Properties

Label 441.4.e.s.226.1
Level $441$
Weight $4$
Character 441.226
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 226.1
Root \(-2.17945 + 3.77492i\) of defining polynomial
Character \(\chi\) \(=\) 441.226
Dual form 441.4.e.s.361.1

$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).

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

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 0.166709 + 0.986006i \(0.446686\pi\)
−0.937261 + 0.348629i \(0.886647\pi\)
\(3\) 0 0
\(4\) −5.50000 9.52628i −0.687500 1.19078i
\(5\) 4.35890 7.54983i 0.389872 0.675278i −0.602560 0.798073i \(-0.705853\pi\)
0.992432 + 0.122796i \(0.0391860\pi\)
\(6\) 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 0.993205 + 0.116379i \(0.0371288\pi\)
−0.395815 + 0.918330i \(0.629538\pi\)
\(12\) 0 0
\(13\) −82.0000 −1.74944 −0.874720 0.484629i \(-0.838954\pi\)
−0.874720 + 0.484629i \(0.838954\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 15.5000 26.8468i 0.242188 0.419481i
\(17\) −39.2301 67.9485i −0.559688 0.969408i −0.997522 0.0703522i \(-0.977588\pi\)
0.437834 0.899056i \(-0.355746\pi\)
\(18\) 0 0
\(19\) −10.0000 + 17.3205i −0.120745 + 0.209137i −0.920062 0.391773i \(-0.871862\pi\)
0.799317 + 0.600910i \(0.205195\pi\)
\(20\) −95.8958 −1.07215
\(21\) 0 0
\(22\) −190.000 −1.84128
\(23\) 65.3835 113.248i 0.592756 1.02668i −0.401103 0.916033i \(-0.631373\pi\)
0.993859 0.110651i \(-0.0352937\pi\)
\(24\) 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 \(-0.214447\pi\)
0.781516 + 0.623885i \(0.214447\pi\)
\(30\) 0 0
\(31\) 78.0000 + 135.100i 0.451910 + 0.782731i 0.998505 0.0546661i \(-0.0174094\pi\)
−0.546595 + 0.837397i \(0.684076\pi\)
\(32\) 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 −0.995240 0.0974576i \(-0.968929\pi\)
0.582021 + 0.813174i \(0.302262\pi\)
\(38\) −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 −0.226161 0.974090i \(-0.572618\pi\)
0.956667 0.291184i \(-0.0940490\pi\)
\(48\) 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 \(-0.101485\pi\)
−0.746259 + 0.665656i \(0.768152\pi\)
\(54\) 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 0.939512 0.342515i \(-0.111279\pi\)
−0.766383 + 0.642384i \(0.777945\pi\)
\(60\) 0 0
\(61\) 395.000 684.160i 0.829091 1.43603i −0.0696607 0.997571i \(-0.522192\pi\)
0.898752 0.438457i \(-0.144475\pi\)
\(62\) −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 0.885386 0.464857i \(-0.153894\pi\)
−0.845271 + 0.534338i \(0.820561\pi\)
\(68\) −431.531 + 747.434i −0.769571 + 1.33294i
\(69\) 0 0
\(70\) 0 0
\(71\) 444.608 0.743172 0.371586 0.928398i \(-0.378814\pi\)
0.371586 + 0.928398i \(0.378814\pi\)
\(72\) 0 0
\(73\) 63.0000 + 109.119i 0.101008 + 0.174951i 0.912100 0.409967i \(-0.134460\pi\)
−0.811092 + 0.584918i \(0.801127\pi\)
\(74\) −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 −0.492966 0.870049i \(-0.664087\pi\)
0.999967 0.00810375i \(-0.00257953\pi\)
\(80\) −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 −0.00190909 + 0.999998i \(0.500608\pi\)
−0.865069 + 0.501652i \(0.832726\pi\)
\(90\) 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 \(-0.637147\pi\)
−0.417653 + 0.908607i \(0.637147\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) 269.500 466.788i 0.269500 0.466788i
