Properties

Label 8001.2.a.u.1.4
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 1.4
Root \(-1.70725\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.70725 q^{2}\) \(+0.914706 q^{4}\) \(-1.08728 q^{5}\) \(+1.00000 q^{7}\) \(+1.85287 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.70725 q^{2}\) \(+0.914706 q^{4}\) \(-1.08728 q^{5}\) \(+1.00000 q^{7}\) \(+1.85287 q^{8}\) \(+1.85625 q^{10}\) \(-1.58139 q^{11}\) \(-5.55528 q^{13}\) \(-1.70725 q^{14}\) \(-4.99273 q^{16}\) \(+3.38289 q^{17}\) \(-4.84199 q^{19}\) \(-0.994538 q^{20}\) \(+2.69983 q^{22}\) \(-7.35331 q^{23}\) \(-3.81783 q^{25}\) \(+9.48427 q^{26}\) \(+0.914706 q^{28}\) \(-4.01548 q^{29}\) \(-8.96014 q^{31}\) \(+4.81810 q^{32}\) \(-5.77544 q^{34}\) \(-1.08728 q^{35}\) \(-3.94006 q^{37}\) \(+8.26650 q^{38}\) \(-2.01458 q^{40}\) \(-6.40603 q^{41}\) \(-8.32135 q^{43}\) \(-1.44651 q^{44}\) \(+12.5539 q^{46}\) \(+2.82123 q^{47}\) \(+1.00000 q^{49}\) \(+6.51800 q^{50}\) \(-5.08145 q^{52}\) \(+2.86232 q^{53}\) \(+1.71941 q^{55}\) \(+1.85287 q^{56}\) \(+6.85544 q^{58}\) \(+3.19939 q^{59}\) \(+15.1992 q^{61}\) \(+15.2972 q^{62}\) \(+1.75975 q^{64}\) \(+6.04013 q^{65}\) \(-14.4412 q^{67}\) \(+3.09435 q^{68}\) \(+1.85625 q^{70}\) \(-4.60022 q^{71}\) \(-11.4194 q^{73}\) \(+6.72667 q^{74}\) \(-4.42900 q^{76}\) \(-1.58139 q^{77}\) \(+5.60203 q^{79}\) \(+5.42847 q^{80}\) \(+10.9367 q^{82}\) \(+6.19625 q^{83}\) \(-3.67813 q^{85}\) \(+14.2066 q^{86}\) \(-2.93010 q^{88}\) \(+14.7613 q^{89}\) \(-5.55528 q^{91}\) \(-6.72612 q^{92}\) \(-4.81655 q^{94}\) \(+5.26458 q^{95}\) \(-4.99491 q^{97}\) \(-1.70725 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 21q^{20} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut +\mathstrut 33q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 31q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 35q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 63q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 46q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.70725 −1.20721 −0.603604 0.797284i \(-0.706269\pi\)
−0.603604 + 0.797284i \(0.706269\pi\)
\(3\) 0 0
\(4\) 0.914706 0.457353
\(5\) −1.08728 −0.486245 −0.243122 0.969996i \(-0.578172\pi\)
−0.243122 + 0.969996i \(0.578172\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.85287 0.655088
\(9\) 0 0
\(10\) 1.85625 0.586999
\(11\) −1.58139 −0.476806 −0.238403 0.971166i \(-0.576624\pi\)
−0.238403 + 0.971166i \(0.576624\pi\)
\(12\) 0 0
\(13\) −5.55528 −1.54076 −0.770379 0.637586i \(-0.779933\pi\)
−0.770379 + 0.637586i \(0.779933\pi\)
\(14\) −1.70725 −0.456282
\(15\) 0 0
\(16\) −4.99273 −1.24818
\(17\) 3.38289 0.820471 0.410236 0.911980i \(-0.365446\pi\)
0.410236 + 0.911980i \(0.365446\pi\)
\(18\) 0 0
\(19\) −4.84199 −1.11083 −0.555415 0.831573i \(-0.687441\pi\)
−0.555415 + 0.831573i \(0.687441\pi\)
\(20\) −0.994538 −0.222386
\(21\) 0 0
\(22\) 2.69983 0.575605
\(23\) −7.35331 −1.53327 −0.766636 0.642082i \(-0.778071\pi\)
−0.766636 + 0.642082i \(0.778071\pi\)
\(24\) 0 0
\(25\) −3.81783 −0.763566
\(26\) 9.48427 1.86002
\(27\) 0 0
\(28\) 0.914706 0.172863
\(29\) −4.01548 −0.745656 −0.372828 0.927900i \(-0.621612\pi\)
−0.372828 + 0.927900i \(0.621612\pi\)
\(30\) 0 0
\(31\) −8.96014 −1.60929 −0.804644 0.593757i \(-0.797644\pi\)
−0.804644 + 0.593757i \(0.797644\pi\)
\(32\) 4.81810 0.851727
\(33\) 0 0
\(34\) −5.77544 −0.990480
\(35\) −1.08728 −0.183783
\(36\) 0 0
\(37\) −3.94006 −0.647742 −0.323871 0.946101i \(-0.604984\pi\)
−0.323871 + 0.946101i \(0.604984\pi\)
\(38\) 8.26650 1.34100
\(39\) 0 0
\(40\) −2.01458 −0.318533
\(41\) −6.40603 −1.00045 −0.500227 0.865894i \(-0.666750\pi\)
−0.500227 + 0.865894i \(0.666750\pi\)
\(42\) 0 0
\(43\) −8.32135 −1.26899 −0.634497 0.772925i \(-0.718793\pi\)
−0.634497 + 0.772925i \(0.718793\pi\)
\(44\) −1.44651 −0.218069
\(45\) 0 0
\(46\) 12.5539 1.85098
\(47\) 2.82123 0.411519 0.205759 0.978603i \(-0.434034\pi\)
0.205759 + 0.978603i \(0.434034\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 6.51800 0.921784
\(51\) 0 0
\(52\) −5.08145 −0.704671
\(53\) 2.86232 0.393170 0.196585 0.980487i \(-0.437015\pi\)
0.196585 + 0.980487i \(0.437015\pi\)
\(54\) 0 0
\(55\) 1.71941 0.231845
\(56\) 1.85287 0.247600
\(57\) 0 0
\(58\) 6.85544 0.900163
\(59\) 3.19939 0.416525 0.208263 0.978073i \(-0.433219\pi\)
0.208263 + 0.978073i \(0.433219\pi\)
\(60\) 0 0
\(61\) 15.1992 1.94606 0.973028 0.230687i \(-0.0740975\pi\)
0.973028 + 0.230687i \(0.0740975\pi\)
\(62\) 15.2972 1.94275
