Properties

Label 9450.2.a.r.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

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: \(0\)
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

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+1.00000 q^{4}\) \(-1.00000 q^{7}\) \(-1.00000 q^{8}\) \(+1.00000 q^{11}\) \(+5.00000 q^{13}\) \(+1.00000 q^{14}\) \(+1.00000 q^{16}\) \(+4.00000 q^{17}\) \(+2.00000 q^{19}\) \(-1.00000 q^{22}\) \(+5.00000 q^{23}\) \(-5.00000 q^{26}\) \(-1.00000 q^{28}\) \(-6.00000 q^{29}\) \(+10.0000 q^{31}\) \(-1.00000 q^{32}\) \(-4.00000 q^{34}\) \(-1.00000 q^{37}\) \(-2.00000 q^{38}\) \(+2.00000 q^{41}\) \(-6.00000 q^{43}\) \(+1.00000 q^{44}\) \(-5.00000 q^{46}\) \(-1.00000 q^{47}\) \(+1.00000 q^{49}\) \(+5.00000 q^{52}\) \(-6.00000 q^{53}\) \(+1.00000 q^{56}\) \(+6.00000 q^{58}\) \(+13.0000 q^{59}\) \(+13.0000 q^{61}\) \(-10.0000 q^{62}\) \(+1.00000 q^{64}\) \(+4.00000 q^{68}\) \(+11.0000 q^{71}\) \(+14.0000 q^{73}\) \(+1.00000 q^{74}\) \(+2.00000 q^{76}\) \(-1.00000 q^{77}\) \(-2.00000 q^{82}\) \(-12.0000 q^{83}\) \(+6.00000 q^{86}\) \(-1.00000 q^{88}\) \(-4.00000 q^{89}\) \(-5.00000 q^{91}\) \(+5.00000 q^{92}\) \(+1.00000 q^{94}\) \(-1.00000 q^{97}\) \(-1.00000 q^{98}\) \(+O(q^{100})\)

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 \(-0.451829\pi\)
0.150756 + 0.988571i \(0.451829\pi\)
\(12\) 0 0
\(13\) 5.00000 1.38675 0.693375 0.720577i \(-0.256123\pi\)
0.693375 + 0.720577i \(0.256123\pi\)
\(14\) 1.00000 0.267261
\(15\) 0 0
\(16\) 1.00000 0.250000
\(17\) 4.00000 0.970143 0.485071 0.874475i \(-0.338794\pi\)
0.485071 + 0.874475i \(0.338794\pi\)
\(18\) 0 0
\(19\) 2.00000 0.458831 0.229416 0.973329i \(-0.426318\pi\)
0.229416 + 0.973329i \(0.426318\pi\)
\(20\) 0 0
\(21\) 0 0
\(22\) −1.00000 −0.213201
\(23\) 5.00000 1.04257 0.521286 0.853382i \(-0.325452\pi\)
0.521286 + 0.853382i \(0.325452\pi\)
\(24\) 0 0
\(25\) 0 0
\(26\) −5.00000 −0.980581
\(27\) 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
\(31\) 10.0000 1.79605 0.898027 0.439941i \(-0.145001\pi\)
0.898027 + 0.439941i \(0.145001\pi\)
\(32\) −1.00000 −0.176777
\(33\) 0 0
\(34\) −4.00000 −0.685994
\(35\) 0 0
\(36\) 0 0
\(37\) −1.00000 −0.164399 −0.0821995 0.996616i \(-0.526194\pi\)
−0.0821995 + 0.996616i \(0.526194\pi\)
\(38\) −2.00000 −0.324443
\(39\) 0 0
\(40\) 0 0
\(41\) 2.00000 0.312348 0.156174 0.987730i \(-0.450084\pi\)
0.156174 + 0.987730i \(0.450084\pi\)
\(42\) 0 0
\(43\) −6.00000 −0.914991 −0.457496 0.889212i \(-0.651253\pi\)
−0.457496 + 0.889212i \(0.651253\pi\)
\(44\) 1.00000 0.150756
\(45\) 0 0
\(46\) −5.00000 −0.737210
\(47\) −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
\(52\) 5.00000 0.693375
\(53\) −6.00000 −0.824163 −0.412082 0.911147i \(-0.635198\pi\)
−0.412082 + 0.911147i \(0.635198\pi\)
\(54\) 0 0
\(55\) 0 0
\(56\) 1.00000 0.133631
\(57\) 0 0
\(58\) 6.00000 0.787839
\(59\) 13.0000 1.69246 0.846228 0.532821i \(-0.178868\pi\)
0.846228 + 0.532821i \(0.178868\pi\)
\(60\) 0 0
\(61\) 13.0000 1.66448 0.832240 0.554416i \(-0.187058\pi\)
0.832240 + 0.554416i \(0.187058\pi\)
\(62\) −10.0000 −1.27000
\(63\) 0 0
\(64\) 1.00000 0.125000
\(65\) 0 0
\(66\) 0 0
\(67\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(68\) 4.00000 0.485071
\(69\) 0 0
\(70\) 0 0
\(71\) 11.0000 1.30546 0.652730 0.757591i \(-0.273624\pi\)
0.652730 + 0.757591i \(0.273624\pi\)
\(72\) 0 0
\(73\) 14.0000 1.63858 0.819288 0.573382i \(-0.194369\pi\)
0.819288 + 0.573382i \(0.194369\pi\)
\(74\) 1.00000 0.116248
\(75\) 0 0
\(76\) 2.00000 0.229416
\(77\) −1.00000 −0.113961
\(78\) 0 0
\(79\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(80\) 0 0
\(81\) 0 0
\(82\) −2.00000 −0.220863
\(83\) −12.0000 −1.31717 −0.658586 0.752506i \(-0.728845\pi\)
−0.658586 + 0.752506i \(0.728845\pi\)
\(84\) 0 0
\(85\) 0 0
\(86\) 6.00000 0.646997
\(87\) 0 0
\(88\) −1.00000 −0.106600
\(89\) −4.00000 −0.423999 −0.212000 0.977270i \(-0.567998\pi\)
−0.212000 + 0.977270i \(0.567998\pi\)
\(90\) 0 0
\(91\) −5.00000 −0.524142
