \(-0.608802\pi\)
−0.335195 + 0.942149i \(0.608802\pi\)
\(648\) 63698.0i 0.151697i
\(649\) 2199.52 74050.7i 0.00522201 0.175809i
\(650\) 522486. 1.23665
\(651\) 26310.7i 0.0620827i
\(652\) 839044. 1.97374
\(653\) 380413. 0.892132 0.446066 0.895000i \(-0.352825\pi\)
0.446066 + 0.895000i \(0.352825\pi\)
\(654\) 479780. 1.12173
\(655\) 1.23398e6i 2.87625i
\(656\) 8826.91 0.0205117
\(657\) 49270.3i 0.114144i
\(658\) 130698. 0.301869
\(659\) 59943.3i 0.138029i −0.997616 0.0690145i \(-0.978015\pi\)
0.997616 0.0690145i \(-0.0219855\pi\)
\(660\) 131866.i 0.302723i
\(661\) −87318.8 −0.199850 −0.0999252 0.994995i \(-0.531860\pi\)
−0.0999252 + 0.994995i \(0.531860\pi\)
\(662\) 1.38630e6i 3.16331i
\(663\) 29093.5i 0.0661864i
\(664\) −386650. −0.876965
\(665\) 121228. 0.274133
\(666\) 308162. 0.694753
\(667\) 129846.i 0.291862i
\(668\) 1.29790e6 2.90864
\(669\) 96420.8 0.215436
\(670\) −219609. −0.489217
\(671\) −43453.6 −0.0965119
\(672\) 20216.0i 0.0447669i
\(673\) 598287.i 1.32093i −0.750857 0.660465i \(-0.770359\pi\)
0.750857 0.660465i \(-0.229641\pi\)
\(674\) −978455. −2.15388
\(675\) 149154. 0.327362
\(676\) −673209. −1.47318
\(677\) 874864. 1.90881 0.954406 0.298512i \(-0.0964902\pi\)
0.954406 + 0.298512i \(0.0964902\pi\)
\(678\) 308164. 0.670382
\(679\) 15794.0i 0.0342572i
\(680\) 274439.i 0.593509i
\(681\) 318628.i 0.687053i
\(682\) 107771.i 0.231705i
\(683\) 742238.i 1.59112i −0.605878 0.795558i \(-0.707178\pi\)
0.605878 0.795558i \(-0.292822\pi\)
\(684\) −344601. −0.736554
\(685\) −1.25507e6 −2.67477
\(686\) 214152.i 0.455066i
\(687\) 448025.i 0.949269i
\(688\) 328319.i 0.693616i
\(689\) 86148.1i 0.181471i
\(690\) −235804. −0.495282
\(691\) 339025.i 0.710028i 0.934861 + 0.355014i \(0.115524\pi\)
−0.934861 + 0.355014i \(0.884476\pi\)
\(692\) 1.08077e6i 2.25695i
\(693\) 3855.30i 0.00802771i
\(694\) 217412. 0.451403
\(695\) −560496. −1.16039
\(696\) 358144.i 0.739332i
\(697\) 5533.85 0.0113910
\(698\) 1.10836e6 2.27493
\(699\) 212520.i 0.434957i
\(700\) 207013. 0.422476
\(701\) 288735.i 0.587576i −0.955871 0.293788i \(-0.905084\pi\)
0.955871 0.293788i \(-0.0949159\pi\)
\(702\) 68949.4 0.139912
\(703\) 748039.i 1.51361i
\(704\) 124327.i 0.250854i
\(705\) 619818.i 1.24706i
\(706\) 1.29800e6 2.60414
\(707\) 101116.i 0.202293i
\(708\) 524717. + 15585.6i 1.04679 + 0.0310925i
\(709\) −65496.9 −0.130295 −0.0651476 0.997876i \(-0.520752\pi\)
−0.0651476 + 0.997876i \(0.520752\pi\)
\(710\) 1.34019e6i 2.65858i
\(711\) −191338. −0.378497
\(712\) −702648. −1.38605
\(713\) −124229. −0.244369
\(714\) 17882.0i 0.0350768i
\(715\) 64046.0 0.125279
\(716\) 684544.i 1.33529i
\(717\) 23064.7 0.0448652
\(718\) 635013.i 1.23178i
\(719\) 616651.i 1.19284i −0.802673 0.596420i \(-0.796589\pi\)
