Properties

Label 8001.2.a.z.1.13
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 32
CM No

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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: \(1\)
Dimension: \(32\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.904420 q^{2}\) \(-1.18202 q^{4}\) \(-0.974726 q^{5}\) \(-1.00000 q^{7}\) \(+2.87789 q^{8}\) \(+O(q^{10})\) \(q\)\(-0.904420 q^{2}\) \(-1.18202 q^{4}\) \(-0.974726 q^{5}\) \(-1.00000 q^{7}\) \(+2.87789 q^{8}\) \(+0.881562 q^{10}\) \(+1.96544 q^{11}\) \(+2.74141 q^{13}\) \(+0.904420 q^{14}\) \(-0.238773 q^{16}\) \(-1.83682 q^{17}\) \(+2.02640 q^{19}\) \(+1.15215 q^{20}\) \(-1.77759 q^{22}\) \(-4.95844 q^{23}\) \(-4.04991 q^{25}\) \(-2.47939 q^{26}\) \(+1.18202 q^{28}\) \(+5.22491 q^{29}\) \(-1.18264 q^{31}\) \(-5.53982 q^{32}\) \(+1.66126 q^{34}\) \(+0.974726 q^{35}\) \(-0.458876 q^{37}\) \(-1.83272 q^{38}\) \(-2.80515 q^{40}\) \(+4.63274 q^{41}\) \(-9.80048 q^{43}\) \(-2.32320 q^{44}\) \(+4.48451 q^{46}\) \(-1.05030 q^{47}\) \(+1.00000 q^{49}\) \(+3.66282 q^{50}\) \(-3.24041 q^{52}\) \(+0.354557 q^{53}\) \(-1.91577 q^{55}\) \(-2.87789 q^{56}\) \(-4.72552 q^{58}\) \(+2.99975 q^{59}\) \(+10.7918 q^{61}\) \(+1.06960 q^{62}\) \(+5.48787 q^{64}\) \(-2.67212 q^{65}\) \(-11.3466 q^{67}\) \(+2.17117 q^{68}\) \(-0.881562 q^{70}\) \(-11.1482 q^{71}\) \(+15.2419 q^{73}\) \(+0.415017 q^{74}\) \(-2.39526 q^{76}\) \(-1.96544 q^{77}\) \(-10.8394 q^{79}\) \(+0.232738 q^{80}\) \(-4.18994 q^{82}\) \(+2.78288 q^{83}\) \(+1.79040 q^{85}\) \(+8.86376 q^{86}\) \(+5.65632 q^{88}\) \(+5.79864 q^{89}\) \(-2.74141 q^{91}\) \(+5.86099 q^{92}\) \(+0.949912 q^{94}\) \(-1.97519 q^{95}\) \(+14.0797 q^{97}\) \(-0.904420 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(32q \) \(\mathstrut +\mathstrut 30q^{4} \) \(\mathstrut -\mathstrut 32q^{7} \) \(\mathstrut -\mathstrut 16q^{10} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut +\mathstrut 18q^{16} \) \(\mathstrut -\mathstrut 30q^{19} \) \(\mathstrut -\mathstrut 10q^{22} \) \(\mathstrut +\mathstrut 36q^{25} \) \(\mathstrut -\mathstrut 30q^{28} \) \(\mathstrut -\mathstrut 58q^{31} \) \(\mathstrut -\mathstrut 34q^{34} \) \(\mathstrut +\mathstrut 8q^{37} \) \(\mathstrut -\mathstrut 34q^{40} \) \(\mathstrut +\mathstrut 6q^{43} \) \(\mathstrut -\mathstrut 36q^{46} \) \(\mathstrut +\mathstrut 32q^{49} \) \(\mathstrut -\mathstrut 56q^{52} \) \(\mathstrut -\mathstrut 88q^{55} \) \(\mathstrut -\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut +\mathstrut 20q^{64} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut +\mathstrut 16q^{70} \) \(\mathstrut -\mathstrut 60q^{73} \) \(\mathstrut -\mathstrut 128q^{76} \) \(\mathstrut -\mathstrut 74q^{79} \) \(\mathstrut -\mathstrut 52q^{82} \) \(\mathstrut -\mathstrut 16q^{85} \) \(\mathstrut -\mathstrut 64q^{88} \) \(\mathstrut +\mathstrut 14q^{91} \) \(\mathstrut -\mathstrut 58q^{94} \) \(\mathstrut -\mathstrut 44q^{97} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.904420 −0.639522 −0.319761 0.947498i \(-0.603603\pi\)
−0.319761 + 0.947498i \(0.603603\pi\)
\(3\) 0 0
\(4\) −1.18202 −0.591012
\(5\) −0.974726 −0.435911 −0.217955 0.975959i \(-0.569939\pi\)
−0.217955 + 0.975959i \(0.569939\pi\)
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 2.87789 1.01749
\(9\) 0 0
\(10\) 0.881562 0.278774
\(11\) 1.96544 0.592603 0.296302 0.955094i \(-0.404247\pi\)
0.296302 + 0.955094i \(0.404247\pi\)
\(12\) 0 0
\(13\) 2.74141 0.760330 0.380165 0.924919i \(-0.375867\pi\)
0.380165 + 0.924919i \(0.375867\pi\)
\(14\) 0.904420 0.241717
\(15\) 0 0
\(16\) −0.238773 −0.0596931
\(17\) −1.83682 −0.445495 −0.222748 0.974876i \(-0.571503\pi\)
−0.222748 + 0.974876i \(0.571503\pi\)
\(18\) 0 0
\(19\) 2.02640 0.464889 0.232444 0.972610i \(-0.425328\pi\)
0.232444 + 0.972610i \(0.425328\pi\)
\(20\) 1.15215 0.257628
\(21\) 0 0
\(22\) −1.77759 −0.378983
\(23\) −4.95844 −1.03391 −0.516953 0.856014i \(-0.672934\pi\)
−0.516953 + 0.856014i \(0.672934\pi\)
\(24\) 0 0
\(25\) −4.04991 −0.809982
\(26\) −2.47939 −0.486248
\(27\) 0 0
\(28\) 1.18202 0.223381
\(29\) 5.22491 0.970242 0.485121 0.874447i \(-0.338776\pi\)
0.485121 + 0.874447i \(0.338776\pi\)
\(30\) 0 0
\(31\) −1.18264 −0.212408 −0.106204 0.994344i \(-0.533870\pi\)
−0.106204 + 0.994344i \(0.533870\pi\)
\(32\) −5.53982 −0.979312
\(33\) 0 0
\(34\) 1.66126 0.284904
\(35\) 0.974726 0.164759
\(36\) 0 0
\(37\) −0.458876 −0.0754388 −0.0377194 0.999288i \(-0.512009\pi\)
−0.0377194 + 0.999288i \(0.512009\pi\)
\(38\) −1.83272 −0.297307
\(39\) 0 0
\(40\) −2.80515 −0.443533
\(41\) 4.63274 0.723512 0.361756 0.932273i \(-0.382177\pi\)
