Properties

Label 252.4.x.a.41.8
Level $252$
Weight $4$
Character 252.41
Analytic conductor $14.868$
Analytic rank $0$
Dimension $48$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 252.x (of order \(6\), degree \(2\), minimal)

Newform invariants

Self dual: no
Analytic conductor: \(14.8684813214\)
Analytic rank: \(0\)
Dimension: \(48\)
Relative dimension: \(24\) over \(\Q(\zeta_{6})\)
Twist minimal: yes
Sato-Tate group: $\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label 41.8
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.8

$q$-expansion

\(f(q)\) \(=\) \(q+(-3.66558 - 3.68287i) q^{3} +(8.29874 - 14.3738i) q^{5} +(18.2297 + 3.26749i) q^{7} +(-0.127054 + 26.9997i) q^{9} +O(q^{10})\) \(q+(-3.66558 - 3.68287i) q^{3} +(8.29874 - 14.3738i) q^{5} +(18.2297 + 3.26749i) q^{7} +(-0.127054 + 26.9997i) q^{9} +(46.2764 - 26.7177i) q^{11} +(11.0474 + 6.37824i) q^{13} +(-83.3566 + 22.1253i) q^{15} +96.7463 q^{17} +54.6996i q^{19} +(-54.7888 - 79.1150i) q^{21} +(-55.6727 - 32.1426i) q^{23} +(-75.2381 - 130.316i) q^{25} +(99.9021 - 98.5016i) q^{27} +(-112.711 + 65.0740i) q^{29} +(-190.618 - 110.053i) q^{31} +(-268.027 - 72.4940i) q^{33} +(198.250 - 234.915i) q^{35} +279.735 q^{37} +(-17.0050 - 64.0662i) q^{39} +(185.308 - 320.963i) q^{41} +(-153.876 - 266.520i) q^{43} +(387.035 + 225.890i) q^{45} +(-163.683 - 283.506i) q^{47} +(321.647 + 119.131i) q^{49} +(-354.631 - 356.304i) q^{51} +451.749i q^{53} -886.892i q^{55} +(201.451 - 200.506i) q^{57} +(-258.739 + 448.148i) q^{59} +(-234.511 + 135.395i) q^{61} +(-90.5373 + 491.782i) q^{63} +(183.360 - 105.863i) q^{65} +(-370.881 + 642.385i) q^{67} +(85.6955 + 322.857i) q^{69} +914.198i q^{71} -337.210i q^{73} +(-204.146 + 754.777i) q^{75} +(930.906 - 335.849i) q^{77} +(-498.583 - 863.570i) q^{79} +(-728.968 - 6.86085i) q^{81} +(-17.0271 - 29.4917i) q^{83} +(802.872 - 1390.61i) q^{85} +(652.812 + 176.568i) q^{87} +208.953 q^{89} +(180.551 + 152.371i) q^{91} +(293.413 + 1105.43i) q^{93} +(786.243 + 453.937i) q^{95} +(-1100.94 + 635.630i) q^{97} +(715.489 + 1252.84i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).

\(n\) \(29\) \(73\) \(127\)
\(\chi(n)\) \(e\left(\frac{5}{6}\right)\) \(-1\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −3.66558 3.68287i −0.705441 0.708769i
\(4\) 0 0
\(5\) 8.29874 14.3738i 0.742262 1.28564i −0.209202 0.977873i \(-0.567086\pi\)
0.951463 0.307762i \(-0.0995802\pi\)
\(6\) 0 0
\(7\) 18.2297 + 3.26749i 0.984314 + 0.176428i
\(8\) 0 0
\(9\) −0.127054 + 26.9997i −0.00470571 + 0.999989i
\(10\) 0 0
\(11\) 46.2764 26.7177i 1.26844 0.732334i 0.293748 0.955883i \(-0.405097\pi\)
0.974693 + 0.223548i \(0.0717641\pi\)
\(12\) 0 0
\(13\) 11.0474 + 6.37824i 0.235693 + 0.136077i 0.613196 0.789931i \(-0.289884\pi\)
−0.377503 + 0.926009i \(0.623217\pi\)
\(14\) 0 0
\(15\) −83.3566 + 22.1253i −1.43484 + 0.380848i
\(16\) 0 0
\(17\) 96.7463 1.38026 0.690130 0.723686i \(-0.257553\pi\)
0.690130 + 0.723686i \(0.257553\pi\)
\(18\) 0 0
\(19\) 54.6996i 0.660471i 0.943899 + 0.330235i \(0.107128\pi\)
−0.943899 + 0.330235i \(0.892872\pi\)
\(20\) 0 0
\(21\) −54.7888 79.1150i −0.569329 0.822110i
\(22\) 0 0
\(23\) −55.6727 32.1426i −0.504720 0.291400i 0.225941 0.974141i \(-0.427454\pi\)
−0.730660 + 0.682741i \(0.760788\pi\)
\(24\) 0 0
\(25\) −75.2381 130.316i −0.601905 1.04253i
\(26\) 0 0
\(27\) 99.9021 98.5016i 0.712080 0.702098i
\(28\) 0 0
\(29\) −112.711 + 65.0740i −0.721724 + 0.416688i −0.815387 0.578916i \(-0.803476\pi\)
0.0936628 + 0.995604i \(0.470142\pi\)
\(30\) 0 0
\(31\) −190.618 110.053i −1.10439 0.637618i −0.167017 0.985954i \(-0.553413\pi\)
−0.937370 + 0.348336i \(0.886747\pi\)
\(32\) 0 0
\(33\) −268.027 72.4940i −1.41387 0.382412i
\(34\) 0 0
\(35\) 198.250 234.915i 0.957440 1.13451i
\(36\) 0 0
\(37\) 279.735 1.24292 0.621462 0.783445i \(-0.286539\pi\)
0.621462 + 0.783445i \(0.286539\pi\)
\(38\) 0 0
\(39\) −17.0050 64.0662i −0.0698201 0.263046i
\(40\) 0 0
\(41\) 185.308 320.963i 0.705861 1.22259i −0.260519 0.965469i \(-0.583894\pi\)
0.966380 0.257118i \(-0.0827729\pi\)
\(42\) 0 0
\(43\) −153.876 266.520i −0.545717 0.945209i −0.998561 0.0536194i \(-0.982924\pi\)
0.452845 0.891589i \(-0.350409\pi\)
\(44\) 0 0
\(45\) 387.035 + 225.890i 1.28213 + 0.748303i
\(46\) 0 0
