Properties

Label 441.4.e.r.361.2
Level $441$
Weight $4$
Character 441.361
Analytic conductor $26.020$
Analytic rank $0$
Dimension $4$
CM no
Inner twists $4$

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Newspace parameters

Level: \( N \) \(=\) \( 441 = 3^{2} \cdot 7^{2} \)
Weight: \( k \) \(=\) \( 4 \)
Character orbit: \([\chi]\) \(=\) 441.e (of order \(3\), degree \(2\), not minimal)

Newform invariants

Self dual: no
Analytic conductor: \(26.0198423125\)
Analytic rank: \(0\)
Dimension: \(4\)
Relative dimension: \(2\) over \(\Q(\zeta_{3})\)
Coefficient field: \(\Q(\sqrt{-3}, \sqrt{19})\)
Defining polynomial: \(x^{4} + 19 x^{2} + 361\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 63)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.2
Root \(2.17945 + 3.77492i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.4.e.r.226.2

$q$-expansion

\(f(q)\) \(=\) \(q+(2.17945 + 3.77492i) q^{2} +(-5.50000 + 9.52628i) q^{4} +(4.35890 + 7.54983i) q^{5} -13.0767 q^{8} +O(q^{10})\) \(q+(2.17945 + 3.77492i) q^{2} +(-5.50000 + 9.52628i) q^{4} +(4.35890 + 7.54983i) q^{5} -13.0767 q^{8} +(-19.0000 + 32.9090i) q^{10} +(-21.7945 + 37.7492i) q^{11} +82.0000 q^{13} +(15.5000 + 26.8468i) q^{16} +(-39.2301 + 67.9485i) q^{17} +(10.0000 + 17.3205i) q^{19} -95.8958 q^{20} -190.000 q^{22} +(-65.3835 - 113.248i) q^{23} +(24.5000 - 42.4352i) q^{25} +(178.715 + 309.543i) q^{26} -244.098 q^{29} +(-78.0000 + 135.100i) q^{31} +(-119.870 + 207.620i) q^{32} -342.000 q^{34} +(-93.0000 - 161.081i) q^{37} +(-43.5890 + 75.4983i) q^{38} +(-57.0000 - 98.7269i) q^{40} +165.638 q^{41} +164.000 q^{43} +(-239.739 - 415.241i) q^{44} +(285.000 - 493.634i) q^{46} +(235.381 + 407.691i) q^{47} +213.586 q^{50} +(-451.000 + 781.155i) q^{52} +(-78.4602 + 135.897i) q^{53} -380.000 q^{55} +(-532.000 - 921.451i) q^{58} +(78.4602 - 135.897i) q^{59} +(-395.000 - 684.160i) q^{61} -679.988 q^{62} -797.000 q^{64} +(357.430 + 619.086i) q^{65} +(22.0000 - 38.1051i) q^{67} +(-431.531 - 747.434i) q^{68} -444.608 q^{71} +(-63.0000 + 109.119i) q^{73} +(405.378 - 702.135i) q^{74} -220.000 q^{76} +(356.000 + 616.610i) q^{79} +(-135.126 + 234.045i) q^{80} +(361.000 + 625.270i) q^{82} +1464.59 q^{83} -684.000 q^{85} +(357.430 + 619.086i) q^{86} +(285.000 - 493.634i) q^{88} +(-727.936 - 1260.82i) q^{89} +1438.44 q^{92} +(-1026.00 + 1777.08i) q^{94} +(-87.1780 + 150.997i) q^{95} +798.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 4q - 22q^{4} + O(q^{10}) \) \( 4q - 22q^{4} - 76q^{10} + 328q^{13} + 62q^{16} + 40q^{19} - 760q^{22} + 98q^{25} - 312q^{31} - 1368q^{34} - 372q^{37} - 228q^{40} + 656q^{43} + 1140q^{46} - 1804q^{52} - 1520q^{55} - 2128q^{58} - 1580q^{61} - 3188q^{64} + 88q^{67} - 252q^{73} - 880q^{76} + 1424q^{79} + 1444q^{82} - 2736q^{85} + 1140q^{88} - 4104q^{94} + 3192q^{97} + O(q^{100}) \)

Character values

We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

\(n\) \(199\) \(344\)
\(\chi(n)\) \(e\left(\frac{2}{3}\right)\) \(1\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 2.17945 + 3.77492i 0.770552 + 1.33463i 0.937261 + 0.348629i \(0.113353\pi\)
−0.166709 + 0.986006i \(0.553314\pi\)
\(3\) 0 0
\(4\) −5.50000 + 9.52628i −0.687500 + 1.19078i
\(5\) 4.35890 + 7.54983i 0.389872 + 0.675278i 0.992432 0.122796i \(-0.0391860\pi\)
−0.602560 + 0.798073i \(0.705853\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −13.0767 −0.577914
\(9\) 0 0
\(10\) −19.0000 + 32.9090i −0.600833 + 1.04067i
\(11\) −21.7945 + 37.7492i −0.597390 + 1.03471i 0.395815 + 0.918330i \(0.370462\pi\)
−0.993205 + 0.116379i \(0.962871\pi\)
\(12\) 0 0
\(13\) 82.0000 1.74944 0.874720 0.484629i \(-0.161046\pi\)
0.874720 + 0.484629i \(0.161046\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 15.5000 + 26.8468i 0.242188 + 0.419481i
\(17\) −39.2301 + 67.9485i −0.559688 + 0.969408i 0.437834 + 0.899056i \(0.355746\pi\)
−0.997522 + 0.0703522i \(0.977588\pi\)
\(18\) 0 0
\(19\) 10.0000 + 17.3205i 0.120745 + 0.209137i 0.920062 0.391773i \(-0.128138\pi\)
−0.799317 + 0.600910i \(0.794805\pi\)
\(20\) −95.8958 −1.07215
\(21\) 0 0
\(22\) −190.000 −1.84128
\(23\) −65.3835 113.248i −0.592756 1.02668i −0.993859 0.110651i \(-0.964706\pi\)
0.401103 0.916033i \(-0.368627\pi\)
\(24\) 0 0
\(25\) 24.5000 42.4352i 0.196000 0.339482i
\(26\) 178.715 + 309.543i 1.34803 + 2.33486i
\(27\) 0 0
\(28\) 0 0
\(29\) −244.098 −1.56303 −0.781516 0.623885i \(-0.785553\pi\)
−0.781516 + 0.623885i \(0.785553\pi\)
\(30\) 0 0
