Properties

Label 177.3.b.a.119.15
Level $177$
Weight $3$
Character 177.119
Analytic conductor $4.823$
Analytic rank $0$
Dimension $38$
CM no
Inner twists $2$

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Newspace parameters

Level: \( N \) \(=\) \( 177 = 3 \cdot 59 \)
Weight: \( k \) \(=\) \( 3 \)
Character orbit: \([\chi]\) \(=\) 177.b (of order \(2\), degree \(1\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(4.82290067918\)
Analytic rank: \(0\)
Dimension: \(38\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label 119.15
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.24

$q$-expansion

\(f(q)\) \(=\) \(q-1.30718i q^{2} +(-2.48886 - 1.67498i) q^{3} +2.29128 q^{4} -3.80837i q^{5} +(-2.18951 + 3.25339i) q^{6} +12.3524 q^{7} -8.22384i q^{8} +(3.38885 + 8.33761i) q^{9} +O(q^{10})\) \(q-1.30718i q^{2} +(-2.48886 - 1.67498i) q^{3} +2.29128 q^{4} -3.80837i q^{5} +(-2.18951 + 3.25339i) q^{6} +12.3524 q^{7} -8.22384i q^{8} +(3.38885 + 8.33761i) q^{9} -4.97823 q^{10} -1.19271i q^{11} +(-5.70267 - 3.83786i) q^{12} -14.6743 q^{13} -16.1468i q^{14} +(-6.37896 + 9.47850i) q^{15} -1.58493 q^{16} -23.0586i q^{17} +(10.8988 - 4.42984i) q^{18} -14.4644 q^{19} -8.72603i q^{20} +(-30.7433 - 20.6900i) q^{21} -1.55909 q^{22} +9.85208i q^{23} +(-13.7748 + 20.4680i) q^{24} +10.4963 q^{25} +19.1820i q^{26} +(5.53098 - 26.4274i) q^{27} +28.3027 q^{28} +46.0717i q^{29} +(12.3901 + 8.33845i) q^{30} -19.2515 q^{31} -30.8236i q^{32} +(-1.99778 + 2.96850i) q^{33} -30.1418 q^{34} -47.0423i q^{35} +(7.76481 + 19.1038i) q^{36} -3.90320 q^{37} +18.9076i q^{38} +(36.5224 + 24.5793i) q^{39} -31.3194 q^{40} -28.4426i q^{41} +(-27.0456 + 40.1870i) q^{42} +57.0037 q^{43} -2.73284i q^{44} +(31.7527 - 12.9060i) q^{45} +12.8784 q^{46} +42.9083i q^{47} +(3.94467 + 2.65473i) q^{48} +103.581 q^{49} -13.7206i q^{50} +(-38.6228 + 57.3897i) q^{51} -33.6230 q^{52} +47.5216i q^{53} +(-34.5454 - 7.22999i) q^{54} -4.54230 q^{55} -101.584i q^{56} +(35.9999 + 24.2277i) q^{57} +60.2240 q^{58} +7.68115i q^{59} +(-14.6160 + 21.7179i) q^{60} +39.9643 q^{61} +25.1652i q^{62} +(41.8603 + 102.989i) q^{63} -46.6317 q^{64} +55.8853i q^{65} +(3.88037 + 2.61146i) q^{66} -54.3907 q^{67} -52.8337i q^{68} +(16.5021 - 24.5205i) q^{69} -61.4928 q^{70} -79.8633i q^{71} +(68.5671 - 27.8694i) q^{72} +123.963 q^{73} +5.10218i q^{74} +(-26.1239 - 17.5812i) q^{75} -33.1420 q^{76} -14.7328i q^{77} +(32.1296 - 47.7414i) q^{78} +28.8678 q^{79} +6.03599i q^{80} +(-58.0314 + 56.5098i) q^{81} -37.1796 q^{82} -2.13566i q^{83} +(-70.4415 - 47.4066i) q^{84} -87.8157 q^{85} -74.5141i q^{86} +(77.1693 - 114.666i) q^{87} -9.80869 q^{88} +161.341i q^{89} +(-16.8705 - 41.5065i) q^{90} -181.263 q^{91} +22.5739i q^{92} +(47.9143 + 32.2460i) q^{93} +56.0889 q^{94} +55.0859i q^{95} +(-51.6290 + 76.7156i) q^{96} +0.232853 q^{97} -135.399i q^{98} +(9.94438 - 4.04193i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + O(q^{10}) \) \( 38q - 76q^{4} - 8q^{6} - 12q^{7} + 20q^{9} + 36q^{10} - 4q^{13} - 17q^{15} + 100q^{16} - 2q^{18} - 28q^{19} - 11q^{21} + 84q^{22} - 6q^{24} - 166q^{25} + 3q^{27} + 12q^{28} + 102q^{30} - 40q^{31} - 46q^{33} - 148q^{34} - 96q^{36} + 112q^{37} + 62q^{39} - 56q^{40} + 14q^{42} + 164q^{43} + 55q^{45} - 4q^{46} - 124q^{48} + 242q^{49} + 52q^{51} + 8q^{52} + 18q^{54} - 228q^{55} - 147q^{57} - 80q^{58} + 128q^{60} + 12q^{61} + 86q^{63} + 48q^{64} - 24q^{66} + 124q^{67} - 240q^{69} + 148q^{70} + 166q^{72} - 192q^{73} - 78q^{75} - 304q^{76} + 244q^{78} + 64q^{79} - 156q^{81} - 180q^{82} + 300q^{84} - 52q^{85} - 83q^{87} - 96q^{88} - 376q^{90} - 332q^{91} + 454q^{93} + 768q^{94} - 722q^{96} + 416q^{97} + 494q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.30718i 0.653590i −0.945095 0.326795i \(-0.894031\pi\)
0.945095 0.326795i \(-0.105969\pi\)
\(3\) −2.48886 1.67498i −0.829620 0.558328i
\(4\) 2.29128 0.572820
\(5\) 3.80837i 0.761674i −0.924642 0.380837i \(-0.875636\pi\)
0.924642 0.380837i \(-0.124364\pi\)
\(6\) −2.18951 + 3.25339i −0.364918 + 0.542232i
\(7\) 12.3524 1.76462 0.882311 0.470666i \(-0.155986\pi\)
0.882311 + 0.470666i \(0.155986\pi\)
\(8\) 8.22384i 1.02798i
\(9\) 3.38885 + 8.33761i 0.376539 + 0.926401i
\(10\) −4.97823 −0.497823
\(11\) 1.19271i 0.108429i −0.998529 0.0542143i \(-0.982735\pi\)
0.998529 0.0542143i \(-0.0172654\pi\)
\(12\) −5.70267 3.83786i −0.475223 0.319821i
\(13\) −14.6743 −1.12880 −0.564398 0.825503i \(-0.690892\pi\)
−0.564398 + 0.825503i \(0.690892\pi\)
\(14\) 16.1468i 1.15334i
\(15\) −6.37896 + 9.47850i −0.425264 + 0.631900i
\(16\) −1.58493 −0.0990581
\(17\) 23.0586i 1.35639i −0.734882 0.678195i \(-0.762763\pi\)
0.734882 0.678195i \(-0.237237\pi\)
\(18\) 10.8988 4.42984i 0.605487 0.246102i
\(19\) −14.4644 −0.761285 −0.380643 0.924722i \(-0.624297\pi\)
−0.380643 + 0.924722i \(0.624297\pi\)
\(20\) 8.72603i 0.436302i
\(21\) −30.7433 20.6900i −1.46397 0.985239i
\(22\) −1.55909 −0.0708679
\(23\) 9.85208i 0.428351i 0.976795 + 0.214176i \(0.0687065\pi\)
−0.976795 + 0.214176i \(0.931294\pi\)
