Properties

Label 8001.2.a.u.1.10
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 0
Dimension 18
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(0\)
Dimension: \(18\)
Coefficient field: \(\mathbb{Q}[x]/(x^{18} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 2\cdot 5 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(0.803961\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.803961 q^{2}\) \(-1.35365 q^{4}\) \(-0.343335 q^{5}\) \(+1.00000 q^{7}\) \(-2.69620 q^{8}\) \(+O(q^{10})\) \(q\)\(+0.803961 q^{2}\) \(-1.35365 q^{4}\) \(-0.343335 q^{5}\) \(+1.00000 q^{7}\) \(-2.69620 q^{8}\) \(-0.276028 q^{10}\) \(-4.04620 q^{11}\) \(-5.07964 q^{13}\) \(+0.803961 q^{14}\) \(+0.539656 q^{16}\) \(+3.48245 q^{17}\) \(-2.23803 q^{19}\) \(+0.464755 q^{20}\) \(-3.25298 q^{22}\) \(+2.35865 q^{23}\) \(-4.88212 q^{25}\) \(-4.08383 q^{26}\) \(-1.35365 q^{28}\) \(-9.24369 q^{29}\) \(+5.54357 q^{31}\) \(+5.82626 q^{32}\) \(+2.79975 q^{34}\) \(-0.343335 q^{35}\) \(+5.87348 q^{37}\) \(-1.79929 q^{38}\) \(+0.925700 q^{40}\) \(+1.66919 q^{41}\) \(-10.3740 q^{43}\) \(+5.47712 q^{44}\) \(+1.89626 q^{46}\) \(+11.9067 q^{47}\) \(+1.00000 q^{49}\) \(-3.92503 q^{50}\) \(+6.87604 q^{52}\) \(-12.9408 q^{53}\) \(+1.38920 q^{55}\) \(-2.69620 q^{56}\) \(-7.43157 q^{58}\) \(-7.20507 q^{59}\) \(-10.3500 q^{61}\) \(+4.45681 q^{62}\) \(+3.60477 q^{64}\) \(+1.74402 q^{65}\) \(-4.97489 q^{67}\) \(-4.71400 q^{68}\) \(-0.276028 q^{70}\) \(-8.55324 q^{71}\) \(+10.9142 q^{73}\) \(+4.72205 q^{74}\) \(+3.02950 q^{76}\) \(-4.04620 q^{77}\) \(+15.8472 q^{79}\) \(-0.185283 q^{80}\) \(+1.34196 q^{82}\) \(+11.6255 q^{83}\) \(-1.19565 q^{85}\) \(-8.34032 q^{86}\) \(+10.9094 q^{88}\) \(+0.366424 q^{89}\) \(-5.07964 q^{91}\) \(-3.19278 q^{92}\) \(+9.57253 q^{94}\) \(+0.768394 q^{95}\) \(-7.75160 q^{97}\) \(+0.803961 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 21q^{20} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut +\mathstrut 33q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 31q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 35q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 63q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 46q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.803961 0.568486 0.284243 0.958752i \(-0.408258\pi\)
0.284243 + 0.958752i \(0.408258\pi\)
\(3\) 0 0
\(4\) −1.35365 −0.676824
\(5\) −0.343335 −0.153544 −0.0767720 0.997049i \(-0.524461\pi\)
−0.0767720 + 0.997049i \(0.524461\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.69620 −0.953251
\(9\) 0 0
\(10\) −0.276028 −0.0872876
\(11\) −4.04620 −1.21997 −0.609987 0.792411i \(-0.708825\pi\)
−0.609987 + 0.792411i \(0.708825\pi\)
\(12\) 0 0
\(13\) −5.07964 −1.40884 −0.704419 0.709784i \(-0.748792\pi\)
−0.704419 + 0.709784i \(0.748792\pi\)
\(14\) 0.803961 0.214867
\(15\) 0 0
\(16\) 0.539656 0.134914
\(17\) 3.48245 0.844617 0.422309 0.906452i \(-0.361220\pi\)
0.422309 + 0.906452i \(0.361220\pi\)
\(18\) 0 0
\(19\) −2.23803 −0.513439 −0.256720 0.966486i \(-0.582642\pi\)
−0.256720 + 0.966486i \(0.582642\pi\)
\(20\) 0.464755 0.103922
\(21\) 0 0
\(22\) −3.25298 −0.693538
\(23\) 2.35865 0.491813 0.245906 0.969294i \(-0.420914\pi\)
0.245906 + 0.969294i \(0.420914\pi\)
\(24\) 0 0
\(25\) −4.88212 −0.976424
\(26\) −4.08383 −0.800905
\(27\) 0 0
\(28\) −1.35365 −0.255815
\(29\) −9.24369 −1.71651 −0.858255 0.513223i \(-0.828451\pi\)
−0.858255 + 0.513223i \(0.828451\pi\)
\(30\) 0 0
\(31\) 5.54357 0.995654 0.497827 0.867276i \(-0.334131\pi\)
0.497827 + 0.867276i \(0.334131\pi\)
\(32\) 5.82626 1.02995
\(33\) 0 0
\(34\) 2.79975 0.480153
\(35\) −0.343335 −0.0580342
\(36\) 0 0
\(37\) 5.87348 0.965594 0.482797 0.875732i \(-0.339621\pi\)
0.482797 + 0.875732i \(0.339621\pi\)
\(38\) −1.79929 −0.291883
\(39\) 0 0
\(40\) 0.925700 0.146366
\(41\) 1.66919 0.260683 0.130342 0.991469i \(-0.458393\pi\)
0.130342 + 0.991469i \(0.458393\pi\)
\(42\) 0 0
\(43\) −10.3740 −1.58203 −0.791013 0.611799i \(-0.790446\pi\)
−0.791013 + 0.611799i \(0.790446\pi\)
\(44\) 5.47712 0.825707
\(45\) 0 0
\(46\) 1.89626 0.279589
\(47\) 11.9067 1.73677 0.868387 0.495887i \(-0.165157\pi\)
0.868387 + 0.495887i \(0.165157\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −3.92503 −0.555083
\(51\) 0 0
\(52\) 6.87604 0.953535
\(53\) −12.9408 −1.77756 −0.888779 0.458336i \(-0.848445\pi\)
−0.888779 + 0.458336i \(0.848445\pi\)
\(54\) 0 0
\(55\) 1.38920 0.187320
\(56\) −2.69620 −0.360295
\(57\) 0 0
\(58\) −7.43157 −0.975812
\(59\) −7.20507 −0.938020 −0.469010 0.883193i \(-0.655389\pi\)
