Properties

Label 8001.2.a.o.1.10
Level 8001
Weight 2
Character 8001.1
Self dual Yes
Analytic conductor 63.888
Analytic rank 1
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8001 = 3^{2} \cdot 7 \cdot 127 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8001.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.8883066572\)
Analytic rank: \(1\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{17}]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.10
Root \(-0.910949\)
Character \(\chi\) = 8001.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.910949 q^{2}\) \(-1.17017 q^{4}\) \(+2.06751 q^{5}\) \(+1.00000 q^{7}\) \(-2.88787 q^{8}\) \(+O(q^{10})\) \(q\)\(+0.910949 q^{2}\) \(-1.17017 q^{4}\) \(+2.06751 q^{5}\) \(+1.00000 q^{7}\) \(-2.88787 q^{8}\) \(+1.88339 q^{10}\) \(-4.76209 q^{11}\) \(+2.03773 q^{13}\) \(+0.910949 q^{14}\) \(-0.290355 q^{16}\) \(-0.854179 q^{17}\) \(+2.23714 q^{19}\) \(-2.41934 q^{20}\) \(-4.33802 q^{22}\) \(-5.99633 q^{23}\) \(-0.725414 q^{25}\) \(+1.85627 q^{26}\) \(-1.17017 q^{28}\) \(+5.46515 q^{29}\) \(+3.43070 q^{31}\) \(+5.51123 q^{32}\) \(-0.778113 q^{34}\) \(+2.06751 q^{35}\) \(+1.22426 q^{37}\) \(+2.03792 q^{38}\) \(-5.97068 q^{40}\) \(+7.05781 q^{41}\) \(-5.15064 q^{43}\) \(+5.57246 q^{44}\) \(-5.46235 q^{46}\) \(-7.66065 q^{47}\) \(+1.00000 q^{49}\) \(-0.660815 q^{50}\) \(-2.38450 q^{52}\) \(+1.39018 q^{53}\) \(-9.84565 q^{55}\) \(-2.88787 q^{56}\) \(+4.97848 q^{58}\) \(-8.77497 q^{59}\) \(+6.04889 q^{61}\) \(+3.12519 q^{62}\) \(+5.60116 q^{64}\) \(+4.21303 q^{65}\) \(-5.42409 q^{67}\) \(+0.999536 q^{68}\) \(+1.88339 q^{70}\) \(+1.57089 q^{71}\) \(-9.67049 q^{73}\) \(+1.11524 q^{74}\) \(-2.61784 q^{76}\) \(-4.76209 q^{77}\) \(-4.49693 q^{79}\) \(-0.600311 q^{80}\) \(+6.42930 q^{82}\) \(-8.88129 q^{83}\) \(-1.76602 q^{85}\) \(-4.69197 q^{86}\) \(+13.7523 q^{88}\) \(-10.1548 q^{89}\) \(+2.03773 q^{91}\) \(+7.01673 q^{92}\) \(-6.97846 q^{94}\) \(+4.62530 q^{95}\) \(+1.09551 q^{97}\) \(+0.910949 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 4q^{2} \) \(\mathstrut +\mathstrut 10q^{4} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 13q^{7} \) \(\mathstrut -\mathstrut 9q^{8} \) \(\mathstrut +\mathstrut 6q^{10} \) \(\mathstrut -\mathstrut 3q^{11} \) \(\mathstrut +\mathstrut 21q^{13} \) \(\mathstrut -\mathstrut 4q^{14} \) \(\mathstrut +\mathstrut 8q^{16} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 29q^{20} \) \(\mathstrut +\mathstrut q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut q^{25} \) \(\mathstrut -\mathstrut 22q^{26} \) \(\mathstrut +\mathstrut 10q^{28} \) \(\mathstrut -\mathstrut 21q^{29} \) \(\mathstrut -\mathstrut 7q^{31} \) \(\mathstrut -\mathstrut 12q^{32} \) \(\mathstrut +\mathstrut 2q^{34} \) \(\mathstrut -\mathstrut 12q^{35} \) \(\mathstrut +\mathstrut 7q^{37} \) \(\mathstrut +\mathstrut 9q^{38} \) \(\mathstrut +\mathstrut 29q^{40} \) \(\mathstrut -\mathstrut 21q^{41} \) \(\mathstrut -\mathstrut 9q^{43} \) \(\mathstrut +\mathstrut 2q^{44} \) \(\mathstrut -\mathstrut 28q^{46} \) \(\mathstrut -\mathstrut 23q^{47} \) \(\mathstrut +\mathstrut 13q^{49} \) \(\mathstrut -\mathstrut 15q^{50} \) \(\mathstrut +\mathstrut 15q^{52} \) \(\mathstrut -\mathstrut 31q^{53} \) \(\mathstrut -\mathstrut 8q^{55} \) \(\mathstrut -\mathstrut 9q^{56} \) \(\mathstrut -\mathstrut 25q^{58} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut +\mathstrut 29q^{61} \) \(\mathstrut +\mathstrut 3q^{62} \) \(\mathstrut +\mathstrut 9q^{64} \) \(\mathstrut -\mathstrut 30q^{65} \) \(\mathstrut -\mathstrut 18q^{67} \) \(\mathstrut -\mathstrut 34q^{68} \) \(\mathstrut +\mathstrut 6q^{70} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 19q^{74} \) \(\mathstrut -\mathstrut 3q^{77} \) \(\mathstrut -\mathstrut 28q^{79} \) \(\mathstrut -\mathstrut 26q^{80} \) \(\mathstrut +\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 26q^{83} \) \(\mathstrut +\mathstrut 20q^{85} \) \(\mathstrut +\mathstrut 2q^{86} \) \(\mathstrut -\mathstrut 17q^{88} \) \(\mathstrut -\mathstrut 44q^{89} \) \(\mathstrut +\mathstrut 21q^{91} \) \(\mathstrut -\mathstrut 6q^{92} \) \(\mathstrut -\mathstrut 9q^{94} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 17q^{97} \) \(\mathstrut -\mathstrut 4q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.910949 0.644138 0.322069 0.946716i \(-0.395622\pi\)
0.322069 + 0.946716i \(0.395622\pi\)
\(3\) 0 0
\(4\) −1.17017 −0.585086
\(5\) 2.06751 0.924617 0.462309 0.886719i \(-0.347021\pi\)
0.462309 + 0.886719i \(0.347021\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) −2.88787 −1.02101
\(9\) 0 0
\(10\) 1.88339 0.595581
\(11\) −4.76209 −1.43582 −0.717912 0.696134i \(-0.754902\pi\)
−0.717912 + 0.696134i \(0.754902\pi\)
\(12\) 0 0
\(13\) 2.03773 0.565166 0.282583 0.959243i \(-0.408809\pi\)