\(24\) −13.7748 + 20.4680i −0.573950 + 0.852833i
\(25\) 10.4963 0.419853
\(26\) 19.1820i 0.737770i
\(27\) 5.53098 26.4274i 0.204851 0.978793i
\(28\) 28.3027 1.01081
\(29\) 46.0717i 1.58868i 0.607475 + 0.794339i \(0.292183\pi\)
−0.607475 + 0.794339i \(0.707817\pi\)
\(30\) 12.3901 + 8.33845i 0.413004 + 0.277948i
\(31\) −19.2515 −0.621017 −0.310508 0.950571i \(-0.600499\pi\)
−0.310508 + 0.950571i \(0.600499\pi\)
\(32\) 30.8236i 0.963236i
\(33\) −1.99778 + 2.96850i −0.0605387 + 0.0899545i
\(34\) −30.1418 −0.886523
\(35\) 47.0423i 1.34407i
\(36\) 7.76481 + 19.1038i 0.215689 + 0.530660i
\(37\) −3.90320 −0.105492 −0.0527459 0.998608i \(-0.516797\pi\)
−0.0527459 + 0.998608i \(0.516797\pi\)
\(38\) 18.9076i 0.497569i
\(39\) 36.5224 + 24.5793i 0.936472 + 0.630239i
\(40\) −31.3194 −0.782985
\(41\) 28.4426i 0.693722i −0.937917 0.346861i \(-0.887248\pi\)
0.937917 0.346861i \(-0.112752\pi\)
\(42\) −27.0456 + 40.1870i −0.643942 + 0.956834i
\(43\) 57.0037 1.32567 0.662834 0.748767i \(-0.269354\pi\)
0.662834 + 0.748767i \(0.269354\pi\)
\(44\) 2.73284i 0.0621100i
\(45\) 31.7527 12.9060i 0.705615 0.286800i
\(46\) 12.8784 0.279966
\(47\) 42.9083i 0.912943i 0.889738 + 0.456472i \(0.150887\pi\)
−0.889738 + 0.456472i \(0.849113\pi\)
\(48\) 3.94467 + 2.65473i 0.0821806 + 0.0553069i
\(49\) 103.581 2.11389
\(50\) 13.7206i 0.274412i
\(51\) −38.6228 + 57.3897i −0.757310 + 1.12529i
\(52\) −33.6230 −0.646596
\(53\) 47.5216i 0.896635i 0.893874 + 0.448317i \(0.147977\pi\)
−0.893874 + 0.448317i \(0.852023\pi\)
\(54\) −34.5454 7.22999i −0.639730 0.133889i
\(55\) −4.54230 −0.0825872
\(56\) 101.584i 1.81400i
\(57\) 35.9999 + 24.2277i 0.631578 + 0.425047i
\(58\) 60.2240 1.03834
\(59\) 7.68115i 0.130189i
\(60\) −14.6160 + 21.7179i −0.243600 + 0.361965i
\(61\) 39.9643 0.655152 0.327576 0.944825i \(-0.393768\pi\)
0.327576 + 0.944825i \(0.393768\pi\)
\(62\) 25.1652i 0.405890i
\(63\) 41.8603 + 102.989i 0.664450 + 1.63475i
\(64\) −46.6317 −0.728620
\(65\) 55.8853i 0.859774i
\(66\) 3.88037 + 2.61146i 0.0587934 + 0.0395675i
\(67\) −54.3907 −0.811802 −0.405901 0.913917i \(-0.633042\pi\)
−0.405901 + 0.913917i \(0.633042\pi\)
\(68\) 52.8337i 0.776966i
\(69\) 16.5021 24.5205i 0.239161 0.355369i
\(70\) −61.4928 −0.878469
\(71\) 79.8633i 1.12484i −0.826853 0.562418i \(-0.809871\pi\)
0.826853 0.562418i \(-0.190129\pi\)
\(72\) 68.5671 27.8694i 0.952321 0.387075i
\(73\) 123.963 1.69813 0.849065 0.528289i \(-0.177166\pi\)
0.849065 + 0.528289i \(0.177166\pi\)
\(74\) 5.10218i 0.0689484i
\(75\) −26.1239 17.5812i −0.348319 0.234416i
\(76\) −33.1420 −0.436079
\(77\) 14.7328i 0.191336i
\(78\) 32.1296 47.7414i 0.411918 0.612069i
\(79\) 28.8678 0.365415 0.182707 0.983167i \(-0.441514\pi\)
0.182707 + 0.983167i \(0.441514\pi\)
\(80\) 6.03599i 0.0754499i
\(81\) −58.0314 + 56.5098i −0.716436 + 0.697652i
\(82\) −37.1796 −0.453410
\(83\) 2.13566i 0.0257309i −0.999917 0.0128654i \(-0.995905\pi\)
0.999917 0.0128654i \(-0.00409531\pi\)
\(84\) −70.4415 47.4066i −0.838589 0.564364i
\(85\) −87.8157 −1.03313
\(86\) 74.5141i 0.866443i
\(87\) 77.1693 114.666i 0.887004 1.31800i
\(88\) −9.80869 −0.111462
\(89\) 161.341i 1.81281i 0.422404 + 0.906407i \(0.361186\pi\)
−0.422404 + 0.906407i \(0.638814\pi\)
\(90\) −16.8705 41.5065i −0.187450 0.461183i
\(91\) −181.263 −1.99190
\(92\) 22.5739i 0.245368i
\(93\) 47.9143 + 32.2460i 0.515208 + 0.346731i
\(94\) 56.0889 0.596691
\(95\) 55.0859i 0.579851i
\(96\) −51.6290 + 76.7156i −0.537802 + 0.799120i
\(97\) 0.232853 0.00240055 0.00120028 0.999999i \(-0.499618\pi\)
0.00120028 + 0.999999i \(0.499618\pi\)
\(98\) 135.399i 1.38162i
\(99\) 9.94438 4.04193i 0.100448 0.0408276i
\(100\) 24.0500 0.240500
\(101\) 84.4713i 0.836349i 0.908367 + 0.418175i \(0.137330\pi\)
−0.908367 + 0.418175i \(0.862670\pi\)
\(102\) 75.0187 + 50.4870i 0.735477 + 0.494971i
\(103\) −29.5611 −0.287001 −0.143501 0.989650i \(-0.545836\pi\)
−0.143501 + 0.989650i \(0.545836\pi\)
\(104\) 120.679i 1.16038i
\(105\) −78.7952 + 117.082i −0.750430 + 1.11506i
\(106\) 62.1194 0.586032
\(107\) 167.005i 1.56080i −0.625281 0.780399i \(-0.715016\pi\)
0.625281 0.780399i \(-0.284984\pi\)
\(108\) 12.6730 60.5526i 0.117343 0.560672i
\(109\) −84.6922 −0.776993 −0.388496 0.921450i \(-0.627005\pi\)
−0.388496 + 0.921450i \(0.627005\pi\)
\(110\) 5.93760i 0.0539782i
\(111\) 9.71451 + 6.53779i 0.0875181 + 0.0588990i
\(112\) −19.5776 −0.174800
\(113\) 192.230i 1.70115i 0.525854 + 0.850575i \(0.323746\pi\)
−0.525854 + 0.850575i \(0.676254\pi\)
\(114\) 31.6700 47.0584i 0.277807 0.412793i
\(115\) 37.5204 0.326264
\(116\) 105.563i 0.910026i
\(117\) −49.7292 122.349i −0.425036 1.04572i
\(118\) 10.0406 0.0850902
\(119\) 284.828i 2.39352i
\(120\) 77.9496 + 52.4595i 0.649580 + 0.437163i
\(121\) 119.577 0.988243
\(122\) 52.2405i 0.428201i
\(123\) −47.6409 + 70.7896i −0.387324 + 0.575525i
\(124\) −44.1106 −0.355730
\(125\) 135.183i 1.08146i
\(126\) 134.625 54.7190i 1.06846 0.434278i
\(127\) 160.912 1.26702 0.633511 0.773734i \(-0.281613\pi\)
0.633511 + 0.773734i \(0.281613\pi\)
