Properties

Label 8020.2.a.c.1.13
Level 8020
Weight 2
Character 8020.1
Self dual Yes
Analytic conductor 64.040
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

Level: \( N \) = \( 8020 = 2^{2} \cdot 5 \cdot 401 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8020.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0400224211\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.13
Character \(\chi\) = 8020.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.172341 q^{3}\) \(-1.00000 q^{5}\) \(+3.94901 q^{7}\) \(-2.97030 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.172341 q^{3}\) \(-1.00000 q^{5}\) \(+3.94901 q^{7}\) \(-2.97030 q^{9}\) \(+2.50533 q^{11}\) \(+5.08392 q^{13}\) \(+0.172341 q^{15}\) \(-5.79588 q^{17}\) \(-1.40336 q^{19}\) \(-0.680578 q^{21}\) \(-4.18550 q^{23}\) \(+1.00000 q^{25}\) \(+1.02893 q^{27}\) \(+3.24974 q^{29}\) \(-2.87221 q^{31}\) \(-0.431771 q^{33}\) \(-3.94901 q^{35}\) \(-2.92358 q^{37}\) \(-0.876169 q^{39}\) \(-11.1289 q^{41}\) \(-1.07418 q^{43}\) \(+2.97030 q^{45}\) \(+0.742520 q^{47}\) \(+8.59469 q^{49}\) \(+0.998869 q^{51}\) \(-7.39320 q^{53}\) \(-2.50533 q^{55}\) \(+0.241857 q^{57}\) \(-13.2989 q^{59}\) \(-13.5530 q^{61}\) \(-11.7297 q^{63}\) \(-5.08392 q^{65}\) \(-0.250028 q^{67}\) \(+0.721335 q^{69}\) \(+1.16282 q^{71}\) \(+9.19316 q^{73}\) \(-0.172341 q^{75}\) \(+9.89356 q^{77}\) \(+10.1231 q^{79}\) \(+8.73357 q^{81}\) \(-10.6880 q^{83}\) \(+5.79588 q^{85}\) \(-0.560065 q^{87}\) \(+14.6364 q^{89}\) \(+20.0765 q^{91}\) \(+0.495000 q^{93}\) \(+1.40336 q^{95}\) \(-3.29704 q^{97}\) \(-7.44157 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut -\mathstrut 28q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 17q^{9} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 3q^{13} \) \(\mathstrut -\mathstrut 3q^{15} \) \(\mathstrut -\mathstrut 10q^{17} \) \(\mathstrut -\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut 12q^{21} \) \(\mathstrut -\mathstrut 23q^{23} \) \(\mathstrut +\mathstrut 28q^{25} \) \(\mathstrut +\mathstrut 9q^{27} \) \(\mathstrut -\mathstrut 37q^{29} \) \(\mathstrut -\mathstrut 11q^{31} \) \(\mathstrut +\mathstrut 2q^{33} \) \(\mathstrut +\mathstrut 4q^{35} \) \(\mathstrut -\mathstrut 3q^{37} \) \(\mathstrut -\mathstrut 19q^{39} \) \(\mathstrut -\mathstrut 30q^{41} \) \(\mathstrut +\mathstrut 13q^{43} \) \(\mathstrut -\mathstrut 17q^{45} \) \(\mathstrut -\mathstrut 15q^{47} \) \(\mathstrut +\mathstrut 12q^{49} \) \(\mathstrut -\mathstrut 8q^{51} \) \(\mathstrut -\mathstrut 35q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut -\mathstrut 22q^{57} \) \(\mathstrut -\mathstrut q^{59} \) \(\mathstrut -\mathstrut 33q^{61} \) \(\mathstrut -\mathstrut 20q^{63} \) \(\mathstrut -\mathstrut 3q^{65} \) \(\mathstrut +\mathstrut 19q^{67} \) \(\mathstrut -\mathstrut 8q^{69} \) \(\mathstrut -\mathstrut 31q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut -\mathstrut 42q^{77} \) \(\mathstrut -\mathstrut 29q^{79} \) \(\mathstrut -\mathstrut 36q^{81} \) \(\mathstrut +\mathstrut 14q^{83} \) \(\mathstrut +\mathstrut 10q^{85} \) \(\mathstrut -\mathstrut 32q^{87} \) \(\mathstrut -\mathstrut 32q^{89} \) \(\mathstrut -\mathstrut 7q^{91} \) \(\mathstrut -\mathstrut 11q^{93} \) \(\mathstrut +\mathstrut 2q^{95} \) \(\mathstrut +\mathstrut 2q^{97} \) \(\mathstrut -\mathstrut 39q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −0.172341 −0.0995013 −0.0497506 0.998762i \(-0.515843\pi\)
−0.0497506 + 0.998762i \(0.515843\pi\)
\(4\) 0 0
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) 3.94901 1.49259 0.746293 0.665618i \(-0.231832\pi\)
0.746293 + 0.665618i \(0.231832\pi\)
\(8\) 0 0
\(9\) −2.97030 −0.990099
\(10\) 0 0
\(11\) 2.50533 0.755384 0.377692 0.925931i \(-0.376718\pi\)
0.377692 + 0.925931i \(0.376718\pi\)
\(12\) 0 0
\(13\) 5.08392 1.41003 0.705013 0.709195i \(-0.250941\pi\)
0.705013 + 0.709195i \(0.250941\pi\)
\(14\) 0 0
\(15\) 0.172341 0.0444983
\(16\) 0 0
\(17\) −5.79588 −1.40571 −0.702853 0.711335i \(-0.748091\pi\)
−0.702853 + 0.711335i \(0.748091\pi\)
\(18\) 0 0
\(19\) −1.40336 −0.321953 −0.160976 0.986958i \(-0.551464\pi\)
−0.160976 + 0.986958i \(0.551464\pi\)
\(20\) 0 0
\(21\) −0.680578 −0.148514
\(22\) 0 0
\(23\) −4.18550 −0.872738 −0.436369 0.899768i \(-0.643736\pi\)
−0.436369 + 0.899768i \(0.643736\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 1.02893 0.198017