\(31\) −78.0000 + 135.100i −0.451910 + 0.782731i −0.998505 0.0546661i \(-0.982591\pi\)
0.546595 + 0.837397i \(0.315924\pi\)
\(32\) −119.870 + 207.620i −0.662193 + 1.14695i
\(33\) 0 0
\(34\) −342.000 −1.72507
\(35\) 0 0
\(36\) 0 0
\(37\) −93.0000 161.081i −0.413219 0.715716i 0.582021 0.813174i \(-0.302262\pi\)
−0.995240 + 0.0974576i \(0.968929\pi\)
\(38\) −43.5890 + 75.4983i −0.186081 + 0.322301i
\(39\) 0 0
\(40\) −57.0000 98.7269i −0.225312 0.390252i
\(41\) 165.638 0.630935 0.315467 0.948936i \(-0.397839\pi\)
0.315467 + 0.948936i \(0.397839\pi\)
\(42\) 0 0
\(43\) 164.000 0.581622 0.290811 0.956780i \(-0.406075\pi\)
0.290811 + 0.956780i \(0.406075\pi\)
\(44\) −239.739 415.241i −0.821411 1.42273i
\(45\) 0 0
\(46\) 285.000 493.634i 0.913499 1.58223i
\(47\) 235.381 + 407.691i 0.730506 + 1.26527i 0.956667 + 0.291184i \(0.0940490\pi\)
−0.226161 + 0.974090i \(0.572618\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 213.586 0.604113
\(51\) 0 0
\(52\) −451.000 + 781.155i −1.20274 + 2.08321i
\(53\) −78.4602 + 135.897i −0.203346 + 0.352205i −0.949604 0.313451i \(-0.898515\pi\)
0.746259 + 0.665656i \(0.231848\pi\)
\(54\) 0 0
\(55\) −380.000 −0.931622
\(56\) 0 0
\(57\) 0 0
\(58\) −532.000 921.451i −1.20440 2.08608i
\(59\) 78.4602 135.897i 0.173130 0.299869i −0.766383 0.642384i \(-0.777945\pi\)
0.939512 + 0.342515i \(0.111279\pi\)
\(60\) 0 0
\(61\) −395.000 684.160i −0.829091 1.43603i −0.898752 0.438457i \(-0.855525\pi\)
0.0696607 0.997571i \(-0.477808\pi\)
\(62\) −679.988 −1.39288
\(63\) 0 0
\(64\) −797.000 −1.55664
\(65\) 357.430 + 619.086i 0.682057 + 1.18136i
\(66\) 0 0
\(67\) 22.0000 38.1051i 0.0401153 0.0694818i −0.845271 0.534338i \(-0.820561\pi\)
0.885386 + 0.464857i \(0.153894\pi\)
\(68\) −431.531 747.434i −0.769571 1.33294i
\(69\) 0 0
\(70\) 0 0
\(71\) −444.608 −0.743172 −0.371586 0.928398i \(-0.621186\pi\)
−0.371586 + 0.928398i \(0.621186\pi\)
\(72\) 0 0
\(73\) −63.0000 + 109.119i −0.101008 + 0.174951i −0.912100 0.409967i \(-0.865540\pi\)
0.811092 + 0.584918i \(0.198873\pi\)
\(74\) 405.378 702.135i 0.636813 1.10299i
\(75\) 0 0
\(76\) −220.000 −0.332049
\(77\) 0 0
\(78\) 0 0
\(79\) 356.000 + 616.610i 0.507002 + 0.878153i 0.999967 + 0.00810375i \(0.00257953\pi\)
−0.492966 + 0.870049i \(0.664087\pi\)
\(80\) −135.126 + 234.045i −0.188844 + 0.327088i
\(81\) 0 0
\(82\) 361.000 + 625.270i 0.486168 + 0.842068i
\(83\) 1464.59 1.93686 0.968432 0.249280i \(-0.0801938\pi\)
0.968432 + 0.249280i \(0.0801938\pi\)
\(84\) 0 0
\(85\) −684.000 −0.872826
\(86\) 357.430 + 619.086i 0.448170 + 0.776254i
\(87\) 0 0
\(88\) 285.000 493.634i 0.345240 0.597973i
\(89\) −727.936 1260.82i −0.866978 1.50165i −0.865069 0.501652i \(-0.832726\pi\)
−0.00190909 0.999998i \(-0.500608\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 1438.44 1.63008
\(93\) 0 0
\(94\) −1026.00 + 1777.08i −1.12579 + 1.94992i
\(95\) −87.1780 + 150.997i −0.0941502 + 0.163073i
\(96\) 0 0
\(97\) 798.000 0.835305 0.417653 0.908607i \(-0.362853\pi\)
0.417653 + 0.908607i \(0.362853\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 269.500 + 466.788i 0.269500 + 0.466788i
\(101\) 204.868 354.842i 0.201833 0.349585i −0.747286 0.664503i \(-0.768643\pi\)
0.949119 + 0.314917i \(0.101977\pi\)
\(102\) 0 0
\(103\) 458.000 + 793.279i 0.438137 + 0.758875i 0.997546 0.0700167i \(-0.0223052\pi\)
−0.559409 + 0.828892i \(0.688972\pi\)
\(104\) −1072.29 −1.01103
\(105\) 0 0
\(106\) −684.000 −0.626754
\(107\) 448.967 + 777.633i 0.405638 + 0.702585i 0.994395 0.105724i \(-0.0337161\pi\)
−0.588758 + 0.808310i \(0.700383\pi\)
\(108\) 0 0
\(109\) 171.000 296.181i 0.150264 0.260266i −0.781060 0.624456i \(-0.785321\pi\)
0.931325 + 0.364190i \(0.118654\pi\)
\(110\) −828.191 1434.47i −0.717863 1.24337i
\(111\) 0 0
\(112\) 0 0
\(113\) 488.197 0.406422 0.203211 0.979135i \(-0.434862\pi\)
0.203211 + 0.979135i \(0.434862\pi\)
\(114\) 0 0
\(115\) 570.000 987.269i 0.462198 0.800550i
\(116\) 1342.54 2325.35i 1.07458 1.86123i
\(117\) 0 0
\(118\) 684.000 0.533621
\(119\) 0 0
\(120\) 0 0
\(121\) −284.500 492.768i −0.213749 0.370224i
\(122\) 1721.77 2982.18i 1.27772 2.21307i
\(123\) 0 0
\(124\) −858.000 1486.10i −0.621376 1.07626i
\(125\) 1516.90 1.08540
\(126\) 0 0
\(127\) 456.000 0.318610 0.159305 0.987229i \(-0.449075\pi\)
0.159305 + 0.987229i \(0.449075\pi\)
\(128\) −778.063 1347.65i −0.537279 0.930595i
\(129\) 0 0
\(130\) −1558.00 + 2698.54i −1.05112 + 1.82059i
\(131\) 749.731 + 1298.57i 0.500033 + 0.866082i 1.00000 3.76230e-5i \(1.19758e-5\pi\)
