Properties

Label 441.4.e.d.361.1
Level $441$
Weight $4$
Character 441.361
Analytic conductor $26.020$
Analytic rank $0$
Dimension $2$
CM no
Inner twists $2$

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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: \(2\)
Coefficient field: \(\Q(\zeta_{6})\)
Defining polynomial: \(x^{2} - x + 1\)
Coefficient ring: \(\Z[a_1, \ldots, a_{4}]\)
Coefficient ring index: \( 1 \)
Twist minimal: no (minimal twist has level 21)
Sato-Tate group: $\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label 361.1
Root \(0.500000 + 0.866025i\) of defining polynomial
Character \(\chi\) \(=\) 441.361
Dual form 441.4.e.d.226.1

$q$-expansion

\(f(q)\) \(=\) \(q+(-1.50000 - 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(9.00000 + 15.5885i) q^{5} -21.0000 q^{8} +O(q^{10})\) \(q+(-1.50000 - 2.59808i) q^{2} +(-0.500000 + 0.866025i) q^{4} +(9.00000 + 15.5885i) q^{5} -21.0000 q^{8} +(27.0000 - 46.7654i) q^{10} +(-18.0000 + 31.1769i) q^{11} +34.0000 q^{13} +(35.5000 + 61.4878i) q^{16} +(-21.0000 + 36.3731i) q^{17} +(-62.0000 - 107.387i) q^{19} -18.0000 q^{20} +108.000 q^{22} +(-99.5000 + 172.339i) q^{25} +(-51.0000 - 88.3346i) q^{26} -102.000 q^{29} +(-80.0000 + 138.564i) q^{31} +(22.5000 - 38.9711i) q^{32} +126.000 q^{34} +(-199.000 - 344.678i) q^{37} +(-186.000 + 322.161i) q^{38} +(-189.000 - 327.358i) q^{40} -318.000 q^{41} -268.000 q^{43} +(-18.0000 - 31.1769i) q^{44} +(-120.000 - 207.846i) q^{47} +597.000 q^{50} +(-17.0000 + 29.4449i) q^{52} +(-249.000 + 431.281i) q^{53} -648.000 q^{55} +(153.000 + 265.004i) q^{58} +(66.0000 - 114.315i) q^{59} +(199.000 + 344.678i) q^{61} +480.000 q^{62} +433.000 q^{64} +(306.000 + 530.008i) q^{65} +(-46.0000 + 79.6743i) q^{67} +(-21.0000 - 36.3731i) q^{68} +720.000 q^{71} +(-251.000 + 434.745i) q^{73} +(-597.000 + 1034.03i) q^{74} +124.000 q^{76} +(512.000 + 886.810i) q^{79} +(-639.000 + 1106.78i) q^{80} +(477.000 + 826.188i) q^{82} -204.000 q^{83} -756.000 q^{85} +(402.000 + 696.284i) q^{86} +(378.000 - 654.715i) q^{88} +(-177.000 - 306.573i) q^{89} +(-360.000 + 623.538i) q^{94} +(1116.00 - 1932.97i) q^{95} +286.000 q^{97} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 2q - 3q^{2} - q^{4} + 18q^{5} - 42q^{8} + O(q^{10}) \) \( 2q - 3q^{2} - q^{4} + 18q^{5} - 42q^{8} + 54q^{10} - 36q^{11} + 68q^{13} + 71q^{16} - 42q^{17} - 124q^{19} - 36q^{20} + 216q^{22} - 199q^{25} - 102q^{26} - 204q^{29} - 160q^{31} + 45q^{32} + 252q^{34} - 398q^{37} - 372q^{38} - 378q^{40} - 636q^{41} - 536q^{43} - 36q^{44} - 240q^{47} + 1194q^{50} - 34q^{52} - 498q^{53} - 1296q^{55} + 306q^{58} + 132q^{59} + 398q^{61} + 960q^{62} + 866q^{64} + 612q^{65} - 92q^{67} - 42q^{68} + 1440q^{71} - 502q^{73} - 1194q^{74} + 248q^{76} + 1024q^{79} - 1278q^{80} + 954q^{82} - 408q^{83} - 1512q^{85} + 804q^{86} + 756q^{88} - 354q^{89} - 720q^{94} + 2232q^{95} + 572q^{97} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.50000 2.59808i −0.530330 0.918559i −0.999374 0.0353837i \(-0.988735\pi\)
0.469044 0.883175i \(-0.344599\pi\)
\(3\) 0 0
\(4\) −0.500000 + 0.866025i −0.0625000 + 0.108253i
\(5\) 9.00000 + 15.5885i 0.804984 + 1.39427i 0.916302 + 0.400489i \(0.131160\pi\)
−0.111317 + 0.993785i \(0.535507\pi\)
\(6\) 0 0
\(7\) 0 0
\(8\) −21.0000 −0.928078
\(9\) 0 0
\(10\) 27.0000 46.7654i 0.853815 1.47885i
\(11\) −18.0000 + 31.1769i −0.493382 + 0.854563i −0.999971 0.00762479i \(-0.997573\pi\)
0.506589 + 0.862188i \(0.330906\pi\)
\(12\) 0 0
\(13\) 34.0000 0.725377 0.362689 0.931910i \(-0.381859\pi\)
0.362689 + 0.931910i \(0.381859\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 35.5000 + 61.4878i 0.554688 + 0.960747i
\(17\) −21.0000 + 36.3731i −0.299603 + 0.518927i −0.976045 0.217568i \(-0.930187\pi\)
0.676442 + 0.736496i \(0.263521\pi\)
\(18\) 0 0
\(19\) −62.0000 107.387i −0.748620 1.29665i −0.948484 0.316824i \(-0.897384\pi\)
0.199865 0.979824i \(-0.435950\pi\)
\(20\) −18.0000 −0.201246
\(21\) 0 0
\(22\) 108.000 1.04662
\(23\) 0 0 0.866025 0.500000i \(-0.166667\pi\)
−0.866025 + 0.500000i \(0.833333\pi\)
\(24\) 0 0
\(25\) −99.5000 + 172.339i −0.796000 + 1.37871i
\(26\) −51.0000 88.3346i −0.384689 0.666301i
\(27\) 0 0
\(28\) 0 0
\(29\) −102.000 −0.653135 −0.326568 0.945174i \(-0.605892\pi\)
−0.326568 + 0.945174i \(0.605892\pi\)
\(30\) 0 0
\(31\) −80.0000 + 138.564i −0.463498 + 0.802801i −0.999132 0.0416484i \(-0.986739\pi\)
0.535635 + 0.844450i \(0.320072\pi\)
