Properties

Label 6040.2.a.p.1.9
Level 6040
Weight 2
Character 6040.1
Self dual Yes
Analytic conductor 48.230
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6040 = 2^{3} \cdot 5 \cdot 151 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6040.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2296428209\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 2^{7} \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.9
Root \(1.02734\)
Character \(\chi\) = 6040.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.02734 q^{3}\) \(+1.00000 q^{5}\) \(+3.96391 q^{7}\) \(-1.94457 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.02734 q^{3}\) \(+1.00000 q^{5}\) \(+3.96391 q^{7}\) \(-1.94457 q^{9}\) \(-0.133682 q^{11}\) \(+2.05488 q^{13}\) \(-1.02734 q^{15}\) \(+1.43734 q^{17}\) \(-7.44046 q^{19}\) \(-4.07229 q^{21}\) \(-6.51346 q^{23}\) \(+1.00000 q^{25}\) \(+5.07976 q^{27}\) \(+3.69856 q^{29}\) \(+6.79194 q^{31}\) \(+0.137337 q^{33}\) \(+3.96391 q^{35}\) \(-10.7260 q^{37}\) \(-2.11106 q^{39}\) \(-11.8991 q^{41}\) \(-3.64630 q^{43}\) \(-1.94457 q^{45}\) \(-6.70849 q^{47}\) \(+8.71260 q^{49}\) \(-1.47664 q^{51}\) \(-11.2211 q^{53}\) \(-0.133682 q^{55}\) \(+7.64389 q^{57}\) \(-0.753474 q^{59}\) \(+3.95271 q^{61}\) \(-7.70811 q^{63}\) \(+2.05488 q^{65}\) \(+0.858406 q^{67}\) \(+6.69154 q^{69}\) \(+2.58753 q^{71}\) \(+8.62749 q^{73}\) \(-1.02734 q^{75}\) \(-0.529905 q^{77}\) \(-10.1509 q^{79}\) \(+0.615076 q^{81}\) \(-16.7116 q^{83}\) \(+1.43734 q^{85}\) \(-3.79968 q^{87}\) \(-6.16458 q^{89}\) \(+8.14538 q^{91}\) \(-6.97763 q^{93}\) \(-7.44046 q^{95}\) \(+0.556936 q^{97}\) \(+0.259955 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(19q \) \(\mathstrut -\mathstrut 5q^{3} \) \(\mathstrut +\mathstrut 19q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 26q^{9} \) \(\mathstrut -\mathstrut 18q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 5q^{15} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut -\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 18q^{21} \) \(\mathstrut -\mathstrut 25q^{23} \) \(\mathstrut +\mathstrut 19q^{25} \) \(\mathstrut -\mathstrut 35q^{27} \) \(\mathstrut -\mathstrut 35q^{29} \) \(\mathstrut -\mathstrut 26q^{31} \) \(\mathstrut -\mathstrut 8q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 48q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut -\mathstrut 21q^{43} \) \(\mathstrut +\mathstrut 26q^{45} \) \(\mathstrut -\mathstrut 40q^{47} \) \(\mathstrut +\mathstrut 23q^{49} \) \(\mathstrut -\mathstrut 32q^{51} \) \(\mathstrut -\mathstrut 3q^{53} \) \(\mathstrut -\mathstrut 18q^{55} \) \(\mathstrut -\mathstrut 13q^{57} \) \(\mathstrut -\mathstrut 28q^{59} \) \(\mathstrut -\mathstrut 46q^{61} \) \(\mathstrut -\mathstrut 53q^{63} \) \(\mathstrut +\mathstrut 5q^{65} \) \(\mathstrut -\mathstrut 42q^{67} \) \(\mathstrut -\mathstrut 31q^{69} \) \(\mathstrut -\mathstrut 46q^{71} \) \(\mathstrut +\mathstrut 31q^{73} \) \(\mathstrut -\mathstrut 5q^{75} \) \(\mathstrut +\mathstrut 15q^{77} \) \(\mathstrut -\mathstrut 56q^{79} \) \(\mathstrut +\mathstrut 31q^{81} \) \(\mathstrut -\mathstrut 25q^{83} \) \(\mathstrut -\mathstrut 4q^{85} \) \(\mathstrut -\mathstrut 20q^{87} \) \(\mathstrut -\mathstrut 7q^{89} \) \(\mathstrut -\mathstrut 61q^{91} \) \(\mathstrut +\mathstrut 29q^{93} \) \(\mathstrut -\mathstrut 27q^{95} \) \(\mathstrut +\mathstrut 39q^{97} \) \(\mathstrut -\mathstrut 52q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) −1.02734 −0.593135 −0.296568 0.955012i \(-0.595842\pi\)
−0.296568 + 0.955012i \(0.595842\pi\)
\(4\) 0 0
\(5\) 1.00000 0.447214
\(6\) 0 0
\(7\) 3.96391 1.49822 0.749109 0.662447i \(-0.230482\pi\)
0.749109 + 0.662447i \(0.230482\pi\)
\(8\) 0 0
\(9\) −1.94457 −0.648191
\(10\) 0 0
\(11\) −0.133682 −0.0403067 −0.0201534 0.999797i \(-0.506415\pi\)
−0.0201534 + 0.999797i \(0.506415\pi\)
\(12\) 0 0
\(13\) 2.05488 0.569922 0.284961 0.958539i \(-0.408019\pi\)
0.284961 + 0.958539i \(0.408019\pi\)
\(14\) 0 0
\(15\) −1.02734 −0.265258
\(16\) 0 0
\(17\) 1.43734 0.348606 0.174303 0.984692i \(-0.444233\pi\)
0.174303 + 0.984692i \(0.444233\pi\)
\(18\) 0 0
\(19\) −7.44046 −1.70696 −0.853480 0.521126i \(-0.825512\pi\)
−0.853480 + 0.521126i \(0.825512\pi\)
\(20\) 0 0
\(21\) −4.07229 −0.888646
\(22\) 0 0
\(23\) −6.51346 −1.35815 −0.679075 0.734069i \(-0.737619\pi\)
