Properties

Label 177.3.b.a.119.6
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 119.6
Character \(\chi\) \(=\) 177.119
Dual form 177.3.b.a.119.33

$q$-expansion

\(f(q)\) \(=\) \(q-3.09739i q^{2} +(1.87116 + 2.34495i) q^{3} -5.59384 q^{4} +8.72041i q^{5} +(7.26322 - 5.79571i) q^{6} -11.2236 q^{7} +4.93675i q^{8} +(-1.99754 + 8.77552i) q^{9} +O(q^{10})\) \(q-3.09739i q^{2} +(1.87116 + 2.34495i) q^{3} -5.59384 q^{4} +8.72041i q^{5} +(7.26322 - 5.79571i) q^{6} -11.2236 q^{7} +4.93675i q^{8} +(-1.99754 + 8.77552i) q^{9} +27.0105 q^{10} +9.18062i q^{11} +(-10.4670 - 13.1173i) q^{12} +7.17130 q^{13} +34.7638i q^{14} +(-20.4489 + 16.3173i) q^{15} -7.08431 q^{16} +10.0383i q^{17} +(27.1812 + 6.18717i) q^{18} +27.7412 q^{19} -48.7806i q^{20} +(-21.0011 - 26.3187i) q^{21} +28.4360 q^{22} -2.46954i q^{23} +(-11.5764 + 9.23743i) q^{24} -51.0456 q^{25} -22.2123i q^{26} +(-24.3158 + 11.7363i) q^{27} +62.7829 q^{28} -42.9540i q^{29} +(50.5410 + 63.3383i) q^{30} +39.9367 q^{31} +41.6899i q^{32} +(-21.5280 + 17.1784i) q^{33} +31.0924 q^{34} -97.8742i q^{35} +(11.1739 - 49.0889i) q^{36} -42.6497 q^{37} -85.9253i q^{38} +(13.4186 + 16.8163i) q^{39} -43.0505 q^{40} -20.2872i q^{41} +(-81.5193 + 65.0486i) q^{42} +56.9139 q^{43} -51.3549i q^{44} +(-76.5262 - 17.4194i) q^{45} -7.64913 q^{46} +47.6938i q^{47} +(-13.2559 - 16.6123i) q^{48} +76.9687 q^{49} +158.108i q^{50} +(-23.5392 + 18.7832i) q^{51} -40.1151 q^{52} +68.4700i q^{53} +(36.3518 + 75.3157i) q^{54} -80.0588 q^{55} -55.4080i q^{56} +(51.9081 + 65.0515i) q^{57} -133.045 q^{58} +7.68115i q^{59} +(114.388 - 91.2762i) q^{60} -31.4105 q^{61} -123.700i q^{62} +(22.4196 - 98.4928i) q^{63} +100.793 q^{64} +62.5367i q^{65} +(53.2082 + 66.6808i) q^{66} +17.2244 q^{67} -56.1524i q^{68} +(5.79093 - 4.62089i) q^{69} -303.155 q^{70} +42.1176i q^{71} +(-43.3226 - 9.86136i) q^{72} +45.5157 q^{73} +132.103i q^{74} +(-95.5143 - 119.699i) q^{75} -155.180 q^{76} -103.039i q^{77} +(52.0867 - 41.5627i) q^{78} +27.8864 q^{79} -61.7781i q^{80} +(-73.0197 - 35.0590i) q^{81} -62.8373 q^{82} +0.101688i q^{83} +(117.477 + 147.222i) q^{84} -87.5378 q^{85} -176.285i q^{86} +(100.725 - 80.3736i) q^{87} -45.3224 q^{88} -34.2875i q^{89} +(-53.9547 + 237.032i) q^{90} -80.4876 q^{91} +13.8142i q^{92} +(74.7279 + 93.6495i) q^{93} +147.727 q^{94} +241.914i q^{95} +(-97.7605 + 78.0083i) q^{96} +59.1817 q^{97} -238.402i q^{98} +(-80.5647 - 18.3387i) 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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 3.09739i 1.54870i −0.632760 0.774348i \(-0.718078\pi\)
0.632760 0.774348i \(-0.281922\pi\)
\(3\) 1.87116 + 2.34495i 0.623719 + 0.781649i
\(4\) −5.59384 −1.39846
\(5\) 8.72041i 1.74408i 0.489432 + 0.872041i \(0.337204\pi\)
−0.489432 + 0.872041i \(0.662796\pi\)
\(6\) 7.26322 5.79571i 1.21054 0.965951i
\(7\) −11.2236 −1.60337 −0.801684 0.597748i \(-0.796062\pi\)
−0.801684 + 0.597748i \(0.796062\pi\)
\(8\) 4.93675i 0.617094i
\(9\) −1.99754 + 8.77552i −0.221949 + 0.975058i
\(10\) 27.0105 2.70105
\(11\) 9.18062i 0.834601i 0.908768 + 0.417301i \(0.137024\pi\)
−0.908768 + 0.417301i \(0.862976\pi\)
\(12\) −10.4670 13.1173i −0.872246 1.09310i
\(13\) 7.17130 0.551638 0.275819 0.961210i \(-0.411051\pi\)
0.275819 + 0.961210i \(0.411051\pi\)
\(14\) 34.7638i 2.48313i
\(15\) −20.4489 + 16.3173i −1.36326 + 1.08782i
\(16\) −7.08431 −0.442770
\(17\) 10.0383i 0.590486i 0.955422 + 0.295243i \(0.0954006\pi\)
−0.955422 + 0.295243i \(0.904599\pi\)
\(18\) 27.1812 + 6.18717i 1.51007 + 0.343732i
\(19\) 27.7412 1.46006 0.730031 0.683414i \(-0.239506\pi\)
0.730031 + 0.683414i \(0.239506\pi\)
\(20\) 48.7806i 2.43903i
\(21\) −21.0011 26.3187i −1.00005 1.25327i
\(22\) 28.4360 1.29254
\(23\) 2.46954i 0.107371i −0.998558 0.0536856i \(-0.982903\pi\)
0.998558 0.0536856i \(-0.0170969\pi\)
\(24\) −11.5764 + 9.23743i −0.482350 + 0.384893i
\(25\) −51.0456 −2.04182
\(26\) 22.2123i 0.854320i
\(27\) −24.3158 + 11.7363i −0.900587 + 0.434676i
\(28\) 62.7829 2.24225
\(29\) 42.9540i 1.48117i −0.671962 0.740586i \(-0.734548\pi\)
0.671962 0.740586i \(-0.265452\pi\)
\(30\) 50.5410 + 63.3383i 1.68470 + 2.11128i
\(31\) 39.9367 1.28828 0.644141 0.764907i \(-0.277215\pi\)
0.644141 + 0.764907i \(0.277215\pi\)
\(32\) 41.6899i 1.30281i
\(33\) −21.5280 + 17.1784i −0.652365 + 0.520557i
\(34\) 31.0924 0.914484
\(35\) 97.8742i 2.79641i
\(36\) 11.1739 49.0889i 0.310387 1.36358i
\(37\) −42.6497 −1.15269 −0.576347 0.817205i \(-0.695522\pi\)
−0.576347 + 0.817205i \(0.695522\pi\)
\(38\) 85.9253i 2.26119i
\(39\) 13.4186 + 16.8163i 0.344067 + 0.431187i
\(40\) −43.0505 −1.07626
\(41\) 20.2872i 0.494809i −0.968912 0.247404i \(-0.920422\pi\)
0.968912 0.247404i \(-0.0795776\pi\)
\(42\) −81.5193 + 65.0486i −1.94094 + 1.54878i
\(43\) 56.9139 1.32358 0.661790 0.749689i \(-0.269797\pi\)
0.661790 + 0.749689i \(0.269797\pi\)
