Properties

Label 8004.2.a.d.1.3
Level 8004
Weight 2
Character 8004.1
Self dual Yes
Analytic conductor 63.912
Analytic rank 1
Dimension 8
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8004 = 2^{2} \cdot 3 \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9122617778\)
Analytic rank: \(1\)
Dimension: \(8\)
Coefficient field: \(\mathbb{Q}[x]/(x^{8} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Root \(-1.03502\)
Character \(\chi\) = 8004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(-1.84132 q^{5}\) \(-2.79101 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(-1.84132 q^{5}\) \(-2.79101 q^{7}\) \(+1.00000 q^{9}\) \(+1.31068 q^{11}\) \(+2.49588 q^{13}\) \(-1.84132 q^{15}\) \(-3.40296 q^{17}\) \(+2.66867 q^{19}\) \(-2.79101 q^{21}\) \(+1.00000 q^{23}\) \(-1.60955 q^{25}\) \(+1.00000 q^{27}\) \(+1.00000 q^{29}\) \(-7.42965 q^{31}\) \(+1.31068 q^{33}\) \(+5.13914 q^{35}\) \(+2.47047 q^{37}\) \(+2.49588 q^{39}\) \(+5.01330 q^{41}\) \(+2.20204 q^{43}\) \(-1.84132 q^{45}\) \(+10.0789 q^{47}\) \(+0.789737 q^{49}\) \(-3.40296 q^{51}\) \(-0.225258 q^{53}\) \(-2.41337 q^{55}\) \(+2.66867 q^{57}\) \(-5.31872 q^{59}\) \(+11.3322 q^{61}\) \(-2.79101 q^{63}\) \(-4.59571 q^{65}\) \(+4.47132 q^{67}\) \(+1.00000 q^{69}\) \(-3.68684 q^{71}\) \(-9.11674 q^{73}\) \(-1.60955 q^{75}\) \(-3.65812 q^{77}\) \(-1.28120 q^{79}\) \(+1.00000 q^{81}\) \(-13.6844 q^{83}\) \(+6.26593 q^{85}\) \(+1.00000 q^{87}\) \(-16.0027 q^{89}\) \(-6.96603 q^{91}\) \(-7.42965 q^{93}\) \(-4.91386 q^{95}\) \(-0.382051 q^{97}\) \(+1.31068 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(8q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(8q \) \(\mathstrut +\mathstrut 8q^{3} \) \(\mathstrut -\mathstrut 5q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 8q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 4q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 3q^{17} \) \(\mathstrut -\mathstrut 5q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut +\mathstrut 8q^{23} \) \(\mathstrut -\mathstrut 5q^{25} \) \(\mathstrut +\mathstrut 8q^{27} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut -\mathstrut 11q^{41} \) \(\mathstrut -\mathstrut 7q^{43} \) \(\mathstrut -\mathstrut 5q^{45} \) \(\mathstrut -\mathstrut 14q^{47} \) \(\mathstrut -\mathstrut 18q^{49} \) \(\mathstrut -\mathstrut 3q^{51} \) \(\mathstrut -\mathstrut 15q^{53} \) \(\mathstrut -\mathstrut 17q^{55} \) \(\mathstrut -\mathstrut 5q^{57} \) \(\mathstrut +\mathstrut 4q^{59} \) \(\mathstrut +\mathstrut q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 5q^{67} \) \(\mathstrut +\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut -\mathstrut 21q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut +\mathstrut 8q^{81} \) \(\mathstrut +\mathstrut 3q^{83} \) \(\mathstrut +\mathstrut 8q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 2q^{93} \) \(\mathstrut -\mathstrut 3q^{95} \) \(\mathstrut -\mathstrut 7q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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 0
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) −1.84132 −0.823462 −0.411731 0.911305i \(-0.635076\pi\)
−0.411731 + 0.911305i \(0.635076\pi\)
\(6\) 0 0
\(7\) −2.79101 −1.05490 −0.527451 0.849585i \(-0.676852\pi\)
−0.527451 + 0.849585i \(0.676852\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) 1.31068 0.395184 0.197592 0.980284i \(-0.436688\pi\)
0.197592 + 0.980284i \(0.436688\pi\)
\(12\) 0 0
\(13\) 2.49588 0.692233 0.346116 0.938192i \(-0.387500\pi\)
0.346116 + 0.938192i \(0.387500\pi\)
\(14\) 0 0
\(15\) −1.84132 −0.475426
\(16\) 0 0
\(17\) −3.40296 −0.825339 −0.412669 0.910881i \(-0.635404\pi\)
−0.412669 + 0.910881i \(0.635404\pi\)
\(18\) 0 0
\(19\) 2.66867 0.612234 0.306117 0.951994i \(-0.400970\pi\)
0.306117 + 0.951994i \(0.400970\pi\)
\(20\) 0 0
\(21\) −2.79101 −0.609048
\(22\) 0 0
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −1.60955 −0.321910
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) −7.42965 −1.33441 −0.667203 0.744876i \(-0.732508\pi\)
−0.667203 + 0.744876i \(0.732508\pi\)
\(32\) 0 0
\(33\) 1.31068 0.228160
\(34\) 0 0
\(35\) 5.13914 0.868673
\(36\) 0 0
\(37\) 2.47047 0.406143 0.203071 0.979164i \(-0.434908\pi\)
0.203071 + 0.979164i \(0.434908\pi\)
\(38\) 0 0
\(39\) 2.49588 0.399661
