Properties

Label 8016.2.a.bg.1.7
Level 8016
Weight 2
Character 8016.1
Self dual Yes
Analytic conductor 64.008
Analytic rank 0
Dimension 13
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8016 = 2^{4} \cdot 3 \cdot 167 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8016.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0080822603\)
Analytic rank: \(0\)
Dimension: \(13\)
Coefficient field: \(\mathbb{Q}[x]/(x^{13} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{13}]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.7
Root \(0.649069\)
Character \(\chi\) = 8016.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{3}\) \(+0.649069 q^{5}\) \(-4.19646 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{3}\) \(+0.649069 q^{5}\) \(-4.19646 q^{7}\) \(+1.00000 q^{9}\) \(-1.95286 q^{11}\) \(+3.07299 q^{13}\) \(-0.649069 q^{15}\) \(+6.85258 q^{17}\) \(-8.04597 q^{19}\) \(+4.19646 q^{21}\) \(+6.50672 q^{23}\) \(-4.57871 q^{25}\) \(-1.00000 q^{27}\) \(-2.52529 q^{29}\) \(-4.14955 q^{31}\) \(+1.95286 q^{33}\) \(-2.72380 q^{35}\) \(-4.94625 q^{37}\) \(-3.07299 q^{39}\) \(+2.05737 q^{41}\) \(-4.35750 q^{43}\) \(+0.649069 q^{45}\) \(+11.2109 q^{47}\) \(+10.6103 q^{49}\) \(-6.85258 q^{51}\) \(-1.69789 q^{53}\) \(-1.26754 q^{55}\) \(+8.04597 q^{57}\) \(+7.31745 q^{59}\) \(-12.5360 q^{61}\) \(-4.19646 q^{63}\) \(+1.99458 q^{65}\) \(+6.97495 q^{67}\) \(-6.50672 q^{69}\) \(-2.84782 q^{71}\) \(-7.78221 q^{73}\) \(+4.57871 q^{75}\) \(+8.19511 q^{77}\) \(+3.29528 q^{79}\) \(+1.00000 q^{81}\) \(-1.99647 q^{83}\) \(+4.44780 q^{85}\) \(+2.52529 q^{87}\) \(-15.9262 q^{89}\) \(-12.8957 q^{91}\) \(+4.14955 q^{93}\) \(-5.22239 q^{95}\) \(+13.7538 q^{97}\) \(-1.95286 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(13q \) \(\mathstrut -\mathstrut 13q^{3} \) \(\mathstrut +\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut q^{7} \) \(\mathstrut +\mathstrut 13q^{9} \) \(\mathstrut -\mathstrut 11q^{11} \) \(\mathstrut +\mathstrut 12q^{13} \) \(\mathstrut -\mathstrut 2q^{15} \) \(\mathstrut +\mathstrut 15q^{17} \) \(\mathstrut -\mathstrut 14q^{19} \) \(\mathstrut +\mathstrut q^{21} \) \(\mathstrut -\mathstrut 9q^{23} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 13q^{27} \) \(\mathstrut -\mathstrut 3q^{29} \) \(\mathstrut +\mathstrut 17q^{31} \) \(\mathstrut +\mathstrut 11q^{33} \) \(\mathstrut -\mathstrut 15q^{35} \) \(\mathstrut +\mathstrut 16q^{37} \) \(\mathstrut -\mathstrut 12q^{39} \) \(\mathstrut +\mathstrut 12q^{41} \) \(\mathstrut -\mathstrut 20q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 6q^{47} \) \(\mathstrut +\mathstrut 26q^{49} \) \(\mathstrut -\mathstrut 15q^{51} \) \(\mathstrut -\mathstrut 12q^{53} \) \(\mathstrut -\mathstrut 7q^{55} \) \(\mathstrut +\mathstrut 14q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut -\mathstrut q^{63} \) \(\mathstrut +\mathstrut 8q^{65} \) \(\mathstrut -\mathstrut 3q^{67} \) \(\mathstrut +\mathstrut 9q^{69} \) \(\mathstrut -\mathstrut 17q^{71} \) \(\mathstrut +\mathstrut 34q^{73} \) \(\mathstrut -\mathstrut 37q^{75} \) \(\mathstrut +\mathstrut 30q^{77} \) \(\mathstrut -\mathstrut 10q^{79} \) \(\mathstrut +\mathstrut 13q^{81} \) \(\mathstrut -\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 25q^{85} \) \(\mathstrut +\mathstrut 3q^{87} \) \(\mathstrut +\mathstrut 25q^{89} \) \(\mathstrut -\mathstrut 29q^{91} \) \(\mathstrut -\mathstrut 17q^{93} \) \(\mathstrut +\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 38q^{97} \) \(\mathstrut -\mathstrut 11q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(5\) 0.649069 0.290273 0.145136 0.989412i \(-0.453638\pi\)
0.145136 + 0.989412i \(0.453638\pi\)
\(6\) 0 0
\(7\) −4.19646 −1.58611 −0.793057 0.609147i \(-0.791512\pi\)
−0.793057 + 0.609147i \(0.791512\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −1.95286 −0.588810 −0.294405 0.955681i \(-0.595121\pi\)
−0.294405 + 0.955681i \(0.595121\pi\)
\(12\) 0 0
\(13\) 3.07299 0.852293 0.426146 0.904654i \(-0.359871\pi\)
0.426146 + 0.904654i \(0.359871\pi\)
\(14\) 0 0
\(15\) −0.649069 −0.167589
\(16\) 0 0
\(17\) 6.85258 1.66200 0.830998 0.556276i \(-0.187770\pi\)
0.830998 + 0.556276i \(0.187770\pi\)
\(18\) 0 0
\(19\) −8.04597 −1.84587 −0.922936 0.384954i \(-0.874217\pi\)
−0.922936 + 0.384954i \(0.874217\pi\)
\(20\) 0 0
\(21\) 4.19646 0.915744
\(22\) 0 0
