Properties

Label 8048.2.a.l.1.1
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(1.61803\)
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.23607 q^{3}\) \(+1.23607 q^{5}\) \(+4.23607 q^{7}\) \(+2.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.23607 q^{3}\) \(+1.23607 q^{5}\) \(+4.23607 q^{7}\) \(+2.00000 q^{9}\) \(+4.23607 q^{11}\) \(-5.47214 q^{13}\) \(-2.76393 q^{15}\) \(+2.00000 q^{17}\) \(+7.70820 q^{19}\) \(-9.47214 q^{21}\) \(-2.23607 q^{23}\) \(-3.47214 q^{25}\) \(+2.23607 q^{27}\) \(-2.76393 q^{29}\) \(-7.70820 q^{31}\) \(-9.47214 q^{33}\) \(+5.23607 q^{35}\) \(-4.47214 q^{37}\) \(+12.2361 q^{39}\) \(-5.23607 q^{41}\) \(-10.2361 q^{43}\) \(+2.47214 q^{45}\) \(-4.23607 q^{47}\) \(+10.9443 q^{49}\) \(-4.47214 q^{51}\) \(-0.472136 q^{53}\) \(+5.23607 q^{55}\) \(-17.2361 q^{57}\) \(-8.94427 q^{59}\) \(+7.47214 q^{61}\) \(+8.47214 q^{63}\) \(-6.76393 q^{65}\) \(-4.70820 q^{67}\) \(+5.00000 q^{69}\) \(-0.763932 q^{71}\) \(-7.52786 q^{73}\) \(+7.76393 q^{75}\) \(+17.9443 q^{77}\) \(-12.9443 q^{79}\) \(-11.0000 q^{81}\) \(-16.7082 q^{83}\) \(+2.47214 q^{85}\) \(+6.18034 q^{87}\) \(-14.4721 q^{89}\) \(-23.1803 q^{91}\) \(+17.2361 q^{93}\) \(+9.52786 q^{95}\) \(-10.0000 q^{97}\) \(+8.47214 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut +\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 4q^{9} \) \(\mathstrut +\mathstrut 4q^{11} \) \(\mathstrut -\mathstrut 2q^{13} \) \(\mathstrut -\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 10q^{29} \) \(\mathstrut -\mathstrut 2q^{31} \) \(\mathstrut -\mathstrut 10q^{33} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{39} \) \(\mathstrut -\mathstrut 6q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut -\mathstrut 4q^{45} \) \(\mathstrut -\mathstrut 4q^{47} \) \(\mathstrut +\mathstrut 4q^{49} \) \(\mathstrut +\mathstrut 8q^{53} \) \(\mathstrut +\mathstrut 6q^{55} \) \(\mathstrut -\mathstrut 30q^{57} \) \(\mathstrut +\mathstrut 6q^{61} \) \(\mathstrut +\mathstrut 8q^{63} \) \(\mathstrut -\mathstrut 18q^{65} \) \(\mathstrut +\mathstrut 4q^{67} \) \(\mathstrut +\mathstrut 10q^{69} \) \(\mathstrut -\mathstrut 6q^{71} \) \(\mathstrut -\mathstrut 24q^{73} \) \(\mathstrut +\mathstrut 20q^{75} \) \(\mathstrut +\mathstrut 18q^{77} \) \(\mathstrut -\mathstrut 8q^{79} \) \(\mathstrut -\mathstrut 22q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 10q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut -\mathstrut 24q^{91} \) \(\mathstrut +\mathstrut 30q^{93} \) \(\mathstrut +\mathstrut 28q^{95} \) \(\mathstrut -\mathstrut 20q^{97} \) \(\mathstrut +\mathstrut 8q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −2.23607 −1.29099 −0.645497 0.763763i \(-0.723350\pi\)
−0.645497 + 0.763763i \(0.723350\pi\)
\(4\) 0 0
\(5\) 1.23607 0.552786 0.276393 0.961045i \(-0.410861\pi\)
0.276393 + 0.961045i \(0.410861\pi\)
\(6\) 0 0
\(7\) 4.23607 1.60108 0.800542 0.599277i \(-0.204545\pi\)
0.800542 + 0.599277i \(0.204545\pi\)
\(8\) 0 0
\(9\) 2.00000 0.666667
\(10\) 0 0
\(11\) 4.23607 1.27722 0.638611 0.769529i \(-0.279509\pi\)
0.638611 + 0.769529i \(0.279509\pi\)
\(12\) 0 0
\(13\) −5.47214 −1.51770 −0.758849 0.651267i \(-0.774238\pi\)
−0.758849 + 0.651267i \(0.774238\pi\)
\(14\) 0 0
\(15\) −2.76393 −0.713644
\(16\) 0 0
\(17\) 2.00000 0.485071 0.242536 0.970143i \(-0.422021\pi\)
0.242536 + 0.970143i \(0.422021\pi\)
\(18\) 0 0
\(19\) 7.70820 1.76838 0.884192 0.467124i \(-0.154710\pi\)
0.884192 + 0.467124i \(0.154710\pi\)
\(20\) 0 0
\(21\) −9.47214 −2.06699
\(22\) 0 0
\(23\) −2.23607 −0.466252 −0.233126 0.972446i \(-0.574896\pi\)
−0.233126 + 0.972446i \(0.574896\pi\)
\(24\) 0 0
\(25\) −3.47214 −0.694427
\(26\) 0 0
\(27\) 2.23607 0.430331
\(28\) 0 0
\(29\) −2.76393 −0.513249 −0.256625 0.966511i \(-0.582610\pi\)
−0.256625 + 0.966511i \(0.582610\pi\)
\(30\) 0 0
\(31\) −7.70820 −1.38443 −0.692217 0.721689i \(-0.743366\pi\)
−0.692217 + 0.721689i \(0.743366\pi\)
\(32\) 0 0
\(33\) −9.47214 −1.64889
\(34\) 0 0
\(35\) 5.23607 0.885057
\(36\) 0 0
\(37\) −4.47214 −0.735215 −0.367607 0.929981i \(-0.619823\pi\)
−0.367607 + 0.929981i \(0.619823\pi\)
\(38\) 0 0
\(39\) 12.2361 1.95934
\(40\) 0 0
\(41\) −5.23607 −0.817736 −0.408868 0.912593i \(-0.634076\pi\)
−0.408868 + 0.912593i \(0.634076\pi\)
