Properties

Label 9450.2.a.cg.1.1
Level 9450
Weight 2
Character 9450.1
Self dual Yes
Analytic conductor 75.459
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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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: \(0\)
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

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-1.00000 q^{7}\) \(+1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-1.00000 q^{7}\) \(+1.00000 q^{8}\) \(-2.00000 q^{11}\) \(-5.00000 q^{13}\) \(-1.00000 q^{14}\) \(+1.00000 q^{16}\) \(-6.00000 q^{17}\) \(+6.00000 q^{19}\) \(-2.00000 q^{22}\) \(+8.00000 q^{23}\) \(-5.00000 q^{26}\) \(-1.00000 q^{28}\) \(+5.00000 q^{29}\) \(+7.00000 q^{31}\) \(+1.00000 q^{32}\) \(-6.00000 q^{34}\) \(-4.00000 q^{37}\) \(+6.00000 q^{38}\) \(-1.00000 q^{41}\) \(-4.00000 q^{43}\) \(-2.00000 q^{44}\) \(+8.00000 q^{46}\) \(+2.00000 q^{47}\) \(+1.00000 q^{49}\) \(-5.00000 q^{52}\) \(-13.0000 q^{53}\) \(-1.00000 q^{56}\) \(+5.00000 q^{58}\) \(-4.00000 q^{59}\) \(-9.00000 q^{61}\) \(+7.00000 q^{62}\) \(+1.00000 q^{64}\) \(+9.00000 q^{67}\) \(-6.00000 q^{68}\) \(+15.0000 q^{71}\) \(+12.0000 q^{73}\) \(-4.00000 q^{74}\) \(+6.00000 q^{76}\) \(+2.00000 q^{77}\) \(+10.0000 q^{79}\) \(-1.00000 q^{82}\) \(-5.00000 q^{83}\) \(-4.00000 q^{86}\) \(-2.00000 q^{88}\) \(-11.0000 q^{89}\) \(+5.00000 q^{91}\) \(+8.00000 q^{92}\) \(+2.00000 q^{94}\) \(+8.00000 q^{97}\) \(+1.00000 q^{98}\) \(+O(q^{100})\)

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
\(11\) −2.00000 −0.603023 −0.301511 0.953463i \(-0.597491\pi\)
−0.301511 + 0.953463i \(0.597491\pi\)
\(12\) 0 0
\(13\) −5.00000 −1.38675 −0.693375 0.720577i \(-0.743877\pi\)
−0.693375 + 0.720577i \(0.743877\pi\)
\(14\) −1.00000 −0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) −6.00000 −1.45521 −0.727607 0.685994i \(-0.759367\pi\)
−0.727607 + 0.685994i \(0.759367\pi\)
\(18\) 0 0
\(19\) 6.00000 1.37649 0.688247 0.725476i \(-0.258380\pi\)
0.688247 + 0.725476i \(0.258380\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −2.00000 −0.426401
\(23\) 8.00000 1.66812 0.834058 0.551677i \(-0.186012\pi\)
0.834058 + 0.551677i \(0.186012\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −5.00000 −0.980581
\(27\) 0 0
\(28\) −1.00000 −0.188982
\(29\) 5.00000 0.928477 0.464238 0.885710i \(-0.346328\pi\)
0.464238 + 0.885710i \(0.346328\pi\)
\(30\) 0 0
\(31\) 7.00000 1.25724 0.628619 0.777714i \(-0.283621\pi\)
0.628619 + 0.777714i \(0.283621\pi\)
\(32\) 1.00000 0.176777
\(33\) 0 0
\(34\) −6.00000 −1.02899
\(35\) 0 0
\(36\) 0 0
\(37\) −4.00000 −0.657596 −0.328798 0.944400i \(-0.606644\pi\)
−0.328798 + 0.944400i \(0.606644\pi\)
\(38\) 6.00000 0.973329
\(39\) 0 0
\(40\) 0 0
\(41\) −1.00000 −0.156174 −0.0780869 0.996947i \(-0.524881\pi\)
−0.0780869 + 0.996947i \(0.524881\pi\)
\(42\) 0 0
\(43\) −4.00000 −0.609994 −0.304997 0.952353i \(-0.598656\pi\)
−0.304997 + 0.952353i \(0.598656\pi\)
\(44\) −2.00000 −0.301511
\(45\) 0 0
\(46\) 8.00000 1.17954
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0 0
\(51\) 0 0
\(52\) −5.00000 −0.693375
\(53\) −13.0000 −1.78569 −0.892844 0.450367i \(-0.851293\pi\)
−0.892844 + 0.450367i \(0.851293\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) −1.00000 −0.133631
\(57\) 0 0
\(58\) 5.00000 0.656532
\(59\) −4.00000 −0.520756 −0.260378 0.965507i \(-0.583847\pi\)
−0.260378 + 0.965507i \(0.583847\pi\)
\(60\) 0 0
\(61\) −9.00000 −1.15233 −0.576166 0.817333i \(-0.695452\pi\)
−0.576166 + 0.817333i \(0.695452\pi\)
\(62\) 7.00000 0.889001
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 9.00000 1.09952 0.549762 0.835321i \(-0.314718\pi\)
0.549762 + 0.835321i \(0.314718\pi\)
\(68\) −6.00000 −0.727607
\(69\) 0 0
\(70\) 0 0
\(71\) 15.0000 1.78017 0.890086 0.455792i \(-0.150644\pi\)
0.890086 + 0.455792i \(0.150644\pi\)
\(72\) 0 0
\(73\) 12.0000 1.40449 0.702247 0.711934i \(-0.252180\pi\)
0.702247 + 0.711934i \(0.252180\pi\)
\(74\) −4.00000 −0.464991
\(75\) 0 0
\(76\) 6.00000 0.688247
\(77\) 2.00000 0.227921
\(78\) 0 0
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −1.00000 −0.110432
\(83\) −5.00000 −0.548821 −0.274411 0.961613i \(-0.588483\pi\)
