Properties

Label 8001.2.a.u.1.11
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 1.11
Root \(0.981962\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.981962 q^{2}\) \(-1.03575 q^{4}\) \(-2.59441 q^{5}\) \(+1.00000 q^{7}\) \(-2.98099 q^{8}\) \(+O(q^{10})\) \(q\)\(+0.981962 q^{2}\) \(-1.03575 q^{4}\) \(-2.59441 q^{5}\) \(+1.00000 q^{7}\) \(-2.98099 q^{8}\) \(-2.54761 q^{10}\) \(+0.832401 q^{11}\) \(-5.10508 q^{13}\) \(+0.981962 q^{14}\) \(-0.855717 q^{16}\) \(-7.10660 q^{17}\) \(-7.54643 q^{19}\) \(+2.68717 q^{20}\) \(+0.817386 q^{22}\) \(-8.33771 q^{23}\) \(+1.73097 q^{25}\) \(-5.01299 q^{26}\) \(-1.03575 q^{28}\) \(+8.62369 q^{29}\) \(-6.02299 q^{31}\) \(+5.12170 q^{32}\) \(-6.97841 q^{34}\) \(-2.59441 q^{35}\) \(-5.52425 q^{37}\) \(-7.41031 q^{38}\) \(+7.73392 q^{40}\) \(+8.68580 q^{41}\) \(+4.88483 q^{43}\) \(-0.862161 q^{44}\) \(-8.18731 q^{46}\) \(-2.27297 q^{47}\) \(+1.00000 q^{49}\) \(+1.69975 q^{50}\) \(+5.28759 q^{52}\) \(-3.81937 q^{53}\) \(-2.15959 q^{55}\) \(-2.98099 q^{56}\) \(+8.46813 q^{58}\) \(+3.88402 q^{59}\) \(-7.64885 q^{61}\) \(-5.91434 q^{62}\) \(+6.74075 q^{64}\) \(+13.2447 q^{65}\) \(+9.03188 q^{67}\) \(+7.36067 q^{68}\) \(-2.54761 q^{70}\) \(+9.47044 q^{71}\) \(-6.75232 q^{73}\) \(-5.42460 q^{74}\) \(+7.81623 q^{76}\) \(+0.832401 q^{77}\) \(+5.46202 q^{79}\) \(+2.22008 q^{80}\) \(+8.52913 q^{82}\) \(-9.63296 q^{83}\) \(+18.4374 q^{85}\) \(+4.79672 q^{86}\) \(-2.48138 q^{88}\) \(-9.34318 q^{89}\) \(-5.10508 q^{91}\) \(+8.63580 q^{92}\) \(-2.23196 q^{94}\) \(+19.5786 q^{95}\) \(-0.647975 q^{97}\) \(+0.981962 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(18q \) \(\mathstrut +\mathstrut 6q^{2} \) \(\mathstrut +\mathstrut 22q^{4} \) \(\mathstrut +\mathstrut 10q^{5} \) \(\mathstrut +\mathstrut 18q^{7} \) \(\mathstrut +\mathstrut 21q^{8} \) \(\mathstrut -\mathstrut 4q^{10} \) \(\mathstrut +\mathstrut 9q^{11} \) \(\mathstrut -\mathstrut 25q^{13} \) \(\mathstrut +\mathstrut 6q^{14} \) \(\mathstrut +\mathstrut 34q^{16} \) \(\mathstrut +\mathstrut 17q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut +\mathstrut 21q^{20} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 14q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 8q^{26} \) \(\mathstrut +\mathstrut 22q^{28} \) \(\mathstrut +\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 19q^{34} \) \(\mathstrut +\mathstrut 10q^{35} \) \(\mathstrut -\mathstrut 15q^{37} \) \(\mathstrut +\mathstrut 22q^{38} \) \(\mathstrut -\mathstrut q^{40} \) \(\mathstrut +\mathstrut 17q^{41} \) \(\mathstrut +\mathstrut q^{43} \) \(\mathstrut +\mathstrut 33q^{44} \) \(\mathstrut +\mathstrut 10q^{46} \) \(\mathstrut +\mathstrut 31q^{47} \) \(\mathstrut +\mathstrut 18q^{49} \) \(\mathstrut +\mathstrut 35q^{50} \) \(\mathstrut -\mathstrut 70q^{52} \) \(\mathstrut +\mathstrut 35q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 21q^{56} \) \(\mathstrut +\mathstrut 3q^{58} \) \(\mathstrut +\mathstrut 46q^{59} \) \(\mathstrut -\mathstrut 5q^{61} \) \(\mathstrut +\mathstrut 10q^{62} \) \(\mathstrut +\mathstrut 63q^{64} \) \(\mathstrut +\mathstrut 12q^{65} \) \(\mathstrut +\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 56q^{68} \) \(\mathstrut -\mathstrut 4q^{70} \) \(\mathstrut +\mathstrut 22q^{71} \) \(\mathstrut -\mathstrut 16q^{73} \) \(\mathstrut -\mathstrut 18q^{74} \) \(\mathstrut +\mathstrut 32q^{76} \) \(\mathstrut +\mathstrut 9q^{77} \) \(\mathstrut +\mathstrut 46q^{79} \) \(\mathstrut +\mathstrut 30q^{80} \) \(\mathstrut -\mathstrut 12q^{82} \) \(\mathstrut +\mathstrut 46q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 18q^{86} \) \(\mathstrut +\mathstrut 30q^{88} \) \(\mathstrut +\mathstrut 42q^{89} \) \(\mathstrut -\mathstrut 25q^{91} \) \(\mathstrut +\mathstrut 48q^{92} \) \(\mathstrut +\mathstrut 3q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut -\mathstrut 35q^{97} \) \(\mathstrut +\mathstrut 6q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.981962 0.694352 0.347176 0.937800i \(-0.387141\pi\)
0.347176 + 0.937800i \(0.387141\pi\)
\(3\) 0 0
\(4\) −1.03575 −0.517876
\(5\) −2.59441 −1.16026 −0.580128 0.814525i \(-0.696998\pi\)
−0.580128 + 0.814525i \(0.696998\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.98099 −1.05394
\(9\) 0 0
\(10\) −2.54761 −0.805626
\(11\) 0.832401 0.250978 0.125489 0.992095i \(-0.459950\pi\)
0.125489 + 0.992095i \(0.459950\pi\)
\(12\) 0 0
\(13\) −5.10508 −1.41589 −0.707947 0.706265i \(-0.750379\pi\)
−0.707947 + 0.706265i \(0.750379\pi\)
\(14\) 0.981962 0.262440
\(15\) 0 0
\(16\) −0.855717 −0.213929
\(17\) −7.10660 −1.72360 −0.861802 0.507245i \(-0.830664\pi\)
−0.861802 + 0.507245i \(0.830664\pi\)
\(18\) 0 0