−0.469010 + 0.883193i \(0.655389\pi\)
\(60\) 0 0
\(61\) −10.3500 −1.32519 −0.662593 0.748980i \(-0.730544\pi\)
−0.662593 + 0.748980i \(0.730544\pi\)
\(62\) 4.45681 0.566015
\(63\) 0 0
\(64\) 3.60477 0.450597
\(65\) 1.74402 0.216319
\(66\) 0 0
\(67\) −4.97489 −0.607779 −0.303890 0.952707i \(-0.598285\pi\)
−0.303890 + 0.952707i \(0.598285\pi\)
\(68\) −4.71400 −0.571657
\(69\) 0 0
\(70\) −0.276028 −0.0329916
\(71\) −8.55324 −1.01508 −0.507541 0.861628i \(-0.669445\pi\)
−0.507541 + 0.861628i \(0.669445\pi\)
\(72\) 0 0
\(73\) 10.9142 1.27741 0.638703 0.769454i \(-0.279471\pi\)
0.638703 + 0.769454i \(0.279471\pi\)
\(74\) 4.72205 0.548927
\(75\) 0 0
\(76\) 3.02950 0.347508
\(77\) −4.04620 −0.461107
\(78\) 0 0
\(79\) 15.8472 1.78295 0.891474 0.453072i \(-0.149672\pi\)
0.891474 + 0.453072i \(0.149672\pi\)
\(80\) −0.185283 −0.0207153
\(81\) 0 0
\(82\) 1.34196 0.148195
\(83\) 11.6255 1.27606 0.638031 0.770010i \(-0.279749\pi\)
0.638031 + 0.770010i \(0.279749\pi\)
\(84\) 0 0
\(85\) −1.19565 −0.129686
\(86\) −8.34032 −0.899360
\(87\) 0 0
\(88\) 10.9094 1.16294
\(89\) 0.366424 0.0388408 0.0194204 0.999811i \(-0.493818\pi\)
0.0194204 + 0.999811i \(0.493818\pi\)
\(90\) 0 0
\(91\) −5.07964 −0.532491
\(92\) −3.19278 −0.332871
\(93\) 0 0
\(94\) 9.57253 0.987332
\(95\) 0.768394 0.0788356
\(96\) 0 0
\(97\) −7.75160 −0.787056 −0.393528 0.919313i \(-0.628746\pi\)
−0.393528 + 0.919313i \(0.628746\pi\)
\(98\) 0.803961 0.0812123
\(99\) 0 0
\(100\) 6.60867 0.660867
\(101\) 13.1619 1.30966 0.654831 0.755776i \(-0.272740\pi\)
0.654831 + 0.755776i \(0.272740\pi\)
\(102\) 0 0
\(103\) −10.2020 −1.00523 −0.502616 0.864510i \(-0.667629\pi\)
−0.502616 + 0.864510i \(0.667629\pi\)
\(104\) 13.6957 1.34298
\(105\) 0 0
\(106\) −10.4039 −1.01052
\(107\) 5.75880 0.556724 0.278362 0.960476i \(-0.410208\pi\)
0.278362 + 0.960476i \(0.410208\pi\)
\(108\) 0 0
\(109\) 10.3606 0.992362 0.496181 0.868219i \(-0.334735\pi\)
0.496181 + 0.868219i \(0.334735\pi\)
\(110\) 1.11686 0.106489
\(111\) 0 0
\(112\) 0.539656 0.0509927
\(113\) 12.1901 1.14675 0.573376 0.819292i \(-0.305633\pi\)
0.573376 + 0.819292i \(0.305633\pi\)
\(114\) 0 0
\(115\) −0.809807 −0.0755149
\(116\) 12.5127 1.16178
\(117\) 0 0
\(118\) −5.79259 −0.533251
\(119\) 3.48245 0.319235
\(120\) 0 0
\(121\) 5.37170 0.488337
\(122\) −8.32101 −0.753349
\(123\) 0 0
\(124\) −7.50403 −0.673882
\(125\) 3.39288 0.303468
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −8.75443 −0.773790
\(129\) 0 0
\(130\) 1.40212 0.122974
\(131\) 11.7624 1.02768 0.513842 0.857885i \(-0.328222\pi\)
0.513842 + 0.857885i \(0.328222\pi\)
\(132\) 0 0
\(133\) −2.23803 −0.194062
\(134\) −3.99961 −0.345514
\(135\) 0 0
\(136\) −9.38937 −0.805132
\(137\) 22.2429 1.90034 0.950169 0.311737i \(-0.100911\pi\)
0.950169 + 0.311737i \(0.100911\pi\)
\(138\) 0 0
\(139\) 4.45596 0.377950 0.188975 0.981982i \(-0.439484\pi\)
0.188975 + 0.981982i \(0.439484\pi\)
\(140\) 0.464755 0.0392789
\(141\) 0 0
\(142\) −6.87646 −0.577060
\(143\) 20.5532 1.71875
\(144\) 0 0
\(145\) 3.17368 0.263560
\(146\) 8.77455 0.726187
\(147\) 0 0
\(148\) −7.95062 −0.653537
\(149\) 18.9721 1.55425 0.777126 0.629345i \(-0.216677\pi\)
0.777126 + 0.629345i \(0.216677\pi\)
\(150\) 0 0
\(151\) −10.7144 −0.871925 −0.435962 0.899965i \(-0.643592\pi\)
−0.435962 + 0.899965i \(0.643592\pi\)
\(152\) 6.03418 0.489436
\(153\) 0 0
\(154\) −3.25298 −0.262133
\(155\) −1.90330 −0.152877
\(156\) 0 0
\(157\) 11.4000 0.909817 0.454909 0.890538i \(-0.349672\pi\)
0.454909 + 0.890538i \(0.349672\pi\)
\(158\) 12.7405 1.01358
\(159\) 0 0
\(160\) −2.00036 −0.158142
\(161\) 2.35865 0.185888
\(162\) 0 0
\(163\) −18.3009 −1.43344 −0.716720 0.697361i \(-0.754357\pi\)
−0.716720 + 0.697361i \(0.754357\pi\)
\(164\) −2.25949 −0.176437
\(165\) 0 0
\(166\) 9.34643 0.725424
\(167\) −13.7796 −1.06630 −0.533150 0.846020i \(-0.678992\pi\)
−0.533150 + 0.846020i \(0.678992\pi\)
\(168\) 0 0
\(169\) 12.8027 0.984825
\(170\) −0.961252 −0.0737246
\(171\) 0 0
\(172\) 14.0428 1.07075
\(173\) 23.7433 1.80517 0.902586 0.430510i \(-0.141666\pi\)
0.902586 + 0.430510i \(0.141666\pi\)
\(174\) 0 0
\(175\) −4.88212 −0.369054
\(176\) −2.18356 −0.164592
\(177\) 0 0
\(178\) 0.294590 0.0220805
\(179\) −6.69909 −0.500714 −0.250357 0.968154i \(-0.580548\pi\)
−0.250357 + 0.968154i \(0.580548\pi\)
\(180\) 0 0
\(181\) 5.85446 0.435159 0.217579 0.976043i \(-0.430184\pi\)
0.217579 + 0.976043i \(0.430184\pi\)
\(182\) −4.08383 −0.302714
\(183\) 0 0
\(184\) −6.35940 −0.468821
