Properties

Label 6004.2.a.g.1.6
Level 6004
Weight 2
Character 6004.1
Self dual Yes
Analytic conductor 47.942
Analytic rank 1
Dimension 27
CM No

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Newspace parameters

Level: \( N \) = \( 6004 = 2^{2} \cdot 19 \cdot 79 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6004.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9421813736\)
Analytic rank: \(1\)
Dimension: \(27\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.6
Character \(\chi\) = 6004.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.00223 q^{3}\) \(-2.46425 q^{5}\) \(+4.06602 q^{7}\) \(+1.00893 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.00223 q^{3}\) \(-2.46425 q^{5}\) \(+4.06602 q^{7}\) \(+1.00893 q^{9}\) \(-3.25056 q^{11}\) \(+4.74938 q^{13}\) \(+4.93400 q^{15}\) \(-4.01211 q^{17}\) \(+1.00000 q^{19}\) \(-8.14112 q^{21}\) \(-2.85930 q^{23}\) \(+1.07253 q^{25}\) \(+3.98658 q^{27}\) \(-3.94076 q^{29}\) \(+2.73532 q^{31}\) \(+6.50837 q^{33}\) \(-10.0197 q^{35}\) \(+2.47454 q^{37}\) \(-9.50936 q^{39}\) \(+7.55017 q^{41}\) \(+2.10768 q^{43}\) \(-2.48626 q^{45}\) \(-12.7138 q^{47}\) \(+9.53253 q^{49}\) \(+8.03317 q^{51}\) \(+13.6739 q^{53}\) \(+8.01019 q^{55}\) \(-2.00223 q^{57}\) \(+6.69652 q^{59}\) \(-14.4098 q^{61}\) \(+4.10234 q^{63}\) \(-11.7037 q^{65}\) \(+2.77431 q^{67}\) \(+5.72498 q^{69}\) \(-11.2617 q^{71}\) \(-9.87501 q^{73}\) \(-2.14745 q^{75}\) \(-13.2168 q^{77}\) \(-1.00000 q^{79}\) \(-11.0089 q^{81}\) \(-13.5101 q^{83}\) \(+9.88684 q^{85}\) \(+7.89032 q^{87}\) \(-1.17737 q^{89}\) \(+19.3111 q^{91}\) \(-5.47675 q^{93}\) \(-2.46425 q^{95}\) \(+7.33863e-5 q^{97}\) \(-3.27959 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(27q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut -\mathstrut 10q^{5} \) \(\mathstrut -\mathstrut 8q^{7} \) \(\mathstrut +\mathstrut 19q^{9} \) \(\mathstrut +\mathstrut 3q^{11} \) \(\mathstrut -\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 17q^{17} \) \(\mathstrut +\mathstrut 27q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut -\mathstrut 11q^{23} \) \(\mathstrut +\mathstrut 13q^{25} \) \(\mathstrut -\mathstrut 7q^{27} \) \(\mathstrut -\mathstrut 39q^{29} \) \(\mathstrut -\mathstrut 27q^{31} \) \(\mathstrut -\mathstrut 18q^{33} \) \(\mathstrut -\mathstrut 5q^{35} \) \(\mathstrut -\mathstrut q^{37} \) \(\mathstrut -\mathstrut 22q^{39} \) \(\mathstrut -\mathstrut 36q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 18q^{45} \) \(\mathstrut -\mathstrut 12q^{47} \) \(\mathstrut +\mathstrut 15q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 28q^{53} \) \(\mathstrut +\mathstrut 5q^{55} \) \(\mathstrut -\mathstrut 4q^{57} \) \(\mathstrut -\mathstrut 30q^{59} \) \(\mathstrut -\mathstrut 6q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 32q^{65} \) \(\mathstrut +\mathstrut 13q^{67} \) \(\mathstrut -\mathstrut 27q^{69} \) \(\mathstrut -\mathstrut 59q^{71} \) \(\mathstrut -\mathstrut 30q^{73} \) \(\mathstrut -\mathstrut 21q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut -\mathstrut 5q^{81} \) \(\mathstrut +\mathstrut 4q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 22q^{87} \) \(\mathstrut -\mathstrut 56q^{89} \) \(\mathstrut -\mathstrut 8q^{91} \) \(\mathstrut -\mathstrut 38q^{93} \) \(\mathstrut -\mathstrut 10q^{95} \) \(\mathstrut -\mathstrut 30q^{97} \) \(\mathstrut +\mathstrut 31q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.00223 −1.15599 −0.577994 0.816041i \(-0.696164\pi\)
−0.577994 + 0.816041i \(0.696164\pi\)
\(4\) 0 0
\(5\) −2.46425 −1.10205 −0.551023 0.834490i \(-0.685762\pi\)
−0.551023 + 0.834490i \(0.685762\pi\)
\(6\) 0 0
\(7\) 4.06602 1.53681 0.768406 0.639963i \(-0.221050\pi\)
0.768406 + 0.639963i \(0.221050\pi\)
\(8\) 0 0
\(9\) 1.00893 0.336310
\(10\) 0 0
\(11\) −3.25056 −0.980080 −0.490040 0.871700i \(-0.663018\pi\)
−0.490040 + 0.871700i \(0.663018\pi\)
\(12\) 0 0
\(13\) 4.74938 1.31724 0.658620 0.752475i \(-0.271140\pi\)
0.658620 + 0.752475i \(0.271140\pi\)
\(14\) 0 0
\(15\) 4.93400 1.27395
\(16\) 0 0
\(17\) −4.01211 −0.973079 −0.486540 0.873659i \(-0.661741\pi\)
−0.486540 + 0.873659i \(0.661741\pi\)
\(18\) 0 0
\(19\) 1.00000 0.229416
\(20\) 0 0
\(21\) −8.14112 −1.77654
\(22\) 0 0
\(23\) −2.85930 −0.596205 −0.298102 0.954534i \(-0.596354\pi\)
−0.298102 + 0.954534i \(0.596354\pi\)