\(92\) 5.00000 0.521286
\(93\) 0 0
\(94\) 1.00000 0.103142
\(95\) 0 0
\(96\) 0 0
\(97\) −1.00000 −0.101535 −0.0507673 0.998711i \(-0.516167\pi\)
−0.0507673 + 0.998711i \(0.516167\pi\)
\(98\) −1.00000 −0.101015
\(99\) 0 0
\(100\) 0 0
\(101\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(102\) 0 0
\(103\) −14.0000 −1.37946 −0.689730 0.724066i \(-0.742271\pi\)
−0.689730 + 0.724066i \(0.742271\pi\)
\(104\) −5.00000 −0.490290
\(105\) 0 0
\(106\) 6.00000 0.582772
\(107\) −19.0000 −1.83680 −0.918400 0.395654i \(-0.870518\pi\)
−0.918400 + 0.395654i \(0.870518\pi\)
\(108\) 0 0
\(109\) 10.0000 0.957826 0.478913 0.877862i \(-0.341031\pi\)
0.478913 + 0.877862i \(0.341031\pi\)
\(110\) 0 0
\(111\) 0 0
\(112\) −1.00000 −0.0944911
\(113\) −10.0000 −0.940721 −0.470360 0.882474i \(-0.655876\pi\)
−0.470360 + 0.882474i \(0.655876\pi\)
\(114\) 0 0
\(115\) 0 0
\(116\) −6.00000 −0.557086
\(117\) 0 0
\(118\) −13.0000 −1.19675
\(119\) −4.00000 −0.366679
\(120\) 0 0
\(121\) −10.0000 −0.909091
\(122\) −13.0000 −1.17696
\(123\) 0 0
\(124\) 10.0000 0.898027
\(125\) 0 0
\(126\) 0 0
\(127\) −6.00000 −0.532414 −0.266207 0.963916i \(-0.585770\pi\)
−0.266207 + 0.963916i \(0.585770\pi\)
\(128\) −1.00000 −0.0883883
\(129\) 0 0
\(130\) 0 0
\(131\) 9.00000 0.786334 0.393167 0.919467i \(-0.371379\pi\)
0.393167 + 0.919467i \(0.371379\pi\)
\(132\) 0 0
\(133\) −2.00000 −0.173422
\(134\) 0 0
\(135\) 0 0
\(136\) −4.00000 −0.342997
\(137\) 2.00000 0.170872 0.0854358 0.996344i \(-0.472772\pi\)
0.0854358 + 0.996344i \(0.472772\pi\)
\(138\) 0 0
\(139\) 20.0000 1.69638 0.848189 0.529694i \(-0.177693\pi\)
0.848189 + 0.529694i \(0.177693\pi\)
\(140\) 0 0
\(141\) 0 0
\(142\) −11.0000 −0.923099
\(143\) 5.00000 0.418121
\(144\) 0 0
\(145\) 0 0
\(146\) −14.0000 −1.15865
\(147\) 0 0
\(148\) −1.00000 −0.0821995
\(149\) −18.0000 −1.47462 −0.737309 0.675556i \(-0.763904\pi\)
−0.737309 + 0.675556i \(0.763904\pi\)
\(150\) 0 0
\(151\) −10.0000 −0.813788 −0.406894 0.913475i \(-0.633388\pi\)
−0.406894 + 0.913475i \(0.633388\pi\)
\(152\) −2.00000 −0.162221
\(153\) 0 0
\(154\) 1.00000 0.0805823
\(155\) 0 0
\(156\) 0 0
\(157\) −14.0000 −1.11732 −0.558661 0.829396i \(-0.688685\pi\)
−0.558661 + 0.829396i \(0.688685\pi\)
\(158\) 0 0
\(159\) 0 0
\(160\) 0 0
\(161\) −5.00000 −0.394055
\(162\) 0 0
\(163\) 18.0000 1.40987 0.704934 0.709273i \(-0.250976\pi\)
0.704934 + 0.709273i \(0.250976\pi\)
\(164\) 2.00000 0.156174
\(165\) 0 0
\(166\) 12.0000 0.931381
\(167\) −5.00000 −0.386912 −0.193456 0.981109i \(-0.561970\pi\)
−0.193456 + 0.981109i \(0.561970\pi\)
\(168\) 0 0
\(169\) 12.0000 0.923077
\(170\) 0 0
\(171\) 0 0
\(172\) −6.00000 −0.457496
\(173\) 16.0000 1.21646 0.608229 0.793762i \(-0.291880\pi\)
0.608229 + 0.793762i \(0.291880\pi\)
\(174\) 0 0
\(175\) 0 0
\(176\) 1.00000 0.0753778
\(177\) 0 0
\(178\) 4.00000 0.299813
\(179\) −23.0000 −1.71910 −0.859550 0.511051i \(-0.829256\pi\)
−0.859550 + 0.511051i \(0.829256\pi\)
\(180\) 0 0
\(181\) 11.0000 0.817624 0.408812 0.912619i \(-0.365943\pi\)
0.408812 + 0.912619i \(0.365943\pi\)
\(182\) 5.00000 0.370625
\(183\) 0 0
\(184\) −5.00000 −0.368605
\(185\) 0 0
\(186\) 0 0
\(187\) 4.00000 0.292509
\(188\) −1.00000 −0.0729325
\(189\) 0 0
\(190\) 0 0
\(191\) −4.00000 −0.289430 −0.144715 0.989473i \(-0.546227\pi\)
−0.144715 + 0.989473i \(0.546227\pi\)
\(192\) 0 0
\(193\) 2.00000 0.143963 0.0719816 0.997406i \(-0.477068\pi\)
0.0719816 + 0.997406i \(0.477068\pi\)
\(194\) 1.00000 0.0717958
\(195\) 0 0
\(196\) 1.00000 0.0714286
\(197\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(198\) 0 0
\(199\) 2.00000 0.141776 0.0708881 0.997484i \(-0.477417\pi\)
0.0708881 + 0.997484i \(0.477417\pi\)
\(200\) 0 0
\(201\) 0 0
\(202\) 0 0
\(203\) 6.00000 0.421117
\(204\) 0 0
\(205\) 0 0
\(206\) 14.0000 0.975426
\(207\) 0 0
\(208\) 5.00000 0.346688
\(209\) 2.00000 0.138343
\(210\) 0 0
\(211\) 20.0000 1.37686 0.688428 0.725304i \(-0.258301\pi\)
0.688428 + 0.725304i \(0.258301\pi\)
\(212\) −6.00000 −0.412082
\(213\) 0 0
\(214\) 19.0000 1.29881
\(215\) 0 0