0.282583 + 0.959243i \(0.408809\pi\)
\(14\) 0.910949 0.243461
\(15\) 0 0
\(16\) −0.290355 −0.0725888
\(17\) −0.854179 −0.207169 −0.103584 0.994621i \(-0.533031\pi\)
−0.103584 + 0.994621i \(0.533031\pi\)
\(18\) 0 0
\(19\) 2.23714 0.513235 0.256617 0.966513i \(-0.417392\pi\)
0.256617 + 0.966513i \(0.417392\pi\)
\(20\) −2.41934 −0.540980
\(21\) 0 0
\(22\) −4.33802 −0.924869
\(23\) −5.99633 −1.25032 −0.625160 0.780496i \(-0.714966\pi\)
−0.625160 + 0.780496i \(0.714966\pi\)
\(24\) 0 0
\(25\) −0.725414 −0.145083
\(26\) 1.85627 0.364045
\(27\) 0 0
\(28\) −1.17017 −0.221142
\(29\) 5.46515 1.01485 0.507427 0.861695i \(-0.330597\pi\)
0.507427 + 0.861695i \(0.330597\pi\)
\(30\) 0 0
\(31\) 3.43070 0.616172 0.308086 0.951358i \(-0.400312\pi\)
0.308086 + 0.951358i \(0.400312\pi\)
\(32\) 5.51123 0.974257
\(33\) 0 0
\(34\) −0.778113 −0.133445
\(35\) 2.06751 0.349472
\(36\) 0 0
\(37\) 1.22426 0.201268 0.100634 0.994924i \(-0.467913\pi\)
0.100634 + 0.994924i \(0.467913\pi\)
\(38\) 2.03792 0.330594
\(39\) 0 0
\(40\) −5.97068 −0.944048
\(41\) 7.05781 1.10224 0.551122 0.834425i \(-0.314200\pi\)
0.551122 + 0.834425i \(0.314200\pi\)
\(42\) 0 0
\(43\) −5.15064 −0.785465 −0.392732 0.919653i \(-0.628470\pi\)
−0.392732 + 0.919653i \(0.628470\pi\)
\(44\) 5.57246 0.840080
\(45\) 0 0
\(46\) −5.46235 −0.805380
\(47\) −7.66065 −1.11742 −0.558710 0.829363i \(-0.688704\pi\)
−0.558710 + 0.829363i \(0.688704\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −0.660815 −0.0934534
\(51\) 0 0
\(52\) −2.38450 −0.330670
\(53\) 1.39018 0.190956 0.0954779 0.995432i \(-0.469562\pi\)
0.0954779 + 0.995432i \(0.469562\pi\)
\(54\) 0 0
\(55\) −9.84565 −1.32759
\(56\) −2.88787 −0.385907
\(57\) 0 0
\(58\) 4.97848 0.653706
\(59\) −8.77497 −1.14240 −0.571202 0.820809i \(-0.693523\pi\)
−0.571202 + 0.820809i \(0.693523\pi\)
\(60\) 0 0
\(61\) 6.04889 0.774481 0.387240 0.921979i \(-0.373428\pi\)
0.387240 + 0.921979i \(0.373428\pi\)
\(62\) 3.12519 0.396900
\(63\) 0 0
\(64\) 5.60116 0.700145
\(65\) 4.21303 0.522562
\(66\) 0 0
\(67\) −5.42409 −0.662658 −0.331329 0.943515i \(-0.607497\pi\)
−0.331329 + 0.943515i \(0.607497\pi\)
\(68\) 0.999536 0.121212
\(69\) 0 0
\(70\) 1.88339 0.225109
\(71\) 1.57089 0.186431 0.0932153 0.995646i \(-0.470286\pi\)
0.0932153 + 0.995646i \(0.470286\pi\)
\(72\) 0 0
\(73\) −9.67049 −1.13185 −0.565923 0.824458i \(-0.691480\pi\)
−0.565923 + 0.824458i \(0.691480\pi\)
\(74\) 1.11524 0.129644
\(75\) 0 0
\(76\) −2.61784 −0.300287
\(77\) −4.76209 −0.542690
\(78\) 0 0
\(79\) −4.49693 −0.505944 −0.252972 0.967474i \(-0.581408\pi\)
−0.252972 + 0.967474i \(0.581408\pi\)
\(80\) −0.600311 −0.0671168
\(81\) 0 0
\(82\) 6.42930 0.709998
\(83\) −8.88129 −0.974848 −0.487424 0.873165i \(-0.662063\pi\)
−0.487424 + 0.873165i \(0.662063\pi\)
\(84\) 0 0
\(85\) −1.76602 −0.191552
\(86\) −4.69197 −0.505948
\(87\) 0 0
\(88\) 13.7523 1.46600
\(89\) −10.1548 −1.07641 −0.538204 0.842815i \(-0.680897\pi\)
−0.538204 + 0.842815i \(0.680897\pi\)
\(90\) 0 0
\(91\) 2.03773 0.213613
\(92\) 7.01673 0.731545
\(93\) 0 0
\(94\) −6.97846 −0.719773
\(95\) 4.62530 0.474546
\(96\) 0 0
\(97\) 1.09551 0.111233 0.0556163 0.998452i \(-0.482288\pi\)
0.0556163 + 0.998452i \(0.482288\pi\)
\(98\) 0.910949 0.0920198
\(99\) 0 0
\(100\) 0.848859 0.0848859
\(101\) −3.53703 −0.351948 −0.175974 0.984395i \(-0.556307\pi\)
−0.175974 + 0.984395i \(0.556307\pi\)
\(102\) 0 0
\(103\) 1.77000 0.174404 0.0872018 0.996191i \(-0.472208\pi\)
0.0872018 + 0.996191i \(0.472208\pi\)
\(104\) −5.88470 −0.577042
\(105\) 0 0
\(106\) 1.26638 0.123002
\(107\) −11.4134 −1.10338 −0.551689 0.834050i \(-0.686017\pi\)
−0.551689 + 0.834050i \(0.686017\pi\)
\(108\) 0 0
\(109\) −15.2946 −1.46496 −0.732480 0.680788i \(-0.761637\pi\)
−0.732480 + 0.680788i \(0.761637\pi\)
\(110\) −8.96889 −0.855150
\(111\) 0 0
\(112\) −0.290355 −0.0274360
\(113\) 15.9081 1.49651 0.748254 0.663413i \(-0.230893\pi\)
0.748254 + 0.663413i \(0.230893\pi\)
\(114\) 0 0
\(115\) −12.3975 −1.15607
\(116\) −6.39517 −0.593776
\(117\) 0 0
\(118\) −7.99355 −0.735866
\(119\) −0.854179 −0.0783024
\(120\) 0 0
\(121\) 11.6775 1.06159
\(122\) 5.51023 0.498873
\(123\) 0 0
\(124\) −4.01451 −0.360514
\(125\) −11.8373 −1.05876
\(126\) 0 0
\(127\) −1.00000 −0.0887357
\(128\) −5.92009 −0.523267
\(129\) 0 0
\(130\) 3.83786 0.336602
\(131\) −14.7361 −1.28750 −0.643749 0.765237i \(-0.722622\pi\)
−0.643749 + 0.765237i \(0.722622\pi\)
\(132\) 0 0
\(133\) 2.23714 0.193985
\(134\) −4.94107 −0.426844
\(135\) 0 0
\(136\) 2.46675 0.211522
\(137\) −7.61686 −0.650752 −0.325376 0.945585i \(-0.605491\pi\)
−0.325376 + 0.945585i \(0.605491\pi\)
\(138\) 0 0
\(139\) 5.10352 0.432875 0.216437 0.976296i \(-0.430556\pi\)
0.216437 + 0.976296i \(0.430556\pi\)
\(140\) −2.41934 −0.204471
\(141\) 0 0
