Properties

Label 252.4.x.a.41.17
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 41.17
Character \(\chi\) \(=\) 252.41
Dual form 252.4.x.a.209.17

$q$-expansion

\(f(q)\) \(=\) \(q+(3.66558 + 3.68287i) q^{3} +(-8.29874 + 14.3738i) q^{5} +(-6.28515 + 17.4212i) q^{7} +(-0.127054 + 26.9997i) q^{9} +O(q^{10})\) \(q+(3.66558 + 3.68287i) q^{3} +(-8.29874 + 14.3738i) q^{5} +(-6.28515 + 17.4212i) q^{7} +(-0.127054 + 26.9997i) q^{9} +(46.2764 - 26.7177i) q^{11} +(-11.0474 - 6.37824i) q^{13} +(-83.3566 + 22.1253i) q^{15} -96.7463 q^{17} -54.6996i q^{19} +(-87.1986 + 40.7113i) q^{21} +(-55.6727 - 32.1426i) q^{23} +(-75.2381 - 130.316i) q^{25} +(-99.9021 + 98.5016i) q^{27} +(-112.711 + 65.0740i) q^{29} +(190.618 + 110.053i) q^{31} +(268.027 + 72.4940i) q^{33} +(-198.250 - 234.915i) q^{35} +279.735 q^{37} +(-17.0050 - 64.0662i) q^{39} +(-185.308 + 320.963i) q^{41} +(-153.876 - 266.520i) q^{43} +(-387.035 - 225.890i) q^{45} +(163.683 + 283.506i) q^{47} +(-263.994 - 218.989i) q^{49} +(-354.631 - 356.304i) q^{51} +451.749i q^{53} +886.892i q^{55} +(201.451 - 200.506i) q^{57} +(258.739 - 448.148i) q^{59} +(234.511 - 135.395i) q^{61} +(-469.568 - 171.910i) q^{63} +(183.360 - 105.863i) q^{65} +(-370.881 + 642.385i) q^{67} +(-85.6955 - 322.857i) q^{69} +914.198i q^{71} +337.210i q^{73} +(204.146 - 754.777i) q^{75} +(174.599 + 974.112i) q^{77} +(-498.583 - 863.570i) q^{79} +(-728.968 - 6.86085i) q^{81} +(17.0271 + 29.4917i) q^{83} +(802.872 - 1390.61i) q^{85} +(-652.812 - 176.568i) q^{87} -208.953 q^{89} +(180.551 - 152.371i) q^{91} +(293.413 + 1105.43i) q^{93} +(786.243 + 453.937i) q^{95} +(1100.94 - 635.630i) q^{97} +(715.489 + 1252.84i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 48q + 6q^{7} + 60q^{9} + O(q^{10}) \) \( 48q + 6q^{7} + 60q^{9} - 12q^{11} + 192q^{15} - 72q^{21} - 408q^{23} - 600q^{25} - 84q^{29} + 336q^{37} + 36q^{39} + 84q^{43} + 318q^{49} - 1812q^{51} - 852q^{57} - 564q^{63} + 2964q^{65} - 588q^{67} + 2400q^{77} + 204q^{79} + 1980q^{81} - 360q^{85} - 1080q^{91} + 2496q^{93} + 300q^{95} - 4968q^{99} + O(q^{100}) \)

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 \(0.432914\pi\)
−0.951463 + 0.307762i \(0.900420\pi\)
\(6\) 0 0
\(7\) −6.28515 + 17.4212i −0.339366 + 0.940654i
\(8\) 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 0.377503 0.926009i \(-0.376783\pi\)
−0.613196 + 0.789931i \(0.710116\pi\)
\(14\) 0 0
\(15\) −83.3566 + 22.1253i −1.43484 + 0.380848i
\(16\) 0 0
\(17\) −96.7463 −1.38026 −0.690130 0.723686i \(-0.742447\pi\)
−0.690130 + 0.723686i \(0.742447\pi\)
\(18\) 0 0
\(19\) 54.6996i 0.660471i −0.943899 0.330235i \(-0.892872\pi\)
0.943899 0.330235i \(-0.107128\pi\)
\(20\) 0 0
\(21\) −87.1986 + 40.7113i −0.906109 + 0.423044i
\(22\) 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 0.937370 0.348336i \(-0.113253\pi\)
0.167017 + 0.985954i \(0.446587\pi\)
\(32\) 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 \(0.416106\pi\)
−0.966380 + 0.257118i \(0.917227\pi\)
\(42\) 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 \(0.00294482\pi\)