\(40\) 0 0
\(41\) 5.01330 0.782945 0.391473 0.920190i \(-0.371966\pi\)
0.391473 + 0.920190i \(0.371966\pi\)
\(42\) 0 0
\(43\) 2.20204 0.335808 0.167904 0.985803i \(-0.446300\pi\)
0.167904 + 0.985803i \(0.446300\pi\)
\(44\) 0 0
\(45\) −1.84132 −0.274487
\(46\) 0 0
\(47\) 10.0789 1.47015 0.735077 0.677984i \(-0.237146\pi\)
0.735077 + 0.677984i \(0.237146\pi\)
\(48\) 0 0
\(49\) 0.789737 0.112820
\(50\) 0 0
\(51\) −3.40296 −0.476510
\(52\) 0 0
\(53\) −0.225258 −0.0309415 −0.0154708 0.999880i \(-0.504925\pi\)
−0.0154708 + 0.999880i \(0.504925\pi\)
\(54\) 0 0
\(55\) −2.41337 −0.325419
\(56\) 0 0
\(57\) 2.66867 0.353474
\(58\) 0 0
\(59\) −5.31872 −0.692439 −0.346219 0.938154i \(-0.612535\pi\)
−0.346219 + 0.938154i \(0.612535\pi\)
\(60\) 0 0
\(61\) 11.3322 1.45094 0.725468 0.688256i \(-0.241623\pi\)
0.725468 + 0.688256i \(0.241623\pi\)
\(62\) 0 0
\(63\) −2.79101 −0.351634
\(64\) 0 0
\(65\) −4.59571 −0.570028
\(66\) 0 0
\(67\) 4.47132 0.546258 0.273129 0.961977i \(-0.411941\pi\)
0.273129 + 0.961977i \(0.411941\pi\)
\(68\) 0 0
\(69\) 1.00000 0.120386
\(70\) 0 0
\(71\) −3.68684 −0.437547 −0.218774 0.975776i \(-0.570206\pi\)
−0.218774 + 0.975776i \(0.570206\pi\)
\(72\) 0 0
\(73\) −9.11674 −1.06703 −0.533517 0.845789i \(-0.679130\pi\)
−0.533517 + 0.845789i \(0.679130\pi\)
\(74\) 0 0
\(75\) −1.60955 −0.185855
\(76\) 0 0
\(77\) −3.65812 −0.416881
\(78\) 0 0
\(79\) −1.28120 −0.144146 −0.0720732 0.997399i \(-0.522962\pi\)
−0.0720732 + 0.997399i \(0.522962\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −13.6844 −1.50206 −0.751028 0.660271i \(-0.770442\pi\)
−0.751028 + 0.660271i \(0.770442\pi\)
\(84\) 0 0
\(85\) 6.26593 0.679635
\(86\) 0 0
\(87\) 1.00000 0.107211
\(88\) 0 0
\(89\) −16.0027 −1.69629 −0.848143 0.529767i \(-0.822280\pi\)
−0.848143 + 0.529767i \(0.822280\pi\)
\(90\) 0 0
\(91\) −6.96603 −0.730238
\(92\) 0 0
\(93\) −7.42965 −0.770419
\(94\) 0 0
\(95\) −4.91386 −0.504152
\(96\) 0 0
\(97\) −0.382051 −0.0387914 −0.0193957 0.999812i \(-0.506174\pi\)
−0.0193957 + 0.999812i \(0.506174\pi\)
\(98\) 0 0
\(99\) 1.31068 0.131728
\(100\) 0 0
\(101\) −8.91275 −0.886852 −0.443426 0.896311i \(-0.646237\pi\)
−0.443426 + 0.896311i \(0.646237\pi\)
\(102\) 0 0
\(103\) −1.72402 −0.169873 −0.0849365 0.996386i \(-0.527069\pi\)
−0.0849365 + 0.996386i \(0.527069\pi\)
\(104\) 0 0
\(105\) 5.13914 0.501528
\(106\) 0 0
\(107\) 8.98490 0.868603 0.434302 0.900767i \(-0.356995\pi\)
0.434302 + 0.900767i \(0.356995\pi\)
\(108\) 0 0
\(109\) −2.52065 −0.241434 −0.120717 0.992687i \(-0.538519\pi\)
−0.120717 + 0.992687i \(0.538519\pi\)
\(110\) 0 0
\(111\) 2.47047 0.234487
\(112\) 0 0
\(113\) 0.730972 0.0687641 0.0343820 0.999409i \(-0.489054\pi\)
0.0343820 + 0.999409i \(0.489054\pi\)
\(114\) 0 0
\(115\) −1.84132 −0.171704
\(116\) 0 0
\(117\) 2.49588 0.230744
\(118\) 0 0
\(119\) 9.49769 0.870652
\(120\) 0 0
\(121\) −9.28212 −0.843829
\(122\) 0 0
\(123\) 5.01330 0.452034
\(124\) 0 0
\(125\) 12.1703 1.08854
\(126\) 0 0
\(127\) −17.3161 −1.53655 −0.768277 0.640118i \(-0.778885\pi\)
−0.768277 + 0.640118i \(0.778885\pi\)
\(128\) 0 0
\(129\) 2.20204 0.193879
\(130\) 0 0
\(131\) 4.66794 0.407840 0.203920 0.978988i \(-0.434632\pi\)
0.203920 + 0.978988i \(0.434632\pi\)
\(132\) 0 0
\(133\) −7.44828 −0.645848
\(134\) 0 0
\(135\) −1.84132 −0.158475
\(136\) 0 0
\(137\) −1.70740 −0.145873 −0.0729366 0.997337i \(-0.523237\pi\)
−0.0729366 + 0.997337i \(0.523237\pi\)
\(138\) 0 0
\(139\) −13.2410 −1.12309 −0.561544 0.827447i \(-0.689792\pi\)
−0.561544 + 0.827447i \(0.689792\pi\)
\(140\) 0 0
\(141\) 10.0789 0.848793
\(142\) 0 0
\(143\) 3.27130 0.273560
\(144\) 0 0
\(145\) −1.84132 −0.152913
\(146\) 0 0
\(147\) 0.789737 0.0651364
\(148\) 0 0
\(149\) 21.2448 1.74044 0.870219 0.492665i \(-0.163977\pi\)
0.870219 + 0.492665i \(0.163977\pi\)
\(150\) 0 0
\(151\) −6.89935 −0.561461 −0.280730 0.959787i \(-0.590577\pi\)
−0.280730 + 0.959787i \(0.590577\pi\)
\(152\) 0 0
\(153\) −3.40296 −0.275113
\(154\) 0 0
\(155\) 13.6804 1.09883
\(156\) 0 0
\(157\) −4.10423 −0.327553 −0.163777 0.986497i \(-0.552368\pi\)
−0.163777 + 0.986497i \(0.552368\pi\)
\(158\) 0 0
\(159\) −0.225258 −0.0178641
\(160\) 0 0
\(161\) −2.79101 −0.219962
\(162\) 0 0
\(163\) −7.13570 −0.558911 −0.279455 0.960159i \(-0.590154\pi\)
−0.279455 + 0.960159i \(0.590154\pi\)
\(164\) 0 0
\(165\) −2.41337 −0.187881