−0.499967 + 0.866044i \(0.666655\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 191.792 0.123644
\(135\) 0 0
\(136\) 513.000 888.542i 0.323451 0.560234i
\(137\) −444.608 + 770.083i −0.277266 + 0.480238i −0.970704 0.240278i \(-0.922762\pi\)
0.693439 + 0.720516i \(0.256095\pi\)
\(138\) 0 0
\(139\) −768.000 −0.468640 −0.234320 0.972160i \(-0.575286\pi\)
−0.234320 + 0.972160i \(0.575286\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −969.000 1678.36i −0.572653 0.991863i
\(143\) −1787.15 + 3095.43i −1.04510 + 1.81016i
\(144\) 0 0
\(145\) −1064.00 1842.90i −0.609382 1.05548i
\(146\) −549.221 −0.311328
\(147\) 0 0
\(148\) 2046.00 1.13635
\(149\) 496.914 + 860.681i 0.273214 + 0.473220i 0.969683 0.244367i \(-0.0785801\pi\)
−0.696469 + 0.717587i \(0.745247\pi\)
\(150\) 0 0
\(151\) 1748.00 3027.62i 0.942054 1.63169i 0.180510 0.983573i \(-0.442225\pi\)
0.761544 0.648113i \(-0.224442\pi\)
\(152\) −130.767 226.495i −0.0697803 0.120863i
\(153\) 0 0
\(154\) 0 0
\(155\) −1359.98 −0.704748
\(156\) 0 0
\(157\) 253.000 438.209i 0.128609 0.222757i −0.794529 0.607226i \(-0.792282\pi\)
0.923138 + 0.384469i \(0.125615\pi\)
\(158\) −1551.77 + 2687.74i −0.781342 + 1.35332i
\(159\) 0 0
\(160\) −2090.00 −1.03268
\(161\) 0 0
\(162\) 0 0
\(163\) 1282.00 + 2220.49i 0.616037 + 1.06701i 0.990202 + 0.139645i \(0.0445961\pi\)
−0.374165 + 0.927362i \(0.622071\pi\)
\(164\) −911.010 + 1577.92i −0.433768 + 0.751308i
\(165\) 0 0
\(166\) 3192.00 + 5528.71i 1.49245 + 2.58500i
\(167\) 645.117 0.298926 0.149463 0.988767i \(-0.452245\pi\)
0.149463 + 0.988767i \(0.452245\pi\)
\(168\) 0 0
\(169\) 4527.00 2.06054
\(170\) −1490.74 2582.04i −0.672558 1.16490i
\(171\) 0 0
\(172\) −902.000 + 1562.31i −0.399865 + 0.692587i
\(173\) 1930.99 + 3344.58i 0.848616 + 1.46985i 0.882443 + 0.470419i \(0.155897\pi\)
−0.0338270 + 0.999428i \(0.510770\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1351.26 −0.578721
\(177\) 0 0
\(178\) 3173.00 5495.80i 1.33610 2.31420i
\(179\) −135.126 + 234.045i −0.0564234 + 0.0977281i −0.892857 0.450339i \(-0.851303\pi\)
0.836434 + 0.548068i \(0.184636\pi\)
\(180\) 0 0
\(181\) 418.000 0.171656 0.0858279 0.996310i \(-0.472646\pi\)
0.0858279 + 0.996310i \(0.472646\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 855.000 + 1480.90i 0.342562 + 0.593335i
\(185\) 810.755 1404.27i 0.322205 0.558075i
\(186\) 0 0
\(187\) −1710.00 2961.81i −0.668704 1.15823i
\(188\) −5178.37 −2.00889
\(189\) 0 0
\(190\) −760.000 −0.290191
\(191\) 762.807 + 1321.22i 0.288978 + 0.500525i 0.973566 0.228406i \(-0.0733512\pi\)
−0.684588 + 0.728930i \(0.740018\pi\)
\(192\) 0 0
\(193\) −679.000 + 1176.06i −0.253241 + 0.438626i −0.964416 0.264389i \(-0.914830\pi\)
0.711175 + 0.703015i \(0.248163\pi\)
\(194\) 1739.20 + 3012.38i 0.643646 + 1.11483i
\(195\) 0 0
\(196\) 0 0
\(197\) −3748.65 −1.35574 −0.677869 0.735183i \(-0.737096\pi\)
−0.677869 + 0.735183i \(0.737096\pi\)
\(198\) 0 0
\(199\) 528.000 914.523i 0.188085 0.325773i −0.756527 0.653963i \(-0.773105\pi\)
0.944612 + 0.328190i \(0.106439\pi\)
\(200\) −320.379 + 554.913i −0.113271 + 0.196191i
\(201\) 0 0
\(202\) 1786.00 0.622092
\(203\) 0 0
\(204\) 0 0
\(205\) 722.000 + 1250.54i 0.245984 + 0.426056i
\(206\) −1996.38 + 3457.82i −0.675214 + 1.16950i
\(207\) 0 0
\(208\) 1271.00 + 2201.44i 0.423692 + 0.733857i
\(209\) −871.780 −0.288528
\(210\) 0 0
\(211\) −3620.00 −1.18110 −0.590548 0.807003i \(-0.701088\pi\)
−0.590548 + 0.807003i \(0.701088\pi\)
\(212\) −863.062 1494.87i −0.279601 0.484283i
\(213\) 0 0
\(214\) −1957.00 + 3389.62i −0.625130 + 1.08276i
\(215\) 714.859 + 1238.17i 0.226758 + 0.392757i
\(216\) 0 0
\(217\) 0 0
\(218\) 1490.74 0.463146
\(219\) 0 0
\(220\) 2090.00 3619.99i 0.640490 1.10936i
\(221\) −3216.87 + 5571.78i −0.979140 + 1.69592i
\(222\) 0 0
\(223\) 5368.00 1.61196 0.805982 0.591940i \(-0.201638\pi\)
0.805982 + 0.591940i \(0.201638\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1064.00 + 1842.90i 0.313169 + 0.542425i
\(227\) 810.755 1404.27i 0.237056 0.410593i −0.722812 0.691045i \(-0.757151\pi\)
0.959868 + 0.280451i \(0.0904842\pi\)
\(228\) 0 0
\(229\) −1093.00 1893.13i −0.315404 0.546295i 0.664119 0.747626i \(-0.268807\pi\)
−0.979523 + 0.201331i \(0.935473\pi\)
\(230\) 4969.14 1.42459
\(231\) 0 0
\(232\) 3192.00 0.903298
\(233\) −2066.12 3578.62i −0.580927 1.00619i −0.995370 0.0961192i \(-0.969357\pi\)
0.414443 0.910075i \(-0.363976\pi\)
\(234\) 0 0
\(235\) −2052.00 + 3554.17i −0.569607 + 0.986589i