−0.491967 + 0.870614i \(0.663722\pi\)
\(48\) 0 0
\(49\) −263.994 218.989i −0.769661 0.638452i
\(50\) 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 \(-0.639916\pi\)
0.996471 0.0839410i \(-0.0267507\pi\)
\(60\) 0 0
\(61\) 234.511 135.395i 0.492230 0.284189i −0.233269 0.972412i \(-0.574942\pi\)
0.725499 + 0.688223i \(0.241609\pi\)
\(62\) 0 0
\(63\) −469.568 171.910i −0.939047 0.343789i
\(64\) 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 \(0.0871311\pi\)
−0.962769 + 0.270325i \(0.912869\pi\)
\(74\) 0 0
\(75\) 204.146 754.777i 0.314304 1.16205i
\(76\) 0 0
\(77\) 174.599 + 974.112i 0.258408 + 1.44169i
\(78\) 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 0.877065 0.480372i \(-0.159498\pi\)
−0.854547 + 0.519374i \(0.826165\pi\)
\(84\) 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 \(-0.539711\pi\)
−0.124433 + 0.992228i \(0.539711\pi\)
\(90\) 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 0.202937 0.979192i \(-0.434951\pi\)
0.949474 + 0.313847i \(0.101618\pi\)
\(98\) 0 0
\(99\) 715.489 + 1252.84i 0.726357 + 1.27187i
\(100\) 0 0
\(101\) −307.124 531.954i −0.302574 0.524073i 0.674144 0.738600i \(-0.264513\pi\)
−0.976718 + 0.214526i \(0.931179\pi\)
\(102\) 0 0
\(103\) 903.410 + 521.584i 0.864229 + 0.498963i 0.865426 0.501036i \(-0.167048\pi\)
−0.00119716 + 0.999999i \(0.500381\pi\)
\(104\) 0 0
\(105\) 138.461 1591.23i 0.128689 1.47894i
\(106\) 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
\(119\) 608.064 1685.43i 0.468413 1.29835i
\(120\) 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 \(0.439163\pi\)
−0.945237 + 0.326384i \(0.894170\pi\)
\(132\) 0 0
\(133\) 952.930 + 343.795i 0.621275 + 0.224141i
\(134\) 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 0.876186 0.481973i \(-0.160080\pi\)
0.0206927 + 0.999786i \(0.493413\pi\)
\(140\) 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
\(147\) −161.182 1774.98i −0.0904360 0.995902i
\(148\) 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 0.260002 0.965608i \(-0.416277\pi\)
−0.706240 + 0.707972i \(0.749610\pi\)
\(158\) 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 −0.982880 0.184246i \(-0.941016\pi\)
0.651001 + 0.759077i \(0.274349\pi\)
\(168\) 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 0.563169 0.826341i \(-0.309582\pi\)
−0.997217 + 0.0745483i \(0.976249\pi\)
\(174\) 0 0
\(175\) 2743.14 491.679i 1.18493 0.212385i
\(176\) 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 \(0.0277173\pi\)
−0.996211 + 0.0869665i \(0.972283\pi\)
\(182\) 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
\(189\) −1088.11 2359.51i −0.418776 0.908090i
\(190\) 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 \(0.0316337\pi\)
−0.995066 + 0.0992166i \(0.968366\pi\)
\(200\) 0 0
\(201\) −3725.32 + 988.807i −1.30728 + 0.346990i
\(202\) 0 0
\(203\) −425.257 2372.56i −0.147030 0.820303i
\(204\) 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 −0.789282 0.614030i \(-0.789547\pi\)
0.137125 + 0.990554i \(0.456214\pi\)
\(224\) 0 0
\(225\) 3528.06 2014.85i 1.04535 0.596992i
\(226\) 0 0
