Properties

Label 9450.2.a.dj.1.1
Level 9450
Weight 2
Character 9450.1
Self dual Yes
Analytic conductor 75.459
Analytic rank 1
Dimension 1
CM No
Inner twists 1

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 9450 = 2 \cdot 3^{3} \cdot 5^{2} \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 9450.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(75.4586299101\)
Analytic rank: \(1\)
Dimension: \(1\)
Coefficient field: \(\mathbb{Q}\)
Coefficient ring: \(\mathbb{Z}\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(0\)
Character \(\chi\) = 9450.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{4}\) \(+1.00000 q^{7}\) \(+1.00000 q^{8}\) \(-1.00000 q^{11}\) \(-3.00000 q^{13}\) \(+1.00000 q^{14}\) \(+1.00000 q^{16}\) \(+8.00000 q^{17}\) \(-3.00000 q^{19}\) \(-1.00000 q^{22}\) \(-6.00000 q^{23}\) \(-3.00000 q^{26}\) \(+1.00000 q^{28}\) \(-6.00000 q^{29}\) \(-4.00000 q^{31}\) \(+1.00000 q^{32}\) \(+8.00000 q^{34}\) \(-2.00000 q^{37}\) \(-3.00000 q^{38}\) \(-11.0000 q^{41}\) \(-1.00000 q^{43}\) \(-1.00000 q^{44}\) \(-6.00000 q^{46}\) \(-1.00000 q^{47}\) \(+1.00000 q^{49}\) \(-3.00000 q^{52}\) \(+1.00000 q^{53}\) \(+1.00000 q^{56}\) \(-6.00000 q^{58}\) \(-10.0000 q^{59}\) \(+4.00000 q^{61}\) \(-4.00000 q^{62}\) \(+1.00000 q^{64}\) \(+3.00000 q^{67}\) \(+8.00000 q^{68}\) \(-8.00000 q^{71}\) \(-11.0000 q^{73}\) \(-2.00000 q^{74}\) \(-3.00000 q^{76}\) \(-1.00000 q^{77}\) \(+4.00000 q^{79}\) \(-11.0000 q^{82}\) \(+11.0000 q^{83}\) \(-1.00000 q^{86}\) \(-1.00000 q^{88}\) \(-7.00000 q^{89}\) \(-3.00000 q^{91}\) \(-6.00000 q^{92}\) \(-1.00000 q^{94}\) \(-2.00000 q^{97}\) \(+1.00000 q^{98}\) \(+O(q^{100})\)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) 0 0
\(4\) 1.00000 0.500000
\(5\) 0 0
\(6\) 0 0
\(7\) 1.00000 0.377964
\(8\) 1.00000 0.353553
\(9\) 0 0
\(10\) 0 0
\(11\) −1.00000 −0.301511 −0.150756 0.988571i \(-0.548171\pi\)
−0.150756 + 0.988571i \(0.548171\pi\)
\(12\) 0 0
\(13\) −3.00000 −0.832050 −0.416025 0.909353i \(-0.636577\pi\)
−0.416025 + 0.909353i \(0.636577\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 8.00000 1.94029 0.970143 0.242536i \(-0.0779791\pi\)
0.970143 + 0.242536i \(0.0779791\pi\)
\(18\) 0 0
\(19\) −3.00000 −0.688247 −0.344124 0.938924i \(-0.611824\pi\)
−0.344124 + 0.938924i \(0.611824\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) −6.00000 −1.25109 −0.625543 0.780189i \(-0.715123\pi\)
−0.625543 + 0.780189i \(0.715123\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −3.00000 −0.588348
\(27\) 0 0
\(28\) 1.00000 0.188982
\(29\) −6.00000 −1.11417 −0.557086 0.830455i \(-0.688081\pi\)
−0.557086 + 0.830455i \(0.688081\pi\)
\(30\) 0 0
\(31\) −4.00000 −0.718421 −0.359211 0.933257i \(-0.616954\pi\)
−0.359211 + 0.933257i \(0.616954\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) 8.00000 1.37199
\(35\) 0 0
\(36\) 0 0
\(37\) −2.00000 −0.328798 −0.164399 0.986394i \(-0.552568\pi\)
−0.164399 + 0.986394i \(0.552568\pi\)
\(38\) −3.00000 −0.486664
\(39\) 0 0
\(40\) 0 0
\(41\) −11.0000 −1.71791 −0.858956 0.512050i \(-0.828886\pi\)
−0.858956 + 0.512050i \(0.828886\pi\)
\(42\) 0 0
\(43\) −1.00000 −0.152499 −0.0762493 0.997089i \(-0.524294\pi\)
−0.0762493 + 0.997089i \(0.524294\pi\)
\(44\) −1.00000 −0.150756
\(45\) 0 0
\(46\) −6.00000 −0.884652
\(47\) −1.00000 −0.145865 −0.0729325 0.997337i \(-0.523236\pi\)
−0.0729325 + 0.997337i \(0.523236\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) −3.00000 −0.416025
\(53\) 1.00000 0.137361 0.0686803 0.997639i \(-0.478121\pi\)
0.0686803 + 0.997639i \(0.478121\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) −6.00000 −0.787839
\(59\) −10.0000 −1.30189 −0.650945 0.759125i \(-0.725627\pi\)
−0.650945 + 0.759125i \(0.725627\pi\)
\(60\) 0 0
\(61\) 4.00000 0.512148 0.256074 0.966657i \(-0.417571\pi\)
0.256074 + 0.966657i \(0.417571\pi\)
\(62\) −4.00000 −0.508001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 3.00000 0.366508 0.183254 0.983066i \(-0.441337\pi\)
0.183254 + 0.983066i \(0.441337\pi\)
\(68\) 8.00000 0.970143
\(69\) 0 0
\(70\) 0 0
\(71\) −8.00000 −0.949425 −0.474713 0.880141i \(-0.657448\pi\)
−0.474713 + 0.880141i \(0.657448\pi\)
\(72\) 0 0
\(73\) −11.0000 −1.28745 −0.643726 0.765256i \(-0.722612\pi\)