\(28\) 0 0
\(29\) 3.24974 0.603462 0.301731 0.953393i \(-0.402436\pi\)
0.301731 + 0.953393i \(0.402436\pi\)
\(30\) 0 0
\(31\) −2.87221 −0.515864 −0.257932 0.966163i \(-0.583041\pi\)
−0.257932 + 0.966163i \(0.583041\pi\)
\(32\) 0 0
\(33\) −0.431771 −0.0751617
\(34\) 0 0
\(35\) −3.94901 −0.667505
\(36\) 0 0
\(37\) −2.92358 −0.480634 −0.240317 0.970695i \(-0.577251\pi\)
−0.240317 + 0.970695i \(0.577251\pi\)
\(38\) 0 0
\(39\) −0.876169 −0.140299
\(40\) 0 0
\(41\) −11.1289 −1.73805 −0.869023 0.494771i \(-0.835252\pi\)
−0.869023 + 0.494771i \(0.835252\pi\)
\(42\) 0 0
\(43\) −1.07418 −0.163811 −0.0819053 0.996640i \(-0.526101\pi\)
−0.0819053 + 0.996640i \(0.526101\pi\)
\(44\) 0 0
\(45\) 2.97030 0.442786
\(46\) 0 0
\(47\) 0.742520 0.108308 0.0541539 0.998533i \(-0.482754\pi\)
0.0541539 + 0.998533i \(0.482754\pi\)
\(48\) 0 0
\(49\) 8.59469 1.22781
\(50\) 0 0
\(51\) 0.998869 0.139870
\(52\) 0 0
\(53\) −7.39320 −1.01553 −0.507767 0.861494i \(-0.669529\pi\)
−0.507767 + 0.861494i \(0.669529\pi\)
\(54\) 0 0
\(55\) −2.50533 −0.337818
\(56\) 0 0
\(57\) 0.241857 0.0320347
\(58\) 0 0
\(59\) −13.2989 −1.73137 −0.865685 0.500589i \(-0.833117\pi\)
−0.865685 + 0.500589i \(0.833117\pi\)
\(60\) 0 0
\(61\) −13.5530 −1.73528 −0.867642 0.497190i \(-0.834365\pi\)
−0.867642 + 0.497190i \(0.834365\pi\)
\(62\) 0 0
\(63\) −11.7297 −1.47781
\(64\) 0 0
\(65\) −5.08392 −0.630583
\(66\) 0 0
\(67\) −0.250028 −0.0305458 −0.0152729 0.999883i \(-0.504862\pi\)
−0.0152729 + 0.999883i \(0.504862\pi\)
\(68\) 0 0
\(69\) 0.721335 0.0868385
\(70\) 0 0
\(71\) 1.16282 0.138001 0.0690006 0.997617i \(-0.478019\pi\)
0.0690006 + 0.997617i \(0.478019\pi\)
\(72\) 0 0
\(73\) 9.19316 1.07598 0.537989 0.842952i \(-0.319184\pi\)
0.537989 + 0.842952i \(0.319184\pi\)
\(74\) 0 0
\(75\) −0.172341 −0.0199003
\(76\) 0 0
\(77\) 9.89356 1.12748
\(78\) 0 0
\(79\) 10.1231 1.13894 0.569471 0.822012i \(-0.307148\pi\)
0.569471 + 0.822012i \(0.307148\pi\)
\(80\) 0 0
\(81\) 8.73357 0.970396
\(82\) 0 0
\(83\) −10.6880 −1.17317 −0.586583 0.809889i \(-0.699527\pi\)
−0.586583 + 0.809889i \(0.699527\pi\)
\(84\) 0 0
\(85\) 5.79588 0.628651
\(86\) 0 0
\(87\) −0.560065 −0.0600453
\(88\) 0 0
\(89\) 14.6364 1.55145 0.775726 0.631069i \(-0.217384\pi\)
0.775726 + 0.631069i \(0.217384\pi\)
\(90\) 0 0
\(91\) 20.0765 2.10458
\(92\) 0 0
\(93\) 0.495000 0.0513292
\(94\) 0 0
\(95\) 1.40336 0.143982
\(96\) 0 0
\(97\) −3.29704 −0.334764 −0.167382 0.985892i \(-0.553531\pi\)
−0.167382 + 0.985892i \(0.553531\pi\)
\(98\) 0 0
\(99\) −7.44157 −0.747906
\(100\) 0 0
\(101\) 8.66341 0.862042 0.431021 0.902342i \(-0.358153\pi\)
0.431021 + 0.902342i \(0.358153\pi\)
\(102\) 0 0
\(103\) 7.45638 0.734699 0.367350 0.930083i \(-0.380265\pi\)
0.367350 + 0.930083i \(0.380265\pi\)
\(104\) 0 0
\(105\) 0.680578 0.0664176
\(106\) 0 0
\(107\) −15.2815 −1.47732 −0.738658 0.674080i \(-0.764540\pi\)
−0.738658 + 0.674080i \(0.764540\pi\)
\(108\) 0 0
\(109\) −4.47754 −0.428871 −0.214435 0.976738i \(-0.568791\pi\)
−0.214435 + 0.976738i \(0.568791\pi\)
\(110\) 0 0
\(111\) 0.503854 0.0478237
\(112\) 0 0
\(113\) −4.16788 −0.392081 −0.196041 0.980596i \(-0.562808\pi\)
−0.196041 + 0.980596i \(0.562808\pi\)
\(114\) 0 0
\(115\) 4.18550 0.390300
\(116\) 0 0
\(117\) −15.1008 −1.39607
\(118\) 0 0
\(119\) −22.8880 −2.09814
\(120\) 0 0
\(121\) −4.72334 −0.429394
\(122\) 0 0
\(123\) 1.91797 0.172938
\(124\) 0 0
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −6.08740 −0.540170 −0.270085 0.962837i \(-0.587052\pi\)
−0.270085 + 0.962837i \(0.587052\pi\)
\(128\) 0 0
\(129\) 0.185125 0.0162994
\(130\) 0 0
\(131\) −0.0374609 −0.00327298 −0.00163649 0.999999i \(-0.500521\pi\)
−0.00163649 + 0.999999i \(0.500521\pi\)
\(132\) 0 0
\(133\) −5.54188 −0.480542
\(134\) 0 0
\(135\) −1.02893 −0.0885561
\(136\) 0 0
\(137\) −16.1557 −1.38027 −0.690136 0.723680i \(-0.742449\pi\)
−0.690136 + 0.723680i \(0.742449\pi\)
\(138\) 0 0
\(139\) −5.26258 −0.446366 −0.223183 0.974777i \(-0.571645\pi\)
−0.223183 + 0.974777i \(0.571645\pi\)
\(140\) 0 0
\(141\) −0.127967 −0.0107768
\(142\) 0 0
\(143\) 12.7369 1.06511
\(144\) 0 0
\(145\) −3.24974 −0.269876
\(146\) 0 0
\(147\) −1.48122 −0.122169
\(148\) 0 0
\(149\) 10.0907 0.826666 0.413333 0.910580i \(-0.364365\pi\)
0.413333 + 0.910580i \(0.364365\pi\)
\(150\) 0 0
\(151\) −14.0956 −1.14708 −0.573541 0.819177i \(-0.694431\pi\)
−0.573541 + 0.819177i \(0.694431\pi\)