\(42\) 0 0
\(43\) −10.2361 −1.56099 −0.780493 0.625165i \(-0.785032\pi\)
−0.780493 + 0.625165i \(0.785032\pi\)
\(44\) 0 0
\(45\) 2.47214 0.368524
\(46\) 0 0
\(47\) −4.23607 −0.617894 −0.308947 0.951079i \(-0.599977\pi\)
−0.308947 + 0.951079i \(0.599977\pi\)
\(48\) 0 0
\(49\) 10.9443 1.56347
\(50\) 0 0
\(51\) −4.47214 −0.626224
\(52\) 0 0
\(53\) −0.472136 −0.0648529 −0.0324264 0.999474i \(-0.510323\pi\)
−0.0324264 + 0.999474i \(0.510323\pi\)
\(54\) 0 0
\(55\) 5.23607 0.706031
\(56\) 0 0
\(57\) −17.2361 −2.28297
\(58\) 0 0
\(59\) −8.94427 −1.16445 −0.582223 0.813029i \(-0.697817\pi\)
−0.582223 + 0.813029i \(0.697817\pi\)
\(60\) 0 0
\(61\) 7.47214 0.956709 0.478354 0.878167i \(-0.341233\pi\)
0.478354 + 0.878167i \(0.341233\pi\)
\(62\) 0 0
\(63\) 8.47214 1.06739
\(64\) 0 0
\(65\) −6.76393 −0.838963
\(66\) 0 0
\(67\) −4.70820 −0.575199 −0.287599 0.957751i \(-0.592857\pi\)
−0.287599 + 0.957751i \(0.592857\pi\)
\(68\) 0 0
\(69\) 5.00000 0.601929
\(70\) 0 0
\(71\) −0.763932 −0.0906621 −0.0453310 0.998972i \(-0.514434\pi\)
−0.0453310 + 0.998972i \(0.514434\pi\)
\(72\) 0 0
\(73\) −7.52786 −0.881070 −0.440535 0.897735i \(-0.645211\pi\)
−0.440535 + 0.897735i \(0.645211\pi\)
\(74\) 0 0
\(75\) 7.76393 0.896502
\(76\) 0 0
\(77\) 17.9443 2.04494
\(78\) 0 0
\(79\) −12.9443 −1.45634 −0.728172 0.685394i \(-0.759630\pi\)
−0.728172 + 0.685394i \(0.759630\pi\)
\(80\) 0 0
\(81\) −11.0000 −1.22222
\(82\) 0 0
\(83\) −16.7082 −1.83396 −0.916982 0.398929i \(-0.869382\pi\)
−0.916982 + 0.398929i \(0.869382\pi\)
\(84\) 0 0
\(85\) 2.47214 0.268141
\(86\) 0 0
\(87\) 6.18034 0.662602
\(88\) 0 0
\(89\) −14.4721 −1.53404 −0.767022 0.641621i \(-0.778262\pi\)
−0.767022 + 0.641621i \(0.778262\pi\)
\(90\) 0 0
\(91\) −23.1803 −2.42996
\(92\) 0 0
\(93\) 17.2361 1.78730
\(94\) 0 0
\(95\) 9.52786 0.977538
\(96\) 0 0
\(97\) −10.0000 −1.01535 −0.507673 0.861550i \(-0.669494\pi\)
−0.507673 + 0.861550i \(0.669494\pi\)
\(98\) 0 0
\(99\) 8.47214 0.851482
\(100\) 0 0
\(101\) −9.70820 −0.966002 −0.483001 0.875620i \(-0.660453\pi\)
−0.483001 + 0.875620i \(0.660453\pi\)
\(102\) 0 0
\(103\) 0.944272 0.0930419 0.0465209 0.998917i \(-0.485187\pi\)
0.0465209 + 0.998917i \(0.485187\pi\)
\(104\) 0 0
\(105\) −11.7082 −1.14260
\(106\) 0 0
\(107\) 8.00000 0.773389 0.386695 0.922208i \(-0.373617\pi\)
0.386695 + 0.922208i \(0.373617\pi\)
\(108\) 0 0
\(109\) 8.47214 0.811483 0.405742 0.913988i \(-0.367013\pi\)
0.405742 + 0.913988i \(0.367013\pi\)
\(110\) 0 0
\(111\) 10.0000 0.949158
\(112\) 0 0
\(113\) −8.52786 −0.802234 −0.401117 0.916027i \(-0.631378\pi\)
−0.401117 + 0.916027i \(0.631378\pi\)
\(114\) 0 0
\(115\) −2.76393 −0.257738
\(116\) 0 0
\(117\) −10.9443 −1.01180
\(118\) 0 0
\(119\) 8.47214 0.776639
\(120\) 0 0
\(121\) 6.94427 0.631297
\(122\) 0 0
\(123\) 11.7082 1.05569
\(124\) 0 0
\(125\) −10.4721 −0.936656
\(126\) 0 0
\(127\) −2.29180 −0.203364 −0.101682 0.994817i \(-0.532422\pi\)
−0.101682 + 0.994817i \(0.532422\pi\)
\(128\) 0 0
\(129\) 22.8885 2.01522
\(130\) 0 0
\(131\) 21.1803 1.85053 0.925267 0.379315i \(-0.123840\pi\)
0.925267 + 0.379315i \(0.123840\pi\)
\(132\) 0 0
\(133\) 32.6525 2.83133
\(134\) 0 0
\(135\) 2.76393 0.237881
\(136\) 0 0
\(137\) −7.23607 −0.618219 −0.309110 0.951026i \(-0.600031\pi\)
−0.309110 + 0.951026i \(0.600031\pi\)
\(138\) 0 0
\(139\) 10.1803 0.863485 0.431743 0.901997i \(-0.357899\pi\)
0.431743 + 0.901997i \(0.357899\pi\)
\(140\) 0 0
\(141\) 9.47214 0.797698
\(142\) 0 0
\(143\) −23.1803 −1.93844
\(144\) 0 0
\(145\) −3.41641 −0.283717
\(146\) 0 0
\(147\) −24.4721 −2.01843
\(148\) 0 0
\(149\) −12.7639 −1.04566 −0.522831 0.852436i \(-0.675124\pi\)
−0.522831 + 0.852436i \(0.675124\pi\)
\(150\) 0 0
\(151\) 18.4721 1.50324 0.751621 0.659596i \(-0.229272\pi\)
0.751621 + 0.659596i \(0.229272\pi\)
\(152\) 0 0
\(153\) 4.00000 0.323381
\(154\) 0 0
\(155\) −9.52786 −0.765296
\(156\) 0 0
\(157\) 12.4721 0.995385 0.497692 0.867354i \(-0.334181\pi\)
0.497692 + 0.867354i \(0.334181\pi\)
\(158\) 0 0
\(159\) 1.05573 0.0837247
\(160\) 0 0
\(161\) −9.47214 −0.746509
\(162\) 0 0
\(163\) 11.7082 0.917057 0.458529 0.888680i \(-0.348377\pi\)
0.458529 + 0.888680i \(0.348377\pi\)
\(164\) 0 0
\(165\) −11.7082 −0.911482
\(166\) 0 0
\(167\) 7.70820 0.596479 0.298239 0.954491i \(-0.403601\pi\)