\(19\) −7.54643 −1.73127 −0.865635 0.500675i \(-0.833085\pi\)
−0.865635 + 0.500675i \(0.833085\pi\)
\(20\) 2.68717 0.600868
\(21\) 0 0
\(22\) 0.817386 0.174267
\(23\) −8.33771 −1.73853 −0.869267 0.494344i \(-0.835408\pi\)
−0.869267 + 0.494344i \(0.835408\pi\)
\(24\) 0 0
\(25\) 1.73097 0.346195
\(26\) −5.01299 −0.983129
\(27\) 0 0
\(28\) −1.03575 −0.195739
\(29\) 8.62369 1.60138 0.800689 0.599080i \(-0.204467\pi\)
0.800689 + 0.599080i \(0.204467\pi\)
\(30\) 0 0
\(31\) −6.02299 −1.08176 −0.540880 0.841100i \(-0.681909\pi\)
−0.540880 + 0.841100i \(0.681909\pi\)
\(32\) 5.12170 0.905397
\(33\) 0 0
\(34\) −6.97841 −1.19679
\(35\) −2.59441 −0.438536
\(36\) 0 0
\(37\) −5.52425 −0.908181 −0.454090 0.890956i \(-0.650036\pi\)
−0.454090 + 0.890956i \(0.650036\pi\)
\(38\) −7.41031 −1.20211
\(39\) 0 0
\(40\) 7.73392 1.22284
\(41\) 8.68580 1.35649 0.678247 0.734834i \(-0.262740\pi\)
0.678247 + 0.734834i \(0.262740\pi\)
\(42\) 0 0
\(43\) 4.88483 0.744930 0.372465 0.928046i \(-0.378513\pi\)
0.372465 + 0.928046i \(0.378513\pi\)
\(44\) −0.862161 −0.129976
\(45\) 0 0
\(46\) −8.18731 −1.20715
\(47\) −2.27297 −0.331546 −0.165773 0.986164i \(-0.553012\pi\)
−0.165773 + 0.986164i \(0.553012\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 1.69975 0.240381
\(51\) 0 0
\(52\) 5.28759 0.733257
\(53\) −3.81937 −0.524631 −0.262316 0.964982i \(-0.584486\pi\)
−0.262316 + 0.964982i \(0.584486\pi\)
\(54\) 0 0
\(55\) −2.15959 −0.291199
\(56\) −2.98099 −0.398352
\(57\) 0 0
\(58\) 8.46813 1.11192
\(59\) 3.88402 0.505656 0.252828 0.967511i \(-0.418639\pi\)
0.252828 + 0.967511i \(0.418639\pi\)
\(60\) 0 0
\(61\) −7.64885 −0.979335 −0.489668 0.871909i \(-0.662882\pi\)
−0.489668 + 0.871909i \(0.662882\pi\)
\(62\) −5.91434 −0.751122
\(63\) 0 0
\(64\) 6.74075 0.842594
\(65\) 13.2447 1.64280
\(66\) 0 0
\(67\) 9.03188 1.10342 0.551710 0.834036i \(-0.313975\pi\)
0.551710 + 0.834036i \(0.313975\pi\)
\(68\) 7.36067 0.892612
\(69\) 0 0
\(70\) −2.54761 −0.304498
\(71\) 9.47044 1.12393 0.561967 0.827160i \(-0.310045\pi\)
0.561967 + 0.827160i \(0.310045\pi\)
\(72\) 0 0
\(73\) −6.75232 −0.790300 −0.395150 0.918617i \(-0.629307\pi\)
−0.395150 + 0.918617i \(0.629307\pi\)
\(74\) −5.42460 −0.630597
\(75\) 0 0
\(76\) 7.81623 0.896583
\(77\) 0.832401 0.0948609
\(78\) 0 0
\(79\) 5.46202 0.614525 0.307262 0.951625i \(-0.400587\pi\)
0.307262 + 0.951625i \(0.400587\pi\)
\(80\) 2.22008 0.248213
\(81\) 0 0
\(82\) 8.52913 0.941885
\(83\) −9.63296 −1.05735 −0.528677 0.848823i \(-0.677312\pi\)
−0.528677 + 0.848823i \(0.677312\pi\)
\(84\) 0 0
\(85\) 18.4374 1.99982
\(86\) 4.79672 0.517244
\(87\) 0 0
\(88\) −2.48138 −0.264516
\(89\) −9.34318 −0.990375 −0.495188 0.868786i \(-0.664901\pi\)
−0.495188 + 0.868786i \(0.664901\pi\)
\(90\) 0 0
\(91\) −5.10508 −0.535158
\(92\) 8.63580 0.900344
\(93\) 0 0
\(94\) −2.23196 −0.230210
\(95\) 19.5786 2.00872
\(96\) 0 0
\(97\) −0.647975 −0.0657918 −0.0328959 0.999459i \(-0.510473\pi\)
−0.0328959 + 0.999459i \(0.510473\pi\)
\(98\) 0.981962 0.0991931
\(99\) 0 0
\(100\) −1.79286 −0.179286
\(101\) −8.32814 −0.828681 −0.414340 0.910122i \(-0.635988\pi\)
−0.414340 + 0.910122i \(0.635988\pi\)
\(102\) 0 0
\(103\) −18.0685 −1.78034 −0.890169 0.455631i \(-0.849414\pi\)
−0.890169 + 0.455631i \(0.849414\pi\)
\(104\) 15.2182 1.49227
\(105\) 0 0
\(106\) −3.75048 −0.364279
\(107\) −11.8426 −1.14487 −0.572434 0.819951i \(-0.694001\pi\)
−0.572434 + 0.819951i \(0.694001\pi\)
\(108\) 0 0
\(109\) 2.81629 0.269752 0.134876 0.990863i \(-0.456936\pi\)
0.134876 + 0.990863i \(0.456936\pi\)
\(110\) −2.12064 −0.202195
\(111\) 0 0
\(112\) −0.855717 −0.0808577
\(113\) −19.7700 −1.85980 −0.929901 0.367811i \(-0.880107\pi\)
−0.929901 + 0.367811i \(0.880107\pi\)
\(114\) 0 0
\(115\) 21.6315 2.01714
\(116\) −8.93199 −0.829315
\(117\) 0 0
\(118\) 3.81395 0.351103
\(119\) −7.10660 −0.651461
\(120\) 0 0
\(121\) −10.3071 −0.937010
\(122\) −7.51088 −0.680003
\(123\) 0 0
\(124\) 6.23832 0.560217
\(125\) 8.48120 0.758582
\(126\) 0 0
\(127\) 1.00000 0.0887357
\(128\) −3.62425 −0.320341
\(129\) 0 0
\(130\) 13.0058 1.14068
\(131\) 22.1245 1.93302 0.966512 0.256622i \(-0.0826095\pi\)
0.966512 + 0.256622i \(0.0826095\pi\)
\(132\) 0 0
\(133\) −7.54643 −0.654359
\(134\) 8.86896 0.766162
\(135\) 0 0
\(136\) 21.1847 1.81657
\(137\) 9.68182 0.827174 0.413587 0.910465i \(-0.364276\pi\)
0.413587 + 0.910465i \(0.364276\pi\)
\(138\) 0 0
\(139\) 4.55040 0.385960 0.192980 0.981203i \(-0.438185\pi\)
0.192980 + 0.981203i \(0.438185\pi\)
\(140\) 2.68717 0.227107
\(141\) 0 0
\(142\) 9.29961 0.780406
\(143\) −4.24948 −0.355359
\(144\) 0 0
\(145\) −22.3734 −1.85801
\(146\) −6.63052 −0.548746
\(147\) 0 0
\(148\) 5.72175 0.470325
\(149\) 23.9402 1.96126 0.980628 0.195880i \(-0.0627562\pi\)
