Properties

Label 8008.2.a.k.1.5
Level 8008
Weight 2
Character 8008.1
Self dual Yes
Analytic conductor 63.944
Analytic rank 0
Dimension 6
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 8008 = 2^{3} \cdot 7 \cdot 11 \cdot 13 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8008.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(63.9442019386\)
Analytic rank: \(0\)
Dimension: \(6\)
Coefficient field: 6.6.244558277.1
Coefficient ring: \(\Z[a_1, a_2, a_3]\)
Coefficient ring index: \( 2^{2} \)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Root \(-0.847024\)
Character \(\chi\) = 8008.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.847024 q^{3}\) \(-2.05840 q^{5}\) \(+1.00000 q^{7}\) \(-2.28255 q^{9}\) \(+O(q^{10})\) \(q\)\(+0.847024 q^{3}\) \(-2.05840 q^{5}\) \(+1.00000 q^{7}\) \(-2.28255 q^{9}\) \(-1.00000 q^{11}\) \(-1.00000 q^{13}\) \(-1.74351 q^{15}\) \(+7.00274 q^{17}\) \(-7.01552 q^{19}\) \(+0.847024 q^{21}\) \(-0.954888 q^{23}\) \(-0.762993 q^{25}\) \(-4.47445 q^{27}\) \(+1.08403 q^{29}\) \(+1.96108 q^{31}\) \(-0.847024 q^{33}\) \(-2.05840 q^{35}\) \(+9.98989 q^{37}\) \(-0.847024 q^{39}\) \(+0.778077 q^{41}\) \(+5.80191 q^{43}\) \(+4.69840 q^{45}\) \(-0.446074 q^{47}\) \(+1.00000 q^{49}\) \(+5.93149 q^{51}\) \(-9.47486 q^{53}\) \(+2.05840 q^{55}\) \(-5.94231 q^{57}\) \(-12.7446 q^{59}\) \(-14.0588 q^{61}\) \(-2.28255 q^{63}\) \(+2.05840 q^{65}\) \(-2.84479 q^{67}\) \(-0.808813 q^{69}\) \(-3.58850 q^{71}\) \(+12.1969 q^{73}\) \(-0.646273 q^{75}\) \(-1.00000 q^{77}\) \(+7.36861 q^{79}\) \(+3.05769 q^{81}\) \(+11.7442 q^{83}\) \(-14.4144 q^{85}\) \(+0.918199 q^{87}\) \(+16.1880 q^{89}\) \(-1.00000 q^{91}\) \(+1.66108 q^{93}\) \(+14.4407 q^{95}\) \(-2.31966 q^{97}\) \(+2.28255 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(6q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(6q \) \(\mathstrut -\mathstrut q^{3} \) \(\mathstrut +\mathstrut q^{5} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 9q^{9} \) \(\mathstrut -\mathstrut 6q^{11} \) \(\mathstrut -\mathstrut 6q^{13} \) \(\mathstrut -\mathstrut q^{15} \) \(\mathstrut +\mathstrut 2q^{19} \) \(\mathstrut -\mathstrut q^{21} \) \(\mathstrut +\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 9q^{25} \) \(\mathstrut -\mathstrut q^{27} \) \(\mathstrut +\mathstrut 14q^{29} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut q^{33} \) \(\mathstrut +\mathstrut q^{35} \) \(\mathstrut -\mathstrut 5q^{37} \) \(\mathstrut +\mathstrut q^{39} \) \(\mathstrut +\mathstrut 12q^{43} \) \(\mathstrut +\mathstrut 2q^{45} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 6q^{49} \) \(\mathstrut -\mathstrut 16q^{51} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut -\mathstrut 12q^{57} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut -\mathstrut 18q^{61} \) \(\mathstrut +\mathstrut 9q^{63} \) \(\mathstrut -\mathstrut q^{65} \) \(\mathstrut -\mathstrut 25q^{67} \) \(\mathstrut +\mathstrut 29q^{69} \) \(\mathstrut -\mathstrut 11q^{71} \) \(\mathstrut +\mathstrut 14q^{73} \) \(\mathstrut -\mathstrut 42q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut +\mathstrut 42q^{81} \) \(\mathstrut +\mathstrut 24q^{83} \) \(\mathstrut -\mathstrut 46q^{85} \) \(\mathstrut -\mathstrut 16q^{87} \) \(\mathstrut +\mathstrut 55q^{89} \) \(\mathstrut -\mathstrut 6q^{91} \) \(\mathstrut +\mathstrut 41q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 9q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 0.847024 0.489029 0.244515 0.969646i \(-0.421371\pi\)
0.244515 + 0.969646i \(0.421371\pi\)
\(4\) 0 0
\(5\) −2.05840 −0.920544 −0.460272 0.887778i \(-0.652248\pi\)
−0.460272 + 0.887778i \(0.652248\pi\)
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 0 0
\(9\) −2.28255 −0.760850
\(10\) 0 0
\(11\) −1.00000 −0.301511
\(12\) 0 0
\(13\) −1.00000 −0.277350
\(14\) 0 0
\(15\) −1.74351 −0.450173
\(16\) 0 0
\(17\) 7.00274 1.69841 0.849207 0.528060i \(-0.177080\pi\)
0.849207 + 0.528060i \(0.177080\pi\)
\(18\) 0 0
\(19\) −7.01552 −1.60947 −0.804735 0.593634i \(-0.797693\pi\)
−0.804735 + 0.593634i \(0.797693\pi\)
\(20\) 0 0
\(21\) 0.847024 0.184836
\(22\) 0 0
\(23\) −0.954888 −0.199108 −0.0995540 0.995032i \(-0.531742\pi\)
−0.0995540 + 0.995032i \(0.531742\pi\)
\(24\) 0 0
\(25\) −0.762993 −0.152599
\(26\) 0 0
\(27\) −4.47445 −0.861107
\(28\) 0 0