0.298239 + 0.954491i \(0.403601\pi\)
\(168\) 0 0
\(169\) 16.9443 1.30341
\(170\) 0 0
\(171\) 15.4164 1.17892
\(172\) 0 0
\(173\) 11.0000 0.836315 0.418157 0.908375i \(-0.362676\pi\)
0.418157 + 0.908375i \(0.362676\pi\)
\(174\) 0 0
\(175\) −14.7082 −1.11184
\(176\) 0 0
\(177\) 20.0000 1.50329
\(178\) 0 0
\(179\) −5.70820 −0.426651 −0.213326 0.976981i \(-0.568430\pi\)
−0.213326 + 0.976981i \(0.568430\pi\)
\(180\) 0 0
\(181\) −20.0000 −1.48659 −0.743294 0.668965i \(-0.766738\pi\)
−0.743294 + 0.668965i \(0.766738\pi\)
\(182\) 0 0
\(183\) −16.7082 −1.23511
\(184\) 0 0
\(185\) −5.52786 −0.406417
\(186\) 0 0
\(187\) 8.47214 0.619544
\(188\) 0 0
\(189\) 9.47214 0.688997
\(190\) 0 0
\(191\) 18.4721 1.33660 0.668298 0.743893i \(-0.267023\pi\)
0.668298 + 0.743893i \(0.267023\pi\)
\(192\) 0 0
\(193\) −6.76393 −0.486878 −0.243439 0.969916i \(-0.578276\pi\)
−0.243439 + 0.969916i \(0.578276\pi\)
\(194\) 0 0
\(195\) 15.1246 1.08310
\(196\) 0 0
\(197\) −20.4164 −1.45461 −0.727304 0.686315i \(-0.759227\pi\)
−0.727304 + 0.686315i \(0.759227\pi\)
\(198\) 0 0
\(199\) −2.47214 −0.175245 −0.0876225 0.996154i \(-0.527927\pi\)
−0.0876225 + 0.996154i \(0.527927\pi\)
\(200\) 0 0
\(201\) 10.5279 0.742578
\(202\) 0 0
\(203\) −11.7082 −0.821755
\(204\) 0 0
\(205\) −6.47214 −0.452034
\(206\) 0 0
\(207\) −4.47214 −0.310835
\(208\) 0 0
\(209\) 32.6525 2.25862
\(210\) 0 0
\(211\) 3.70820 0.255283 0.127642 0.991820i \(-0.459259\pi\)
0.127642 + 0.991820i \(0.459259\pi\)
\(212\) 0 0
\(213\) 1.70820 0.117044
\(214\) 0 0
\(215\) −12.6525 −0.862892
\(216\) 0 0
\(217\) −32.6525 −2.21659
\(218\) 0 0
\(219\) 16.8328 1.13746
\(220\) 0 0
\(221\) −10.9443 −0.736191
\(222\) 0 0
\(223\) −3.76393 −0.252052 −0.126026 0.992027i \(-0.540222\pi\)
−0.126026 + 0.992027i \(0.540222\pi\)
\(224\) 0 0
\(225\) −6.94427 −0.462951
\(226\) 0 0
\(227\) −11.7082 −0.777101 −0.388550 0.921427i \(-0.627024\pi\)
−0.388550 + 0.921427i \(0.627024\pi\)
\(228\) 0 0
\(229\) 18.4164 1.21699 0.608495 0.793558i \(-0.291773\pi\)
0.608495 + 0.793558i \(0.291773\pi\)
\(230\) 0 0
\(231\) −40.1246 −2.64001
\(232\) 0 0
\(233\) 22.4164 1.46855 0.734274 0.678853i \(-0.237523\pi\)
0.734274 + 0.678853i \(0.237523\pi\)
\(234\) 0 0
\(235\) −5.23607 −0.341563
\(236\) 0 0
\(237\) 28.9443 1.88013
\(238\) 0 0
\(239\) 25.4164 1.64405 0.822025 0.569451i \(-0.192844\pi\)
0.822025 + 0.569451i \(0.192844\pi\)
\(240\) 0 0
\(241\) −4.94427 −0.318489 −0.159244 0.987239i \(-0.550906\pi\)
−0.159244 + 0.987239i \(0.550906\pi\)
\(242\) 0 0
\(243\) 17.8885 1.14755
\(244\) 0 0
\(245\) 13.5279 0.864264
\(246\) 0 0
\(247\) −42.1803 −2.68387
\(248\) 0 0
\(249\) 37.3607 2.36764
\(250\) 0 0
\(251\) 4.18034 0.263861 0.131930 0.991259i \(-0.457882\pi\)
0.131930 + 0.991259i \(0.457882\pi\)
\(252\) 0 0
\(253\) −9.47214 −0.595508
\(254\) 0 0
\(255\) −5.52786 −0.346168
\(256\) 0 0
\(257\) 10.0557 0.627259 0.313630 0.949545i \(-0.398455\pi\)
0.313630 + 0.949545i \(0.398455\pi\)
\(258\) 0 0
\(259\) −18.9443 −1.17714
\(260\) 0 0
\(261\) −5.52786 −0.342166
\(262\) 0 0
\(263\) −16.1246 −0.994286 −0.497143 0.867669i \(-0.665618\pi\)
−0.497143 + 0.867669i \(0.665618\pi\)
\(264\) 0 0
\(265\) −0.583592 −0.0358498
\(266\) 0 0
\(267\) 32.3607 1.98044
\(268\) 0 0
\(269\) 16.9443 1.03311 0.516555 0.856254i \(-0.327214\pi\)
0.516555 + 0.856254i \(0.327214\pi\)
\(270\) 0 0
\(271\) −26.7082 −1.62241 −0.811204 0.584763i \(-0.801187\pi\)
−0.811204 + 0.584763i \(0.801187\pi\)
\(272\) 0 0
\(273\) 51.8328 3.13706
\(274\) 0 0
\(275\) −14.7082 −0.886938
\(276\) 0 0
\(277\) 26.1803 1.57302 0.786512 0.617575i \(-0.211885\pi\)
0.786512 + 0.617575i \(0.211885\pi\)
\(278\) 0 0
\(279\) −15.4164 −0.922956
\(280\) 0 0
\(281\) −28.4164 −1.69518 −0.847590 0.530651i \(-0.821947\pi\)
−0.847590 + 0.530651i \(0.821947\pi\)
\(282\) 0 0
\(283\) 18.4721 1.09805 0.549027 0.835804i \(-0.314998\pi\)
0.549027 + 0.835804i \(0.314998\pi\)
\(284\) 0 0
\(285\) −21.3050 −1.26200
\(286\) 0 0
\(287\) −22.1803 −1.30926
\(288\) 0 0
\(289\) −13.0000 −0.764706
\(290\) 0 0
\(291\) 22.3607 1.31081
\(292\) 0 0
\(293\) 5.00000 0.292103 0.146052 0.989277i \(-0.453343\pi\)
0.146052 + 0.989277i \(0.453343\pi\)
\(294\) 0 0
\(295\) −11.0557 −0.643689
\(296\) 0 0
\(297\) 9.47214 0.549629
\(298\) 0 0