\(63\) 0 0
\(64\) 1.75975 0.219968
\(65\) 6.04013 0.749186
\(66\) 0 0
\(67\) −14.4412 −1.76427 −0.882137 0.470992i \(-0.843896\pi\)
−0.882137 + 0.470992i \(0.843896\pi\)
\(68\) 3.09435 0.375245
\(69\) 0 0
\(70\) 1.85625 0.221865
\(71\) −4.60022 −0.545946 −0.272973 0.962022i \(-0.588007\pi\)
−0.272973 + 0.962022i \(0.588007\pi\)
\(72\) 0 0
\(73\) −11.4194 −1.33654 −0.668272 0.743917i \(-0.732966\pi\)
−0.668272 + 0.743917i \(0.732966\pi\)
\(74\) 6.72667 0.781960
\(75\) 0 0
\(76\) −4.42900 −0.508042
\(77\) −1.58139 −0.180216
\(78\) 0 0
\(79\) 5.60203 0.630278 0.315139 0.949046i \(-0.397949\pi\)
0.315139 + 0.949046i \(0.397949\pi\)
\(80\) 5.42847 0.606921
\(81\) 0 0
\(82\) 10.9367 1.20776
\(83\) 6.19625 0.680127 0.340064 0.940402i \(-0.389551\pi\)
0.340064 + 0.940402i \(0.389551\pi\)
\(84\) 0 0
\(85\) −3.67813 −0.398950
\(86\) 14.2066 1.53194
\(87\) 0 0
\(88\) −2.93010 −0.312350
\(89\) 14.7613 1.56470 0.782349 0.622840i \(-0.214021\pi\)
0.782349 + 0.622840i \(0.214021\pi\)
\(90\) 0 0
\(91\) −5.55528 −0.582352
\(92\) −6.72612 −0.701247
\(93\) 0 0
\(94\) −4.81655 −0.496789
\(95\) 5.26458 0.540135
\(96\) 0 0
\(97\) −4.99491 −0.507157 −0.253578 0.967315i \(-0.581608\pi\)
−0.253578 + 0.967315i \(0.581608\pi\)
\(98\) −1.70725 −0.172458
\(99\) 0 0
\(100\) −3.49219 −0.349219
\(101\) −15.3793 −1.53030 −0.765148 0.643854i \(-0.777334\pi\)
−0.765148 + 0.643854i \(0.777334\pi\)
\(102\) 0 0
\(103\) 18.4573 1.81866 0.909328 0.416080i \(-0.136596\pi\)
0.909328 + 0.416080i \(0.136596\pi\)
\(104\) −10.2932 −1.00933
\(105\) 0 0
\(106\) −4.88670 −0.474639
\(107\) 3.34462 0.323336 0.161668 0.986845i \(-0.448313\pi\)
0.161668 + 0.986845i \(0.448313\pi\)
\(108\) 0 0
\(109\) −2.86219 −0.274148 −0.137074 0.990561i \(-0.543770\pi\)
−0.137074 + 0.990561i \(0.543770\pi\)
\(110\) −2.93546 −0.279885
\(111\) 0 0
\(112\) −4.99273 −0.471768
\(113\) 6.64072 0.624706 0.312353 0.949966i \(-0.398883\pi\)
0.312353 + 0.949966i \(0.398883\pi\)
\(114\) 0 0
\(115\) 7.99508 0.745545
\(116\) −3.67299 −0.341028
\(117\) 0 0
\(118\) −5.46217 −0.502833
\(119\) 3.38289 0.310109
\(120\) 0 0
\(121\) −8.49921 −0.772656
\(122\) −25.9488 −2.34930
\(123\) 0 0
\(124\) −8.19590 −0.736013
\(125\) 9.58742 0.857525
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −12.6405 −1.11728
\(129\) 0 0
\(130\) −10.3120 −0.904424
\(131\) 6.22354 0.543753 0.271876 0.962332i \(-0.412356\pi\)
0.271876 + 0.962332i \(0.412356\pi\)
\(132\) 0 0
\(133\) −4.84199 −0.419854
\(134\) 24.6548 2.12985
\(135\) 0 0
\(136\) 6.26805 0.537481
\(137\) −0.432704 −0.0369684 −0.0184842 0.999829i \(-0.505884\pi\)
−0.0184842 + 0.999829i \(0.505884\pi\)
\(138\) 0 0
\(139\) −6.17897 −0.524093 −0.262047 0.965055i \(-0.584397\pi\)
−0.262047 + 0.965055i \(0.584397\pi\)
\(140\) −0.994538 −0.0840538
\(141\) 0 0
\(142\) 7.85373 0.659070
\(143\) 8.78506 0.734644
\(144\) 0 0
\(145\) 4.36594 0.362571
\(146\) 19.4958 1.61349
\(147\) 0 0
\(148\) −3.60400 −0.296247
\(149\) −13.4075 −1.09838 −0.549191 0.835697i \(-0.685064\pi\)
−0.549191 + 0.835697i \(0.685064\pi\)
\(150\) 0 0
\(151\) 11.2770 0.917708 0.458854 0.888512i \(-0.348260\pi\)
0.458854 + 0.888512i \(0.348260\pi\)
\(152\) −8.97158 −0.727691
\(153\) 0 0
\(154\) 2.69983 0.217558
\(155\) 9.74214 0.782508
\(156\) 0 0
\(157\) −20.5897 −1.64323 −0.821617 0.570040i \(-0.806928\pi\)
−0.821617 + 0.570040i \(0.806928\pi\)
\(158\) −9.56408 −0.760877
\(159\) 0 0
\(160\) −5.23860 −0.414148
\(161\) −7.35331 −0.579522
\(162\) 0 0
\(163\) 13.6441 1.06869 0.534343 0.845268i \(-0.320559\pi\)
0.534343 + 0.845268i \(0.320559\pi\)
\(164\) −5.85964 −0.457561
\(165\) 0 0
\(166\) −10.5786 −0.821055
\(167\) 24.9692 1.93218 0.966089 0.258210i \(-0.0831325\pi\)
0.966089 + 0.258210i \(0.0831325\pi\)
\(168\) 0 0
\(169\) 17.8612 1.37394
\(170\) 6.27950 0.481616
\(171\) 0 0
\(172\) −7.61159 −0.580378
\(173\) 7.80876 0.593689 0.296845 0.954926i \(-0.404066\pi\)
0.296845 + 0.954926i \(0.404066\pi\)
\(174\) 0 0
\(175\) −3.81783 −0.288601
\(176\) 7.89544 0.595141
\(177\) 0 0
\(178\) −25.2013 −1.88892
\(179\) 20.4507 1.52856 0.764279 0.644886i \(-0.223095\pi\)
0.764279 + 0.644886i \(0.223095\pi\)
\(180\) 0 0
\(181\) −4.32280 −0.321311 −0.160656 0.987011i \(-0.551361\pi\)
−0.160656 + 0.987011i \(0.551361\pi\)
\(182\) 9.48427 0.703021
\(183\) 0 0
\(184\) −13.6247 −1.00443
\(185\) 4.28393 0.314961
\(186\) 0 0
\(187\) −5.34966 −0.391206
\(188\) 2.58060 0.188210
\(189\) 0 0
\(190\) −8.98797 −0.652056
\(191\) −18.8230 −1.36198 −0.680992 0.732291i \(-0.738451\pi\)