0.361756 + 0.932273i \(0.382177\pi\)
\(42\) 0 0
\(43\) −9.80048 −1.49456 −0.747280 0.664509i \(-0.768641\pi\)
−0.747280 + 0.664509i \(0.768641\pi\)
\(44\) −2.32320 −0.350235
\(45\) 0 0
\(46\) 4.48451 0.661205
\(47\) −1.05030 −0.153202 −0.0766010 0.997062i \(-0.524407\pi\)
−0.0766010 + 0.997062i \(0.524407\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 3.66282 0.518001
\(51\) 0 0
\(52\) −3.24041 −0.449364
\(53\) 0.354557 0.0487021 0.0243511 0.999703i \(-0.492248\pi\)
0.0243511 + 0.999703i \(0.492248\pi\)
\(54\) 0 0
\(55\) −1.91577 −0.258322
\(56\) −2.87789 −0.384574
\(57\) 0 0
\(58\) −4.72552 −0.620491
\(59\) 2.99975 0.390534 0.195267 0.980750i \(-0.437443\pi\)
0.195267 + 0.980750i \(0.437443\pi\)
\(60\) 0 0
\(61\) 10.7918 1.38174 0.690872 0.722977i \(-0.257227\pi\)
0.690872 + 0.722977i \(0.257227\pi\)
\(62\) 1.06960 0.135839
\(63\) 0 0
\(64\) 5.48787 0.685984
\(65\) −2.67212 −0.331436
\(66\) 0 0
\(67\) −11.3466 −1.38621 −0.693104 0.720837i \(-0.743757\pi\)
−0.693104 + 0.720837i \(0.743757\pi\)
\(68\) 2.17117 0.263293
\(69\) 0 0
\(70\) −0.881562 −0.105367
\(71\) −11.1482 −1.32305 −0.661525 0.749923i \(-0.730091\pi\)
−0.661525 + 0.749923i \(0.730091\pi\)
\(72\) 0 0
\(73\) 15.2419 1.78393 0.891966 0.452102i \(-0.149326\pi\)
0.891966 + 0.452102i \(0.149326\pi\)
\(74\) 0.415017 0.0482447
\(75\) 0 0
\(76\) −2.39526 −0.274755
\(77\) −1.96544 −0.223983
\(78\) 0 0
\(79\) −10.8394 −1.21953 −0.609764 0.792583i \(-0.708736\pi\)
−0.609764 + 0.792583i \(0.708736\pi\)
\(80\) 0.232738 0.0260209
\(81\) 0 0
\(82\) −4.18994 −0.462702
\(83\) 2.78288 0.305461 0.152730 0.988268i \(-0.451193\pi\)
0.152730 + 0.988268i \(0.451193\pi\)
\(84\) 0 0
\(85\) 1.79040 0.194196
\(86\) 8.86376 0.955804
\(87\) 0 0
\(88\) 5.65632 0.602966
\(89\) 5.79864 0.614655 0.307327 0.951604i \(-0.400565\pi\)
0.307327 + 0.951604i \(0.400565\pi\)
\(90\) 0 0
\(91\) −2.74141 −0.287378
\(92\) 5.86099 0.611051
\(93\) 0 0
\(94\) 0.949912 0.0979760
\(95\) −1.97519 −0.202650
\(96\) 0 0
\(97\) 14.0797 1.42957 0.714787 0.699343i \(-0.246524\pi\)
0.714787 + 0.699343i \(0.246524\pi\)
\(98\) −0.904420 −0.0913603
\(99\) 0 0
\(100\) 4.78709 0.478709
\(101\) −18.6908 −1.85980 −0.929901 0.367809i \(-0.880108\pi\)
−0.929901 + 0.367809i \(0.880108\pi\)
\(102\) 0 0
\(103\) −11.2067 −1.10423 −0.552114 0.833768i \(-0.686179\pi\)
−0.552114 + 0.833768i \(0.686179\pi\)
\(104\) 7.88947 0.773626
\(105\) 0 0
\(106\) −0.320668 −0.0311461
\(107\) −0.851347 −0.0823028 −0.0411514 0.999153i \(-0.513103\pi\)
−0.0411514 + 0.999153i \(0.513103\pi\)
\(108\) 0 0
\(109\) 5.23394 0.501320 0.250660 0.968075i \(-0.419352\pi\)
0.250660 + 0.968075i \(0.419352\pi\)
\(110\) 1.73266 0.165203
\(111\) 0 0
\(112\) 0.238773 0.0225619
\(113\) 20.4549 1.92424 0.962118 0.272634i \(-0.0878949\pi\)
0.962118 + 0.272634i \(0.0878949\pi\)
\(114\) 0 0
\(115\) 4.83312 0.450690
\(116\) −6.17597 −0.573424
\(117\) 0 0
\(118\) −2.71304 −0.249755
\(119\) 1.83682 0.168381
\(120\) 0 0
\(121\) −7.13704 −0.648822
\(122\) −9.76030 −0.883656
\(123\) 0 0
\(124\) 1.39790 0.125536
\(125\) 8.82118 0.788990
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) 6.11630 0.540610
\(129\) 0 0
\(130\) 2.41672 0.211961
\(131\) 4.73386 0.413600 0.206800 0.978383i \(-0.433695\pi\)
0.206800 + 0.978383i \(0.433695\pi\)
\(132\) 0 0
\(133\) −2.02640 −0.175712
\(134\) 10.2621 0.886511
\(135\) 0 0
\(136\) −5.28617 −0.453285
\(137\) −2.27099 −0.194024 −0.0970118 0.995283i \(-0.530928\pi\)
−0.0970118 + 0.995283i \(0.530928\pi\)
\(138\) 0 0
\(139\) −1.52891 −0.129680 −0.0648402 0.997896i \(-0.520654\pi\)
−0.0648402 + 0.997896i \(0.520654\pi\)
\(140\) −1.15215 −0.0973743
\(141\) 0 0
\(142\) 10.0827 0.846120
\(143\) 5.38808 0.450574
\(144\) 0 0
\(145\) −5.09286 −0.422939
\(146\) −13.7851 −1.14086
\(147\) 0 0
\(148\) 0.542402 0.0445852
\(149\) 3.83317 0.314025 0.157013 0.987597i \(-0.449814\pi\)
0.157013 + 0.987597i \(0.449814\pi\)
\(150\) 0 0
\(151\) −14.1993 −1.15553 −0.577763 0.816205i \(-0.696074\pi\)
−0.577763 + 0.816205i \(0.696074\pi\)
\(152\) 5.83176 0.473018
\(153\) 0 0
\(154\) 1.77759 0.143242
\(155\) 1.15275 0.0925908
\(156\) 0 0
\(157\) 5.23858 0.418084 0.209042 0.977907i \(-0.432965\pi\)
0.209042 + 0.977907i \(0.432965\pi\)
\(158\) 9.80338 0.779915
\(159\) 0 0
\(160\) 5.39981 0.426892
\(161\) 4.95844 0.390780
\(162\) 0 0
\(163\) 3.56149 0.278957 0.139479 0.990225i \(-0.455457\pi\)
0.139479 + 0.990225i \(0.455457\pi\)
\(164\) −5.47601 −0.427604
\(165\) 0 0
\(166\) −2.51689 −0.195349
\(167\) 15.4593 1.19628 0.598140 0.801392i \(-0.295907\pi\)
0.598140 + 0.801392i \(0.295907\pi\)
\(168\) 0 0
\(169\) −5.48467 −0.421898
