Properties

Label 8048.2.a.v.1.23
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

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Newspace parameters

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

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.23
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.98770 q^{3}\) \(+0.688613 q^{5}\) \(+1.63548 q^{7}\) \(+0.950962 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.98770 q^{3}\) \(+0.688613 q^{5}\) \(+1.63548 q^{7}\) \(+0.950962 q^{9}\) \(-1.13439 q^{11}\) \(-4.69083 q^{13}\) \(+1.36876 q^{15}\) \(+3.66450 q^{17}\) \(+0.478156 q^{19}\) \(+3.25084 q^{21}\) \(-4.93137 q^{23}\) \(-4.52581 q^{25}\) \(-4.07288 q^{27}\) \(+3.04650 q^{29}\) \(-7.78407 q^{31}\) \(-2.25484 q^{33}\) \(+1.12621 q^{35}\) \(-1.05854 q^{37}\) \(-9.32397 q^{39}\) \(-10.5669 q^{41}\) \(+3.06948 q^{43}\) \(+0.654845 q^{45}\) \(-11.5743 q^{47}\) \(-4.32522 q^{49}\) \(+7.28393 q^{51}\) \(+6.59289 q^{53}\) \(-0.781158 q^{55}\) \(+0.950432 q^{57}\) \(+2.97184 q^{59}\) \(-9.43833 q^{61}\) \(+1.55527 q^{63}\) \(-3.23016 q^{65}\) \(+8.15913 q^{67}\) \(-9.80210 q^{69}\) \(-11.2051 q^{71}\) \(-2.52633 q^{73}\) \(-8.99597 q^{75}\) \(-1.85527 q^{77}\) \(+0.930221 q^{79}\) \(-10.9486 q^{81}\) \(-1.69982 q^{83}\) \(+2.52342 q^{85}\) \(+6.05554 q^{87}\) \(+1.82823 q^{89}\) \(-7.67173 q^{91}\) \(-15.4724 q^{93}\) \(+0.329264 q^{95}\) \(+12.4565 q^{97}\) \(-1.07876 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.98770 1.14760 0.573800 0.818995i \(-0.305469\pi\)
0.573800 + 0.818995i \(0.305469\pi\)
\(4\) 0 0
\(5\) 0.688613 0.307957 0.153979 0.988074i \(-0.450791\pi\)
0.153979 + 0.988074i \(0.450791\pi\)
\(6\) 0 0
\(7\) 1.63548 0.618152 0.309076 0.951037i \(-0.399980\pi\)
0.309076 + 0.951037i \(0.399980\pi\)
\(8\) 0 0
\(9\) 0.950962 0.316987
\(10\) 0 0
\(11\) −1.13439 −0.342033 −0.171016 0.985268i \(-0.554705\pi\)
−0.171016 + 0.985268i \(0.554705\pi\)
\(12\) 0 0
\(13\) −4.69083 −1.30100 −0.650501 0.759506i \(-0.725441\pi\)
−0.650501 + 0.759506i \(0.725441\pi\)
\(14\) 0 0
\(15\) 1.36876 0.353412
\(16\) 0 0
\(17\) 3.66450 0.888771 0.444385 0.895836i \(-0.353422\pi\)
0.444385 + 0.895836i \(0.353422\pi\)
\(18\) 0 0
\(19\) 0.478156 0.109697 0.0548483 0.998495i \(-0.482532\pi\)
0.0548483 + 0.998495i \(0.482532\pi\)
\(20\) 0 0
\(21\) 3.25084 0.709391
\(22\) 0 0
\(23\) −4.93137 −1.02826 −0.514131 0.857712i \(-0.671885\pi\)
−0.514131 + 0.857712i \(0.671885\pi\)
\(24\) 0 0
\(25\) −4.52581 −0.905162
\(26\) 0 0
\(27\) −4.07288 −0.783826
\(28\) 0 0
\(29\) 3.04650 0.565721 0.282860 0.959161i \(-0.408717\pi\)
0.282860 + 0.959161i \(0.408717\pi\)
\(30\) 0 0
\(31\) −7.78407 −1.39806 −0.699030 0.715092i \(-0.746385\pi\)
−0.699030 + 0.715092i \(0.746385\pi\)
\(32\) 0 0
\(33\) −2.25484 −0.392517
\(34\) 0 0
\(35\) 1.12621 0.190364
\(36\) 0 0
\(37\) −1.05854 −0.174023 −0.0870113 0.996207i \(-0.527732\pi\)
−0.0870113 + 0.996207i \(0.527732\pi\)
\(38\) 0 0
\(39\) −9.32397 −1.49303
\(40\) 0 0
\(41\) −10.5669 −1.65027 −0.825134 0.564937i \(-0.808901\pi\)
−0.825134 + 0.564937i \(0.808901\pi\)
\(42\) 0 0
\(43\) 3.06948 0.468092 0.234046 0.972226i \(-0.424803\pi\)
0.234046 + 0.972226i \(0.424803\pi\)
\(44\) 0 0
\(45\) 0.654845 0.0976185
\(46\) 0 0
\(47\) −11.5743 −1.68829 −0.844145 0.536114i \(-0.819892\pi\)
−0.844145 + 0.536114i \(0.819892\pi\)
\(48\) 0 0
\(49\) −4.32522 −0.617889
\(50\) 0 0
\(51\) 7.28393 1.01995
\(52\) 0 0
\(53\) 6.59289 0.905603 0.452801 0.891611i \(-0.350425\pi\)
0.452801 + 0.891611i \(0.350425\pi\)
\(54\) 0 0
\(55\) −0.781158 −0.105331
\(56\) 0 0
\(57\) 0.950432 0.125888
\(58\) 0 0
\(59\) 2.97184 0.386900 0.193450 0.981110i \(-0.438032\pi\)
0.193450 + 0.981110i \(0.438032\pi\)
\(60\) 0 0
\(61\) −9.43833 −1.20845 −0.604227 0.796812i \(-0.706518\pi\)
−0.604227 + 0.796812i \(0.706518\pi\)
\(62\) 0 0
\(63\) 1.55527 0.195946
\(64\) 0 0
\(65\) −3.23016 −0.400653
\(66\) 0 0
\(67\) 8.15913 0.996796 0.498398 0.866948i \(-0.333922\pi\)
0.498398 + 0.866948i \(0.333922\pi\)
\(68\) 0 0
\(69\) −9.80210 −1.18003
\(70\) 0 0
\(71\) −11.2051 −1.32981 −0.664903 0.746930i \(-0.731527\pi\)