−0.274411 + 0.961613i \(0.588483\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) −4.00000 −0.431331
\(87\) 0 0
\(88\) −2.00000 −0.213201
\(89\) −11.0000 −1.16600 −0.582999 0.812473i \(-0.698121\pi\)
−0.582999 + 0.812473i \(0.698121\pi\)
\(90\) 0 0
\(91\) 5.00000 0.524142
\(92\) 8.00000 0.834058
\(93\) 0 0
\(94\) 2.00000 0.206284
\(95\) 0 0
\(96\) 0 0
\(97\) 8.00000 0.812277 0.406138 0.913812i \(-0.366875\pi\)
0.406138 + 0.913812i \(0.366875\pi\)
\(98\) 1.00000 0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) 12.0000 1.19404 0.597022 0.802225i \(-0.296350\pi\)
0.597022 + 0.802225i \(0.296350\pi\)
\(102\) 0 0
\(103\) −16.0000 −1.57653 −0.788263 0.615338i \(-0.789020\pi\)
−0.788263 + 0.615338i \(0.789020\pi\)
\(104\) −5.00000 −0.490290
\(105\) 0 0
\(106\) −13.0000 −1.26267
\(107\) 10.0000 0.966736 0.483368 0.875417i \(-0.339413\pi\)
0.483368 + 0.875417i \(0.339413\pi\)
\(108\) 0 0
\(109\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) 12.0000 1.12887 0.564433 0.825479i \(-0.309095\pi\)
0.564433 + 0.825479i \(0.309095\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) 5.00000 0.464238
\(117\) 0 0
\(118\) −4.00000 −0.368230
\(119\) 6.00000 0.550019
\(120\) 0 0
\(121\) −7.00000 −0.636364
\(122\) −9.00000 −0.814822
\(123\) 0 0
\(124\) 7.00000 0.628619
\(125\) 0 0
\(126\) 0 0
\(127\) −8.00000 −0.709885 −0.354943 0.934888i \(-0.615500\pi\)
−0.354943 + 0.934888i \(0.615500\pi\)
\(128\) 1.00000 0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) −1.00000 −0.0873704 −0.0436852 0.999045i \(-0.513910\pi\)
−0.0436852 + 0.999045i \(0.513910\pi\)
\(132\) 0 0
\(133\) −6.00000 −0.520266
\(134\) 9.00000 0.777482
\(135\) 0 0
\(136\) −6.00000 −0.514496
\(137\) 12.0000 1.02523 0.512615 0.858619i \(-0.328677\pi\)
0.512615 + 0.858619i \(0.328677\pi\)
\(138\) 0 0
\(139\) 14.0000 1.18746 0.593732 0.804663i \(-0.297654\pi\)
0.593732 + 0.804663i \(0.297654\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) 15.0000 1.25877
\(143\) 10.0000 0.836242
\(144\) 0 0
\(145\) 0 0
\(146\) 12.0000 0.993127
\(147\) 0 0
\(148\) −4.00000 −0.328798
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 0 0
\(151\) 24.0000 1.95309 0.976546 0.215308i \(-0.0690756\pi\)
0.976546 + 0.215308i \(0.0690756\pi\)
\(152\) 6.00000 0.486664
\(153\) 0 0
\(154\) 2.00000 0.161165
\(155\) 0 0
\(156\) 0 0
\(157\) 17.0000 1.35675 0.678374 0.734717i \(-0.262685\pi\)
0.678374 + 0.734717i \(0.262685\pi\)
\(158\) 10.0000 0.795557
\(159\) 0 0
\(160\) 0 0
\(161\) −8.00000 −0.630488
\(162\) 0 0
\(163\) 7.00000 0.548282 0.274141 0.961689i \(-0.411606\pi\)
0.274141 + 0.961689i \(0.411606\pi\)
\(164\) −1.00000 −0.0780869
\(165\) 0 0
\(166\) −5.00000 −0.388075
\(167\) 12.0000 0.928588 0.464294 0.885681i \(-0.346308\pi\)
0.464294 + 0.885681i \(0.346308\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) −4.00000 −0.304997
\(173\) 6.00000 0.456172 0.228086 0.973641i \(-0.426753\pi\)
0.228086 + 0.973641i \(0.426753\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) −2.00000 −0.150756
\(177\) 0 0
\(178\) −11.0000 −0.824485
\(179\) 10.0000 0.747435 0.373718 0.927543i \(-0.378083\pi\)
0.373718 + 0.927543i \(0.378083\pi\)
\(180\) 0 0
\(181\) 3.00000 0.222988 0.111494 0.993765i \(-0.464436\pi\)
0.111494 + 0.993765i \(0.464436\pi\)
\(182\) 5.00000 0.370625
\(183\) 0 0
\(184\) 8.00000 0.589768
\(185\) 0 0
\(186\) 0 0
\(187\) 12.0000 0.877527
\(188\) 2.00000 0.145865
\(189\) 0 0
\(190\) 0 0
\(191\) 15.0000 1.08536 0.542681 0.839939i \(-0.317409\pi\)
0.542681 + 0.839939i \(0.317409\pi\)
\(192\) 0 0
\(193\) 25.0000 1.79954 0.899770 0.436365i \(-0.143734\pi\)
0.899770 + 0.436365i \(0.143734\pi\)
\(194\) 8.00000 0.574367
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) −5.00000 −0.356235 −0.178118 0.984009i \(-0.557001\pi\)
−0.178118 + 0.984009i \(0.557001\pi\)
\(198\) 0 0
\(199\) 27.0000 1.91398 0.956990 0.290122i \(-0.0936959\pi\)
0.956990 + 0.290122i \(0.0936959\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 12.0000 0.844317
\(203\) −5.00000 −0.350931
\(204\) 0 0
\(205\) 0 0
\(206\) −16.0000 −1.11477
\(207\) 0 0
\(208\) −5.00000 −0.346688