\(216\) 0 0
\(217\) −10.0000 −0.678844
\(218\) −10.0000 −0.677285
\(219\) 0 0
\(220\) 0 0
\(221\) 20.0000 1.34535
\(222\) 0 0
\(223\) 6.00000 0.401790 0.200895 0.979613i \(-0.435615\pi\)
0.200895 + 0.979613i \(0.435615\pi\)
\(224\) 1.00000 0.0668153
\(225\) 0 0
\(226\) 10.0000 0.665190
\(227\) 3.00000 0.199117 0.0995585 0.995032i \(-0.468257\pi\)
0.0995585 + 0.995032i \(0.468257\pi\)
\(228\) 0 0
\(229\) 19.0000 1.25556 0.627778 0.778393i \(-0.283965\pi\)
0.627778 + 0.778393i \(0.283965\pi\)
\(230\) 0 0
\(231\) 0 0
\(232\) 6.00000 0.393919
\(233\) 8.00000 0.524097 0.262049 0.965055i \(-0.415602\pi\)
0.262049 + 0.965055i \(0.415602\pi\)
\(234\) 0 0
\(235\) 0 0
\(236\) 13.0000 0.846228
\(237\) 0 0
\(238\) 4.00000 0.259281
\(239\) −19.0000 −1.22901 −0.614504 0.788914i \(-0.710644\pi\)
−0.614504 + 0.788914i \(0.710644\pi\)
\(240\) 0 0
\(241\) −15.0000 −0.966235 −0.483117 0.875556i \(-0.660496\pi\)
−0.483117 + 0.875556i \(0.660496\pi\)
\(242\) 10.0000 0.642824
\(243\) 0 0
\(244\) 13.0000 0.832240
\(245\) 0 0
\(246\) 0 0
\(247\) 10.0000 0.636285
\(248\) −10.0000 −0.635001
\(249\) 0 0
\(250\) 0 0
\(251\) 1.00000 0.0631194 0.0315597 0.999502i \(-0.489953\pi\)
0.0315597 + 0.999502i \(0.489953\pi\)
\(252\) 0 0
\(253\) 5.00000 0.314347
\(254\) 6.00000 0.376473
\(255\) 0 0
\(256\) 1.00000 0.0625000
\(257\) −8.00000 −0.499026 −0.249513 0.968371i \(-0.580271\pi\)
−0.249513 + 0.968371i \(0.580271\pi\)
\(258\) 0 0
\(259\) 1.00000 0.0621370
\(260\) 0 0
\(261\) 0 0
\(262\) −9.00000 −0.556022
\(263\) −3.00000 −0.184988 −0.0924940 0.995713i \(-0.529484\pi\)
−0.0924940 + 0.995713i \(0.529484\pi\)
\(264\) 0 0
\(265\) 0 0
\(266\) 2.00000 0.122628
\(267\) 0 0
\(268\) 0 0
\(269\) −24.0000 −1.46331 −0.731653 0.681677i \(-0.761251\pi\)
−0.731653 + 0.681677i \(0.761251\pi\)
\(270\) 0 0
\(271\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(272\) 4.00000 0.242536
\(273\) 0 0
\(274\) −2.00000 −0.120824
\(275\) 0 0
\(276\) 0 0
\(277\) −2.00000 −0.120168 −0.0600842 0.998193i \(-0.519137\pi\)
−0.0600842 + 0.998193i \(0.519137\pi\)
\(278\) −20.0000 −1.19952
\(279\) 0 0
\(280\) 0 0
\(281\) −14.0000 −0.835170 −0.417585 0.908638i \(-0.637123\pi\)
−0.417585 + 0.908638i \(0.637123\pi\)
\(282\) 0 0
\(283\) −14.0000 −0.832214 −0.416107 0.909316i \(-0.636606\pi\)
−0.416107 + 0.909316i \(0.636606\pi\)
\(284\) 11.0000 0.652730
\(285\) 0 0
\(286\) −5.00000 −0.295656
\(287\) −2.00000 −0.118056
\(288\) 0 0
\(289\) −1.00000 −0.0588235
\(290\) 0 0
\(291\) 0 0
\(292\) 14.0000 0.819288
\(293\) 24.0000 1.40209 0.701047 0.713115i \(-0.252716\pi\)
0.701047 + 0.713115i \(0.252716\pi\)
\(294\) 0 0
\(295\) 0 0
\(296\) 1.00000 0.0581238
\(297\) 0 0
\(298\) 18.0000 1.04271
\(299\) 25.0000 1.44579
\(300\) 0 0
\(301\) 6.00000 0.345834
\(302\) 10.0000 0.575435
\(303\) 0 0
\(304\) 2.00000 0.114708
\(305\) 0 0
\(306\) 0 0
\(307\) −2.00000 −0.114146 −0.0570730 0.998370i \(-0.518177\pi\)
−0.0570730 + 0.998370i \(0.518177\pi\)
\(308\) −1.00000 −0.0569803
\(309\) 0 0
\(310\) 0 0
\(311\) 11.0000 0.623753 0.311876 0.950123i \(-0.399043\pi\)
0.311876 + 0.950123i \(0.399043\pi\)
\(312\) 0 0
\(313\) 2.00000 0.113047 0.0565233 0.998401i \(-0.481998\pi\)
0.0565233 + 0.998401i \(0.481998\pi\)
\(314\) 14.0000 0.790066
\(315\) 0 0
\(316\) 0 0
\(317\) 10.0000 0.561656 0.280828 0.959758i \(-0.409391\pi\)
0.280828 + 0.959758i \(0.409391\pi\)
\(318\) 0 0
\(319\) −6.00000 −0.335936
\(320\) 0 0
\(321\) 0 0
\(322\) 5.00000 0.278639
\(323\) 8.00000 0.445132
\(324\) 0 0
\(325\) 0 0
\(326\) −18.0000 −0.996928
\(327\) 0 0
\(328\) −2.00000 −0.110432
\(329\) 1.00000 0.0551318
\(330\) 0 0
\(331\) 22.0000 1.20923 0.604615 0.796518i \(-0.293327\pi\)
0.604615 + 0.796518i \(0.293327\pi\)
\(332\) −12.0000 −0.658586
\(333\) 0 0
\(334\) 5.00000 0.273588
\(335\) 0 0
\(336\) 0 0
\(337\) −2.00000 −0.108947 −0.0544735 0.998515i \(-0.517348\pi\)
−0.0544735 + 0.998515i \(0.517348\pi\)
\(338\) −12.0000 −0.652714
\(339\) 0 0
\(340\) 0 0
\(341\) 10.0000 0.541530