−0.643726 + 0.765256i \(0.722612\pi\)
\(74\) −2.00000 −0.232495
\(75\) 0 0
\(76\) −3.00000 −0.344124
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 4.00000 0.450035 0.225018 0.974355i \(-0.427756\pi\)
0.225018 + 0.974355i \(0.427756\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −11.0000 −1.21475
\(83\) 11.0000 1.20741 0.603703 0.797209i \(-0.293691\pi\)
0.603703 + 0.797209i \(0.293691\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −1.00000 −0.107833
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) −7.00000 −0.741999 −0.370999 0.928633i \(-0.620985\pi\)
−0.370999 + 0.928633i \(0.620985\pi\)
\(90\) 0 0
\(91\) −3.00000 −0.314485
\(92\) −6.00000 −0.625543
\(93\) 0 0
\(94\) −1.00000 −0.103142
\(95\) 0 0
\(96\) 0 0
\(97\) −2.00000 −0.203069 −0.101535 0.994832i \(-0.532375\pi\)
−0.101535 + 0.994832i \(0.532375\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) 15.0000 1.49256 0.746278 0.665635i \(-0.231839\pi\)
0.746278 + 0.665635i \(0.231839\pi\)
\(102\) 0 0
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −3.00000 −0.294174
\(105\) 0 0
\(106\) 1.00000 0.0971286
\(107\) 12.0000 1.16008 0.580042 0.814587i \(-0.303036\pi\)
0.580042 + 0.814587i \(0.303036\pi\)
\(108\) 0 0
\(109\) −9.00000 −0.862044 −0.431022 0.902342i \(-0.641847\pi\)
−0.431022 + 0.902342i \(0.641847\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) 1.00000 0.0944911
\(113\) −13.0000 −1.22294 −0.611469 0.791269i \(-0.709421\pi\)
−0.611469 + 0.791269i \(0.709421\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) −10.0000 −0.920575
\(119\) 8.00000 0.733359
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) 4.00000 0.362143
\(123\) 0 0
\(124\) −4.00000 −0.359211
\(125\) 0 0
\(126\) 0 0
\(127\) 5.00000 0.443678 0.221839 0.975083i \(-0.428794\pi\)
0.221839 + 0.975083i \(0.428794\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 4.00000 0.349482 0.174741 0.984614i \(-0.444091\pi\)
0.174741 + 0.984614i \(0.444091\pi\)
\(132\) 0 0
\(133\) −3.00000 −0.260133
\(134\) 3.00000 0.259161
\(135\) 0 0
\(136\) 8.00000 0.685994
\(137\) −3.00000 −0.256307 −0.128154 0.991754i \(-0.540905\pi\)
−0.128154 + 0.991754i \(0.540905\pi\)
\(138\) 0 0
\(139\) −20.0000 −1.69638 −0.848189 0.529694i \(-0.822307\pi\)
−0.848189 + 0.529694i \(0.822307\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −8.00000 −0.671345
\(143\) 3.00000 0.250873
\(144\) 0 0
\(145\) 0 0
\(146\) −11.0000 −0.910366
\(147\) 0 0
\(148\) −2.00000 −0.164399
\(149\) 18.0000 1.47462 0.737309 0.675556i \(-0.236096\pi\)
0.737309 + 0.675556i \(0.236096\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) −3.00000 −0.243332
\(153\) 0 0
\(154\) −1.00000 −0.0805823
\(155\) 0 0
\(156\) 0 0
\(157\) −22.0000 −1.75579 −0.877896 0.478852i \(-0.841053\pi\)
−0.877896 + 0.478852i \(0.841053\pi\)
\(158\) 4.00000 0.318223
\(159\) 0 0
\(160\) 0 0
\(161\) −6.00000 −0.472866
\(162\) 0 0
\(163\) 16.0000 1.25322 0.626608 0.779334i \(-0.284443\pi\)
0.626608 + 0.779334i \(0.284443\pi\)
\(164\) −11.0000 −0.858956
\(165\) 0 0
\(166\) 11.0000 0.853766
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) −4.00000 −0.307692
\(170\) 0 0
\(171\) 0 0
\(172\) −1.00000 −0.0762493
\(173\) 2.00000 0.152057 0.0760286 0.997106i \(-0.475776\pi\)
0.0760286 + 0.997106i \(0.475776\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −1.00000 −0.0753778
\(177\) 0 0
\(178\) −7.00000 −0.524672
\(179\) −3.00000 −0.224231 −0.112115 0.993695i \(-0.535763\pi\)
−0.112115 + 0.993695i \(0.535763\pi\)
\(180\) 0 0
\(181\) −14.0000 −1.04061 −0.520306 0.853980i \(-0.674182\pi\)
−0.520306 + 0.853980i \(0.674182\pi\)
\(182\) −3.00000 −0.222375
\(183\) 0 0
\(184\) −6.00000 −0.442326
\(185\) 0 0
\(186\) 0 0
\(187\) −8.00000 −0.585018
\(188\) −1.00000 −0.0729325
\(189\) 0 0
\(190\) 0 0
\(191\) 3.00000 0.217072 0.108536 0.994092i \(-0.465384\pi\)
0.108536 + 0.994092i \(0.465384\pi\)
\(192\) 0 0
\(193\) 10.0000 0.719816 0.359908 0.932988i \(-0.382808\pi\)
0.359908 + 0.932988i \(0.382808\pi\)
\(194\) −2.00000 −0.143592
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 11.0000 0.783718 0.391859 0.920025i \(-0.371832\pi\)
0.391859 + 0.920025i \(0.371832\pi\)
\(198\) 0 0
