Properties

Label 6004.2.a.g.1.15
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.267543 q^{3}\) \(+3.98483 q^{5}\) \(-3.08625 q^{7}\) \(-2.92842 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.267543 q^{3}\) \(+3.98483 q^{5}\) \(-3.08625 q^{7}\) \(-2.92842 q^{9}\) \(+5.66644 q^{11}\) \(-4.10489 q^{13}\) \(+1.06611 q^{15}\) \(+0.737930 q^{17}\) \(+1.00000 q^{19}\) \(-0.825706 q^{21}\) \(-6.58466 q^{23}\) \(+10.8789 q^{25}\) \(-1.58611 q^{27}\) \(-7.16235 q^{29}\) \(-7.97038 q^{31}\) \(+1.51602 q^{33}\) \(-12.2982 q^{35}\) \(+4.21298 q^{37}\) \(-1.09824 q^{39}\) \(-10.2411 q^{41}\) \(-0.0742958 q^{43}\) \(-11.6693 q^{45}\) \(-6.74831 q^{47}\) \(+2.52497 q^{49}\) \(+0.197428 q^{51}\) \(+6.32796 q^{53}\) \(+22.5798 q^{55}\) \(+0.267543 q^{57}\) \(+4.35950 q^{59}\) \(-15.4906 q^{61}\) \(+9.03785 q^{63}\) \(-16.3573 q^{65}\) \(+1.03751 q^{67}\) \(-1.76168 q^{69}\) \(-2.60621 q^{71}\) \(-1.11620 q^{73}\) \(+2.91057 q^{75}\) \(-17.4881 q^{77}\) \(-1.00000 q^{79}\) \(+8.36091 q^{81}\) \(+17.0678 q^{83}\) \(+2.94052 q^{85}\) \(-1.91624 q^{87}\) \(-5.80665 q^{89}\) \(+12.6687 q^{91}\) \(-2.13242 q^{93}\) \(+3.98483 q^{95}\) \(-8.59304 q^{97}\) \(-16.5937 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 39q^{29} \) \(\mathstrut -\mathstrut 27q^{31} \) \(\mathstrut -\mathstrut 18q^{33} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 22q^{39} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 28q^{53} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut -\mathstrut 27q^{69} \) \(\mathstrut -\mathstrut 59q^{71} \) \(\mathstrut -\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 21q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut -\mathstrut 5q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 56q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 38q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 31q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 0
\(3\) 0.267543 0.154466 0.0772330 0.997013i \(-0.475391\pi\)
0.0772330 + 0.997013i \(0.475391\pi\)
\(4\) 0 0
\(5\) 3.98483 1.78207 0.891035 0.453934i \(-0.149980\pi\)
0.891035 + 0.453934i \(0.149980\pi\)
\(6\) 0 0
\(7\) −3.08625 −1.16649 −0.583247 0.812295i \(-0.698218\pi\)
−0.583247 + 0.812295i \(0.698218\pi\)
\(8\) 0 0
\(9\) −2.92842 −0.976140
\(10\) 0 0
\(11\) 5.66644 1.70850 0.854248 0.519866i \(-0.174018\pi\)
0.854248 + 0.519866i \(0.174018\pi\)
\(12\) 0 0
\(13\) −4.10489 −1.13849 −0.569246 0.822167i \(-0.692765\pi\)
−0.569246 + 0.822167i \(0.692765\pi\)
\(14\) 0 0
\(15\) 1.06611 0.275269
\(16\) 0 0
\(17\) 0.737930 0.178974 0.0894871 0.995988i \(-0.471477\pi\)
0.0894871 + 0.995988i \(0.471477\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −0.825706 −0.180184
\(22\) 0 0
\(23\) −6.58466 −1.37300 −0.686498 0.727132i \(-0.740853\pi\)
−0.686498 + 0.727132i \(0.740853\pi\)
\(24\) 0 0
\(25\) 10.8789 2.17578
\(26\) 0 0
\(27\) −1.58611 −0.305247
\(28\) 0 0
\(29\) −7.16235 −1.33002 −0.665008 0.746837i \(-0.731572\pi\)
−0.665008 + 0.746837i \(0.731572\pi\)
\(30\) 0 0
\(31\) −7.97038 −1.43152 −0.715761 0.698345i \(-0.753920\pi\)
−0.715761 + 0.698345i \(0.753920\pi\)
\(32\) 0 0
\(33\) 1.51602 0.263904
\(34\) 0 0
\(35\) −12.2982 −2.07878
\(36\) 0 0
\(37\) 4.21298 0.692610 0.346305 0.938122i \(-0.387436\pi\)
0.346305 + 0.938122i \(0.387436\pi\)
\(38\) 0 0
\(39\) −1.09824 −0.175858
\(40\) 0 0
\(41\) −10.2411 −1.59939 −0.799697 0.600404i \(-0.795006\pi\)
−0.799697 + 0.600404i \(0.795006\pi\)
\(42\) 0 0
\(43\) −0.0742958 −0.0113300 −0.00566501 0.999984i \(-0.501803\pi\)
−0.00566501 + 0.999984i \(0.501803\pi\)
\(44\) 0 0
\(45\) −11.6693 −1.73955
\(46\) 0 0
\(47\) −6.74831 −0.984342 −0.492171 0.870499i \(-0.663796\pi\)
−0.492171 + 0.870499i \(0.663796\pi\)
\(48\) 0 0
\(49\) 2.52497 0.360710
\(50\) 0 0
\(51\) 0.197428 0.0276454
\(52\) 0 0
\(53\) 6.32796 0.869212 0.434606 0.900621i \(-0.356888\pi\)
0.434606 + 0.900621i \(0.356888\pi\)
\(54\) 0 0
\(55\) 22.5798 3.04466
\(56\) 0 0
\(57\) 0.267543 0.0354369
\(58\) 0 0
\(59\) 4.35950 0.567558 0.283779 0.958890i \(-0.408412\pi\)
0.283779 + 0.958890i \(0.408412\pi\)
\(60\) 0 0
\(61\) −15.4906 −1.98337 −0.991685 0.128691i \(-0.958922\pi\)