\(23\) 6.50672 1.35675 0.678373 0.734718i \(-0.262686\pi\)
0.678373 + 0.734718i \(0.262686\pi\)
\(24\) 0 0
\(25\) −4.57871 −0.915742
\(26\) 0 0
\(27\) −1.00000 −0.192450
\(28\) 0 0
\(29\) −2.52529 −0.468935 −0.234468 0.972124i \(-0.575335\pi\)
−0.234468 + 0.972124i \(0.575335\pi\)
\(30\) 0 0
\(31\) −4.14955 −0.745281 −0.372640 0.927976i \(-0.621547\pi\)
−0.372640 + 0.927976i \(0.621547\pi\)
\(32\) 0 0
\(33\) 1.95286 0.339949
\(34\) 0 0
\(35\) −2.72380 −0.460406
\(36\) 0 0
\(37\) −4.94625 −0.813159 −0.406579 0.913615i \(-0.633279\pi\)
−0.406579 + 0.913615i \(0.633279\pi\)
\(38\) 0 0
\(39\) −3.07299 −0.492072
\(40\) 0 0
\(41\) 2.05737 0.321308 0.160654 0.987011i \(-0.448640\pi\)
0.160654 + 0.987011i \(0.448640\pi\)
\(42\) 0 0
\(43\) −4.35750 −0.664512 −0.332256 0.943189i \(-0.607810\pi\)
−0.332256 + 0.943189i \(0.607810\pi\)
\(44\) 0 0
\(45\) 0.649069 0.0967576
\(46\) 0 0
\(47\) 11.2109 1.63528 0.817641 0.575728i \(-0.195281\pi\)
0.817641 + 0.575728i \(0.195281\pi\)
\(48\) 0 0
\(49\) 10.6103 1.51576
\(50\) 0 0
\(51\) −6.85258 −0.959554
\(52\) 0 0
\(53\) −1.69789 −0.233224 −0.116612 0.993178i \(-0.537203\pi\)
−0.116612 + 0.993178i \(0.537203\pi\)
\(54\) 0 0
\(55\) −1.26754 −0.170915
\(56\) 0 0
\(57\) 8.04597 1.06571
\(58\) 0 0
\(59\) 7.31745 0.952651 0.476326 0.879269i \(-0.341968\pi\)
0.476326 + 0.879269i \(0.341968\pi\)
\(60\) 0 0
\(61\) −12.5360 −1.60507 −0.802534 0.596607i \(-0.796515\pi\)
−0.802534 + 0.596607i \(0.796515\pi\)
\(62\) 0 0
\(63\) −4.19646 −0.528705
\(64\) 0 0
\(65\) 1.99458 0.247397
\(66\) 0 0
\(67\) 6.97495 0.852126 0.426063 0.904694i \(-0.359900\pi\)
0.426063 + 0.904694i \(0.359900\pi\)
\(68\) 0 0
\(69\) −6.50672 −0.783317
\(70\) 0 0
\(71\) −2.84782 −0.337974 −0.168987 0.985618i \(-0.554050\pi\)
−0.168987 + 0.985618i \(0.554050\pi\)
\(72\) 0 0
\(73\) −7.78221 −0.910839 −0.455420 0.890277i \(-0.650511\pi\)
−0.455420 + 0.890277i \(0.650511\pi\)
\(74\) 0 0
\(75\) 4.57871 0.528704
\(76\) 0 0
\(77\) 8.19511 0.933920
\(78\) 0 0
\(79\) 3.29528 0.370747 0.185374 0.982668i \(-0.440650\pi\)
0.185374 + 0.982668i \(0.440650\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) −1.99647 −0.219141 −0.109571 0.993979i \(-0.534948\pi\)
−0.109571 + 0.993979i \(0.534948\pi\)
\(84\) 0 0
\(85\) 4.44780 0.482432
\(86\) 0 0
\(87\) 2.52529 0.270740
\(88\) 0 0
\(89\) −15.9262 −1.68817 −0.844086 0.536207i \(-0.819857\pi\)
−0.844086 + 0.536207i \(0.819857\pi\)
\(90\) 0 0
\(91\) −12.8957 −1.35183
\(92\) 0 0
\(93\) 4.14955 0.430288
\(94\) 0 0
\(95\) −5.22239 −0.535806
\(96\) 0 0
\(97\) 13.7538 1.39649 0.698243 0.715861i \(-0.253966\pi\)
0.698243 + 0.715861i \(0.253966\pi\)
\(98\) 0 0
\(99\) −1.95286 −0.196270
\(100\) 0 0
\(101\) −2.39371 −0.238183 −0.119092 0.992883i \(-0.537998\pi\)
−0.119092 + 0.992883i \(0.537998\pi\)
\(102\) 0 0
\(103\) 0.185299 0.0182581 0.00912904 0.999958i \(-0.497094\pi\)
0.00912904 + 0.999958i \(0.497094\pi\)
\(104\) 0 0
\(105\) 2.72380 0.265815
\(106\) 0 0
\(107\) 10.1993 0.986002 0.493001 0.870029i \(-0.335900\pi\)
0.493001 + 0.870029i \(0.335900\pi\)
\(108\) 0 0
\(109\) −11.3264 −1.08487 −0.542437 0.840097i \(-0.682498\pi\)
−0.542437 + 0.840097i \(0.682498\pi\)
\(110\) 0 0
\(111\) 4.94625 0.469477
\(112\) 0 0
\(113\) 1.85199 0.174221 0.0871104 0.996199i \(-0.472237\pi\)
0.0871104 + 0.996199i \(0.472237\pi\)
\(114\) 0 0
\(115\) 4.22331 0.393826
\(116\) 0 0
\(117\) 3.07299 0.284098
\(118\) 0 0
\(119\) −28.7566 −2.63612
\(120\) 0 0
\(121\) −7.18633 −0.653303
\(122\) 0 0
\(123\) −2.05737 −0.185507
\(124\) 0 0
\(125\) −6.21725 −0.556087
\(126\) 0 0
\(127\) −10.4107 −0.923802 −0.461901 0.886931i \(-0.652833\pi\)
−0.461901 + 0.886931i \(0.652833\pi\)
\(128\) 0 0
\(129\) 4.35750 0.383656
\(130\) 0 0
\(131\) 15.5093 1.35506 0.677528 0.735497i \(-0.263051\pi\)
0.677528 + 0.735497i \(0.263051\pi\)
\(132\) 0 0
\(133\) 33.7646 2.92776
\(134\) 0 0
\(135\) −0.649069 −0.0558630
\(136\) 0 0
\(137\) 16.4624 1.40648 0.703239 0.710954i \(-0.251736\pi\)
0.703239 + 0.710954i \(0.251736\pi\)
\(138\) 0 0
\(139\) −19.8190 −1.68102 −0.840512 0.541793i \(-0.817746\pi\)
−0.840512 + 0.541793i \(0.817746\pi\)
\(140\) 0 0
\(141\) −11.2109 −0.944131
\(142\) 0 0
\(143\) −6.00111 −0.501838
\(144\) 0 0
\(145\) −1.63909 −0.136119
\(146\) 0 0
\(147\) −10.6103 −0.875124
\(148\) 0 0
\(149\) 9.90281 0.811269 0.405635 0.914035i \(-0.367051\pi\)
0.405635 + 0.914035i \(0.367051\pi\)