\(142\) 1.43100 0.120087
\(143\) −9.70387 −0.811478
\(144\) 0 0
\(145\) 11.2992 0.938351
\(146\) −8.80933 −0.729065
\(147\) 0 0
\(148\) −1.43260 −0.117759
\(149\) 0.345030 0.0282659 0.0141330 0.999900i \(-0.495501\pi\)
0.0141330 + 0.999900i \(0.495501\pi\)
\(150\) 0 0
\(151\) 6.54380 0.532527 0.266264 0.963900i \(-0.414211\pi\)
0.266264 + 0.963900i \(0.414211\pi\)
\(152\) −6.46056 −0.524020
\(153\) 0 0
\(154\) −4.33802 −0.349568
\(155\) 7.09300 0.569724
\(156\) 0 0
\(157\) 5.25736 0.419583 0.209792 0.977746i \(-0.432721\pi\)
0.209792 + 0.977746i \(0.432721\pi\)
\(158\) −4.09647 −0.325898
\(159\) 0 0
\(160\) 11.3945 0.900815
\(161\) −5.99633 −0.472577
\(162\) 0 0
\(163\) −4.27474 −0.334824 −0.167412 0.985887i \(-0.553541\pi\)
−0.167412 + 0.985887i \(0.553541\pi\)
\(164\) −8.25885 −0.644907
\(165\) 0 0
\(166\) −8.09040 −0.627937
\(167\) −15.9971 −1.23790 −0.618948 0.785432i \(-0.712441\pi\)
−0.618948 + 0.785432i \(0.712441\pi\)
\(168\) 0 0
\(169\) −8.84764 −0.680588
\(170\) −1.60876 −0.123386
\(171\) 0 0
\(172\) 6.02713 0.459564
\(173\) −7.16537 −0.544773 −0.272387 0.962188i \(-0.587813\pi\)
−0.272387 + 0.962188i \(0.587813\pi\)
\(174\) 0 0
\(175\) −0.725414 −0.0548361
\(176\) 1.38270 0.104225
\(177\) 0 0
\(178\) −9.25051 −0.693355
\(179\) −0.409220 −0.0305866 −0.0152933 0.999883i \(-0.504868\pi\)
−0.0152933 + 0.999883i \(0.504868\pi\)
\(180\) 0 0
\(181\) −10.5918 −0.787279 −0.393639 0.919265i \(-0.628784\pi\)
−0.393639 + 0.919265i \(0.628784\pi\)
\(182\) 1.85627 0.137596
\(183\) 0 0
\(184\) 17.3166 1.27660
\(185\) 2.53117 0.186096
\(186\) 0 0
\(187\) 4.06767 0.297458
\(188\) 8.96427 0.653787
\(189\) 0 0
\(190\) 4.21341 0.305673
\(191\) −14.3830 −1.04072 −0.520358 0.853948i \(-0.674201\pi\)
−0.520358 + 0.853948i \(0.674201\pi\)
\(192\) 0 0
\(193\) 4.91728 0.353954 0.176977 0.984215i \(-0.443368\pi\)
0.176977 + 0.984215i \(0.443368\pi\)
\(194\) 0.997957 0.0716491
\(195\) 0 0
\(196\) −1.17017 −0.0835837
\(197\) 18.4666 1.31569 0.657846 0.753152i \(-0.271468\pi\)
0.657846 + 0.753152i \(0.271468\pi\)
\(198\) 0 0
\(199\) −15.1069 −1.07090 −0.535450 0.844567i \(-0.679858\pi\)
−0.535450 + 0.844567i \(0.679858\pi\)
\(200\) 2.09490 0.148132
\(201\) 0 0
\(202\) −3.22206 −0.226703
\(203\) 5.46515 0.383578
\(204\) 0 0
\(205\) 14.5921 1.01915
\(206\) 1.61238 0.112340
\(207\) 0 0
\(208\) −0.591666 −0.0410247
\(209\) −10.6535 −0.736915
\(210\) 0 0
\(211\) 8.27452 0.569641 0.284821 0.958581i \(-0.408066\pi\)
0.284821 + 0.958581i \(0.408066\pi\)
\(212\) −1.62675 −0.111726
\(213\) 0 0
\(214\) −10.3971 −0.710728
\(215\) −10.6490 −0.726254
\(216\) 0 0
\(217\) 3.43070 0.232891
\(218\) −13.9326 −0.943637
\(219\) 0 0
\(220\) 11.5211 0.776753
\(221\) −1.74059 −0.117085
\(222\) 0 0
\(223\) 9.20017 0.616089 0.308044 0.951372i \(-0.400325\pi\)
0.308044 + 0.951372i \(0.400325\pi\)
\(224\) 5.51123 0.368235
\(225\) 0 0
\(226\) 14.4915 0.963958
\(227\) −4.61206 −0.306113 −0.153057 0.988217i \(-0.548912\pi\)
−0.153057 + 0.988217i \(0.548912\pi\)
\(228\) 0 0
\(229\) 8.47798 0.560240 0.280120 0.959965i \(-0.409626\pi\)
0.280120 + 0.959965i \(0.409626\pi\)
\(230\) −11.2934 −0.744668
\(231\) 0 0
\(232\) −15.7826 −1.03618
\(233\) 11.9704 0.784209 0.392104 0.919921i \(-0.371747\pi\)
0.392104 + 0.919921i \(0.371747\pi\)
\(234\) 0 0
\(235\) −15.8384 −1.03319
\(236\) 10.2682 0.668404
\(237\) 0 0
\(238\) −0.778113 −0.0504376
\(239\) 20.9024 1.35206 0.676031 0.736873i \(-0.263699\pi\)
0.676031 + 0.736873i \(0.263699\pi\)
\(240\) 0 0
\(241\) 5.81959 0.374873 0.187436 0.982277i \(-0.439982\pi\)
0.187436 + 0.982277i \(0.439982\pi\)
\(242\) 10.6376 0.683810
\(243\) 0 0
\(244\) −7.07824 −0.453138
\(245\) 2.06751 0.132088
\(246\) 0 0
\(247\) 4.55869 0.290063
\(248\) −9.90740 −0.629121
\(249\) 0 0
\(250\) −10.7832 −0.681990
\(251\) −0.00650335 −0.000410488 0 −0.000205244 1.00000i \(-0.500065\pi\)
−0.000205244 1.00000i \(0.500065\pi\)
\(252\) 0 0
\(253\) 28.5550 1.79524
\(254\) −0.910949 −0.0571580
\(255\) 0 0
\(256\) −16.5952 −1.03720
\(257\) −21.6261 −1.34900 −0.674498 0.738276i \(-0.735640\pi\)
−0.674498 + 0.738276i \(0.735640\pi\)
\(258\) 0 0
\(259\) 1.22426 0.0760721
\(260\) −4.92997 −0.305744
\(261\) 0 0
\(262\) −13.4238 −0.829326
\(263\) −6.14267 −0.378773 −0.189386 0.981903i \(-0.560650\pi\)
−0.189386 + 0.981903i \(0.560650\pi\)
\(264\) 0 0
\(265\) 2.87421 0.176561
\(266\) 2.03792 0.124953
\(267\) 0 0
\(268\) 6.34712 0.387712
\(269\) 20.1163 1.22651 0.613255 0.789885i \(-0.289860\pi\)
0.613255 + 0.789885i \(0.289860\pi\)
\(270\) 0 0
\(271\) −13.3909 −0.813440 −0.406720 0.913553i \(-0.633327\pi\)
−0.406720 + 0.913553i \(0.633327\pi\)
\(272\) 0.248015 0.0150381
\(273\) 0 0
\(274\) −6.93857 −0.419174
\(275\) 3.45449 0.208313
\(276\) 0 0
\(277\) 8.05697 0.484096 0.242048 0.970264i \(-0.422181\pi\)