\(236\) 863.062 + 1494.87i 0.238053 + 0.412320i
\(237\) 0 0
\(238\) 0 0
\(239\) 4838.38 1.30949 0.654746 0.755849i \(-0.272776\pi\)
0.654746 + 0.755849i \(0.272776\pi\)
\(240\) 0 0
\(241\) −643.000 + 1113.71i −0.171864 + 0.297678i −0.939072 0.343722i \(-0.888312\pi\)
0.767207 + 0.641399i \(0.221646\pi\)
\(242\) 1240.11 2147.93i 0.329409 0.570554i
\(243\) 0 0
\(244\) 8690.00 2.28000
\(245\) 0 0
\(246\) 0 0
\(247\) 820.000 + 1420.28i 0.211236 + 0.365872i
\(248\) 1019.98 1766.66i 0.261165 0.452351i
\(249\) 0 0
\(250\) 3306.00 + 5726.16i 0.836359 + 1.44862i
\(251\) 1795.87 0.451610 0.225805 0.974173i \(-0.427499\pi\)
0.225805 + 0.974173i \(0.427499\pi\)
\(252\) 0 0
\(253\) 5700.00 1.41643
\(254\) 993.829 + 1721.36i 0.245505 + 0.425228i
\(255\) 0 0
\(256\) 203.500 352.472i 0.0496826 0.0860528i
\(257\) −972.034 1683.61i −0.235929 0.408642i 0.723613 0.690206i \(-0.242480\pi\)
−0.959542 + 0.281564i \(0.909147\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −7863.45 −1.87566
\(261\) 0 0
\(262\) −3268.00 + 5660.34i −0.770602 + 1.33472i
\(263\) 2672.01 4628.05i 0.626475 1.08509i −0.361779 0.932264i \(-0.617830\pi\)
0.988254 0.152822i \(-0.0488362\pi\)
\(264\) 0 0
\(265\) −1368.00 −0.317115
\(266\) 0 0
\(267\) 0 0
\(268\) 242.000 + 419.156i 0.0551586 + 0.0955375i
\(269\) −2000.73 + 3465.37i −0.453483 + 0.785456i −0.998600 0.0529046i \(-0.983152\pi\)
0.545117 + 0.838360i \(0.316485\pi\)
\(270\) 0 0
\(271\) −1394.00 2414.48i −0.312470 0.541215i 0.666426 0.745571i \(-0.267823\pi\)
−0.978897 + 0.204356i \(0.934490\pi\)
\(272\) −2432.27 −0.542198
\(273\) 0 0
\(274\) −3876.00 −0.854590
\(275\) 1067.93 + 1849.71i 0.234177 + 0.405606i
\(276\) 0 0
\(277\) 2281.00 3950.81i 0.494773 0.856971i −0.505209 0.862997i \(-0.668585\pi\)
0.999982 + 0.00602561i \(0.00191802\pi\)
\(278\) −1673.82 2899.14i −0.361111 0.625463i
\(279\) 0 0
\(280\) 0 0
\(281\) 1551.77 0.329433 0.164717 0.986341i \(-0.447329\pi\)
0.164717 + 0.986341i \(0.447329\pi\)
\(282\) 0 0
\(283\) 3394.00 5878.58i 0.712906 1.23479i −0.250856 0.968024i \(-0.580712\pi\)
0.963762 0.266765i \(-0.0859547\pi\)
\(284\) 2445.34 4235.46i 0.510931 0.884958i
\(285\) 0 0
\(286\) −15580.0 −3.22121
\(287\) 0 0
\(288\) 0 0
\(289\) −621.500 1076.47i −0.126501 0.219106i
\(290\) 4637.87 8033.02i 0.939121 1.62660i
\(291\) 0 0
\(292\) −693.000 1200.31i −0.138886 0.240558i
\(293\) −1142.03 −0.227707 −0.113854 0.993498i \(-0.536319\pi\)
−0.113854 + 0.993498i \(0.536319\pi\)
\(294\) 0 0
\(295\) 1368.00 0.269993
\(296\) 1216.13 + 2106.40i 0.238805 + 0.413622i
\(297\) 0 0
\(298\) −2166.00 + 3751.62i −0.421050 + 0.729281i
\(299\) −5361.45 9286.30i −1.03699 1.79612i
\(300\) 0 0
\(301\) 0 0
\(302\) 15238.7 2.90361
\(303\) 0 0
\(304\) −310.000 + 536.936i −0.0584859 + 0.101301i
\(305\) 3443.53 5964.37i 0.646479 1.11973i
\(306\) 0 0
\(307\) 532.000 0.0989018 0.0494509 0.998777i \(-0.484253\pi\)
0.0494509 + 0.998777i \(0.484253\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2964.00 5133.80i −0.543045 0.940581i
\(311\) 3269.17 5662.38i 0.596070 1.03242i −0.397325 0.917678i \(-0.630061\pi\)
0.993395 0.114746i \(-0.0366054\pi\)
\(312\) 0 0
\(313\) −2497.00 4324.93i −0.450923 0.781021i 0.547521 0.836792i \(-0.315572\pi\)
−0.998444 + 0.0557711i \(0.982238\pi\)
\(314\) 2205.60 0.396399
\(315\) 0 0
\(316\) −7832.00 −1.39425
\(317\) −235.381 407.691i −0.0417044 0.0722341i 0.844420 0.535682i \(-0.179945\pi\)
−0.886124 + 0.463448i \(0.846612\pi\)
\(318\) 0 0
\(319\) 5320.00 9214.51i 0.933739 1.61728i
\(320\) −3474.04 6017.22i −0.606890 1.05116i
\(321\) 0 0
\(322\) 0 0
\(323\) −1569.20 −0.270318
\(324\) 0 0
\(325\) 2009.00 3479.69i 0.342890 0.593903i
\(326\) −5588.11 + 9678.89i −0.949376 + 1.64437i
\(327\) 0 0
\(328\) −2166.00 −0.364626
\(329\) 0 0
\(330\) 0 0
\(331\) −1294.00 2241.27i −0.214878 0.372180i 0.738357 0.674410i \(-0.235602\pi\)
−0.953235 + 0.302230i \(0.902269\pi\)
\(332\) −8055.25 + 13952.1i −1.33159 + 2.30639i
\(333\) 0 0
\(334\) 1406.00 + 2435.26i 0.230338 + 0.398957i
\(335\) 383.583 0.0625594
\(336\) 0 0
\(337\) 238.000 0.0384709 0.0192354 0.999815i \(-0.493877\pi\)
0.0192354 + 0.999815i \(0.493877\pi\)
\(338\) 9866.37 + 17089.1i 1.58775 + 2.75006i
\(339\) 0 0
\(340\) 3762.00 6515.98i 0.600068 1.03935i
\(341\) −3399.94 5888.87i −0.539933 0.935191i
\(342\) 0 0
\(343\) 0 0
\(344\) −2144.58 −0.336128
\(345\) 0 0
\(346\) −8417.00 + 14578.7i −1.30781 + 2.26519i
\(347\) 3526.35 6107.82i 0.545546 0.944913i −0.453027 0.891497i \(-0.649656\pi\)
