Properties

Label 8015.2.a.l.1.25
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.25
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q-0.614026 q^{2} -1.52615 q^{3} -1.62297 q^{4} -1.00000 q^{5} +0.937096 q^{6} -1.00000 q^{7} +2.22460 q^{8} -0.670866 q^{9} +O(q^{10})\) \(q-0.614026 q^{2} -1.52615 q^{3} -1.62297 q^{4} -1.00000 q^{5} +0.937096 q^{6} -1.00000 q^{7} +2.22460 q^{8} -0.670866 q^{9} +0.614026 q^{10} -1.70380 q^{11} +2.47690 q^{12} -4.10542 q^{13} +0.614026 q^{14} +1.52615 q^{15} +1.87998 q^{16} -0.650974 q^{17} +0.411929 q^{18} +6.66509 q^{19} +1.62297 q^{20} +1.52615 q^{21} +1.04618 q^{22} +1.46015 q^{23} -3.39507 q^{24} +1.00000 q^{25} +2.52083 q^{26} +5.60229 q^{27} +1.62297 q^{28} -8.37011 q^{29} -0.937096 q^{30} +6.49153 q^{31} -5.60356 q^{32} +2.60025 q^{33} +0.399715 q^{34} +1.00000 q^{35} +1.08880 q^{36} +1.26083 q^{37} -4.09254 q^{38} +6.26549 q^{39} -2.22460 q^{40} -11.8525 q^{41} -0.937096 q^{42} -2.32014 q^{43} +2.76522 q^{44} +0.670866 q^{45} -0.896571 q^{46} -6.47208 q^{47} -2.86914 q^{48} +1.00000 q^{49} -0.614026 q^{50} +0.993484 q^{51} +6.66298 q^{52} -3.55565 q^{53} -3.43995 q^{54} +1.70380 q^{55} -2.22460 q^{56} -10.1719 q^{57} +5.13947 q^{58} -2.36574 q^{59} -2.47690 q^{60} -8.50184 q^{61} -3.98597 q^{62} +0.670866 q^{63} -0.319237 q^{64} +4.10542 q^{65} -1.59662 q^{66} +10.4007 q^{67} +1.05651 q^{68} -2.22841 q^{69} -0.614026 q^{70} -6.68333 q^{71} -1.49241 q^{72} -8.71692 q^{73} -0.774180 q^{74} -1.52615 q^{75} -10.8173 q^{76} +1.70380 q^{77} -3.84717 q^{78} +3.26503 q^{79} -1.87998 q^{80} -6.53734 q^{81} +7.27774 q^{82} +14.2987 q^{83} -2.47690 q^{84} +0.650974 q^{85} +1.42463 q^{86} +12.7740 q^{87} -3.79027 q^{88} -11.1853 q^{89} -0.411929 q^{90} +4.10542 q^{91} -2.36979 q^{92} -9.90705 q^{93} +3.97403 q^{94} -6.66509 q^{95} +8.55187 q^{96} -9.95302 q^{97} -0.614026 q^{98} +1.14302 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} + O(q^{10}) \) \( 62q + 2q^{2} + 11q^{3} + 64q^{4} - 62q^{5} + 3q^{6} - 62q^{7} + 15q^{8} + 69q^{9} - 2q^{10} - 13q^{11} + 37q^{12} + 31q^{13} - 2q^{14} - 11q^{15} + 64q^{16} + 30q^{17} + 18q^{18} + 20q^{19} - 64q^{20} - 11q^{21} + 7q^{22} + 29q^{24} + 62q^{25} + 59q^{27} - 64q^{28} - 29q^{29} - 3q^{30} + 20q^{31} + 22q^{32} + 72q^{33} + 13q^{34} + 62q^{35} + 53q^{36} + 35q^{37} + 34q^{38} - 6q^{39} - 15q^{40} + 13q^{41} - 3q^{42} - 4q^{43} - 44q^{44} - 69q^{45} - 19q^{46} + 58q^{47} + 64q^{48} + 62q^{49} + 2q^{50} - 30q^{51} + 82q^{52} + 18q^{53} + 22q^{54} + 13q^{55} - 15q^{56} + 21q^{57} + 18q^{58} - 11q^{59} - 37q^{60} + 24q^{61} + 48q^{62} - 69q^{63} + 65q^{64} - 31q^{65} + 25q^{66} - 6q^{67} + 65q^{68} + 27q^{69} + 2q^{70} - 35q^{71} + 53q^{72} + 116q^{73} - 69q^{74} + 11q^{75} + 65q^{76} + 13q^{77} + 102q^{78} - 83q^{79} - 64q^{80} + 126q^{81} + 71q^{82} + 84q^{83} - 37q^{84} - 30q^{85} + 24q^{86} + 49q^{87} + 20q^{88} - 16q^{89} - 18q^{90} - 31q^{91} + 19q^{92} + 65q^{93} + 54q^{94} - 20q^{95} + 17q^{96} + 155q^{97} + 2q^{98} + 6q^{99} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.614026 −0.434182 −0.217091 0.976151i \(-0.569657\pi\)
−0.217091 + 0.976151i \(0.569657\pi\)
\(3\) −1.52615 −0.881123 −0.440562 0.897722i \(-0.645221\pi\)
−0.440562 + 0.897722i \(0.645221\pi\)
\(4\) −1.62297 −0.811486
\(5\) −1.00000 −0.447214
\(6\) 0.937096 0.382568
\(7\) −1.00000 −0.377964
\(8\) 2.22460 0.786514
\(9\) −0.670866 −0.223622
\(10\) 0.614026 0.194172
\(11\) −1.70380 −0.513714 −0.256857 0.966449i \(-0.582687\pi\)
−0.256857 + 0.966449i \(0.582687\pi\)
\(12\) 2.47690 0.715019
\(13\) −4.10542 −1.13864 −0.569319 0.822116i \(-0.692793\pi\)
−0.569319 + 0.822116i \(0.692793\pi\)
\(14\) 0.614026 0.164105
\(15\) 1.52615 0.394050
\(16\) 1.87998 0.469996
\(17\) −0.650974 −0.157884 −0.0789422 0.996879i \(-0.525154\pi\)
−0.0789422 + 0.996879i \(0.525154\pi\)
\(18\) 0.411929 0.0970927
\(19\) 6.66509 1.52908 0.764538 0.644578i \(-0.222967\pi\)
0.764538 + 0.644578i \(0.222967\pi\)
\(20\) 1.62297 0.362908
\(21\) 1.52615 0.333033
\(22\) 1.04618 0.223046
\(23\) 1.46015 0.304463 0.152231 0.988345i \(-0.451354\pi\)
0.152231 + 0.988345i \(0.451354\pi\)
\(24\) −3.39507 −0.693016
\(25\) 1.00000 0.200000
\(26\) 2.52083 0.494376
\(27\) 5.60229 1.07816
\(28\) 1.62297 0.306713
\(29\) −8.37011 −1.55429 −0.777146 0.629321i \(-0.783333\pi\)
−0.777146 + 0.629321i \(0.783333\pi\)
\(30\) −0.937096 −0.171089
\(31\) 6.49153 1.16591 0.582956 0.812503i \(-0.301896\pi\)
0.582956 + 0.812503i \(0.301896\pi\)
\(32\) −5.60356 −0.990578
\(33\) 2.60025 0.452646
\(34\) 0.399715 0.0685506
\(35\) 1.00000 0.169031
\(36\) 1.08880 0.181466
\(37\) 1.26083 0.207279 0.103639 0.994615i \(-0.466951\pi\)
0.103639 + 0.994615i \(0.466951\pi\)
\(38\) −4.09254 −0.663897
\(39\) 6.26549 1.00328
\(40\) −2.22460 −0.351740
\(41\) −11.8525 −1.85105 −0.925525 0.378686i \(-0.876376\pi\)
−0.925525 + 0.378686i \(0.876376\pi\)
\(42\) −0.937096 −0.144597
\(43\) −2.32014 −0.353818 −0.176909 0.984227i \(-0.556610\pi\)
−0.176909 + 0.984227i \(0.556610\pi\)
\(44\) 2.76522 0.416872
\(45\) 0.670866 0.100007
\(46\) −0.896571 −0.132192
\(47\) −6.47208 −0.944050 −0.472025 0.881585i \(-0.656477\pi\)
−0.472025 + 0.881585i \(0.656477\pi\)
\(48\) −2.86914 −0.414124