\(209\) −12.0000 −0.830057
\(210\) 0 0
\(211\) −4.00000 −0.275371 −0.137686 0.990476i \(-0.543966\pi\)
−0.137686 + 0.990476i \(0.543966\pi\)
\(212\) −13.0000 −0.892844
\(213\) 0 0
\(214\) 10.0000 0.683586
\(215\) 0 0
\(216\) 0 0
\(217\) −7.00000 −0.475191
\(218\) 0 0
\(219\) 0 0
\(220\) 0 0
\(221\) 30.0000 2.01802
\(222\) 0 0
\(223\) 21.0000 1.40626 0.703132 0.711059i \(-0.251784\pi\)
0.703132 + 0.711059i \(0.251784\pi\)
\(224\) −1.00000 −0.0668153
\(225\) 0 0
\(226\) 12.0000 0.798228
\(227\) 19.0000 1.26107 0.630537 0.776159i \(-0.282835\pi\)
0.630537 + 0.776159i \(0.282835\pi\)
\(228\) 0 0
\(229\) −22.0000 −1.45380 −0.726900 0.686743i \(-0.759040\pi\)
−0.726900 + 0.686743i \(0.759040\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 5.00000 0.328266
\(233\) −6.00000 −0.393073 −0.196537 0.980497i \(-0.562969\pi\)
−0.196537 + 0.980497i \(0.562969\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) −4.00000 −0.260378
\(237\) 0 0
\(238\) 6.00000 0.388922
\(239\) 24.0000 1.55243 0.776215 0.630468i \(-0.217137\pi\)
0.776215 + 0.630468i \(0.217137\pi\)
\(240\) 0 0
\(241\) 16.0000 1.03065 0.515325 0.856995i \(-0.327671\pi\)
0.515325 + 0.856995i \(0.327671\pi\)
\(242\) −7.00000 −0.449977
\(243\) 0 0
\(244\) −9.00000 −0.576166
\(245\) 0 0
\(246\) 0 0
\(247\) −30.0000 −1.90885
\(248\) 7.00000 0.444500
\(249\) 0 0
\(250\) 0 0
\(251\) −13.0000 −0.820553 −0.410276 0.911961i \(-0.634568\pi\)
−0.410276 + 0.911961i \(0.634568\pi\)
\(252\) 0 0
\(253\) −16.0000 −1.00591
\(254\) −8.00000 −0.501965
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −7.00000 −0.436648 −0.218324 0.975876i \(-0.570059\pi\)
−0.218324 + 0.975876i \(0.570059\pi\)
\(258\) 0 0
\(259\) 4.00000 0.248548
\(260\) 0 0
\(261\) 0 0
\(262\) −1.00000 −0.0617802
\(263\) −27.0000 −1.66489 −0.832446 0.554107i \(-0.813060\pi\)
−0.832446 + 0.554107i \(0.813060\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) −6.00000 −0.367884
\(267\) 0 0
\(268\) 9.00000 0.549762
\(269\) −20.0000 −1.21942 −0.609711 0.792624i \(-0.708714\pi\)
−0.609711 + 0.792624i \(0.708714\pi\)
\(270\) 0 0
\(271\) 5.00000 0.303728 0.151864 0.988401i \(-0.451472\pi\)
0.151864 + 0.988401i \(0.451472\pi\)
\(272\) −6.00000 −0.363803
\(273\) 0 0
\(274\) 12.0000 0.724947
\(275\) 0 0
\(276\) 0 0
\(277\) 8.00000 0.480673 0.240337 0.970690i \(-0.422742\pi\)
0.240337 + 0.970690i \(0.422742\pi\)
\(278\) 14.0000 0.839664
\(279\) 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
\(283\) −26.0000 −1.54554 −0.772770 0.634686i \(-0.781129\pi\)
−0.772770 + 0.634686i \(0.781129\pi\)
\(284\) 15.0000 0.890086
\(285\) 0 0
\(286\) 10.0000 0.591312
\(287\) 1.00000 0.0590281
\(288\) 0 0
\(289\) 19.0000 1.11765
\(290\) 0 0
\(291\) 0 0
\(292\) 12.0000 0.702247
\(293\) −6.00000 −0.350524 −0.175262 0.984522i \(-0.556077\pi\)
−0.175262 + 0.984522i \(0.556077\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) −4.00000 −0.232495
\(297\) 0 0
\(298\) −18.0000 −1.04271
\(299\) −40.0000 −2.31326
\(300\) 0 0
\(301\) 4.00000 0.230556
\(302\) 24.0000 1.38104
\(303\) 0 0
\(304\) 6.00000 0.344124
\(305\) 0 0
\(306\) 0 0
\(307\) 20.0000 1.14146 0.570730 0.821138i \(-0.306660\pi\)
0.570730 + 0.821138i \(0.306660\pi\)
\(308\) 2.00000 0.113961
\(309\) 0 0
\(310\) 0 0
\(311\) −18.0000 −1.02069 −0.510343 0.859971i \(-0.670482\pi\)
−0.510343 + 0.859971i \(0.670482\pi\)
\(312\) 0 0
\(313\) −30.0000 −1.69570 −0.847850 0.530236i \(-0.822103\pi\)
−0.847850 + 0.530236i \(0.822103\pi\)
\(314\) 17.0000 0.959366
\(315\) 0 0
\(316\) 10.0000 0.562544
\(317\) 3.00000 0.168497 0.0842484 0.996445i \(-0.473151\pi\)
0.0842484 + 0.996445i \(0.473151\pi\)
\(318\) 0 0
\(319\) −10.0000 −0.559893
\(320\) 0 0
\(321\) 0 0
\(322\) −8.00000 −0.445823
\(323\) −36.0000 −2.00309
\(324\) 0 0
\(325\) 0 0
\(326\) 7.00000 0.387694
\(327\) 0 0
\(328\) −1.00000 −0.0552158
\(329\) −2.00000 −0.110264
\(330\) 0 0
\(331\) 20.0000 1.09930 0.549650 0.835395i \(-0.314761\pi\)
0.549650 + 0.835395i \(0.314761\pi\)
\(332\) −5.00000 −0.274411
\(333\) 0 0
\(334\) 12.0000 0.656611
\(335\) 0 0
\(336\) 0 0
\(337\) 18.0000 0.980522 0.490261 0.871576i \(-0.336901\pi\)
0.490261 + 0.871576i \(0.336901\pi\)