\(166\) 0 0
\(167\) −2.57124 −0.198968 −0.0994842 0.995039i \(-0.531719\pi\)
−0.0994842 + 0.995039i \(0.531719\pi\)
\(168\) 0 0
\(169\) −6.77058 −0.520813
\(170\) 0 0
\(171\) 2.66867 0.204078
\(172\) 0 0
\(173\) 6.34813 0.482639 0.241320 0.970446i \(-0.422420\pi\)
0.241320 + 0.970446i \(0.422420\pi\)
\(174\) 0 0
\(175\) 4.49227 0.339584
\(176\) 0 0
\(177\) −5.31872 −0.399780
\(178\) 0 0
\(179\) 13.2017 0.986739 0.493369 0.869820i \(-0.335765\pi\)
0.493369 + 0.869820i \(0.335765\pi\)
\(180\) 0 0
\(181\) −3.44048 −0.255729 −0.127864 0.991792i \(-0.540812\pi\)
−0.127864 + 0.991792i \(0.540812\pi\)
\(182\) 0 0
\(183\) 11.3322 0.837698
\(184\) 0 0
\(185\) −4.54892 −0.334443
\(186\) 0 0
\(187\) −4.46018 −0.326161
\(188\) 0 0
\(189\) −2.79101 −0.203016
\(190\) 0 0
\(191\) −13.0228 −0.942298 −0.471149 0.882054i \(-0.656161\pi\)
−0.471149 + 0.882054i \(0.656161\pi\)
\(192\) 0 0
\(193\) −3.25619 −0.234386 −0.117193 0.993109i \(-0.537390\pi\)
−0.117193 + 0.993109i \(0.537390\pi\)
\(194\) 0 0
\(195\) −4.59571 −0.329106
\(196\) 0 0
\(197\) −12.8117 −0.912794 −0.456397 0.889776i \(-0.650860\pi\)
−0.456397 + 0.889776i \(0.650860\pi\)
\(198\) 0 0
\(199\) −0.641529 −0.0454768 −0.0227384 0.999741i \(-0.507238\pi\)
−0.0227384 + 0.999741i \(0.507238\pi\)
\(200\) 0 0
\(201\) 4.47132 0.315382
\(202\) 0 0
\(203\) −2.79101 −0.195891
\(204\) 0 0
\(205\) −9.23107 −0.644726
\(206\) 0 0
\(207\) 1.00000 0.0695048
\(208\) 0 0
\(209\) 3.49776 0.241945
\(210\) 0 0
\(211\) −21.1764 −1.45785 −0.728923 0.684596i \(-0.759979\pi\)
−0.728923 + 0.684596i \(0.759979\pi\)
\(212\) 0 0
\(213\) −3.68684 −0.252618
\(214\) 0 0
\(215\) −4.05466 −0.276525
\(216\) 0 0
\(217\) 20.7362 1.40767
\(218\) 0 0
\(219\) −9.11674 −0.616052
\(220\) 0 0
\(221\) −8.49338 −0.571327
\(222\) 0 0
\(223\) 0.964487 0.0645868 0.0322934 0.999478i \(-0.489719\pi\)
0.0322934 + 0.999478i \(0.489719\pi\)
\(224\) 0 0
\(225\) −1.60955 −0.107303
\(226\) 0 0
\(227\) 0.721082 0.0478599 0.0239299 0.999714i \(-0.492382\pi\)
0.0239299 + 0.999714i \(0.492382\pi\)
\(228\) 0 0
\(229\) 4.60402 0.304242 0.152121 0.988362i \(-0.451390\pi\)
0.152121 + 0.988362i \(0.451390\pi\)
\(230\) 0 0
\(231\) −3.65812 −0.240686
\(232\) 0 0
\(233\) −23.2612 −1.52389 −0.761947 0.647640i \(-0.775756\pi\)
−0.761947 + 0.647640i \(0.775756\pi\)
\(234\) 0 0
\(235\) −18.5584 −1.21062
\(236\) 0 0
\(237\) −1.28120 −0.0832229
\(238\) 0 0
\(239\) 9.82598 0.635590 0.317795 0.948159i \(-0.397058\pi\)
0.317795 + 0.948159i \(0.397058\pi\)
\(240\) 0 0
\(241\) −0.446152 −0.0287392 −0.0143696 0.999897i \(-0.504574\pi\)
−0.0143696 + 0.999897i \(0.504574\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −1.45416 −0.0929027
\(246\) 0 0
\(247\) 6.66068 0.423809
\(248\) 0 0
\(249\) −13.6844 −0.867212
\(250\) 0 0
\(251\) 24.8713 1.56987 0.784933 0.619581i \(-0.212698\pi\)
0.784933 + 0.619581i \(0.212698\pi\)
\(252\) 0 0
\(253\) 1.31068 0.0824016
\(254\) 0 0
\(255\) 6.26593 0.392388
\(256\) 0 0
\(257\) −18.7469 −1.16940 −0.584699 0.811251i \(-0.698787\pi\)
−0.584699 + 0.811251i \(0.698787\pi\)
\(258\) 0 0
\(259\) −6.89510 −0.428441
\(260\) 0 0
\(261\) 1.00000 0.0618984
\(262\) 0 0
\(263\) −29.0245 −1.78973 −0.894863 0.446341i \(-0.852727\pi\)
−0.894863 + 0.446341i \(0.852727\pi\)
\(264\) 0 0
\(265\) 0.414771 0.0254792
\(266\) 0 0
\(267\) −16.0027 −0.979352
\(268\) 0 0
\(269\) −30.8162 −1.87890 −0.939450 0.342686i \(-0.888663\pi\)
−0.939450 + 0.342686i \(0.888663\pi\)
\(270\) 0 0
\(271\) 30.3061 1.84096 0.920482 0.390784i \(-0.127796\pi\)
0.920482 + 0.390784i \(0.127796\pi\)
\(272\) 0 0
\(273\) −6.96603 −0.421603
\(274\) 0 0
\(275\) −2.10960 −0.127214
\(276\) 0 0
\(277\) 10.1153 0.607767 0.303883 0.952709i \(-0.401717\pi\)
0.303883 + 0.952709i \(0.401717\pi\)
\(278\) 0 0
\(279\) −7.42965 −0.444802
\(280\) 0 0
\(281\) −5.35616 −0.319521 −0.159761 0.987156i \(-0.551072\pi\)
−0.159761 + 0.987156i \(0.551072\pi\)
\(282\) 0 0
\(283\) 15.3122 0.910216 0.455108 0.890436i \(-0.349601\pi\)
0.455108 + 0.890436i \(0.349601\pi\)
\(284\) 0 0
\(285\) −4.91386 −0.291072
\(286\) 0 0
\(287\) −13.9922 −0.825931
\(288\) 0 0
\(289\) −5.41987 −0.318816
\(290\) 0 0
\(291\) −0.382051 −0.0223962
\(292\) 0 0
\(293\) 20.0293 1.17012 0.585062 0.810989i \(-0.301070\pi\)
0.585062 + 0.810989i \(0.301070\pi\)
\(294\) 0 0
\(295\) 9.79346 0.570197