\(185\) −2.01657 −0.148261
\(186\) 0 0
\(187\) −14.0907 −1.03041
\(188\) −16.1175 −1.17549
\(189\) 0 0
\(190\) 0.617759 0.0448169
\(191\) −6.96386 −0.503887 −0.251944 0.967742i \(-0.581070\pi\)
−0.251944 + 0.967742i \(0.581070\pi\)
\(192\) 0 0
\(193\) −4.33351 −0.311933 −0.155966 0.987762i \(-0.549849\pi\)
−0.155966 + 0.987762i \(0.549849\pi\)
\(194\) −6.23198 −0.447430
\(195\) 0 0
\(196\) −1.35365 −0.0966891
\(197\) −6.88472 −0.490516 −0.245258 0.969458i \(-0.578873\pi\)
−0.245258 + 0.969458i \(0.578873\pi\)
\(198\) 0 0
\(199\) −6.03022 −0.427471 −0.213735 0.976892i \(-0.568563\pi\)
−0.213735 + 0.976892i \(0.568563\pi\)
\(200\) 13.1632 0.930777
\(201\) 0 0
\(202\) 10.5817 0.744524
\(203\) −9.24369 −0.648780
\(204\) 0 0
\(205\) −0.573091 −0.0400264
\(206\) −8.20199 −0.571460
\(207\) 0 0
\(208\) −2.74126 −0.190072
\(209\) 9.05551 0.626383
\(210\) 0 0
\(211\) −18.7052 −1.28772 −0.643858 0.765145i \(-0.722667\pi\)
−0.643858 + 0.765145i \(0.722667\pi\)
\(212\) 17.5173 1.20309
\(213\) 0 0
\(214\) 4.62985 0.316490
\(215\) 3.56177 0.242911
\(216\) 0 0
\(217\) 5.54357 0.376322
\(218\) 8.32948 0.564144
\(219\) 0 0
\(220\) −1.88049 −0.126782
\(221\) −17.6896 −1.18993
\(222\) 0 0
\(223\) −10.6279 −0.711696 −0.355848 0.934544i \(-0.615808\pi\)
−0.355848 + 0.934544i \(0.615808\pi\)
\(224\) 5.82626 0.389284
\(225\) 0 0
\(226\) 9.80039 0.651912
\(227\) 2.03230 0.134888 0.0674442 0.997723i \(-0.478516\pi\)
0.0674442 + 0.997723i \(0.478516\pi\)
\(228\) 0 0
\(229\) 14.7071 0.971873 0.485937 0.873994i \(-0.338479\pi\)
0.485937 + 0.873994i \(0.338479\pi\)
\(230\) −0.651053 −0.0429292
\(231\) 0 0
\(232\) 24.9228 1.63627
\(233\) 18.8646 1.23586 0.617932 0.786232i \(-0.287971\pi\)
0.617932 + 0.786232i \(0.287971\pi\)
\(234\) 0 0
\(235\) −4.08799 −0.266671
\(236\) 9.75313 0.634874
\(237\) 0 0
\(238\) 2.79975 0.181481
\(239\) −3.80322 −0.246010 −0.123005 0.992406i \(-0.539253\pi\)
−0.123005 + 0.992406i \(0.539253\pi\)
\(240\) 0 0
\(241\) −23.5196 −1.51503 −0.757515 0.652818i \(-0.773587\pi\)
−0.757515 + 0.652818i \(0.773587\pi\)
\(242\) 4.31864 0.277613
\(243\) 0 0
\(244\) 14.0103 0.896917
\(245\) −0.343335 −0.0219349
\(246\) 0 0
\(247\) 11.3684 0.723353
\(248\) −14.9466 −0.949108
\(249\) 0 0
\(250\) 2.72774 0.172517
\(251\) 24.4633 1.54411 0.772056 0.635555i \(-0.219228\pi\)
0.772056 + 0.635555i \(0.219228\pi\)
\(252\) 0 0
\(253\) −9.54357 −0.599999
\(254\) 0.803961 0.0504450
\(255\) 0 0
\(256\) −14.2478 −0.890485
\(257\) 1.68358 0.105019 0.0525096 0.998620i \(-0.483278\pi\)
0.0525096 + 0.998620i \(0.483278\pi\)
\(258\) 0 0
\(259\) 5.87348 0.364960
\(260\) −2.36078 −0.146410
\(261\) 0 0
\(262\) 9.45649 0.584224
\(263\) 22.2555 1.37233 0.686166 0.727445i \(-0.259292\pi\)
0.686166 + 0.727445i \(0.259292\pi\)
\(264\) 0 0
\(265\) 4.44303 0.272933
\(266\) −1.79929 −0.110321
\(267\) 0 0
\(268\) 6.73425 0.411360
\(269\) −10.4180 −0.635195 −0.317597 0.948226i \(-0.602876\pi\)
−0.317597 + 0.948226i \(0.602876\pi\)
\(270\) 0 0
\(271\) 2.90437 0.176428 0.0882141 0.996102i \(-0.471884\pi\)
0.0882141 + 0.996102i \(0.471884\pi\)
\(272\) 1.87932 0.113951
\(273\) 0 0
\(274\) 17.8824 1.08031
\(275\) 19.7540 1.19121
\(276\) 0 0
\(277\) 15.7288 0.945054 0.472527 0.881316i \(-0.343342\pi\)
0.472527 + 0.881316i \(0.343342\pi\)
\(278\) 3.58242 0.214859
\(279\) 0 0
\(280\) 0.925700 0.0553211
\(281\) 27.1991 1.62256 0.811280 0.584657i \(-0.198771\pi\)
0.811280 + 0.584657i \(0.198771\pi\)
\(282\) 0 0
\(283\) 11.1363 0.661982 0.330991 0.943634i \(-0.392617\pi\)
0.330991 + 0.943634i \(0.392617\pi\)
\(284\) 11.5781 0.687032
\(285\) 0 0
\(286\) 16.5240 0.977083
\(287\) 1.66919 0.0985290
\(288\) 0 0
\(289\) −4.87257 −0.286622
\(290\) 2.55152 0.149830
\(291\) 0 0
\(292\) −14.7739 −0.864578
\(293\) −22.3106 −1.30340 −0.651700 0.758477i \(-0.725944\pi\)
−0.651700 + 0.758477i \(0.725944\pi\)
\(294\) 0 0
\(295\) 2.47375 0.144027
\(296\) −15.8361 −0.920454
\(297\) 0 0
\(298\) 15.2528 0.883570
\(299\) −11.9811 −0.692885
\(300\) 0 0
\(301\) −10.3740 −0.597950
\(302\) −8.61395 −0.495677
\(303\) 0 0
\(304\) −1.20777 −0.0692702
\(305\) 3.55353 0.203474
\(306\) 0 0
\(307\) 20.8361 1.18918 0.594588 0.804030i \(-0.297315\pi\)
0.594588 + 0.804030i \(0.297315\pi\)
\(308\) 5.47712 0.312088
\(309\) 0 0
\(310\) −1.53018 −0.0869083
\(311\) −7.05946 −0.400305 −0.200153 0.979765i \(-0.564144\pi\)
−0.200153 + 0.979765i \(0.564144\pi\)
\(312\) 0 0
\(313\) 8.81011 0.497977 0.248988 0.968506i \(-0.419902\pi\)
0.248988 + 0.968506i \(0.419902\pi\)
\(314\) 9.16513 0.517218