\(47\) −163.683 283.506i −0.507990 0.879865i −0.999957 0.00925130i \(-0.997055\pi\)
0.491967 0.870614i \(-0.336278\pi\)
\(48\) 0 0
\(49\) 321.647 + 119.131i 0.937747 + 0.347320i
\(50\) 0 0
\(51\) −354.631 356.304i −0.973692 0.978285i
\(52\) 0 0
\(53\) 451.749i 1.17080i 0.810744 + 0.585401i \(0.199063\pi\)
−0.810744 + 0.585401i \(0.800937\pi\)
\(54\) 0 0
\(55\) 886.892i 2.17434i
\(56\) 0 0
\(57\) 201.451 200.506i 0.468121 0.465923i
\(58\) 0 0
\(59\) −258.739 + 448.148i −0.570930 + 0.988880i 0.425540 + 0.904939i \(0.360084\pi\)
−0.996471 + 0.0839410i \(0.973249\pi\)
\(60\) 0 0
\(61\) −234.511 + 135.395i −0.492230 + 0.284189i −0.725499 0.688223i \(-0.758391\pi\)
0.233269 + 0.972412i \(0.425058\pi\)
\(62\) 0 0
\(63\) −90.5373 + 491.782i −0.181058 + 0.983472i
\(64\) 0 0
\(65\) 183.360 105.863i 0.349892 0.202010i
\(66\) 0 0
\(67\) −370.881 + 642.385i −0.676274 + 1.17134i 0.299821 + 0.953996i \(0.403073\pi\)
−0.976095 + 0.217345i \(0.930260\pi\)
\(68\) 0 0
\(69\) 85.6955 + 322.857i 0.149515 + 0.563295i
\(70\) 0 0
\(71\) 914.198i 1.52810i 0.645155 + 0.764051i \(0.276793\pi\)
−0.645155 + 0.764051i \(0.723207\pi\)
\(72\) 0 0
\(73\) 337.210i 0.540650i −0.962769 0.270325i \(-0.912869\pi\)
0.962769 0.270325i \(-0.0871311\pi\)
\(74\) 0 0
\(75\) −204.146 + 754.777i −0.314304 + 1.16205i
\(76\) 0 0
\(77\) 930.906 335.849i 1.37775 0.497059i
\(78\) 0 0
\(79\) −498.583 863.570i −0.710062 1.22986i −0.964833 0.262863i \(-0.915333\pi\)
0.254771 0.967001i \(-0.418000\pi\)
\(80\) 0 0
\(81\) −728.968 6.86085i −0.999956 0.00941131i
\(82\) 0 0
\(83\) −17.0271 29.4917i −0.0225176 0.0390016i 0.854547 0.519374i \(-0.173835\pi\)
−0.877065 + 0.480372i \(0.840502\pi\)
\(84\) 0 0
\(85\) 802.872 1390.61i 1.02451 1.77451i
\(86\) 0 0
\(87\) 652.812 + 176.568i 0.804469 + 0.217587i
\(88\) 0 0
\(89\) 208.953 0.248865 0.124433 0.992228i \(-0.460289\pi\)
0.124433 + 0.992228i \(0.460289\pi\)
\(90\) 0 0
\(91\) 180.551 + 152.371i 0.207988 + 0.175526i
\(92\) 0 0
\(93\) 293.413 + 1105.43i 0.327156 + 1.23256i
\(94\) 0 0
\(95\) 786.243 + 453.937i 0.849124 + 0.490242i
\(96\) 0 0
\(97\) −1100.94 + 635.630i −1.15241 + 0.665345i −0.949474 0.313847i \(-0.898382\pi\)
−0.202937 + 0.979192i \(0.565049\pi\)
\(98\) 0 0
\(99\) 715.489 + 1252.84i 0.726357 + 1.27187i
\(100\) 0 0
\(101\) 307.124 + 531.954i 0.302574 + 0.524073i 0.976718 0.214526i \(-0.0688208\pi\)
−0.674144 + 0.738600i \(0.735487\pi\)
\(102\) 0 0
\(103\) −903.410 521.584i −0.864229 0.498963i 0.00119716 0.999999i \(-0.499619\pi\)
−0.865426 + 0.501036i \(0.832952\pi\)
\(104\) 0 0
\(105\) −1591.86 + 130.971i −1.47952 + 0.121729i
\(106\) 0 0
\(107\) 1128.83i 1.01989i 0.860207 + 0.509945i \(0.170334\pi\)
−0.860207 + 0.509945i \(0.829666\pi\)
\(108\) 0 0
\(109\) 1555.72 1.36707 0.683535 0.729918i \(-0.260442\pi\)
0.683535 + 0.729918i \(0.260442\pi\)
\(110\) 0 0
\(111\) −1025.39 1030.23i −0.876809 0.880945i
\(112\) 0 0
\(113\) 223.834 + 129.231i 0.186341 + 0.107584i 0.590269 0.807207i \(-0.299022\pi\)
−0.403927 + 0.914791i \(0.632355\pi\)
\(114\) 0 0
\(115\) −924.026 + 533.487i −0.749268 + 0.432590i
\(116\) 0 0
\(117\) −173.614 + 297.467i −0.137185 + 0.235050i
\(118\) 0 0
\(119\) 1763.66 + 316.117i 1.35861 + 0.243516i
\(120\) 0 0
\(121\) 762.167 1320.11i 0.572628 0.991820i
\(122\) 0 0
\(123\) −1861.33 + 494.050i −1.36447 + 0.362171i
\(124\) 0 0
\(125\) −422.841 −0.302560
\(126\) 0 0
\(127\) −586.759 −0.409972 −0.204986 0.978765i \(-0.565715\pi\)
−0.204986 + 0.978765i \(0.565715\pi\)
\(128\) 0 0
\(129\) −417.516 + 1543.66i −0.284963 + 1.05358i
\(130\) 0 0
\(131\) 1132.43 1961.43i 0.755275 1.30817i −0.189962 0.981791i \(-0.560837\pi\)
0.945237 0.326384i \(-0.105830\pi\)
\(132\) 0 0
\(133\) −178.730 + 997.159i −0.116525 + 0.650110i
\(134\) 0 0
\(135\) −586.785 2253.42i −0.374092 1.43662i
\(136\) 0 0
\(137\) 1654.71 955.347i 1.03191 0.595772i 0.114377 0.993437i \(-0.463513\pi\)
0.917531 + 0.397665i \(0.130179\pi\)
\(138\) 0 0
\(139\) −1469.79 848.585i −0.896879 0.517813i −0.0206927 0.999786i \(-0.506587\pi\)
−0.876186 + 0.481973i \(0.839920\pi\)
\(140\) 0 0
\(141\) −444.126 + 1642.04i −0.265263 + 0.980741i
\(142\) 0 0
\(143\) 681.647 0.398617
\(144\) 0 0
\(145\) 2160.13i 1.23717i
\(146\) 0 0
\(147\) −740.280 1621.27i −0.415355 0.909659i
\(148\) 0 0
\(149\) −140.294 80.9987i −0.0771364 0.0445347i 0.460936 0.887434i \(-0.347514\pi\)