\(199\) 23.0000 1.63043 0.815213 0.579161i \(-0.196620\pi\)
0.815213 + 0.579161i \(0.196620\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 15.0000 1.05540
\(203\) −6.00000 −0.421117
\(204\) 0 0
\(205\) 0 0
\(206\) 8.00000 0.557386
\(207\) 0 0
\(208\) −3.00000 −0.208013
\(209\) 3.00000 0.207514
\(210\) 0 0
\(211\) −26.0000 −1.78991 −0.894957 0.446153i \(-0.852794\pi\)
−0.894957 + 0.446153i \(0.852794\pi\)
\(212\) 1.00000 0.0686803
\(213\) 0 0
\(214\) 12.0000 0.820303
\(215\) 0 0
\(216\) 0 0
\(217\) −4.00000 −0.271538
\(218\) −9.00000 −0.609557
\(219\) 0 0
\(220\) 0 0
\(221\) −24.0000 −1.61441
\(222\) 0 0
\(223\) 2.00000 0.133930 0.0669650 0.997755i \(-0.478668\pi\)
0.0669650 + 0.997755i \(0.478668\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) −13.0000 −0.864747
\(227\) 11.0000 0.730096 0.365048 0.930989i \(-0.381053\pi\)
0.365048 + 0.930989i \(0.381053\pi\)
\(228\) 0 0
\(229\) −14.0000 −0.925146 −0.462573 0.886581i \(-0.653074\pi\)
−0.462573 + 0.886581i \(0.653074\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) −6.00000 −0.393919
\(233\) −9.00000 −0.589610 −0.294805 0.955557i \(-0.595255\pi\)
−0.294805 + 0.955557i \(0.595255\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −10.0000 −0.650945
\(237\) 0 0
\(238\) 8.00000 0.518563
\(239\) 8.00000 0.517477 0.258738 0.965947i \(-0.416693\pi\)
0.258738 + 0.965947i \(0.416693\pi\)
\(240\) 0 0
\(241\) −20.0000 −1.28831 −0.644157 0.764894i \(-0.722792\pi\)
−0.644157 + 0.764894i \(0.722792\pi\)
\(242\) −10.0000 −0.642824
\(243\) 0 0
\(244\) 4.00000 0.256074
\(245\) 0 0
\(246\) 0 0
\(247\) 9.00000 0.572656
\(248\) −4.00000 −0.254000
\(249\) 0 0
\(250\) 0 0
\(251\) −30.0000 −1.89358 −0.946792 0.321847i \(-0.895696\pi\)
−0.946792 + 0.321847i \(0.895696\pi\)
\(252\) 0 0
\(253\) 6.00000 0.377217
\(254\) 5.00000 0.313728
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) 20.0000 1.24757 0.623783 0.781598i \(-0.285595\pi\)
0.623783 + 0.781598i \(0.285595\pi\)
\(258\) 0 0
\(259\) −2.00000 −0.124274
\(260\) 0 0
\(261\) 0 0
\(262\) 4.00000 0.247121
\(263\) −16.0000 −0.986602 −0.493301 0.869859i \(-0.664210\pi\)
−0.493301 + 0.869859i \(0.664210\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −3.00000 −0.183942
\(267\) 0 0
\(268\) 3.00000 0.183254
\(269\) 6.00000 0.365826 0.182913 0.983129i \(-0.441447\pi\)
0.182913 + 0.983129i \(0.441447\pi\)
\(270\) 0 0
\(271\) −27.0000 −1.64013 −0.820067 0.572268i \(-0.806064\pi\)
−0.820067 + 0.572268i \(0.806064\pi\)
\(272\) 8.00000 0.485071
\(273\) 0 0
\(274\) −3.00000 −0.181237
\(275\) 0 0
\(276\) 0 0
\(277\) −18.0000 −1.08152 −0.540758 0.841178i \(-0.681862\pi\)
−0.540758 + 0.841178i \(0.681862\pi\)
\(278\) −20.0000 −1.19952
\(279\) 0 0
\(280\) 0 0
\(281\) 10.0000 0.596550 0.298275 0.954480i \(-0.403589\pi\)
0.298275 + 0.954480i \(0.403589\pi\)
\(282\) 0 0
\(283\) 22.0000 1.30776 0.653882 0.756596i \(-0.273139\pi\)
0.653882 + 0.756596i \(0.273139\pi\)
\(284\) −8.00000 −0.474713
\(285\) 0 0
\(286\) 3.00000 0.177394
\(287\) −11.0000 −0.649309
\(288\) 0 0
\(289\) 47.0000 2.76471
\(290\) 0 0
\(291\) 0 0
\(292\) −11.0000 −0.643726
\(293\) −14.0000 −0.817889 −0.408944 0.912559i \(-0.634103\pi\)
−0.408944 + 0.912559i \(0.634103\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −2.00000 −0.116248
\(297\) 0 0
\(298\) 18.0000 1.04271
\(299\) 18.0000 1.04097
\(300\) 0 0
\(301\) −1.00000 −0.0576390
\(302\) −10.0000 −0.575435
\(303\) 0 0
\(304\) −3.00000 −0.172062
\(305\) 0 0
\(306\) 0 0
\(307\) −28.0000 −1.59804 −0.799022 0.601302i \(-0.794649\pi\)
−0.799022 + 0.601302i \(0.794649\pi\)
\(308\) −1.00000 −0.0569803
\(309\) 0 0
\(310\) 0 0
\(311\) 18.0000 1.02069 0.510343 0.859971i \(-0.329518\pi\)
0.510343 + 0.859971i \(0.329518\pi\)
\(312\) 0 0
\(313\) −29.0000 −1.63918 −0.819588 0.572953i \(-0.805798\pi\)
−0.819588 + 0.572953i \(0.805798\pi\)
\(314\) −22.0000 −1.24153
\(315\) 0 0
\(316\) 4.00000 0.225018
\(317\) −23.0000 −1.29181 −0.645904 0.763418i \(-0.723520\pi\)
−0.645904 + 0.763418i \(0.723520\pi\)
\(318\) 0 0
\(319\) 6.00000 0.335936
\(320\) 0 0
\(321\) 0 0
\(322\) −6.00000 −0.334367
\(323\) −24.0000 −1.33540
\(324\) 0 0
\(325\) 0 0
\(326\) 16.0000 0.886158
\(327\) 0 0
\(328\) −11.0000 −0.607373
\(329\) −1.00000 −0.0551318