\(227\) 1344.84 + 2329.34i 0.393218 + 0.681073i 0.992872 0.119186i \(-0.0380286\pi\)
−0.599654 + 0.800259i \(0.704695\pi\)
\(228\) 0 0
\(229\) 3562.03 + 2056.54i 1.02788 + 0.593449i 0.916378 0.400314i \(-0.131099\pi\)
0.111507 + 0.993764i \(0.464432\pi\)
\(230\) 0 0
\(231\) −2947.52 + 4213.71i −0.839535 + 1.20018i
\(232\) 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 −0.422041 0.906577i \(-0.638686\pi\)
0.574098 + 0.818786i \(0.305353\pi\)
\(242\) 0 0
\(243\) −2646.82 2709.84i −0.698739 0.715376i
\(244\) 0 0
\(245\) 5338.53 1977.27i 1.39211 0.515605i
\(246\) 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 \(-0.572970\pi\)
−0.227239 + 0.973839i \(0.572970\pi\)
\(252\) 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 −0.710936 0.703256i \(-0.751729\pi\)
0.964506 + 0.264061i \(0.0850619\pi\)
\(258\) 0 0
\(259\) −1758.18 + 4873.31i −0.421806 + 1.16916i
\(260\) 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 \(-0.323735\pi\)
0.525882 + 0.850557i \(0.323735\pi\)
\(270\) 0 0
\(271\) 5685.82i 1.27450i −0.770658 0.637249i \(-0.780072\pi\)
0.770658 0.637249i \(-0.219928\pi\)
\(272\) 0 0
\(273\) 1222.99 + 106.418i 0.271130 + 0.0235924i
\(274\) 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 −0.205006 0.978761i \(-0.565721\pi\)
−0.950135 + 0.311840i \(0.899055\pi\)
\(284\) 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 −0.931960 0.362561i \(-0.881902\pi\)
0.779967 + 0.625820i \(0.215236\pi\)
\(294\) 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
\(301\) 5610.23 1005.57i 1.07431 0.192559i
\(302\) 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 \(0.0187423\pi\)
−0.998267 + 0.0588466i \(0.981258\pi\)
\(308\) 0 0
\(309\) 1390.59 + 5239.05i 0.256013 + 0.964527i
\(310\) 0 0
\(311\) 2222.36 3849.24i 0.405204 0.701833i −0.589142 0.808030i \(-0.700534\pi\)
0.994345 + 0.106197i \(0.0338673\pi\)
\(312\) 0 0
\(313\) 8892.94 5134.34i 1.60594 0.927189i 0.615673 0.788002i \(-0.288884\pi\)
0.990266 0.139187i \(-0.0444490\pi\)
\(314\) 0 0
\(315\) 6367.83 5322.85i 1.13901 0.952091i
\(316\) 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
\(329\) −5967.78 + 1069.66i −1.00004 + 0.179247i
\(330\) 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 −0.458813 0.888533i \(-0.651725\pi\)
0.540086 + 0.841610i \(0.318392\pi\)
\(350\) 0 0
\(351\) 1731.93 450.991i 0.263372 0.0685815i
\(352\) 0 0
\(353\) −2592.39 4490.16i −0.390876 0.677017i 0.601689 0.798730i \(-0.294495\pi\)
−0.992565 + 0.121713i \(0.961161\pi\)
\(354\) 0 0
\(355\) −13140.5 7586.69i −1.96458 1.13425i
\(356\) 0 0
\(357\) 8436.14 3938.66i 1.25067 0.583911i
\(358\) 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 0.261698 0.965150i \(-0.415718\pi\)
0.966693 + 0.255938i \(0.0823844\pi\)
\(368\) 0 0
\(369\) −8642.37 5044.05i −1.21925 0.711606i
\(370\) 0 0
\(371\) −7870.00 2839.31i −1.10132 0.397331i
\(372\) 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 −0.768069 0.640367i \(-0.778782\pi\)
0.938609 + 0.344983i \(0.112115\pi\)
\(384\) 0 0
\(385\) −15450.7 5574.24i −2.04530 0.737895i