−0.538072 + 0.842899i \(0.680847\pi\)
\(150\) 0 0
\(151\) 1536.40 + 2661.13i 0.828017 + 1.43417i 0.899591 + 0.436732i \(0.143864\pi\)
−0.0715744 + 0.997435i \(0.522802\pi\)
\(152\) 0 0
\(153\) −12.2920 + 2612.12i −0.00649510 + 1.38024i
\(154\) 0 0
\(155\) −3163.77 + 1826.61i −1.63949 + 0.946558i
\(156\) 0 0
\(157\) 877.841 + 506.822i 0.446238 + 0.257636i 0.706240 0.707972i \(-0.250390\pi\)
−0.260002 + 0.965608i \(0.583723\pi\)
\(158\) 0 0
\(159\) 1663.73 1655.92i 0.829828 0.825932i
\(160\) 0 0
\(161\) −909.873 767.862i −0.445391 0.375876i
\(162\) 0 0
\(163\) 1297.23 0.623356 0.311678 0.950188i \(-0.399109\pi\)
0.311678 + 0.950188i \(0.399109\pi\)
\(164\) 0 0
\(165\) −3266.31 + 3250.97i −1.54110 + 1.53387i
\(166\) 0 0
\(167\) 716.233 1240.55i 0.331879 0.574831i −0.651001 0.759077i \(-0.725651\pi\)
0.982880 + 0.184246i \(0.0589842\pi\)
\(168\) 0 0
\(169\) −1017.14 1761.73i −0.462966 0.801880i
\(170\) 0 0
\(171\) −1476.87 6.94981i −0.660463 0.00310798i
\(172\) 0 0
\(173\) 987.659 + 1710.68i 0.434048 + 0.751793i 0.997217 0.0745483i \(-0.0237515\pi\)
−0.563169 + 0.826341i \(0.690418\pi\)
\(174\) 0 0
\(175\) −945.765 2621.47i −0.408532 1.13237i
\(176\) 0 0
\(177\) 2598.90 689.823i 1.10365 0.292939i
\(178\) 0 0
\(179\) 2310.07i 0.964595i 0.876007 + 0.482298i \(0.160198\pi\)
−0.876007 + 0.482298i \(0.839802\pi\)
\(180\) 0 0
\(181\) 423.545i 0.173933i −0.996211 0.0869665i \(-0.972283\pi\)
0.996211 0.0869665i \(-0.0277173\pi\)
\(182\) 0 0
\(183\) 1358.26 + 367.372i 0.548663 + 0.148398i
\(184\) 0 0
\(185\) 2321.45 4020.87i 0.922574 1.59795i
\(186\) 0 0
\(187\) 4477.06 2584.83i 1.75078 1.01081i
\(188\) 0 0
\(189\) 2143.04 1469.23i 0.824780 0.565454i
\(190\) 0 0
\(191\) 2030.43 1172.27i 0.769197 0.444096i −0.0633911 0.997989i \(-0.520192\pi\)
0.832588 + 0.553893i \(0.186858\pi\)
\(192\) 0 0
\(193\) −2025.36 + 3508.02i −0.755380 + 1.30836i 0.189805 + 0.981822i \(0.439214\pi\)
−0.945185 + 0.326535i \(0.894119\pi\)
\(194\) 0 0
\(195\) −1062.00 287.241i −0.390006 0.105486i
\(196\) 0 0
\(197\) 3659.21i 1.32339i 0.749773 + 0.661695i \(0.230163\pi\)
−0.749773 + 0.661695i \(0.769837\pi\)
\(198\) 0 0
\(199\) 557.050i 0.198433i −0.995066 0.0992166i \(-0.968366\pi\)
0.995066 0.0992166i \(-0.0316337\pi\)
\(200\) 0 0
\(201\) 3725.32 988.807i 1.30728 0.346990i
\(202\) 0 0
\(203\) −2267.33 + 817.999i −0.783918 + 0.282819i
\(204\) 0 0
\(205\) −3075.65 5327.18i −1.04787 1.81496i
\(206\) 0 0
\(207\) 874.915 1499.06i 0.293772 0.503343i
\(208\) 0 0
\(209\) 1461.45 + 2531.30i 0.483685 + 0.837768i
\(210\) 0 0
\(211\) 2195.03 3801.91i 0.716173 1.24045i −0.246333 0.969185i \(-0.579226\pi\)
0.962505 0.271262i \(-0.0874410\pi\)
\(212\) 0 0
\(213\) 3366.87 3351.06i 1.08307 1.07799i
\(214\) 0 0
\(215\) −5107.89 −1.62026
\(216\) 0 0
\(217\) −3115.32 2629.08i −0.974569 0.822460i
\(218\) 0 0
\(219\) −1241.90 + 1236.07i −0.383196 + 0.381397i
\(220\) 0 0
\(221\) 1068.80 + 617.071i 0.325318 + 0.187822i
\(222\) 0 0
\(223\) 2171.75 1253.86i 0.652157 0.376523i −0.137125 0.990554i \(-0.543786\pi\)
0.789282 + 0.614030i \(0.210453\pi\)
\(224\) 0 0
\(225\) 3528.06 2014.85i 1.04535 0.596992i
\(226\) 0 0
\(227\) −1344.84 2329.34i −0.393218 0.681073i 0.599654 0.800259i \(-0.295305\pi\)
−0.992872 + 0.119186i \(0.961971\pi\)
\(228\) 0 0
\(229\) −3562.03 2056.54i −1.02788 0.593449i −0.111507 0.993764i \(-0.535568\pi\)
−0.916378 + 0.400314i \(0.868901\pi\)
\(230\) 0 0
\(231\) −4649.20 2197.32i −1.32422 0.625858i
\(232\) 0 0
\(233\) 2621.07i 0.736960i −0.929636 0.368480i \(-0.879878\pi\)
0.929636 0.368480i \(-0.120122\pi\)
\(234\) 0 0
\(235\) −5433.43 −1.50825
\(236\) 0 0
\(237\) −1352.82 + 5001.70i −0.370782 + 1.37087i
\(238\) 0 0
\(239\) −4446.09 2566.95i −1.20332 0.694738i −0.242029 0.970269i \(-0.577813\pi\)
−0.961292 + 0.275531i \(0.911146\pi\)
\(240\) 0 0
\(241\) −568.896 + 328.452i −0.152057 + 0.0877903i −0.574098 0.818786i \(-0.694647\pi\)
0.422041 + 0.906577i \(0.361314\pi\)
\(242\) 0 0
\(243\) 2646.82 + 2709.84i 0.698739 + 0.715376i
\(244\) 0 0
\(245\) 4381.63 3634.67i 1.14258 0.947797i
\(246\) 0 0
\(247\) −348.887 + 604.290i −0.0898752 + 0.155668i
\(248\) 0 0
\(249\) −46.2001 + 170.813i −0.0117583 + 0.0434731i
\(250\) 0 0
\(251\) 1807.27 0.454479 0.227239 0.973839i \(-0.427030\pi\)