0.980628 + 0.195880i \(0.0627562\pi\)
\(150\) 0 0
\(151\) −11.2109 −0.912329 −0.456164 0.889896i \(-0.650777\pi\)
−0.456164 + 0.889896i \(0.650777\pi\)
\(152\) 22.4959 1.82465
\(153\) 0 0
\(154\) 0.817386 0.0658669
\(155\) 15.6261 1.25512
\(156\) 0 0
\(157\) −0.154475 −0.0123284 −0.00616422 0.999981i \(-0.501962\pi\)
−0.00616422 + 0.999981i \(0.501962\pi\)
\(158\) 5.36349 0.426696
\(159\) 0 0
\(160\) −13.2878 −1.05049
\(161\) −8.33771 −0.657104
\(162\) 0 0
\(163\) −11.4755 −0.898831 −0.449415 0.893323i \(-0.648368\pi\)
−0.449415 + 0.893323i \(0.648368\pi\)
\(164\) −8.99633 −0.702496
\(165\) 0 0
\(166\) −9.45920 −0.734176
\(167\) 1.57208 0.121651 0.0608255 0.998148i \(-0.480627\pi\)
0.0608255 + 0.998148i \(0.480627\pi\)
\(168\) 0 0
\(169\) 13.0619 1.00476
\(170\) 18.1049 1.38858
\(171\) 0 0
\(172\) −5.05947 −0.385781
\(173\) 24.4378 1.85797 0.928985 0.370117i \(-0.120682\pi\)
0.928985 + 0.370117i \(0.120682\pi\)
\(174\) 0 0
\(175\) 1.73097 0.130849
\(176\) −0.712300 −0.0536916
\(177\) 0 0
\(178\) −9.17464 −0.687669
\(179\) 8.38681 0.626860 0.313430 0.949611i \(-0.398522\pi\)
0.313430 + 0.949611i \(0.398522\pi\)
\(180\) 0 0
\(181\) −11.9980 −0.891806 −0.445903 0.895081i \(-0.647117\pi\)
−0.445903 + 0.895081i \(0.647117\pi\)
\(182\) −5.01299 −0.371588
\(183\) 0 0
\(184\) 24.8546 1.83231
\(185\) 14.3322 1.05372
\(186\) 0 0
\(187\) −5.91554 −0.432587
\(188\) 2.35423 0.171700
\(189\) 0 0
\(190\) 19.2254 1.39476
\(191\) 3.62612 0.262377 0.131188 0.991357i \(-0.458121\pi\)
0.131188 + 0.991357i \(0.458121\pi\)
\(192\) 0 0
\(193\) −20.6742 −1.48816 −0.744081 0.668089i \(-0.767112\pi\)
−0.744081 + 0.668089i \(0.767112\pi\)
\(194\) −0.636286 −0.0456827
\(195\) 0 0
\(196\) −1.03575 −0.0739822
\(197\) 22.7186 1.61863 0.809315 0.587374i \(-0.199838\pi\)
0.809315 + 0.587374i \(0.199838\pi\)
\(198\) 0 0
\(199\) 13.5397 0.959803 0.479901 0.877322i \(-0.340672\pi\)
0.479901 + 0.877322i \(0.340672\pi\)
\(200\) −5.16002 −0.364868
\(201\) 0 0
\(202\) −8.17791 −0.575396
\(203\) 8.62369 0.605264
\(204\) 0 0
\(205\) −22.5346 −1.57388
\(206\) −17.7425 −1.23618
\(207\) 0 0
\(208\) 4.36850 0.302901
\(209\) −6.28166 −0.434512
\(210\) 0 0
\(211\) −0.844287 −0.0581231 −0.0290615 0.999578i \(-0.509252\pi\)
−0.0290615 + 0.999578i \(0.509252\pi\)
\(212\) 3.95592 0.271694
\(213\) 0 0
\(214\) −11.6290 −0.794941
\(215\) −12.6733 −0.864310
\(216\) 0 0
\(217\) −6.02299 −0.408867
\(218\) 2.76549 0.187303
\(219\) 0 0
\(220\) 2.23680 0.150805
\(221\) 36.2798 2.44044
\(222\) 0 0
\(223\) 1.45728 0.0975867 0.0487934 0.998809i \(-0.484462\pi\)
0.0487934 + 0.998809i \(0.484462\pi\)
\(224\) 5.12170 0.342208
\(225\) 0 0
\(226\) −19.4133 −1.29136
\(227\) −19.2589 −1.27825 −0.639127 0.769101i \(-0.720704\pi\)
−0.639127 + 0.769101i \(0.720704\pi\)
\(228\) 0 0
\(229\) −9.93419 −0.656470 −0.328235 0.944596i \(-0.606454\pi\)
−0.328235 + 0.944596i \(0.606454\pi\)
\(230\) 21.2413 1.40061
\(231\) 0 0
\(232\) −25.7071 −1.68776
\(233\) 16.6806 1.09278 0.546390 0.837531i \(-0.316001\pi\)
0.546390 + 0.837531i \(0.316001\pi\)
\(234\) 0 0
\(235\) 5.89701 0.384678
\(236\) −4.02287 −0.261867
\(237\) 0 0
\(238\) −6.97841 −0.452343
\(239\) −7.56639 −0.489429 −0.244715 0.969595i \(-0.578694\pi\)
−0.244715 + 0.969595i \(0.578694\pi\)
\(240\) 0 0
\(241\) 3.45538 0.222580 0.111290 0.993788i \(-0.464502\pi\)
0.111290 + 0.993788i \(0.464502\pi\)
\(242\) −10.1212 −0.650614
\(243\) 0 0
\(244\) 7.92231 0.507174
\(245\) −2.59441 −0.165751
\(246\) 0 0
\(247\) 38.5251 2.45130
\(248\) 17.9545 1.14011
\(249\) 0 0
\(250\) 8.32822 0.526723
\(251\) 3.24187 0.204625 0.102313 0.994752i \(-0.467376\pi\)
0.102313 + 0.994752i \(0.467376\pi\)
\(252\) 0 0
\(253\) −6.94032 −0.436334
\(254\) 0.981962 0.0616138
\(255\) 0 0
\(256\) −17.0404 −1.06502
\(257\) −2.15313 −0.134308 −0.0671542 0.997743i \(-0.521392\pi\)
−0.0671542 + 0.997743i \(0.521392\pi\)
\(258\) 0 0
\(259\) −5.52425 −0.343260
\(260\) −13.7182 −0.850766
\(261\) 0 0
\(262\) 21.7254 1.34220
\(263\) −12.2970 −0.758264 −0.379132 0.925343i \(-0.623777\pi\)
−0.379132 + 0.925343i \(0.623777\pi\)
\(264\) 0 0
\(265\) 9.90903 0.608707
\(266\) −7.41031 −0.454355
\(267\) 0 0
\(268\) −9.35478 −0.571434
\(269\) −28.2317 −1.72132 −0.860659 0.509183i \(-0.829948\pi\)
−0.860659 + 0.509183i \(0.829948\pi\)
\(270\) 0 0
\(271\) 8.79041 0.533980 0.266990 0.963699i \(-0.413971\pi\)
0.266990 + 0.963699i \(0.413971\pi\)
\(272\) 6.08124 0.368729
\(273\) 0 0
\(274\) 9.50718 0.574350
\(275\) 1.44086 0.0868874
\(276\) 0 0
\(277\) −7.19056 −0.432039 −0.216019 0.976389i \(-0.569307\pi\)
−0.216019 + 0.976389i \(0.569307\pi\)
\(278\) 4.46832 0.267992
\(279\) 0 0
\(280\) 7.73392 0.462190
\(281\) 0.601253 0.0358678 0.0179339 0.999839i \(-0.494291\pi\)