\(150\) 0 0
\(151\) −3.84338 −0.312770 −0.156385 0.987696i \(-0.549984\pi\)
−0.156385 + 0.987696i \(0.549984\pi\)
\(152\) 0 0
\(153\) 6.85258 0.553999
\(154\) 0 0
\(155\) −2.69334 −0.216335
\(156\) 0 0
\(157\) 6.26403 0.499924 0.249962 0.968256i \(-0.419582\pi\)
0.249962 + 0.968256i \(0.419582\pi\)
\(158\) 0 0
\(159\) 1.69789 0.134652
\(160\) 0 0
\(161\) −27.3052 −2.15195
\(162\) 0 0
\(163\) 15.4625 1.21111 0.605557 0.795802i \(-0.292950\pi\)
0.605557 + 0.795802i \(0.292950\pi\)
\(164\) 0 0
\(165\) 1.26754 0.0986780
\(166\) 0 0
\(167\) 1.00000 0.0773823
\(168\) 0 0
\(169\) −3.55676 −0.273597
\(170\) 0 0
\(171\) −8.04597 −0.615290
\(172\) 0 0
\(173\) −4.68343 −0.356075 −0.178037 0.984024i \(-0.556975\pi\)
−0.178037 + 0.984024i \(0.556975\pi\)
\(174\) 0 0
\(175\) 19.2144 1.45247
\(176\) 0 0
\(177\) −7.31745 −0.550014
\(178\) 0 0
\(179\) 23.5932 1.76344 0.881720 0.471773i \(-0.156386\pi\)
0.881720 + 0.471773i \(0.156386\pi\)
\(180\) 0 0
\(181\) 6.72533 0.499890 0.249945 0.968260i \(-0.419588\pi\)
0.249945 + 0.968260i \(0.419588\pi\)
\(182\) 0 0
\(183\) 12.5360 0.926686
\(184\) 0 0
\(185\) −3.21046 −0.236038
\(186\) 0 0
\(187\) −13.3821 −0.978599
\(188\) 0 0
\(189\) 4.19646 0.305248
\(190\) 0 0
\(191\) −10.7649 −0.778922 −0.389461 0.921043i \(-0.627339\pi\)
−0.389461 + 0.921043i \(0.627339\pi\)
\(192\) 0 0
\(193\) 17.0021 1.22384 0.611918 0.790921i \(-0.290398\pi\)
0.611918 + 0.790921i \(0.290398\pi\)
\(194\) 0 0
\(195\) −1.99458 −0.142835
\(196\) 0 0
\(197\) 10.7297 0.764461 0.382230 0.924067i \(-0.375156\pi\)
0.382230 + 0.924067i \(0.375156\pi\)
\(198\) 0 0
\(199\) 12.9427 0.917486 0.458743 0.888569i \(-0.348300\pi\)
0.458743 + 0.888569i \(0.348300\pi\)
\(200\) 0 0
\(201\) −6.97495 −0.491975
\(202\) 0 0
\(203\) 10.5973 0.743785
\(204\) 0 0
\(205\) 1.33538 0.0932669
\(206\) 0 0
\(207\) 6.50672 0.452248
\(208\) 0 0
\(209\) 15.7127 1.08687
\(210\) 0 0
\(211\) 0.727181 0.0500612 0.0250306 0.999687i \(-0.492032\pi\)
0.0250306 + 0.999687i \(0.492032\pi\)
\(212\) 0 0
\(213\) 2.84782 0.195129
\(214\) 0 0
\(215\) −2.82832 −0.192890
\(216\) 0 0
\(217\) 17.4134 1.18210
\(218\) 0 0
\(219\) 7.78221 0.525873
\(220\) 0 0
\(221\) 21.0579 1.41651
\(222\) 0 0
\(223\) 22.1726 1.48478 0.742392 0.669966i \(-0.233691\pi\)
0.742392 + 0.669966i \(0.233691\pi\)
\(224\) 0 0
\(225\) −4.57871 −0.305247
\(226\) 0 0
\(227\) −6.28074 −0.416867 −0.208434 0.978037i \(-0.566837\pi\)
−0.208434 + 0.978037i \(0.566837\pi\)
\(228\) 0 0
\(229\) 21.3981 1.41402 0.707012 0.707201i \(-0.250043\pi\)
0.707012 + 0.707201i \(0.250043\pi\)
\(230\) 0 0
\(231\) −8.19511 −0.539199
\(232\) 0 0
\(233\) −22.8556 −1.49732 −0.748659 0.662956i \(-0.769302\pi\)
−0.748659 + 0.662956i \(0.769302\pi\)
\(234\) 0 0
\(235\) 7.27667 0.474678
\(236\) 0 0
\(237\) −3.29528 −0.214051
\(238\) 0 0
\(239\) 21.7956 1.40984 0.704920 0.709287i \(-0.250983\pi\)
0.704920 + 0.709287i \(0.250983\pi\)
\(240\) 0 0
\(241\) −3.28924 −0.211878 −0.105939 0.994373i \(-0.533785\pi\)
−0.105939 + 0.994373i \(0.533785\pi\)
\(242\) 0 0
\(243\) −1.00000 −0.0641500
\(244\) 0 0
\(245\) 6.88683 0.439983
\(246\) 0 0
\(247\) −24.7251 −1.57322
\(248\) 0 0
\(249\) 1.99647 0.126521
\(250\) 0 0
\(251\) −12.5801 −0.794050 −0.397025 0.917808i \(-0.629957\pi\)
−0.397025 + 0.917808i \(0.629957\pi\)
\(252\) 0 0
\(253\) −12.7067 −0.798865
\(254\) 0 0
\(255\) −4.44780 −0.278532
\(256\) 0 0
\(257\) 4.03469 0.251677 0.125839 0.992051i \(-0.459838\pi\)
0.125839 + 0.992051i \(0.459838\pi\)
\(258\) 0 0
\(259\) 20.7568 1.28976
\(260\) 0 0
\(261\) −2.52529 −0.156312
\(262\) 0 0
\(263\) 12.0597 0.743631 0.371815 0.928307i \(-0.378735\pi\)
0.371815 + 0.928307i \(0.378735\pi\)
\(264\) 0 0
\(265\) −1.10205 −0.0676984
\(266\) 0 0
\(267\) 15.9262 0.974667
\(268\) 0 0
\(269\) −0.441761 −0.0269346 −0.0134673 0.999909i \(-0.504287\pi\)
−0.0134673 + 0.999909i \(0.504287\pi\)
\(270\) 0 0
\(271\) 21.7472 1.32105 0.660523 0.750806i \(-0.270334\pi\)
0.660523 + 0.750806i \(0.270334\pi\)
\(272\) 0 0
\(273\) 12.8957 0.780482
\(274\) 0 0
\(275\) 8.94158 0.539198
\(276\) 0 0
\(277\) −12.7062 −0.763442 −0.381721 0.924278i \(-0.624669\pi\)
−0.381721 + 0.924278i \(0.624669\pi\)
\(278\) 0 0
\(279\) −4.14955 −0.248427
\(280\) 0 0
\(281\) 24.6981 1.47336 0.736682 0.676240i \(-0.236392\pi\)
0.736682 + 0.676240i \(0.236392\pi\)
\(282\) 0 0
\(283\) −5.77605 −0.343350 −0.171675 0.985154i \(-0.554918\pi\)