\(24\) 0 0
\(25\) 1.07253 0.214506
\(26\) 0 0
\(27\) 3.98658 0.767218
\(28\) 0 0
\(29\) −3.94076 −0.731782 −0.365891 0.930658i \(-0.619236\pi\)
−0.365891 + 0.930658i \(0.619236\pi\)
\(30\) 0 0
\(31\) 2.73532 0.491279 0.245639 0.969361i \(-0.421002\pi\)
0.245639 + 0.969361i \(0.421002\pi\)
\(32\) 0 0
\(33\) 6.50837 1.13296
\(34\) 0 0
\(35\) −10.0197 −1.69364
\(36\) 0 0
\(37\) 2.47454 0.406812 0.203406 0.979094i \(-0.434799\pi\)
0.203406 + 0.979094i \(0.434799\pi\)
\(38\) 0 0
\(39\) −9.50936 −1.52272
\(40\) 0 0
\(41\) 7.55017 1.17914 0.589569 0.807718i \(-0.299298\pi\)
0.589569 + 0.807718i \(0.299298\pi\)
\(42\) 0 0
\(43\) 2.10768 0.321418 0.160709 0.987002i \(-0.448622\pi\)
0.160709 + 0.987002i \(0.448622\pi\)
\(44\) 0 0
\(45\) −2.48626 −0.370630
\(46\) 0 0
\(47\) −12.7138 −1.85450 −0.927252 0.374437i \(-0.877836\pi\)
−0.927252 + 0.374437i \(0.877836\pi\)
\(48\) 0 0
\(49\) 9.53253 1.36179
\(50\) 0 0
\(51\) 8.03317 1.12487
\(52\) 0 0
\(53\) 13.6739 1.87825 0.939125 0.343576i \(-0.111638\pi\)
0.939125 + 0.343576i \(0.111638\pi\)
\(54\) 0 0
\(55\) 8.01019 1.08009
\(56\) 0 0
\(57\) −2.00223 −0.265202
\(58\) 0 0
\(59\) 6.69652 0.871812 0.435906 0.899992i \(-0.356428\pi\)
0.435906 + 0.899992i \(0.356428\pi\)
\(60\) 0 0
\(61\) −14.4098 −1.84498 −0.922492 0.386016i \(-0.873851\pi\)
−0.922492 + 0.386016i \(0.873851\pi\)
\(62\) 0 0
\(63\) 4.10234 0.516846
\(64\) 0 0
\(65\) −11.7037 −1.45166
\(66\) 0 0
\(67\) 2.77431 0.338936 0.169468 0.985536i \(-0.445795\pi\)
0.169468 + 0.985536i \(0.445795\pi\)
\(68\) 0 0
\(69\) 5.72498 0.689206
\(70\) 0 0
\(71\) −11.2617 −1.33651 −0.668257 0.743931i \(-0.732959\pi\)
−0.668257 + 0.743931i \(0.732959\pi\)
\(72\) 0 0
\(73\) −9.87501 −1.15578 −0.577891 0.816114i \(-0.696124\pi\)
−0.577891 + 0.816114i \(0.696124\pi\)
\(74\) 0 0
\(75\) −2.14745 −0.247967
\(76\) 0 0
\(77\) −13.2168 −1.50620
\(78\) 0 0
\(79\) −1.00000 −0.112509
\(80\) 0 0
\(81\) −11.0089 −1.22321
\(82\) 0 0
\(83\) −13.5101 −1.48293 −0.741463 0.670994i \(-0.765868\pi\)
−0.741463 + 0.670994i \(0.765868\pi\)
\(84\) 0 0
\(85\) 9.88684 1.07238
\(86\) 0 0
\(87\) 7.89032 0.845932
\(88\) 0 0
\(89\) −1.17737 −0.124801 −0.0624007 0.998051i \(-0.519876\pi\)
−0.0624007 + 0.998051i \(0.519876\pi\)
\(90\) 0 0
\(91\) 19.3111 2.02435
\(92\) 0 0
\(93\) −5.47675 −0.567913
\(94\) 0 0
\(95\) −2.46425 −0.252827
\(96\) 0 0
\(97\) 7.33863e−5 0 7.45125e−6 0 3.72562e−6 1.00000i \(-0.499999\pi\)
3.72562e−6 1.00000i \(0.499999\pi\)
\(98\) 0 0
\(99\) −3.27959 −0.329611
\(100\) 0 0
\(101\) 17.9605 1.78714 0.893568 0.448928i \(-0.148194\pi\)
0.893568 + 0.448928i \(0.148194\pi\)
\(102\) 0 0
\(103\) 9.84993 0.970542 0.485271 0.874364i \(-0.338721\pi\)
0.485271 + 0.874364i \(0.338721\pi\)
\(104\) 0 0
\(105\) 20.0618 1.95783
\(106\) 0 0
\(107\) 14.9143 1.44182 0.720908 0.693030i \(-0.243725\pi\)
0.720908 + 0.693030i \(0.243725\pi\)
\(108\) 0 0
\(109\) 3.56298 0.341272 0.170636 0.985334i \(-0.445418\pi\)
0.170636 + 0.985334i \(0.445418\pi\)
\(110\) 0 0
\(111\) −4.95461 −0.470271
\(112\) 0 0
\(113\) 11.6812 1.09888 0.549438 0.835534i \(-0.314842\pi\)
0.549438 + 0.835534i \(0.314842\pi\)
\(114\) 0 0
\(115\) 7.04603 0.657045
\(116\) 0 0
\(117\) 4.79180 0.443002
\(118\) 0 0
\(119\) −16.3133 −1.49544
\(120\) 0 0
\(121\) −0.433870 −0.0394427
\(122\) 0 0
\(123\) −15.1172 −1.36307
\(124\) 0 0
\(125\) 9.67827 0.865651
\(126\) 0 0
\(127\) 15.1253 1.34216 0.671079 0.741386i \(-0.265831\pi\)
0.671079 + 0.741386i \(0.265831\pi\)
\(128\) 0 0
\(129\) −4.22007 −0.371556
\(130\) 0 0
\(131\) 16.2713 1.42163 0.710816 0.703378i \(-0.248326\pi\)
0.710816 + 0.703378i \(0.248326\pi\)
\(132\) 0 0
\(133\) 4.06602 0.352569
\(134\) 0 0
\(135\) −9.82393 −0.845510
\(136\) 0 0
\(137\) −5.54441 −0.473691 −0.236846 0.971547i \(-0.576114\pi\)
−0.236846 + 0.971547i \(0.576114\pi\)
\(138\) 0 0
\(139\) 12.8476 1.08972 0.544858 0.838528i \(-0.316583\pi\)
0.544858 + 0.838528i \(0.316583\pi\)
\(140\) 0 0
\(141\) 25.4561 2.14379
\(142\) 0 0
\(143\) −15.4381 −1.29100
\(144\) 0 0
\(145\) 9.71103 0.806457
\(146\) 0 0
\(147\) −19.0863 −1.57421
\(148\) 0 0
\(149\) 0.322118 0.0263889 0.0131945 0.999913i \(-0.495800\pi\)
0.0131945 + 0.999913i \(0.495800\pi\)
\(150\) 0 0
\(151\) 14.6173 1.18954 0.594770 0.803896i \(-0.297243\pi\)
0.594770 + 0.803896i \(0.297243\pi\)
\(152\) 0 0
\(153\) −4.04794 −0.327257
\(154\) 0 0