\(44\) 51.3549i 1.16716i
\(45\) −76.5262 17.4194i −1.70058 0.387098i
\(46\) −7.64913 −0.166285
\(47\) 47.6938i 1.01476i 0.861722 + 0.507381i \(0.169386\pi\)
−0.861722 + 0.507381i \(0.830614\pi\)
\(48\) −13.2559 16.6123i −0.276164 0.346090i
\(49\) 76.9687 1.57079
\(50\) 158.108i 3.16216i
\(51\) −23.5392 + 18.7832i −0.461553 + 0.368297i
\(52\) −40.1151 −0.771444
\(53\) 68.4700i 1.29189i 0.763386 + 0.645943i \(0.223536\pi\)
−0.763386 + 0.645943i \(0.776464\pi\)
\(54\) 36.3518 + 75.3157i 0.673181 + 1.39474i
\(55\) −80.0588 −1.45561
\(56\) 55.4080i 0.989428i
\(57\) 51.9081 + 65.0515i 0.910668 + 1.14125i
\(58\) −133.045 −2.29388
\(59\) 7.68115i 0.130189i
\(60\) 114.388 91.2762i 1.90646 1.52127i
\(61\) −31.4105 −0.514926 −0.257463 0.966288i \(-0.582887\pi\)
−0.257463 + 0.966288i \(0.582887\pi\)
\(62\) 123.700i 1.99516i
\(63\) 22.4196 98.4928i 0.355866 1.56338i
\(64\) 100.793 1.57489
\(65\) 62.5367i 0.962102i
\(66\) 53.2082 + 66.6808i 0.806184 + 1.01032i
\(67\) 17.2244 0.257081 0.128540 0.991704i \(-0.458971\pi\)
0.128540 + 0.991704i \(0.458971\pi\)
\(68\) 56.1524i 0.825771i
\(69\) 5.79093 4.62089i 0.0839266 0.0669695i
\(70\) −303.155 −4.33078
\(71\) 42.1176i 0.593205i 0.955001 + 0.296603i \(0.0958536\pi\)
−0.955001 + 0.296603i \(0.904146\pi\)
\(72\) −43.3226 9.86136i −0.601702 0.136963i
\(73\) 45.5157 0.623503 0.311751 0.950164i \(-0.399084\pi\)
0.311751 + 0.950164i \(0.399084\pi\)
\(74\) 132.103i 1.78517i
\(75\) −95.5143 119.699i −1.27352 1.59599i
\(76\) −155.180 −2.04184
\(77\) 103.039i 1.33817i
\(78\) 52.0867 41.5627i 0.667778 0.532856i
\(79\) 27.8864 0.352993 0.176496 0.984301i \(-0.443524\pi\)
0.176496 + 0.984301i \(0.443524\pi\)
\(80\) 61.7781i 0.772227i
\(81\) −73.0197 35.0590i −0.901477 0.432827i
\(82\) −62.8373 −0.766308
\(83\) 0.101688i 0.00122516i 1.00000 0.000612579i \(0.000194990\pi\)
−1.00000 0.000612579i \(0.999805\pi\)
\(84\) 117.477 + 147.222i 1.39853 + 1.75265i
\(85\) −87.5378 −1.02986
\(86\) 176.285i 2.04982i
\(87\) 100.725 80.3736i 1.15776 0.923835i
\(88\) −45.3224 −0.515027
\(89\) 34.2875i 0.385252i −0.981272 0.192626i \(-0.938300\pi\)
0.981272 0.192626i \(-0.0617005\pi\)
\(90\) −53.9547 + 237.032i −0.599496 + 2.63369i
\(91\) −80.4876 −0.884479
\(92\) 13.8142i 0.150154i
\(93\) 74.7279 + 93.6495i 0.803526 + 1.00698i
\(94\) 147.727 1.57156
\(95\) 241.914i 2.54647i
\(96\) −97.7605 + 78.0083i −1.01834 + 0.812587i
\(97\) 59.1817 0.610121 0.305061 0.952333i \(-0.401323\pi\)
0.305061 + 0.952333i \(0.401323\pi\)
\(98\) 238.402i 2.43268i
\(99\) −80.5647 18.3387i −0.813785 0.185239i
\(100\) 285.541 2.85541
\(101\) 109.102i 1.08022i −0.841594 0.540110i \(-0.818383\pi\)
0.841594 0.540110i \(-0.181617\pi\)
\(102\) 58.1788 + 72.9101i 0.570381 + 0.714805i
\(103\) 84.9548 0.824804 0.412402 0.911002i \(-0.364690\pi\)
0.412402 + 0.911002i \(0.364690\pi\)
\(104\) 35.4029i 0.340412i
\(105\) 229.510 183.138i 2.18581 1.74417i
\(106\) 212.078 2.00074
\(107\) 132.466i 1.23800i 0.785389 + 0.619002i \(0.212463\pi\)
−0.785389 + 0.619002i \(0.787537\pi\)
\(108\) 136.019 65.6508i 1.25943 0.607877i
\(109\) 42.8315 0.392950 0.196475 0.980509i \(-0.437051\pi\)
0.196475 + 0.980509i \(0.437051\pi\)
\(110\) 247.973i 2.25430i
\(111\) −79.8042 100.011i −0.718957 0.901001i
\(112\) 79.5113 0.709923
\(113\) 13.7032i 0.121267i 0.998160 + 0.0606334i \(0.0193121\pi\)
−0.998160 + 0.0606334i \(0.980688\pi\)
\(114\) 201.490 160.780i 1.76746 1.41035i
\(115\) 21.5354 0.187264
\(116\) 240.278i 2.07136i
\(117\) −14.3250 + 62.9319i −0.122436 + 0.537879i
\(118\) 23.7915 0.201623
\(119\) 112.665i 0.946766i
\(120\) −80.5542 100.951i −0.671285 0.841259i
\(121\) 36.7163 0.303440
\(122\) 97.2906i 0.797464i
\(123\) 47.5723 37.9605i 0.386767 0.308622i
\(124\) −223.400 −1.80161
\(125\) 227.128i 1.81703i
\(126\) −305.071 69.4422i −2.42120 0.551128i
\(127\) −54.3557 −0.427998 −0.213999 0.976834i \(-0.568649\pi\)
−0.213999 + 0.976834i \(0.568649\pi\)
\(128\) 145.435i 1.13621i
\(129\) 106.495 + 133.460i 0.825542 + 1.03457i
\(130\) 193.701 1.49000
\(131\) 85.5392i 0.652971i 0.945202 + 0.326485i \(0.105864\pi\)
−0.945202 + 0.326485i \(0.894136\pi\)
\(132\) 120.424 96.0931i 0.912306 0.727978i
\(133\) −311.355 −2.34102
\(134\) 53.3507i 0.398140i
\(135\) −102.345 212.044i −0.758111 1.57070i
\(136\) −49.5564 −0.364385
\(137\) 29.0403i 0.211973i −0.994368 0.105986i \(-0.966200\pi\)
0.994368 0.105986i \(-0.0338000\pi\)
\(138\) −14.3127 17.9368i −0.103715 0.129977i
\(139\) −2.50546 −0.0180249 −0.00901243 0.999959i \(-0.502869\pi\)
−0.00901243 + 0.999959i \(0.502869\pi\)
\(140\) 547.493i 3.91066i
\(141\) −111.839 + 89.2427i −0.793188 + 0.632927i
\(142\) 130.455 0.918694
\(143\) 65.8369i 0.460398i
\(144\) 14.1512 62.1686i 0.0982723 0.431726i
\(145\) 374.576 2.58328
\(146\) 140.980i 0.965616i
\(147\) 144.020 + 180.487i 0.979731 + 1.22781i