\(29\) 1.08403 0.201299 0.100650 0.994922i \(-0.467908\pi\)
0.100650 + 0.994922i \(0.467908\pi\)
\(30\) 0 0
\(31\) 1.96108 0.352221 0.176110 0.984370i \(-0.443648\pi\)
0.176110 + 0.984370i \(0.443648\pi\)
\(32\) 0 0
\(33\) −0.847024 −0.147448
\(34\) 0 0
\(35\) −2.05840 −0.347933
\(36\) 0 0
\(37\) 9.98989 1.64233 0.821164 0.570693i \(-0.193325\pi\)
0.821164 + 0.570693i \(0.193325\pi\)
\(38\) 0 0
\(39\) −0.847024 −0.135632
\(40\) 0 0
\(41\) 0.778077 0.121515 0.0607576 0.998153i \(-0.480648\pi\)
0.0607576 + 0.998153i \(0.480648\pi\)
\(42\) 0 0
\(43\) 5.80191 0.884783 0.442392 0.896822i \(-0.354130\pi\)
0.442392 + 0.896822i \(0.354130\pi\)
\(44\) 0 0
\(45\) 4.69840 0.700396
\(46\) 0 0
\(47\) −0.446074 −0.0650666 −0.0325333 0.999471i \(-0.510358\pi\)
−0.0325333 + 0.999471i \(0.510358\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 5.93149 0.830574
\(52\) 0 0
\(53\) −9.47486 −1.30147 −0.650736 0.759304i \(-0.725540\pi\)
−0.650736 + 0.759304i \(0.725540\pi\)
\(54\) 0 0
\(55\) 2.05840 0.277554
\(56\) 0 0
\(57\) −5.94231 −0.787078
\(58\) 0 0
\(59\) −12.7446 −1.65921 −0.829605 0.558350i \(-0.811435\pi\)
−0.829605 + 0.558350i \(0.811435\pi\)
\(60\) 0 0
\(61\) −14.0588 −1.80005 −0.900024 0.435839i \(-0.856452\pi\)
−0.900024 + 0.435839i \(0.856452\pi\)
\(62\) 0 0
\(63\) −2.28255 −0.287574
\(64\) 0 0
\(65\) 2.05840 0.255313
\(66\) 0 0
\(67\) −2.84479 −0.347547 −0.173773 0.984786i \(-0.555596\pi\)
−0.173773 + 0.984786i \(0.555596\pi\)
\(68\) 0 0
\(69\) −0.808813 −0.0973696
\(70\) 0 0
\(71\) −3.58850 −0.425877 −0.212939 0.977066i \(-0.568303\pi\)
−0.212939 + 0.977066i \(0.568303\pi\)
\(72\) 0 0
\(73\) 12.1969 1.42753 0.713767 0.700383i \(-0.246987\pi\)
0.713767 + 0.700383i \(0.246987\pi\)
\(74\) 0 0
\(75\) −0.646273 −0.0746252
\(76\) 0 0
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 7.36861 0.829034 0.414517 0.910042i \(-0.363951\pi\)
0.414517 + 0.910042i \(0.363951\pi\)
\(80\) 0 0
\(81\) 3.05769 0.339744
\(82\) 0 0
\(83\) 11.7442 1.28910 0.644548 0.764564i \(-0.277046\pi\)
0.644548 + 0.764564i \(0.277046\pi\)
\(84\) 0 0
\(85\) −14.4144 −1.56346
\(86\) 0 0
\(87\) 0.918199 0.0984413
\(88\) 0 0
\(89\) 16.1880 1.71592 0.857961 0.513715i \(-0.171731\pi\)
0.857961 + 0.513715i \(0.171731\pi\)
\(90\) 0 0
\(91\) −1.00000 −0.104828
\(92\) 0 0
\(93\) 1.66108 0.172246
\(94\) 0 0
\(95\) 14.4407 1.48159
\(96\) 0 0
\(97\) −2.31966 −0.235526 −0.117763 0.993042i \(-0.537572\pi\)
−0.117763 + 0.993042i \(0.537572\pi\)
\(98\) 0 0
\(99\) 2.28255 0.229405
\(100\) 0 0
\(101\) 11.5762 1.15187 0.575935 0.817495i \(-0.304638\pi\)
0.575935 + 0.817495i \(0.304638\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) 0 0
\(105\) −1.74351 −0.170149
\(106\) 0 0
\(107\) 1.72408 0.166673 0.0833363 0.996521i \(-0.473442\pi\)
0.0833363 + 0.996521i \(0.473442\pi\)
\(108\) 0 0
\(109\) −11.9315 −1.14283 −0.571415 0.820662i \(-0.693605\pi\)
−0.571415 + 0.820662i \(0.693605\pi\)
\(110\) 0 0
\(111\) 8.46167 0.803146
\(112\) 0 0
\(113\) −16.9821 −1.59754 −0.798770 0.601637i \(-0.794515\pi\)
−0.798770 + 0.601637i \(0.794515\pi\)
\(114\) 0 0
\(115\) 1.96554 0.183288
\(116\) 0 0
\(117\) 2.28255 0.211022
\(118\) 0 0
\(119\) 7.00274 0.641940
\(120\) 0 0
\(121\) 1.00000 0.0909091
\(122\) 0 0
\(123\) 0.659050 0.0594245
\(124\) 0 0
\(125\) 11.8625 1.06102
\(126\) 0 0
\(127\) −4.13628 −0.367035 −0.183518 0.983016i \(-0.558748\pi\)
−0.183518 + 0.983016i \(0.558748\pi\)
\(128\) 0 0
\(129\) 4.91436 0.432685
\(130\) 0 0
\(131\) 7.36427 0.643420 0.321710 0.946838i \(-0.395742\pi\)
0.321710 + 0.946838i \(0.395742\pi\)
\(132\) 0 0
\(133\) −7.01552 −0.608322
\(134\) 0 0
\(135\) 9.21019 0.792687
\(136\) 0 0
\(137\) 7.96108 0.680161 0.340081 0.940396i \(-0.389546\pi\)
0.340081 + 0.940396i \(0.389546\pi\)
\(138\) 0 0
\(139\) 7.81085 0.662507 0.331254 0.943542i \(-0.392528\pi\)
0.331254 + 0.943542i \(0.392528\pi\)
\(140\) 0 0
\(141\) −0.377836 −0.0318195
\(142\) 0 0
\(143\) 1.00000 0.0836242
\(144\) 0 0
\(145\) −2.23137 −0.185305
\(146\) 0 0
\(147\) 0.847024 0.0698613
\(148\) 0 0
\(149\) 19.3196 1.58272 0.791361 0.611349i \(-0.209373\pi\)
0.791361 + 0.611349i \(0.209373\pi\)
\(150\) 0 0
\(151\) 17.3075 1.40846 0.704231 0.709971i \(-0.251292\pi\)
0.704231 + 0.709971i \(0.251292\pi\)
\(152\) 0 0
\(153\) −15.9841 −1.29224
\(154\) 0 0
\(155\) −4.03669 −0.324235
\(156\) 0 0
\(157\) 14.8929 1.18859 0.594293 0.804248i \(-0.297432\pi\)