−0.664903 + 0.746930i \(0.731527\pi\)
\(72\) 0 0
\(73\) −2.52633 −0.295685 −0.147842 0.989011i \(-0.547233\pi\)
−0.147842 + 0.989011i \(0.547233\pi\)
\(74\) 0 0
\(75\) −8.99597 −1.03876
\(76\) 0 0
\(77\) −1.85527 −0.211428
\(78\) 0 0
\(79\) 0.930221 0.104658 0.0523290 0.998630i \(-0.483336\pi\)
0.0523290 + 0.998630i \(0.483336\pi\)
\(80\) 0 0
\(81\) −10.9486 −1.21651
\(82\) 0 0
\(83\) −1.69982 −0.186579 −0.0932897 0.995639i \(-0.529738\pi\)
−0.0932897 + 0.995639i \(0.529738\pi\)
\(84\) 0 0
\(85\) 2.52342 0.273703
\(86\) 0 0
\(87\) 6.05554 0.649222
\(88\) 0 0
\(89\) 1.82823 0.193792 0.0968960 0.995295i \(-0.469109\pi\)
0.0968960 + 0.995295i \(0.469109\pi\)
\(90\) 0 0
\(91\) −7.67173 −0.804216
\(92\) 0 0
\(93\) −15.4724 −1.60442
\(94\) 0 0
\(95\) 0.329264 0.0337818
\(96\) 0 0
\(97\) 12.4565 1.26477 0.632385 0.774654i \(-0.282076\pi\)
0.632385 + 0.774654i \(0.282076\pi\)
\(98\) 0 0
\(99\) −1.07876 −0.108420
\(100\) 0 0
\(101\) −3.76622 −0.374753 −0.187377 0.982288i \(-0.559998\pi\)
−0.187377 + 0.982288i \(0.559998\pi\)
\(102\) 0 0
\(103\) 17.1753 1.69233 0.846166 0.532920i \(-0.178905\pi\)
0.846166 + 0.532920i \(0.178905\pi\)
\(104\) 0 0
\(105\) 2.23857 0.218462
\(106\) 0 0
\(107\) 6.01484 0.581477 0.290738 0.956803i \(-0.406099\pi\)
0.290738 + 0.956803i \(0.406099\pi\)
\(108\) 0 0
\(109\) −2.39418 −0.229320 −0.114660 0.993405i \(-0.536578\pi\)
−0.114660 + 0.993405i \(0.536578\pi\)
\(110\) 0 0
\(111\) −2.10406 −0.199709
\(112\) 0 0
\(113\) 10.4392 0.982042 0.491021 0.871148i \(-0.336624\pi\)
0.491021 + 0.871148i \(0.336624\pi\)
\(114\) 0 0
\(115\) −3.39581 −0.316661
\(116\) 0 0
\(117\) −4.46080 −0.412401
\(118\) 0 0
\(119\) 5.99319 0.549395
\(120\) 0 0
\(121\) −9.71315 −0.883014
\(122\) 0 0
\(123\) −21.0038 −1.89385
\(124\) 0 0
\(125\) −6.55960 −0.586708
\(126\) 0 0
\(127\) 9.11409 0.808745 0.404372 0.914594i \(-0.367490\pi\)
0.404372 + 0.914594i \(0.367490\pi\)
\(128\) 0 0
\(129\) 6.10122 0.537182
\(130\) 0 0
\(131\) −8.76960 −0.766203 −0.383102 0.923706i \(-0.625144\pi\)
−0.383102 + 0.923706i \(0.625144\pi\)
\(132\) 0 0
\(133\) 0.782012 0.0678091
\(134\) 0 0
\(135\) −2.80464 −0.241385
\(136\) 0 0
\(137\) −10.1477 −0.866976 −0.433488 0.901159i \(-0.642717\pi\)
−0.433488 + 0.901159i \(0.642717\pi\)
\(138\) 0 0
\(139\) −17.0009 −1.44200 −0.720999 0.692936i \(-0.756317\pi\)
−0.720999 + 0.692936i \(0.756317\pi\)
\(140\) 0 0
\(141\) −23.0063 −1.93748
\(142\) 0 0
\(143\) 5.32124 0.444985
\(144\) 0 0
\(145\) 2.09786 0.174218
\(146\) 0 0
\(147\) −8.59725 −0.709089
\(148\) 0 0
\(149\) 9.22613 0.755834 0.377917 0.925839i \(-0.376640\pi\)
0.377917 + 0.925839i \(0.376640\pi\)
\(150\) 0 0
\(151\) 16.7011 1.35912 0.679558 0.733622i \(-0.262172\pi\)
0.679558 + 0.733622i \(0.262172\pi\)
\(152\) 0 0
\(153\) 3.48479 0.281729
\(154\) 0 0
\(155\) −5.36021 −0.430543
\(156\) 0 0
\(157\) 5.27599 0.421070 0.210535 0.977586i \(-0.432479\pi\)
0.210535 + 0.977586i \(0.432479\pi\)
\(158\) 0 0
\(159\) 13.1047 1.03927
\(160\) 0 0
\(161\) −8.06514 −0.635622
\(162\) 0 0
\(163\) 19.8148 1.55202 0.776008 0.630722i \(-0.217241\pi\)
0.776008 + 0.630722i \(0.217241\pi\)
\(164\) 0 0
\(165\) −1.55271 −0.120878
\(166\) 0 0
\(167\) 4.80319 0.371682 0.185841 0.982580i \(-0.440499\pi\)
0.185841 + 0.982580i \(0.440499\pi\)
\(168\) 0 0
\(169\) 9.00385 0.692604
\(170\) 0 0
\(171\) 0.454708 0.0347724
\(172\) 0 0
\(173\) 2.26005 0.171828 0.0859141 0.996303i \(-0.472619\pi\)
0.0859141 + 0.996303i \(0.472619\pi\)
\(174\) 0 0
\(175\) −7.40185 −0.559528
\(176\) 0 0
\(177\) 5.90713 0.444007
\(178\) 0 0
\(179\) 1.15821 0.0865690 0.0432845 0.999063i \(-0.486218\pi\)
0.0432845 + 0.999063i \(0.486218\pi\)
\(180\) 0 0
\(181\) −18.8463 −1.40083 −0.700417 0.713734i \(-0.747003\pi\)
−0.700417 + 0.713734i \(0.747003\pi\)
\(182\) 0 0
\(183\) −18.7606 −1.38682
\(184\) 0 0
\(185\) −0.728923 −0.0535915
\(186\) 0 0
\(187\) −4.15698 −0.303988
\(188\) 0 0
\(189\) −6.66109 −0.484523
\(190\) 0 0
\(191\) −6.90350 −0.499520 −0.249760 0.968308i \(-0.580352\pi\)
−0.249760 + 0.968308i \(0.580352\pi\)
\(192\) 0 0
\(193\) 7.69003 0.553540 0.276770 0.960936i \(-0.410736\pi\)
0.276770 + 0.960936i \(0.410736\pi\)