\(152\) 0 0
\(153\) 17.2155 1.39179
\(154\) 0 0
\(155\) 2.87221 0.230701
\(156\) 0 0
\(157\) −4.50373 −0.359436 −0.179718 0.983718i \(-0.557519\pi\)
−0.179718 + 0.983718i \(0.557519\pi\)
\(158\) 0 0
\(159\) 1.27415 0.101047
\(160\) 0 0
\(161\) −16.5286 −1.30264
\(162\) 0 0
\(163\) −2.08183 −0.163062 −0.0815308 0.996671i \(-0.525981\pi\)
−0.0815308 + 0.996671i \(0.525981\pi\)
\(164\) 0 0
\(165\) 0.431771 0.0336133
\(166\) 0 0
\(167\) −14.2807 −1.10508 −0.552538 0.833488i \(-0.686341\pi\)
−0.552538 + 0.833488i \(0.686341\pi\)
\(168\) 0 0
\(169\) 12.8462 0.988172
\(170\) 0 0
\(171\) 4.16839 0.318765
\(172\) 0 0
\(173\) 15.9731 1.21441 0.607206 0.794545i \(-0.292290\pi\)
0.607206 + 0.794545i \(0.292290\pi\)
\(174\) 0 0
\(175\) 3.94901 0.298517
\(176\) 0 0
\(177\) 2.29195 0.172274
\(178\) 0 0
\(179\) −11.8862 −0.888414 −0.444207 0.895924i \(-0.646515\pi\)
−0.444207 + 0.895924i \(0.646515\pi\)
\(180\) 0 0
\(181\) 23.4450 1.74266 0.871328 0.490701i \(-0.163259\pi\)
0.871328 + 0.490701i \(0.163259\pi\)
\(182\) 0 0
\(183\) 2.33574 0.172663
\(184\) 0 0
\(185\) 2.92358 0.214946
\(186\) 0 0
\(187\) −14.5206 −1.06185
\(188\) 0 0
\(189\) 4.06325 0.295558
\(190\) 0 0
\(191\) 11.0712 0.801084 0.400542 0.916278i \(-0.368822\pi\)
0.400542 + 0.916278i \(0.368822\pi\)
\(192\) 0 0
\(193\) 13.6691 0.983923 0.491961 0.870617i \(-0.336280\pi\)
0.491961 + 0.870617i \(0.336280\pi\)
\(194\) 0 0
\(195\) 0.876169 0.0627438
\(196\) 0 0
\(197\) 5.96193 0.424770 0.212385 0.977186i \(-0.431877\pi\)
0.212385 + 0.977186i \(0.431877\pi\)
\(198\) 0 0
\(199\) 12.2406 0.867712 0.433856 0.900982i \(-0.357153\pi\)
0.433856 + 0.900982i \(0.357153\pi\)
\(200\) 0 0
\(201\) 0.0430902 0.00303935
\(202\) 0 0
\(203\) 12.8333 0.900719
\(204\) 0 0
\(205\) 11.1289 0.777278
\(206\) 0 0
\(207\) 12.4322 0.864097
\(208\) 0 0
\(209\) −3.51587 −0.243198
\(210\) 0 0
\(211\) −16.8163 −1.15768 −0.578841 0.815441i \(-0.696495\pi\)
−0.578841 + 0.815441i \(0.696495\pi\)
\(212\) 0 0
\(213\) −0.200402 −0.0137313
\(214\) 0 0
\(215\) 1.07418 0.0732583
\(216\) 0 0
\(217\) −11.3424 −0.769972
\(218\) 0 0
\(219\) −1.58436 −0.107061
\(220\) 0 0
\(221\) −29.4658 −1.98208
\(222\) 0 0
\(223\) 12.1078 0.810798 0.405399 0.914140i \(-0.367133\pi\)
0.405399 + 0.914140i \(0.367133\pi\)
\(224\) 0 0
\(225\) −2.97030 −0.198020
\(226\) 0 0
\(227\) 8.55660 0.567922 0.283961 0.958836i \(-0.408351\pi\)
0.283961 + 0.958836i \(0.408351\pi\)
\(228\) 0 0
\(229\) 19.5042 1.28887 0.644437 0.764657i \(-0.277092\pi\)
0.644437 + 0.764657i \(0.277092\pi\)
\(230\) 0 0
\(231\) −1.70507 −0.112185
\(232\) 0 0
\(233\) 16.1430 1.05756 0.528782 0.848758i \(-0.322649\pi\)
0.528782 + 0.848758i \(0.322649\pi\)
\(234\) 0 0
\(235\) −0.742520 −0.0484367
\(236\) 0 0
\(237\) −1.74463 −0.113326
\(238\) 0 0
\(239\) 20.4042 1.31984 0.659919 0.751337i \(-0.270590\pi\)
0.659919 + 0.751337i \(0.270590\pi\)
\(240\) 0 0
\(241\) −16.6841 −1.07472 −0.537358 0.843354i \(-0.680578\pi\)
−0.537358 + 0.843354i \(0.680578\pi\)
\(242\) 0 0
\(243\) −4.59194 −0.294573
\(244\) 0 0
\(245\) −8.59469 −0.549095
\(246\) 0 0
\(247\) −7.13456 −0.453961
\(248\) 0 0
\(249\) 1.84199 0.116732
\(250\) 0 0
\(251\) −9.38049 −0.592091 −0.296046 0.955174i \(-0.595668\pi\)
−0.296046 + 0.955174i \(0.595668\pi\)
\(252\) 0 0
\(253\) −10.4861 −0.659253
\(254\) 0 0
\(255\) −0.998869 −0.0625516
\(256\) 0 0
\(257\) −13.7357 −0.856807 −0.428404 0.903587i \(-0.640924\pi\)
−0.428404 + 0.903587i \(0.640924\pi\)
\(258\) 0 0
\(259\) −11.5453 −0.717387
\(260\) 0 0
\(261\) −9.65271 −0.597488
\(262\) 0 0
\(263\) −12.0127 −0.740735 −0.370368 0.928885i \(-0.620768\pi\)
−0.370368 + 0.928885i \(0.620768\pi\)
\(264\) 0 0
\(265\) 7.39320 0.454161
\(266\) 0 0
\(267\) −2.52245 −0.154372
\(268\) 0 0
\(269\) −16.4260 −1.00151 −0.500755 0.865589i \(-0.666944\pi\)
−0.500755 + 0.865589i \(0.666944\pi\)
\(270\) 0 0
\(271\) −8.82884 −0.536314 −0.268157 0.963375i \(-0.586415\pi\)
−0.268157 + 0.963375i \(0.586415\pi\)
\(272\) 0 0
\(273\) −3.46000 −0.209409
\(274\) 0 0
\(275\) 2.50533 0.151077
\(276\) 0 0
\(277\) −9.90537 −0.595156 −0.297578 0.954698i \(-0.596179\pi\)
−0.297578 + 0.954698i \(0.596179\pi\)
\(278\) 0 0
\(279\) 8.53132 0.510757
\(280\) 0 0
\(281\) −8.53454 −0.509128 −0.254564 0.967056i \(-0.581932\pi\)
−0.254564 + 0.967056i \(0.581932\pi\)
\(282\) 0 0
\(283\) −25.4398 −1.51224 −0.756120 0.654433i \(-0.772907\pi\)