\(170\) −1.61927 −0.124193
\(171\) 0 0
\(172\) 11.5844 0.883303
\(173\) 13.8233 1.05097 0.525484 0.850804i \(-0.323884\pi\)
0.525484 + 0.850804i \(0.323884\pi\)
\(174\) 0 0
\(175\) 4.04991 0.306144
\(176\) −0.469294 −0.0353743
\(177\) 0 0
\(178\) −5.24441 −0.393085
\(179\) 24.2437 1.81206 0.906028 0.423218i \(-0.139099\pi\)
0.906028 + 0.423218i \(0.139099\pi\)
\(180\) 0 0
\(181\) −19.1972 −1.42692 −0.713460 0.700696i \(-0.752873\pi\)
−0.713460 + 0.700696i \(0.752873\pi\)
\(182\) 2.47939 0.183784
\(183\) 0 0
\(184\) −14.2698 −1.05199
\(185\) 0.447278 0.0328846
\(186\) 0 0
\(187\) −3.61017 −0.264002
\(188\) 1.24148 0.0905442
\(189\) 0 0
\(190\) 1.78640 0.129599
\(191\) −7.51446 −0.543727 −0.271864 0.962336i \(-0.587640\pi\)
−0.271864 + 0.962336i \(0.587640\pi\)
\(192\) 0 0
\(193\) −4.90984 −0.353418 −0.176709 0.984263i \(-0.556545\pi\)
−0.176709 + 0.984263i \(0.556545\pi\)
\(194\) −12.7339 −0.914243
\(195\) 0 0
\(196\) −1.18202 −0.0844303
\(197\) 23.6073 1.68195 0.840975 0.541074i \(-0.181982\pi\)
0.840975 + 0.541074i \(0.181982\pi\)
\(198\) 0 0
\(199\) −6.60082 −0.467920 −0.233960 0.972246i \(-0.575168\pi\)
−0.233960 + 0.972246i \(0.575168\pi\)
\(200\) −11.6552 −0.824146
\(201\) 0 0
\(202\) 16.9043 1.18938
\(203\) −5.22491 −0.366717
\(204\) 0 0
\(205\) −4.51565 −0.315387
\(206\) 10.1356 0.706178
\(207\) 0 0
\(208\) −0.654573 −0.0453865
\(209\) 3.98278 0.275495
\(210\) 0 0
\(211\) −15.9501 −1.09805 −0.549024 0.835806i \(-0.685001\pi\)
−0.549024 + 0.835806i \(0.685001\pi\)
\(212\) −0.419094 −0.0287835
\(213\) 0 0
\(214\) 0.769976 0.0526345
\(215\) 9.55278 0.651494
\(216\) 0 0
\(217\) 1.18264 0.0802826
\(218\) −4.73368 −0.320605
\(219\) 0 0
\(220\) 2.26448 0.152671
\(221\) −5.03549 −0.338724
\(222\) 0 0
\(223\) 10.7130 0.717399 0.358699 0.933453i \(-0.383220\pi\)
0.358699 + 0.933453i \(0.383220\pi\)
\(224\) 5.53982 0.370145
\(225\) 0 0
\(226\) −18.4998 −1.23059
\(227\) −3.94057 −0.261545 −0.130772 0.991412i \(-0.541746\pi\)
−0.130772 + 0.991412i \(0.541746\pi\)
\(228\) 0 0
\(229\) −18.2625 −1.20682 −0.603409 0.797432i \(-0.706191\pi\)
−0.603409 + 0.797432i \(0.706191\pi\)
\(230\) −4.37117 −0.288226
\(231\) 0 0
\(232\) 15.0367 0.987208
\(233\) 8.66383 0.567587 0.283793 0.958885i \(-0.408407\pi\)
0.283793 + 0.958885i \(0.408407\pi\)
\(234\) 0 0
\(235\) 1.02375 0.0667823
\(236\) −3.54578 −0.230810
\(237\) 0 0
\(238\) −1.66126 −0.107684
\(239\) 3.60516 0.233198 0.116599 0.993179i \(-0.462801\pi\)
0.116599 + 0.993179i \(0.462801\pi\)
\(240\) 0 0
\(241\) −6.19669 −0.399164 −0.199582 0.979881i \(-0.563958\pi\)
−0.199582 + 0.979881i \(0.563958\pi\)
\(242\) 6.45488 0.414936
\(243\) 0 0
\(244\) −12.7561 −0.816628
\(245\) −0.974726 −0.0622729
\(246\) 0 0
\(247\) 5.55520 0.353469
\(248\) −3.40350 −0.216122
\(249\) 0 0
\(250\) −7.97805 −0.504576
\(251\) 0.903566 0.0570326 0.0285163 0.999593i \(-0.490922\pi\)
0.0285163 + 0.999593i \(0.490922\pi\)
\(252\) 0 0
\(253\) −9.74552 −0.612696
\(254\) 0.904420 0.0567484
\(255\) 0 0
\(256\) −16.5075 −1.03172
\(257\) −8.84869 −0.551966 −0.275983 0.961162i \(-0.589003\pi\)
−0.275983 + 0.961162i \(0.589003\pi\)
\(258\) 0 0
\(259\) 0.458876 0.0285132
\(260\) 3.15851 0.195883
\(261\) 0 0
\(262\) −4.28140 −0.264506
\(263\) 1.87830 0.115821 0.0579104 0.998322i \(-0.481556\pi\)
0.0579104 + 0.998322i \(0.481556\pi\)
\(264\) 0 0
\(265\) −0.345595 −0.0212298
\(266\) 1.83272 0.112371
\(267\) 0 0
\(268\) 13.4120 0.819266
\(269\) −27.5980 −1.68268 −0.841339 0.540507i \(-0.818232\pi\)
−0.841339 + 0.540507i \(0.818232\pi\)
\(270\) 0 0
\(271\) −1.69809 −0.103151 −0.0515757 0.998669i \(-0.516424\pi\)
−0.0515757 + 0.998669i \(0.516424\pi\)
\(272\) 0.438583 0.0265930
\(273\) 0 0
\(274\) 2.05393 0.124082
\(275\) −7.95986 −0.479998
\(276\) 0 0
\(277\) −7.81718 −0.469689 −0.234844 0.972033i \(-0.575458\pi\)
−0.234844 + 0.972033i \(0.575458\pi\)
\(278\) 1.38278 0.0829334
\(279\) 0 0
\(280\) 2.80515 0.167640
\(281\) 27.2136 1.62343 0.811713 0.584056i \(-0.198535\pi\)
0.811713 + 0.584056i \(0.198535\pi\)
\(282\) 0 0
\(283\) −28.2507 −1.67933 −0.839663 0.543107i \(-0.817248\pi\)
−0.839663 + 0.543107i \(0.817248\pi\)
\(284\) 13.1775 0.781939
\(285\) 0 0
\(286\) −4.87309 −0.288152
\(287\) −4.63274 −0.273462
\(288\) 0 0
\(289\) −13.6261 −0.801534
\(290\) 4.60608 0.270478
\(291\) 0 0
\(292\) −18.0163 −1.05433
\(293\) −28.5553 −1.66822 −0.834108 0.551601i \(-0.814017\pi\)
−0.834108 + 0.551601i \(0.814017\pi\)
\(294\) 0 0
\(295\) −2.92393 −0.170238
\(296\) −1.32059 −0.0767579
\(297\) 0 0
\(298\) −3.46679 −0.200826
\(299\) −13.5931 −0.786110
\(300\) 0 0
\(301\) 9.80048 0.564891