\(155\) −6.74052 −0.541412
\(156\) 0 0
\(157\) −8.46486 −0.675569 −0.337785 0.941223i \(-0.609678\pi\)
−0.337785 + 0.941223i \(0.609678\pi\)
\(158\) 0 0
\(159\) −27.3782 −2.17124
\(160\) 0 0
\(161\) −11.6260 −0.916255
\(162\) 0 0
\(163\) −14.4811 −1.13424 −0.567122 0.823634i \(-0.691943\pi\)
−0.567122 + 0.823634i \(0.691943\pi\)
\(164\) 0 0
\(165\) −16.0383 −1.24858
\(166\) 0 0
\(167\) −17.2913 −1.33804 −0.669022 0.743242i \(-0.733287\pi\)
−0.669022 + 0.743242i \(0.733287\pi\)
\(168\) 0 0
\(169\) 9.55660 0.735123
\(170\) 0 0
\(171\) 1.00893 0.0771549
\(172\) 0 0
\(173\) −9.49577 −0.721950 −0.360975 0.932575i \(-0.617556\pi\)
−0.360975 + 0.932575i \(0.617556\pi\)
\(174\) 0 0
\(175\) 4.36093 0.329655
\(176\) 0 0
\(177\) −13.4080 −1.00781
\(178\) 0 0
\(179\) −18.1435 −1.35611 −0.678054 0.735012i \(-0.737176\pi\)
−0.678054 + 0.735012i \(0.737176\pi\)
\(180\) 0 0
\(181\) 12.0309 0.894247 0.447123 0.894472i \(-0.352448\pi\)
0.447123 + 0.894472i \(0.352448\pi\)
\(182\) 0 0
\(183\) 28.8517 2.13278
\(184\) 0 0
\(185\) −6.09790 −0.448326
\(186\) 0 0
\(187\) 13.0416 0.953696
\(188\) 0 0
\(189\) 16.2095 1.17907
\(190\) 0 0
\(191\) −11.5961 −0.839062 −0.419531 0.907741i \(-0.637805\pi\)
−0.419531 + 0.907741i \(0.637805\pi\)
\(192\) 0 0
\(193\) −20.3110 −1.46201 −0.731007 0.682370i \(-0.760950\pi\)
−0.731007 + 0.682370i \(0.760950\pi\)
\(194\) 0 0
\(195\) 23.4334 1.67810
\(196\) 0 0
\(197\) 13.4712 0.959781 0.479890 0.877329i \(-0.340676\pi\)
0.479890 + 0.877329i \(0.340676\pi\)
\(198\) 0 0
\(199\) −17.9671 −1.27366 −0.636829 0.771005i \(-0.719754\pi\)
−0.636829 + 0.771005i \(0.719754\pi\)
\(200\) 0 0
\(201\) −5.55482 −0.391807
\(202\) 0 0
\(203\) −16.0232 −1.12461
\(204\) 0 0
\(205\) −18.6055 −1.29946
\(206\) 0 0
\(207\) −2.88484 −0.200510
\(208\) 0 0
\(209\) −3.25056 −0.224846
\(210\) 0 0
\(211\) −0.281244 −0.0193616 −0.00968081 0.999953i \(-0.503082\pi\)
−0.00968081 + 0.999953i \(0.503082\pi\)
\(212\) 0 0
\(213\) 22.5485 1.54500
\(214\) 0 0
\(215\) −5.19386 −0.354218
\(216\) 0 0
\(217\) 11.1219 0.755003
\(218\) 0 0
\(219\) 19.7721 1.33607
\(220\) 0 0
\(221\) −19.0550 −1.28178
\(222\) 0 0
\(223\) −26.6025 −1.78143 −0.890716 0.454560i \(-0.849797\pi\)
−0.890716 + 0.454560i \(0.849797\pi\)
\(224\) 0 0
\(225\) 1.08211 0.0721406
\(226\) 0 0
\(227\) −23.1329 −1.53539 −0.767693 0.640818i \(-0.778595\pi\)
−0.767693 + 0.640818i \(0.778595\pi\)
\(228\) 0 0
\(229\) −1.77613 −0.117370 −0.0586851 0.998277i \(-0.518691\pi\)
−0.0586851 + 0.998277i \(0.518691\pi\)
\(230\) 0 0
\(231\) 26.4632 1.74115
\(232\) 0 0
\(233\) −19.3010 −1.26445 −0.632226 0.774784i \(-0.717859\pi\)
−0.632226 + 0.774784i \(0.717859\pi\)
\(234\) 0 0
\(235\) 31.3301 2.04375
\(236\) 0 0
\(237\) 2.00223 0.130059
\(238\) 0 0
\(239\) −2.93699 −0.189978 −0.0949892 0.995478i \(-0.530282\pi\)
−0.0949892 + 0.995478i \(0.530282\pi\)
\(240\) 0 0
\(241\) −10.6645 −0.686959 −0.343480 0.939160i \(-0.611606\pi\)
−0.343480 + 0.939160i \(0.611606\pi\)
\(242\) 0 0
\(243\) 10.0825 0.646795
\(244\) 0 0
\(245\) −23.4905 −1.50076
\(246\) 0 0
\(247\) 4.74938 0.302196
\(248\) 0 0
\(249\) 27.0504 1.71425
\(250\) 0 0
\(251\) 23.0155 1.45272 0.726362 0.687313i \(-0.241210\pi\)
0.726362 + 0.687313i \(0.241210\pi\)
\(252\) 0 0
\(253\) 9.29432 0.584329
\(254\) 0 0
\(255\) −19.7957 −1.23966
\(256\) 0 0
\(257\) −18.3997 −1.14774 −0.573870 0.818946i \(-0.694559\pi\)
−0.573870 + 0.818946i \(0.694559\pi\)
\(258\) 0 0
\(259\) 10.0615 0.625194
\(260\) 0 0
\(261\) −3.97596 −0.246106
\(262\) 0 0
\(263\) 29.1100 1.79500 0.897500 0.441015i \(-0.145381\pi\)
0.897500 + 0.441015i \(0.145381\pi\)
\(264\) 0 0
\(265\) −33.6958 −2.06992
\(266\) 0 0
\(267\) 2.35738 0.144269
\(268\) 0 0
\(269\) −21.6268 −1.31861 −0.659306 0.751875i \(-0.729150\pi\)
−0.659306 + 0.751875i \(0.729150\pi\)
\(270\) 0 0
\(271\) −15.0903 −0.916672 −0.458336 0.888779i \(-0.651554\pi\)
−0.458336 + 0.888779i \(0.651554\pi\)
\(272\) 0 0
\(273\) −38.6652 −2.34013
\(274\) 0 0
\(275\) −3.48632 −0.210233
\(276\) 0 0
\(277\) −6.41202 −0.385261 −0.192631 0.981271i \(-0.561702\pi\)
−0.192631 + 0.981271i \(0.561702\pi\)
\(278\) 0 0
\(279\) 2.75975 0.165222
\(280\) 0 0
\(281\) −13.4042 −0.799626 −0.399813 0.916597i \(-0.630925\pi\)
−0.399813 + 0.916597i \(0.630925\pi\)
\(282\) 0 0
\(283\) −0.998663 −0.0593644 −0.0296822 0.999559i \(-0.509450\pi\)
−0.0296822 + 0.999559i \(0.509450\pi\)