0.242048 + 0.970264i \(0.422181\pi\)
\(278\) 4.64905 0.278831
\(279\) 0 0
\(280\) −5.97068 −0.356816
\(281\) −27.8734 −1.66279 −0.831395 0.555682i \(-0.812457\pi\)
−0.831395 + 0.555682i \(0.812457\pi\)
\(282\) 0 0
\(283\) −10.1043 −0.600639 −0.300320 0.953839i \(-0.597093\pi\)
−0.300320 + 0.953839i \(0.597093\pi\)
\(284\) −1.83821 −0.109078
\(285\) 0 0
\(286\) −8.83973 −0.522704
\(287\) 7.05781 0.416609
\(288\) 0 0
\(289\) −16.2704 −0.957081
\(290\) 10.2930 0.604428
\(291\) 0 0
\(292\) 11.3161 0.662227
\(293\) −5.16465 −0.301722 −0.150861 0.988555i \(-0.548205\pi\)
−0.150861 + 0.988555i \(0.548205\pi\)
\(294\) 0 0
\(295\) −18.1423 −1.05629
\(296\) −3.53551 −0.205497
\(297\) 0 0
\(298\) 0.314305 0.0182072
\(299\) −12.2189 −0.706638
\(300\) 0 0
\(301\) −5.15064 −0.296878
\(302\) 5.96107 0.343021
\(303\) 0 0
\(304\) −0.649565 −0.0372551
\(305\) 12.5061 0.716098
\(306\) 0 0
\(307\) 3.03374 0.173144 0.0865722 0.996246i \(-0.472409\pi\)
0.0865722 + 0.996246i \(0.472409\pi\)
\(308\) 5.57246 0.317520
\(309\) 0 0
\(310\) 6.46136 0.366981
\(311\) −22.1371 −1.25528 −0.627640 0.778504i \(-0.715979\pi\)
−0.627640 + 0.778504i \(0.715979\pi\)
\(312\) 0 0
\(313\) 9.66850 0.546496 0.273248 0.961944i \(-0.411902\pi\)
0.273248 + 0.961944i \(0.411902\pi\)
\(314\) 4.78919 0.270270
\(315\) 0 0
\(316\) 5.26218 0.296021
\(317\) 9.91891 0.557101 0.278551 0.960422i \(-0.410146\pi\)
0.278551 + 0.960422i \(0.410146\pi\)
\(318\) 0 0
\(319\) −26.0255 −1.45715
\(320\) 11.5804 0.647366
\(321\) 0 0
\(322\) −5.46235 −0.304405
\(323\) −1.91092 −0.106326
\(324\) 0 0
\(325\) −1.47820 −0.0819958
\(326\) −3.89408 −0.215673
\(327\) 0 0
\(328\) −20.3820 −1.12541
\(329\) −7.66065 −0.422345
\(330\) 0 0
\(331\) 22.7606 1.25104 0.625518 0.780210i \(-0.284888\pi\)
0.625518 + 0.780210i \(0.284888\pi\)
\(332\) 10.3926 0.570370
\(333\) 0 0
\(334\) −14.5726 −0.797376
\(335\) −11.2143 −0.612705
\(336\) 0 0
\(337\) 16.9411 0.922840 0.461420 0.887182i \(-0.347340\pi\)
0.461420 + 0.887182i \(0.347340\pi\)
\(338\) −8.05975 −0.438393
\(339\) 0 0
\(340\) 2.06655 0.112074
\(341\) −16.3373 −0.884715
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 14.8743 0.801971
\(345\) 0 0
\(346\) −6.52729 −0.350909
\(347\) −35.6135 −1.91183 −0.955917 0.293636i \(-0.905135\pi\)
−0.955917 + 0.293636i \(0.905135\pi\)
\(348\) 0 0
\(349\) −0.202587 −0.0108443 −0.00542213 0.999985i \(-0.501726\pi\)
−0.00542213 + 0.999985i \(0.501726\pi\)
\(350\) −0.660815 −0.0353221
\(351\) 0 0
\(352\) −26.2450 −1.39886
\(353\) −14.0659 −0.748653 −0.374327 0.927297i \(-0.622126\pi\)
−0.374327 + 0.927297i \(0.622126\pi\)
\(354\) 0 0
\(355\) 3.24783 0.172377
\(356\) 11.8829 0.629791
\(357\) 0 0
\(358\) −0.372779 −0.0197020
\(359\) 9.61467 0.507443 0.253722 0.967277i \(-0.418345\pi\)
0.253722 + 0.967277i \(0.418345\pi\)
\(360\) 0 0
\(361\) −13.9952 −0.736590
\(362\) −9.64855 −0.507116
\(363\) 0 0
\(364\) −2.38450 −0.124982
\(365\) −19.9938 −1.04652
\(366\) 0 0
\(367\) −23.8796 −1.24651 −0.623254 0.782020i \(-0.714190\pi\)
−0.623254 + 0.782020i \(0.714190\pi\)
\(368\) 1.74106 0.0907592
\(369\) 0 0
\(370\) 2.30577 0.119871
\(371\) 1.39018 0.0721745
\(372\) 0 0
\(373\) 19.0393 0.985816 0.492908 0.870081i \(-0.335934\pi\)
0.492908 + 0.870081i \(0.335934\pi\)
\(374\) 3.70544 0.191604
\(375\) 0 0
\(376\) 22.1229 1.14090
\(377\) 11.1365 0.573560
\(378\) 0 0
\(379\) −8.43150 −0.433097 −0.216548 0.976272i \(-0.569480\pi\)
−0.216548 + 0.976272i \(0.569480\pi\)
\(380\) −5.41240 −0.277650
\(381\) 0 0
\(382\) −13.1022 −0.670365
\(383\) 22.7597 1.16296 0.581482 0.813559i \(-0.302473\pi\)
0.581482 + 0.813559i \(0.302473\pi\)
\(384\) 0 0
\(385\) −9.84565 −0.501781
\(386\) 4.47939 0.227995
\(387\) 0 0
\(388\) −1.28194 −0.0650806
\(389\) −15.4243 −0.782041 −0.391021 0.920382i \(-0.627878\pi\)
−0.391021 + 0.920382i \(0.627878\pi\)
\(390\) 0 0
\(391\) 5.12194 0.259027
\(392\) −2.88787 −0.145859
\(393\) 0 0
\(394\) 16.8222 0.847488
\(395\) −9.29743 −0.467804
\(396\) 0 0
\(397\) −7.28576 −0.365662 −0.182831 0.983144i \(-0.558526\pi\)
−0.182831 + 0.983144i \(0.558526\pi\)
\(398\) −13.7616 −0.689807
\(399\) 0 0
\(400\) 0.210628 0.0105314
\(401\) −25.8458 −1.29068 −0.645340 0.763896i \(-0.723284\pi\)
−0.645340 + 0.763896i \(0.723284\pi\)
\(402\) 0 0
\(403\) 6.99086 0.348239
\(404\) 4.13894 0.205920
\(405\) 0 0
\(406\) 4.97848 0.247078
\(407\) −5.83005 −0.288985
\(408\) 0 0
\(409\) −18.8712 −0.933120 −0.466560 0.884490i \(-0.654507\pi\)
−0.466560 + 0.884490i \(0.654507\pi\)
\(410\) 13.2926 0.656476
\(411\) 0 0
\(412\) −2.07121 −0.102041
\(413\) −8.77497 −0.431788
\(414\) 0 0
\(415\) −18.3621 −0.901361
\(416\) 11.2304 0.550617
\(417\) 0 0
\(418\) −9.70476 −0.474675
\(419\) −36.8364 −1.79958 −0.899788 0.436328i \(-0.856279\pi\)
−0.899788 + 0.436328i \(0.856279\pi\)