\(32\) 22.5000 38.9711i 0.124296 0.215287i
\(33\) 0 0
\(34\) 126.000 0.635554
\(35\) 0 0
\(36\) 0 0
\(37\) −199.000 344.678i −0.884200 1.53148i −0.846628 0.532185i \(-0.821371\pi\)
−0.0375721 0.999294i \(-0.511962\pi\)
\(38\) −186.000 + 322.161i −0.794031 + 1.37530i
\(39\) 0 0
\(40\) −189.000 327.358i −0.747088 1.29399i
\(41\) −318.000 −1.21130 −0.605649 0.795732i \(-0.707087\pi\)
−0.605649 + 0.795732i \(0.707087\pi\)
\(42\) 0 0
\(43\) −268.000 −0.950456 −0.475228 0.879863i \(-0.657634\pi\)
−0.475228 + 0.879863i \(0.657634\pi\)
\(44\) −18.0000 31.1769i −0.0616728 0.106820i
\(45\) 0 0
\(46\) 0 0
\(47\) −120.000 207.846i −0.372421 0.645053i 0.617516 0.786558i \(-0.288139\pi\)
−0.989937 + 0.141506i \(0.954806\pi\)
\(48\) 0 0
\(49\) 0 0
\(50\) 597.000 1.68857
\(51\) 0 0
\(52\) −17.0000 + 29.4449i −0.0453361 + 0.0785244i
\(53\) −249.000 + 431.281i −0.645335 + 1.11775i 0.338888 + 0.940827i \(0.389949\pi\)
−0.984224 + 0.176927i \(0.943384\pi\)
\(54\) 0 0
\(55\) −648.000 −1.58866
\(56\) 0 0
\(57\) 0 0
\(58\) 153.000 + 265.004i 0.346377 + 0.599943i
\(59\) 66.0000 114.315i 0.145635 0.252247i −0.783975 0.620793i \(-0.786811\pi\)
0.929610 + 0.368546i \(0.120144\pi\)
\(60\) 0 0
\(61\) 199.000 + 344.678i 0.417694 + 0.723467i 0.995707 0.0925602i \(-0.0295051\pi\)
−0.578013 + 0.816028i \(0.696172\pi\)
\(62\) 480.000 0.983227
\(63\) 0 0
\(64\) 433.000 0.845703
\(65\) 306.000 + 530.008i 0.583917 + 1.01137i
\(66\) 0 0
\(67\) −46.0000 + 79.6743i −0.0838775 + 0.145280i −0.904912 0.425598i \(-0.860064\pi\)
0.821035 + 0.570878i \(0.193397\pi\)
\(68\) −21.0000 36.3731i −0.0374504 0.0648659i
\(69\) 0 0
\(70\) 0 0
\(71\) 720.000 1.20350 0.601748 0.798686i \(-0.294471\pi\)
0.601748 + 0.798686i \(0.294471\pi\)
\(72\) 0 0
\(73\) −251.000 + 434.745i −0.402429 + 0.697028i −0.994019 0.109212i \(-0.965167\pi\)
0.591589 + 0.806239i \(0.298501\pi\)
\(74\) −597.000 + 1034.03i −0.937836 + 1.62438i
\(75\) 0 0
\(76\) 124.000 0.187155
\(77\) 0 0
\(78\) 0 0
\(79\) 512.000 + 886.810i 0.729171 + 1.26296i 0.957234 + 0.289315i \(0.0934274\pi\)
−0.228063 + 0.973646i \(0.573239\pi\)
\(80\) −639.000 + 1106.78i −0.893030 + 1.54677i
\(81\) 0 0
\(82\) 477.000 + 826.188i 0.642388 + 1.11265i
\(83\) −204.000 −0.269782 −0.134891 0.990860i \(-0.543068\pi\)
−0.134891 + 0.990860i \(0.543068\pi\)
\(84\) 0 0
\(85\) −756.000 −0.964703
\(86\) 402.000 + 696.284i 0.504056 + 0.873050i
\(87\) 0 0
\(88\) 378.000 654.715i 0.457897 0.793101i
\(89\) −177.000 306.573i −0.210809 0.365131i 0.741159 0.671329i \(-0.234276\pi\)
−0.951968 + 0.306198i \(0.900943\pi\)
\(90\) 0 0
\(91\) 0 0
\(92\) 0 0
\(93\) 0 0
\(94\) −360.000 + 623.538i −0.395012 + 0.684182i
\(95\) 1116.00 1932.97i 1.20525 2.08756i
\(96\) 0 0
\(97\) 286.000 0.299370 0.149685 0.988734i \(-0.452174\pi\)
0.149685 + 0.988734i \(0.452174\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −99.5000 172.339i −0.0995000 0.172339i
\(101\) −207.000 + 358.535i −0.203933 + 0.353223i −0.949792 0.312881i \(-0.898706\pi\)
0.745859 + 0.666104i \(0.232039\pi\)
\(102\) 0 0
\(103\) 28.0000 + 48.4974i 0.0267857 + 0.0463941i 0.879107 0.476624i \(-0.158140\pi\)
−0.852322 + 0.523018i \(0.824806\pi\)
\(104\) −714.000 −0.673206
\(105\) 0 0
\(106\) 1494.00 1.36896
\(107\) 6.00000 + 10.3923i 0.00542095 + 0.00938936i 0.868723 0.495298i \(-0.164941\pi\)
−0.863302 + 0.504687i \(0.831608\pi\)
\(108\) 0 0
\(109\) −739.000 + 1279.99i −0.649389 + 1.12477i 0.333880 + 0.942615i \(0.391642\pi\)
−0.983269 + 0.182159i \(0.941692\pi\)
\(110\) 972.000 + 1683.55i 0.842514 + 1.45928i
\(111\) 0 0
\(112\) 0 0
\(113\) −402.000 −0.334664 −0.167332 0.985901i \(-0.553515\pi\)
−0.167332 + 0.985901i \(0.553515\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 51.0000 88.3346i 0.0408210 0.0707040i
\(117\) 0 0
\(118\) −396.000 −0.308939
\(119\) 0 0
\(120\) 0 0
\(121\) 17.5000 + 30.3109i 0.0131480 + 0.0227730i
\(122\) 597.000 1034.03i 0.443031 0.767353i
\(123\) 0 0
\(124\) −80.0000 138.564i −0.0579372 0.100350i
\(125\) −1332.00 −0.953102
\(126\) 0 0
\(127\) 1280.00 0.894344 0.447172 0.894448i \(-0.352431\pi\)
0.447172 + 0.894448i \(0.352431\pi\)
\(128\) −829.500 1436.74i −0.572798 0.992115i
\(129\) 0 0
\(130\) 918.000 1590.02i 0.619338 1.07272i
\(131\) −882.000 1527.67i −0.588250 1.01888i −0.994462 0.105099i \(-0.966484\pi\)
0.406212 0.913779i \(-0.366849\pi\)
\(132\) 0 0
\(133\) 0 0
\(134\) 276.000 0.177931
\(135\) 0 0
\(136\) 441.000 763.834i 0.278055 0.481605i