\(128\) 62.3382i 0.487017i
\(129\) −141.874 95.4803i −1.09980 0.740158i
\(130\) 73.0522 0.561940
\(131\) 63.6841i 0.486138i −0.970009 0.243069i \(-0.921846\pi\)
0.970009 0.243069i \(-0.0781541\pi\)
\(132\) −4.57747 + 6.80166i −0.0346778 + 0.0515277i
\(133\) −178.670 −1.34338
\(134\) 71.0985i 0.530586i
\(135\) −100.645 21.0640i −0.745521 0.156030i
\(136\) −189.630 −1.39434
\(137\) 33.4272i 0.243994i 0.992530 + 0.121997i \(0.0389299\pi\)
−0.992530 + 0.121997i \(0.961070\pi\)
\(138\) −32.0527 21.5712i −0.232266 0.156313i
\(139\) −91.5357 −0.658530 −0.329265 0.944237i \(-0.606801\pi\)
−0.329265 + 0.944237i \(0.606801\pi\)
\(140\) 107.787i 0.769908i
\(141\) 71.8708 106.793i 0.509722 0.757396i
\(142\) −104.396 −0.735182
\(143\) 17.5023i 0.122394i
\(144\) −5.37109 13.2145i −0.0372992 0.0917675i
\(145\) 175.458 1.21005
\(146\) 162.043i 1.10988i
\(147\) −257.798 173.496i −1.75373 1.18025i
\(148\) −8.94331 −0.0604278
\(149\) 144.503i 0.969822i 0.874564 + 0.484911i \(0.161148\pi\)
−0.874564 + 0.484911i \(0.838852\pi\)
\(150\) −22.9818 + 34.1486i −0.153212 + 0.227658i
\(151\) −253.295 −1.67745 −0.838726 0.544554i \(-0.816699\pi\)
−0.838726 + 0.544554i \(0.816699\pi\)
\(152\) 118.953i 0.782586i
\(153\) 192.254 78.1423i 1.25656 0.510734i
\(154\) −19.2585 −0.125055
\(155\) 73.3169i 0.473012i
\(156\) 83.6830 + 56.3180i 0.536429 + 0.361013i
\(157\) 179.184 1.14130 0.570651 0.821193i \(-0.306691\pi\)
0.570651 + 0.821193i \(0.306691\pi\)
\(158\) 37.7354i 0.238832i
\(159\) 79.5980 118.275i 0.500617 0.743866i
\(160\) −117.388 −0.733672
\(161\) 121.696i 0.755878i
\(162\) 73.8686 + 75.8575i 0.455979 + 0.468256i
\(163\) −103.948 −0.637715 −0.318858 0.947803i \(-0.603299\pi\)
−0.318858 + 0.947803i \(0.603299\pi\)
\(164\) 65.1699i 0.397377i
\(165\) 11.3051 + 7.60828i 0.0685160 + 0.0461108i
\(166\) −2.79170 −0.0168175
\(167\) 199.086i 1.19213i 0.802935 + 0.596066i \(0.203271\pi\)
−0.802935 + 0.596066i \(0.796729\pi\)
\(168\) −170.151 + 252.828i −1.01281 + 1.50493i
\(169\) 46.3364 0.274180
\(170\) 114.791i 0.675241i
\(171\) −49.0178 120.599i −0.286654 0.705255i
\(172\) 130.611 0.759368
\(173\) 9.56148i 0.0552687i −0.999618 0.0276343i \(-0.991203\pi\)
0.999618 0.0276343i \(-0.00879741\pi\)
\(174\) −149.889 100.874i −0.861432 0.579737i
\(175\) 129.654 0.740882
\(176\) 1.89037i 0.0107407i
\(177\) 12.8658 19.1173i 0.0726881 0.108007i
\(178\) 210.901 1.18484
\(179\) 154.856i 0.865119i 0.901605 + 0.432560i \(0.142390\pi\)
−0.901605 + 0.432560i \(0.857610\pi\)
\(180\) 72.7542 29.5712i 0.404190 0.164285i
\(181\) 244.908 1.35308 0.676542 0.736404i \(-0.263478\pi\)
0.676542 + 0.736404i \(0.263478\pi\)
\(182\) 236.943i 1.30189i
\(183\) −99.4654 66.9395i −0.543527 0.365790i
\(184\) 81.0219 0.440336
\(185\) 14.8648i 0.0803503i
\(186\) 42.1513 62.6327i 0.226620 0.336735i
\(187\) −27.5023 −0.147071
\(188\) 98.3149i 0.522952i
\(189\) 68.3206 326.441i 0.361485 1.72720i
\(190\) 72.0072 0.378985
\(191\) 199.587i 1.04496i −0.852652 0.522480i \(-0.825007\pi\)
0.852652 0.522480i \(-0.174993\pi\)
\(192\) 116.060 + 78.1074i 0.604478 + 0.406809i
\(193\) 305.794 1.58442 0.792212 0.610245i \(-0.208929\pi\)
0.792212 + 0.610245i \(0.208929\pi\)
\(194\) 0.304381i 0.00156898i
\(195\) 93.6071 139.091i 0.480036 0.713286i
\(196\) 237.332 1.21088
\(197\) 39.8596i 0.202333i 0.994870 + 0.101166i \(0.0322575\pi\)
−0.994870 + 0.101166i \(0.967743\pi\)
\(198\) −5.28354 12.9991i −0.0266845 0.0656521i
\(199\) −181.977 −0.914456 −0.457228 0.889350i \(-0.651158\pi\)
−0.457228 + 0.889350i \(0.651158\pi\)
\(200\) 86.3201i 0.431600i
\(201\) 135.371 + 91.1036i 0.673487 + 0.453252i
\(202\) 110.419 0.546630
\(203\) 569.094i 2.80342i
\(204\) −88.4957 + 131.496i −0.433802 + 0.644587i
\(205\) −108.320 −0.528390
\(206\) 38.6417i 0.187581i
\(207\) −82.1428 + 33.3873i −0.396825 + 0.161291i
\(208\) 23.2578 0.111816
\(209\) 17.2519i 0.0825451i
\(210\) 153.047 + 103.000i 0.728796 + 0.490474i
\(211\) 10.4581 0.0495646 0.0247823 0.999693i \(-0.492111\pi\)
0.0247823 + 0.999693i \(0.492111\pi\)
\(212\) 108.885i 0.513610i
\(213\) −133.770 + 198.769i −0.628027 + 0.933186i
\(214\) −218.306 −1.02012
\(215\) 217.091i 1.00973i
\(216\) −217.335 45.4859i −1.00618 0.210583i
\(217\) −237.802 −1.09586
\(218\) 110.708i 0.507835i
\(219\) −308.528 207.637i −1.40880 0.948114i
\(220\) −10.4077 −0.0473076
\(221\) 338.370i 1.53109i
\(222\) 8.54608 12.6986i 0.0384958 0.0572010i
\(223\) 83.7996 0.375783 0.187891 0.982190i \(-0.439835\pi\)
0.187891 + 0.982190i \(0.439835\pi\)
\(224\) 380.744i 1.69975i
\(225\) 35.5705 + 87.5142i 0.158091 + 0.388952i
\(226\) 251.279 1.11186
\(227\) 294.024i 1.29526i 0.761956 + 0.647629i \(0.224239\pi\)
−0.761956 + 0.647629i \(0.775761\pi\)
\(228\) 82.4859 + 55.5124i 0.361780 + 0.243475i
\(229\) −329.219 −1.43764 −0.718818 0.695198i \(-0.755317\pi\)
−0.718818 + 0.695198i \(0.755317\pi\)
\(230\) 49.0459i 0.213243i
\(231\) −24.6773 + 36.6680i −0.106828 + 0.158736i
\(232\) 378.886 1.63313
\(233\) 63.0754i 0.270710i 0.990797 + 0.135355i \(0.0432174\pi\)