\(338\) 12.0000 0.652714
\(339\) 0 0
\(340\) 0 0
\(341\) −14.0000 −0.758143
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −4.00000 −0.215666
\(345\) 0 0
\(346\) 6.00000 0.322562
\(347\) −8.00000 −0.429463 −0.214731 0.976673i \(-0.568888\pi\)
−0.214731 + 0.976673i \(0.568888\pi\)
\(348\) 0 0
\(349\) 21.0000 1.12410 0.562052 0.827102i \(-0.310012\pi\)
0.562052 + 0.827102i \(0.310012\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −2.00000 −0.106600
\(353\) −9.00000 −0.479022 −0.239511 0.970894i \(-0.576987\pi\)
−0.239511 + 0.970894i \(0.576987\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −11.0000 −0.582999
\(357\) 0 0
\(358\) 10.0000 0.528516
\(359\) 17.0000 0.897226 0.448613 0.893726i \(-0.351918\pi\)
0.448613 + 0.893726i \(0.351918\pi\)
\(360\) 0 0
\(361\) 17.0000 0.894737
\(362\) 3.00000 0.157676
\(363\) 0 0
\(364\) 5.00000 0.262071
\(365\) 0 0
\(366\) 0 0
\(367\) −8.00000 −0.417597 −0.208798 0.977959i \(-0.566955\pi\)
−0.208798 + 0.977959i \(0.566955\pi\)
\(368\) 8.00000 0.417029
\(369\) 0 0
\(370\) 0 0
\(371\) 13.0000 0.674926
\(372\) 0 0
\(373\) −30.0000 −1.55334 −0.776671 0.629907i \(-0.783093\pi\)
−0.776671 + 0.629907i \(0.783093\pi\)
\(374\) 12.0000 0.620505
\(375\) 0 0
\(376\) 2.00000 0.103142
\(377\) −25.0000 −1.28757
\(378\) 0 0
\(379\) 11.0000 0.565032 0.282516 0.959263i \(-0.408831\pi\)
0.282516 + 0.959263i \(0.408831\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 15.0000 0.767467
\(383\) −14.0000 −0.715367 −0.357683 0.933843i \(-0.616433\pi\)
−0.357683 + 0.933843i \(0.616433\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) 25.0000 1.27247
\(387\) 0 0
\(388\) 8.00000 0.406138
\(389\) −22.0000 −1.11544 −0.557722 0.830028i \(-0.688325\pi\)
−0.557722 + 0.830028i \(0.688325\pi\)
\(390\) 0 0
\(391\) −48.0000 −2.42746
\(392\) 1.00000 0.0505076
\(393\) 0 0
\(394\) −5.00000 −0.251896
\(395\) 0 0
\(396\) 0 0
\(397\) 29.0000 1.45547 0.727734 0.685859i \(-0.240573\pi\)
0.727734 + 0.685859i \(0.240573\pi\)
\(398\) 27.0000 1.35339
\(399\) 0 0
\(400\) 0 0
\(401\) 14.0000 0.699127 0.349563 0.936913i \(-0.386330\pi\)
0.349563 + 0.936913i \(0.386330\pi\)
\(402\) 0 0
\(403\) −35.0000 −1.74347
\(404\) 12.0000 0.597022
\(405\) 0 0
\(406\) −5.00000 −0.248146
\(407\) 8.00000 0.396545
\(408\) 0 0
\(409\) −16.0000 −0.791149 −0.395575 0.918434i \(-0.629455\pi\)
−0.395575 + 0.918434i \(0.629455\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −16.0000 −0.788263
\(413\) 4.00000 0.196827
\(414\) 0 0
\(415\) 0 0
\(416\) −5.00000 −0.245145
\(417\) 0 0
\(418\) −12.0000 −0.586939
\(419\) −1.00000 −0.0488532 −0.0244266 0.999702i \(-0.507776\pi\)
−0.0244266 + 0.999702i \(0.507776\pi\)
\(420\) 0 0
\(421\) −14.0000 −0.682318 −0.341159 0.940006i \(-0.610819\pi\)
−0.341159 + 0.940006i \(0.610819\pi\)
\(422\) −4.00000 −0.194717
\(423\) 0 0
\(424\) −13.0000 −0.631336
\(425\) 0 0
\(426\) 0 0
\(427\) 9.00000 0.435541
\(428\) 10.0000 0.483368
\(429\) 0 0
\(430\) 0 0
\(431\) −21.0000 −1.01153 −0.505767 0.862670i \(-0.668791\pi\)
−0.505767 + 0.862670i \(0.668791\pi\)
\(432\) 0 0
\(433\) −20.0000 −0.961139 −0.480569 0.876957i \(-0.659570\pi\)
−0.480569 + 0.876957i \(0.659570\pi\)
\(434\) −7.00000 −0.336011
\(435\) 0 0
\(436\) 0 0
\(437\) 48.0000 2.29615
\(438\) 0 0
\(439\) −16.0000 −0.763638 −0.381819 0.924237i \(-0.624702\pi\)
−0.381819 + 0.924237i \(0.624702\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) 30.0000 1.42695
\(443\) 2.00000 0.0950229 0.0475114 0.998871i \(-0.484871\pi\)
0.0475114 + 0.998871i \(0.484871\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) 21.0000 0.994379
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) −8.00000 −0.377543 −0.188772 0.982021i \(-0.560451\pi\)
−0.188772 + 0.982021i \(0.560451\pi\)
\(450\) 0 0
\(451\) 2.00000 0.0941763
\(452\) 12.0000 0.564433
\(453\) 0 0
\(454\) 19.0000 0.891714
\(455\) 0 0
\(456\) 0 0
\(457\) 42.0000 1.96468 0.982339 0.187112i \(-0.0599128\pi\)
0.982339 + 0.187112i \(0.0599128\pi\)
\(458\) −22.0000 −1.02799
\(459\) 0 0
\(460\) 0 0
\(461\) 18.0000 0.838344 0.419172 0.907907i \(-0.362320\pi\)
0.419172 + 0.907907i \(0.362320\pi\)
\(462\) 0 0
\(463\) −4.00000 −0.185896 −0.0929479 0.995671i \(-0.529629\pi\)