−0.991685 + 0.128691i \(0.958922\pi\)
\(62\) 0 0
\(63\) 9.03785 1.13866
\(64\) 0 0
\(65\) −16.3573 −2.02887
\(66\) 0 0
\(67\) 1.03751 0.126752 0.0633759 0.997990i \(-0.479813\pi\)
0.0633759 + 0.997990i \(0.479813\pi\)
\(68\) 0 0
\(69\) −1.76168 −0.212081
\(70\) 0 0
\(71\) −2.60621 −0.309300 −0.154650 0.987969i \(-0.549425\pi\)
−0.154650 + 0.987969i \(0.549425\pi\)
\(72\) 0 0
\(73\) −1.11620 −0.130642 −0.0653208 0.997864i \(-0.520807\pi\)
−0.0653208 + 0.997864i \(0.520807\pi\)
\(74\) 0 0
\(75\) 2.91057 0.336083
\(76\) 0 0
\(77\) −17.4881 −1.99295
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) 8.36091 0.928990
\(82\) 0 0
\(83\) 17.0678 1.87343 0.936717 0.350086i \(-0.113848\pi\)
0.936717 + 0.350086i \(0.113848\pi\)
\(84\) 0 0
\(85\) 2.94052 0.318945
\(86\) 0 0
\(87\) −1.91624 −0.205442
\(88\) 0 0
\(89\) −5.80665 −0.615503 −0.307752 0.951467i \(-0.599577\pi\)
−0.307752 + 0.951467i \(0.599577\pi\)
\(90\) 0 0
\(91\) 12.6687 1.32805
\(92\) 0 0
\(93\) −2.13242 −0.221122
\(94\) 0 0
\(95\) 3.98483 0.408835
\(96\) 0 0
\(97\) −8.59304 −0.872491 −0.436246 0.899828i \(-0.643692\pi\)
−0.436246 + 0.899828i \(0.643692\pi\)
\(98\) 0 0
\(99\) −16.5937 −1.66773
\(100\) 0 0
\(101\) −3.24212 −0.322603 −0.161302 0.986905i \(-0.551569\pi\)
−0.161302 + 0.986905i \(0.551569\pi\)
\(102\) 0 0
\(103\) −3.50418 −0.345277 −0.172638 0.984985i \(-0.555229\pi\)
−0.172638 + 0.984985i \(0.555229\pi\)
\(104\) 0 0
\(105\) −3.29030 −0.321100
\(106\) 0 0
\(107\) 16.3533 1.58094 0.790468 0.612504i \(-0.209837\pi\)
0.790468 + 0.612504i \(0.209837\pi\)
\(108\) 0 0
\(109\) −4.32019 −0.413799 −0.206900 0.978362i \(-0.566337\pi\)
−0.206900 + 0.978362i \(0.566337\pi\)
\(110\) 0 0
\(111\) 1.12715 0.106985
\(112\) 0 0
\(113\) −1.94549 −0.183016 −0.0915082 0.995804i \(-0.529169\pi\)
−0.0915082 + 0.995804i \(0.529169\pi\)
\(114\) 0 0
\(115\) −26.2387 −2.44678
\(116\) 0 0
\(117\) 12.0209 1.11133
\(118\) 0 0
\(119\) −2.27744 −0.208772
\(120\) 0 0
\(121\) 21.1085 1.91896
\(122\) 0 0
\(123\) −2.73994 −0.247052
\(124\) 0 0
\(125\) 23.4263 2.09531
\(126\) 0 0
\(127\) −14.4542 −1.28261 −0.641303 0.767288i \(-0.721606\pi\)
−0.641303 + 0.767288i \(0.721606\pi\)
\(128\) 0 0
\(129\) −0.0198773 −0.00175010
\(130\) 0 0
\(131\) 9.52369 0.832089 0.416045 0.909344i \(-0.363416\pi\)
0.416045 + 0.909344i \(0.363416\pi\)
\(132\) 0 0
\(133\) −3.08625 −0.267612
\(134\) 0 0
\(135\) −6.32037 −0.543971
\(136\) 0 0
\(137\) −8.32265 −0.711052 −0.355526 0.934666i \(-0.615698\pi\)
−0.355526 + 0.934666i \(0.615698\pi\)
\(138\) 0 0
\(139\) 8.68277 0.736463 0.368231 0.929734i \(-0.379963\pi\)
0.368231 + 0.929734i \(0.379963\pi\)
\(140\) 0 0
\(141\) −1.80546 −0.152047
\(142\) 0 0
\(143\) −23.2601 −1.94511
\(144\) 0 0
\(145\) −28.5408 −2.37018
\(146\) 0 0
\(147\) 0.675537 0.0557174
\(148\) 0 0
\(149\) −11.1694 −0.915035 −0.457518 0.889201i \(-0.651261\pi\)
−0.457518 + 0.889201i \(0.651261\pi\)
\(150\) 0 0
\(151\) −10.0572 −0.818445 −0.409222 0.912435i \(-0.634200\pi\)
−0.409222 + 0.912435i \(0.634200\pi\)
\(152\) 0 0
\(153\) −2.16097 −0.174704
\(154\) 0 0
\(155\) −31.7606 −2.55107
\(156\) 0 0
\(157\) −19.1717 −1.53007 −0.765033 0.643990i \(-0.777278\pi\)
−0.765033 + 0.643990i \(0.777278\pi\)
\(158\) 0 0
\(159\) 1.69300 0.134264
\(160\) 0 0
\(161\) 20.3219 1.60159
\(162\) 0 0
\(163\) −12.2144 −0.956702 −0.478351 0.878169i \(-0.658765\pi\)
−0.478351 + 0.878169i \(0.658765\pi\)
\(164\) 0 0
\(165\) 6.04107 0.470296
\(166\) 0 0
\(167\) −10.5405 −0.815645 −0.407822 0.913061i \(-0.633712\pi\)
−0.407822 + 0.913061i \(0.633712\pi\)
\(168\) 0 0
\(169\) 3.85015 0.296165
\(170\) 0 0
\(171\) −2.92842 −0.223942
\(172\) 0 0
\(173\) 9.79404 0.744627 0.372314 0.928107i \(-0.378565\pi\)
0.372314 + 0.928107i \(0.378565\pi\)
\(174\) 0 0
\(175\) −33.5750 −2.53803
\(176\) 0 0
\(177\) 1.16635 0.0876685
\(178\) 0 0
\(179\) 14.6238 1.09303 0.546515 0.837449i \(-0.315954\pi\)
0.546515 + 0.837449i \(0.315954\pi\)
\(180\) 0 0
\(181\) 6.12088 0.454962 0.227481 0.973783i \(-0.426951\pi\)
0.227481 + 0.973783i \(0.426951\pi\)
\(182\) 0 0
\(183\) −4.14441 −0.306363
\(184\) 0 0
\(185\) 16.7880 1.23428
\(186\) 0 0
\(187\) 4.18143 0.305777
\(188\) 0 0