0.0179339 + 0.999839i \(0.494291\pi\)
\(282\) 0 0
\(283\) 32.0154 1.90312 0.951560 0.307462i \(-0.0994797\pi\)
0.951560 + 0.307462i \(0.0994797\pi\)
\(284\) −9.80902 −0.582058
\(285\) 0 0
\(286\) −4.17282 −0.246744
\(287\) 8.68580 0.512707
\(288\) 0 0
\(289\) 33.5038 1.97081
\(290\) −21.9698 −1.29011
\(291\) 0 0
\(292\) 6.99373 0.409277
\(293\) 23.4909 1.37235 0.686175 0.727436i \(-0.259288\pi\)
0.686175 + 0.727436i \(0.259288\pi\)
\(294\) 0 0
\(295\) −10.0767 −0.586690
\(296\) 16.4677 0.957168
\(297\) 0 0
\(298\) 23.5083 1.36180
\(299\) 42.5647 2.46158
\(300\) 0 0
\(301\) 4.88483 0.281557
\(302\) −11.0087 −0.633477
\(303\) 0 0
\(304\) 6.45761 0.370369
\(305\) 19.8443 1.13628
\(306\) 0 0
\(307\) −17.5946 −1.00418 −0.502088 0.864816i \(-0.667435\pi\)
−0.502088 + 0.864816i \(0.667435\pi\)
\(308\) −0.862161 −0.0491262
\(309\) 0 0
\(310\) 15.3442 0.871494
\(311\) 19.6113 1.11205 0.556026 0.831165i \(-0.312325\pi\)
0.556026 + 0.831165i \(0.312325\pi\)
\(312\) 0 0
\(313\) −16.1312 −0.911787 −0.455893 0.890034i \(-0.650680\pi\)
−0.455893 + 0.890034i \(0.650680\pi\)
\(314\) −0.151688 −0.00856028
\(315\) 0 0
\(316\) −5.65729 −0.318247
\(317\) −6.34583 −0.356417 −0.178209 0.983993i \(-0.557030\pi\)
−0.178209 + 0.983993i \(0.557030\pi\)
\(318\) 0 0
\(319\) 7.17837 0.401912
\(320\) −17.4883 −0.977625
\(321\) 0 0
\(322\) −8.18731 −0.456261
\(323\) 53.6295 2.98402
\(324\) 0 0
\(325\) −8.83676 −0.490175
\(326\) −11.2685 −0.624105
\(327\) 0 0
\(328\) −25.8923 −1.42966
\(329\) −2.27297 −0.125313
\(330\) 0 0
\(331\) −1.36803 −0.0751938 −0.0375969 0.999293i \(-0.511970\pi\)
−0.0375969 + 0.999293i \(0.511970\pi\)
\(332\) 9.97735 0.547578
\(333\) 0 0
\(334\) 1.54372 0.0844686
\(335\) −23.4324 −1.28025
\(336\) 0 0
\(337\) −10.0731 −0.548719 −0.274359 0.961627i \(-0.588466\pi\)
−0.274359 + 0.961627i \(0.588466\pi\)
\(338\) 12.8262 0.697655
\(339\) 0 0
\(340\) −19.0966 −1.03566
\(341\) −5.01354 −0.271499
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −14.5616 −0.785111
\(345\) 0 0
\(346\) 23.9970 1.29009
\(347\) −11.8342 −0.635295 −0.317647 0.948209i \(-0.602893\pi\)
−0.317647 + 0.948209i \(0.602893\pi\)
\(348\) 0 0
\(349\) 13.7100 0.733880 0.366940 0.930245i \(-0.380405\pi\)
0.366940 + 0.930245i \(0.380405\pi\)
\(350\) 1.69975 0.0908554
\(351\) 0 0
\(352\) 4.26331 0.227235
\(353\) 24.2687 1.29169 0.645846 0.763468i \(-0.276505\pi\)
0.645846 + 0.763468i \(0.276505\pi\)
\(354\) 0 0
\(355\) −24.5702 −1.30405
\(356\) 9.67721 0.512891
\(357\) 0 0
\(358\) 8.23553 0.435261
\(359\) −4.37238 −0.230765 −0.115383 0.993321i \(-0.536809\pi\)
−0.115383 + 0.993321i \(0.536809\pi\)
\(360\) 0 0
\(361\) 37.9486 1.99730
\(362\) −11.7816 −0.619227
\(363\) 0 0
\(364\) 5.28759 0.277145
\(365\) 17.5183 0.916950
\(366\) 0 0
\(367\) 22.4911 1.17403 0.587013 0.809578i \(-0.300304\pi\)
0.587013 + 0.809578i \(0.300304\pi\)
\(368\) 7.13472 0.371923
\(369\) 0 0
\(370\) 14.0736 0.731654
\(371\) −3.81937 −0.198292
\(372\) 0 0
\(373\) 12.0199 0.622367 0.311183 0.950350i \(-0.399275\pi\)
0.311183 + 0.950350i \(0.399275\pi\)
\(374\) −5.80884 −0.300368
\(375\) 0 0
\(376\) 6.77569 0.349430
\(377\) −44.0246 −2.26738
\(378\) 0 0
\(379\) −3.53055 −0.181352 −0.0906761 0.995880i \(-0.528903\pi\)
−0.0906761 + 0.995880i \(0.528903\pi\)
\(380\) −20.2785 −1.04027
\(381\) 0 0
\(382\) 3.56071 0.182182
\(383\) −27.7234 −1.41660 −0.708299 0.705913i \(-0.750537\pi\)
−0.708299 + 0.705913i \(0.750537\pi\)
\(384\) 0 0
\(385\) −2.15959 −0.110063
\(386\) −20.3013 −1.03331
\(387\) 0 0
\(388\) 0.671140 0.0340720
\(389\) 3.79519 0.192424 0.0962118 0.995361i \(-0.469327\pi\)
0.0962118 + 0.995361i \(0.469327\pi\)
\(390\) 0 0
\(391\) 59.2528 2.99654
\(392\) −2.98099 −0.150563
\(393\) 0 0
\(394\) 22.3088 1.12390
\(395\) −14.1707 −0.713006
\(396\) 0 0
\(397\) −21.7337 −1.09078 −0.545392 0.838181i \(-0.683619\pi\)
−0.545392 + 0.838181i \(0.683619\pi\)
\(398\) 13.2955 0.666441
\(399\) 0 0
\(400\) −1.48122 −0.0740612
\(401\) 1.98537 0.0991445 0.0495723 0.998771i \(-0.484214\pi\)
0.0495723 + 0.998771i \(0.484214\pi\)
\(402\) 0 0
\(403\) 30.7478 1.53166
\(404\) 8.62588 0.429154
\(405\) 0 0
\(406\) 8.46813 0.420266
\(407\) −4.59839 −0.227934
\(408\) 0 0
\(409\) −36.7841 −1.81886 −0.909429 0.415859i \(-0.863481\pi\)
−0.909429 + 0.415859i \(0.863481\pi\)
\(410\) −22.1281 −1.09283
\(411\) 0 0
\(412\) 18.7144 0.921993
\(413\) 3.88402 0.191120
\(414\) 0 0
\(415\) 24.9919 1.22680
\(416\) −26.1467 −1.28195
\(417\) 0 0
\(418\) −6.16835 −0.301704
\(419\) 1.04076 0.0508444 0.0254222 0.999677i \(-0.491907\pi\)
0.0254222 + 0.999677i \(0.491907\pi\)
\(420\) 0 0
\(421\) −7.51888 −0.366448 −0.183224 0.983071i \(-0.558653\pi\)
−0.183224 + 0.983071i \(0.558653\pi\)
\(422\) −0.829057 −0.0403579