−0.0929479 + 0.995671i \(0.529629\pi\)
\(464\) 5.00000 0.232119
\(465\) 0 0
\(466\) −6.00000 −0.277945
\(467\) −21.0000 −0.971764 −0.485882 0.874024i \(-0.661502\pi\)
−0.485882 + 0.874024i \(0.661502\pi\)
\(468\) 0 0
\(469\) −9.00000 −0.415581
\(470\) 0 0
\(471\) 0 0
\(472\) −4.00000 −0.184115
\(473\) 8.00000 0.367840
\(474\) 0 0
\(475\) 0 0
\(476\) 6.00000 0.275010
\(477\) 0 0
\(478\) 24.0000 1.09773
\(479\) −16.0000 −0.731059 −0.365529 0.930800i \(-0.619112\pi\)
−0.365529 + 0.930800i \(0.619112\pi\)
\(480\) 0 0
\(481\) 20.0000 0.911922
\(482\) 16.0000 0.728780
\(483\) 0 0
\(484\) −7.00000 −0.318182
\(485\) 0 0
\(486\) 0 0
\(487\) 8.00000 0.362515 0.181257 0.983436i \(-0.441983\pi\)
0.181257 + 0.983436i \(0.441983\pi\)
\(488\) −9.00000 −0.407411
\(489\) 0 0
\(490\) 0 0
\(491\) −26.0000 −1.17336 −0.586682 0.809818i \(-0.699566\pi\)
−0.586682 + 0.809818i \(0.699566\pi\)
\(492\) 0 0
\(493\) −30.0000 −1.35113
\(494\) −30.0000 −1.34976
\(495\) 0 0
\(496\) 7.00000 0.314309
\(497\) −15.0000 −0.672842
\(498\) 0 0
\(499\) 25.0000 1.11915 0.559577 0.828778i \(-0.310964\pi\)
0.559577 + 0.828778i \(0.310964\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −13.0000 −0.580218
\(503\) 30.0000 1.33763 0.668817 0.743427i \(-0.266801\pi\)
0.668817 + 0.743427i \(0.266801\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −16.0000 −0.711287
\(507\) 0 0
\(508\) −8.00000 −0.354943
\(509\) −26.0000 −1.15243 −0.576215 0.817298i \(-0.695471\pi\)
−0.576215 + 0.817298i \(0.695471\pi\)
\(510\) 0 0
\(511\) −12.0000 −0.530849
\(512\) 1.00000 0.0441942
\(513\) 0 0
\(514\) −7.00000 −0.308757
\(515\) 0 0
\(516\) 0 0
\(517\) −4.00000 −0.175920
\(518\) 4.00000 0.175750
\(519\) 0 0
\(520\) 0 0
\(521\) 33.0000 1.44576 0.722878 0.690976i \(-0.242819\pi\)
0.722878 + 0.690976i \(0.242819\pi\)
\(522\) 0 0
\(523\) −4.00000 −0.174908 −0.0874539 0.996169i \(-0.527873\pi\)
−0.0874539 + 0.996169i \(0.527873\pi\)
\(524\) −1.00000 −0.0436852
\(525\) 0 0
\(526\) −27.0000 −1.17726
\(527\) −42.0000 −1.82955
\(528\) 0 0
\(529\) 41.0000 1.78261
\(530\) 0 0
\(531\) 0 0
\(532\) −6.00000 −0.260133
\(533\) 5.00000 0.216574
\(534\) 0 0
\(535\) 0 0
\(536\) 9.00000 0.388741
\(537\) 0 0
\(538\) −20.0000 −0.862261
\(539\) −2.00000 −0.0861461
\(540\) 0 0
\(541\) −10.0000 −0.429934 −0.214967 0.976621i \(-0.568964\pi\)
−0.214967 + 0.976621i \(0.568964\pi\)
\(542\) 5.00000 0.214768
\(543\) 0 0
\(544\) −6.00000 −0.257248
\(545\) 0 0
\(546\) 0 0
\(547\) 13.0000 0.555840 0.277920 0.960604i \(-0.410355\pi\)
0.277920 + 0.960604i \(0.410355\pi\)
\(548\) 12.0000 0.512615
\(549\) 0 0
\(550\) 0 0
\(551\) 30.0000 1.27804
\(552\) 0 0
\(553\) −10.0000 −0.425243
\(554\) 8.00000 0.339887
\(555\) 0 0
\(556\) 14.0000 0.593732
\(557\) −3.00000 −0.127114 −0.0635570 0.997978i \(-0.520244\pi\)
−0.0635570 + 0.997978i \(0.520244\pi\)
\(558\) 0 0
\(559\) 20.0000 0.845910
\(560\) 0 0
\(561\) 0 0
\(562\) 10.0000 0.421825
\(563\) −4.00000 −0.168580 −0.0842900 0.996441i \(-0.526862\pi\)
−0.0842900 + 0.996441i \(0.526862\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) −26.0000 −1.09286
\(567\) 0 0
\(568\) 15.0000 0.629386
\(569\) −18.0000 −0.754599 −0.377300 0.926091i \(-0.623147\pi\)
−0.377300 + 0.926091i \(0.623147\pi\)
\(570\) 0 0
\(571\) 1.00000 0.0418487 0.0209243 0.999781i \(-0.493339\pi\)
0.0209243 + 0.999781i \(0.493339\pi\)
\(572\) 10.0000 0.418121
\(573\) 0 0
\(574\) 1.00000 0.0417392
\(575\) 0 0
\(576\) 0 0
\(577\) −32.0000 −1.33218 −0.666089 0.745873i \(-0.732033\pi\)
−0.666089 + 0.745873i \(0.732033\pi\)
\(578\) 19.0000 0.790296
\(579\) 0 0
\(580\) 0 0
\(581\) 5.00000 0.207435
\(582\) 0 0
\(583\) 26.0000 1.07681
\(584\) 12.0000 0.496564
\(585\) 0 0
\(586\) −6.00000 −0.247858
\(587\) −12.0000 −0.495293 −0.247647 0.968850i \(-0.579657\pi\)
−0.247647 + 0.968850i \(0.579657\pi\)
\(588\) 0 0
\(589\) 42.0000 1.73058
\(590\) 0 0
\(591\) 0 0
\(592\) −4.00000 −0.164399
\(593\) 14.0000 0.574911 0.287456 0.957794i \(-0.407191\pi\)
0.287456 + 0.957794i \(0.407191\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) −40.0000 −1.63572
\(599\) 13.0000 0.531166 0.265583 0.964088i \(-0.414436\pi\)