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 6.00000 0.323498
\(345\) 0 0
\(346\) −16.0000 −0.860165
\(347\) 12.0000 0.644194 0.322097 0.946707i \(-0.395612\pi\)
0.322097 + 0.946707i \(0.395612\pi\)
\(348\) 0 0
\(349\) −10.0000 −0.535288 −0.267644 0.963518i \(-0.586245\pi\)
−0.267644 + 0.963518i \(0.586245\pi\)
\(350\) 0 0
\(351\) 0 0
\(352\) −1.00000 −0.0533002
\(353\) −6.00000 −0.319348 −0.159674 0.987170i \(-0.551044\pi\)
−0.159674 + 0.987170i \(0.551044\pi\)
\(354\) 0 0
\(355\) 0 0
\(356\) −4.00000 −0.212000
\(357\) 0 0
\(358\) 23.0000 1.21559
\(359\) 25.0000 1.31945 0.659725 0.751507i \(-0.270673\pi\)
0.659725 + 0.751507i \(0.270673\pi\)
\(360\) 0 0
\(361\) −15.0000 −0.789474
\(362\) −11.0000 −0.578147
\(363\) 0 0
\(364\) −5.00000 −0.262071
\(365\) 0 0
\(366\) 0 0
\(367\) −28.0000 −1.46159 −0.730794 0.682598i \(-0.760850\pi\)
−0.730794 + 0.682598i \(0.760850\pi\)
\(368\) 5.00000 0.260643
\(369\) 0 0
\(370\) 0 0
\(371\) 6.00000 0.311504
\(372\) 0 0
\(373\) 22.0000 1.13912 0.569558 0.821951i \(-0.307114\pi\)
0.569558 + 0.821951i \(0.307114\pi\)
\(374\) −4.00000 −0.206835
\(375\) 0 0
\(376\) 1.00000 0.0515711
\(377\) −30.0000 −1.54508
\(378\) 0 0
\(379\) 10.0000 0.513665 0.256833 0.966456i \(-0.417321\pi\)
0.256833 + 0.966456i \(0.417321\pi\)
\(380\) 0 0
\(381\) 0 0
\(382\) 4.00000 0.204658
\(383\) 15.0000 0.766464 0.383232 0.923652i \(-0.374811\pi\)
0.383232 + 0.923652i \(0.374811\pi\)
\(384\) 0 0
\(385\) 0 0
\(386\) −2.00000 −0.101797
\(387\) 0 0
\(388\) −1.00000 −0.0507673
\(389\) −6.00000 −0.304212 −0.152106 0.988364i \(-0.548606\pi\)
−0.152106 + 0.988364i \(0.548606\pi\)
\(390\) 0 0
\(391\) 20.0000 1.01144
\(392\) −1.00000 −0.0505076
\(393\) 0 0
\(394\) 0 0
\(395\) 0 0
\(396\) 0 0
\(397\) −1.00000 −0.0501886 −0.0250943 0.999685i \(-0.507989\pi\)
−0.0250943 + 0.999685i \(0.507989\pi\)
\(398\) −2.00000 −0.100251
\(399\) 0 0
\(400\) 0 0
\(401\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(402\) 0 0
\(403\) 50.0000 2.49068
\(404\) 0 0
\(405\) 0 0
\(406\) −6.00000 −0.297775
\(407\) −1.00000 −0.0495682
\(408\) 0 0
\(409\) 37.0000 1.82953 0.914766 0.403984i \(-0.132375\pi\)
0.914766 + 0.403984i \(0.132375\pi\)
\(410\) 0 0
\(411\) 0 0
\(412\) −14.0000 −0.689730
\(413\) −13.0000 −0.639688
\(414\) 0 0
\(415\) 0 0
\(416\) −5.00000 −0.245145
\(417\) 0 0
\(418\) −2.00000 −0.0978232
\(419\) −12.0000 −0.586238 −0.293119 0.956076i \(-0.594693\pi\)
−0.293119 + 0.956076i \(0.594693\pi\)
\(420\) 0 0
\(421\) 19.0000 0.926003 0.463002 0.886357i \(-0.346772\pi\)
0.463002 + 0.886357i \(0.346772\pi\)
\(422\) −20.0000 −0.973585
\(423\) 0 0
\(424\) 6.00000 0.291386
\(425\) 0 0
\(426\) 0 0
\(427\) −13.0000 −0.629114
\(428\) −19.0000 −0.918400
\(429\) 0 0
\(430\) 0 0
\(431\) 33.0000 1.58955 0.794777 0.606902i \(-0.207588\pi\)
0.794777 + 0.606902i \(0.207588\pi\)
\(432\) 0 0
\(433\) 33.0000 1.58588 0.792939 0.609301i \(-0.208550\pi\)
0.792939 + 0.609301i \(0.208550\pi\)
\(434\) 10.0000 0.480015
\(435\) 0 0
\(436\) 10.0000 0.478913
\(437\) 10.0000 0.478365
\(438\) 0 0
\(439\) 32.0000 1.52728 0.763638 0.645644i \(-0.223411\pi\)
0.763638 + 0.645644i \(0.223411\pi\)
\(440\) 0 0
\(441\) 0 0
\(442\) −20.0000 −0.951303
\(443\) 31.0000 1.47285 0.736427 0.676517i \(-0.236511\pi\)
0.736427 + 0.676517i \(0.236511\pi\)
\(444\) 0 0
\(445\) 0 0
\(446\) −6.00000 −0.284108
\(447\) 0 0
\(448\) −1.00000 −0.0472456
\(449\) −38.0000 −1.79333 −0.896665 0.442709i \(-0.854018\pi\)
−0.896665 + 0.442709i \(0.854018\pi\)
\(450\) 0 0
\(451\) 2.00000 0.0941763
\(452\) −10.0000 −0.470360
\(453\) 0 0
\(454\) −3.00000 −0.140797
\(455\) 0 0
\(456\) 0 0
\(457\) −13.0000 −0.608114 −0.304057 0.952654i \(-0.598341\pi\)
−0.304057 + 0.952654i \(0.598341\pi\)
\(458\) −19.0000 −0.887812
\(459\) 0 0
\(460\) 0 0
\(461\) 20.0000 0.931493 0.465746 0.884918i \(-0.345786\pi\)
0.465746 + 0.884918i \(0.345786\pi\)
\(462\) 0 0
\(463\) 34.0000 1.58011 0.790057 0.613033i \(-0.210051\pi\)
0.790057 + 0.613033i \(0.210051\pi\)
\(464\) −6.00000 −0.278543
\(465\) 0 0
\(466\) −8.00000 −0.370593