\(420\) 0 0
\(421\) 1.66960 0.0813711 0.0406855 0.999172i \(-0.487046\pi\)
0.0406855 + 0.999172i \(0.487046\pi\)
\(422\) 7.53767 0.366928
\(423\) 0 0
\(424\) −4.01465 −0.194969
\(425\) 0.619633 0.0300566
\(426\) 0 0
\(427\) 6.04889 0.292726
\(428\) 13.3557 0.645571
\(429\) 0 0
\(430\) −9.70068 −0.467808
\(431\) −22.4575 −1.08174 −0.540869 0.841107i \(-0.681905\pi\)
−0.540869 + 0.841107i \(0.681905\pi\)
\(432\) 0 0
\(433\) 34.2436 1.64564 0.822822 0.568299i \(-0.192398\pi\)
0.822822 + 0.568299i \(0.192398\pi\)
\(434\) 3.12519 0.150014
\(435\) 0 0
\(436\) 17.8974 0.857128
\(437\) −13.4146 −0.641708
\(438\) 0 0
\(439\) 21.2700 1.01516 0.507581 0.861604i \(-0.330540\pi\)
0.507581 + 0.861604i \(0.330540\pi\)
\(440\) 28.4329 1.35549
\(441\) 0 0
\(442\) −1.58559 −0.0754187
\(443\) 30.7912 1.46294 0.731468 0.681876i \(-0.238835\pi\)
0.731468 + 0.681876i \(0.238835\pi\)
\(444\) 0 0
\(445\) −20.9951 −0.995265
\(446\) 8.38089 0.396846
\(447\) 0 0
\(448\) 5.60116 0.264630
\(449\) −26.8456 −1.26692 −0.633462 0.773774i \(-0.718367\pi\)
−0.633462 + 0.773774i \(0.718367\pi\)
\(450\) 0 0
\(451\) −33.6099 −1.58263
\(452\) −18.6152 −0.875585
\(453\) 0 0
\(454\) −4.20135 −0.197179
\(455\) 4.21303 0.197510
\(456\) 0 0
\(457\) 2.07317 0.0969789 0.0484895 0.998824i \(-0.484559\pi\)
0.0484895 + 0.998824i \(0.484559\pi\)
\(458\) 7.72300 0.360872
\(459\) 0 0
\(460\) 14.5071 0.676399
\(461\) −37.8084 −1.76091 −0.880455 0.474129i \(-0.842763\pi\)
−0.880455 + 0.474129i \(0.842763\pi\)
\(462\) 0 0
\(463\) 30.4977 1.41735 0.708674 0.705536i \(-0.249294\pi\)
0.708674 + 0.705536i \(0.249294\pi\)
\(464\) −1.58683 −0.0736669
\(465\) 0 0
\(466\) 10.9045 0.505139
\(467\) 7.92034 0.366509 0.183255 0.983065i \(-0.441337\pi\)
0.183255 + 0.983065i \(0.441337\pi\)
\(468\) 0 0
\(469\) −5.42409 −0.250461
\(470\) −14.4280 −0.665515
\(471\) 0 0
\(472\) 25.3409 1.16641
\(473\) 24.5278 1.12779
\(474\) 0 0
\(475\) −1.62285 −0.0744616
\(476\) 0.999536 0.0458137
\(477\) 0 0
\(478\) 19.0410 0.870915
\(479\) 34.0782 1.55707 0.778537 0.627599i \(-0.215962\pi\)
0.778537 + 0.627599i \(0.215962\pi\)
\(480\) 0 0
\(481\) 2.49472 0.113750
\(482\) 5.30135 0.241470
\(483\) 0 0
\(484\) −13.6647 −0.621121
\(485\) 2.26498 0.102848
\(486\) 0 0
\(487\) −10.7347 −0.486436 −0.243218 0.969972i \(-0.578203\pi\)
−0.243218 + 0.969972i \(0.578203\pi\)
\(488\) −17.4684 −0.790756
\(489\) 0 0
\(490\) 1.88339 0.0850831
\(491\) 35.6179 1.60741 0.803707 0.595025i \(-0.202858\pi\)
0.803707 + 0.595025i \(0.202858\pi\)
\(492\) 0 0
\(493\) −4.66822 −0.210246
\(494\) 4.15274 0.186841
\(495\) 0 0
\(496\) −0.996122 −0.0447272
\(497\) 1.57089 0.0704641
\(498\) 0 0
\(499\) −29.5279 −1.32185 −0.660925 0.750452i \(-0.729836\pi\)
−0.660925 + 0.750452i \(0.729836\pi\)
\(500\) 13.8517 0.619467
\(501\) 0 0
\(502\) −0.00592422 −0.000264411 0
\(503\) 21.5076 0.958976 0.479488 0.877549i \(-0.340822\pi\)
0.479488 + 0.877549i \(0.340822\pi\)
\(504\) 0 0
\(505\) −7.31284 −0.325417
\(506\) 26.0122 1.15638
\(507\) 0 0
\(508\) 1.17017 0.0519180
\(509\) 20.3805 0.903348 0.451674 0.892183i \(-0.350827\pi\)
0.451674 + 0.892183i \(0.350827\pi\)
\(510\) 0 0
\(511\) −9.67049 −0.427797
\(512\) −3.27723 −0.144834
\(513\) 0 0
\(514\) −19.7002 −0.868941
\(515\) 3.65949 0.161257
\(516\) 0 0
\(517\) 36.4807 1.60442
\(518\) 1.11524 0.0490009
\(519\) 0 0
\(520\) −12.1667 −0.533543
\(521\) 35.3393 1.54824 0.774122 0.633037i \(-0.218192\pi\)
0.774122 + 0.633037i \(0.218192\pi\)
\(522\) 0 0
\(523\) 41.3525 1.80822 0.904110 0.427300i \(-0.140535\pi\)
0.904110 + 0.427300i \(0.140535\pi\)
\(524\) 17.2437 0.753297
\(525\) 0 0
\(526\) −5.59566 −0.243982
\(527\) −2.93043 −0.127652
\(528\) 0 0
\(529\) 12.9559 0.563302
\(530\) 2.61826 0.113730
\(531\) 0 0
\(532\) −2.61784 −0.113498
\(533\) 14.3819 0.622951
\(534\) 0 0
\(535\) −23.5974 −1.02020
\(536\) 15.6640 0.676584
\(537\) 0 0
\(538\) 18.3249 0.790042
\(539\) −4.76209 −0.205118
\(540\) 0 0
\(541\) 25.4880 1.09582 0.547908 0.836539i \(-0.315424\pi\)
0.547908 + 0.836539i \(0.315424\pi\)
\(542\) −12.1984 −0.523968
\(543\) 0 0
\(544\) −4.70758 −0.201836
\(545\) −31.6218 −1.35453
\(546\) 0 0
\(547\) 30.4992 1.30405 0.652025 0.758198i \(-0.273920\pi\)
0.652025 + 0.758198i \(0.273920\pi\)
\(548\) 8.91303 0.380746
\(549\) 0 0
\(550\) 3.14686 0.134183
\(551\) 12.2263 0.520858
\(552\) 0 0
\(553\) −4.49693 −0.191229
\(554\) 7.33949 0.311825
\(555\) 0 0
\(556\) −5.97199 −0.253269
\(557\) −36.9759 −1.56672 −0.783361 0.621568i \(-0.786496\pi\)
−0.783361 + 0.621568i \(0.786496\pi\)
\(558\) 0 0
\(559\) −10.4956 −0.443918
\(560\) −0.600311 −0.0253678
\(561\) 0 0
\(562\) −25.3913 −1.07107
\(563\) −36.8641 −1.55363 −0.776817 0.629726i \(-0.783167\pi\)
−0.776817 + 0.629726i \(0.783167\pi\)
\(564\) 0 0
\(565\) 32.8901 1.38370