−0.680992 + 0.732291i \(0.738451\pi\)
\(192\) 0 0
\(193\) 4.03163 0.290203 0.145102 0.989417i \(-0.453649\pi\)
0.145102 + 0.989417i \(0.453649\pi\)
\(194\) 8.52757 0.612244
\(195\) 0 0
\(196\) 0.914706 0.0653362
\(197\) −8.77313 −0.625060 −0.312530 0.949908i \(-0.601176\pi\)
−0.312530 + 0.949908i \(0.601176\pi\)
\(198\) 0 0
\(199\) −16.1994 −1.14835 −0.574174 0.818734i \(-0.694677\pi\)
−0.574174 + 0.818734i \(0.694677\pi\)
\(200\) −7.07394 −0.500203
\(201\) 0 0
\(202\) 26.2563 1.84739
\(203\) −4.01548 −0.281832
\(204\) 0 0
\(205\) 6.96513 0.486465
\(206\) −31.5113 −2.19550
\(207\) 0 0
\(208\) 27.7360 1.92315
\(209\) 7.65707 0.529651
\(210\) 0 0
\(211\) −6.64122 −0.457200 −0.228600 0.973520i \(-0.573415\pi\)
−0.228600 + 0.973520i \(0.573415\pi\)
\(212\) 2.61818 0.179818
\(213\) 0 0
\(214\) −5.71010 −0.390334
\(215\) 9.04760 0.617041
\(216\) 0 0
\(217\) −8.96014 −0.608254
\(218\) 4.88648 0.330954
\(219\) 0 0
\(220\) 1.57275 0.106035
\(221\) −18.7929 −1.26415
\(222\) 0 0
\(223\) 18.9937 1.27192 0.635958 0.771724i \(-0.280605\pi\)
0.635958 + 0.771724i \(0.280605\pi\)
\(224\) 4.81810 0.321923
\(225\) 0 0
\(226\) −11.3374 −0.754151
\(227\) −9.18958 −0.609934 −0.304967 0.952363i \(-0.598645\pi\)
−0.304967 + 0.952363i \(0.598645\pi\)
\(228\) 0 0
\(229\) 0.707717 0.0467672 0.0233836 0.999727i \(-0.492556\pi\)
0.0233836 + 0.999727i \(0.492556\pi\)
\(230\) −13.6496 −0.900029
\(231\) 0 0
\(232\) −7.44016 −0.488471
\(233\) 13.4302 0.879842 0.439921 0.898036i \(-0.355006\pi\)
0.439921 + 0.898036i \(0.355006\pi\)
\(234\) 0 0
\(235\) −3.06746 −0.200099
\(236\) 2.92650 0.190499
\(237\) 0 0
\(238\) −5.77544 −0.374366
\(239\) 0.623102 0.0403051 0.0201526 0.999797i \(-0.493585\pi\)
0.0201526 + 0.999797i \(0.493585\pi\)
\(240\) 0 0
\(241\) 0.924991 0.0595839 0.0297920 0.999556i \(-0.490516\pi\)
0.0297920 + 0.999556i \(0.490516\pi\)
\(242\) 14.5103 0.932757
\(243\) 0 0
\(244\) 13.9028 0.890035
\(245\) −1.08728 −0.0694635
\(246\) 0 0
\(247\) 26.8987 1.71152
\(248\) −16.6020 −1.05423
\(249\) 0 0
\(250\) −16.3681 −1.03521
\(251\) −11.3142 −0.714146 −0.357073 0.934077i \(-0.616225\pi\)
−0.357073 + 0.934077i \(0.616225\pi\)
\(252\) 0 0
\(253\) 11.6284 0.731074
\(254\) −1.70725 −0.107122
\(255\) 0 0
\(256\) 18.0611 1.12882
\(257\) −22.4836 −1.40249 −0.701244 0.712921i \(-0.747372\pi\)
−0.701244 + 0.712921i \(0.747372\pi\)
\(258\) 0 0
\(259\) −3.94006 −0.244823
\(260\) 5.52494 0.342642
\(261\) 0 0
\(262\) −10.6251 −0.656423
\(263\) −7.25932 −0.447629 −0.223814 0.974632i \(-0.571851\pi\)
−0.223814 + 0.974632i \(0.571851\pi\)
\(264\) 0 0
\(265\) −3.11213 −0.191177
\(266\) 8.26650 0.506852
\(267\) 0 0
\(268\) −13.2095 −0.806897
\(269\) 5.61611 0.342420 0.171210 0.985235i \(-0.445232\pi\)
0.171210 + 0.985235i \(0.445232\pi\)
\(270\) 0 0
\(271\) 15.4371 0.937737 0.468869 0.883268i \(-0.344662\pi\)
0.468869 + 0.883268i \(0.344662\pi\)
\(272\) −16.8898 −1.02410
\(273\) 0 0
\(274\) 0.738734 0.0446286
\(275\) 6.03747 0.364073
\(276\) 0 0
\(277\) 21.4310 1.28767 0.643833 0.765166i \(-0.277343\pi\)
0.643833 + 0.765166i \(0.277343\pi\)
\(278\) 10.5491 0.632690
\(279\) 0 0
\(280\) −2.01458 −0.120394
\(281\) −18.1891 −1.08507 −0.542535 0.840033i \(-0.682535\pi\)
−0.542535 + 0.840033i \(0.682535\pi\)
\(282\) 0 0
\(283\) −6.98641 −0.415299 −0.207649 0.978203i \(-0.566581\pi\)
−0.207649 + 0.978203i \(0.566581\pi\)
\(284\) −4.20785 −0.249690
\(285\) 0 0
\(286\) −14.9983 −0.886868
\(287\) −6.40603 −0.378136
\(288\) 0 0
\(289\) −5.55606 −0.326827
\(290\) −7.45375 −0.437699
\(291\) 0 0
\(292\) −10.4454 −0.611272
\(293\) −3.67122 −0.214475 −0.107237 0.994233i \(-0.534201\pi\)
−0.107237 + 0.994233i \(0.534201\pi\)
\(294\) 0 0
\(295\) −3.47862 −0.202533
\(296\) −7.30042 −0.424328
\(297\) 0 0
\(298\) 22.8899 1.32598
\(299\) 40.8497 2.36240
\(300\) 0 0
\(301\) −8.32135 −0.479634
\(302\) −19.2526 −1.10786
\(303\) 0 0
\(304\) 24.1747 1.38652
\(305\) −16.5257 −0.946259
\(306\) 0 0
\(307\) 0.782621 0.0446666 0.0223333 0.999751i \(-0.492891\pi\)
0.0223333 + 0.999751i \(0.492891\pi\)
\(308\) −1.44651 −0.0824223
\(309\) 0 0
\(310\) −16.6323 −0.944650
\(311\) −27.4489 −1.55649 −0.778243 0.627963i \(-0.783889\pi\)
−0.778243 + 0.627963i \(0.783889\pi\)
\(312\) 0 0
\(313\) −17.6863 −0.999690 −0.499845 0.866115i \(-0.666610\pi\)
−0.499845 + 0.866115i \(0.666610\pi\)
\(314\) 35.1517 1.98373
\(315\) 0 0
\(316\) 5.12422 0.288260
\(317\) −5.84866 −0.328493 −0.164247 0.986419i \(-0.552519\pi\)