−0.679075 + 0.734069i \(0.737619\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 0 0
\(27\) 5.07976 0.977600
\(28\) 0 0
\(29\) 3.69856 0.686806 0.343403 0.939188i \(-0.388420\pi\)
0.343403 + 0.939188i \(0.388420\pi\)
\(30\) 0 0
\(31\) 6.79194 1.21987 0.609934 0.792452i \(-0.291196\pi\)
0.609934 + 0.792452i \(0.291196\pi\)
\(32\) 0 0
\(33\) 0.137337 0.0239073
\(34\) 0 0
\(35\) 3.96391 0.670023
\(36\) 0 0
\(37\) −10.7260 −1.76335 −0.881675 0.471858i \(-0.843584\pi\)
−0.881675 + 0.471858i \(0.843584\pi\)
\(38\) 0 0
\(39\) −2.11106 −0.338041
\(40\) 0 0
\(41\) −11.8991 −1.85832 −0.929161 0.369676i \(-0.879469\pi\)
−0.929161 + 0.369676i \(0.879469\pi\)
\(42\) 0 0
\(43\) −3.64630 −0.556056 −0.278028 0.960573i \(-0.589681\pi\)
−0.278028 + 0.960573i \(0.589681\pi\)
\(44\) 0 0
\(45\) −1.94457 −0.289880
\(46\) 0 0
\(47\) −6.70849 −0.978534 −0.489267 0.872134i \(-0.662736\pi\)
−0.489267 + 0.872134i \(0.662736\pi\)
\(48\) 0 0
\(49\) 8.71260 1.24466
\(50\) 0 0
\(51\) −1.47664 −0.206771
\(52\) 0 0
\(53\) −11.2211 −1.54134 −0.770670 0.637234i \(-0.780078\pi\)
−0.770670 + 0.637234i \(0.780078\pi\)
\(54\) 0 0
\(55\) −0.133682 −0.0180257
\(56\) 0 0
\(57\) 7.64389 1.01246
\(58\) 0 0
\(59\) −0.753474 −0.0980939 −0.0490470 0.998796i \(-0.515618\pi\)
−0.0490470 + 0.998796i \(0.515618\pi\)
\(60\) 0 0
\(61\) 3.95271 0.506093 0.253046 0.967454i \(-0.418567\pi\)
0.253046 + 0.967454i \(0.418567\pi\)
\(62\) 0 0
\(63\) −7.70811 −0.971131
\(64\) 0 0
\(65\) 2.05488 0.254877
\(66\) 0 0
\(67\) 0.858406 0.104871 0.0524355 0.998624i \(-0.483302\pi\)
0.0524355 + 0.998624i \(0.483302\pi\)
\(68\) 0 0
\(69\) 6.69154 0.805566
\(70\) 0 0
\(71\) 2.58753 0.307083 0.153541 0.988142i \(-0.450932\pi\)
0.153541 + 0.988142i \(0.450932\pi\)
\(72\) 0 0
\(73\) 8.62749 1.00977 0.504886 0.863186i \(-0.331535\pi\)
0.504886 + 0.863186i \(0.331535\pi\)
\(74\) 0 0
\(75\) −1.02734 −0.118627
\(76\) 0 0
\(77\) −0.529905 −0.0603883
\(78\) 0 0
\(79\) −10.1509 −1.14207 −0.571033 0.820927i \(-0.693457\pi\)
−0.571033 + 0.820927i \(0.693457\pi\)
\(80\) 0 0
\(81\) 0.615076 0.0683418
\(82\) 0 0
\(83\) −16.7116 −1.83433 −0.917167 0.398504i \(-0.869530\pi\)
−0.917167 + 0.398504i \(0.869530\pi\)
\(84\) 0 0
\(85\) 1.43734 0.155901
\(86\) 0 0
\(87\) −3.79968 −0.407369
\(88\) 0 0
\(89\) −6.16458 −0.653444 −0.326722 0.945120i \(-0.605944\pi\)
−0.326722 + 0.945120i \(0.605944\pi\)
\(90\) 0 0
\(91\) 8.14538 0.853867
\(92\) 0 0
\(93\) −6.97763 −0.723547
\(94\) 0 0
\(95\) −7.44046 −0.763375
\(96\) 0 0
\(97\) 0.556936 0.0565482 0.0282741 0.999600i \(-0.490999\pi\)
0.0282741 + 0.999600i \(0.490999\pi\)
\(98\) 0 0
\(99\) 0.259955 0.0261264
\(100\) 0 0
\(101\) 3.80987 0.379097 0.189548 0.981871i \(-0.439298\pi\)
0.189548 + 0.981871i \(0.439298\pi\)
\(102\) 0 0
\(103\) 1.50594 0.148384 0.0741922 0.997244i \(-0.476362\pi\)
0.0741922 + 0.997244i \(0.476362\pi\)
\(104\) 0 0
\(105\) −4.07229 −0.397414
\(106\) 0 0
\(107\) −1.03707 −0.100258 −0.0501288 0.998743i \(-0.515963\pi\)
−0.0501288 + 0.998743i \(0.515963\pi\)
\(108\) 0 0
\(109\) 11.2279 1.07544 0.537721 0.843123i \(-0.319286\pi\)
0.537721 + 0.843123i \(0.319286\pi\)
\(110\) 0 0
\(111\) 11.0193 1.04590
\(112\) 0 0
\(113\) −1.67887 −0.157935 −0.0789675 0.996877i \(-0.525162\pi\)
−0.0789675 + 0.996877i \(0.525162\pi\)
\(114\) 0 0
\(115\) −6.51346 −0.607383
\(116\) 0 0
\(117\) −3.99587 −0.369418
\(118\) 0 0
\(119\) 5.69749 0.522288
\(120\) 0 0
\(121\) −10.9821 −0.998375
\(122\) 0 0
\(123\) 12.2244 1.10224
\(124\) 0 0
\(125\) 1.00000 0.0894427
\(126\) 0 0
\(127\) 10.0216 0.889275 0.444637 0.895711i \(-0.353333\pi\)
0.444637 + 0.895711i \(0.353333\pi\)
\(128\) 0 0
\(129\) 3.74599 0.329816
\(130\) 0 0
\(131\) −15.0967 −1.31901 −0.659503 0.751702i \(-0.729233\pi\)
−0.659503 + 0.751702i \(0.729233\pi\)
\(132\) 0 0
\(133\) −29.4933 −2.55740
\(134\) 0 0
\(135\) 5.07976 0.437196
\(136\) 0 0
\(137\) 2.54668 0.217578 0.108789 0.994065i \(-0.465303\pi\)
0.108789 + 0.994065i \(0.465303\pi\)
\(138\) 0 0
\(139\) −16.1062 −1.36611 −0.683054 0.730368i \(-0.739349\pi\)
−0.683054 + 0.730368i \(0.739349\pi\)
\(140\) 0 0
\(141\) 6.89190 0.580403
\(142\) 0 0
\(143\) −0.274702 −0.0229717
\(144\) 0 0
\(145\) 3.69856 0.307149
\(146\) 0 0
\(147\) −8.95080 −0.738250
\(148\) 0 0
\(149\) 22.5893 1.85058 0.925292 0.379255i \(-0.123820\pi\)
0.925292 + 0.379255i \(0.123820\pi\)
\(150\) 0 0
\(151\) 1.00000 0.0813788
\(152\) 0 0