\(423\) 0 0
\(424\) 11.3855 0.552930
\(425\) −12.3013 −0.596702
\(426\) 0 0
\(427\) −7.64885 −0.370154
\(428\) 12.2660 0.592899
\(429\) 0 0
\(430\) −12.4447 −0.600135
\(431\) 27.1064 1.30567 0.652834 0.757501i \(-0.273580\pi\)
0.652834 + 0.757501i \(0.273580\pi\)
\(432\) 0 0
\(433\) 26.6125 1.27891 0.639457 0.768827i \(-0.279159\pi\)
0.639457 + 0.768827i \(0.279159\pi\)
\(434\) −5.91434 −0.283898
\(435\) 0 0
\(436\) −2.91698 −0.139698
\(437\) 62.9200 3.00987
\(438\) 0 0
\(439\) −3.69046 −0.176136 −0.0880681 0.996114i \(-0.528069\pi\)
−0.0880681 + 0.996114i \(0.528069\pi\)
\(440\) 6.43773 0.306907
\(441\) 0 0
\(442\) 35.6253 1.69452
\(443\) 9.76106 0.463762 0.231881 0.972744i \(-0.425512\pi\)
0.231881 + 0.972744i \(0.425512\pi\)
\(444\) 0 0
\(445\) 24.2401 1.14909
\(446\) 1.43099 0.0677595
\(447\) 0 0
\(448\) 6.74075 0.318470
\(449\) −41.3985 −1.95372 −0.976858 0.213887i \(-0.931388\pi\)
−0.976858 + 0.213887i \(0.931388\pi\)
\(450\) 0 0
\(451\) 7.23008 0.340451
\(452\) 20.4768 0.963146
\(453\) 0 0
\(454\) −18.9115 −0.887559
\(455\) 13.2447 0.620920
\(456\) 0 0
\(457\) 26.3294 1.23164 0.615820 0.787887i \(-0.288825\pi\)
0.615820 + 0.787887i \(0.288825\pi\)
\(458\) −9.75500 −0.455821
\(459\) 0 0
\(460\) −22.4048 −1.04463
\(461\) 27.2734 1.27025 0.635125 0.772409i \(-0.280948\pi\)
0.635125 + 0.772409i \(0.280948\pi\)
\(462\) 0 0
\(463\) −37.5923 −1.74706 −0.873531 0.486769i \(-0.838175\pi\)
−0.873531 + 0.486769i \(0.838175\pi\)
\(464\) −7.37944 −0.342582
\(465\) 0 0
\(466\) 16.3797 0.758774
\(467\) −25.9161 −1.19925 −0.599626 0.800280i \(-0.704684\pi\)
−0.599626 + 0.800280i \(0.704684\pi\)
\(468\) 0 0
\(469\) 9.03188 0.417054
\(470\) 5.79064 0.267102
\(471\) 0 0
\(472\) −11.5782 −0.532931
\(473\) 4.06614 0.186961
\(474\) 0 0
\(475\) −13.0627 −0.599357
\(476\) 7.36067 0.337376
\(477\) 0 0
\(478\) −7.42991 −0.339836
\(479\) 13.5335 0.618361 0.309180 0.951003i \(-0.399945\pi\)
0.309180 + 0.951003i \(0.399945\pi\)
\(480\) 0 0
\(481\) 28.2017 1.28589
\(482\) 3.39305 0.154549
\(483\) 0 0
\(484\) 10.6756 0.485255
\(485\) 1.68111 0.0763354
\(486\) 0 0
\(487\) 17.0640 0.773243 0.386622 0.922238i \(-0.373642\pi\)
0.386622 + 0.922238i \(0.373642\pi\)
\(488\) 22.8012 1.03216
\(489\) 0 0
\(490\) −2.54761 −0.115089
\(491\) −40.2689 −1.81731 −0.908655 0.417547i \(-0.862890\pi\)
−0.908655 + 0.417547i \(0.862890\pi\)
\(492\) 0 0
\(493\) −61.2851 −2.76014
\(494\) 37.8302 1.70206
\(495\) 0 0
\(496\) 5.15397 0.231420
\(497\) 9.47044 0.424807
\(498\) 0 0
\(499\) −11.2792 −0.504927 −0.252463 0.967606i \(-0.581241\pi\)
−0.252463 + 0.967606i \(0.581241\pi\)
\(500\) −8.78441 −0.392851
\(501\) 0 0
\(502\) 3.18339 0.142082
\(503\) 0.345174 0.0153905 0.00769527 0.999970i \(-0.497550\pi\)
0.00769527 + 0.999970i \(0.497550\pi\)
\(504\) 0 0
\(505\) 21.6066 0.961482
\(506\) −6.81513 −0.302970
\(507\) 0 0
\(508\) −1.03575 −0.0459540
\(509\) 36.5704 1.62095 0.810476 0.585771i \(-0.199208\pi\)
0.810476 + 0.585771i \(0.199208\pi\)
\(510\) 0 0
\(511\) −6.75232 −0.298705
\(512\) −9.48450 −0.419160
\(513\) 0 0
\(514\) −2.11429 −0.0932573
\(515\) 46.8770 2.06565
\(516\) 0 0
\(517\) −1.89202 −0.0832109
\(518\) −5.42460 −0.238343
\(519\) 0 0
\(520\) −39.4823 −1.73141
\(521\) −5.93817 −0.260156 −0.130078 0.991504i \(-0.541523\pi\)
−0.130078 + 0.991504i \(0.541523\pi\)
\(522\) 0 0
\(523\) −40.8155 −1.78474 −0.892368 0.451309i \(-0.850957\pi\)
−0.892368 + 0.451309i \(0.850957\pi\)
\(524\) −22.9154 −1.00107
\(525\) 0 0
\(526\) −12.0752 −0.526502
\(527\) 42.8030 1.86453
\(528\) 0 0
\(529\) 46.5175 2.02250
\(530\) 9.73029 0.422657
\(531\) 0 0
\(532\) 7.81623 0.338876
\(533\) −44.3417 −1.92065
\(534\) 0 0
\(535\) 30.7246 1.32834
\(536\) −26.9240 −1.16294
\(537\) 0 0
\(538\) −27.7224 −1.19520
\(539\) 0.832401 0.0358541
\(540\) 0 0
\(541\) −29.7773 −1.28023 −0.640114 0.768280i \(-0.721113\pi\)
−0.640114 + 0.768280i \(0.721113\pi\)
\(542\) 8.63185 0.370770
\(543\) 0 0
\(544\) −36.3979 −1.56055
\(545\) −7.30662 −0.312981
\(546\) 0 0
\(547\) −32.4777 −1.38865 −0.694323 0.719663i \(-0.744296\pi\)
−0.694323 + 0.719663i \(0.744296\pi\)
\(548\) −10.0280 −0.428373
\(549\) 0 0
\(550\) 1.41487 0.0603304
\(551\) −65.0781 −2.77242
\(552\) 0 0
\(553\) 5.46202 0.232269
\(554\) −7.06085 −0.299987
\(555\) 0 0
\(556\) −4.71308 −0.199879
\(557\) −7.30357 −0.309462 −0.154731 0.987957i \(-0.549451\pi\)
−0.154731 + 0.987957i \(0.549451\pi\)
\(558\) 0 0
\(559\) −24.9375 −1.05474
\(560\) 2.22008 0.0938156
\(561\) 0 0
\(562\) 0.590408 0.0249049
\(563\) −20.9917 −0.884695 −0.442348 0.896844i \(-0.645854\pi\)
−0.442348 + 0.896844i \(0.645854\pi\)
\(564\) 0 0
\(565\) 51.2914 2.15785
\(566\) 31.4379 1.32144
\(567\) 0 0
\(568\) −28.2313 −1.18456