\(386\) 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 \(-0.697017\pi\)
0.580177 0.814491i \(-0.302983\pi\)
\(398\) 0 0
\(399\) 2226.89 + 4769.73i 0.279408 + 0.598458i
\(400\) 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 0.101325 0.994853i \(-0.467692\pi\)
−0.810906 + 0.585177i \(0.801025\pi\)
\(410\) 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 −0.663888 0.747832i \(-0.731095\pi\)
0.979586 + 0.201028i \(0.0644281\pi\)
\(420\) 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
\(427\) 884.802 + 4936.43i 0.100278 + 0.559462i
\(428\) 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 \(0.352476\pi\)
−0.447047 + 0.894511i \(0.647524\pi\)
\(434\) 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 −0.874180 0.485603i \(-0.838600\pi\)
−0.0165456 + 0.999863i \(0.505267\pi\)
\(440\) 0 0
\(441\) 5946.18 7099.93i 0.642067 0.766649i
\(442\) 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
\(455\) 691.810 + 3859.70i 0.0712803 + 0.397683i
\(456\) 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 0.940965 0.338505i \(-0.109921\pi\)
−0.763636 + 0.645647i \(0.776588\pi\)
\(462\) 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 \(-0.469636\pi\)
0.0952474 + 0.995454i \(0.469636\pi\)
\(468\) 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 \(-0.862748\pi\)
0.0922775 0.995733i \(-0.470585\pi\)
\(480\) 0 0
\(481\) −3090.36 1784.22i −0.292948 0.169134i
\(482\) 0 0
\(483\) 6163.14 + 536.285i 0.580606 + 0.0505214i
\(484\) 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
\(497\) −15926.4 5745.87i −1.43742 0.518586i
\(498\) 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 \(-0.443585\pi\)
0.176307 + 0.984335i \(0.443585\pi\)
\(504\) 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 \(0.426309\pi\)
−0.957644 + 0.287956i \(0.907024\pi\)
\(510\) 0 0
\(511\) −5874.59 2119.41i −0.508565 0.183478i
\(512\) 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 \(-0.624812\pi\)
−0.382137 + 0.924106i \(0.624812\pi\)
\(522\) 0 0
\(523\) 13218.7i 1.10519i −0.833450 0.552596i \(-0.813637\pi\)
0.833450 0.552596i \(-0.186363\pi\)
\(524\) 0 0
\(525\) 11866.0 + 8300.35i 0.986428 + 0.690013i
\(526\) 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
\(553\) 18178.1 3258.22i 1.39785 0.250549i
\(554\) 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 −0.966548 0.256486i \(-0.917435\pi\)
0.705397 + 0.708812i \(0.250769\pi\)
\(564\) 0 0
\(565\) −3715.08 + 2144.90i −0.276628 + 0.159711i
\(566\) 0 0
\(567\) 4701.19 12656.3i 0.348204 0.937419i
\(568\) 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 \(-0.898645\pi\)
0.949733 0.313062i \(-0.101355\pi\)
\(578\) 0 0
\(579\) −20343.7 + 5399.81i −1.46020 + 0.387579i
\(580\) 0 0
\(581\) −620.798 + 111.271i −0.0443288 + 0.00794546i
\(582\) 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 0.577921 0.816093i \(-0.303864\pi\)
−0.995718 + 0.0924479i \(0.970531\pi\)
\(588\) 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 \(-0.355036\pi\)
0.439838 + 0.898077i \(0.355036\pi\)