\(299\) 12.2361 0.707630
\(300\) 0 0
\(301\) −43.3607 −2.49927
\(302\) 0 0
\(303\) 21.7082 1.24710
\(304\) 0 0
\(305\) 9.23607 0.528856
\(306\) 0 0
\(307\) −9.41641 −0.537423 −0.268711 0.963221i \(-0.586598\pi\)
−0.268711 + 0.963221i \(0.586598\pi\)
\(308\) 0 0
\(309\) −2.11146 −0.120117
\(310\) 0 0
\(311\) 5.81966 0.330003 0.165001 0.986293i \(-0.447237\pi\)
0.165001 + 0.986293i \(0.447237\pi\)
\(312\) 0 0
\(313\) −30.9443 −1.74907 −0.874537 0.484959i \(-0.838834\pi\)
−0.874537 + 0.484959i \(0.838834\pi\)
\(314\) 0 0
\(315\) 10.4721 0.590038
\(316\) 0 0
\(317\) −8.05573 −0.452455 −0.226227 0.974075i \(-0.572639\pi\)
−0.226227 + 0.974075i \(0.572639\pi\)
\(318\) 0 0
\(319\) −11.7082 −0.655534
\(320\) 0 0
\(321\) −17.8885 −0.998441
\(322\) 0 0
\(323\) 15.4164 0.857792
\(324\) 0 0
\(325\) 19.0000 1.05393
\(326\) 0 0
\(327\) −18.9443 −1.04762
\(328\) 0 0
\(329\) −17.9443 −0.989300
\(330\) 0 0
\(331\) −10.9443 −0.601552 −0.300776 0.953695i \(-0.597246\pi\)
−0.300776 + 0.953695i \(0.597246\pi\)
\(332\) 0 0
\(333\) −8.94427 −0.490143
\(334\) 0 0
\(335\) −5.81966 −0.317962
\(336\) 0 0
\(337\) −30.9443 −1.68564 −0.842821 0.538194i \(-0.819107\pi\)
−0.842821 + 0.538194i \(0.819107\pi\)
\(338\) 0 0
\(339\) 19.0689 1.03568
\(340\) 0 0
\(341\) −32.6525 −1.76823
\(342\) 0 0
\(343\) 16.7082 0.902158
\(344\) 0 0
\(345\) 6.18034 0.332738
\(346\) 0 0
\(347\) 8.00000 0.429463 0.214731 0.976673i \(-0.431112\pi\)
0.214731 + 0.976673i \(0.431112\pi\)
\(348\) 0 0
\(349\) 12.0000 0.642345 0.321173 0.947021i \(-0.395923\pi\)
0.321173 + 0.947021i \(0.395923\pi\)
\(350\) 0 0
\(351\) −12.2361 −0.653113
\(352\) 0 0
\(353\) −24.7639 −1.31805 −0.659026 0.752121i \(-0.729031\pi\)
−0.659026 + 0.752121i \(0.729031\pi\)
\(354\) 0 0
\(355\) −0.944272 −0.0501167
\(356\) 0 0
\(357\) −18.9443 −1.00264
\(358\) 0 0
\(359\) 9.70820 0.512379 0.256190 0.966627i \(-0.417533\pi\)
0.256190 + 0.966627i \(0.417533\pi\)
\(360\) 0 0
\(361\) 40.4164 2.12718
\(362\) 0 0
\(363\) −15.5279 −0.815001
\(364\) 0 0
\(365\) −9.30495 −0.487043
\(366\) 0 0
\(367\) 2.23607 0.116722 0.0583609 0.998296i \(-0.481413\pi\)
0.0583609 + 0.998296i \(0.481413\pi\)
\(368\) 0 0
\(369\) −10.4721 −0.545158
\(370\) 0 0
\(371\) −2.00000 −0.103835
\(372\) 0 0
\(373\) 26.3050 1.36202 0.681009 0.732275i \(-0.261541\pi\)
0.681009 + 0.732275i \(0.261541\pi\)
\(374\) 0 0
\(375\) 23.4164 1.20922
\(376\) 0 0
\(377\) 15.1246 0.778957
\(378\) 0 0
\(379\) 6.70820 0.344577 0.172289 0.985047i \(-0.444884\pi\)
0.172289 + 0.985047i \(0.444884\pi\)
\(380\) 0 0
\(381\) 5.12461 0.262542
\(382\) 0 0
\(383\) 12.9443 0.661421 0.330711 0.943732i \(-0.392712\pi\)
0.330711 + 0.943732i \(0.392712\pi\)
\(384\) 0 0
\(385\) 22.1803 1.13041
\(386\) 0 0
\(387\) −20.4721 −1.04066
\(388\) 0 0
\(389\) 16.8328 0.853458 0.426729 0.904380i \(-0.359666\pi\)
0.426729 + 0.904380i \(0.359666\pi\)
\(390\) 0 0
\(391\) −4.47214 −0.226166
\(392\) 0 0
\(393\) −47.3607 −2.38903
\(394\) 0 0
\(395\) −16.0000 −0.805047
\(396\) 0 0
\(397\) 37.3607 1.87508 0.937539 0.347879i \(-0.113098\pi\)
0.937539 + 0.347879i \(0.113098\pi\)
\(398\) 0 0
\(399\) −73.0132 −3.65523
\(400\) 0 0
\(401\) 12.4164 0.620046 0.310023 0.950729i \(-0.399663\pi\)
0.310023 + 0.950729i \(0.399663\pi\)
\(402\) 0 0
\(403\) 42.1803 2.10115
\(404\) 0 0
\(405\) −13.5967 −0.675628
\(406\) 0 0
\(407\) −18.9443 −0.939033
\(408\) 0 0
\(409\) 1.70820 0.0844652 0.0422326 0.999108i \(-0.486553\pi\)
0.0422326 + 0.999108i \(0.486553\pi\)
\(410\) 0 0
\(411\) 16.1803 0.798117
\(412\) 0 0
\(413\) −37.8885 −1.86437
\(414\) 0 0
\(415\) −20.6525 −1.01379
\(416\) 0 0
\(417\) −22.7639 −1.11475
\(418\) 0 0
\(419\) 8.29180 0.405081 0.202540 0.979274i \(-0.435080\pi\)
0.202540 + 0.979274i \(0.435080\pi\)
\(420\) 0 0
\(421\) −5.05573 −0.246401 −0.123201 0.992382i \(-0.539316\pi\)
−0.123201 + 0.992382i \(0.539316\pi\)
\(422\) 0 0
\(423\) −8.47214 −0.411929
\(424\) 0 0
\(425\) −6.94427 −0.336847
\(426\) 0 0
\(427\) 31.6525 1.53177
\(428\) 0 0
\(429\) 51.8328 2.50251
\(430\) 0 0
\(431\) −1.34752 −0.0649080 −0.0324540 0.999473i \(-0.510332\pi\)
−0.0324540 + 0.999473i \(0.510332\pi\)
\(432\) 0 0
\(433\) 20.4721 0.983828 0.491914 0.870644i \(-0.336297\pi\)
0.491914 + 0.870644i \(0.336297\pi\)
\(434\) 0 0