0.998572 0.0534159i \(-0.0170109\pi\)
\(348\) 0 0
\(349\) −10850.0 −1.66415 −0.832073 0.554666i \(-0.812846\pi\)
−0.832073 + 0.554666i \(0.812846\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5225.00 9049.97i −0.791175 1.37035i
\(353\) 2645.85 4582.75i 0.398936 0.690978i −0.594659 0.803978i \(-0.702713\pi\)
0.993595 + 0.113000i \(0.0360462\pi\)
\(354\) 0 0
\(355\) −1938.00 3356.71i −0.289742 0.501848i
\(356\) 16014.6 2.38419
\(357\) 0 0
\(358\) −1178.00 −0.173908
\(359\) −2410.47 4175.06i −0.354373 0.613792i 0.632638 0.774448i \(-0.281972\pi\)
−0.987010 + 0.160656i \(0.948639\pi\)
\(360\) 0 0
\(361\) 3229.50 5593.66i 0.470841 0.815521i
\(362\) 911.010 + 1577.92i 0.132270 + 0.229098i
\(363\) 0 0
\(364\) 0 0
\(365\) −1098.44 −0.157521
\(366\) 0 0
\(367\) −5856.00 + 10142.9i −0.832917 + 1.44266i 0.0627973 + 0.998026i \(0.479998\pi\)
−0.895715 + 0.444629i \(0.853336\pi\)
\(368\) 2026.89 3510.67i 0.287116 0.497300i
\(369\) 0 0
\(370\) 7068.00 0.993102
\(371\) 0 0
\(372\) 0 0
\(373\) 5225.00 + 9049.97i 0.725309 + 1.25627i 0.958847 + 0.283924i \(0.0916364\pi\)
−0.233538 + 0.972348i \(0.575030\pi\)
\(374\) 7453.72 12910.2i 1.03054 1.78495i
\(375\) 0 0
\(376\) −3078.00 5331.25i −0.422169 0.731219i
\(377\) −20016.1 −2.73443
\(378\) 0 0
\(379\) −756.000 −0.102462 −0.0512310 0.998687i \(-0.516314\pi\)
−0.0512310 + 0.998687i \(0.516314\pi\)
\(380\) −958.958 1660.96i −0.129457 0.224225i
\(381\) 0 0
\(382\) −3325.00 + 5759.07i −0.445345 + 0.771360i
\(383\) 3190.71 + 5526.48i 0.425686 + 0.737310i 0.996484 0.0837802i \(-0.0266994\pi\)
−0.570798 + 0.821091i \(0.693366\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −5919.38 −0.780541
\(387\) 0 0
\(388\) −4389.00 + 7601.97i −0.574272 + 0.994669i
\(389\) −209.227 + 362.392i −0.0272705 + 0.0472339i −0.879339 0.476197i \(-0.842015\pi\)
0.852068 + 0.523431i \(0.175348\pi\)
\(390\) 0 0
\(391\) 10260.0 1.32703
\(392\) 0 0
\(393\) 0 0
\(394\) −8170.00 14150.9i −1.04467 1.80942i
\(395\) −3103.54 + 5375.48i −0.395331 + 0.684734i
\(396\) 0 0
\(397\) 2901.00 + 5024.68i 0.366743 + 0.635218i 0.989054 0.147552i \(-0.0471395\pi\)
−0.622311 + 0.782770i \(0.713806\pi\)
\(398\) 4603.00 0.579717
\(399\) 0 0
\(400\) 1519.00 0.189875
\(401\) −2066.12 3578.62i −0.257299 0.445655i 0.708218 0.705994i \(-0.249499\pi\)
−0.965517 + 0.260338i \(0.916166\pi\)
\(402\) 0 0
\(403\) −6396.00 + 11078.2i −0.790589 + 1.36934i
\(404\) 2253.55 + 3903.26i 0.277521 + 0.480680i
\(405\) 0 0
\(406\) 0 0
\(407\) 8107.55 0.987411
\(408\) 0 0
\(409\) 665.000 1151.81i 0.0803964 0.139251i −0.823024 0.568007i \(-0.807715\pi\)
0.903420 + 0.428756i \(0.141048\pi\)
\(410\) −3147.13 + 5450.98i −0.379086 + 0.656597i
\(411\) 0 0
\(412\) −10076.0 −1.20488
\(413\) 0 0
\(414\) 0 0
\(415\) 6384.00 + 11057.4i 0.755128 + 1.30792i
\(416\) −9829.32 + 17024.9i −1.15847 + 2.00652i
\(417\) 0 0
\(418\) −1900.00 3290.90i −0.222325 0.385079i
\(419\) −10409.1 −1.21364 −0.606820 0.794839i \(-0.707555\pi\)
−0.606820 + 0.794839i \(0.707555\pi\)
\(420\) 0 0
\(421\) −12274.0 −1.42090 −0.710449 0.703749i \(-0.751508\pi\)
−0.710449 + 0.703749i \(0.751508\pi\)
\(422\) −7889.61 13665.2i −0.910095 1.57633i
\(423\) 0 0
\(424\) 1026.00 1777.08i 0.117516 0.203544i
\(425\) 1922.27 + 3329.48i 0.219398 + 0.380008i
\(426\) 0 0
\(427\) 0 0
\(428\) −9877.27 −1.11550
\(429\) 0 0
\(430\) −3116.00 + 5397.07i −0.349458 + 0.605279i
\(431\) −2340.73 + 4054.26i −0.261598 + 0.453102i −0.966667 0.256037i \(-0.917583\pi\)
0.705068 + 0.709139i \(0.250916\pi\)
\(432\) 0 0
\(433\) 5770.00 0.640389 0.320195 0.947352i \(-0.396252\pi\)
0.320195 + 0.947352i \(0.396252\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) 1881.00 + 3257.99i 0.206614 + 0.357865i
\(437\) 1307.67 2264.95i 0.143145 0.247934i
\(438\) 0 0
\(439\) 936.000 + 1621.20i 0.101760 + 0.176254i 0.912410 0.409277i \(-0.134219\pi\)
−0.810650 + 0.585532i \(0.800886\pi\)
\(440\) 4969.14 0.538397
\(441\) 0 0
\(442\) −28044.0 −3.01791
\(443\) −5557.60 9626.04i −0.596048 1.03239i −0.993398 0.114719i \(-0.963403\pi\)
0.397350 0.917667i \(-0.369930\pi\)
\(444\) 0 0
\(445\) 6346.00 10991.6i 0.676021 1.17090i
\(446\) 11699.3 + 20263.8i 1.24210 + 2.15138i
\(447\) 0 0
\(448\) 0 0
\(449\) 7636.79 0.802678 0.401339 0.915930i \(-0.368545\pi\)
0.401339 + 0.915930i \(0.368545\pi\)
\(450\) 0 0
\(451\) −3610.00 + 6252.70i −0.376914 + 0.652834i
\(452\) −2685.08 + 4650.70i −0.279415 + 0.483961i
\(453\) 0 0
\(454\) 7068.00 0.730656
\(455\) 0 0
\(456\) 0 0