\(302\) 12.8422 0.738984
\(303\) 0 0
\(304\) −0.483850 −0.0277507
\(305\) −10.5190 −0.602317
\(306\) 0 0
\(307\) 27.6944 1.58060 0.790301 0.612719i \(-0.209924\pi\)
0.790301 + 0.612719i \(0.209924\pi\)
\(308\) 2.32320 0.132377
\(309\) 0 0
\(310\) −1.04257 −0.0592139
\(311\) 9.66622 0.548121 0.274061 0.961712i \(-0.411633\pi\)
0.274061 + 0.961712i \(0.411633\pi\)
\(312\) 0 0
\(313\) 5.52701 0.312405 0.156203 0.987725i \(-0.450075\pi\)
0.156203 + 0.987725i \(0.450075\pi\)
\(314\) −4.73788 −0.267374
\(315\) 0 0
\(316\) 12.8124 0.720756
\(317\) 11.9503 0.671193 0.335597 0.942006i \(-0.391062\pi\)
0.335597 + 0.942006i \(0.391062\pi\)
\(318\) 0 0
\(319\) 10.2693 0.574968
\(320\) −5.34917 −0.299028
\(321\) 0 0
\(322\) −4.48451 −0.249912
\(323\) −3.72215 −0.207106
\(324\) 0 0
\(325\) −11.1025 −0.615854
\(326\) −3.22108 −0.178399
\(327\) 0 0
\(328\) 13.3325 0.736164
\(329\) 1.05030 0.0579049
\(330\) 0 0
\(331\) −15.3085 −0.841432 −0.420716 0.907192i \(-0.638221\pi\)
−0.420716 + 0.907192i \(0.638221\pi\)
\(332\) −3.28943 −0.180531
\(333\) 0 0
\(334\) −13.9817 −0.765047
\(335\) 11.0598 0.604263
\(336\) 0 0
\(337\) −24.6748 −1.34412 −0.672062 0.740495i \(-0.734591\pi\)
−0.672062 + 0.740495i \(0.734591\pi\)
\(338\) 4.96045 0.269813
\(339\) 0 0
\(340\) −2.11629 −0.114772
\(341\) −2.32440 −0.125874
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −28.2047 −1.52069
\(345\) 0 0
\(346\) −12.5021 −0.672117
\(347\) 16.4238 0.881674 0.440837 0.897587i \(-0.354682\pi\)
0.440837 + 0.897587i \(0.354682\pi\)
\(348\) 0 0
\(349\) −14.5558 −0.779156 −0.389578 0.920994i \(-0.627379\pi\)
−0.389578 + 0.920994i \(0.627379\pi\)
\(350\) −3.66282 −0.195786
\(351\) 0 0
\(352\) −10.8882 −0.580343
\(353\) −6.68260 −0.355679 −0.177839 0.984060i \(-0.556911\pi\)
−0.177839 + 0.984060i \(0.556911\pi\)
\(354\) 0 0
\(355\) 10.8665 0.576732
\(356\) −6.85413 −0.363268
\(357\) 0 0
\(358\) −21.9265 −1.15885
\(359\) −31.4312 −1.65888 −0.829439 0.558598i \(-0.811340\pi\)
−0.829439 + 0.558598i \(0.811340\pi\)
\(360\) 0 0
\(361\) −14.8937 −0.783878
\(362\) 17.3624 0.912547
\(363\) 0 0
\(364\) 3.24041 0.169844
\(365\) −14.8567 −0.777635
\(366\) 0 0
\(367\) −33.1243 −1.72907 −0.864537 0.502570i \(-0.832388\pi\)
−0.864537 + 0.502570i \(0.832388\pi\)
\(368\) 1.18394 0.0617171
\(369\) 0 0
\(370\) −0.404528 −0.0210304
\(371\) −0.354557 −0.0184077
\(372\) 0 0
\(373\) −14.3474 −0.742883 −0.371441 0.928456i \(-0.621136\pi\)
−0.371441 + 0.928456i \(0.621136\pi\)
\(374\) 3.26511 0.168835
\(375\) 0 0
\(376\) −3.02264 −0.155881
\(377\) 14.3236 0.737704
\(378\) 0 0
\(379\) 10.7475 0.552061 0.276031 0.961149i \(-0.410981\pi\)
0.276031 + 0.961149i \(0.410981\pi\)
\(380\) 2.33472 0.119769
\(381\) 0 0
\(382\) 6.79623 0.347725
\(383\) −15.3578 −0.784746 −0.392373 0.919806i \(-0.628346\pi\)
−0.392373 + 0.919806i \(0.628346\pi\)
\(384\) 0 0
\(385\) 1.91577 0.0976365
\(386\) 4.44056 0.226019
\(387\) 0 0
\(388\) −16.6425 −0.844895
\(389\) −26.9989 −1.36890 −0.684449 0.729061i \(-0.739957\pi\)
−0.684449 + 0.729061i \(0.739957\pi\)
\(390\) 0 0
\(391\) 9.10778 0.460600
\(392\) 2.87789 0.145355
\(393\) 0 0
\(394\) −21.3509 −1.07564
\(395\) 10.5654 0.531605
\(396\) 0 0
\(397\) 9.42370 0.472962 0.236481 0.971636i \(-0.424006\pi\)
0.236481 + 0.971636i \(0.424006\pi\)
\(398\) 5.96992 0.299245
\(399\) 0 0
\(400\) 0.967007 0.0483504
\(401\) 27.0326 1.34994 0.674972 0.737843i \(-0.264155\pi\)
0.674972 + 0.737843i \(0.264155\pi\)
\(402\) 0 0
\(403\) −3.24209 −0.161500
\(404\) 22.0929 1.09917
\(405\) 0 0
\(406\) 4.72552 0.234523
\(407\) −0.901894 −0.0447052
\(408\) 0 0
\(409\) −1.53002 −0.0756546 −0.0378273 0.999284i \(-0.512044\pi\)
−0.0378273 + 0.999284i \(0.512044\pi\)
\(410\) 4.08405 0.201697
\(411\) 0 0
\(412\) 13.2466 0.652612
\(413\) −2.99975 −0.147608
\(414\) 0 0
\(415\) −2.71254 −0.133153
\(416\) −15.1869 −0.744600
\(417\) 0 0
\(418\) −3.60211 −0.176185
\(419\) −24.5561 −1.19964 −0.599821 0.800134i \(-0.704761\pi\)
−0.599821 + 0.800134i \(0.704761\pi\)
\(420\) 0 0
\(421\) −17.0319 −0.830082 −0.415041 0.909803i \(-0.636233\pi\)
−0.415041 + 0.909803i \(0.636233\pi\)
\(422\) 14.4256 0.702226
\(423\) 0 0
\(424\) 1.02037 0.0495538
\(425\) 7.43897 0.360843
\(426\) 0 0
\(427\) −10.7918 −0.522250
\(428\) 1.00631 0.0486420
\(429\) 0 0
\(430\) −8.63973 −0.416645
\(431\) −19.1165 −0.920807 −0.460404 0.887710i \(-0.652295\pi\)
−0.460404 + 0.887710i \(0.652295\pi\)
\(432\) 0 0
\(433\) −20.3990 −0.980314 −0.490157 0.871634i \(-0.663061\pi\)
−0.490157 + 0.871634i \(0.663061\pi\)
\(434\) −1.06960 −0.0513425
\(435\) 0 0
\(436\) −6.18664 −0.296286
\(437\) −10.0478 −0.480651
\(438\) 0 0