\(296\) 0 0
\(297\) 1.31068 0.0760533
\(298\) 0 0
\(299\) 2.49588 0.144341
\(300\) 0 0
\(301\) −6.14592 −0.354245
\(302\) 0 0
\(303\) −8.91275 −0.512024
\(304\) 0 0
\(305\) −20.8661 −1.19479
\(306\) 0 0
\(307\) −29.9678 −1.71035 −0.855176 0.518337i \(-0.826551\pi\)
−0.855176 + 0.518337i \(0.826551\pi\)
\(308\) 0 0
\(309\) −1.72402 −0.0980762
\(310\) 0 0
\(311\) 20.1613 1.14324 0.571620 0.820518i \(-0.306315\pi\)
0.571620 + 0.820518i \(0.306315\pi\)
\(312\) 0 0
\(313\) −9.24273 −0.522430 −0.261215 0.965281i \(-0.584123\pi\)
−0.261215 + 0.965281i \(0.584123\pi\)
\(314\) 0 0
\(315\) 5.13914 0.289558
\(316\) 0 0
\(317\) 2.91035 0.163462 0.0817308 0.996654i \(-0.473955\pi\)
0.0817308 + 0.996654i \(0.473955\pi\)
\(318\) 0 0
\(319\) 1.31068 0.0733839
\(320\) 0 0
\(321\) 8.98490 0.501488
\(322\) 0 0
\(323\) −9.08136 −0.505301
\(324\) 0 0
\(325\) −4.01724 −0.222837
\(326\) 0 0
\(327\) −2.52065 −0.139392
\(328\) 0 0
\(329\) −28.1302 −1.55087
\(330\) 0 0
\(331\) −23.1303 −1.27135 −0.635677 0.771955i \(-0.719279\pi\)
−0.635677 + 0.771955i \(0.719279\pi\)
\(332\) 0 0
\(333\) 2.47047 0.135381
\(334\) 0 0
\(335\) −8.23312 −0.449823
\(336\) 0 0
\(337\) −2.73470 −0.148969 −0.0744843 0.997222i \(-0.523731\pi\)
−0.0744843 + 0.997222i \(0.523731\pi\)
\(338\) 0 0
\(339\) 0.730972 0.0397010
\(340\) 0 0
\(341\) −9.73788 −0.527336
\(342\) 0 0
\(343\) 17.3329 0.935889
\(344\) 0 0
\(345\) −1.84132 −0.0991332
\(346\) 0 0
\(347\) −13.6496 −0.732747 −0.366374 0.930468i \(-0.619401\pi\)
−0.366374 + 0.930468i \(0.619401\pi\)
\(348\) 0 0
\(349\) −16.3981 −0.877771 −0.438886 0.898543i \(-0.644627\pi\)
−0.438886 + 0.898543i \(0.644627\pi\)
\(350\) 0 0
\(351\) 2.49588 0.133220
\(352\) 0 0
\(353\) −11.1416 −0.593008 −0.296504 0.955032i \(-0.595821\pi\)
−0.296504 + 0.955032i \(0.595821\pi\)
\(354\) 0 0
\(355\) 6.78864 0.360304
\(356\) 0 0
\(357\) 9.49769 0.502671
\(358\) 0 0
\(359\) −15.2834 −0.806626 −0.403313 0.915062i \(-0.632141\pi\)
−0.403313 + 0.915062i \(0.632141\pi\)
\(360\) 0 0
\(361\) −11.8782 −0.625169
\(362\) 0 0
\(363\) −9.28212 −0.487185
\(364\) 0 0
\(365\) 16.7868 0.878662
\(366\) 0 0
\(367\) −34.4019 −1.79576 −0.897882 0.440237i \(-0.854895\pi\)
−0.897882 + 0.440237i \(0.854895\pi\)
\(368\) 0 0
\(369\) 5.01330 0.260982
\(370\) 0 0
\(371\) 0.628697 0.0326403
\(372\) 0 0
\(373\) −18.0848 −0.936393 −0.468197 0.883624i \(-0.655096\pi\)
−0.468197 + 0.883624i \(0.655096\pi\)
\(374\) 0 0
\(375\) 12.1703 0.628471
\(376\) 0 0
\(377\) 2.49588 0.128544
\(378\) 0 0
\(379\) 6.85047 0.351885 0.175943 0.984400i \(-0.443703\pi\)
0.175943 + 0.984400i \(0.443703\pi\)
\(380\) 0 0
\(381\) −17.3161 −0.887130
\(382\) 0 0
\(383\) 7.08057 0.361800 0.180900 0.983501i \(-0.442099\pi\)
0.180900 + 0.983501i \(0.442099\pi\)
\(384\) 0 0
\(385\) 6.73575 0.343286
\(386\) 0 0
\(387\) 2.20204 0.111936
\(388\) 0 0
\(389\) 13.4254 0.680693 0.340347 0.940300i \(-0.389456\pi\)
0.340347 + 0.940300i \(0.389456\pi\)
\(390\) 0 0
\(391\) −3.40296 −0.172095
\(392\) 0 0
\(393\) 4.66794 0.235467
\(394\) 0 0
\(395\) 2.35910 0.118699
\(396\) 0 0
\(397\) 34.0450 1.70867 0.854335 0.519723i \(-0.173965\pi\)
0.854335 + 0.519723i \(0.173965\pi\)
\(398\) 0 0
\(399\) −7.44828 −0.372880
\(400\) 0 0
\(401\) −34.5040 −1.72305 −0.861524 0.507717i \(-0.830490\pi\)
−0.861524 + 0.507717i \(0.830490\pi\)
\(402\) 0 0
\(403\) −18.5435 −0.923719
\(404\) 0 0
\(405\) −1.84132 −0.0914958
\(406\) 0 0
\(407\) 3.23799 0.160501
\(408\) 0 0
\(409\) −34.8839 −1.72490 −0.862449 0.506145i \(-0.831070\pi\)
−0.862449 + 0.506145i \(0.831070\pi\)
\(410\) 0 0
\(411\) −1.70740 −0.0842199
\(412\) 0 0
\(413\) 14.8446 0.730455
\(414\) 0 0
\(415\) 25.1973 1.23689
\(416\) 0 0
\(417\) −13.2410 −0.648415
\(418\) 0 0
\(419\) −1.38156 −0.0674937 −0.0337468 0.999430i \(-0.510744\pi\)
−0.0337468 + 0.999430i \(0.510744\pi\)
\(420\) 0 0
\(421\) 17.2379 0.840125 0.420062 0.907495i \(-0.362008\pi\)
0.420062 + 0.907495i \(0.362008\pi\)
\(422\) 0 0
\(423\) 10.0789 0.490051
\(424\) 0 0
\(425\) 5.47723 0.265685
\(426\) 0 0
\(427\) −31.6282 −1.53060
\(428\) 0 0
\(429\) 3.27130 0.157940
\(430\) 0 0
\(431\) 15.1235 0.728474 0.364237 0.931306i \(-0.381330\pi\)
0.364237 + 0.931306i \(0.381330\pi\)
\(432\) 0 0
\(433\) 5.90927 0.283981 0.141991 0.989868i \(-0.454650\pi\)
0.141991 + 0.989868i \(0.454650\pi\)