\(284\) 0 0
\(285\) 4.93400 0.292265
\(286\) 0 0
\(287\) 30.6992 1.81211
\(288\) 0 0
\(289\) −0.902990 −0.0531171
\(290\) 0 0
\(291\) −0.000146936 0 −8.61356e−6 0
\(292\) 0 0
\(293\) −23.3856 −1.36620 −0.683102 0.730323i \(-0.739369\pi\)
−0.683102 + 0.730323i \(0.739369\pi\)
\(294\) 0 0
\(295\) −16.5019 −0.960778
\(296\) 0 0
\(297\) −12.9586 −0.751935
\(298\) 0 0
\(299\) −13.5799 −0.785345
\(300\) 0 0
\(301\) 8.56988 0.493960
\(302\) 0 0
\(303\) −35.9611 −2.06591
\(304\) 0 0
\(305\) 35.5093 2.03326
\(306\) 0 0
\(307\) −14.9284 −0.852006 −0.426003 0.904722i \(-0.640079\pi\)
−0.426003 + 0.904722i \(0.640079\pi\)
\(308\) 0 0
\(309\) −19.7218 −1.12194
\(310\) 0 0
\(311\) −9.23525 −0.523683 −0.261841 0.965111i \(-0.584330\pi\)
−0.261841 + 0.965111i \(0.584330\pi\)
\(312\) 0 0
\(313\) −8.52864 −0.482067 −0.241034 0.970517i \(-0.577486\pi\)
−0.241034 + 0.970517i \(0.577486\pi\)
\(314\) 0 0
\(315\) −10.1092 −0.569588
\(316\) 0 0
\(317\) −7.92737 −0.445245 −0.222623 0.974905i \(-0.571462\pi\)
−0.222623 + 0.974905i \(0.571462\pi\)
\(318\) 0 0
\(319\) 12.8097 0.717205
\(320\) 0 0
\(321\) −29.8618 −1.66672
\(322\) 0 0
\(323\) −4.01211 −0.223240
\(324\) 0 0
\(325\) 5.09385 0.282556
\(326\) 0 0
\(327\) −7.13392 −0.394507
\(328\) 0 0
\(329\) −51.6948 −2.85002
\(330\) 0 0
\(331\) −0.769875 −0.0423162 −0.0211581 0.999776i \(-0.506735\pi\)
−0.0211581 + 0.999776i \(0.506735\pi\)
\(332\) 0 0
\(333\) 2.49664 0.136815
\(334\) 0 0
\(335\) −6.83660 −0.373524
\(336\) 0 0
\(337\) −32.4512 −1.76773 −0.883865 0.467743i \(-0.845067\pi\)
−0.883865 + 0.467743i \(0.845067\pi\)
\(338\) 0 0
\(339\) −23.3885 −1.27029
\(340\) 0 0
\(341\) −8.89133 −0.481493
\(342\) 0 0
\(343\) 10.2973 0.556004
\(344\) 0 0
\(345\) −14.1078 −0.759537
\(346\) 0 0
\(347\) −24.4051 −1.31014 −0.655068 0.755570i \(-0.727360\pi\)
−0.655068 + 0.755570i \(0.727360\pi\)
\(348\) 0 0
\(349\) −27.5557 −1.47502 −0.737512 0.675334i \(-0.763999\pi\)
−0.737512 + 0.675334i \(0.763999\pi\)
\(350\) 0 0
\(351\) 18.9338 1.01061
\(352\) 0 0
\(353\) −22.7223 −1.20938 −0.604692 0.796459i \(-0.706704\pi\)
−0.604692 + 0.796459i \(0.706704\pi\)
\(354\) 0 0
\(355\) 27.7516 1.47290
\(356\) 0 0
\(357\) 32.6630 1.72871
\(358\) 0 0
\(359\) 9.45014 0.498759 0.249380 0.968406i \(-0.419773\pi\)
0.249380 + 0.968406i \(0.419773\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) 0.868707 0.0455953
\(364\) 0 0
\(365\) 24.3345 1.27373
\(366\) 0 0
\(367\) 37.2296 1.94337 0.971686 0.236278i \(-0.0759275\pi\)
0.971686 + 0.236278i \(0.0759275\pi\)
\(368\) 0 0
\(369\) 7.61760 0.396557
\(370\) 0 0
\(371\) 55.5982 2.88652
\(372\) 0 0
\(373\) −12.0405 −0.623433 −0.311716 0.950175i \(-0.600904\pi\)
−0.311716 + 0.950175i \(0.600904\pi\)
\(374\) 0 0
\(375\) −19.3781 −1.00068
\(376\) 0 0
\(377\) −18.7162 −0.963933
\(378\) 0 0
\(379\) −10.2690 −0.527482 −0.263741 0.964593i \(-0.584957\pi\)
−0.263741 + 0.964593i \(0.584957\pi\)
\(380\) 0 0
\(381\) −30.2844 −1.55152
\(382\) 0 0
\(383\) −5.19047 −0.265221 −0.132610 0.991168i \(-0.542336\pi\)
−0.132610 + 0.991168i \(0.542336\pi\)
\(384\) 0 0
\(385\) 32.5696 1.65990
\(386\) 0 0
\(387\) 2.12651 0.108096
\(388\) 0 0
\(389\) 23.4606 1.18950 0.594751 0.803910i \(-0.297251\pi\)
0.594751 + 0.803910i \(0.297251\pi\)
\(390\) 0 0
\(391\) 11.4718 0.580155
\(392\) 0 0
\(393\) −32.5789 −1.64339
\(394\) 0 0
\(395\) 2.46425 0.123990
\(396\) 0 0
\(397\) 13.4816 0.676622 0.338311 0.941034i \(-0.390144\pi\)
0.338311 + 0.941034i \(0.390144\pi\)
\(398\) 0 0
\(399\) −8.14112 −0.407566
\(400\) 0 0
\(401\) −35.1207 −1.75384 −0.876922 0.480634i \(-0.840407\pi\)
−0.876922 + 0.480634i \(0.840407\pi\)
\(402\) 0 0
\(403\) 12.9911 0.647132
\(404\) 0 0
\(405\) 27.1286 1.34803
\(406\) 0 0
\(407\) −8.04365 −0.398709
\(408\) 0 0
\(409\) 27.5142 1.36049 0.680244 0.732986i \(-0.261874\pi\)
0.680244 + 0.732986i \(0.261874\pi\)
\(410\) 0 0
\(411\) 11.1012 0.547582
\(412\) 0 0
\(413\) 27.2282 1.33981
\(414\) 0 0
\(415\) 33.2923 1.63425
\(416\) 0 0
\(417\) −25.7238 −1.25970
\(418\) 0 0
\(419\) 32.8683 1.60572 0.802862 0.596166i \(-0.203310\pi\)
0.802862 + 0.596166i \(0.203310\pi\)
\(420\) 0 0
\(421\) 8.07512 0.393557 0.196779 0.980448i \(-0.436952\pi\)
0.196779 + 0.980448i \(0.436952\pi\)
\(422\) 0 0
\(423\) −12.8274 −0.623689
\(424\) 0 0
\(425\) −4.30311 −0.208731
\(426\) 0 0
\(427\) −58.5905 −2.83539