\(194\) 0 0
\(195\) −6.42061 −0.459789
\(196\) 0 0
\(197\) −15.5059 −1.10475 −0.552373 0.833597i \(-0.686278\pi\)
−0.552373 + 0.833597i \(0.686278\pi\)
\(198\) 0 0
\(199\) 0.786271 0.0557373 0.0278686 0.999612i \(-0.491128\pi\)
0.0278686 + 0.999612i \(0.491128\pi\)
\(200\) 0 0
\(201\) 16.2179 1.14392
\(202\) 0 0
\(203\) 4.98248 0.349701
\(204\) 0 0
\(205\) −7.27649 −0.508212
\(206\) 0 0
\(207\) −4.68955 −0.325946
\(208\) 0 0
\(209\) −0.542417 −0.0375198
\(210\) 0 0
\(211\) 3.63528 0.250263 0.125131 0.992140i \(-0.460065\pi\)
0.125131 + 0.992140i \(0.460065\pi\)
\(212\) 0 0
\(213\) −22.2725 −1.52609
\(214\) 0 0
\(215\) 2.11369 0.144152
\(216\) 0 0
\(217\) −12.7307 −0.864213
\(218\) 0 0
\(219\) −5.02160 −0.339328
\(220\) 0 0
\(221\) −17.1895 −1.15629
\(222\) 0 0
\(223\) 16.5480 1.10814 0.554068 0.832471i \(-0.313075\pi\)
0.554068 + 0.832471i \(0.313075\pi\)
\(224\) 0 0
\(225\) −4.30387 −0.286925
\(226\) 0 0
\(227\) 2.79658 0.185616 0.0928079 0.995684i \(-0.470416\pi\)
0.0928079 + 0.995684i \(0.470416\pi\)
\(228\) 0 0
\(229\) −25.4607 −1.68249 −0.841245 0.540655i \(-0.818177\pi\)
−0.841245 + 0.540655i \(0.818177\pi\)
\(230\) 0 0
\(231\) −3.68773 −0.242635
\(232\) 0 0
\(233\) −21.8036 −1.42840 −0.714201 0.699940i \(-0.753210\pi\)
−0.714201 + 0.699940i \(0.753210\pi\)
\(234\) 0 0
\(235\) −7.97024 −0.519921
\(236\) 0 0
\(237\) 1.84900 0.120106
\(238\) 0 0
\(239\) −9.61699 −0.622071 −0.311036 0.950398i \(-0.600676\pi\)
−0.311036 + 0.950398i \(0.600676\pi\)
\(240\) 0 0
\(241\) −16.3250 −1.05158 −0.525792 0.850613i \(-0.676231\pi\)
−0.525792 + 0.850613i \(0.676231\pi\)
\(242\) 0 0
\(243\) −9.54384 −0.612237
\(244\) 0 0
\(245\) −2.97840 −0.190283
\(246\) 0 0
\(247\) −2.24295 −0.142715
\(248\) 0 0
\(249\) −3.37874 −0.214119
\(250\) 0 0
\(251\) 18.7773 1.18521 0.592606 0.805493i \(-0.298099\pi\)
0.592606 + 0.805493i \(0.298099\pi\)
\(252\) 0 0
\(253\) 5.59412 0.351699
\(254\) 0 0
\(255\) 5.01581 0.314102
\(256\) 0 0
\(257\) 17.3296 1.08099 0.540495 0.841347i \(-0.318237\pi\)
0.540495 + 0.841347i \(0.318237\pi\)
\(258\) 0 0
\(259\) −1.73121 −0.107572
\(260\) 0 0
\(261\) 2.89711 0.179326
\(262\) 0 0
\(263\) −12.5842 −0.775974 −0.387987 0.921665i \(-0.626830\pi\)
−0.387987 + 0.921665i \(0.626830\pi\)
\(264\) 0 0
\(265\) 4.53995 0.278887
\(266\) 0 0
\(267\) 3.63398 0.222396
\(268\) 0 0
\(269\) −12.8277 −0.782122 −0.391061 0.920365i \(-0.627892\pi\)
−0.391061 + 0.920365i \(0.627892\pi\)
\(270\) 0 0
\(271\) 7.41634 0.450511 0.225255 0.974300i \(-0.427678\pi\)
0.225255 + 0.974300i \(0.427678\pi\)
\(272\) 0 0
\(273\) −15.2491 −0.922919
\(274\) 0 0
\(275\) 5.13405 0.309595
\(276\) 0 0
\(277\) −17.6508 −1.06053 −0.530266 0.847831i \(-0.677908\pi\)
−0.530266 + 0.847831i \(0.677908\pi\)
\(278\) 0 0
\(279\) −7.40236 −0.443167
\(280\) 0 0
\(281\) −1.73057 −0.103237 −0.0516187 0.998667i \(-0.516438\pi\)
−0.0516187 + 0.998667i \(0.516438\pi\)
\(282\) 0 0
\(283\) 25.1645 1.49587 0.747936 0.663771i \(-0.231045\pi\)
0.747936 + 0.663771i \(0.231045\pi\)
\(284\) 0 0
\(285\) 0.654480 0.0387680
\(286\) 0 0
\(287\) −17.2819 −1.02012
\(288\) 0 0
\(289\) −3.57148 −0.210087
\(290\) 0 0
\(291\) 24.7599 1.45145
\(292\) 0 0
\(293\) 14.5820 0.851890 0.425945 0.904749i \(-0.359942\pi\)
0.425945 + 0.904749i \(0.359942\pi\)
\(294\) 0 0
\(295\) 2.04645 0.119149
\(296\) 0 0
\(297\) 4.62025 0.268094
\(298\) 0 0
\(299\) 23.1322 1.33777
\(300\) 0 0
\(301\) 5.02006 0.289352
\(302\) 0 0
\(303\) −7.48613 −0.430067
\(304\) 0 0
\(305\) −6.49935 −0.372152
\(306\) 0 0
\(307\) 6.19489 0.353561 0.176781 0.984250i \(-0.443432\pi\)
0.176781 + 0.984250i \(0.443432\pi\)
\(308\) 0 0
\(309\) 34.1394 1.94212
\(310\) 0 0
\(311\) 27.2078 1.54281 0.771406 0.636344i \(-0.219554\pi\)
0.771406 + 0.636344i \(0.219554\pi\)
\(312\) 0 0
\(313\) 25.7176 1.45365 0.726823 0.686824i \(-0.240996\pi\)
0.726823 + 0.686824i \(0.240996\pi\)
\(314\) 0 0
\(315\) 1.07098 0.0603430
\(316\) 0 0
\(317\) 0.151691 0.00851982 0.00425991 0.999991i \(-0.498644\pi\)
0.00425991 + 0.999991i \(0.498644\pi\)
\(318\) 0 0
\(319\) −3.45593 −0.193495
\(320\) 0 0
\(321\) 11.9557 0.667303