\(137\) −1179.00 + 2042.09i −0.735246 + 1.27348i 0.219369 + 0.975642i \(0.429600\pi\)
−0.954615 + 0.297842i \(0.903733\pi\)
\(138\) 0 0
\(139\) 52.0000 0.0317308 0.0158654 0.999874i \(-0.494950\pi\)
0.0158654 + 0.999874i \(0.494950\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −1080.00 1870.61i −0.638251 1.10548i
\(143\) −612.000 + 1060.02i −0.357888 + 0.619881i
\(144\) 0 0
\(145\) −918.000 1590.02i −0.525764 0.910650i
\(146\) 1506.00 0.853681
\(147\) 0 0
\(148\) 398.000 0.221050
\(149\) −873.000 1512.08i −0.479993 0.831372i 0.519744 0.854322i \(-0.326027\pi\)
−0.999737 + 0.0229501i \(0.992694\pi\)
\(150\) 0 0
\(151\) 116.000 200.918i 0.0625162 0.108281i −0.833073 0.553163i \(-0.813421\pi\)
0.895590 + 0.444881i \(0.146754\pi\)
\(152\) 1302.00 + 2255.13i 0.694777 + 1.20339i
\(153\) 0 0
\(154\) 0 0
\(155\) −2880.00 −1.49243
\(156\) 0 0
\(157\) 847.000 1467.05i 0.430560 0.745752i −0.566361 0.824157i \(-0.691649\pi\)
0.996922 + 0.0784048i \(0.0249827\pi\)
\(158\) 1536.00 2660.43i 0.773403 1.33957i
\(159\) 0 0
\(160\) 810.000 0.400226
\(161\) 0 0
\(162\) 0 0
\(163\) 1466.00 + 2539.19i 0.704454 + 1.22015i 0.966888 + 0.255200i \(0.0821413\pi\)
−0.262434 + 0.964950i \(0.584525\pi\)
\(164\) 159.000 275.396i 0.0757062 0.131127i
\(165\) 0 0
\(166\) 306.000 + 530.008i 0.143074 + 0.247811i
\(167\) 1176.00 0.544920 0.272460 0.962167i \(-0.412163\pi\)
0.272460 + 0.962167i \(0.412163\pi\)
\(168\) 0 0
\(169\) −1041.00 −0.473828
\(170\) 1134.00 + 1964.15i 0.511611 + 0.886136i
\(171\) 0 0
\(172\) 134.000 232.095i 0.0594035 0.102890i
\(173\) −435.000 753.442i −0.191170 0.331116i 0.754468 0.656337i \(-0.227895\pi\)
−0.945638 + 0.325220i \(0.894562\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2556.00 −1.09469
\(177\) 0 0
\(178\) −531.000 + 919.719i −0.223596 + 0.387280i
\(179\) −1158.00 + 2005.71i −0.483536 + 0.837509i −0.999821 0.0189075i \(-0.993981\pi\)
0.516285 + 0.856417i \(0.327315\pi\)
\(180\) 0 0
\(181\) 106.000 0.0435299 0.0217650 0.999763i \(-0.493071\pi\)
0.0217650 + 0.999763i \(0.493071\pi\)
\(182\) 0 0
\(183\) 0 0
\(184\) 0 0
\(185\) 3582.00 6204.21i 1.42353 2.46563i
\(186\) 0 0
\(187\) −756.000 1309.43i −0.295637 0.512059i
\(188\) 240.000 0.0931053
\(189\) 0 0
\(190\) −6696.00 −2.55673
\(191\) −564.000 976.877i −0.213663 0.370075i 0.739195 0.673491i \(-0.235206\pi\)
−0.952858 + 0.303416i \(0.901873\pi\)
\(192\) 0 0
\(193\) −2017.00 + 3493.55i −0.752263 + 1.30296i 0.194460 + 0.980910i \(0.437705\pi\)
−0.946723 + 0.322048i \(0.895629\pi\)
\(194\) −429.000 743.050i −0.158765 0.274989i
\(195\) 0 0
\(196\) 0 0
\(197\) 1314.00 0.475221 0.237611 0.971360i \(-0.423636\pi\)
0.237611 + 0.971360i \(0.423636\pi\)
\(198\) 0 0
\(199\) 2548.00 4413.27i 0.907653 1.57210i 0.0903369 0.995911i \(-0.471206\pi\)
0.817316 0.576190i \(-0.195461\pi\)
\(200\) 2089.50 3619.12i 0.738750 1.27955i
\(201\) 0 0
\(202\) 1242.00 0.432608
\(203\) 0 0
\(204\) 0 0
\(205\) −2862.00 4957.13i −0.975077 1.68888i
\(206\) 84.0000 145.492i 0.0284105 0.0492084i
\(207\) 0 0
\(208\) 1207.00 + 2090.59i 0.402358 + 0.696904i
\(209\) 4464.00 1.47742
\(210\) 0 0
\(211\) −3076.00 −1.00360 −0.501802 0.864982i \(-0.667330\pi\)
−0.501802 + 0.864982i \(0.667330\pi\)
\(212\) −249.000 431.281i −0.0806669 0.139719i
\(213\) 0 0
\(214\) 18.0000 31.1769i 0.00574979 0.00995893i
\(215\) −2412.00 4177.71i −0.765102 1.32520i
\(216\) 0 0
\(217\) 0 0
\(218\) 4434.00 1.37756
\(219\) 0 0
\(220\) 324.000 561.184i 0.0992913 0.171977i
\(221\) −714.000 + 1236.68i −0.217325 + 0.376418i
\(222\) 0 0
\(223\) 1888.00 0.566950 0.283475 0.958980i \(-0.408513\pi\)
0.283475 + 0.958980i \(0.408513\pi\)
\(224\) 0 0
\(225\) 0 0
\(226\) 603.000 + 1044.43i 0.177482 + 0.307408i
\(227\) 2358.00 4084.18i 0.689454 1.19417i −0.282561 0.959249i \(-0.591184\pi\)
0.972015 0.234919i \(-0.0754826\pi\)
\(228\) 0 0
\(229\) −845.000 1463.58i −0.243839 0.422342i 0.717965 0.696079i \(-0.245074\pi\)
−0.961805 + 0.273737i \(0.911740\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 2142.00 0.606160
\(233\) 69.0000 + 119.512i 0.0194006 + 0.0336028i 0.875563 0.483104i \(-0.160491\pi\)
−0.856162 + 0.516707i \(0.827158\pi\)
\(234\) 0 0
\(235\) 2160.00 3741.23i 0.599587 1.03851i
\(236\) 66.0000 + 114.315i 0.0182044 + 0.0315309i
\(237\) 0 0
\(238\) 0 0
\(239\) −1896.00 −0.513147 −0.256573 0.966525i \(-0.582594\pi\)
−0.256573 + 0.966525i \(0.582594\pi\)
\(240\) 0 0
\(241\) −1799.00 + 3115.96i −0.480846 + 0.832849i −0.999758 0.0219782i \(-0.993004\pi\)