−0.990797 + 0.135355i \(0.956783\pi\)
\(234\) −159.932 + 65.0051i −0.683471 + 0.277799i
\(235\) 163.411 0.695365
\(236\) 17.5996i 0.0745748i
\(237\) −71.8478 48.3531i −0.303155 0.204021i
\(238\) −372.322 −1.56438
\(239\) 264.038i 1.10476i 0.833593 + 0.552380i \(0.186280\pi\)
−0.833593 + 0.552380i \(0.813720\pi\)
\(240\) 10.1102 15.0227i 0.0421258 0.0625948i
\(241\) −38.4617 −0.159592 −0.0797961 0.996811i \(-0.525427\pi\)
−0.0797961 + 0.996811i \(0.525427\pi\)
\(242\) 156.309i 0.645906i
\(243\) 239.085 43.4435i 0.983889 0.178780i
\(244\) 91.5692 0.375284
\(245\) 394.474i 1.61010i
\(246\) 92.5348 + 62.2753i 0.376158 + 0.253151i
\(247\) 212.256 0.859336
\(248\) 158.321i 0.638392i
\(249\) −3.57720 + 5.31537i −0.0143663 + 0.0213469i
\(250\) −176.709 −0.706835
\(251\) 120.243i 0.479055i −0.970890 0.239528i \(-0.923007\pi\)
0.970890 0.239528i \(-0.0769926\pi\)
\(252\) 95.9137 + 235.977i 0.380610 + 0.936415i
\(253\) 11.7507 0.0464455
\(254\) 210.341i 0.828113i
\(255\) 218.561 + 147.090i 0.857102 + 0.576824i
\(256\) −268.014 −1.04693
\(257\) 249.489i 0.970773i −0.874300 0.485387i \(-0.838679\pi\)
0.874300 0.485387i \(-0.161321\pi\)
\(258\) −124.810 + 185.455i −0.483760 + 0.718819i
\(259\) −48.2137 −0.186153
\(260\) 128.049i 0.492496i
\(261\) −384.127 + 156.130i −1.47175 + 0.598199i
\(262\) −83.2466 −0.317735
\(263\) 202.885i 0.771424i −0.922619 0.385712i \(-0.873956\pi\)
0.922619 0.385712i \(-0.126044\pi\)
\(264\) 24.4125 + 16.4294i 0.0924714 + 0.0622326i
\(265\) 180.980 0.682943
\(266\) 233.554i 0.878021i
\(267\) 270.243 401.554i 1.01215 1.50395i
\(268\) −124.624 −0.465016
\(269\) 474.375i 1.76347i −0.471741 0.881737i \(-0.656374\pi\)
0.471741 0.881737i \(-0.343626\pi\)
\(270\) −27.5345 + 131.562i −0.101980 + 0.487265i
\(271\) −184.439 −0.680585 −0.340293 0.940320i \(-0.610526\pi\)
−0.340293 + 0.940320i \(0.610526\pi\)
\(272\) 36.5463i 0.134361i
\(273\) 451.138 + 303.612i 1.65252 + 1.11213i
\(274\) 43.6954 0.159472
\(275\) 12.5191i 0.0455241i
\(276\) 37.8109 56.1832i 0.136996 0.203562i
\(277\) −376.578 −1.35949 −0.679744 0.733450i \(-0.737909\pi\)
−0.679744 + 0.733450i \(0.737909\pi\)
\(278\) 119.654i 0.430409i
\(279\) −65.2406 160.512i −0.233837 0.575310i
\(280\) −386.869 −1.38167
\(281\) 360.072i 1.28140i −0.767793 0.640698i \(-0.778645\pi\)
0.767793 0.640698i \(-0.221355\pi\)
\(282\) −139.598 93.9481i −0.495027 0.333149i
\(283\) −342.882 −1.21160 −0.605799 0.795618i \(-0.707146\pi\)
−0.605799 + 0.795618i \(0.707146\pi\)
\(284\) 182.989i 0.644328i
\(285\) 92.2680 137.101i 0.323747 0.481056i
\(286\) 22.8787 0.0799954
\(287\) 351.333i 1.22416i
\(288\) 256.995 104.457i 0.892343 0.362696i
\(289\) −242.700 −0.839792
\(290\) 229.355i 0.790880i
\(291\) −0.579540 0.390026i −0.00199155 0.00134030i
\(292\) 284.035 0.972722
\(293\) 137.522i 0.469359i −0.972073 0.234679i \(-0.924596\pi\)
0.972073 0.234679i \(-0.0754040\pi\)
\(294\) −226.791 + 336.989i −0.771397 + 1.14622i
\(295\) 29.2526 0.0991615
\(296\) 32.0992i 0.108443i
\(297\) −31.5204 6.59688i −0.106129 0.0222117i
\(298\) 188.892 0.633866
\(299\) 144.573i 0.483521i
\(300\) −59.8571 40.2834i −0.199524 0.134278i
\(301\) 704.130 2.33930
\(302\) 331.103i 1.09637i
\(303\) 141.488 210.237i 0.466957 0.693852i
\(304\) 22.9251 0.0754115
\(305\) 152.199i 0.499012i
\(306\) −102.146 251.310i −0.333811 0.821276i
\(307\) −71.9236 −0.234279 −0.117139 0.993115i \(-0.537372\pi\)
−0.117139 + 0.993115i \(0.537372\pi\)
\(308\) 33.7570i 0.109601i
\(309\) 73.5735 + 49.5144i 0.238102 + 0.160241i
\(310\) 95.8384 0.309156
\(311\) 33.3440i 0.107215i 0.998562 + 0.0536077i \(0.0170720\pi\)
−0.998562 + 0.0536077i \(0.982928\pi\)
\(312\) 202.136 300.354i 0.647872 0.962674i
\(313\) −163.093 −0.521065 −0.260532 0.965465i \(-0.583898\pi\)
−0.260532 + 0.965465i \(0.583898\pi\)
\(314\) 234.226i 0.745944i
\(315\) 392.220 159.420i 1.24514 0.506094i
\(316\) 66.1441 0.209317
\(317\) 408.609i 1.28899i 0.764609 + 0.644494i \(0.222932\pi\)
−0.764609 + 0.644494i \(0.777068\pi\)
\(318\) −154.606 104.049i −0.486184 0.327198i
\(319\) 54.9503 0.172258
\(320\) 177.591i 0.554971i
\(321\) −279.732 + 415.653i −0.871438 + 1.29487i
\(322\) 159.079 0.494035
\(323\) 333.530i 1.03260i
\(324\) −132.966 + 129.480i −0.410389 + 0.399629i
\(325\) −154.027 −0.473928
\(326\) 135.878i 0.416805i
\(327\) 210.787 + 141.858i 0.644609 + 0.433817i
\(328\) −233.907 −0.713132
\(329\) 530.019i 1.61100i
\(330\) 9.94539 14.7779i 0.0301376 0.0447814i
\(331\) −593.300 −1.79245 −0.896224 0.443603i \(-0.853700\pi\)
−0.896224 + 0.443603i \(0.853700\pi\)
\(332\) 4.89340i 0.0147392i
\(333\) −13.2274 32.5433i −0.0397218 0.0977276i
\(334\) 260.242 0.779167
\(335\) 207.140i 0.618328i
\(336\) 48.7259 + 32.7922i 0.145018 + 0.0975958i
\(337\) 324.138 0.961833 0.480917 0.876766i \(-0.340304\pi\)
0.480917 + 0.876766i \(0.340304\pi\)
\(338\) 60.5701i 0.179201i
\(339\) 321.982 478.434i 0.949800 1.41131i
\(340\) −201.210 −0.591795
\(341\) 22.9616i 0.0673360i
\(342\) −157.644 + 64.0751i −0.460948 + 0.187354i