\(434\) 0 0
\(435\) −1.84132 −0.0882844
\(436\) 0 0
\(437\) 2.66867 0.127660
\(438\) 0 0
\(439\) −6.02290 −0.287457 −0.143729 0.989617i \(-0.545909\pi\)
−0.143729 + 0.989617i \(0.545909\pi\)
\(440\) 0 0
\(441\) 0.789737 0.0376065
\(442\) 0 0
\(443\) 40.0603 1.90332 0.951660 0.307154i \(-0.0993765\pi\)
0.951660 + 0.307154i \(0.0993765\pi\)
\(444\) 0 0
\(445\) 29.4661 1.39683
\(446\) 0 0
\(447\) 21.2448 1.00484
\(448\) 0 0
\(449\) −1.37150 −0.0647252 −0.0323626 0.999476i \(-0.510303\pi\)
−0.0323626 + 0.999476i \(0.510303\pi\)
\(450\) 0 0
\(451\) 6.57082 0.309408
\(452\) 0 0
\(453\) −6.89935 −0.324160
\(454\) 0 0
\(455\) 12.8267 0.601324
\(456\) 0 0
\(457\) −39.6704 −1.85570 −0.927851 0.372952i \(-0.878346\pi\)
−0.927851 + 0.372952i \(0.878346\pi\)
\(458\) 0 0
\(459\) −3.40296 −0.158837
\(460\) 0 0
\(461\) 15.9461 0.742686 0.371343 0.928496i \(-0.378897\pi\)
0.371343 + 0.928496i \(0.378897\pi\)
\(462\) 0 0
\(463\) −23.4418 −1.08943 −0.544716 0.838621i \(-0.683363\pi\)
−0.544716 + 0.838621i \(0.683363\pi\)
\(464\) 0 0
\(465\) 13.6804 0.634411
\(466\) 0 0
\(467\) 23.4489 1.08508 0.542542 0.840029i \(-0.317462\pi\)
0.542542 + 0.840029i \(0.317462\pi\)
\(468\) 0 0
\(469\) −12.4795 −0.576249
\(470\) 0 0
\(471\) −4.10423 −0.189113
\(472\) 0 0
\(473\) 2.88617 0.132706
\(474\) 0 0
\(475\) −4.29535 −0.197084
\(476\) 0 0
\(477\) −0.225258 −0.0103138
\(478\) 0 0
\(479\) −39.7274 −1.81519 −0.907595 0.419847i \(-0.862084\pi\)
−0.907595 + 0.419847i \(0.862084\pi\)
\(480\) 0 0
\(481\) 6.16600 0.281145
\(482\) 0 0
\(483\) −2.79101 −0.126995
\(484\) 0 0
\(485\) 0.703477 0.0319432
\(486\) 0 0
\(487\) −24.2376 −1.09831 −0.549156 0.835720i \(-0.685051\pi\)
−0.549156 + 0.835720i \(0.685051\pi\)
\(488\) 0 0
\(489\) −7.13570 −0.322687
\(490\) 0 0
\(491\) 6.61956 0.298737 0.149368 0.988782i \(-0.452276\pi\)
0.149368 + 0.988782i \(0.452276\pi\)
\(492\) 0 0
\(493\) −3.40296 −0.153262
\(494\) 0 0
\(495\) −2.41337 −0.108473
\(496\) 0 0
\(497\) 10.2900 0.461570
\(498\) 0 0
\(499\) −2.22263 −0.0994986 −0.0497493 0.998762i \(-0.515842\pi\)
−0.0497493 + 0.998762i \(0.515842\pi\)
\(500\) 0 0
\(501\) −2.57124 −0.114874
\(502\) 0 0
\(503\) −35.3252 −1.57507 −0.787536 0.616269i \(-0.788643\pi\)
−0.787536 + 0.616269i \(0.788643\pi\)
\(504\) 0 0
\(505\) 16.4112 0.730289
\(506\) 0 0
\(507\) −6.77058 −0.300692
\(508\) 0 0
\(509\) −8.24953 −0.365654 −0.182827 0.983145i \(-0.558525\pi\)
−0.182827 + 0.983145i \(0.558525\pi\)
\(510\) 0 0
\(511\) 25.4449 1.12562
\(512\) 0 0
\(513\) 2.66867 0.117825
\(514\) 0 0
\(515\) 3.17447 0.139884
\(516\) 0 0
\(517\) 13.2101 0.580982
\(518\) 0 0
\(519\) 6.34813 0.278652
\(520\) 0 0
\(521\) −10.3404 −0.453020 −0.226510 0.974009i \(-0.572732\pi\)
−0.226510 + 0.974009i \(0.572732\pi\)
\(522\) 0 0
\(523\) 12.8697 0.562754 0.281377 0.959597i \(-0.409209\pi\)
0.281377 + 0.959597i \(0.409209\pi\)
\(524\) 0 0
\(525\) 4.49227 0.196059
\(526\) 0 0
\(527\) 25.2828 1.10134
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) 0 0
\(531\) −5.31872 −0.230813
\(532\) 0 0
\(533\) 12.5126 0.541981
\(534\) 0 0
\(535\) −16.5441 −0.715262
\(536\) 0 0
\(537\) 13.2017 0.569694
\(538\) 0 0
\(539\) 1.03509 0.0445846
\(540\) 0 0
\(541\) −26.5276 −1.14051 −0.570255 0.821468i \(-0.693156\pi\)
−0.570255 + 0.821468i \(0.693156\pi\)
\(542\) 0 0
\(543\) −3.44048 −0.147645
\(544\) 0 0
\(545\) 4.64131 0.198812
\(546\) 0 0
\(547\) −27.7253 −1.18545 −0.592724 0.805406i \(-0.701947\pi\)
−0.592724 + 0.805406i \(0.701947\pi\)
\(548\) 0 0
\(549\) 11.3322 0.483645
\(550\) 0 0
\(551\) 2.66867 0.113689
\(552\) 0 0
\(553\) 3.57584 0.152060
\(554\) 0 0
\(555\) −4.54892 −0.193091
\(556\) 0 0
\(557\) −6.61863 −0.280440 −0.140220 0.990120i \(-0.544781\pi\)
−0.140220 + 0.990120i \(0.544781\pi\)
\(558\) 0 0
\(559\) 5.49603 0.232457
\(560\) 0 0
\(561\) −4.46018 −0.188309
\(562\) 0 0
\(563\) −4.44737 −0.187434 −0.0937172 0.995599i \(-0.529875\pi\)
−0.0937172 + 0.995599i \(0.529875\pi\)
\(564\) 0 0
\(565\) −1.34595 −0.0566246
\(566\) 0 0
\(567\) −2.79101 −0.117211
\(568\) 0 0
\(569\) −27.7708 −1.16421 −0.582106 0.813113i \(-0.697771\pi\)
−0.582106 + 0.813113i \(0.697771\pi\)
\(570\) 0 0
\(571\) 19.7301 0.825679 0.412839 0.910804i \(-0.364537\pi\)
0.412839 + 0.910804i \(0.364537\pi\)
\(572\) 0 0
\(573\) −13.0228 −0.544036
\(574\) 0 0
\(575\) −1.60955 −0.0671229