\(566\) −9.20452 −0.386895
\(567\) 0 0
\(568\) −4.53652 −0.190348
\(569\) −12.5246 −0.525057 −0.262529 0.964924i \(-0.584556\pi\)
−0.262529 + 0.964924i \(0.584556\pi\)
\(570\) 0 0
\(571\) 13.9998 0.585875 0.292937 0.956132i \(-0.405367\pi\)
0.292937 + 0.956132i \(0.405367\pi\)
\(572\) 11.3552 0.474784
\(573\) 0 0
\(574\) 6.42930 0.268354
\(575\) 4.34982 0.181400
\(576\) 0 0
\(577\) −31.7993 −1.32382 −0.661911 0.749582i \(-0.730254\pi\)
−0.661911 + 0.749582i \(0.730254\pi\)
\(578\) −14.8215 −0.616493
\(579\) 0 0
\(580\) −13.2221 −0.549016
\(581\) −8.88129 −0.368458
\(582\) 0 0
\(583\) −6.62016 −0.274179
\(584\) 27.9271 1.15563
\(585\) 0 0
\(586\) −4.70474 −0.194351
\(587\) −0.697457 −0.0287871 −0.0143936 0.999896i \(-0.504582\pi\)
−0.0143936 + 0.999896i \(0.504582\pi\)
\(588\) 0 0
\(589\) 7.67496 0.316241
\(590\) −16.5267 −0.680395
\(591\) 0 0
\(592\) −0.355471 −0.0146098
\(593\) −8.07973 −0.331795 −0.165897 0.986143i \(-0.553052\pi\)
−0.165897 + 0.986143i \(0.553052\pi\)
\(594\) 0 0
\(595\) −1.76602 −0.0723998
\(596\) −0.403744 −0.0165380
\(597\) 0 0
\(598\) −11.1308 −0.455173
\(599\) −15.7153 −0.642108 −0.321054 0.947061i \(-0.604037\pi\)
−0.321054 + 0.947061i \(0.604037\pi\)
\(600\) 0 0
\(601\) −40.1903 −1.63939 −0.819697 0.572797i \(-0.805858\pi\)
−0.819697 + 0.572797i \(0.805858\pi\)
\(602\) −4.69197 −0.191230
\(603\) 0 0
\(604\) −7.65737 −0.311574
\(605\) 24.1433 0.981564
\(606\) 0 0
\(607\) −4.34490 −0.176354 −0.0881770 0.996105i \(-0.528104\pi\)
−0.0881770 + 0.996105i \(0.528104\pi\)
\(608\) 12.3294 0.500023
\(609\) 0 0
\(610\) 11.3924 0.461266
\(611\) −15.6104 −0.631528
\(612\) 0 0
\(613\) 16.5086 0.666775 0.333388 0.942790i \(-0.391808\pi\)
0.333388 + 0.942790i \(0.391808\pi\)
\(614\) 2.76358 0.111529
\(615\) 0 0
\(616\) 13.7523 0.554095
\(617\) 35.3853 1.42456 0.712280 0.701896i \(-0.247663\pi\)
0.712280 + 0.701896i \(0.247663\pi\)
\(618\) 0 0
\(619\) 5.41450 0.217627 0.108814 0.994062i \(-0.465295\pi\)
0.108814 + 0.994062i \(0.465295\pi\)
\(620\) −8.30003 −0.333337
\(621\) 0 0
\(622\) −20.1658 −0.808574
\(623\) −10.1548 −0.406844
\(624\) 0 0
\(625\) −20.8467 −0.833868
\(626\) 8.80751 0.352019
\(627\) 0 0
\(628\) −6.15202 −0.245492
\(629\) −1.04574 −0.0416964
\(630\) 0 0
\(631\) −4.17145 −0.166063 −0.0830315 0.996547i \(-0.526460\pi\)
−0.0830315 + 0.996547i \(0.526460\pi\)
\(632\) 12.9865 0.516576
\(633\) 0 0
\(634\) 9.03562 0.358850
\(635\) −2.06751 −0.0820465
\(636\) 0 0
\(637\) 2.03773 0.0807380
\(638\) −23.7079 −0.938606
\(639\) 0 0
\(640\) −12.2398 −0.483822
\(641\) −4.95692 −0.195787 −0.0978933 0.995197i \(-0.531210\pi\)
−0.0978933 + 0.995197i \(0.531210\pi\)
\(642\) 0 0
\(643\) −14.0285 −0.553230 −0.276615 0.960981i \(-0.589213\pi\)
−0.276615 + 0.960981i \(0.589213\pi\)
\(644\) 7.01673 0.276498
\(645\) 0 0
\(646\) −1.74075 −0.0684888
\(647\) 15.8380 0.622658 0.311329 0.950302i \(-0.399226\pi\)
0.311329 + 0.950302i \(0.399226\pi\)
\(648\) 0 0
\(649\) 41.7872 1.64029
\(650\) −1.34657 −0.0528167
\(651\) 0 0
\(652\) 5.00219 0.195901
\(653\) −29.1768 −1.14178 −0.570888 0.821028i \(-0.693401\pi\)
−0.570888 + 0.821028i \(0.693401\pi\)
\(654\) 0 0
\(655\) −30.4670 −1.19044
\(656\) −2.04927 −0.0800105
\(657\) 0 0
\(658\) −6.97846 −0.272049
\(659\) 3.36477 0.131073 0.0655364 0.997850i \(-0.479124\pi\)
0.0655364 + 0.997850i \(0.479124\pi\)
\(660\) 0 0
\(661\) −3.56055 −0.138489 −0.0692447 0.997600i \(-0.522059\pi\)
−0.0692447 + 0.997600i \(0.522059\pi\)
\(662\) 20.7337 0.805840
\(663\) 0 0
\(664\) 25.6480 0.995334
\(665\) 4.62530 0.179362
\(666\) 0 0
\(667\) −32.7708 −1.26889
\(668\) 18.7194 0.724275
\(669\) 0 0
\(670\) −10.2157 −0.394667
\(671\) −28.8053 −1.11202
\(672\) 0 0
\(673\) −6.79286 −0.261845 −0.130923 0.991393i \(-0.541794\pi\)
−0.130923 + 0.991393i \(0.541794\pi\)
\(674\) 15.4325 0.594437
\(675\) 0 0
\(676\) 10.3533 0.398202
\(677\) −3.52953 −0.135651 −0.0678254 0.997697i \(-0.521606\pi\)
−0.0678254 + 0.997697i \(0.521606\pi\)
\(678\) 0 0
\(679\) 1.09551 0.0420419
\(680\) 5.10003 0.195577
\(681\) 0 0
\(682\) −14.8825 −0.569879
\(683\) −36.8948 −1.41174 −0.705871 0.708341i \(-0.749444\pi\)
−0.705871 + 0.708341i \(0.749444\pi\)
\(684\) 0 0
\(685\) −15.7479 −0.601696
\(686\) 0.910949 0.0347802
\(687\) 0 0
\(688\) 1.49551 0.0570159
\(689\) 2.83282 0.107922
\(690\) 0 0
\(691\) −0.939809 −0.0357520 −0.0178760 0.999840i \(-0.505690\pi\)
−0.0178760 + 0.999840i \(0.505690\pi\)
\(692\) 8.38472 0.318739
\(693\) 0 0
\(694\) −32.4421 −1.23149
\(695\) 10.5516 0.400244
\(696\) 0 0
\(697\) −6.02863 −0.228351
\(698\) −0.184547 −0.00698520
\(699\) 0 0
\(700\) 0.848859 0.0320839
\(701\) 15.3128 0.578356 0.289178 0.957275i \(-0.406618\pi\)
0.289178 + 0.957275i \(0.406618\pi\)
\(702\) 0 0
\(703\) 2.73885 0.103298
\(704\) −26.6732 −1.00529
\(705\) 0 0