\(467\) −13.0000 −0.601568 −0.300784 0.953692i \(-0.597248\pi\)
−0.300784 + 0.953692i \(0.597248\pi\)
\(468\) 0 0
\(469\) 0 0
\(470\) 0 0
\(471\) 0 0
\(472\) −13.0000 −0.598374
\(473\) −6.00000 −0.275880
\(474\) 0 0
\(475\) 0 0
\(476\) −4.00000 −0.183340
\(477\) 0 0
\(478\) 19.0000 0.869040
\(479\) 24.0000 1.09659 0.548294 0.836286i \(-0.315277\pi\)
0.548294 + 0.836286i \(0.315277\pi\)
\(480\) 0 0
\(481\) −5.00000 −0.227980
\(482\) 15.0000 0.683231
\(483\) 0 0
\(484\) −10.0000 −0.454545
\(485\) 0 0
\(486\) 0 0
\(487\) −12.0000 −0.543772 −0.271886 0.962329i \(-0.587647\pi\)
−0.271886 + 0.962329i \(0.587647\pi\)
\(488\) −13.0000 −0.588482
\(489\) 0 0
\(490\) 0 0
\(491\) −36.0000 −1.62466 −0.812329 0.583200i \(-0.801800\pi\)
−0.812329 + 0.583200i \(0.801800\pi\)
\(492\) 0 0
\(493\) −24.0000 −1.08091
\(494\) −10.0000 −0.449921
\(495\) 0 0
\(496\) 10.0000 0.449013
\(497\) −11.0000 −0.493417
\(498\) 0 0
\(499\) 40.0000 1.79065 0.895323 0.445418i \(-0.146945\pi\)
0.895323 + 0.445418i \(0.146945\pi\)
\(500\) 0 0
\(501\) 0 0
\(502\) −1.00000 −0.0446322
\(503\) −4.00000 −0.178351 −0.0891756 0.996016i \(-0.528423\pi\)
−0.0891756 + 0.996016i \(0.528423\pi\)
\(504\) 0 0
\(505\) 0 0
\(506\) −5.00000 −0.222277
\(507\) 0 0
\(508\) −6.00000 −0.266207
\(509\) −22.0000 −0.975133 −0.487566 0.873086i \(-0.662115\pi\)
−0.487566 + 0.873086i \(0.662115\pi\)
\(510\) 0 0
\(511\) −14.0000 −0.619324
\(512\) −1.00000 −0.0441942
\(513\) 0 0
\(514\) 8.00000 0.352865
\(515\) 0 0
\(516\) 0 0
\(517\) −1.00000 −0.0439799
\(518\) −1.00000 −0.0439375
\(519\) 0 0
\(520\) 0 0
\(521\) −12.0000 −0.525730 −0.262865 0.964833i \(-0.584667\pi\)
−0.262865 + 0.964833i \(0.584667\pi\)
\(522\) 0 0
\(523\) −8.00000 −0.349816 −0.174908 0.984585i \(-0.555963\pi\)
−0.174908 + 0.984585i \(0.555963\pi\)
\(524\) 9.00000 0.393167
\(525\) 0 0
\(526\) 3.00000 0.130806
\(527\) 40.0000 1.74243
\(528\) 0 0
\(529\) 2.00000 0.0869565
\(530\) 0 0
\(531\) 0 0
\(532\) −2.00000 −0.0867110
\(533\) 10.0000 0.433148
\(534\) 0 0
\(535\) 0 0
\(536\) 0 0
\(537\) 0 0
\(538\) 24.0000 1.03471
\(539\) 1.00000 0.0430730
\(540\) 0 0
\(541\) −37.0000 −1.59075 −0.795377 0.606115i \(-0.792727\pi\)
−0.795377 + 0.606115i \(0.792727\pi\)
\(542\) 0 0
\(543\) 0 0
\(544\) −4.00000 −0.171499
\(545\) 0 0
\(546\) 0 0
\(547\) 8.00000 0.342055 0.171028 0.985266i \(-0.445291\pi\)
0.171028 + 0.985266i \(0.445291\pi\)
\(548\) 2.00000 0.0854358
\(549\) 0 0
\(550\) 0 0
\(551\) −12.0000 −0.511217
\(552\) 0 0
\(553\) 0 0
\(554\) 2.00000 0.0849719
\(555\) 0 0
\(556\) 20.0000 0.848189
\(557\) −40.0000 −1.69485 −0.847427 0.530912i \(-0.821850\pi\)
−0.847427 + 0.530912i \(0.821850\pi\)
\(558\) 0 0
\(559\) −30.0000 −1.26886
\(560\) 0 0
\(561\) 0 0
\(562\) 14.0000 0.590554
\(563\) 21.0000 0.885044 0.442522 0.896758i \(-0.354084\pi\)
0.442522 + 0.896758i \(0.354084\pi\)
\(564\) 0 0
\(565\) 0 0
\(566\) 14.0000 0.588464
\(567\) 0 0
\(568\) −11.0000 −0.461550
\(569\) 18.0000 0.754599 0.377300 0.926091i \(-0.376853\pi\)
0.377300 + 0.926091i \(0.376853\pi\)
\(570\) 0 0
\(571\) 10.0000 0.418487 0.209243 0.977864i \(-0.432900\pi\)
0.209243 + 0.977864i \(0.432900\pi\)
\(572\) 5.00000 0.209061
\(573\) 0 0
\(574\) 2.00000 0.0834784
\(575\) 0 0
\(576\) 0 0
\(577\) 1.00000 0.0416305 0.0208153 0.999783i \(-0.493374\pi\)
0.0208153 + 0.999783i \(0.493374\pi\)
\(578\) 1.00000 0.0415945
\(579\) 0 0
\(580\) 0 0
\(581\) 12.0000 0.497844
\(582\) 0 0
\(583\) −6.00000 −0.248495
\(584\) −14.0000 −0.579324
\(585\) 0 0
\(586\) −24.0000 −0.991431
\(587\) 36.0000 1.48588 0.742940 0.669359i \(-0.233431\pi\)
0.742940 + 0.669359i \(0.233431\pi\)
\(588\) 0 0
\(589\) 20.0000 0.824086
\(590\) 0 0
\(591\) 0 0
\(592\) −1.00000 −0.0410997
\(593\) −24.0000 −0.985562 −0.492781 0.870153i \(-0.664020\pi\)
−0.492781 + 0.870153i \(0.664020\pi\)
\(594\) 0 0
\(595\) 0 0
\(596\) −18.0000 −0.737309
\(597\) 0 0
\(598\) −25.0000 −1.02233
\(599\) −4.00000 −0.163436 −0.0817178 0.996656i \(-0.526041\pi\)
−0.0817178 + 0.996656i \(0.526041\pi\)
\(600\) 0 0