−0.756120 + 0.654433i \(0.772907\pi\)
\(284\) 0 0
\(285\) −0.241857 −0.0143263
\(286\) 0 0
\(287\) −43.9483 −2.59418
\(288\) 0 0
\(289\) 16.5922 0.976011
\(290\) 0 0
\(291\) 0.568216 0.0333094
\(292\) 0 0
\(293\) −25.1395 −1.46867 −0.734334 0.678788i \(-0.762505\pi\)
−0.734334 + 0.678788i \(0.762505\pi\)
\(294\) 0 0
\(295\) 13.2989 0.774292
\(296\) 0 0
\(297\) 2.57780 0.149579
\(298\) 0 0
\(299\) −21.2788 −1.23058
\(300\) 0 0
\(301\) −4.24194 −0.244501
\(302\) 0 0
\(303\) −1.49306 −0.0857743
\(304\) 0 0
\(305\) 13.5530 0.776042
\(306\) 0 0
\(307\) 11.7002 0.667767 0.333884 0.942614i \(-0.391641\pi\)
0.333884 + 0.942614i \(0.391641\pi\)
\(308\) 0 0
\(309\) −1.28504 −0.0731035
\(310\) 0 0
\(311\) 3.84370 0.217956 0.108978 0.994044i \(-0.465242\pi\)
0.108978 + 0.994044i \(0.465242\pi\)
\(312\) 0 0
\(313\) −26.2050 −1.48119 −0.740596 0.671951i \(-0.765457\pi\)
−0.740596 + 0.671951i \(0.765457\pi\)
\(314\) 0 0
\(315\) 11.7297 0.660896
\(316\) 0 0
\(317\) 27.3801 1.53782 0.768911 0.639356i \(-0.220799\pi\)
0.768911 + 0.639356i \(0.220799\pi\)
\(318\) 0 0
\(319\) 8.14167 0.455846
\(320\) 0 0
\(321\) 2.63363 0.146995
\(322\) 0 0
\(323\) 8.13369 0.452571
\(324\) 0 0
\(325\) 5.08392 0.282005
\(326\) 0 0
\(327\) 0.771665 0.0426732
\(328\) 0 0
\(329\) 2.93222 0.161659
\(330\) 0 0
\(331\) 0.294394 0.0161814 0.00809068 0.999967i \(-0.497425\pi\)
0.00809068 + 0.999967i \(0.497425\pi\)
\(332\) 0 0
\(333\) 8.68391 0.475875
\(334\) 0 0
\(335\) 0.250028 0.0136605
\(336\) 0 0
\(337\) −18.2719 −0.995333 −0.497667 0.867368i \(-0.665810\pi\)
−0.497667 + 0.867368i \(0.665810\pi\)
\(338\) 0 0
\(339\) 0.718298 0.0390126
\(340\) 0 0
\(341\) −7.19582 −0.389676
\(342\) 0 0
\(343\) 6.29746 0.340031
\(344\) 0 0
\(345\) −0.721335 −0.0388354
\(346\) 0 0
\(347\) −27.2663 −1.46373 −0.731866 0.681449i \(-0.761350\pi\)
−0.731866 + 0.681449i \(0.761350\pi\)
\(348\) 0 0
\(349\) 14.2024 0.760235 0.380117 0.924938i \(-0.375884\pi\)
0.380117 + 0.924938i \(0.375884\pi\)
\(350\) 0 0
\(351\) 5.23099 0.279210
\(352\) 0 0
\(353\) −12.9886 −0.691316 −0.345658 0.938361i \(-0.612344\pi\)
−0.345658 + 0.938361i \(0.612344\pi\)
\(354\) 0 0
\(355\) −1.16282 −0.0617160
\(356\) 0 0
\(357\) 3.94454 0.208767
\(358\) 0 0
\(359\) −25.7593 −1.35952 −0.679762 0.733432i \(-0.737917\pi\)
−0.679762 + 0.733432i \(0.737917\pi\)
\(360\) 0 0
\(361\) −17.0306 −0.896347
\(362\) 0 0
\(363\) 0.814026 0.0427253
\(364\) 0 0
\(365\) −9.19316 −0.481192
\(366\) 0 0
\(367\) 2.93246 0.153073 0.0765366 0.997067i \(-0.475614\pi\)
0.0765366 + 0.997067i \(0.475614\pi\)
\(368\) 0 0
\(369\) 33.0562 1.72084
\(370\) 0 0
\(371\) −29.1958 −1.51577
\(372\) 0 0
\(373\) −3.42751 −0.177470 −0.0887350 0.996055i \(-0.528282\pi\)
−0.0887350 + 0.996055i \(0.528282\pi\)
\(374\) 0 0
\(375\) 0.172341 0.00889967
\(376\) 0 0
\(377\) 16.5214 0.850897
\(378\) 0 0
\(379\) −9.04806 −0.464768 −0.232384 0.972624i \(-0.574653\pi\)
−0.232384 + 0.972624i \(0.574653\pi\)
\(380\) 0 0
\(381\) 1.04911 0.0537476
\(382\) 0 0
\(383\) 25.7643 1.31650 0.658248 0.752801i \(-0.271298\pi\)
0.658248 + 0.752801i \(0.271298\pi\)
\(384\) 0 0
\(385\) −9.89356 −0.504223
\(386\) 0 0
\(387\) 3.19063 0.162189
\(388\) 0 0
\(389\) 27.9374 1.41648 0.708240 0.705971i \(-0.249489\pi\)
0.708240 + 0.705971i \(0.249489\pi\)
\(390\) 0 0
\(391\) 24.2587 1.22681
\(392\) 0 0
\(393\) 0.00645607 0.000325665 0
\(394\) 0 0
\(395\) −10.1231 −0.509350
\(396\) 0 0
\(397\) 22.9558 1.15212 0.576060 0.817407i \(-0.304589\pi\)
0.576060 + 0.817407i \(0.304589\pi\)
\(398\) 0 0
\(399\) 0.955095 0.0478145
\(400\) 0 0
\(401\) 1.00000 0.0499376
\(402\) 0 0
\(403\) −14.6021 −0.727382
\(404\) 0 0
\(405\) −8.73357 −0.433975
\(406\) 0 0
\(407\) −7.32452 −0.363063
\(408\) 0 0
\(409\) 12.4661 0.616410 0.308205 0.951320i \(-0.400272\pi\)
0.308205 + 0.951320i \(0.400272\pi\)
\(410\) 0 0
\(411\) 2.78429 0.137339
\(412\) 0 0
\(413\) −52.5175 −2.58422
\(414\) 0 0
\(415\) 10.6880 0.524656
\(416\) 0 0
\(417\) 0.906960 0.0444140
\(418\) 0 0
\(419\) −0.822135 −0.0401639 −0.0200820 0.999798i \(-0.506393\pi\)
−0.0200820 + 0.999798i \(0.506393\pi\)
\(420\) 0 0
\(421\) 3.89826 0.189990 0.0949948 0.995478i \(-0.469717\pi\)
0.0949948 + 0.995478i \(0.469717\pi\)
\(422\) 0 0
\(423\) −2.20551 −0.107235
\(424\) 0 0
\(425\) −5.79588 −0.281141
\(426\) 0 0
\(427\) −53.5209 −2.59006
\(428\) 0 0
\(429\) −2.19509 −0.105980
\(430\) 0 0