\(322\) 0 0
\(323\) 1.75220 0.0974950
\(324\) 0 0
\(325\) 21.2298 1.17762
\(326\) 0 0
\(327\) −4.75891 −0.263168
\(328\) 0 0
\(329\) −18.9295 −1.04362
\(330\) 0 0
\(331\) 9.22563 0.507087 0.253543 0.967324i \(-0.418404\pi\)
0.253543 + 0.967324i \(0.418404\pi\)
\(332\) 0 0
\(333\) −1.00663 −0.0551630
\(334\) 0 0
\(335\) 5.61848 0.306970
\(336\) 0 0
\(337\) −10.3200 −0.562167 −0.281084 0.959683i \(-0.590694\pi\)
−0.281084 + 0.959683i \(0.590694\pi\)
\(338\) 0 0
\(339\) 20.7501 1.12699
\(340\) 0 0
\(341\) 8.83020 0.478182
\(342\) 0 0
\(343\) −18.5221 −1.00010
\(344\) 0 0
\(345\) −6.74985 −0.363400
\(346\) 0 0
\(347\) −25.5483 −1.37150 −0.685752 0.727836i \(-0.740526\pi\)
−0.685752 + 0.727836i \(0.740526\pi\)
\(348\) 0 0
\(349\) −28.3172 −1.51578 −0.757892 0.652380i \(-0.773771\pi\)
−0.757892 + 0.652380i \(0.773771\pi\)
\(350\) 0 0
\(351\) 19.1052 1.01976
\(352\) 0 0
\(353\) −3.73049 −0.198554 −0.0992769 0.995060i \(-0.531653\pi\)
−0.0992769 + 0.995060i \(0.531653\pi\)
\(354\) 0 0
\(355\) −7.71601 −0.409523
\(356\) 0 0
\(357\) 11.9127 0.630486
\(358\) 0 0
\(359\) 21.5508 1.13741 0.568704 0.822543i \(-0.307445\pi\)
0.568704 + 0.822543i \(0.307445\pi\)
\(360\) 0 0
\(361\) −18.7714 −0.987967
\(362\) 0 0
\(363\) −19.3069 −1.01335
\(364\) 0 0
\(365\) −1.73967 −0.0910582
\(366\) 0 0
\(367\) −11.7230 −0.611934 −0.305967 0.952042i \(-0.598980\pi\)
−0.305967 + 0.952042i \(0.598980\pi\)
\(368\) 0 0
\(369\) −10.0487 −0.523114
\(370\) 0 0
\(371\) 10.7825 0.559800
\(372\) 0 0
\(373\) −11.0782 −0.573608 −0.286804 0.957989i \(-0.592593\pi\)
−0.286804 + 0.957989i \(0.592593\pi\)
\(374\) 0 0
\(375\) −13.0385 −0.673307
\(376\) 0 0
\(377\) −14.2906 −0.736004
\(378\) 0 0
\(379\) 19.5312 1.00325 0.501626 0.865085i \(-0.332736\pi\)
0.501626 + 0.865085i \(0.332736\pi\)
\(380\) 0 0
\(381\) 18.1161 0.928116
\(382\) 0 0
\(383\) −9.11161 −0.465582 −0.232791 0.972527i \(-0.574786\pi\)
−0.232791 + 0.972527i \(0.574786\pi\)
\(384\) 0 0
\(385\) −1.27756 −0.0651107
\(386\) 0 0
\(387\) 2.91896 0.148379
\(388\) 0 0
\(389\) −27.0768 −1.37285 −0.686424 0.727202i \(-0.740820\pi\)
−0.686424 + 0.727202i \(0.740820\pi\)
\(390\) 0 0
\(391\) −18.0710 −0.913889
\(392\) 0 0
\(393\) −17.4314 −0.879296
\(394\) 0 0
\(395\) 0.640562 0.0322302
\(396\) 0 0
\(397\) 23.5084 1.17985 0.589927 0.807457i \(-0.299157\pi\)
0.589927 + 0.807457i \(0.299157\pi\)
\(398\) 0 0
\(399\) 1.55441 0.0778177
\(400\) 0 0
\(401\) 35.8354 1.78954 0.894768 0.446531i \(-0.147341\pi\)
0.894768 + 0.446531i \(0.147341\pi\)
\(402\) 0 0
\(403\) 36.5137 1.81888
\(404\) 0 0
\(405\) −7.53932 −0.374632
\(406\) 0 0
\(407\) 1.20080 0.0595214
\(408\) 0 0
\(409\) 29.5592 1.46161 0.730804 0.682587i \(-0.239145\pi\)
0.730804 + 0.682587i \(0.239145\pi\)
\(410\) 0 0
\(411\) −20.1706 −0.994943
\(412\) 0 0
\(413\) 4.86037 0.239163
\(414\) 0 0
\(415\) −1.17052 −0.0574585
\(416\) 0 0
\(417\) −33.7927 −1.65484
\(418\) 0 0
\(419\) −7.19483 −0.351491 −0.175745 0.984436i \(-0.556234\pi\)
−0.175745 + 0.984436i \(0.556234\pi\)
\(420\) 0 0
\(421\) −33.0736 −1.61191 −0.805954 0.591978i \(-0.798347\pi\)
−0.805954 + 0.591978i \(0.798347\pi\)
\(422\) 0 0
\(423\) −11.0068 −0.535167
\(424\) 0 0
\(425\) −16.5848 −0.804482
\(426\) 0 0
\(427\) −15.4361 −0.747008
\(428\) 0 0
\(429\) 10.5770 0.510665
\(430\) 0 0
\(431\) 19.4849 0.938553 0.469276 0.883051i \(-0.344515\pi\)
0.469276 + 0.883051i \(0.344515\pi\)
\(432\) 0 0
\(433\) 30.7444 1.47748 0.738740 0.673991i \(-0.235421\pi\)
0.738740 + 0.673991i \(0.235421\pi\)
\(434\) 0 0
\(435\) 4.16992 0.199932
\(436\) 0 0
\(437\) −2.35797 −0.112797
\(438\) 0 0
\(439\) −19.0872 −0.910983 −0.455491 0.890240i \(-0.650536\pi\)
−0.455491 + 0.890240i \(0.650536\pi\)
\(440\) 0 0
\(441\) −4.11312 −0.195863
\(442\) 0 0
\(443\) 7.77156 0.369238 0.184619 0.982810i \(-0.440895\pi\)
0.184619 + 0.982810i \(0.440895\pi\)
\(444\) 0 0
\(445\) 1.25894 0.0596796
\(446\) 0 0
\(447\) 18.3388 0.867396
\(448\) 0 0
\(449\) 29.9281 1.41239 0.706197 0.708015i \(-0.250409\pi\)
0.706197 + 0.708015i \(0.250409\pi\)
\(450\) 0 0
\(451\) 11.9870 0.564446
\(452\) 0 0
\(453\) 33.1968 1.55972
\(454\) 0 0
\(455\) −5.28285 −0.247664