\(330\) 0 0
\(331\) 34.0000 1.86881 0.934405 0.356214i \(-0.115932\pi\)
0.934405 + 0.356214i \(0.115932\pi\)
\(332\) 11.0000 0.603703
\(333\) 0 0
\(334\) 12.0000 0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) 8.00000 0.435788 0.217894 0.975972i \(-0.430081\pi\)
0.217894 + 0.975972i \(0.430081\pi\)
\(338\) −4.00000 −0.217571
\(339\) 0 0
\(340\) 0 0
\(341\) 4.00000 0.216612
\(342\) 0 0
\(343\) 1.00000 0.0539949
\(344\) −1.00000 −0.0539164
\(345\) 0 0
\(346\) 2.00000 0.107521
\(347\) −2.00000 −0.107366 −0.0536828 0.998558i \(-0.517096\pi\)
−0.0536828 + 0.998558i \(0.517096\pi\)
\(348\) 0 0
\(349\) 10.0000 0.535288 0.267644 0.963518i \(-0.413755\pi\)
0.267644 + 0.963518i \(0.413755\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.00000 −0.0533002
\(353\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −7.00000 −0.370999
\(357\) 0 0
\(358\) −3.00000 −0.158555
\(359\) 1.00000 0.0527780 0.0263890 0.999652i \(-0.491599\pi\)
0.0263890 + 0.999652i \(0.491599\pi\)
\(360\) 0 0
\(361\) −10.0000 −0.526316
\(362\) −14.0000 −0.735824
\(363\) 0 0
\(364\) −3.00000 −0.157243
\(365\) 0 0
\(366\) 0 0
\(367\) −10.0000 −0.521996 −0.260998 0.965339i \(-0.584052\pi\)
−0.260998 + 0.965339i \(0.584052\pi\)
\(368\) −6.00000 −0.312772
\(369\) 0 0
\(370\) 0 0
\(371\) 1.00000 0.0519174
\(372\) 0 0
\(373\) −32.0000 −1.65690 −0.828449 0.560065i \(-0.810776\pi\)
−0.828449 + 0.560065i \(0.810776\pi\)
\(374\) −8.00000 −0.413670
\(375\) 0 0
\(376\) −1.00000 −0.0515711
\(377\) 18.0000 0.927047
\(378\) 0 0
\(379\) 12.0000 0.616399 0.308199 0.951322i \(-0.400274\pi\)
0.308199 + 0.951322i \(0.400274\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 3.00000 0.153493
\(383\) −24.0000 −1.22634 −0.613171 0.789950i \(-0.710106\pi\)
−0.613171 + 0.789950i \(0.710106\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 10.0000 0.508987
\(387\) 0 0
\(388\) −2.00000 −0.101535
\(389\) −26.0000 −1.31825 −0.659126 0.752032i \(-0.729074\pi\)
−0.659126 + 0.752032i \(0.729074\pi\)
\(390\) 0 0
\(391\) −48.0000 −2.42746
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) 11.0000 0.554172
\(395\) 0 0
\(396\) 0 0
\(397\) 14.0000 0.702640 0.351320 0.936255i \(-0.385733\pi\)
0.351320 + 0.936255i \(0.385733\pi\)
\(398\) 23.0000 1.15289
\(399\) 0 0
\(400\) 0 0
\(401\) 20.0000 0.998752 0.499376 0.866385i \(-0.333563\pi\)
0.499376 + 0.866385i \(0.333563\pi\)
\(402\) 0 0
\(403\) 12.0000 0.597763
\(404\) 15.0000 0.746278
\(405\) 0 0
\(406\) −6.00000 −0.297775
\(407\) 2.00000 0.0991363
\(408\) 0 0
\(409\) −18.0000 −0.890043 −0.445021 0.895520i \(-0.646804\pi\)
−0.445021 + 0.895520i \(0.646804\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) 8.00000 0.394132
\(413\) −10.0000 −0.492068
\(414\) 0 0
\(415\) 0 0
\(416\) −3.00000 −0.147087
\(417\) 0 0
\(418\) 3.00000 0.146735
\(419\) 18.0000 0.879358 0.439679 0.898155i \(-0.355092\pi\)
0.439679 + 0.898155i \(0.355092\pi\)
\(420\) 0 0
\(421\) −1.00000 −0.0487370 −0.0243685 0.999703i \(-0.507758\pi\)
−0.0243685 + 0.999703i \(0.507758\pi\)
\(422\) −26.0000 −1.26566
\(423\) 0 0
\(424\) 1.00000 0.0485643
\(425\) 0 0
\(426\) 0 0
\(427\) 4.00000 0.193574
\(428\) 12.0000 0.580042
\(429\) 0 0
\(430\) 0 0
\(431\) −9.00000 −0.433515 −0.216757 0.976226i \(-0.569548\pi\)
−0.216757 + 0.976226i \(0.569548\pi\)
\(432\) 0 0
\(433\) 7.00000 0.336399 0.168199 0.985753i \(-0.446205\pi\)
0.168199 + 0.985753i \(0.446205\pi\)
\(434\) −4.00000 −0.192006
\(435\) 0 0
\(436\) −9.00000 −0.431022
\(437\) 18.0000 0.861057
\(438\) 0 0
\(439\) −11.0000 −0.525001 −0.262501 0.964932i \(-0.584547\pi\)
−0.262501 + 0.964932i \(0.584547\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −24.0000 −1.14156
\(443\) 16.0000 0.760183 0.380091 0.924949i \(-0.375893\pi\)
0.380091 + 0.924949i \(0.375893\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 2.00000 0.0947027
\(447\) 0 0
\(448\) 1.00000 0.0472456
\(449\) 36.0000 1.69895 0.849473 0.527633i \(-0.176920\pi\)
0.849473 + 0.527633i \(0.176920\pi\)
\(450\) 0 0
\(451\) 11.0000 0.517970
\(452\) −13.0000 −0.611469
\(453\) 0 0
\(454\) 11.0000 0.516256
\(455\) 0 0
\(456\) 0 0
\(457\) −16.0000 −0.748448 −0.374224 0.927338i \(-0.622091\pi\)
−0.374224 + 0.927338i \(0.622091\pi\)