\(439\) 25.7152 1.22732 0.613661 0.789570i \(-0.289696\pi\)
0.613661 + 0.789570i \(0.289696\pi\)
\(440\) −5.51336 −0.262839
\(441\) 0 0
\(442\) 4.55420 0.216621
\(443\) 1.86722 0.0887145 0.0443572 0.999016i \(-0.485876\pi\)
0.0443572 + 0.999016i \(0.485876\pi\)
\(444\) 0 0
\(445\) −5.65209 −0.267935
\(446\) −9.68910 −0.458792
\(447\) 0 0
\(448\) −5.48787 −0.259278
\(449\) −31.0418 −1.46495 −0.732477 0.680792i \(-0.761636\pi\)
−0.732477 + 0.680792i \(0.761636\pi\)
\(450\) 0 0
\(451\) 9.10538 0.428756
\(452\) −24.1782 −1.13725
\(453\) 0 0
\(454\) 3.56393 0.167264
\(455\) 2.67212 0.125271
\(456\) 0 0
\(457\) −6.64753 −0.310958 −0.155479 0.987839i \(-0.549692\pi\)
−0.155479 + 0.987839i \(0.549692\pi\)
\(458\) 16.5170 0.771787
\(459\) 0 0
\(460\) −5.71286 −0.266363
\(461\) −39.1504 −1.82342 −0.911709 0.410837i \(-0.865237\pi\)
−0.911709 + 0.410837i \(0.865237\pi\)
\(462\) 0 0
\(463\) 3.32152 0.154364 0.0771821 0.997017i \(-0.475408\pi\)
0.0771821 + 0.997017i \(0.475408\pi\)
\(464\) −1.24757 −0.0579168
\(465\) 0 0
\(466\) −7.83575 −0.362984
\(467\) 4.67881 0.216509 0.108255 0.994123i \(-0.465474\pi\)
0.108255 + 0.994123i \(0.465474\pi\)
\(468\) 0 0
\(469\) 11.3466 0.523938
\(470\) −0.925904 −0.0427088
\(471\) 0 0
\(472\) 8.63294 0.397363
\(473\) −19.2623 −0.885681
\(474\) 0 0
\(475\) −8.20675 −0.376552
\(476\) −2.17117 −0.0995154
\(477\) 0 0
\(478\) −3.26058 −0.149135
\(479\) 13.8988 0.635054 0.317527 0.948249i \(-0.397148\pi\)
0.317527 + 0.948249i \(0.397148\pi\)
\(480\) 0 0
\(481\) −1.25797 −0.0573584
\(482\) 5.60442 0.255274
\(483\) 0 0
\(484\) 8.43615 0.383461
\(485\) −13.7238 −0.623166
\(486\) 0 0
\(487\) 40.1874 1.82106 0.910532 0.413439i \(-0.135673\pi\)
0.910532 + 0.413439i \(0.135673\pi\)
\(488\) 31.0575 1.40591
\(489\) 0 0
\(490\) 0.881562 0.0398249
\(491\) −19.5893 −0.884052 −0.442026 0.897002i \(-0.645740\pi\)
−0.442026 + 0.897002i \(0.645740\pi\)
\(492\) 0 0
\(493\) −9.59724 −0.432238
\(494\) −5.02424 −0.226051
\(495\) 0 0
\(496\) 0.282381 0.0126793
\(497\) 11.1482 0.500066
\(498\) 0 0
\(499\) −12.0588 −0.539826 −0.269913 0.962885i \(-0.586995\pi\)
−0.269913 + 0.962885i \(0.586995\pi\)
\(500\) −10.4268 −0.466303
\(501\) 0 0
\(502\) −0.817203 −0.0364736
\(503\) 16.7958 0.748889 0.374444 0.927249i \(-0.377833\pi\)
0.374444 + 0.927249i \(0.377833\pi\)
\(504\) 0 0
\(505\) 18.2184 0.810707
\(506\) 8.81405 0.391832
\(507\) 0 0
\(508\) 1.18202 0.0524438
\(509\) 3.01771 0.133758 0.0668789 0.997761i \(-0.478696\pi\)
0.0668789 + 0.997761i \(0.478696\pi\)
\(510\) 0 0
\(511\) −15.2419 −0.674263
\(512\) 2.69708 0.119195
\(513\) 0 0
\(514\) 8.00294 0.352994
\(515\) 10.9235 0.481345
\(516\) 0 0
\(517\) −2.06430 −0.0907880
\(518\) −0.415017 −0.0182348
\(519\) 0 0
\(520\) −7.69007 −0.337232
\(521\) −39.2726 −1.72056 −0.860281 0.509819i \(-0.829712\pi\)
−0.860281 + 0.509819i \(0.829712\pi\)
\(522\) 0 0
\(523\) −8.32811 −0.364163 −0.182081 0.983283i \(-0.558283\pi\)
−0.182081 + 0.983283i \(0.558283\pi\)
\(524\) −5.59554 −0.244442
\(525\) 0 0
\(526\) −1.69877 −0.0740700
\(527\) 2.17230 0.0946267
\(528\) 0 0
\(529\) 1.58611 0.0689615
\(530\) 0.312564 0.0135769
\(531\) 0 0
\(532\) 2.39526 0.103848
\(533\) 12.7002 0.550108
\(534\) 0 0
\(535\) 0.829830 0.0358767
\(536\) −32.6542 −1.41045
\(537\) 0 0
\(538\) 24.9602 1.07611
\(539\) 1.96544 0.0846576
\(540\) 0 0
\(541\) 25.5876 1.10010 0.550048 0.835133i \(-0.314609\pi\)
0.550048 + 0.835133i \(0.314609\pi\)
\(542\) 1.53579 0.0659676
\(543\) 0 0
\(544\) 10.1757 0.436279
\(545\) −5.10165 −0.218531
\(546\) 0 0
\(547\) −9.33215 −0.399014 −0.199507 0.979896i \(-0.563934\pi\)
−0.199507 + 0.979896i \(0.563934\pi\)
\(548\) 2.68436 0.114670
\(549\) 0 0
\(550\) 7.19906 0.306969
\(551\) 10.5878 0.451055
\(552\) 0 0
\(553\) 10.8394 0.460939
\(554\) 7.07001 0.300376
\(555\) 0 0
\(556\) 1.80721 0.0766426
\(557\) 29.0421 1.23055 0.615276 0.788312i \(-0.289045\pi\)
0.615276 + 0.788312i \(0.289045\pi\)
\(558\) 0 0
\(559\) −26.8671 −1.13636
\(560\) −0.232738 −0.00983496
\(561\) 0 0
\(562\) −24.6125 −1.03822
\(563\) −42.9533 −1.81027 −0.905134 0.425127i \(-0.860229\pi\)
−0.905134 + 0.425127i \(0.860229\pi\)
\(564\) 0 0
\(565\) −19.9379 −0.838795
\(566\) 25.5505 1.07397
\(567\) 0 0
\(568\) −32.0833 −1.34619
\(569\) 17.8917 0.750060 0.375030 0.927013i \(-0.377632\pi\)
0.375030 + 0.927013i \(0.377632\pi\)
\(570\) 0 0
\(571\) 16.4317 0.687646 0.343823 0.939035i \(-0.388278\pi\)
0.343823 + 0.939035i \(0.388278\pi\)
\(572\) −6.36884 −0.266295
\(573\) 0 0
\(574\) 4.18994 0.174885
\(575\) 20.0812 0.837445
\(576\) 0 0
\(577\) −44.9708 −1.87216 −0.936079 0.351789i \(-0.885574\pi\)