\(101\) 204.868 + 354.842i 0.201833 + 0.349585i 0.949119 0.314917i \(-0.101977\pi\)
−0.747286 + 0.664503i \(0.768643\pi\)
\(102\) 0 0
\(103\) −458.000 + 793.279i −0.438137 + 0.758875i −0.997546 0.0700167i \(-0.977695\pi\)
0.559409 + 0.828892i \(0.311028\pi\)
\(104\) −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 \(-0.966284\pi\)
0.588758 + 0.808310i \(0.299617\pi\)
\(108\) 0 0
\(109\) 171.000 + 296.181i 0.150264 + 0.260266i 0.931325 0.364190i \(-0.118654\pi\)
−0.781060 + 0.624456i \(0.785321\pi\)
\(110\) −828.191 + 1434.47i −0.717863 + 1.24337i
\(111\) 0 0
\(112\) 0 0
\(113\) −488.197 −0.406422 −0.203211 0.979135i \(-0.565138\pi\)
−0.203211 + 0.979135i \(0.565138\pi\)
\(114\) 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 −0.499967 0.866044i \(-0.666655\pi\)
1.00000 3.76230e-5i \(-1.19758e-5\pi\)
\(132\) 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 \(-0.0772384\pi\)
−0.693439 + 0.720516i \(0.743905\pi\)
\(138\) 0 0
\(139\) 768.000 0.468640 0.234320 0.972160i \(-0.424714\pi\)
0.234320 + 0.972160i \(0.424714\pi\)
\(140\) 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 \(-0.921420\pi\)
0.696469 + 0.717587i \(0.254753\pi\)
\(150\) 0 0
\(151\) 1748.00 + 3027.62i 0.942054 + 1.63169i 0.761544 + 0.648113i \(0.224442\pi\)
0.180510 + 0.983573i \(0.442225\pi\)
\(152\) −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 \(-0.207718\pi\)
−0.923138 + 0.384469i \(0.874385\pi\)
\(158\) 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 −0.374165 0.927362i \(-0.622071\pi\)
0.990202 0.139645i \(-0.0445961\pi\)
\(164\) −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 −0.0338270 0.999428i \(-0.510770\pi\)
0.882443 0.470419i \(-0.155897\pi\)
\(174\) 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 \(-0.148697\pi\)
−0.836434 + 0.548068i \(0.815364\pi\)
\(180\) 0 0
\(181\) −418.000 −0.171656 −0.0858279 0.996310i \(-0.527354\pi\)
−0.0858279 + 0.996310i \(0.527354\pi\)
\(182\) 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 \(-0.926649\pi\)
0.684588 + 0.728930i \(0.259982\pi\)
\(192\) 0 0
\(193\) −679.000 1176.06i −0.253241 0.438626i 0.711175 0.703015i \(-0.248163\pi\)
−0.964416 + 0.264389i \(0.914830\pi\)
\(194\) 1739.20 3012.38i 0.643646 1.11483i
\(195\) 0 0
\(196\) 0 0
\(197\) 3748.65 1.35574 0.677869 0.735183i \(-0.262904\pi\)
0.677869 + 0.735183i \(0.262904\pi\)
\(198\) 0 0
\(199\) −528.000 914.523i −0.188085 0.325773i 0.756527 0.653963i \(-0.226895\pi\)
−0.944612 + 0.328190i \(0.893561\pi\)
\(200\) 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 \(-0.798362\pi\)
−0.805982 + 0.591940i \(0.798362\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 1064.00 1842.90i 0.313169 0.542425i
\(227\) 810.755 + 1404.27i 0.237056 + 0.410593i 0.959868 0.280451i \(-0.0904842\pi\)
−0.722812 + 0.691045i \(0.757151\pi\)
\(228\) 0 0
\(229\) 1093.00 1893.13i 0.315404 0.546295i −0.664119 0.747626i \(-0.731193\pi\)
0.979523 + 0.201331i \(0.0645267\pi\)
\(230\) 4969.14 1.42459
\(231\) 0 0
\(232\) 3192.00 0.903298
\(233\) 2066.12 3578.62i 0.580927 1.00619i −0.414443 0.910075i \(-0.636024\pi\)
0.995370 0.0961192i \(-0.0306430\pi\)
\(234\) 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 \(-0.727224\pi\)
−0.654746 + 0.755849i \(0.727224\pi\)
\(240\) 0 0
\(241\) 643.000 + 1113.71i 0.171864 + 0.297678i 0.939072 0.343722i \(-0.111688\pi\)