0.227239 + 0.973839i \(0.427030\pi\)
\(252\) 0 0
\(253\) −3435.10 −0.853609
\(254\) 0 0
\(255\) −8064.44 + 2140.54i −1.98045 + 0.525669i
\(256\) 0 0
\(257\) −1044.71 + 1809.50i −0.253570 + 0.439196i −0.964506 0.264061i \(-0.914938\pi\)
0.710936 + 0.703256i \(0.248271\pi\)
\(258\) 0 0
\(259\) 5099.50 + 914.030i 1.22343 + 0.219286i
\(260\) 0 0
\(261\) −1742.66 3051.44i −0.413287 0.723677i
\(262\) 0 0
\(263\) −4219.35 + 2436.05i −0.989265 + 0.571152i −0.905054 0.425296i \(-0.860170\pi\)
−0.0842101 + 0.996448i \(0.526837\pi\)
\(264\) 0 0
\(265\) 6493.37 + 3748.95i 1.50522 + 0.869042i
\(266\) 0 0
\(267\) −765.935 769.548i −0.175560 0.176388i
\(268\) 0 0
\(269\) −4640.31 −1.05176 −0.525882 0.850557i \(-0.676265\pi\)
−0.525882 + 0.850557i \(0.676265\pi\)
\(270\) 0 0
\(271\) 5685.82i 1.27450i 0.770658 + 0.637249i \(0.219928\pi\)
−0.770658 + 0.637249i \(0.780072\pi\)
\(272\) 0 0
\(273\) −100.662 1223.47i −0.0223163 0.271238i
\(274\) 0 0
\(275\) −6963.49 4020.37i −1.52696 0.881591i
\(276\) 0 0
\(277\) 2507.59 + 4343.28i 0.543923 + 0.942103i 0.998674 + 0.0514839i \(0.0163951\pi\)
−0.454751 + 0.890619i \(0.650272\pi\)
\(278\) 0 0
\(279\) 2995.62 5132.64i 0.642808 1.10137i
\(280\) 0 0
\(281\) 4421.84 2552.95i 0.938736 0.541979i 0.0491721 0.998790i \(-0.484342\pi\)
0.889564 + 0.456811i \(0.151008\pi\)
\(282\) 0 0
\(283\) 5499.39 + 3175.07i 1.15514 + 0.666921i 0.950135 0.311840i \(-0.100945\pi\)
0.205006 + 0.978761i \(0.434279\pi\)
\(284\) 0 0
\(285\) −1210.24 4559.57i −0.251539 0.947670i
\(286\) 0 0
\(287\) 4426.87 5245.59i 0.910486 1.07888i
\(288\) 0 0
\(289\) 4446.84 0.905117
\(290\) 0 0
\(291\) 6376.54 + 1724.68i 1.28453 + 0.347431i
\(292\) 0 0
\(293\) 762.297 1320.34i 0.151993 0.263259i −0.779967 0.625820i \(-0.784764\pi\)
0.931960 + 0.362561i \(0.118098\pi\)
\(294\) 0 0
\(295\) 4294.41 + 7438.13i 0.847560 + 1.46802i
\(296\) 0 0
\(297\) 1991.37 7227.45i 0.389061 1.41205i
\(298\) 0 0
\(299\) −410.027 710.188i −0.0793059 0.137362i
\(300\) 0 0
\(301\) −1934.26 5361.38i −0.370395 1.02666i
\(302\) 0 0
\(303\) 833.330 3081.02i 0.157999 0.584158i
\(304\) 0 0
\(305\) 4494.43i 0.843771i
\(306\) 0 0
\(307\) 633.080i 0.117693i −0.998267 0.0588466i \(-0.981258\pi\)
0.998267 0.0588466i \(-0.0187423\pi\)
\(308\) 0 0
\(309\) 1390.59 + 5239.05i 0.256013 + 0.964527i
\(310\) 0 0
\(311\) −2222.36 + 3849.24i −0.405204 + 0.701833i −0.994345 0.106197i \(-0.966133\pi\)
0.589142 + 0.808030i \(0.299466\pi\)
\(312\) 0 0
\(313\) −8892.94 + 5134.34i −1.60594 + 0.927189i −0.615673 + 0.788002i \(0.711116\pi\)
−0.990266 + 0.139187i \(0.955551\pi\)
\(314\) 0 0
\(315\) 6317.46 + 5382.54i 1.12999 + 0.962768i
\(316\) 0 0
\(317\) 1625.88 938.700i 0.288070 0.166318i −0.349001 0.937122i \(-0.613479\pi\)
0.637071 + 0.770805i \(0.280146\pi\)
\(318\) 0 0
\(319\) −3477.25 + 6022.78i −0.610309 + 1.05709i
\(320\) 0 0
\(321\) 4157.34 4137.82i 0.722866 0.719472i
\(322\) 0 0
\(323\) 5291.98i 0.911621i
\(324\) 0 0
\(325\) 1919.55i 0.327623i
\(326\) 0 0
\(327\) −5702.60 5729.50i −0.964387 0.968936i
\(328\) 0 0
\(329\) −2057.54 5703.08i −0.344789 0.955687i
\(330\) 0 0
\(331\) 1549.03 + 2683.00i 0.257228 + 0.445531i 0.965498 0.260410i \(-0.0838576\pi\)
−0.708271 + 0.705941i \(0.750524\pi\)
\(332\) 0 0
\(333\) −35.5415 + 7552.76i −0.00584883 + 1.24291i
\(334\) 0 0
\(335\) 6155.69 + 10662.0i 1.00394 + 1.73888i
\(336\) 0 0
\(337\) −5445.10 + 9431.18i −0.880158 + 1.52448i −0.0289934 + 0.999580i \(0.509230\pi\)
−0.851165 + 0.524899i \(0.824103\pi\)
\(338\) 0 0
\(339\) −344.542 1298.06i −0.0552005 0.207967i
\(340\) 0 0
\(341\) −11761.5 −1.86780
\(342\) 0 0
\(343\) 5474.29 + 3222.70i 0.861760 + 0.507317i
\(344\) 0 0
\(345\) 5351.85 + 1447.53i 0.835171 + 0.225891i
\(346\) 0 0
\(347\) −3226.80 1862.99i −0.499203 0.288215i 0.229181 0.973384i \(-0.426395\pi\)
−0.728385 + 0.685169i \(0.759729\pi\)
\(348\) 0 0
\(349\) −529.889 + 305.931i −0.0812730 + 0.0469230i −0.540086 0.841610i \(-0.681608\pi\)
0.458813 + 0.888533i \(0.348275\pi\)
\(350\) 0 0
\(351\) 1731.93 450.991i 0.263372 0.0685815i
\(352\) 0 0
\(353\) 2592.39 + 4490.16i 0.390876 + 0.677017i 0.992565 0.121713i \(-0.0388388\pi\)
−0.601689 + 0.798730i \(0.705505\pi\)
\(354\) 0 0
\(355\) 13140.5 + 7586.69i 1.96458 + 1.13425i
\(356\) 0 0
\(357\) −5300.62 7654.08i −0.785822 1.13473i