\(601\) 23.0000 0.938190 0.469095 0.883148i \(-0.344580\pi\)
0.469095 + 0.883148i \(0.344580\pi\)
\(602\) −6.00000 −0.244542
\(603\) 0 0
\(604\) −10.0000 −0.406894
\(605\) 0 0
\(606\) 0 0
\(607\) −30.0000 −1.21766 −0.608831 0.793300i \(-0.708361\pi\)
−0.608831 + 0.793300i \(0.708361\pi\)
\(608\) −2.00000 −0.0811107
\(609\) 0 0
\(610\) 0 0
\(611\) −5.00000 −0.202278
\(612\) 0 0
\(613\) −29.0000 −1.17130 −0.585649 0.810564i \(-0.699160\pi\)
−0.585649 + 0.810564i \(0.699160\pi\)
\(614\) 2.00000 0.0807134
\(615\) 0 0
\(616\) 1.00000 0.0402911
\(617\) −34.0000 −1.36879 −0.684394 0.729112i \(-0.739933\pi\)
−0.684394 + 0.729112i \(0.739933\pi\)
\(618\) 0 0
\(619\) −2.00000 −0.0803868 −0.0401934 0.999192i \(-0.512797\pi\)
−0.0401934 + 0.999192i \(0.512797\pi\)
\(620\) 0 0
\(621\) 0 0
\(622\) −11.0000 −0.441060
\(623\) 4.00000 0.160257
\(624\) 0 0
\(625\) 0 0
\(626\) −2.00000 −0.0799361
\(627\) 0 0
\(628\) −14.0000 −0.558661
\(629\) −4.00000 −0.159490
\(630\) 0 0
\(631\) −18.0000 −0.716569 −0.358284 0.933613i \(-0.616638\pi\)
−0.358284 + 0.933613i \(0.616638\pi\)
\(632\) 0 0
\(633\) 0 0
\(634\) −10.0000 −0.397151
\(635\) 0 0
\(636\) 0 0
\(637\) 5.00000 0.198107
\(638\) 6.00000 0.237542
\(639\) 0 0
\(640\) 0 0
\(641\) −12.0000 −0.473972 −0.236986 0.971513i \(-0.576159\pi\)
−0.236986 + 0.971513i \(0.576159\pi\)
\(642\) 0 0
\(643\) 14.0000 0.552106 0.276053 0.961142i \(-0.410973\pi\)
0.276053 + 0.961142i \(0.410973\pi\)
\(644\) −5.00000 −0.197028
\(645\) 0 0
\(646\) −8.00000 −0.314756
\(647\) 23.0000 0.904223 0.452112 0.891961i \(-0.350671\pi\)
0.452112 + 0.891961i \(0.350671\pi\)
\(648\) 0 0
\(649\) 13.0000 0.510295
\(650\) 0 0
\(651\) 0 0
\(652\) 18.0000 0.704934
\(653\) −8.00000 −0.313064 −0.156532 0.987673i \(-0.550031\pi\)
−0.156532 + 0.987673i \(0.550031\pi\)
\(654\) 0 0
\(655\) 0 0
\(656\) 2.00000 0.0780869
\(657\) 0 0
\(658\) −1.00000 −0.0389841
\(659\) 4.00000 0.155818 0.0779089 0.996960i \(-0.475176\pi\)
0.0779089 + 0.996960i \(0.475176\pi\)
\(660\) 0 0
\(661\) 5.00000 0.194477 0.0972387 0.995261i \(-0.468999\pi\)
0.0972387 + 0.995261i \(0.468999\pi\)
\(662\) −22.0000 −0.855054
\(663\) 0 0
\(664\) 12.0000 0.465690
\(665\) 0 0
\(666\) 0 0
\(667\) −30.0000 −1.16160
\(668\) −5.00000 −0.193456
\(669\) 0 0
\(670\) 0 0
\(671\) 13.0000 0.501859
\(672\) 0 0
\(673\) −23.0000 −0.886585 −0.443292 0.896377i \(-0.646190\pi\)
−0.443292 + 0.896377i \(0.646190\pi\)
\(674\) 2.00000 0.0770371
\(675\) 0 0
\(676\) 12.0000 0.461538
\(677\) 42.0000 1.61419 0.807096 0.590421i \(-0.201038\pi\)
0.807096 + 0.590421i \(0.201038\pi\)
\(678\) 0 0
\(679\) 1.00000 0.0383765
\(680\) 0 0
\(681\) 0 0
\(682\) −10.0000 −0.382920
\(683\) 37.0000 1.41577 0.707883 0.706330i \(-0.249650\pi\)
0.707883 + 0.706330i \(0.249650\pi\)
\(684\) 0 0
\(685\) 0 0
\(686\) 1.00000 0.0381802
\(687\) 0 0
\(688\) −6.00000 −0.228748
\(689\) −30.0000 −1.14291
\(690\) 0 0
\(691\) −38.0000 −1.44559 −0.722794 0.691063i \(-0.757142\pi\)
−0.722794 + 0.691063i \(0.757142\pi\)
\(692\) 16.0000 0.608229
\(693\) 0 0
\(694\) −12.0000 −0.455514
\(695\) 0 0
\(696\) 0 0
\(697\) 8.00000 0.303022
\(698\) 10.0000 0.378506
\(699\) 0 0
\(700\) 0 0
\(701\) 48.0000 1.81293 0.906467 0.422276i \(-0.138769\pi\)
0.906467 + 0.422276i \(0.138769\pi\)
\(702\) 0 0
\(703\) −2.00000 −0.0754314
\(704\) 1.00000 0.0376889
\(705\) 0 0
\(706\) 6.00000 0.225813
\(707\) 0 0
\(708\) 0 0
\(709\) −17.0000 −0.638448 −0.319224 0.947679i \(-0.603422\pi\)
−0.319224 + 0.947679i \(0.603422\pi\)
\(710\) 0 0
\(711\) 0 0
\(712\) 4.00000 0.149906
\(713\) 50.0000 1.87251
\(714\) 0 0
\(715\) 0 0
\(716\) −23.0000 −0.859550
\(717\) 0 0
\(718\) −25.0000 −0.932992
\(719\) 45.0000 1.67822 0.839108 0.543964i \(-0.183077\pi\)
0.839108 + 0.543964i \(0.183077\pi\)
\(720\) 0 0
\(721\) 14.0000 0.521387
\(722\) 15.0000 0.558242
\(723\) 0 0
\(724\) 11.0000 0.408812
\(725\) 0 0
\(726\) 0 0
\(727\) −12.0000 −0.445055 −0.222528 0.974926i \(-0.571431\pi\)
−0.222528 + 0.974926i \(0.571431\pi\)
\(728\) 5.00000 0.185312
\(729\) 0 0