\(49\) 1.00000 0.142857
\(50\) −0.614026 −0.0868364
\(51\) 0.993484 0.139116
\(52\) 6.66298 0.923990
\(53\) −3.55565 −0.488406 −0.244203 0.969724i \(-0.578526\pi\)
−0.244203 + 0.969724i \(0.578526\pi\)
\(54\) −3.43995 −0.468118
\(55\) 1.70380 0.229740
\(56\) −2.22460 −0.297275
\(57\) −10.1719 −1.34730
\(58\) 5.13947 0.674845
\(59\) −2.36574 −0.307993 −0.153996 0.988071i \(-0.549214\pi\)
−0.153996 + 0.988071i \(0.549214\pi\)
\(60\) −2.47690 −0.319766
\(61\) −8.50184 −1.08855 −0.544274 0.838907i \(-0.683195\pi\)
−0.544274 + 0.838907i \(0.683195\pi\)
\(62\) −3.98597 −0.506218
\(63\) 0.670866 0.0845212
\(64\) −0.319237 −0.0399047
\(65\) 4.10542 0.509215
\(66\) −1.59662 −0.196531
\(67\) 10.4007 1.27065 0.635327 0.772243i \(-0.280865\pi\)
0.635327 + 0.772243i \(0.280865\pi\)
\(68\) 1.05651 0.128121
\(69\) −2.22841 −0.268269
\(70\) −0.614026 −0.0733901
\(71\) −6.68333 −0.793166 −0.396583 0.917999i \(-0.629804\pi\)
−0.396583 + 0.917999i \(0.629804\pi\)
\(72\) −1.49241 −0.175882
\(73\) −8.71692 −1.02024 −0.510119 0.860104i \(-0.670399\pi\)
−0.510119 + 0.860104i \(0.670399\pi\)
\(74\) −0.774180 −0.0899966
\(75\) −1.52615 −0.176225
\(76\) −10.8173 −1.24082
\(77\) 1.70380 0.194166
\(78\) −3.84717 −0.435606
\(79\) 3.26503 0.367345 0.183672 0.982988i \(-0.441201\pi\)
0.183672 + 0.982988i \(0.441201\pi\)
\(80\) −1.87998 −0.210188
\(81\) −6.53734 −0.726371
\(82\) 7.27774 0.803692
\(83\) 14.2987 1.56949 0.784745 0.619818i \(-0.212794\pi\)
0.784745 + 0.619818i \(0.212794\pi\)
\(84\) −2.47690 −0.270252
\(85\) 0.650974 0.0706081
\(86\) 1.42463 0.153622
\(87\) 12.7740 1.36952
\(88\) −3.79027 −0.404044
\(89\) −11.1853 −1.18564 −0.592821 0.805335i \(-0.701986\pi\)
−0.592821 + 0.805335i \(0.701986\pi\)
\(90\) −0.411929 −0.0434212
\(91\) 4.10542 0.430365
\(92\) −2.36979 −0.247067
\(93\) −9.90705 −1.02731
\(94\) 3.97403 0.409889
\(95\) −6.66509 −0.683824
\(96\) 8.55187 0.872821
\(97\) −9.95302 −1.01058 −0.505288 0.862951i \(-0.668614\pi\)
−0.505288 + 0.862951i \(0.668614\pi\)
\(98\) −0.614026 −0.0620260
\(99\) 1.14302 0.114878
\(100\) −1.62297 −0.162297
\(101\) −13.4985 −1.34315 −0.671577 0.740935i \(-0.734383\pi\)
−0.671577 + 0.740935i \(0.734383\pi\)
\(102\) −0.610025 −0.0604015
\(103\) 8.95643 0.882503 0.441251 0.897384i \(-0.354535\pi\)
0.441251 + 0.897384i \(0.354535\pi\)
\(104\) −9.13291 −0.895556
\(105\) −1.52615 −0.148937
\(106\) 2.18326 0.212057
\(107\) −13.7420 −1.32849 −0.664245 0.747515i \(-0.731247\pi\)
−0.664245 + 0.747515i \(0.731247\pi\)
\(108\) −9.09236 −0.874913
\(109\) 4.23676 0.405808 0.202904 0.979199i \(-0.434962\pi\)
0.202904 + 0.979199i \(0.434962\pi\)
\(110\) −1.04618 −0.0997490
\(111\) −1.92421 −0.182638
\(112\) −1.87998 −0.177642
\(113\) −20.3245 −1.91197 −0.955986 0.293411i \(-0.905209\pi\)
−0.955986 + 0.293411i \(0.905209\pi\)
\(114\) 6.24583 0.584975
\(115\) −1.46015 −0.136160
\(116\) 13.5845 1.26129
\(117\) 2.75419 0.254625
\(118\) 1.45262 0.133725
\(119\) 0.650974 0.0596747
\(120\) 3.39507 0.309926
\(121\) −8.09707 −0.736097
\(122\) 5.22035 0.472628
\(123\) 18.0887 1.63100
\(124\) −10.5356 −0.946122
\(125\) −1.00000 −0.0894427
\(126\) −0.411929 −0.0366976
\(127\) −5.18231 −0.459855 −0.229928 0.973208i \(-0.573849\pi\)
−0.229928 + 0.973208i \(0.573849\pi\)
\(128\) 11.4031 1.00790
\(129\) 3.54089 0.311758
\(130\) −2.52083 −0.221092
\(131\) −21.1192 −1.84520 −0.922598 0.385762i \(-0.873939\pi\)
−0.922598 + 0.385762i \(0.873939\pi\)
\(132\) −4.22014 −0.367316
\(133\) −6.66509 −0.577937
\(134\) −6.38633 −0.551695
\(135\) −5.60229 −0.482169
\(136\) −1.44816 −0.124178
\(137\) 13.2511 1.13212 0.566060 0.824364i \(-0.308467\pi\)
0.566060 + 0.824364i \(0.308467\pi\)
\(138\) 1.36830 0.116478
\(139\) 4.86864 0.412953 0.206476 0.978452i \(-0.433800\pi\)
0.206476 + 0.978452i \(0.433800\pi\)
\(140\) −1.62297 −0.137166
\(141\) 9.87737 0.831824
\(142\) 4.10374 0.344378
\(143\) 6.99481 0.584935
\(144\) −1.26122 −0.105101
\(145\) 8.37011 0.695100
\(146\) 5.35241 0.442969
\(147\) −1.52615 −0.125875
\(148\) −2.04629 −0.168204
\(149\) 9.15495 0.750003 0.375001 0.927024i \(-0.377642\pi\)
0.375001 + 0.927024i \(0.377642\pi\)
\(150\) 0.937096 0.0765135
\(151\) 20.6800 1.68291 0.841456 0.540326i \(-0.181699\pi\)
0.841456 + 0.540326i \(0.181699\pi\)
\(152\) 14.8272 1.20264
\(153\) 0.436717 0.0353064
\(154\) −1.04618 −0.0843033
\(155\) −6.49153 −0.521412
\(156\) −10.1687 −0.814149
\(157\) 1.97961 0.157990 0.0789950 0.996875i \(-0.474829\pi\)
0.0789950 + 0.996875i \(0.474829\pi\)
\(158\) −2.00481 −0.159494
\(159\) 5.42646 0.430346
\(160\) 5.60356 0.443000
\(161\) −1.46015 −0.115076
\(162\) 4.01410 0.315377
\(163\) −22.4027 −1.75471 −0.877357 0.479838i \(-0.840696\pi\)
−0.877357 + 0.479838i \(0.840696\pi\)
\(164\) 19.2363 1.50210
\(165\) −2.60025 −0.202429
\(166\) −8.77980 −0.681444
\(167\) 19.4040 1.50152 0.750762 0.660572i \(-0.229686\pi\)
0.750762 + 0.660572i \(0.229686\pi\)
\(168\) 3.39507 0.261935
\(169\) 3.85448 0.296498
\(170\) −0.399715 −0.0306567
\(171\) −4.47138 −0.341935
\(172\) 3.76553 0.287119
\(173\) −23.2766 −1.76968 −0.884842 0.465891i \(-0.845734\pi\)
−0.884842 + 0.465891i \(0.845734\pi\)
\(174\) −7.84360 −0.594622
\(175\) −1.00000 −0.0755929
\(176\) −3.20311 −0.241444
\(177\) 3.61047 0.271379