\(358\) 0 0
\(359\) 10228.9i 1.50379i −0.659280 0.751897i \(-0.729139\pi\)
0.659280 0.751897i \(-0.270861\pi\)
\(360\) 0 0
\(361\) 3866.96 0.563778
\(362\) 0 0
\(363\) −7655.59 + 2032.01i −1.10693 + 0.293810i
\(364\) 0 0
\(365\) −4847.00 2798.42i −0.695078 0.401304i
\(366\) 0 0
\(367\) −8636.46 + 4986.26i −1.22839 + 0.709212i −0.966693 0.255938i \(-0.917616\pi\)
−0.261698 + 0.965150i \(0.584282\pi\)
\(368\) 0 0
\(369\) 8642.37 + 5044.05i 1.21925 + 0.711606i
\(370\) 0 0
\(371\) −1476.08 + 8235.27i −0.206562 + 1.15244i
\(372\) 0 0
\(373\) −4230.45 + 7327.36i −0.587251 + 1.01715i 0.407340 + 0.913277i \(0.366457\pi\)
−0.994591 + 0.103872i \(0.966877\pi\)
\(374\) 0 0
\(375\) 1549.96 + 1557.27i 0.213439 + 0.214445i
\(376\) 0 0
\(377\) −1660.23 −0.226807
\(378\) 0 0
\(379\) −1.71044 −0.000231819 −0.000115910 1.00000i \(-0.500037\pi\)
−0.000115910 1.00000i \(0.500037\pi\)
\(380\) 0 0
\(381\) 2150.81 + 2160.96i 0.289211 + 0.290575i
\(382\) 0 0
\(383\) −1278.28 + 2214.04i −0.170540 + 0.295384i −0.938609 0.344983i \(-0.887885\pi\)
0.768069 + 0.640367i \(0.221218\pi\)
\(384\) 0 0
\(385\) 2897.91 16167.8i 0.383613 2.14023i
\(386\) 0 0
\(387\) 7215.52 4120.73i 0.947766 0.541263i
\(388\) 0 0
\(389\) 2061.39 1190.14i 0.268680 0.155123i −0.359607 0.933104i \(-0.617089\pi\)
0.628288 + 0.777981i \(0.283756\pi\)
\(390\) 0 0
\(391\) −5386.12 3109.68i −0.696644 0.402208i
\(392\) 0 0
\(393\) −11374.7 + 3019.18i −1.46000 + 0.387525i
\(394\) 0 0
\(395\) −16550.4 −2.10821
\(396\) 0 0
\(397\) 12885.5i 1.62898i 0.580177 + 0.814491i \(0.302983\pi\)
−0.580177 + 0.814491i \(0.697017\pi\)
\(398\) 0 0
\(399\) 4327.56 2996.93i 0.542979 0.376025i
\(400\) 0 0
\(401\) 6388.40 + 3688.35i 0.795565 + 0.459320i 0.841918 0.539605i \(-0.181427\pi\)
−0.0463529 + 0.998925i \(0.514760\pi\)
\(402\) 0 0
\(403\) −1403.89 2431.61i −0.173531 0.300564i
\(404\) 0 0
\(405\) −6148.13 + 10421.1i −0.754328 + 1.27859i
\(406\) 0 0
\(407\) 12945.1 7473.87i 1.57657 0.910236i
\(408\) 0 0
\(409\) 5869.30 + 3388.64i 0.709580 + 0.409676i 0.810906 0.585177i \(-0.198975\pi\)
−0.101325 + 0.994853i \(0.532308\pi\)
\(410\) 0 0
\(411\) −9583.88 2592.18i −1.15021 0.311101i
\(412\) 0 0
\(413\) −6181.06 + 7324.20i −0.736440 + 0.872641i
\(414\) 0 0
\(415\) −565.212 −0.0668558
\(416\) 0 0
\(417\) 2262.41 + 8523.61i 0.265686 + 1.00097i
\(418\) 0 0
\(419\) −2707.65 + 4689.79i −0.315698 + 0.546804i −0.979586 0.201028i \(-0.935572\pi\)
0.663888 + 0.747832i \(0.268905\pi\)
\(420\) 0 0
\(421\) −409.136 708.644i −0.0473636 0.0820361i 0.841372 0.540457i \(-0.181749\pi\)
−0.888735 + 0.458421i \(0.848415\pi\)
\(422\) 0 0
\(423\) 7675.39 4383.36i 0.882246 0.503844i
\(424\) 0 0
\(425\) −7279.01 12607.6i −0.830785 1.43896i
\(426\) 0 0
\(427\) −4717.47 + 1701.95i −0.534647 + 0.192888i
\(428\) 0 0
\(429\) −2498.63 2510.42i −0.281201 0.282527i
\(430\) 0 0
\(431\) 10300.0i 1.15113i 0.817757 + 0.575564i \(0.195217\pi\)
−0.817757 + 0.575564i \(0.804783\pi\)
\(432\) 0 0
\(433\) 16119.3i 1.78902i −0.447047 0.894511i \(-0.647524\pi\)
0.447047 0.894511i \(-0.352476\pi\)
\(434\) 0 0
\(435\) 7955.47 7918.12i 0.876864 0.872747i
\(436\) 0 0
\(437\) 1758.19 3045.27i 0.192461 0.333353i
\(438\) 0 0
\(439\) 8192.95 4730.20i 0.890725 0.514260i 0.0165456 0.999863i \(-0.494733\pi\)
0.874180 + 0.485603i \(0.161400\pi\)
\(440\) 0 0
\(441\) −3257.36 + 8669.24i −0.351729 + 0.936102i
\(442\) 0 0
\(443\) 3327.36 1921.05i 0.356857 0.206032i −0.310844 0.950461i \(-0.600612\pi\)
0.667701 + 0.744429i \(0.267278\pi\)
\(444\) 0 0
\(445\) 1734.05 3003.46i 0.184723 0.319950i
\(446\) 0 0
\(447\) 215.951 + 813.591i 0.0228504 + 0.0860885i
\(448\) 0 0
\(449\) 15663.0i 1.64628i −0.567837 0.823141i \(-0.692220\pi\)
0.567837 0.823141i \(-0.307780\pi\)
\(450\) 0 0
\(451\) 19804.0i 2.06770i
\(452\) 0 0
\(453\) 4168.78 15412.9i 0.432376 1.59859i
\(454\) 0 0
\(455\) 3688.50 1330.73i 0.380043 0.137111i
\(456\) 0 0
\(457\) −2476.59 4289.58i −0.253501 0.439077i 0.710986 0.703206i \(-0.248249\pi\)
−0.964487 + 0.264129i \(0.914915\pi\)
\(458\) 0 0
\(459\) 9665.15 9529.66i 0.982856 0.969078i
\(460\) 0 0
\(461\) −1755.21 3040.12i −0.177329 0.307142i 0.763636 0.645647i \(-0.223412\pi\)
−0.940965 + 0.338505i \(0.890079\pi\)
\(462\) 0 0
\(463\) −7086.75 + 12274.6i −0.711338 + 1.23207i 0.253017 + 0.967462i \(0.418577\pi\)