0.518913 + 0.854827i \(0.326337\pi\)
\(242\) 52.5000 90.9327i 0.0139456 0.0241544i
\(243\) 0 0
\(244\) −398.000 −0.104424
\(245\) 0 0
\(246\) 0 0
\(247\) −2108.00 3651.16i −0.543032 0.940558i
\(248\) 1680.00 2909.85i 0.430162 0.745062i
\(249\) 0 0
\(250\) 1998.00 + 3460.64i 0.505458 + 0.875480i
\(251\) −3060.00 −0.769504 −0.384752 0.923020i \(-0.625713\pi\)
−0.384752 + 0.923020i \(0.625713\pi\)
\(252\) 0 0
\(253\) 0 0
\(254\) −1920.00 3325.54i −0.474297 0.821507i
\(255\) 0 0
\(256\) −756.500 + 1310.30i −0.184692 + 0.319897i
\(257\) 3411.00 + 5908.03i 0.827908 + 1.43398i 0.899676 + 0.436557i \(0.143802\pi\)
−0.0717686 + 0.997421i \(0.522864\pi\)
\(258\) 0 0
\(259\) 0 0
\(260\) −612.000 −0.145979
\(261\) 0 0
\(262\) −2646.00 + 4583.01i −0.623933 + 1.08068i
\(263\) 1296.00 2244.74i 0.303858 0.526298i −0.673148 0.739508i \(-0.735058\pi\)
0.977007 + 0.213209i \(0.0683917\pi\)
\(264\) 0 0
\(265\) −8964.00 −2.07794
\(266\) 0 0
\(267\) 0 0
\(268\) −46.0000 79.6743i −0.0104847 0.0181600i
\(269\) −4107.00 + 7113.53i −0.930886 + 1.61234i −0.149074 + 0.988826i \(0.547629\pi\)
−0.781811 + 0.623515i \(0.785704\pi\)
\(270\) 0 0
\(271\) −2672.00 4628.04i −0.598939 1.03739i −0.992978 0.118299i \(-0.962256\pi\)
0.394039 0.919094i \(-0.371077\pi\)
\(272\) −2982.00 −0.664744
\(273\) 0 0
\(274\) 7074.00 1.55969
\(275\) −3582.00 6204.21i −0.785464 1.36046i
\(276\) 0 0
\(277\) 3257.00 5641.29i 0.706477 1.22365i −0.259679 0.965695i \(-0.583617\pi\)
0.966156 0.257959i \(-0.0830500\pi\)
\(278\) −78.0000 135.100i −0.0168278 0.0291466i
\(279\) 0 0
\(280\) 0 0
\(281\) −6618.00 −1.40497 −0.702485 0.711698i \(-0.747926\pi\)
−0.702485 + 0.711698i \(0.747926\pi\)
\(282\) 0 0
\(283\) 1630.00 2823.24i 0.342380 0.593019i −0.642494 0.766290i \(-0.722100\pi\)
0.984874 + 0.173271i \(0.0554338\pi\)
\(284\) −360.000 + 623.538i −0.0752186 + 0.130282i
\(285\) 0 0
\(286\) 3672.00 0.759195
\(287\) 0 0
\(288\) 0 0
\(289\) 1574.50 + 2727.11i 0.320476 + 0.555081i
\(290\) −2754.00 + 4770.07i −0.557657 + 0.965890i
\(291\) 0 0
\(292\) −251.000 434.745i −0.0503036 0.0871285i
\(293\) 5118.00 1.02047 0.510233 0.860036i \(-0.329559\pi\)
0.510233 + 0.860036i \(0.329559\pi\)
\(294\) 0 0
\(295\) 2376.00 0.468936
\(296\) 4179.00 + 7238.24i 0.820606 + 1.42133i
\(297\) 0 0
\(298\) −2619.00 + 4536.24i −0.509109 + 0.881803i
\(299\) 0 0
\(300\) 0 0
\(301\) 0 0
\(302\) −696.000 −0.132617
\(303\) 0 0
\(304\) 4402.00 7624.49i 0.830500 1.43847i
\(305\) −3582.00 + 6204.21i −0.672475 + 1.16476i
\(306\) 0 0
\(307\) −452.000 −0.0840293 −0.0420147 0.999117i \(-0.513378\pi\)
−0.0420147 + 0.999117i \(0.513378\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4320.00 + 7482.46i 0.791482 + 1.37089i
\(311\) −2508.00 + 4343.98i −0.457285 + 0.792041i −0.998816 0.0486397i \(-0.984511\pi\)
0.541531 + 0.840681i \(0.317845\pi\)
\(312\) 0 0
\(313\) 2701.00 + 4678.27i 0.487762 + 0.844829i 0.999901 0.0140739i \(-0.00448001\pi\)
−0.512139 + 0.858903i \(0.671147\pi\)
\(314\) −5082.00 −0.913356
\(315\) 0 0
\(316\) −1024.00 −0.182293
\(317\) 5043.00 + 8734.73i 0.893511 + 1.54761i 0.835636 + 0.549283i \(0.185099\pi\)
0.0578751 + 0.998324i \(0.481567\pi\)
\(318\) 0 0
\(319\) 1836.00 3180.05i 0.322245 0.558145i
\(320\) 3897.00 + 6749.80i 0.680778 + 1.17914i
\(321\) 0 0
\(322\) 0 0
\(323\) 5208.00 0.897154
\(324\) 0 0
\(325\) −3383.00 + 5859.53i −0.577400 + 1.00009i
\(326\) 4398.00 7617.56i 0.747186 1.29416i
\(327\) 0 0
\(328\) 6678.00 1.12418
\(329\) 0 0
\(330\) 0 0
\(331\) 4022.00 + 6966.31i 0.667883 + 1.15681i 0.978495 + 0.206270i \(0.0661325\pi\)
−0.310613 + 0.950537i \(0.600534\pi\)
\(332\) 102.000 176.669i 0.0168614 0.0292048i
\(333\) 0 0
\(334\) −1764.00 3055.34i −0.288987 0.500541i
\(335\) −1656.00 −0.270080
\(336\) 0 0
\(337\) 4178.00 0.675342 0.337671 0.941264i \(-0.390361\pi\)
0.337671 + 0.941264i \(0.390361\pi\)
\(338\) 1561.50 + 2704.60i 0.251285 + 0.435239i
\(339\) 0 0
\(340\) 378.000 654.715i 0.0602939 0.104432i
\(341\) −2880.00 4988.31i −0.457363 0.792176i
\(342\) 0 0
\(343\) 0 0
\(344\) 5628.00 0.882097
\(345\) 0 0
\(346\) −1305.00 + 2260.33i −0.202767 + 0.351202i
\(347\) 78.0000 135.100i 0.0120670 0.0209007i −0.859929 0.510414i \(-0.829492\pi\)
0.871996 + 0.489513i \(0.162826\pi\)
\(348\) 0 0
\(349\) 12418.0 1.90464 0.952321 0.305097i \(-0.0986888\pi\)
0.952321 + 0.305097i \(0.0986888\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) 810.000 + 1402.96i 0.122651 + 0.212438i