\(315\) 0 0
\(316\) −21.4515 −1.20674
\(317\) 9.91942 0.557130 0.278565 0.960417i \(-0.410141\pi\)
0.278565 + 0.960417i \(0.410141\pi\)
\(318\) 0 0
\(319\) 37.4018 2.09410
\(320\) −1.23764 −0.0691864
\(321\) 0 0
\(322\) 1.89626 0.105675
\(323\) −7.79382 −0.433660
\(324\) 0 0
\(325\) 24.7994 1.37562
\(326\) −14.7132 −0.814890
\(327\) 0 0
\(328\) −4.50046 −0.248497
\(329\) 11.9067 0.656439
\(330\) 0 0
\(331\) −4.64788 −0.255471 −0.127735 0.991808i \(-0.540771\pi\)
−0.127735 + 0.991808i \(0.540771\pi\)
\(332\) −15.7368 −0.863669
\(333\) 0 0
\(334\) −11.0783 −0.606177
\(335\) 1.70805 0.0933209
\(336\) 0 0
\(337\) 20.2867 1.10509 0.552545 0.833483i \(-0.313657\pi\)
0.552545 + 0.833483i \(0.313657\pi\)
\(338\) 10.2929 0.559859
\(339\) 0 0
\(340\) 1.61848 0.0877745
\(341\) −22.4304 −1.21467
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 27.9705 1.50807
\(345\) 0 0
\(346\) 19.0887 1.02621
\(347\) 7.49407 0.402303 0.201151 0.979560i \(-0.435532\pi\)
0.201151 + 0.979560i \(0.435532\pi\)
\(348\) 0 0
\(349\) −32.3002 −1.72899 −0.864496 0.502640i \(-0.832362\pi\)
−0.864496 + 0.502640i \(0.832362\pi\)
\(350\) −3.92503 −0.209802
\(351\) 0 0
\(352\) −23.5742 −1.25651
\(353\) −20.5000 −1.09110 −0.545552 0.838077i \(-0.683680\pi\)
−0.545552 + 0.838077i \(0.683680\pi\)
\(354\) 0 0
\(355\) 2.93662 0.155860
\(356\) −0.496009 −0.0262884
\(357\) 0 0
\(358\) −5.38581 −0.284649
\(359\) 24.6060 1.29866 0.649328 0.760508i \(-0.275050\pi\)
0.649328 + 0.760508i \(0.275050\pi\)
\(360\) 0 0
\(361\) −13.9912 −0.736380
\(362\) 4.70675 0.247382
\(363\) 0 0
\(364\) 6.87604 0.360402
\(365\) −3.74721 −0.196138
\(366\) 0 0
\(367\) 15.9470 0.832429 0.416214 0.909267i \(-0.363357\pi\)
0.416214 + 0.909267i \(0.363357\pi\)
\(368\) 1.27286 0.0663525
\(369\) 0 0
\(370\) −1.62124 −0.0842845
\(371\) −12.9408 −0.671854
\(372\) 0 0
\(373\) −28.0230 −1.45098 −0.725488 0.688235i \(-0.758386\pi\)
−0.725488 + 0.688235i \(0.758386\pi\)
\(374\) −11.3283 −0.585774
\(375\) 0 0
\(376\) −32.1029 −1.65558
\(377\) 46.9546 2.41829
\(378\) 0 0
\(379\) 32.1526 1.65157 0.825783 0.563987i \(-0.190733\pi\)
0.825783 + 0.563987i \(0.190733\pi\)
\(380\) −1.04013 −0.0533578
\(381\) 0 0
\(382\) −5.59867 −0.286453
\(383\) 21.9187 1.11999 0.559996 0.828495i \(-0.310803\pi\)
0.559996 + 0.828495i \(0.310803\pi\)
\(384\) 0 0
\(385\) 1.38920 0.0708002
\(386\) −3.48397 −0.177329
\(387\) 0 0
\(388\) 10.4929 0.532698
\(389\) −0.259292 −0.0131466 −0.00657331 0.999978i \(-0.502092\pi\)
−0.00657331 + 0.999978i \(0.502092\pi\)
\(390\) 0 0
\(391\) 8.21387 0.415394
\(392\) −2.69620 −0.136179
\(393\) 0 0
\(394\) −5.53504 −0.278852
\(395\) −5.44089 −0.273761
\(396\) 0 0
\(397\) 8.76662 0.439984 0.219992 0.975502i \(-0.429397\pi\)
0.219992 + 0.975502i \(0.429397\pi\)
\(398\) −4.84805 −0.243011
\(399\) 0 0
\(400\) −2.63467 −0.131733
\(401\) 12.3572 0.617091 0.308546 0.951210i \(-0.400158\pi\)
0.308546 + 0.951210i \(0.400158\pi\)
\(402\) 0 0
\(403\) −28.1593 −1.40272
\(404\) −17.8166 −0.886410
\(405\) 0 0
\(406\) −7.43157 −0.368822
\(407\) −23.7653 −1.17800
\(408\) 0 0
\(409\) 10.7862 0.533346 0.266673 0.963787i \(-0.414076\pi\)
0.266673 + 0.963787i \(0.414076\pi\)
\(410\) −0.460742 −0.0227544
\(411\) 0 0
\(412\) 13.8099 0.680365
\(413\) −7.20507 −0.354538
\(414\) 0 0
\(415\) −3.99143 −0.195932
\(416\) −29.5953 −1.45103
\(417\) 0 0
\(418\) 7.28027 0.356090
\(419\) 17.4411 0.852054 0.426027 0.904710i \(-0.359913\pi\)
0.426027 + 0.904710i \(0.359913\pi\)
\(420\) 0 0
\(421\) −40.2522 −1.96177 −0.980886 0.194583i \(-0.937665\pi\)
−0.980886 + 0.194583i \(0.937665\pi\)
\(422\) −15.0382 −0.732048
\(423\) 0 0
\(424\) 34.8910 1.69446
\(425\) −17.0017 −0.824705
\(426\) 0 0
\(427\) −10.3500 −0.500873
\(428\) −7.79538 −0.376804
\(429\) 0 0
\(430\) 2.86352 0.138091
\(431\) −5.00922 −0.241286 −0.120643 0.992696i \(-0.538496\pi\)
−0.120643 + 0.992696i \(0.538496\pi\)
\(432\) 0 0
\(433\) 26.9224 1.29381 0.646904 0.762571i \(-0.276063\pi\)
0.646904 + 0.762571i \(0.276063\pi\)
\(434\) 4.45681 0.213934
\(435\) 0 0
\(436\) −14.0245 −0.671654
\(437\) −5.27873 −0.252516
\(438\) 0 0
\(439\) −30.1663 −1.43976 −0.719879 0.694099i \(-0.755803\pi\)
−0.719879 + 0.694099i \(0.755803\pi\)
\(440\) −3.74556 −0.178563
\(441\) 0 0
\(442\) −14.2217 −0.676458
\(443\) −30.6696 −1.45716 −0.728579 0.684962i \(-0.759819\pi\)
−0.728579 + 0.684962i \(0.759819\pi\)
\(444\) 0 0
\(445\) −0.125806 −0.00596378
\(446\) −8.54440 −0.404589
\(447\) 0 0
\(448\) 3.60477 0.170309
\(449\) 12.2072 0.576093 0.288047 0.957616i \(-0.406994\pi\)