\(189\) 4.89513 0.356068
\(190\) 0 0
\(191\) 0.507669 0.0367336 0.0183668 0.999831i \(-0.494153\pi\)
0.0183668 + 0.999831i \(0.494153\pi\)
\(192\) 0 0
\(193\) 1.57498 0.113370 0.0566849 0.998392i \(-0.481947\pi\)
0.0566849 + 0.998392i \(0.481947\pi\)
\(194\) 0 0
\(195\) −4.37628 −0.313392
\(196\) 0 0
\(197\) −5.76214 −0.410535 −0.205268 0.978706i \(-0.565807\pi\)
−0.205268 + 0.978706i \(0.565807\pi\)
\(198\) 0 0
\(199\) 13.5143 0.958005 0.479003 0.877814i \(-0.340998\pi\)
0.479003 + 0.877814i \(0.340998\pi\)
\(200\) 0 0
\(201\) 0.277578 0.0195788
\(202\) 0 0
\(203\) 22.1048 1.55146
\(204\) 0 0
\(205\) −40.8091 −2.85023
\(206\) 0 0
\(207\) 19.2827 1.34024
\(208\) 0 0
\(209\) 5.66644 0.391956
\(210\) 0 0
\(211\) −5.33274 −0.367121 −0.183561 0.983008i \(-0.558762\pi\)
−0.183561 + 0.983008i \(0.558762\pi\)
\(212\) 0 0
\(213\) −0.697272 −0.0477763
\(214\) 0 0
\(215\) −0.296056 −0.0201909
\(216\) 0 0
\(217\) 24.5986 1.66986
\(218\) 0 0
\(219\) −0.298632 −0.0201797
\(220\) 0 0
\(221\) −3.02912 −0.203761
\(222\) 0 0
\(223\) −7.27422 −0.487118 −0.243559 0.969886i \(-0.578315\pi\)
−0.243559 + 0.969886i \(0.578315\pi\)
\(224\) 0 0
\(225\) −31.8579 −2.12386
\(226\) 0 0
\(227\) −16.7390 −1.11101 −0.555503 0.831514i \(-0.687474\pi\)
−0.555503 + 0.831514i \(0.687474\pi\)
\(228\) 0 0
\(229\) 25.4085 1.67904 0.839522 0.543326i \(-0.182835\pi\)
0.839522 + 0.543326i \(0.182835\pi\)
\(230\) 0 0
\(231\) −4.67881 −0.307843
\(232\) 0 0
\(233\) 23.9450 1.56869 0.784344 0.620326i \(-0.213000\pi\)
0.784344 + 0.620326i \(0.213000\pi\)
\(234\) 0 0
\(235\) −26.8909 −1.75417
\(236\) 0 0
\(237\) −0.267543 −0.0173788
\(238\) 0 0
\(239\) 10.8368 0.700976 0.350488 0.936567i \(-0.386016\pi\)
0.350488 + 0.936567i \(0.386016\pi\)
\(240\) 0 0
\(241\) −17.8010 −1.14666 −0.573331 0.819324i \(-0.694349\pi\)
−0.573331 + 0.819324i \(0.694349\pi\)
\(242\) 0 0
\(243\) 6.99523 0.448744
\(244\) 0 0
\(245\) 10.0616 0.642810
\(246\) 0 0
\(247\) −4.10489 −0.261188
\(248\) 0 0
\(249\) 4.56637 0.289382
\(250\) 0 0
\(251\) 8.05985 0.508733 0.254367 0.967108i \(-0.418133\pi\)
0.254367 + 0.967108i \(0.418133\pi\)
\(252\) 0 0
\(253\) −37.3116 −2.34576
\(254\) 0 0
\(255\) 0.786717 0.0492661
\(256\) 0 0
\(257\) 31.1377 1.94232 0.971159 0.238433i \(-0.0766339\pi\)
0.971159 + 0.238433i \(0.0766339\pi\)
\(258\) 0 0
\(259\) −13.0023 −0.807926
\(260\) 0 0
\(261\) 20.9744 1.29828
\(262\) 0 0
\(263\) −1.28299 −0.0791123 −0.0395561 0.999217i \(-0.512594\pi\)
−0.0395561 + 0.999217i \(0.512594\pi\)
\(264\) 0 0
\(265\) 25.2159 1.54900
\(266\) 0 0
\(267\) −1.55353 −0.0950744
\(268\) 0 0
\(269\) −10.2559 −0.625316 −0.312658 0.949866i \(-0.601219\pi\)
−0.312658 + 0.949866i \(0.601219\pi\)
\(270\) 0 0
\(271\) −2.81545 −0.171026 −0.0855132 0.996337i \(-0.527253\pi\)
−0.0855132 + 0.996337i \(0.527253\pi\)
\(272\) 0 0
\(273\) 3.38943 0.205138
\(274\) 0 0
\(275\) 61.6445 3.71730
\(276\) 0 0
\(277\) −26.4165 −1.58722 −0.793608 0.608429i \(-0.791800\pi\)
−0.793608 + 0.608429i \(0.791800\pi\)
\(278\) 0 0
\(279\) 23.3406 1.39737
\(280\) 0 0
\(281\) −11.1123 −0.662905 −0.331452 0.943472i \(-0.607539\pi\)
−0.331452 + 0.943472i \(0.607539\pi\)
\(282\) 0 0
\(283\) 17.0505 1.01354 0.506772 0.862080i \(-0.330838\pi\)
0.506772 + 0.862080i \(0.330838\pi\)
\(284\) 0 0
\(285\) 1.06611 0.0631511
\(286\) 0 0
\(287\) 31.6067 1.86568
\(288\) 0 0
\(289\) −16.4555 −0.967968
\(290\) 0 0
\(291\) −2.29901 −0.134770
\(292\) 0 0
\(293\) −15.0465 −0.879027 −0.439514 0.898236i \(-0.644849\pi\)
−0.439514 + 0.898236i \(0.644849\pi\)
\(294\) 0 0
\(295\) 17.3719 1.01143
\(296\) 0 0
\(297\) −8.98758 −0.521512
\(298\) 0 0
\(299\) 27.0293 1.56315
\(300\) 0 0
\(301\) 0.229296 0.0132164
\(302\) 0 0
\(303\) −0.867408 −0.0498313
\(304\) 0 0
\(305\) −61.7275 −3.53450
\(306\) 0 0
\(307\) −10.5847 −0.604103 −0.302051 0.953292i \(-0.597671\pi\)
−0.302051 + 0.953292i \(0.597671\pi\)
\(308\) 0 0
\(309\) −0.937518 −0.0533335
\(310\) 0 0
\(311\) 19.3012 1.09447 0.547236 0.836979i \(-0.315680\pi\)
0.547236 + 0.836979i \(0.315680\pi\)
\(312\) 0 0
\(313\) −19.1934 −1.08487 −0.542437 0.840097i \(-0.682498\pi\)
−0.542437 + 0.840097i \(0.682498\pi\)
\(314\) 0 0
\(315\) 36.0143 2.02918