\(178\) 6.86807 0.514784
\(179\) 4.71244 0.352224 0.176112 0.984370i \(-0.443648\pi\)
0.176112 + 0.984370i \(0.443648\pi\)
\(180\) −1.08880 −0.0811541
\(181\) 7.10961 0.528453 0.264227 0.964461i \(-0.414883\pi\)
0.264227 + 0.964461i \(0.414883\pi\)
\(182\) −2.52083 −0.186857
\(183\) 12.9751 0.959146
\(184\) 3.24825 0.239464
\(185\) −1.26083 −0.0926978
\(186\) 6.08318 0.446041
\(187\) 1.10913 0.0811075
\(188\) 10.5040 0.766084
\(189\) −5.60229 −0.407507
\(190\) 4.09254 0.296904
\(191\) −26.7248 −1.93374 −0.966869 0.255274i \(-0.917834\pi\)
−0.966869 + 0.255274i \(0.917834\pi\)
\(192\) 0.487204 0.0351609
\(193\) −8.12503 −0.584853 −0.292426 0.956288i \(-0.594463\pi\)
−0.292426 + 0.956288i \(0.594463\pi\)
\(194\) 6.11141 0.438774
\(195\) −6.26549 −0.448681
\(196\) −1.62297 −0.115927
\(197\) 15.0454 1.07194 0.535971 0.844236i \(-0.319946\pi\)
0.535971 + 0.844236i \(0.319946\pi\)
\(198\) −0.701844 −0.0498779
\(199\) −6.73146 −0.477181 −0.238590 0.971120i \(-0.576685\pi\)
−0.238590 + 0.971120i \(0.576685\pi\)
\(200\) 2.22460 0.157303
\(201\) −15.8731 −1.11960
\(202\) 8.28845 0.583173
\(203\) 8.37011 0.587467
\(204\) −1.61240 −0.112890
\(205\) 11.8525 0.827815
\(206\) −5.49948 −0.383167
\(207\) −0.979567 −0.0680846
\(208\) −7.71812 −0.535155
\(209\) −11.3560 −0.785509
\(210\) 0.937096 0.0646657
\(211\) 10.7127 0.737490 0.368745 0.929531i \(-0.379788\pi\)
0.368745 + 0.929531i \(0.379788\pi\)
\(212\) 5.77072 0.396335
\(213\) 10.1998 0.698876
\(214\) 8.43795 0.576807
\(215\) 2.32014 0.158232
\(216\) 12.4629 0.847990
\(217\) −6.49153 −0.440674
\(218\) −2.60148 −0.176195
\(219\) 13.3033 0.898955
\(220\) −2.76522 −0.186431
\(221\) 2.67252 0.179773
\(222\) 1.18151 0.0792981
\(223\) −0.791955 −0.0530332 −0.0265166 0.999648i \(-0.508441\pi\)
−0.0265166 + 0.999648i \(0.508441\pi\)
\(224\) 5.60356 0.374403
\(225\) −0.670866 −0.0447244
\(226\) 12.4798 0.830144
\(227\) −27.2216 −1.80676 −0.903380 0.428841i \(-0.858922\pi\)
−0.903380 + 0.428841i \(0.858922\pi\)
\(228\) 16.5088 1.09332
\(229\) 1.00000 0.0660819
\(230\) 0.896571 0.0591182
\(231\) −2.60025 −0.171084
\(232\) −18.6201 −1.22247
\(233\) −0.912968 −0.0598105 −0.0299053 0.999553i \(-0.509521\pi\)
−0.0299053 + 0.999553i \(0.509521\pi\)
\(234\) −1.69114 −0.110553
\(235\) 6.47208 0.422192
\(236\) 3.83952 0.249932
\(237\) −4.98293 −0.323676
\(238\) −0.399715 −0.0259097
\(239\) 1.61620 0.104543 0.0522717 0.998633i \(-0.483354\pi\)
0.0522717 + 0.998633i \(0.483354\pi\)
\(240\) 2.86914 0.185202
\(241\) −28.1724 −1.81474 −0.907372 0.420328i \(-0.861915\pi\)
−0.907372 + 0.420328i \(0.861915\pi\)
\(242\) 4.97181 0.319600
\(243\) −6.82992 −0.438139
\(244\) 13.7982 0.883342
\(245\) −1.00000 −0.0638877
\(246\) −11.1069 −0.708152
\(247\) −27.3630 −1.74107
\(248\) 14.4410 0.917007
\(249\) −21.8220 −1.38291
\(250\) 0.614026 0.0388344
\(251\) 1.63256 0.103046 0.0515230 0.998672i \(-0.483592\pi\)
0.0515230 + 0.998672i \(0.483592\pi\)
\(252\) −1.08880 −0.0685878
\(253\) −2.48780 −0.156407
\(254\) 3.18207 0.199661
\(255\) −0.993484 −0.0622144
\(256\) −6.36334 −0.397709
\(257\) 17.5786 1.09652 0.548260 0.836308i \(-0.315290\pi\)
0.548260 + 0.836308i \(0.315290\pi\)
\(258\) −2.17420 −0.135359
\(259\) −1.26083 −0.0783439
\(260\) −6.66298 −0.413221
\(261\) 5.61523 0.347574
\(262\) 12.9678 0.801151
\(263\) 23.2886 1.43603 0.718017 0.696025i \(-0.245050\pi\)
0.718017 + 0.696025i \(0.245050\pi\)
\(264\) 5.78452 0.356012
\(265\) 3.55565 0.218422
\(266\) 4.09254 0.250930
\(267\) 17.0705 1.04470
\(268\) −16.8801 −1.03112
\(269\) 18.2182 1.11078 0.555391 0.831590i \(-0.312569\pi\)
0.555391 + 0.831590i \(0.312569\pi\)
\(270\) 3.43995 0.209349
\(271\) 26.1341 1.58753 0.793766 0.608223i \(-0.208117\pi\)
0.793766 + 0.608223i \(0.208117\pi\)
\(272\) −1.22382 −0.0742050
\(273\) −6.26549 −0.379205
\(274\) −8.13653 −0.491546
\(275\) −1.70380 −0.102743
\(276\) 3.61665 0.217697
\(277\) 8.61757 0.517779 0.258890 0.965907i \(-0.416643\pi\)
0.258890 + 0.965907i \(0.416643\pi\)
\(278\) −2.98947 −0.179297
\(279\) −4.35495 −0.260724
\(280\) 2.22460 0.132945
\(281\) 5.89380 0.351595 0.175797 0.984426i \(-0.443750\pi\)
0.175797 + 0.984426i \(0.443750\pi\)
\(282\) −6.06496 −0.361163
\(283\) −2.92384 −0.173804 −0.0869022 0.996217i \(-0.527697\pi\)
−0.0869022 + 0.996217i \(0.527697\pi\)
\(284\) 10.8469 0.643643
\(285\) 10.1719 0.602533
\(286\) −4.29499 −0.253968
\(287\) 11.8525 0.699631
\(288\) 3.75924 0.221515
\(289\) −16.5762 −0.975073
\(290\) −5.13947 −0.301800
\(291\) 15.1898 0.890441
\(292\) 14.1473 0.827909
\(293\) −1.88521 −0.110135 −0.0550675 0.998483i \(-0.517537\pi\)
−0.0550675 + 0.998483i \(0.517537\pi\)
\(294\) 0.937096 0.0546525
\(295\) 2.36574 0.137738
\(296\) 2.80483 0.163028
\(297\) −9.54517 −0.553867
\(298\) −5.62138 −0.325638
\(299\) −5.99454 −0.346673
\(300\) 2.47690 0.143004
\(301\) 2.32014 0.133731
\(302\) −12.6980 −0.730690
\(303\) 20.6008 1.18348
\(304\) 12.5303 0.718659
\(305\) 8.50184 0.486814
\(306\) −0.268155 −0.0153294
\(307\) 9.93303 0.566908 0.283454 0.958986i \(-0.408520\pi\)
0.283454 + 0.958986i \(0.408520\pi\)
\(308\) −2.76522 −0.157563
\(309\) −13.6688 −0.777594
\(310\) 3.98597 0.226388
\(311\) −3.37095 −0.191149 −0.0955745 0.995422i \(-0.530469\pi\)