0.288047 + 0.957616i \(0.406994\pi\)
\(450\) 0 0
\(451\) −6.75386 −0.318027
\(452\) −16.5012 −0.776149
\(453\) 0 0
\(454\) 1.63389 0.0766822
\(455\) 1.74402 0.0817608
\(456\) 0 0
\(457\) −32.4700 −1.51888 −0.759442 0.650575i \(-0.774528\pi\)
−0.759442 + 0.650575i \(0.774528\pi\)
\(458\) 11.8239 0.552496
\(459\) 0 0
\(460\) 1.09619 0.0511103
\(461\) 12.1968 0.568060 0.284030 0.958815i \(-0.408329\pi\)
0.284030 + 0.958815i \(0.408329\pi\)
\(462\) 0 0
\(463\) 35.1369 1.63295 0.816475 0.577380i \(-0.195925\pi\)
0.816475 + 0.577380i \(0.195925\pi\)
\(464\) −4.98842 −0.231582
\(465\) 0 0
\(466\) 15.1664 0.702571
\(467\) 17.0341 0.788246 0.394123 0.919058i \(-0.371048\pi\)
0.394123 + 0.919058i \(0.371048\pi\)
\(468\) 0 0
\(469\) −4.97489 −0.229719
\(470\) −3.28659 −0.151599
\(471\) 0 0
\(472\) 19.4263 0.894169
\(473\) 41.9754 1.93003
\(474\) 0 0
\(475\) 10.9263 0.501335
\(476\) −4.71400 −0.216066
\(477\) 0 0
\(478\) −3.05764 −0.139853
\(479\) −12.1072 −0.553190 −0.276595 0.960987i \(-0.589206\pi\)
−0.276595 + 0.960987i \(0.589206\pi\)
\(480\) 0 0
\(481\) −29.8352 −1.36037
\(482\) −18.9088 −0.861273
\(483\) 0 0
\(484\) −7.27139 −0.330518
\(485\) 2.66140 0.120848
\(486\) 0 0
\(487\) 15.5980 0.706812 0.353406 0.935470i \(-0.385023\pi\)
0.353406 + 0.935470i \(0.385023\pi\)
\(488\) 27.9057 1.26323
\(489\) 0 0
\(490\) −0.276028 −0.0124697
\(491\) −8.87764 −0.400642 −0.200321 0.979730i \(-0.564199\pi\)
−0.200321 + 0.979730i \(0.564199\pi\)
\(492\) 0 0
\(493\) −32.1907 −1.44979
\(494\) 9.13973 0.411216
\(495\) 0 0
\(496\) 2.99162 0.134328
\(497\) −8.55324 −0.383665
\(498\) 0 0
\(499\) 15.3071 0.685241 0.342620 0.939474i \(-0.388686\pi\)
0.342620 + 0.939474i \(0.388686\pi\)
\(500\) −4.59276 −0.205394
\(501\) 0 0
\(502\) 19.6676 0.877806
\(503\) 14.5352 0.648091 0.324045 0.946042i \(-0.394957\pi\)
0.324045 + 0.946042i \(0.394957\pi\)
\(504\) 0 0
\(505\) −4.51895 −0.201091
\(506\) −7.67265 −0.341091
\(507\) 0 0
\(508\) −1.35365 −0.0600584
\(509\) 29.5667 1.31052 0.655260 0.755403i \(-0.272559\pi\)
0.655260 + 0.755403i \(0.272559\pi\)
\(510\) 0 0
\(511\) 10.9142 0.482814
\(512\) 6.05422 0.267561
\(513\) 0 0
\(514\) 1.35354 0.0597019
\(515\) 3.50270 0.154347
\(516\) 0 0
\(517\) −48.1769 −2.11882
\(518\) 4.72205 0.207475
\(519\) 0 0
\(520\) −4.70222 −0.206206
\(521\) 14.6876 0.643478 0.321739 0.946828i \(-0.395733\pi\)
0.321739 + 0.946828i \(0.395733\pi\)
\(522\) 0 0
\(523\) 16.6693 0.728897 0.364448 0.931224i \(-0.381258\pi\)
0.364448 + 0.931224i \(0.381258\pi\)
\(524\) −15.9221 −0.695561
\(525\) 0 0
\(526\) 17.8925 0.780152
\(527\) 19.3052 0.840946
\(528\) 0 0
\(529\) −17.4368 −0.758120
\(530\) 3.57202 0.155159
\(531\) 0 0
\(532\) 3.02950 0.131346
\(533\) −8.47887 −0.367261
\(534\) 0 0
\(535\) −1.97720 −0.0854817
\(536\) 13.4133 0.579366
\(537\) 0 0
\(538\) −8.37563 −0.361099
\(539\) −4.04620 −0.174282
\(540\) 0 0
\(541\) −9.00282 −0.387061 −0.193531 0.981094i \(-0.561994\pi\)
−0.193531 + 0.981094i \(0.561994\pi\)
\(542\) 2.33500 0.100297
\(543\) 0 0
\(544\) 20.2896 0.869911
\(545\) −3.55714 −0.152371
\(546\) 0 0
\(547\) 34.5632 1.47782 0.738909 0.673805i \(-0.235341\pi\)
0.738909 + 0.673805i \(0.235341\pi\)
\(548\) −30.1090 −1.28619
\(549\) 0 0
\(550\) 15.8815 0.677187
\(551\) 20.6877 0.881324
\(552\) 0 0
\(553\) 15.8472 0.673891
\(554\) 12.6454 0.537250
\(555\) 0 0
\(556\) −6.03180 −0.255805
\(557\) −5.54071 −0.234767 −0.117384 0.993087i \(-0.537451\pi\)
−0.117384 + 0.993087i \(0.537451\pi\)
\(558\) 0 0
\(559\) 52.6964 2.22882
\(560\) −0.185283 −0.00782963
\(561\) 0 0
\(562\) 21.8670 0.922403
\(563\) 32.8794 1.38570 0.692852 0.721080i \(-0.256354\pi\)
0.692852 + 0.721080i \(0.256354\pi\)
\(564\) 0 0
\(565\) −4.18530 −0.176077
\(566\) 8.95311 0.376327
\(567\) 0 0
\(568\) 23.0612 0.967628
\(569\) −39.4015 −1.65180 −0.825898 0.563819i \(-0.809331\pi\)
−0.825898 + 0.563819i \(0.809331\pi\)
\(570\) 0 0
\(571\) −8.97776 −0.375707 −0.187854 0.982197i \(-0.560153\pi\)
−0.187854 + 0.982197i \(0.560153\pi\)
\(572\) −27.8218 −1.16329
\(573\) 0 0
\(574\) 1.34196 0.0560124
\(575\) −11.5152 −0.480218
\(576\) 0 0
\(577\) 29.6596 1.23474 0.617372 0.786671i \(-0.288197\pi\)
0.617372 + 0.786671i \(0.288197\pi\)
\(578\) −3.91736 −0.162941
\(579\) 0 0
\(580\) −4.29605 −0.178384
\(581\) 11.6255 0.482306
\(582\) 0 0
\(583\) 52.3611 2.16857
\(584\) −29.4268 −1.21769
\(585\) 0 0
\(586\) −17.9369 −0.740964
\(587\) −24.2422 −1.00058 −0.500292 0.865857i \(-0.666774\pi\)
−0.500292 + 0.865857i \(0.666774\pi\)