\(343\) 674.201 1.96560
\(344\) 468.789i 1.36276i
\(345\) −93.3829 62.8460i −0.270675 0.182162i
\(346\) −12.4986 −0.0361231
\(347\) 390.559i 1.12553i −0.826617 0.562765i \(-0.809738\pi\)
0.826617 0.562765i \(-0.190262\pi\)
\(348\) 176.816 262.732i 0.508093 0.754976i
\(349\) 42.3900 0.121461 0.0607306 0.998154i \(-0.480657\pi\)
0.0607306 + 0.998154i \(0.480657\pi\)
\(350\) 169.482i 0.484233i
\(351\) −81.1635 + 387.805i −0.231235 + 1.10486i
\(352\) −36.7637 −0.104442
\(353\) 192.382i 0.544991i −0.962157 0.272496i \(-0.912151\pi\)
0.962157 0.272496i \(-0.0878490\pi\)
\(354\) −24.9898 16.8179i −0.0705926 0.0475083i
\(355\) −304.149 −0.856758
\(356\) 369.676i 1.03842i
\(357\) −477.083 + 708.898i −1.33637 + 1.98571i
\(358\) 202.425 0.565434
\(359\) 594.058i 1.65476i −0.561644 0.827379i \(-0.689831\pi\)
0.561644 0.827379i \(-0.310169\pi\)
\(360\) −106.137 261.129i −0.294825 0.725358i
\(361\) −151.780 −0.420445
\(362\) 320.139i 0.884362i
\(363\) −297.612 200.290i −0.819867 0.551764i
\(364\) −415.323 −1.14100
\(365\) 472.099i 1.29342i
\(366\) −87.5020 + 130.019i −0.239077 + 0.355244i
\(367\) −575.716 −1.56871 −0.784354 0.620313i \(-0.787006\pi\)
−0.784354 + 0.620313i \(0.787006\pi\)
\(368\) 15.6148i 0.0424316i
\(369\) 237.143 96.3877i 0.642664 0.261213i
\(370\) 19.4310 0.0525162
\(371\) 587.004i 1.58222i
\(372\) 109.785 + 73.8845i 0.295121 + 0.198614i
\(373\) −411.683 −1.10371 −0.551853 0.833941i \(-0.686079\pi\)
−0.551853 + 0.833941i \(0.686079\pi\)
\(374\) 35.9505i 0.0961244i
\(375\) −226.430 + 336.452i −0.603812 + 0.897205i
\(376\) 352.871 0.938487
\(377\) 676.071i 1.79329i
\(378\) −426.717 89.3074i −1.12888 0.236263i
\(379\) 485.114 1.27998 0.639991 0.768382i \(-0.278938\pi\)
0.639991 + 0.768382i \(0.278938\pi\)
\(380\) 126.217i 0.332150i
\(381\) −400.487 269.525i −1.05115 0.707414i
\(382\) −260.897 −0.682975
\(383\) 353.447i 0.922838i 0.887182 + 0.461419i \(0.152659\pi\)
−0.887182 + 0.461419i \(0.847341\pi\)
\(384\) −104.416 + 155.151i −0.271915 + 0.404039i
\(385\) −56.1081 −0.145735
\(386\) 399.728i 1.03556i
\(387\) 193.177 + 475.274i 0.499166 + 1.22810i
\(388\) 0.533532 0.00137508
\(389\) 111.760i 0.287302i 0.989628 + 0.143651i \(0.0458842\pi\)
−0.989628 + 0.143651i \(0.954116\pi\)
\(390\) −181.817 122.361i −0.466197 0.313747i
\(391\) 227.175 0.581011
\(392\) 851.831i 2.17304i
\(393\) −106.670 + 158.501i −0.271424 + 0.403310i
\(394\) 52.1037 0.132243
\(395\) 109.939i 0.278327i
\(396\) 22.7854 9.26120i 0.0575388 0.0233869i
\(397\) −612.174 −1.54200 −0.771001 0.636834i \(-0.780243\pi\)
−0.771001 + 0.636834i \(0.780243\pi\)
\(398\) 237.876i 0.597679i
\(399\) 444.684 + 299.269i 1.11450 + 0.750048i
\(400\) −16.6359 −0.0415898
\(401\) 409.763i 1.02185i 0.859625 + 0.510926i \(0.170697\pi\)
−0.859625 + 0.510926i \(0.829303\pi\)
\(402\) 119.089 176.954i 0.296241 0.440185i
\(403\) 282.503 0.701001
\(404\) 193.547i 0.479077i
\(405\) 215.210 + 221.005i 0.531384 + 0.545691i
\(406\) 743.908 1.83229
\(407\) 4.65540i 0.0114383i
\(408\) 471.964 + 317.628i 1.15677 + 0.778500i
\(409\) −572.552 −1.39988 −0.699941 0.714201i \(-0.746790\pi\)
−0.699941 + 0.714201i \(0.746790\pi\)
\(410\) 141.594i 0.345350i
\(411\) 55.9901 83.1957i 0.136229 0.202423i
\(412\) −67.7327 −0.164400
\(413\) 94.8803i 0.229734i
\(414\) 43.6432 + 107.375i 0.105418 + 0.259361i
\(415\) −8.13340 −0.0195985
\(416\) 452.316i 1.08730i
\(417\) 227.820 + 153.321i 0.546330 + 0.367676i
\(418\) 22.5514 0.0539507
\(419\) 350.684i 0.836955i −0.908227 0.418478i \(-0.862564\pi\)
0.908227 0.418478i \(-0.137436\pi\)
\(420\) −180.542 + 268.267i −0.429861 + 0.638731i
\(421\) 566.440 1.34546 0.672732 0.739886i \(-0.265121\pi\)
0.672732 + 0.739886i \(0.265121\pi\)
\(422\) 13.6707i 0.0323949i
\(423\) −357.753 + 145.410i −0.845751 + 0.343759i
\(424\) 390.810 0.921722
\(425\) 242.031i 0.569484i
\(426\) 259.827 + 174.861i 0.609922 + 0.410473i
\(427\) 493.653 1.15610
\(428\) 382.656i 0.894056i
\(429\) 29.3161 43.5608i 0.0683359 0.101540i
\(430\) −283.777 −0.659947
\(431\) 321.611i 0.746196i 0.927792 + 0.373098i \(0.121705\pi\)
−0.927792 + 0.373098i \(0.878295\pi\)
\(432\) −8.76621 + 41.8856i −0.0202922 + 0.0969573i
\(433\) 288.242 0.665685 0.332843 0.942982i \(-0.391992\pi\)
0.332843 + 0.942982i \(0.391992\pi\)
\(434\) 310.850i 0.716243i
\(435\) −436.690 293.889i −1.00389 0.675607i
\(436\) −194.053 −0.445077
\(437\) 142.505i 0.326098i
\(438\) −271.419 + 403.301i −0.619678 + 0.920780i
\(439\) −207.559 −0.472801 −0.236400 0.971656i \(-0.575968\pi\)
−0.236400 + 0.971656i \(0.575968\pi\)
\(440\) 37.3551i 0.0848980i
\(441\) 351.020 + 863.615i 0.795964 + 1.95831i
\(442\) 442.311 1.00070
\(443\) 658.077i 1.48550i −0.669568 0.742751i \(-0.733521\pi\)
0.669568 0.742751i \(-0.266479\pi\)
\(444\) 22.2586 + 14.9799i 0.0501321 + 0.0337385i
\(445\) 614.444 1.38077
\(446\) 109.541i 0.245608i
\(447\) 242.041 359.649i 0.541479 0.804584i
\(448\) −576.011 −1.28574
\(449\) 575.777i 1.28235i 0.767393 + 0.641177i \(0.221554\pi\)
−0.767393 + 0.641177i \(0.778446\pi\)