−0.164247 + 0.986419i \(0.552519\pi\)
\(318\) 0 0
\(319\) 6.35004 0.355534
\(320\) −1.91333 −0.106958
\(321\) 0 0
\(322\) 12.5539 0.699604
\(323\) −16.3799 −0.911404
\(324\) 0 0
\(325\) 21.2091 1.17647
\(326\) −23.2939 −1.29013
\(327\) 0 0
\(328\) −11.8695 −0.655386
\(329\) 2.82123 0.155540
\(330\) 0 0
\(331\) −6.76050 −0.371591 −0.185795 0.982588i \(-0.559486\pi\)
−0.185795 + 0.982588i \(0.559486\pi\)
\(332\) 5.66775 0.311058
\(333\) 0 0
\(334\) −42.6288 −2.33254
\(335\) 15.7016 0.857869
\(336\) 0 0
\(337\) 21.7933 1.18715 0.593577 0.804777i \(-0.297715\pi\)
0.593577 + 0.804777i \(0.297715\pi\)
\(338\) −30.4935 −1.65863
\(339\) 0 0
\(340\) −3.36441 −0.182461
\(341\) 14.1695 0.767319
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −15.4184 −0.831302
\(345\) 0 0
\(346\) −13.3315 −0.716707
\(347\) −26.0834 −1.40023 −0.700115 0.714030i \(-0.746868\pi\)
−0.700115 + 0.714030i \(0.746868\pi\)
\(348\) 0 0
\(349\) −33.5729 −1.79711 −0.898557 0.438856i \(-0.855384\pi\)
−0.898557 + 0.438856i \(0.855384\pi\)
\(350\) 6.51800 0.348402
\(351\) 0 0
\(352\) −7.61928 −0.406109
\(353\) 27.4331 1.46011 0.730057 0.683386i \(-0.239493\pi\)
0.730057 + 0.683386i \(0.239493\pi\)
\(354\) 0 0
\(355\) 5.00171 0.265463
\(356\) 13.5023 0.715619
\(357\) 0 0
\(358\) −34.9145 −1.84529
\(359\) −6.58084 −0.347324 −0.173662 0.984805i \(-0.555560\pi\)
−0.173662 + 0.984805i \(0.555560\pi\)
\(360\) 0 0
\(361\) 4.44491 0.233943
\(362\) 7.38010 0.387889
\(363\) 0 0
\(364\) −5.08145 −0.266341
\(365\) 12.4161 0.649887
\(366\) 0 0
\(367\) 23.1790 1.20994 0.604968 0.796250i \(-0.293186\pi\)
0.604968 + 0.796250i \(0.293186\pi\)
\(368\) 36.7131 1.91380
\(369\) 0 0
\(370\) −7.31375 −0.380224
\(371\) 2.86232 0.148604
\(372\) 0 0
\(373\) 14.4055 0.745886 0.372943 0.927854i \(-0.378349\pi\)
0.372943 + 0.927854i \(0.378349\pi\)
\(374\) 9.13321 0.472267
\(375\) 0 0
\(376\) 5.22737 0.269581
\(377\) 22.3072 1.14888
\(378\) 0 0
\(379\) 19.3549 0.994194 0.497097 0.867695i \(-0.334399\pi\)
0.497097 + 0.867695i \(0.334399\pi\)
\(380\) 4.81555 0.247032
\(381\) 0 0
\(382\) 32.1356 1.64420
\(383\) −21.4947 −1.09833 −0.549163 0.835715i \(-0.685054\pi\)
−0.549163 + 0.835715i \(0.685054\pi\)
\(384\) 0 0
\(385\) 1.71941 0.0876290
\(386\) −6.88301 −0.350336
\(387\) 0 0
\(388\) −4.56888 −0.231950
\(389\) −24.0187 −1.21779 −0.608897 0.793249i \(-0.708388\pi\)
−0.608897 + 0.793249i \(0.708388\pi\)
\(390\) 0 0
\(391\) −24.8754 −1.25800
\(392\) 1.85287 0.0935840
\(393\) 0 0
\(394\) 14.9779 0.754578
\(395\) −6.09096 −0.306469
\(396\) 0 0
\(397\) −22.9033 −1.14948 −0.574741 0.818336i \(-0.694897\pi\)
−0.574741 + 0.818336i \(0.694897\pi\)
\(398\) 27.6565 1.38629
\(399\) 0 0
\(400\) 19.0614 0.953069
\(401\) 36.2294 1.80921 0.904606 0.426249i \(-0.140165\pi\)
0.904606 + 0.426249i \(0.140165\pi\)
\(402\) 0 0
\(403\) 49.7761 2.47953
\(404\) −14.0675 −0.699886
\(405\) 0 0
\(406\) 6.85544 0.340230
\(407\) 6.23077 0.308848
\(408\) 0 0
\(409\) 10.3032 0.509461 0.254731 0.967012i \(-0.418013\pi\)
0.254731 + 0.967012i \(0.418013\pi\)
\(410\) −11.8912 −0.587265
\(411\) 0 0
\(412\) 16.8830 0.831768
\(413\) 3.19939 0.157432
\(414\) 0 0
\(415\) −6.73704 −0.330708
\(416\) −26.7659 −1.31231
\(417\) 0 0
\(418\) −13.0725 −0.639399
\(419\) −34.4188 −1.68147 −0.840735 0.541446i \(-0.817877\pi\)
−0.840735 + 0.541446i \(0.817877\pi\)
\(420\) 0 0
\(421\) 5.58303 0.272100 0.136050 0.990702i \(-0.456559\pi\)
0.136050 + 0.990702i \(0.456559\pi\)
\(422\) 11.3382 0.551936
\(423\) 0 0
\(424\) 5.30351 0.257561
\(425\) −12.9153 −0.626484
\(426\) 0 0
\(427\) 15.1992 0.735540
\(428\) 3.05934 0.147879
\(429\) 0 0
\(430\) −15.4465 −0.744898
\(431\) 6.32096 0.304470 0.152235 0.988344i \(-0.451353\pi\)
0.152235 + 0.988344i \(0.451353\pi\)
\(432\) 0 0
\(433\) 2.42420 0.116500 0.0582498 0.998302i \(-0.481448\pi\)
0.0582498 + 0.998302i \(0.481448\pi\)
\(434\) 15.2972 0.734289
\(435\) 0 0
\(436\) −2.61807 −0.125383
\(437\) 35.6047 1.70320
\(438\) 0 0
\(439\) 20.2577 0.966845 0.483423 0.875387i \(-0.339393\pi\)
0.483423 + 0.875387i \(0.339393\pi\)
\(440\) 3.18583 0.151879
\(441\) 0 0
\(442\) 32.0842 1.52609
\(443\) 22.8915 1.08761 0.543804 0.839212i \(-0.316983\pi\)
0.543804 + 0.839212i \(0.316983\pi\)
\(444\) 0 0
\(445\) −16.0496 −0.760826
\(446\) −32.4271 −1.53547
\(447\) 0 0
\(448\) 1.75975 0.0831402
\(449\) 6.07459 0.286677 0.143339 0.989674i \(-0.454216\pi\)
0.143339 + 0.989674i \(0.454216\pi\)
\(450\) 0 0
\(451\) 10.1304 0.477023