\(431\) −10.3758 −0.499787 −0.249893 0.968273i \(-0.580396\pi\)
−0.249893 + 0.968273i \(0.580396\pi\)
\(432\) 0 0
\(433\) 0.266162 0.0127909 0.00639547 0.999980i \(-0.497964\pi\)
0.00639547 + 0.999980i \(0.497964\pi\)
\(434\) 0 0
\(435\) 0.560065 0.0268531
\(436\) 0 0
\(437\) 5.87376 0.280980
\(438\) 0 0
\(439\) 17.4599 0.833317 0.416658 0.909063i \(-0.363201\pi\)
0.416658 + 0.909063i \(0.363201\pi\)
\(440\) 0 0
\(441\) −25.5288 −1.21566
\(442\) 0 0
\(443\) −3.30611 −0.157078 −0.0785390 0.996911i \(-0.525026\pi\)
−0.0785390 + 0.996911i \(0.525026\pi\)
\(444\) 0 0
\(445\) −14.6364 −0.693831
\(446\) 0 0
\(447\) −1.73905 −0.0822544
\(448\) 0 0
\(449\) −40.4136 −1.90724 −0.953619 0.301018i \(-0.902674\pi\)
−0.953619 + 0.301018i \(0.902674\pi\)
\(450\) 0 0
\(451\) −27.8816 −1.31289
\(452\) 0 0
\(453\) 2.42925 0.114136
\(454\) 0 0
\(455\) −20.0765 −0.941199
\(456\) 0 0
\(457\) −10.7329 −0.502065 −0.251033 0.967979i \(-0.580770\pi\)
−0.251033 + 0.967979i \(0.580770\pi\)
\(458\) 0 0
\(459\) −5.96355 −0.278354
\(460\) 0 0
\(461\) 0.208109 0.00969258 0.00484629 0.999988i \(-0.498457\pi\)
0.00484629 + 0.999988i \(0.498457\pi\)
\(462\) 0 0
\(463\) −16.3676 −0.760665 −0.380332 0.924850i \(-0.624190\pi\)
−0.380332 + 0.924850i \(0.624190\pi\)
\(464\) 0 0
\(465\) −0.495000 −0.0229551
\(466\) 0 0
\(467\) −21.3688 −0.988829 −0.494415 0.869226i \(-0.664618\pi\)
−0.494415 + 0.869226i \(0.664618\pi\)
\(468\) 0 0
\(469\) −0.987364 −0.0455922
\(470\) 0 0
\(471\) 0.776178 0.0357644
\(472\) 0 0
\(473\) −2.69117 −0.123740
\(474\) 0 0
\(475\) −1.40336 −0.0643905
\(476\) 0 0
\(477\) 21.9600 1.00548
\(478\) 0 0
\(479\) −29.5482 −1.35009 −0.675047 0.737775i \(-0.735877\pi\)
−0.675047 + 0.737775i \(0.735877\pi\)
\(480\) 0 0
\(481\) −14.8632 −0.677706
\(482\) 0 0
\(483\) 2.84856 0.129614
\(484\) 0 0
\(485\) 3.29704 0.149711
\(486\) 0 0
\(487\) 20.3957 0.924218 0.462109 0.886823i \(-0.347093\pi\)
0.462109 + 0.886823i \(0.347093\pi\)
\(488\) 0 0
\(489\) 0.358786 0.0162249
\(490\) 0 0
\(491\) 15.0246 0.678053 0.339026 0.940777i \(-0.389902\pi\)
0.339026 + 0.940777i \(0.389902\pi\)
\(492\) 0 0
\(493\) −18.8351 −0.848291
\(494\) 0 0
\(495\) 7.44157 0.334474
\(496\) 0 0
\(497\) 4.59198 0.205979
\(498\) 0 0
\(499\) 15.9864 0.715648 0.357824 0.933789i \(-0.383519\pi\)
0.357824 + 0.933789i \(0.383519\pi\)
\(500\) 0 0
\(501\) 2.46116 0.109957
\(502\) 0 0
\(503\) 11.8103 0.526594 0.263297 0.964715i \(-0.415190\pi\)
0.263297 + 0.964715i \(0.415190\pi\)
\(504\) 0 0
\(505\) −8.66341 −0.385517
\(506\) 0 0
\(507\) −2.21394 −0.0983244
\(508\) 0 0
\(509\) −44.2108 −1.95961 −0.979805 0.199954i \(-0.935921\pi\)
−0.979805 + 0.199954i \(0.935921\pi\)
\(510\) 0 0
\(511\) 36.3039 1.60599
\(512\) 0 0
\(513\) −1.44396 −0.0637522
\(514\) 0 0
\(515\) −7.45638 −0.328568
\(516\) 0 0
\(517\) 1.86026 0.0818140
\(518\) 0 0
\(519\) −2.75282 −0.120836
\(520\) 0 0
\(521\) −14.7082 −0.644380 −0.322190 0.946675i \(-0.604419\pi\)
−0.322190 + 0.946675i \(0.604419\pi\)
\(522\) 0 0
\(523\) −6.92390 −0.302761 −0.151380 0.988476i \(-0.548372\pi\)
−0.151380 + 0.988476i \(0.548372\pi\)
\(524\) 0 0
\(525\) −0.680578 −0.0297028
\(526\) 0 0
\(527\) 16.6470 0.725154
\(528\) 0 0
\(529\) −5.48156 −0.238329
\(530\) 0 0
\(531\) 39.5017 1.71423
\(532\) 0 0
\(533\) −56.5786 −2.45069
\(534\) 0 0
\(535\) 15.2815 0.660676
\(536\) 0 0
\(537\) 2.04848 0.0883984
\(538\) 0 0
\(539\) 21.5325 0.927471
\(540\) 0 0
\(541\) −33.3206 −1.43256 −0.716282 0.697811i \(-0.754157\pi\)
−0.716282 + 0.697811i \(0.754157\pi\)
\(542\) 0 0
\(543\) −4.04055 −0.173397
\(544\) 0 0
\(545\) 4.47754 0.191797
\(546\) 0 0
\(547\) −19.6932 −0.842021 −0.421011 0.907056i \(-0.638324\pi\)
−0.421011 + 0.907056i \(0.638324\pi\)
\(548\) 0 0
\(549\) 40.2564 1.71810
\(550\) 0 0
\(551\) −4.56055 −0.194286
\(552\) 0 0
\(553\) 39.9764 1.69997
\(554\) 0 0
\(555\) −0.503854 −0.0213874
\(556\) 0 0
\(557\) −39.1600 −1.65926 −0.829632 0.558310i \(-0.811450\pi\)
−0.829632 + 0.558310i \(0.811450\pi\)
\(558\) 0 0
\(559\) −5.46104 −0.230977
\(560\) 0 0
\(561\) 2.50249 0.105655
\(562\) 0 0
\(563\) 30.2992 1.27696 0.638480 0.769638i \(-0.279564\pi\)
0.638480 + 0.769638i \(0.279564\pi\)
\(564\) 0 0
\(565\) 4.16788 0.175344
\(566\) 0 0
\(567\) 34.4890 1.44840
\(568\) 0 0
\(569\) −26.9939 −1.13164 −0.565822 0.824528i \(-0.691441\pi\)
−0.565822 + 0.824528i \(0.691441\pi\)
\(570\) 0 0