\(576\) 0 0
\(577\) 25.1301 1.04618 0.523091 0.852277i \(-0.324779\pi\)
0.523091 + 0.852277i \(0.324779\pi\)
\(578\) 0 0
\(579\) −3.25619 −0.135323
\(580\) 0 0
\(581\) 38.1932 1.58452
\(582\) 0 0
\(583\) −0.295240 −0.0122276
\(584\) 0 0
\(585\) −4.59571 −0.190009
\(586\) 0 0
\(587\) 0.444202 0.0183342 0.00916710 0.999958i \(-0.497082\pi\)
0.00916710 + 0.999958i \(0.497082\pi\)
\(588\) 0 0
\(589\) −19.8273 −0.816969
\(590\) 0 0
\(591\) −12.8117 −0.527002
\(592\) 0 0
\(593\) 2.18109 0.0895666 0.0447833 0.998997i \(-0.485740\pi\)
0.0447833 + 0.998997i \(0.485740\pi\)
\(594\) 0 0
\(595\) −17.4883 −0.716949
\(596\) 0 0
\(597\) −0.641529 −0.0262560
\(598\) 0 0
\(599\) −11.5022 −0.469969 −0.234984 0.971999i \(-0.575504\pi\)
−0.234984 + 0.971999i \(0.575504\pi\)
\(600\) 0 0
\(601\) 22.5290 0.918979 0.459489 0.888183i \(-0.348032\pi\)
0.459489 + 0.888183i \(0.348032\pi\)
\(602\) 0 0
\(603\) 4.47132 0.182086
\(604\) 0 0
\(605\) 17.0913 0.694862
\(606\) 0 0
\(607\) −28.5352 −1.15821 −0.579104 0.815254i \(-0.696597\pi\)
−0.579104 + 0.815254i \(0.696597\pi\)
\(608\) 0 0
\(609\) −2.79101 −0.113097
\(610\) 0 0
\(611\) 25.1557 1.01769
\(612\) 0 0
\(613\) 2.67998 0.108243 0.0541217 0.998534i \(-0.482764\pi\)
0.0541217 + 0.998534i \(0.482764\pi\)
\(614\) 0 0
\(615\) −9.23107 −0.372233
\(616\) 0 0
\(617\) 14.8179 0.596546 0.298273 0.954481i \(-0.403589\pi\)
0.298273 + 0.954481i \(0.403589\pi\)
\(618\) 0 0
\(619\) −29.8951 −1.20159 −0.600793 0.799404i \(-0.705149\pi\)
−0.600793 + 0.799404i \(0.705149\pi\)
\(620\) 0 0
\(621\) 1.00000 0.0401286
\(622\) 0 0
\(623\) 44.6638 1.78942
\(624\) 0 0
\(625\) −14.3616 −0.574464
\(626\) 0 0
\(627\) 3.49776 0.139687
\(628\) 0 0
\(629\) −8.40690 −0.335205
\(630\) 0 0
\(631\) 21.3013 0.847993 0.423996 0.905664i \(-0.360627\pi\)
0.423996 + 0.905664i \(0.360627\pi\)
\(632\) 0 0
\(633\) −21.1764 −0.841688
\(634\) 0 0
\(635\) 31.8844 1.26529
\(636\) 0 0
\(637\) 1.97109 0.0780975
\(638\) 0 0
\(639\) −3.68684 −0.145849
\(640\) 0 0
\(641\) −10.5956 −0.418502 −0.209251 0.977862i \(-0.567103\pi\)
−0.209251 + 0.977862i \(0.567103\pi\)
\(642\) 0 0
\(643\) 5.99622 0.236468 0.118234 0.992986i \(-0.462277\pi\)
0.118234 + 0.992986i \(0.462277\pi\)
\(644\) 0 0
\(645\) −4.05466 −0.159652
\(646\) 0 0
\(647\) 39.5310 1.55412 0.777062 0.629424i \(-0.216709\pi\)
0.777062 + 0.629424i \(0.216709\pi\)
\(648\) 0 0
\(649\) −6.97113 −0.273641
\(650\) 0 0
\(651\) 20.7362 0.812717
\(652\) 0 0
\(653\) 5.01241 0.196151 0.0980754 0.995179i \(-0.468731\pi\)
0.0980754 + 0.995179i \(0.468731\pi\)
\(654\) 0 0
\(655\) −8.59517 −0.335841
\(656\) 0 0
\(657\) −9.11674 −0.355678
\(658\) 0 0
\(659\) 12.0968 0.471225 0.235612 0.971847i \(-0.424290\pi\)
0.235612 + 0.971847i \(0.424290\pi\)
\(660\) 0 0
\(661\) 44.6828 1.73796 0.868980 0.494847i \(-0.164776\pi\)
0.868980 + 0.494847i \(0.164776\pi\)
\(662\) 0 0
\(663\) −8.49338 −0.329856
\(664\) 0 0
\(665\) 13.7146 0.531831
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) 0 0
\(669\) 0.964487 0.0372892
\(670\) 0 0
\(671\) 14.8528 0.573387
\(672\) 0 0
\(673\) 9.38496 0.361764 0.180882 0.983505i \(-0.442105\pi\)
0.180882 + 0.983505i \(0.442105\pi\)
\(674\) 0 0
\(675\) −1.60955 −0.0619516
\(676\) 0 0
\(677\) 41.0590 1.57802 0.789012 0.614378i \(-0.210593\pi\)
0.789012 + 0.614378i \(0.210593\pi\)
\(678\) 0 0
\(679\) 1.06631 0.0409211
\(680\) 0 0
\(681\) 0.721082 0.0276319
\(682\) 0 0
\(683\) −0.237475 −0.00908675 −0.00454337 0.999990i \(-0.501446\pi\)
−0.00454337 + 0.999990i \(0.501446\pi\)
\(684\) 0 0
\(685\) 3.14387 0.120121
\(686\) 0 0
\(687\) 4.60402 0.175654
\(688\) 0 0
\(689\) −0.562217 −0.0214187
\(690\) 0 0
\(691\) −18.1078 −0.688852 −0.344426 0.938813i \(-0.611926\pi\)
−0.344426 + 0.938813i \(0.611926\pi\)
\(692\) 0 0
\(693\) −3.65812 −0.138960
\(694\) 0 0
\(695\) 24.3809 0.924821
\(696\) 0 0
\(697\) −17.0600 −0.646195
\(698\) 0 0
\(699\) −23.2612 −0.879820
\(700\) 0 0
\(701\) 3.16563 0.119564 0.0597821 0.998211i \(-0.480959\pi\)
0.0597821 + 0.998211i \(0.480959\pi\)
\(702\) 0 0
\(703\) 6.59286 0.248654
\(704\) 0 0
\(705\) −18.5584 −0.698949
\(706\) 0 0
\(707\) 24.8756 0.935542
\(708\) 0 0
\(709\) −31.0905 −1.16763 −0.583814 0.811887i \(-0.698440\pi\)
−0.583814 + 0.811887i \(0.698440\pi\)
\(710\) 0 0
\(711\) −1.28120 −0.0480488
\(712\) 0 0
\(713\) −7.42965 −0.278243