\(452\) 6.07431 0.285712
\(453\) 0 0
\(454\) 15.6889 0.736318
\(455\) 6.04013 0.283166
\(456\) 0 0
\(457\) 12.0326 0.562862 0.281431 0.959582i \(-0.409191\pi\)
0.281431 + 0.959582i \(0.409191\pi\)
\(458\) −1.20825 −0.0564578
\(459\) 0 0
\(460\) 7.31315 0.340977
\(461\) 35.2714 1.64275 0.821377 0.570386i \(-0.193206\pi\)
0.821377 + 0.570386i \(0.193206\pi\)
\(462\) 0 0
\(463\) 41.2830 1.91858 0.959291 0.282420i \(-0.0911372\pi\)
0.959291 + 0.282420i \(0.0911372\pi\)
\(464\) 20.0482 0.930714
\(465\) 0 0
\(466\) −22.9287 −1.06215
\(467\) −3.10679 −0.143765 −0.0718825 0.997413i \(-0.522901\pi\)
−0.0718825 + 0.997413i \(0.522901\pi\)
\(468\) 0 0
\(469\) −14.4412 −0.666833
\(470\) 5.23692 0.241561
\(471\) 0 0
\(472\) 5.92805 0.272861
\(473\) 13.1593 0.605064
\(474\) 0 0
\(475\) 18.4859 0.848192
\(476\) 3.09435 0.141829
\(477\) 0 0
\(478\) −1.06379 −0.0486567
\(479\) 15.5577 0.710848 0.355424 0.934705i \(-0.384336\pi\)
0.355424 + 0.934705i \(0.384336\pi\)
\(480\) 0 0
\(481\) 21.8882 0.998014
\(482\) −1.57919 −0.0719302
\(483\) 0 0
\(484\) −7.77428 −0.353377
\(485\) 5.43085 0.246602
\(486\) 0 0
\(487\) −29.6687 −1.34442 −0.672210 0.740361i \(-0.734655\pi\)
−0.672210 + 0.740361i \(0.734655\pi\)
\(488\) 28.1621 1.27484
\(489\) 0 0
\(490\) 1.85625 0.0838570
\(491\) −0.760535 −0.0343225 −0.0171612 0.999853i \(-0.505463\pi\)
−0.0171612 + 0.999853i \(0.505463\pi\)
\(492\) 0 0
\(493\) −13.5839 −0.611790
\(494\) −45.9228 −2.06616
\(495\) 0 0
\(496\) 44.7355 2.00868
\(497\) −4.60022 −0.206348
\(498\) 0 0
\(499\) −16.4337 −0.735673 −0.367837 0.929890i \(-0.619901\pi\)
−0.367837 + 0.929890i \(0.619901\pi\)
\(500\) 8.76967 0.392192
\(501\) 0 0
\(502\) 19.3162 0.862123
\(503\) −38.5672 −1.71963 −0.859813 0.510610i \(-0.829420\pi\)
−0.859813 + 0.510610i \(0.829420\pi\)
\(504\) 0 0
\(505\) 16.7215 0.744098
\(506\) −19.8527 −0.882559
\(507\) 0 0
\(508\) 0.914706 0.0405835
\(509\) 26.3389 1.16745 0.583726 0.811951i \(-0.301594\pi\)
0.583726 + 0.811951i \(0.301594\pi\)
\(510\) 0 0
\(511\) −11.4194 −0.505166
\(512\) −5.55371 −0.245442
\(513\) 0 0
\(514\) 38.3852 1.69310
\(515\) −20.0682 −0.884312
\(516\) 0 0
\(517\) −4.46146 −0.196215
\(518\) 6.72667 0.295553
\(519\) 0 0
\(520\) 11.1916 0.490783
\(521\) −12.5229 −0.548640 −0.274320 0.961638i \(-0.588453\pi\)
−0.274320 + 0.961638i \(0.588453\pi\)
\(522\) 0 0
\(523\) −29.0101 −1.26852 −0.634261 0.773119i \(-0.718696\pi\)
−0.634261 + 0.773119i \(0.718696\pi\)
\(524\) 5.69271 0.248687
\(525\) 0 0
\(526\) 12.3935 0.540382
\(527\) −30.3112 −1.32037
\(528\) 0 0
\(529\) 31.0712 1.35092
\(530\) 5.31320 0.230790
\(531\) 0 0
\(532\) −4.42900 −0.192022
\(533\) 35.5873 1.54146
\(534\) 0 0
\(535\) −3.63652 −0.157220
\(536\) −26.7577 −1.15576
\(537\) 0 0
\(538\) −9.58812 −0.413373
\(539\) −1.58139 −0.0681152
\(540\) 0 0
\(541\) −19.1020 −0.821260 −0.410630 0.911802i \(-0.634691\pi\)
−0.410630 + 0.911802i \(0.634691\pi\)
\(542\) −26.3550 −1.13204
\(543\) 0 0
\(544\) 16.2991 0.698818
\(545\) 3.11199 0.133303
\(546\) 0 0
\(547\) −38.1266 −1.63018 −0.815089 0.579336i \(-0.803312\pi\)
−0.815089 + 0.579336i \(0.803312\pi\)
\(548\) −0.395797 −0.0169076
\(549\) 0 0
\(550\) −10.3075 −0.439513
\(551\) 19.4429 0.828297
\(552\) 0 0
\(553\) 5.60203 0.238223
\(554\) −36.5882 −1.55448
\(555\) 0 0
\(556\) −5.65194 −0.239696
\(557\) 15.8515 0.671649 0.335825 0.941925i \(-0.390985\pi\)
0.335825 + 0.941925i \(0.390985\pi\)
\(558\) 0 0
\(559\) 46.2275 1.95521
\(560\) 5.42847 0.229395
\(561\) 0 0
\(562\) 31.0533 1.30991
\(563\) −12.5290 −0.528035 −0.264017 0.964518i \(-0.585048\pi\)
−0.264017 + 0.964518i \(0.585048\pi\)
\(564\) 0 0
\(565\) −7.22030 −0.303760
\(566\) 11.9276 0.501352
\(567\) 0 0
\(568\) −8.52360 −0.357642
\(569\) 26.3672 1.10537 0.552685 0.833390i \(-0.313603\pi\)
0.552685 + 0.833390i \(0.313603\pi\)
\(570\) 0 0
\(571\) 24.5409 1.02700 0.513502 0.858089i \(-0.328348\pi\)
0.513502 + 0.858089i \(0.328348\pi\)
\(572\) 8.03575 0.335992
\(573\) 0 0
\(574\) 10.9367 0.456489
\(575\) 28.0737 1.17075
\(576\) 0 0
\(577\) −28.3026 −1.17825 −0.589126 0.808042i \(-0.700528\pi\)
−0.589126 + 0.808042i \(0.700528\pi\)
\(578\) 9.48559 0.394549
\(579\) 0 0
\(580\) 3.99355 0.165823
\(581\) 6.19625 0.257064
\(582\) 0 0
\(583\) −4.52644 −0.187466
\(584\) −21.1587 −0.875554
\(585\) 0 0
\(586\) 6.26769 0.258916
\(587\) 7.70006 0.317815 0.158908 0.987293i \(-0.449203\pi\)
0.158908 + 0.987293i \(0.449203\pi\)
\(588\) 0 0
\(589\) 43.3849 1.78765
\(590\) 5.93888 0.244500