−0.767207 + 0.641399i \(0.778354\pi\)
\(242\) −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 −0.959542 0.281564i \(-0.909147\pi\)
0.723613 + 0.690206i \(0.242480\pi\)
\(258\) 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 −0.988254 0.152822i \(-0.951164\pi\)
0.361779 0.932264i \(-0.382170\pi\)
\(264\) 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 0.545117 0.838360i \(-0.316485\pi\)
−0.998600 + 0.0529046i \(0.983152\pi\)
\(270\) 0 0
\(271\) 1394.00 2414.48i 0.312470 0.541215i −0.666426 0.745571i \(-0.732177\pi\)
0.978897 + 0.204356i \(0.0655102\pi\)
\(272\) −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 0.999982 0.00602561i \(-0.00191802\pi\)
−0.505209 + 0.862997i \(0.668585\pi\)
\(278\) −1673.82 + 2899.14i −0.361111 + 0.625463i
\(279\) 0 0
\(280\) 0 0
\(281\) −1551.77 −0.329433 −0.164717 0.986341i \(-0.552671\pi\)
−0.164717 + 0.986341i \(0.552671\pi\)
\(282\) 0 0
\(283\) −3394.00 5878.58i −0.712906 1.23479i −0.963762 0.266765i \(-0.914045\pi\)
0.250856 0.968024i \(-0.419288\pi\)
\(284\) −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 \(-0.515747\pi\)
−0.0494509 + 0.998777i \(0.515747\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) −2964.00 + 5133.80i −0.543045 + 0.940581i
\(311\) 3269.17 + 5662.38i 0.596070 + 1.03242i 0.993395 + 0.114746i \(0.0366054\pi\)
−0.397325 + 0.917678i \(0.630061\pi\)
\(312\) 0 0
\(313\) 2497.00 4324.93i 0.450923 0.781021i −0.547521 0.836792i \(-0.684428\pi\)
0.998444 + 0.0557711i \(0.0177617\pi\)
\(314\) 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 \(-0.820055\pi\)
0.886124 + 0.463448i \(0.153388\pi\)
\(318\) 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 −0.953235 0.302230i \(-0.902269\pi\)
0.738357 + 0.674410i \(0.235602\pi\)
\(332\) −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 −0.998572 0.0534159i \(-0.982989\pi\)
0.453027 0.891497i \(-0.350344\pi\)
\(348\) 0 0
\(349\) 10850.0 1.66415 0.832073 0.554666i \(-0.187154\pi\)
0.832073 + 0.554666i \(0.187154\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −5225.00 + 9049.97i −0.791175 + 1.37035i
\(353\) 2645.85 + 4582.75i 0.398936 + 0.690978i 0.993595 0.113000i \(-0.0360462\pi\)
−0.594659 + 0.803978i \(0.702713\pi\)
\(354\) 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 \(-0.718028\pi\)
0.987010 + 0.160656i \(0.0513611\pi\)
\(360\) 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 0.895715 + 0.444629i \(0.146664\pi\)
−0.0627973 + 0.998026i \(0.520002\pi\)
\(368\) −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 −0.233538 0.972348i \(-0.575030\pi\)
0.958847 0.283924i \(-0.0916364\pi\)
\(374\) 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 −0.570798 0.821091i \(-0.693366\pi\)
0.996484 + 0.0837802i \(0.0266994\pi\)
\(384\) 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 \(-0.157985\pi\)
−0.852068 + 0.523431i \(0.824652\pi\)
\(390\) 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 \(-0.952861\pi\)
0.622311 + 0.782770i \(0.286194\pi\)
\(398\) 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 \(-0.750501\pi\)
0.965517 + 0.260338i \(0.0838340\pi\)
\(402\) 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 \(-0.192285\pi\)
−0.903420 + 0.428756i \(0.858952\pi\)
\(410\) 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 \(-0.0824171\pi\)