\(714\) 0 0
\(715\) −6.02350 −0.225266
\(716\) 0 0
\(717\) 9.82598 0.366958
\(718\) 0 0
\(719\) 15.6141 0.582309 0.291154 0.956676i \(-0.405961\pi\)
0.291154 + 0.956676i \(0.405961\pi\)
\(720\) 0 0
\(721\) 4.81176 0.179199
\(722\) 0 0
\(723\) −0.446152 −0.0165926
\(724\) 0 0
\(725\) −1.60955 −0.0597772
\(726\) 0 0
\(727\) 7.95160 0.294909 0.147454 0.989069i \(-0.452892\pi\)
0.147454 + 0.989069i \(0.452892\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −7.49346 −0.277156
\(732\) 0 0
\(733\) −5.71166 −0.210965 −0.105482 0.994421i \(-0.533639\pi\)
−0.105482 + 0.994421i \(0.533639\pi\)
\(734\) 0 0
\(735\) −1.45416 −0.0536374
\(736\) 0 0
\(737\) 5.86046 0.215873
\(738\) 0 0
\(739\) 7.90655 0.290847 0.145424 0.989369i \(-0.453546\pi\)
0.145424 + 0.989369i \(0.453546\pi\)
\(740\) 0 0
\(741\) 6.66068 0.244686
\(742\) 0 0
\(743\) 40.3623 1.48075 0.740375 0.672194i \(-0.234648\pi\)
0.740375 + 0.672194i \(0.234648\pi\)
\(744\) 0 0
\(745\) −39.1183 −1.43318
\(746\) 0 0
\(747\) −13.6844 −0.500685
\(748\) 0 0
\(749\) −25.0770 −0.916292
\(750\) 0 0
\(751\) 54.5012 1.98878 0.994389 0.105783i \(-0.0337350\pi\)
0.994389 + 0.105783i \(0.0337350\pi\)
\(752\) 0 0
\(753\) 24.8713 0.906362
\(754\) 0 0
\(755\) 12.7039 0.462342
\(756\) 0 0
\(757\) 43.2504 1.57196 0.785980 0.618251i \(-0.212159\pi\)
0.785980 + 0.618251i \(0.212159\pi\)
\(758\) 0 0
\(759\) 1.31068 0.0475746
\(760\) 0 0
\(761\) 34.9295 1.26619 0.633096 0.774073i \(-0.281784\pi\)
0.633096 + 0.774073i \(0.281784\pi\)
\(762\) 0 0
\(763\) 7.03515 0.254690
\(764\) 0 0
\(765\) 6.26593 0.226545
\(766\) 0 0
\(767\) −13.2749 −0.479329
\(768\) 0 0
\(769\) 0.322606 0.0116335 0.00581673 0.999983i \(-0.498148\pi\)
0.00581673 + 0.999983i \(0.498148\pi\)
\(770\) 0 0
\(771\) −18.7469 −0.675152
\(772\) 0 0
\(773\) −11.7294 −0.421878 −0.210939 0.977499i \(-0.567652\pi\)
−0.210939 + 0.977499i \(0.567652\pi\)
\(774\) 0 0
\(775\) 11.9584 0.429558
\(776\) 0 0
\(777\) −6.89510 −0.247360
\(778\) 0 0
\(779\) 13.3788 0.479346
\(780\) 0 0
\(781\) −4.83226 −0.172912
\(782\) 0 0
\(783\) 1.00000 0.0357371
\(784\) 0 0
\(785\) 7.55719 0.269728
\(786\) 0 0
\(787\) −29.7868 −1.06179 −0.530893 0.847439i \(-0.678143\pi\)
−0.530893 + 0.847439i \(0.678143\pi\)
\(788\) 0 0
\(789\) −29.0245 −1.03330
\(790\) 0 0
\(791\) −2.04015 −0.0725394
\(792\) 0 0
\(793\) 28.2838 1.00439
\(794\) 0 0
\(795\) 0.414771 0.0147104
\(796\) 0 0
\(797\) −14.1416 −0.500921 −0.250460 0.968127i \(-0.580582\pi\)
−0.250460 + 0.968127i \(0.580582\pi\)
\(798\) 0 0
\(799\) −34.2980 −1.21337
\(800\) 0 0
\(801\) −16.0027 −0.565429
\(802\) 0 0
\(803\) −11.9491 −0.421675
\(804\) 0 0
\(805\) 5.13914 0.181131
\(806\) 0 0
\(807\) −30.8162 −1.08478
\(808\) 0 0
\(809\) 24.6028 0.864989 0.432495 0.901637i \(-0.357633\pi\)
0.432495 + 0.901637i \(0.357633\pi\)
\(810\) 0 0
\(811\) 45.8185 1.60890 0.804452 0.594018i \(-0.202459\pi\)
0.804452 + 0.594018i \(0.202459\pi\)
\(812\) 0 0
\(813\) 30.3061 1.06288
\(814\) 0 0
\(815\) 13.1391 0.460242
\(816\) 0 0
\(817\) 5.87652 0.205593
\(818\) 0 0
\(819\) −6.96603 −0.243413
\(820\) 0 0
\(821\) 30.1401 1.05190 0.525948 0.850517i \(-0.323711\pi\)
0.525948 + 0.850517i \(0.323711\pi\)
\(822\) 0 0
\(823\) −24.8868 −0.867499 −0.433749 0.901034i \(-0.642810\pi\)
−0.433749 + 0.901034i \(0.642810\pi\)
\(824\) 0 0
\(825\) −2.10960 −0.0734469
\(826\) 0 0
\(827\) 16.4625 0.572459 0.286229 0.958161i \(-0.407598\pi\)
0.286229 + 0.958161i \(0.407598\pi\)
\(828\) 0 0
\(829\) −10.1519 −0.352589 −0.176295 0.984337i \(-0.556411\pi\)
−0.176295 + 0.984337i \(0.556411\pi\)
\(830\) 0 0
\(831\) 10.1153 0.350894
\(832\) 0 0
\(833\) −2.68744 −0.0931144
\(834\) 0 0
\(835\) 4.73447 0.163843
\(836\) 0 0
\(837\) −7.42965 −0.256806
\(838\) 0 0
\(839\) 7.98039 0.275514 0.137757 0.990466i \(-0.456011\pi\)
0.137757 + 0.990466i \(0.456011\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 0 0
\(843\) −5.35616 −0.184476
\(844\) 0 0
\(845\) 12.4668 0.428870
\(846\) 0 0
\(847\) 25.9065 0.890158
\(848\) 0 0
\(849\) 15.3122 0.525514
\(850\) 0 0
\(851\) 2.47047 0.0846866
\(852\) 0 0
\(853\) −18.3786 −0.629270 −0.314635 0.949213i \(-0.601882\pi\)
−0.314635 + 0.949213i \(0.601882\pi\)
\(854\) 0 0
\(855\) −4.91386 −0.168051
\(856\) 0 0
\(857\) 34.3869 1.17464 0.587318 0.809357i \(-0.300184\pi\)
0.587318 + 0.809357i \(0.300184\pi\)