\(148\) 238.575 1.61200
\(149\) 133.203i 0.893978i −0.894540 0.446989i \(-0.852496\pi\)
0.894540 0.446989i \(-0.147504\pi\)
\(150\) −370.755 + 295.845i −2.47170 + 1.97230i
\(151\) −34.6793 −0.229665 −0.114832 0.993385i \(-0.536633\pi\)
−0.114832 + 0.993385i \(0.536633\pi\)
\(152\) 136.951i 0.900995i
\(153\) −88.0910 20.0518i −0.575758 0.131058i
\(154\) −319.153 −2.07242
\(155\) 348.265i 2.24687i
\(156\) −75.0616 94.0677i −0.481164 0.602998i
\(157\) −269.832 −1.71867 −0.859336 0.511411i \(-0.829123\pi\)
−0.859336 + 0.511411i \(0.829123\pi\)
\(158\) 86.3752i 0.546679i
\(159\) −160.558 + 128.118i −1.00980 + 0.805774i
\(160\) −363.553 −2.27221
\(161\) 27.7171i 0.172156i
\(162\) −108.591 + 226.171i −0.670317 + 1.39611i
\(163\) 164.306 1.00801 0.504006 0.863700i \(-0.331859\pi\)
0.504006 + 0.863700i \(0.331859\pi\)
\(164\) 113.483i 0.691970i
\(165\) −149.803 187.733i −0.907894 1.13778i
\(166\) 0.314968 0.00189740
\(167\) 268.971i 1.61060i −0.592864 0.805302i \(-0.702003\pi\)
0.592864 0.805302i \(-0.297997\pi\)
\(168\) 129.929 103.677i 0.773385 0.617125i
\(169\) −117.573 −0.695695
\(170\) 271.139i 1.59493i
\(171\) −55.4141 + 243.443i −0.324059 + 1.42364i
\(172\) −318.367 −1.85097
\(173\) 155.110i 0.896589i 0.893886 + 0.448295i \(0.147968\pi\)
−0.893886 + 0.448295i \(0.852032\pi\)
\(174\) −248.949 311.984i −1.43074 1.79301i
\(175\) 572.914 3.27379
\(176\) 65.0384i 0.369536i
\(177\) −18.0119 + 14.3726i −0.101762 + 0.0812013i
\(178\) −106.202 −0.596639
\(179\) 203.005i 1.13411i −0.823681 0.567053i \(-0.808083\pi\)
0.823681 0.567053i \(-0.191917\pi\)
\(180\) 428.075 + 97.4413i 2.37820 + 0.541340i
\(181\) 214.747 1.18645 0.593223 0.805038i \(-0.297855\pi\)
0.593223 + 0.805038i \(0.297855\pi\)
\(182\) 249.302i 1.36979i
\(183\) −58.7739 73.6559i −0.321169 0.402491i
\(184\) 12.1915 0.0662581
\(185\) 371.923i 2.01039i
\(186\) 290.069 231.462i 1.55951 1.24442i
\(187\) −92.1574 −0.492821
\(188\) 266.792i 1.41911i
\(189\) 272.911 131.723i 1.44397 0.696946i
\(190\) 749.304 3.94370
\(191\) 89.7848i 0.470078i −0.971986 0.235039i \(-0.924478\pi\)
0.971986 0.235039i \(-0.0755217\pi\)
\(192\) 188.599 + 236.353i 0.982286 + 1.23101i
\(193\) 46.0334 0.238515 0.119258 0.992863i \(-0.461949\pi\)
0.119258 + 0.992863i \(0.461949\pi\)
\(194\) 183.309i 0.944892i
\(195\) −146.645 + 117.016i −0.752026 + 0.600082i
\(196\) −430.550 −2.19669
\(197\) 202.962i 1.03026i −0.857111 0.515132i \(-0.827743\pi\)
0.857111 0.515132i \(-0.172257\pi\)
\(198\) −56.8020 + 249.541i −0.286879 + 1.26031i
\(199\) −80.7470 −0.405764 −0.202882 0.979203i \(-0.565031\pi\)
−0.202882 + 0.979203i \(0.565031\pi\)
\(200\) 251.999i 1.26000i
\(201\) 32.2296 + 40.3903i 0.160346 + 0.200947i
\(202\) −337.933 −1.67293
\(203\) 482.097i 2.37486i
\(204\) 131.674 105.070i 0.645463 0.515049i
\(205\) 176.912 0.862987
\(206\) 263.138i 1.27737i
\(207\) 21.6715 + 4.93301i 0.104693 + 0.0238309i
\(208\) −50.8037 −0.244249
\(209\) 254.681i 1.21857i
\(210\) −567.250 710.882i −2.70119 3.38515i
\(211\) −80.3144 −0.380637 −0.190318 0.981722i \(-0.560952\pi\)
−0.190318 + 0.981722i \(0.560952\pi\)
\(212\) 383.010i 1.80665i
\(213\) −98.7634 + 78.8086i −0.463678 + 0.369993i
\(214\) 410.301 1.91729
\(215\) 496.313i 2.30843i
\(216\) −57.9390 120.041i −0.268236 0.555746i
\(217\) −448.233 −2.06559
\(218\) 132.666i 0.608560i
\(219\) 85.1670 + 106.732i 0.388891 + 0.487360i
\(220\) 447.836 2.03562
\(221\) 71.9874i 0.325735i
\(222\) −309.774 + 247.185i −1.39538 + 1.11345i
\(223\) −1.92218 −0.00861964 −0.00430982 0.999991i \(-0.501372\pi\)
−0.00430982 + 0.999991i \(0.501372\pi\)
\(224\) 467.910i 2.08888i
\(225\) 101.966 447.952i 0.453181 1.99090i
\(226\) 42.4440 0.187806
\(227\) 169.954i 0.748696i 0.927288 + 0.374348i \(0.122134\pi\)
−0.927288 + 0.374348i \(0.877866\pi\)
\(228\) −290.366 363.888i −1.27353 1.59600i
\(229\) 112.375 0.490722 0.245361 0.969432i \(-0.421094\pi\)
0.245361 + 0.969432i \(0.421094\pi\)
\(230\) 66.7036i 0.290016i
\(231\) 241.622 192.803i 1.04598 0.834644i
\(232\) 212.053 0.914021
\(233\) 342.532i 1.47010i 0.678015 + 0.735048i \(0.262840\pi\)
−0.678015 + 0.735048i \(0.737160\pi\)
\(234\) 194.925 + 44.3700i 0.833012 + 0.189616i
\(235\) −415.910 −1.76983
\(236\) 42.9671i 0.182064i
\(237\) 52.1799 + 65.3922i 0.220168 + 0.275916i
\(238\) −348.968 −1.46625
\(239\) 61.3192i 0.256566i −0.991738 0.128283i \(-0.959053\pi\)
0.991738 0.128283i \(-0.0409466\pi\)
\(240\) 144.866 115.597i 0.603610 0.481652i
\(241\) −107.066 −0.444257 −0.222129 0.975017i \(-0.571300\pi\)
−0.222129 + 0.975017i \(0.571300\pi\)
\(242\) 113.725i 0.469937i
\(243\) −54.4199 236.828i −0.223950 0.974601i
\(244\) 175.705 0.720103
\(245\) 671.199i 2.73959i
\(246\) −117.578 147.350i −0.477961 0.598984i
\(247\) 198.940 0.805426
\(248\) 197.158i 0.794991i
\(249\) −0.238453 + 0.190274i −0.000957643 + 0.000764154i
\(250\) −703.506 −2.81402