−0.0955745 + 0.995422i \(0.530469\pi\)
\(312\) 13.9382 0.789095
\(313\) −5.06918 −0.286527 −0.143264 0.989685i \(-0.545760\pi\)
−0.143264 + 0.989685i \(0.545760\pi\)
\(314\) −1.21553 −0.0685964
\(315\) −0.670866 −0.0377990
\(316\) −5.29905 −0.298095
\(317\) −18.0527 −1.01394 −0.506971 0.861963i \(-0.669235\pi\)
−0.506971 + 0.861963i \(0.669235\pi\)
\(318\) −3.33199 −0.186849
\(319\) 14.2610 0.798462
\(320\) 0.319237 0.0178459
\(321\) 20.9724 1.17056
\(322\) 0.896571 0.0499640
\(323\) −4.33880 −0.241417
\(324\) 10.6099 0.589440
\(325\) −4.10542 −0.227728
\(326\) 13.7558 0.761865
\(327\) −6.46593 −0.357567
\(328\) −26.3671 −1.45588
\(329\) 6.47208 0.356817
\(330\) 1.59662 0.0878911
\(331\) −25.2651 −1.38869 −0.694347 0.719640i \(-0.744307\pi\)
−0.694347 + 0.719640i \(0.744307\pi\)
\(332\) −23.2065 −1.27362
\(333\) −0.845846 −0.0463521
\(334\) −11.9145 −0.651935
\(335\) −10.4007 −0.568254
\(336\) 2.86914 0.156524
\(337\) 0.219020 0.0119308 0.00596540 0.999982i \(-0.498101\pi\)
0.00596540 + 0.999982i \(0.498101\pi\)
\(338\) −2.36675 −0.128734
\(339\) 31.0183 1.68468
\(340\) −1.05651 −0.0572975
\(341\) −11.0603 −0.598946
\(342\) 2.74555 0.148462
\(343\) −1.00000 −0.0539949
\(344\) −5.16139 −0.278283
\(345\) 2.22841 0.119974
\(346\) 14.2924 0.768365
\(347\) −14.1836 −0.761417 −0.380708 0.924695i \(-0.624320\pi\)
−0.380708 + 0.924695i \(0.624320\pi\)
\(348\) −20.7319 −1.11135
\(349\) −15.8976 −0.850977 −0.425489 0.904964i \(-0.639898\pi\)
−0.425489 + 0.904964i \(0.639898\pi\)
\(350\) 0.614026 0.0328211
\(351\) −22.9998 −1.22764
\(352\) 9.54733 0.508874
\(353\) 0.474151 0.0252365 0.0126182 0.999920i \(-0.495983\pi\)
0.0126182 + 0.999920i \(0.495983\pi\)
\(354\) −2.21692 −0.117828
\(355\) 6.68333 0.354714
\(356\) 18.1535 0.962131
\(357\) −0.993484 −0.0525808
\(358\) −2.89356 −0.152929
\(359\) −16.5748 −0.874783 −0.437392 0.899271i \(-0.644098\pi\)
−0.437392 + 0.899271i \(0.644098\pi\)
\(360\) 1.49241 0.0786568
\(361\) 25.4234 1.33807
\(362\) −4.36549 −0.229445
\(363\) 12.3573 0.648593
\(364\) −6.66298 −0.349235
\(365\) 8.71692 0.456264
\(366\) −7.96704 −0.416444
\(367\) 0.494832 0.0258300 0.0129150 0.999917i \(-0.495889\pi\)
0.0129150 + 0.999917i \(0.495889\pi\)
\(368\) 2.74506 0.143096
\(369\) 7.95144 0.413936
\(370\) 0.774180 0.0402477
\(371\) 3.55565 0.184600
\(372\) 16.0789 0.833650
\(373\) 28.1173 1.45586 0.727929 0.685653i \(-0.240483\pi\)
0.727929 + 0.685653i \(0.240483\pi\)
\(374\) −0.681034 −0.0352154
\(375\) 1.52615 0.0788100
\(376\) −14.3978 −0.742509
\(377\) 34.3628 1.76978
\(378\) 3.43995 0.176932
\(379\) −29.6898 −1.52506 −0.762531 0.646951i \(-0.776044\pi\)
−0.762531 + 0.646951i \(0.776044\pi\)
\(380\) 10.8173 0.554913
\(381\) 7.90898 0.405189
\(382\) 16.4097 0.839594
\(383\) −20.5508 −1.05009 −0.525047 0.851073i \(-0.675952\pi\)
−0.525047 + 0.851073i \(0.675952\pi\)
\(384\) −17.4029 −0.888087
\(385\) −1.70380 −0.0868336
\(386\) 4.98898 0.253932
\(387\) 1.55651 0.0791216
\(388\) 16.1535 0.820068
\(389\) −0.330569 −0.0167605 −0.00838025 0.999965i \(-0.502668\pi\)
−0.00838025 + 0.999965i \(0.502668\pi\)
\(390\) 3.84717 0.194809
\(391\) −0.950521 −0.0480699
\(392\) 2.22460 0.112359
\(393\) 32.2311 1.62585
\(394\) −9.23828 −0.465418
\(395\) −3.26503 −0.164282
\(396\) −1.85509 −0.0932218
\(397\) −1.94539 −0.0976365 −0.0488183 0.998808i \(-0.515546\pi\)
−0.0488183 + 0.998808i \(0.515546\pi\)
\(398\) 4.13329 0.207183
\(399\) 10.1719 0.509233
\(400\) 1.87998 0.0939991
\(401\) −6.31723 −0.315467 −0.157734 0.987482i \(-0.550419\pi\)
−0.157734 + 0.987482i \(0.550419\pi\)
\(402\) 9.74650 0.486111
\(403\) −26.6505 −1.32755
\(404\) 21.9077 1.08995
\(405\) 6.53734 0.324843
\(406\) −5.13947 −0.255067
\(407\) −2.14819 −0.106482
\(408\) 2.21010 0.109416
\(409\) 15.5184 0.767337 0.383669 0.923471i \(-0.374660\pi\)
0.383669 + 0.923471i \(0.374660\pi\)
\(410\) −7.27774 −0.359422
\(411\) −20.2232 −0.997537
\(412\) −14.5360 −0.716139
\(413\) 2.36574 0.116410
\(414\) 0.601479 0.0295611
\(415\) −14.2987 −0.701898
\(416\) 23.0050 1.12791
\(417\) −7.43027 −0.363862
\(418\) 6.97286 0.341054
\(419\) 35.1368 1.71655 0.858273 0.513193i \(-0.171538\pi\)
0.858273 + 0.513193i \(0.171538\pi\)
\(420\) 2.47690 0.120860
\(421\) −3.27712 −0.159717 −0.0798585 0.996806i \(-0.525447\pi\)
−0.0798585 + 0.996806i \(0.525447\pi\)
\(422\) −6.57785 −0.320205
\(423\) 4.34190 0.211110
\(424\) −7.90990 −0.384139
\(425\) −0.650974 −0.0315769
\(426\) −6.26292 −0.303440
\(427\) 8.50184 0.411433
\(428\) 22.3029 1.07805
\(429\) −10.6751 −0.515400
\(430\) −1.42463 −0.0687016
\(431\) −0.0630480 −0.00303692 −0.00151846 0.999999i \(-0.500483\pi\)
−0.00151846 + 0.999999i \(0.500483\pi\)
\(432\) 10.5322 0.506731
\(433\) 27.6159 1.32714 0.663568 0.748116i \(-0.269041\pi\)
0.663568 + 0.748116i \(0.269041\pi\)
\(434\) 3.98597 0.191333
\(435\) −12.7740 −0.612469
\(436\) −6.87615 −0.329308
\(437\) 9.73205 0.465547
\(438\) −8.16859 −0.390310
\(439\) −9.96936 −0.475812 −0.237906 0.971288i \(-0.576461\pi\)
−0.237906 + 0.971288i \(0.576461\pi\)
\(440\) 3.79027 0.180694
\(441\) −0.670866 −0.0319460
\(442\) −1.64100 −0.0780543
\(443\) 29.9622 1.42355 0.711774 0.702408i \(-0.247892\pi\)
0.711774 + 0.702408i \(0.247892\pi\)