\(428\) 0 0
\(429\) 30.9107 1.49238
\(430\) 0 0
\(431\) 9.24355 0.445246 0.222623 0.974905i \(-0.428538\pi\)
0.222623 + 0.974905i \(0.428538\pi\)
\(432\) 0 0
\(433\) 2.55366 0.122721 0.0613606 0.998116i \(-0.480456\pi\)
0.0613606 + 0.998116i \(0.480456\pi\)
\(434\) 0 0
\(435\) −19.4437 −0.932256
\(436\) 0 0
\(437\) −2.85930 −0.136779
\(438\) 0 0
\(439\) −13.6258 −0.650325 −0.325162 0.945658i \(-0.605419\pi\)
−0.325162 + 0.945658i \(0.605419\pi\)
\(440\) 0 0
\(441\) 9.61767 0.457984
\(442\) 0 0
\(443\) −34.2056 −1.62516 −0.812578 0.582852i \(-0.801937\pi\)
−0.812578 + 0.582852i \(0.801937\pi\)
\(444\) 0 0
\(445\) 2.90135 0.137537
\(446\) 0 0
\(447\) −0.644955 −0.0305053
\(448\) 0 0
\(449\) −7.38903 −0.348710 −0.174355 0.984683i \(-0.555784\pi\)
−0.174355 + 0.984683i \(0.555784\pi\)
\(450\) 0 0
\(451\) −24.5423 −1.15565
\(452\) 0 0
\(453\) −29.2673 −1.37510
\(454\) 0 0
\(455\) −47.5873 −2.23093
\(456\) 0 0
\(457\) 9.45614 0.442340 0.221170 0.975235i \(-0.429013\pi\)
0.221170 + 0.975235i \(0.429013\pi\)
\(458\) 0 0
\(459\) −15.9946 −0.746564
\(460\) 0 0
\(461\) −41.3261 −1.92475 −0.962374 0.271728i \(-0.912405\pi\)
−0.962374 + 0.271728i \(0.912405\pi\)
\(462\) 0 0
\(463\) −8.85669 −0.411605 −0.205803 0.978594i \(-0.565981\pi\)
−0.205803 + 0.978594i \(0.565981\pi\)
\(464\) 0 0
\(465\) 13.4961 0.625866
\(466\) 0 0
\(467\) 27.5092 1.27297 0.636487 0.771287i \(-0.280387\pi\)
0.636487 + 0.771287i \(0.280387\pi\)
\(468\) 0 0
\(469\) 11.2804 0.520881
\(470\) 0 0
\(471\) 16.9486 0.780950
\(472\) 0 0
\(473\) −6.85114 −0.315016
\(474\) 0 0
\(475\) 1.07253 0.0492111
\(476\) 0 0
\(477\) 13.7960 0.631675
\(478\) 0 0
\(479\) −27.6175 −1.26188 −0.630938 0.775834i \(-0.717330\pi\)
−0.630938 + 0.775834i \(0.717330\pi\)
\(480\) 0 0
\(481\) 11.7525 0.535870
\(482\) 0 0
\(483\) 23.2779 1.05918
\(484\) 0 0
\(485\) −0.000180842 0 −8.21162e−6 0
\(486\) 0 0
\(487\) 39.0331 1.76876 0.884380 0.466767i \(-0.154582\pi\)
0.884380 + 0.466767i \(0.154582\pi\)
\(488\) 0 0
\(489\) 28.9944 1.31117
\(490\) 0 0
\(491\) 7.74681 0.349609 0.174804 0.984603i \(-0.444071\pi\)
0.174804 + 0.984603i \(0.444071\pi\)
\(492\) 0 0
\(493\) 15.8108 0.712081
\(494\) 0 0
\(495\) 8.08173 0.363247
\(496\) 0 0
\(497\) −45.7902 −2.05397
\(498\) 0 0
\(499\) −10.3219 −0.462073 −0.231037 0.972945i \(-0.574212\pi\)
−0.231037 + 0.972945i \(0.574212\pi\)
\(500\) 0 0
\(501\) 34.6213 1.54676
\(502\) 0 0
\(503\) 36.9413 1.64713 0.823567 0.567220i \(-0.191981\pi\)
0.823567 + 0.567220i \(0.191981\pi\)
\(504\) 0 0
\(505\) −44.2592 −1.96951
\(506\) 0 0
\(507\) −19.1345 −0.849794
\(508\) 0 0
\(509\) 32.8827 1.45750 0.728751 0.684779i \(-0.240101\pi\)
0.728751 + 0.684779i \(0.240101\pi\)
\(510\) 0 0
\(511\) −40.1520 −1.77622
\(512\) 0 0
\(513\) 3.98658 0.176012
\(514\) 0 0
\(515\) −24.2727 −1.06958
\(516\) 0 0
\(517\) 41.3271 1.81756
\(518\) 0 0
\(519\) 19.0127 0.834567
\(520\) 0 0
\(521\) 22.6280 0.991353 0.495676 0.868507i \(-0.334920\pi\)
0.495676 + 0.868507i \(0.334920\pi\)
\(522\) 0 0
\(523\) 19.7042 0.861606 0.430803 0.902446i \(-0.358230\pi\)
0.430803 + 0.902446i \(0.358230\pi\)
\(524\) 0 0
\(525\) −8.73159 −0.381078
\(526\) 0 0
\(527\) −10.9744 −0.478053
\(528\) 0 0
\(529\) −14.8244 −0.644540
\(530\) 0 0
\(531\) 6.75633 0.293200
\(532\) 0 0
\(533\) 35.8586 1.55321
\(534\) 0 0
\(535\) −36.7525 −1.58895
\(536\) 0 0
\(537\) 36.3275 1.56765
\(538\) 0 0
\(539\) −30.9861 −1.33466
\(540\) 0 0
\(541\) −43.5457 −1.87217 −0.936087 0.351768i \(-0.885581\pi\)
−0.936087 + 0.351768i \(0.885581\pi\)
\(542\) 0 0
\(543\) −24.0886 −1.03374
\(544\) 0 0
\(545\) −8.78009 −0.376098
\(546\) 0 0
\(547\) −40.2915 −1.72274 −0.861370 0.507978i \(-0.830393\pi\)
−0.861370 + 0.507978i \(0.830393\pi\)
\(548\) 0 0
\(549\) −14.5385 −0.620487
\(550\) 0 0
\(551\) −3.94076 −0.167882
\(552\) 0 0
\(553\) −4.06602 −0.172905
\(554\) 0 0
\(555\) 12.2094 0.518260
\(556\) 0 0
\(557\) −22.4154 −0.949773 −0.474887 0.880047i \(-0.657511\pi\)
−0.474887 + 0.880047i \(0.657511\pi\)
\(558\) 0 0
\(559\) 10.0102 0.423385
\(560\) 0 0
\(561\) −26.1123 −1.10246
\(562\) 0 0
\(563\) 30.7726 1.29691 0.648456 0.761252i \(-0.275415\pi\)
0.648456 + 0.761252i \(0.275415\pi\)
\(564\) 0 0
\(565\) −28.7855 −1.21101
\(566\) 0 0
\(567\) −44.7622 −1.87984
\(568\) 0 0
\(569\) −21.1833 −0.888052 −0.444026 0.896014i \(-0.646450\pi\)
−0.444026 + 0.896014i \(0.646450\pi\)