\(251\) 82.0368i 0.326840i 0.986557 + 0.163420i \(0.0522525\pi\)
−0.986557 + 0.163420i \(0.947747\pi\)
\(252\) −125.411 + 550.953i −0.497664 + 2.18632i
\(253\) 22.6719 0.0896122
\(254\) 168.361i 0.662839i
\(255\) −163.797 205.271i −0.642341 0.804986i
\(256\) −47.2985 −0.184760
\(257\) 499.557i 1.94380i 0.235391 + 0.971901i \(0.424363\pi\)
−0.235391 + 0.971901i \(0.575637\pi\)
\(258\) 413.378 329.857i 1.60224 1.27851i
\(259\) 478.682 1.84819
\(260\) 349.820i 1.34546i
\(261\) 376.944 + 85.8023i 1.44423 + 0.328745i
\(262\) 264.948 1.01125
\(263\) 41.9833i 0.159632i −0.996810 0.0798161i \(-0.974567\pi\)
0.996810 0.0798161i \(-0.0254333\pi\)
\(264\) −84.8053 106.279i −0.321232 0.402570i
\(265\) −597.086 −2.25316
\(266\) 964.389i 3.62552i
\(267\) 80.4022 64.1572i 0.301132 0.240289i
\(268\) −96.3506 −0.359517
\(269\) 246.564i 0.916596i −0.888799 0.458298i \(-0.848459\pi\)
0.888799 0.458298i \(-0.151541\pi\)
\(270\) −656.784 + 317.003i −2.43253 + 1.17408i
\(271\) 454.843 1.67839 0.839194 0.543831i \(-0.183027\pi\)
0.839194 + 0.543831i \(0.183027\pi\)
\(272\) 71.1142i 0.261449i
\(273\) −150.605 188.739i −0.551666 0.691352i
\(274\) −89.9492 −0.328282
\(275\) 468.630i 1.70411i
\(276\) −32.3936 + 25.8485i −0.117368 + 0.0936542i
\(277\) −523.363 −1.88940 −0.944699 0.327939i \(-0.893646\pi\)
−0.944699 + 0.327939i \(0.893646\pi\)
\(278\) 7.76038i 0.0279150i
\(279\) −79.7753 + 350.466i −0.285933 + 1.25615i
\(280\) 483.180 1.72564
\(281\) 327.127i 1.16415i −0.813134 0.582077i \(-0.802240\pi\)
0.813134 0.582077i \(-0.197760\pi\)
\(282\) 276.420 + 346.411i 0.980211 + 1.22841i
\(283\) 435.705 1.53959 0.769796 0.638290i \(-0.220358\pi\)
0.769796 + 0.638290i \(0.220358\pi\)
\(284\) 235.599i 0.829574i
\(285\) −567.276 + 452.660i −1.99044 + 1.58828i
\(286\) 203.923 0.713017
\(287\) 227.694i 0.793361i
\(288\) −365.851 83.2773i −1.27031 0.289157i
\(289\) 188.233 0.651326
\(290\) 1160.21i 4.00072i
\(291\) 110.738 + 138.778i 0.380544 + 0.476900i
\(292\) −254.608 −0.871944
\(293\) 228.463i 0.779736i −0.920871 0.389868i \(-0.872521\pi\)
0.920871 0.389868i \(-0.127479\pi\)
\(294\) 559.040 446.088i 1.90150 1.51731i
\(295\) −66.9828 −0.227060
\(296\) 210.551i 0.711320i
\(297\) −107.746 223.234i −0.362781 0.751631i
\(298\) −412.581 −1.38450
\(299\) 17.7098i 0.0592301i
\(300\) 534.292 + 669.578i 1.78097 + 2.23193i
\(301\) −638.778 −2.12219
\(302\) 107.416i 0.355681i
\(303\) 255.839 204.147i 0.844353 0.673754i
\(304\) −196.527 −0.646471
\(305\) 273.912i 0.898073i
\(306\) −62.1084 + 272.852i −0.202969 + 0.891675i
\(307\) −374.581 −1.22013 −0.610067 0.792350i \(-0.708858\pi\)
−0.610067 + 0.792350i \(0.708858\pi\)
\(308\) 576.386i 1.87138i
\(309\) 158.964 + 199.214i 0.514446 + 0.644707i
\(310\) 1078.71 3.47972
\(311\) 187.947i 0.604331i 0.953256 + 0.302165i \(0.0977095\pi\)
−0.953256 + 0.302165i \(0.902291\pi\)
\(312\) −83.0178 + 66.2444i −0.266083 + 0.212322i
\(313\) 621.024 1.98410 0.992052 0.125832i \(-0.0401599\pi\)
0.992052 + 0.125832i \(0.0401599\pi\)
\(314\) 835.774i 2.66170i
\(315\) 858.898 + 195.508i 2.72666 + 0.620660i
\(316\) −155.992 −0.493646
\(317\) 313.420i 0.988706i −0.869261 0.494353i \(-0.835405\pi\)
0.869261 0.494353i \(-0.164595\pi\)
\(318\) 396.832 + 497.312i 1.24790 + 1.56388i
\(319\) 394.344 1.23619
\(320\) 878.954i 2.74673i
\(321\) −310.627 + 247.866i −0.967684 + 0.772167i
\(322\) 85.8506 0.266617
\(323\) 278.473i 0.862146i
\(324\) 408.460 + 196.114i 1.26068 + 0.605291i
\(325\) −366.063 −1.12635
\(326\) 508.920i 1.56111i
\(327\) 80.1445 + 100.438i 0.245090 + 0.307149i
\(328\) 100.153 0.305343
\(329\) 535.296i 1.62704i
\(330\) −581.484 + 463.997i −1.76207 + 1.40605i
\(331\) 125.021 0.377707 0.188853 0.982005i \(-0.439523\pi\)
0.188853 + 0.982005i \(0.439523\pi\)
\(332\) 0.568827i 0.00171333i
\(333\) 85.1945 374.273i 0.255839 1.12394i
\(334\) −833.109 −2.49434
\(335\) 150.204i 0.448370i
\(336\) 148.778 + 186.450i 0.442792 + 0.554910i
\(337\) −422.805 −1.25461 −0.627307 0.778772i \(-0.715843\pi\)
−0.627307 + 0.778772i \(0.715843\pi\)
\(338\) 364.168i 1.07742i
\(339\) −32.1332 + 25.6408i −0.0947881 + 0.0756364i
\(340\) 489.672 1.44021
\(341\) 366.644i 1.07520i
\(342\) 754.039 + 171.639i 2.20479 + 0.501869i
\(343\) −313.908 −0.915185
\(344\) 280.970i 0.816773i
\(345\) 40.2961 + 50.4993i 0.116800 + 0.146375i
\(346\) 480.436 1.38854
\(347\) 285.316i 0.822235i 0.911582 + 0.411118i \(0.134861\pi\)
−0.911582 + 0.411118i \(0.865139\pi\)
\(348\) −563.438 + 449.597i −1.61907 + 1.29195i
\(349\) −146.999 −0.421202 −0.210601 0.977572i \(-0.567542\pi\)
−0.210601 + 0.977572i \(0.567542\pi\)
\(350\) 1774.54i 5.07011i
\(351\) −174.376 + 84.1642i −0.496798 + 0.239784i
\(352\) −382.739 −1.08733
\(353\) 372.881i 1.05632i −0.849145 0.528160i \(-0.822882\pi\)
0.849145 0.528160i \(-0.177118\pi\)
\(354\) 44.5177 + 55.7898i 0.125756 + 0.157598i