−0.936079 + 0.351789i \(0.885574\pi\)
\(578\) 12.3237 0.512598
\(579\) 0 0
\(580\) 6.01988 0.249962
\(581\) −2.78288 −0.115453
\(582\) 0 0
\(583\) 0.696861 0.0288610
\(584\) 43.8646 1.81513
\(585\) 0 0
\(586\) 25.8260 1.06686
\(587\) 6.71570 0.277186 0.138593 0.990349i \(-0.455742\pi\)
0.138593 + 0.990349i \(0.455742\pi\)
\(588\) 0 0
\(589\) −2.39650 −0.0987461
\(590\) 2.64446 0.108871
\(591\) 0 0
\(592\) 0.109567 0.00450318
\(593\) 16.3420 0.671085 0.335543 0.942025i \(-0.391080\pi\)
0.335543 + 0.942025i \(0.391080\pi\)
\(594\) 0 0
\(595\) −1.79040 −0.0733992
\(596\) −4.53089 −0.185593
\(597\) 0 0
\(598\) 12.2939 0.502735
\(599\) 18.6301 0.761207 0.380603 0.924738i \(-0.375716\pi\)
0.380603 + 0.924738i \(0.375716\pi\)
\(600\) 0 0
\(601\) 19.0537 0.777217 0.388608 0.921403i \(-0.372956\pi\)
0.388608 + 0.921403i \(0.372956\pi\)
\(602\) −8.86376 −0.361260
\(603\) 0 0
\(604\) 16.7839 0.682929
\(605\) 6.95665 0.282828
\(606\) 0 0
\(607\) −45.4627 −1.84527 −0.922636 0.385672i \(-0.873970\pi\)
−0.922636 + 0.385672i \(0.873970\pi\)
\(608\) −11.2259 −0.455271
\(609\) 0 0
\(610\) 9.51361 0.385195
\(611\) −2.87930 −0.116484
\(612\) 0 0
\(613\) 41.9261 1.69338 0.846689 0.532088i \(-0.178592\pi\)
0.846689 + 0.532088i \(0.178592\pi\)
\(614\) −25.0474 −1.01083
\(615\) 0 0
\(616\) −5.65632 −0.227900
\(617\) −26.3445 −1.06059 −0.530295 0.847813i \(-0.677919\pi\)
−0.530295 + 0.847813i \(0.677919\pi\)
\(618\) 0 0
\(619\) 15.1455 0.608748 0.304374 0.952553i \(-0.401553\pi\)
0.304374 + 0.952553i \(0.401553\pi\)
\(620\) −1.36257 −0.0547223
\(621\) 0 0
\(622\) −8.74233 −0.350536
\(623\) −5.79864 −0.232318
\(624\) 0 0
\(625\) 11.6513 0.466053
\(626\) −4.99874 −0.199790
\(627\) 0 0
\(628\) −6.19213 −0.247093
\(629\) 0.842875 0.0336076
\(630\) 0 0
\(631\) 37.6323 1.49812 0.749060 0.662502i \(-0.230506\pi\)
0.749060 + 0.662502i \(0.230506\pi\)
\(632\) −31.1946 −1.24085
\(633\) 0 0
\(634\) −10.8081 −0.429243
\(635\) 0.974726 0.0386808
\(636\) 0 0
\(637\) 2.74141 0.108619
\(638\) −9.28773 −0.367705
\(639\) 0 0
\(640\) −5.96172 −0.235657
\(641\) 16.6216 0.656513 0.328256 0.944589i \(-0.393539\pi\)
0.328256 + 0.944589i \(0.393539\pi\)
\(642\) 0 0
\(643\) −39.1067 −1.54222 −0.771109 0.636703i \(-0.780298\pi\)
−0.771109 + 0.636703i \(0.780298\pi\)
\(644\) −5.86099 −0.230955
\(645\) 0 0
\(646\) 3.36639 0.132449
\(647\) −42.9546 −1.68872 −0.844360 0.535776i \(-0.820019\pi\)
−0.844360 + 0.535776i \(0.820019\pi\)
\(648\) 0 0
\(649\) 5.89584 0.231432
\(650\) 10.0413 0.393852
\(651\) 0 0
\(652\) −4.20976 −0.164867
\(653\) −23.8090 −0.931719 −0.465859 0.884859i \(-0.654255\pi\)
−0.465859 + 0.884859i \(0.654255\pi\)
\(654\) 0 0
\(655\) −4.61422 −0.180292
\(656\) −1.10617 −0.0431887
\(657\) 0 0
\(658\) −0.949912 −0.0370314
\(659\) 30.9550 1.20583 0.602917 0.797804i \(-0.294005\pi\)
0.602917 + 0.797804i \(0.294005\pi\)
\(660\) 0 0
\(661\) −29.0899 −1.13147 −0.565733 0.824588i \(-0.691407\pi\)
−0.565733 + 0.824588i \(0.691407\pi\)
\(662\) 13.8453 0.538114
\(663\) 0 0
\(664\) 8.00881 0.310802
\(665\) 1.97519 0.0765945
\(666\) 0 0
\(667\) −25.9074 −1.00314
\(668\) −18.2733 −0.707015
\(669\) 0 0
\(670\) −10.0027 −0.386439
\(671\) 21.2106 0.818826
\(672\) 0 0
\(673\) −3.04793 −0.117489 −0.0587446 0.998273i \(-0.518710\pi\)
−0.0587446 + 0.998273i \(0.518710\pi\)
\(674\) 22.3164 0.859597
\(675\) 0 0
\(676\) 6.48301 0.249347
\(677\) −29.7290 −1.14258 −0.571289 0.820749i \(-0.693556\pi\)
−0.571289 + 0.820749i \(0.693556\pi\)
\(678\) 0 0
\(679\) −14.0797 −0.540328
\(680\) 5.15257 0.197592
\(681\) 0 0
\(682\) 2.10224 0.0804989
\(683\) −28.7088 −1.09851 −0.549256 0.835654i \(-0.685089\pi\)
−0.549256 + 0.835654i \(0.685089\pi\)
\(684\) 0 0
\(685\) 2.21359 0.0845770
\(686\) 0.904420 0.0345309
\(687\) 0 0
\(688\) 2.34009 0.0892149
\(689\) 0.971985 0.0370297
\(690\) 0 0
\(691\) −36.9473 −1.40554 −0.702772 0.711416i \(-0.748054\pi\)
−0.702772 + 0.711416i \(0.748054\pi\)
\(692\) −16.3395 −0.621134
\(693\) 0 0
\(694\) −14.8540 −0.563850
\(695\) 1.49027 0.0565290
\(696\) 0 0
\(697\) −8.50953 −0.322321
\(698\) 13.1646 0.498287
\(699\) 0 0
\(700\) −4.78709 −0.180935
\(701\) −3.28373 −0.124025 −0.0620123 0.998075i \(-0.519752\pi\)
−0.0620123 + 0.998075i \(0.519752\pi\)
\(702\) 0 0
\(703\) −0.929868 −0.0350707
\(704\) 10.7861 0.406516
\(705\) 0 0
\(706\) 6.04388 0.227464
\(707\) 18.6908 0.702939
\(708\) 0 0
\(709\) 13.0439 0.489874 0.244937 0.969539i \(-0.421233\pi\)
0.244937 + 0.969539i \(0.421233\pi\)
\(710\) −9.82784 −0.368832
\(711\) 0 0
\(712\) 16.6878 0.625403
\(713\) 5.86403 0.219610
\(714\) 0 0
\(715\) −5.25190 −0.196410
\(716\) −28.6566 −1.07095