\(569\) 9.59641 0.402302 0.201151 0.979560i \(-0.435532\pi\)
0.201151 + 0.979560i \(0.435532\pi\)
\(570\) 0 0
\(571\) −29.0968 −1.21766 −0.608831 0.793300i \(-0.708361\pi\)
−0.608831 + 0.793300i \(0.708361\pi\)
\(572\) 4.40140 0.184032
\(573\) 0 0
\(574\) 8.52913 0.355999
\(575\) −14.4324 −0.601871
\(576\) 0 0
\(577\) 35.6413 1.48377 0.741883 0.670530i \(-0.233933\pi\)
0.741883 + 0.670530i \(0.233933\pi\)
\(578\) 32.8994 1.36843
\(579\) 0 0
\(580\) 23.1733 0.962218
\(581\) −9.63296 −0.399642
\(582\) 0 0
\(583\) −3.17925 −0.131671
\(584\) 20.1286 0.832928
\(585\) 0 0
\(586\) 23.0671 0.952894
\(587\) 21.8864 0.903349 0.451674 0.892183i \(-0.350827\pi\)
0.451674 + 0.892183i \(0.350827\pi\)
\(588\) 0 0
\(589\) 45.4521 1.87282
\(590\) −9.89497 −0.407369
\(591\) 0 0
\(592\) 4.72719 0.194286
\(593\) 6.80864 0.279597 0.139799 0.990180i \(-0.455354\pi\)
0.139799 + 0.990180i \(0.455354\pi\)
\(594\) 0 0
\(595\) 18.4374 0.755862
\(596\) −24.7961 −1.01569
\(597\) 0 0
\(598\) 41.7969 1.70920
\(599\) 27.9609 1.14245 0.571225 0.820794i \(-0.306468\pi\)
0.571225 + 0.820794i \(0.306468\pi\)
\(600\) 0 0
\(601\) 9.23744 0.376803 0.188401 0.982092i \(-0.439669\pi\)
0.188401 + 0.982092i \(0.439669\pi\)
\(602\) 4.79672 0.195500
\(603\) 0 0
\(604\) 11.6117 0.472473
\(605\) 26.7409 1.08717
\(606\) 0 0
\(607\) −6.28025 −0.254907 −0.127454 0.991845i \(-0.540680\pi\)
−0.127454 + 0.991845i \(0.540680\pi\)
\(608\) −38.6506 −1.56749
\(609\) 0 0
\(610\) 19.4863 0.788978
\(611\) 11.6037 0.469434
\(612\) 0 0
\(613\) −15.5564 −0.628316 −0.314158 0.949371i \(-0.601722\pi\)
−0.314158 + 0.949371i \(0.601722\pi\)
\(614\) −17.2772 −0.697252
\(615\) 0 0
\(616\) −2.48138 −0.0999777
\(617\) −19.0545 −0.767106 −0.383553 0.923519i \(-0.625300\pi\)
−0.383553 + 0.923519i \(0.625300\pi\)
\(618\) 0 0
\(619\) 24.7065 0.993037 0.496519 0.868026i \(-0.334611\pi\)
0.496519 + 0.868026i \(0.334611\pi\)
\(620\) −16.1848 −0.649996
\(621\) 0 0
\(622\) 19.2575 0.772155
\(623\) −9.34318 −0.374327
\(624\) 0 0
\(625\) −30.6586 −1.22634
\(626\) −15.8402 −0.633101
\(627\) 0 0
\(628\) 0.159998 0.00638460
\(629\) 39.2586 1.56534
\(630\) 0 0
\(631\) −12.9423 −0.515224 −0.257612 0.966248i \(-0.582936\pi\)
−0.257612 + 0.966248i \(0.582936\pi\)
\(632\) −16.2822 −0.647672
\(633\) 0 0
\(634\) −6.23136 −0.247479
\(635\) −2.59441 −0.102956
\(636\) 0 0
\(637\) −5.10508 −0.202271
\(638\) 7.04888 0.279068
\(639\) 0 0
\(640\) 9.40279 0.371678
\(641\) −27.1939 −1.07409 −0.537047 0.843553i \(-0.680460\pi\)
−0.537047 + 0.843553i \(0.680460\pi\)
\(642\) 0 0
\(643\) 4.58228 0.180707 0.0903537 0.995910i \(-0.471200\pi\)
0.0903537 + 0.995910i \(0.471200\pi\)
\(644\) 8.63580 0.340298
\(645\) 0 0
\(646\) 52.6621 2.07196
\(647\) 12.4292 0.488642 0.244321 0.969694i \(-0.421435\pi\)
0.244321 + 0.969694i \(0.421435\pi\)
\(648\) 0 0
\(649\) 3.23306 0.126909
\(650\) −8.67736 −0.340354
\(651\) 0 0
\(652\) 11.8858 0.465482
\(653\) −7.35908 −0.287983 −0.143992 0.989579i \(-0.545994\pi\)
−0.143992 + 0.989579i \(0.545994\pi\)
\(654\) 0 0
\(655\) −57.4000 −2.24280
\(656\) −7.43259 −0.290194
\(657\) 0 0
\(658\) −2.23196 −0.0870111
\(659\) −22.2982 −0.868613 −0.434307 0.900765i \(-0.643007\pi\)
−0.434307 + 0.900765i \(0.643007\pi\)
\(660\) 0 0
\(661\) −31.4767 −1.22430 −0.612151 0.790741i \(-0.709695\pi\)
−0.612151 + 0.790741i \(0.709695\pi\)
\(662\) −1.34335 −0.0522109
\(663\) 0 0
\(664\) 28.7158 1.11439
\(665\) 19.5786 0.759224
\(666\) 0 0
\(667\) −71.9018 −2.78405
\(668\) −1.62828 −0.0630001
\(669\) 0 0
\(670\) −23.0097 −0.888944
\(671\) −6.36692 −0.245792
\(672\) 0 0
\(673\) 26.0157 1.00283 0.501416 0.865206i \(-0.332813\pi\)
0.501416 + 0.865206i \(0.332813\pi\)
\(674\) −9.89144 −0.381004
\(675\) 0 0
\(676\) −13.5288 −0.520340
\(677\) −50.1304 −1.92667 −0.963334 0.268306i \(-0.913536\pi\)
−0.963334 + 0.268306i \(0.913536\pi\)
\(678\) 0 0
\(679\) −0.647975 −0.0248670
\(680\) −54.9619 −2.10769
\(681\) 0 0
\(682\) −4.92311 −0.188515
\(683\) −44.8648 −1.71670 −0.858352 0.513060i \(-0.828512\pi\)
−0.858352 + 0.513060i \(0.828512\pi\)
\(684\) 0 0
\(685\) −25.1186 −0.959733
\(686\) 0.981962 0.0374915
\(687\) 0 0
\(688\) −4.18003 −0.159362
\(689\) 19.4982 0.742823
\(690\) 0 0
\(691\) 29.4106 1.11883 0.559416 0.828887i \(-0.311026\pi\)
0.559416 + 0.828887i \(0.311026\pi\)
\(692\) −25.3115 −0.962198
\(693\) 0 0
\(694\) −11.6208 −0.441118
\(695\) −11.8056 −0.447812
\(696\) 0 0
\(697\) −61.7265 −2.33806
\(698\) 13.4627 0.509571
\(699\) 0 0
\(700\) −1.79286 −0.0677637
\(701\) 3.93713 0.148703 0.0743517 0.997232i \(-0.476311\pi\)
0.0743517 + 0.997232i \(0.476311\pi\)
\(702\) 0 0
\(703\) 41.6884 1.57231
\(704\) 5.61101 0.211473
\(705\) 0 0
\(706\) 23.8309 0.896888
\(707\) −8.32814 −0.313212
\(708\) 0 0