\(355\) −367.282 −1.03460
\(356\) 191.799i 0.538760i
\(357\) 264.194 210.814i 0.740039 0.590516i
\(358\) −628.787 −1.75639
\(359\) 74.5446i 0.207645i −0.994596 0.103823i \(-0.966893\pi\)
0.994596 0.103823i \(-0.0331074\pi\)
\(360\) 85.9951 377.791i 0.238875 1.04942i
\(361\) 408.572 1.13178
\(362\) 665.154i 1.83744i
\(363\) 68.7019 + 86.0977i 0.189262 + 0.237184i
\(364\) 450.235 1.23691
\(365\) 396.916i 1.08744i
\(366\) −228.141 + 182.046i −0.623336 + 0.497393i
\(367\) 639.738 1.74316 0.871578 0.490257i \(-0.163097\pi\)
0.871578 + 0.490257i \(0.163097\pi\)
\(368\) 17.4950i 0.0475407i
\(369\) 178.030 + 40.5244i 0.482467 + 0.109822i
\(370\) −1151.99 −3.11349
\(371\) 768.478i 2.07137i
\(372\) −418.016 523.860i −1.12370 1.40823i
\(373\) −272.666 −0.731008 −0.365504 0.930810i \(-0.619103\pi\)
−0.365504 + 0.930810i \(0.619103\pi\)
\(374\) 285.448i 0.763229i
\(375\) 532.604 424.993i 1.42028 1.13331i
\(376\) −235.453 −0.626204
\(377\) 308.036i 0.817071i
\(378\) −407.997 845.312i −1.07936 2.23627i
\(379\) 473.984 1.25062 0.625309 0.780377i \(-0.284973\pi\)
0.625309 + 0.780377i \(0.284973\pi\)
\(380\) 1353.23i 3.56113i
\(381\) −101.708 127.461i −0.266950 0.334544i
\(382\) −278.099 −0.728007
\(383\) 297.241i 0.776086i −0.921641 0.388043i \(-0.873151\pi\)
0.921641 0.388043i \(-0.126849\pi\)
\(384\) 341.037 272.132i 0.888118 0.708676i
\(385\) 898.546 2.33388
\(386\) 142.584i 0.369388i
\(387\) −113.688 + 499.450i −0.293767 + 1.29057i
\(388\) −331.053 −0.853230
\(389\) 147.396i 0.378910i 0.981889 + 0.189455i \(0.0606721\pi\)
−0.981889 + 0.189455i \(0.939328\pi\)
\(390\) 362.444 + 454.217i 0.929344 + 1.16466i
\(391\) 24.7899 0.0634012
\(392\) 379.975i 0.969324i
\(393\) −200.585 + 160.057i −0.510394 + 0.407270i
\(394\) −628.653 −1.59557
\(395\) 243.181i 0.615649i
\(396\) 450.666 + 102.584i 1.13805 + 0.259049i
\(397\) −671.197 −1.69067 −0.845336 0.534235i \(-0.820600\pi\)
−0.845336 + 0.534235i \(0.820600\pi\)
\(398\) 250.105i 0.628405i
\(399\) −582.594 730.111i −1.46014 1.82985i
\(400\) 361.623 0.904057
\(401\) 420.309i 1.04815i 0.851671 + 0.524076i \(0.175589\pi\)
−0.851671 + 0.524076i \(0.824411\pi\)
\(402\) 125.105 99.8276i 0.311205 0.248327i
\(403\) 286.398 0.710666
\(404\) 610.301i 1.51065i
\(405\) 305.729 636.762i 0.754885 1.57225i
\(406\) 1493.24 3.67794
\(407\) 391.550i 0.962040i
\(408\) −92.7278 116.207i −0.227274 0.284821i
\(409\) −119.098 −0.291193 −0.145597 0.989344i \(-0.546510\pi\)
−0.145597 + 0.989344i \(0.546510\pi\)
\(410\) 547.967i 1.33651i
\(411\) 68.0979 54.3389i 0.165688 0.132212i
\(412\) −475.223 −1.15345
\(413\) 86.2099i 0.208741i
\(414\) 15.2795 67.1251i 0.0369069 0.162138i
\(415\) −0.886762 −0.00213678
\(416\) 298.971i 0.718679i
\(417\) −4.68810 5.87516i −0.0112424 0.0140891i
\(418\) 788.847 1.88719
\(419\) 744.229i 1.77620i 0.459648 + 0.888101i \(0.347975\pi\)
−0.459648 + 0.888101i \(0.652025\pi\)
\(420\) −1283.84 + 1024.44i −3.05676 + 2.43915i
\(421\) −364.752 −0.866393 −0.433197 0.901299i \(-0.642614\pi\)
−0.433197 + 0.901299i \(0.642614\pi\)
\(422\) 248.765i 0.589491i
\(423\) −418.539 95.2704i −0.989453 0.225226i
\(424\) −338.019 −0.797215
\(425\) 512.409i 1.20567i
\(426\) 244.101 + 305.909i 0.573007 + 0.718096i
\(427\) 352.538 0.825616
\(428\) 740.996i 1.73130i
\(429\) −154.384 + 123.191i −0.359869 + 0.287159i
\(430\) 1537.28 3.57506
\(431\) 64.3549i 0.149315i 0.997209 + 0.0746576i \(0.0237864\pi\)
−0.997209 + 0.0746576i \(0.976214\pi\)
\(432\) 172.261 83.1433i 0.398752 0.192461i
\(433\) −399.530 −0.922701 −0.461351 0.887218i \(-0.652635\pi\)
−0.461351 + 0.887218i \(0.652635\pi\)
\(434\) 1388.35i 3.19897i
\(435\) 700.891 + 878.361i 1.61124 + 2.01922i
\(436\) −239.593 −0.549524
\(437\) 68.5079i 0.156769i
\(438\) 330.590 263.796i 0.754773 0.602273i
\(439\) −757.730 −1.72604 −0.863019 0.505172i \(-0.831429\pi\)
−0.863019 + 0.505172i \(0.831429\pi\)
\(440\) 395.230i 0.898250i
\(441\) −153.748 + 675.440i −0.348635 + 1.53161i
\(442\) 222.973 0.504464
\(443\) 397.689i 0.897717i −0.893603 0.448859i \(-0.851831\pi\)
0.893603 0.448859i \(-0.148169\pi\)
\(444\) 446.412 + 559.446i 1.00543 + 1.26001i
\(445\) 299.001 0.671912
\(446\) 5.95374i 0.0133492i
\(447\) 312.353 249.243i 0.698776 0.557591i
\(448\) −1131.25 −2.52512
\(449\) 219.751i 0.489424i 0.969596 + 0.244712i \(0.0786934\pi\)
−0.969596 + 0.244712i \(0.921307\pi\)
\(450\) −1387.48 315.828i −3.08329 0.701840i
\(451\) 186.249 0.412968
\(452\) 76.6533i 0.169587i
\(453\) −64.8905 81.3212i −0.143246 0.179517i
\(454\) 526.414 1.15950
\(455\) 701.885i 1.54260i
\(456\) −321.143 + 256.257i −0.704261 + 0.561967i
\(457\) 416.283 0.910903 0.455451 0.890261i \(-0.349478\pi\)
0.455451 + 0.890261i \(0.349478\pi\)
\(458\) 348.070i 0.759979i
\(459\) −117.812 244.089i −0.256670 0.531784i
\(460\) −120.466 −0.261882