\(717\) 0 0
\(718\) 28.4271 1.06089
\(719\) −22.6400 −0.844329 −0.422165 0.906519i \(-0.638730\pi\)
−0.422165 + 0.906519i \(0.638730\pi\)
\(720\) 0 0
\(721\) 11.2067 0.417359
\(722\) 13.4702 0.501307
\(723\) 0 0
\(724\) 22.6916 0.843327
\(725\) −21.1604 −0.785878
\(726\) 0 0
\(727\) −13.0887 −0.485435 −0.242717 0.970097i \(-0.578039\pi\)
−0.242717 + 0.970097i \(0.578039\pi\)
\(728\) −7.88947 −0.292403
\(729\) 0 0
\(730\) 13.4367 0.497315
\(731\) 18.0018 0.665819
\(732\) 0 0
\(733\) 1.28284 0.0473828 0.0236914 0.999719i \(-0.492458\pi\)
0.0236914 + 0.999719i \(0.492458\pi\)
\(734\) 29.9583 1.10578
\(735\) 0 0
\(736\) 27.4689 1.01252
\(737\) −22.3011 −0.821471
\(738\) 0 0
\(739\) −25.5084 −0.938341 −0.469171 0.883108i \(-0.655447\pi\)
−0.469171 + 0.883108i \(0.655447\pi\)
\(740\) −0.528693 −0.0194352
\(741\) 0 0
\(742\) 0.320668 0.0117721
\(743\) 7.17039 0.263056 0.131528 0.991312i \(-0.458012\pi\)
0.131528 + 0.991312i \(0.458012\pi\)
\(744\) 0 0
\(745\) −3.73629 −0.136887
\(746\) 12.9761 0.475090
\(747\) 0 0
\(748\) 4.26731 0.156028
\(749\) 0.851347 0.0311076
\(750\) 0 0
\(751\) −3.47503 −0.126805 −0.0634027 0.997988i \(-0.520195\pi\)
−0.0634027 + 0.997988i \(0.520195\pi\)
\(752\) 0.250783 0.00914510
\(753\) 0 0
\(754\) −12.9546 −0.471778
\(755\) 13.8405 0.503706
\(756\) 0 0
\(757\) 24.2740 0.882254 0.441127 0.897445i \(-0.354579\pi\)
0.441127 + 0.897445i \(0.354579\pi\)
\(758\) −9.72025 −0.353055
\(759\) 0 0
\(760\) −5.68437 −0.206194
\(761\) −18.2719 −0.662355 −0.331178 0.943568i \(-0.607446\pi\)
−0.331178 + 0.943568i \(0.607446\pi\)
\(762\) 0 0
\(763\) −5.23394 −0.189481
\(764\) 8.88227 0.321349
\(765\) 0 0
\(766\) 13.8899 0.501862
\(767\) 8.22355 0.296935
\(768\) 0 0
\(769\) 10.0830 0.363601 0.181801 0.983335i \(-0.441807\pi\)
0.181801 + 0.983335i \(0.441807\pi\)
\(770\) −1.73266 −0.0624407
\(771\) 0 0
\(772\) 5.80355 0.208874
\(773\) 17.1958 0.618490 0.309245 0.950982i \(-0.399924\pi\)
0.309245 + 0.950982i \(0.399924\pi\)
\(774\) 0 0
\(775\) 4.78957 0.172047
\(776\) 40.5197 1.45457
\(777\) 0 0
\(778\) 24.4183 0.875440
\(779\) 9.38780 0.336353
\(780\) 0 0
\(781\) −21.9112 −0.784044
\(782\) −8.23726 −0.294564
\(783\) 0 0
\(784\) −0.238773 −0.00852759
\(785\) −5.10618 −0.182247
\(786\) 0 0
\(787\) 6.09963 0.217428 0.108714 0.994073i \(-0.465327\pi\)
0.108714 + 0.994073i \(0.465327\pi\)
\(788\) −27.9044 −0.994053
\(789\) 0 0
\(790\) −9.55561 −0.339973
\(791\) −20.4549 −0.727293
\(792\) 0 0
\(793\) 29.5847 1.05058
\(794\) −8.52299 −0.302470
\(795\) 0 0
\(796\) 7.80233 0.276546
\(797\) 12.7977 0.453318 0.226659 0.973974i \(-0.427220\pi\)
0.226659 + 0.973974i \(0.427220\pi\)
\(798\) 0 0
\(799\) 1.92922 0.0682507
\(800\) 22.4358 0.793225
\(801\) 0 0
\(802\) −24.4489 −0.863319
\(803\) 29.9571 1.05716
\(804\) 0 0
\(805\) −4.83312 −0.170345
\(806\) 2.93222 0.103283
\(807\) 0 0
\(808\) −53.7900 −1.89232
\(809\) −8.95423 −0.314814 −0.157407 0.987534i \(-0.550313\pi\)
−0.157407 + 0.987534i \(0.550313\pi\)
\(810\) 0 0
\(811\) −1.49580 −0.0525247 −0.0262623 0.999655i \(-0.508361\pi\)
−0.0262623 + 0.999655i \(0.508361\pi\)
\(812\) 6.17597 0.216734
\(813\) 0 0
\(814\) 0.815692 0.0285900
\(815\) −3.47147 −0.121600
\(816\) 0 0
\(817\) −19.8597 −0.694804
\(818\) 1.38378 0.0483828
\(819\) 0 0
\(820\) 5.33761 0.186397
\(821\) −53.6744 −1.87325 −0.936625 0.350334i \(-0.886068\pi\)
−0.936625 + 0.350334i \(0.886068\pi\)
\(822\) 0 0
\(823\) −9.21268 −0.321134 −0.160567 0.987025i \(-0.551332\pi\)
−0.160567 + 0.987025i \(0.551332\pi\)
\(824\) −32.2516 −1.12354
\(825\) 0 0
\(826\) 2.71304 0.0943986
\(827\) 47.7919 1.66189 0.830944 0.556356i \(-0.187801\pi\)
0.830944 + 0.556356i \(0.187801\pi\)
\(828\) 0 0
\(829\) 12.8026 0.444654 0.222327 0.974972i \(-0.428635\pi\)
0.222327 + 0.974972i \(0.428635\pi\)
\(830\) 2.45328 0.0851546
\(831\) 0 0
\(832\) 15.0445 0.521575
\(833\) −1.83682 −0.0636422
\(834\) 0 0
\(835\) −15.0686 −0.521471
\(836\) −4.70774 −0.162821
\(837\) 0 0
\(838\) 22.2090 0.767197
\(839\) 26.8790 0.927965 0.463982 0.885844i \(-0.346420\pi\)
0.463982 + 0.885844i \(0.346420\pi\)
\(840\) 0 0
\(841\) −1.70029 −0.0586307
\(842\) 15.4040 0.530856
\(843\) 0 0
\(844\) 18.8534 0.648960
\(845\) 5.34605 0.183910
\(846\) 0 0
\(847\) 7.13704 0.245232
\(848\) −0.0846584 −0.00290718
\(849\) 0 0
\(850\) −6.72796 −0.230767
\(851\) 2.27531 0.0779966
\(852\) 0 0
\(853\) −1.36355 −0.0466870 −0.0233435 0.999728i \(-0.507431\pi\)
−0.0233435 + 0.999728i \(0.507431\pi\)
\(854\) 9.76030 0.333991
\(855\) 0 0
\(856\) −2.45008 −0.0837421
\(857\) 25.6174 0.875075 0.437537 0.899200i \(-0.355851\pi\)
0.437537 + 0.899200i \(0.355851\pi\)
