Properties

Label 8021.2.a.a.1.6
Level 8021
Weight 2
Character 8021.1
Self dual Yes
Analytic conductor 64.048
Analytic rank 1
Dimension 134
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8021 = 13 \cdot 617 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8021.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0480074613\)
Analytic rank: \(1\)
Dimension: \(134\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 8021.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.55271 q^{2} -2.07589 q^{3} +4.51632 q^{4} +1.36107 q^{5} +5.29914 q^{6} -3.73550 q^{7} -6.42344 q^{8} +1.30931 q^{9} +O(q^{10})\) \(q-2.55271 q^{2} -2.07589 q^{3} +4.51632 q^{4} +1.36107 q^{5} +5.29914 q^{6} -3.73550 q^{7} -6.42344 q^{8} +1.30931 q^{9} -3.47441 q^{10} -4.88732 q^{11} -9.37538 q^{12} +1.00000 q^{13} +9.53564 q^{14} -2.82543 q^{15} +7.36452 q^{16} +5.80287 q^{17} -3.34228 q^{18} +3.30043 q^{19} +6.14703 q^{20} +7.75447 q^{21} +12.4759 q^{22} -2.29061 q^{23} +13.3343 q^{24} -3.14749 q^{25} -2.55271 q^{26} +3.50968 q^{27} -16.8707 q^{28} -4.85362 q^{29} +7.21249 q^{30} -4.25817 q^{31} -5.95260 q^{32} +10.1455 q^{33} -14.8130 q^{34} -5.08427 q^{35} +5.91326 q^{36} +1.06475 q^{37} -8.42504 q^{38} -2.07589 q^{39} -8.74275 q^{40} +2.21441 q^{41} -19.7949 q^{42} -9.13392 q^{43} -22.0727 q^{44} +1.78206 q^{45} +5.84727 q^{46} +5.48436 q^{47} -15.2879 q^{48} +6.95394 q^{49} +8.03462 q^{50} -12.0461 q^{51} +4.51632 q^{52} -6.59148 q^{53} -8.95920 q^{54} -6.65198 q^{55} +23.9947 q^{56} -6.85132 q^{57} +12.3899 q^{58} +2.08444 q^{59} -12.7605 q^{60} +9.96838 q^{61} +10.8699 q^{62} -4.89092 q^{63} +0.466219 q^{64} +1.36107 q^{65} -25.8986 q^{66} +3.89134 q^{67} +26.2076 q^{68} +4.75506 q^{69} +12.9787 q^{70} -3.43870 q^{71} -8.41026 q^{72} +14.4044 q^{73} -2.71799 q^{74} +6.53383 q^{75} +14.9058 q^{76} +18.2566 q^{77} +5.29914 q^{78} -10.0130 q^{79} +10.0236 q^{80} -11.2136 q^{81} -5.65274 q^{82} -13.0394 q^{83} +35.0217 q^{84} +7.89811 q^{85} +23.3162 q^{86} +10.0756 q^{87} +31.3934 q^{88} +4.18128 q^{89} -4.54908 q^{90} -3.73550 q^{91} -10.3451 q^{92} +8.83948 q^{93} -14.0000 q^{94} +4.49212 q^{95} +12.3569 q^{96} +11.5663 q^{97} -17.7514 q^{98} -6.39901 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 134q - 6q^{2} - 33q^{3} + 98q^{4} - 8q^{5} - 16q^{6} - 32q^{7} - 15q^{8} + 101q^{9} + O(q^{10}) \) \( 134q - 6q^{2} - 33q^{3} + 98q^{4} - 8q^{5} - 16q^{6} - 32q^{7} - 15q^{8} + 101q^{9} - 33q^{10} - 47q^{11} - 53q^{12} + 134q^{13} - 28q^{14} - 30q^{15} + 30q^{16} - 17q^{17} - 14q^{18} - 87q^{19} - 12q^{20} - 24q^{21} - 52q^{22} - 44q^{23} - 36q^{24} + 58q^{25} - 6q^{26} - 117q^{27} - 71q^{28} - 42q^{29} - 21q^{30} - 82q^{31} - 31q^{32} + 12q^{33} - 30q^{34} - 54q^{35} + 32q^{36} - 55q^{37} - 12q^{38} - 33q^{39} - 86q^{40} - 16q^{41} + 6q^{42} - 148q^{43} - 54q^{44} - 24q^{45} - 57q^{46} - 21q^{47} - 82q^{48} + 12q^{49} - 17q^{50} - 123q^{51} + 98q^{52} - 17q^{53} - 10q^{54} - 148q^{55} - 47q^{56} - q^{57} - 58q^{58} - 64q^{59} - 16q^{60} - 112q^{61} - 15q^{62} - 58q^{63} - 65q^{64} - 8q^{65} - 20q^{66} - 110q^{67} - 8q^{68} - 57q^{69} - 40q^{70} - 78q^{71} - 28q^{72} - 43q^{73} - 52q^{74} - 150q^{75} - 96q^{76} - 24q^{77} - 16q^{78} - 228q^{79} + 20q^{80} + 54q^{81} - 89q^{82} - 12q^{83} + 6q^{84} - 77q^{85} + 29q^{86} - 77q^{87} - 95q^{88} - 32q^{89} - 46q^{90} - 32q^{91} - 62q^{92} - 9q^{93} - 87q^{94} - 61q^{95} - 54q^{96} - 38q^{97} + 6q^{98} - 193q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.55271 −1.80504 −0.902519 0.430650i \(-0.858284\pi\)
−0.902519 + 0.430650i \(0.858284\pi\)
\(3\) −2.07589 −1.19851 −0.599257 0.800557i \(-0.704537\pi\)
−0.599257 + 0.800557i \(0.704537\pi\)
\(4\) 4.51632 2.25816
\(5\) 1.36107 0.608689 0.304344 0.952562i \(-0.401563\pi\)
0.304344 + 0.952562i \(0.401563\pi\)
\(6\) 5.29914 2.16336
\(7\) −3.73550 −1.41189 −0.705943 0.708269i \(-0.749476\pi\)
−0.705943 + 0.708269i \(0.749476\pi\)
\(8\) −6.42344 −2.27103
\(9\) 1.30931 0.436436
\(10\) −3.47441 −1.09871
\(11\) −4.88732 −1.47358 −0.736791 0.676121i \(-0.763660\pi\)
−0.736791 + 0.676121i \(0.763660\pi\)
\(12\) −9.37538 −2.70644
\(13\) 1.00000 0.277350
\(14\) 9.53564 2.54851
\(15\) −2.82543 −0.729522
\(16\) 7.36452 1.84113
\(17\) 5.80287 1.40740 0.703701 0.710496i \(-0.251529\pi\)
0.703701 + 0.710496i \(0.251529\pi\)
\(18\) −3.34228 −0.787784
\(19\) 3.30043 0.757171 0.378585 0.925566i \(-0.376411\pi\)
0.378585 + 0.925566i \(0.376411\pi\)
\(20\) 6.14703 1.37452
\(21\) 7.75447 1.69216
\(22\) 12.4759 2.65987
\(23\) −2.29061 −0.477626 −0.238813 0.971066i \(-0.576758\pi\)
−0.238813 + 0.971066i \(0.576758\pi\)
\(24\) 13.3343 2.72186
\(25\) −3.14749 −0.629498
\(26\) −2.55271 −0.500627
\(27\) 3.50968 0.675439
\(28\) −16.8707 −3.18826
\(29\) −4.85362 −0.901294 −0.450647 0.892702i \(-0.648807\pi\)
−0.450647 + 0.892702i \(0.648807\pi\)
\(30\) 7.21249 1.31682
\(31\) −4.25817 −0.764790 −0.382395 0.923999i \(-0.624901\pi\)
−0.382395 + 0.923999i \(0.624901\pi\)
\(32\) −5.95260 −1.05228
\(33\) 10.1455 1.76611
\(34\) −14.8130 −2.54041
\(35\) −5.08427 −0.859399
\(36\) 5.91326 0.985543
\(37\) 1.06475 0.175044 0.0875219 0.996163i \(-0.472105\pi\)
0.0875219 + 0.996163i \(0.472105\pi\)
\(38\) −8.42504 −1.36672