−0.171675 + 0.985154i \(0.554918\pi\)
\(284\) 0 0
\(285\) 5.22239 0.309348
\(286\) 0 0
\(287\) −8.63370 −0.509631
\(288\) 0 0
\(289\) 29.9579 1.76223
\(290\) 0 0
\(291\) −13.7538 −0.806261
\(292\) 0 0
\(293\) 14.9087 0.870973 0.435486 0.900195i \(-0.356576\pi\)
0.435486 + 0.900195i \(0.356576\pi\)
\(294\) 0 0
\(295\) 4.74954 0.276529
\(296\) 0 0
\(297\) 1.95286 0.113316
\(298\) 0 0
\(299\) 19.9951 1.15634
\(300\) 0 0
\(301\) 18.2861 1.05399
\(302\) 0 0
\(303\) 2.39371 0.137515
\(304\) 0 0
\(305\) −8.13672 −0.465907
\(306\) 0 0
\(307\) −2.60592 −0.148728 −0.0743638 0.997231i \(-0.523693\pi\)
−0.0743638 + 0.997231i \(0.523693\pi\)
\(308\) 0 0
\(309\) −0.185299 −0.0105413
\(310\) 0 0
\(311\) 5.88680 0.333810 0.166905 0.985973i \(-0.446623\pi\)
0.166905 + 0.985973i \(0.446623\pi\)
\(312\) 0 0
\(313\) 29.5589 1.67077 0.835384 0.549667i \(-0.185245\pi\)
0.835384 + 0.549667i \(0.185245\pi\)
\(314\) 0 0
\(315\) −2.72380 −0.153469
\(316\) 0 0
\(317\) 27.3897 1.53836 0.769180 0.639032i \(-0.220665\pi\)
0.769180 + 0.639032i \(0.220665\pi\)
\(318\) 0 0
\(319\) 4.93155 0.276114
\(320\) 0 0
\(321\) −10.1993 −0.569268
\(322\) 0 0
\(323\) −55.1357 −3.06783
\(324\) 0 0
\(325\) −14.0703 −0.780480
\(326\) 0 0
\(327\) 11.3264 0.626352
\(328\) 0 0
\(329\) −47.0463 −2.59375
\(330\) 0 0
\(331\) −25.0680 −1.37786 −0.688931 0.724827i \(-0.741920\pi\)
−0.688931 + 0.724827i \(0.741920\pi\)
\(332\) 0 0
\(333\) −4.94625 −0.271053
\(334\) 0 0
\(335\) 4.52723 0.247349
\(336\) 0 0
\(337\) −20.0351 −1.09138 −0.545691 0.837987i \(-0.683733\pi\)
−0.545691 + 0.837987i \(0.683733\pi\)
\(338\) 0 0
\(339\) −1.85199 −0.100586
\(340\) 0 0
\(341\) 8.10349 0.438829
\(342\) 0 0
\(343\) −15.1505 −0.818052
\(344\) 0 0
\(345\) −4.22331 −0.227376
\(346\) 0 0
\(347\) −27.6121 −1.48229 −0.741147 0.671343i \(-0.765718\pi\)
−0.741147 + 0.671343i \(0.765718\pi\)
\(348\) 0 0
\(349\) 23.2868 1.24652 0.623258 0.782016i \(-0.285809\pi\)
0.623258 + 0.782016i \(0.285809\pi\)
\(350\) 0 0
\(351\) −3.07299 −0.164024
\(352\) 0 0
\(353\) −27.0763 −1.44112 −0.720562 0.693390i \(-0.756116\pi\)
−0.720562 + 0.693390i \(0.756116\pi\)
\(354\) 0 0
\(355\) −1.84843 −0.0981045
\(356\) 0 0
\(357\) 28.7566 1.52196
\(358\) 0 0
\(359\) 10.5945 0.559156 0.279578 0.960123i \(-0.409805\pi\)
0.279578 + 0.960123i \(0.409805\pi\)
\(360\) 0 0
\(361\) 45.7376 2.40724
\(362\) 0 0
\(363\) 7.18633 0.377185
\(364\) 0 0
\(365\) −5.05120 −0.264392
\(366\) 0 0
\(367\) −8.01577 −0.418420 −0.209210 0.977871i \(-0.567089\pi\)
−0.209210 + 0.977871i \(0.567089\pi\)
\(368\) 0 0
\(369\) 2.05737 0.107103
\(370\) 0 0
\(371\) 7.12515 0.369919
\(372\) 0 0
\(373\) −0.337791 −0.0174902 −0.00874508 0.999962i \(-0.502784\pi\)
−0.00874508 + 0.999962i \(0.502784\pi\)
\(374\) 0 0
\(375\) 6.21725 0.321057
\(376\) 0 0
\(377\) −7.76019 −0.399670
\(378\) 0 0
\(379\) −31.4233 −1.61411 −0.807054 0.590477i \(-0.798940\pi\)
−0.807054 + 0.590477i \(0.798940\pi\)
\(380\) 0 0
\(381\) 10.4107 0.533357
\(382\) 0 0
\(383\) 23.6461 1.20826 0.604129 0.796887i \(-0.293521\pi\)
0.604129 + 0.796887i \(0.293521\pi\)
\(384\) 0 0
\(385\) 5.31920 0.271091
\(386\) 0 0
\(387\) −4.35750 −0.221504
\(388\) 0 0
\(389\) 9.30638 0.471852 0.235926 0.971771i \(-0.424188\pi\)
0.235926 + 0.971771i \(0.424188\pi\)
\(390\) 0 0
\(391\) 44.5879 2.25490
\(392\) 0 0
\(393\) −15.5093 −0.782342
\(394\) 0 0
\(395\) 2.13886 0.107618
\(396\) 0 0
\(397\) 5.29743 0.265870 0.132935 0.991125i \(-0.457560\pi\)
0.132935 + 0.991125i \(0.457560\pi\)
\(398\) 0 0
\(399\) −33.7646 −1.69034
\(400\) 0 0
\(401\) 24.1903 1.20801 0.604004 0.796982i \(-0.293571\pi\)
0.604004 + 0.796982i \(0.293571\pi\)
\(402\) 0 0
\(403\) −12.7515 −0.635198
\(404\) 0 0
\(405\) 0.649069 0.0322525
\(406\) 0 0
\(407\) 9.65934 0.478796
\(408\) 0 0
\(409\) −26.6321 −1.31687 −0.658436 0.752637i \(-0.728782\pi\)
−0.658436 + 0.752637i \(0.728782\pi\)
\(410\) 0 0
\(411\) −16.4624 −0.812030
\(412\) 0 0
\(413\) −30.7074 −1.51101
\(414\) 0 0
\(415\) −1.29585 −0.0636107
\(416\) 0 0
\(417\) 19.8190 0.970540
\(418\) 0 0
\(419\) 16.8970 0.825473 0.412737 0.910850i \(-0.364573\pi\)
0.412737 + 0.910850i \(0.364573\pi\)
\(420\) 0 0
\(421\) 13.6534 0.665428 0.332714 0.943028i \(-0.392036\pi\)
0.332714 + 0.943028i \(0.392036\pi\)
\(422\) 0 0
\(423\) 11.2109 0.545094
\(424\) 0 0
\(425\) −31.3760 −1.52196
\(426\) 0 0