\(458\) −14.0000 −0.654177
\(459\) 0 0
\(460\) 0 0
\(461\) −1.00000 −0.0465746 −0.0232873 0.999729i \(-0.507413\pi\)
−0.0232873 + 0.999729i \(0.507413\pi\)
\(462\) 0 0
\(463\) −17.0000 −0.790057 −0.395029 0.918669i \(-0.629265\pi\)
−0.395029 + 0.918669i \(0.629265\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −9.00000 −0.416917
\(467\) −28.0000 −1.29569 −0.647843 0.761774i \(-0.724329\pi\)
−0.647843 + 0.761774i \(0.724329\pi\)
\(468\) 0 0
\(469\) 3.00000 0.138527
\(470\) 0 0
\(471\) 0 0
\(472\) −10.0000 −0.460287
\(473\) 1.00000 0.0459800
\(474\) 0 0
\(475\) 0 0
\(476\) 8.00000 0.366679
\(477\) 0 0
\(478\) 8.00000 0.365911
\(479\) 12.0000 0.548294 0.274147 0.961688i \(-0.411605\pi\)
0.274147 + 0.961688i \(0.411605\pi\)
\(480\) 0 0
\(481\) 6.00000 0.273576
\(482\) −20.0000 −0.910975
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) 0 0
\(486\) 0 0
\(487\) −11.0000 −0.498458 −0.249229 0.968445i \(-0.580177\pi\)
−0.249229 + 0.968445i \(0.580177\pi\)
\(488\) 4.00000 0.181071
\(489\) 0 0
\(490\) 0 0
\(491\) 36.0000 1.62466 0.812329 0.583200i \(-0.198200\pi\)
0.812329 + 0.583200i \(0.198200\pi\)
\(492\) 0 0
\(493\) −48.0000 −2.16181
\(494\) 9.00000 0.404929
\(495\) 0 0
\(496\) −4.00000 −0.179605
\(497\) −8.00000 −0.358849
\(498\) 0 0
\(499\) 18.0000 0.805791 0.402895 0.915246i \(-0.368004\pi\)
0.402895 + 0.915246i \(0.368004\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −30.0000 −1.33897
\(503\) 21.0000 0.936344 0.468172 0.883637i \(-0.344913\pi\)
0.468172 + 0.883637i \(0.344913\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) 6.00000 0.266733
\(507\) 0 0
\(508\) 5.00000 0.221839
\(509\) 26.0000 1.15243 0.576215 0.817298i \(-0.304529\pi\)
0.576215 + 0.817298i \(0.304529\pi\)
\(510\) 0 0
\(511\) −11.0000 −0.486611
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) 20.0000 0.882162
\(515\) 0 0
\(516\) 0 0
\(517\) 1.00000 0.0439799
\(518\) −2.00000 −0.0878750
\(519\) 0 0
\(520\) 0 0
\(521\) −35.0000 −1.53338 −0.766689 0.642019i \(-0.778097\pi\)
−0.766689 + 0.642019i \(0.778097\pi\)
\(522\) 0 0
\(523\) 26.0000 1.13690 0.568450 0.822718i \(-0.307543\pi\)
0.568450 + 0.822718i \(0.307543\pi\)
\(524\) 4.00000 0.174741
\(525\) 0 0
\(526\) −16.0000 −0.697633
\(527\) −32.0000 −1.39394
\(528\) 0 0
\(529\) 13.0000 0.565217
\(530\) 0 0
\(531\) 0 0
\(532\) −3.00000 −0.130066
\(533\) 33.0000 1.42939
\(534\) 0 0
\(535\) 0 0
\(536\) 3.00000 0.129580
\(537\) 0 0
\(538\) 6.00000 0.258678
\(539\) −1.00000 −0.0430730
\(540\) 0 0
\(541\) 9.00000 0.386940 0.193470 0.981106i \(-0.438026\pi\)
0.193470 + 0.981106i \(0.438026\pi\)
\(542\) −27.0000 −1.15975
\(543\) 0 0
\(544\) 8.00000 0.342997
\(545\) 0 0
\(546\) 0 0
\(547\) 24.0000 1.02617 0.513083 0.858339i \(-0.328503\pi\)
0.513083 + 0.858339i \(0.328503\pi\)
\(548\) −3.00000 −0.128154
\(549\) 0 0
\(550\) 0 0
\(551\) 18.0000 0.766826
\(552\) 0 0
\(553\) 4.00000 0.170097
\(554\) −18.0000 −0.764747
\(555\) 0 0
\(556\) −20.0000 −0.848189
\(557\) 46.0000 1.94908 0.974541 0.224208i \(-0.0719796\pi\)
0.974541 + 0.224208i \(0.0719796\pi\)
\(558\) 0 0
\(559\) 3.00000 0.126886
\(560\) 0 0
\(561\) 0 0
\(562\) 10.0000 0.421825
\(563\) 11.0000 0.463595 0.231797 0.972764i \(-0.425539\pi\)
0.231797 + 0.972764i \(0.425539\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 22.0000 0.924729
\(567\) 0 0
\(568\) −8.00000 −0.335673
\(569\) 18.0000 0.754599 0.377300 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) 0 0
\(571\) 36.0000 1.50655 0.753277 0.657704i \(-0.228472\pi\)
0.753277 + 0.657704i \(0.228472\pi\)
\(572\) 3.00000 0.125436
\(573\) 0 0
\(574\) −11.0000 −0.459131
\(575\) 0 0
\(576\) 0 0
\(577\) −25.0000 −1.04076 −0.520382 0.853934i \(-0.674210\pi\)
−0.520382 + 0.853934i \(0.674210\pi\)
\(578\) 47.0000 1.95494
\(579\) 0 0
\(580\) 0 0
\(581\) 11.0000 0.456357
\(582\) 0 0
\(583\) −1.00000 −0.0414158
\(584\) −11.0000 −0.455183
\(585\) 0 0
\(586\) −14.0000 −0.578335
\(587\) 20.0000 0.825488 0.412744 0.910847i \(-0.364570\pi\)
0.412744 + 0.910847i \(0.364570\pi\)
\(588\) 0 0
\(589\) 12.0000 0.494451
\(590\) 0 0
\(591\) 0 0
\(592\) −2.00000 −0.0821995
\(593\) −48.0000 −1.97112 −0.985562 0.169316i \(-0.945844\pi\)