\(456\) 0 0
\(457\) −6.17193 −0.288711 −0.144355 0.989526i \(-0.546111\pi\)
−0.144355 + 0.989526i \(0.546111\pi\)
\(458\) 0 0
\(459\) −14.9250 −0.696641
\(460\) 0 0
\(461\) −7.54136 −0.351236 −0.175618 0.984458i \(-0.556192\pi\)
−0.175618 + 0.984458i \(0.556192\pi\)
\(462\) 0 0
\(463\) −27.2246 −1.26523 −0.632616 0.774465i \(-0.718019\pi\)
−0.632616 + 0.774465i \(0.718019\pi\)
\(464\) 0 0
\(465\) −10.6545 −0.494091
\(466\) 0 0
\(467\) 7.15705 0.331189 0.165594 0.986194i \(-0.447046\pi\)
0.165594 + 0.986194i \(0.447046\pi\)
\(468\) 0 0
\(469\) 13.3441 0.616171
\(470\) 0 0
\(471\) 10.4871 0.483220
\(472\) 0 0
\(473\) −3.48200 −0.160103
\(474\) 0 0
\(475\) −2.16404 −0.0992932
\(476\) 0 0
\(477\) 6.26958 0.287064
\(478\) 0 0
\(479\) 2.80206 0.128029 0.0640147 0.997949i \(-0.479610\pi\)
0.0640147 + 0.997949i \(0.479610\pi\)
\(480\) 0 0
\(481\) 4.96542 0.226404
\(482\) 0 0
\(483\) −16.0311 −0.729440
\(484\) 0 0
\(485\) 8.57774 0.389495
\(486\) 0 0
\(487\) −28.0145 −1.26946 −0.634730 0.772734i \(-0.718889\pi\)
−0.634730 + 0.772734i \(0.718889\pi\)
\(488\) 0 0
\(489\) 39.3860 1.78110
\(490\) 0 0
\(491\) 23.9111 1.07909 0.539547 0.841955i \(-0.318595\pi\)
0.539547 + 0.841955i \(0.318595\pi\)
\(492\) 0 0
\(493\) 11.1639 0.502796
\(494\) 0 0
\(495\) −0.742852 −0.0333887
\(496\) 0 0
\(497\) −18.3257 −0.822022
\(498\) 0 0
\(499\) −25.9335 −1.16094 −0.580472 0.814280i \(-0.697132\pi\)
−0.580472 + 0.814280i \(0.697132\pi\)
\(500\) 0 0
\(501\) 9.54732 0.426543
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −2.59347 −0.115408
\(506\) 0 0
\(507\) 17.8970 0.794832
\(508\) 0 0
\(509\) −24.1748 −1.07153 −0.535764 0.844368i \(-0.679976\pi\)
−0.535764 + 0.844368i \(0.679976\pi\)
\(510\) 0 0
\(511\) −4.13175 −0.182778
\(512\) 0 0
\(513\) −1.94747 −0.0859830
\(514\) 0 0
\(515\) 11.8271 0.521166
\(516\) 0 0
\(517\) 13.1299 0.577450
\(518\) 0 0
\(519\) 4.49230 0.197190
\(520\) 0 0
\(521\) −3.71497 −0.162756 −0.0813779 0.996683i \(-0.525932\pi\)
−0.0813779 + 0.996683i \(0.525932\pi\)
\(522\) 0 0
\(523\) −2.17027 −0.0948991 −0.0474495 0.998874i \(-0.515109\pi\)
−0.0474495 + 0.998874i \(0.515109\pi\)
\(524\) 0 0
\(525\) −14.7127 −0.642114
\(526\) 0 0
\(527\) −28.5247 −1.24256
\(528\) 0 0
\(529\) 1.31843 0.0573229
\(530\) 0 0
\(531\) 2.82610 0.122642
\(532\) 0 0
\(533\) 49.5674 2.14700
\(534\) 0 0
\(535\) 4.14190 0.179070
\(536\) 0 0
\(537\) 2.30218 0.0993466
\(538\) 0 0
\(539\) 4.90650 0.211338
\(540\) 0 0
\(541\) −14.3982 −0.619025 −0.309513 0.950895i \(-0.600166\pi\)
−0.309513 + 0.950895i \(0.600166\pi\)
\(542\) 0 0
\(543\) −37.4608 −1.60760
\(544\) 0 0
\(545\) −1.64866 −0.0706208
\(546\) 0 0
\(547\) 10.3525 0.442643 0.221321 0.975201i \(-0.428963\pi\)
0.221321 + 0.975201i \(0.428963\pi\)
\(548\) 0 0
\(549\) −8.97549 −0.383064
\(550\) 0 0
\(551\) 1.45670 0.0620576
\(552\) 0 0
\(553\) 1.52135 0.0646945
\(554\) 0 0
\(555\) −1.44888 −0.0615017
\(556\) 0 0
\(557\) −28.3766 −1.20235 −0.601177 0.799116i \(-0.705301\pi\)
−0.601177 + 0.799116i \(0.705301\pi\)
\(558\) 0 0
\(559\) −14.3984 −0.608988
\(560\) 0 0
\(561\) −8.26284 −0.348857
\(562\) 0 0
\(563\) 33.5183 1.41263 0.706313 0.707900i \(-0.250357\pi\)
0.706313 + 0.707900i \(0.250357\pi\)
\(564\) 0 0
\(565\) 7.18860 0.302427
\(566\) 0 0
\(567\) −17.9061 −0.751985
\(568\) 0 0
\(569\) −31.3435 −1.31399 −0.656994 0.753896i \(-0.728172\pi\)
−0.656994 + 0.753896i \(0.728172\pi\)
\(570\) 0 0
\(571\) −32.7332 −1.36984 −0.684921 0.728617i \(-0.740163\pi\)
−0.684921 + 0.728617i \(0.740163\pi\)
\(572\) 0 0
\(573\) −13.7221 −0.573249
\(574\) 0 0
\(575\) 22.3185 0.930744
\(576\) 0 0
\(577\) 34.9784 1.45617 0.728085 0.685487i \(-0.240411\pi\)
0.728085 + 0.685487i \(0.240411\pi\)
\(578\) 0 0
\(579\) 15.2855 0.635243
\(580\) 0 0
\(581\) −2.78001 −0.115334
\(582\) 0 0
\(583\) −7.47893 −0.309746
\(584\) 0 0
\(585\) −3.07176 −0.127002
\(586\) 0 0
\(587\) −27.2112 −1.12313 −0.561563 0.827434i \(-0.689800\pi\)
−0.561563 + 0.827434i \(0.689800\pi\)
\(588\) 0 0
\(589\) −3.72200 −0.153362
\(590\) 0 0
\(591\) −30.8210 −1.26781
\(592\) 0 0
\(593\) −8.86207 −0.363921 −0.181961 0.983306i \(-0.558244\pi\)