−0.705068 + 0.709139i \(0.749084\pi\)
\(432\) 0 0
\(433\) −5770.00 −0.640389 −0.320195 0.947352i \(-0.603748\pi\)
−0.320195 + 0.947352i \(0.603748\pi\)
\(434\) 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 \(-0.865781\pi\)
0.810650 + 0.585532i \(0.199114\pi\)
\(440\) 4969.14 0.538397
\(441\) 0 0
\(442\) −28044.0 −3.01791
\(443\) 5557.60 9626.04i 0.596048 1.03239i −0.397350 0.917667i \(-0.630070\pi\)
0.993398 0.114719i \(-0.0365966\pi\)
\(444\) 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 \(-0.631455\pi\)
−0.401339 + 0.915930i \(0.631455\pi\)
\(450\) 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 0.159858 + 0.987140i \(0.448896\pi\)
−0.934817 + 0.355129i \(0.884437\pi\)
\(458\) 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 −0.769426 0.638736i \(-0.779458\pi\)
0.937874 + 0.346975i \(0.112791\pi\)
\(468\) 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 0.938586 0.345047i \(-0.112137\pi\)
−0.768112 + 0.640316i \(0.778804\pi\)
\(480\) 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 0.578433 0.815730i \(-0.303665\pi\)
−0.995659 + 0.0930722i \(0.970331\pi\)
\(488\) 5165.30 8946.55i 0.479143 0.829901i
\(489\) 0 0
\(490\) 0 0
\(491\) 5169.65 0.475159 0.237580 0.971368i \(-0.423646\pi\)
0.237580 + 0.971368i \(0.423646\pi\)
\(492\) 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 −0.940759 0.339075i \(-0.889886\pi\)
0.764027 + 0.645184i \(0.223219\pi\)
\(500\) −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 −0.570961 0.820977i \(-0.693429\pi\)
0.996468 + 0.0839787i \(0.0267628\pi\)
\(510\) 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 0.667429 0.744673i \(-0.267395\pi\)
−0.978621 + 0.205674i \(0.934061\pi\)
\(522\) 0 0
\(523\) −1384.00 + 2397.16i −0.115713 + 0.200421i −0.918065 0.396431i \(-0.870249\pi\)
0.802351 + 0.596852i \(0.203582\pi\)
\(524\) −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 0.335502 + 0.942040i \(0.391094\pi\)
−0.983581 + 0.180467i \(0.942239\pi\)
\(542\) 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 −0.865287 0.501276i \(-0.832864\pi\)
−0.00147399 0.999999i \(-0.500469\pi\)
\(558\) 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 0.565625 0.824662i \(-0.308635\pi\)
−0.996991 + 0.0775149i \(0.975301\pi\)
\(564\) 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 \(-0.813489\pi\)
0.895495 + 0.445073i \(0.146822\pi\)
\(570\) 0 0
\(571\) −5614.00 9723.73i −0.411451 0.712654i 0.583598 0.812043i \(-0.301645\pi\)
−0.995049 + 0.0993888i \(0.968311\pi\)
\(572\) −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 \(-0.143105\pi\)
−0.826677 + 0.562677i \(0.809772\pi\)
\(578\) −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 −0.997487 0.0708515i \(-0.977428\pi\)
0.560103 + 0.828423i \(0.310762\pi\)
\(594\) 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 \(-0.0605081\pi\)
−0.654628 + 0.755951i \(0.727175\pi\)
\(600\) 0 0
\(601\) 10758.0 0.730163 0.365082 0.930976i \(-0.381041\pi\)
0.365082 + 0.930976i \(0.381041\pi\)
\(602\) 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 0.249509 + 0.968372i \(0.419731\pi\)
−0.963390 + 0.268105i \(0.913603\pi\)
\(608\) −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 0.944665 0.328038i \(-0.106387\pi\)
−0.756421 + 0.654085i \(0.773054\pi\)