0.594293 + 0.804248i \(0.297432\pi\)
\(158\) 0 0
\(159\) −8.02543 −0.636458
\(160\) 0 0
\(161\) −0.954888 −0.0752557
\(162\) 0 0
\(163\) 9.03934 0.708016 0.354008 0.935242i \(-0.384819\pi\)
0.354008 + 0.935242i \(0.384819\pi\)
\(164\) 0 0
\(165\) 1.74351 0.135732
\(166\) 0 0
\(167\) −1.58894 −0.122956 −0.0614778 0.998108i \(-0.519581\pi\)
−0.0614778 + 0.998108i \(0.519581\pi\)
\(168\) 0 0
\(169\) 1.00000 0.0769231
\(170\) 0 0
\(171\) 16.0133 1.22457
\(172\) 0 0
\(173\) −12.4036 −0.943029 −0.471515 0.881858i \(-0.656293\pi\)
−0.471515 + 0.881858i \(0.656293\pi\)
\(174\) 0 0
\(175\) −0.762993 −0.0576769
\(176\) 0 0
\(177\) −10.7950 −0.811403
\(178\) 0 0
\(179\) 10.7913 0.806579 0.403289 0.915073i \(-0.367867\pi\)
0.403289 + 0.915073i \(0.367867\pi\)
\(180\) 0 0
\(181\) −18.2294 −1.35498 −0.677492 0.735530i \(-0.736933\pi\)
−0.677492 + 0.735530i \(0.736933\pi\)
\(182\) 0 0
\(183\) −11.9082 −0.880277
\(184\) 0 0
\(185\) −20.5632 −1.51183
\(186\) 0 0
\(187\) −7.00274 −0.512091
\(188\) 0 0
\(189\) −4.47445 −0.325468
\(190\) 0 0
\(191\) −13.7640 −0.995928 −0.497964 0.867198i \(-0.665919\pi\)
−0.497964 + 0.867198i \(0.665919\pi\)
\(192\) 0 0
\(193\) 17.7080 1.27465 0.637324 0.770596i \(-0.280041\pi\)
0.637324 + 0.770596i \(0.280041\pi\)
\(194\) 0 0
\(195\) 1.74351 0.124856
\(196\) 0 0
\(197\) −8.53507 −0.608099 −0.304049 0.952656i \(-0.598339\pi\)
−0.304049 + 0.952656i \(0.598339\pi\)
\(198\) 0 0
\(199\) 22.4069 1.58838 0.794190 0.607669i \(-0.207895\pi\)
0.794190 + 0.607669i \(0.207895\pi\)
\(200\) 0 0
\(201\) −2.40961 −0.169961
\(202\) 0 0
\(203\) 1.08403 0.0760840
\(204\) 0 0
\(205\) −1.60159 −0.111860
\(206\) 0 0
\(207\) 2.17958 0.151491
\(208\) 0 0
\(209\) 7.01552 0.485273
\(210\) 0 0
\(211\) −25.7597 −1.77337 −0.886686 0.462372i \(-0.846999\pi\)
−0.886686 + 0.462372i \(0.846999\pi\)
\(212\) 0 0
\(213\) −3.03955 −0.208266
\(214\) 0 0
\(215\) −11.9426 −0.814482
\(216\) 0 0
\(217\) 1.96108 0.133127
\(218\) 0 0
\(219\) 10.3310 0.698106
\(220\) 0 0
\(221\) −7.00274 −0.471055
\(222\) 0 0
\(223\) −22.3058 −1.49371 −0.746853 0.664990i \(-0.768436\pi\)
−0.746853 + 0.664990i \(0.768436\pi\)
\(224\) 0 0
\(225\) 1.74157 0.116105
\(226\) 0 0
\(227\) 22.0432 1.46306 0.731530 0.681809i \(-0.238807\pi\)
0.731530 + 0.681809i \(0.238807\pi\)
\(228\) 0 0
\(229\) 19.1420 1.26494 0.632468 0.774586i \(-0.282042\pi\)
0.632468 + 0.774586i \(0.282042\pi\)
\(230\) 0 0
\(231\) −0.847024 −0.0557301
\(232\) 0 0
\(233\) 0.614135 0.0402333 0.0201167 0.999798i \(-0.493596\pi\)
0.0201167 + 0.999798i \(0.493596\pi\)
\(234\) 0 0
\(235\) 0.918199 0.0598967
\(236\) 0 0
\(237\) 6.24139 0.405422
\(238\) 0 0
\(239\) 26.5486 1.71729 0.858643 0.512574i \(-0.171308\pi\)
0.858643 + 0.512574i \(0.171308\pi\)
\(240\) 0 0
\(241\) −13.6212 −0.877418 −0.438709 0.898629i \(-0.644564\pi\)
−0.438709 + 0.898629i \(0.644564\pi\)
\(242\) 0 0
\(243\) 16.0133 1.02725
\(244\) 0 0
\(245\) −2.05840 −0.131506
\(246\) 0 0
\(247\) 7.01552 0.446387
\(248\) 0 0
\(249\) 9.94763 0.630406
\(250\) 0 0
\(251\) −2.14862 −0.135620 −0.0678099 0.997698i \(-0.521601\pi\)
−0.0678099 + 0.997698i \(0.521601\pi\)
\(252\) 0 0
\(253\) 0.954888 0.0600333
\(254\) 0 0
\(255\) −12.2094 −0.764580
\(256\) 0 0
\(257\) 7.58000 0.472828 0.236414 0.971652i \(-0.424028\pi\)
0.236414 + 0.971652i \(0.424028\pi\)
\(258\) 0 0
\(259\) 9.98989 0.620741
\(260\) 0 0
\(261\) −2.47435 −0.153159
\(262\) 0 0
\(263\) 10.5846 0.652673 0.326337 0.945254i \(-0.394186\pi\)
0.326337 + 0.945254i \(0.394186\pi\)
\(264\) 0 0
\(265\) 19.5031 1.19806
\(266\) 0 0
\(267\) 13.7116 0.839136
\(268\) 0 0
\(269\) 1.78702 0.108957 0.0544784 0.998515i \(-0.482650\pi\)
0.0544784 + 0.998515i \(0.482650\pi\)
\(270\) 0 0
\(271\) 10.4330 0.633761 0.316881 0.948465i \(-0.397365\pi\)
0.316881 + 0.948465i \(0.397365\pi\)
\(272\) 0 0
\(273\) −0.847024 −0.0512642
\(274\) 0 0
\(275\) 0.762993 0.0460102
\(276\) 0 0
\(277\) 12.0759 0.725573 0.362787 0.931872i \(-0.381825\pi\)
0.362787 + 0.931872i \(0.381825\pi\)
\(278\) 0 0
\(279\) −4.47627 −0.267987
\(280\) 0 0
\(281\) 24.8892 1.48476 0.742382 0.669976i \(-0.233696\pi\)
0.742382 + 0.669976i \(0.233696\pi\)
\(282\) 0 0
\(283\) −3.45416 −0.205328 −0.102664 0.994716i \(-0.532737\pi\)
−0.102664 + 0.994716i \(0.532737\pi\)
\(284\) 0 0
\(285\) 12.2316 0.724540
\(286\) 0 0
\(287\) 0.778077 0.0459285