\(709\) 28.9928 1.08885 0.544423 0.838811i \(-0.316749\pi\)
0.544423 + 0.838811i \(0.316749\pi\)
\(710\) −24.1270 −0.905470
\(711\) 0 0
\(712\) 27.8519 1.04380
\(713\) 50.2179 1.88068
\(714\) 0 0
\(715\) 11.0249 0.412308
\(716\) −8.68665 −0.324635
\(717\) 0 0
\(718\) −4.29351 −0.160232
\(719\) 33.2336 1.23940 0.619701 0.784838i \(-0.287254\pi\)
0.619701 + 0.784838i \(0.287254\pi\)
\(720\) 0 0
\(721\) −18.0685 −0.672904
\(722\) 37.2641 1.38683
\(723\) 0 0
\(724\) 12.4270 0.461845
\(725\) 14.9274 0.554389
\(726\) 0 0
\(727\) −19.0117 −0.705105 −0.352552 0.935792i \(-0.614686\pi\)
−0.352552 + 0.935792i \(0.614686\pi\)
\(728\) 15.2182 0.564024
\(729\) 0 0
\(730\) 17.2023 0.636686
\(731\) −34.7146 −1.28396
\(732\) 0 0
\(733\) −30.5354 −1.12785 −0.563925 0.825826i \(-0.690709\pi\)
−0.563925 + 0.825826i \(0.690709\pi\)
\(734\) 22.0854 0.815187
\(735\) 0 0
\(736\) −42.7033 −1.57406
\(737\) 7.51815 0.276935
\(738\) 0 0
\(739\) −2.93682 −0.108033 −0.0540163 0.998540i \(-0.517202\pi\)
−0.0540163 + 0.998540i \(0.517202\pi\)
\(740\) −14.8446 −0.545697
\(741\) 0 0
\(742\) −3.75048 −0.137684
\(743\) −37.7443 −1.38470 −0.692352 0.721560i \(-0.743426\pi\)
−0.692352 + 0.721560i \(0.743426\pi\)
\(744\) 0 0
\(745\) −62.1107 −2.27556
\(746\) 11.8031 0.432141
\(747\) 0 0
\(748\) 6.12703 0.224026
\(749\) −11.8426 −0.432719
\(750\) 0 0
\(751\) 2.36132 0.0861657 0.0430828 0.999072i \(-0.486282\pi\)
0.0430828 + 0.999072i \(0.486282\pi\)
\(752\) 1.94502 0.0709274
\(753\) 0 0
\(754\) −43.2305 −1.57436
\(755\) 29.0857 1.05854
\(756\) 0 0
\(757\) 42.6822 1.55131 0.775655 0.631157i \(-0.217420\pi\)
0.775655 + 0.631157i \(0.217420\pi\)
\(758\) −3.46687 −0.125922
\(759\) 0 0
\(760\) −58.3635 −2.11707
\(761\) 43.9063 1.59160 0.795802 0.605558i \(-0.207050\pi\)
0.795802 + 0.605558i \(0.207050\pi\)
\(762\) 0 0
\(763\) 2.81629 0.101957
\(764\) −3.75576 −0.135878
\(765\) 0 0
\(766\) −27.2233 −0.983617
\(767\) −19.8282 −0.715955
\(768\) 0 0
\(769\) 34.9812 1.26145 0.630727 0.776005i \(-0.282757\pi\)
0.630727 + 0.776005i \(0.282757\pi\)
\(770\) −2.12064 −0.0764224
\(771\) 0 0
\(772\) 21.4133 0.770683
\(773\) 3.10373 0.111633 0.0558166 0.998441i \(-0.482224\pi\)
0.0558166 + 0.998441i \(0.482224\pi\)
\(774\) 0 0
\(775\) −10.4256 −0.374500
\(776\) 1.93161 0.0693406
\(777\) 0 0
\(778\) 3.72673 0.133610
\(779\) −65.5468 −2.34846
\(780\) 0 0
\(781\) 7.88320 0.282083
\(782\) 58.1840 2.08065
\(783\) 0 0
\(784\) −0.855717 −0.0305613
\(785\) 0.400772 0.0143042
\(786\) 0 0
\(787\) −36.8082 −1.31207 −0.656036 0.754730i \(-0.727768\pi\)
−0.656036 + 0.754730i \(0.727768\pi\)
\(788\) −23.5308 −0.838250
\(789\) 0 0
\(790\) −13.9151 −0.495077
\(791\) −19.7700 −0.702939
\(792\) 0 0
\(793\) 39.0480 1.38664
\(794\) −21.3417 −0.757388
\(795\) 0 0
\(796\) −14.0237 −0.497059
\(797\) −38.1550 −1.35152 −0.675759 0.737122i \(-0.736184\pi\)
−0.675759 + 0.737122i \(0.736184\pi\)
\(798\) 0 0
\(799\) 16.1531 0.571454
\(800\) 8.86553 0.313444
\(801\) 0 0
\(802\) 1.94956 0.0688412
\(803\) −5.62064 −0.198348
\(804\) 0 0
\(805\) 21.6315 0.762409
\(806\) 30.1932 1.06351
\(807\) 0 0
\(808\) 24.8261 0.873379
\(809\) −22.3583 −0.786076 −0.393038 0.919522i \(-0.628576\pi\)
−0.393038 + 0.919522i \(0.628576\pi\)
\(810\) 0 0
\(811\) −47.2102 −1.65777 −0.828887 0.559416i \(-0.811025\pi\)
−0.828887 + 0.559416i \(0.811025\pi\)
\(812\) −8.93199 −0.313452
\(813\) 0 0
\(814\) −4.51544 −0.158266
\(815\) 29.7722 1.04287
\(816\) 0 0
\(817\) −36.8631 −1.28968
\(818\) −36.1206 −1.26293
\(819\) 0 0
\(820\) 23.3402 0.815075
\(821\) −2.65321 −0.0925975 −0.0462988 0.998928i \(-0.514743\pi\)
−0.0462988 + 0.998928i \(0.514743\pi\)
\(822\) 0 0
\(823\) 46.5374 1.62219 0.811095 0.584914i \(-0.198872\pi\)
0.811095 + 0.584914i \(0.198872\pi\)
\(824\) 53.8619 1.87637
\(825\) 0 0
\(826\) 3.81395 0.132704
\(827\) −23.3068 −0.810458 −0.405229 0.914215i \(-0.632808\pi\)
−0.405229 + 0.914215i \(0.632808\pi\)
\(828\) 0 0
\(829\) −20.0978 −0.698025 −0.349012 0.937118i \(-0.613483\pi\)
−0.349012 + 0.937118i \(0.613483\pi\)
\(830\) 24.5411 0.851832
\(831\) 0 0
\(832\) −34.4121 −1.19302
\(833\) −7.10660 −0.246229
\(834\) 0 0
\(835\) −4.07862 −0.141146
\(836\) 6.50624 0.225023
\(837\) 0 0
\(838\) 1.02199 0.0353039
\(839\) 49.4669 1.70779 0.853894 0.520447i \(-0.174235\pi\)
0.853894 + 0.520447i \(0.174235\pi\)
\(840\) 0 0
\(841\) 45.3680 1.56441
\(842\) −7.38325 −0.254444
\(843\) 0 0
\(844\) 0.874471 0.0301005
\(845\) −33.8878 −1.16578
\(846\) 0 0
\(847\) −10.3071 −0.354156
\(848\) 3.26830 0.112234
\(849\) 0 0
\(850\) −12.0794 −0.414321
\(851\) 46.0596 1.57890
\(852\) 0 0
\(853\) 7.99651 0.273795 0.136898 0.990585i \(-0.456287\pi\)
0.136898 + 0.990585i \(0.456287\pi\)
\(854\) −7.51088 −0.257017