\(614\) 1159.47 2008.26i 0.0762089 0.131998i
\(615\) 0 0
\(616\) 0 0
\(617\) 6747.58 0.440271 0.220135 0.975469i \(-0.429350\pi\)
0.220135 + 0.975469i \(0.429350\pi\)
\(618\) 0 0
\(619\) −940.000 1628.13i −0.0610368 0.105719i 0.833892 0.551927i \(-0.186107\pi\)
−0.894929 + 0.446208i \(0.852774\pi\)
\(620\) −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 −0.919001 0.394255i \(-0.871003\pi\)
0.118066 0.993006i \(-0.462331\pi\)
\(642\) 0 0
\(643\) −24788.0 −1.52029 −0.760143 0.649756i \(-0.774871\pi\)
−0.760143 + 0.649756i \(0.774871\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −3420.00 + 5923.61i −0.208294 + 0.360776i
\(647\) 14236.2 + 24657.8i 0.865041 + 1.49829i 0.867007 + 0.498296i \(0.166041\pi\)
−0.00196599 + 0.999998i \(0.500626\pi\)
\(648\) 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 \(-0.864314\pi\)
0.813340 + 0.581789i \(0.197647\pi\)
\(654\) 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 \(-0.488926\pi\)
0.0347842 + 0.999395i \(0.488926\pi\)
\(660\) 0 0
\(661\) 5795.00 + 10037.2i 0.340998 + 0.590625i 0.984618 0.174720i \(-0.0559019\pi\)
−0.643621 + 0.765345i \(0.722569\pi\)
\(662\) −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 0.333661 + 0.942693i \(0.391716\pi\)
−0.983227 + 0.182388i \(0.941617\pi\)
\(678\) 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 0.971080 + 0.238754i \(0.0767390\pi\)
−0.278773 + 0.960357i \(0.589928\pi\)
\(684\) 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 \(-0.927582\pi\)
0.682449 + 0.730933i \(0.260915\pi\)
\(692\) −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 \(-0.391138\pi\)
0.335373 + 0.942085i \(0.391138\pi\)
\(702\) 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 −0.625361 0.780336i \(-0.715048\pi\)
0.988471 + 0.151411i \(0.0483816\pi\)
\(710\) 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 −0.896745 0.442548i \(-0.854075\pi\)
0.831630 + 0.555329i \(0.187408\pi\)
\(720\) 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 \(-0.505034\pi\)
−0.0158147 + 0.999875i \(0.505034\pi\)
\(728\) 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 0.490651 + 0.871356i \(0.336759\pi\)
−0.999942 + 0.0107622i \(0.996574\pi\)
\(734\) −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 0.977645 0.210263i \(-0.0674321\pi\)
−0.670916 + 0.741534i \(0.734099\pi\)
\(740\) 8918.31 15447.0i 0.443032 0.767353i
\(741\) 0 0
\(742\) 0 0
\(743\) 29736.4 1.46827 0.734134 0.679005i \(-0.237588\pi\)
0.734134 + 0.679005i \(0.237588\pi\)
\(744\) 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 −0.999402 0.0345721i \(-0.988993\pi\)
0.529641 + 0.848222i \(0.322326\pi\)
\(752\) −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 0.0316342 0.999500i \(-0.489929\pi\)
0.849775 0.527146i \(-0.176738\pi\)
\(762\) 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 \(-0.179171\pi\)
0.845720 + 0.533627i \(0.179171\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −7469.00 + 12936.7i −0.348206 + 0.603111i
\(773\) −265.893 460.540i −0.0123719 0.0214288i 0.859773 0.510676i \(-0.170605\pi\)
−0.872145 + 0.489247i \(0.837272\pi\)
\(774\) 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 \(-0.174857\pi\)
−0.878602 + 0.477554i \(0.841523\pi\)
\(788\) −20617.6 35710.7i −0.932070 1.61439i
\(789\) 0 0
\(790\) 27056.0 1.21849