\(316\) 0 0
\(317\) 5.46787 0.307106 0.153553 0.988140i \(-0.450928\pi\)
0.153553 + 0.988140i \(0.450928\pi\)
\(318\) 0 0
\(319\) −40.5850 −2.27232
\(320\) 0 0
\(321\) 4.37522 0.244201
\(322\) 0 0
\(323\) 0.737930 0.0410595
\(324\) 0 0
\(325\) −44.6566 −2.47710
\(326\) 0 0
\(327\) −1.15584 −0.0639180
\(328\) 0 0
\(329\) 20.8270 1.14823
\(330\) 0 0
\(331\) −18.4884 −1.01622 −0.508108 0.861293i \(-0.669655\pi\)
−0.508108 + 0.861293i \(0.669655\pi\)
\(332\) 0 0
\(333\) −12.3374 −0.676085
\(334\) 0 0
\(335\) 4.13429 0.225881
\(336\) 0 0
\(337\) 9.87107 0.537711 0.268856 0.963180i \(-0.413355\pi\)
0.268856 + 0.963180i \(0.413355\pi\)
\(338\) 0 0
\(339\) −0.520503 −0.0282698
\(340\) 0 0
\(341\) −45.1636 −2.44575
\(342\) 0 0
\(343\) 13.8111 0.745729
\(344\) 0 0
\(345\) −7.02000 −0.377944
\(346\) 0 0
\(347\) 5.72655 0.307417 0.153709 0.988116i \(-0.450878\pi\)
0.153709 + 0.988116i \(0.450878\pi\)
\(348\) 0 0
\(349\) −15.5689 −0.833382 −0.416691 0.909048i \(-0.636810\pi\)
−0.416691 + 0.909048i \(0.636810\pi\)
\(350\) 0 0
\(351\) 6.51080 0.347521
\(352\) 0 0
\(353\) 1.82597 0.0971865 0.0485933 0.998819i \(-0.484526\pi\)
0.0485933 + 0.998819i \(0.484526\pi\)
\(354\) 0 0
\(355\) −10.3853 −0.551194
\(356\) 0 0
\(357\) −0.609313 −0.0322483
\(358\) 0 0
\(359\) −13.8860 −0.732876 −0.366438 0.930442i \(-0.619423\pi\)
−0.366438 + 0.930442i \(0.619423\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 5.64744 0.296413
\(364\) 0 0
\(365\) −4.44788 −0.232813
\(366\) 0 0
\(367\) 24.2946 1.26817 0.634085 0.773264i \(-0.281377\pi\)
0.634085 + 0.773264i \(0.281377\pi\)
\(368\) 0 0
\(369\) 29.9903 1.56123
\(370\) 0 0
\(371\) −19.5297 −1.01393
\(372\) 0 0
\(373\) −25.6746 −1.32938 −0.664690 0.747119i \(-0.731437\pi\)
−0.664690 + 0.747119i \(0.731437\pi\)
\(374\) 0 0
\(375\) 6.26755 0.323655
\(376\) 0 0
\(377\) 29.4007 1.51421
\(378\) 0 0
\(379\) −29.5409 −1.51741 −0.758706 0.651433i \(-0.774168\pi\)
−0.758706 + 0.651433i \(0.774168\pi\)
\(380\) 0 0
\(381\) −3.86713 −0.198119
\(382\) 0 0
\(383\) 19.3035 0.986364 0.493182 0.869926i \(-0.335834\pi\)
0.493182 + 0.869926i \(0.335834\pi\)
\(384\) 0 0
\(385\) −69.6870 −3.55158
\(386\) 0 0
\(387\) 0.217570 0.0110597
\(388\) 0 0
\(389\) −7.82362 −0.396673 −0.198337 0.980134i \(-0.563554\pi\)
−0.198337 + 0.980134i \(0.563554\pi\)
\(390\) 0 0
\(391\) −4.85901 −0.245731
\(392\) 0 0
\(393\) 2.54800 0.128530
\(394\) 0 0
\(395\) −3.98483 −0.200499
\(396\) 0 0
\(397\) −15.2982 −0.767793 −0.383897 0.923376i \(-0.625418\pi\)
−0.383897 + 0.923376i \(0.625418\pi\)
\(398\) 0 0
\(399\) −0.825706 −0.0413370
\(400\) 0 0
\(401\) 3.46073 0.172821 0.0864104 0.996260i \(-0.472460\pi\)
0.0864104 + 0.996260i \(0.472460\pi\)
\(402\) 0 0
\(403\) 32.7175 1.62978
\(404\) 0 0
\(405\) 33.3168 1.65553
\(406\) 0 0
\(407\) 23.8726 1.18332
\(408\) 0 0
\(409\) 33.6841 1.66557 0.832785 0.553596i \(-0.186745\pi\)
0.832785 + 0.553596i \(0.186745\pi\)
\(410\) 0 0
\(411\) −2.22667 −0.109833
\(412\) 0 0
\(413\) −13.4545 −0.662053
\(414\) 0 0
\(415\) 68.0123 3.33859
\(416\) 0 0
\(417\) 2.32301 0.113758
\(418\) 0 0
\(419\) −12.6607 −0.618516 −0.309258 0.950978i \(-0.600081\pi\)
−0.309258 + 0.950978i \(0.600081\pi\)
\(420\) 0 0
\(421\) 24.9508 1.21603 0.608013 0.793927i \(-0.291967\pi\)
0.608013 + 0.793927i \(0.291967\pi\)
\(422\) 0 0
\(423\) 19.7619 0.960855
\(424\) 0 0
\(425\) 8.02784 0.389408
\(426\) 0 0
\(427\) 47.8080 2.31359
\(428\) 0 0
\(429\) −6.22308 −0.300453
\(430\) 0 0
\(431\) 5.25871 0.253303 0.126652 0.991947i \(-0.459577\pi\)
0.126652 + 0.991947i \(0.459577\pi\)
\(432\) 0 0
\(433\) 29.1341 1.40010 0.700048 0.714096i \(-0.253162\pi\)
0.700048 + 0.714096i \(0.253162\pi\)
\(434\) 0 0
\(435\) −7.63588 −0.366112
\(436\) 0 0
\(437\) −6.58466 −0.314987
\(438\) 0 0
\(439\) −14.5518 −0.694522 −0.347261 0.937769i \(-0.612888\pi\)
−0.347261 + 0.937769i \(0.612888\pi\)
\(440\) 0 0
\(441\) −7.39417 −0.352103
\(442\) 0 0
\(443\) 30.3678 1.44282 0.721409 0.692509i \(-0.243495\pi\)
0.721409 + 0.692509i \(0.243495\pi\)
\(444\) 0 0
\(445\) −23.1385 −1.09687
\(446\) 0 0
\(447\) −2.98830 −0.141342
\(448\) 0 0
\(449\) −26.7498 −1.26240 −0.631201 0.775619i \(-0.717438\pi\)