−0.181961 + 0.983306i \(0.558244\pi\)
\(594\) 0 0
\(595\) 4.12699 0.169190
\(596\) 0 0
\(597\) 1.56287 0.0639641
\(598\) 0 0
\(599\) 33.0116 1.34882 0.674409 0.738358i \(-0.264398\pi\)
0.674409 + 0.738358i \(0.264398\pi\)
\(600\) 0 0
\(601\) −27.2290 −1.11069 −0.555347 0.831619i \(-0.687414\pi\)
−0.555347 + 0.831619i \(0.687414\pi\)
\(602\) 0 0
\(603\) 7.75902 0.315972
\(604\) 0 0
\(605\) −6.68860 −0.271930
\(606\) 0 0
\(607\) 18.8180 0.763798 0.381899 0.924204i \(-0.375270\pi\)
0.381899 + 0.924204i \(0.375270\pi\)
\(608\) 0 0
\(609\) 9.90368 0.401317
\(610\) 0 0
\(611\) 54.2932 2.19647
\(612\) 0 0
\(613\) 9.12383 0.368508 0.184254 0.982879i \(-0.441013\pi\)
0.184254 + 0.982879i \(0.441013\pi\)
\(614\) 0 0
\(615\) −14.4635 −0.583224
\(616\) 0 0
\(617\) 30.4208 1.22469 0.612347 0.790589i \(-0.290226\pi\)
0.612347 + 0.790589i \(0.290226\pi\)
\(618\) 0 0
\(619\) −8.07959 −0.324746 −0.162373 0.986729i \(-0.551915\pi\)
−0.162373 + 0.986729i \(0.551915\pi\)
\(620\) 0 0
\(621\) 20.0849 0.805978
\(622\) 0 0
\(623\) 2.99003 0.119793
\(624\) 0 0
\(625\) 18.1120 0.724481
\(626\) 0 0
\(627\) −1.07816 −0.0430577
\(628\) 0 0
\(629\) −3.87901 −0.154666
\(630\) 0 0
\(631\) 14.3458 0.571097 0.285549 0.958364i \(-0.407824\pi\)
0.285549 + 0.958364i \(0.407824\pi\)
\(632\) 0 0
\(633\) 7.22585 0.287202
\(634\) 0 0
\(635\) 6.27608 0.249059
\(636\) 0 0
\(637\) 20.2889 0.803874
\(638\) 0 0
\(639\) −10.6557 −0.421532
\(640\) 0 0
\(641\) −29.8780 −1.18011 −0.590055 0.807363i \(-0.700894\pi\)
−0.590055 + 0.807363i \(0.700894\pi\)
\(642\) 0 0
\(643\) −35.0867 −1.38369 −0.691843 0.722048i \(-0.743201\pi\)
−0.691843 + 0.722048i \(0.743201\pi\)
\(644\) 0 0
\(645\) 4.20138 0.165429
\(646\) 0 0
\(647\) 16.1457 0.634751 0.317376 0.948300i \(-0.397198\pi\)
0.317376 + 0.948300i \(0.397198\pi\)
\(648\) 0 0
\(649\) −3.37123 −0.132333
\(650\) 0 0
\(651\) −25.3048 −0.991772
\(652\) 0 0
\(653\) 3.36679 0.131753 0.0658764 0.997828i \(-0.479016\pi\)
0.0658764 + 0.997828i \(0.479016\pi\)
\(654\) 0 0
\(655\) −6.03886 −0.235958
\(656\) 0 0
\(657\) −2.40244 −0.0937283
\(658\) 0 0
\(659\) 2.72422 0.106120 0.0530602 0.998591i \(-0.483102\pi\)
0.0530602 + 0.998591i \(0.483102\pi\)
\(660\) 0 0
\(661\) −31.3598 −1.21975 −0.609877 0.792496i \(-0.708781\pi\)
−0.609877 + 0.792496i \(0.708781\pi\)
\(662\) 0 0
\(663\) −34.1676 −1.32696
\(664\) 0 0
\(665\) 0.538504 0.0208823
\(666\) 0 0
\(667\) −15.0234 −0.581709
\(668\) 0 0
\(669\) 32.8925 1.27170
\(670\) 0 0
\(671\) 10.7068 0.413331
\(672\) 0 0
\(673\) −38.8250 −1.49659 −0.748296 0.663365i \(-0.769128\pi\)
−0.748296 + 0.663365i \(0.769128\pi\)
\(674\) 0 0
\(675\) 18.4331 0.709490
\(676\) 0 0
\(677\) 43.3006 1.66418 0.832089 0.554642i \(-0.187145\pi\)
0.832089 + 0.554642i \(0.187145\pi\)
\(678\) 0 0
\(679\) 20.3724 0.781819
\(680\) 0 0
\(681\) 5.55878 0.213013
\(682\) 0 0
\(683\) −37.1515 −1.42156 −0.710782 0.703412i \(-0.751659\pi\)
−0.710782 + 0.703412i \(0.751659\pi\)
\(684\) 0 0
\(685\) −6.98784 −0.266992
\(686\) 0 0
\(687\) −50.6083 −1.93083
\(688\) 0 0
\(689\) −30.9261 −1.17819
\(690\) 0 0
\(691\) −47.0789 −1.79097 −0.895483 0.445096i \(-0.853169\pi\)
−0.895483 + 0.445096i \(0.853169\pi\)
\(692\) 0 0
\(693\) −1.76429 −0.0670200
\(694\) 0 0
\(695\) −11.7070 −0.444073
\(696\) 0 0
\(697\) −38.7223 −1.46671
\(698\) 0 0
\(699\) −43.3391 −1.63924
\(700\) 0 0
\(701\) −18.2836 −0.690564 −0.345282 0.938499i \(-0.612217\pi\)
−0.345282 + 0.938499i \(0.612217\pi\)
\(702\) 0 0
\(703\) −0.506147 −0.0190897
\(704\) 0 0
\(705\) −15.8425 −0.596662
\(706\) 0 0
\(707\) −6.15956 −0.231654
\(708\) 0 0
\(709\) 4.10860 0.154302 0.0771508 0.997019i \(-0.475418\pi\)
0.0771508 + 0.997019i \(0.475418\pi\)
\(710\) 0 0
\(711\) 0.884604 0.0331752
\(712\) 0 0
\(713\) 38.3862 1.43757
\(714\) 0 0
\(715\) 3.66428 0.137036
\(716\) 0 0
\(717\) −19.1157 −0.713889
\(718\) 0 0
\(719\) 4.33485 0.161663 0.0808314 0.996728i \(-0.474242\pi\)
0.0808314 + 0.996728i \(0.474242\pi\)
\(720\) 0 0
\(721\) 28.0898 1.04612
\(722\) 0 0
\(723\) −32.4492 −1.20680
\(724\) 0 0
\(725\) −13.7879 −0.512069
\(726\) 0 0
\(727\) 21.4778 0.796568 0.398284 0.917262i \(-0.369606\pi\)