0.265583 + 0.964088i \(0.414436\pi\)
\(600\) 0 0
\(601\) −8.00000 −0.326327 −0.163163 0.986599i \(-0.552170\pi\)
−0.163163 + 0.986599i \(0.552170\pi\)
\(602\) 4.00000 0.163028
\(603\) 0 0
\(604\) 24.0000 0.976546
\(605\) 0 0
\(606\) 0 0
\(607\) 29.0000 1.17707 0.588537 0.808470i \(-0.299704\pi\)
0.588537 + 0.808470i \(0.299704\pi\)
\(608\) 6.00000 0.243332
\(609\) 0 0
\(610\) 0 0
\(611\) −10.0000 −0.404557
\(612\) 0 0
\(613\) 16.0000 0.646234 0.323117 0.946359i \(-0.395269\pi\)
0.323117 + 0.946359i \(0.395269\pi\)
\(614\) 20.0000 0.807134
\(615\) 0 0
\(616\) 2.00000 0.0805823
\(617\) 8.00000 0.322068 0.161034 0.986949i \(-0.448517\pi\)
0.161034 + 0.986949i \(0.448517\pi\)
\(618\) 0 0
\(619\) 2.00000 0.0803868 0.0401934 0.999192i \(-0.487203\pi\)
0.0401934 + 0.999192i \(0.487203\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −18.0000 −0.721734
\(623\) 11.0000 0.440706
\(624\) 0 0
\(625\) 0 0
\(626\) −30.0000 −1.19904
\(627\) 0 0
\(628\) 17.0000 0.678374
\(629\) 24.0000 0.956943
\(630\) 0 0
\(631\) 40.0000 1.59237 0.796187 0.605050i \(-0.206847\pi\)
0.796187 + 0.605050i \(0.206847\pi\)
\(632\) 10.0000 0.397779
\(633\) 0 0
\(634\) 3.00000 0.119145
\(635\) 0 0
\(636\) 0 0
\(637\) −5.00000 −0.198107
\(638\) −10.0000 −0.395904
\(639\) 0 0
\(640\) 0 0
\(641\) −36.0000 −1.42191 −0.710957 0.703235i \(-0.751738\pi\)
−0.710957 + 0.703235i \(0.751738\pi\)
\(642\) 0 0
\(643\) 20.0000 0.788723 0.394362 0.918955i \(-0.370966\pi\)
0.394362 + 0.918955i \(0.370966\pi\)
\(644\) −8.00000 −0.315244
\(645\) 0 0
\(646\) −36.0000 −1.41640
\(647\) −22.0000 −0.864909 −0.432455 0.901656i \(-0.642352\pi\)
−0.432455 + 0.901656i \(0.642352\pi\)
\(648\) 0 0
\(649\) 8.00000 0.314027
\(650\) 0 0
\(651\) 0 0
\(652\) 7.00000 0.274141
\(653\) −25.0000 −0.978326 −0.489163 0.872192i \(-0.662698\pi\)
−0.489163 + 0.872192i \(0.662698\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) −1.00000 −0.0390434
\(657\) 0 0
\(658\) −2.00000 −0.0779681
\(659\) 12.0000 0.467454 0.233727 0.972302i \(-0.424908\pi\)
0.233727 + 0.972302i \(0.424908\pi\)
\(660\) 0 0
\(661\) 18.0000 0.700119 0.350059 0.936727i \(-0.386161\pi\)
0.350059 + 0.936727i \(0.386161\pi\)
\(662\) 20.0000 0.777322
\(663\) 0 0
\(664\) −5.00000 −0.194038
\(665\) 0 0
\(666\) 0 0
\(667\) 40.0000 1.54881
\(668\) 12.0000 0.464294
\(669\) 0 0
\(670\) 0 0
\(671\) 18.0000 0.694882
\(672\) 0 0
\(673\) 19.0000 0.732396 0.366198 0.930537i \(-0.380659\pi\)
0.366198 + 0.930537i \(0.380659\pi\)
\(674\) 18.0000 0.693334
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) 34.0000 1.30673 0.653363 0.757045i \(-0.273358\pi\)
0.653363 + 0.757045i \(0.273358\pi\)
\(678\) 0 0
\(679\) −8.00000 −0.307012
\(680\) 0 0
\(681\) 0 0
\(682\) −14.0000 −0.536088
\(683\) −40.0000 −1.53056 −0.765279 0.643699i \(-0.777399\pi\)
−0.765279 + 0.643699i \(0.777399\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) −1.00000 −0.0381802
\(687\) 0 0
\(688\) −4.00000 −0.152499
\(689\) 65.0000 2.47630
\(690\) 0 0
\(691\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) −8.00000 −0.303676
\(695\) 0 0
\(696\) 0 0
\(697\) 6.00000 0.227266
\(698\) 21.0000 0.794862
\(699\) 0 0
\(700\) 0 0
\(701\) −15.0000 −0.566542 −0.283271 0.959040i \(-0.591420\pi\)
−0.283271 + 0.959040i \(0.591420\pi\)
\(702\) 0 0
\(703\) −24.0000 −0.905177
\(704\) −2.00000 −0.0753778
\(705\) 0 0
\(706\) −9.00000 −0.338719
\(707\) −12.0000 −0.451306
\(708\) 0 0
\(709\) 2.00000 0.0751116 0.0375558 0.999295i \(-0.488043\pi\)
0.0375558 + 0.999295i \(0.488043\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) −11.0000 −0.412242
\(713\) 56.0000 2.09722
\(714\) 0 0
\(715\) 0 0
\(716\) 10.0000 0.373718
\(717\) 0 0
\(718\) 17.0000 0.634434
\(719\) 16.0000 0.596699 0.298350 0.954457i \(-0.403564\pi\)
0.298350 + 0.954457i \(0.403564\pi\)
\(720\) 0 0
\(721\) 16.0000 0.595871
\(722\) 17.0000 0.632674
\(723\) 0 0
\(724\) 3.00000 0.111494
\(725\) 0 0
\(726\) 0 0
\(727\) −13.0000 −0.482143 −0.241072 0.970507i \(-0.577499\pi\)
−0.241072 + 0.970507i \(0.577499\pi\)
\(728\) 5.00000 0.185312
\(729\) 0 0
\(730\) 0 0
\(731\) 24.0000 0.887672
\(732\) 0 0
\(733\) 14.0000 0.517102 0.258551 0.965998i \(-0.416755\pi\)