−0.631201 + 0.775619i \(0.717438\pi\)
\(450\) 0 0
\(451\) −58.0306 −2.73256
\(452\) 0 0
\(453\) −2.69074 −0.126422
\(454\) 0 0
\(455\) 50.4828 2.36667
\(456\) 0 0
\(457\) 5.00356 0.234057 0.117028 0.993129i \(-0.462663\pi\)
0.117028 + 0.993129i \(0.462663\pi\)
\(458\) 0 0
\(459\) −1.17044 −0.0546313
\(460\) 0 0
\(461\) 14.3969 0.670530 0.335265 0.942124i \(-0.391174\pi\)
0.335265 + 0.942124i \(0.391174\pi\)
\(462\) 0 0
\(463\) 20.9455 0.973418 0.486709 0.873564i \(-0.338197\pi\)
0.486709 + 0.873564i \(0.338197\pi\)
\(464\) 0 0
\(465\) −8.49733 −0.394054
\(466\) 0 0
\(467\) 17.3177 0.801368 0.400684 0.916216i \(-0.368773\pi\)
0.400684 + 0.916216i \(0.368773\pi\)
\(468\) 0 0
\(469\) −3.20201 −0.147855
\(470\) 0 0
\(471\) −5.12925 −0.236343
\(472\) 0 0
\(473\) −0.420993 −0.0193573
\(474\) 0 0
\(475\) 10.8789 0.499157
\(476\) 0 0
\(477\) −18.5309 −0.848473
\(478\) 0 0
\(479\) −4.75877 −0.217434 −0.108717 0.994073i \(-0.534674\pi\)
−0.108717 + 0.994073i \(0.534674\pi\)
\(480\) 0 0
\(481\) −17.2938 −0.788532
\(482\) 0 0
\(483\) 5.43699 0.247392
\(484\) 0 0
\(485\) −34.2418 −1.55484
\(486\) 0 0
\(487\) −22.0088 −0.997315 −0.498658 0.866799i \(-0.666173\pi\)
−0.498658 + 0.866799i \(0.666173\pi\)
\(488\) 0 0
\(489\) −3.26787 −0.147778
\(490\) 0 0
\(491\) 13.3411 0.602075 0.301037 0.953612i \(-0.402667\pi\)
0.301037 + 0.953612i \(0.402667\pi\)
\(492\) 0 0
\(493\) −5.28531 −0.238038
\(494\) 0 0
\(495\) −66.1231 −2.97201
\(496\) 0 0
\(497\) 8.04342 0.360797
\(498\) 0 0
\(499\) 17.3197 0.775336 0.387668 0.921799i \(-0.373281\pi\)
0.387668 + 0.921799i \(0.373281\pi\)
\(500\) 0 0
\(501\) −2.82003 −0.125989
\(502\) 0 0
\(503\) 22.4785 1.00227 0.501134 0.865369i \(-0.332916\pi\)
0.501134 + 0.865369i \(0.332916\pi\)
\(504\) 0 0
\(505\) −12.9193 −0.574902
\(506\) 0 0
\(507\) 1.03008 0.0457475
\(508\) 0 0
\(509\) −26.6450 −1.18102 −0.590510 0.807030i \(-0.701074\pi\)
−0.590510 + 0.807030i \(0.701074\pi\)
\(510\) 0 0
\(511\) 3.44489 0.152393
\(512\) 0 0
\(513\) −1.58611 −0.0700284
\(514\) 0 0
\(515\) −13.9636 −0.615308
\(516\) 0 0
\(517\) −38.2389 −1.68174
\(518\) 0 0
\(519\) 2.62033 0.115020
\(520\) 0 0
\(521\) −24.9282 −1.09213 −0.546063 0.837744i \(-0.683874\pi\)
−0.546063 + 0.837744i \(0.683874\pi\)
\(522\) 0 0
\(523\) −35.9077 −1.57013 −0.785067 0.619411i \(-0.787372\pi\)
−0.785067 + 0.619411i \(0.787372\pi\)
\(524\) 0 0
\(525\) −8.98275 −0.392039
\(526\) 0 0
\(527\) −5.88158 −0.256206
\(528\) 0 0
\(529\) 20.3577 0.885119
\(530\) 0 0
\(531\) −12.7664 −0.554016
\(532\) 0 0
\(533\) 42.0387 1.82090
\(534\) 0 0
\(535\) 65.1652 2.81734
\(536\) 0 0
\(537\) 3.91248 0.168836
\(538\) 0 0
\(539\) 14.3076 0.616271
\(540\) 0 0
\(541\) −44.0737 −1.89488 −0.947438 0.319940i \(-0.896337\pi\)
−0.947438 + 0.319940i \(0.896337\pi\)
\(542\) 0 0
\(543\) 1.63760 0.0702761
\(544\) 0 0
\(545\) −17.2152 −0.737420
\(546\) 0 0
\(547\) −22.8305 −0.976164 −0.488082 0.872798i \(-0.662303\pi\)
−0.488082 + 0.872798i \(0.662303\pi\)
\(548\) 0 0
\(549\) 45.3630 1.93605
\(550\) 0 0
\(551\) −7.16235 −0.305126
\(552\) 0 0
\(553\) 3.08625 0.131241
\(554\) 0 0
\(555\) 4.49152 0.190654
\(556\) 0 0
\(557\) −38.0115 −1.61060 −0.805298 0.592870i \(-0.797995\pi\)
−0.805298 + 0.592870i \(0.797995\pi\)
\(558\) 0 0
\(559\) 0.304977 0.0128991
\(560\) 0 0
\(561\) 1.11871 0.0472321
\(562\) 0 0
\(563\) 12.3346 0.519842 0.259921 0.965630i \(-0.416304\pi\)
0.259921 + 0.965630i \(0.416304\pi\)
\(564\) 0 0
\(565\) −7.75245 −0.326148
\(566\) 0 0
\(567\) −25.8039 −1.08366
\(568\) 0 0
\(569\) 34.3615 1.44051 0.720254 0.693711i \(-0.244025\pi\)
0.720254 + 0.693711i \(0.244025\pi\)
\(570\) 0 0
\(571\) −20.2425 −0.847122 −0.423561 0.905867i \(-0.639220\pi\)
−0.423561 + 0.905867i \(0.639220\pi\)
\(572\) 0 0
\(573\) 0.135823 0.00567410
\(574\) 0 0
\(575\) −71.6337 −2.98733
\(576\) 0 0
\(577\) −21.6444 −0.901069 −0.450535 0.892759i \(-0.648767\pi\)
−0.450535 + 0.892759i \(0.648767\pi\)
\(578\) 0 0
\(579\) 0.421376 0.0175118
\(580\) 0 0
\(581\) −52.6756 −2.18535
\(582\) 0 0
\(583\) 35.8570 1.48504
\(584\) 0 0
\(585\) 47.9011 1.98047
\(586\) 0 0
\(587\) −33.0794 −1.36533 −0.682666 0.730730i \(-0.739180\pi\)
−0.682666 + 0.730730i \(0.739180\pi\)
