Properties

Label 121.2.a.a.1.1
Level 121
Weight 2
Character 121.1
Self dual Yes
Analytic conductor 0.966
Analytic rank 0
Dimension 1
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 121 = 11^{2} \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 121.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(0.966189864457\)
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 \(\chi\) = 121.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.00000 q^{2}\) \(+2.00000 q^{3}\) \(-1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-2.00000 q^{6}\) \(+2.00000 q^{7}\) \(+3.00000 q^{8}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.00000 q^{2}\) \(+2.00000 q^{3}\) \(-1.00000 q^{4}\) \(+1.00000 q^{5}\) \(-2.00000 q^{6}\) \(+2.00000 q^{7}\) \(+3.00000 q^{8}\) \(+1.00000 q^{9}\) \(-1.00000 q^{10}\) \(-2.00000 q^{12}\) \(-1.00000 q^{13}\) \(-2.00000 q^{14}\) \(+2.00000 q^{15}\) \(-1.00000 q^{16}\) \(+5.00000 q^{17}\) \(-1.00000 q^{18}\) \(-6.00000 q^{19}\) \(-1.00000 q^{20}\) \(+4.00000 q^{21}\) \(+2.00000 q^{23}\) \(+6.00000 q^{24}\) \(-4.00000 q^{25}\) \(+1.00000 q^{26}\) \(-4.00000 q^{27}\) \(-2.00000 q^{28}\) \(-9.00000 q^{29}\) \(-2.00000 q^{30}\) \(-2.00000 q^{31}\) \(-5.00000 q^{32}\) \(-5.00000 q^{34}\) \(+2.00000 q^{35}\) \(-1.00000 q^{36}\) \(-3.00000 q^{37}\) \(+6.00000 q^{38}\) \(-2.00000 q^{39}\) \(+3.00000 q^{40}\) \(+5.00000 q^{41}\) \(-4.00000 q^{42}\) \(+1.00000 q^{45}\) \(-2.00000 q^{46}\) \(+2.00000 q^{47}\) \(-2.00000 q^{48}\) \(-3.00000 q^{49}\) \(+4.00000 q^{50}\) \(+10.0000 q^{51}\) \(+1.00000 q^{52}\) \(+9.00000 q^{53}\) \(+4.00000 q^{54}\) \(+6.00000 q^{56}\) \(-12.0000 q^{57}\) \(+9.00000 q^{58}\) \(+8.00000 q^{59}\) \(-2.00000 q^{60}\) \(-6.00000 q^{61}\) \(+2.00000 q^{62}\) \(+2.00000 q^{63}\) \(+7.00000 q^{64}\) \(-1.00000 q^{65}\) \(+2.00000 q^{67}\) \(-5.00000 q^{68}\) \(+4.00000 q^{69}\) \(-2.00000 q^{70}\) \(+12.0000 q^{71}\) \(+3.00000 q^{72}\) \(+2.00000 q^{73}\) \(+3.00000 q^{74}\) \(-8.00000 q^{75}\) \(+6.00000 q^{76}\) \(+2.00000 q^{78}\) \(+10.0000 q^{79}\) \(-1.00000 q^{80}\) \(-11.0000 q^{81}\) \(-5.00000 q^{82}\) \(-6.00000 q^{83}\) \(-4.00000 q^{84}\) \(+5.00000 q^{85}\) \(-18.0000 q^{87}\) \(-9.00000 q^{89}\) \(-1.00000 q^{90}\) \(-2.00000 q^{91}\) \(-2.00000 q^{92}\) \(-4.00000 q^{93}\) \(-2.00000 q^{94}\) \(-6.00000 q^{95}\) \(-10.0000 q^{96}\) \(-13.0000 q^{97}\) \(+3.00000 q^{98}\) \(+O(q^{100})\)

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 −0.353553 0.935414i \(-0.615027\pi\)