\(450\) 114.397 46.4971i 0.254215 0.103327i
\(451\) −33.9239 −0.0752192
\(452\) 440.452i 0.974452i
\(453\) 630.417 + 424.266i 1.39165 + 0.936569i
\(454\) 384.342 0.846568
\(455\) 690.316i 1.51718i
\(456\) 199.245 296.058i 0.436940 0.649249i
\(457\) −716.921 −1.56876 −0.784378 0.620284i \(-0.787017\pi\)
−0.784378 + 0.620284i \(0.787017\pi\)
\(458\) 430.348i 0.939625i
\(459\) −609.380 127.537i −1.32762 0.277858i
\(460\) 85.9696 0.186890
\(461\) 570.888i 1.23837i 0.785246 + 0.619184i \(0.212536\pi\)
−0.785246 + 0.619184i \(0.787464\pi\)
\(462\) 47.9317 + 32.2577i 0.103748 + 0.0698218i
\(463\) −297.331 −0.642183 −0.321091 0.947048i \(-0.604050\pi\)
−0.321091 + 0.947048i \(0.604050\pi\)
\(464\) 73.0203i 0.157371i
\(465\) 122.805 182.475i 0.264096 0.392420i
\(466\) 82.4509 0.176933
\(467\) 402.518i 0.861923i −0.902370 0.430961i \(-0.858175\pi\)
0.902370 0.430961i \(-0.141825\pi\)
\(468\) −113.943 280.335i −0.243469 0.599007i
\(469\) −671.854 −1.43252
\(470\) 213.607i 0.454484i
\(471\) −445.965 300.131i −0.946847 0.637221i
\(472\) 63.1685 0.133832
\(473\) 67.9891i 0.143740i
\(474\) −63.2062 + 93.9181i −0.133346 + 0.198140i
\(475\) −151.823 −0.319628
\(476\) 652.621i 1.37105i
\(477\) −396.217 + 161.044i −0.830643 + 0.337618i
\(478\) 345.145 0.722060
\(479\) 628.870i 1.31288i 0.754378 + 0.656440i \(0.227939\pi\)
−0.754378 + 0.656440i \(0.772061\pi\)
\(480\) 292.161 + 196.622i 0.608669 + 0.409630i
\(481\) 57.2768 0.119079
\(482\) 50.2764i 0.104308i
\(483\) 203.840 302.885i 0.422028 0.627092i
\(484\) 273.985 0.566085
\(485\) 0.886792i 0.00182844i
\(486\) −56.7885 312.527i −0.116849 0.643060i
\(487\) 481.364 0.988428 0.494214 0.869340i \(-0.335456\pi\)
0.494214 + 0.869340i \(0.335456\pi\)
\(488\) 328.660i 0.673483i
\(489\) 258.711 + 174.111i 0.529062 + 0.356055i
\(490\) −515.648 −1.05234
\(491\) 739.745i 1.50661i 0.657671 + 0.753305i \(0.271542\pi\)
−0.657671 + 0.753305i \(0.728458\pi\)
\(492\) −109.159 + 162.199i −0.221867 + 0.329672i
\(493\) 1062.35 2.15487
\(494\) 277.457i 0.561654i
\(495\) −15.3932 37.8719i −0.0310973 0.0765089i
\(496\) 30.5123 0.0615167
\(497\) 986.500i 1.98491i
\(498\) 6.94815 + 4.67605i 0.0139521 + 0.00938966i
\(499\) −630.412 −1.26335 −0.631675 0.775233i \(-0.717632\pi\)
−0.631675 + 0.775233i \(0.717632\pi\)
\(500\) 309.742i 0.619484i
\(501\) 333.466 495.498i 0.665601 0.989017i
\(502\) −157.179 −0.313106
\(503\) 375.876i 0.747269i −0.927576 0.373635i \(-0.878111\pi\)
0.927576 0.373635i \(-0.121889\pi\)
\(504\) 846.966 344.253i 1.68049 0.683041i
\(505\) 321.698 0.637025
\(506\) 15.3603i 0.0303564i
\(507\) −115.325 77.6128i −0.227465 0.153082i
\(508\) 368.694 0.725775
\(509\) 539.451i 1.05982i 0.848052 + 0.529912i \(0.177775\pi\)
−0.848052 + 0.529912i \(0.822225\pi\)
\(510\) 192.273 285.699i 0.377006 0.560194i
\(511\) 1531.24 2.99656
\(512\) 100.990i 0.197246i
\(513\) −80.0024 + 382.257i −0.155950 + 0.745141i
\(514\) −326.127 −0.634488
\(515\) 112.580i 0.218601i
\(516\) −325.073 218.772i −0.629987 0.423977i
\(517\) 51.1774 0.0989891
\(518\) 63.0240i 0.121668i
\(519\) −16.0153 + 23.7972i −0.0308581 + 0.0458520i
\(520\) 459.592 0.883830
\(521\) 143.060i 0.274587i 0.990530 + 0.137293i \(0.0438403\pi\)
−0.990530 + 0.137293i \(0.956160\pi\)
\(522\) 204.090 + 502.124i 0.390977 + 0.961923i
\(523\) 447.990 0.856578 0.428289 0.903642i \(-0.359117\pi\)
0.428289 + 0.903642i \(0.359117\pi\)
\(524\) 145.918i 0.278469i
\(525\) −322.692 217.169i −0.614651 0.413655i
\(526\) −265.207 −0.504195
\(527\) 443.913i 0.842340i
\(528\) 3.16634 4.70486i 0.00599685 0.00891072i
\(529\) 431.937 0.816515
\(530\) 236.574i 0.446365i
\(531\) −64.0424 + 26.0303i −0.120607 + 0.0490212i
\(532\) −409.382 −0.769515
\(533\) 417.376i 0.783070i
\(534\) −524.904 353.256i −0.982966 0.661529i
\(535\) −636.019 −1.18882
\(536\) 447.300i 0.834516i
\(537\) 259.382 385.416i 0.483021 0.717720i
\(538\) −620.094 −1.15259
\(539\) 123.542i 0.229206i
\(540\) −230.607 48.2635i −0.427049 0.0893769i
\(541\) −165.991 −0.306823 −0.153412 0.988162i \(-0.549026\pi\)
−0.153412 + 0.988162i \(0.549026\pi\)
\(542\) 241.095i 0.444824i
\(543\) −609.542 410.217i −1.12255 0.755465i
\(544\) −710.749 −1.30652
\(545\) 322.539i 0.591815i
\(546\) 396.876 589.719i 0.726880 1.08007i
\(547\) 472.010 0.862907 0.431453 0.902135i \(-0.358001\pi\)
0.431453 + 0.902135i \(0.358001\pi\)
\(548\) 76.5911i 0.139765i
\(549\) 135.433 + 333.206i 0.246690 + 0.606933i
\(550\) −16.3648 −0.0297541
\(551\) 666.400i 1.20944i
\(552\) −201.652 135.710i −0.365312 0.245852i
\(553\) 356.585 0.644819
\(554\) 492.255i 0.888548i
\(555\) 24.8983 36.9964i 0.0448618 0.0666602i
\(556\) −209.734 −0.377219
\(557\) 355.959i 0.639064i 0.947575 + 0.319532i \(0.103526\pi\)
−0.947575 + 0.319532i \(0.896474\pi\)
\(558\) −209.818 + 85.2812i −0.376017 + 0.152834i
\(559\) −836.492 −1.49641
\(560\) 74.5588i 0.133141i
\(561\) 68.4495 + 46.0660i 0.122013 + 0.0821141i
\(562\) −470.680 −0.837508
\(563\) 230.539i 0.409483i −0.978816 0.204741i \(-0.934365\pi\)
0.978816 0.204741i \(-0.0656353\pi\)