\(435\) 7.63932 0.366277
\(436\) 0 0
\(437\) −17.2361 −0.824513
\(438\) 0 0
\(439\) 17.8885 0.853774 0.426887 0.904305i \(-0.359610\pi\)
0.426887 + 0.904305i \(0.359610\pi\)
\(440\) 0 0
\(441\) 21.8885 1.04231
\(442\) 0 0
\(443\) −23.1803 −1.10133 −0.550666 0.834726i \(-0.685626\pi\)
−0.550666 + 0.834726i \(0.685626\pi\)
\(444\) 0 0
\(445\) −17.8885 −0.847998
\(446\) 0 0
\(447\) 28.5410 1.34994
\(448\) 0 0
\(449\) 19.5967 0.924828 0.462414 0.886664i \(-0.346983\pi\)
0.462414 + 0.886664i \(0.346983\pi\)
\(450\) 0 0
\(451\) −22.1803 −1.04443
\(452\) 0 0
\(453\) −41.3050 −1.94068
\(454\) 0 0
\(455\) −28.6525 −1.34325
\(456\) 0 0
\(457\) −22.3607 −1.04599 −0.522994 0.852336i \(-0.675185\pi\)
−0.522994 + 0.852336i \(0.675185\pi\)
\(458\) 0 0
\(459\) 4.47214 0.208741
\(460\) 0 0
\(461\) −16.0689 −0.748403 −0.374201 0.927348i \(-0.622083\pi\)
−0.374201 + 0.927348i \(0.622083\pi\)
\(462\) 0 0
\(463\) −16.5967 −0.771316 −0.385658 0.922642i \(-0.626026\pi\)
−0.385658 + 0.922642i \(0.626026\pi\)
\(464\) 0 0
\(465\) 21.3050 0.987993
\(466\) 0 0
\(467\) 8.29180 0.383699 0.191849 0.981424i \(-0.438552\pi\)
0.191849 + 0.981424i \(0.438552\pi\)
\(468\) 0 0
\(469\) −19.9443 −0.920941
\(470\) 0 0
\(471\) −27.8885 −1.28504
\(472\) 0 0
\(473\) −43.3607 −1.99373
\(474\) 0 0
\(475\) −26.7639 −1.22801
\(476\) 0 0
\(477\) −0.944272 −0.0432352
\(478\) 0 0
\(479\) 12.9443 0.591439 0.295719 0.955275i \(-0.404441\pi\)
0.295719 + 0.955275i \(0.404441\pi\)
\(480\) 0 0
\(481\) 24.4721 1.11583
\(482\) 0 0
\(483\) 21.1803 0.963739
\(484\) 0 0
\(485\) −12.3607 −0.561270
\(486\) 0 0
\(487\) −35.5967 −1.61304 −0.806521 0.591205i \(-0.798652\pi\)
−0.806521 + 0.591205i \(0.798652\pi\)
\(488\) 0 0
\(489\) −26.1803 −1.18392
\(490\) 0 0
\(491\) 1.12461 0.0507530 0.0253765 0.999678i \(-0.491922\pi\)
0.0253765 + 0.999678i \(0.491922\pi\)
\(492\) 0 0
\(493\) −5.52786 −0.248962
\(494\) 0 0
\(495\) 10.4721 0.470688
\(496\) 0 0
\(497\) −3.23607 −0.145157
\(498\) 0 0
\(499\) 35.8885 1.60659 0.803296 0.595580i \(-0.203078\pi\)
0.803296 + 0.595580i \(0.203078\pi\)
\(500\) 0 0
\(501\) −17.2361 −0.770051
\(502\) 0 0
\(503\) 1.00000 0.0445878
\(504\) 0 0
\(505\) −12.0000 −0.533993
\(506\) 0 0
\(507\) −37.8885 −1.68269
\(508\) 0 0
\(509\) 14.8885 0.659923 0.329962 0.943994i \(-0.392964\pi\)
0.329962 + 0.943994i \(0.392964\pi\)
\(510\) 0 0
\(511\) −31.8885 −1.41067
\(512\) 0 0
\(513\) 17.2361 0.760991
\(514\) 0 0
\(515\) 1.16718 0.0514323
\(516\) 0 0
\(517\) −17.9443 −0.789188
\(518\) 0 0
\(519\) −24.5967 −1.07968
\(520\) 0 0
\(521\) −41.0000 −1.79624 −0.898121 0.439748i \(-0.855068\pi\)
−0.898121 + 0.439748i \(0.855068\pi\)
\(522\) 0 0
\(523\) −12.3607 −0.540495 −0.270247 0.962791i \(-0.587105\pi\)
−0.270247 + 0.962791i \(0.587105\pi\)
\(524\) 0 0
\(525\) 32.8885 1.43537
\(526\) 0 0
\(527\) −15.4164 −0.671549
\(528\) 0 0
\(529\) −18.0000 −0.782609
\(530\) 0 0
\(531\) −17.8885 −0.776297
\(532\) 0 0
\(533\) 28.6525 1.24108
\(534\) 0 0
\(535\) 9.88854 0.427519
\(536\) 0 0
\(537\) 12.7639 0.550804
\(538\) 0 0
\(539\) 46.3607 1.99690
\(540\) 0 0
\(541\) 6.65248 0.286012 0.143006 0.989722i \(-0.454323\pi\)
0.143006 + 0.989722i \(0.454323\pi\)
\(542\) 0 0
\(543\) 44.7214 1.91918
\(544\) 0 0
\(545\) 10.4721 0.448577
\(546\) 0 0
\(547\) −36.3607 −1.55467 −0.777335 0.629087i \(-0.783429\pi\)
−0.777335 + 0.629087i \(0.783429\pi\)
\(548\) 0 0
\(549\) 14.9443 0.637806
\(550\) 0 0
\(551\) −21.3050 −0.907621
\(552\) 0 0
\(553\) −54.8328 −2.33173
\(554\) 0 0
\(555\) 12.3607 0.524682
\(556\) 0 0
\(557\) −37.2492 −1.57830 −0.789150 0.614200i \(-0.789479\pi\)
−0.789150 + 0.614200i \(0.789479\pi\)
\(558\) 0 0
\(559\) 56.0132 2.36910
\(560\) 0 0
\(561\) −18.9443 −0.799828
\(562\) 0 0
\(563\) −35.7082 −1.50492 −0.752461 0.658637i \(-0.771133\pi\)
−0.752461 + 0.658637i \(0.771133\pi\)
\(564\) 0 0
\(565\) −10.5410 −0.443464
\(566\) 0 0
\(567\) −46.5967 −1.95688
\(568\) 0 0
\(569\) 39.3050 1.64775 0.823875 0.566772i \(-0.191808\pi\)
0.823875 + 0.566772i \(0.191808\pi\)
\(570\) 0 0
\(571\) −15.8885 −0.664915 −0.332457 0.943118i \(-0.607878\pi\)
−0.332457 + 0.943118i \(0.607878\pi\)
\(572\) 0 0
\(573\) −41.3050 −1.72554
\(574\) 0 0
\(575\) 7.76393 0.323778
\(576\) 0 0
\(577\) −22.3607 −0.930887 −0.465444 0.885078i \(-0.654105\pi\)