−0.353553 + 0.935414i \(0.615027\pi\)
\(3\) 2.00000 1.15470 0.577350 0.816497i \(-0.304087\pi\)
0.577350 + 0.816497i \(0.304087\pi\)
\(4\) −1.00000 −0.500000
\(5\) 1.00000 0.447214 0.223607 0.974679i \(-0.428217\pi\)
0.223607 + 0.974679i \(0.428217\pi\)
\(6\) −2.00000 −0.816497
\(7\) 2.00000 0.755929 0.377964 0.925820i \(-0.376624\pi\)
0.377964 + 0.925820i \(0.376624\pi\)
\(8\) 3.00000 1.06066
\(9\) 1.00000 0.333333
\(10\) −1.00000 −0.316228
\(11\) 0 0
\(12\) −2.00000 −0.577350
\(13\) −1.00000 −0.277350 −0.138675 0.990338i \(-0.544284\pi\)
−0.138675 + 0.990338i \(0.544284\pi\)
\(14\) −2.00000 −0.534522
\(15\) 2.00000 0.516398
\(16\) −1.00000 −0.250000
\(17\) 5.00000 1.21268 0.606339 0.795206i \(-0.292637\pi\)
0.606339 + 0.795206i \(0.292637\pi\)
\(18\) −1.00000 −0.235702
\(19\) −6.00000 −1.37649 −0.688247 0.725476i \(-0.741620\pi\)
−0.688247 + 0.725476i \(0.741620\pi\)
\(20\) −1.00000 −0.223607
\(21\) 4.00000 0.872872
\(22\) 0 0
\(23\) 2.00000 0.417029 0.208514 0.978019i \(-0.433137\pi\)
0.208514 + 0.978019i \(0.433137\pi\)
\(24\) 6.00000 1.22474
\(25\) −4.00000 −0.800000
\(26\) 1.00000 0.196116
\(27\) −4.00000 −0.769800
\(28\) −2.00000 −0.377964
\(29\) −9.00000 −1.67126 −0.835629 0.549294i \(-0.814897\pi\)
−0.835629 + 0.549294i \(0.814897\pi\)
\(30\) −2.00000 −0.365148
\(31\) −2.00000 −0.359211 −0.179605 0.983739i \(-0.557482\pi\)
−0.179605 + 0.983739i \(0.557482\pi\)
\(32\) −5.00000 −0.883883
\(33\) 0 0
\(34\) −5.00000 −0.857493
\(35\) 2.00000 0.338062
\(36\) −1.00000 −0.166667
\(37\) −3.00000 −0.493197 −0.246598 0.969118i \(-0.579313\pi\)
−0.246598 + 0.969118i \(0.579313\pi\)
\(38\) 6.00000 0.973329
\(39\) −2.00000 −0.320256
\(40\) 3.00000 0.474342
\(41\) 5.00000 0.780869 0.390434 0.920631i \(-0.372325\pi\)
0.390434 + 0.920631i \(0.372325\pi\)
\(42\) −4.00000 −0.617213
\(43\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(44\) 0 0
\(45\) 1.00000 0.149071
\(46\) −2.00000 −0.294884
\(47\) 2.00000 0.291730 0.145865 0.989305i \(-0.453403\pi\)
0.145865 + 0.989305i \(0.453403\pi\)
\(48\) −2.00000 −0.288675
\(49\) −3.00000 −0.428571
\(50\) 4.00000 0.565685
\(51\) 10.0000 1.40028
\(52\) 1.00000 0.138675
\(53\) 9.00000 1.23625 0.618123 0.786082i \(-0.287894\pi\)
0.618123 + 0.786082i \(0.287894\pi\)
\(54\) 4.00000 0.544331
\(55\) 0 0
\(56\) 6.00000 0.801784
\(57\) −12.0000 −1.58944
\(58\) 9.00000 1.18176
\(59\) 8.00000 1.04151 0.520756 0.853706i \(-0.325650\pi\)