\(427\) 52.6068 2.54582
\(428\) 0 0
\(429\) 6.00111 0.289737
\(430\) 0 0
\(431\) −3.15760 −0.152096 −0.0760481 0.997104i \(-0.524230\pi\)
−0.0760481 + 0.997104i \(0.524230\pi\)
\(432\) 0 0
\(433\) −3.19183 −0.153390 −0.0766948 0.997055i \(-0.524437\pi\)
−0.0766948 + 0.997055i \(0.524437\pi\)
\(434\) 0 0
\(435\) 1.63909 0.0785884
\(436\) 0 0
\(437\) −52.3529 −2.50438
\(438\) 0 0
\(439\) −24.3383 −1.16160 −0.580801 0.814046i \(-0.697261\pi\)
−0.580801 + 0.814046i \(0.697261\pi\)
\(440\) 0 0
\(441\) 10.6103 0.505253
\(442\) 0 0
\(443\) 2.32690 0.110554 0.0552772 0.998471i \(-0.482396\pi\)
0.0552772 + 0.998471i \(0.482396\pi\)
\(444\) 0 0
\(445\) −10.3372 −0.490030
\(446\) 0 0
\(447\) −9.90281 −0.468387
\(448\) 0 0
\(449\) 18.9408 0.893869 0.446935 0.894567i \(-0.352516\pi\)
0.446935 + 0.894567i \(0.352516\pi\)
\(450\) 0 0
\(451\) −4.01777 −0.189189
\(452\) 0 0
\(453\) 3.84338 0.180578
\(454\) 0 0
\(455\) −8.37019 −0.392400
\(456\) 0 0
\(457\) −7.00613 −0.327733 −0.163867 0.986483i \(-0.552397\pi\)
−0.163867 + 0.986483i \(0.552397\pi\)
\(458\) 0 0
\(459\) −6.85258 −0.319851
\(460\) 0 0
\(461\) 29.9382 1.39436 0.697182 0.716895i \(-0.254437\pi\)
0.697182 + 0.716895i \(0.254437\pi\)
\(462\) 0 0
\(463\) 28.6425 1.33113 0.665564 0.746341i \(-0.268191\pi\)
0.665564 + 0.746341i \(0.268191\pi\)
\(464\) 0 0
\(465\) 2.69334 0.124901
\(466\) 0 0
\(467\) 10.2858 0.475970 0.237985 0.971269i \(-0.423513\pi\)
0.237985 + 0.971269i \(0.423513\pi\)
\(468\) 0 0
\(469\) −29.2701 −1.35157
\(470\) 0 0
\(471\) −6.26403 −0.288631
\(472\) 0 0
\(473\) 8.50959 0.391271
\(474\) 0 0
\(475\) 36.8401 1.69034
\(476\) 0 0
\(477\) −1.69789 −0.0777412
\(478\) 0 0
\(479\) 35.9258 1.64149 0.820745 0.571295i \(-0.193559\pi\)
0.820745 + 0.571295i \(0.193559\pi\)
\(480\) 0 0
\(481\) −15.1998 −0.693050
\(482\) 0 0
\(483\) 27.3052 1.24243
\(484\) 0 0
\(485\) 8.92716 0.405362
\(486\) 0 0
\(487\) 24.5681 1.11329 0.556644 0.830751i \(-0.312089\pi\)
0.556644 + 0.830751i \(0.312089\pi\)
\(488\) 0 0
\(489\) −15.4625 −0.699237
\(490\) 0 0
\(491\) 14.0673 0.634848 0.317424 0.948284i \(-0.397182\pi\)
0.317424 + 0.948284i \(0.397182\pi\)
\(492\) 0 0
\(493\) −17.3048 −0.779368
\(494\) 0 0
\(495\) −1.26754 −0.0569718
\(496\) 0 0
\(497\) 11.9508 0.536065
\(498\) 0 0
\(499\) −28.3654 −1.26981 −0.634905 0.772590i \(-0.718961\pi\)
−0.634905 + 0.772590i \(0.718961\pi\)
\(500\) 0 0
\(501\) −1.00000 −0.0446767
\(502\) 0 0
\(503\) 3.29871 0.147082 0.0735412 0.997292i \(-0.476570\pi\)
0.0735412 + 0.997292i \(0.476570\pi\)
\(504\) 0 0
\(505\) −1.55369 −0.0691381
\(506\) 0 0
\(507\) 3.55676 0.157961
\(508\) 0 0
\(509\) −13.2600 −0.587738 −0.293869 0.955846i \(-0.594943\pi\)
−0.293869 + 0.955846i \(0.594943\pi\)
\(510\) 0 0
\(511\) 32.6578 1.44470
\(512\) 0 0
\(513\) 8.04597 0.355238
\(514\) 0 0
\(515\) 0.120272 0.00529982
\(516\) 0 0
\(517\) −21.8934 −0.962870
\(518\) 0 0
\(519\) 4.68343 0.205580
\(520\) 0 0
\(521\) 23.0586 1.01022 0.505108 0.863056i \(-0.331453\pi\)
0.505108 + 0.863056i \(0.331453\pi\)
\(522\) 0 0
\(523\) 5.08722 0.222449 0.111224 0.993795i \(-0.464523\pi\)
0.111224 + 0.993795i \(0.464523\pi\)
\(524\) 0 0
\(525\) −19.2144 −0.838585
\(526\) 0 0
\(527\) −28.4351 −1.23865
\(528\) 0 0
\(529\) 19.3374 0.840758
\(530\) 0 0
\(531\) 7.31745 0.317550
\(532\) 0 0
\(533\) 6.32228 0.273848
\(534\) 0 0
\(535\) 6.62004 0.286209
\(536\) 0 0
\(537\) −23.5932 −1.01812
\(538\) 0 0
\(539\) −20.7205 −0.892493
\(540\) 0 0
\(541\) 6.83762 0.293972 0.146986 0.989139i \(-0.453043\pi\)
0.146986 + 0.989139i \(0.453043\pi\)
\(542\) 0 0
\(543\) −6.72533 −0.288611
\(544\) 0 0
\(545\) −7.35163 −0.314909
\(546\) 0 0
\(547\) 2.89764 0.123894 0.0619470 0.998079i \(-0.480269\pi\)
0.0619470 + 0.998079i \(0.480269\pi\)
\(548\) 0 0
\(549\) −12.5360 −0.535022
\(550\) 0 0
\(551\) 20.3184 0.865594
\(552\) 0 0
\(553\) −13.8285 −0.588048
\(554\) 0 0
\(555\) 3.21046 0.136276
\(556\) 0 0
\(557\) 1.11407 0.0472045 0.0236023 0.999721i \(-0.492486\pi\)
0.0236023 + 0.999721i \(0.492486\pi\)
\(558\) 0 0
\(559\) −13.3905 −0.566359
\(560\) 0 0
\(561\) 13.3821 0.564995
\(562\) 0 0
\(563\) 26.2894 1.10797 0.553984 0.832527i \(-0.313107\pi\)
0.553984 + 0.832527i \(0.313107\pi\)
\(564\) 0 0
\(565\) 1.20207 0.0505715
\(566\) 0 0
\(567\) −4.19646 −0.176235
\(568\) 0 0
\(569\) 29.5405 1.23840 0.619200 0.785233i \(-0.287457\pi\)
0.619200 + 0.785233i \(0.287457\pi\)