\(457\) −7571.00 13113.4i −0.774959 1.34227i −0.934817 0.355129i \(-0.884437\pi\)
0.159858 0.987140i \(-0.448896\pi\)
\(458\) 4764.28 8251.97i 0.486070 0.841898i
\(459\) 0 0
\(460\) 6270.00 + 10860.0i 0.635522 + 1.10076i
\(461\) 13190.0 1.33258 0.666292 0.745691i \(-0.267881\pi\)
0.666292 + 0.745691i \(0.267881\pi\)
\(462\) 0 0
\(463\) 9328.00 0.936304 0.468152 0.883648i \(-0.344920\pi\)
0.468152 + 0.883648i \(0.344920\pi\)
\(464\) −3783.52 6553.26i −0.378547 0.655662i
\(465\) 0 0
\(466\) 9006.00 15598.8i 0.895268 1.55065i
\(467\) 1699.97 + 2944.44i 0.168448 + 0.291761i 0.937874 0.346975i \(-0.112791\pi\)
−0.769426 + 0.638736i \(0.779458\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −17888.9 −1.75565
\(471\) 0 0
\(472\) −1026.00 + 1777.08i −0.100054 + 0.173299i
\(473\) −3574.30 + 6190.86i −0.347455 + 0.601810i
\(474\) 0 0
\(475\) 980.000 0.0946642
\(476\) 0 0
\(477\) 0 0
\(478\) 10545.0 + 18264.5i 1.00903 + 1.74769i
\(479\) 1787.15 3095.43i 0.170474 0.295269i −0.768112 0.640316i \(-0.778804\pi\)
0.938586 + 0.345047i \(0.112137\pi\)
\(480\) 0 0
\(481\) −7626.00 13208.6i −0.722902 1.25210i
\(482\) −5605.54 −0.529721
\(483\) 0 0
\(484\) 6259.00 0.587810
\(485\) 3478.40 + 6024.77i 0.325662 + 0.564063i
\(486\) 0 0
\(487\) −4484.00 + 7766.52i −0.417227 + 0.722658i −0.995659 0.0930722i \(-0.970331\pi\)
0.578433 + 0.815730i \(0.303665\pi\)
\(488\) 5165.30 + 8946.55i 0.479143 + 0.829901i
\(489\) 0 0
\(490\) 0 0
\(491\) −5169.65 −0.475159 −0.237580 0.971368i \(-0.576354\pi\)
−0.237580 + 0.971368i \(0.576354\pi\)
\(492\) 0 0
\(493\) 9576.00 16586.1i 0.874810 1.51522i
\(494\) −3574.30 + 6190.86i −0.325537 + 0.563846i
\(495\) 0 0
\(496\) −4836.00 −0.437788
\(497\) 0 0
\(498\) 0 0
\(499\) −1970.00 3412.14i −0.176732 0.306109i 0.764027 0.645184i \(-0.223219\pi\)
−0.940759 + 0.339075i \(0.889886\pi\)
\(500\) −8342.93 + 14450.4i −0.746215 + 1.29248i
\(501\) 0 0
\(502\) 3914.00 + 6779.25i 0.347989 + 0.602734i
\(503\) −10252.1 −0.908787 −0.454394 0.890801i \(-0.650144\pi\)
−0.454394 + 0.890801i \(0.650144\pi\)
\(504\) 0 0
\(505\) 3572.00 0.314756
\(506\) 12422.9 + 21517.0i 1.09143 + 1.89041i
\(507\) 0 0
\(508\) −2508.00 + 4343.98i −0.219044 + 0.379396i
\(509\) 4886.33 + 8463.36i 0.425506 + 0.736998i 0.996468 0.0839787i \(-0.0267628\pi\)
−0.570961 + 0.820977i \(0.693429\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −10674.9 −0.921426
\(513\) 0 0
\(514\) 4237.00 7338.70i 0.363592 0.629759i
\(515\) −3992.75 + 6915.65i −0.341634 + 0.591728i
\(516\) 0 0
\(517\) −20520.0 −1.74559
\(518\) 0 0
\(519\) 0 0
\(520\) −4674.00 8095.61i −0.394170 0.682723i
\(521\) −3700.71 + 6409.81i −0.311192 + 0.539000i −0.978621 0.205674i \(-0.934061\pi\)
0.667429 + 0.744673i \(0.267395\pi\)
\(522\) 0 0
\(523\) 1384.00 + 2397.16i 0.115713 + 0.200421i 0.918065 0.396431i \(-0.129751\pi\)
−0.802351 + 0.596852i \(0.796418\pi\)
\(524\) −16494.1 −1.37509
\(525\) 0 0
\(526\) 23294.0 1.93093
\(527\) −6119.89 10600.0i −0.505857 0.876170i
\(528\) 0 0
\(529\) −2466.50 + 4272.10i −0.202720 + 0.351122i
\(530\) −2981.49 5164.09i −0.244354 0.423233i
\(531\) 0 0
\(532\) 0 0
\(533\) 13582.3 1.10378
\(534\) 0 0
\(535\) −3914.00 + 6779.25i −0.316293 + 0.547836i
\(536\) −287.687 + 498.289i −0.0231832 + 0.0401545i
\(537\) 0 0
\(538\) −17442.0 −1.39773
\(539\) 0 0
\(540\) 0 0
\(541\) −8155.00 14124.9i −0.648079 1.12251i −0.983581 0.180467i \(-0.942239\pi\)
0.335502 0.942040i \(-0.391094\pi\)
\(542\) 6076.31 10524.5i 0.481549 0.834068i
\(543\) 0 0
\(544\) −9405.00 16289.9i −0.741243 1.28387i
\(545\) 2981.49 0.234336
\(546\) 0 0
\(547\) 11140.0 0.870771 0.435386 0.900244i \(-0.356612\pi\)
0.435386 + 0.900244i \(0.356612\pi\)
\(548\) −4890.68 8470.91i −0.381240 0.660328i
\(549\) 0 0
\(550\) −4655.00 + 8062.70i −0.360891 + 0.625081i
\(551\) −2440.98 4227.91i −0.188728 0.326887i
\(552\) 0 0
\(553\) 0 0
\(554\) 19885.3 1.52499
\(555\) 0 0
\(556\) 4224.00 7316.18i 0.322190 0.558049i
\(557\) 11394.2 19735.3i 0.866761 1.50127i 0.00147399 0.999999i \(-0.499531\pi\)
0.865287 0.501276i \(-0.167136\pi\)
\(558\) 0 0
\(559\) 13448.0 1.01751
\(560\) 0 0
\(561\) 0 0
\(562\) 3382.00 + 5857.80i 0.253845 + 0.439673i
\(563\) −5762.46 + 9980.88i −0.431366 + 0.747147i −0.996991 0.0775149i \(-0.975301\pi\)
0.565625 + 0.824662i \(0.308635\pi\)
\(564\) 0 0
\(565\) 2128.00 + 3685.80i 0.158452 + 0.274448i
\(566\) 29588.2 2.19732
\(567\) 0 0
\(568\) 5814.00 0.429489
\(569\) −845.626 1464.67i −0.0623032 0.107912i 0.833191 0.552985i \(-0.186511\pi\)