\(570\) 0 0
\(571\) −29.3932 −1.23007 −0.615034 0.788500i \(-0.710858\pi\)
−0.615034 + 0.788500i \(0.710858\pi\)
\(572\) 0 0
\(573\) 23.2180 0.969946
\(574\) 0 0
\(575\) −3.06668 −0.127890
\(576\) 0 0
\(577\) 5.88503 0.244997 0.122499 0.992469i \(-0.460909\pi\)
0.122499 + 0.992469i \(0.460909\pi\)
\(578\) 0 0
\(579\) 40.6672 1.69007
\(580\) 0 0
\(581\) −54.9324 −2.27898
\(582\) 0 0
\(583\) −44.4477 −1.84084
\(584\) 0 0
\(585\) −11.8082 −0.488208
\(586\) 0 0
\(587\) 17.8053 0.734903 0.367452 0.930043i \(-0.380230\pi\)
0.367452 + 0.930043i \(0.380230\pi\)
\(588\) 0 0
\(589\) 2.73532 0.112707
\(590\) 0 0
\(591\) −26.9724 −1.10950
\(592\) 0 0
\(593\) −8.60392 −0.353321 −0.176660 0.984272i \(-0.556529\pi\)
−0.176660 + 0.984272i \(0.556529\pi\)
\(594\) 0 0
\(595\) 40.2001 1.64804
\(596\) 0 0
\(597\) 35.9744 1.47233
\(598\) 0 0
\(599\) 33.4644 1.36732 0.683660 0.729801i \(-0.260387\pi\)
0.683660 + 0.729801i \(0.260387\pi\)
\(600\) 0 0
\(601\) −10.2715 −0.418983 −0.209491 0.977810i \(-0.567181\pi\)
−0.209491 + 0.977810i \(0.567181\pi\)
\(602\) 0 0
\(603\) 2.79909 0.113988
\(604\) 0 0
\(605\) 1.06916 0.0434677
\(606\) 0 0
\(607\) 30.0027 1.21777 0.608886 0.793258i \(-0.291617\pi\)
0.608886 + 0.793258i \(0.291617\pi\)
\(608\) 0 0
\(609\) 32.0822 1.30004
\(610\) 0 0
\(611\) −60.3829 −2.44283
\(612\) 0 0
\(613\) −34.5067 −1.39371 −0.696856 0.717211i \(-0.745419\pi\)
−0.696856 + 0.717211i \(0.745419\pi\)
\(614\) 0 0
\(615\) 37.2525 1.50217
\(616\) 0 0
\(617\) −45.6129 −1.83631 −0.918154 0.396224i \(-0.870320\pi\)
−0.918154 + 0.396224i \(0.870320\pi\)
\(618\) 0 0
\(619\) 11.1456 0.447980 0.223990 0.974591i \(-0.428092\pi\)
0.223990 + 0.974591i \(0.428092\pi\)
\(620\) 0 0
\(621\) −11.3988 −0.457419
\(622\) 0 0
\(623\) −4.78723 −0.191796
\(624\) 0 0
\(625\) −29.2123 −1.16849
\(626\) 0 0
\(627\) 6.50837 0.259919
\(628\) 0 0
\(629\) −9.92814 −0.395861
\(630\) 0 0
\(631\) 49.4569 1.96885 0.984423 0.175815i \(-0.0562561\pi\)
0.984423 + 0.175815i \(0.0562561\pi\)
\(632\) 0 0
\(633\) 0.563115 0.0223818
\(634\) 0 0
\(635\) −37.2726 −1.47912
\(636\) 0 0
\(637\) 45.2736 1.79381
\(638\) 0 0
\(639\) −11.3622 −0.449484
\(640\) 0 0
\(641\) 26.8188 1.05928 0.529639 0.848223i \(-0.322327\pi\)
0.529639 + 0.848223i \(0.322327\pi\)
\(642\) 0 0
\(643\) −24.3253 −0.959298 −0.479649 0.877461i \(-0.659236\pi\)
−0.479649 + 0.877461i \(0.659236\pi\)
\(644\) 0 0
\(645\) 10.3993 0.409472
\(646\) 0 0
\(647\) −22.2968 −0.876580 −0.438290 0.898834i \(-0.644416\pi\)
−0.438290 + 0.898834i \(0.644416\pi\)
\(648\) 0 0
\(649\) −21.7674 −0.854446
\(650\) 0 0
\(651\) −22.2686 −0.872775
\(652\) 0 0
\(653\) 33.5260 1.31197 0.655987 0.754772i \(-0.272252\pi\)
0.655987 + 0.754772i \(0.272252\pi\)
\(654\) 0 0
\(655\) −40.0966 −1.56670
\(656\) 0 0
\(657\) −9.96320 −0.388702
\(658\) 0 0
\(659\) −31.8937 −1.24240 −0.621202 0.783651i \(-0.713355\pi\)
−0.621202 + 0.783651i \(0.713355\pi\)
\(660\) 0 0
\(661\) 8.28363 0.322196 0.161098 0.986938i \(-0.448497\pi\)
0.161098 + 0.986938i \(0.448497\pi\)
\(662\) 0 0
\(663\) 38.1526 1.48172
\(664\) 0 0
\(665\) −10.0197 −0.388547
\(666\) 0 0
\(667\) 11.2678 0.436292
\(668\) 0 0
\(669\) 53.2643 2.05932
\(670\) 0 0
\(671\) 46.8398 1.80823
\(672\) 0 0
\(673\) 40.2386 1.55108 0.775541 0.631297i \(-0.217477\pi\)
0.775541 + 0.631297i \(0.217477\pi\)
\(674\) 0 0
\(675\) 4.27573 0.164573
\(676\) 0 0
\(677\) −9.54961 −0.367021 −0.183511 0.983018i \(-0.558746\pi\)
−0.183511 + 0.983018i \(0.558746\pi\)
\(678\) 0 0
\(679\) 0.000298390 0 1.14512e−5 0
\(680\) 0 0
\(681\) 46.3175 1.77489
\(682\) 0 0
\(683\) 13.3845 0.512143 0.256072 0.966658i \(-0.417572\pi\)
0.256072 + 0.966658i \(0.417572\pi\)
\(684\) 0 0
\(685\) 13.6628 0.522030
\(686\) 0 0
\(687\) 3.55623 0.135679
\(688\) 0 0
\(689\) 64.9424 2.47411
\(690\) 0 0
\(691\) −42.0952 −1.60138 −0.800689 0.599080i \(-0.795533\pi\)
−0.800689 + 0.599080i \(0.795533\pi\)
\(692\) 0 0
\(693\) −13.3349 −0.506550
\(694\) 0 0
\(695\) −31.6596 −1.20092
\(696\) 0 0
\(697\) −30.2921 −1.14739
\(698\) 0 0
\(699\) 38.6451 1.46169
\(700\) 0 0
\(701\) −16.2520 −0.613831 −0.306916 0.951737i \(-0.599297\pi\)
−0.306916 + 0.951737i \(0.599297\pi\)
\(702\) 0 0
\(703\) 2.47454 0.0933292
\(704\) 0 0
\(705\) −62.7301 −2.36255
\(706\) 0 0
\(707\) 73.0278 2.74649
\(708\) 0 0
\(709\) 12.5642 0.471859 0.235929 0.971770i \(-0.424187\pi\)