−0.964355 + 0.264611i \(0.914756\pi\)
\(464\) 0 0
\(465\) 18324.2 + 4956.20i 1.82745 + 0.494276i
\(466\) 0 0
\(467\) −1922.47 −0.190495 −0.0952474 0.995454i \(-0.530364\pi\)
−0.0952474 + 0.995454i \(0.530364\pi\)
\(468\) 0 0
\(469\) −8860.05 + 10498.7i −0.872323 + 1.03365i
\(470\) 0 0
\(471\) −1351.24 5090.77i −0.132191 0.498026i
\(472\) 0 0
\(473\) −14241.6 8222.39i −1.38442 0.799294i
\(474\) 0 0
\(475\) 7128.24 4115.49i 0.688560 0.397541i
\(476\) 0 0
\(477\) −12197.1 57.3966i −1.17079 0.00550945i
\(478\) 0 0
\(479\) 8556.48 + 14820.3i 0.816192 + 1.41369i 0.908469 + 0.417952i \(0.137252\pi\)
−0.0922775 + 0.995733i \(0.529415\pi\)
\(480\) 0 0
\(481\) 3090.36 + 1784.22i 0.292948 + 0.169134i
\(482\) 0 0
\(483\) 507.277 + 6165.60i 0.0477887 + 0.580838i
\(484\) 0 0
\(485\) 21099.7i 1.97544i
\(486\) 0 0
\(487\) 3067.21 0.285397 0.142699 0.989766i \(-0.454422\pi\)
0.142699 + 0.989766i \(0.454422\pi\)
\(488\) 0 0
\(489\) −4755.11 4777.54i −0.439741 0.441815i
\(490\) 0 0
\(491\) 7470.97 + 4313.37i 0.686681 + 0.396455i 0.802367 0.596831i \(-0.203574\pi\)
−0.115687 + 0.993286i \(0.536907\pi\)
\(492\) 0 0
\(493\) −10904.4 + 6295.67i −0.996167 + 0.575137i
\(494\) 0 0
\(495\) 23945.8 + 112.683i 2.17431 + 0.0102318i
\(496\) 0 0
\(497\) −2987.13 + 16665.6i −0.269600 + 1.50413i
\(498\) 0 0
\(499\) 6142.19 10638.6i 0.551026 0.954406i −0.447174 0.894447i \(-0.647570\pi\)
0.998201 0.0599589i \(-0.0190970\pi\)
\(500\) 0 0
\(501\) −7194.20 + 1909.55i −0.641543 + 0.170284i
\(502\) 0 0
\(503\) −3977.87 −0.352613 −0.176307 0.984335i \(-0.556415\pi\)
−0.176307 + 0.984335i \(0.556415\pi\)
\(504\) 0 0
\(505\) 10195.0 0.898356
\(506\) 0 0
\(507\) −2759.83 + 10203.7i −0.241752 + 0.893815i
\(508\) 0 0
\(509\) 8362.32 14484.0i 0.728199 1.26128i −0.229444 0.973322i \(-0.573691\pi\)
0.957644 0.287956i \(-0.0929758\pi\)
\(510\) 0 0
\(511\) 1101.83 6147.25i 0.0953856 0.532169i
\(512\) 0 0
\(513\) 5388.00 + 5464.60i 0.463715 + 0.470308i
\(514\) 0 0
\(515\) −14994.3 + 8656.97i −1.28297 + 0.740722i
\(516\) 0 0
\(517\) −15149.3 8746.43i −1.28871 0.744038i
\(518\) 0 0
\(519\) 2679.85 9908.03i 0.226652 0.837985i
\(520\) 0 0
\(521\) 9088.77 0.764273 0.382137 0.924106i \(-0.375188\pi\)
0.382137 + 0.924106i \(0.375188\pi\)
\(522\) 0 0
\(523\) 13218.7i 1.10519i 0.833450 + 0.552596i \(0.186363\pi\)
−0.833450 + 0.552596i \(0.813637\pi\)
\(524\) 0 0
\(525\) −6187.76 + 13092.3i −0.514392 + 1.08837i
\(526\) 0 0
\(527\) −18441.6 10647.2i −1.52434 0.880078i
\(528\) 0 0
\(529\) −4017.20 6958.00i −0.330172 0.571875i
\(530\) 0 0
\(531\) −12067.0 7042.80i −0.986183 0.575577i
\(532\) 0 0
\(533\) 4094.36 2363.88i 0.332733 0.192103i
\(534\) 0 0
\(535\) 16225.6 + 9367.87i 1.31121 + 0.757025i
\(536\) 0 0
\(537\) 8507.68 8467.74i 0.683675 0.680465i
\(538\) 0 0
\(539\) 18067.6 3080.72i 1.44383 0.246189i
\(540\) 0 0
\(541\) −20011.9 −1.59035 −0.795174 0.606382i \(-0.792620\pi\)
−0.795174 + 0.606382i \(0.792620\pi\)
\(542\) 0 0
\(543\) −1559.86 + 1552.54i −0.123278 + 0.122699i
\(544\) 0 0
\(545\) 12910.5 22361.6i 1.01472 1.75755i
\(546\) 0 0
\(547\) 8725.59 + 15113.2i 0.682046 + 1.18134i 0.974355 + 0.225015i \(0.0722430\pi\)
−0.292309 + 0.956324i \(0.594424\pi\)
\(548\) 0 0
\(549\) −3625.82 6348.92i −0.281870 0.493562i
\(550\) 0 0
\(551\) −3559.52 6165.27i −0.275210 0.476678i
\(552\) 0 0
\(553\) −6267.33 17371.8i −0.481942 1.33585i
\(554\) 0 0
\(555\) −23317.8 + 6189.21i −1.78340 + 0.473365i
\(556\) 0 0
\(557\) 15169.7i 1.15397i −0.816754 0.576986i \(-0.804229\pi\)
0.816754 0.576986i \(-0.195771\pi\)
\(558\) 0 0
\(559\) 3925.82i 0.297039i
\(560\) 0 0
\(561\) −25930.6 7013.53i −1.95150 0.527828i
\(562\) 0 0
\(563\) 3488.62 6042.47i 0.261151 0.452326i −0.705397 0.708812i \(-0.749231\pi\)
0.966548 + 0.256486i \(0.0825647\pi\)
\(564\) 0 0
\(565\) 3715.08 2144.90i 0.276628 0.159711i
\(566\) 0 0
\(567\) −13266.5 2506.96i −0.982610 0.185684i
\(568\) 0 0
\(569\) 17354.8 10019.8i 1.27865 0.738227i 0.302047 0.953293i \(-0.402330\pi\)
0.976600 + 0.215066i \(0.0689967\pi\)
\(570\) 0 0
\(571\) 8327.71 14424.0i 0.610339 1.05714i −0.380844 0.924639i \(-0.624366\pi\)
0.991183 0.132500i \(-0.0423003\pi\)
\(572\) 0 0
\(573\) −11760.0 3180.76i −0.857385 0.231899i
\(574\) 0 0
\(575\) 9673.40i 0.701580i
\(576\) 0 0