0.398284 + 0.917262i \(0.369606\pi\)
\(728\) 0 0
\(729\) 13.8754 0.513902
\(730\) 0 0
\(731\) 11.2481 0.416026
\(732\) 0 0
\(733\) −18.2602 −0.674457 −0.337228 0.941423i \(-0.609489\pi\)
−0.337228 + 0.941423i \(0.609489\pi\)
\(734\) 0 0
\(735\) −5.92018 −0.218369
\(736\) 0 0
\(737\) −9.25566 −0.340937
\(738\) 0 0
\(739\) −3.24461 −0.119355 −0.0596775 0.998218i \(-0.519007\pi\)
−0.0596775 + 0.998218i \(0.519007\pi\)
\(740\) 0 0
\(741\) −4.45831 −0.163780
\(742\) 0 0
\(743\) −20.5402 −0.753547 −0.376773 0.926305i \(-0.622966\pi\)
−0.376773 + 0.926305i \(0.622966\pi\)
\(744\) 0 0
\(745\) 6.35323 0.232765
\(746\) 0 0
\(747\) −1.61646 −0.0591433
\(748\) 0 0
\(749\) 9.83713 0.359441
\(750\) 0 0
\(751\) −28.0632 −1.02404 −0.512021 0.858973i \(-0.671103\pi\)
−0.512021 + 0.858973i \(0.671103\pi\)
\(752\) 0 0
\(753\) 37.3237 1.36015
\(754\) 0 0
\(755\) 11.5006 0.418549
\(756\) 0 0
\(757\) −33.1412 −1.20454 −0.602268 0.798294i \(-0.705736\pi\)
−0.602268 + 0.798294i \(0.705736\pi\)
\(758\) 0 0
\(759\) 11.1194 0.403610
\(760\) 0 0
\(761\) 2.25043 0.0815781 0.0407890 0.999168i \(-0.487013\pi\)
0.0407890 + 0.999168i \(0.487013\pi\)
\(762\) 0 0
\(763\) −3.91561 −0.141755
\(764\) 0 0
\(765\) 2.39967 0.0867604
\(766\) 0 0
\(767\) −13.9404 −0.503358
\(768\) 0 0
\(769\) 49.3766 1.78056 0.890282 0.455409i \(-0.150507\pi\)
0.890282 + 0.455409i \(0.150507\pi\)
\(770\) 0 0
\(771\) 34.4461 1.24055
\(772\) 0 0
\(773\) 8.11729 0.291959 0.145979 0.989288i \(-0.453367\pi\)
0.145979 + 0.989288i \(0.453367\pi\)
\(774\) 0 0
\(775\) 35.2293 1.26547
\(776\) 0 0
\(777\) −3.44114 −0.123450
\(778\) 0 0
\(779\) −5.05262 −0.181029
\(780\) 0 0
\(781\) 12.7110 0.454837
\(782\) 0 0
\(783\) −12.4080 −0.443427
\(784\) 0 0
\(785\) 3.63312 0.129672
\(786\) 0 0
\(787\) −23.6961 −0.844676 −0.422338 0.906438i \(-0.638790\pi\)
−0.422338 + 0.906438i \(0.638790\pi\)
\(788\) 0 0
\(789\) −25.0136 −0.890509
\(790\) 0 0
\(791\) 17.0731 0.607051
\(792\) 0 0
\(793\) 44.2735 1.57220
\(794\) 0 0
\(795\) 9.02406 0.320051
\(796\) 0 0
\(797\) −14.1640 −0.501714 −0.250857 0.968024i \(-0.580712\pi\)
−0.250857 + 0.968024i \(0.580712\pi\)
\(798\) 0 0
\(799\) −42.4141 −1.50050
\(800\) 0 0
\(801\) 1.73858 0.0614296
\(802\) 0 0
\(803\) 2.86586 0.101134
\(804\) 0 0
\(805\) −5.55376 −0.195744
\(806\) 0 0
\(807\) −25.4977 −0.897563
\(808\) 0 0
\(809\) 52.5347 1.84702 0.923510 0.383574i \(-0.125307\pi\)
0.923510 + 0.383574i \(0.125307\pi\)
\(810\) 0 0
\(811\) 38.8247 1.36332 0.681660 0.731669i \(-0.261259\pi\)
0.681660 + 0.731669i \(0.261259\pi\)
\(812\) 0 0
\(813\) 14.7415 0.517007
\(814\) 0 0
\(815\) 13.6447 0.477955
\(816\) 0 0
\(817\) 1.46769 0.0513480
\(818\) 0 0
\(819\) −7.29552 −0.254926
\(820\) 0 0
\(821\) 20.5192 0.716127 0.358063 0.933697i \(-0.383437\pi\)
0.358063 + 0.933697i \(0.383437\pi\)
\(822\) 0 0
\(823\) −50.2425 −1.75134 −0.875672 0.482907i \(-0.839581\pi\)
−0.875672 + 0.482907i \(0.839581\pi\)
\(824\) 0 0
\(825\) 10.2050 0.355291
\(826\) 0 0
\(827\) −2.50670 −0.0871664 −0.0435832 0.999050i \(-0.513877\pi\)
−0.0435832 + 0.999050i \(0.513877\pi\)
\(828\) 0 0
\(829\) 48.4355 1.68223 0.841117 0.540852i \(-0.181898\pi\)
0.841117 + 0.540852i \(0.181898\pi\)
\(830\) 0 0
\(831\) −35.0845 −1.21707
\(832\) 0 0
\(833\) −15.8498 −0.549161
\(834\) 0 0
\(835\) 3.30754 0.114462
\(836\) 0 0
\(837\) 31.7036 1.09584
\(838\) 0 0
\(839\) −20.8801 −0.720861 −0.360430 0.932786i \(-0.617370\pi\)
−0.360430 + 0.932786i \(0.617370\pi\)
\(840\) 0 0
\(841\) −19.7188 −0.679960
\(842\) 0 0
\(843\) −3.43986 −0.118475
\(844\) 0 0
\(845\) 6.20017 0.213292
\(846\) 0 0
\(847\) −15.8856 −0.545836
\(848\) 0 0
\(849\) 50.0194 1.71666
\(850\) 0 0
\(851\) 5.22005 0.178941
\(852\) 0 0
\(853\) −22.0276 −0.754211 −0.377105 0.926170i \(-0.623081\pi\)
−0.377105 + 0.926170i \(0.623081\pi\)
\(854\) 0 0
\(855\) 0.313118 0.0107084
\(856\) 0 0
\(857\) 28.4292 0.971124 0.485562 0.874202i \(-0.338615\pi\)
0.485562 + 0.874202i \(0.338615\pi\)
\(858\) 0 0
\(859\) 36.9251 1.25987 0.629935 0.776648i \(-0.283082\pi\)
0.629935 + 0.776648i \(0.283082\pi\)
\(860\) 0 0
\(861\) −34.3512 −1.17069