\(461\) 387.495i 0.840554i −0.907396 0.420277i \(-0.861933\pi\)
0.907396 0.420277i \(-0.138067\pi\)
\(462\) −597.186 748.397i −1.29261 1.61991i
\(463\) −445.696 −0.962626 −0.481313 0.876549i \(-0.659840\pi\)
−0.481313 + 0.876549i \(0.659840\pi\)
\(464\) 304.299i 0.655817i
\(465\) −816.662 + 651.658i −1.75626 + 1.40142i
\(466\) 1060.96 2.27673
\(467\) 805.049i 1.72387i −0.507016 0.861937i \(-0.669251\pi\)
0.507016 0.861937i \(-0.330749\pi\)
\(468\) 80.1316 352.031i 0.171221 0.752203i
\(469\) −193.319 −0.412195
\(470\) 1288.24i 2.74093i
\(471\) −504.897 632.741i −1.07197 1.34340i
\(472\) −37.9199 −0.0803387
\(473\) 522.505i 1.10466i
\(474\) 202.545 161.622i 0.427311 0.340974i
\(475\) −1416.06 −2.98119
\(476\) 630.231i 1.32402i
\(477\) −600.860 136.772i −1.25966 0.286733i
\(478\) −189.930 −0.397343
\(479\) 199.257i 0.415986i 0.978130 + 0.207993i \(0.0666931\pi\)
−0.978130 + 0.207993i \(0.933307\pi\)
\(480\) −680.265 852.512i −1.41722 1.77607i
\(481\) −305.853 −0.635870
\(482\) 331.625i 0.688019i
\(483\) −64.9950 + 51.8630i −0.134565 + 0.107377i
\(484\) −205.385 −0.424349
\(485\) 516.089i 1.06410i
\(486\) −733.549 + 168.560i −1.50936 + 0.346831i
\(487\) −558.507 −1.14683 −0.573416 0.819264i \(-0.694382\pi\)
−0.573416 + 0.819264i \(0.694382\pi\)
\(488\) 155.066i 0.317757i
\(489\) 307.442 + 385.289i 0.628717 + 0.787912i
\(490\) 2078.97 4.24279
\(491\) 947.072i 1.92886i −0.264332 0.964432i \(-0.585152\pi\)
0.264332 0.964432i \(-0.414848\pi\)
\(492\) −266.112 + 212.345i −0.540878 + 0.431595i
\(493\) 431.183 0.874611
\(494\) 616.196i 1.24736i
\(495\) 159.921 702.558i 0.323072 1.41931i
\(496\) −282.924 −0.570412
\(497\) 472.710i 0.951126i
\(498\) 0.589354 + 0.738583i 0.00118344 + 0.00148310i
\(499\) −454.602 −0.911026 −0.455513 0.890229i \(-0.650544\pi\)
−0.455513 + 0.890229i \(0.650544\pi\)
\(500\) 1270.52i 2.54104i
\(501\) 630.722 503.287i 1.25893 1.00456i
\(502\) 254.100 0.506176
\(503\) 818.520i 1.62728i 0.581372 + 0.813638i \(0.302516\pi\)
−0.581372 + 0.813638i \(0.697484\pi\)
\(504\) 486.234 + 110.680i 0.964750 + 0.219603i
\(505\) 951.417 1.88399
\(506\) 70.2237i 0.138782i
\(507\) −219.997 275.701i −0.433918 0.543789i
\(508\) 304.057 0.598538
\(509\) 329.331i 0.647017i −0.946225 0.323508i \(-0.895138\pi\)
0.946225 0.323508i \(-0.104862\pi\)
\(510\) −635.806 + 507.343i −1.24668 + 0.994791i
\(511\) −510.849 −0.999705
\(512\) 435.238i 0.850074i
\(513\) −674.550 + 325.577i −1.31491 + 0.634654i
\(514\) 1547.32 3.01036
\(515\) 740.841i 1.43853i
\(516\) −595.716 746.554i −1.15449 1.44681i
\(517\) −437.859 −0.846922
\(518\) 1482.66i 2.86229i
\(519\) −363.724 + 290.235i −0.700818 + 0.559220i
\(520\) −308.728 −0.593707
\(521\) 128.469i 0.246581i −0.992371 0.123290i \(-0.960655\pi\)
0.992371 0.123290i \(-0.0393447\pi\)
\(522\) 265.764 1167.54i 0.509126 2.23667i
\(523\) −131.827 −0.252060 −0.126030 0.992026i \(-0.540224\pi\)
−0.126030 + 0.992026i \(0.540224\pi\)
\(524\) 478.493i 0.913154i
\(525\) 1072.01 + 1343.45i 2.04193 + 2.55896i
\(526\) −130.039 −0.247222
\(527\) 400.896i 0.760713i
\(528\) 152.511 121.697i 0.288847 0.230487i
\(529\) 522.901 0.988471
\(530\) 1849.41i 3.48945i
\(531\) −67.4061 15.3434i −0.126942 0.0288953i
\(532\) 1741.67 3.27382
\(533\) 145.485i 0.272955i
\(534\) −198.720 249.037i −0.372135 0.466362i
\(535\) −1155.16 −2.15918
\(536\) 85.0325i 0.158643i
\(537\) 476.036 379.855i 0.886473 0.707364i
\(538\) −763.706 −1.41953
\(539\) 706.620i 1.31098i
\(540\) 572.502 + 1186.14i 1.06019 + 2.19656i
\(541\) 524.830 0.970110 0.485055 0.874484i \(-0.338800\pi\)
0.485055 + 0.874484i \(0.338800\pi\)
\(542\) 1408.83i 2.59931i
\(543\) 401.825 + 503.569i 0.740009 + 0.927383i
\(544\) −418.494 −0.769291
\(545\) 373.508i 0.685337i
\(546\) −584.599 + 466.483i −1.07069 + 0.854364i
\(547\) 181.429 0.331680 0.165840 0.986153i \(-0.446966\pi\)
0.165840 + 0.986153i \(0.446966\pi\)
\(548\) 162.447i 0.296436i
\(549\) 62.7437 275.643i 0.114287 0.502083i
\(550\) −1451.53 −2.63915
\(551\) 1191.59i 2.16260i
\(552\) 22.8122 + 28.5884i 0.0413264 + 0.0517906i
\(553\) −312.986 −0.565977
\(554\) 1621.06i 2.92610i
\(555\) 872.138 695.926i 1.57142 1.25392i
\(556\) 14.0151 0.0252070
\(557\) 549.889i 0.987234i −0.869680 0.493617i \(-0.835675\pi\)
0.869680 0.493617i \(-0.164325\pi\)
\(558\) 1085.53 + 247.095i 1.94540 + 0.442823i
\(559\) 408.147 0.730137
\(560\) 693.372i 1.23816i
\(561\) −172.441 216.104i −0.307382 0.385212i
\(562\) −1013.24 −1.80292
\(563\) 374.249i 0.664741i 0.943149 + 0.332370i \(0.107848\pi\)
−0.943149 + 0.332370i \(0.892152\pi\)
\(564\) 625.612 499.209i 1.10924 0.885123i
\(565\) −119.497 −0.211499
\(566\) 1349.55i 2.38436i
\(567\) 819.542 + 393.487i 1.44540 + 0.693980i
\(568\) −207.924 −0.366063
\(569\) 812.694i 1.42828i −0.700000 0.714142i \(-0.746817\pi\)
0.700000 0.714142i \(-0.253183\pi\)
\(570\) 1402.07 + 1757.08i 2.45976 + 3.08259i