\(577\) 8678.08i 0.626123i 0.949733 + 0.313062i \(0.101355\pi\)
−0.949733 + 0.313062i \(0.898645\pi\)
\(578\) 0 0
\(579\) 20343.7 5399.81i 1.46020 0.387579i
\(580\) 0 0
\(581\) −214.035 593.262i −0.0152834 0.0423626i
\(582\) 0 0
\(583\) 12069.7 + 20905.3i 0.857419 + 1.48509i
\(584\) 0 0
\(585\) 2834.97 + 4964.11i 0.200361 + 0.350839i
\(586\) 0 0
\(587\) 5941.85 + 10291.6i 0.417796 + 0.723645i 0.995718 0.0924479i \(-0.0294692\pi\)
−0.577921 + 0.816093i \(0.696136\pi\)
\(588\) 0 0
\(589\) 6019.87 10426.7i 0.421128 0.729415i
\(590\) 0 0
\(591\) 13476.4 13413.1i 0.937977 0.933574i
\(592\) 0 0
\(593\) −12702.9 −0.879675 −0.439838 0.898077i \(-0.644964\pi\)
−0.439838 + 0.898077i \(0.644964\pi\)
\(594\) 0 0
\(595\) 19180.0 22727.2i 1.32152 1.56592i
\(596\) 0 0
\(597\) −2051.54 + 2041.91i −0.140643 + 0.139983i
\(598\) 0 0
\(599\) 20674.6 + 11936.5i 1.41025 + 0.814209i 0.995412 0.0956853i \(-0.0305042\pi\)
0.414840 + 0.909894i \(0.363838\pi\)
\(600\) 0 0
\(601\) −9016.55 + 5205.71i −0.611968 + 0.353320i −0.773735 0.633509i \(-0.781614\pi\)
0.161767 + 0.986829i \(0.448281\pi\)
\(602\) 0 0
\(603\) −17297.1 10095.3i −1.16815 0.681778i
\(604\) 0 0
\(605\) −12650.1 21910.5i −0.850079 1.47238i
\(606\) 0 0
\(607\) −13446.8 7763.51i −0.899158 0.519129i −0.0222310 0.999753i \(-0.507077\pi\)
−0.876927 + 0.480624i \(0.840410\pi\)
\(608\) 0 0
\(609\) 11323.7 + 5351.84i 0.753461 + 0.356104i
\(610\) 0 0
\(611\) 4176.03i 0.276504i
\(612\) 0 0
\(613\) −9275.88 −0.611173 −0.305587 0.952164i \(-0.598853\pi\)
−0.305587 + 0.952164i \(0.598853\pi\)
\(614\) 0 0
\(615\) −8345.27 + 30854.4i −0.547177 + 2.02304i
\(616\) 0 0
\(617\) 2687.23 + 1551.47i 0.175338 + 0.101232i 0.585101 0.810961i \(-0.301055\pi\)
−0.409762 + 0.912192i \(0.634388\pi\)
\(618\) 0 0
\(619\) −5859.30 + 3382.87i −0.380460 + 0.219659i −0.678019 0.735045i \(-0.737161\pi\)
0.297558 + 0.954704i \(0.403828\pi\)
\(620\) 0 0
\(621\) −8727.92 + 2272.73i −0.563992 + 0.146862i
\(622\) 0 0
\(623\) 3809.17 + 682.752i 0.244962 + 0.0439067i
\(624\) 0 0
\(625\) 5895.72 10211.7i 0.377326 0.653548i
\(626\) 0 0
\(627\) 3965.39 14661.0i 0.252572 0.933817i
\(628\) 0 0
\(629\) 27063.3 1.71556
\(630\) 0 0
\(631\) −4096.60 −0.258452 −0.129226 0.991615i \(-0.541249\pi\)
−0.129226 + 0.991615i \(0.541249\pi\)
\(632\) 0 0
\(633\) −22048.0 + 5852.18i −1.38441 + 0.367462i
\(634\) 0 0
\(635\) −4869.36 + 8433.98i −0.304307 + 0.527075i
\(636\) 0 0
\(637\) 2793.53 + 3367.63i 0.173758 + 0.209467i
\(638\) 0 0
\(639\) −24683.1 116.153i −1.52809 0.00719081i
\(640\) 0 0
\(641\) 15136.8 8739.26i 0.932713 0.538502i 0.0450444 0.998985i \(-0.485657\pi\)
0.887669 + 0.460483i \(0.152324\pi\)
\(642\) 0 0
\(643\) −8965.15 5176.03i −0.549846 0.317454i 0.199214 0.979956i \(-0.436161\pi\)
−0.749060 + 0.662502i \(0.769495\pi\)
\(644\) 0 0
\(645\) 18723.4 + 18811.7i 1.14300 + 1.14839i
\(646\) 0 0
\(647\) 13536.7 0.822539 0.411269 0.911514i \(-0.365086\pi\)
0.411269 + 0.911514i \(0.365086\pi\)
\(648\) 0 0
\(649\) 27651.6i 1.67245i
\(650\) 0 0
\(651\) 1736.87 + 21110.4i 0.104567 + 1.27094i
\(652\) 0 0
\(653\) 20174.8 + 11647.9i 1.20904 + 0.698039i 0.962549 0.271106i \(-0.0873895\pi\)
0.246490 + 0.969145i \(0.420723\pi\)
\(654\) 0 0
\(655\) −18795.5 32554.8i −1.12122 1.94202i
\(656\) 0 0
\(657\) 9104.57 + 42.8439i 0.540644 + 0.00254414i
\(658\) 0 0
\(659\) −1032.74 + 596.254i −0.0610469 + 0.0352454i −0.530213 0.847865i \(-0.677888\pi\)
0.469166 + 0.883110i \(0.344555\pi\)
\(660\) 0 0
\(661\) 10922.7 + 6306.24i 0.642731 + 0.371081i 0.785666 0.618651i \(-0.212321\pi\)
−0.142935 + 0.989732i \(0.545654\pi\)
\(662\) 0 0
\(663\) −1645.17 6198.17i −0.0963699 0.363072i
\(664\) 0 0
\(665\) 12849.8 + 10844.2i 0.749312 + 0.632361i
\(666\) 0 0
\(667\) 8366.60 0.485691
\(668\) 0 0
\(669\) −12578.5 3402.15i −0.726927 0.196614i
\(670\) 0 0
\(671\) −7234.87 + 12531.2i −0.416243 + 0.720954i
\(672\) 0 0
\(673\) −12824.0 22211.8i −0.734515 1.27222i −0.954936 0.296813i \(-0.904076\pi\)
0.220421 0.975405i \(-0.429257\pi\)
\(674\) 0 0
\(675\) −20352.8 5607.79i −1.16056 0.319769i
\(676\) 0 0
\(677\) −7049.87 12210.7i −0.400220 0.693201i 0.593533 0.804810i \(-0.297733\pi\)
−0.993752 + 0.111609i \(0.964399\pi\)
\(678\) 0 0
\(679\) −22146.8 + 7990.05i −1.25172 + 0.451591i
\(680\) 0 0
\(681\) −3649.01 + 13491.3i −0.205331 + 0.759157i