\(444\) 3.12294 0.148208
\(445\) 11.1853 0.530235
\(446\) 0.486281 0.0230261
\(447\) −13.9718 −0.660845
\(448\) 0.319237 0.0150825
\(449\) −12.6265 −0.595881 −0.297941 0.954584i \(-0.596300\pi\)
−0.297941 + 0.954584i \(0.596300\pi\)
\(450\) 0.411929 0.0194185
\(451\) 20.1943 0.950911
\(452\) 32.9862 1.55154
\(453\) −31.5607 −1.48285
\(454\) 16.7148 0.784462
\(455\) −4.10542 −0.192465
\(456\) −22.6285 −1.05967
\(457\) 30.8998 1.44543 0.722717 0.691144i \(-0.242893\pi\)
0.722717 + 0.691144i \(0.242893\pi\)
\(458\) −0.614026 −0.0286915
\(459\) −3.64695 −0.170225
\(460\) 2.36979 0.110492
\(461\) −11.0706 −0.515610 −0.257805 0.966197i \(-0.582999\pi\)
−0.257805 + 0.966197i \(0.582999\pi\)
\(462\) 1.59662 0.0742816
\(463\) −17.9537 −0.834380 −0.417190 0.908819i \(-0.636985\pi\)
−0.417190 + 0.908819i \(0.636985\pi\)
\(464\) −15.7357 −0.730510
\(465\) 9.90705 0.459428
\(466\) 0.560586 0.0259687
\(467\) −1.37295 −0.0635323 −0.0317662 0.999495i \(-0.510113\pi\)
−0.0317662 + 0.999495i \(0.510113\pi\)
\(468\) −4.46997 −0.206624
\(469\) −10.4007 −0.480262
\(470\) −3.97403 −0.183308
\(471\) −3.02118 −0.139209
\(472\) −5.26281 −0.242241
\(473\) 3.95305 0.181762
\(474\) 3.05965 0.140534
\(475\) 6.66509 0.305815
\(476\) −1.05651 −0.0484252
\(477\) 2.38537 0.109218
\(478\) −0.992390 −0.0453908
\(479\) 21.0535 0.961959 0.480980 0.876732i \(-0.340281\pi\)
0.480980 + 0.876732i \(0.340281\pi\)
\(480\) −8.55187 −0.390338
\(481\) −5.17622 −0.236015
\(482\) 17.2986 0.787929
\(483\) 2.22841 0.101396
\(484\) 13.1413 0.597333
\(485\) 9.95302 0.451943
\(486\) 4.19375 0.190232
\(487\) 0.203246 0.00920995 0.00460497 0.999989i \(-0.498534\pi\)
0.00460497 + 0.999989i \(0.498534\pi\)
\(488\) −18.9132 −0.856159
\(489\) 34.1899 1.54612
\(490\) 0.614026 0.0277389
\(491\) −1.55121 −0.0700053 −0.0350027 0.999387i \(-0.511144\pi\)
−0.0350027 + 0.999387i \(0.511144\pi\)
\(492\) −29.3575 −1.32354
\(493\) 5.44873 0.245398
\(494\) 16.8016 0.755939
\(495\) −1.14302 −0.0513750
\(496\) 12.2040 0.547974
\(497\) 6.68333 0.299788
\(498\) 13.3993 0.600436
\(499\) −15.2494 −0.682655 −0.341327 0.939944i \(-0.610876\pi\)
−0.341327 + 0.939944i \(0.610876\pi\)
\(500\) 1.62297 0.0725815
\(501\) −29.6134 −1.32303
\(502\) −1.00243 −0.0447407
\(503\) 28.6358 1.27681 0.638404 0.769701i \(-0.279595\pi\)
0.638404 + 0.769701i \(0.279595\pi\)
\(504\) 1.49241 0.0664771
\(505\) 13.4985 0.600677
\(506\) 1.52758 0.0679091
\(507\) −5.88251 −0.261252
\(508\) 8.41074 0.373166
\(509\) 37.1774 1.64786 0.823930 0.566692i \(-0.191777\pi\)
0.823930 + 0.566692i \(0.191777\pi\)
\(510\) 0.610025 0.0270124
\(511\) 8.71692 0.385614
\(512\) −18.8990 −0.835226
\(513\) 37.3398 1.64859
\(514\) −10.7937 −0.476089
\(515\) −8.95643 −0.394667
\(516\) −5.74676 −0.252987
\(517\) 11.0271 0.484972
\(518\) 0.774180 0.0340155
\(519\) 35.5235 1.55931
\(520\) 9.13291 0.400505
\(521\) 4.82404 0.211345 0.105673 0.994401i \(-0.466300\pi\)
0.105673 + 0.994401i \(0.466300\pi\)
\(522\) −3.44789 −0.150910
\(523\) −2.45696 −0.107435 −0.0537177 0.998556i \(-0.517107\pi\)
−0.0537177 + 0.998556i \(0.517107\pi\)
\(524\) 34.2759 1.49735
\(525\) 1.52615 0.0666066
\(526\) −14.2998 −0.623500
\(527\) −4.22582 −0.184080
\(528\) 4.88843 0.212742
\(529\) −20.8680 −0.907302
\(530\) −2.18326 −0.0948349
\(531\) 1.58709 0.0688739
\(532\) 10.8173 0.468987
\(533\) 48.6595 2.10768
\(534\) −10.4817 −0.453588
\(535\) 13.7420 0.594119
\(536\) 23.1375 0.999387
\(537\) −7.19189 −0.310353
\(538\) −11.1864 −0.482281
\(539\) −1.70380 −0.0733878
\(540\) 9.09236 0.391273
\(541\) −29.2787 −1.25879 −0.629394 0.777086i \(-0.716697\pi\)
−0.629394 + 0.777086i \(0.716697\pi\)
\(542\) −16.0470 −0.689278
\(543\) −10.8503 −0.465633
\(544\) 3.64777 0.156397
\(545\) −4.23676 −0.181483
\(546\) 3.84717 0.164644
\(547\) 35.1000 1.50077 0.750384 0.661003i \(-0.229869\pi\)
0.750384 + 0.661003i \(0.229869\pi\)
\(548\) −21.5062 −0.918700
\(549\) 5.70360 0.243424
\(550\) 1.04618 0.0446091
\(551\) −55.7876 −2.37663
\(552\) −4.95732 −0.210998
\(553\) −3.26503 −0.138843
\(554\) −5.29141 −0.224810
\(555\) 1.92421 0.0816782
\(556\) −7.90166 −0.335105
\(557\) −35.8948 −1.52091 −0.760455 0.649391i \(-0.775024\pi\)
−0.760455 + 0.649391i \(0.775024\pi\)
\(558\) 2.67405 0.113202
\(559\) 9.52516 0.402871
\(560\) 1.87998 0.0794438
\(561\) −1.69270 −0.0714657
\(562\) −3.61895 −0.152656
\(563\) 38.7271 1.63215 0.816076 0.577944i \(-0.196145\pi\)
0.816076 + 0.577944i \(0.196145\pi\)
\(564\) −16.0307 −0.675014
\(565\) 20.3245 0.855060
\(566\) 1.79532 0.0754627
\(567\) 6.53734 0.274542
\(568\) −14.8677 −0.623836
\(569\) 36.0813 1.51261 0.756303 0.654221i \(-0.227003\pi\)
0.756303 + 0.654221i \(0.227003\pi\)
\(570\) −6.24583 −0.261609
\(571\) 16.5581 0.692937 0.346468 0.938062i \(-0.387381\pi\)
0.346468 + 0.938062i \(0.387381\pi\)
\(572\) −11.3524 −0.474667
\(573\) 40.7860 1.70386
\(574\) −7.27774 −0.303767
\(575\) 1.46015 0.0608926
\(576\) 0.214166 0.00892356
\(577\) −1.51921 −0.0632457 −0.0316228 0.999500i \(-0.510068\pi\)
−0.0316228 + 0.999500i \(0.510068\pi\)
\(578\) 10.1782 0.423359
\(579\) 12.4000 0.515327
\(580\) −13.5845 −0.564064
\(581\) −14.2987 −0.593212
\(582\) −9.32693 −0.386614
\(583\) 6.05811 0.250901
\(584\) −19.3916 −0.802432