\(730\) 0 0
\(731\) −24.0000 −0.887672
\(732\) 0 0
\(733\) 9.00000 0.332423 0.166211 0.986090i \(-0.446847\pi\)
0.166211 + 0.986090i \(0.446847\pi\)
\(734\) 28.0000 1.03350
\(735\) 0 0
\(736\) −5.00000 −0.184302
\(737\) 0 0
\(738\) 0 0
\(739\) 48.0000 1.76571 0.882854 0.469647i \(-0.155619\pi\)
0.882854 + 0.469647i \(0.155619\pi\)
\(740\) 0 0
\(741\) 0 0
\(742\) −6.00000 −0.220267
\(743\) −39.0000 −1.43077 −0.715386 0.698730i \(-0.753749\pi\)
−0.715386 + 0.698730i \(0.753749\pi\)
\(744\) 0 0
\(745\) 0 0
\(746\) −22.0000 −0.805477
\(747\) 0 0
\(748\) 4.00000 0.146254
\(749\) 19.0000 0.694245
\(750\) 0 0
\(751\) 40.0000 1.45962 0.729810 0.683650i \(-0.239608\pi\)
0.729810 + 0.683650i \(0.239608\pi\)
\(752\) −1.00000 −0.0364662
\(753\) 0 0
\(754\) 30.0000 1.09254
\(755\) 0 0
\(756\) 0 0
\(757\) −23.0000 −0.835949 −0.417975 0.908459i \(-0.637260\pi\)
−0.417975 + 0.908459i \(0.637260\pi\)
\(758\) −10.0000 −0.363216
\(759\) 0 0
\(760\) 0 0
\(761\) 50.0000 1.81250 0.906249 0.422744i \(-0.138933\pi\)
0.906249 + 0.422744i \(0.138933\pi\)
\(762\) 0 0
\(763\) −10.0000 −0.362024
\(764\) −4.00000 −0.144715
\(765\) 0 0
\(766\) −15.0000 −0.541972
\(767\) 65.0000 2.34701
\(768\) 0 0
\(769\) −14.0000 −0.504853 −0.252426 0.967616i \(-0.581229\pi\)
−0.252426 + 0.967616i \(0.581229\pi\)
\(770\) 0 0
\(771\) 0 0
\(772\) 2.00000 0.0719816
\(773\) −10.0000 −0.359675 −0.179838 0.983696i \(-0.557557\pi\)
−0.179838 + 0.983696i \(0.557557\pi\)
\(774\) 0 0
\(775\) 0 0
\(776\) 1.00000 0.0358979
\(777\) 0 0
\(778\) 6.00000 0.215110
\(779\) 4.00000 0.143315
\(780\) 0 0
\(781\) 11.0000 0.393611
\(782\) −20.0000 −0.715199
\(783\) 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 \(0.693188\pi\)
\(788\) 0 0
\(789\) 0 0
\(790\) 0 0
\(791\) 10.0000 0.355559
\(792\) 0 0
\(793\) 65.0000 2.30822
\(794\) 1.00000 0.0354887
\(795\) 0 0
\(796\) 2.00000 0.0708881
\(797\) −42.0000 −1.48772 −0.743858 0.668338i \(-0.767006\pi\)
−0.743858 + 0.668338i \(0.767006\pi\)
\(798\) 0 0
\(799\) −4.00000 −0.141510
\(800\) 0 0
\(801\) 0 0
\(802\) 0 0
\(803\) 14.0000 0.494049
\(804\) 0 0
\(805\) 0 0
\(806\) −50.0000 −1.76117
\(807\) 0 0
\(808\) 0 0
\(809\) 22.0000 0.773479 0.386739 0.922189i \(-0.373601\pi\)
0.386739 + 0.922189i \(0.373601\pi\)
\(810\) 0 0
\(811\) −12.0000 −0.421377 −0.210688 0.977553i \(-0.567571\pi\)
−0.210688 + 0.977553i \(0.567571\pi\)
\(812\) 6.00000 0.210559
\(813\) 0 0
\(814\) 1.00000 0.0350500
\(815\) 0 0
\(816\) 0 0
\(817\) −12.0000 −0.419827
\(818\) −37.0000 −1.29367
\(819\) 0 0
\(820\) 0 0
\(821\) −2.00000 −0.0698005 −0.0349002 0.999391i \(-0.511111\pi\)
−0.0349002 + 0.999391i \(0.511111\pi\)
\(822\) 0 0
\(823\) −22.0000 −0.766872 −0.383436 0.923567i \(-0.625259\pi\)
−0.383436 + 0.923567i \(0.625259\pi\)
\(824\) 14.0000 0.487713
\(825\) 0 0
\(826\) 13.0000 0.452328
\(827\) 39.0000 1.35616 0.678081 0.734987i \(-0.262812\pi\)
0.678081 + 0.734987i \(0.262812\pi\)
\(828\) 0 0
\(829\) 11.0000 0.382046 0.191023 0.981586i \(-0.438820\pi\)
0.191023 + 0.981586i \(0.438820\pi\)
\(830\) 0 0
\(831\) 0 0
\(832\) 5.00000 0.173344
\(833\) 4.00000 0.138592
\(834\) 0 0
\(835\) 0 0
\(836\) 2.00000 0.0691714
\(837\) 0 0
\(838\) 12.0000 0.414533
\(839\) 9.00000 0.310715 0.155357 0.987858i \(-0.450347\pi\)
0.155357 + 0.987858i \(0.450347\pi\)
\(840\) 0 0
\(841\) 7.00000 0.241379
\(842\) −19.0000 −0.654783
\(843\) 0 0
\(844\) 20.0000 0.688428
\(845\) 0 0
\(846\) 0 0
\(847\) 10.0000 0.343604
\(848\) −6.00000 −0.206041
\(849\) 0 0
\(850\) 0 0
\(851\) −5.00000 −0.171398
\(852\) 0 0
\(853\) 11.0000 0.376633 0.188316 0.982108i \(-0.439697\pi\)
0.188316 + 0.982108i \(0.439697\pi\)
\(854\) 13.0000 0.444851
\(855\) 0 0
\(856\) 19.0000 0.649407
\(857\) 52.0000 1.77629 0.888143 0.459567i \(-0.151995\pi\)
0.888143 + 0.459567i \(0.151995\pi\)
\(858\) 0 0
\(859\) −10.0000 −0.341196 −0.170598 0.985341i \(-0.554570\pi\)
−0.170598 + 0.985341i \(0.554570\pi\)
\(860\) 0 0
\(861\) 0 0
\(862\) −33.0000 −1.12398
\(863\) −24.0000 −0.816970 −0.408485 0.912765i \(-0.633943\pi\)