−0.985562 + 0.169316i \(0.945844\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) 18.0000 0.737309
\(597\) 0 0
\(598\) 18.0000 0.736075
\(599\) 9.00000 0.367730 0.183865 0.982952i \(-0.441139\pi\)
0.183865 + 0.982952i \(0.441139\pi\)
\(600\) 0 0
\(601\) 12.0000 0.489490 0.244745 0.969587i \(-0.421296\pi\)
0.244745 + 0.969587i \(0.421296\pi\)
\(602\) −1.00000 −0.0407570
\(603\) 0 0
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) 0 0
\(607\) −34.0000 −1.38002 −0.690009 0.723801i \(-0.742393\pi\)
−0.690009 + 0.723801i \(0.742393\pi\)
\(608\) −3.00000 −0.121666
\(609\) 0 0
\(610\) 0 0
\(611\) 3.00000 0.121367
\(612\) 0 0
\(613\) 36.0000 1.45403 0.727013 0.686624i \(-0.240908\pi\)
0.727013 + 0.686624i \(0.240908\pi\)
\(614\) −28.0000 −1.12999
\(615\) 0 0
\(616\) −1.00000 −0.0402911
\(617\) 14.0000 0.563619 0.281809 0.959470i \(-0.409065\pi\)
0.281809 + 0.959470i \(0.409065\pi\)
\(618\) 0 0
\(619\) 11.0000 0.442127 0.221064 0.975259i \(-0.429047\pi\)
0.221064 + 0.975259i \(0.429047\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) 18.0000 0.721734
\(623\) −7.00000 −0.280449
\(624\) 0 0
\(625\) 0 0
\(626\) −29.0000 −1.15907
\(627\) 0 0
\(628\) −22.0000 −0.877896
\(629\) −16.0000 −0.637962
\(630\) 0 0
\(631\) −34.0000 −1.35352 −0.676759 0.736204i \(-0.736616\pi\)
−0.676759 + 0.736204i \(0.736616\pi\)
\(632\) 4.00000 0.159111
\(633\) 0 0
\(634\) −23.0000 −0.913447
\(635\) 0 0
\(636\) 0 0
\(637\) −3.00000 −0.118864
\(638\) 6.00000 0.237542
\(639\) 0 0
\(640\) 0 0
\(641\) 28.0000 1.10593 0.552967 0.833203i \(-0.313496\pi\)
0.552967 + 0.833203i \(0.313496\pi\)
\(642\) 0 0
\(643\) −16.0000 −0.630978 −0.315489 0.948929i \(-0.602169\pi\)
−0.315489 + 0.948929i \(0.602169\pi\)
\(644\) −6.00000 −0.236433
\(645\) 0 0
\(646\) −24.0000 −0.944267
\(647\) 7.00000 0.275198 0.137599 0.990488i \(-0.456061\pi\)
0.137599 + 0.990488i \(0.456061\pi\)
\(648\) 0 0
\(649\) 10.0000 0.392534
\(650\) 0 0
\(651\) 0 0
\(652\) 16.0000 0.626608
\(653\) −22.0000 −0.860927 −0.430463 0.902608i \(-0.641650\pi\)
−0.430463 + 0.902608i \(0.641650\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −11.0000 −0.429478
\(657\) 0 0
\(658\) −1.00000 −0.0389841
\(659\) 8.00000 0.311636 0.155818 0.987786i \(-0.450199\pi\)
0.155818 + 0.987786i \(0.450199\pi\)
\(660\) 0 0
\(661\) −14.0000 −0.544537 −0.272268 0.962221i \(-0.587774\pi\)
−0.272268 + 0.962221i \(0.587774\pi\)
\(662\) 34.0000 1.32145
\(663\) 0 0
\(664\) 11.0000 0.426883
\(665\) 0 0
\(666\) 0 0
\(667\) 36.0000 1.39393
\(668\) 12.0000 0.464294
\(669\) 0 0
\(670\) 0 0
\(671\) −4.00000 −0.154418
\(672\) 0 0
\(673\) 32.0000 1.23351 0.616755 0.787155i \(-0.288447\pi\)
0.616755 + 0.787155i \(0.288447\pi\)
\(674\) 8.00000 0.308148
\(675\) 0 0
\(676\) −4.00000 −0.153846
\(677\) −30.0000 −1.15299 −0.576497 0.817099i \(-0.695581\pi\)
−0.576497 + 0.817099i \(0.695581\pi\)
\(678\) 0 0
\(679\) −2.00000 −0.0767530
\(680\) 0 0
\(681\) 0 0
\(682\) 4.00000 0.153168
\(683\) 2.00000 0.0765279 0.0382639 0.999268i \(-0.487817\pi\)
0.0382639 + 0.999268i \(0.487817\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) −1.00000 −0.0381246
\(689\) −3.00000 −0.114291
\(690\) 0 0
\(691\) −35.0000 −1.33146 −0.665731 0.746191i \(-0.731880\pi\)
−0.665731 + 0.746191i \(0.731880\pi\)
\(692\) 2.00000 0.0760286
\(693\) 0 0
\(694\) −2.00000 −0.0759190
\(695\) 0 0
\(696\) 0 0
\(697\) −88.0000 −3.33324
\(698\) 10.0000 0.378506
\(699\) 0 0
\(700\) 0 0
\(701\) 32.0000 1.20862 0.604312 0.796748i \(-0.293448\pi\)
0.604312 + 0.796748i \(0.293448\pi\)
\(702\) 0 0
\(703\) 6.00000 0.226294
\(704\) −1.00000 −0.0376889
\(705\) 0 0
\(706\) 0 0
\(707\) 15.0000 0.564133
\(708\) 0 0
\(709\) 25.0000 0.938895 0.469447 0.882960i \(-0.344453\pi\)
0.469447 + 0.882960i \(0.344453\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −7.00000 −0.262336
\(713\) 24.0000 0.898807
\(714\) 0 0
\(715\) 0 0
\(716\) −3.00000 −0.112115
\(717\) 0 0
\(718\) 1.00000 0.0373197
\(719\) −48.0000 −1.79010 −0.895049 0.445968i \(-0.852860\pi\)
−0.895049 + 0.445968i \(0.852860\pi\)
\(720\) 0 0
\(721\) 8.00000 0.297936
\(722\) −10.0000 −0.372161
\(723\) 0 0
\(724\) −14.0000 −0.520306
\(725\) 0 0
\(726\) 0 0
\(727\) 24.0000 0.890111 0.445055 0.895503i \(-0.353184\pi\)
0.445055 + 0.895503i \(0.353184\pi\)