\(706\) −12.8133 −0.482236
\(707\) −3.53703 −0.133024
\(708\) 0 0
\(709\) −20.5964 −0.773515 −0.386757 0.922182i \(-0.626405\pi\)
−0.386757 + 0.922182i \(0.626405\pi\)
\(710\) 2.95861 0.111035
\(711\) 0 0
\(712\) 29.3257 1.09903
\(713\) −20.5716 −0.770413
\(714\) 0 0
\(715\) −20.0628 −0.750307
\(716\) 0.478858 0.0178958
\(717\) 0 0
\(718\) 8.75848 0.326864
\(719\) −25.9093 −0.966255 −0.483128 0.875550i \(-0.660499\pi\)
−0.483128 + 0.875550i \(0.660499\pi\)
\(720\) 0 0
\(721\) 1.77000 0.0659184
\(722\) −12.7489 −0.474466
\(723\) 0 0
\(724\) 12.3942 0.460626
\(725\) −3.96450 −0.147238
\(726\) 0 0
\(727\) 33.5208 1.24322 0.621609 0.783328i \(-0.286479\pi\)
0.621609 + 0.783328i \(0.286479\pi\)
\(728\) −5.88470 −0.218102
\(729\) 0 0
\(730\) −18.2133 −0.674106
\(731\) 4.39956 0.162724
\(732\) 0 0
\(733\) 8.91851 0.329413 0.164706 0.986343i \(-0.447332\pi\)
0.164706 + 0.986343i \(0.447332\pi\)
\(734\) −21.7531 −0.802923
\(735\) 0 0
\(736\) −33.0472 −1.21813
\(737\) 25.8300 0.951460
\(738\) 0 0
\(739\) −17.5441 −0.645368 −0.322684 0.946507i \(-0.604585\pi\)
−0.322684 + 0.946507i \(0.604585\pi\)
\(740\) −2.96191 −0.108882
\(741\) 0 0
\(742\) 1.26638 0.0464904
\(743\) 31.3395 1.14973 0.574867 0.818247i \(-0.305054\pi\)
0.574867 + 0.818247i \(0.305054\pi\)
\(744\) 0 0
\(745\) 0.713352 0.0261352
\(746\) 17.3438 0.635002
\(747\) 0 0
\(748\) −4.75988 −0.174038
\(749\) −11.4134 −0.417038
\(750\) 0 0
\(751\) 44.1522 1.61114 0.805568 0.592503i \(-0.201860\pi\)
0.805568 + 0.592503i \(0.201860\pi\)
\(752\) 2.22431 0.0811122
\(753\) 0 0
\(754\) 10.1448 0.369452
\(755\) 13.5294 0.492384
\(756\) 0 0
\(757\) −17.5802 −0.638964 −0.319482 0.947592i \(-0.603509\pi\)
−0.319482 + 0.947592i \(0.603509\pi\)
\(758\) −7.68066 −0.278974
\(759\) 0 0
\(760\) −13.3572 −0.484518
\(761\) 15.5785 0.564720 0.282360 0.959308i \(-0.408883\pi\)
0.282360 + 0.959308i \(0.408883\pi\)
\(762\) 0 0
\(763\) −15.2946 −0.553703
\(764\) 16.8305 0.608908
\(765\) 0 0
\(766\) 20.7329 0.749110
\(767\) −17.8811 −0.645648
\(768\) 0 0
\(769\) −26.4832 −0.955009 −0.477505 0.878629i \(-0.658459\pi\)
−0.477505 + 0.878629i \(0.658459\pi\)
\(770\) −8.96889 −0.323216
\(771\) 0 0
\(772\) −5.75406 −0.207093
\(773\) 4.85564 0.174645 0.0873226 0.996180i \(-0.472169\pi\)
0.0873226 + 0.996180i \(0.472169\pi\)
\(774\) 0 0
\(775\) −2.48868 −0.0893960
\(776\) −3.16369 −0.113570
\(777\) 0 0
\(778\) −14.0507 −0.503743
\(779\) 15.7893 0.565710
\(780\) 0 0
\(781\) −7.48072 −0.267681
\(782\) 4.66582 0.166850
\(783\) 0 0
\(784\) −0.290355 −0.0103698
\(785\) 10.8696 0.387954
\(786\) 0 0
\(787\) −6.95194 −0.247810 −0.123905 0.992294i \(-0.539542\pi\)
−0.123905 + 0.992294i \(0.539542\pi\)
\(788\) −21.6091 −0.769793
\(789\) 0 0
\(790\) −8.46949 −0.301331
\(791\) 15.9081 0.565627
\(792\) 0 0
\(793\) 12.3260 0.437710
\(794\) −6.63695 −0.235537
\(795\) 0 0
\(796\) 17.6777 0.626568
\(797\) −26.4161 −0.935705 −0.467852 0.883807i \(-0.654972\pi\)
−0.467852 + 0.883807i \(0.654972\pi\)
\(798\) 0 0
\(799\) 6.54356 0.231495
\(800\) −3.99792 −0.141348
\(801\) 0 0
\(802\) −23.5442 −0.831376
\(803\) 46.0517 1.62513
\(804\) 0 0
\(805\) −12.3975 −0.436953
\(806\) 6.36832 0.224314
\(807\) 0 0
\(808\) 10.2145 0.359344
\(809\) 20.0526 0.705010 0.352505 0.935810i \(-0.385330\pi\)
0.352505 + 0.935810i \(0.385330\pi\)
\(810\) 0 0
\(811\) −6.59746 −0.231668 −0.115834 0.993269i \(-0.536954\pi\)
−0.115834 + 0.993269i \(0.536954\pi\)
\(812\) −6.39517 −0.224426
\(813\) 0 0
\(814\) −5.31088 −0.186146
\(815\) −8.83807 −0.309584
\(816\) 0 0
\(817\) −11.5227 −0.403128
\(818\) −17.1907 −0.601058
\(819\) 0 0
\(820\) −17.0752 −0.596293
\(821\) −32.1085 −1.12060 −0.560298 0.828291i \(-0.689313\pi\)
−0.560298 + 0.828291i \(0.689313\pi\)
\(822\) 0 0
\(823\) 53.0767 1.85014 0.925069 0.379799i \(-0.124007\pi\)
0.925069 + 0.379799i \(0.124007\pi\)
\(824\) −5.11153 −0.178069
\(825\) 0 0
\(826\) −7.99355 −0.278131
\(827\) 5.72183 0.198968 0.0994838 0.995039i \(-0.468281\pi\)
0.0994838 + 0.995039i \(0.468281\pi\)
\(828\) 0 0
\(829\) 36.9131 1.28204 0.641022 0.767522i \(-0.278511\pi\)
0.641022 + 0.767522i \(0.278511\pi\)
\(830\) −16.7270 −0.580601
\(831\) 0 0
\(832\) 11.4137 0.395698
\(833\) −0.854179 −0.0295955
\(834\) 0 0
\(835\) −33.0742 −1.14458
\(836\) 12.4664 0.431158
\(837\) 0 0
\(838\) −33.5561 −1.15918
\(839\) 35.8828 1.23881 0.619406 0.785071i \(-0.287374\pi\)
0.619406 + 0.785071i \(0.287374\pi\)
\(840\) 0 0
\(841\) 0.867890 0.0299272
\(842\) 1.52092 0.0524142
\(843\) 0 0
\(844\) −9.68261 −0.333289
\(845\) −18.2926 −0.629283
\(846\) 0 0
\(847\) 11.6775 0.401243
\(848\) −0.403646 −0.0138612
\(849\) 0 0
\(850\) 0.564454 0.0193606
\(851\) −7.34109 −0.251649
\(852\) 0 0
\(853\) 38.1872 1.30750 0.653752 0.756709i \(-0.273194\pi\)
0.653752 + 0.756709i \(0.273194\pi\)
