Properties

Label 441.4.e.b.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.b.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 \(-0.868840\pi\)
0.111317 0.993785i \(-0.464493\pi\)
\(6\) 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 \(-0.618141\pi\)
−0.362689 + 0.931910i \(0.618141\pi\)
\(14\) 0 0
\(15\) 0 0
\(16\) 35.5000 + 61.4878i 0.554688 + 0.960747i
\(17\) 21.0000 36.3731i 0.299603 0.518927i −0.676442 0.736496i \(-0.736479\pi\)
0.976045 + 0.217568i \(0.0698125\pi\)
\(18\) 0 0
\(19\) 62.0000 + 107.387i 0.748620 + 1.29665i 0.948484 + 0.316824i \(0.102616\pi\)
−0.199865 + 0.979824i \(0.564050\pi\)
\(20\) 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 −0.535635 0.844450i \(-0.679928\pi\)
0.999132 + 0.0416484i \(0.0132609\pi\)
\(32\) 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 \(-0.292913\pi\)
0.605649 + 0.795732i \(0.292913\pi\)
\(42\) 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 0.989937 0.141506i \(-0.0451943\pi\)
−0.617516 + 0.786558i \(0.711861\pi\)
\(48\) 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 −0.929610 0.368546i \(-0.879856\pi\)
0.783975 + 0.620793i \(0.213189\pi\)
\(60\) 0 0
\(61\) −199.000 344.678i −0.417694 0.723467i 0.578013 0.816028i \(-0.303828\pi\)
−0.995707 + 0.0925602i \(0.970495\pi\)
\(62\) −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 −0.591589 0.806239i \(-0.701499\pi\)
0.994019 + 0.109212i \(0.0348326\pi\)
\(74\) −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 \(-0.456932\pi\)
0.134891 + 0.990860i \(0.456932\pi\)
\(84\) 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 0.951968 0.306198i \(-0.0990570\pi\)
−0.741159 + 0.671329i \(0.765724\pi\)
\(90\) 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 \(-0.547826\pi\)
−0.149685 + 0.988734i \(0.547826\pi\)
\(98\) 0 0
\(99\) 0 0
\(100\) −99.5000 172.339i −0.0995000 0.172339i
\(101\) 207.000 358.535i 0.203933 0.353223i −0.745859 0.666104i \(-0.767961\pi\)
0.949792 + 0.312881i \(0.101294\pi\)
\(102\) 0 0
\(103\) −28.0000 48.4974i −0.0267857 0.0463941i 0.852322 0.523018i \(-0.175194\pi\)
−0.879107 + 0.476624i \(0.841860\pi\)
\(104\) 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 \(0.0335161\pi\)
−0.406212 + 0.913779i \(0.633151\pi\)
\(132\) 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 \(-0.505050\pi\)
−0.0158654 + 0.999874i \(0.505050\pi\)
\(140\) 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 −0.996922 0.0784048i \(-0.975017\pi\)
0.566361 + 0.824157i \(0.308351\pi\)
\(158\) 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 \(-0.587837\pi\)
−0.272460 + 0.962167i \(0.587837\pi\)
\(168\) 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 0.945638 0.325220i \(-0.105438\pi\)
−0.754468 + 0.656337i \(0.772105\pi\)
\(174\) 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 \(-0.506929\pi\)
−0.0217650 + 0.999763i \(0.506929\pi\)
\(182\) 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 \(0.528794\pi\)
−0.817316 + 0.576190i \(0.804539\pi\)
\(200\) 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 \(-0.591487\pi\)
−0.283475 + 0.958980i \(0.591487\pi\)
\(224\) 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 \(0.408816\pi\)
−0.972015 + 0.234919i \(0.924517\pi\)
\(228\) 0 0
\(229\) 845.000 + 1463.58i 0.243839 + 0.422342i 0.961805 0.273737i \(-0.0882598\pi\)
−0.717965 + 0.696079i \(0.754926\pi\)
\(230\) 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 −0.518913 0.854827i \(-0.673663\pi\)
0.999758 + 0.0219782i \(0.00699644\pi\)
\(242\) 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 \(-0.374287\pi\)
0.384752 + 0.923020i \(0.374287\pi\)
\(252\) 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 \(-0.856198\pi\)
0.0717686 0.997421i \(-0.477136\pi\)
\(258\) 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 \(-0.452371\pi\)
0.781811 0.623515i \(-0.214296\pi\)
\(270\) 0 0
\(271\) 2672.00 + 4628.04i 0.598939 + 1.03739i 0.992978 + 0.118299i \(0.0377441\pi\)
−0.394039 + 0.919094i \(0.628923\pi\)
\(272\) 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 −0.984874 0.173271i \(-0.944566\pi\)
0.642494 + 0.766290i \(0.277900\pi\)
\(284\) −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 \(-0.670441\pi\)
−0.510233 + 0.860036i \(0.670441\pi\)
\(294\) 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 \(-0.486622\pi\)
0.0420147 + 0.999117i \(0.486622\pi\)
\(308\) 0 0
\(309\) 0 0
\(310\) 4320.00 + 7482.46i 0.791482 + 1.37089i
\(311\) 2508.00 4343.98i 0.457285 0.792041i −0.541531 0.840681i \(-0.682155\pi\)
0.998816 + 0.0486397i \(0.0154886\pi\)
\(312\) 0 0
\(313\) −2701.00 4678.27i −0.487762 0.844829i 0.512139 0.858903i \(-0.328853\pi\)
−0.999901 + 0.0140739i \(0.995520\pi\)