0.258551 + 0.965998i \(0.416755\pi\)
\(734\) −8.00000 −0.295285
\(735\) 0 0
\(736\) 8.00000 0.294884
\(737\) −18.0000 −0.663039
\(738\) 0 0
\(739\) 11.0000 0.404642 0.202321 0.979319i \(-0.435152\pi\)
0.202321 + 0.979319i \(0.435152\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) 13.0000 0.477245
\(743\) −37.0000 −1.35740 −0.678699 0.734416i \(-0.737456\pi\)
−0.678699 + 0.734416i \(0.737456\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −30.0000 −1.09838
\(747\) 0 0
\(748\) 12.0000 0.438763
\(749\) −10.0000 −0.365392
\(750\) 0 0
\(751\) −40.0000 −1.45962 −0.729810 0.683650i \(-0.760392\pi\)
−0.729810 + 0.683650i \(0.760392\pi\)
\(752\) 2.00000 0.0729325
\(753\) 0 0
\(754\) −25.0000 −0.910446
\(755\) 0 0
\(756\) 0 0
\(757\) −34.0000 −1.23575 −0.617876 0.786276i \(-0.712006\pi\)
−0.617876 + 0.786276i \(0.712006\pi\)
\(758\) 11.0000 0.399538
\(759\) 0 0
\(760\) 0 0
\(761\) −21.0000 −0.761249 −0.380625 0.924730i \(-0.624291\pi\)
−0.380625 + 0.924730i \(0.624291\pi\)
\(762\) 0 0
\(763\) 0 0
\(764\) 15.0000 0.542681
\(765\) 0 0
\(766\) −14.0000 −0.505841
\(767\) 20.0000 0.722158
\(768\) 0 0
\(769\) 34.0000 1.22607 0.613036 0.790055i \(-0.289948\pi\)
0.613036 + 0.790055i \(0.289948\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 25.0000 0.899770
\(773\) −42.0000 −1.51064 −0.755318 0.655359i \(-0.772517\pi\)
−0.755318 + 0.655359i \(0.772517\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 8.00000 0.287183
\(777\) 0 0
\(778\) −22.0000 −0.788738
\(779\) −6.00000 −0.214972
\(780\) 0 0
\(781\) −30.0000 −1.07348
\(782\) −48.0000 −1.71648
\(783\) 0 0
\(784\) 1.00000 0.0357143
\(785\) 0 0
\(786\) 0 0
\(787\) −32.0000 −1.14068 −0.570338 0.821410i \(-0.693188\pi\)
−0.570338 + 0.821410i \(0.693188\pi\)
\(788\) −5.00000 −0.178118
\(789\) 0 0
\(790\) 0 0
\(791\) −12.0000 −0.426671
\(792\) 0 0
\(793\) 45.0000 1.59800
\(794\) 29.0000 1.02917
\(795\) 0 0
\(796\) 27.0000 0.956990
\(797\) −48.0000 −1.70025 −0.850124 0.526583i \(-0.823473\pi\)
−0.850124 + 0.526583i \(0.823473\pi\)
\(798\) 0 0
\(799\) −12.0000 −0.424529
\(800\) 0 0
\(801\) 0 0
\(802\) 14.0000 0.494357
\(803\) −24.0000 −0.846942
\(804\) 0 0
\(805\) 0 0
\(806\) −35.0000 −1.23282
\(807\) 0 0
\(808\) 12.0000 0.422159
\(809\) 12.0000 0.421898 0.210949 0.977497i \(-0.432345\pi\)
0.210949 + 0.977497i \(0.432345\pi\)
\(810\) 0 0
\(811\) 6.00000 0.210688 0.105344 0.994436i \(-0.466406\pi\)
0.105344 + 0.994436i \(0.466406\pi\)
\(812\) −5.00000 −0.175466
\(813\) 0 0
\(814\) 8.00000 0.280400
\(815\) 0 0
\(816\) 0 0
\(817\) −24.0000 −0.839654
\(818\) −16.0000 −0.559427
\(819\) 0 0
\(820\) 0 0
\(821\) 39.0000 1.36111 0.680555 0.732697i \(-0.261739\pi\)
0.680555 + 0.732697i \(0.261739\pi\)
\(822\) 0 0
\(823\) −18.0000 −0.627441 −0.313720 0.949515i \(-0.601575\pi\)
−0.313720 + 0.949515i \(0.601575\pi\)
\(824\) −16.0000 −0.557386
\(825\) 0 0
\(826\) 4.00000 0.139178
\(827\) −44.0000 −1.53003 −0.765015 0.644013i \(-0.777268\pi\)
−0.765015 + 0.644013i \(0.777268\pi\)
\(828\) 0 0
\(829\) 13.0000 0.451509 0.225754 0.974184i \(-0.427515\pi\)
0.225754 + 0.974184i \(0.427515\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) −5.00000 −0.173344
\(833\) −6.00000 −0.207888
\(834\) 0 0
\(835\) 0 0
\(836\) −12.0000 −0.415029
\(837\) 0 0
\(838\) −1.00000 −0.0345444
\(839\) −56.0000 −1.93333 −0.966667 0.256036i \(-0.917584\pi\)
−0.966667 + 0.256036i \(0.917584\pi\)
\(840\) 0 0
\(841\) −4.00000 −0.137931
\(842\) −14.0000 −0.482472
\(843\) 0 0
\(844\) −4.00000 −0.137686
\(845\) 0 0
\(846\) 0 0
\(847\) 7.00000 0.240523
\(848\) −13.0000 −0.446422
\(849\) 0 0
\(850\) 0 0
\(851\) −32.0000 −1.09695
\(852\) 0 0
\(853\) −26.0000 −0.890223 −0.445112 0.895475i \(-0.646836\pi\)
−0.445112 + 0.895475i \(0.646836\pi\)
\(854\) 9.00000 0.307974
\(855\) 0 0
\(856\) 10.0000 0.341793
\(857\) 23.0000 0.785665 0.392833 0.919610i \(-0.371495\pi\)
0.392833 + 0.919610i \(0.371495\pi\)
\(858\) 0 0
\(859\) 30.0000 1.02359 0.511793 0.859109i \(-0.328981\pi\)
0.511793 + 0.859109i \(0.328981\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −21.0000 −0.715263
\(863\) −13.0000 −0.442525 −0.221263 0.975214i \(-0.571018\pi\)