\(39\) −2.07589 −0.332408
\(40\) −8.74275 −1.38235
\(41\) 2.21441 0.345833 0.172916 0.984937i \(-0.444681\pi\)
0.172916 + 0.984937i \(0.444681\pi\)
\(42\) −19.7949 −3.05442
\(43\) −9.13392 −1.39291 −0.696455 0.717600i \(-0.745240\pi\)
−0.696455 + 0.717600i \(0.745240\pi\)
\(44\) −22.0727 −3.32758
\(45\) 1.78206 0.265654
\(46\) 5.84727 0.862133
\(47\) 5.48436 0.799976 0.399988 0.916520i \(-0.369014\pi\)
0.399988 + 0.916520i \(0.369014\pi\)
\(48\) −15.2879 −2.20662
\(49\) 6.95394 0.993420
\(50\) 8.03462 1.13627
\(51\) −12.0461 −1.68679
\(52\) 4.51632 0.626301
\(53\) −6.59148 −0.905409 −0.452704 0.891661i \(-0.649541\pi\)
−0.452704 + 0.891661i \(0.649541\pi\)
\(54\) −8.95920 −1.21919
\(55\) −6.65198 −0.896952
\(56\) 23.9947 3.20643
\(57\) −6.85132 −0.907480
\(58\) 12.3899 1.62687
\(59\) 2.08444 0.271371 0.135685 0.990752i \(-0.456676\pi\)
0.135685 + 0.990752i \(0.456676\pi\)
\(60\) −12.7605 −1.64738
\(61\) 9.96838 1.27632 0.638160 0.769904i \(-0.279696\pi\)
0.638160 + 0.769904i \(0.279696\pi\)
\(62\) 10.8699 1.38047
\(63\) −4.89092 −0.616198
\(64\) 0.466219 0.0582773
\(65\) 1.36107 0.168820
\(66\) −25.8986 −3.18789
\(67\) 3.89134 0.475403 0.237702 0.971338i \(-0.423606\pi\)
0.237702 + 0.971338i \(0.423606\pi\)
\(68\) 26.2076 3.17814
\(69\) 4.75506 0.572441
\(70\) 12.9787 1.55125
\(71\) −3.43870 −0.408099 −0.204050 0.978961i \(-0.565410\pi\)
−0.204050 + 0.978961i \(0.565410\pi\)
\(72\) −8.41026 −0.991159
\(73\) 14.4044 1.68590 0.842952 0.537989i \(-0.180816\pi\)
0.842952 + 0.537989i \(0.180816\pi\)
\(74\) −2.71799 −0.315960
\(75\) 6.53383 0.754462
\(76\) 14.9058 1.70981
\(77\) 18.2566 2.08053
\(78\) 5.29914 0.600009
\(79\) −10.0130 −1.12656 −0.563278 0.826268i \(-0.690460\pi\)
−0.563278 + 0.826268i \(0.690460\pi\)
\(80\) 10.0236 1.12068
\(81\) −11.2136 −1.24596
\(82\) −5.65274 −0.624241
\(83\) −13.0394 −1.43126 −0.715631 0.698479i \(-0.753861\pi\)
−0.715631 + 0.698479i \(0.753861\pi\)
\(84\) 35.0217 3.82118
\(85\) 7.89811 0.856670
\(86\) 23.3162 2.51426
\(87\) 10.0756 1.08021
\(88\) 31.3934 3.34654
\(89\) 4.18128 0.443215 0.221608 0.975136i \(-0.428870\pi\)
0.221608 + 0.975136i \(0.428870\pi\)
\(90\) −4.54908 −0.479515
\(91\) −3.73550 −0.391587
\(92\) −10.3451 −1.07856
\(93\) 8.83948 0.916611
\(94\) −14.0000 −1.44399
\(95\) 4.49212 0.460881
\(96\) 12.3569 1.26117
\(97\) 11.5663 1.17438 0.587189 0.809450i \(-0.300235\pi\)
0.587189 + 0.809450i \(0.300235\pi\)
\(98\) −17.7514 −1.79316
\(99\) −6.39901 −0.643124
\(100\) −14.2151 −1.42151
\(101\) 8.60246 0.855977 0.427988 0.903784i \(-0.359222\pi\)
0.427988 + 0.903784i \(0.359222\pi\)
\(102\) 30.7502 3.04472
\(103\) 0.650032 0.0640495 0.0320248 0.999487i \(-0.489804\pi\)
0.0320248 + 0.999487i \(0.489804\pi\)
\(104\) −6.42344 −0.629870
\(105\) 10.5544 1.03000
\(106\) 16.8261 1.63430
\(107\) 14.3528 1.38753 0.693766 0.720200i \(-0.255950\pi\)
0.693766 + 0.720200i \(0.255950\pi\)
\(108\) 15.8509 1.52525
\(109\) −8.21938 −0.787274 −0.393637 0.919266i \(-0.628783\pi\)
−0.393637 + 0.919266i \(0.628783\pi\)
\(110\) 16.9806 1.61903
\(111\) −2.21030 −0.209792
\(112\) −27.5102 −2.59946
\(113\) 10.3605 0.974632 0.487316 0.873226i \(-0.337976\pi\)
0.487316 + 0.873226i \(0.337976\pi\)
\(114\) 17.4894 1.63804
\(115\) −3.11768 −0.290726
\(116\) −21.9205 −2.03527
\(117\) 1.30931 0.121046
\(118\) −5.32097 −0.489835
\(119\) −21.6766 −1.98709
\(120\) 18.1490 1.65677
\(121\) 12.8859 1.17144
\(122\) −25.4464 −2.30381
\(123\) −4.59687 −0.414485
\(124\) −19.2313 −1.72702
\(125\) −11.0893 −0.991857
\(126\) 12.4851 1.11226
\(127\) −2.48293 −0.220324 −0.110162 0.993914i \(-0.535137\pi\)
−0.110162 + 0.993914i \(0.535137\pi\)
\(128\) 10.7151 0.947089
\(129\) 18.9610 1.66942
\(130\) −3.47441 −0.304726
\(131\) −3.92300 −0.342754 −0.171377 0.985206i \(-0.554822\pi\)
−0.171377 + 0.985206i \(0.554822\pi\)
\(132\) 45.8204 3.98816
\(133\) −12.3288 −1.06904
\(134\) −9.93347 −0.858121
\(135\) 4.77693 0.411132
\(136\) −37.2744 −3.19625
\(137\) 16.5088 1.41044 0.705221 0.708988i \(-0.250848\pi\)
0.705221 + 0.708988i \(0.250848\pi\)
\(138\) −12.1383 −1.03328
\(139\) −15.4693 −1.31209 −0.656046 0.754721i \(-0.727772\pi\)
−0.656046 + 0.754721i \(0.727772\pi\)
\(140\) −22.9622 −1.94066
\(141\) −11.3849 −0.958782
\(142\) 8.77801 0.736634
\(143\) −4.88732 −0.408698
\(144\) 9.64243 0.803536
\(145\) −6.60611 −0.548608
\(146\) −36.7702 −3.04312
\(147\) −14.4356 −1.19063
\(148\) 4.80875 0.395277
\(149\) −3.36452 −0.275632 −0.137816 0.990458i \(-0.544008\pi\)
−0.137816 + 0.990458i \(0.544008\pi\)
\(150\) −16.6790 −1.36183
\(151\) 2.57118 0.209240 0.104620 0.994512i \(-0.466637\pi\)
0.104620 + 0.994512i \(0.466637\pi\)
\(152\) −21.2001 −1.71956
\(153\) 7.59775 0.614241
\(154\) −46.6037 −3.75543
\(155\) −5.79566 −0.465519
\(156\) −9.37538 −0.750631
\(157\) −1.72677 −0.137811 −0.0689054 0.997623i \(-0.521951\pi\)
−0.0689054 + 0.997623i \(0.521951\pi\)
\(158\) 25.5604 2.03347
\(159\) 13.6832 1.08515
\(160\) −8.10191 −0.640512
\(161\) 8.55658 0.674353
\(162\) 28.6251 2.24900
\(163\) −1.42754 −0.111814 −0.0559069 0.998436i \(-0.517805\pi\)
−0.0559069 + 0.998436i \(0.517805\pi\)
\(164\) 10.0010 0.780946
\(165\) 13.8088 1.07501
\(166\) 33.2858 2.58348