\(585\) −2.75419 −0.113872
\(586\) 1.15757 0.0478186
\(587\) 40.0689 1.65382 0.826910 0.562334i \(-0.190097\pi\)
0.826910 + 0.562334i \(0.190097\pi\)
\(588\) 2.47690 0.102146
\(589\) 43.2666 1.78277
\(590\) −1.45262 −0.0598036
\(591\) −22.9616 −0.944513
\(592\) 2.37033 0.0974200
\(593\) 32.6835 1.34215 0.671075 0.741390i \(-0.265833\pi\)
0.671075 + 0.741390i \(0.265833\pi\)
\(594\) 5.86098 0.240479
\(595\) −0.650974 −0.0266873
\(596\) −14.8582 −0.608617
\(597\) 10.2732 0.420455
\(598\) 3.68080 0.150519
\(599\) −46.7229 −1.90904 −0.954522 0.298140i \(-0.903634\pi\)
−0.954522 + 0.298140i \(0.903634\pi\)
\(600\) −3.39507 −0.138603
\(601\) −22.2308 −0.906812 −0.453406 0.891304i \(-0.649791\pi\)
−0.453406 + 0.891304i \(0.649791\pi\)
\(602\) −1.42463 −0.0580635
\(603\) −6.97751 −0.284146
\(604\) −33.5630 −1.36566
\(605\) 8.09707 0.329193
\(606\) −12.6494 −0.513847
\(607\) 46.3587 1.88164 0.940821 0.338904i \(-0.110056\pi\)
0.940821 + 0.338904i \(0.110056\pi\)
\(608\) −37.3482 −1.51467
\(609\) −12.7740 −0.517631
\(610\) −5.22035 −0.211366
\(611\) 26.5706 1.07493
\(612\) −0.708779 −0.0286507
\(613\) 21.5486 0.870341 0.435171 0.900348i \(-0.356688\pi\)
0.435171 + 0.900348i \(0.356688\pi\)
\(614\) −6.09914 −0.246141
\(615\) −18.0887 −0.729407
\(616\) 3.79027 0.152714
\(617\) 21.2545 0.855676 0.427838 0.903856i \(-0.359275\pi\)
0.427838 + 0.903856i \(0.359275\pi\)
\(618\) 8.39303 0.337617
\(619\) 23.5322 0.945838 0.472919 0.881106i \(-0.343200\pi\)
0.472919 + 0.881106i \(0.343200\pi\)
\(620\) 10.5356 0.423119
\(621\) 8.18020 0.328260
\(622\) 2.06985 0.0829934
\(623\) 11.1853 0.448130
\(624\) 11.7790 0.471538
\(625\) 1.00000 0.0400000
\(626\) 3.11261 0.124405
\(627\) 17.3309 0.692130
\(628\) −3.21285 −0.128207
\(629\) −0.820765 −0.0327261
\(630\) 0.411929 0.0164117
\(631\) −20.2740 −0.807097 −0.403548 0.914958i \(-0.632223\pi\)
−0.403548 + 0.914958i \(0.632223\pi\)
\(632\) 7.26338 0.288922
\(633\) −16.3491 −0.649820
\(634\) 11.0848 0.440235
\(635\) 5.18231 0.205654
\(636\) −8.80699 −0.349220
\(637\) −4.10542 −0.162663
\(638\) −8.75661 −0.346678
\(639\) 4.48362 0.177369
\(640\) −11.4031 −0.450748
\(641\) 0.259133 0.0102351 0.00511757 0.999987i \(-0.498371\pi\)
0.00511757 + 0.999987i \(0.498371\pi\)
\(642\) −12.8776 −0.508238
\(643\) −13.9887 −0.551661 −0.275830 0.961206i \(-0.588953\pi\)
−0.275830 + 0.961206i \(0.588953\pi\)
\(644\) 2.36979 0.0933827
\(645\) −3.54089 −0.139422
\(646\) 2.66414 0.104819
\(647\) 40.2024 1.58052 0.790260 0.612771i \(-0.209945\pi\)
0.790260 + 0.612771i \(0.209945\pi\)
\(648\) −14.5430 −0.571301
\(649\) 4.03074 0.158220
\(650\) 2.52083 0.0988753
\(651\) 9.90705 0.388288
\(652\) 36.3590 1.42393
\(653\) −18.9775 −0.742647 −0.371324 0.928504i \(-0.621096\pi\)
−0.371324 + 0.928504i \(0.621096\pi\)
\(654\) 3.97025 0.155249
\(655\) 21.1192 0.825197
\(656\) −22.2825 −0.869986
\(657\) 5.84789 0.228148
\(658\) −3.97403 −0.154924
\(659\) −3.35032 −0.130510 −0.0652549 0.997869i \(-0.520786\pi\)
−0.0652549 + 0.997869i \(0.520786\pi\)
\(660\) 4.22014 0.164269
\(661\) −4.74806 −0.184678 −0.0923391 0.995728i \(-0.529434\pi\)
−0.0923391 + 0.995728i \(0.529434\pi\)
\(662\) 15.5134 0.602946
\(663\) −4.07867 −0.158402
\(664\) 31.8090 1.23443
\(665\) 6.66509 0.258461
\(666\) 0.519371 0.0201252
\(667\) −12.2216 −0.473224
\(668\) −31.4921 −1.21847
\(669\) 1.20864 0.0467288
\(670\) 6.38633 0.246725
\(671\) 14.4854 0.559203
\(672\) −8.55187 −0.329895
\(673\) −32.3093 −1.24543 −0.622716 0.782448i \(-0.713971\pi\)
−0.622716 + 0.782448i \(0.713971\pi\)
\(674\) −0.134484 −0.00518013
\(675\) 5.60229 0.215632
\(676\) −6.25571 −0.240604
\(677\) 37.3496 1.43546 0.717731 0.696321i \(-0.245181\pi\)
0.717731 + 0.696321i \(0.245181\pi\)
\(678\) −19.0460 −0.731459
\(679\) 9.95302 0.381962
\(680\) 1.44816 0.0555343
\(681\) 41.5442 1.59198
\(682\) 6.79128 0.260052
\(683\) −18.9079 −0.723489 −0.361745 0.932277i \(-0.617819\pi\)
−0.361745 + 0.932277i \(0.617819\pi\)
\(684\) 7.25693 0.277476
\(685\) −13.2511 −0.506299
\(686\) 0.614026 0.0234436
\(687\) −1.52615 −0.0582263
\(688\) −4.36183 −0.166293
\(689\) 14.5974 0.556118
\(690\) −1.36830 −0.0520904
\(691\) 47.6790 1.81379 0.906897 0.421353i \(-0.138445\pi\)
0.906897 + 0.421353i \(0.138445\pi\)
\(692\) 37.7772 1.43607
\(693\) −1.14302 −0.0434198
\(694\) 8.70911 0.330593
\(695\) −4.86864 −0.184678
\(696\) 28.4171 1.07715
\(697\) 7.71567 0.292252
\(698\) 9.76152 0.369479
\(699\) 1.39333 0.0527004
\(700\) 1.62297 0.0613426
\(701\) −11.7448 −0.443594 −0.221797 0.975093i \(-0.571192\pi\)
−0.221797 + 0.975093i \(0.571192\pi\)
\(702\) 14.1225 0.533018
\(703\) 8.40352 0.316945
\(704\) 0.543916 0.0204996
\(705\) −9.87737 −0.372003
\(706\) −0.291141 −0.0109572
\(707\) 13.4985 0.507665
\(708\) −5.85969 −0.220221
\(709\) −11.9291 −0.448008 −0.224004 0.974588i \(-0.571913\pi\)
−0.224004 + 0.974588i \(0.571913\pi\)
\(710\) −4.10374 −0.154011
\(711\) −2.19040 −0.0821464
\(712\) −24.8828 −0.932524
\(713\) 9.47862 0.354977
\(714\) 0.610025 0.0228296
\(715\) −6.99481 −0.261591
\(716\) −7.64816 −0.285825
\(717\) −2.46657 −0.0921156
\(718\) 10.1773 0.379815
\(719\) 29.9119 1.11553 0.557764 0.830000i \(-0.311660\pi\)
0.557764 + 0.830000i \(0.311660\pi\)
\(720\) 1.26122 0.0470028