−0.465444 + 0.885078i \(0.654105\pi\)
\(578\) 0 0
\(579\) 15.1246 0.628557
\(580\) 0 0
\(581\) −70.7771 −2.93633
\(582\) 0 0
\(583\) −2.00000 −0.0828315
\(584\) 0 0
\(585\) −13.5279 −0.559308
\(586\) 0 0
\(587\) 14.8328 0.612216 0.306108 0.951997i \(-0.400973\pi\)
0.306108 + 0.951997i \(0.400973\pi\)
\(588\) 0 0
\(589\) −59.4164 −2.44821
\(590\) 0 0
\(591\) 45.6525 1.87789
\(592\) 0 0
\(593\) 16.4721 0.676430 0.338215 0.941069i \(-0.390177\pi\)
0.338215 + 0.941069i \(0.390177\pi\)
\(594\) 0 0
\(595\) 10.4721 0.429316
\(596\) 0 0
\(597\) 5.52786 0.226240
\(598\) 0 0
\(599\) −25.5279 −1.04304 −0.521520 0.853239i \(-0.674635\pi\)
−0.521520 + 0.853239i \(0.674635\pi\)
\(600\) 0 0
\(601\) −9.47214 −0.386376 −0.193188 0.981162i \(-0.561883\pi\)
−0.193188 + 0.981162i \(0.561883\pi\)
\(602\) 0 0
\(603\) −9.41641 −0.383466
\(604\) 0 0
\(605\) 8.58359 0.348973
\(606\) 0 0
\(607\) −10.2361 −0.415469 −0.207735 0.978185i \(-0.566609\pi\)
−0.207735 + 0.978185i \(0.566609\pi\)
\(608\) 0 0
\(609\) 26.1803 1.06088
\(610\) 0 0
\(611\) 23.1803 0.937776
\(612\) 0 0
\(613\) 7.81966 0.315833 0.157917 0.987452i \(-0.449522\pi\)
0.157917 + 0.987452i \(0.449522\pi\)
\(614\) 0 0
\(615\) 14.4721 0.583573
\(616\) 0 0
\(617\) −23.8885 −0.961717 −0.480858 0.876798i \(-0.659675\pi\)
−0.480858 + 0.876798i \(0.659675\pi\)
\(618\) 0 0
\(619\) −31.7082 −1.27446 −0.637230 0.770674i \(-0.719920\pi\)
−0.637230 + 0.770674i \(0.719920\pi\)
\(620\) 0 0
\(621\) −5.00000 −0.200643
\(622\) 0 0
\(623\) −61.3050 −2.45613
\(624\) 0 0
\(625\) 4.41641 0.176656
\(626\) 0 0
\(627\) −73.0132 −2.91586
\(628\) 0 0
\(629\) −8.94427 −0.356631
\(630\) 0 0
\(631\) −12.2361 −0.487110 −0.243555 0.969887i \(-0.578314\pi\)
−0.243555 + 0.969887i \(0.578314\pi\)
\(632\) 0 0
\(633\) −8.29180 −0.329569
\(634\) 0 0
\(635\) −2.83282 −0.112417
\(636\) 0 0
\(637\) −59.8885 −2.37287
\(638\) 0 0
\(639\) −1.52786 −0.0604414
\(640\) 0 0
\(641\) −10.4164 −0.411423 −0.205712 0.978613i \(-0.565951\pi\)
−0.205712 + 0.978613i \(0.565951\pi\)
\(642\) 0 0
\(643\) −21.0557 −0.830357 −0.415178 0.909740i \(-0.636281\pi\)
−0.415178 + 0.909740i \(0.636281\pi\)
\(644\) 0 0
\(645\) 28.2918 1.11399
\(646\) 0 0
\(647\) 44.9443 1.76694 0.883471 0.468486i \(-0.155200\pi\)
0.883471 + 0.468486i \(0.155200\pi\)
\(648\) 0 0
\(649\) −37.8885 −1.48726
\(650\) 0 0
\(651\) 73.0132 2.86161
\(652\) 0 0
\(653\) 9.00000 0.352197 0.176099 0.984373i \(-0.443652\pi\)
0.176099 + 0.984373i \(0.443652\pi\)
\(654\) 0 0
\(655\) 26.1803 1.02295
\(656\) 0 0
\(657\) −15.0557 −0.587380
\(658\) 0 0
\(659\) −30.0132 −1.16915 −0.584573 0.811341i \(-0.698738\pi\)
−0.584573 + 0.811341i \(0.698738\pi\)
\(660\) 0 0
\(661\) −47.3607 −1.84212 −0.921058 0.389424i \(-0.872674\pi\)
−0.921058 + 0.389424i \(0.872674\pi\)
\(662\) 0 0
\(663\) 24.4721 0.950419
\(664\) 0 0
\(665\) 40.3607 1.56512
\(666\) 0 0
\(667\) 6.18034 0.239304
\(668\) 0 0
\(669\) 8.41641 0.325397
\(670\) 0 0
\(671\) 31.6525 1.22193
\(672\) 0 0
\(673\) 22.9443 0.884437 0.442218 0.896907i \(-0.354192\pi\)
0.442218 + 0.896907i \(0.354192\pi\)
\(674\) 0 0
\(675\) −7.76393 −0.298834
\(676\) 0 0
\(677\) 27.5279 1.05798 0.528991 0.848628i \(-0.322571\pi\)
0.528991 + 0.848628i \(0.322571\pi\)
\(678\) 0 0
\(679\) −42.3607 −1.62565
\(680\) 0 0
\(681\) 26.1803 1.00323
\(682\) 0 0
\(683\) 23.8197 0.911434 0.455717 0.890125i \(-0.349383\pi\)
0.455717 + 0.890125i \(0.349383\pi\)
\(684\) 0 0
\(685\) −8.94427 −0.341743
\(686\) 0 0
\(687\) −41.1803 −1.57113
\(688\) 0 0
\(689\) 2.58359 0.0984270
\(690\) 0 0
\(691\) 8.00000 0.304334 0.152167 0.988355i \(-0.451375\pi\)
0.152167 + 0.988355i \(0.451375\pi\)
\(692\) 0 0
\(693\) 35.8885 1.36329
\(694\) 0 0
\(695\) 12.5836 0.477323
\(696\) 0 0
\(697\) −10.4721 −0.396660
\(698\) 0 0
\(699\) −50.1246 −1.89589
\(700\) 0 0
\(701\) 9.00000 0.339925 0.169963 0.985451i \(-0.445635\pi\)
0.169963 + 0.985451i \(0.445635\pi\)
\(702\) 0 0
\(703\) −34.4721 −1.30014
\(704\) 0 0
\(705\) 11.7082 0.440956
\(706\) 0 0
\(707\) −41.1246 −1.54665
\(708\) 0 0
\(709\) 30.0000 1.12667 0.563337 0.826227i \(-0.309517\pi\)
0.563337 + 0.826227i \(0.309517\pi\)
\(710\) 0 0
\(711\) −25.8885 −0.970896
\(712\) 0 0
\(713\) 17.2361 0.645496
\(714\) 0 0
\(715\) −28.6525 −1.07154
\(716\) 0 0