\(167\) 23.7322 1.83646 0.918228 0.396053i \(-0.129620\pi\)
0.918228 + 0.396053i \(0.129620\pi\)
\(168\) −49.8104 −3.84295
\(169\) 1.00000 0.0769231
\(170\) −20.1616 −1.54632
\(171\) 4.32128 0.330457
\(172\) −41.2517 −3.14542
\(173\) −23.9529 −1.82111 −0.910553 0.413391i \(-0.864344\pi\)
−0.910553 + 0.413391i \(0.864344\pi\)
\(174\) −25.7200 −1.94983
\(175\) 11.7574 0.888779
\(176\) −35.9927 −2.71305
\(177\) −4.32706 −0.325242
\(178\) −10.6736 −0.800020
\(179\) 6.23682 0.466162 0.233081 0.972457i \(-0.425119\pi\)
0.233081 + 0.972457i \(0.425119\pi\)
\(180\) 8.04836 0.599889
\(181\) −10.1627 −0.755384 −0.377692 0.925931i \(-0.623282\pi\)
−0.377692 + 0.925931i \(0.623282\pi\)
\(182\) 9.53564 0.706828
\(183\) −20.6932 −1.52969
\(184\) 14.7136 1.08470
\(185\) 1.44920 0.106547
\(186\) −22.5646 −1.65452
\(187\) −28.3604 −2.07392
\(188\) 24.7691 1.80647
\(189\) −13.1104 −0.953643
\(190\) −11.4671 −0.831908
\(191\) 15.4706 1.11941 0.559707 0.828691i \(-0.310914\pi\)
0.559707 + 0.828691i \(0.310914\pi\)
\(192\) −0.967817 −0.0698462
\(193\) 11.0404 0.794704 0.397352 0.917666i \(-0.369929\pi\)
0.397352 + 0.917666i \(0.369929\pi\)
\(194\) −29.5253 −2.11980
\(195\) −2.82543 −0.202333
\(196\) 31.4062 2.24330
\(197\) 21.9129 1.56123 0.780616 0.625011i \(-0.214905\pi\)
0.780616 + 0.625011i \(0.214905\pi\)
\(198\) 16.3348 1.16086
\(199\) 7.15543 0.507235 0.253617 0.967305i \(-0.418380\pi\)
0.253617 + 0.967305i \(0.418380\pi\)
\(200\) 20.2177 1.42961
\(201\) −8.07799 −0.569778
\(202\) −21.9596 −1.54507
\(203\) 18.1307 1.27252
\(204\) −54.4041 −3.80905
\(205\) 3.01397 0.210505
\(206\) −1.65934 −0.115612
\(207\) −2.99912 −0.208453
\(208\) 7.36452 0.510638
\(209\) −16.1303 −1.11575
\(210\) −26.9423 −1.85919
\(211\) −10.4315 −0.718133 −0.359067 0.933312i \(-0.616905\pi\)
−0.359067 + 0.933312i \(0.616905\pi\)
\(212\) −29.7692 −2.04456
\(213\) 7.13836 0.489113
\(214\) −36.6384 −2.50455
\(215\) −12.4319 −0.847849
\(216\) −22.5442 −1.53394
\(217\) 15.9064 1.07980
\(218\) 20.9817 1.42106
\(219\) −29.9018 −2.02058
\(220\) −30.0425 −2.02546
\(221\) 5.80287 0.390343
\(222\) 5.64225 0.378683
\(223\) −6.92170 −0.463511 −0.231756 0.972774i \(-0.574447\pi\)
−0.231756 + 0.972774i \(0.574447\pi\)
\(224\) 22.2359 1.48570
\(225\) −4.12104 −0.274736
\(226\) −26.4473 −1.75925
\(227\) 20.0822 1.33290 0.666452 0.745548i \(-0.267812\pi\)
0.666452 + 0.745548i \(0.267812\pi\)
\(228\) −30.9428 −2.04924
\(229\) 20.7822 1.37333 0.686664 0.726975i \(-0.259075\pi\)
0.686664 + 0.726975i \(0.259075\pi\)
\(230\) 7.95854 0.524771
\(231\) −37.8986 −2.49354
\(232\) 31.1769 2.04687
\(233\) −17.0089 −1.11429 −0.557144 0.830416i \(-0.688103\pi\)
−0.557144 + 0.830416i \(0.688103\pi\)
\(234\) −3.34228 −0.218492
\(235\) 7.46459 0.486936
\(236\) 9.41400 0.612799
\(237\) 20.7859 1.35019
\(238\) 55.3340 3.58677
\(239\) 19.5527 1.26476 0.632379 0.774659i \(-0.282079\pi\)
0.632379 + 0.774659i \(0.282079\pi\)
\(240\) −20.8079 −1.34315
\(241\) −13.5152 −0.870591 −0.435296 0.900288i \(-0.643356\pi\)
−0.435296 + 0.900288i \(0.643356\pi\)
\(242\) −32.8938 −2.11450
\(243\) 12.7492 0.817861
\(244\) 45.0204 2.88214
\(245\) 9.46480 0.604684
\(246\) 11.7345 0.748162
\(247\) 3.30043 0.210001
\(248\) 27.3521 1.73686
\(249\) 27.0684 1.71539
\(250\) 28.3078 1.79034
\(251\) −4.47371 −0.282378 −0.141189 0.989983i \(-0.545093\pi\)
−0.141189 + 0.989983i \(0.545093\pi\)
\(252\) −22.0890 −1.39147
\(253\) 11.1950 0.703821
\(254\) 6.33819 0.397694
\(255\) −16.3956 −1.02673
\(256\) −28.2849 −1.76781
\(257\) −21.3628 −1.33257 −0.666286 0.745696i \(-0.732117\pi\)
−0.666286 + 0.745696i \(0.732117\pi\)
\(258\) −48.4019 −3.01337
\(259\) −3.97737 −0.247142
\(260\) 6.14703 0.381223
\(261\) −6.35489 −0.393358
\(262\) 10.0143 0.618684
\(263\) −19.1099 −1.17837 −0.589183 0.808000i \(-0.700550\pi\)
−0.589183 + 0.808000i \(0.700550\pi\)
\(264\) −65.1691 −4.01088
\(265\) −8.97146 −0.551112
\(266\) 31.4717 1.92965
\(267\) −8.67987 −0.531200
\(268\) 17.5746 1.07354
\(269\) −27.5063 −1.67709 −0.838545 0.544832i \(-0.816593\pi\)
−0.838545 + 0.544832i \(0.816593\pi\)
\(270\) −12.1941 −0.742109
\(271\) −4.34067 −0.263677 −0.131838 0.991271i \(-0.542088\pi\)
−0.131838 + 0.991271i \(0.542088\pi\)
\(272\) 42.7353 2.59121
\(273\) 7.75447 0.469322
\(274\) −42.1421 −2.54590
\(275\) 15.3828 0.927616
\(276\) 21.4754 1.29267
\(277\) 21.7042 1.30408 0.652040 0.758185i \(-0.273913\pi\)
0.652040 + 0.758185i \(0.273913\pi\)
\(278\) 39.4887 2.36838
\(279\) −5.57526 −0.333782
\(280\) 32.6585 1.95172
\(281\) −2.73391 −0.163092 −0.0815458 0.996670i \(-0.525986\pi\)
−0.0815458 + 0.996670i \(0.525986\pi\)
\(282\) 29.0624 1.73064
\(283\) −24.8911 −1.47962 −0.739810 0.672816i \(-0.765085\pi\)
−0.739810 + 0.672816i \(0.765085\pi\)
\(284\) −15.5303 −0.921554
\(285\) −9.32513 −0.552373
\(286\) 12.4759 0.737715
\(287\) −8.27192 −0.488276
\(288\) −7.79379 −0.459254
\(289\) 16.6733 0.980781
\(290\) 16.8635 0.990258
\(291\) −24.0103 −1.40751
\(292\) 65.0548 3.80704
\(293\) 16.8027 0.981625 0.490813 0.871265i \(-0.336700\pi\)
0.490813 + 0.871265i \(0.336700\pi\)
\(294\) 36.8499 2.14913
\(295\) 2.83707 0.165181
\(296\) −6.83935 −0.397529
\(297\) −17.1529 −0.995314
\(298\) 8.58864 0.497526
\(299\) −2.29061 −0.132470