\(570\) 0 0
\(571\) 17.4949 0.732139 0.366069 0.930588i \(-0.380703\pi\)
0.366069 + 0.930588i \(0.380703\pi\)
\(572\) 0 0
\(573\) 10.7649 0.449711
\(574\) 0 0
\(575\) −29.7924 −1.24243
\(576\) 0 0
\(577\) −24.5885 −1.02363 −0.511816 0.859095i \(-0.671027\pi\)
−0.511816 + 0.859095i \(0.671027\pi\)
\(578\) 0 0
\(579\) −17.0021 −0.706582
\(580\) 0 0
\(581\) 8.37812 0.347583
\(582\) 0 0
\(583\) 3.31575 0.137324
\(584\) 0 0
\(585\) 1.99458 0.0824658
\(586\) 0 0
\(587\) −7.38624 −0.304863 −0.152431 0.988314i \(-0.548710\pi\)
−0.152431 + 0.988314i \(0.548710\pi\)
\(588\) 0 0
\(589\) 33.3871 1.37569
\(590\) 0 0
\(591\) −10.7297 −0.441361
\(592\) 0 0
\(593\) −3.49026 −0.143328 −0.0716640 0.997429i \(-0.522831\pi\)
−0.0716640 + 0.997429i \(0.522831\pi\)
\(594\) 0 0
\(595\) −18.6650 −0.765192
\(596\) 0 0
\(597\) −12.9427 −0.529711
\(598\) 0 0
\(599\) −19.5847 −0.800211 −0.400105 0.916469i \(-0.631026\pi\)
−0.400105 + 0.916469i \(0.631026\pi\)
\(600\) 0 0
\(601\) 9.07252 0.370076 0.185038 0.982731i \(-0.440759\pi\)
0.185038 + 0.982731i \(0.440759\pi\)
\(602\) 0 0
\(603\) 6.97495 0.284042
\(604\) 0 0
\(605\) −4.66443 −0.189636
\(606\) 0 0
\(607\) −42.6413 −1.73076 −0.865379 0.501119i \(-0.832922\pi\)
−0.865379 + 0.501119i \(0.832922\pi\)
\(608\) 0 0
\(609\) −10.5973 −0.429424
\(610\) 0 0
\(611\) 34.4510 1.39374
\(612\) 0 0
\(613\) 30.2567 1.22206 0.611028 0.791609i \(-0.290756\pi\)
0.611028 + 0.791609i \(0.290756\pi\)
\(614\) 0 0
\(615\) −1.33538 −0.0538477
\(616\) 0 0
\(617\) 22.7488 0.915831 0.457915 0.888996i \(-0.348596\pi\)
0.457915 + 0.888996i \(0.348596\pi\)
\(618\) 0 0
\(619\) 3.82335 0.153674 0.0768368 0.997044i \(-0.475518\pi\)
0.0768368 + 0.997044i \(0.475518\pi\)
\(620\) 0 0
\(621\) −6.50672 −0.261106
\(622\) 0 0
\(623\) 66.8337 2.67764
\(624\) 0 0
\(625\) 18.8581 0.754325
\(626\) 0 0
\(627\) −15.7127 −0.627503
\(628\) 0 0
\(629\) −33.8946 −1.35147
\(630\) 0 0
\(631\) 10.5670 0.420666 0.210333 0.977630i \(-0.432545\pi\)
0.210333 + 0.977630i \(0.432545\pi\)
\(632\) 0 0
\(633\) −0.727181 −0.0289028
\(634\) 0 0
\(635\) −6.75728 −0.268155
\(636\) 0 0
\(637\) 32.6053 1.29187
\(638\) 0 0
\(639\) −2.84782 −0.112658
\(640\) 0 0
\(641\) −24.3166 −0.960447 −0.480223 0.877146i \(-0.659444\pi\)
−0.480223 + 0.877146i \(0.659444\pi\)
\(642\) 0 0
\(643\) −12.6719 −0.499733 −0.249866 0.968280i \(-0.580387\pi\)
−0.249866 + 0.968280i \(0.580387\pi\)
\(644\) 0 0
\(645\) 2.82832 0.111365
\(646\) 0 0
\(647\) −11.2943 −0.444024 −0.222012 0.975044i \(-0.571262\pi\)
−0.222012 + 0.975044i \(0.571262\pi\)
\(648\) 0 0
\(649\) −14.2900 −0.560930
\(650\) 0 0
\(651\) −17.4134 −0.682486
\(652\) 0 0
\(653\) −40.4706 −1.58374 −0.791869 0.610691i \(-0.790892\pi\)
−0.791869 + 0.610691i \(0.790892\pi\)
\(654\) 0 0
\(655\) 10.0666 0.393336
\(656\) 0 0
\(657\) −7.78221 −0.303613
\(658\) 0 0
\(659\) 13.5779 0.528921 0.264460 0.964397i \(-0.414806\pi\)
0.264460 + 0.964397i \(0.414806\pi\)
\(660\) 0 0
\(661\) −38.4128 −1.49408 −0.747041 0.664777i \(-0.768526\pi\)
−0.747041 + 0.664777i \(0.768526\pi\)
\(662\) 0 0
\(663\) −21.0579 −0.817821
\(664\) 0 0
\(665\) 21.9156 0.849849
\(666\) 0 0
\(667\) −16.4314 −0.636226
\(668\) 0 0
\(669\) −22.1726 −0.857240
\(670\) 0 0
\(671\) 24.4810 0.945079
\(672\) 0 0
\(673\) 33.7593 1.30132 0.650662 0.759367i \(-0.274491\pi\)
0.650662 + 0.759367i \(0.274491\pi\)
\(674\) 0 0
\(675\) 4.57871 0.176235
\(676\) 0 0
\(677\) −0.268807 −0.0103311 −0.00516555 0.999987i \(-0.501644\pi\)
−0.00516555 + 0.999987i \(0.501644\pi\)
\(678\) 0 0
\(679\) −57.7173 −2.21499
\(680\) 0 0
\(681\) 6.28074 0.240678
\(682\) 0 0
\(683\) 42.6332 1.63131 0.815656 0.578537i \(-0.196376\pi\)
0.815656 + 0.578537i \(0.196376\pi\)
\(684\) 0 0
\(685\) 10.6852 0.408262
\(686\) 0 0
\(687\) −21.3981 −0.816387
\(688\) 0 0
\(689\) −5.21760 −0.198775
\(690\) 0 0
\(691\) −14.9041 −0.566979 −0.283490 0.958975i \(-0.591492\pi\)
−0.283490 + 0.958975i \(0.591492\pi\)
\(692\) 0 0
\(693\) 8.19511 0.311307
\(694\) 0 0
\(695\) −12.8639 −0.487955
\(696\) 0 0
\(697\) 14.0983 0.534012
\(698\) 0 0
\(699\) 22.8556 0.864476
\(700\) 0 0
\(701\) −46.9108 −1.77180 −0.885898 0.463880i \(-0.846457\pi\)
−0.885898 + 0.463880i \(0.846457\pi\)
\(702\) 0 0
\(703\) 39.7974 1.50099
\(704\) 0 0
\(705\) −7.27667 −0.274055
\(706\) 0 0
\(707\) 10.0451 0.377786
\(708\) 0 0
\(709\) 38.2929 1.43812 0.719059 0.694949i \(-0.244573\pi\)