\(153\) −2.79501 −0.225963
\(154\) 0 0
\(155\) 6.79194 0.545542
\(156\) 0 0
\(157\) −4.54438 −0.362681 −0.181340 0.983420i \(-0.558044\pi\)
−0.181340 + 0.983420i \(0.558044\pi\)
\(158\) 0 0
\(159\) 11.5279 0.914223
\(160\) 0 0
\(161\) −25.8188 −2.03480
\(162\) 0 0
\(163\) −22.4641 −1.75952 −0.879761 0.475416i \(-0.842298\pi\)
−0.879761 + 0.475416i \(0.842298\pi\)
\(164\) 0 0
\(165\) 0.137337 0.0106917
\(166\) 0 0
\(167\) 19.9065 1.54041 0.770206 0.637795i \(-0.220153\pi\)
0.770206 + 0.637795i \(0.220153\pi\)
\(168\) 0 0
\(169\) −8.77745 −0.675189
\(170\) 0 0
\(171\) 14.4685 1.10643
\(172\) 0 0
\(173\) 10.6650 0.810842 0.405421 0.914130i \(-0.367125\pi\)
0.405421 + 0.914130i \(0.367125\pi\)
\(174\) 0 0
\(175\) 3.96391 0.299644
\(176\) 0 0
\(177\) 0.774074 0.0581830
\(178\) 0 0
\(179\) 19.0173 1.42142 0.710711 0.703484i \(-0.248373\pi\)
0.710711 + 0.703484i \(0.248373\pi\)
\(180\) 0 0
\(181\) 1.31287 0.0975850 0.0487925 0.998809i \(-0.484463\pi\)
0.0487925 + 0.998809i \(0.484463\pi\)
\(182\) 0 0
\(183\) −4.06078 −0.300181
\(184\) 0 0
\(185\) −10.7260 −0.788594
\(186\) 0 0
\(187\) −0.192147 −0.0140512
\(188\) 0 0
\(189\) 20.1357 1.46466
\(190\) 0 0
\(191\) 6.03989 0.437031 0.218516 0.975833i \(-0.429879\pi\)
0.218516 + 0.975833i \(0.429879\pi\)
\(192\) 0 0
\(193\) −2.26958 −0.163368 −0.0816840 0.996658i \(-0.526030\pi\)
−0.0816840 + 0.996658i \(0.526030\pi\)
\(194\) 0 0
\(195\) −2.11106 −0.151176
\(196\) 0 0
\(197\) 21.3797 1.52324 0.761621 0.648023i \(-0.224404\pi\)
0.761621 + 0.648023i \(0.224404\pi\)
\(198\) 0 0
\(199\) 17.8996 1.26887 0.634433 0.772978i \(-0.281234\pi\)
0.634433 + 0.772978i \(0.281234\pi\)
\(200\) 0 0
\(201\) −0.881875 −0.0622027
\(202\) 0 0
\(203\) 14.6608 1.02898
\(204\) 0 0
\(205\) −11.8991 −0.831067
\(206\) 0 0
\(207\) 12.6659 0.880340
\(208\) 0 0
\(209\) 0.994658 0.0688019
\(210\) 0 0
\(211\) 4.87449 0.335574 0.167787 0.985823i \(-0.446338\pi\)
0.167787 + 0.985823i \(0.446338\pi\)
\(212\) 0 0
\(213\) −2.65827 −0.182142
\(214\) 0 0
\(215\) −3.64630 −0.248676
\(216\) 0 0
\(217\) 26.9227 1.82763
\(218\) 0 0
\(219\) −8.86337 −0.598931
\(220\) 0 0
\(221\) 2.95357 0.198678
\(222\) 0 0
\(223\) −2.06676 −0.138400 −0.0692002 0.997603i \(-0.522045\pi\)
−0.0692002 + 0.997603i \(0.522045\pi\)
\(224\) 0 0
\(225\) −1.94457 −0.129638
\(226\) 0 0
\(227\) −27.3298 −1.81394 −0.906972 0.421191i \(-0.861612\pi\)
−0.906972 + 0.421191i \(0.861612\pi\)
\(228\) 0 0
\(229\) −4.24658 −0.280622 −0.140311 0.990107i \(-0.544810\pi\)
−0.140311 + 0.990107i \(0.544810\pi\)
\(230\) 0 0
\(231\) 0.544393 0.0358184
\(232\) 0 0
\(233\) 3.54497 0.232239 0.116119 0.993235i \(-0.462954\pi\)
0.116119 + 0.993235i \(0.462954\pi\)
\(234\) 0 0
\(235\) −6.70849 −0.437614
\(236\) 0 0
\(237\) 10.4284 0.677400
\(238\) 0 0
\(239\) −15.2406 −0.985834 −0.492917 0.870076i \(-0.664069\pi\)
−0.492917 + 0.870076i \(0.664069\pi\)
\(240\) 0 0
\(241\) 20.6270 1.32870 0.664351 0.747421i \(-0.268708\pi\)
0.664351 + 0.747421i \(0.268708\pi\)
\(242\) 0 0
\(243\) −15.8712 −1.01814
\(244\) 0 0
\(245\) 8.71260 0.556627
\(246\) 0 0
\(247\) −15.2893 −0.972834
\(248\) 0 0
\(249\) 17.1685 1.08801
\(250\) 0 0
\(251\) −28.5890 −1.80452 −0.902259 0.431194i \(-0.858093\pi\)
−0.902259 + 0.431194i \(0.858093\pi\)
\(252\) 0 0
\(253\) 0.870734 0.0547426
\(254\) 0 0
\(255\) −1.47664 −0.0924706
\(256\) 0 0
\(257\) 6.63056 0.413603 0.206801 0.978383i \(-0.433695\pi\)
0.206801 + 0.978383i \(0.433695\pi\)
\(258\) 0 0
\(259\) −42.5171 −2.64188
\(260\) 0 0
\(261\) −7.19212 −0.445181
\(262\) 0 0
\(263\) −10.5541 −0.650791 −0.325396 0.945578i \(-0.605497\pi\)
−0.325396 + 0.945578i \(0.605497\pi\)
\(264\) 0 0
\(265\) −11.2211 −0.689308
\(266\) 0 0
\(267\) 6.33312 0.387581
\(268\) 0 0
\(269\) −28.1483 −1.71623 −0.858116 0.513456i \(-0.828365\pi\)
−0.858116 + 0.513456i \(0.828365\pi\)
\(270\) 0 0
\(271\) 1.01280 0.0615233 0.0307616 0.999527i \(-0.490207\pi\)
0.0307616 + 0.999527i \(0.490207\pi\)
\(272\) 0 0
\(273\) −8.36807 −0.506459
\(274\) 0 0
\(275\) −0.133682 −0.00806135
\(276\) 0 0
\(277\) 21.3520 1.28292 0.641458 0.767158i \(-0.278330\pi\)
0.641458 + 0.767158i \(0.278330\pi\)
\(278\) 0 0
\(279\) −13.2074 −0.790707
\(280\) 0 0
\(281\) −8.92765 −0.532579 −0.266290 0.963893i \(-0.585798\pi\)
−0.266290 + 0.963893i \(0.585798\pi\)
\(282\) 0 0
\(283\) 6.24757 0.371380 0.185690 0.982608i \(-0.440548\pi\)
0.185690 + 0.982608i \(0.440548\pi\)