\(728\) −3.00000 −0.111187
\(729\) 0 0
\(730\) 0 0
\(731\) −8.00000 −0.295891
\(732\) 0 0
\(733\) 5.00000 0.184679 0.0923396 0.995728i \(-0.470565\pi\)
0.0923396 + 0.995728i \(0.470565\pi\)
\(734\) −10.0000 −0.369107
\(735\) 0 0
\(736\) −6.00000 −0.221163
\(737\) −3.00000 −0.110506
\(738\) 0 0
\(739\) −8.00000 −0.294285 −0.147142 0.989115i \(-0.547008\pi\)
−0.147142 + 0.989115i \(0.547008\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 1.00000 0.0367112
\(743\) 6.00000 0.220119 0.110059 0.993925i \(-0.464896\pi\)
0.110059 + 0.993925i \(0.464896\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −32.0000 −1.17160
\(747\) 0 0
\(748\) −8.00000 −0.292509
\(749\) 12.0000 0.438470
\(750\) 0 0
\(751\) −34.0000 −1.24068 −0.620339 0.784334i \(-0.713005\pi\)
−0.620339 + 0.784334i \(0.713005\pi\)
\(752\) −1.00000 −0.0364662
\(753\) 0 0
\(754\) 18.0000 0.655521
\(755\) 0 0
\(756\) 0 0
\(757\) −28.0000 −1.01768 −0.508839 0.860862i \(-0.669925\pi\)
−0.508839 + 0.860862i \(0.669925\pi\)
\(758\) 12.0000 0.435860
\(759\) 0 0
\(760\) 0 0
\(761\) −42.0000 −1.52250 −0.761249 0.648459i \(-0.775414\pi\)
−0.761249 + 0.648459i \(0.775414\pi\)
\(762\) 0 0
\(763\) −9.00000 −0.325822
\(764\) 3.00000 0.108536
\(765\) 0 0
\(766\) −24.0000 −0.867155
\(767\) 30.0000 1.08324
\(768\) 0 0
\(769\) 4.00000 0.144244 0.0721218 0.997396i \(-0.477023\pi\)
0.0721218 + 0.997396i \(0.477023\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 10.0000 0.359908
\(773\) −6.00000 −0.215805 −0.107903 0.994161i \(-0.534413\pi\)
−0.107903 + 0.994161i \(0.534413\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) −2.00000 −0.0717958
\(777\) 0 0
\(778\) −26.0000 −0.932145
\(779\) 33.0000 1.18235
\(780\) 0 0
\(781\) 8.00000 0.286263
\(782\) −48.0000 −1.71648
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) −28.0000 −0.998092 −0.499046 0.866575i \(-0.666316\pi\)
−0.499046 + 0.866575i \(0.666316\pi\)
\(788\) 11.0000 0.391859
\(789\) 0 0
\(790\) 0 0
\(791\) −13.0000 −0.462227
\(792\) 0 0
\(793\) −12.0000 −0.426132
\(794\) 14.0000 0.496841
\(795\) 0 0
\(796\) 23.0000 0.815213
\(797\) 12.0000 0.425062 0.212531 0.977154i \(-0.431829\pi\)
0.212531 + 0.977154i \(0.431829\pi\)
\(798\) 0 0
\(799\) −8.00000 −0.283020
\(800\) 0 0
\(801\) 0 0
\(802\) 20.0000 0.706225
\(803\) 11.0000 0.388182
\(804\) 0 0
\(805\) 0 0
\(806\) 12.0000 0.422682
\(807\) 0 0
\(808\) 15.0000 0.527698
\(809\) −18.0000 −0.632846 −0.316423 0.948618i \(-0.602482\pi\)
−0.316423 + 0.948618i \(0.602482\pi\)
\(810\) 0 0
\(811\) 29.0000 1.01833 0.509164 0.860670i \(-0.329955\pi\)
0.509164 + 0.860670i \(0.329955\pi\)
\(812\) −6.00000 −0.210559
\(813\) 0 0
\(814\) 2.00000 0.0701000
\(815\) 0 0
\(816\) 0 0
\(817\) 3.00000 0.104957
\(818\) −18.0000 −0.629355
\(819\) 0 0
\(820\) 0 0
\(821\) −42.0000 −1.46581 −0.732905 0.680331i \(-0.761836\pi\)
−0.732905 + 0.680331i \(0.761836\pi\)
\(822\) 0 0
\(823\) −37.0000 −1.28974 −0.644869 0.764293i \(-0.723088\pi\)
−0.644869 + 0.764293i \(0.723088\pi\)
\(824\) 8.00000 0.278693
\(825\) 0 0
\(826\) −10.0000 −0.347945
\(827\) 32.0000 1.11275 0.556375 0.830932i \(-0.312192\pi\)
0.556375 + 0.830932i \(0.312192\pi\)
\(828\) 0 0
\(829\) −16.0000 −0.555703 −0.277851 0.960624i \(-0.589622\pi\)
−0.277851 + 0.960624i \(0.589622\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −3.00000 −0.104006
\(833\) 8.00000 0.277184
\(834\) 0 0
\(835\) 0 0
\(836\) 3.00000 0.103757
\(837\) 0 0
\(838\) 18.0000 0.621800
\(839\) −50.0000 −1.72619 −0.863096 0.505040i \(-0.831478\pi\)
−0.863096 + 0.505040i \(0.831478\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −1.00000 −0.0344623
\(843\) 0 0
\(844\) −26.0000 −0.894957
\(845\) 0 0
\(846\) 0 0
\(847\) −10.0000 −0.343604
\(848\) 1.00000 0.0343401
\(849\) 0 0
\(850\) 0 0
\(851\) 12.0000 0.411355
\(852\) 0 0
\(853\) 22.0000 0.753266 0.376633 0.926363i \(-0.377082\pi\)
0.376633 + 0.926363i \(0.377082\pi\)
\(854\) 4.00000 0.136877
\(855\) 0 0
\(856\) 12.0000 0.410152
\(857\) −18.0000 −0.614868 −0.307434 0.951569i \(-0.599470\pi\)
−0.307434 + 0.951569i \(0.599470\pi\)
\(858\) 0 0
\(859\) −3.00000 −0.102359 −0.0511793 0.998689i \(-0.516298\pi\)
−0.0511793 + 0.998689i \(0.516298\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −9.00000 −0.306541