−0.408485 + 0.912765i \(0.633943\pi\)
\(864\) 0 0
\(865\) 0 0
\(866\) −33.0000 −1.12139
\(867\) 0 0
\(868\) −10.0000 −0.339422
\(869\) 0 0
\(870\) 0 0
\(871\) 0 0
\(872\) −10.0000 −0.338643
\(873\) 0 0
\(874\) −10.0000 −0.338255
\(875\) 0 0
\(876\) 0 0
\(877\) 43.0000 1.45201 0.726003 0.687691i \(-0.241376\pi\)
0.726003 + 0.687691i \(0.241376\pi\)
\(878\) −32.0000 −1.07995
\(879\) 0 0
\(880\) 0 0
\(881\) −12.0000 −0.404290 −0.202145 0.979356i \(-0.564791\pi\)
−0.202145 + 0.979356i \(0.564791\pi\)
\(882\) 0 0
\(883\) 20.0000 0.673054 0.336527 0.941674i \(-0.390748\pi\)
0.336527 + 0.941674i \(0.390748\pi\)
\(884\) 20.0000 0.672673
\(885\) 0 0
\(886\) −31.0000 −1.04147
\(887\) 5.00000 0.167884 0.0839418 0.996471i \(-0.473249\pi\)
0.0839418 + 0.996471i \(0.473249\pi\)
\(888\) 0 0
\(889\) 6.00000 0.201234
\(890\) 0 0
\(891\) 0 0
\(892\) 6.00000 0.200895
\(893\) −2.00000 −0.0669274
\(894\) 0 0
\(895\) 0 0
\(896\) 1.00000 0.0334077
\(897\) 0 0
\(898\) 38.0000 1.26808
\(899\) −60.0000 −2.00111
\(900\) 0 0
\(901\) −24.0000 −0.799556
\(902\) −2.00000 −0.0665927
\(903\) 0 0
\(904\) 10.0000 0.332595
\(905\) 0 0
\(906\) 0 0
\(907\) 54.0000 1.79304 0.896520 0.443003i \(-0.146087\pi\)
0.896520 + 0.443003i \(0.146087\pi\)
\(908\) 3.00000 0.0995585
\(909\) 0 0
\(910\) 0 0
\(911\) −27.0000 −0.894550 −0.447275 0.894397i \(-0.647605\pi\)
−0.447275 + 0.894397i \(0.647605\pi\)
\(912\) 0 0
\(913\) −12.0000 −0.397142
\(914\) 13.0000 0.430002
\(915\) 0 0
\(916\) 19.0000 0.627778
\(917\) −9.00000 −0.297206
\(918\) 0 0
\(919\) −26.0000 −0.857661 −0.428830 0.903385i \(-0.641074\pi\)
−0.428830 + 0.903385i \(0.641074\pi\)
\(920\) 0 0
\(921\) 0 0
\(922\) −20.0000 −0.658665
\(923\) 55.0000 1.81035
\(924\) 0 0
\(925\) 0 0
\(926\) −34.0000 −1.11731
\(927\) 0 0
\(928\) 6.00000 0.196960
\(929\) 10.0000 0.328089 0.164045 0.986453i \(-0.447546\pi\)
0.164045 + 0.986453i \(0.447546\pi\)
\(930\) 0 0
\(931\) 2.00000 0.0655474
\(932\) 8.00000 0.262049
\(933\) 0 0
\(934\) 13.0000 0.425373
\(935\) 0 0
\(936\) 0 0
\(937\) −51.0000 −1.66610 −0.833049 0.553200i \(-0.813407\pi\)
−0.833049 + 0.553200i \(0.813407\pi\)
\(938\) 0 0
\(939\) 0 0
\(940\) 0 0
\(941\) −48.0000 −1.56476 −0.782378 0.622804i \(-0.785993\pi\)
−0.782378 + 0.622804i \(0.785993\pi\)
\(942\) 0 0
\(943\) 10.0000 0.325645
\(944\) 13.0000 0.423114
\(945\) 0 0
\(946\) 6.00000 0.195077
\(947\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(948\) 0 0
\(949\) 70.0000 2.27230
\(950\) 0 0
\(951\) 0 0
\(952\) 4.00000 0.129641
\(953\) 36.0000 1.16615 0.583077 0.812417i \(-0.301849\pi\)
0.583077 + 0.812417i \(0.301849\pi\)
\(954\) 0 0
\(955\) 0 0
\(956\) −19.0000 −0.614504
\(957\) 0 0
\(958\) −24.0000 −0.775405
\(959\) −2.00000 −0.0645834
\(960\) 0 0
\(961\) 69.0000 2.22581
\(962\) 5.00000 0.161206
\(963\) 0 0
\(964\) −15.0000 −0.483117
\(965\) 0 0
\(966\) 0 0
\(967\) 8.00000 0.257263 0.128631 0.991692i \(-0.458942\pi\)
0.128631 + 0.991692i \(0.458942\pi\)
\(968\) 10.0000 0.321412
\(969\) 0 0
\(970\) 0 0
\(971\) 45.0000 1.44412 0.722059 0.691831i \(-0.243196\pi\)
0.722059 + 0.691831i \(0.243196\pi\)
\(972\) 0 0
\(973\) −20.0000 −0.641171
\(974\) 12.0000 0.384505
\(975\) 0 0
\(976\) 13.0000 0.416120
\(977\) 12.0000 0.383914 0.191957 0.981403i \(-0.438517\pi\)
0.191957 + 0.981403i \(0.438517\pi\)
\(978\) 0 0
\(979\) −4.00000 −0.127841
\(980\) 0 0
\(981\) 0 0
\(982\) 36.0000 1.14881
\(983\) 31.0000 0.988746 0.494373 0.869250i \(-0.335398\pi\)
0.494373 + 0.869250i \(0.335398\pi\)
\(984\) 0 0
\(985\) 0 0
\(986\) 24.0000 0.764316
\(987\) 0 0
\(988\) 10.0000 0.318142
\(989\) −30.0000 −0.953945
\(990\) 0 0
\(991\) −20.0000 −0.635321 −0.317660 0.948205i \(-0.602897\pi\)
−0.317660 + 0.948205i \(0.602897\pi\)
\(992\) −10.0000 −0.317500
\(993\) 0 0
\(994\) 11.0000 0.348899
\(995\) 0 0
\(996\) 0 0
\(997\) 7.00000 0.221692 0.110846 0.993838i \(-0.464644\pi\)
0.110846 + 0.993838i \(0.464644\pi\)
\(998\) −40.0000 −1.26618
\(999\) 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 \(a_p\))