\(284\) 0 0
\(285\) 7.64389 0.452785
\(286\) 0 0
\(287\) −47.1668 −2.78417
\(288\) 0 0
\(289\) −14.9341 −0.878474
\(290\) 0 0
\(291\) −0.572162 −0.0335408
\(292\) 0 0
\(293\) 0.327469 0.0191309 0.00956546 0.999954i \(-0.496955\pi\)
0.00956546 + 0.999954i \(0.496955\pi\)
\(294\) 0 0
\(295\) −0.753474 −0.0438689
\(296\) 0 0
\(297\) −0.679074 −0.0394039
\(298\) 0 0
\(299\) −13.3844 −0.774040
\(300\) 0 0
\(301\) −14.4536 −0.833093
\(302\) 0 0
\(303\) −3.91404 −0.224856
\(304\) 0 0
\(305\) 3.95271 0.226332
\(306\) 0 0
\(307\) −7.36459 −0.420319 −0.210160 0.977667i \(-0.567398\pi\)
−0.210160 + 0.977667i \(0.567398\pi\)
\(308\) 0 0
\(309\) −1.54711 −0.0880121
\(310\) 0 0
\(311\) −10.0965 −0.572522 −0.286261 0.958152i \(-0.592413\pi\)
−0.286261 + 0.958152i \(0.592413\pi\)
\(312\) 0 0
\(313\) −5.37945 −0.304064 −0.152032 0.988376i \(-0.548582\pi\)
−0.152032 + 0.988376i \(0.548582\pi\)
\(314\) 0 0
\(315\) −7.70811 −0.434303
\(316\) 0 0
\(317\) −3.47050 −0.194923 −0.0974614 0.995239i \(-0.531072\pi\)
−0.0974614 + 0.995239i \(0.531072\pi\)
\(318\) 0 0
\(319\) −0.494432 −0.0276829
\(320\) 0 0
\(321\) 1.06543 0.0594663
\(322\) 0 0
\(323\) −10.6945 −0.595056
\(324\) 0 0
\(325\) 2.05488 0.113984
\(326\) 0 0
\(327\) −11.5349 −0.637882
\(328\) 0 0
\(329\) −26.5919 −1.46606
\(330\) 0 0
\(331\) −16.3616 −0.899315 −0.449657 0.893201i \(-0.648454\pi\)
−0.449657 + 0.893201i \(0.648454\pi\)
\(332\) 0 0
\(333\) 20.8576 1.14299
\(334\) 0 0
\(335\) 0.858406 0.0468997
\(336\) 0 0
\(337\) 5.16717 0.281474 0.140737 0.990047i \(-0.455053\pi\)
0.140737 + 0.990047i \(0.455053\pi\)
\(338\) 0 0
\(339\) 1.72477 0.0936768
\(340\) 0 0
\(341\) −0.907962 −0.0491689
\(342\) 0 0
\(343\) 6.78858 0.366549
\(344\) 0 0
\(345\) 6.69154 0.360260
\(346\) 0 0
\(347\) −4.09030 −0.219579 −0.109790 0.993955i \(-0.535018\pi\)
−0.109790 + 0.993955i \(0.535018\pi\)
\(348\) 0 0
\(349\) 26.4790 1.41739 0.708695 0.705515i \(-0.249284\pi\)
0.708695 + 0.705515i \(0.249284\pi\)
\(350\) 0 0
\(351\) 10.4383 0.557156
\(352\) 0 0
\(353\) −1.17028 −0.0622879 −0.0311440 0.999515i \(-0.509915\pi\)
−0.0311440 + 0.999515i \(0.509915\pi\)
\(354\) 0 0
\(355\) 2.58753 0.137332
\(356\) 0 0
\(357\) −5.85326 −0.309787
\(358\) 0 0
\(359\) −13.6986 −0.722984 −0.361492 0.932375i \(-0.617732\pi\)
−0.361492 + 0.932375i \(0.617732\pi\)
\(360\) 0 0
\(361\) 36.3605 1.91371
\(362\) 0 0
\(363\) 11.2824 0.592172
\(364\) 0 0
\(365\) 8.62749 0.451583
\(366\) 0 0
\(367\) 9.03348 0.471544 0.235772 0.971808i \(-0.424238\pi\)
0.235772 + 0.971808i \(0.424238\pi\)
\(368\) 0 0
\(369\) 23.1386 1.20455
\(370\) 0 0
\(371\) −44.4796 −2.30926
\(372\) 0 0
\(373\) −11.8393 −0.613013 −0.306507 0.951868i \(-0.599160\pi\)
−0.306507 + 0.951868i \(0.599160\pi\)
\(374\) 0 0
\(375\) −1.02734 −0.0530516
\(376\) 0 0
\(377\) 7.60011 0.391426
\(378\) 0 0
\(379\) −27.7124 −1.42349 −0.711744 0.702439i \(-0.752094\pi\)
−0.711744 + 0.702439i \(0.752094\pi\)
\(380\) 0 0
\(381\) −10.2956 −0.527460
\(382\) 0 0
\(383\) −22.5967 −1.15464 −0.577319 0.816519i \(-0.695901\pi\)
−0.577319 + 0.816519i \(0.695901\pi\)
\(384\) 0 0
\(385\) −0.529905 −0.0270065
\(386\) 0 0
\(387\) 7.09050 0.360430
\(388\) 0 0
\(389\) −14.0430 −0.712007 −0.356004 0.934485i \(-0.615861\pi\)
−0.356004 + 0.934485i \(0.615861\pi\)
\(390\) 0 0
\(391\) −9.36205 −0.473459
\(392\) 0 0
\(393\) 15.5095 0.782349
\(394\) 0 0
\(395\) −10.1509 −0.510748
\(396\) 0 0
\(397\) 3.14697 0.157942 0.0789711 0.996877i \(-0.474837\pi\)
0.0789711 + 0.996877i \(0.474837\pi\)
\(398\) 0 0
\(399\) 30.2997 1.51688
\(400\) 0 0
\(401\) 27.3354 1.36506 0.682532 0.730856i \(-0.260879\pi\)
0.682532 + 0.730856i \(0.260879\pi\)
\(402\) 0 0
\(403\) 13.9566 0.695230
\(404\) 0 0
\(405\) 0.615076 0.0305634
\(406\) 0 0
\(407\) 1.43388 0.0710749
\(408\) 0 0
\(409\) −27.9743 −1.38324 −0.691621 0.722261i \(-0.743103\pi\)
−0.691621 + 0.722261i \(0.743103\pi\)
\(410\) 0 0
\(411\) −2.61631 −0.129053
\(412\) 0 0
\(413\) −2.98670 −0.146966
\(414\) 0 0
\(415\) −16.7116 −0.820339
\(416\) 0 0
\(417\) 16.5465 0.810287
\(418\) 0 0
\(419\) −12.3654 −0.604091 −0.302045 0.953294i \(-0.597669\pi\)
−0.302045 + 0.953294i \(0.597669\pi\)
\(420\) 0 0
\(421\) 9.47148 0.461612 0.230806 0.973000i \(-0.425864\pi\)
0.230806 + 0.973000i \(0.425864\pi\)
\(422\) 0 0
\(423\) 13.0451 0.634276
\(424\) 0 0
\(425\) 1.43734 0.0697212
\(426\) 0 0
\(427\) 15.6682 0.758237