\(854\) 5.51023 0.188556
\(855\) 0 0
\(856\) 32.9605 1.12657
\(857\) 5.39552 0.184308 0.0921538 0.995745i \(-0.470625\pi\)
0.0921538 + 0.995745i \(0.470625\pi\)
\(858\) 0 0
\(859\) −22.8095 −0.778250 −0.389125 0.921185i \(-0.627223\pi\)
−0.389125 + 0.921185i \(0.627223\pi\)
\(860\) 12.4611 0.424921
\(861\) 0 0
\(862\) −20.4576 −0.696789
\(863\) −15.7818 −0.537220 −0.268610 0.963249i \(-0.586564\pi\)
−0.268610 + 0.963249i \(0.586564\pi\)
\(864\) 0 0
\(865\) −14.8145 −0.503707
\(866\) 31.1942 1.06002
\(867\) 0 0
\(868\) −4.01451 −0.136261
\(869\) 21.4148 0.726446
\(870\) 0 0
\(871\) −11.0529 −0.374512
\(872\) 44.1689 1.49575
\(873\) 0 0
\(874\) −12.2200 −0.413349
\(875\) −11.8373 −0.400175
\(876\) 0 0
\(877\) −27.3621 −0.923952 −0.461976 0.886892i \(-0.652859\pi\)
−0.461976 + 0.886892i \(0.652859\pi\)
\(878\) 19.3759 0.653905
\(879\) 0 0
\(880\) 2.85873 0.0963679
\(881\) 39.0186 1.31457 0.657284 0.753643i \(-0.271705\pi\)
0.657284 + 0.753643i \(0.271705\pi\)
\(882\) 0 0
\(883\) −47.1651 −1.58723 −0.793616 0.608419i \(-0.791804\pi\)
−0.793616 + 0.608419i \(0.791804\pi\)
\(884\) 2.03679 0.0685046
\(885\) 0 0
\(886\) 28.0493 0.942333
\(887\) −1.26669 −0.0425313 −0.0212656 0.999774i \(-0.506770\pi\)
−0.0212656 + 0.999774i \(0.506770\pi\)
\(888\) 0 0
\(889\) −1.00000 −0.0335389
\(890\) −19.1255 −0.641088
\(891\) 0 0
\(892\) −10.7658 −0.360465
\(893\) −17.1379 −0.573499
\(894\) 0 0
\(895\) −0.846066 −0.0282809
\(896\) −5.92009 −0.197776
\(897\) 0 0
\(898\) −24.4550 −0.816074
\(899\) 18.7493 0.625324
\(900\) 0 0
\(901\) −1.18746 −0.0395601
\(902\) −30.6169 −1.01943
\(903\) 0 0
\(904\) −45.9404 −1.52796
\(905\) −21.8985 −0.727931
\(906\) 0 0
\(907\) −14.3655 −0.476999 −0.238500 0.971143i \(-0.576656\pi\)
−0.238500 + 0.971143i \(0.576656\pi\)
\(908\) 5.39690 0.179102
\(909\) 0 0
\(910\) 3.83786 0.127224
\(911\) 15.5385 0.514812 0.257406 0.966303i \(-0.417132\pi\)
0.257406 + 0.966303i \(0.417132\pi\)
\(912\) 0 0
\(913\) 42.2935 1.39971
\(914\) 1.88855 0.0624678
\(915\) 0 0
\(916\) −9.92069 −0.327789
\(917\) −14.7361 −0.486628
\(918\) 0 0
\(919\) 0.672694 0.0221901 0.0110951 0.999938i \(-0.496468\pi\)
0.0110951 + 0.999938i \(0.496468\pi\)
\(920\) 35.8022 1.18036
\(921\) 0 0
\(922\) −34.4415 −1.13427
\(923\) 3.20106 0.105364
\(924\) 0 0
\(925\) −0.888098 −0.0292005
\(926\) 27.7819 0.912968
\(927\) 0 0
\(928\) 30.1197 0.988728
\(929\) −49.6218 −1.62804 −0.814020 0.580837i \(-0.802725\pi\)
−0.814020 + 0.580837i \(0.802725\pi\)
\(930\) 0 0
\(931\) 2.23714 0.0733193
\(932\) −14.0075 −0.458829
\(933\) 0 0
\(934\) 7.21502 0.236083
\(935\) 8.40995 0.275035
\(936\) 0 0
\(937\) −26.7103 −0.872586 −0.436293 0.899805i \(-0.643709\pi\)
−0.436293 + 0.899805i \(0.643709\pi\)
\(938\) −4.94107 −0.161332
\(939\) 0 0
\(940\) 18.5337 0.604503
\(941\) 12.6965 0.413895 0.206948 0.978352i \(-0.433647\pi\)
0.206948 + 0.978352i \(0.433647\pi\)
\(942\) 0 0
\(943\) −42.3209 −1.37816
\(944\) 2.54786 0.0829257
\(945\) 0 0
\(946\) 22.3436 0.726452
\(947\) 38.5444 1.25253 0.626263 0.779612i \(-0.284584\pi\)
0.626263 + 0.779612i \(0.284584\pi\)
\(948\) 0 0
\(949\) −19.7059 −0.639680
\(950\) −1.47834 −0.0479636
\(951\) 0 0
\(952\) 2.46675 0.0799479
\(953\) 20.6289 0.668235 0.334118 0.942531i \(-0.391562\pi\)
0.334118 + 0.942531i \(0.391562\pi\)
\(954\) 0 0
\(955\) −29.7369 −0.962263
\(956\) −24.4594 −0.791072
\(957\) 0 0
\(958\) 31.0435 1.00297
\(959\) −7.61686 −0.245961
\(960\) 0 0
\(961\) −19.2303 −0.620332
\(962\) 2.27257 0.0732705
\(963\) 0 0
\(964\) −6.80992 −0.219333
\(965\) 10.1665 0.327272
\(966\) 0 0
\(967\) −12.4906 −0.401669 −0.200835 0.979625i \(-0.564365\pi\)
−0.200835 + 0.979625i \(0.564365\pi\)
\(968\) −33.7230 −1.08390
\(969\) 0 0
\(970\) 2.06328 0.0662480
\(971\) −38.8901 −1.24804 −0.624022 0.781407i \(-0.714502\pi\)
−0.624022 + 0.781407i \(0.714502\pi\)
\(972\) 0 0
\(973\) 5.10352 0.163611
\(974\) −9.77877 −0.313332
\(975\) 0 0
\(976\) −1.75633 −0.0562186
\(977\) 17.5486 0.561428 0.280714 0.959791i \(-0.409429\pi\)
0.280714 + 0.959791i \(0.409429\pi\)
\(978\) 0 0
\(979\) 48.3581 1.54553
\(980\) −2.41934 −0.0772829
\(981\) 0 0
\(982\) 32.4461 1.03540
\(983\) −35.7325 −1.13969 −0.569845 0.821752i \(-0.692997\pi\)
−0.569845 + 0.821752i \(0.692997\pi\)
\(984\) 0 0
\(985\) 38.1799 1.21651
\(986\) −4.25251 −0.135427
\(987\) 0 0
\(988\) −5.33446 −0.169712
\(989\) 30.8849 0.982083
\(990\) 0 0
\(991\) 38.7774 1.23180 0.615902 0.787822i \(-0.288792\pi\)
0.615902 + 0.787822i \(0.288792\pi\)
\(992\) 18.9074 0.600310
\(993\) 0 0
\(994\) 1.43100 0.0453886
\(995\) −31.2336 −0.990172
\(996\) 0 0
\(997\) 58.7906 1.86192 0.930958 0.365127i \(-0.118974\pi\)
0.930958 + 0.365127i \(0.118974\pi\)
\(998\) −26.8984 −0.851455
\(999\) 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 \(a_p\))