\(717\) −56.8328 −2.12246
\(718\) 0 0
\(719\) 9.88854 0.368780 0.184390 0.982853i \(-0.440969\pi\)
0.184390 + 0.982853i \(0.440969\pi\)
\(720\) 0 0
\(721\) 4.00000 0.148968
\(722\) 0 0
\(723\) 11.0557 0.411167
\(724\) 0 0
\(725\) 9.59675 0.356414
\(726\) 0 0
\(727\) −21.0689 −0.781402 −0.390701 0.920518i \(-0.627767\pi\)
−0.390701 + 0.920518i \(0.627767\pi\)
\(728\) 0 0
\(729\) −7.00000 −0.259259
\(730\) 0 0
\(731\) −20.4721 −0.757189
\(732\) 0 0
\(733\) −29.2361 −1.07986 −0.539929 0.841710i \(-0.681549\pi\)
−0.539929 + 0.841710i \(0.681549\pi\)
\(734\) 0 0
\(735\) −30.2492 −1.11576
\(736\) 0 0
\(737\) −19.9443 −0.734657
\(738\) 0 0
\(739\) 30.2361 1.11225 0.556126 0.831098i \(-0.312287\pi\)
0.556126 + 0.831098i \(0.312287\pi\)
\(740\) 0 0
\(741\) 94.3181 3.46486
\(742\) 0 0
\(743\) 36.2918 1.33142 0.665708 0.746212i \(-0.268129\pi\)
0.665708 + 0.746212i \(0.268129\pi\)
\(744\) 0 0
\(745\) −15.7771 −0.578028
\(746\) 0 0
\(747\) −33.4164 −1.22264
\(748\) 0 0
\(749\) 33.8885 1.23826
\(750\) 0 0
\(751\) 40.3607 1.47278 0.736391 0.676556i \(-0.236528\pi\)
0.736391 + 0.676556i \(0.236528\pi\)
\(752\) 0 0
\(753\) −9.34752 −0.340643
\(754\) 0 0
\(755\) 22.8328 0.830971
\(756\) 0 0
\(757\) 42.3607 1.53963 0.769813 0.638270i \(-0.220350\pi\)
0.769813 + 0.638270i \(0.220350\pi\)
\(758\) 0 0
\(759\) 21.1803 0.768798
\(760\) 0 0
\(761\) 7.00000 0.253750 0.126875 0.991919i \(-0.459505\pi\)
0.126875 + 0.991919i \(0.459505\pi\)
\(762\) 0 0
\(763\) 35.8885 1.29925
\(764\) 0 0
\(765\) 4.94427 0.178761
\(766\) 0 0
\(767\) 48.9443 1.76728
\(768\) 0 0
\(769\) 45.7771 1.65076 0.825382 0.564575i \(-0.190960\pi\)
0.825382 + 0.564575i \(0.190960\pi\)
\(770\) 0 0
\(771\) −22.4853 −0.809788
\(772\) 0 0
\(773\) 33.5967 1.20839 0.604196 0.796836i \(-0.293495\pi\)
0.604196 + 0.796836i \(0.293495\pi\)
\(774\) 0 0
\(775\) 26.7639 0.961389
\(776\) 0 0
\(777\) 42.3607 1.51968
\(778\) 0 0
\(779\) −40.3607 −1.44607
\(780\) 0 0
\(781\) −3.23607 −0.115796
\(782\) 0 0
\(783\) −6.18034 −0.220867
\(784\) 0 0
\(785\) 15.4164 0.550235
\(786\) 0 0
\(787\) −52.0689 −1.85606 −0.928028 0.372511i \(-0.878497\pi\)
−0.928028 + 0.372511i \(0.878497\pi\)
\(788\) 0 0
\(789\) 36.0557 1.28362
\(790\) 0 0
\(791\) −36.1246 −1.28444
\(792\) 0 0
\(793\) −40.8885 −1.45199
\(794\) 0 0
\(795\) 1.30495 0.0462819
\(796\) 0 0
\(797\) −4.83282 −0.171187 −0.0855936 0.996330i \(-0.527279\pi\)
−0.0855936 + 0.996330i \(0.527279\pi\)
\(798\) 0 0
\(799\) −8.47214 −0.299723
\(800\) 0 0
\(801\) −28.9443 −1.02270
\(802\) 0 0
\(803\) −31.8885 −1.12532
\(804\) 0 0
\(805\) −11.7082 −0.412660
\(806\) 0 0
\(807\) −37.8885 −1.33374
\(808\) 0 0
\(809\) −6.18034 −0.217289 −0.108645 0.994081i \(-0.534651\pi\)
−0.108645 + 0.994081i \(0.534651\pi\)
\(810\) 0 0
\(811\) 8.23607 0.289207 0.144604 0.989490i \(-0.453809\pi\)
0.144604 + 0.989490i \(0.453809\pi\)
\(812\) 0 0
\(813\) 59.7214 2.09452
\(814\) 0 0
\(815\) 14.4721 0.506937
\(816\) 0 0
\(817\) −78.9017 −2.76042
\(818\) 0 0
\(819\) −46.3607 −1.61997
\(820\) 0 0
\(821\) 40.9443 1.42896 0.714482 0.699653i \(-0.246662\pi\)
0.714482 + 0.699653i \(0.246662\pi\)
\(822\) 0 0
\(823\) 24.1803 0.842874 0.421437 0.906858i \(-0.361526\pi\)
0.421437 + 0.906858i \(0.361526\pi\)
\(824\) 0 0
\(825\) 32.8885 1.14503
\(826\) 0 0
\(827\) −8.00000 −0.278187 −0.139094 0.990279i \(-0.544419\pi\)
−0.139094 + 0.990279i \(0.544419\pi\)
\(828\) 0 0
\(829\) −45.5967 −1.58364 −0.791820 0.610754i \(-0.790866\pi\)
−0.791820 + 0.610754i \(0.790866\pi\)
\(830\) 0 0
\(831\) −58.5410 −2.03077
\(832\) 0 0
\(833\) 21.8885 0.758393
\(834\) 0 0
\(835\) 9.52786 0.329725
\(836\) 0 0
\(837\) −17.2361 −0.595766
\(838\) 0 0
\(839\) −34.5967 −1.19441 −0.597206 0.802088i \(-0.703723\pi\)
−0.597206 + 0.802088i \(0.703723\pi\)
\(840\) 0 0
\(841\) −21.3607 −0.736575
\(842\) 0 0
\(843\) 63.5410 2.18847
\(844\) 0 0
\(845\) 20.9443 0.720505
\(846\) 0 0
\(847\) 29.4164 1.01076
\(848\) 0 0
\(849\) −41.3050 −1.41758
\(850\) 0 0
\(851\) 10.0000 0.342796
\(852\) 0 0
\(853\) 15.8328 0.542105 0.271053 0.962565i \(-0.412628\pi\)
0.271053 + 0.962565i \(0.412628\pi\)
\(854\) 0 0
\(855\) 19.0557 0.651692
\(856\) 0 0
\(857\) 16.0557 0.548453 0.274227 0.961665i \(-0.411578\pi\)
0.274227 + 0.961665i \(0.411578\pi\)
\(858\) 0 0