\(428\) 0 0
\(429\) 0.282212 0.0136253
\(430\) 0 0
\(431\) −28.0707 −1.35212 −0.676060 0.736847i \(-0.736314\pi\)
−0.676060 + 0.736847i \(0.736314\pi\)
\(432\) 0 0
\(433\) −0.360158 −0.0173081 −0.00865405 0.999963i \(-0.502755\pi\)
−0.00865405 + 0.999963i \(0.502755\pi\)
\(434\) 0 0
\(435\) −3.79968 −0.182181
\(436\) 0 0
\(437\) 48.4631 2.31831
\(438\) 0 0
\(439\) 3.13899 0.149816 0.0749078 0.997190i \(-0.476134\pi\)
0.0749078 + 0.997190i \(0.476134\pi\)
\(440\) 0 0
\(441\) −16.9423 −0.806775
\(442\) 0 0
\(443\) 34.0600 1.61824 0.809119 0.587644i \(-0.199945\pi\)
0.809119 + 0.587644i \(0.199945\pi\)
\(444\) 0 0
\(445\) −6.16458 −0.292229
\(446\) 0 0
\(447\) −23.2069 −1.09765
\(448\) 0 0
\(449\) −15.2927 −0.721709 −0.360854 0.932622i \(-0.617515\pi\)
−0.360854 + 0.932622i \(0.617515\pi\)
\(450\) 0 0
\(451\) 1.59069 0.0749029
\(452\) 0 0
\(453\) −1.02734 −0.0482687
\(454\) 0 0
\(455\) 8.14538 0.381861
\(456\) 0 0
\(457\) −2.66399 −0.124616 −0.0623082 0.998057i \(-0.519846\pi\)
−0.0623082 + 0.998057i \(0.519846\pi\)
\(458\) 0 0
\(459\) 7.30134 0.340797
\(460\) 0 0
\(461\) −23.9871 −1.11719 −0.558595 0.829440i \(-0.688659\pi\)
−0.558595 + 0.829440i \(0.688659\pi\)
\(462\) 0 0
\(463\) 38.0725 1.76938 0.884689 0.466181i \(-0.154371\pi\)
0.884689 + 0.466181i \(0.154371\pi\)
\(464\) 0 0
\(465\) −6.97763 −0.323580
\(466\) 0 0
\(467\) −37.8268 −1.75042 −0.875208 0.483748i \(-0.839275\pi\)
−0.875208 + 0.483748i \(0.839275\pi\)
\(468\) 0 0
\(469\) 3.40265 0.157120
\(470\) 0 0
\(471\) 4.66862 0.215119
\(472\) 0 0
\(473\) 0.487446 0.0224128
\(474\) 0 0
\(475\) −7.44046 −0.341392
\(476\) 0 0
\(477\) 21.8203 0.999083
\(478\) 0 0
\(479\) 6.00495 0.274373 0.137187 0.990545i \(-0.456194\pi\)
0.137187 + 0.990545i \(0.456194\pi\)
\(480\) 0 0
\(481\) −22.0408 −1.00497
\(482\) 0 0
\(483\) 26.5247 1.20691
\(484\) 0 0
\(485\) 0.556936 0.0252891
\(486\) 0 0
\(487\) 2.20663 0.0999917 0.0499959 0.998749i \(-0.484079\pi\)
0.0499959 + 0.998749i \(0.484079\pi\)
\(488\) 0 0
\(489\) 23.0783 1.04363
\(490\) 0 0
\(491\) −9.98970 −0.450829 −0.225414 0.974263i \(-0.572374\pi\)
−0.225414 + 0.974263i \(0.572374\pi\)
\(492\) 0 0
\(493\) 5.31609 0.239425
\(494\) 0 0
\(495\) 0.259955 0.0116841
\(496\) 0 0
\(497\) 10.2567 0.460077
\(498\) 0 0
\(499\) −15.2215 −0.681409 −0.340704 0.940171i \(-0.610665\pi\)
−0.340704 + 0.940171i \(0.610665\pi\)
\(500\) 0 0
\(501\) −20.4508 −0.913673
\(502\) 0 0
\(503\) 16.9678 0.756559 0.378279 0.925691i \(-0.376516\pi\)
0.378279 + 0.925691i \(0.376516\pi\)
\(504\) 0 0
\(505\) 3.80987 0.169537
\(506\) 0 0
\(507\) 9.01743 0.400478
\(508\) 0 0
\(509\) 6.68393 0.296260 0.148130 0.988968i \(-0.452675\pi\)
0.148130 + 0.988968i \(0.452675\pi\)
\(510\) 0 0
\(511\) 34.1986 1.51286
\(512\) 0 0
\(513\) −37.7957 −1.66872
\(514\) 0 0
\(515\) 1.50594 0.0663596
\(516\) 0 0
\(517\) 0.896806 0.0394415
\(518\) 0 0
\(519\) −10.9565 −0.480939
\(520\) 0 0
\(521\) 3.08733 0.135259 0.0676293 0.997711i \(-0.478456\pi\)
0.0676293 + 0.997711i \(0.478456\pi\)
\(522\) 0 0
\(523\) −38.7765 −1.69558 −0.847789 0.530334i \(-0.822067\pi\)
−0.847789 + 0.530334i \(0.822067\pi\)
\(524\) 0 0
\(525\) −4.07229 −0.177729
\(526\) 0 0
\(527\) 9.76233 0.425254
\(528\) 0 0
\(529\) 19.4251 0.844571
\(530\) 0 0
\(531\) 1.46518 0.0635836
\(532\) 0 0
\(533\) −24.4512 −1.05910
\(534\) 0 0
\(535\) −1.03707 −0.0448365
\(536\) 0 0
\(537\) −19.5373 −0.843095
\(538\) 0 0
\(539\) −1.16472 −0.0501680
\(540\) 0 0
\(541\) 0.0182391 0.000784158 0 0.000392079 1.00000i \(-0.499875\pi\)
0.000392079 1.00000i \(0.499875\pi\)
\(542\) 0 0
\(543\) −1.34877 −0.0578811
\(544\) 0 0
\(545\) 11.2279 0.480952
\(546\) 0 0
\(547\) 8.21039 0.351051 0.175526 0.984475i \(-0.443838\pi\)
0.175526 + 0.984475i \(0.443838\pi\)
\(548\) 0 0
\(549\) −7.68633 −0.328045
\(550\) 0 0
\(551\) −27.5190 −1.17235
\(552\) 0 0
\(553\) −40.2373 −1.71106
\(554\) 0 0
\(555\) 11.0193 0.467743
\(556\) 0 0
\(557\) −14.3446 −0.607801 −0.303901 0.952704i \(-0.598289\pi\)
−0.303901 + 0.952704i \(0.598289\pi\)
\(558\) 0 0
\(559\) −7.49273 −0.316909
\(560\) 0 0
\(561\) 0.197400 0.00833425
\(562\) 0 0
\(563\) −37.8903 −1.59689 −0.798444 0.602069i \(-0.794343\pi\)
−0.798444 + 0.602069i \(0.794343\pi\)
\(564\) 0 0
\(565\) −1.67887 −0.0706306
\(566\) 0 0
\(567\) 2.43811 0.102391
\(568\) 0 0
\(569\) −23.3786 −0.980083 −0.490041 0.871699i \(-0.663018\pi\)