−0.221263 + 0.975214i \(0.571018\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −20.0000 −0.679628
\(867\) 0 0
\(868\) −7.00000 −0.237595
\(869\) −20.0000 −0.678454
\(870\) 0 0
\(871\) −45.0000 −1.52477
\(872\) 0 0
\(873\) 0 0
\(874\) 48.0000 1.62362
\(875\) 0 0
\(876\) 0 0
\(877\) 44.0000 1.48577 0.742887 0.669417i \(-0.233456\pi\)
0.742887 + 0.669417i \(0.233456\pi\)
\(878\) −16.0000 −0.539974
\(879\) 0 0
\(880\) 0 0
\(881\) 35.0000 1.17918 0.589590 0.807703i \(-0.299289\pi\)
0.589590 + 0.807703i \(0.299289\pi\)
\(882\) 0 0
\(883\) −12.0000 −0.403832 −0.201916 0.979403i \(-0.564717\pi\)
−0.201916 + 0.979403i \(0.564717\pi\)
\(884\) 30.0000 1.00901
\(885\) 0 0
\(886\) 2.00000 0.0671913
\(887\) −56.0000 −1.88030 −0.940148 0.340766i \(-0.889313\pi\)
−0.940148 + 0.340766i \(0.889313\pi\)
\(888\) 0 0
\(889\) 8.00000 0.268311
\(890\) 0 0
\(891\) 0 0
\(892\) 21.0000 0.703132
\(893\) 12.0000 0.401565
\(894\) 0 0
\(895\) 0 0
\(896\) −1.00000 −0.0334077
\(897\) 0 0
\(898\) −8.00000 −0.266963
\(899\) 35.0000 1.16732
\(900\) 0 0
\(901\) 78.0000 2.59856
\(902\) 2.00000 0.0665927
\(903\) 0 0
\(904\) 12.0000 0.399114
\(905\) 0 0
\(906\) 0 0
\(907\) 17.0000 0.564476 0.282238 0.959344i \(-0.408923\pi\)
0.282238 + 0.959344i \(0.408923\pi\)
\(908\) 19.0000 0.630537
\(909\) 0 0
\(910\) 0 0
\(911\) 53.0000 1.75597 0.877984 0.478690i \(-0.158888\pi\)
0.877984 + 0.478690i \(0.158888\pi\)
\(912\) 0 0
\(913\) 10.0000 0.330952
\(914\) 42.0000 1.38924
\(915\) 0 0
\(916\) −22.0000 −0.726900
\(917\) 1.00000 0.0330229
\(918\) 0 0
\(919\) −6.00000 −0.197922 −0.0989609 0.995091i \(-0.531552\pi\)
−0.0989609 + 0.995091i \(0.531552\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) 18.0000 0.592798
\(923\) −75.0000 −2.46866
\(924\) 0 0
\(925\) 0 0
\(926\) −4.00000 −0.131448
\(927\) 0 0
\(928\) 5.00000 0.164133
\(929\) 15.0000 0.492134 0.246067 0.969253i \(-0.420862\pi\)
0.246067 + 0.969253i \(0.420862\pi\)
\(930\) 0 0
\(931\) 6.00000 0.196642
\(932\) −6.00000 −0.196537
\(933\) 0 0
\(934\) −21.0000 −0.687141
\(935\) 0 0
\(936\) 0 0
\(937\) −18.0000 −0.588034 −0.294017 0.955800i \(-0.594992\pi\)
−0.294017 + 0.955800i \(0.594992\pi\)
\(938\) −9.00000 −0.293860
\(939\) 0 0
\(940\) 0 0
\(941\) 42.0000 1.36916 0.684580 0.728937i \(-0.259985\pi\)
0.684580 + 0.728937i \(0.259985\pi\)
\(942\) 0 0
\(943\) −8.00000 −0.260516
\(944\) −4.00000 −0.130189
\(945\) 0 0
\(946\) 8.00000 0.260102
\(947\) 32.0000 1.03986 0.519930 0.854209i \(-0.325958\pi\)
0.519930 + 0.854209i \(0.325958\pi\)
\(948\) 0 0
\(949\) −60.0000 −1.94768
\(950\) 0 0
\(951\) 0 0
\(952\) 6.00000 0.194461
\(953\) −58.0000 −1.87880 −0.939402 0.342817i \(-0.888619\pi\)
−0.939402 + 0.342817i \(0.888619\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) 24.0000 0.776215
\(957\) 0 0
\(958\) −16.0000 −0.516937
\(959\) −12.0000 −0.387500
\(960\) 0 0
\(961\) 18.0000 0.580645
\(962\) 20.0000 0.644826
\(963\) 0 0
\(964\) 16.0000 0.515325
\(965\) 0 0
\(966\) 0 0
\(967\) −14.0000 −0.450210 −0.225105 0.974335i \(-0.572272\pi\)
−0.225105 + 0.974335i \(0.572272\pi\)
\(968\) −7.00000 −0.224989
\(969\) 0 0
\(970\) 0 0
\(971\) 3.00000 0.0962746 0.0481373 0.998841i \(-0.484672\pi\)
0.0481373 + 0.998841i \(0.484672\pi\)
\(972\) 0 0
\(973\) −14.0000 −0.448819
\(974\) 8.00000 0.256337
\(975\) 0 0
\(976\) −9.00000 −0.288083
\(977\) −42.0000 −1.34370 −0.671850 0.740688i \(-0.734500\pi\)
−0.671850 + 0.740688i \(0.734500\pi\)
\(978\) 0 0
\(979\) 22.0000 0.703123
\(980\) 0 0
\(981\) 0 0
\(982\) −26.0000 −0.829693
\(983\) −4.00000 −0.127580 −0.0637901 0.997963i \(-0.520319\pi\)
−0.0637901 + 0.997963i \(0.520319\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) −30.0000 −0.955395
\(987\) 0 0
\(988\) −30.0000 −0.954427
\(989\) −32.0000 −1.01754
\(990\) 0 0
\(991\) 22.0000 0.698853 0.349427 0.936964i \(-0.386376\pi\)
0.349427 + 0.936964i \(0.386376\pi\)
\(992\) 7.00000 0.222250
\(993\) 0 0
\(994\) −15.0000 −0.475771
\(995\) 0 0
\(996\) 0 0
\(997\) 59.0000 1.86855 0.934274 0.356555i \(-0.116049\pi\)
0.934274 + 0.356555i \(0.116049\pi\)
\(998\) 25.0000 0.791361
\(999\) 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 \(a_p\))