\(288\) 0 0
\(289\) 32.0384 1.88461
\(290\) 0 0
\(291\) −1.96481 −0.115179
\(292\) 0 0
\(293\) 6.01926 0.351649 0.175824 0.984422i \(-0.443741\pi\)
0.175824 + 0.984422i \(0.443741\pi\)
\(294\) 0 0
\(295\) 26.2336 1.52738
\(296\) 0 0
\(297\) 4.47445 0.259634
\(298\) 0 0
\(299\) 0.954888 0.0552226
\(300\) 0 0
\(301\) 5.80191 0.334417
\(302\) 0 0
\(303\) 9.80528 0.563299
\(304\) 0 0
\(305\) 28.9387 1.65702
\(306\) 0 0
\(307\) −29.0598 −1.65853 −0.829266 0.558854i \(-0.811241\pi\)
−0.829266 + 0.558854i \(0.811241\pi\)
\(308\) 0 0
\(309\) 6.77619 0.385484
\(310\) 0 0
\(311\) 20.0052 1.13439 0.567196 0.823583i \(-0.308028\pi\)
0.567196 + 0.823583i \(0.308028\pi\)
\(312\) 0 0
\(313\) −15.9725 −0.902820 −0.451410 0.892317i \(-0.649079\pi\)
−0.451410 + 0.892317i \(0.649079\pi\)
\(314\) 0 0
\(315\) 4.69840 0.264725
\(316\) 0 0
\(317\) 8.67790 0.487399 0.243700 0.969851i \(-0.421639\pi\)
0.243700 + 0.969851i \(0.421639\pi\)
\(318\) 0 0
\(319\) −1.08403 −0.0606940
\(320\) 0 0
\(321\) 1.46033 0.0815078
\(322\) 0 0
\(323\) −49.1278 −2.73355
\(324\) 0 0
\(325\) 0.762993 0.0423233
\(326\) 0 0
\(327\) −10.1063 −0.558877
\(328\) 0 0
\(329\) −0.446074 −0.0245929
\(330\) 0 0
\(331\) 5.49282 0.301913 0.150956 0.988540i \(-0.451765\pi\)
0.150956 + 0.988540i \(0.451765\pi\)
\(332\) 0 0
\(333\) −22.8024 −1.24957
\(334\) 0 0
\(335\) 5.85572 0.319932
\(336\) 0 0
\(337\) 14.2610 0.776848 0.388424 0.921481i \(-0.373020\pi\)
0.388424 + 0.921481i \(0.373020\pi\)
\(338\) 0 0
\(339\) −14.3842 −0.781244
\(340\) 0 0
\(341\) −1.96108 −0.106199
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) 0 0
\(345\) 1.66486 0.0896330
\(346\) 0 0
\(347\) −15.4487 −0.829329 −0.414664 0.909974i \(-0.636101\pi\)
−0.414664 + 0.909974i \(0.636101\pi\)
\(348\) 0 0
\(349\) 11.8542 0.634540 0.317270 0.948335i \(-0.397234\pi\)
0.317270 + 0.948335i \(0.397234\pi\)
\(350\) 0 0
\(351\) 4.47445 0.238828
\(352\) 0 0
\(353\) −27.2777 −1.45185 −0.725924 0.687775i \(-0.758587\pi\)
−0.725924 + 0.687775i \(0.758587\pi\)
\(354\) 0 0
\(355\) 7.38657 0.392039
\(356\) 0 0
\(357\) 5.93149 0.313928
\(358\) 0 0
\(359\) −15.5630 −0.821382 −0.410691 0.911775i \(-0.634713\pi\)
−0.410691 + 0.911775i \(0.634713\pi\)
\(360\) 0 0
\(361\) 30.2175 1.59039
\(362\) 0 0
\(363\) 0.847024 0.0444572
\(364\) 0 0
\(365\) −25.1060 −1.31411
\(366\) 0 0
\(367\) 0.566283 0.0295597 0.0147799 0.999891i \(-0.495295\pi\)
0.0147799 + 0.999891i \(0.495295\pi\)
\(368\) 0 0
\(369\) −1.77600 −0.0924549
\(370\) 0 0
\(371\) −9.47486 −0.491910
\(372\) 0 0
\(373\) 28.8743 1.49505 0.747527 0.664231i \(-0.231241\pi\)
0.747527 + 0.664231i \(0.231241\pi\)
\(374\) 0 0
\(375\) 10.0479 0.518869
\(376\) 0 0
\(377\) −1.08403 −0.0558304
\(378\) 0 0
\(379\) −13.1086 −0.673341 −0.336671 0.941622i \(-0.609301\pi\)
−0.336671 + 0.941622i \(0.609301\pi\)
\(380\) 0 0
\(381\) −3.50353 −0.179491
\(382\) 0 0
\(383\) 13.8278 0.706566 0.353283 0.935516i \(-0.385065\pi\)
0.353283 + 0.935516i \(0.385065\pi\)
\(384\) 0 0
\(385\) 2.05840 0.104906
\(386\) 0 0
\(387\) −13.2432 −0.673188
\(388\) 0 0
\(389\) 14.3584 0.728000 0.364000 0.931399i \(-0.381411\pi\)
0.364000 + 0.931399i \(0.381411\pi\)
\(390\) 0 0
\(391\) −6.68683 −0.338168
\(392\) 0 0
\(393\) 6.23771 0.314651
\(394\) 0 0
\(395\) −15.1675 −0.763162
\(396\) 0 0
\(397\) 12.0548 0.605011 0.302506 0.953148i \(-0.402177\pi\)
0.302506 + 0.953148i \(0.402177\pi\)
\(398\) 0 0
\(399\) −5.94231 −0.297488
\(400\) 0 0
\(401\) −4.87701 −0.243546 −0.121773 0.992558i \(-0.538858\pi\)
−0.121773 + 0.992558i \(0.538858\pi\)
\(402\) 0 0
\(403\) −1.96108 −0.0976884
\(404\) 0 0
\(405\) −6.29395 −0.312749
\(406\) 0 0
\(407\) −9.98989 −0.495180
\(408\) 0 0
\(409\) 22.7296 1.12390 0.561952 0.827170i \(-0.310050\pi\)
0.561952 + 0.827170i \(0.310050\pi\)
\(410\) 0 0
\(411\) 6.74322 0.332619
\(412\) 0 0
\(413\) −12.7446 −0.627123
\(414\) 0 0
\(415\) −24.1743 −1.18667
\(416\) 0 0
\(417\) 6.61597 0.323985
\(418\) 0 0
\(419\) −28.3492 −1.38495 −0.692474 0.721443i \(-0.743479\pi\)
−0.692474 + 0.721443i \(0.743479\pi\)
\(420\) 0 0
\(421\) 19.1169 0.931701 0.465850 0.884864i \(-0.345749\pi\)
0.465850 + 0.884864i \(0.345749\pi\)
\(422\) 0 0
\(423\) 1.01819 0.0495060
\(424\) 0 0
\(425\) −5.34304 −0.259176
\(426\) 0 0
\(427\) −14.0588 −0.680355
\(428\) 0 0
\(429\) 0.847024 0.0408947
\(430\) 0 0
\(431\) 18.2876 0.880881 0.440440 0.897782i \(-0.354822\pi\)