−0.490041 + 0.871699i \(0.663018\pi\)
\(570\) 0 0
\(571\) −37.0058 −1.54864 −0.774321 0.632793i \(-0.781909\pi\)
−0.774321 + 0.632793i \(0.781909\pi\)
\(572\) 0 0
\(573\) −6.20503 −0.259219
\(574\) 0 0
\(575\) −6.51346 −0.271630
\(576\) 0 0
\(577\) 27.2057 1.13259 0.566293 0.824204i \(-0.308377\pi\)
0.566293 + 0.824204i \(0.308377\pi\)
\(578\) 0 0
\(579\) 2.33163 0.0968993
\(580\) 0 0
\(581\) −66.2432 −2.74823
\(582\) 0 0
\(583\) 1.50007 0.0621264
\(584\) 0 0
\(585\) −3.99587 −0.165209
\(586\) 0 0
\(587\) 15.7726 0.651004 0.325502 0.945541i \(-0.394467\pi\)
0.325502 + 0.945541i \(0.394467\pi\)
\(588\) 0 0
\(589\) −50.5352 −2.08227
\(590\) 0 0
\(591\) −21.9642 −0.903488
\(592\) 0 0
\(593\) 36.8998 1.51529 0.757647 0.652664i \(-0.226349\pi\)
0.757647 + 0.652664i \(0.226349\pi\)
\(594\) 0 0
\(595\) 5.69749 0.233574
\(596\) 0 0
\(597\) −18.3889 −0.752609
\(598\) 0 0
\(599\) −2.35830 −0.0963574 −0.0481787 0.998839i \(-0.515342\pi\)
−0.0481787 + 0.998839i \(0.515342\pi\)
\(600\) 0 0
\(601\) 7.63950 0.311622 0.155811 0.987787i \(-0.450201\pi\)
0.155811 + 0.987787i \(0.450201\pi\)
\(602\) 0 0
\(603\) −1.66923 −0.0679764
\(604\) 0 0
\(605\) −10.9821 −0.446487
\(606\) 0 0
\(607\) −4.10217 −0.166502 −0.0832510 0.996529i \(-0.526530\pi\)
−0.0832510 + 0.996529i \(0.526530\pi\)
\(608\) 0 0
\(609\) −15.0616 −0.610327
\(610\) 0 0
\(611\) −13.7852 −0.557688
\(612\) 0 0
\(613\) 0.291089 0.0117570 0.00587849 0.999983i \(-0.498129\pi\)
0.00587849 + 0.999983i \(0.498129\pi\)
\(614\) 0 0
\(615\) 12.2244 0.492935
\(616\) 0 0
\(617\) 38.8169 1.56271 0.781356 0.624086i \(-0.214529\pi\)
0.781356 + 0.624086i \(0.214529\pi\)
\(618\) 0 0
\(619\) 19.1127 0.768203 0.384101 0.923291i \(-0.374511\pi\)
0.384101 + 0.923291i \(0.374511\pi\)
\(620\) 0 0
\(621\) −33.0868 −1.32773
\(622\) 0 0
\(623\) −24.4358 −0.979001
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0 0
\(627\) −1.02185 −0.0408088
\(628\) 0 0
\(629\) −15.4170 −0.614715
\(630\) 0 0
\(631\) 14.9259 0.594190 0.297095 0.954848i \(-0.403982\pi\)
0.297095 + 0.954848i \(0.403982\pi\)
\(632\) 0 0
\(633\) −5.00776 −0.199041
\(634\) 0 0
\(635\) 10.0216 0.397696
\(636\) 0 0
\(637\) 17.9034 0.709357
\(638\) 0 0
\(639\) −5.03163 −0.199048
\(640\) 0 0
\(641\) 18.7962 0.742404 0.371202 0.928552i \(-0.378946\pi\)
0.371202 + 0.928552i \(0.378946\pi\)
\(642\) 0 0
\(643\) −40.4370 −1.59468 −0.797340 0.603531i \(-0.793760\pi\)
−0.797340 + 0.603531i \(0.793760\pi\)
\(644\) 0 0
\(645\) 3.74599 0.147498
\(646\) 0 0
\(647\) 2.42847 0.0954728 0.0477364 0.998860i \(-0.484799\pi\)
0.0477364 + 0.998860i \(0.484799\pi\)
\(648\) 0 0
\(649\) 0.100726 0.00395385
\(650\) 0 0
\(651\) −27.6587 −1.08403
\(652\) 0 0
\(653\) 1.12265 0.0439328 0.0219664 0.999759i \(-0.493007\pi\)
0.0219664 + 0.999759i \(0.493007\pi\)
\(654\) 0 0
\(655\) −15.0967 −0.589878
\(656\) 0 0
\(657\) −16.7768 −0.654524
\(658\) 0 0
\(659\) 27.1554 1.05782 0.528912 0.848676i \(-0.322600\pi\)
0.528912 + 0.848676i \(0.322600\pi\)
\(660\) 0 0
\(661\) −35.7346 −1.38992 −0.694958 0.719050i \(-0.744577\pi\)
−0.694958 + 0.719050i \(0.744577\pi\)
\(662\) 0 0
\(663\) −3.03432 −0.117843
\(664\) 0 0
\(665\) −29.4933 −1.14370
\(666\) 0 0
\(667\) −24.0904 −0.932785
\(668\) 0 0
\(669\) 2.12326 0.0820901
\(670\) 0 0
\(671\) −0.528408 −0.0203989
\(672\) 0 0
\(673\) 10.6470 0.410413 0.205207 0.978719i \(-0.434213\pi\)
0.205207 + 0.978719i \(0.434213\pi\)
\(674\) 0 0
\(675\) 5.07976 0.195520
\(676\) 0 0
\(677\) 11.1032 0.426729 0.213364 0.976973i \(-0.431558\pi\)
0.213364 + 0.976973i \(0.431558\pi\)
\(678\) 0 0
\(679\) 2.20764 0.0847216
\(680\) 0 0
\(681\) 28.0770 1.07591
\(682\) 0 0
\(683\) −18.9637 −0.725626 −0.362813 0.931862i \(-0.618184\pi\)
−0.362813 + 0.931862i \(0.618184\pi\)
\(684\) 0 0
\(685\) 2.54668 0.0973036
\(686\) 0 0
\(687\) 4.36268 0.166447
\(688\) 0 0
\(689\) −23.0581 −0.878444
\(690\) 0 0
\(691\) 15.8152 0.601639 0.300820 0.953681i \(-0.402740\pi\)
0.300820 + 0.953681i \(0.402740\pi\)
\(692\) 0 0
\(693\) 1.03044 0.0391431
\(694\) 0 0
\(695\) −16.1062 −0.610942
\(696\) 0 0
\(697\) −17.1030 −0.647822
\(698\) 0 0
\(699\) −3.64189 −0.137749
\(700\) 0 0
\(701\) 49.1451 1.85619 0.928093 0.372348i \(-0.121447\pi\)
0.928093 + 0.372348i \(0.121447\pi\)
\(702\) 0 0
\(703\) 79.8067 3.00997
\(704\) 0 0
\(705\) 6.89190 0.259564
\(706\) 0 0
\(707\) 15.1020 0.567969
\(708\) 0 0