\(855\) 0 0
\(856\) 35.3027 1.20662
\(857\) 21.7094 0.741579 0.370790 0.928717i \(-0.379087\pi\)
0.370790 + 0.928717i \(0.379087\pi\)
\(858\) 0 0
\(859\) 8.50670 0.290245 0.145122 0.989414i \(-0.453642\pi\)
0.145122 + 0.989414i \(0.453642\pi\)
\(860\) 13.1264 0.447605
\(861\) 0 0
\(862\) 26.6174 0.906593
\(863\) −31.9233 −1.08668 −0.543341 0.839512i \(-0.682841\pi\)
−0.543341 + 0.839512i \(0.682841\pi\)
\(864\) 0 0
\(865\) −63.4017 −2.15572
\(866\) 26.1324 0.888016
\(867\) 0 0
\(868\) 6.23832 0.211742
\(869\) 4.54659 0.154232
\(870\) 0 0
\(871\) −46.1085 −1.56233
\(872\) −8.39534 −0.284302
\(873\) 0 0
\(874\) 61.7850 2.08991
\(875\) 8.48120 0.286717
\(876\) 0 0
\(877\) −42.5730 −1.43759 −0.718793 0.695224i \(-0.755305\pi\)
−0.718793 + 0.695224i \(0.755305\pi\)
\(878\) −3.62389 −0.122300
\(879\) 0 0
\(880\) 1.84800 0.0622961
\(881\) 35.2691 1.18825 0.594124 0.804374i \(-0.297499\pi\)
0.594124 + 0.804374i \(0.297499\pi\)
\(882\) 0 0
\(883\) −21.3815 −0.719546 −0.359773 0.933040i \(-0.617146\pi\)
−0.359773 + 0.933040i \(0.617146\pi\)
\(884\) −37.5768 −1.26384
\(885\) 0 0
\(886\) 9.58498 0.322014
\(887\) −37.3935 −1.25555 −0.627776 0.778394i \(-0.716035\pi\)
−0.627776 + 0.778394i \(0.716035\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 23.8028 0.797872
\(891\) 0 0
\(892\) −1.50938 −0.0505378
\(893\) 17.1528 0.573996
\(894\) 0 0
\(895\) −21.7588 −0.727318
\(896\) −3.62425 −0.121078
\(897\) 0 0
\(898\) −40.6518 −1.35657
\(899\) −51.9404 −1.73231
\(900\) 0 0
\(901\) 27.1428 0.904257
\(902\) 7.09966 0.236393
\(903\) 0 0
\(904\) 58.9341 1.96012
\(905\) 31.1278 1.03472
\(906\) 0 0
\(907\) 9.53781 0.316698 0.158349 0.987383i \(-0.449383\pi\)
0.158349 + 0.987383i \(0.449383\pi\)
\(908\) 19.9474 0.661977
\(909\) 0 0
\(910\) 13.0058 0.431137
\(911\) 47.6465 1.57860 0.789300 0.614008i \(-0.210444\pi\)
0.789300 + 0.614008i \(0.210444\pi\)
\(912\) 0 0
\(913\) −8.01849 −0.265373
\(914\) 25.8545 0.855191
\(915\) 0 0
\(916\) 10.2894 0.339970
\(917\) 22.1245 0.730614
\(918\) 0 0
\(919\) 32.1422 1.06027 0.530136 0.847913i \(-0.322141\pi\)
0.530136 + 0.847913i \(0.322141\pi\)
\(920\) −64.4832 −2.12595
\(921\) 0 0
\(922\) 26.7815 0.882001
\(923\) −48.3473 −1.59137
\(924\) 0 0
\(925\) −9.56233 −0.314407
\(926\) −36.9142 −1.21307
\(927\) 0 0
\(928\) 44.1680 1.44988
\(929\) −21.6067 −0.708892 −0.354446 0.935076i \(-0.615331\pi\)
−0.354446 + 0.935076i \(0.615331\pi\)
\(930\) 0 0
\(931\) −7.54643 −0.247324
\(932\) −17.2769 −0.565925
\(933\) 0 0
\(934\) −25.4486 −0.832703
\(935\) 15.3474 0.501912
\(936\) 0 0
\(937\) −2.03535 −0.0664920 −0.0332460 0.999447i \(-0.510584\pi\)
−0.0332460 + 0.999447i \(0.510584\pi\)
\(938\) 8.86896 0.289582
\(939\) 0 0
\(940\) −6.10783 −0.199216
\(941\) −30.7135 −1.00123 −0.500616 0.865670i \(-0.666893\pi\)
−0.500616 + 0.865670i \(0.666893\pi\)
\(942\) 0 0
\(943\) −72.4197 −2.35831
\(944\) −3.32362 −0.108175
\(945\) 0 0
\(946\) 3.99280 0.129817
\(947\) 29.7046 0.965271 0.482636 0.875821i \(-0.339680\pi\)
0.482636 + 0.875821i \(0.339680\pi\)
\(948\) 0 0
\(949\) 34.4712 1.11898
\(950\) −12.8270 −0.416164
\(951\) 0 0
\(952\) 21.1847 0.686600
\(953\) 3.51868 0.113981 0.0569907 0.998375i \(-0.481849\pi\)
0.0569907 + 0.998375i \(0.481849\pi\)
\(954\) 0 0
\(955\) −9.40764 −0.304424
\(956\) 7.83690 0.253463
\(957\) 0 0
\(958\) 13.2894 0.429360
\(959\) 9.68182 0.312642
\(960\) 0 0
\(961\) 5.27637 0.170205
\(962\) 27.6930 0.892859
\(963\) 0 0
\(964\) −3.57891 −0.115269
\(965\) 53.6374 1.72665
\(966\) 0 0
\(967\) −14.7718 −0.475028 −0.237514 0.971384i \(-0.576333\pi\)
−0.237514 + 0.971384i \(0.576333\pi\)
\(968\) 30.7254 0.987552
\(969\) 0 0
\(970\) 1.65079 0.0530036
\(971\) −6.76299 −0.217035 −0.108517 0.994095i \(-0.534610\pi\)
−0.108517 + 0.994095i \(0.534610\pi\)
\(972\) 0 0
\(973\) 4.55040 0.145879
\(974\) 16.7562 0.536903
\(975\) 0 0
\(976\) 6.54525 0.209508
\(977\) −7.10433 −0.227288 −0.113644 0.993522i \(-0.536252\pi\)
−0.113644 + 0.993522i \(0.536252\pi\)
\(978\) 0 0
\(979\) −7.77728 −0.248563
\(980\) 2.68717 0.0858383
\(981\) 0 0
\(982\) −39.5425 −1.26185
\(983\) −15.7760 −0.503175 −0.251588 0.967835i \(-0.580953\pi\)
−0.251588 + 0.967835i \(0.580953\pi\)
\(984\) 0 0
\(985\) −58.9413 −1.87803
\(986\) −60.1796 −1.91651
\(987\) 0 0
\(988\) −39.9025 −1.26947
\(989\) −40.7283 −1.29509
\(990\) 0 0
\(991\) 50.7213 1.61121 0.805607 0.592450i \(-0.201839\pi\)
0.805607 + 0.592450i \(0.201839\pi\)
\(992\) −30.8479 −0.979423
\(993\) 0 0
\(994\) 9.29961 0.294966
\(995\) −35.1275 −1.11362
\(996\) 0 0
\(997\) 11.3933 0.360829 0.180415 0.983591i \(-0.442256\pi\)
0.180415 + 0.983591i \(0.442256\pi\)
\(998\) −11.0758 −0.350597
\(999\) 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 \(a_p\))