\(721\) −8.95643 −0.333555
\(722\) −15.6106 −0.580968
\(723\) 42.9953 1.59901
\(724\) −11.5387 −0.428833
\(725\) −8.37011 −0.310858
\(726\) −7.58773 −0.281607
\(727\) 43.6537 1.61903 0.809514 0.587101i \(-0.199731\pi\)
0.809514 + 0.587101i \(0.199731\pi\)
\(728\) 9.13291 0.338488
\(729\) 30.0355 1.11243
\(730\) −5.35241 −0.198102
\(731\) 1.51035 0.0558624
\(732\) −21.0582 −0.778333
\(733\) −34.8525 −1.28731 −0.643653 0.765318i \(-0.722582\pi\)
−0.643653 + 0.765318i \(0.722582\pi\)
\(734\) −0.303840 −0.0112149
\(735\) 1.52615 0.0562929
\(736\) −8.18205 −0.301594
\(737\) −17.7208 −0.652753
\(738\) −4.88239 −0.179723
\(739\) 21.8890 0.805200 0.402600 0.915376i \(-0.368107\pi\)
0.402600 + 0.915376i \(0.368107\pi\)
\(740\) 2.04629 0.0752230
\(741\) 41.7600 1.53409
\(742\) −2.18326 −0.0801501
\(743\) 36.3758 1.33450 0.667249 0.744835i \(-0.267472\pi\)
0.667249 + 0.744835i \(0.267472\pi\)
\(744\) −22.0392 −0.807996
\(745\) −9.15495 −0.335411
\(746\) −17.2647 −0.632107
\(747\) −9.59254 −0.350973
\(748\) −1.80008 −0.0658176
\(749\) 13.7420 0.502122
\(750\) −0.937096 −0.0342179
\(751\) −39.5992 −1.44500 −0.722498 0.691373i \(-0.757006\pi\)
−0.722498 + 0.691373i \(0.757006\pi\)
\(752\) −12.1674 −0.443700
\(753\) −2.49152 −0.0907962
\(754\) −21.0997 −0.768405
\(755\) −20.6800 −0.752621
\(756\) 9.09236 0.330686
\(757\) −50.8769 −1.84915 −0.924577 0.380995i \(-0.875581\pi\)
−0.924577 + 0.380995i \(0.875581\pi\)
\(758\) 18.2303 0.662155
\(759\) 3.79676 0.137814
\(760\) −14.8272 −0.537837
\(761\) −37.8763 −1.37302 −0.686508 0.727122i \(-0.740857\pi\)
−0.686508 + 0.727122i \(0.740857\pi\)
\(762\) −4.85632 −0.175926
\(763\) −4.23676 −0.153381
\(764\) 43.3736 1.56920
\(765\) −0.436717 −0.0157895
\(766\) 12.6187 0.455932
\(767\) 9.71234 0.350692
\(768\) 9.71142 0.350431
\(769\) 47.2577 1.70415 0.852077 0.523416i \(-0.175343\pi\)
0.852077 + 0.523416i \(0.175343\pi\)
\(770\) 1.04618 0.0377016
\(771\) −26.8275 −0.966169
\(772\) 13.1867 0.474600
\(773\) 6.76995 0.243498 0.121749 0.992561i \(-0.461150\pi\)
0.121749 + 0.992561i \(0.461150\pi\)
\(774\) −0.955734 −0.0343532
\(775\) 6.49153 0.233183
\(776\) −22.1415 −0.794832
\(777\) 1.92421 0.0690306
\(778\) 0.202978 0.00727710
\(779\) −78.9980 −2.83040
\(780\) 10.1687 0.364098
\(781\) 11.3870 0.407461
\(782\) 0.583645 0.0208711
\(783\) −46.8918 −1.67578
\(784\) 1.87998 0.0671422
\(785\) −1.97961 −0.0706553
\(786\) −19.7908 −0.705913
\(787\) 33.5533 1.19605 0.598024 0.801479i \(-0.295953\pi\)
0.598024 + 0.801479i \(0.295953\pi\)
\(788\) −24.4183 −0.869867
\(789\) −35.5418 −1.26532
\(790\) 2.00481 0.0713281
\(791\) 20.3245 0.722658
\(792\) 2.54276 0.0903531
\(793\) 34.9036 1.23946
\(794\) 1.19452 0.0423920
\(795\) −5.42646 −0.192457
\(796\) 10.9250 0.387225
\(797\) 0.832832 0.0295004 0.0147502 0.999891i \(-0.495305\pi\)
0.0147502 + 0.999891i \(0.495305\pi\)
\(798\) −6.24583 −0.221100
\(799\) 4.21316 0.149051
\(800\) −5.60356 −0.198116
\(801\) 7.50385 0.265136
\(802\) 3.87894 0.136970
\(803\) 14.8519 0.524111
\(804\) 25.7616 0.908542
\(805\) 1.46015 0.0514636
\(806\) 16.3641 0.576400
\(807\) −27.8037 −0.978735
\(808\) −30.0288 −1.05641
\(809\) 36.6078 1.28706 0.643530 0.765421i \(-0.277469\pi\)
0.643530 + 0.765421i \(0.277469\pi\)
\(810\) −4.01410 −0.141041
\(811\) −21.3984 −0.751400 −0.375700 0.926741i \(-0.622598\pi\)
−0.375700 + 0.926741i \(0.622598\pi\)
\(812\) −13.5845 −0.476721
\(813\) −39.8845 −1.39881
\(814\) 1.31905 0.0462325
\(815\) 22.4027 0.784732
\(816\) 1.86773 0.0653838
\(817\) −15.4640 −0.541015
\(818\) −9.52872 −0.333164
\(819\) −2.75419 −0.0962391
\(820\) −19.2363 −0.671760
\(821\) −39.4128 −1.37552 −0.687758 0.725940i \(-0.741405\pi\)
−0.687758 + 0.725940i \(0.741405\pi\)
\(822\) 12.4176 0.433113
\(823\) −4.12219 −0.143691 −0.0718453 0.997416i \(-0.522889\pi\)
−0.0718453 + 0.997416i \(0.522889\pi\)
\(824\) 19.9245 0.694101
\(825\) 2.60025 0.0905291
\(826\) −1.45262 −0.0505432
\(827\) 45.6118 1.58608 0.793038 0.609172i \(-0.208498\pi\)
0.793038 + 0.609172i \(0.208498\pi\)
\(828\) 1.58981 0.0552497
\(829\) 52.2860 1.81597 0.907984 0.419004i \(-0.137621\pi\)
0.907984 + 0.419004i \(0.137621\pi\)
\(830\) 8.77980 0.304751
\(831\) −13.1517 −0.456227
\(832\) 1.31060 0.0454370
\(833\) −0.650974 −0.0225549
\(834\) 4.56238 0.157982
\(835\) −19.4040 −0.671502
\(836\) 18.4304 0.637429
\(837\) 36.3674 1.25704
\(838\) −21.5749 −0.745293
\(839\) −40.3138 −1.39179 −0.695893 0.718145i \(-0.744991\pi\)
−0.695893 + 0.718145i \(0.744991\pi\)
\(840\) −3.39507 −0.117141
\(841\) 41.0588 1.41582
\(842\) 2.01224 0.0693462
\(843\) −8.99483 −0.309798
\(844\) −17.3864 −0.598463
\(845\) −3.85448 −0.132598
\(846\) −2.66604 −0.0916603
\(847\) 8.09707 0.278219
\(848\) −6.68457 −0.229549
\(849\) 4.46222 0.153143
\(850\) 0.399715 0.0137101
\(851\) 1.84100 0.0631086
\(852\) −16.5539 −0.567129
\(853\) −33.6098 −1.15078 −0.575389 0.817880i \(-0.695149\pi\)
−0.575389 + 0.817880i \(0.695149\pi\)
\(854\) −5.22035 −0.178637
\(855\) 4.47138 0.152918
\(856\) −30.5705 −1.04488
\(857\) −18.8306 −0.643240 −0.321620 0.946869i \(-0.604227\pi\)
−0.321620 + 0.946869i \(0.604227\pi\)
\(858\) 6.55480 0.223777
\(859\) −17.1295 −0.584452 −0.292226 0.956349i \(-0.594396\pi\)