−0.895495 + 0.445073i \(0.853178\pi\)
\(570\) 0 0
\(571\) −5614.00 + 9723.73i −0.411451 + 0.712654i −0.995049 0.0993888i \(-0.968311\pi\)
0.583598 + 0.812043i \(0.301645\pi\)
\(572\) −19658.6 34049.8i −1.43701 2.48897i
\(573\) 0 0
\(574\) 0 0
\(575\) −6407.58 −0.464721
\(576\) 0 0
\(577\) −1025.00 + 1775.35i −0.0739537 + 0.128092i −0.900631 0.434585i \(-0.856895\pi\)
0.826677 + 0.562677i \(0.190228\pi\)
\(578\) 2709.06 4692.22i 0.194951 0.337666i
\(579\) 0 0
\(580\) 23408.0 1.67580
\(581\) 0 0
\(582\) 0 0
\(583\) −3420.00 5923.61i −0.242954 0.420808i
\(584\) 823.832 1426.92i 0.0583740 0.101107i
\(585\) 0 0
\(586\) −2489.00 4311.07i −0.175460 0.303906i
\(587\) −18394.6 −1.29340 −0.646699 0.762745i \(-0.723851\pi\)
−0.646699 + 0.762745i \(0.723851\pi\)
\(588\) 0 0
\(589\) −3120.00 −0.218264
\(590\) 2981.49 + 5164.09i 0.208044 + 0.360343i
\(591\) 0 0
\(592\) 2883.00 4993.50i 0.200153 0.346675i
\(593\) −6316.04 10939.7i −0.437384 0.757572i 0.560103 0.828423i \(-0.310762\pi\)
−0.997487 + 0.0708515i \(0.977428\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −10932.1 −0.751337
\(597\) 0 0
\(598\) 23370.0 40478.0i 1.59811 2.76801i
\(599\) −4799.15 + 8312.37i −0.327359 + 0.567002i −0.981987 0.188949i \(-0.939492\pi\)
0.654628 + 0.755951i \(0.272825\pi\)
\(600\) 0 0
\(601\) −10758.0 −0.730163 −0.365082 0.930976i \(-0.618959\pi\)
−0.365082 + 0.930976i \(0.618959\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 19228.0 + 33303.9i 1.29532 + 2.24357i
\(605\) 2480.21 4295.86i 0.166669 0.288680i
\(606\) 0 0
\(607\) 10676.0 + 18491.4i 0.713881 + 1.23648i 0.963390 + 0.268105i \(0.0863974\pi\)
−0.249509 + 0.968372i \(0.580269\pi\)
\(608\) −4794.79 −0.319826
\(609\) 0 0
\(610\) 30020.0 1.99258
\(611\) 19301.2 + 33430.7i 1.27798 + 2.21352i
\(612\) 0 0
\(613\) 2857.00 4948.47i 0.188243 0.326047i −0.756421 0.654085i \(-0.773054\pi\)
0.944665 + 0.328038i \(0.106387\pi\)
\(614\) 1159.47 + 2008.26i 0.0762089 + 0.131998i
\(615\) 0 0
\(616\) 0 0
\(617\) −6747.58 −0.440271 −0.220135 0.975469i \(-0.570650\pi\)
−0.220135 + 0.975469i \(0.570650\pi\)
\(618\) 0 0
\(619\) 940.000 1628.13i 0.0610368 0.105719i −0.833892 0.551927i \(-0.813893\pi\)
0.894929 + 0.446208i \(0.147226\pi\)
\(620\) 7479.87 12955.5i 0.484514 0.839203i
\(621\) 0 0
\(622\) 28500.0 1.83721
\(623\) 0 0
\(624\) 0 0
\(625\) 3549.50 + 6147.91i 0.227168 + 0.393467i
\(626\) 10884.2 18851.9i 0.694918 1.20363i
\(627\) 0 0
\(628\) 2783.00 + 4820.30i 0.176837 + 0.306291i
\(629\) 14593.6 0.925095
\(630\) 0 0
\(631\) −28888.0 −1.82252 −0.911262 0.411826i \(-0.864891\pi\)
−0.911262 + 0.411826i \(0.864891\pi\)
\(632\) −4655.30 8063.22i −0.293003 0.507497i
\(633\) 0 0
\(634\) 1026.00 1777.08i 0.0642708 0.111320i
\(635\) 1987.66 + 3442.72i 0.124217 + 0.215150i
\(636\) 0 0
\(637\) 0 0
\(638\) 46378.7 2.87798
\(639\) 0 0
\(640\) 6783.00 11748.5i 0.418940 0.725625i
\(641\) 12998.2 22513.6i 0.800935 1.38726i −0.118066 0.993006i \(-0.537669\pi\)
0.919001 0.394255i \(-0.128997\pi\)
\(642\) 0 0
\(643\) 24788.0 1.52029 0.760143 0.649756i \(-0.225129\pi\)
0.760143 + 0.649756i \(0.225129\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3420.00 5923.61i −0.208294 0.360776i
\(647\) 14236.2 24657.8i 0.865041 1.49829i −0.00196599 0.999998i \(-0.500626\pi\)
0.867007 0.498296i \(-0.166041\pi\)
\(648\) 0 0
\(649\) 3420.00 + 5923.61i 0.206852 + 0.358278i
\(650\) 17514.1 1.05686
\(651\) 0 0
\(652\) −28204.0 −1.69410
\(653\) 1621.51 + 2808.54i 0.0971740 + 0.168310i 0.910514 0.413479i \(-0.135686\pi\)
−0.813340 + 0.581789i \(0.802353\pi\)
\(654\) 0 0
\(655\) −6536.00 + 11320.7i −0.389897 + 0.675322i
\(656\) 2567.39 + 4446.85i 0.152805 + 0.264665i
\(657\) 0 0
\(658\) 0 0
\(659\) −1176.90 −0.0695685 −0.0347842 0.999395i \(-0.511074\pi\)
−0.0347842 + 0.999395i \(0.511074\pi\)
\(660\) 0 0
\(661\) −5795.00 + 10037.2i −0.340998 + 0.590625i −0.984618 0.174720i \(-0.944098\pi\)
0.643621 + 0.765345i \(0.277431\pi\)
\(662\) 5640.42 9769.49i 0.331149 0.573568i
\(663\) 0 0
\(664\) −19152.0 −1.11934
\(665\) 0 0
\(666\) 0 0
\(667\) 15960.0 + 27643.5i 0.926497 + 1.60474i
\(668\) −3548.14 + 6145.57i −0.205512 + 0.355957i
\(669\) 0 0
\(670\) 836.000 + 1447.99i 0.0482052 + 0.0834939i
\(671\) 34435.3 1.98116
\(672\) 0 0
\(673\) 23062.0 1.32091 0.660457 0.750864i \(-0.270363\pi\)
0.660457 + 0.750864i \(0.270363\pi\)
\(674\) 518.709 + 898.430i 0.0296438 + 0.0513446i
\(675\) 0 0
\(676\) −24898.5 + 43125.5i −1.41662 + 2.45366i