\(300\) 29.5089 1.70370
\(301\) 34.1197 1.96663
\(302\) −6.56347 −0.377685
\(303\) −17.8577 −1.02590
\(304\) 24.3061 1.39405
\(305\) 13.5677 0.776882
\(306\) −19.3948 −1.10873
\(307\) 19.7951 1.12977 0.564884 0.825170i \(-0.308921\pi\)
0.564884 + 0.825170i \(0.308921\pi\)
\(308\) 82.4525 4.69817
\(309\) −1.34939 −0.0767642
\(310\) 14.7946 0.840279
\(311\) 30.9577 1.75545 0.877726 0.479162i \(-0.159060\pi\)
0.877726 + 0.479162i \(0.159060\pi\)
\(312\) 13.3343 0.754908
\(313\) 26.5276 1.49943 0.749715 0.661761i \(-0.230191\pi\)
0.749715 + 0.661761i \(0.230191\pi\)
\(314\) 4.40793 0.248754
\(315\) −6.65688 −0.375073
\(316\) −45.2221 −2.54394
\(317\) 18.5159 1.03996 0.519978 0.854179i \(-0.325940\pi\)
0.519978 + 0.854179i \(0.325940\pi\)
\(318\) −34.9291 −1.95873
\(319\) 23.7212 1.32813
\(320\) 0.634556 0.0354728
\(321\) −29.7947 −1.66298
\(322\) −21.8425 −1.21723
\(323\) 19.1520 1.06564
\(324\) −50.6444 −2.81358
\(325\) −3.14749 −0.174591
\(326\) 3.64410 0.201828
\(327\) 17.0625 0.943559
\(328\) −14.2241 −0.785396
\(329\) −20.4868 −1.12947
\(330\) −35.2497 −1.94043
\(331\) 31.3284 1.72196 0.860982 0.508636i \(-0.169850\pi\)
0.860982 + 0.508636i \(0.169850\pi\)
\(332\) −58.8902 −3.23202
\(333\) 1.39409 0.0763954
\(334\) −60.5815 −3.31487
\(335\) 5.29639 0.289373
\(336\) 57.1080 3.11550
\(337\) −21.0246 −1.14528 −0.572641 0.819806i \(-0.694081\pi\)
−0.572641 + 0.819806i \(0.694081\pi\)
\(338\) −2.55271 −0.138849
\(339\) −21.5072 −1.16811
\(340\) 35.6704 1.93450
\(341\) 20.8110 1.12698
\(342\) −11.0310 −0.596487
\(343\) 0.172047 0.00928966
\(344\) 58.6712 3.16334
\(345\) 6.47196 0.348439
\(346\) 61.1448 3.28717
\(347\) 25.6493 1.37692 0.688462 0.725272i \(-0.258286\pi\)
0.688462 + 0.725272i \(0.258286\pi\)
\(348\) 45.5045 2.43930
\(349\) −26.8489 −1.43719 −0.718594 0.695430i \(-0.755214\pi\)
−0.718594 + 0.695430i \(0.755214\pi\)
\(350\) −30.0133 −1.60428
\(351\) 3.50968 0.187333
\(352\) 29.0922 1.55062
\(353\) 9.48184 0.504667 0.252334 0.967640i \(-0.418802\pi\)
0.252334 + 0.967640i \(0.418802\pi\)
\(354\) 11.0457 0.587074
\(355\) −4.68032 −0.248405
\(356\) 18.8840 1.00085
\(357\) 44.9982 2.38156
\(358\) −15.9208 −0.841440
\(359\) −8.05040 −0.424884 −0.212442 0.977174i \(-0.568142\pi\)
−0.212442 + 0.977174i \(0.568142\pi\)
\(360\) −11.4470 −0.603307
\(361\) −8.10715 −0.426692
\(362\) 25.9423 1.36350
\(363\) −26.7496 −1.40399
\(364\) −16.8707 −0.884266
\(365\) 19.6053 1.02619
\(366\) 52.8238 2.76114
\(367\) 16.1764 0.844402 0.422201 0.906502i \(-0.361258\pi\)
0.422201 + 0.906502i \(0.361258\pi\)
\(368\) −16.8693 −0.879372
\(369\) 2.89935 0.150934
\(370\) −3.69938 −0.192322
\(371\) 24.6224 1.27833
\(372\) 39.9219 2.06986
\(373\) 6.89791 0.357160 0.178580 0.983925i \(-0.442850\pi\)
0.178580 + 0.983925i \(0.442850\pi\)
\(374\) 72.3960 3.74351
\(375\) 23.0201 1.18875
\(376\) −35.2284 −1.81677
\(377\) −4.85362 −0.249974
\(378\) 33.4671 1.72136
\(379\) −25.2251 −1.29573 −0.647864 0.761756i \(-0.724338\pi\)
−0.647864 + 0.761756i \(0.724338\pi\)
\(380\) 20.2878 1.04074
\(381\) 5.15428 0.264062
\(382\) −39.4919 −2.02058
\(383\) 27.1912 1.38940 0.694701 0.719298i \(-0.255536\pi\)
0.694701 + 0.719298i \(0.255536\pi\)
\(384\) −22.2433 −1.13510
\(385\) 24.8484 1.26639
\(386\) −28.1829 −1.43447
\(387\) −11.9591 −0.607916
\(388\) 52.2371 2.65193
\(389\) 2.30112 0.116672 0.0583358 0.998297i \(-0.481421\pi\)
0.0583358 + 0.998297i \(0.481421\pi\)
\(390\) 7.21249 0.365219
\(391\) −13.2921 −0.672212
\(392\) −44.6682 −2.25609
\(393\) 8.14370 0.410795
\(394\) −55.9374 −2.81808
\(395\) −13.6284 −0.685722
\(396\) −28.9000 −1.45228
\(397\) 11.1675 0.560481 0.280240 0.959930i \(-0.409586\pi\)
0.280240 + 0.959930i \(0.409586\pi\)
\(398\) −18.2657 −0.915578
\(399\) 25.5931 1.28126
\(400\) −23.1798 −1.15899
\(401\) −35.3692 −1.76625 −0.883127 0.469133i \(-0.844566\pi\)
−0.883127 + 0.469133i \(0.844566\pi\)
\(402\) 20.6208 1.02847
\(403\) −4.25817 −0.212114
\(404\) 38.8515 1.93293
\(405\) −15.2625 −0.758402
\(406\) −46.2824 −2.29695
\(407\) −5.20377 −0.257941
\(408\) 77.3774 3.83075
\(409\) 11.2279 0.555182 0.277591 0.960699i \(-0.410464\pi\)
0.277591 + 0.960699i \(0.410464\pi\)
\(410\) −7.69378 −0.379969
\(411\) −34.2704 −1.69043
\(412\) 2.93575 0.144634
\(413\) −7.78642 −0.383145
\(414\) 7.65588 0.376266
\(415\) −17.7475 −0.871193
\(416\) −5.95260 −0.291850
\(417\) 32.1126 1.57256
\(418\) 41.1758 2.01398
\(419\) 25.2443 1.23326 0.616631 0.787252i \(-0.288497\pi\)
0.616631 + 0.787252i \(0.288497\pi\)
\(420\) 47.6670 2.32591
\(421\) −20.9770 −1.02236 −0.511179 0.859474i \(-0.670791\pi\)
−0.511179 + 0.859474i \(0.670791\pi\)
\(422\) 26.6286 1.29626
\(423\) 7.18072 0.349138
\(424\) 42.3399 2.05621
\(425\) −18.2645 −0.885957
\(426\) −18.2222 −0.882867
\(427\) −37.2369 −1.80202
\(428\) 64.8216 3.13327
\(429\) 10.1455 0.489830
\(430\) 31.7350 1.53040
\(431\) 18.4094 0.886751 0.443375 0.896336i \(-0.353781\pi\)
0.443375 + 0.896336i \(0.353781\pi\)
\(432\) 25.8471 1.24357
\(433\) 4.44301 0.213517 0.106759 0.994285i \(-0.465953\pi\)
0.106759 + 0.994285i \(0.465953\pi\)
\(434\) −40.6044 −1.94907
\(435\) 13.7135 0.657514
\(436\) −37.1214 −1.77779
\(437\) −7.56001 −0.361644
\(438\) 76.3307 3.64722