−0.292226 + 0.956349i \(0.594396\pi\)
\(860\) −3.76553 −0.128403
\(861\) −18.0887 −0.616461
\(862\) 0.0387131 0.00131857
\(863\) 20.8003 0.708051 0.354026 0.935236i \(-0.384813\pi\)
0.354026 + 0.935236i \(0.384813\pi\)
\(864\) −31.3928 −1.06800
\(865\) 23.2766 0.791427
\(866\) −16.9569 −0.576218
\(867\) 25.2978 0.859159
\(868\) 10.5356 0.357601
\(869\) −5.56295 −0.188710
\(870\) 7.84360 0.265923
\(871\) −42.6994 −1.44682
\(872\) 9.42509 0.319174
\(873\) 6.67714 0.225987
\(874\) −5.97573 −0.202132
\(875\) 1.00000 0.0338062
\(876\) −21.5909 −0.729490
\(877\) −26.1079 −0.881600 −0.440800 0.897605i \(-0.645305\pi\)
−0.440800 + 0.897605i \(0.645305\pi\)
\(878\) 6.12145 0.206589
\(879\) 2.87711 0.0970425
\(880\) 3.20311 0.107977
\(881\) −3.17163 −0.106855 −0.0534275 0.998572i \(-0.517015\pi\)
−0.0534275 + 0.998572i \(0.517015\pi\)
\(882\) 0.411929 0.0138704
\(883\) 0.325001 0.0109371 0.00546857 0.999985i \(-0.498259\pi\)
0.00546857 + 0.999985i \(0.498259\pi\)
\(884\) −4.33743 −0.145884
\(885\) −3.61047 −0.121365
\(886\) −18.3976 −0.618079
\(887\) −40.4310 −1.35754 −0.678770 0.734350i \(-0.737487\pi\)
−0.678770 + 0.734350i \(0.737487\pi\)
\(888\) −4.28060 −0.143647
\(889\) 5.18231 0.173809
\(890\) −6.86807 −0.230218
\(891\) 11.1383 0.373147
\(892\) 1.28532 0.0430357
\(893\) −43.1370 −1.44352
\(894\) 8.57907 0.286927
\(895\) −4.71244 −0.157520
\(896\) −11.4031 −0.380952
\(897\) 9.14857 0.305462
\(898\) 7.75300 0.258721
\(899\) −54.3348 −1.81217
\(900\) 1.08880 0.0362932
\(901\) 2.31464 0.0771118
\(902\) −12.3998 −0.412868
\(903\) −3.54089 −0.117833
\(904\) −45.2140 −1.50379
\(905\) −7.10961 −0.236332
\(906\) 19.3791 0.643827
\(907\) −15.6741 −0.520449 −0.260225 0.965548i \(-0.583797\pi\)
−0.260225 + 0.965548i \(0.583797\pi\)
\(908\) 44.1799 1.46616
\(909\) 9.05571 0.300359
\(910\) 2.52083 0.0835649
\(911\) −29.4928 −0.977139 −0.488570 0.872525i \(-0.662481\pi\)
−0.488570 + 0.872525i \(0.662481\pi\)
\(912\) −19.1230 −0.633227
\(913\) −24.3622 −0.806270
\(914\) −18.9733 −0.627581
\(915\) −12.9751 −0.428943
\(916\) −1.62297 −0.0536245
\(917\) 21.1192 0.697419
\(918\) 2.23932 0.0739086
\(919\) 38.2326 1.26118 0.630589 0.776117i \(-0.282814\pi\)
0.630589 + 0.776117i \(0.282814\pi\)
\(920\) −3.24825 −0.107092
\(921\) −15.1593 −0.499516
\(922\) 6.79765 0.223869
\(923\) 27.4379 0.903129
\(924\) 4.22014 0.138832
\(925\) 1.26083 0.0414557
\(926\) 11.0240 0.362273
\(927\) −6.00856 −0.197347
\(928\) 46.9024 1.53965
\(929\) 13.2421 0.434460 0.217230 0.976120i \(-0.430298\pi\)
0.217230 + 0.976120i \(0.430298\pi\)
\(930\) −6.08318 −0.199475
\(931\) 6.66509 0.218439
\(932\) 1.48172 0.0485354
\(933\) 5.14457 0.168426
\(934\) 0.843024 0.0275846
\(935\) −1.10913 −0.0362724
\(936\) 6.12696 0.200266
\(937\) −13.6877 −0.447158 −0.223579 0.974686i \(-0.571774\pi\)
−0.223579 + 0.974686i \(0.571774\pi\)
\(938\) 6.38633 0.208521
\(939\) 7.73633 0.252466
\(940\) −10.5040 −0.342603
\(941\) −28.2048 −0.919449 −0.459725 0.888062i \(-0.652052\pi\)
−0.459725 + 0.888062i \(0.652052\pi\)
\(942\) 1.85508 0.0604419
\(943\) −17.3065 −0.563576
\(944\) −4.44754 −0.144755
\(945\) 5.60229 0.182243
\(946\) −2.42728 −0.0789176
\(947\) −38.4049 −1.24799 −0.623996 0.781428i \(-0.714492\pi\)
−0.623996 + 0.781428i \(0.714492\pi\)
\(948\) 8.08715 0.262658
\(949\) 35.7866 1.16168
\(950\) −4.09254 −0.132779
\(951\) 27.5512 0.893408
\(952\) 1.44816 0.0469350
\(953\) 15.3032 0.495719 0.247860 0.968796i \(-0.420273\pi\)
0.247860 + 0.968796i \(0.420273\pi\)
\(954\) −1.46468 −0.0474207
\(955\) 26.7248 0.864794
\(956\) −2.62305 −0.0848355
\(957\) −21.7644 −0.703543
\(958\) −12.9274 −0.417665
\(959\) −13.2511 −0.427901
\(960\) −0.487204 −0.0157244
\(961\) 11.1399 0.359353
\(962\) 3.17833 0.102474
\(963\) 9.21905 0.297080
\(964\) 45.7230 1.47264
\(965\) 8.12503 0.261554
\(966\) −1.36830 −0.0440244
\(967\) 17.0172 0.547237 0.273619 0.961838i \(-0.411779\pi\)
0.273619 + 0.961838i \(0.411779\pi\)
\(968\) −18.0127 −0.578951
\(969\) 6.62166 0.212718
\(970\) −6.11141 −0.196226
\(971\) −44.5645 −1.43014 −0.715071 0.699052i \(-0.753606\pi\)
−0.715071 + 0.699052i \(0.753606\pi\)
\(972\) 11.0848 0.355544
\(973\) −4.86864 −0.156081
\(974\) −0.124798 −0.00399879
\(975\) 6.26549 0.200656
\(976\) −15.9833 −0.511613
\(977\) 42.6678 1.36506 0.682532 0.730856i \(-0.260879\pi\)
0.682532 + 0.730856i \(0.260879\pi\)
\(978\) −20.9935 −0.671297
\(979\) 19.0575 0.609081
\(980\) 1.62297 0.0518439
\(981\) −2.84230 −0.0907476
\(982\) 0.952486 0.0303950
\(983\) −42.8223 −1.36582 −0.682909 0.730503i \(-0.739286\pi\)
−0.682909 + 0.730503i \(0.739286\pi\)
\(984\) 40.2401 1.28281
\(985\) −15.0454 −0.479387
\(986\) −3.34566 −0.106548
\(987\) −9.87737 −0.314400
\(988\) 44.4094 1.41285
\(989\) −3.38776 −0.107725
\(990\) 0.701844 0.0223061
\(991\) 57.8421 1.83741 0.918707 0.394940i \(-0.129235\pi\)
0.918707 + 0.394940i \(0.129235\pi\)
\(992\) −36.3756 −1.15493
\(993\) 38.5583 1.22361
\(994\) −4.10374 −0.130163
\(995\) 6.73146 0.213402
\(996\) 35.4165 1.12222
\(997\) −24.1233 −0.763991 −0.381996 0.924164i \(-0.624763\pi\)
−0.381996 + 0.924164i \(0.624763\pi\)
\(998\) 9.36350 0.296396
\(999\) 7.06352 0.223480
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 \(a_p\))