\(314\) 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 \(-0.901311\pi\)
−0.952321 + 0.305097i \(0.901311\pi\)
\(350\) 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 \(0.367656\pi\)
−0.994192 + 0.107618i \(0.965678\pi\)
\(354\) 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 −0.700791 0.713367i \(-0.747169\pi\)
0.968189 + 0.250219i \(0.0805027\pi\)
\(368\) 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 0.929032 0.369999i \(-0.120642\pi\)
−0.784945 + 0.619566i \(0.787309\pi\)
\(384\) 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 0.995081 0.0990641i \(-0.0315849\pi\)
−0.583333 + 0.812233i \(0.698252\pi\)
\(398\) 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 −0.655474 0.755218i \(-0.727531\pi\)
0.981775 + 0.190048i \(0.0608645\pi\)
\(410\) −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 \(-0.776387\pi\)
−0.763229 + 0.646128i \(0.776387\pi\)
\(420\) 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 \(-0.422905\pi\)
0.239841 + 0.970812i \(0.422905\pi\)
\(434\) 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 0.999935 0.0113909i \(-0.00362592\pi\)
−0.509832 + 0.860274i \(0.670293\pi\)
\(440\) −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 \(-0.412558\pi\)
0.271264 + 0.962505i \(0.412558\pi\)
\(462\) 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 0.956418 0.292002i \(-0.0943213\pi\)
−0.731090 + 0.682281i \(0.760988\pi\)
\(468\) 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 −0.991715 0.128461i \(-0.958996\pi\)
0.607108 + 0.794620i \(0.292330\pi\)
\(480\) 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 \(-0.406213\pi\)
0.290397 + 0.956906i \(0.406213\pi\)
\(504\) 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 0.920351 0.391094i \(-0.127903\pi\)
−0.798873 + 0.601500i \(0.794570\pi\)
\(510\) 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 \(0.381515\pi\)
−0.988566 + 0.150791i \(0.951818\pi\)
\(522\) 0 0
\(523\) −8830.00 15294.0i −0.738258 1.27870i −0.953279 0.302091i \(-0.902315\pi\)
0.215021 0.976609i \(-0.431018\pi\)
\(524\) −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 \(0.398315\pi\)
−0.979235 + 0.202730i \(0.935019\pi\)
\(564\) 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 −0.866061 0.499938i \(-0.833356\pi\)
0.865989 + 0.500062i \(0.166690\pi\)
\(578\) 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 \(-0.877521\pi\)
−0.926881 + 0.375354i \(0.877521\pi\)
\(588\) 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 0.903064 0.429507i \(-0.141313\pi\)
−0.823496 + 0.567323i \(0.807979\pi\)
\(594\) 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 \(-0.186472\pi\)
0.833260 + 0.552881i \(0.186472\pi\)
\(602\) 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 \(-0.976406\pi\)
0.434495 0.900674i \(-0.356927\pi\)
\(608\) 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 \(-0.665957\pi\)
0.999998 0.00223050i \(-0.000709990\pi\)
\(620\) 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 \(-0.622266\pi\)
−0.374735 + 0.927132i \(0.622266\pi\)
\(644\) 0 0
\(645\) 0 0
\(646\) −7812.00 13530.8i −0.475788 0.824089i
\(647\) 6780.00 11743.3i 0.411977 0.713566i −0.583129 0.812380i \(-0.698172\pi\)
0.995106 + 0.0988143i \(0.0315050\pi\)
\(648\) 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 \(0.338415\pi\)
−0.999873 + 0.0159643i \(0.994918\pi\)
\(662\) 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 \(-0.908346\pi\)
0.233484 0.972361i \(-0.424987\pi\)
\(678\) 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 \(-0.894944\pi\)
0.192349 0.981326i \(-0.438389\pi\)
\(692\) −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 0.601683 0.798735i \(-0.294497\pi\)
−0.992566 + 0.121705i \(0.961164\pi\)
\(720\) 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 \(-0.817274\pi\)
−0.839708 + 0.543038i \(0.817274\pi\)
\(728\) 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 0.940163 0.340726i \(-0.110673\pi\)
−0.765158 + 0.643842i \(0.777339\pi\)
\(734\) −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 0.970086 0.242763i \(-0.0780536\pi\)
−0.695281 + 0.718738i \(0.744720\pi\)
\(762\) 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 \(-0.436150\pi\)
0.199249 + 0.979949i \(0.436150\pi\)
\(770\) 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 \(0.437562\pi\)
−0.946868 + 0.321623i \(0.895772\pi\)
\(774\) 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 \(0.369112\pi\)
−0.993690 + 0.112164i \(0.964222\pi\)
\(788\) −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 \(-0.0867931\pi\)
0.963056 + 0.269302i \(0.0867931\pi\)
\(798\) 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
\(805\) 0 0