\(862\) 0 0
\(863\) 49.4592 1.68361 0.841805 0.539782i \(-0.181493\pi\)
0.841805 + 0.539782i \(0.181493\pi\)
\(864\) 0 0
\(865\) 1.55630 0.0529157
\(866\) 0 0
\(867\) −7.09903 −0.241096
\(868\) 0 0
\(869\) −1.05524 −0.0357964
\(870\) 0 0
\(871\) −38.2731 −1.29683
\(872\) 0 0
\(873\) 11.8457 0.400916
\(874\) 0 0
\(875\) −10.7281 −0.362675
\(876\) 0 0
\(877\) −20.1086 −0.679019 −0.339510 0.940603i \(-0.610261\pi\)
−0.339510 + 0.940603i \(0.610261\pi\)
\(878\) 0 0
\(879\) 28.9847 0.977630
\(880\) 0 0
\(881\) 41.6742 1.40404 0.702020 0.712157i \(-0.252282\pi\)
0.702020 + 0.712157i \(0.252282\pi\)
\(882\) 0 0
\(883\) −21.4623 −0.722265 −0.361132 0.932515i \(-0.617610\pi\)
−0.361132 + 0.932515i \(0.617610\pi\)
\(884\) 0 0
\(885\) 4.06773 0.136735
\(886\) 0 0
\(887\) −51.6761 −1.73512 −0.867558 0.497337i \(-0.834311\pi\)
−0.867558 + 0.497337i \(0.834311\pi\)
\(888\) 0 0
\(889\) 14.9059 0.499927
\(890\) 0 0
\(891\) 12.4200 0.416085
\(892\) 0 0
\(893\) −5.53434 −0.185200
\(894\) 0 0
\(895\) 0.797561 0.0266595
\(896\) 0 0
\(897\) 45.9799 1.53523
\(898\) 0 0
\(899\) −23.7142 −0.790912
\(900\) 0 0
\(901\) 24.1596 0.804873
\(902\) 0 0
\(903\) 9.97839 0.332060
\(904\) 0 0
\(905\) −12.9778 −0.431397
\(906\) 0 0
\(907\) 32.5649 1.08130 0.540650 0.841248i \(-0.318178\pi\)
0.540650 + 0.841248i \(0.318178\pi\)
\(908\) 0 0
\(909\) −3.58153 −0.118792
\(910\) 0 0
\(911\) −38.1120 −1.26271 −0.631354 0.775495i \(-0.717500\pi\)
−0.631354 + 0.775495i \(0.717500\pi\)
\(912\) 0 0
\(913\) 1.92826 0.0638163
\(914\) 0 0
\(915\) −12.9188 −0.427082
\(916\) 0 0
\(917\) −14.3425 −0.473630
\(918\) 0 0
\(919\) −30.5828 −1.00883 −0.504417 0.863460i \(-0.668293\pi\)
−0.504417 + 0.863460i \(0.668293\pi\)
\(920\) 0 0
\(921\) 12.3136 0.405747
\(922\) 0 0
\(923\) 52.5614 1.73008
\(924\) 0 0
\(925\) 4.79075 0.157519
\(926\) 0 0
\(927\) 16.3330 0.536448
\(928\) 0 0
\(929\) 2.30989 0.0757851 0.0378926 0.999282i \(-0.487936\pi\)
0.0378926 + 0.999282i \(0.487936\pi\)
\(930\) 0 0
\(931\) −2.06813 −0.0677802
\(932\) 0 0
\(933\) 54.0810 1.77053
\(934\) 0 0
\(935\) −2.86255 −0.0936154
\(936\) 0 0
\(937\) −22.8337 −0.745945 −0.372973 0.927842i \(-0.621662\pi\)
−0.372973 + 0.927842i \(0.621662\pi\)
\(938\) 0 0
\(939\) 51.1190 1.66821
\(940\) 0 0
\(941\) 34.0397 1.10966 0.554831 0.831963i \(-0.312783\pi\)
0.554831 + 0.831963i \(0.312783\pi\)
\(942\) 0 0
\(943\) 52.1092 1.69691
\(944\) 0 0
\(945\) −4.58691 −0.149212
\(946\) 0 0
\(947\) 19.1614 0.622661 0.311331 0.950302i \(-0.399225\pi\)
0.311331 + 0.950302i \(0.399225\pi\)
\(948\) 0 0
\(949\) 11.8506 0.384686
\(950\) 0 0
\(951\) 0.301517 0.00977736
\(952\) 0 0
\(953\) 19.3222 0.625908 0.312954 0.949768i \(-0.398681\pi\)
0.312954 + 0.949768i \(0.398681\pi\)
\(954\) 0 0
\(955\) −4.75384 −0.153831
\(956\) 0 0
\(957\) −6.86936 −0.222055
\(958\) 0 0
\(959\) −16.5963 −0.535923
\(960\) 0 0
\(961\) 29.5918 0.954574
\(962\) 0 0
\(963\) 5.71988 0.184321
\(964\) 0 0
\(965\) 5.29545 0.170467
\(966\) 0 0
\(967\) 59.2613 1.90572 0.952858 0.303416i \(-0.0981272\pi\)
0.952858 + 0.303416i \(0.0981272\pi\)
\(968\) 0 0
\(969\) 3.48285 0.111885
\(970\) 0 0
\(971\) −39.7605 −1.27598 −0.637988 0.770047i \(-0.720233\pi\)
−0.637988 + 0.770047i \(0.720233\pi\)
\(972\) 0 0
\(973\) −27.8046 −0.891373
\(974\) 0 0
\(975\) 42.1985 1.35143
\(976\) 0 0
\(977\) 23.7820 0.760855 0.380427 0.924811i \(-0.375777\pi\)
0.380427 + 0.924811i \(0.375777\pi\)
\(978\) 0 0
\(979\) −2.07393 −0.0662832
\(980\) 0 0
\(981\) −2.27677 −0.0726916
\(982\) 0 0
\(983\) 28.7374 0.916581 0.458290 0.888802i \(-0.348462\pi\)
0.458290 + 0.888802i \(0.348462\pi\)
\(984\) 0 0
\(985\) −10.6775 −0.340214
\(986\) 0 0
\(987\) −37.6263 −1.19766
\(988\) 0 0
\(989\) −15.1368 −0.481321
\(990\) 0 0
\(991\) −24.1020 −0.765626 −0.382813 0.923826i \(-0.625045\pi\)
−0.382813 + 0.923826i \(0.625045\pi\)
\(992\) 0 0
\(993\) 18.3378 0.581933
\(994\) 0 0
\(995\) 0.541436 0.0171647
\(996\) 0 0
\(997\) −15.6418 −0.495381 −0.247690 0.968839i \(-0.579672\pi\)
−0.247690 + 0.968839i \(0.579672\pi\)
\(998\) 0 0
\(999\) 4.31130 0.136403
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 \(a_p\))