0.440440 + 0.897782i \(0.354822\pi\)
\(432\) 0 0
\(433\) −34.8733 −1.67590 −0.837951 0.545745i \(-0.816247\pi\)
−0.837951 + 0.545745i \(0.816247\pi\)
\(434\) 0 0
\(435\) −1.89002 −0.0906195
\(436\) 0 0
\(437\) 6.69903 0.320458
\(438\) 0 0
\(439\) 3.24713 0.154977 0.0774886 0.996993i \(-0.475310\pi\)
0.0774886 + 0.996993i \(0.475310\pi\)
\(440\) 0 0
\(441\) −2.28255 −0.108693
\(442\) 0 0
\(443\) −1.51826 −0.0721346 −0.0360673 0.999349i \(-0.511483\pi\)
−0.0360673 + 0.999349i \(0.511483\pi\)
\(444\) 0 0
\(445\) −33.3213 −1.57958
\(446\) 0 0
\(447\) 16.3641 0.773997
\(448\) 0 0
\(449\) −29.6637 −1.39992 −0.699958 0.714184i \(-0.746798\pi\)
−0.699958 + 0.714184i \(0.746798\pi\)
\(450\) 0 0
\(451\) −0.778077 −0.0366382
\(452\) 0 0
\(453\) 14.6598 0.688779
\(454\) 0 0
\(455\) 2.05840 0.0964992
\(456\) 0 0
\(457\) 10.3474 0.484031 0.242015 0.970272i \(-0.422192\pi\)
0.242015 + 0.970272i \(0.422192\pi\)
\(458\) 0 0
\(459\) −31.3334 −1.46252
\(460\) 0 0
\(461\) 30.8769 1.43808 0.719040 0.694969i \(-0.244582\pi\)
0.719040 + 0.694969i \(0.244582\pi\)
\(462\) 0 0
\(463\) 27.1572 1.26210 0.631052 0.775741i \(-0.282624\pi\)
0.631052 + 0.775741i \(0.282624\pi\)
\(464\) 0 0
\(465\) −3.41917 −0.158560
\(466\) 0 0
\(467\) 6.54107 0.302685 0.151342 0.988481i \(-0.451640\pi\)
0.151342 + 0.988481i \(0.451640\pi\)
\(468\) 0 0
\(469\) −2.84479 −0.131360
\(470\) 0 0
\(471\) 12.6147 0.581254
\(472\) 0 0
\(473\) −5.80191 −0.266772
\(474\) 0 0
\(475\) 5.35279 0.245603
\(476\) 0 0
\(477\) 21.6269 0.990226
\(478\) 0 0
\(479\) 33.9419 1.55085 0.775424 0.631441i \(-0.217536\pi\)
0.775424 + 0.631441i \(0.217536\pi\)
\(480\) 0 0
\(481\) −9.98989 −0.455500
\(482\) 0 0
\(483\) −0.808813 −0.0368023
\(484\) 0 0
\(485\) 4.77478 0.216812
\(486\) 0 0
\(487\) 5.51228 0.249785 0.124893 0.992170i \(-0.460141\pi\)
0.124893 + 0.992170i \(0.460141\pi\)
\(488\) 0 0
\(489\) 7.65653 0.346240
\(490\) 0 0
\(491\) −2.04625 −0.0923461 −0.0461731 0.998933i \(-0.514703\pi\)
−0.0461731 + 0.998933i \(0.514703\pi\)
\(492\) 0 0
\(493\) 7.59118 0.341890
\(494\) 0 0
\(495\) −4.69840 −0.211177
\(496\) 0 0
\(497\) −3.58850 −0.160966
\(498\) 0 0
\(499\) −21.7391 −0.973177 −0.486589 0.873631i \(-0.661759\pi\)
−0.486589 + 0.873631i \(0.661759\pi\)
\(500\) 0 0
\(501\) −1.34587 −0.0601289
\(502\) 0 0
\(503\) −35.4668 −1.58139 −0.790693 0.612213i \(-0.790280\pi\)
−0.790693 + 0.612213i \(0.790280\pi\)
\(504\) 0 0
\(505\) −23.8284 −1.06035
\(506\) 0 0
\(507\) 0.847024 0.0376176
\(508\) 0 0
\(509\) 14.8093 0.656410 0.328205 0.944607i \(-0.393556\pi\)
0.328205 + 0.944607i \(0.393556\pi\)
\(510\) 0 0
\(511\) 12.1969 0.539557
\(512\) 0 0
\(513\) 31.3905 1.38593
\(514\) 0 0
\(515\) −16.4672 −0.725631
\(516\) 0 0
\(517\) 0.446074 0.0196183
\(518\) 0 0
\(519\) −10.5062 −0.461169
\(520\) 0 0
\(521\) 30.3786 1.33091 0.665456 0.746437i \(-0.268237\pi\)
0.665456 + 0.746437i \(0.268237\pi\)
\(522\) 0 0
\(523\) −8.28572 −0.362309 −0.181155 0.983455i \(-0.557983\pi\)
−0.181155 + 0.983455i \(0.557983\pi\)
\(524\) 0 0
\(525\) −0.646273 −0.0282057
\(526\) 0 0
\(527\) 13.7329 0.598217
\(528\) 0 0
\(529\) −22.0882 −0.960356
\(530\) 0 0
\(531\) 29.0903 1.26241
\(532\) 0 0
\(533\) −0.778077 −0.0337023
\(534\) 0 0
\(535\) −3.54883 −0.153430
\(536\) 0 0
\(537\) 9.14047 0.394441
\(538\) 0 0
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 4.24152 0.182357 0.0911787 0.995835i \(-0.470937\pi\)
0.0911787 + 0.995835i \(0.470937\pi\)
\(542\) 0 0
\(543\) −15.4408 −0.662627
\(544\) 0 0
\(545\) 24.5598 1.05202
\(546\) 0 0
\(547\) −30.0700 −1.28570 −0.642850 0.765992i \(-0.722248\pi\)
−0.642850 + 0.765992i \(0.722248\pi\)
\(548\) 0 0
\(549\) 32.0900 1.36957
\(550\) 0 0
\(551\) −7.60503 −0.323985
\(552\) 0 0
\(553\) 7.36861 0.313345
\(554\) 0 0
\(555\) −17.4175 −0.739331
\(556\) 0 0
\(557\) 20.9958 0.889619 0.444809 0.895625i \(-0.353271\pi\)
0.444809 + 0.895625i \(0.353271\pi\)
\(558\) 0 0
\(559\) −5.80191 −0.245395
\(560\) 0 0
\(561\) −5.93149 −0.250428
\(562\) 0 0
\(563\) −7.07309 −0.298095 −0.149048 0.988830i \(-0.547621\pi\)
−0.149048 + 0.988830i \(0.547621\pi\)
\(564\) 0 0
\(565\) 34.9559 1.47061
\(566\) 0 0
\(567\) 3.05769 0.128411
\(568\) 0 0
\(569\) 30.2441 1.26790 0.633948 0.773375i \(-0.281433\pi\)
0.633948 + 0.773375i \(0.281433\pi\)
\(570\) 0 0
\(571\) −44.4850 −1.86164 −0.930820 0.365477i \(-0.880906\pi\)