\(588\) 0 0
\(589\) −12.4067 −0.511208
\(590\) 1.98880 0.0818776
\(591\) 0 0
\(592\) 3.16966 0.130272
\(593\) −4.03464 −0.165683 −0.0828413 0.996563i \(-0.526399\pi\)
−0.0828413 + 0.996563i \(0.526399\pi\)
\(594\) 0 0
\(595\) −1.19565 −0.0490167
\(596\) −25.6815 −1.05195
\(597\) 0 0
\(598\) −9.63233 −0.393895
\(599\) −13.9844 −0.571386 −0.285693 0.958321i \(-0.592224\pi\)
−0.285693 + 0.958321i \(0.592224\pi\)
\(600\) 0 0
\(601\) 2.49583 0.101807 0.0509034 0.998704i \(-0.483790\pi\)
0.0509034 + 0.998704i \(0.483790\pi\)
\(602\) −8.34032 −0.339926
\(603\) 0 0
\(604\) 14.5035 0.590139
\(605\) −1.84429 −0.0749812
\(606\) 0 0
\(607\) −31.0017 −1.25832 −0.629160 0.777276i \(-0.716601\pi\)
−0.629160 + 0.777276i \(0.716601\pi\)
\(608\) −13.0394 −0.528816
\(609\) 0 0
\(610\) 2.85689 0.115672
\(611\) −60.4818 −2.44683
\(612\) 0 0
\(613\) 16.1533 0.652424 0.326212 0.945297i \(-0.394228\pi\)
0.326212 + 0.945297i \(0.394228\pi\)
\(614\) 16.7514 0.676030
\(615\) 0 0
\(616\) 10.9094 0.439550
\(617\) 28.2570 1.13759 0.568793 0.822481i \(-0.307411\pi\)
0.568793 + 0.822481i \(0.307411\pi\)
\(618\) 0 0
\(619\) 8.17631 0.328634 0.164317 0.986408i \(-0.447458\pi\)
0.164317 + 0.986408i \(0.447458\pi\)
\(620\) 2.57640 0.103471
\(621\) 0 0
\(622\) −5.67553 −0.227568
\(623\) 0.366424 0.0146805
\(624\) 0 0
\(625\) 23.2457 0.929828
\(626\) 7.08298 0.283093
\(627\) 0 0
\(628\) −15.4315 −0.615786
\(629\) 20.4541 0.815558
\(630\) 0 0
\(631\) −4.89122 −0.194716 −0.0973582 0.995249i \(-0.531039\pi\)
−0.0973582 + 0.995249i \(0.531039\pi\)
\(632\) −42.7272 −1.69960
\(633\) 0 0
\(634\) 7.97483 0.316721
\(635\) −0.343335 −0.0136248
\(636\) 0 0
\(637\) −5.07964 −0.201263
\(638\) 30.0696 1.19047
\(639\) 0 0
\(640\) 3.00570 0.118811
\(641\) 25.5390 1.00873 0.504364 0.863491i \(-0.331727\pi\)
0.504364 + 0.863491i \(0.331727\pi\)
\(642\) 0 0
\(643\) −1.19858 −0.0472675 −0.0236338 0.999721i \(-0.507524\pi\)
−0.0236338 + 0.999721i \(0.507524\pi\)
\(644\) −3.19278 −0.125813
\(645\) 0 0
\(646\) −6.26592 −0.246529
\(647\) 18.5349 0.728684 0.364342 0.931265i \(-0.381294\pi\)
0.364342 + 0.931265i \(0.381294\pi\)
\(648\) 0 0
\(649\) 29.1531 1.14436
\(650\) 19.9377 0.782023
\(651\) 0 0
\(652\) 24.7730 0.970186
\(653\) 17.4806 0.684070 0.342035 0.939687i \(-0.388884\pi\)
0.342035 + 0.939687i \(0.388884\pi\)
\(654\) 0 0
\(655\) −4.03844 −0.157795
\(656\) 0.900788 0.0351699
\(657\) 0 0
\(658\) 9.57253 0.373176
\(659\) −14.2329 −0.554433 −0.277217 0.960807i \(-0.589412\pi\)
−0.277217 + 0.960807i \(0.589412\pi\)
\(660\) 0 0
\(661\) 41.6188 1.61878 0.809392 0.587269i \(-0.199797\pi\)
0.809392 + 0.587269i \(0.199797\pi\)
\(662\) −3.73671 −0.145231
\(663\) 0 0
\(664\) −31.3446 −1.21641
\(665\) 0.768394 0.0297970
\(666\) 0 0
\(667\) −21.8027 −0.844202
\(668\) 18.6528 0.721698
\(669\) 0 0
\(670\) 1.37321 0.0530516
\(671\) 41.8782 1.61669
\(672\) 0 0
\(673\) −7.84024 −0.302219 −0.151110 0.988517i \(-0.548285\pi\)
−0.151110 + 0.988517i \(0.548285\pi\)
\(674\) 16.3097 0.628228
\(675\) 0 0
\(676\) −17.3304 −0.666553
\(677\) −10.4000 −0.399704 −0.199852 0.979826i \(-0.564046\pi\)
−0.199852 + 0.979826i \(0.564046\pi\)
\(678\) 0 0
\(679\) −7.75160 −0.297479
\(680\) 3.22370 0.123623
\(681\) 0 0
\(682\) −18.0331 −0.690524
\(683\) −30.2573 −1.15776 −0.578882 0.815412i \(-0.696511\pi\)
−0.578882 + 0.815412i \(0.696511\pi\)
\(684\) 0 0
\(685\) −7.63676 −0.291786
\(686\) 0.803961 0.0306954
\(687\) 0 0
\(688\) −5.59842 −0.213438
\(689\) 65.7347 2.50429
\(690\) 0 0
\(691\) −23.7198 −0.902343 −0.451172 0.892437i \(-0.648994\pi\)
−0.451172 + 0.892437i \(0.648994\pi\)
\(692\) −32.1401 −1.22178
\(693\) 0 0
\(694\) 6.02494 0.228704
\(695\) −1.52989 −0.0580319
\(696\) 0 0
\(697\) 5.81286 0.220178
\(698\) −25.9681 −0.982907
\(699\) 0 0
\(700\) 6.60867 0.249784
\(701\) 33.5878 1.26859 0.634297 0.773090i \(-0.281290\pi\)
0.634297 + 0.773090i \(0.281290\pi\)
\(702\) 0 0
\(703\) −13.1450 −0.495774
\(704\) −14.5856 −0.549716
\(705\) 0 0
\(706\) −16.4812 −0.620277
\(707\) 13.1619 0.495005
\(708\) 0 0
\(709\) −27.9016 −1.04787 −0.523933 0.851759i \(-0.675536\pi\)
−0.523933 + 0.851759i \(0.675536\pi\)
\(710\) 2.36093 0.0886041
\(711\) 0 0
\(712\) −0.987952 −0.0370251
\(713\) 13.0753 0.489675
\(714\) 0 0
\(715\) −7.05664 −0.263903
\(716\) 9.06821 0.338895
\(717\) 0 0
\(718\) 19.7823 0.738268
\(719\) 8.25535 0.307873 0.153936 0.988081i \(-0.450805\pi\)
0.153936 + 0.988081i \(0.450805\pi\)
\(720\) 0 0
\(721\) −10.2020 −0.379942
\(722\) −11.2484 −0.418622
\(723\) 0 0