\(571\) −42.1830 −1.76530 −0.882651 0.470029i \(-0.844244\pi\)
−0.882651 + 0.470029i \(0.844244\pi\)
\(572\) 0 0
\(573\) −1.90802 −0.0797089
\(574\) 0 0
\(575\) −4.18550 −0.174548
\(576\) 0 0
\(577\) −13.0524 −0.543377 −0.271689 0.962385i \(-0.587582\pi\)
−0.271689 + 0.962385i \(0.587582\pi\)
\(578\) 0 0
\(579\) −2.35575 −0.0979016
\(580\) 0 0
\(581\) −42.2072 −1.75105
\(582\) 0 0
\(583\) −18.5224 −0.767119
\(584\) 0 0
\(585\) 15.1008 0.624339
\(586\) 0 0
\(587\) 34.1703 1.41036 0.705179 0.709029i \(-0.250867\pi\)
0.705179 + 0.709029i \(0.250867\pi\)
\(588\) 0 0
\(589\) 4.03074 0.166084
\(590\) 0 0
\(591\) −1.02749 −0.0422652
\(592\) 0 0
\(593\) −12.6877 −0.521019 −0.260510 0.965471i \(-0.583891\pi\)
−0.260510 + 0.965471i \(0.583891\pi\)
\(594\) 0 0
\(595\) 22.8880 0.938316
\(596\) 0 0
\(597\) −2.10956 −0.0863385
\(598\) 0 0
\(599\) 43.2204 1.76594 0.882969 0.469432i \(-0.155541\pi\)
0.882969 + 0.469432i \(0.155541\pi\)
\(600\) 0 0
\(601\) 5.16914 0.210854 0.105427 0.994427i \(-0.466379\pi\)
0.105427 + 0.994427i \(0.466379\pi\)
\(602\) 0 0
\(603\) 0.742658 0.0302434
\(604\) 0 0
\(605\) 4.72334 0.192031
\(606\) 0 0
\(607\) −20.0138 −0.812333 −0.406167 0.913799i \(-0.633135\pi\)
−0.406167 + 0.913799i \(0.633135\pi\)
\(608\) 0 0
\(609\) −2.21170 −0.0896227
\(610\) 0 0
\(611\) 3.77491 0.152717
\(612\) 0 0
\(613\) 44.9835 1.81687 0.908434 0.418029i \(-0.137279\pi\)
0.908434 + 0.418029i \(0.137279\pi\)
\(614\) 0 0
\(615\) −1.91797 −0.0773402
\(616\) 0 0
\(617\) 5.50806 0.221746 0.110873 0.993835i \(-0.464635\pi\)
0.110873 + 0.993835i \(0.464635\pi\)
\(618\) 0 0
\(619\) −2.84120 −0.114198 −0.0570988 0.998369i \(-0.518185\pi\)
−0.0570988 + 0.998369i \(0.518185\pi\)
\(620\) 0 0
\(621\) −4.30659 −0.172817
\(622\) 0 0
\(623\) 57.7992 2.31568
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) 0.605930 0.0241985
\(628\) 0 0
\(629\) 16.9447 0.675630
\(630\) 0 0
\(631\) 37.5017 1.49292 0.746459 0.665432i \(-0.231753\pi\)
0.746459 + 0.665432i \(0.231753\pi\)
\(632\) 0 0
\(633\) 2.89814 0.115191
\(634\) 0 0
\(635\) 6.08740 0.241571
\(636\) 0 0
\(637\) 43.6947 1.73125
\(638\) 0 0
\(639\) −3.45392 −0.136635
\(640\) 0 0
\(641\) 0.515023 0.0203422 0.0101711 0.999948i \(-0.496762\pi\)
0.0101711 + 0.999948i \(0.496762\pi\)
\(642\) 0 0
\(643\) 34.7070 1.36871 0.684356 0.729148i \(-0.260083\pi\)
0.684356 + 0.729148i \(0.260083\pi\)
\(644\) 0 0
\(645\) −0.185125 −0.00728930
\(646\) 0 0
\(647\) −2.06179 −0.0810574 −0.0405287 0.999178i \(-0.512904\pi\)
−0.0405287 + 0.999178i \(0.512904\pi\)
\(648\) 0 0
\(649\) −33.3181 −1.30785
\(650\) 0 0
\(651\) 1.95476 0.0766132
\(652\) 0 0
\(653\) −4.21345 −0.164885 −0.0824426 0.996596i \(-0.526272\pi\)
−0.0824426 + 0.996596i \(0.526272\pi\)
\(654\) 0 0
\(655\) 0.0374609 0.00146372
\(656\) 0 0
\(657\) −27.3064 −1.06533
\(658\) 0 0
\(659\) 40.3729 1.57271 0.786353 0.617777i \(-0.211967\pi\)
0.786353 + 0.617777i \(0.211967\pi\)
\(660\) 0 0
\(661\) −2.51668 −0.0978876 −0.0489438 0.998802i \(-0.515586\pi\)
−0.0489438 + 0.998802i \(0.515586\pi\)
\(662\) 0 0
\(663\) 5.07817 0.197220
\(664\) 0 0
\(665\) 5.54188 0.214905
\(666\) 0 0
\(667\) −13.6018 −0.526664
\(668\) 0 0
\(669\) −2.08667 −0.0806755
\(670\) 0 0
\(671\) −33.9547 −1.31081
\(672\) 0 0
\(673\) 24.0961 0.928836 0.464418 0.885616i \(-0.346264\pi\)
0.464418 + 0.885616i \(0.346264\pi\)
\(674\) 0 0
\(675\) 1.02893 0.0396035
\(676\) 0 0
\(677\) 27.5605 1.05923 0.529617 0.848237i \(-0.322336\pi\)
0.529617 + 0.848237i \(0.322336\pi\)
\(678\) 0 0
\(679\) −13.0201 −0.499664
\(680\) 0 0
\(681\) −1.47466 −0.0565089
\(682\) 0 0
\(683\) 31.1261 1.19101 0.595504 0.803352i \(-0.296952\pi\)
0.595504 + 0.803352i \(0.296952\pi\)
\(684\) 0 0
\(685\) 16.1557 0.617276
\(686\) 0 0
\(687\) −3.36138 −0.128245
\(688\) 0 0
\(689\) −37.5864 −1.43193
\(690\) 0 0
\(691\) −10.8852 −0.414094 −0.207047 0.978331i \(-0.566385\pi\)
−0.207047 + 0.978331i \(0.566385\pi\)
\(692\) 0 0
\(693\) −29.3868 −1.11631
\(694\) 0 0
\(695\) 5.26258 0.199621
\(696\) 0 0
\(697\) 64.5019 2.44318
\(698\) 0 0
\(699\) −2.78211 −0.105229
\(700\) 0 0
\(701\) −35.7814 −1.35145 −0.675723 0.737156i \(-0.736168\pi\)
−0.675723 + 0.737156i \(0.736168\pi\)
\(702\) 0 0
\(703\) 4.10283 0.154741
\(704\) 0 0
\(705\) 0.127967 0.00481951
\(706\) 0 0
\(707\) 34.2119 1.28667
\(708\) 0 0
\(709\) 33.6583 1.26406 0.632031 0.774943i \(-0.282221\pi\)
0.632031 + 0.774943i \(0.282221\pi\)