\(588\) 0 0
\(589\) −7.97038 −0.328414
\(590\) 0 0
\(591\) −1.54162 −0.0634138
\(592\) 0 0
\(593\) 36.4590 1.49719 0.748595 0.663028i \(-0.230729\pi\)
0.748595 + 0.663028i \(0.230729\pi\)
\(594\) 0 0
\(595\) −9.07521 −0.372047
\(596\) 0 0
\(597\) 3.61566 0.147979
\(598\) 0 0
\(599\) 22.1215 0.903862 0.451931 0.892053i \(-0.350735\pi\)
0.451931 + 0.892053i \(0.350735\pi\)
\(600\) 0 0
\(601\) −17.6738 −0.720930 −0.360465 0.932773i \(-0.617382\pi\)
−0.360465 + 0.932773i \(0.617382\pi\)
\(602\) 0 0
\(603\) −3.03826 −0.123727
\(604\) 0 0
\(605\) 84.1138 3.41971
\(606\) 0 0
\(607\) 28.6143 1.16142 0.580708 0.814112i \(-0.302776\pi\)
0.580708 + 0.814112i \(0.302776\pi\)
\(608\) 0 0
\(609\) 5.91400 0.239647
\(610\) 0 0
\(611\) 27.7011 1.12067
\(612\) 0 0
\(613\) 16.9460 0.684444 0.342222 0.939619i \(-0.388820\pi\)
0.342222 + 0.939619i \(0.388820\pi\)
\(614\) 0 0
\(615\) −10.9182 −0.440264
\(616\) 0 0
\(617\) −29.5611 −1.19009 −0.595043 0.803694i \(-0.702865\pi\)
−0.595043 + 0.803694i \(0.702865\pi\)
\(618\) 0 0
\(619\) −20.8148 −0.836617 −0.418309 0.908305i \(-0.637377\pi\)
−0.418309 + 0.908305i \(0.637377\pi\)
\(620\) 0 0
\(621\) 10.4440 0.419102
\(622\) 0 0
\(623\) 17.9208 0.717981
\(624\) 0 0
\(625\) 38.9555 1.55822
\(626\) 0 0
\(627\) 1.51602 0.0605438
\(628\) 0 0
\(629\) 3.10889 0.123959
\(630\) 0 0
\(631\) −39.1313 −1.55779 −0.778896 0.627153i \(-0.784220\pi\)
−0.778896 + 0.627153i \(0.784220\pi\)
\(632\) 0 0
\(633\) −1.42674 −0.0567077
\(634\) 0 0
\(635\) −57.5977 −2.28569
\(636\) 0 0
\(637\) −10.3647 −0.410665
\(638\) 0 0
\(639\) 7.63207 0.301920
\(640\) 0 0
\(641\) −45.6850 −1.80445 −0.902224 0.431268i \(-0.858066\pi\)
−0.902224 + 0.431268i \(0.858066\pi\)
\(642\) 0 0
\(643\) −10.2820 −0.405484 −0.202742 0.979232i \(-0.564985\pi\)
−0.202742 + 0.979232i \(0.564985\pi\)
\(644\) 0 0
\(645\) −0.0792078 −0.00311881
\(646\) 0 0
\(647\) −6.89390 −0.271027 −0.135514 0.990775i \(-0.543268\pi\)
−0.135514 + 0.990775i \(0.543268\pi\)
\(648\) 0 0
\(649\) 24.7028 0.969670
\(650\) 0 0
\(651\) 6.58119 0.257937
\(652\) 0 0
\(653\) 11.8571 0.464004 0.232002 0.972715i \(-0.425472\pi\)
0.232002 + 0.972715i \(0.425472\pi\)
\(654\) 0 0
\(655\) 37.9503 1.48284
\(656\) 0 0
\(657\) 3.26871 0.127525
\(658\) 0 0
\(659\) 7.88681 0.307227 0.153613 0.988131i \(-0.450909\pi\)
0.153613 + 0.988131i \(0.450909\pi\)
\(660\) 0 0
\(661\) −5.94556 −0.231256 −0.115628 0.993293i \(-0.536888\pi\)
−0.115628 + 0.993293i \(0.536888\pi\)
\(662\) 0 0
\(663\) −0.810421 −0.0314741
\(664\) 0 0
\(665\) −12.2982 −0.476904
\(666\) 0 0
\(667\) 47.1616 1.82611
\(668\) 0 0
\(669\) −1.94617 −0.0752432
\(670\) 0 0
\(671\) −87.7766 −3.38858
\(672\) 0 0
\(673\) −49.8614 −1.92202 −0.961008 0.276520i \(-0.910819\pi\)
−0.961008 + 0.276520i \(0.910819\pi\)
\(674\) 0 0
\(675\) −17.2551 −0.664148
\(676\) 0 0
\(677\) −8.28532 −0.318431 −0.159215 0.987244i \(-0.550896\pi\)
−0.159215 + 0.987244i \(0.550896\pi\)
\(678\) 0 0
\(679\) 26.5203 1.01776
\(680\) 0 0
\(681\) −4.47840 −0.171613
\(682\) 0 0
\(683\) 31.1620 1.19238 0.596190 0.802844i \(-0.296681\pi\)
0.596190 + 0.802844i \(0.296681\pi\)
\(684\) 0 0
\(685\) −33.1644 −1.26714
\(686\) 0 0
\(687\) 6.79788 0.259355
\(688\) 0 0
\(689\) −25.9756 −0.989592
\(690\) 0 0
\(691\) 5.78987 0.220257 0.110128 0.993917i \(-0.464874\pi\)
0.110128 + 0.993917i \(0.464874\pi\)
\(692\) 0 0
\(693\) 51.2124 1.94540
\(694\) 0 0
\(695\) 34.5994 1.31243
\(696\) 0 0
\(697\) −7.55722 −0.286250
\(698\) 0 0
\(699\) 6.40631 0.242309
\(700\) 0 0
\(701\) 13.7565 0.519576 0.259788 0.965666i \(-0.416347\pi\)
0.259788 + 0.965666i \(0.416347\pi\)
\(702\) 0 0
\(703\) 4.21298 0.158896
\(704\) 0 0
\(705\) −7.19446 −0.270959
\(706\) 0 0
\(707\) 10.0060 0.376315
\(708\) 0 0
\(709\) −0.784026 −0.0294447 −0.0147224 0.999892i \(-0.504686\pi\)
−0.0147224 + 0.999892i \(0.504686\pi\)
\(710\) 0 0
\(711\) 2.92842 0.109824
\(712\) 0 0
\(713\) 52.4822 1.96547
\(714\) 0 0
\(715\) −92.6876 −3.46632
\(716\) 0 0
\(717\) 2.89932 0.108277
\(718\) 0 0
\(719\) 38.4772 1.43496 0.717479 0.696581i \(-0.245296\pi\)
0.717479 + 0.696581i \(0.245296\pi\)
\(720\) 0 0
\(721\) 10.8148 0.402763
\(722\) 0 0
\(723\) −4.76253 −0.177120