\(439\) 7.39785 0.353080 0.176540 0.984293i \(-0.443510\pi\)
0.176540 + 0.984293i \(0.443510\pi\)
\(440\) 42.7286 2.03700
\(441\) 9.10486 0.433565
\(442\) −14.8130 −0.704584
\(443\) −21.1177 −1.00333 −0.501667 0.865061i \(-0.667280\pi\)
−0.501667 + 0.865061i \(0.667280\pi\)
\(444\) −9.98243 −0.473745
\(445\) 5.69102 0.269780
\(446\) 17.6691 0.836655
\(447\) 6.98436 0.330349
\(448\) −1.74156 −0.0822809
\(449\) −5.25241 −0.247876 −0.123938 0.992290i \(-0.539552\pi\)
−0.123938 + 0.992290i \(0.539552\pi\)
\(450\) 10.5198 0.495908
\(451\) −10.8225 −0.509613
\(452\) 46.7913 2.20088
\(453\) −5.33748 −0.250777
\(454\) −51.2641 −2.40594
\(455\) −5.08427 −0.238354
\(456\) 44.0091 2.06091
\(457\) −24.7501 −1.15776 −0.578881 0.815412i \(-0.696510\pi\)
−0.578881 + 0.815412i \(0.696510\pi\)
\(458\) −53.0509 −2.47891
\(459\) 20.3662 0.950614
\(460\) −14.0805 −0.656505
\(461\) 8.69173 0.404814 0.202407 0.979301i \(-0.435124\pi\)
0.202407 + 0.979301i \(0.435124\pi\)
\(462\) 96.7440 4.50094
\(463\) −3.42601 −0.159220 −0.0796101 0.996826i \(-0.525368\pi\)
−0.0796101 + 0.996826i \(0.525368\pi\)
\(464\) −35.7446 −1.65940
\(465\) 12.0311 0.557931
\(466\) 43.4187 2.01133
\(467\) −22.0391 −1.01985 −0.509924 0.860220i \(-0.670326\pi\)
−0.509924 + 0.860220i \(0.670326\pi\)
\(468\) 5.91326 0.273341
\(469\) −14.5361 −0.671215
\(470\) −19.0549 −0.878938
\(471\) 3.58457 0.165168
\(472\) −13.3893 −0.616291
\(473\) 44.6404 2.05257
\(474\) −53.0605 −2.43715
\(475\) −10.3881 −0.476637
\(476\) −97.8985 −4.48717
\(477\) −8.63028 −0.395153
\(478\) −49.9123 −2.28293
\(479\) −23.5978 −1.07821 −0.539106 0.842238i \(-0.681238\pi\)
−0.539106 + 0.842238i \(0.681238\pi\)
\(480\) 16.8186 0.767663
\(481\) 1.06475 0.0485484
\(482\) 34.5004 1.57145
\(483\) −17.7625 −0.808222
\(484\) 58.1967 2.64530
\(485\) 15.7425 0.714831
\(486\) −32.5450 −1.47627
\(487\) −34.1718 −1.54847 −0.774237 0.632896i \(-0.781866\pi\)
−0.774237 + 0.632896i \(0.781866\pi\)
\(488\) −64.0313 −2.89856
\(489\) 2.96342 0.134010
\(490\) −24.1609 −1.09148
\(491\) 42.6421 1.92441 0.962205 0.272326i \(-0.0877929\pi\)
0.962205 + 0.272326i \(0.0877929\pi\)
\(492\) −20.7609 −0.935975
\(493\) −28.1649 −1.26848
\(494\) −8.42504 −0.379060
\(495\) −8.70949 −0.391463
\(496\) −31.3594 −1.40808
\(497\) 12.8453 0.576189
\(498\) −69.0976 −3.09634
\(499\) 0.703466 0.0314915 0.0157457 0.999876i \(-0.494988\pi\)
0.0157457 + 0.999876i \(0.494988\pi\)
\(500\) −50.0829 −2.23977
\(501\) −49.2654 −2.20102
\(502\) 11.4201 0.509703
\(503\) −10.7356 −0.478677 −0.239338 0.970936i \(-0.576930\pi\)
−0.239338 + 0.970936i \(0.576930\pi\)
\(504\) 31.4165 1.39940
\(505\) 11.7085 0.521024
\(506\) −28.5775 −1.27042
\(507\) −2.07589 −0.0921934
\(508\) −11.2137 −0.497528
\(509\) −4.60768 −0.204232 −0.102116 0.994772i \(-0.532561\pi\)
−0.102116 + 0.994772i \(0.532561\pi\)
\(510\) 41.8531 1.85329
\(511\) −53.8075 −2.38030
\(512\) 50.7730 2.24387
\(513\) 11.5835 0.511423
\(514\) 54.5329 2.40534
\(515\) 0.884738 0.0389862
\(516\) 85.6340 3.76982
\(517\) −26.8038 −1.17883
\(518\) 10.1531 0.446100
\(519\) 49.7236 2.18262
\(520\) −8.74275 −0.383395
\(521\) 33.9789 1.48864 0.744320 0.667823i \(-0.232774\pi\)
0.744320 + 0.667823i \(0.232774\pi\)
\(522\) 16.2222 0.710025
\(523\) −6.64383 −0.290515 −0.145257 0.989394i \(-0.546401\pi\)
−0.145257 + 0.989394i \(0.546401\pi\)
\(524\) −17.7175 −0.773993
\(525\) −24.4071 −1.06521
\(526\) 48.7820 2.12700
\(527\) −24.7096 −1.07637
\(528\) 74.7169 3.25163
\(529\) −17.7531 −0.771873
\(530\) 22.9015 0.994778
\(531\) 2.72918 0.118436
\(532\) −55.6806 −2.41406
\(533\) 2.21441 0.0959167
\(534\) 22.1572 0.958835
\(535\) 19.5351 0.844576
\(536\) −24.9958 −1.07965
\(537\) −12.9469 −0.558702
\(538\) 70.2156 3.02721
\(539\) −33.9861 −1.46389
\(540\) 21.5741 0.928403
\(541\) −13.8517 −0.595530 −0.297765 0.954639i \(-0.596241\pi\)
−0.297765 + 0.954639i \(0.596241\pi\)
\(542\) 11.0805 0.475947
\(543\) 21.0965 0.905338
\(544\) −34.5422 −1.48098
\(545\) −11.1871 −0.479205
\(546\) −19.7949 −0.847144
\(547\) 7.34951 0.314242 0.157121 0.987579i \(-0.449779\pi\)
0.157121 + 0.987579i \(0.449779\pi\)
\(548\) 74.5590 3.18500
\(549\) 13.0517 0.557032
\(550\) −39.2677 −1.67438
\(551\) −16.0190 −0.682434
\(552\) −30.5438 −1.30003
\(553\) 37.4037 1.59057
\(554\) −55.4045 −2.35391
\(555\) −3.00837 −0.127698
\(556\) −69.8645 −2.96291
\(557\) 25.2031 1.06789 0.533945 0.845519i \(-0.320709\pi\)
0.533945 + 0.845519i \(0.320709\pi\)
\(558\) 14.2320 0.602489
\(559\) −9.13392 −0.386324
\(560\) −37.4432 −1.58227
\(561\) 58.8731 2.48562
\(562\) 6.97888 0.294386
\(563\) 4.75109 0.200235 0.100117 0.994976i \(-0.468078\pi\)
0.100117 + 0.994976i \(0.468078\pi\)
\(564\) −51.4179 −2.16508
\(565\) 14.1013 0.593247
\(566\) 63.5396 2.67077
\(567\) 41.8885 1.75915
\(568\) 22.0883 0.926805
\(569\) −38.6353 −1.61968 −0.809838 0.586654i \(-0.800445\pi\)
−0.809838 + 0.586654i \(0.800445\pi\)
\(570\) 23.8043 0.997054
\(571\) −2.44392 −0.102275 −0.0511374 0.998692i \(-0.516285\pi\)
−0.0511374 + 0.998692i \(0.516285\pi\)
\(572\) −22.0727 −0.922906
\(573\) −32.1152 −1.34163
\(574\) 21.1158 0.881357
\(575\) 7.20968 0.300665
\(576\) 0.610424 0.0254343
\(577\) −24.4592 −1.01825 −0.509125 0.860692i \(-0.670031\pi\)