\(594\) 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 −0.161767 0.986829i \(-0.551719\pi\)
0.773735 + 0.633509i \(0.218386\pi\)
\(602\) 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 0.876927 0.480624i \(-0.159590\pi\)
0.0222310 + 0.999753i \(0.492923\pi\)
\(608\) 0 0
\(609\) 7179.03 10263.0i 0.477683 0.682886i
\(610\) 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 −0.297558 0.954704i \(-0.596172\pi\)
0.678019 + 0.735045i \(0.262839\pi\)
\(620\) 0 0
\(621\) 8727.92 2272.73i 0.563992 0.146862i
\(622\) 0 0
\(623\) 1313.30 3640.21i 0.0844564 0.234096i
\(624\) 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
\(637\) 1519.69 + 4103.09i 0.0945249 + 0.255212i
\(638\) 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 0.749060 0.662502i \(-0.230505\pi\)
−0.199214 + 0.979956i \(0.563839\pi\)
\(644\) 0 0
\(645\) 18723.4 + 18811.7i 1.14300 + 1.14839i
\(646\) 0 0
\(647\) −13536.7 −0.822539 −0.411269 0.911514i \(-0.634914\pi\)
−0.411269 + 0.911514i \(0.634914\pi\)
\(648\) 0 0
\(649\) 27651.6i 1.67245i
\(650\) 0 0
\(651\) −21102.0 1836.19i −1.27043 0.110547i
\(652\) 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 0.142935 0.989732i \(-0.454346\pi\)
−0.785666 + 0.618651i \(0.787679\pi\)
\(662\) 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 0.993752 0.111609i \(-0.0356005\pi\)
−0.593533 + 0.804810i \(0.702267\pi\)
\(678\) 0 0
\(679\) 4153.82 + 23174.7i 0.234770 + 1.30982i
\(680\) 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 \(-0.330963\pi\)
0.999972 0.00744663i \(-0.00237036\pi\)
\(692\) 0 0
\(693\) −26322.9 + 4590.36i −1.44289 + 0.251621i
\(694\) 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
\(707\) 11197.6 2007.04i 0.595655 0.106765i
\(708\) 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 \(-0.110262\pi\)
0.940601 + 0.339514i \(0.110262\pi\)
\(720\) 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 −0.920193 0.391465i \(-0.871968\pi\)
−0.121078 + 0.992643i \(0.538635\pi\)
\(728\) 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 0.844975 0.534806i \(-0.179615\pi\)
−0.0406678 + 0.999173i \(0.512949\pi\)
\(734\) 0 0
\(735\) 26850.8 + 12413.3i 1.34749 + 0.622952i
\(736\) 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
\(749\) −19665.6 7094.87i −0.959364 0.346116i
\(750\) 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 −0.569300 0.822130i \(-0.692786\pi\)
0.996635 + 0.0819631i \(0.0261190\pi\)
\(762\) 0 0
\(763\) −9777.90 + 27102.4i −0.463937 + 1.28594i
\(764\) 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 0.388248 0.921555i \(-0.373081\pi\)
−0.603966 + 0.797010i \(0.706414\pi\)
\(770\) 0 0
\(771\) 10493.6 2785.31i 0.490167 0.130104i
\(772\) 0 0
\(773\) 21593.6 1.00475 0.502373 0.864651i \(-0.332460\pi\)
0.502373 + 0.864651i \(0.332460\pi\)
\(774\) 0 0
\(775\) 33120.8i 1.53514i
\(776\) 0 0
\(777\) −24392.5 + 11388.4i −1.12622 + 0.525812i
\(778\) 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 0.989783 0.142581i \(-0.0455402\pi\)
0.371413 + 0.928468i \(0.378874\pi\)
\(788\) 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
\(796\)