\(863\) −14.0000 −0.476566 −0.238283 0.971196i \(-0.576585\pi\)
−0.238283 + 0.971196i \(0.576585\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) 7.00000 0.237870
\(867\) 0 0
\(868\) −4.00000 −0.135769
\(869\) −4.00000 −0.135691
\(870\) 0 0
\(871\) −9.00000 −0.304953
\(872\) −9.00000 −0.304778
\(873\) 0 0
\(874\) 18.0000 0.608859
\(875\) 0 0
\(876\) 0 0
\(877\) 28.0000 0.945493 0.472746 0.881199i \(-0.343263\pi\)
0.472746 + 0.881199i \(0.343263\pi\)
\(878\) −11.0000 −0.371232
\(879\) 0 0
\(880\) 0 0
\(881\) −50.0000 −1.68454 −0.842271 0.539054i \(-0.818782\pi\)
−0.842271 + 0.539054i \(0.818782\pi\)
\(882\) 0 0
\(883\) −36.0000 −1.21150 −0.605748 0.795656i \(-0.707126\pi\)
−0.605748 + 0.795656i \(0.707126\pi\)
\(884\) −24.0000 −0.807207
\(885\) 0 0
\(886\) 16.0000 0.537531
\(887\) −37.0000 −1.24234 −0.621169 0.783676i \(-0.713342\pi\)
−0.621169 + 0.783676i \(0.713342\pi\)
\(888\) 0 0
\(889\) 5.00000 0.167695
\(890\) 0 0
\(891\) 0 0
\(892\) 2.00000 0.0669650
\(893\) 3.00000 0.100391
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 36.0000 1.20134
\(899\) 24.0000 0.800445
\(900\) 0 0
\(901\) 8.00000 0.266519
\(902\) 11.0000 0.366260
\(903\) 0 0
\(904\) −13.0000 −0.432374
\(905\) 0 0
\(906\) 0 0
\(907\) −17.0000 −0.564476 −0.282238 0.959344i \(-0.591077\pi\)
−0.282238 + 0.959344i \(0.591077\pi\)
\(908\) 11.0000 0.365048
\(909\) 0 0
\(910\) 0 0
\(911\) 33.0000 1.09334 0.546669 0.837349i \(-0.315895\pi\)
0.546669 + 0.837349i \(0.315895\pi\)
\(912\) 0 0
\(913\) −11.0000 −0.364047
\(914\) −16.0000 −0.529233
\(915\) 0 0
\(916\) −14.0000 −0.462573
\(917\) 4.00000 0.132092
\(918\) 0 0
\(919\) −28.0000 −0.923635 −0.461817 0.886975i \(-0.652802\pi\)
−0.461817 + 0.886975i \(0.652802\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −1.00000 −0.0329332
\(923\) 24.0000 0.789970
\(924\) 0 0
\(925\) 0 0
\(926\) −17.0000 −0.558655
\(927\) 0 0
\(928\) −6.00000 −0.196960
\(929\) 35.0000 1.14831 0.574156 0.818746i \(-0.305330\pi\)
0.574156 + 0.818746i \(0.305330\pi\)
\(930\) 0 0
\(931\) −3.00000 −0.0983210
\(932\) −9.00000 −0.294805
\(933\) 0 0
\(934\) −28.0000 −0.916188
\(935\) 0 0
\(936\) 0 0
\(937\) 37.0000 1.20874 0.604369 0.796705i \(-0.293425\pi\)
0.604369 + 0.796705i \(0.293425\pi\)
\(938\) 3.00000 0.0979535
\(939\) 0 0
\(940\) 0 0
\(941\) −23.0000 −0.749779 −0.374889 0.927070i \(-0.622319\pi\)
−0.374889 + 0.927070i \(0.622319\pi\)
\(942\) 0 0
\(943\) 66.0000 2.14926
\(944\) −10.0000 −0.325472
\(945\) 0 0
\(946\) 1.00000 0.0325128
\(947\) 8.00000 0.259965 0.129983 0.991516i \(-0.458508\pi\)
0.129983 + 0.991516i \(0.458508\pi\)
\(948\) 0 0
\(949\) 33.0000 1.07123
\(950\) 0 0
\(951\) 0 0
\(952\) 8.00000 0.259281
\(953\) −42.0000 −1.36051 −0.680257 0.732974i \(-0.738132\pi\)
−0.680257 + 0.732974i \(0.738132\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 8.00000 0.258738
\(957\) 0 0
\(958\) 12.0000 0.387702
\(959\) −3.00000 −0.0968751
\(960\) 0 0
\(961\) −15.0000 −0.483871
\(962\) 6.00000 0.193448
\(963\) 0 0
\(964\) −20.0000 −0.644157
\(965\) 0 0
\(966\) 0 0
\(967\) 35.0000 1.12552 0.562762 0.826619i \(-0.309739\pi\)
0.562762 + 0.826619i \(0.309739\pi\)
\(968\) −10.0000 −0.321412
\(969\) 0 0
\(970\) 0 0
\(971\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(972\) 0 0
\(973\) −20.0000 −0.641171
\(974\) −11.0000 −0.352463
\(975\) 0 0
\(976\) 4.00000 0.128037
\(977\) 3.00000 0.0959785 0.0479893 0.998848i \(-0.484719\pi\)
0.0479893 + 0.998848i \(0.484719\pi\)
\(978\) 0 0
\(979\) 7.00000 0.223721
\(980\) 0 0
\(981\) 0 0
\(982\) 36.0000 1.14881
\(983\) 56.0000 1.78612 0.893061 0.449935i \(-0.148553\pi\)
0.893061 + 0.449935i \(0.148553\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −48.0000 −1.52863
\(987\) 0 0
\(988\) 9.00000 0.286328
\(989\) 6.00000 0.190789
\(990\) 0 0
\(991\) −44.0000 −1.39771 −0.698853 0.715265i \(-0.746306\pi\)
−0.698853 + 0.715265i \(0.746306\pi\)
\(992\) −4.00000 −0.127000
\(993\) 0 0
\(994\) −8.00000 −0.253745
\(995\) 0 0
\(996\) 0 0
\(997\) 10.0000 0.316703 0.158352 0.987383i \(-0.449382\pi\)
0.158352 + 0.987383i \(0.449382\pi\)
\(998\) 18.0000 0.569780
\(999\) 0 0
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 \(a_p\))