−0.509125 + 0.860692i \(0.670031\pi\)
\(578\) −42.5620 −1.77035
\(579\) −22.9186 −0.952464
\(580\) −29.8353 −1.23885
\(581\) 48.7087 2.02078
\(582\) 61.2913 2.54061
\(583\) 32.2146 1.33419
\(584\) −92.5255 −3.82873
\(585\) 1.78206 0.0736791
\(586\) −42.8924 −1.77187
\(587\) 5.84639 0.241306 0.120653 0.992695i \(-0.461501\pi\)
0.120653 + 0.992695i \(0.461501\pi\)
\(588\) −65.1958 −2.68863
\(589\) −14.0538 −0.579076
\(590\) −7.24221 −0.298157
\(591\) −45.4888 −1.87116
\(592\) 7.84137 0.322278
\(593\) −24.0382 −0.987131 −0.493565 0.869709i \(-0.664307\pi\)
−0.493565 + 0.869709i \(0.664307\pi\)
\(594\) 43.7865 1.79658
\(595\) −29.5034 −1.20952
\(596\) −15.1953 −0.622422
\(597\) −14.8539 −0.607928
\(598\) 5.84727 0.239113
\(599\) −15.1623 −0.619513 −0.309757 0.950816i \(-0.600248\pi\)
−0.309757 + 0.950816i \(0.600248\pi\)
\(600\) −41.9697 −1.71340
\(601\) 27.9902 1.14174 0.570871 0.821040i \(-0.306606\pi\)
0.570871 + 0.821040i \(0.306606\pi\)
\(602\) −87.0978 −3.54984
\(603\) 5.09497 0.207483
\(604\) 11.6123 0.472497
\(605\) 17.5385 0.713043
\(606\) 45.5856 1.85179
\(607\) −34.2677 −1.39088 −0.695441 0.718583i \(-0.744791\pi\)
−0.695441 + 0.718583i \(0.744791\pi\)
\(608\) −19.6462 −0.796757
\(609\) −37.6373 −1.52514
\(610\) −34.6343 −1.40230
\(611\) 5.48436 0.221873
\(612\) 34.3139 1.38706
\(613\) 5.33028 0.215288 0.107644 0.994189i \(-0.465669\pi\)
0.107644 + 0.994189i \(0.465669\pi\)
\(614\) −50.5312 −2.03927
\(615\) −6.25666 −0.252293
\(616\) −117.270 −4.72494
\(617\) 1.00000 0.0402585
\(618\) 3.44461 0.138562
\(619\) −31.4298 −1.26327 −0.631634 0.775266i \(-0.717616\pi\)
−0.631634 + 0.775266i \(0.717616\pi\)
\(620\) −26.1751 −1.05122
\(621\) −8.03933 −0.322607
\(622\) −79.0261 −3.16866
\(623\) −15.6192 −0.625769
\(624\) −15.2879 −0.612006
\(625\) 0.644135 0.0257654
\(626\) −67.7173 −2.70653
\(627\) 33.4846 1.33725
\(628\) −7.79863 −0.311199
\(629\) 6.17860 0.246357
\(630\) 16.9931 0.677021
\(631\) 3.86645 0.153921 0.0769604 0.997034i \(-0.475479\pi\)
0.0769604 + 0.997034i \(0.475479\pi\)
\(632\) 64.3181 2.55844
\(633\) 21.6546 0.860693
\(634\) −47.2657 −1.87716
\(635\) −3.37944 −0.134109
\(636\) 61.7976 2.45043
\(637\) 6.95394 0.275525
\(638\) −60.5532 −2.39733
\(639\) −4.50233 −0.178109
\(640\) 14.5840 0.576482
\(641\) 22.1898 0.876445 0.438223 0.898867i \(-0.355608\pi\)
0.438223 + 0.898867i \(0.355608\pi\)
\(642\) 76.0572 3.00174
\(643\) −7.13709 −0.281459 −0.140730 0.990048i \(-0.544945\pi\)
−0.140730 + 0.990048i \(0.544945\pi\)
\(644\) 38.6443 1.52280
\(645\) 25.8072 1.01616
\(646\) −48.8894 −1.92353
\(647\) 23.8764 0.938677 0.469339 0.883018i \(-0.344492\pi\)
0.469339 + 0.883018i \(0.344492\pi\)
\(648\) 72.0301 2.82961
\(649\) −10.1873 −0.399887
\(650\) 8.03462 0.315144
\(651\) −33.0199 −1.29415
\(652\) −6.44724 −0.252493
\(653\) 20.6710 0.808918 0.404459 0.914556i \(-0.367460\pi\)
0.404459 + 0.914556i \(0.367460\pi\)
\(654\) −43.5556 −1.70316
\(655\) −5.33947 −0.208630
\(656\) 16.3081 0.636723
\(657\) 18.8598 0.735789
\(658\) 52.2968 2.03874
\(659\) 21.0827 0.821264 0.410632 0.911801i \(-0.365308\pi\)
0.410632 + 0.911801i \(0.365308\pi\)
\(660\) 62.3648 2.42755
\(661\) −7.64481 −0.297349 −0.148674 0.988886i \(-0.547501\pi\)
−0.148674 + 0.988886i \(0.547501\pi\)
\(662\) −79.9722 −3.10821
\(663\) −12.0461 −0.467832
\(664\) 83.7579 3.25044
\(665\) −16.7803 −0.650712
\(666\) −3.55869 −0.137897
\(667\) 11.1178 0.430482
\(668\) 107.182 4.14701
\(669\) 14.3687 0.555525
\(670\) −13.5201 −0.522329
\(671\) −48.7186 −1.88076
\(672\) −46.1593 −1.78063
\(673\) −34.1328 −1.31572 −0.657862 0.753138i \(-0.728539\pi\)
−0.657862 + 0.753138i \(0.728539\pi\)
\(674\) 53.6697 2.06728
\(675\) −11.0467 −0.425187
\(676\) 4.51632 0.173705
\(677\) −29.7101 −1.14185 −0.570926 0.821001i \(-0.693416\pi\)
−0.570926 + 0.821001i \(0.693416\pi\)
\(678\) 54.9016 2.10848
\(679\) −43.2058 −1.65809
\(680\) −50.7330 −1.94552
\(681\) −41.6884 −1.59750
\(682\) −53.1245 −2.03424
\(683\) −15.5337 −0.594382 −0.297191 0.954818i \(-0.596050\pi\)
−0.297191 + 0.954818i \(0.596050\pi\)
\(684\) 19.5163 0.746225
\(685\) 22.4696 0.858520
\(686\) −0.439186 −0.0167682
\(687\) −43.1415 −1.64595
\(688\) −67.2670 −2.56453
\(689\) −6.59148 −0.251115
\(690\) −16.5210 −0.628945
\(691\) −37.8103 −1.43837 −0.719186 0.694817i \(-0.755485\pi\)
−0.719186 + 0.694817i \(0.755485\pi\)
\(692\) −108.179 −4.11235
\(693\) 23.9035 0.908018
\(694\) −65.4751 −2.48540
\(695\) −21.0548 −0.798656
\(696\) −64.7198 −2.45320
\(697\) 12.8499 0.486726
\(698\) 68.5374 2.59418
\(699\) 35.3085 1.33549
\(700\) 53.1004 2.00701
\(701\) 45.7661 1.72856 0.864280 0.503011i \(-0.167775\pi\)
0.864280 + 0.503011i \(0.167775\pi\)
\(702\) −8.95920 −0.338143
\(703\) 3.51413 0.132538
\(704\) −2.27856 −0.0858764
\(705\) −15.4957 −0.583600
\(706\) −24.2044 −0.910944
\(707\) −32.1345 −1.20854
\(708\) −19.5424 −0.734449
\(709\) −6.20926 −0.233194 −0.116597 0.993179i \(-0.537199\pi\)
−0.116597 + 0.993179i \(0.537199\pi\)
\(710\) 11.9475 0.448381
\(711\) −13.1102 −0.491670
\(712\) −26.8582 −1.00655
\(713\) 9.75382 0.365283
\(714\) −114.867 −4.29880
\(715\) −6.65198 −0.248770
\(716\) 28.1675 1.05267
\(717\) −40.5892 −1.51583