0.802673 0.596420i \(-0.203411\pi\)
\(720\) −135267. −0.260932
\(721\) 87819.5i 0.168935i
\(722\) 423217.i 0.811875i
\(723\) −340409. −0.651214
\(724\) 39186.5 0.0747583
\(725\) −838624. −1.59548
\(726\) 494673.i 0.938524i
\(727\) 79727.7 0.150848 0.0754241 0.997152i \(-0.475969\pi\)
0.0754241 + 0.997152i \(0.475969\pi\)
\(728\) 42938.5 0.0810186
\(729\) 19683.0 0.0370370
\(730\) −503082. −0.944045
\(731\) 205833.i 0.385194i
\(732\) 307909.i 0.574645i
\(733\) −797529. −1.48436 −0.742179 0.670202i \(-0.766207\pi\)
−0.742179 + 0.670202i \(0.766207\pi\)
\(734\) 1.68167e6 3.12139
\(735\) 502989. 0.931073
\(736\) −95452.7 −0.176211
\(737\) −16953.1 −0.0312115
\(738\) 13114.8i 0.0240796i
\(739\) 924588.i 1.69301i −0.532381 0.846505i \(-0.678703\pi\)
0.532381 0.846505i \(-0.321297\pi\)
\(740\) 2.02832e6i 3.70402i
\(741\) 167369.i 0.304817i
\(742\) 52950.0i 0.0961741i
\(743\) 671065. 1.21559 0.607795 0.794094i \(-0.292054\pi\)
0.607795 + 0.794094i \(0.292054\pi\)
\(744\) −342652. −0.619024
\(745\) 740637.i 1.33442i
\(746\) 439202.i 0.789200i
\(747\) 119477.i 0.214113i
\(748\) 47216.1i 0.0843893i
\(749\) 1777.81 0.00316900
\(750\) 627640.i 1.11580i
\(751\) 405680.i 0.719289i −0.933089 0.359645i \(-0.882898\pi\)
0.933089 0.359645i \(-0.117102\pi\)
\(752\) 354000.i 0.625989i
\(753\) −137600. −0.242676
\(754\) −387670. −0.681898
\(755\) 1.60628e6i 2.81791i
\(756\) 27318.3 0.0477981
\(757\) −843491. −1.47193 −0.735967 0.677017i \(-0.763272\pi\)
−0.735967 + 0.677017i \(0.763272\pi\)
\(758\) 404755.i 0.704457i
\(759\) −18203.3 −0.0315985
\(760\) 1.57879e6i 2.73337i
\(761\) −953711. −1.64682 −0.823412 0.567444i \(-0.807932\pi\)
−0.823412 + 0.567444i \(0.807932\pi\)
\(762\) 436112.i 0.751084i
\(763\) 92326.0i 0.158590i
\(764\) 1.01476e6i 1.73850i
\(765\) −84802.9 −0.144906
\(766\) 358645.i 0.611234i
\(767\) 7569.75 254849.i 0.0128674 0.433205i
\(768\) −557489. −0.945178
\(769\) 551211.i 0.932106i −0.884757 0.466053i \(-0.845676\pi\)
0.884757 0.466053i \(-0.154324\pi\)
\(770\) 39365.2 0.0663943
\(771\) −382075. −0.642747
\(772\) 814421. 1.36651
\(773\) 98128.0i 0.164223i −0.996623 0.0821115i \(-0.973834\pi\)
0.996623 0.0821115i \(-0.0261664\pi\)
\(774\) 487808. 0.814267
\(775\) 802348.i 1.33586i
\(776\) 205689. 0.341577
\(777\) 59300.9i 0.0982244i
\(778\) 330187.i 0.545508i
\(779\) 31835.2 0.0524605
\(780\) 453824.i 0.745931i
\(781\) 103458.i 0.169614i
\(782\) 84432.2 0.138068
\(783\) −110668. −0.180509
\(784\) −287274. −0.467374
\(785\) 1.13708e6i 1.84524i
\(786\) 1.04713e6 1.69494
\(787\) 975267. 1.57461 0.787307 0.616561i \(-0.211475\pi\)
0.787307 + 0.616561i \(0.211475\pi\)
\(788\) 251303. 0.404712
\(789\) −301570. −0.484433