\(709\) 12.2932 0.461681 0.230840 0.972992i \(-0.425852\pi\)
0.230840 + 0.972992i \(0.425852\pi\)
\(710\) 0 0
\(711\) 19.7392 0.740277
\(712\) 0 0
\(713\) −44.2390 −1.65676
\(714\) 0 0
\(715\) −0.274702 −0.0102733
\(716\) 0 0
\(717\) 15.6573 0.584733
\(718\) 0 0
\(719\) 14.6066 0.544735 0.272368 0.962193i \(-0.412193\pi\)
0.272368 + 0.962193i \(0.412193\pi\)
\(720\) 0 0
\(721\) 5.96941 0.222312
\(722\) 0 0
\(723\) −21.1910 −0.788100
\(724\) 0 0
\(725\) 3.69856 0.137361
\(726\) 0 0
\(727\) −13.7835 −0.511200 −0.255600 0.966783i \(-0.582273\pi\)
−0.255600 + 0.966783i \(0.582273\pi\)
\(728\) 0 0
\(729\) 14.4599 0.535550
\(730\) 0 0
\(731\) −5.24098 −0.193845
\(732\) 0 0
\(733\) 36.9036 1.36306 0.681532 0.731788i \(-0.261314\pi\)
0.681532 + 0.731788i \(0.261314\pi\)
\(734\) 0 0
\(735\) −8.95080 −0.330155
\(736\) 0 0
\(737\) −0.114754 −0.00422701
\(738\) 0 0
\(739\) 18.6989 0.687849 0.343924 0.938997i \(-0.388244\pi\)
0.343924 + 0.938997i \(0.388244\pi\)
\(740\) 0 0
\(741\) 15.7073 0.577022
\(742\) 0 0
\(743\) −39.5144 −1.44964 −0.724822 0.688936i \(-0.758078\pi\)
−0.724822 + 0.688936i \(0.758078\pi\)
\(744\) 0 0
\(745\) 22.5893 0.827606
\(746\) 0 0
\(747\) 32.4969 1.18900
\(748\) 0 0
\(749\) −4.11086 −0.150208
\(750\) 0 0
\(751\) 27.1120 0.989332 0.494666 0.869083i \(-0.335290\pi\)
0.494666 + 0.869083i \(0.335290\pi\)
\(752\) 0 0
\(753\) 29.3706 1.07032
\(754\) 0 0
\(755\) 1.00000 0.0363937
\(756\) 0 0
\(757\) 23.5912 0.857436 0.428718 0.903438i \(-0.358965\pi\)
0.428718 + 0.903438i \(0.358965\pi\)
\(758\) 0 0
\(759\) −0.894540 −0.0324697
\(760\) 0 0
\(761\) −47.2953 −1.71445 −0.857227 0.514938i \(-0.827815\pi\)
−0.857227 + 0.514938i \(0.827815\pi\)
\(762\) 0 0
\(763\) 44.5065 1.61124
\(764\) 0 0
\(765\) −2.79501 −0.101054
\(766\) 0 0
\(767\) −1.54830 −0.0559059
\(768\) 0 0
\(769\) −30.4354 −1.09753 −0.548765 0.835977i \(-0.684902\pi\)
−0.548765 + 0.835977i \(0.684902\pi\)
\(770\) 0 0
\(771\) −6.81184 −0.245322
\(772\) 0 0
\(773\) −11.2118 −0.403260 −0.201630 0.979462i \(-0.564624\pi\)
−0.201630 + 0.979462i \(0.564624\pi\)
\(774\) 0 0
\(775\) 6.79194 0.243974
\(776\) 0 0
\(777\) 43.6795 1.56699
\(778\) 0 0
\(779\) 88.5345 3.17208
\(780\) 0 0
\(781\) −0.345906 −0.0123775
\(782\) 0 0
\(783\) 18.7878 0.671421
\(784\) 0 0
\(785\) −4.54438 −0.162196
\(786\) 0 0
\(787\) 13.9000 0.495480 0.247740 0.968827i \(-0.420312\pi\)
0.247740 + 0.968827i \(0.420312\pi\)
\(788\) 0 0
\(789\) 10.8426 0.386007
\(790\) 0 0
\(791\) −6.65490 −0.236621
\(792\) 0 0
\(793\) 8.12236 0.288434
\(794\) 0 0
\(795\) 11.5279 0.408853
\(796\) 0 0
\(797\) 37.8572 1.34097 0.670486 0.741923i \(-0.266086\pi\)
0.670486 + 0.741923i \(0.266086\pi\)
\(798\) 0 0
\(799\) −9.64238 −0.341123
\(800\) 0 0
\(801\) 11.9875 0.423556
\(802\) 0 0
\(803\) −1.15334 −0.0407006
\(804\) 0 0
\(805\) −25.8188 −0.909992
\(806\) 0 0
\(807\) 28.9179 1.01796
\(808\) 0 0
\(809\) −24.7911 −0.871607 −0.435804 0.900042i \(-0.643536\pi\)
−0.435804 + 0.900042i \(0.643536\pi\)
\(810\) 0 0
\(811\) 25.7289 0.903463 0.451732 0.892154i \(-0.350806\pi\)
0.451732 + 0.892154i \(0.350806\pi\)
\(812\) 0 0
\(813\) −1.04049 −0.0364916
\(814\) 0 0
\(815\) −22.4641 −0.786882
\(816\) 0 0
\(817\) 27.1302 0.949165
\(818\) 0 0
\(819\) −15.8393 −0.553469
\(820\) 0 0
\(821\) −6.07179 −0.211907 −0.105953 0.994371i \(-0.533789\pi\)
−0.105953 + 0.994371i \(0.533789\pi\)
\(822\) 0 0
\(823\) 10.0513 0.350367 0.175184 0.984536i \(-0.443948\pi\)
0.175184 + 0.984536i \(0.443948\pi\)
\(824\) 0 0
\(825\) 0.137337 0.00478147
\(826\) 0 0
\(827\) 15.6283 0.543450 0.271725 0.962375i \(-0.412406\pi\)
0.271725 + 0.962375i \(0.412406\pi\)
\(828\) 0 0
\(829\) 45.3019 1.57340 0.786700 0.617335i \(-0.211788\pi\)
0.786700 + 0.617335i \(0.211788\pi\)
\(830\) 0 0
\(831\) −21.9358 −0.760943
\(832\) 0 0
\(833\) 12.5230 0.433895
\(834\) 0 0
\(835\) 19.9065 0.688893
\(836\) 0 0
\(837\) 34.5014 1.19254
\(838\) 0 0
\(839\) 15.1343 0.522494 0.261247 0.965272i \(-0.415866\pi\)
0.261247 + 0.965272i \(0.415866\pi\)
\(840\) 0 0
\(841\) −15.3206 −0.528298
\(842\) 0 0
\(843\) 9.17174 0.315891
\(844\) 0 0
\(845\) −8.77745 −0.301954
\(846\) 0 0
\(847\) −43.5322 −1.49578
\(848\) 0 0
\(849\) −6.41838 −0.220278
\(850\) 0 0
\(851\) 69.8636 2.39489
\(852\) 0 0
\(853\) 31.6754 1.08455 0.542273 0.840202i \(-0.317564\pi\)
0.542273 + 0.840202i \(0.317564\pi\)
\(854\) 0 0
\(855\) 14.4685 0.494813
\(856\) 0 0