\(724\) −7.92488 −0.294526
\(725\) 45.1288 1.67604
\(726\) 0 0
\(727\) 25.7683 0.955694 0.477847 0.878443i \(-0.341417\pi\)
0.477847 + 0.878443i \(0.341417\pi\)
\(728\) 13.6957 0.507597
\(729\) 0 0
\(730\) −3.01261 −0.111502
\(731\) −36.1270 −1.33621
\(732\) 0 0
\(733\) −41.2704 −1.52436 −0.762179 0.647366i \(-0.775870\pi\)
−0.762179 + 0.647366i \(0.775870\pi\)
\(734\) 12.8208 0.473224
\(735\) 0 0
\(736\) 13.7421 0.506541
\(737\) 20.1294 0.741475
\(738\) 0 0
\(739\) −12.2673 −0.451260 −0.225630 0.974213i \(-0.572444\pi\)
−0.225630 + 0.974213i \(0.572444\pi\)
\(740\) 2.72973 0.100347
\(741\) 0 0
\(742\) −10.4039 −0.381939
\(743\) −30.3770 −1.11443 −0.557213 0.830370i \(-0.688129\pi\)
−0.557213 + 0.830370i \(0.688129\pi\)
\(744\) 0 0
\(745\) −6.51377 −0.238646
\(746\) −22.5294 −0.824859
\(747\) 0 0
\(748\) 19.0738 0.697407
\(749\) 5.75880 0.210422
\(750\) 0 0
\(751\) 38.9352 1.42076 0.710382 0.703816i \(-0.248522\pi\)
0.710382 + 0.703816i \(0.248522\pi\)
\(752\) 6.42554 0.234315
\(753\) 0 0
\(754\) 37.7497 1.37476
\(755\) 3.67862 0.133879
\(756\) 0 0
\(757\) 0.998200 0.0362802 0.0181401 0.999835i \(-0.494226\pi\)
0.0181401 + 0.999835i \(0.494226\pi\)
\(758\) 25.8494 0.938892
\(759\) 0 0
\(760\) −2.07174 −0.0751501
\(761\) −49.1530 −1.78180 −0.890898 0.454204i \(-0.849924\pi\)
−0.890898 + 0.454204i \(0.849924\pi\)
\(762\) 0 0
\(763\) 10.3606 0.375077
\(764\) 9.42662 0.341043
\(765\) 0 0
\(766\) 17.6218 0.636700
\(767\) 36.5992 1.32152
\(768\) 0 0
\(769\) −49.4560 −1.78343 −0.891715 0.452598i \(-0.850497\pi\)
−0.891715 + 0.452598i \(0.850497\pi\)
\(770\) 1.11686 0.0402489
\(771\) 0 0
\(772\) 5.86604 0.211124
\(773\) 18.8474 0.677893 0.338946 0.940806i \(-0.389929\pi\)
0.338946 + 0.940806i \(0.389929\pi\)
\(774\) 0 0
\(775\) −27.0644 −0.972181
\(776\) 20.8999 0.750261
\(777\) 0 0
\(778\) −0.208460 −0.00747367
\(779\) −3.73569 −0.133845
\(780\) 0 0
\(781\) 34.6081 1.23837
\(782\) 6.60363 0.236145
\(783\) 0 0
\(784\) 0.539656 0.0192734
\(785\) −3.91401 −0.139697
\(786\) 0 0
\(787\) 32.2531 1.14970 0.574849 0.818259i \(-0.305061\pi\)
0.574849 + 0.818259i \(0.305061\pi\)
\(788\) 9.31949 0.331993
\(789\) 0 0
\(790\) −4.37426 −0.155629
\(791\) 12.1901 0.433431
\(792\) 0 0
\(793\) 52.5744 1.86697
\(794\) 7.04802 0.250125
\(795\) 0 0
\(796\) 8.16279 0.289322
\(797\) −21.3937 −0.757805 −0.378902 0.925437i \(-0.623698\pi\)
−0.378902 + 0.925437i \(0.623698\pi\)
\(798\) 0 0
\(799\) 41.4645 1.46691
\(800\) −28.4445 −1.00567
\(801\) 0 0
\(802\) 9.93474 0.350808
\(803\) −44.1608 −1.55840
\(804\) 0 0
\(805\) −0.809807 −0.0285420
\(806\) −22.6390 −0.797424
\(807\) 0 0
\(808\) −35.4872 −1.24844
\(809\) 10.7150 0.376721 0.188360 0.982100i \(-0.439683\pi\)
0.188360 + 0.982100i \(0.439683\pi\)
\(810\) 0 0
\(811\) 8.31984 0.292149 0.146075 0.989274i \(-0.453336\pi\)
0.146075 + 0.989274i \(0.453336\pi\)
\(812\) 12.5127 0.439110
\(813\) 0 0
\(814\) −19.1063 −0.669677
\(815\) 6.28335 0.220096
\(816\) 0 0
\(817\) 23.2174 0.812275
\(818\) 8.67172 0.303200
\(819\) 0 0
\(820\) 0.775763 0.0270908
\(821\) 5.64944 0.197167 0.0985834 0.995129i \(-0.468569\pi\)
0.0985834 + 0.995129i \(0.468569\pi\)
\(822\) 0 0
\(823\) −17.7394 −0.618356 −0.309178 0.951004i \(-0.600054\pi\)
−0.309178 + 0.951004i \(0.600054\pi\)
\(824\) 27.5066 0.958238
\(825\) 0 0
\(826\) −5.79259 −0.201550
\(827\) −19.4735 −0.677160 −0.338580 0.940938i \(-0.609947\pi\)
−0.338580 + 0.940938i \(0.609947\pi\)
\(828\) 0 0
\(829\) −7.64454 −0.265506 −0.132753 0.991149i \(-0.542382\pi\)
−0.132753 + 0.991149i \(0.542382\pi\)
\(830\) −3.20896 −0.111384
\(831\) 0 0
\(832\) −18.3109 −0.634818
\(833\) 3.48245 0.120660
\(834\) 0 0
\(835\) 4.73103 0.163724
\(836\) −12.2580 −0.423951
\(837\) 0 0
\(838\) 14.0220 0.484381
\(839\) −36.5165 −1.26069 −0.630345 0.776315i \(-0.717087\pi\)
−0.630345 + 0.776315i \(0.717087\pi\)
\(840\) 0 0
\(841\) 56.4459 1.94641
\(842\) −32.3612 −1.11524
\(843\) 0 0
\(844\) 25.3202 0.871557
\(845\) −4.39562 −0.151214
\(846\) 0 0
\(847\) 5.37170 0.184574
\(848\) −6.98359 −0.239818
\(849\) 0 0
\(850\) −13.6687 −0.468833
\(851\) 13.8535 0.474892
\(852\) 0 0
\(853\) −17.2119 −0.589325 −0.294663 0.955601i \(-0.595207\pi\)
−0.294663 + 0.955601i \(0.595207\pi\)
\(854\) −8.32101 −0.284739
\(855\) 0 0
\(856\) −15.5269 −0.530698
\(857\) −36.8613 −1.25916 −0.629579 0.776937i \(-0.716773\pi\)
−0.629579 + 0.776937i \(0.716773\pi\)
\(858\) 0 0
\(859\) −39.9500 −1.36308 −0.681538 0.731783i \(-0.738688\pi\)
−0.681538 + 0.731783i \(0.738688\pi\)
\(860\) −4.82138 −0.164408