\(682\) 0 0
\(683\) 6066.68i 0.339875i 0.985455 + 0.169938i \(0.0543567\pi\)
−0.985455 + 0.169938i \(0.945643\pi\)
\(684\) 0 0
\(685\) 31712.7i 1.76888i
\(686\) 0 0
\(687\) 5482.94 + 20656.9i 0.304494 + 1.14718i
\(688\) 0 0
\(689\) −2881.37 + 4990.67i −0.159320 + 0.275950i
\(690\) 0 0
\(691\) −27362.7 + 15797.9i −1.50641 + 0.869725i −0.506435 + 0.862278i \(0.669037\pi\)
−0.999972 + 0.00744663i \(0.997630\pi\)
\(692\) 0 0
\(693\) 8949.54 + 25176.8i 0.490570 + 1.38007i
\(694\) 0 0
\(695\) −24394.8 + 14084.4i −1.33144 + 0.768706i
\(696\) 0 0
\(697\) 17927.9 31052.0i 0.974271 1.68749i
\(698\) 0 0
\(699\) −9653.04 + 9607.73i −0.522334 + 0.519882i
\(700\) 0 0
\(701\) 14828.2i 0.798936i 0.916747 + 0.399468i \(0.130805\pi\)
−0.916747 + 0.399468i \(0.869195\pi\)
\(702\) 0 0
\(703\) 15301.4i 0.820914i
\(704\) 0 0
\(705\) 19916.7 + 20010.6i 1.06398 + 1.06900i
\(706\) 0 0
\(707\) 3860.63 + 10700.9i 0.205366 + 0.569235i
\(708\) 0 0
\(709\) 10513.5 + 18210.0i 0.556903 + 0.964584i 0.997753 + 0.0670034i \(0.0213438\pi\)
−0.440850 + 0.897581i \(0.645323\pi\)
\(710\) 0 0
\(711\) 23379.5 13351.9i 1.23319 0.704267i
\(712\) 0 0
\(713\) 7074.80 + 12253.9i 0.371604 + 0.643636i
\(714\) 0 0
\(715\) 5656.81 9797.88i 0.295878 0.512476i
\(716\) 0 0
\(717\) 6843.75 + 25783.7i 0.356464 + 1.34297i
\(718\) 0 0
\(719\) −36268.4 −1.88120 −0.940601 0.339514i \(-0.889738\pi\)
−0.940601 + 0.339514i \(0.889738\pi\)
\(720\) 0 0
\(721\) −14764.7 12460.2i −0.762642 0.643610i
\(722\) 0 0
\(723\) 3294.98 + 891.202i 0.169491 + 0.0458425i
\(724\) 0 0
\(725\) 16960.4 + 9792.09i 0.868819 + 0.501613i
\(726\) 0 0
\(727\) 20411.1 11784.3i 1.04127 0.601178i 0.121078 0.992643i \(-0.461365\pi\)
0.920193 + 0.391465i \(0.128032\pi\)
\(728\) 0 0
\(729\) 277.859 19681.0i 0.0141167 0.999900i
\(730\) 0 0
\(731\) −14886.9 25784.8i −0.753231 1.30463i
\(732\) 0 0
\(733\) −15961.7 9215.47i −0.804307 0.464367i 0.0406678 0.999173i \(-0.487051\pi\)
−0.844975 + 0.534806i \(0.820385\pi\)
\(734\) 0 0
\(735\) −29447.2 2813.82i −1.47779 0.141210i
\(736\) 0 0
\(737\) 39636.3i 1.98104i
\(738\) 0 0
\(739\) −2029.42 −0.101020 −0.0505098 0.998724i \(-0.516085\pi\)
−0.0505098 + 0.998724i \(0.516085\pi\)
\(740\) 0 0
\(741\) 3504.40 930.168i 0.173734 0.0461142i
\(742\) 0 0
\(743\) 1592.75 + 919.575i 0.0786438 + 0.0454050i 0.538806 0.842430i \(-0.318875\pi\)
−0.460162 + 0.887835i \(0.652209\pi\)
\(744\) 0 0
\(745\) −2328.52 + 1344.37i −0.114511 + 0.0661128i
\(746\) 0 0
\(747\) 798.431 455.978i 0.0391072 0.0223338i
\(748\) 0 0
\(749\) −3688.44 + 20578.3i −0.179937 + 1.00389i
\(750\) 0 0
\(751\) 1091.30 1890.19i 0.0530254 0.0918427i −0.838294 0.545218i \(-0.816447\pi\)
0.891320 + 0.453375i \(0.149780\pi\)
\(752\) 0 0
\(753\) −6624.71 6655.95i −0.320608 0.322120i
\(754\) 0 0
\(755\) 51000.8 2.45842
\(756\) 0 0
\(757\) 14605.5 0.701250 0.350625 0.936516i \(-0.385969\pi\)
0.350625 + 0.936516i \(0.385969\pi\)
\(758\) 0 0
\(759\) 12591.6 + 12651.0i 0.602171 + 0.605011i
\(760\) 0 0
\(761\) −8971.11 + 15538.4i −0.427336 + 0.740167i −0.996635 0.0819631i \(-0.973881\pi\)
0.569300 + 0.822130i \(0.307214\pi\)
\(762\) 0 0
\(763\) 28360.3 + 5083.28i 1.34563 + 0.241189i
\(764\) 0 0
\(765\) 37444.2 + 21854.0i 1.76967 + 1.03285i
\(766\) 0 0
\(767\) −5716.80 + 3300.60i −0.269129 + 0.155381i
\(768\) 0 0
\(769\) 4600.21 + 2655.93i 0.215719 + 0.124545i 0.603966 0.797010i \(-0.293586\pi\)
−0.388248 + 0.921555i \(0.626919\pi\)
\(770\) 0 0
\(771\) 10493.6 2785.31i 0.490167 0.130104i
\(772\) 0 0
\(773\) −21593.6 −1.00475 −0.502373 0.864651i \(-0.667540\pi\)
−0.502373 + 0.864651i \(0.667540\pi\)
\(774\) 0 0
\(775\) 33120.8i 1.53514i
\(776\) 0 0
\(777\) −15326.4 22131.2i −0.707632 1.02182i
\(778\) 0 0
\(779\) 17556.6 + 10136.3i 0.807483 + 0.466200i
\(780\) 0 0
\(781\) 24425.2 + 42305.7i 1.11908 + 1.93831i
\(782\) 0 0
\(783\) −4850.22 + 17603.3i −0.221370 + 0.803436i
\(784\) 0 0
\(785\) 14569.9 8411.96i 0.662451 0.382466i
\(786\) 0 0
\(787\) −30052.6 17350.9i −1.36120 0.785887i −0.371413 0.928468i \(-0.621126\pi\)
−0.989783 + 0.142581i \(0.954460\pi\)
\(788\) 0 0
\(789\) 24438.0 + 6609.81i 1.10268 + 0.298245i
\(790\) 0 0
\(791\) 3658.18 + 3087.22i 0.164437 + 0.138772i
\(792\) 0 0
\(793\) −3454.33 −0.154687
\(794\) 0 0
\(795\) −9995.07 37656.3i −0.445898 1.67991i