−0.930820 + 0.365477i \(0.880906\pi\)
\(572\) 0 0
\(573\) −11.6584 −0.487038
\(574\) 0 0
\(575\) 0.728573 0.0303836
\(576\) 0 0
\(577\) −17.1854 −0.715436 −0.357718 0.933830i \(-0.616445\pi\)
−0.357718 + 0.933830i \(0.616445\pi\)
\(578\) 0 0
\(579\) 14.9991 0.623340
\(580\) 0 0
\(581\) 11.7442 0.487232
\(582\) 0 0
\(583\) 9.47486 0.392409
\(584\) 0 0
\(585\) −4.69840 −0.194255
\(586\) 0 0
\(587\) 23.7916 0.981986 0.490993 0.871164i \(-0.336634\pi\)
0.490993 + 0.871164i \(0.336634\pi\)
\(588\) 0 0
\(589\) −13.7580 −0.566889
\(590\) 0 0
\(591\) −7.22941 −0.297378
\(592\) 0 0
\(593\) 13.5745 0.557440 0.278720 0.960372i \(-0.410090\pi\)
0.278720 + 0.960372i \(0.410090\pi\)
\(594\) 0 0
\(595\) −14.4144 −0.590934
\(596\) 0 0
\(597\) 18.9791 0.776765
\(598\) 0 0
\(599\) 5.89645 0.240923 0.120461 0.992718i \(-0.461563\pi\)
0.120461 + 0.992718i \(0.461563\pi\)
\(600\) 0 0
\(601\) 33.1942 1.35402 0.677009 0.735974i \(-0.263276\pi\)
0.677009 + 0.735974i \(0.263276\pi\)
\(602\) 0 0
\(603\) 6.49339 0.264431
\(604\) 0 0
\(605\) −2.05840 −0.0836858
\(606\) 0 0
\(607\) −20.9580 −0.850660 −0.425330 0.905038i \(-0.639842\pi\)
−0.425330 + 0.905038i \(0.639842\pi\)
\(608\) 0 0
\(609\) 0.918199 0.0372073
\(610\) 0 0
\(611\) 0.446074 0.0180462
\(612\) 0 0
\(613\) −12.3458 −0.498641 −0.249321 0.968421i \(-0.580207\pi\)
−0.249321 + 0.968421i \(0.580207\pi\)
\(614\) 0 0
\(615\) −1.35659 −0.0547029
\(616\) 0 0
\(617\) −1.32308 −0.0532653 −0.0266327 0.999645i \(-0.508478\pi\)
−0.0266327 + 0.999645i \(0.508478\pi\)
\(618\) 0 0
\(619\) −26.3498 −1.05909 −0.529544 0.848282i \(-0.677637\pi\)
−0.529544 + 0.848282i \(0.677637\pi\)
\(620\) 0 0
\(621\) 4.27259 0.171453
\(622\) 0 0
\(623\) 16.1880 0.648557
\(624\) 0 0
\(625\) −20.6029 −0.824115
\(626\) 0 0
\(627\) 5.94231 0.237313
\(628\) 0 0
\(629\) 69.9566 2.78935
\(630\) 0 0
\(631\) −31.4368 −1.25148 −0.625740 0.780032i \(-0.715203\pi\)
−0.625740 + 0.780032i \(0.715203\pi\)
\(632\) 0 0
\(633\) −21.8191 −0.867231
\(634\) 0 0
\(635\) 8.51411 0.337872
\(636\) 0 0
\(637\) −1.00000 −0.0396214
\(638\) 0 0
\(639\) 8.19094 0.324029
\(640\) 0 0
\(641\) −12.2758 −0.484865 −0.242433 0.970168i \(-0.577945\pi\)
−0.242433 + 0.970168i \(0.577945\pi\)
\(642\) 0 0
\(643\) 8.29219 0.327012 0.163506 0.986542i \(-0.447720\pi\)
0.163506 + 0.986542i \(0.447720\pi\)
\(644\) 0 0
\(645\) −10.1157 −0.398306
\(646\) 0 0
\(647\) −20.0570 −0.788524 −0.394262 0.918998i \(-0.629000\pi\)
−0.394262 + 0.918998i \(0.629000\pi\)
\(648\) 0 0
\(649\) 12.7446 0.500271
\(650\) 0 0
\(651\) 1.66108 0.0651030
\(652\) 0 0
\(653\) −15.2082 −0.595142 −0.297571 0.954700i \(-0.596176\pi\)
−0.297571 + 0.954700i \(0.596176\pi\)
\(654\) 0 0
\(655\) −15.1586 −0.592296
\(656\) 0 0
\(657\) −27.8400 −1.08614
\(658\) 0 0
\(659\) 26.5095 1.03266 0.516332 0.856388i \(-0.327297\pi\)
0.516332 + 0.856388i \(0.327297\pi\)
\(660\) 0 0
\(661\) −46.1291 −1.79422 −0.897108 0.441812i \(-0.854336\pi\)
−0.897108 + 0.441812i \(0.854336\pi\)
\(662\) 0 0
\(663\) −5.93149 −0.230360
\(664\) 0 0
\(665\) 14.4407 0.559988
\(666\) 0 0
\(667\) −1.03513 −0.0400803
\(668\) 0 0
\(669\) −18.8935 −0.730466
\(670\) 0 0
\(671\) 14.0588 0.542735
\(672\) 0 0
\(673\) −0.602701 −0.0232324 −0.0116162 0.999933i \(-0.503698\pi\)
−0.0116162 + 0.999933i \(0.503698\pi\)
\(674\) 0 0
\(675\) 3.41397 0.131404
\(676\) 0 0
\(677\) 44.3981 1.70636 0.853178 0.521620i \(-0.174672\pi\)
0.853178 + 0.521620i \(0.174672\pi\)
\(678\) 0 0
\(679\) −2.31966 −0.0890203
\(680\) 0 0
\(681\) 18.6711 0.715479
\(682\) 0 0
\(683\) −5.09430 −0.194928 −0.0974640 0.995239i \(-0.531073\pi\)
−0.0974640 + 0.995239i \(0.531073\pi\)
\(684\) 0 0
\(685\) −16.3871 −0.626118
\(686\) 0 0
\(687\) 16.2137 0.618591
\(688\) 0 0
\(689\) 9.47486 0.360964
\(690\) 0 0
\(691\) −6.70988 −0.255256 −0.127628 0.991822i \(-0.540736\pi\)
−0.127628 + 0.991822i \(0.540736\pi\)
\(692\) 0 0
\(693\) 2.28255 0.0867069
\(694\) 0 0
\(695\) −16.0778 −0.609867
\(696\) 0 0
\(697\) 5.44867 0.206383
\(698\) 0 0
\(699\) 0.520187 0.0196753
\(700\) 0 0
\(701\) −11.6510 −0.440051 −0.220025 0.975494i \(-0.570614\pi\)
−0.220025 + 0.975494i \(0.570614\pi\)
\(702\) 0 0
\(703\) −70.0842 −2.64328
\(704\) 0 0
\(705\) 0.777736 0.0292912
\(706\) 0 0
\(707\) 11.5762 0.435366
\(708\) 0 0
\(709\) −1.01867 −0.0382569 −0.0191284 0.999817i \(-0.506089\pi\)
−0.0191284 + 0.999817i \(0.506089\pi\)