\(724\) 0 0
\(725\) −77.9183 −2.89381
\(726\) 0 0
\(727\) 40.6305 1.50690 0.753451 0.657504i \(-0.228388\pi\)
0.753451 + 0.657504i \(0.228388\pi\)
\(728\) 0 0
\(729\) −23.2112 −0.859674
\(730\) 0 0
\(731\) −0.0548251 −0.00202778
\(732\) 0 0
\(733\) 35.4159 1.30812 0.654059 0.756444i \(-0.273065\pi\)
0.654059 + 0.756444i \(0.273065\pi\)
\(734\) 0 0
\(735\) 2.69190 0.0992923
\(736\) 0 0
\(737\) 5.87897 0.216555
\(738\) 0 0
\(739\) 27.6195 1.01600 0.508000 0.861357i \(-0.330385\pi\)
0.508000 + 0.861357i \(0.330385\pi\)
\(740\) 0 0
\(741\) −1.09824 −0.0403447
\(742\) 0 0
\(743\) −52.1845 −1.91446 −0.957232 0.289323i \(-0.906570\pi\)
−0.957232 + 0.289323i \(0.906570\pi\)
\(744\) 0 0
\(745\) −44.5083 −1.63066
\(746\) 0 0
\(747\) −49.9817 −1.82874
\(748\) 0 0
\(749\) −50.4705 −1.84415
\(750\) 0 0
\(751\) −4.68961 −0.171126 −0.0855632 0.996333i \(-0.527269\pi\)
−0.0855632 + 0.996333i \(0.527269\pi\)
\(752\) 0 0
\(753\) 2.15636 0.0785820
\(754\) 0 0
\(755\) −40.0763 −1.45853
\(756\) 0 0
\(757\) 13.5813 0.493620 0.246810 0.969064i \(-0.420618\pi\)
0.246810 + 0.969064i \(0.420618\pi\)
\(758\) 0 0
\(759\) −9.98245 −0.362340
\(760\) 0 0
\(761\) 23.4668 0.850671 0.425336 0.905036i \(-0.360156\pi\)
0.425336 + 0.905036i \(0.360156\pi\)
\(762\) 0 0
\(763\) 13.3332 0.482695
\(764\) 0 0
\(765\) −8.61109 −0.311335
\(766\) 0 0
\(767\) −17.8953 −0.646161
\(768\) 0 0
\(769\) −37.3675 −1.34751 −0.673753 0.738956i \(-0.735319\pi\)
−0.673753 + 0.738956i \(0.735319\pi\)
\(770\) 0 0
\(771\) 8.33068 0.300022
\(772\) 0 0
\(773\) 53.4358 1.92195 0.960977 0.276630i \(-0.0892176\pi\)
0.960977 + 0.276630i \(0.0892176\pi\)
\(774\) 0 0
\(775\) −86.7087 −3.11467
\(776\) 0 0
\(777\) −3.47869 −0.124797
\(778\) 0 0
\(779\) −10.2411 −0.366926
\(780\) 0 0
\(781\) −14.7679 −0.528437
\(782\) 0 0
\(783\) 11.3603 0.405983
\(784\) 0 0
\(785\) −76.3959 −2.72669
\(786\) 0 0
\(787\) 41.9471 1.49525 0.747626 0.664120i \(-0.231194\pi\)
0.747626 + 0.664120i \(0.231194\pi\)
\(788\) 0 0
\(789\) −0.343254 −0.0122202
\(790\) 0 0
\(791\) 6.00428 0.213488
\(792\) 0 0
\(793\) 63.5873 2.25805
\(794\) 0 0
\(795\) 6.74633 0.239268
\(796\) 0 0
\(797\) 20.7217 0.734001 0.367000 0.930221i \(-0.380385\pi\)
0.367000 + 0.930221i \(0.380385\pi\)
\(798\) 0 0
\(799\) −4.97978 −0.176172
\(800\) 0 0
\(801\) 17.0043 0.600818
\(802\) 0 0
\(803\) −6.32489 −0.223201
\(804\) 0 0
\(805\) 80.9795 2.85415
\(806\) 0 0
\(807\) −2.74391 −0.0965901
\(808\) 0 0
\(809\) −25.2923 −0.889229 −0.444614 0.895722i \(-0.646659\pi\)
−0.444614 + 0.895722i \(0.646659\pi\)
\(810\) 0 0
\(811\) −10.4491 −0.366919 −0.183460 0.983027i \(-0.558730\pi\)
−0.183460 + 0.983027i \(0.558730\pi\)
\(812\) 0 0
\(813\) −0.753254 −0.0264178
\(814\) 0 0
\(815\) −48.6721 −1.70491
\(816\) 0 0
\(817\) −0.0742958 −0.00259928
\(818\) 0 0
\(819\) −37.0994 −1.29636
\(820\) 0 0
\(821\) 7.67738 0.267942 0.133971 0.990985i \(-0.457227\pi\)
0.133971 + 0.990985i \(0.457227\pi\)
\(822\) 0 0
\(823\) −28.4103 −0.990320 −0.495160 0.868802i \(-0.664891\pi\)
−0.495160 + 0.868802i \(0.664891\pi\)
\(824\) 0 0
\(825\) 16.4925 0.574197
\(826\) 0 0
\(827\) 6.35233 0.220892 0.110446 0.993882i \(-0.464772\pi\)
0.110446 + 0.993882i \(0.464772\pi\)
\(828\) 0 0
\(829\) −40.9232 −1.42132 −0.710660 0.703535i \(-0.751604\pi\)
−0.710660 + 0.703535i \(0.751604\pi\)
\(830\) 0 0
\(831\) −7.06756 −0.245171
\(832\) 0 0
\(833\) 1.86325 0.0645577
\(834\) 0 0
\(835\) −42.0019 −1.45354
\(836\) 0 0
\(837\) 12.6419 0.436967
\(838\) 0 0
\(839\) 14.5133 0.501056 0.250528 0.968109i \(-0.419396\pi\)
0.250528 + 0.968109i \(0.419396\pi\)
\(840\) 0 0
\(841\) 22.2993 0.768940
\(842\) 0 0
\(843\) −2.97302 −0.102396
\(844\) 0 0
\(845\) 15.3422 0.527787
\(846\) 0 0
\(847\) −65.1462 −2.23845
\(848\) 0 0
\(849\) 4.56173 0.156558
\(850\) 0 0
\(851\) −27.7411 −0.950951
\(852\) 0 0
\(853\) 28.0533 0.960526 0.480263 0.877125i \(-0.340541\pi\)
0.480263 + 0.877125i \(0.340541\pi\)
\(854\) 0 0
\(855\) −11.6693 −0.399080
\(856\) 0 0
\(857\) −16.1110 −0.550342 −0.275171 0.961395i \(-0.588734\pi\)
−0.275171 + 0.961395i \(0.588734\pi\)
\(858\) 0 0
\(859\) −27.4236 −0.935682 −0.467841 0.883813i \(-0.654968\pi\)
−0.467841 + 0.883813i \(0.654968\pi\)