\(353\) 3915.00 6780.98i 0.590296 1.02242i −0.403897 0.914805i \(-0.632344\pi\)
0.994192 0.107618i \(-0.0343222\pi\)
\(354\) 0 0
\(355\) 6480.00 + 11223.7i 0.968796 + 1.67800i
\(356\) 354.000 0.0527021
\(357\) 0 0
\(358\) 6948.00 1.02574
\(359\) −4656.00 8064.43i −0.684497 1.18558i −0.973595 0.228283i \(-0.926689\pi\)
0.289098 0.957299i \(-0.406645\pi\)
\(360\) 0 0
\(361\) −4258.50 + 7375.94i −0.620863 + 1.07537i
\(362\) −159.000 275.396i −0.0230852 0.0399848i
\(363\) 0 0
\(364\) 0 0
\(365\) −9036.00 −1.29580
\(366\) 0 0
\(367\) −1880.00 + 3256.26i −0.267398 + 0.463148i −0.968189 0.250219i \(-0.919497\pi\)
0.700791 + 0.713367i \(0.252831\pi\)
\(368\) 0 0
\(369\) 0 0
\(370\) −21492.0 −3.01977
\(371\) 0 0
\(372\) 0 0
\(373\) −2935.00 5083.57i −0.407422 0.705676i 0.587178 0.809458i \(-0.300239\pi\)
−0.994600 + 0.103782i \(0.966906\pi\)
\(374\) −2268.00 + 3928.29i −0.313571 + 0.543121i
\(375\) 0 0
\(376\) 2520.00 + 4364.77i 0.345636 + 0.598659i
\(377\) −3468.00 −0.473769
\(378\) 0 0
\(379\) −1852.00 −0.251005 −0.125502 0.992093i \(-0.540054\pi\)
−0.125502 + 0.992093i \(0.540054\pi\)
\(380\) 1116.00 + 1932.97i 0.150657 + 0.260945i
\(381\) 0 0
\(382\) −1692.00 + 2930.63i −0.226624 + 0.392524i
\(383\) −1080.00 1870.61i −0.144087 0.249566i 0.784945 0.619566i \(-0.212691\pi\)
−0.929032 + 0.369999i \(0.879358\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 12102.0 1.59579
\(387\) 0 0
\(388\) −143.000 + 247.683i −0.0187106 + 0.0324078i
\(389\) −3393.00 + 5876.85i −0.442241 + 0.765985i −0.997855 0.0654557i \(-0.979150\pi\)
0.555614 + 0.831440i \(0.312483\pi\)
\(390\) 0 0
\(391\) 0 0
\(392\) 0 0
\(393\) 0 0
\(394\) −1971.00 3413.87i −0.252024 0.436519i
\(395\) −9216.00 + 15962.6i −1.17394 + 2.03333i
\(396\) 0 0
\(397\) −3257.00 5641.29i −0.411748 0.713169i 0.583333 0.812233i \(-0.301748\pi\)
−0.995081 + 0.0990641i \(0.968415\pi\)
\(398\) −15288.0 −1.92542
\(399\) 0 0
\(400\) −14129.0 −1.76612
\(401\) 1665.00 + 2883.86i 0.207347 + 0.359135i 0.950878 0.309566i \(-0.100184\pi\)
−0.743531 + 0.668701i \(0.766850\pi\)
\(402\) 0 0
\(403\) −2720.00 + 4711.18i −0.336211 + 0.582334i
\(404\) −207.000 358.535i −0.0254917 0.0441529i
\(405\) 0 0
\(406\) 0 0
\(407\) 14328.0 1.74499
\(408\) 0 0
\(409\) −2699.00 + 4674.81i −0.326301 + 0.565169i −0.981775 0.190048i \(-0.939136\pi\)
0.655474 + 0.755218i \(0.272469\pi\)
\(410\) −8586.00 + 14871.4i −1.03423 + 1.79133i
\(411\) 0 0
\(412\) −56.0000 −0.00669641
\(413\) 0 0
\(414\) 0 0
\(415\) −1836.00 3180.05i −0.217170 0.376150i
\(416\) 765.000 1325.02i 0.0901616 0.156164i
\(417\) 0 0
\(418\) −6696.00 11597.8i −0.783522 1.35710i
\(419\) 13092.0 1.52646 0.763229 0.646128i \(-0.223613\pi\)
0.763229 + 0.646128i \(0.223613\pi\)
\(420\) 0 0
\(421\) −322.000 −0.0372763 −0.0186381 0.999826i \(-0.505933\pi\)
−0.0186381 + 0.999826i \(0.505933\pi\)
\(422\) 4614.00 + 7991.68i 0.532242 + 0.921870i
\(423\) 0 0
\(424\) 5229.00 9056.89i 0.598921 1.03736i
\(425\) −4179.00 7238.24i −0.476968 0.826132i
\(426\) 0 0
\(427\) 0 0
\(428\) −12.0000 −0.00135524
\(429\) 0 0
\(430\) −7236.00 + 12533.1i −0.811514 + 1.40558i
\(431\) 1308.00 2265.52i 0.146181 0.253193i −0.783632 0.621226i \(-0.786635\pi\)
0.929813 + 0.368032i \(0.119968\pi\)
\(432\) 0 0
\(433\) −4322.00 −0.479681 −0.239841 0.970812i \(-0.577095\pi\)
−0.239841 + 0.970812i \(0.577095\pi\)
\(434\) 0 0
\(435\) 0 0
\(436\) −739.000 1279.99i −0.0811736 0.140597i
\(437\) 0 0
\(438\) 0 0
\(439\) −4508.00 7808.09i −0.490103 0.848883i 0.509832 0.860274i \(-0.329707\pi\)
−0.999935 + 0.0113909i \(0.996374\pi\)
\(440\) 13608.0 1.47440
\(441\) 0 0
\(442\) 4284.00 0.461016
\(443\) −2634.00 4562.22i −0.282495 0.489295i 0.689504 0.724282i \(-0.257829\pi\)
−0.971999 + 0.234987i \(0.924495\pi\)
\(444\) 0 0
\(445\) 3186.00 5518.31i 0.339395 0.587850i
\(446\) −2832.00 4905.17i −0.300671 0.520777i
\(447\) 0 0
\(448\) 0 0
\(449\) 5310.00 0.558117 0.279058 0.960274i \(-0.409978\pi\)
0.279058 + 0.960274i \(0.409978\pi\)
\(450\) 0 0
\(451\) 5724.00 9914.26i 0.597633 1.03513i
\(452\) 201.000 348.142i 0.0209165 0.0362284i
\(453\) 0 0
\(454\) −14148.0 −1.46255
\(455\) 0 0
\(456\) 0 0
\(457\) −7885.00 13657.2i −0.807100 1.39794i −0.914864 0.403762i \(-0.867702\pi\)
0.107764 0.994177i \(-0.465631\pi\)
\(458\) −2535.00 + 4390.75i −0.258631 + 0.447961i
\(459\) 0 0
\(460\) 0 0
\(461\) −5370.00 −0.542529 −0.271264 0.962505i \(-0.587442\pi\)
−0.271264 + 0.962505i \(0.587442\pi\)
\(462\) 0 0