\(858\) 0 0
\(859\) −25.9662 −0.885956 −0.442978 0.896532i \(-0.646078\pi\)
−0.442978 + 0.896532i \(0.646078\pi\)
\(860\) −11.2916 −0.385041
\(861\) 0 0
\(862\) 17.2893 0.588876
\(863\) −28.3650 −0.965554 −0.482777 0.875743i \(-0.660372\pi\)
−0.482777 + 0.875743i \(0.660372\pi\)
\(864\) 0 0
\(865\) −13.4739 −0.458128
\(866\) 18.4493 0.626932
\(867\) 0 0
\(868\) −1.39790 −0.0474480
\(869\) −21.3042 −0.722696
\(870\) 0 0
\(871\) −31.1057 −1.05398
\(872\) 15.0627 0.510087
\(873\) 0 0
\(874\) 9.08744 0.307387
\(875\) −8.82118 −0.298210
\(876\) 0 0
\(877\) 12.1836 0.411411 0.205705 0.978614i \(-0.434051\pi\)
0.205705 + 0.978614i \(0.434051\pi\)
\(878\) −23.2574 −0.784899
\(879\) 0 0
\(880\) 0.457432 0.0154200
\(881\) 14.3304 0.482804 0.241402 0.970425i \(-0.422393\pi\)
0.241402 + 0.970425i \(0.422393\pi\)
\(882\) 0 0
\(883\) −51.3214 −1.72710 −0.863552 0.504260i \(-0.831765\pi\)
−0.863552 + 0.504260i \(0.831765\pi\)
\(884\) 5.95207 0.200190
\(885\) 0 0
\(886\) −1.68876 −0.0567348
\(887\) 24.4353 0.820458 0.410229 0.911982i \(-0.365449\pi\)
0.410229 + 0.911982i \(0.365449\pi\)
\(888\) 0 0
\(889\) 1.00000 0.0335389
\(890\) 5.11186 0.171350
\(891\) 0 0
\(892\) −12.6631 −0.423991
\(893\) −2.12833 −0.0712219
\(894\) 0 0
\(895\) −23.6309 −0.789894
\(896\) −6.11630 −0.204331
\(897\) 0 0
\(898\) 28.0748 0.936869
\(899\) −6.17917 −0.206087
\(900\) 0 0
\(901\) −0.651258 −0.0216966
\(902\) −8.23509 −0.274199
\(903\) 0 0
\(904\) 58.8669 1.95788
\(905\) 18.7120 0.622010
\(906\) 0 0
\(907\) 28.7487 0.954584 0.477292 0.878745i \(-0.341618\pi\)
0.477292 + 0.878745i \(0.341618\pi\)
\(908\) 4.65785 0.154576
\(909\) 0 0
\(910\) −2.41672 −0.0801136
\(911\) −27.4863 −0.910662 −0.455331 0.890322i \(-0.650479\pi\)
−0.455331 + 0.890322i \(0.650479\pi\)
\(912\) 0 0
\(913\) 5.46959 0.181017
\(914\) 6.01216 0.198865
\(915\) 0 0
\(916\) 21.5867 0.713244
\(917\) −4.73386 −0.156326
\(918\) 0 0
\(919\) −15.9691 −0.526771 −0.263385 0.964691i \(-0.584839\pi\)
−0.263385 + 0.964691i \(0.584839\pi\)
\(920\) 13.9092 0.458572
\(921\) 0 0
\(922\) 35.4085 1.16612
\(923\) −30.5618 −1.00596
\(924\) 0 0
\(925\) 1.85841 0.0611040
\(926\) −3.00405 −0.0987193
\(927\) 0 0
\(928\) −28.9451 −0.950169
\(929\) 12.7716 0.419023 0.209511 0.977806i \(-0.432813\pi\)
0.209511 + 0.977806i \(0.432813\pi\)
\(930\) 0 0
\(931\) 2.02640 0.0664127
\(932\) −10.2409 −0.335450
\(933\) 0 0
\(934\) −4.23161 −0.138462
\(935\) 3.51893 0.115081
\(936\) 0 0
\(937\) 52.7627 1.72368 0.861842 0.507178i \(-0.169311\pi\)
0.861842 + 0.507178i \(0.169311\pi\)
\(938\) −10.2621 −0.335069
\(939\) 0 0
\(940\) −1.21010 −0.0394692
\(941\) −51.2315 −1.67010 −0.835049 0.550176i \(-0.814561\pi\)
−0.835049 + 0.550176i \(0.814561\pi\)
\(942\) 0 0
\(943\) −22.9712 −0.748044
\(944\) −0.716258 −0.0233122
\(945\) 0 0
\(946\) 17.4212 0.566412
\(947\) −2.89717 −0.0941455 −0.0470727 0.998891i \(-0.514989\pi\)
−0.0470727 + 0.998891i \(0.514989\pi\)
\(948\) 0 0
\(949\) 41.7844 1.35638
\(950\) 7.42236 0.240813
\(951\) 0 0
\(952\) 5.28617 0.171326
\(953\) 50.7174 1.64290 0.821448 0.570283i \(-0.193166\pi\)
0.821448 + 0.570283i \(0.193166\pi\)
\(954\) 0 0
\(955\) 7.32454 0.237016
\(956\) −4.26138 −0.137823
\(957\) 0 0
\(958\) −12.5704 −0.406131
\(959\) 2.27099 0.0733341
\(960\) 0 0
\(961\) −29.6014 −0.954883
\(962\) 1.13773 0.0366819
\(963\) 0 0
\(964\) 7.32464 0.235911
\(965\) 4.78575 0.154059
\(966\) 0 0
\(967\) 0.226419 0.00728114 0.00364057 0.999993i \(-0.498841\pi\)
0.00364057 + 0.999993i \(0.498841\pi\)
\(968\) −20.5396 −0.660167
\(969\) 0 0
\(970\) 12.4121 0.398528
\(971\) −18.1946 −0.583894 −0.291947 0.956435i \(-0.594303\pi\)
−0.291947 + 0.956435i \(0.594303\pi\)
\(972\) 0 0
\(973\) 1.52891 0.0490146
\(974\) −36.3463 −1.16461
\(975\) 0 0
\(976\) −2.57678 −0.0824807
\(977\) −35.6302 −1.13991 −0.569956 0.821675i \(-0.693040\pi\)
−0.569956 + 0.821675i \(0.693040\pi\)
\(978\) 0 0
\(979\) 11.3969 0.364246
\(980\) 1.15215 0.0368040
\(981\) 0 0
\(982\) 17.7170 0.565371
\(983\) 30.5746 0.975179 0.487589 0.873073i \(-0.337876\pi\)
0.487589 + 0.873073i \(0.337876\pi\)
\(984\) 0 0
\(985\) −23.0106 −0.733180
\(986\) 8.67994 0.276426
\(987\) 0 0
\(988\) −6.56638 −0.208904
\(989\) 48.5951 1.54523
\(990\) 0 0
\(991\) 29.5461 0.938561 0.469281 0.883049i \(-0.344513\pi\)
0.469281 + 0.883049i \(0.344513\pi\)
\(992\) 6.55160 0.208014
\(993\) 0 0
\(994\) −10.0827 −0.319803
\(995\) 6.43399 0.203971
\(996\) 0 0
\(997\) −7.43799 −0.235563 −0.117782 0.993040i \(-0.537578\pi\)
−0.117782 + 0.993040i \(0.537578\pi\)
\(998\) 10.9062 0.345230
\(999\) 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 \(a_p\))