\(860\) 0 0
\(861\) 8.45615 0.288185
\(862\) 0 0
\(863\) 52.5151 1.78764 0.893818 0.448430i \(-0.148017\pi\)
0.893818 + 0.448430i \(0.148017\pi\)
\(864\) 0 0
\(865\) 39.0276 1.32698
\(866\) 0 0
\(867\) −4.40254 −0.149518
\(868\) 0 0
\(869\) −5.66644 −0.192221
\(870\) 0 0
\(871\) −4.25886 −0.144306
\(872\) 0 0
\(873\) 25.1640 0.851674
\(874\) 0 0
\(875\) −72.2996 −2.44417
\(876\) 0 0
\(877\) −31.6799 −1.06975 −0.534876 0.844930i \(-0.679642\pi\)
−0.534876 + 0.844930i \(0.679642\pi\)
\(878\) 0 0
\(879\) −4.02559 −0.135780
\(880\) 0 0
\(881\) −1.08430 −0.0365308 −0.0182654 0.999833i \(-0.505814\pi\)
−0.0182654 + 0.999833i \(0.505814\pi\)
\(882\) 0 0
\(883\) −14.6799 −0.494018 −0.247009 0.969013i \(-0.579448\pi\)
−0.247009 + 0.969013i \(0.579448\pi\)
\(884\) 0 0
\(885\) 4.64772 0.156231
\(886\) 0 0
\(887\) −34.9533 −1.17362 −0.586809 0.809725i \(-0.699616\pi\)
−0.586809 + 0.809725i \(0.699616\pi\)
\(888\) 0 0
\(889\) 44.6094 1.49615
\(890\) 0 0
\(891\) 47.3766 1.58717
\(892\) 0 0
\(893\) −6.74831 −0.225823
\(894\) 0 0
\(895\) 58.2732 1.94786
\(896\) 0 0
\(897\) 7.23151 0.241453
\(898\) 0 0
\(899\) 57.0866 1.90395
\(900\) 0 0
\(901\) 4.66959 0.155567
\(902\) 0 0
\(903\) 0.0613465 0.00204148
\(904\) 0 0
\(905\) 24.3907 0.810774
\(906\) 0 0
\(907\) 48.8899 1.62336 0.811682 0.584100i \(-0.198552\pi\)
0.811682 + 0.584100i \(0.198552\pi\)
\(908\) 0 0
\(909\) 9.49431 0.314906
\(910\) 0 0
\(911\) −27.9939 −0.927479 −0.463739 0.885972i \(-0.653493\pi\)
−0.463739 + 0.885972i \(0.653493\pi\)
\(912\) 0 0
\(913\) 96.7136 3.20075
\(914\) 0 0
\(915\) −16.5148 −0.545961
\(916\) 0 0
\(917\) −29.3925 −0.970627
\(918\) 0 0
\(919\) 38.2174 1.26068 0.630338 0.776321i \(-0.282916\pi\)
0.630338 + 0.776321i \(0.282916\pi\)
\(920\) 0 0
\(921\) −2.83187 −0.0933134
\(922\) 0 0
\(923\) 10.6982 0.352136
\(924\) 0 0
\(925\) 45.8325 1.50696
\(926\) 0 0
\(927\) 10.2617 0.337039
\(928\) 0 0
\(929\) 26.9191 0.883187 0.441594 0.897215i \(-0.354413\pi\)
0.441594 + 0.897215i \(0.354413\pi\)
\(930\) 0 0
\(931\) 2.52497 0.0827525
\(932\) 0 0
\(933\) 5.16390 0.169059
\(934\) 0 0
\(935\) 16.6623 0.544915
\(936\) 0 0
\(937\) −45.1360 −1.47453 −0.737265 0.675604i \(-0.763883\pi\)
−0.737265 + 0.675604i \(0.763883\pi\)
\(938\) 0 0
\(939\) −5.13505 −0.167576
\(940\) 0 0
\(941\) −23.2948 −0.759387 −0.379694 0.925112i \(-0.623971\pi\)
−0.379694 + 0.925112i \(0.623971\pi\)
\(942\) 0 0
\(943\) 67.4342 2.19596
\(944\) 0 0
\(945\) 19.5063 0.634539
\(946\) 0 0
\(947\) −2.33510 −0.0758807 −0.0379403 0.999280i \(-0.512080\pi\)
−0.0379403 + 0.999280i \(0.512080\pi\)
\(948\) 0 0
\(949\) 4.58189 0.148735
\(950\) 0 0
\(951\) 1.46289 0.0474375
\(952\) 0 0
\(953\) −33.1929 −1.07522 −0.537612 0.843192i \(-0.680673\pi\)
−0.537612 + 0.843192i \(0.680673\pi\)
\(954\) 0 0
\(955\) 2.02297 0.0654619
\(956\) 0 0
\(957\) −10.8582 −0.350997
\(958\) 0 0
\(959\) 25.6858 0.829438
\(960\) 0 0
\(961\) 32.5269 1.04926
\(962\) 0 0
\(963\) −47.8894 −1.54321
\(964\) 0 0
\(965\) 6.27604 0.202033
\(966\) 0 0
\(967\) 46.3742 1.49129 0.745647 0.666342i \(-0.232141\pi\)
0.745647 + 0.666342i \(0.232141\pi\)
\(968\) 0 0
\(969\) 0.197428 0.00634230
\(970\) 0 0
\(971\) −38.2017 −1.22595 −0.612975 0.790102i \(-0.710028\pi\)
−0.612975 + 0.790102i \(0.710028\pi\)
\(972\) 0 0
\(973\) −26.7972 −0.859080
\(974\) 0 0
\(975\) −11.9476 −0.382628
\(976\) 0 0
\(977\) 5.15462 0.164911 0.0824554 0.996595i \(-0.473724\pi\)
0.0824554 + 0.996595i \(0.473724\pi\)
\(978\) 0 0
\(979\) −32.9030 −1.05158
\(980\) 0 0
\(981\) 12.6513 0.403926
\(982\) 0 0
\(983\) 41.7510 1.33165 0.665826 0.746107i \(-0.268079\pi\)
0.665826 + 0.746107i \(0.268079\pi\)
\(984\) 0 0
\(985\) −22.9612 −0.731603
\(986\) 0 0
\(987\) 5.57212 0.177362
\(988\) 0 0
\(989\) 0.489213 0.0155561
\(990\) 0 0
\(991\) 40.0015 1.27069 0.635344 0.772229i \(-0.280858\pi\)
0.635344 + 0.772229i \(0.280858\pi\)
\(992\) 0 0
\(993\) −4.94645 −0.156971
\(994\) 0 0
\(995\) 53.8523 1.70723
\(996\) 0 0
\(997\) −33.6269 −1.06497 −0.532487 0.846438i \(-0.678743\pi\)
−0.532487 + 0.846438i \(0.678743\pi\)
\(998\) 0 0
\(999\) −6.68225 −0.211417
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 \(a_p\))