\(710\) 0 0
\(711\) −30.0687 −1.12767
\(712\) 0 0
\(713\) 12.0216 0.450214
\(714\) 0 0
\(715\) −12.7369 −0.476332
\(716\) 0 0
\(717\) −3.51649 −0.131326
\(718\) 0 0
\(719\) 10.6906 0.398690 0.199345 0.979929i \(-0.436119\pi\)
0.199345 + 0.979929i \(0.436119\pi\)
\(720\) 0 0
\(721\) 29.4453 1.09660
\(722\) 0 0
\(723\) 2.87536 0.106936
\(724\) 0 0
\(725\) 3.24974 0.120692
\(726\) 0 0
\(727\) 39.8500 1.47795 0.738977 0.673731i \(-0.235309\pi\)
0.738977 + 0.673731i \(0.235309\pi\)
\(728\) 0 0
\(729\) −25.4093 −0.941086
\(730\) 0 0
\(731\) 6.22580 0.230270
\(732\) 0 0
\(733\) −24.7794 −0.915248 −0.457624 0.889146i \(-0.651299\pi\)
−0.457624 + 0.889146i \(0.651299\pi\)
\(734\) 0 0
\(735\) 1.48122 0.0546356
\(736\) 0 0
\(737\) −0.626402 −0.0230738
\(738\) 0 0
\(739\) −25.5981 −0.941640 −0.470820 0.882229i \(-0.656042\pi\)
−0.470820 + 0.882229i \(0.656042\pi\)
\(740\) 0 0
\(741\) 1.22958 0.0451697
\(742\) 0 0
\(743\) −33.9505 −1.24552 −0.622762 0.782411i \(-0.713989\pi\)
−0.622762 + 0.782411i \(0.713989\pi\)
\(744\) 0 0
\(745\) −10.0907 −0.369696
\(746\) 0 0
\(747\) 31.7467 1.16155
\(748\) 0 0
\(749\) −60.3468 −2.20502
\(750\) 0 0
\(751\) −22.5974 −0.824589 −0.412295 0.911051i \(-0.635273\pi\)
−0.412295 + 0.911051i \(0.635273\pi\)
\(752\) 0 0
\(753\) 1.61665 0.0589139
\(754\) 0 0
\(755\) 14.0956 0.512991
\(756\) 0 0
\(757\) −5.22886 −0.190046 −0.0950231 0.995475i \(-0.530292\pi\)
−0.0950231 + 0.995475i \(0.530292\pi\)
\(758\) 0 0
\(759\) 1.80718 0.0655965
\(760\) 0 0
\(761\) −38.7689 −1.40537 −0.702686 0.711500i \(-0.748016\pi\)
−0.702686 + 0.711500i \(0.748016\pi\)
\(762\) 0 0
\(763\) −17.6819 −0.640126
\(764\) 0 0
\(765\) −17.2155 −0.622427
\(766\) 0 0
\(767\) −67.6106 −2.44128
\(768\) 0 0
\(769\) 0.509032 0.0183562 0.00917808 0.999958i \(-0.497078\pi\)
0.00917808 + 0.999958i \(0.497078\pi\)
\(770\) 0 0
\(771\) 2.36722 0.0852535
\(772\) 0 0
\(773\) 31.6275 1.13756 0.568781 0.822489i \(-0.307415\pi\)
0.568781 + 0.822489i \(0.307415\pi\)
\(774\) 0 0
\(775\) −2.87221 −0.103173
\(776\) 0 0
\(777\) 1.98972 0.0713809
\(778\) 0 0
\(779\) 15.6179 0.559569
\(780\) 0 0
\(781\) 2.91324 0.104244
\(782\) 0 0
\(783\) 3.34375 0.119496
\(784\) 0 0
\(785\) 4.50373 0.160745
\(786\) 0 0
\(787\) −18.1207 −0.645931 −0.322966 0.946411i \(-0.604680\pi\)
−0.322966 + 0.946411i \(0.604680\pi\)
\(788\) 0 0
\(789\) 2.07029 0.0737041
\(790\) 0 0
\(791\) −16.4590 −0.585215
\(792\) 0 0
\(793\) −68.9023 −2.44679
\(794\) 0 0
\(795\) −1.27415 −0.0451896
\(796\) 0 0
\(797\) 6.00102 0.212567 0.106284 0.994336i \(-0.466105\pi\)
0.106284 + 0.994336i \(0.466105\pi\)
\(798\) 0 0
\(799\) −4.30356 −0.152249
\(800\) 0 0
\(801\) −43.4744 −1.53609
\(802\) 0 0
\(803\) 23.0319 0.812777
\(804\) 0 0
\(805\) 16.5286 0.582557
\(806\) 0 0
\(807\) 2.83087 0.0996515
\(808\) 0 0
\(809\) −23.3365 −0.820468 −0.410234 0.911980i \(-0.634553\pi\)
−0.410234 + 0.911980i \(0.634553\pi\)
\(810\) 0 0
\(811\) 50.0159 1.75630 0.878149 0.478388i \(-0.158779\pi\)
0.878149 + 0.478388i \(0.158779\pi\)
\(812\) 0 0
\(813\) 1.52157 0.0533639
\(814\) 0 0
\(815\) 2.08183 0.0729234
\(816\) 0 0
\(817\) 1.50746 0.0527392
\(818\) 0 0
\(819\) −59.6331 −2.08375
\(820\) 0 0
\(821\) −41.1312 −1.43549 −0.717745 0.696306i \(-0.754826\pi\)
−0.717745 + 0.696306i \(0.754826\pi\)
\(822\) 0 0
\(823\) −40.1532 −1.39965 −0.699827 0.714313i \(-0.746739\pi\)
−0.699827 + 0.714313i \(0.746739\pi\)
\(824\) 0 0
\(825\) −0.431771 −0.0150323
\(826\) 0 0
\(827\) 20.0711 0.697941 0.348971 0.937134i \(-0.386531\pi\)
0.348971 + 0.937134i \(0.386531\pi\)
\(828\) 0 0
\(829\) 16.0369 0.556985 0.278492 0.960438i \(-0.410165\pi\)
0.278492 + 0.960438i \(0.410165\pi\)
\(830\) 0 0
\(831\) 1.70710 0.0592188
\(832\) 0 0
\(833\) −49.8138 −1.72594
\(834\) 0 0
\(835\) 14.2807 0.494205
\(836\) 0 0
\(837\) −2.95530 −0.102150
\(838\) 0 0
\(839\) 50.7575 1.75234 0.876172 0.481998i \(-0.160089\pi\)
0.876172 + 0.481998i \(0.160089\pi\)
\(840\) 0 0
\(841\) −18.4392 −0.635833
\(842\) 0 0
\(843\) 1.47085 0.0506589
\(844\) 0 0
\(845\) −12.8462 −0.441924
\(846\) 0 0
\(847\) −18.6525 −0.640908
\(848\) 0 0
\(849\) 4.38433 0.150470
\(850\) 0 0
\(851\) 12.2367 0.419467
\(852\) 0 0
\(853\) 9.68631 0.331653 0.165826 0.986155i \(-0.446971\pi\)
0.165826 + 0.986155i \(0.446971\pi\)
\(854\) 0 0
\(855\) −4.16839 −0.142556
\(856\) 0 0
\(857\) 3.41593 0.116686 0.0583430 0.998297i \(-0.481418\pi\)