\(710\) 0 0
\(711\) −16.8192 −0.630771
\(712\) 0 0
\(713\) −1.87261 −0.0701299
\(714\) 0 0
\(715\) −2.05840 −0.0769798
\(716\) 0 0
\(717\) 22.4873 0.839803
\(718\) 0 0
\(719\) 23.5816 0.879444 0.439722 0.898134i \(-0.355077\pi\)
0.439722 + 0.898134i \(0.355077\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) 0 0
\(723\) −11.5375 −0.429083
\(724\) 0 0
\(725\) −0.827108 −0.0307180
\(726\) 0 0
\(727\) −11.1740 −0.414419 −0.207210 0.978297i \(-0.566438\pi\)
−0.207210 + 0.978297i \(0.566438\pi\)
\(728\) 0 0
\(729\) 4.39055 0.162613
\(730\) 0 0
\(731\) 40.6293 1.50273
\(732\) 0 0
\(733\) −24.3061 −0.897765 −0.448883 0.893591i \(-0.648178\pi\)
−0.448883 + 0.893591i \(0.648178\pi\)
\(734\) 0 0
\(735\) −1.74351 −0.0643104
\(736\) 0 0
\(737\) 2.84479 0.104789
\(738\) 0 0
\(739\) 23.5386 0.865882 0.432941 0.901422i \(-0.357476\pi\)
0.432941 + 0.901422i \(0.357476\pi\)
\(740\) 0 0
\(741\) 5.94231 0.218296
\(742\) 0 0
\(743\) 24.0351 0.881763 0.440882 0.897565i \(-0.354666\pi\)
0.440882 + 0.897565i \(0.354666\pi\)
\(744\) 0 0
\(745\) −39.7674 −1.45697
\(746\) 0 0
\(747\) −26.8068 −0.980809
\(748\) 0 0
\(749\) 1.72408 0.0629963
\(750\) 0 0
\(751\) −12.7741 −0.466133 −0.233066 0.972461i \(-0.574876\pi\)
−0.233066 + 0.972461i \(0.574876\pi\)
\(752\) 0 0
\(753\) −1.81993 −0.0663221
\(754\) 0 0
\(755\) −35.6257 −1.29655
\(756\) 0 0
\(757\) 48.1026 1.74832 0.874159 0.485640i \(-0.161413\pi\)
0.874159 + 0.485640i \(0.161413\pi\)
\(758\) 0 0
\(759\) 0.808813 0.0293580
\(760\) 0 0
\(761\) 7.03639 0.255069 0.127534 0.991834i \(-0.459294\pi\)
0.127534 + 0.991834i \(0.459294\pi\)
\(762\) 0 0
\(763\) −11.9315 −0.431949
\(764\) 0 0
\(765\) 32.9017 1.18956
\(766\) 0 0
\(767\) 12.7446 0.460182
\(768\) 0 0
\(769\) −21.1847 −0.763939 −0.381969 0.924175i \(-0.624754\pi\)
−0.381969 + 0.924175i \(0.624754\pi\)
\(770\) 0 0
\(771\) 6.42044 0.231227
\(772\) 0 0
\(773\) −4.60216 −0.165528 −0.0827640 0.996569i \(-0.526375\pi\)
−0.0827640 + 0.996569i \(0.526375\pi\)
\(774\) 0 0
\(775\) −1.49629 −0.0537484
\(776\) 0 0
\(777\) 8.46167 0.303561
\(778\) 0 0
\(779\) −5.45862 −0.195575
\(780\) 0 0
\(781\) 3.58850 0.128407
\(782\) 0 0
\(783\) −4.85043 −0.173340
\(784\) 0 0
\(785\) −30.6556 −1.09415
\(786\) 0 0
\(787\) 45.6855 1.62851 0.814255 0.580507i \(-0.197146\pi\)
0.814255 + 0.580507i \(0.197146\pi\)
\(788\) 0 0
\(789\) 8.96539 0.319176
\(790\) 0 0
\(791\) −16.9821 −0.603813
\(792\) 0 0
\(793\) 14.0588 0.499244
\(794\) 0 0
\(795\) 16.5195 0.585888
\(796\) 0 0
\(797\) 44.4936 1.57604 0.788021 0.615648i \(-0.211106\pi\)
0.788021 + 0.615648i \(0.211106\pi\)
\(798\) 0 0
\(799\) −3.12374 −0.110510
\(800\) 0 0
\(801\) −36.9499 −1.30556
\(802\) 0 0
\(803\) −12.1969 −0.430418
\(804\) 0 0
\(805\) 1.96554 0.0692762
\(806\) 0 0
\(807\) 1.51365 0.0532831
\(808\) 0 0
\(809\) 22.9932 0.808397 0.404199 0.914671i \(-0.367550\pi\)
0.404199 + 0.914671i \(0.367550\pi\)
\(810\) 0 0
\(811\) 27.1126 0.952053 0.476027 0.879431i \(-0.342077\pi\)
0.476027 + 0.879431i \(0.342077\pi\)
\(812\) 0 0
\(813\) 8.83702 0.309928
\(814\) 0 0
\(815\) −18.6066 −0.651759
\(816\) 0 0
\(817\) −40.7034 −1.42403
\(818\) 0 0
\(819\) 2.28255 0.0797588
\(820\) 0 0
\(821\) −34.9418 −1.21948 −0.609739 0.792602i \(-0.708726\pi\)
−0.609739 + 0.792602i \(0.708726\pi\)
\(822\) 0 0
\(823\) −22.2465 −0.775463 −0.387731 0.921772i \(-0.626741\pi\)
−0.387731 + 0.921772i \(0.626741\pi\)
\(824\) 0 0
\(825\) 0.646273 0.0225004
\(826\) 0 0
\(827\) −26.1421 −0.909051 −0.454525 0.890734i \(-0.650191\pi\)
−0.454525 + 0.890734i \(0.650191\pi\)
\(828\) 0 0
\(829\) −18.4368 −0.640336 −0.320168 0.947361i \(-0.603739\pi\)
−0.320168 + 0.947361i \(0.603739\pi\)
\(830\) 0 0
\(831\) 10.2286 0.354827
\(832\) 0 0
\(833\) 7.00274 0.242631
\(834\) 0 0
\(835\) 3.27066 0.113186
\(836\) 0 0
\(837\) −8.77475 −0.303300
\(838\) 0 0
\(839\) 35.7978 1.23588 0.617938 0.786227i \(-0.287968\pi\)
0.617938 + 0.786227i \(0.287968\pi\)
\(840\) 0 0
\(841\) −27.8249 −0.959479
\(842\) 0 0
\(843\) 21.0817 0.726093
\(844\) 0 0
\(845\) −2.05840 −0.0708111
\(846\) 0 0
\(847\) 1.00000 0.0343604
\(848\) 0 0
\(849\) −2.92575 −0.100412
\(850\) 0 0
\(851\) −9.53922 −0.327000
\(852\) 0 0
\(853\) 9.48563 0.324782 0.162391 0.986726i \(-0.448079\pi\)
0.162391 + 0.986726i \(0.448079\pi\)
\(854\) 0 0
\(855\) −32.9617 −1.12727
\(856\) 0 0