\(591\) 0 0
\(592\) 19.6716 0.808499
\(593\) −25.5437 −1.04895 −0.524477 0.851424i \(-0.675739\pi\)
−0.524477 + 0.851424i \(0.675739\pi\)
\(594\) 0 0
\(595\) −3.67813 −0.150789
\(596\) −12.2639 −0.502348
\(597\) 0 0
\(598\) −69.7408 −2.85191
\(599\) 25.6812 1.04930 0.524652 0.851317i \(-0.324196\pi\)
0.524652 + 0.851317i \(0.324196\pi\)
\(600\) 0 0
\(601\) −33.8437 −1.38051 −0.690256 0.723565i \(-0.742502\pi\)
−0.690256 + 0.723565i \(0.742502\pi\)
\(602\) 14.2066 0.579019
\(603\) 0 0
\(604\) 10.3151 0.419717
\(605\) 9.24099 0.375700
\(606\) 0 0
\(607\) −15.9169 −0.646046 −0.323023 0.946391i \(-0.604699\pi\)
−0.323023 + 0.946391i \(0.604699\pi\)
\(608\) −23.3292 −0.946124
\(609\) 0 0
\(610\) 28.2135 1.14233
\(611\) −15.6727 −0.634051
\(612\) 0 0
\(613\) −26.9742 −1.08948 −0.544740 0.838605i \(-0.683372\pi\)
−0.544740 + 0.838605i \(0.683372\pi\)
\(614\) −1.33613 −0.0539219
\(615\) 0 0
\(616\) −2.93010 −0.118057
\(617\) 45.1074 1.81596 0.907979 0.419016i \(-0.137625\pi\)
0.907979 + 0.419016i \(0.137625\pi\)
\(618\) 0 0
\(619\) −24.4678 −0.983443 −0.491722 0.870752i \(-0.663632\pi\)
−0.491722 + 0.870752i \(0.663632\pi\)
\(620\) 8.91120 0.357882
\(621\) 0 0
\(622\) 46.8622 1.87900
\(623\) 14.7613 0.591400
\(624\) 0 0
\(625\) 8.66499 0.346600
\(626\) 30.1950 1.20683
\(627\) 0 0
\(628\) −18.8335 −0.751538
\(629\) −13.3288 −0.531454
\(630\) 0 0
\(631\) 4.21378 0.167748 0.0838740 0.996476i \(-0.473271\pi\)
0.0838740 + 0.996476i \(0.473271\pi\)
\(632\) 10.3798 0.412888
\(633\) 0 0
\(634\) 9.98513 0.396560
\(635\) −1.08728 −0.0431472
\(636\) 0 0
\(637\) −5.55528 −0.220108
\(638\) −10.8411 −0.429204
\(639\) 0 0
\(640\) 13.7437 0.543269
\(641\) −42.2656 −1.66939 −0.834696 0.550711i \(-0.814357\pi\)
−0.834696 + 0.550711i \(0.814357\pi\)
\(642\) 0 0
\(643\) 18.5428 0.731257 0.365628 0.930761i \(-0.380854\pi\)
0.365628 + 0.930761i \(0.380854\pi\)
\(644\) −6.72612 −0.265046
\(645\) 0 0
\(646\) 27.9647 1.10025
\(647\) −22.4540 −0.882760 −0.441380 0.897320i \(-0.645511\pi\)
−0.441380 + 0.897320i \(0.645511\pi\)
\(648\) 0 0
\(649\) −5.05948 −0.198602
\(650\) −36.2093 −1.42025
\(651\) 0 0
\(652\) 12.4803 0.488767
\(653\) 36.2822 1.41983 0.709917 0.704285i \(-0.248732\pi\)
0.709917 + 0.704285i \(0.248732\pi\)
\(654\) 0 0
\(655\) −6.76670 −0.264397
\(656\) 31.9836 1.24875
\(657\) 0 0
\(658\) −4.81655 −0.187769
\(659\) −15.1601 −0.590555 −0.295278 0.955412i \(-0.595412\pi\)
−0.295278 + 0.955412i \(0.595412\pi\)
\(660\) 0 0
\(661\) 2.70883 0.105361 0.0526805 0.998611i \(-0.483223\pi\)
0.0526805 + 0.998611i \(0.483223\pi\)
\(662\) 11.5419 0.448587
\(663\) 0 0
\(664\) 11.4808 0.445543
\(665\) 5.26458 0.204152
\(666\) 0 0
\(667\) 29.5271 1.14329
\(668\) 22.8395 0.883688
\(669\) 0 0
\(670\) −26.8065 −1.03563
\(671\) −24.0358 −0.927892
\(672\) 0 0
\(673\) 12.1551 0.468545 0.234273 0.972171i \(-0.424729\pi\)
0.234273 + 0.972171i \(0.424729\pi\)
\(674\) −37.2066 −1.43314
\(675\) 0 0
\(676\) 16.3377 0.628375
\(677\) −18.2524 −0.701498 −0.350749 0.936469i \(-0.614073\pi\)
−0.350749 + 0.936469i \(0.614073\pi\)
\(678\) 0 0
\(679\) −4.99491 −0.191687
\(680\) −6.81510 −0.261347
\(681\) 0 0
\(682\) −24.1908 −0.926314
\(683\) 14.5033 0.554955 0.277478 0.960732i \(-0.410502\pi\)
0.277478 + 0.960732i \(0.410502\pi\)
\(684\) 0 0
\(685\) 0.470468 0.0179757
\(686\) −1.70725 −0.0651832
\(687\) 0 0
\(688\) 41.5462 1.58393
\(689\) −15.9010 −0.605781
\(690\) 0 0
\(691\) 34.0254 1.29439 0.647193 0.762326i \(-0.275943\pi\)
0.647193 + 0.762326i \(0.275943\pi\)
\(692\) 7.14273 0.271526
\(693\) 0 0
\(694\) 44.5309 1.69037
\(695\) 6.71825 0.254838
\(696\) 0 0
\(697\) −21.6709 −0.820844
\(698\) 57.3173 2.16949
\(699\) 0 0
\(700\) −3.49219 −0.131993
\(701\) 20.9705 0.792043 0.396022 0.918241i \(-0.370391\pi\)
0.396022 + 0.918241i \(0.370391\pi\)
\(702\) 0 0
\(703\) 19.0778 0.719531
\(704\) −2.78284 −0.104882
\(705\) 0 0
\(706\) −46.8351 −1.76266
\(707\) −15.3793 −0.578398
\(708\) 0 0
\(709\) −12.8542 −0.482749 −0.241375 0.970432i \(-0.577598\pi\)
−0.241375 + 0.970432i \(0.577598\pi\)
\(710\) −8.53917 −0.320469
\(711\) 0 0
\(712\) 27.3508 1.02501
\(713\) 65.8867 2.46748
\(714\) 0 0
\(715\) −9.55179 −0.357217
\(716\) 18.7064 0.699091
\(717\) 0 0
\(718\) 11.2352 0.419292
\(719\) −16.2432 −0.605768 −0.302884 0.953027i \(-0.597949\pi\)
−0.302884 + 0.953027i \(0.597949\pi\)
\(720\) 0 0
\(721\) 18.4573 0.687387
\(722\) −7.58858 −0.282418
\(723\) 0 0
\(724\) −3.95409 −0.146953
\(725\) 15.3304 0.569358