\(571\) 537.470 0.941278 0.470639 0.882326i \(-0.344023\pi\)
0.470639 + 0.882326i \(0.344023\pi\)
\(572\) 368.281i 0.643848i
\(573\) 210.541 168.001i 0.367435 0.293196i
\(574\) 705.259 1.22867
\(575\) 126.059i 0.219233i
\(576\) −201.338 + 884.509i −0.349545 + 1.53561i
\(577\) 115.099 0.199479 0.0997395 0.995014i \(-0.468199\pi\)
0.0997395 + 0.995014i \(0.468199\pi\)
\(578\) 583.032i 1.00871i
\(579\) 86.1358 + 107.946i 0.148766 + 0.186435i
\(580\) −2095.32 −3.61262
\(581\) 1.14130i 0.00196438i
\(582\) 429.850 343.000i 0.738574 0.589347i
\(583\) −628.597 −1.07821
\(584\) 224.700i 0.384760i
\(585\) −548.792 124.920i −0.938106 0.213538i
\(586\) −707.638 −1.20757
\(587\) 280.527i 0.477899i −0.971032 0.238950i \(-0.923197\pi\)
0.971032 0.238950i \(-0.0768031\pi\)
\(588\) −805.627 1009.62i −1.37011 1.71704i
\(589\) 1107.89 1.88097
\(590\) 207.472i 0.351647i
\(591\) 475.935 379.774i 0.805305 0.642596i
\(592\) 302.143 0.510377
\(593\) 189.070i 0.318837i 0.987211 + 0.159418i \(0.0509619\pi\)
−0.987211 + 0.159418i \(0.949038\pi\)
\(594\) −691.445 + 333.732i −1.16405 + 0.561838i
\(595\) 982.487 1.65124
\(596\) 745.114i 1.25019i
\(597\) −151.090 189.347i −0.253082 0.317165i
\(598\) −54.8542 −0.0917294
\(599\) 305.707i 0.510363i 0.966893 + 0.255182i \(0.0821352\pi\)
−0.966893 + 0.255182i \(0.917865\pi\)
\(600\) 590.925 471.530i 0.984874 0.785884i
\(601\) 1136.72 1.89138 0.945688 0.325076i \(-0.105390\pi\)
0.945688 + 0.325076i \(0.105390\pi\)
\(602\) 1978.55i 3.28662i
\(603\) −34.4065 + 151.153i −0.0570588 + 0.250669i
\(604\) 193.991 0.321177
\(605\) 320.181i 0.529225i
\(606\) −632.325 792.434i −1.04344 1.30765i
\(607\) −677.066 −1.11543 −0.557715 0.830033i \(-0.688322\pi\)
−0.557715 + 0.830033i \(0.688322\pi\)
\(608\) 1156.53i 1.90218i
\(609\) −1130.49 + 902.079i −1.85631 + 1.48125i
\(610\) −848.414 −1.39084
\(611\) 342.027i 0.559782i
\(612\) 492.767 + 112.167i 0.805175 + 0.183279i
\(613\) −747.057 −1.21869 −0.609345 0.792905i \(-0.708567\pi\)
−0.609345 + 0.792905i \(0.708567\pi\)
\(614\) 1160.23i 1.88962i
\(615\) 331.031 + 414.850i 0.538262 + 0.674553i
\(616\) 508.679 0.825778
\(617\) 19.4217i 0.0314777i 0.999876 + 0.0157388i \(0.00501003\pi\)
−0.999876 + 0.0157388i \(0.994990\pi\)
\(618\) 617.045 492.373i 0.998455 0.796720i
\(619\) 477.200 0.770921 0.385460 0.922724i \(-0.374043\pi\)
0.385460 + 0.922724i \(0.374043\pi\)
\(620\) 1948.14i 3.14216i
\(621\) 28.9831 + 60.0489i 0.0466717 + 0.0966971i
\(622\) 582.145 0.935925
\(623\) 384.828i 0.617701i
\(624\) −95.0617 119.132i −0.152342 0.190917i
\(625\) 704.513 1.12722
\(626\) 1923.56i 3.07277i
\(627\) −597.213 + 476.548i −0.952493 + 0.760045i
\(628\) 1509.39 2.40350
\(629\) 428.128i 0.680649i
\(630\) 605.564 2660.34i 0.961213 4.22277i
\(631\) 360.411 0.571174 0.285587 0.958353i \(-0.407811\pi\)
0.285587 + 0.958353i \(0.407811\pi\)
\(632\) 137.668i 0.217830i
\(633\) −150.281 188.333i −0.237410 0.297524i
\(634\) −970.784 −1.53121
\(635\) 474.004i 0.746464i
\(636\) 898.138 716.672i 1.41217 1.12684i
\(637\) 551.965 0.866507
\(638\) 1221.44i 1.91448i
\(639\) −369.604 84.1316i −0.578409 0.131661i
\(640\) 1268.25 1.98165
\(641\) 239.172i 0.373123i −0.982443 0.186562i \(-0.940266\pi\)
0.982443 0.186562i \(-0.0597344\pi\)
\(642\) 767.737 + 962.133i 1.19585 + 1.49865i
\(643\) −491.031 −0.763657 −0.381828 0.924233i \(-0.624705\pi\)
−0.381828 + 0.924233i \(0.624705\pi\)
\(644\) 155.045i 0.240753i
\(645\) −1163.83 + 928.680i −1.80438 + 1.43981i
\(646\) 862.541 1.33520
\(647\) 1065.46i 1.64677i 0.567480 + 0.823387i \(0.307918\pi\)
−0.567480 + 0.823387i \(0.692082\pi\)
\(648\) 173.077 360.480i 0.267094 0.556296i
\(649\) −70.5177 −0.108656
\(650\) 1133.84i 1.74437i
\(651\) −838.715 1051.08i −1.28835 1.61457i
\(652\) −919.102 −1.40967
\(653\) 245.954i 0.376652i 0.982107 + 0.188326i \(0.0603062\pi\)
−0.982107 + 0.188326i \(0.939694\pi\)
\(654\) 311.095 248.239i 0.475680 0.379570i
\(655\) −745.937 −1.13884
\(656\) 143.721i 0.219086i
\(657\) −90.9195 + 399.424i −0.138386 + 0.607952i
\(658\) −1658.02 −2.51979
\(659\) 230.272i 0.349426i −0.984619 0.174713i \(-0.944100\pi\)
0.984619 0.174713i \(-0.0558997\pi\)
\(660\) 837.971 + 1050.15i 1.26965 + 1.59114i
\(661\) 703.422 1.06418 0.532089 0.846688i \(-0.321407\pi\)
0.532089 + 0.846688i \(0.321407\pi\)
\(662\) 387.239i 0.584953i
\(663\) −168.806 + 134.700i −0.254610 + 0.203167i
\(664\) −0.502009 −0.000756037
\(665\) 2715.14i 4.08292i
\(666\) −1159.27 263.881i −1.74065 0.396217i
\(667\) −106.076 −0.159035
\(668\) 1504.58i 2.25237i
\(669\) −3.59670 4.50741i −0.00537623 0.00673753i
\(670\) 465.240 0.694389
\(671\) 288.368i 0.429758i
\(672\) 1097.22 875.533i 1.63277 1.30288i
\(673\) −590.571 −0.877520 −0.438760 0.898604i \(-0.644582\pi\)
−0.438760 + 0.898604i \(0.644582\pi\)
\(674\) 1309.59i 1.94302i
\(675\) 1241.22 599.084i 1.83884 0.887532i