0.235929 + 0.971770i \(0.424187\pi\)
\(710\) 0 0
\(711\) −1.00893 −0.0378379
\(712\) 0 0
\(713\) −7.82111 −0.292903
\(714\) 0 0
\(715\) 38.0434 1.42274
\(716\) 0 0
\(717\) 5.88054 0.219613
\(718\) 0 0
\(719\) 27.9035 1.04063 0.520313 0.853976i \(-0.325815\pi\)
0.520313 + 0.853976i \(0.325815\pi\)
\(720\) 0 0
\(721\) 40.0500 1.49154
\(722\) 0 0
\(723\) 21.3527 0.794117
\(724\) 0 0
\(725\) −4.22659 −0.156972
\(726\) 0 0
\(727\) 17.8993 0.663850 0.331925 0.943306i \(-0.392302\pi\)
0.331925 + 0.943306i \(0.392302\pi\)
\(728\) 0 0
\(729\) 12.8390 0.475518
\(730\) 0 0
\(731\) −8.45625 −0.312766
\(732\) 0 0
\(733\) −30.6676 −1.13273 −0.566367 0.824153i \(-0.691651\pi\)
−0.566367 + 0.824153i \(0.691651\pi\)
\(734\) 0 0
\(735\) 47.0335 1.73486
\(736\) 0 0
\(737\) −9.01807 −0.332185
\(738\) 0 0
\(739\) −18.9825 −0.698281 −0.349141 0.937070i \(-0.613526\pi\)
−0.349141 + 0.937070i \(0.613526\pi\)
\(740\) 0 0
\(741\) −9.50936 −0.349335
\(742\) 0 0
\(743\) −2.74872 −0.100841 −0.0504203 0.998728i \(-0.516056\pi\)
−0.0504203 + 0.998728i \(0.516056\pi\)
\(744\) 0 0
\(745\) −0.793780 −0.0290818
\(746\) 0 0
\(747\) −13.6308 −0.498724
\(748\) 0 0
\(749\) 60.6417 2.21580
\(750\) 0 0
\(751\) −37.3254 −1.36202 −0.681011 0.732273i \(-0.738459\pi\)
−0.681011 + 0.732273i \(0.738459\pi\)
\(752\) 0 0
\(753\) −46.0823 −1.67933
\(754\) 0 0
\(755\) −36.0207 −1.31093
\(756\) 0 0
\(757\) −12.0263 −0.437105 −0.218553 0.975825i \(-0.570133\pi\)
−0.218553 + 0.975825i \(0.570133\pi\)
\(758\) 0 0
\(759\) −18.6094 −0.675478
\(760\) 0 0
\(761\) −34.3634 −1.24567 −0.622835 0.782353i \(-0.714019\pi\)
−0.622835 + 0.782353i \(0.714019\pi\)
\(762\) 0 0
\(763\) 14.4872 0.524471
\(764\) 0 0
\(765\) 9.97514 0.360652
\(766\) 0 0
\(767\) 31.8043 1.14839
\(768\) 0 0
\(769\) 28.2503 1.01873 0.509367 0.860550i \(-0.329880\pi\)
0.509367 + 0.860550i \(0.329880\pi\)
\(770\) 0 0
\(771\) 36.8404 1.32677
\(772\) 0 0
\(773\) −35.8882 −1.29081 −0.645404 0.763841i \(-0.723311\pi\)
−0.645404 + 0.763841i \(0.723311\pi\)
\(774\) 0 0
\(775\) 2.93372 0.105382
\(776\) 0 0
\(777\) −20.1455 −0.722718
\(778\) 0 0
\(779\) 7.55017 0.270513
\(780\) 0 0
\(781\) 36.6067 1.30989
\(782\) 0 0
\(783\) −15.7102 −0.561436
\(784\) 0 0
\(785\) 20.8595 0.744508
\(786\) 0 0
\(787\) −19.3714 −0.690516 −0.345258 0.938508i \(-0.612209\pi\)
−0.345258 + 0.938508i \(0.612209\pi\)
\(788\) 0 0
\(789\) −58.2850 −2.07500
\(790\) 0 0
\(791\) 47.4961 1.68877
\(792\) 0 0
\(793\) −68.4375 −2.43029
\(794\) 0 0
\(795\) 67.4669 2.39280
\(796\) 0 0
\(797\) 48.8991 1.73209 0.866047 0.499963i \(-0.166653\pi\)
0.866047 + 0.499963i \(0.166653\pi\)
\(798\) 0 0
\(799\) 51.0093 1.80458
\(800\) 0 0
\(801\) −1.18789 −0.0419720
\(802\) 0 0
\(803\) 32.0993 1.13276
\(804\) 0 0
\(805\) 28.6493 1.00976
\(806\) 0 0
\(807\) 43.3019 1.52430
\(808\) 0 0
\(809\) −27.5666 −0.969192 −0.484596 0.874738i \(-0.661033\pi\)
−0.484596 + 0.874738i \(0.661033\pi\)
\(810\) 0 0
\(811\) 24.5523 0.862148 0.431074 0.902317i \(-0.358135\pi\)
0.431074 + 0.902317i \(0.358135\pi\)
\(812\) 0 0
\(813\) 30.2143 1.05966
\(814\) 0 0
\(815\) 35.6850 1.24999
\(816\) 0 0
\(817\) 2.10768 0.0737384
\(818\) 0 0
\(819\) 19.4836 0.680810
\(820\) 0 0
\(821\) −18.8845 −0.659075 −0.329537 0.944143i \(-0.606893\pi\)
−0.329537 + 0.944143i \(0.606893\pi\)
\(822\) 0 0
\(823\) 37.3110 1.30058 0.650291 0.759685i \(-0.274647\pi\)
0.650291 + 0.759685i \(0.274647\pi\)
\(824\) 0 0
\(825\) 6.98042 0.243027
\(826\) 0 0
\(827\) 35.4380 1.23230 0.616150 0.787629i \(-0.288691\pi\)
0.616150 + 0.787629i \(0.288691\pi\)
\(828\) 0 0
\(829\) 21.6258 0.751096 0.375548 0.926803i \(-0.377454\pi\)
0.375548 + 0.926803i \(0.377454\pi\)
\(830\) 0 0
\(831\) 12.8384 0.445358
\(832\) 0 0
\(833\) −38.2456 −1.32513
\(834\) 0 0
\(835\) 42.6102 1.47459
\(836\) 0 0
\(837\) 10.9046 0.376918
\(838\) 0 0
\(839\) 6.88368 0.237651 0.118825 0.992915i \(-0.462087\pi\)
0.118825 + 0.992915i \(0.462087\pi\)
\(840\) 0 0
\(841\) −13.4704 −0.464496
\(842\) 0 0
\(843\) 26.8383 0.924359
\(844\) 0 0
\(845\) −23.5499 −0.810140
\(846\) 0 0
\(847\) −1.76412 −0.0606160
\(848\) 0 0
\(849\) 1.99955 0.0686245
\(850\) 0 0
\(851\) −7.07546 −0.242544
\(852\) 0 0
\(853\) −20.5202 −0.702597 −0.351298 0.936264i \(-0.614260\pi\)
−0.351298 + 0.936264i \(0.614260\pi\)
\(854\) 0 0
\(855\) −2.48626 −0.0850283
\(856\) 0 0