\(726\) 0 0
\(727\) −31.2233 −1.15801 −0.579003 0.815325i \(-0.696558\pi\)
−0.579003 + 0.815325i \(0.696558\pi\)
\(728\) −10.2932 −0.381492
\(729\) 0 0
\(730\) −21.1974 −0.784549
\(731\) −28.1502 −1.04117
\(732\) 0 0
\(733\) −9.59601 −0.354437 −0.177218 0.984172i \(-0.556710\pi\)
−0.177218 + 0.984172i \(0.556710\pi\)
\(734\) −39.5724 −1.46065
\(735\) 0 0
\(736\) −35.4290 −1.30593
\(737\) 22.8372 0.841218
\(738\) 0 0
\(739\) 16.5843 0.610065 0.305032 0.952342i \(-0.401333\pi\)
0.305032 + 0.952342i \(0.401333\pi\)
\(740\) 3.91854 0.144048
\(741\) 0 0
\(742\) −4.88670 −0.179397
\(743\) 44.5444 1.63418 0.817088 0.576513i \(-0.195587\pi\)
0.817088 + 0.576513i \(0.195587\pi\)
\(744\) 0 0
\(745\) 14.5776 0.534082
\(746\) −24.5937 −0.900440
\(747\) 0 0
\(748\) −4.89337 −0.178919
\(749\) 3.34462 0.122210
\(750\) 0 0
\(751\) −6.32997 −0.230984 −0.115492 0.993308i \(-0.536844\pi\)
−0.115492 + 0.993308i \(0.536844\pi\)
\(752\) −14.0856 −0.513650
\(753\) 0 0
\(754\) −38.0839 −1.38693
\(755\) −12.2612 −0.446230
\(756\) 0 0
\(757\) 46.6198 1.69442 0.847212 0.531255i \(-0.178279\pi\)
0.847212 + 0.531255i \(0.178279\pi\)
\(758\) −33.0436 −1.20020
\(759\) 0 0
\(760\) 9.75458 0.353836
\(761\) −22.2626 −0.807017 −0.403509 0.914976i \(-0.632209\pi\)
−0.403509 + 0.914976i \(0.632209\pi\)
\(762\) 0 0
\(763\) −2.86219 −0.103618
\(764\) −17.2175 −0.622908
\(765\) 0 0
\(766\) 36.6968 1.32591
\(767\) −17.7735 −0.641765
\(768\) 0 0
\(769\) −45.6713 −1.64695 −0.823475 0.567352i \(-0.807968\pi\)
−0.823475 + 0.567352i \(0.807968\pi\)
\(770\) −2.93546 −0.105787
\(771\) 0 0
\(772\) 3.68776 0.132725
\(773\) 18.8556 0.678189 0.339094 0.940752i \(-0.389879\pi\)
0.339094 + 0.940752i \(0.389879\pi\)
\(774\) 0 0
\(775\) 34.2083 1.22880
\(776\) −9.25492 −0.332232
\(777\) 0 0
\(778\) 41.0059 1.47013
\(779\) 31.0180 1.11133
\(780\) 0 0
\(781\) 7.27473 0.260310
\(782\) 42.4686 1.51867
\(783\) 0 0
\(784\) −4.99273 −0.178312
\(785\) 22.3866 0.799014
\(786\) 0 0
\(787\) −12.6245 −0.450015 −0.225008 0.974357i \(-0.572241\pi\)
−0.225008 + 0.974357i \(0.572241\pi\)
\(788\) −8.02484 −0.285873
\(789\) 0 0
\(790\) 10.3988 0.369972
\(791\) 6.64072 0.236117
\(792\) 0 0
\(793\) −84.4358 −2.99840
\(794\) 39.1016 1.38766
\(795\) 0 0
\(796\) −14.8177 −0.525200
\(797\) 30.7074 1.08771 0.543856 0.839178i \(-0.316964\pi\)
0.543856 + 0.839178i \(0.316964\pi\)
\(798\) 0 0
\(799\) 9.54391 0.337639
\(800\) −18.3947 −0.650350
\(801\) 0 0
\(802\) −61.8527 −2.18410
\(803\) 18.0586 0.637273
\(804\) 0 0
\(805\) 7.99508 0.281790
\(806\) −84.9803 −2.99330
\(807\) 0 0
\(808\) −28.4958 −1.00248
\(809\) 18.4310 0.648001 0.324001 0.946057i \(-0.394972\pi\)
0.324001 + 0.946057i \(0.394972\pi\)
\(810\) 0 0
\(811\) 7.64652 0.268506 0.134253 0.990947i \(-0.457137\pi\)
0.134253 + 0.990947i \(0.457137\pi\)
\(812\) −3.67299 −0.128897
\(813\) 0 0
\(814\) −10.6375 −0.372844
\(815\) −14.8349 −0.519643
\(816\) 0 0
\(817\) 40.2919 1.40964
\(818\) −17.5902 −0.615026
\(819\) 0 0
\(820\) 6.37104 0.222487
\(821\) −9.83737 −0.343326 −0.171663 0.985156i \(-0.554914\pi\)
−0.171663 + 0.985156i \(0.554914\pi\)
\(822\) 0 0
\(823\) −9.32310 −0.324983 −0.162491 0.986710i \(-0.551953\pi\)
−0.162491 + 0.986710i \(0.551953\pi\)
\(824\) 34.1990 1.19138
\(825\) 0 0
\(826\) −5.46217 −0.190053
\(827\) 4.19232 0.145781 0.0728906 0.997340i \(-0.476778\pi\)
0.0728906 + 0.997340i \(0.476778\pi\)
\(828\) 0 0
\(829\) 3.57413 0.124135 0.0620673 0.998072i \(-0.480231\pi\)
0.0620673 + 0.998072i \(0.480231\pi\)
\(830\) 11.5018 0.399234
\(831\) 0 0
\(832\) −9.77590 −0.338918
\(833\) 3.38289 0.117210
\(834\) 0 0
\(835\) −27.1485 −0.939511
\(836\) 7.00397 0.242238
\(837\) 0 0
\(838\) 58.7616 2.02989
\(839\) 46.2021 1.59507 0.797537 0.603270i \(-0.206136\pi\)
0.797537 + 0.603270i \(0.206136\pi\)
\(840\) 0 0
\(841\) −12.8759 −0.443996
\(842\) −9.53164 −0.328482
\(843\) 0 0
\(844\) −6.07477 −0.209102
\(845\) −19.4200 −0.668070
\(846\) 0 0
\(847\) −8.49921 −0.292036
\(848\) −14.2908 −0.490748
\(849\) 0 0
\(850\) 22.0497 0.756297
\(851\) 28.9725 0.993164
\(852\) 0 0
\(853\) −41.5480 −1.42257 −0.711287 0.702901i \(-0.751888\pi\)
−0.711287 + 0.702901i \(0.751888\pi\)
\(854\) −25.9488 −0.887950
\(855\) 0 0
\(856\) 6.19713 0.211814
\(857\) −34.9505 −1.19389 −0.596943 0.802284i \(-0.703618\pi\)
−0.596943 + 0.802284i \(0.703618\pi\)
\(858\) 0 0
\(859\) 14.3297 0.488922 0.244461 0.969659i \(-0.421389\pi\)
0.244461 + 0.969659i \(0.421389\pi\)
\(860\) 8.27590 0.282206