0.719059 + 0.694949i \(0.244573\pi\)
\(710\) 0 0
\(711\) 3.29528 0.123582
\(712\) 0 0
\(713\) −27.0000 −1.01116
\(714\) 0 0
\(715\) −3.89514 −0.145670
\(716\) 0 0
\(717\) −21.7956 −0.813971
\(718\) 0 0
\(719\) −15.4361 −0.575670 −0.287835 0.957680i \(-0.592936\pi\)
−0.287835 + 0.957680i \(0.592936\pi\)
\(720\) 0 0
\(721\) −0.777601 −0.0289594
\(722\) 0 0
\(723\) 3.28924 0.122328
\(724\) 0 0
\(725\) 11.5626 0.429424
\(726\) 0 0
\(727\) −28.7752 −1.06721 −0.533606 0.845733i \(-0.679163\pi\)
−0.533606 + 0.845733i \(0.679163\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −29.8601 −1.10442
\(732\) 0 0
\(733\) 16.2197 0.599088 0.299544 0.954082i \(-0.403165\pi\)
0.299544 + 0.954082i \(0.403165\pi\)
\(734\) 0 0
\(735\) −6.88683 −0.254024
\(736\) 0 0
\(737\) −13.6211 −0.501740
\(738\) 0 0
\(739\) −40.9725 −1.50720 −0.753599 0.657334i \(-0.771684\pi\)
−0.753599 + 0.657334i \(0.771684\pi\)
\(740\) 0 0
\(741\) 24.7251 0.908301
\(742\) 0 0
\(743\) 9.94574 0.364874 0.182437 0.983218i \(-0.441601\pi\)
0.182437 + 0.983218i \(0.441601\pi\)
\(744\) 0 0
\(745\) 6.42761 0.235489
\(746\) 0 0
\(747\) −1.99647 −0.0730471
\(748\) 0 0
\(749\) −42.8009 −1.56391
\(750\) 0 0
\(751\) 36.5092 1.33224 0.666121 0.745844i \(-0.267954\pi\)
0.666121 + 0.745844i \(0.267954\pi\)
\(752\) 0 0
\(753\) 12.5801 0.458445
\(754\) 0 0
\(755\) −2.49462 −0.0907885
\(756\) 0 0
\(757\) 45.9732 1.67092 0.835462 0.549549i \(-0.185200\pi\)
0.835462 + 0.549549i \(0.185200\pi\)
\(758\) 0 0
\(759\) 12.7067 0.461225
\(760\) 0 0
\(761\) −9.48336 −0.343771 −0.171886 0.985117i \(-0.554986\pi\)
−0.171886 + 0.985117i \(0.554986\pi\)
\(762\) 0 0
\(763\) 47.5309 1.72073
\(764\) 0 0
\(765\) 4.44780 0.160811
\(766\) 0 0
\(767\) 22.4864 0.811938
\(768\) 0 0
\(769\) 11.3149 0.408027 0.204014 0.978968i \(-0.434601\pi\)
0.204014 + 0.978968i \(0.434601\pi\)
\(770\) 0 0
\(771\) −4.03469 −0.145306
\(772\) 0 0
\(773\) 22.0938 0.794659 0.397329 0.917676i \(-0.369937\pi\)
0.397329 + 0.917676i \(0.369937\pi\)
\(774\) 0 0
\(775\) 18.9996 0.682485
\(776\) 0 0
\(777\) −20.7568 −0.744645
\(778\) 0 0
\(779\) −16.5536 −0.593093
\(780\) 0 0
\(781\) 5.56139 0.199002
\(782\) 0 0
\(783\) 2.52529 0.0902466
\(784\) 0 0
\(785\) 4.06579 0.145114
\(786\) 0 0
\(787\) 27.3069 0.973385 0.486692 0.873573i \(-0.338203\pi\)
0.486692 + 0.873573i \(0.338203\pi\)
\(788\) 0 0
\(789\) −12.0597 −0.429335
\(790\) 0 0
\(791\) −7.77182 −0.276334
\(792\) 0 0
\(793\) −38.5229 −1.36799
\(794\) 0 0
\(795\) 1.10205 0.0390857
\(796\) 0 0
\(797\) −28.3415 −1.00391 −0.501953 0.864895i \(-0.667385\pi\)
−0.501953 + 0.864895i \(0.667385\pi\)
\(798\) 0 0
\(799\) 76.8239 2.71783
\(800\) 0 0
\(801\) −15.9262 −0.562724
\(802\) 0 0
\(803\) 15.1976 0.536311
\(804\) 0 0
\(805\) −17.7230 −0.624653
\(806\) 0 0
\(807\) 0.441761 0.0155507
\(808\) 0 0
\(809\) 33.8936 1.19163 0.595817 0.803120i \(-0.296828\pi\)
0.595817 + 0.803120i \(0.296828\pi\)
\(810\) 0 0
\(811\) −22.7048 −0.797275 −0.398637 0.917109i \(-0.630517\pi\)
−0.398637 + 0.917109i \(0.630517\pi\)
\(812\) 0 0
\(813\) −21.7472 −0.762707
\(814\) 0 0
\(815\) 10.0362 0.351553
\(816\) 0 0
\(817\) 35.0603 1.22660
\(818\) 0 0
\(819\) −12.8957 −0.450611
\(820\) 0 0
\(821\) 0.663314 0.0231498 0.0115749 0.999933i \(-0.496316\pi\)
0.0115749 + 0.999933i \(0.496316\pi\)
\(822\) 0 0
\(823\) 41.4039 1.44325 0.721624 0.692285i \(-0.243396\pi\)
0.721624 + 0.692285i \(0.243396\pi\)
\(824\) 0 0
\(825\) −8.94158 −0.311306
\(826\) 0 0
\(827\) −17.6369 −0.613296 −0.306648 0.951823i \(-0.599207\pi\)
−0.306648 + 0.951823i \(0.599207\pi\)
\(828\) 0 0
\(829\) 11.8064 0.410053 0.205027 0.978756i \(-0.434272\pi\)
0.205027 + 0.978756i \(0.434272\pi\)
\(830\) 0 0
\(831\) 12.7062 0.440774
\(832\) 0 0
\(833\) 72.7080 2.51918
\(834\) 0 0
\(835\) 0.649069 0.0224620
\(836\) 0 0
\(837\) 4.14955 0.143429
\(838\) 0 0
\(839\) 42.9529 1.48290 0.741449 0.671010i \(-0.234139\pi\)
0.741449 + 0.671010i \(0.234139\pi\)
\(840\) 0 0
\(841\) −22.6229 −0.780100
\(842\) 0 0
\(843\) −24.6981 −0.850647
\(844\) 0 0
\(845\) −2.30858 −0.0794177
\(846\) 0 0
\(847\) 30.1572 1.03621
\(848\) 0 0
\(849\) 5.77605 0.198233
\(850\) 0 0
\(851\) −32.1839 −1.10325
\(852\) 0 0
\(853\) 31.7110 1.08576 0.542882 0.839809i \(-0.317333\pi\)
0.542882 + 0.839809i \(0.317333\pi\)
\(854\) 0 0
\(855\) −5.22239 −0.178602
\(856\) 0 0