\(463\) −3328.00 −0.334050 −0.167025 0.985953i \(-0.553416\pi\)
−0.167025 + 0.985953i \(0.553416\pi\)
\(464\) −3621.00 6271.76i −0.362286 0.627498i
\(465\) 0 0
\(466\) 207.000 358.535i 0.0205774 0.0356412i
\(467\) −2274.00 3938.68i −0.225328 0.390280i 0.731090 0.682281i \(-0.239012\pi\)
−0.956418 + 0.292002i \(0.905679\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) −12960.0 −1.27192
\(471\) 0 0
\(472\) −1386.00 + 2400.62i −0.135161 + 0.234105i
\(473\) 4824.00 8355.41i 0.468938 0.812225i
\(474\) 0 0
\(475\) 24676.0 2.38361
\(476\) 0 0
\(477\) 0 0
\(478\) 2844.00 + 4925.95i 0.272137 + 0.471355i
\(479\) 4032.00 6983.63i 0.384607 0.666159i −0.607108 0.794620i \(-0.707670\pi\)
0.991715 + 0.128461i \(0.0410036\pi\)
\(480\) 0 0
\(481\) −6766.00 11719.1i −0.641378 1.11090i
\(482\) 10794.0 1.02003
\(483\) 0 0
\(484\) −35.0000 −0.00328700
\(485\) 2574.00 + 4458.30i 0.240988 + 0.417404i
\(486\) 0 0
\(487\) −8308.00 + 14389.9i −0.773042 + 1.33895i 0.162847 + 0.986651i \(0.447932\pi\)
−0.935888 + 0.352296i \(0.885401\pi\)
\(488\) −4179.00 7238.24i −0.387653 0.671434i
\(489\) 0 0
\(490\) 0 0
\(491\) 7140.00 0.656260 0.328130 0.944633i \(-0.393582\pi\)
0.328130 + 0.944633i \(0.393582\pi\)
\(492\) 0 0
\(493\) 2142.00 3710.05i 0.195681 0.338930i
\(494\) −6324.00 + 10953.5i −0.575972 + 0.997613i
\(495\) 0 0
\(496\) −11360.0 −1.02839
\(497\) 0 0
\(498\) 0 0
\(499\) 4562.00 + 7901.62i 0.409265 + 0.708868i 0.994808 0.101774i \(-0.0324519\pi\)
−0.585543 + 0.810642i \(0.699119\pi\)
\(500\) 666.000 1153.55i 0.0595689 0.103176i
\(501\) 0 0
\(502\) 4590.00 + 7950.11i 0.408091 + 0.706834i
\(503\) −6552.00 −0.580794 −0.290397 0.956906i \(-0.593787\pi\)
−0.290397 + 0.956906i \(0.593787\pi\)
\(504\) 0 0
\(505\) −7452.00 −0.656653
\(506\) 0 0
\(507\) 0 0
\(508\) −640.000 + 1108.51i −0.0558965 + 0.0968155i
\(509\) −1395.00 2416.21i −0.121478 0.210406i 0.798873 0.601500i \(-0.205430\pi\)
−0.920351 + 0.391094i \(0.872097\pi\)
\(510\) 0 0
\(511\) 0 0
\(512\) −8733.00 −0.753804
\(513\) 0 0
\(514\) 10233.0 17724.1i 0.878129 1.52096i
\(515\) −504.000 + 872.954i −0.0431241 + 0.0746931i
\(516\) 0 0
\(517\) 8640.00 0.734984
\(518\) 0 0
\(519\) 0 0
\(520\) −6426.00 11130.2i −0.541921 0.938634i
\(521\) 7431.00 12870.9i 0.624871 1.08231i −0.363694 0.931518i \(-0.618485\pi\)
0.988566 0.150791i \(-0.0481820\pi\)
\(522\) 0 0
\(523\) 8830.00 + 15294.0i 0.738258 + 1.27870i 0.953279 + 0.302091i \(0.0976846\pi\)
−0.215021 + 0.976609i \(0.568982\pi\)
\(524\) 1764.00 0.147062
\(525\) 0 0
\(526\) −7776.00 −0.644581
\(527\) −3360.00 5819.69i −0.277730 0.481043i
\(528\) 0 0
\(529\) 6083.50 10536.9i 0.500000 0.866025i
\(530\) 13446.0 + 23289.2i 1.10199 + 1.90871i
\(531\) 0 0
\(532\) 0 0
\(533\) −10812.0 −0.878649
\(534\) 0 0
\(535\) −108.000 + 187.061i −0.00872756 + 0.0151166i
\(536\) 966.000 1673.16i 0.0778449 0.134831i
\(537\) 0 0
\(538\) 24642.0 1.97471
\(539\) 0 0
\(540\) 0 0
\(541\) 9917.00 + 17176.7i 0.788106 + 1.36504i 0.927126 + 0.374749i \(0.122271\pi\)
−0.139021 + 0.990290i \(0.544395\pi\)
\(542\) −8016.00 + 13884.1i −0.635271 + 1.10032i
\(543\) 0 0
\(544\) 945.000 + 1636.79i 0.0744789 + 0.129001i
\(545\) −26604.0 −2.09099
\(546\) 0 0
\(547\) 20972.0 1.63930 0.819651 0.572863i \(-0.194167\pi\)
0.819651 + 0.572863i \(0.194167\pi\)
\(548\) −1179.00 2042.09i −0.0919058 0.159186i
\(549\) 0 0
\(550\) −10746.0 + 18612.6i −0.833111 + 1.44299i
\(551\) 6324.00 + 10953.5i 0.488950 + 0.846886i
\(552\) 0 0
\(553\) 0 0
\(554\) −19542.0 −1.49866
\(555\) 0 0
\(556\) −26.0000 + 45.0333i −0.00198318 + 0.00343496i
\(557\) 10587.0 18337.2i 0.805360 1.39492i −0.110688 0.993855i \(-0.535305\pi\)
0.916048 0.401069i \(-0.131361\pi\)
\(558\) 0 0
\(559\) −9112.00 −0.689439
\(560\) 0 0
\(561\) 0 0
\(562\) 9927.00 + 17194.1i 0.745098 + 1.29055i
\(563\) 8886.00 15391.0i 0.665187 1.15214i −0.314048 0.949407i \(-0.601685\pi\)
0.979235 0.202730i \(-0.0649815\pi\)
\(564\) 0 0
\(565\) −3618.00 6266.56i −0.269399 0.466613i
\(566\) −9780.00 −0.726297
\(567\) 0 0
\(568\) −15120.0 −1.11694
\(569\) 4125.00 + 7144.71i 0.303917 + 0.526400i 0.977020 0.213149i \(-0.0683720\pi\)
−0.673102 + 0.739549i \(0.735039\pi\)
\(570\) 0 0
\(571\) −10378.0 + 17975.2i −0.760606 + 1.31741i 0.181933 + 0.983311i \(0.441765\pi\)
−0.942539 + 0.334097i \(0.891569\pi\)
\(572\) −612.000 1060.02i −0.0447360 0.0774851i
\(573\) 0 0
\(574\) 0 0
\(575\) 0 0
\(576\) 0 0
\(577\) 1.00000 1.73205i 7.21500e−5 0.000124967i −0.865989 0.500062i \(-0.833310\pi\)