\(861\) 0 0
\(862\) −10.7915 −0.367559
\(863\) 4.68464 0.159467 0.0797334 0.996816i \(-0.474593\pi\)
0.0797334 + 0.996816i \(0.474593\pi\)
\(864\) 0 0
\(865\) −8.49028 −0.288678
\(866\) −4.13871 −0.140639
\(867\) 0 0
\(868\) −8.19590 −0.278187
\(869\) −8.85899 −0.300521
\(870\) 0 0
\(871\) 80.2250 2.71832
\(872\) −5.30327 −0.179591
\(873\) 0 0
\(874\) −60.7862 −2.05612
\(875\) 9.58742 0.324114
\(876\) 0 0
\(877\) −29.4874 −0.995719 −0.497859 0.867258i \(-0.665880\pi\)
−0.497859 + 0.867258i \(0.665880\pi\)
\(878\) −34.5849 −1.16718
\(879\) 0 0
\(880\) −8.58452 −0.289384
\(881\) 55.1122 1.85678 0.928389 0.371610i \(-0.121194\pi\)
0.928389 + 0.371610i \(0.121194\pi\)
\(882\) 0 0
\(883\) −30.1318 −1.01402 −0.507008 0.861942i \(-0.669248\pi\)
−0.507008 + 0.861942i \(0.669248\pi\)
\(884\) −17.1900 −0.578162
\(885\) 0 0
\(886\) −39.0816 −1.31297
\(887\) −23.2940 −0.782137 −0.391069 0.920362i \(-0.627894\pi\)
−0.391069 + 0.920362i \(0.627894\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 27.4008 0.918476
\(891\) 0 0
\(892\) 17.3737 0.581714
\(893\) −13.6604 −0.457128
\(894\) 0 0
\(895\) −22.2356 −0.743253
\(896\) −12.6405 −0.422290
\(897\) 0 0
\(898\) −10.3708 −0.346080
\(899\) 35.9793 1.19998
\(900\) 0 0
\(901\) 9.68292 0.322585
\(902\) −17.2952 −0.575866
\(903\) 0 0
\(904\) 12.3044 0.409238
\(905\) 4.70007 0.156236
\(906\) 0 0
\(907\) −3.20187 −0.106316 −0.0531582 0.998586i \(-0.516929\pi\)
−0.0531582 + 0.998586i \(0.516929\pi\)
\(908\) −8.40577 −0.278955
\(909\) 0 0
\(910\) −10.3120 −0.341840
\(911\) 1.03289 0.0342212 0.0171106 0.999854i \(-0.494553\pi\)
0.0171106 + 0.999854i \(0.494553\pi\)
\(912\) 0 0
\(913\) −9.79868 −0.324289
\(914\) −20.5427 −0.679492
\(915\) 0 0
\(916\) 0.647353 0.0213891
\(917\) 6.22354 0.205519
\(918\) 0 0
\(919\) −3.56770 −0.117688 −0.0588438 0.998267i \(-0.518741\pi\)
−0.0588438 + 0.998267i \(0.518741\pi\)
\(920\) 14.8138 0.488398
\(921\) 0 0
\(922\) −60.2172 −1.98315
\(923\) 25.5555 0.841171
\(924\) 0 0
\(925\) 15.0425 0.494594
\(926\) −70.4804 −2.31613
\(927\) 0 0
\(928\) −19.3470 −0.635096
\(929\) 0.360409 0.0118246 0.00591231 0.999983i \(-0.498118\pi\)
0.00591231 + 0.999983i \(0.498118\pi\)
\(930\) 0 0
\(931\) −4.84199 −0.158690
\(932\) 12.2847 0.402399
\(933\) 0 0
\(934\) 5.30407 0.173554
\(935\) 5.81656 0.190222
\(936\) 0 0
\(937\) −11.7931 −0.385265 −0.192633 0.981271i \(-0.561703\pi\)
−0.192633 + 0.981271i \(0.561703\pi\)
\(938\) 24.6548 0.805007
\(939\) 0 0
\(940\) −2.80582 −0.0915159
\(941\) 14.0874 0.459236 0.229618 0.973281i \(-0.426252\pi\)
0.229618 + 0.973281i \(0.426252\pi\)
\(942\) 0 0
\(943\) 47.1056 1.53397
\(944\) −15.9737 −0.519899
\(945\) 0 0
\(946\) −22.4662 −0.730439
\(947\) 42.7570 1.38941 0.694707 0.719292i \(-0.255534\pi\)
0.694707 + 0.719292i \(0.255534\pi\)
\(948\) 0 0
\(949\) 63.4382 2.05929
\(950\) −31.5601 −1.02394
\(951\) 0 0
\(952\) 6.26805 0.203149
\(953\) 36.7785 1.19137 0.595686 0.803218i \(-0.296880\pi\)
0.595686 + 0.803218i \(0.296880\pi\)
\(954\) 0 0
\(955\) 20.4658 0.662257
\(956\) 0.569956 0.0184337
\(957\) 0 0
\(958\) −26.5608 −0.858142
\(959\) −0.432704 −0.0139727
\(960\) 0 0
\(961\) 49.2841 1.58981
\(962\) −37.3686 −1.20481
\(963\) 0 0
\(964\) 0.846095 0.0272509
\(965\) −4.38350 −0.141110
\(966\) 0 0
\(967\) 25.7951 0.829515 0.414757 0.909932i \(-0.363866\pi\)
0.414757 + 0.909932i \(0.363866\pi\)
\(968\) −15.7479 −0.506157
\(969\) 0 0
\(970\) −9.27183 −0.297700
\(971\) 40.2676 1.29225 0.646124 0.763232i \(-0.276389\pi\)
0.646124 + 0.763232i \(0.276389\pi\)
\(972\) 0 0
\(973\) −6.17897 −0.198089
\(974\) 50.6520 1.62299
\(975\) 0 0
\(976\) −75.8853 −2.42903
\(977\) 23.0942 0.738848 0.369424 0.929261i \(-0.379555\pi\)
0.369424 + 0.929261i \(0.379555\pi\)
\(978\) 0 0
\(979\) −23.3434 −0.746058
\(980\) −0.994538 −0.0317694
\(981\) 0 0
\(982\) 1.29842 0.0414344
\(983\) −23.8772 −0.761563 −0.380781 0.924665i \(-0.624345\pi\)
−0.380781 + 0.924665i \(0.624345\pi\)
\(984\) 0 0
\(985\) 9.53882 0.303932
\(986\) 23.1912 0.738558
\(987\) 0 0
\(988\) 24.6044 0.782769
\(989\) 61.1895 1.94571
\(990\) 0 0
\(991\) 13.5689 0.431031 0.215516 0.976500i \(-0.430857\pi\)
0.215516 + 0.976500i \(0.430857\pi\)
\(992\) −43.1708 −1.37067
\(993\) 0 0
\(994\) 7.85373 0.249105
\(995\) 17.6132 0.558378
\(996\) 0 0
\(997\) 53.5594 1.69624 0.848121 0.529803i \(-0.177734\pi\)
0.848121 + 0.529803i \(0.177734\pi\)
\(998\) 28.0564 0.888111
\(999\) 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 \(a_p\))