\(857\) 42.3228 1.44572 0.722860 0.690995i \(-0.242827\pi\)
0.722860 + 0.690995i \(0.242827\pi\)
\(858\) 0 0
\(859\) −56.6416 −1.93259 −0.966294 0.257443i \(-0.917120\pi\)
−0.966294 + 0.257443i \(0.917120\pi\)
\(860\) 0 0
\(861\) 48.4564 1.65139
\(862\) 0 0
\(863\) −0.0497365 −0.00169305 −0.000846524 1.00000i \(-0.500269\pi\)
−0.000846524 1.00000i \(0.500269\pi\)
\(864\) 0 0
\(865\) 10.6650 0.362620
\(866\) 0 0
\(867\) 15.3424 0.521054
\(868\) 0 0
\(869\) 1.35700 0.0460330
\(870\) 0 0
\(871\) 1.76392 0.0597683
\(872\) 0 0
\(873\) −1.08300 −0.0366540
\(874\) 0 0
\(875\) 3.96391 0.134005
\(876\) 0 0
\(877\) −54.5613 −1.84241 −0.921203 0.389083i \(-0.872792\pi\)
−0.921203 + 0.389083i \(0.872792\pi\)
\(878\) 0 0
\(879\) −0.336422 −0.0113472
\(880\) 0 0
\(881\) −29.4965 −0.993763 −0.496881 0.867818i \(-0.665522\pi\)
−0.496881 + 0.867818i \(0.665522\pi\)
\(882\) 0 0
\(883\) −37.0908 −1.24820 −0.624102 0.781343i \(-0.714535\pi\)
−0.624102 + 0.781343i \(0.714535\pi\)
\(884\) 0 0
\(885\) 0.774074 0.0260202
\(886\) 0 0
\(887\) −47.4882 −1.59450 −0.797250 0.603650i \(-0.793713\pi\)
−0.797250 + 0.603650i \(0.793713\pi\)
\(888\) 0 0
\(889\) 39.7248 1.33233
\(890\) 0 0
\(891\) −0.0822248 −0.00275464
\(892\) 0 0
\(893\) 49.9143 1.67032
\(894\) 0 0
\(895\) 19.0173 0.635679
\(896\) 0 0
\(897\) 13.7503 0.459110
\(898\) 0 0
\(899\) 25.1204 0.837812
\(900\) 0 0
\(901\) −16.1286 −0.537321
\(902\) 0 0
\(903\) 14.8488 0.494137
\(904\) 0 0
\(905\) 1.31287 0.0436413
\(906\) 0 0
\(907\) 13.4378 0.446196 0.223098 0.974796i \(-0.428383\pi\)
0.223098 + 0.974796i \(0.428383\pi\)
\(908\) 0 0
\(909\) −7.40857 −0.245727
\(910\) 0 0
\(911\) 8.50824 0.281891 0.140945 0.990017i \(-0.454986\pi\)
0.140945 + 0.990017i \(0.454986\pi\)
\(912\) 0 0
\(913\) 2.23404 0.0739360
\(914\) 0 0
\(915\) −4.06078 −0.134245
\(916\) 0 0
\(917\) −59.8421 −1.97616
\(918\) 0 0
\(919\) −21.1993 −0.699300 −0.349650 0.936880i \(-0.613699\pi\)
−0.349650 + 0.936880i \(0.613699\pi\)
\(920\) 0 0
\(921\) 7.56594 0.249306
\(922\) 0 0
\(923\) 5.31706 0.175013
\(924\) 0 0
\(925\) −10.7260 −0.352670
\(926\) 0 0
\(927\) −2.92840 −0.0961814
\(928\) 0 0
\(929\) 21.0555 0.690808 0.345404 0.938454i \(-0.387742\pi\)
0.345404 + 0.938454i \(0.387742\pi\)
\(930\) 0 0
\(931\) −64.8257 −2.12458
\(932\) 0 0
\(933\) 10.3726 0.339583
\(934\) 0 0
\(935\) −0.192147 −0.00628388
\(936\) 0 0
\(937\) 16.3528 0.534222 0.267111 0.963666i \(-0.413931\pi\)
0.267111 + 0.963666i \(0.413931\pi\)
\(938\) 0 0
\(939\) 5.52652 0.180351
\(940\) 0 0
\(941\) −47.7196 −1.55561 −0.777807 0.628503i \(-0.783668\pi\)
−0.777807 + 0.628503i \(0.783668\pi\)
\(942\) 0 0
\(943\) 77.5040 2.52388
\(944\) 0 0
\(945\) 20.1357 0.655015
\(946\) 0 0
\(947\) 28.7202 0.933281 0.466641 0.884447i \(-0.345464\pi\)
0.466641 + 0.884447i \(0.345464\pi\)
\(948\) 0 0
\(949\) 17.7285 0.575491
\(950\) 0 0
\(951\) 3.56538 0.115616
\(952\) 0 0
\(953\) −18.5233 −0.600029 −0.300015 0.953935i \(-0.596992\pi\)
−0.300015 + 0.953935i \(0.596992\pi\)
\(954\) 0 0
\(955\) 6.03989 0.195446
\(956\) 0 0
\(957\) 0.507950 0.0164197
\(958\) 0 0
\(959\) 10.0948 0.325979
\(960\) 0 0
\(961\) 15.1304 0.488079
\(962\) 0 0
\(963\) 2.01666 0.0649860
\(964\) 0 0
\(965\) −2.26958 −0.0730604
\(966\) 0 0
\(967\) 41.7628 1.34300 0.671501 0.741004i \(-0.265650\pi\)
0.671501 + 0.741004i \(0.265650\pi\)
\(968\) 0 0
\(969\) 10.9869 0.352949
\(970\) 0 0
\(971\) −41.5280 −1.33270 −0.666348 0.745641i \(-0.732143\pi\)
−0.666348 + 0.745641i \(0.732143\pi\)
\(972\) 0 0
\(973\) −63.8435 −2.04673
\(974\) 0 0
\(975\) −2.11106 −0.0676082
\(976\) 0 0
\(977\) −10.3955 −0.332582 −0.166291 0.986077i \(-0.553179\pi\)
−0.166291 + 0.986077i \(0.553179\pi\)
\(978\) 0 0
\(979\) 0.824095 0.0263382
\(980\) 0 0
\(981\) −21.8335 −0.697091
\(982\) 0 0
\(983\) 54.5823 1.74091 0.870453 0.492251i \(-0.163826\pi\)
0.870453 + 0.492251i \(0.163826\pi\)
\(984\) 0 0
\(985\) 21.3797 0.681215
\(986\) 0 0
\(987\) 27.3189 0.869570
\(988\) 0 0
\(989\) 23.7500 0.755208
\(990\) 0 0
\(991\) 21.8329 0.693543 0.346772 0.937950i \(-0.387278\pi\)
0.346772 + 0.937950i \(0.387278\pi\)
\(992\) 0 0
\(993\) 16.8089 0.533415
\(994\) 0 0
\(995\) 17.8996 0.567454
\(996\) 0 0
\(997\) −50.3450 −1.59444 −0.797221 0.603688i \(-0.793697\pi\)
−0.797221 + 0.603688i \(0.793697\pi\)
\(998\) 0 0
\(999\) −54.4857 −1.72385
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 \(a_p\))