0.866061 + 0.499938i \(0.166644\pi\)
\(578\) 4723.50 8181.34i 0.339916 0.588753i
\(579\) 0 0
\(580\) 1836.00 0.131441
\(581\) 0 0
\(582\) 0 0
\(583\) −8964.00 15526.1i −0.636794 1.10296i
\(584\) 5271.00 9129.64i 0.373485 0.646896i
\(585\) 0 0
\(586\) −7677.00 13297.0i −0.541184 0.937359i
\(587\) 26364.0 1.85376 0.926881 0.375354i \(-0.122479\pi\)
0.926881 + 0.375354i \(0.122479\pi\)
\(588\) 0 0
\(589\) 19840.0 1.38793
\(590\) −3564.00 6173.03i −0.248691 0.430745i
\(591\) 0 0
\(592\) 14129.0 24472.1i 0.980909 1.69898i
\(593\) −1149.00 1990.13i −0.0795679 0.137816i 0.823496 0.567323i \(-0.192021\pi\)
−0.903064 + 0.429507i \(0.858687\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 1746.00 0.119998
\(597\) 0 0
\(598\) 0 0
\(599\) 1536.00 2660.43i 0.104773 0.181473i −0.808872 0.587984i \(-0.799922\pi\)
0.913646 + 0.406512i \(0.133255\pi\)
\(600\) 0 0
\(601\) −24554.0 −1.66652 −0.833260 0.552881i \(-0.813528\pi\)
−0.833260 + 0.552881i \(0.813528\pi\)
\(602\) 0 0
\(603\) 0 0
\(604\) 116.000 + 200.918i 0.00781452 + 0.0135352i
\(605\) −315.000 + 545.596i −0.0211679 + 0.0366639i
\(606\) 0 0
\(607\) 8416.00 + 14576.9i 0.562759 + 0.974728i 0.997254 + 0.0740535i \(0.0235935\pi\)
−0.434495 + 0.900674i \(0.643073\pi\)
\(608\) −5580.00 −0.372202
\(609\) 0 0
\(610\) 21492.0 1.42653
\(611\) −4080.00 7066.77i −0.270146 0.467906i
\(612\) 0 0
\(613\) 1241.00 2149.48i 0.0817676 0.141626i −0.822242 0.569139i \(-0.807277\pi\)
0.904009 + 0.427513i \(0.140610\pi\)
\(614\) 678.000 + 1174.33i 0.0445633 + 0.0771859i
\(615\) 0 0
\(616\) 0 0
\(617\) 15798.0 1.03080 0.515400 0.856950i \(-0.327643\pi\)
0.515400 + 0.856950i \(0.327643\pi\)
\(618\) 0 0
\(619\) −7730.00 + 13388.8i −0.501930 + 0.869369i 0.498067 + 0.867138i \(0.334043\pi\)
−0.999998 + 0.00223050i \(0.999290\pi\)
\(620\) 1440.00 2494.15i 0.0932771 0.161561i
\(621\) 0 0
\(622\) 15048.0 0.970048
\(623\) 0 0
\(624\) 0 0
\(625\) 449.500 + 778.557i 0.0287680 + 0.0498276i
\(626\) 8103.00 14034.8i 0.517350 0.896076i
\(627\) 0 0
\(628\) 847.000 + 1467.05i 0.0538200 + 0.0932190i
\(629\) 16716.0 1.05964
\(630\) 0 0
\(631\) −7720.00 −0.487050 −0.243525 0.969895i \(-0.578304\pi\)
−0.243525 + 0.969895i \(0.578304\pi\)
\(632\) −10752.0 18623.0i −0.676727 1.17213i
\(633\) 0 0
\(634\) 15129.0 26204.2i 0.947712 1.64149i
\(635\) 11520.0 + 19953.2i 0.719933 + 1.24696i
\(636\) 0 0
\(637\) 0 0
\(638\) −11016.0 −0.683586
\(639\) 0 0
\(640\) 14931.0 25861.3i 0.922187 1.59727i
\(641\) −8631.00 + 14949.3i −0.531832 + 0.921159i 0.467478 + 0.884005i \(0.345163\pi\)
−0.999310 + 0.0371545i \(0.988171\pi\)
\(642\) 0 0
\(643\) 12220.0 0.749471 0.374735 0.927132i \(-0.377734\pi\)
0.374735 + 0.927132i \(0.377734\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −7812.00 13530.8i −0.475788 0.824089i
\(647\) −6780.00 + 11743.3i −0.411977 + 0.713566i −0.995106 0.0988143i \(-0.968495\pi\)
0.583129 + 0.812380i \(0.301828\pi\)
\(648\) 0 0
\(649\) 2376.00 + 4115.35i 0.143707 + 0.248909i
\(650\) 20298.0 1.22485
\(651\) 0 0
\(652\) −2932.00 −0.176113
\(653\) 11547.0 + 20000.0i 0.691989 + 1.19856i 0.971185 + 0.238326i \(0.0765988\pi\)
−0.279196 + 0.960234i \(0.590068\pi\)
\(654\) 0 0
\(655\) 15876.0 27498.0i 0.947064 1.64036i
\(656\) −11289.0 19553.1i −0.671892 1.16375i
\(657\) 0 0
\(658\) 0 0
\(659\) −22548.0 −1.33285 −0.666423 0.745574i \(-0.732175\pi\)
−0.666423 + 0.745574i \(0.732175\pi\)
\(660\) 0 0
\(661\) 8731.00 15122.5i 0.513762 0.889862i −0.486111 0.873897i \(-0.661585\pi\)
0.999873 0.0159643i \(-0.00508182\pi\)
\(662\) 12066.0 20898.9i 0.708396 1.22698i
\(663\) 0 0
\(664\) 4284.00 0.250379
\(665\) 0 0
\(666\) 0 0
\(667\) 0 0
\(668\) −588.000 + 1018.45i −0.0340575 + 0.0589893i
\(669\) 0 0
\(670\) 2484.00 + 4302.41i 0.143232 + 0.248085i
\(671\) −14328.0 −0.824331
\(672\) 0 0
\(673\) −22462.0 −1.28655 −0.643274 0.765636i \(-0.722424\pi\)
−0.643274 + 0.765636i \(0.722424\pi\)
\(674\) −6267.00 10854.8i −0.358154 0.620341i
\(675\) 0 0
\(676\) 520.500 901.532i 0.0296142 0.0512934i
\(677\) 12777.0 + 22130.4i 0.725347 + 1.25634i 0.958831 + 0.283977i \(0.0916541\pi\)
−0.233484 + 0.972361i \(0.575013\pi\)
\(678\) 0 0
\(679\) 0 0
\(680\) 15876.0 0.895319
\(681\) 0 0
\(682\) −8640.00 + 14964.9i −0.485107 + 0.840229i
\(683\) 4638.00 8033.25i 0.259836 0.450050i −0.706362 0.707851i \(-0.749665\pi\)
0.966198 + 0.257802i \(0.0829981\pi\)
\(684\) 0 0
\(685\) −42444.0 −2.36745
\(686\) 0 0
\(687\) 0 0