\(859\) 14.2918 0.487630 0.243815 0.969822i \(-0.421601\pi\)
0.243815 + 0.969822i \(0.421601\pi\)
\(860\) 0 0
\(861\) 49.5967 1.69025
\(862\) 0 0
\(863\) −7.23607 −0.246319 −0.123159 0.992387i \(-0.539303\pi\)
−0.123159 + 0.992387i \(0.539303\pi\)
\(864\) 0 0
\(865\) 13.5967 0.462303
\(866\) 0 0
\(867\) 29.0689 0.987231
\(868\) 0 0
\(869\) −54.8328 −1.86008
\(870\) 0 0
\(871\) 25.7639 0.872978
\(872\) 0 0
\(873\) −20.0000 −0.676897
\(874\) 0 0
\(875\) −44.3607 −1.49966
\(876\) 0 0
\(877\) −17.7771 −0.600290 −0.300145 0.953894i \(-0.597035\pi\)
−0.300145 + 0.953894i \(0.597035\pi\)
\(878\) 0 0
\(879\) −11.1803 −0.377104
\(880\) 0 0
\(881\) −11.8885 −0.400535 −0.200268 0.979741i \(-0.564181\pi\)
−0.200268 + 0.979741i \(0.564181\pi\)
\(882\) 0 0
\(883\) −41.5279 −1.39752 −0.698762 0.715354i \(-0.746265\pi\)
−0.698762 + 0.715354i \(0.746265\pi\)
\(884\) 0 0
\(885\) 24.7214 0.830999
\(886\) 0 0
\(887\) 40.7214 1.36729 0.683645 0.729815i \(-0.260394\pi\)
0.683645 + 0.729815i \(0.260394\pi\)
\(888\) 0 0
\(889\) −9.70820 −0.325603
\(890\) 0 0
\(891\) −46.5967 −1.56105
\(892\) 0 0
\(893\) −32.6525 −1.09267
\(894\) 0 0
\(895\) −7.05573 −0.235847
\(896\) 0 0
\(897\) −27.3607 −0.913547
\(898\) 0 0
\(899\) 21.3050 0.710560
\(900\) 0 0
\(901\) −0.944272 −0.0314583
\(902\) 0 0
\(903\) 96.9574 3.22654
\(904\) 0 0
\(905\) −24.7214 −0.821766
\(906\) 0 0
\(907\) 2.94427 0.0977629 0.0488815 0.998805i \(-0.484434\pi\)
0.0488815 + 0.998805i \(0.484434\pi\)
\(908\) 0 0
\(909\) −19.4164 −0.644002
\(910\) 0 0
\(911\) −6.76393 −0.224099 −0.112050 0.993703i \(-0.535742\pi\)
−0.112050 + 0.993703i \(0.535742\pi\)
\(912\) 0 0
\(913\) −70.7771 −2.34238
\(914\) 0 0
\(915\) −20.6525 −0.682750
\(916\) 0 0
\(917\) 89.7214 2.96286
\(918\) 0 0
\(919\) −4.94427 −0.163096 −0.0815482 0.996669i \(-0.525986\pi\)
−0.0815482 + 0.996669i \(0.525986\pi\)
\(920\) 0 0
\(921\) 21.0557 0.693810
\(922\) 0 0
\(923\) 4.18034 0.137598
\(924\) 0 0
\(925\) 15.5279 0.510553
\(926\) 0 0
\(927\) 1.88854 0.0620279
\(928\) 0 0
\(929\) 26.6525 0.874439 0.437220 0.899355i \(-0.355963\pi\)
0.437220 + 0.899355i \(0.355963\pi\)
\(930\) 0 0
\(931\) 84.3607 2.76481
\(932\) 0 0
\(933\) −13.0132 −0.426032
\(934\) 0 0
\(935\) 10.4721 0.342475
\(936\) 0 0
\(937\) −16.0689 −0.524948 −0.262474 0.964939i \(-0.584538\pi\)
−0.262474 + 0.964939i \(0.584538\pi\)
\(938\) 0 0
\(939\) 69.1935 2.25804
\(940\) 0 0
\(941\) 36.4164 1.18714 0.593570 0.804782i \(-0.297718\pi\)
0.593570 + 0.804782i \(0.297718\pi\)
\(942\) 0 0
\(943\) 11.7082 0.381272
\(944\) 0 0
\(945\) 11.7082 0.380868
\(946\) 0 0
\(947\) 29.2361 0.950045 0.475022 0.879974i \(-0.342440\pi\)
0.475022 + 0.879974i \(0.342440\pi\)
\(948\) 0 0
\(949\) 41.1935 1.33720
\(950\) 0 0
\(951\) 18.0132 0.584117
\(952\) 0 0
\(953\) 20.0557 0.649669 0.324834 0.945771i \(-0.394691\pi\)
0.324834 + 0.945771i \(0.394691\pi\)
\(954\) 0 0
\(955\) 22.8328 0.738853
\(956\) 0 0
\(957\) 26.1803 0.846290
\(958\) 0 0
\(959\) −30.6525 −0.989820
\(960\) 0 0
\(961\) 28.4164 0.916658
\(962\) 0 0
\(963\) 16.0000 0.515593
\(964\) 0 0
\(965\) −8.36068 −0.269140
\(966\) 0 0
\(967\) −61.3050 −1.97143 −0.985717 0.168409i \(-0.946137\pi\)
−0.985717 + 0.168409i \(0.946137\pi\)
\(968\) 0 0
\(969\) −34.4721 −1.10740
\(970\) 0 0
\(971\) 57.0689 1.83143 0.915714 0.401831i \(-0.131626\pi\)
0.915714 + 0.401831i \(0.131626\pi\)
\(972\) 0 0
\(973\) 43.1246 1.38251
\(974\) 0 0
\(975\) −42.4853 −1.36062
\(976\) 0 0
\(977\) 39.8885 1.27615 0.638074 0.769975i \(-0.279731\pi\)
0.638074 + 0.769975i \(0.279731\pi\)
\(978\) 0 0
\(979\) −61.3050 −1.95931
\(980\) 0 0
\(981\) 16.9443 0.540989
\(982\) 0 0
\(983\) 39.2361 1.25144 0.625718 0.780049i \(-0.284806\pi\)
0.625718 + 0.780049i \(0.284806\pi\)
\(984\) 0 0
\(985\) −25.2361 −0.804088
\(986\) 0 0
\(987\) 40.1246 1.27718
\(988\) 0 0
\(989\) 22.8885 0.727813
\(990\) 0 0
\(991\) 36.9574 1.17399 0.586996 0.809590i \(-0.300311\pi\)
0.586996 + 0.809590i \(0.300311\pi\)
\(992\) 0 0
\(993\) 24.4721 0.776600
\(994\) 0 0
\(995\) −3.05573 −0.0968731
\(996\) 0 0
\(997\) −2.06888 −0.0655222 −0.0327611 0.999463i \(-0.510430\pi\)
−0.0327611 + 0.999463i \(0.510430\pi\)
\(998\) 0 0
\(999\) −10.0000 −0.316386
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 \(a_p\))