\(564\) 164.676 244.692i 0.291979 0.433851i
\(565\) 732.083 1.29572
\(566\) 448.209i 0.791888i
\(567\) −716.824 + 698.030i −1.26424 + 1.23109i
\(568\) −656.783 −1.15631
\(569\) 562.742i 0.989002i −0.869177 0.494501i \(-0.835351\pi\)
0.869177 0.494501i \(-0.164649\pi\)
\(570\) −179.216 120.611i −0.314414 0.211598i
\(571\) 674.756 1.18171 0.590854 0.806778i \(-0.298791\pi\)
0.590854 + 0.806778i \(0.298791\pi\)
\(572\) 40.1027i 0.0701095i
\(573\) −334.306 + 496.745i −0.583430 + 0.866919i
\(574\) −459.256 −0.800097
\(575\) 103.411i 0.179845i
\(576\) −158.028 388.797i −0.274354 0.674994i
\(577\) −379.150 −0.657105 −0.328553 0.944486i \(-0.606561\pi\)
−0.328553 + 0.944486i \(0.606561\pi\)
\(578\) 317.253i 0.548880i
\(579\) −761.079 512.200i −1.31447 0.884629i
\(580\) 402.023 0.693143
\(581\) 26.3805i 0.0454053i
\(582\) −0.509834 + 0.757563i −0.000876004 + 0.00130165i
\(583\) 56.6798 0.0972208
\(584\) 1019.46i 1.74564i
\(585\) −465.950 + 189.387i −0.796495 + 0.323739i
\(586\) −179.766 −0.306768
\(587\) 555.352i 0.946085i 0.881040 + 0.473042i \(0.156844\pi\)
−0.881040 + 0.473042i \(0.843156\pi\)
\(588\) −590.687 397.528i −1.00457 0.676068i
\(589\) 278.462 0.472771
\(590\) 38.2385i 0.0648110i
\(591\) 66.7642 99.2049i 0.112968 0.167859i
\(592\) 6.18629 0.0104498
\(593\) 228.099i 0.384653i −0.981331 0.192327i \(-0.938397\pi\)
0.981331 0.192327i \(-0.0616033\pi\)
\(594\) −8.62331 + 41.2028i −0.0145174 + 0.0693650i
\(595\) −1084.73 −1.82308
\(596\) 331.098i 0.555533i
\(597\) 452.915 + 304.808i 0.758651 + 0.510566i
\(598\) −188.983 −0.316025
\(599\) 21.5391i 0.0359584i 0.999838 + 0.0179792i \(0.00572327\pi\)
−0.999838 + 0.0179792i \(0.994277\pi\)
\(600\) −144.585 + 214.839i −0.240975 + 0.358064i
\(601\) 602.048 1.00174 0.500872 0.865521i \(-0.333013\pi\)
0.500872 + 0.865521i \(0.333013\pi\)
\(602\) 920.425i 1.52895i
\(603\) −184.322 453.488i −0.305675 0.752054i
\(604\) −580.370 −0.960878
\(605\) 455.395i 0.752719i
\(606\) −274.818 184.950i −0.453495 0.305199i
\(607\) −113.664 −0.187256 −0.0936281 0.995607i \(-0.529846\pi\)
−0.0936281 + 0.995607i \(0.529846\pi\)
\(608\) 445.845i 0.733298i
\(609\) 953.223 1416.39i 1.56523 2.32577i
\(610\) −198.951 −0.326149
\(611\) 629.652i 1.03053i
\(612\) 440.507 179.046i 0.719782 0.292558i
\(613\) −160.198 −0.261335 −0.130667 0.991426i \(-0.541712\pi\)
−0.130667 + 0.991426i \(0.541712\pi\)
\(614\) 94.0172i 0.153122i
\(615\) 269.593 + 181.434i 0.438363 + 0.295015i
\(616\) −121.160 −0.196689
\(617\) 274.258i 0.444502i −0.974990 0.222251i \(-0.928660\pi\)
0.974990 0.222251i \(-0.0713404\pi\)
\(618\) 64.7243 96.1738i 0.104732 0.155621i
\(619\) 270.664 0.437261 0.218630 0.975808i \(-0.429841\pi\)
0.218630 + 0.975808i \(0.429841\pi\)
\(620\) 167.989i 0.270951i
\(621\) 260.365 + 54.4917i 0.419267 + 0.0877482i
\(622\) 43.5866 0.0700749
\(623\) 1992.94i 3.19893i
\(624\) −57.8854 38.9564i −0.0927651 0.0624302i
\(625\) −252.419 −0.403870
\(626\) 213.192i 0.340563i
\(627\) 28.8967 42.9376i 0.0460873 0.0684811i
\(628\) 410.562 0.653760
\(629\) 90.0023i 0.143088i
\(630\) −208.390 512.703i −0.330778 0.813814i
\(631\) −927.683 −1.47018 −0.735090 0.677970i \(-0.762860\pi\)
−0.735090 + 0.677970i \(0.762860\pi\)
\(632\) 237.404i 0.375639i
\(633\) −26.0288 17.5172i −0.0411198 0.0276733i
\(634\) 534.126 0.842470
\(635\) 612.811i 0.965057i
\(636\) 182.381 271.000i 0.286763 0.426101i
\(637\) −1519.98 −2.38615
\(638\) 71.8300i 0.112586i
\(639\) 665.869 270.645i 1.04205 0.423545i
\(640\) −237.407 −0.370948
\(641\) 1000.42i 1.56072i −0.625330 0.780360i \(-0.715036\pi\)
0.625330 0.780360i \(-0.284964\pi\)
\(642\) 543.334 + 365.660i 0.846315 + 0.569564i
\(643\) 932.909 1.45087 0.725434 0.688291i \(-0.241639\pi\)
0.725434 + 0.688291i \(0.241639\pi\)
\(644\) 278.840i 0.432982i
\(645\) −363.624 + 540.310i −0.563759 + 0.837689i
\(646\) 435.984 0.674897
\(647\) 517.452i 0.799772i −0.916565 0.399886i \(-0.869050\pi\)
0.916565 0.399886i \(-0.130950\pi\)
\(648\) 464.728 + 477.240i 0.717173 + 0.736482i
\(649\) 9.16141 0.0141162
\(650\) 201.341i 0.309755i
\(651\) 591.855 + 398.314i 0.909147 + 0.611849i
\(652\) −238.173 −0.365296
\(653\) 301.747i 0.462094i −0.972943 0.231047i \(-0.925785\pi\)
0.972943 0.231047i \(-0.0742151\pi\)
\(654\) 185.434 275.537i 0.283539 0.421310i
\(655\) −242.532 −0.370278
\(656\) 45.0795i 0.0687187i
\(657\) 420.094 + 1033.56i 0.639412 + 1.57315i
\(658\) 692.831 1.05293
\(659\) 710.758i 1.07854i 0.842133 + 0.539270i \(0.181300\pi\)
−0.842133 + 0.539270i \(0.818700\pi\)
\(660\) 25.9032 + 17.4327i 0.0392473 + 0.0264132i
\(661\) 824.370 1.24716 0.623578 0.781761i \(-0.285678\pi\)
0.623578 + 0.781761i \(0.285678\pi\)
\(662\) 775.550i 1.17153i
\(663\) 566.765 842.156i 0.854849 1.27022i
\(664\) −17.5634 −0.0264508
\(665\) 680.440i 1.02322i
\(666\) −42.5400 + 17.2905i −0.0638738 + 0.0259618i
\(667\) −453.902 −0.680512
\(668\) 456.162i 0.682877i
\(669\) −208.565 140.363i −0.311757 0.209810i
\(670\) 270.769 0.404133
\(671\) 47.6659i 0.0710372i
\(672\) −637.740 + 947.618i −0.949018 + 1.41015i