\(857\) 41.6406 1.42242 0.711208 0.702982i \(-0.248148\pi\)
0.711208 + 0.702982i \(0.248148\pi\)
\(858\) 0 0
\(859\) 16.0745 0.548456 0.274228 0.961665i \(-0.411578\pi\)
0.274228 + 0.961665i \(0.411578\pi\)
\(860\) 0 0
\(861\) 0.659050 0.0224604
\(862\) 0 0
\(863\) 23.1835 0.789175 0.394587 0.918858i \(-0.370888\pi\)
0.394587 + 0.918858i \(0.370888\pi\)
\(864\) 0 0
\(865\) 25.5316 0.868100
\(866\) 0 0
\(867\) 27.1373 0.921629
\(868\) 0 0
\(869\) −7.36861 −0.249963
\(870\) 0 0
\(871\) 2.84479 0.0963922
\(872\) 0 0
\(873\) 5.29474 0.179200
\(874\) 0 0
\(875\) 11.8625 0.401027
\(876\) 0 0
\(877\) 10.1993 0.344407 0.172204 0.985061i \(-0.444911\pi\)
0.172204 + 0.985061i \(0.444911\pi\)
\(878\) 0 0
\(879\) 5.09845 0.171967
\(880\) 0 0
\(881\) −9.98907 −0.336540 −0.168270 0.985741i \(-0.553818\pi\)
−0.168270 + 0.985741i \(0.553818\pi\)
\(882\) 0 0
\(883\) 11.5738 0.389489 0.194744 0.980854i \(-0.437612\pi\)
0.194744 + 0.980854i \(0.437612\pi\)
\(884\) 0 0
\(885\) 22.2204 0.746932
\(886\) 0 0
\(887\) 32.8788 1.10396 0.551980 0.833857i \(-0.313872\pi\)
0.551980 + 0.833857i \(0.313872\pi\)
\(888\) 0 0
\(889\) −4.13628 −0.138726
\(890\) 0 0
\(891\) −3.05769 −0.102437
\(892\) 0 0
\(893\) 3.12944 0.104723
\(894\) 0 0
\(895\) −22.2128 −0.742491
\(896\) 0 0
\(897\) 0.808813 0.0270055
\(898\) 0 0
\(899\) 2.12587 0.0709018
\(900\) 0 0
\(901\) −66.3500 −2.21044
\(902\) 0 0
\(903\) 4.91436 0.163540
\(904\) 0 0
\(905\) 37.5235 1.24732
\(906\) 0 0
\(907\) 23.1471 0.768587 0.384294 0.923211i \(-0.374445\pi\)
0.384294 + 0.923211i \(0.374445\pi\)
\(908\) 0 0
\(909\) −26.4232 −0.876401
\(910\) 0 0
\(911\) 21.2258 0.703241 0.351621 0.936143i \(-0.385631\pi\)
0.351621 + 0.936143i \(0.385631\pi\)
\(912\) 0 0
\(913\) −11.7442 −0.388677
\(914\) 0 0
\(915\) 24.5118 0.810333
\(916\) 0 0
\(917\) 7.36427 0.243190
\(918\) 0 0
\(919\) −49.3406 −1.62760 −0.813798 0.581147i \(-0.802604\pi\)
−0.813798 + 0.581147i \(0.802604\pi\)
\(920\) 0 0
\(921\) −24.6144 −0.811071
\(922\) 0 0
\(923\) 3.58850 0.118117
\(924\) 0 0
\(925\) −7.62222 −0.250617
\(926\) 0 0
\(927\) −18.2604 −0.599750
\(928\) 0 0
\(929\) 31.4298 1.03118 0.515589 0.856836i \(-0.327573\pi\)
0.515589 + 0.856836i \(0.327573\pi\)
\(930\) 0 0
\(931\) −7.01552 −0.229924
\(932\) 0 0
\(933\) 16.9449 0.554751
\(934\) 0 0
\(935\) 14.4144 0.471402
\(936\) 0 0
\(937\) −33.6828 −1.10037 −0.550185 0.835043i \(-0.685443\pi\)
−0.550185 + 0.835043i \(0.685443\pi\)
\(938\) 0 0
\(939\) −13.5291 −0.441505
\(940\) 0 0
\(941\) −33.0345 −1.07689 −0.538447 0.842659i \(-0.680989\pi\)
−0.538447 + 0.842659i \(0.680989\pi\)
\(942\) 0 0
\(943\) −0.742977 −0.0241947
\(944\) 0 0
\(945\) 9.21019 0.299608
\(946\) 0 0
\(947\) −27.2385 −0.885133 −0.442567 0.896736i \(-0.645932\pi\)
−0.442567 + 0.896736i \(0.645932\pi\)
\(948\) 0 0
\(949\) −12.1969 −0.395927
\(950\) 0 0
\(951\) 7.35038 0.238352
\(952\) 0 0
\(953\) −44.0094 −1.42560 −0.712802 0.701366i \(-0.752574\pi\)
−0.712802 + 0.701366i \(0.752574\pi\)
\(954\) 0 0
\(955\) 28.3318 0.916796
\(956\) 0 0
\(957\) −0.918199 −0.0296812
\(958\) 0 0
\(959\) 7.96108 0.257077
\(960\) 0 0
\(961\) −27.1542 −0.875941
\(962\) 0 0
\(963\) −3.93529 −0.126813
\(964\) 0 0
\(965\) −36.4501 −1.17337
\(966\) 0 0
\(967\) −27.8204 −0.894644 −0.447322 0.894373i \(-0.647622\pi\)
−0.447322 + 0.894373i \(0.647622\pi\)
\(968\) 0 0
\(969\) −41.6124 −1.33678
\(970\) 0 0
\(971\) −35.1246 −1.12720 −0.563600 0.826048i \(-0.690584\pi\)
−0.563600 + 0.826048i \(0.690584\pi\)
\(972\) 0 0
\(973\) 7.81085 0.250404
\(974\) 0 0
\(975\) 0.646273 0.0206973
\(976\) 0 0
\(977\) −35.8641 −1.14739 −0.573697 0.819067i \(-0.694491\pi\)
−0.573697 + 0.819067i \(0.694491\pi\)
\(978\) 0 0
\(979\) −16.1880 −0.517370
\(980\) 0 0
\(981\) 27.2342 0.869522
\(982\) 0 0
\(983\) 39.0977 1.24702 0.623512 0.781814i \(-0.285705\pi\)
0.623512 + 0.781814i \(0.285705\pi\)
\(984\) 0 0
\(985\) 17.5686 0.559782
\(986\) 0 0
\(987\) −0.377836 −0.0120266
\(988\) 0 0
\(989\) −5.54018 −0.176167
\(990\) 0 0
\(991\) −14.2785 −0.453572 −0.226786 0.973945i \(-0.572822\pi\)
−0.226786 + 0.973945i \(0.572822\pi\)
\(992\) 0 0
\(993\) 4.65255 0.147644
\(994\) 0 0
\(995\) −46.1223 −1.46217
\(996\) 0 0
\(997\) −19.0422 −0.603072 −0.301536 0.953455i \(-0.597499\pi\)
−0.301536 + 0.953455i \(0.597499\pi\)
\(998\) 0 0
\(999\) −44.6992 −1.41422
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 \(a_p\))