\(688\) −9514.00 16478.7i −0.527206 0.913148i
\(689\) −8466.00 + 14663.5i −0.468112 + 0.810793i
\(690\) 0 0
\(691\) 13690.0 + 23711.8i 0.753679 + 1.30541i 0.946028 + 0.324084i \(0.105056\pi\)
−0.192349 + 0.981326i \(0.561611\pi\)
\(692\) 870.000 0.0477925
\(693\) 0 0
\(694\) −468.000 −0.0255980
\(695\) 468.000 + 810.600i 0.0255428 + 0.0442414i
\(696\) 0 0
\(697\) 6678.00 11566.6i 0.362909 0.628576i
\(698\) −18627.0 32262.9i −1.01009 1.74953i
\(699\) 0 0
\(700\) 0 0
\(701\) −25830.0 −1.39171 −0.695853 0.718184i \(-0.744973\pi\)
−0.695853 + 0.718184i \(0.744973\pi\)
\(702\) 0 0
\(703\) −24676.0 + 42740.1i −1.32386 + 2.29299i
\(704\) −7794.00 + 13499.6i −0.417255 + 0.722707i
\(705\) 0 0
\(706\) −23490.0 −1.25221
\(707\) 0 0
\(708\) 0 0
\(709\) 3113.00 + 5391.87i 0.164896 + 0.285608i 0.936618 0.350351i \(-0.113938\pi\)
−0.771722 + 0.635959i \(0.780605\pi\)
\(710\) 19440.0 33671.1i 1.02756 1.77979i
\(711\) 0 0
\(712\) 3717.00 + 6438.03i 0.195647 + 0.338870i
\(713\) 0 0
\(714\) 0 0
\(715\) −22032.0 −1.15238
\(716\) −1158.00 2005.71i −0.0604420 0.104689i
\(717\) 0 0
\(718\) −13968.0 + 24193.3i −0.726018 + 1.25750i
\(719\) 7536.00 + 13052.7i 0.390884 + 0.677030i 0.992566 0.121705i \(-0.0388361\pi\)
−0.601683 + 0.798735i \(0.705503\pi\)
\(720\) 0 0
\(721\) 0 0
\(722\) 25551.0 1.31705
\(723\) 0 0
\(724\) −53.0000 + 91.7987i −0.00272062 + 0.00471225i
\(725\) 10149.0 17578.6i 0.519896 0.900486i
\(726\) 0 0
\(727\) 32920.0 1.67942 0.839708 0.543038i \(-0.182726\pi\)
0.839708 + 0.543038i \(0.182726\pi\)
\(728\) 0 0
\(729\) 0 0
\(730\) 13554.0 + 23476.2i 0.687200 + 1.19027i
\(731\) 5628.00 9747.98i 0.284759 0.493218i
\(732\) 0 0
\(733\) −3473.00 6015.41i −0.175004 0.303116i 0.765158 0.643842i \(-0.222661\pi\)
−0.940163 + 0.340726i \(0.889327\pi\)
\(734\) 11280.0 0.567238
\(735\) 0 0
\(736\) 0 0
\(737\) −1656.00 2868.28i −0.0827674 0.143357i
\(738\) 0 0
\(739\) 1178.00 2040.36i 0.0586379 0.101564i −0.835216 0.549922i \(-0.814658\pi\)
0.893854 + 0.448358i \(0.147991\pi\)
\(740\) 3582.00 + 6204.21i 0.177942 + 0.308204i
\(741\) 0 0
\(742\) 0 0
\(743\) 23520.0 1.16133 0.580663 0.814144i \(-0.302793\pi\)
0.580663 + 0.814144i \(0.302793\pi\)
\(744\) 0 0
\(745\) 15714.0 27217.4i 0.772774 1.33848i
\(746\) −8805.00 + 15250.7i −0.432137 + 0.748483i
\(747\) 0 0
\(748\) 1512.00 0.0739094
\(749\) 0 0
\(750\) 0 0
\(751\) −1504.00 2605.00i −0.0730782 0.126575i 0.827171 0.561951i \(-0.189949\pi\)
−0.900249 + 0.435376i \(0.856616\pi\)
\(752\) 8520.00 14757.1i 0.413155 0.715605i
\(753\) 0 0
\(754\) 5202.00 + 9010.13i 0.251254 + 0.435185i
\(755\) 4176.00 0.201298
\(756\) 0 0
\(757\) −20770.0 −0.997224 −0.498612 0.866825i \(-0.666157\pi\)
−0.498612 + 0.866825i \(0.666157\pi\)
\(758\) 2778.00 + 4811.64i 0.133115 + 0.230563i
\(759\) 0 0
\(760\) −23436.0 + 40592.3i −1.11857 + 1.93742i
\(761\) −5769.00 9992.20i −0.274804 0.475975i 0.695281 0.718738i \(-0.255280\pi\)
−0.970086 + 0.242763i \(0.921946\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 1128.00 0.0534157
\(765\) 0 0
\(766\) −3240.00 + 5611.84i −0.152828 + 0.264705i
\(767\) 2244.00 3886.72i 0.105640 0.182974i
\(768\) 0 0
\(769\) −8498.00 −0.398499 −0.199249 0.979949i \(-0.563850\pi\)
−0.199249 + 0.979949i \(0.563850\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) −2017.00 3493.55i −0.0940329 0.162870i
\(773\) 16161.0 27991.7i 0.751967 1.30245i −0.194901 0.980823i \(-0.562438\pi\)
0.946868 0.321623i \(-0.104228\pi\)
\(774\) 0 0
\(775\) −15920.0 27574.2i −0.737888 1.27806i
\(776\) −6006.00 −0.277839
\(777\) 0 0
\(778\) 20358.0 0.938136
\(779\) 19716.0 + 34149.1i 0.906802 + 1.57063i
\(780\) 0 0
\(781\) −12960.0 + 22447.4i −0.593784 + 1.02846i
\(782\) 0 0
\(783\) 0 0
\(784\) 0 0
\(785\) 30492.0 1.38638
\(786\) 0 0
\(787\) 13114.0 22714.1i 0.593982 1.02881i −0.399708 0.916643i \(-0.630888\pi\)
0.993690 0.112164i \(-0.0357782\pi\)
\(788\) −657.000 + 1137.96i −0.0297013 + 0.0514442i
\(789\) 0 0
\(790\) 55296.0 2.49031
\(791\) 0 0
\(792\) 0 0
\(793\) 6766.00 + 11719.1i 0.302986 + 0.524787i
\(794\) −9771.00 + 16923.9i −0.436725 + 0.756430i
\(795\) 0 0
\(796\) 2548.00 + 4413.27i 0.113457 + 0.196513i
\(797\) −43338.0 −1.92611 −0.963056 0.269302i \(-0.913207\pi\)
−0.963056 + 0.269302i \(0.913207\pi\)
\(798\) 0 0
\(799\) 10080.0 0.446314
\(800\) 4477.50 + 7755.26i 0.197879 + 0.342737i
\(801\) 0 0
\(802\) 4995.00 8651.59i 0.219925 0.380921i
\(803\) −9036.00 15650.8i −0.397103 0.687802i
\(804\) 0 0
\(805\)