\(858\) 0 0
\(859\) −36.1092 −1.23203 −0.616014 0.787735i \(-0.711254\pi\)
−0.616014 + 0.787735i \(0.711254\pi\)
\(860\) 0 0
\(861\) −13.9922 −0.476852
\(862\) 0 0
\(863\) 24.6333 0.838528 0.419264 0.907864i \(-0.362288\pi\)
0.419264 + 0.907864i \(0.362288\pi\)
\(864\) 0 0
\(865\) −11.6889 −0.397435
\(866\) 0 0
\(867\) −5.41987 −0.184068
\(868\) 0 0
\(869\) −1.67924 −0.0569644
\(870\) 0 0
\(871\) 11.1599 0.378138
\(872\) 0 0
\(873\) −0.382051 −0.0129305
\(874\) 0 0
\(875\) −33.9674 −1.14831
\(876\) 0 0
\(877\) −0.299645 −0.0101183 −0.00505914 0.999987i \(-0.501610\pi\)
−0.00505914 + 0.999987i \(0.501610\pi\)
\(878\) 0 0
\(879\) 20.0293 0.675571
\(880\) 0 0
\(881\) 17.4170 0.586792 0.293396 0.955991i \(-0.405215\pi\)
0.293396 + 0.955991i \(0.405215\pi\)
\(882\) 0 0
\(883\) 58.5341 1.96983 0.984915 0.173038i \(-0.0553583\pi\)
0.984915 + 0.173038i \(0.0553583\pi\)
\(884\) 0 0
\(885\) 9.79346 0.329203
\(886\) 0 0
\(887\) 11.9826 0.402337 0.201169 0.979557i \(-0.435526\pi\)
0.201169 + 0.979557i \(0.435526\pi\)
\(888\) 0 0
\(889\) 48.3293 1.62091
\(890\) 0 0
\(891\) 1.31068 0.0439094
\(892\) 0 0
\(893\) 26.8971 0.900078
\(894\) 0 0
\(895\) −24.3085 −0.812542
\(896\) 0 0
\(897\) 2.49588 0.0833351
\(898\) 0 0
\(899\) −7.42965 −0.247793
\(900\) 0 0
\(901\) 0.766543 0.0255372
\(902\) 0 0
\(903\) −6.14592 −0.204523
\(904\) 0 0
\(905\) 6.33501 0.210583
\(906\) 0 0
\(907\) −28.4906 −0.946016 −0.473008 0.881058i \(-0.656832\pi\)
−0.473008 + 0.881058i \(0.656832\pi\)
\(908\) 0 0
\(909\) −8.91275 −0.295617
\(910\) 0 0
\(911\) −46.1639 −1.52948 −0.764739 0.644340i \(-0.777132\pi\)
−0.764739 + 0.644340i \(0.777132\pi\)
\(912\) 0 0
\(913\) −17.9358 −0.593589
\(914\) 0 0
\(915\) −20.8661 −0.689813
\(916\) 0 0
\(917\) −13.0283 −0.430232
\(918\) 0 0
\(919\) −28.8727 −0.952421 −0.476211 0.879331i \(-0.657990\pi\)
−0.476211 + 0.879331i \(0.657990\pi\)
\(920\) 0 0
\(921\) −29.9678 −0.987473
\(922\) 0 0
\(923\) −9.20191 −0.302885
\(924\) 0 0
\(925\) −3.97634 −0.130741
\(926\) 0 0
\(927\) −1.72402 −0.0566243
\(928\) 0 0
\(929\) −8.26220 −0.271074 −0.135537 0.990772i \(-0.543276\pi\)
−0.135537 + 0.990772i \(0.543276\pi\)
\(930\) 0 0
\(931\) 2.10755 0.0690720
\(932\) 0 0
\(933\) 20.1613 0.660050
\(934\) 0 0
\(935\) 8.21262 0.268581
\(936\) 0 0
\(937\) −42.0102 −1.37241 −0.686207 0.727406i \(-0.740726\pi\)
−0.686207 + 0.727406i \(0.740726\pi\)
\(938\) 0 0
\(939\) −9.24273 −0.301625
\(940\) 0 0
\(941\) −20.2044 −0.658646 −0.329323 0.944217i \(-0.606820\pi\)
−0.329323 + 0.944217i \(0.606820\pi\)
\(942\) 0 0
\(943\) 5.01330 0.163255
\(944\) 0 0
\(945\) 5.13914 0.167176
\(946\) 0 0
\(947\) −17.8025 −0.578503 −0.289251 0.957253i \(-0.593406\pi\)
−0.289251 + 0.957253i \(0.593406\pi\)
\(948\) 0 0
\(949\) −22.7543 −0.738636
\(950\) 0 0
\(951\) 2.91035 0.0943745
\(952\) 0 0
\(953\) 7.84427 0.254101 0.127050 0.991896i \(-0.459449\pi\)
0.127050 + 0.991896i \(0.459449\pi\)
\(954\) 0 0
\(955\) 23.9791 0.775947
\(956\) 0 0
\(957\) 1.31068 0.0423682
\(958\) 0 0
\(959\) 4.76537 0.153882
\(960\) 0 0
\(961\) 24.1998 0.780637
\(962\) 0 0
\(963\) 8.98490 0.289534
\(964\) 0 0
\(965\) 5.99568 0.193008
\(966\) 0 0
\(967\) −9.66288 −0.310737 −0.155369 0.987857i \(-0.549657\pi\)
−0.155369 + 0.987857i \(0.549657\pi\)
\(968\) 0 0
\(969\) −9.08136 −0.291735
\(970\) 0 0
\(971\) −18.3599 −0.589196 −0.294598 0.955621i \(-0.595186\pi\)
−0.294598 + 0.955621i \(0.595186\pi\)
\(972\) 0 0
\(973\) 36.9558 1.18475
\(974\) 0 0
\(975\) −4.01724 −0.128655
\(976\) 0 0
\(977\) 4.09208 0.130917 0.0654586 0.997855i \(-0.479149\pi\)
0.0654586 + 0.997855i \(0.479149\pi\)
\(978\) 0 0
\(979\) −20.9744 −0.670346
\(980\) 0 0
\(981\) −2.52065 −0.0804781
\(982\) 0 0
\(983\) −4.24113 −0.135271 −0.0676356 0.997710i \(-0.521546\pi\)
−0.0676356 + 0.997710i \(0.521546\pi\)
\(984\) 0 0
\(985\) 23.5904 0.751652
\(986\) 0 0
\(987\) −28.1302 −0.895394
\(988\) 0 0
\(989\) 2.20204 0.0700208
\(990\) 0 0
\(991\) −58.6987 −1.86463 −0.932313 0.361654i \(-0.882212\pi\)
−0.932313 + 0.361654i \(0.882212\pi\)
\(992\) 0 0
\(993\) −23.1303 −0.734017
\(994\) 0 0
\(995\) 1.18126 0.0374484
\(996\) 0 0
\(997\) 21.2189 0.672009 0.336005 0.941860i \(-0.390924\pi\)
0.336005 + 0.941860i \(0.390924\pi\)
\(998\) 0 0
\(999\) 2.47047 0.0781622
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 \(a_p\))