0.0583430 + 0.998297i \(0.481418\pi\)
\(858\) 0 0
\(859\) −46.1090 −1.57322 −0.786609 0.617451i \(-0.788165\pi\)
−0.786609 + 0.617451i \(0.788165\pi\)
\(860\) 0 0
\(861\) 7.57410 0.258125
\(862\) 0 0
\(863\) 0.419035 0.0142641 0.00713206 0.999975i \(-0.497730\pi\)
0.00713206 + 0.999975i \(0.497730\pi\)
\(864\) 0 0
\(865\) −15.9731 −0.543101
\(866\) 0 0
\(867\) −2.85952 −0.0971143
\(868\) 0 0
\(869\) 25.3618 0.860338
\(870\) 0 0
\(871\) −1.27112 −0.0430704
\(872\) 0 0
\(873\) 9.79320 0.331450
\(874\) 0 0
\(875\) −3.94901 −0.133501
\(876\) 0 0
\(877\) −27.8069 −0.938971 −0.469486 0.882940i \(-0.655561\pi\)
−0.469486 + 0.882940i \(0.655561\pi\)
\(878\) 0 0
\(879\) 4.33258 0.146134
\(880\) 0 0
\(881\) −16.0861 −0.541955 −0.270978 0.962586i \(-0.587347\pi\)
−0.270978 + 0.962586i \(0.587347\pi\)
\(882\) 0 0
\(883\) 22.1778 0.746342 0.373171 0.927763i \(-0.378270\pi\)
0.373171 + 0.927763i \(0.378270\pi\)
\(884\) 0 0
\(885\) −2.29195 −0.0770431
\(886\) 0 0
\(887\) 23.5203 0.789734 0.394867 0.918738i \(-0.370791\pi\)
0.394867 + 0.918738i \(0.370791\pi\)
\(888\) 0 0
\(889\) −24.0392 −0.806250
\(890\) 0 0
\(891\) 21.8804 0.733022
\(892\) 0 0
\(893\) −1.04202 −0.0348699
\(894\) 0 0
\(895\) 11.8862 0.397311
\(896\) 0 0
\(897\) 3.66721 0.122445
\(898\) 0 0
\(899\) −9.33395 −0.311305
\(900\) 0 0
\(901\) 42.8501 1.42754
\(902\) 0 0
\(903\) 0.731062 0.0243282
\(904\) 0 0
\(905\) −23.4450 −0.779340
\(906\) 0 0
\(907\) −29.9251 −0.993646 −0.496823 0.867852i \(-0.665500\pi\)
−0.496823 + 0.867852i \(0.665500\pi\)
\(908\) 0 0
\(909\) −25.7329 −0.853507
\(910\) 0 0
\(911\) 56.2978 1.86523 0.932614 0.360875i \(-0.117522\pi\)
0.932614 + 0.360875i \(0.117522\pi\)
\(912\) 0 0
\(913\) −26.7771 −0.886191
\(914\) 0 0
\(915\) −2.33574 −0.0772172
\(916\) 0 0
\(917\) −0.147934 −0.00488520
\(918\) 0 0
\(919\) 12.1010 0.399175 0.199588 0.979880i \(-0.436040\pi\)
0.199588 + 0.979880i \(0.436040\pi\)
\(920\) 0 0
\(921\) −2.01643 −0.0664437
\(922\) 0 0
\(923\) 5.91167 0.194585
\(924\) 0 0
\(925\) −2.92358 −0.0961267
\(926\) 0 0
\(927\) −22.1477 −0.727425
\(928\) 0 0
\(929\) 23.6374 0.775518 0.387759 0.921761i \(-0.373249\pi\)
0.387759 + 0.921761i \(0.373249\pi\)
\(930\) 0 0
\(931\) −12.0614 −0.395298
\(932\) 0 0
\(933\) −0.662428 −0.0216869
\(934\) 0 0
\(935\) 14.5206 0.474873
\(936\) 0 0
\(937\) 22.1206 0.722648 0.361324 0.932440i \(-0.382325\pi\)
0.361324 + 0.932440i \(0.382325\pi\)
\(938\) 0 0
\(939\) 4.51620 0.147381
\(940\) 0 0
\(941\) −17.4606 −0.569200 −0.284600 0.958646i \(-0.591861\pi\)
−0.284600 + 0.958646i \(0.591861\pi\)
\(942\) 0 0
\(943\) 46.5802 1.51686
\(944\) 0 0
\(945\) −4.06325 −0.132178
\(946\) 0 0
\(947\) 41.9493 1.36317 0.681585 0.731739i \(-0.261291\pi\)
0.681585 + 0.731739i \(0.261291\pi\)
\(948\) 0 0
\(949\) 46.7373 1.51716
\(950\) 0 0
\(951\) −4.71873 −0.153015
\(952\) 0 0
\(953\) −23.4034 −0.758112 −0.379056 0.925374i \(-0.623751\pi\)
−0.379056 + 0.925374i \(0.623751\pi\)
\(954\) 0 0
\(955\) −11.0712 −0.358256
\(956\) 0 0
\(957\) −1.40315 −0.0453573
\(958\) 0 0
\(959\) −63.7989 −2.06017
\(960\) 0 0
\(961\) −22.7504 −0.733884
\(962\) 0 0
\(963\) 45.3906 1.46269
\(964\) 0 0
\(965\) −13.6691 −0.440024
\(966\) 0 0
\(967\) 26.4024 0.849045 0.424523 0.905417i \(-0.360442\pi\)
0.424523 + 0.905417i \(0.360442\pi\)
\(968\) 0 0
\(969\) −1.40177 −0.0450314
\(970\) 0 0
\(971\) −43.3895 −1.39243 −0.696217 0.717831i \(-0.745135\pi\)
−0.696217 + 0.717831i \(0.745135\pi\)
\(972\) 0 0
\(973\) −20.7820 −0.666240
\(974\) 0 0
\(975\) −0.876169 −0.0280599
\(976\) 0 0
\(977\) −49.4544 −1.58219 −0.791093 0.611696i \(-0.790488\pi\)
−0.791093 + 0.611696i \(0.790488\pi\)
\(978\) 0 0
\(979\) 36.6689 1.17194
\(980\) 0 0
\(981\) 13.2996 0.424625
\(982\) 0 0
\(983\) 30.6175 0.976546 0.488273 0.872691i \(-0.337627\pi\)
0.488273 + 0.872691i \(0.337627\pi\)
\(984\) 0 0
\(985\) −5.96193 −0.189963
\(986\) 0 0
\(987\) −0.505343 −0.0160852
\(988\) 0 0
\(989\) 4.49598 0.142964
\(990\) 0 0
\(991\) −20.6310 −0.655365 −0.327682 0.944788i \(-0.606268\pi\)
−0.327682 + 0.944788i \(0.606268\pi\)
\(992\) 0 0
\(993\) −0.0507362 −0.00161007
\(994\) 0 0
\(995\) −12.2406 −0.388053
\(996\) 0 0
\(997\) −10.6969 −0.338775 −0.169388 0.985550i \(-0.554179\pi\)
−0.169388 + 0.985550i \(0.554179\pi\)
\(998\) 0 0
\(999\) −3.00816 −0.0951739
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 \(a_p\))