\(718\) 20.5503 0.766931
\(719\) −35.1400 −1.31050 −0.655250 0.755412i \(-0.727437\pi\)
−0.655250 + 0.755412i \(0.727437\pi\)
\(720\) 13.1240 0.489103
\(721\) −2.42819 −0.0904306
\(722\) 20.6952 0.770196
\(723\) 28.0561 1.04342
\(724\) −45.8978 −1.70578
\(725\) 15.2767 0.567363
\(726\) 68.2839 2.53425
\(727\) −17.2991 −0.641587 −0.320794 0.947149i \(-0.603950\pi\)
−0.320794 + 0.947149i \(0.603950\pi\)
\(728\) 23.9947 0.889304
\(729\) 7.17502 0.265741
\(730\) −50.0467 −1.85231
\(731\) −53.0029 −1.96038
\(732\) −93.4573 −3.45428
\(733\) 11.0049 0.406473 0.203237 0.979130i \(-0.434854\pi\)
0.203237 + 0.979130i \(0.434854\pi\)
\(734\) −41.2937 −1.52418
\(735\) −19.6479 −0.724722
\(736\) 13.6351 0.502597
\(737\) −19.0182 −0.700546
\(738\) −7.40119 −0.272441
\(739\) −14.3816 −0.529034 −0.264517 0.964381i \(-0.585213\pi\)
−0.264517 + 0.964381i \(0.585213\pi\)
\(740\) 6.54505 0.240601
\(741\) −6.85132 −0.251690
\(742\) −62.8539 −2.30744
\(743\) −28.5428 −1.04713 −0.523567 0.851984i \(-0.675399\pi\)
−0.523567 + 0.851984i \(0.675399\pi\)
\(744\) −56.7798 −2.08165
\(745\) −4.57935 −0.167774
\(746\) −17.6083 −0.644687
\(747\) −17.0726 −0.624654
\(748\) −128.085 −4.68325
\(749\) −53.6147 −1.95904
\(750\) −58.7637 −2.14575
\(751\) 35.2304 1.28557 0.642787 0.766045i \(-0.277778\pi\)
0.642787 + 0.766045i \(0.277778\pi\)
\(752\) 40.3897 1.47286
\(753\) 9.28692 0.338434
\(754\) 12.3899 0.451213
\(755\) 3.49955 0.127362
\(756\) −59.2109 −2.15348
\(757\) −17.5013 −0.636095 −0.318047 0.948075i \(-0.603027\pi\)
−0.318047 + 0.948075i \(0.603027\pi\)
\(758\) 64.3924 2.33884
\(759\) −23.2395 −0.843539
\(760\) −28.8548 −1.04667
\(761\) −26.5406 −0.962094 −0.481047 0.876695i \(-0.659743\pi\)
−0.481047 + 0.876695i \(0.659743\pi\)
\(762\) −13.1574 −0.476641
\(763\) 30.7035 1.11154
\(764\) 69.8702 2.52782
\(765\) 10.3411 0.373882
\(766\) −69.4111 −2.50792
\(767\) 2.08444 0.0752648
\(768\) 58.7163 2.11874
\(769\) −26.3614 −0.950617 −0.475309 0.879819i \(-0.657664\pi\)
−0.475309 + 0.879819i \(0.657664\pi\)
\(770\) −63.4308 −2.28589
\(771\) 44.3467 1.59711
\(772\) 49.8619 1.79457
\(773\) −1.44656 −0.0520290 −0.0260145 0.999662i \(-0.508282\pi\)
−0.0260145 + 0.999662i \(0.508282\pi\)
\(774\) 30.5282 1.09731
\(775\) 13.4025 0.481433
\(776\) −74.2953 −2.66705
\(777\) 8.25657 0.296203
\(778\) −5.87410 −0.210597
\(779\) 7.30851 0.261854
\(780\) −12.7605 −0.456901
\(781\) 16.8060 0.601367
\(782\) 33.9309 1.21337
\(783\) −17.0347 −0.608770
\(784\) 51.2125 1.82902
\(785\) −2.35025 −0.0838839
\(786\) −20.7885 −0.741501
\(787\) −14.2075 −0.506444 −0.253222 0.967408i \(-0.581490\pi\)
−0.253222 + 0.967408i \(0.581490\pi\)
\(788\) 98.9659 3.52551
\(789\) 39.6700 1.41229
\(790\) 34.7895 1.23775
\(791\) −38.7015 −1.37607
\(792\) 41.1036 1.46055
\(793\) 9.96838 0.353988
\(794\) −28.5074 −1.01169
\(795\) 18.6237 0.660516
\(796\) 32.3162 1.14542
\(797\) 2.33266 0.0826272 0.0413136 0.999146i \(-0.486846\pi\)
0.0413136 + 0.999146i \(0.486846\pi\)
\(798\) −65.3317 −2.31272
\(799\) 31.8250 1.12589
\(800\) 18.7358 0.662409
\(801\) 5.47459 0.193435
\(802\) 90.2873 3.18816
\(803\) −70.3987 −2.48432
\(804\) −36.4828 −1.28665
\(805\) 11.6461 0.410471
\(806\) 10.8699 0.382875
\(807\) 57.1000 2.01002
\(808\) −55.2574 −1.94395
\(809\) 41.6494 1.46431 0.732157 0.681136i \(-0.238514\pi\)
0.732157 + 0.681136i \(0.238514\pi\)
\(810\) 38.9608 1.36894
\(811\) 9.19350 0.322828 0.161414 0.986887i \(-0.448395\pi\)
0.161414 + 0.986887i \(0.448395\pi\)
\(812\) 81.8840 2.87357
\(813\) 9.01074 0.316020
\(814\) 13.2837 0.465593
\(815\) −1.94299 −0.0680598
\(816\) −88.7138 −3.10560
\(817\) −30.1459 −1.05467
\(818\) −28.6615 −1.00213
\(819\) −4.89092 −0.170903
\(820\) 13.6120 0.475353
\(821\) 49.0509 1.71189 0.855945 0.517068i \(-0.172976\pi\)
0.855945 + 0.517068i \(0.172976\pi\)
\(822\) 87.4824 3.05130
\(823\) 16.6587 0.580686 0.290343 0.956923i \(-0.406231\pi\)
0.290343 + 0.956923i \(0.406231\pi\)
\(824\) −4.17544 −0.145458
\(825\) −31.9329 −1.11176
\(826\) 19.8765 0.691591
\(827\) −22.4839 −0.781841 −0.390920 0.920424i \(-0.627843\pi\)
−0.390920 + 0.920424i \(0.627843\pi\)
\(828\) −13.5450 −0.470721
\(829\) −3.29885 −0.114574 −0.0572870 0.998358i \(-0.518245\pi\)
−0.0572870 + 0.998358i \(0.518245\pi\)
\(830\) 45.3043 1.57254
\(831\) −45.0555 −1.56296
\(832\) 0.466219 0.0161632
\(833\) 40.3528 1.39814
\(834\) −81.9741 −2.83853
\(835\) 32.3012 1.11783
\(836\) −72.8494 −2.51955
\(837\) −14.9448 −0.516569
\(838\) −64.4412 −2.22609
\(839\) 50.9527 1.75908 0.879542 0.475822i \(-0.157849\pi\)
0.879542 + 0.475822i \(0.157849\pi\)
\(840\) −67.7954 −2.33916
\(841\) −5.44238 −0.187668
\(842\) 53.5483 1.84539
\(843\) 5.67530 0.195468
\(844\) −47.1120 −1.62166
\(845\) 1.36107 0.0468222
\(846\) −18.3303 −0.630208
\(847\) −48.1351 −1.65394
\(848\) −48.5431 −1.66698
\(849\) 51.6710 1.77335
\(850\) 46.6239 1.59919
\(851\) −2.43893 −0.0836054
\(852\) 32.2392 1.10450
\(853\) 12.3854 0.424069 0.212034 0.977262i \(-0.431991\pi\)
0.212034 + 0.977262i \(0.431991\pi\)
\(854\) 95.0549 3.25271
\(855\) 5.88157 0.201145
\(856\) −92.1940 −3.15113
\(857\) 12.1022 0.413403 0.206702 0.978404i \(-0.433727\pi\)
0.206702 + 0.978404i \(0.433727\pi\)
\(858\) −25.8986 −0.884162