\(861\) 0 0
\(862\) −4.02722 −0.137168
\(863\) 4.30869 0.146670 0.0733348 0.997307i \(-0.476636\pi\)
0.0733348 + 0.997307i \(0.476636\pi\)
\(864\) 0 0
\(865\) −8.15191 −0.277173
\(866\) 21.6446 0.735512
\(867\) 0 0
\(868\) −7.50403 −0.254704
\(869\) −64.1208 −2.17515
\(870\) 0 0
\(871\) 25.2706 0.856263
\(872\) −27.9341 −0.945970
\(873\) 0 0
\(874\) −4.24389 −0.143552
\(875\) 3.39288 0.114700
\(876\) 0 0
\(877\) −41.7064 −1.40832 −0.704162 0.710039i \(-0.748677\pi\)
−0.704162 + 0.710039i \(0.748677\pi\)
\(878\) −24.2525 −0.818483
\(879\) 0 0
\(880\) 0.749691 0.0252721
\(881\) −14.6304 −0.492910 −0.246455 0.969154i \(-0.579266\pi\)
−0.246455 + 0.969154i \(0.579266\pi\)
\(882\) 0 0
\(883\) 20.2903 0.682821 0.341411 0.939914i \(-0.389095\pi\)
0.341411 + 0.939914i \(0.389095\pi\)
\(884\) 23.9454 0.805372
\(885\) 0 0
\(886\) −24.6572 −0.828374
\(887\) 14.1451 0.474945 0.237473 0.971394i \(-0.423681\pi\)
0.237473 + 0.971394i \(0.423681\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) −0.101143 −0.00339033
\(891\) 0 0
\(892\) 14.3864 0.481692
\(893\) −26.6476 −0.891728
\(894\) 0 0
\(895\) 2.30003 0.0768816
\(896\) −8.75443 −0.292465
\(897\) 0 0
\(898\) 9.81410 0.327501
\(899\) −51.2430 −1.70905
\(900\) 0 0
\(901\) −45.0657 −1.50136
\(902\) −5.42984 −0.180794
\(903\) 0 0
\(904\) −32.8671 −1.09314
\(905\) −2.01004 −0.0668160
\(906\) 0 0
\(907\) −53.2224 −1.76722 −0.883611 0.468223i \(-0.844895\pi\)
−0.883611 + 0.468223i \(0.844895\pi\)
\(908\) −2.75102 −0.0912957
\(909\) 0 0
\(910\) 1.40212 0.0464799
\(911\) −35.5787 −1.17877 −0.589387 0.807851i \(-0.700631\pi\)
−0.589387 + 0.807851i \(0.700631\pi\)
\(912\) 0 0
\(913\) −47.0390 −1.55676
\(914\) −26.1046 −0.863464
\(915\) 0 0
\(916\) −19.9082 −0.657787
\(917\) 11.7624 0.388428
\(918\) 0 0
\(919\) 55.8133 1.84111 0.920556 0.390610i \(-0.127736\pi\)
0.920556 + 0.390610i \(0.127736\pi\)
\(920\) 2.18340 0.0719847
\(921\) 0 0
\(922\) 9.80571 0.322934
\(923\) 43.4473 1.43009
\(924\) 0 0
\(925\) −28.6751 −0.942830
\(926\) 28.2487 0.928310
\(927\) 0 0
\(928\) −53.8562 −1.76792
\(929\) −18.8585 −0.618726 −0.309363 0.950944i \(-0.600116\pi\)
−0.309363 + 0.950944i \(0.600116\pi\)
\(930\) 0 0
\(931\) −2.23803 −0.0733485
\(932\) −25.5361 −0.836462
\(933\) 0 0
\(934\) 13.6948 0.448107
\(935\) 4.83782 0.158213
\(936\) 0 0
\(937\) −36.7884 −1.20183 −0.600913 0.799315i \(-0.705196\pi\)
−0.600913 + 0.799315i \(0.705196\pi\)
\(938\) −3.99961 −0.130592
\(939\) 0 0
\(940\) 5.53370 0.180489
\(941\) 16.0773 0.524105 0.262053 0.965054i \(-0.415601\pi\)
0.262053 + 0.965054i \(0.415601\pi\)
\(942\) 0 0
\(943\) 3.93703 0.128207
\(944\) −3.88826 −0.126552
\(945\) 0 0
\(946\) 33.7466 1.09720
\(947\) 40.8039 1.32595 0.662974 0.748642i \(-0.269294\pi\)
0.662974 + 0.748642i \(0.269294\pi\)
\(948\) 0 0
\(949\) −55.4400 −1.79966
\(950\) 8.78434 0.285002
\(951\) 0 0
\(952\) −9.38937 −0.304311
\(953\) −2.02328 −0.0655406 −0.0327703 0.999463i \(-0.510433\pi\)
−0.0327703 + 0.999463i \(0.510433\pi\)
\(954\) 0 0
\(955\) 2.39094 0.0773689
\(956\) 5.14823 0.166506
\(957\) 0 0
\(958\) −9.73368 −0.314481
\(959\) 22.2429 0.718260
\(960\) 0 0
\(961\) −0.268875 −0.00867340
\(962\) −23.9863 −0.773349
\(963\) 0 0
\(964\) 31.8372 1.02541
\(965\) 1.48785 0.0478954
\(966\) 0 0
\(967\) 54.7174 1.75959 0.879796 0.475351i \(-0.157679\pi\)
0.879796 + 0.475351i \(0.157679\pi\)
\(968\) −14.4832 −0.465507
\(969\) 0 0
\(970\) 2.13966 0.0687002
\(971\) −13.3453 −0.428271 −0.214136 0.976804i \(-0.568693\pi\)
−0.214136 + 0.976804i \(0.568693\pi\)
\(972\) 0 0
\(973\) 4.45596 0.142852
\(974\) 12.5402 0.401812
\(975\) 0 0
\(976\) −5.58546 −0.178786
\(977\) −30.3067 −0.969596 −0.484798 0.874626i \(-0.661107\pi\)
−0.484798 + 0.874626i \(0.661107\pi\)
\(978\) 0 0
\(979\) −1.48262 −0.0473848
\(980\) 0.464755 0.0148460
\(981\) 0 0
\(982\) −7.13727 −0.227759
\(983\) −25.8700 −0.825124 −0.412562 0.910930i \(-0.635366\pi\)
−0.412562 + 0.910930i \(0.635366\pi\)
\(984\) 0 0
\(985\) 2.36377 0.0753158
\(986\) −25.8800 −0.824188
\(987\) 0 0
\(988\) −15.3888 −0.489582
\(989\) −24.4688 −0.778061
\(990\) 0 0
\(991\) −19.5822 −0.622050 −0.311025 0.950402i \(-0.600672\pi\)
−0.311025 + 0.950402i \(0.600672\pi\)
\(992\) 32.2983 1.02547
\(993\) 0 0
\(994\) −6.87646 −0.218108
\(995\) 2.07038 0.0656356
\(996\) 0 0
\(997\) −51.3683 −1.62685 −0.813425 0.581670i \(-0.802399\pi\)
−0.813425 + 0.581670i \(0.802399\pi\)
\(998\) 12.3063 0.389550
\(999\) 0 0
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 \(a_p\))