\(673\) −866.939 −1.28817 −0.644085 0.764954i \(-0.722762\pi\)
−0.644085 + 0.764954i \(0.722762\pi\)
\(674\) 423.707i 0.628645i
\(675\) 58.0550 277.391i 0.0860073 0.410949i
\(676\) 106.170 0.157056
\(677\) 678.127i 1.00167i −0.865544 0.500833i \(-0.833027\pi\)
0.865544 0.500833i \(-0.166973\pi\)
\(678\) −625.399 420.889i −0.922418 0.620780i
\(679\) 2.87629 0.00423607
\(680\) 722.182i 1.06203i
\(681\) 492.485 731.784i 0.723179 1.07457i
\(682\) 30.0149 0.0440101
\(683\) 775.837i 1.13592i −0.823055 0.567962i \(-0.807732\pi\)
0.823055 0.567962i \(-0.192268\pi\)
\(684\) −112.313 276.325i −0.164201 0.403984i
\(685\) 127.303 0.185844
\(686\) 881.303i 1.28470i
\(687\) 819.380 + 551.436i 1.19269 + 0.802673i
\(688\) −90.3468 −0.131318
\(689\) 697.349i 1.01212i
\(690\) −82.1511 + 122.068i −0.119060 + 0.176911i
\(691\) −12.5020 −0.0180926 −0.00904632 0.999959i \(-0.502880\pi\)
−0.00904632 + 0.999959i \(0.502880\pi\)
\(692\) 21.9080i 0.0316590i
\(693\) 122.837 49.9274i 0.177253 0.0720453i
\(694\) −510.531 −0.735635
\(695\) 348.602i 0.501585i
\(696\) −942.994 634.628i −1.35488 0.911822i
\(697\) −655.847 −0.940957
\(698\) 55.4114i 0.0793859i
\(699\) 105.650 156.986i 0.151145 0.224586i
\(700\) 297.074 0.424392
\(701\) 256.833i 0.366381i 0.983077 + 0.183191i \(0.0586426\pi\)
−0.983077 + 0.183191i \(0.941357\pi\)
\(702\) 506.931 + 106.095i 0.722124 + 0.151133i
\(703\) 56.4575 0.0803093
\(704\) 55.6183i 0.0790032i
\(705\) −406.707 273.710i −0.576889 0.388242i
\(706\) −251.478 −0.356201
\(707\) 1043.42i 1.47584i
\(708\) 29.4791 43.8031i 0.0416372 0.0618687i
\(709\) 738.720 1.04192 0.520959 0.853582i \(-0.325574\pi\)
0.520959 + 0.853582i \(0.325574\pi\)
\(710\) 397.578i 0.559969i
\(711\) 97.8286 + 240.688i 0.137593 + 0.338521i
\(712\) 1326.84 1.86354
\(713\) 189.667i 0.266013i
\(714\) 926.658 + 623.634i 1.29784 + 0.873437i
\(715\) 66.6552 0.0932241
\(716\) 354.819i 0.495557i
\(717\) 442.259 657.153i 0.616818 0.916531i
\(718\) −776.541 −1.08153
\(719\) 319.264i 0.444039i 0.975042 + 0.222020i \(0.0712649\pi\)
−0.975042 + 0.222020i \(0.928735\pi\)
\(720\) −50.3257 + 20.4551i −0.0698969 + 0.0284099i
\(721\) −365.149 −0.506448
\(722\) 198.405i 0.274798i
\(723\) 95.7259 + 64.4228i 0.132401 + 0.0891048i
\(724\) 561.153 0.775073
\(725\) 483.583i 0.667011i
\(726\) −261.816 + 389.032i −0.360628 + 0.535857i
\(727\) 548.565 0.754559 0.377280 0.926099i \(-0.376860\pi\)
0.377280 + 0.926099i \(0.376860\pi\)
\(728\) 1490.68i 2.04763i
\(729\) −667.817 292.339i −0.916072 0.401014i
\(730\) −617.118 −0.845367
\(731\) 1314.43i 1.79812i
\(732\) −227.903 153.377i −0.311343 0.209531i
\(733\) 45.2936 0.0617921 0.0308960 0.999523i \(-0.490164\pi\)
0.0308960 + 0.999523i \(0.490164\pi\)
\(734\) 752.565i 1.02529i
\(735\) −660.737 + 981.790i −0.898962 + 1.33577i
\(736\) 303.676 0.412604
\(737\) 64.8726i 0.0880225i
\(738\) −125.996 309.989i −0.170727 0.420039i
\(739\) 549.302 0.743304 0.371652 0.928372i \(-0.378791\pi\)
0.371652 + 0.928372i \(0.378791\pi\)
\(740\) 34.0594i 0.0460262i
\(741\) −528.275 355.525i −0.712922 0.479791i
\(742\) 767.321 1.03413
\(743\) 343.910i 0.462867i 0.972851 + 0.231433i \(0.0743415\pi\)
−0.972851 + 0.231433i \(0.925658\pi\)
\(744\) 265.186 394.040i 0.356433 0.529623i
\(745\) 550.322 0.738688
\(746\) 538.144i 0.721372i
\(747\) 17.8063 7.23745i 0.0238371 0.00968869i
\(748\) −63.0155 −0.0842454
\(749\) 2062.91i 2.75422i
\(750\) 439.803 + 295.984i 0.586405 + 0.394646i
\(751\) 354.918 0.472594 0.236297 0.971681i \(-0.424066\pi\)
0.236297 + 0.971681i \(0.424066\pi\)
\(752\) 68.0066i 0.0904344i
\(753\) −201.405 + 299.268i −0.267470 + 0.397434i
\(754\) −883.747 −1.17208
\(755\) 964.642i 1.27767i
\(756\) 156.542 747.967i 0.207066 0.989374i
\(757\) −235.656 −0.311303 −0.155651 0.987812i \(-0.549748\pi\)
−0.155651 + 0.987812i \(0.549748\pi\)
\(758\) 634.131i 0.836585i
\(759\) −29.2459 19.6823i −0.0385321 0.0259318i
\(760\) 453.017 0.596075
\(761\) 75.3637i 0.0990325i −0.998773 0.0495162i \(-0.984232\pi\)
0.998773 0.0495162i \(-0.0157680\pi\)
\(762\) −352.317 + 523.509i −0.462359 + 0.687019i
\(763\) −1046.15 −1.37110
\(764\) 457.310i 0.598573i
\(765\) −297.595 732.173i −0.389013 0.957089i
\(766\) 462.019 0.603158
\(767\) 112.716i 0.146957i
\(768\) 667.050 + 448.919i 0.868554 + 0.584530i
\(769\) −324.938 −0.422546 −0.211273 0.977427i \(-0.567761\pi\)
−0.211273 + 0.977427i \(0.567761\pi\)
\(770\) 73.3434i 0.0952512i
\(771\) −417.890 + 620.943i −0.542010 + 0.805373i
\(772\) 700.659 0.907590
\(773\) 675.310i 0.873622i −0.899553 0.436811i \(-0.856108\pi\)
0.899553 0.436811i \(-0.143892\pi\)
\(774\) 621.270 252.517i 0.802674 0.326250i
\(775\) −202.070 −0.260736
\(776\) 1.91495i 0.00246772i
\(777\) 119.997 + 80.7571i 0.154436 + 0.103935i
\(778\) 146.091 0.187778
\(779\) 411.406i 0.528120i
\(780\) 214.480 318.696i 0.274974 0.408584i
\(781\) −95.2541 −0.121964
\(782\) 296.959i 0.379743i
\(783\) 1217.55 + 254.821i 1.55499 + 0.325442i
\(784\) −164.168 −0.209398
\(785\) 682.401i 0.869300i
\(