\(857\) −43.9632 −1.50175 −0.750877 0.660442i \(-0.770369\pi\)
−0.750877 + 0.660442i \(0.770369\pi\)
\(858\) 0 0
\(859\) 28.7001 0.979234 0.489617 0.871938i \(-0.337137\pi\)
0.489617 + 0.871938i \(0.337137\pi\)
\(860\) 0 0
\(861\) 8.63370 0.294236
\(862\) 0 0
\(863\) 42.6438 1.45161 0.725806 0.687899i \(-0.241467\pi\)
0.725806 + 0.687899i \(0.241467\pi\)
\(864\) 0 0
\(865\) −3.03987 −0.103359
\(866\) 0 0
\(867\) −29.9579 −1.01742
\(868\) 0 0
\(869\) −6.43521 −0.218300
\(870\) 0 0
\(871\) 21.4339 0.726261
\(872\) 0 0
\(873\) 13.7538 0.465495
\(874\) 0 0
\(875\) 26.0905 0.882018
\(876\) 0 0
\(877\) −15.1091 −0.510199 −0.255099 0.966915i \(-0.582108\pi\)
−0.255099 + 0.966915i \(0.582108\pi\)
\(878\) 0 0
\(879\) −14.9087 −0.502856
\(880\) 0 0
\(881\) −14.5387 −0.489820 −0.244910 0.969546i \(-0.578758\pi\)
−0.244910 + 0.969546i \(0.578758\pi\)
\(882\) 0 0
\(883\) −6.92350 −0.232994 −0.116497 0.993191i \(-0.537167\pi\)
−0.116497 + 0.993191i \(0.537167\pi\)
\(884\) 0 0
\(885\) −4.74954 −0.159654
\(886\) 0 0
\(887\) 45.7047 1.53461 0.767306 0.641281i \(-0.221597\pi\)
0.767306 + 0.641281i \(0.221597\pi\)
\(888\) 0 0
\(889\) 43.6882 1.46526
\(890\) 0 0
\(891\) −1.95286 −0.0654233
\(892\) 0 0
\(893\) −90.2028 −3.01852
\(894\) 0 0
\(895\) 15.3136 0.511878
\(896\) 0 0
\(897\) −19.9951 −0.667616
\(898\) 0 0
\(899\) 10.4788 0.349488
\(900\) 0 0
\(901\) −11.6350 −0.387616
\(902\) 0 0
\(903\) −18.2861 −0.608523
\(904\) 0 0
\(905\) 4.36520 0.145104
\(906\) 0 0
\(907\) −28.7584 −0.954907 −0.477453 0.878657i \(-0.658440\pi\)
−0.477453 + 0.878657i \(0.658440\pi\)
\(908\) 0 0
\(909\) −2.39371 −0.0793945
\(910\) 0 0
\(911\) −3.33280 −0.110421 −0.0552103 0.998475i \(-0.517583\pi\)
−0.0552103 + 0.998475i \(0.517583\pi\)
\(912\) 0 0
\(913\) 3.89883 0.129032
\(914\) 0 0
\(915\) 8.13672 0.268992
\(916\) 0 0
\(917\) −65.0843 −2.14927
\(918\) 0 0
\(919\) −45.6696 −1.50650 −0.753250 0.657735i \(-0.771515\pi\)
−0.753250 + 0.657735i \(0.771515\pi\)
\(920\) 0 0
\(921\) 2.60592 0.0858679
\(922\) 0 0
\(923\) −8.75130 −0.288052
\(924\) 0 0
\(925\) 22.6474 0.744643
\(926\) 0 0
\(927\) 0.185299 0.00608602
\(928\) 0 0
\(929\) 41.0210 1.34586 0.672928 0.739708i \(-0.265037\pi\)
0.672928 + 0.739708i \(0.265037\pi\)
\(930\) 0 0
\(931\) −85.3702 −2.79789
\(932\) 0 0
\(933\) −5.88680 −0.192725
\(934\) 0 0
\(935\) −8.68594 −0.284061
\(936\) 0 0
\(937\) 0.449676 0.0146903 0.00734514 0.999973i \(-0.497662\pi\)
0.00734514 + 0.999973i \(0.497662\pi\)
\(938\) 0 0
\(939\) −29.5589 −0.964618
\(940\) 0 0
\(941\) −24.2530 −0.790626 −0.395313 0.918546i \(-0.629364\pi\)
−0.395313 + 0.918546i \(0.629364\pi\)
\(942\) 0 0
\(943\) 13.3868 0.435933
\(944\) 0 0
\(945\) 2.72380 0.0886051
\(946\) 0 0
\(947\) −42.4970 −1.38097 −0.690484 0.723348i \(-0.742602\pi\)
−0.690484 + 0.723348i \(0.742602\pi\)
\(948\) 0 0
\(949\) −23.9146 −0.776302
\(950\) 0 0
\(951\) −27.3897 −0.888173
\(952\) 0 0
\(953\) 17.5025 0.566961 0.283480 0.958978i \(-0.408511\pi\)
0.283480 + 0.958978i \(0.408511\pi\)
\(954\) 0 0
\(955\) −6.98718 −0.226100
\(956\) 0 0
\(957\) −4.93155 −0.159414
\(958\) 0 0
\(959\) −69.0839 −2.23083
\(960\) 0 0
\(961\) −13.7813 −0.444557
\(962\) 0 0
\(963\) 10.1993 0.328667
\(964\) 0 0
\(965\) 11.0355 0.355246
\(966\) 0 0
\(967\) 16.8865 0.543032 0.271516 0.962434i \(-0.412475\pi\)
0.271516 + 0.962434i \(0.412475\pi\)
\(968\) 0 0
\(969\) 55.1357 1.77121
\(970\) 0 0
\(971\) 54.6352 1.75333 0.876664 0.481103i \(-0.159764\pi\)
0.876664 + 0.481103i \(0.159764\pi\)
\(972\) 0 0
\(973\) 83.1696 2.66630
\(974\) 0 0
\(975\) 14.0703 0.450610
\(976\) 0 0
\(977\) −18.6725 −0.597386 −0.298693 0.954349i \(-0.596551\pi\)
−0.298693 + 0.954349i \(0.596551\pi\)
\(978\) 0 0
\(979\) 31.1016 0.994013
\(980\) 0 0
\(981\) −11.3264 −0.361625
\(982\) 0 0
\(983\) −46.7507 −1.49112 −0.745558 0.666441i \(-0.767817\pi\)
−0.745558 + 0.666441i \(0.767817\pi\)
\(984\) 0 0
\(985\) 6.96433 0.221902
\(986\) 0 0
\(987\) 47.0463 1.49750
\(988\) 0 0
\(989\) −28.3530 −0.901574
\(990\) 0 0
\(991\) 46.7105 1.48381 0.741904 0.670506i \(-0.233923\pi\)
0.741904 + 0.670506i \(0.233923\pi\)
\(992\) 0 0
\(993\) 25.0680 0.795509
\(994\) 0 0
\(995\) 8.40074 0.266321
\(996\) 0 0
\(997\) −59.1332 −1.87277 −0.936383 0.350979i \(-0.885849\pi\)
−0.936383 + 0.350979i \(0.885849\pi\)
\(998\) 0 0
\(999\) 4.94625 0.156492
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 \(a_p\))