\(677\) −11442.1 19818.3i −0.649566 1.12508i −0.983227 0.182388i \(-0.941617\pi\)
0.333661 0.942693i \(-0.391716\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 8944.46 0.504418
\(681\) 0 0
\(682\) 14820.0 25669.0i 0.832093 1.44123i
\(683\) −12357.5 + 21403.8i −0.692307 + 1.19911i 0.278773 + 0.960357i \(0.410072\pi\)
−0.971080 + 0.238754i \(0.923261\pi\)
\(684\) 0 0
\(685\) −7752.00 −0.432392
\(686\) 0 0
\(687\) 0 0
\(688\) 2542.00 + 4402.87i 0.140862 + 0.243980i
\(689\) −6433.73 + 11143.6i −0.355741 + 0.616162i
\(690\) 0 0
\(691\) 5300.00 + 9179.87i 0.291782 + 0.505382i 0.974231 0.225552i \(-0.0724184\pi\)
−0.682449 + 0.730933i \(0.739085\pi\)
\(692\) −42481.8 −2.33369
\(693\) 0 0
\(694\) 30742.0 1.68148
\(695\) −3347.63 5798.27i −0.182709 0.316462i
\(696\) 0 0
\(697\) −6498.00 + 11254.9i −0.353127 + 0.611633i
\(698\) −23647.0 40957.9i −1.28231 2.22103i
\(699\) 0 0
\(700\) 0 0
\(701\) −12449.0 −0.670746 −0.335373 0.942085i \(-0.608862\pi\)
−0.335373 + 0.942085i \(0.608862\pi\)
\(702\) 0 0
\(703\) 1860.00 3221.61i 0.0997884 0.172839i
\(704\) 17370.2 30086.1i 0.929921 1.61067i
\(705\) 0 0
\(706\) 23066.0 1.22960
\(707\) 0 0
\(708\) 0 0
\(709\) 6855.00 + 11873.2i 0.363110 + 0.628925i 0.988471 0.151411i \(-0.0483816\pi\)
−0.625361 + 0.780336i \(0.715048\pi\)
\(710\) 8447.55 14631.6i 0.446522 0.773399i
\(711\) 0 0
\(712\) 9519.00 + 16487.4i 0.501039 + 0.867825i
\(713\) 20399.6 1.07149
\(714\) 0 0
\(715\) −31160.0 −1.62982
\(716\) −1486.38 2574.49i −0.0775821 0.134376i
\(717\) 0 0
\(718\) 10507.0 18198.7i 0.546125 0.945916i
\(719\) −1255.36 2174.35i −0.0651142 0.112781i 0.831630 0.555329i \(-0.187408\pi\)
−0.896745 + 0.442548i \(0.854075\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 28154.1 1.45123
\(723\) 0 0
\(724\) −2299.00 + 3981.98i −0.118013 + 0.204405i
\(725\) −5980.41 + 10358.4i −0.306354 + 0.530621i
\(726\) 0 0
\(727\) 620.000 0.0316293 0.0158147 0.999875i \(-0.494966\pi\)
0.0158147 + 0.999875i \(0.494966\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) −2394.00 4146.53i −0.121378 0.210233i
\(731\) −6433.73 + 11143.6i −0.325527 + 0.563829i
\(732\) 0 0
\(733\) 10107.0 + 17505.8i 0.509291 + 0.882119i 0.999942 + 0.0107622i \(0.00342577\pi\)
−0.490651 + 0.871356i \(0.663241\pi\)
\(734\) −51051.4 −2.56722
\(735\) 0 0
\(736\) 31350.0 1.57008
\(737\) 958.958 + 1660.96i 0.0479290 + 0.0830154i
\(738\) 0 0
\(739\) 6162.00 10672.9i 0.306729 0.531270i −0.670916 0.741534i \(-0.734099\pi\)
0.977645 + 0.210263i \(0.0674321\pi\)
\(740\) 8918.31 + 15447.0i 0.443032 + 0.767353i
\(741\) 0 0
\(742\) 0 0
\(743\) −29736.4 −1.46827 −0.734134 0.679005i \(-0.762412\pi\)
−0.734134 + 0.679005i \(0.762412\pi\)
\(744\) 0 0
\(745\) −4332.00 + 7503.24i −0.213037 + 0.368990i
\(746\) −22775.2 + 39447.9i −1.11778 + 1.93605i
\(747\) 0 0
\(748\) 37620.0 1.83894
\(749\) 0 0
\(750\) 0 0
\(751\) −9668.00 16745.5i −0.469761 0.813650i 0.529641 0.848222i \(-0.322326\pi\)
−0.999402 + 0.0345721i \(0.988993\pi\)
\(752\) −7296.80 + 12638.4i −0.353839 + 0.612867i
\(753\) 0 0
\(754\) −43624.0 75559.0i −2.10702 3.64946i
\(755\) 30477.4 1.46912
\(756\) 0 0
\(757\) 15986.0 0.767531 0.383766 0.923431i \(-0.374627\pi\)
0.383766 + 0.923431i \(0.374627\pi\)
\(758\) −1647.66 2853.84i −0.0789523 0.136749i
\(759\) 0 0
\(760\) 1140.00 1974.54i 0.0544107 0.0942421i
\(761\) 18503.5 + 32049.0i 0.881409 + 1.52665i 0.849775 + 0.527146i \(0.176738\pi\)
0.0316342 + 0.999500i \(0.489929\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) −16781.8 −0.794690
\(765\) 0 0
\(766\) −13908.0 + 24089.4i −0.656027 + 1.13627i
\(767\) 6433.73 11143.6i 0.302880 0.524603i
\(768\) 0 0
\(769\) −36070.0 −1.69144 −0.845720 0.533627i \(-0.820829\pi\)
−0.845720 + 0.533627i \(0.820829\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7469.00 12936.7i −0.348206 0.603111i
\(773\) −265.893 + 460.540i −0.0123719 + 0.0214288i −0.872145 0.489247i \(-0.837272\pi\)
0.859773 + 0.510676i \(0.170605\pi\)
\(774\) 0 0
\(775\) 3822.00 + 6619.90i 0.177149 + 0.306831i
\(776\) −10435.2 −0.482735
\(777\) 0 0
\(778\) −1824.00 −0.0840534
\(779\) 1656.38 + 2868.94i 0.0761823 + 0.131952i
\(780\) 0 0
\(781\) 9690.00 16783.6i 0.443963 0.768967i
\(782\) 22361.2 + 38730.7i 1.02255 + 1.77111i
\(783\) 0 0
\(784\) 0 0
\(785\) 4411.21 0.200564
\(786\) 0 0
\(787\) 568.000 983.805i 0.0257268 0.0445602i −0.852875 0.522115i \(-0.825143\pi\)
0.878602 + 0.477554i \(0.158477\pi\)
\(788\) 20617.6 35710.7i 0.932070 1.61439i
\(789\) 0 0
\(790\) −27056.0