\(676\) 657.682 0.972902
\(677\) 233.839i 0.345405i 0.984974 + 0.172702i \(0.0552499\pi\)
−0.984974 + 0.172702i \(0.944750\pi\)
\(678\) 79.4195 + 99.5290i 0.117138 + 0.146798i
\(679\) −664.231 −0.978249
\(680\) 432.152i 0.635518i
\(681\) −398.533 + 318.011i −0.585217 + 0.466976i
\(682\) 1135.64 1.66516
\(683\) 143.102i 0.209519i 0.994498 + 0.104760i \(0.0334073\pi\)
−0.994498 + 0.104760i \(0.966593\pi\)
\(684\) 309.978 1361.78i 0.453184 1.99091i
\(685\) 253.243 0.369698
\(686\) 972.298i 1.41734i
\(687\) 210.272 + 263.514i 0.306072 + 0.383572i
\(688\) −403.196 −0.586041
\(689\) 491.018i 0.712654i
\(690\) 156.416 124.813i 0.226690 0.180888i
\(691\) 73.3360 0.106130 0.0530651 0.998591i \(-0.483101\pi\)
0.0530651 + 0.998591i \(0.483101\pi\)
\(692\) 867.660i 1.25384i
\(693\) 904.224 + 205.825i 1.30480 + 0.297006i
\(694\) 883.734 1.27339
\(695\) 21.8486i 0.0314368i
\(696\) 396.784 + 497.253i 0.570092 + 0.714443i
\(697\) 203.648 0.292178
\(698\) 455.315i 0.652314i
\(699\) −803.220 + 640.932i −1.14910 + 0.916927i
\(700\) −3204.79 −4.57827
\(701\) 888.614i 1.26764i 0.773482 + 0.633819i \(0.218513\pi\)
−0.773482 + 0.633819i \(0.781487\pi\)
\(702\) 260.689 + 540.111i 0.371353 + 0.769389i
\(703\) −1183.15 −1.68300
\(704\) 925.339i 1.31440i
\(705\) −778.233 975.286i −1.10388 1.38339i
\(706\) −1154.96 −1.63592
\(707\) 1224.52i 1.73199i
\(708\) 100.756 80.3982i 0.142310 0.113557i
\(709\) −23.4690 −0.0331015 −0.0165508 0.999863i \(-0.505269\pi\)
−0.0165508 + 0.999863i \(0.505269\pi\)
\(710\) 1137.62i 1.60228i
\(711\) −55.7043 + 244.718i −0.0783464 + 0.344189i
\(712\) 169.269 0.237737
\(713\) 98.6253i 0.138324i
\(714\) −652.975 818.312i −0.914530 1.14610i
\(715\) −574.125 −0.802972
\(716\) 1135.58i 1.58600i
\(717\) 143.790 114.738i 0.200544 0.160025i
\(718\) −230.894 −0.321579
\(719\) 25.0099i 0.0347842i −0.999849 0.0173921i \(-0.994464\pi\)
0.999849 0.0173921i \(-0.00553636\pi\)
\(720\) 542.135 + 123.404i 0.752966 + 0.171395i
\(721\) −953.496 −1.32246
\(722\) 1265.51i 1.75278i
\(723\) −200.337 251.064i −0.277092 0.347253i
\(724\) −1201.26 −1.65920
\(725\) 2192.61i 3.02429i
\(726\) 266.678 212.797i 0.367326 0.293109i
\(727\) 1393.92 1.91736 0.958680 0.284488i \(-0.0918236\pi\)
0.958680 + 0.284488i \(0.0918236\pi\)
\(728\) 397.347i 0.545806i
\(729\) 453.520 570.754i 0.622113 0.782927i
\(730\) 1229.40 1.68411
\(731\) 571.317i 0.781555i
\(732\) 328.772 + 412.019i 0.449142 + 0.562868i
\(733\) 235.168 0.320829 0.160415 0.987050i \(-0.448717\pi\)
0.160415 + 0.987050i \(0.448717\pi\)
\(734\) 1981.52i 2.69962i
\(735\) −1573.92 + 1255.92i −2.14139 + 1.70873i
\(736\) 102.955 0.139884
\(737\) 158.131i 0.214560i
\(738\) 125.520 551.430i 0.170081 0.747195i
\(739\) 892.737 1.20803 0.604017 0.796971i \(-0.293566\pi\)
0.604017 + 0.796971i \(0.293566\pi\)
\(740\) 2080.48i 2.81145i
\(741\) 372.248 + 466.504i 0.502359 + 0.629560i
\(742\) −2380.28 −3.20792
\(743\) 282.415i 0.380101i 0.981774 + 0.190050i \(0.0608651\pi\)
−0.981774 + 0.190050i \(0.939135\pi\)
\(744\) −462.324 + 368.913i −0.621403 + 0.495851i
\(745\) 1161.58 1.55917
\(746\) 844.553i 1.13211i
\(747\) −0.892366 0.203126i −0.00119460 0.000271923i
\(748\) 515.514 0.689190
\(749\) 1486.75i 1.98498i
\(750\) −1316.37 1649.68i −1.75516 2.19958i
\(751\) 583.942 0.777552 0.388776 0.921332i \(-0.372898\pi\)
0.388776 + 0.921332i \(0.372898\pi\)
\(752\) 337.878i 0.449306i
\(753\) −192.372 + 153.504i −0.255474 + 0.203856i
\(754\) −954.107 −1.26539
\(755\) 302.418i 0.400554i
\(756\) −1526.62 + 736.836i −2.01934 + 0.974651i
\(757\) 540.866 0.714486 0.357243 0.934011i \(-0.383717\pi\)
0.357243 + 0.934011i \(0.383717\pi\)
\(758\) 1468.12i 1.93683i
\(759\) 42.4227 + 53.1643i 0.0558928 + 0.0700452i
\(760\) −1194.27 −1.57141
\(761\) 657.957i 0.864595i −0.901731 0.432298i \(-0.857703\pi\)
0.901731 0.432298i \(-0.142297\pi\)
\(762\) −394.798 + 315.030i −0.518107 + 0.413425i
\(763\) −480.723 −0.630043
\(764\) 502.242i 0.657385i
\(765\) 174.860 768.190i 0.228576 1.00417i
\(766\) −920.672 −1.20192
\(767\) 55.0838i 0.0718172i
\(768\) −88.5028 110.912i −0.115238 0.144417i
\(769\) 557.505 0.724974 0.362487 0.931989i \(-0.381928\pi\)
0.362487 + 0.931989i \(0.381928\pi\)
\(770\) 2783.15i 3.61448i
\(771\) −1171.43 + 934.750i −1.51937 + 1.21239i
\(772\) −257.504 −0.333554
\(773\) 499.019i 0.645561i −0.946474 0.322781i \(-0.895382\pi\)
0.946474 0.322781i \(-0.104618\pi\)
\(774\) 1546.99 + 352.136i 1.99870 + 0.454956i
\(775\) −2038.60 −2.63045
\(776\) 292.165i 0.376502i
\(777\) 895.689 + 1122.48i 1.15275 + 1.44464i
\(778\) 456.543 0.586816
\(779\) 562.789i 0.722451i
\(780\) 820.309 654.568i 1.05168 0.839190i
\(781\) −386.665 −0.495090
\(782\) 76.7840i 0.0981892i
\(783\) 504.119 + 1044.46i 0.643830 + 1.33392i
\(784\) −545.270 −0.695498
\(785\) 2353.04i 2.99751i
\(786\) 495.760 + 621.290i 0.630738 + 0.790445i