\(859\) −37.7943 −1.28952 −0.644762 0.764383i \(-0.723044\pi\)
−0.644762 + 0.764383i \(0.723044\pi\)
\(860\) −56.1465 −1.91458
\(861\) 17.1716 0.585206
\(862\) −46.9939 −1.60062
\(863\) −4.44037 −0.151152 −0.0755760 0.997140i \(-0.524080\pi\)
−0.0755760 + 0.997140i \(0.524080\pi\)
\(864\) −20.8918 −0.710752
\(865\) −32.6016 −1.10849
\(866\) −11.3417 −0.385407
\(867\) −34.6118 −1.17548
\(868\) 71.8383 2.43835
\(869\) 48.9369 1.66007
\(870\) −35.0067 −1.18684
\(871\) 3.89134 0.131853
\(872\) 52.7967 1.78792
\(873\) 15.1438 0.512541
\(874\) 19.2985 0.652782
\(875\) 41.4241 1.40039
\(876\) −135.046 −4.56279
\(877\) 9.20474 0.310822 0.155411 0.987850i \(-0.450330\pi\)
0.155411 + 0.987850i \(0.450330\pi\)
\(878\) −18.8846 −0.637323
\(879\) −34.8805 −1.17649
\(880\) −48.9886 −1.65141
\(881\) 9.42216 0.317441 0.158720 0.987324i \(-0.449263\pi\)
0.158720 + 0.987324i \(0.449263\pi\)
\(882\) −23.2421 −0.782601
\(883\) −16.4594 −0.553903 −0.276951 0.960884i \(-0.589324\pi\)
−0.276951 + 0.960884i \(0.589324\pi\)
\(884\) 26.2076 0.881458
\(885\) −5.88943 −0.197971
\(886\) 53.9074 1.81105
\(887\) −7.75556 −0.260406 −0.130203 0.991487i \(-0.541563\pi\)
−0.130203 + 0.991487i \(0.541563\pi\)
\(888\) 14.1977 0.476444
\(889\) 9.27497 0.311073
\(890\) −14.5275 −0.486963
\(891\) 54.8046 1.83602
\(892\) −31.2606 −1.04668
\(893\) 18.1007 0.605718
\(894\) −17.8290 −0.596292
\(895\) 8.48875 0.283748
\(896\) −40.0262 −1.33718
\(897\) 4.75506 0.158767
\(898\) 13.4079 0.447426
\(899\) 20.6675 0.689301
\(900\) −18.6119 −0.620397
\(901\) −38.2495 −1.27427
\(902\) 27.6267 0.919870
\(903\) −70.8288 −2.35703
\(904\) −66.5499 −2.21342
\(905\) −13.8321 −0.459794
\(906\) 13.6250 0.452661
\(907\) 23.3230 0.774428 0.387214 0.921990i \(-0.373437\pi\)
0.387214 + 0.921990i \(0.373437\pi\)
\(908\) 90.6978 3.00991
\(909\) 11.2633 0.373579
\(910\) 12.9787 0.430239
\(911\) −23.0399 −0.763346 −0.381673 0.924297i \(-0.624652\pi\)
−0.381673 + 0.924297i \(0.624652\pi\)
\(912\) −50.4567 −1.67079
\(913\) 63.7277 2.10908
\(914\) 63.1798 2.08980
\(915\) −28.1649 −0.931104
\(916\) 93.8592 3.10119
\(917\) 14.6543 0.483929
\(918\) −51.9891 −1.71589
\(919\) 26.2708 0.866594 0.433297 0.901251i \(-0.357350\pi\)
0.433297 + 0.901251i \(0.357350\pi\)
\(920\) 20.0263 0.660246
\(921\) −41.0925 −1.35404
\(922\) −22.1874 −0.730705
\(923\) −3.43870 −0.113186
\(924\) −171.162 −5.63082
\(925\) −3.35129 −0.110190
\(926\) 8.74560 0.287398
\(927\) 0.851092 0.0279535
\(928\) 28.8917 0.948415
\(929\) −51.9540 −1.70456 −0.852278 0.523088i \(-0.824780\pi\)
−0.852278 + 0.523088i \(0.824780\pi\)
\(930\) −30.7120 −1.00709
\(931\) 22.9510 0.752189
\(932\) −76.8175 −2.51624
\(933\) −64.2648 −2.10393
\(934\) 56.2594 1.84086
\(935\) −38.6005 −1.26237
\(936\) −8.41026 −0.274898
\(937\) 49.9266 1.63103 0.815515 0.578736i \(-0.196454\pi\)
0.815515 + 0.578736i \(0.196454\pi\)
\(938\) 37.1065 1.21157
\(939\) −55.0684 −1.79709
\(940\) 33.7125 1.09958
\(941\) −42.4897 −1.38513 −0.692563 0.721358i \(-0.743518\pi\)
−0.692563 + 0.721358i \(0.743518\pi\)
\(942\) −9.15036 −0.298135
\(943\) −5.07236 −0.165179
\(944\) 15.3509 0.499629
\(945\) −17.8442 −0.580472
\(946\) −113.954 −3.70496
\(947\) −27.6213 −0.897571 −0.448785 0.893640i \(-0.648143\pi\)
−0.448785 + 0.893640i \(0.648143\pi\)
\(948\) 93.8760 3.04895
\(949\) 14.4044 0.467586
\(950\) 26.5177 0.860349
\(951\) −38.4369 −1.24640
\(952\) 139.238 4.51274
\(953\) 9.71699 0.314764 0.157382 0.987538i \(-0.449695\pi\)
0.157382 + 0.987538i \(0.449695\pi\)
\(954\) 22.0306 0.713266
\(955\) 21.0566 0.681374
\(956\) 88.3062 2.85603
\(957\) −49.2425 −1.59178
\(958\) 60.2384 1.94621
\(959\) −61.6686 −1.99138
\(960\) −1.31727 −0.0425146
\(961\) −12.8680 −0.415097
\(962\) −2.71799 −0.0876317
\(963\) 18.7922 0.605570
\(964\) −61.0390 −1.96593
\(965\) 15.0267 0.483727
\(966\) 45.3425 1.45887
\(967\) −33.7635 −1.08576 −0.542880 0.839810i \(-0.682666\pi\)
−0.542880 + 0.839810i \(0.682666\pi\)
\(968\) −82.7715 −2.66038
\(969\) −39.7573 −1.27719
\(970\) −40.1861 −1.29030
\(971\) 14.3791 0.461448 0.230724 0.973019i \(-0.425891\pi\)
0.230724 + 0.973019i \(0.425891\pi\)
\(972\) 57.5795 1.84686
\(973\) 57.7857 1.85252
\(974\) 87.2308 2.79505
\(975\) 6.53383 0.209250
\(976\) 73.4123 2.34987
\(977\) 25.6326 0.820060 0.410030 0.912072i \(-0.365518\pi\)
0.410030 + 0.912072i \(0.365518\pi\)
\(978\) −7.56474 −0.241894
\(979\) −20.4352 −0.653113
\(980\) 42.7461 1.36547
\(981\) −10.7617 −0.343595
\(982\) −108.853 −3.47363
\(983\) 19.5646 0.624014 0.312007 0.950080i \(-0.398999\pi\)
0.312007 + 0.950080i \(0.398999\pi\)
\(984\) 29.5277 0.941308
\(985\) 29.8250 0.950305
\(986\) 71.8968 2.28966
\(987\) 42.5283 1.35369
\(988\) 14.9058 0.474217
\(989\) 20.9223 0.665290
\(990\) 22.2328 0.706605
\(991\) −14.2308 −0.452055 −0.226028 0.974121i \(-0.572574\pi\)
−0.226028 + 0.974121i \(0.572574\pi\)
\(992\) 25.3472 0.804774
\(993\) −65.0342 −2.06380
\(994\) −32.7902 −1.04004
\(995\) 9.73904 0.308748
\(996\) 122.249 3.87362
\(997\) −28.6632 −0.907772 −0.453886 0.891060i \(-0.649963\pi\)
−0.453886 + 0.891060i \(0.649963\pi\)
\(998\) −1.79574 −0.0568433
\(999\) 3.73693 0.118231
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 \(a_p\))