\(857\) −48.6493 −1.66183 −0.830914 0.556401i \(-0.812182\pi\)
−0.830914 + 0.556401i \(0.812182\pi\)
\(858\) 0 0
\(859\) −36.1468 −1.23331 −0.616656 0.787232i \(-0.711513\pi\)
−0.616656 + 0.787232i \(0.711513\pi\)
\(860\) 0 0
\(861\) −61.4668 −2.09478
\(862\) 0 0
\(863\) −34.4735 −1.17349 −0.586746 0.809771i \(-0.699591\pi\)
−0.586746 + 0.809771i \(0.699591\pi\)
\(864\) 0 0
\(865\) 23.4000 0.795623
\(866\) 0 0
\(867\) 1.80800 0.0614027
\(868\) 0 0
\(869\) 3.25056 0.110268
\(870\) 0 0
\(871\) 13.1763 0.446461
\(872\) 0 0
\(873\) 7.40417e−5 0 2.50593e−6 0
\(874\) 0 0
\(875\) 39.3521 1.33034
\(876\) 0 0
\(877\) −2.96081 −0.0999794 −0.0499897 0.998750i \(-0.515919\pi\)
−0.0499897 + 0.998750i \(0.515919\pi\)
\(878\) 0 0
\(879\) 46.8235 1.57932
\(880\) 0 0
\(881\) 32.6950 1.10152 0.550761 0.834663i \(-0.314338\pi\)
0.550761 + 0.834663i \(0.314338\pi\)
\(882\) 0 0
\(883\) 35.3221 1.18868 0.594342 0.804212i \(-0.297412\pi\)
0.594342 + 0.804212i \(0.297412\pi\)
\(884\) 0 0
\(885\) 33.0406 1.11065
\(886\) 0 0
\(887\) 18.4807 0.620520 0.310260 0.950652i \(-0.399584\pi\)
0.310260 + 0.950652i \(0.399584\pi\)
\(888\) 0 0
\(889\) 61.5000 2.06264
\(890\) 0 0
\(891\) 35.7849 1.19884
\(892\) 0 0
\(893\) −12.7138 −0.425453
\(894\) 0 0
\(895\) 44.7101 1.49449
\(896\) 0 0
\(897\) 27.1901 0.907851
\(898\) 0 0
\(899\) −10.7793 −0.359509
\(900\) 0 0
\(901\) −54.8610 −1.82769
\(902\) 0 0
\(903\) −17.1589 −0.571012
\(904\) 0 0
\(905\) −29.6471 −0.985502
\(906\) 0 0
\(907\) 40.0208 1.32887 0.664435 0.747346i \(-0.268672\pi\)
0.664435 + 0.747346i \(0.268672\pi\)
\(908\) 0 0
\(909\) 18.1209 0.601033
\(910\) 0 0
\(911\) 7.01189 0.232314 0.116157 0.993231i \(-0.462942\pi\)
0.116157 + 0.993231i \(0.462942\pi\)
\(912\) 0 0
\(913\) 43.9154 1.45339
\(914\) 0 0
\(915\) −71.0979 −2.35042
\(916\) 0 0
\(917\) 66.1595 2.18478
\(918\) 0 0
\(919\) −18.3016 −0.603715 −0.301858 0.953353i \(-0.597607\pi\)
−0.301858 + 0.953353i \(0.597607\pi\)
\(920\) 0 0
\(921\) 29.8900 0.984910
\(922\) 0 0
\(923\) −53.4859 −1.76051
\(924\) 0 0
\(925\) 2.65402 0.0872637
\(926\) 0 0
\(927\) 9.93790 0.326403
\(928\) 0 0
\(929\) 2.70469 0.0887379 0.0443689 0.999015i \(-0.485872\pi\)
0.0443689 + 0.999015i \(0.485872\pi\)
\(930\) 0 0
\(931\) 9.53253 0.312416
\(932\) 0 0
\(933\) 18.4911 0.605371
\(934\) 0 0
\(935\) −32.1377 −1.05102
\(936\) 0 0
\(937\) 22.1781 0.724528 0.362264 0.932075i \(-0.382004\pi\)
0.362264 + 0.932075i \(0.382004\pi\)
\(938\) 0 0
\(939\) 17.0763 0.557265
\(940\) 0 0
\(941\) 10.3706 0.338071 0.169036 0.985610i \(-0.445935\pi\)
0.169036 + 0.985610i \(0.445935\pi\)
\(942\) 0 0
\(943\) −21.5882 −0.703008
\(944\) 0 0
\(945\) −39.9443 −1.29939
\(946\) 0 0
\(947\) −36.9437 −1.20051 −0.600255 0.799809i \(-0.704934\pi\)
−0.600255 + 0.799809i \(0.704934\pi\)
\(948\) 0 0
\(949\) −46.9001 −1.52244
\(950\) 0 0
\(951\) 15.8724 0.514699
\(952\) 0 0
\(953\) −10.5283 −0.341046 −0.170523 0.985354i \(-0.554546\pi\)
−0.170523 + 0.985354i \(0.554546\pi\)
\(954\) 0 0
\(955\) 28.5756 0.924685
\(956\) 0 0
\(957\) −25.6480 −0.829081
\(958\) 0 0
\(959\) −22.5437 −0.727974
\(960\) 0 0
\(961\) −23.5180 −0.758645
\(962\) 0 0
\(963\) 15.0475 0.484898
\(964\) 0 0
\(965\) 50.0513 1.61121
\(966\) 0 0
\(967\) 34.7791 1.11842 0.559210 0.829026i \(-0.311105\pi\)
0.559210 + 0.829026i \(0.311105\pi\)
\(968\) 0 0
\(969\) 8.03317 0.258063
\(970\) 0 0
\(971\) 41.6332 1.33607 0.668036 0.744129i \(-0.267135\pi\)
0.668036 + 0.744129i \(0.267135\pi\)
\(972\) 0 0
\(973\) 52.2385 1.67469
\(974\) 0 0
\(975\) −10.1991 −0.326632
\(976\) 0 0
\(977\) −14.7360 −0.471448 −0.235724 0.971820i \(-0.575746\pi\)
−0.235724 + 0.971820i \(0.575746\pi\)
\(978\) 0 0
\(979\) 3.82713 0.122315
\(980\) 0 0
\(981\) 3.59481 0.114773
\(982\) 0 0
\(983\) 28.7435 0.916775 0.458388 0.888752i \(-0.348427\pi\)
0.458388 + 0.888752i \(0.348427\pi\)
\(984\) 0 0
\(985\) −33.1963 −1.05772
\(986\) 0 0
\(987\) 103.505 3.29460
\(988\) 0 0
\(989\) −6.02649 −0.191631
\(990\) 0 0
\(991\) −53.3287 −1.69404 −0.847022 0.531558i \(-0.821607\pi\)
−0.847022 + 0.531558i \(0.821607\pi\)
\(992\) 0 0
\(993\) 1.54147 0.0489170
\(994\) 0 0
\(995\) 44.2756 1.40363
\(996\) 0 0
\(997\) −49.0112 −1.55220 −0.776101 0.630609i \(-0.782805\pi\)
−0.776101 + 0.630609i \(0.782805\pi\)
\(998\) 0 0
\(999\) 9.86497 0.312114
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 \(a_p\))