0.520756 + 0.853706i \(0.325650\pi\)
\(60\) −2.00000 −0.258199
\(61\) −6.00000 −0.768221 −0.384111 0.923287i \(-0.625492\pi\)
−0.384111 + 0.923287i \(0.625492\pi\)
\(62\) 2.00000 0.254000
\(63\) 2.00000 0.251976
\(64\) 7.00000 0.875000
\(65\) −1.00000 −0.124035
\(66\) 0 0
\(67\) 2.00000 0.244339 0.122169 0.992509i \(-0.461015\pi\)
0.122169 + 0.992509i \(0.461015\pi\)
\(68\) −5.00000 −0.606339
\(69\) 4.00000 0.481543
\(70\) −2.00000 −0.239046
\(71\) 12.0000 1.42414 0.712069 0.702109i \(-0.247758\pi\)
0.712069 + 0.702109i \(0.247758\pi\)
\(72\) 3.00000 0.353553
\(73\) 2.00000 0.234082 0.117041 0.993127i \(-0.462659\pi\)
0.117041 + 0.993127i \(0.462659\pi\)
\(74\) 3.00000 0.348743
\(75\) −8.00000 −0.923760
\(76\) 6.00000 0.688247
\(77\) 0 0
\(78\) 2.00000 0.226455
\(79\) 10.0000 1.12509 0.562544 0.826767i \(-0.309823\pi\)
0.562544 + 0.826767i \(0.309823\pi\)
\(80\) −1.00000 −0.111803
\(81\) −11.0000 −1.22222
\(82\) −5.00000 −0.552158
\(83\) −6.00000 −0.658586 −0.329293 0.944228i \(-0.606810\pi\)
−0.329293 + 0.944228i \(0.606810\pi\)
\(84\) −4.00000 −0.436436
\(85\) 5.00000 0.542326
\(86\) 0 0
\(87\) −18.0000 −1.92980
\(88\) 0 0
\(89\) −9.00000 −0.953998 −0.476999 0.878904i \(-0.658275\pi\)
−0.476999 + 0.878904i \(0.658275\pi\)
\(90\) −1.00000 −0.105409
\(91\) −2.00000 −0.209657
\(92\) −2.00000 −0.208514
\(93\) −4.00000 −0.414781
\(94\) −2.00000 −0.206284
\(95\) −6.00000 −0.615587
\(96\) −10.0000 −1.02062
\(97\) −13.0000 −1.31995 −0.659975 0.751288i \(-0.729433\pi\)
−0.659975 + 0.751288i \(0.729433\pi\)
\(98\) 3.00000 0.303046
\(99\) 0 0
\(100\) 4.00000 0.400000
\(101\) 10.0000 0.995037 0.497519 0.867453i \(-0.334245\pi\)
0.497519 + 0.867453i \(0.334245\pi\)
\(102\) −10.0000 −0.990148
\(103\) 8.00000 0.788263 0.394132 0.919054i \(-0.371045\pi\)
0.394132 + 0.919054i \(0.371045\pi\)
\(104\) −3.00000 −0.294174
\(105\) 4.00000 0.390360
\(106\) −9.00000 −0.874157
\(107\) −6.00000 −0.580042 −0.290021 0.957020i \(-0.593662\pi\)
−0.290021 + 0.957020i \(0.593662\pi\)
\(108\) 4.00000 0.384900
\(109\) 11.0000 1.05361 0.526804 0.849987i \(-0.323390\pi\)
0.526804 + 0.849987i \(0.323390\pi\)
\(110\) 0 0
\(111\) −6.00000 −0.569495
\(112\) −2.00000 −0.188982
\(113\) −9.00000 −0.846649 −0.423324 0.905978i \(-0.639137\pi\)
−0.423324 + 0.905978i \(0.639137\pi\)
\(114\) 12.0000 1.12390
\(115\) 2.00000 0.186501
\(116\) 9.00000 0.835629
\(117\) −1.00000 −0.0924500
\(118\) −8.00000 −0.736460
\(119\) 10.0000 0.916698
\(120\) 6.00000 0.547723
\(121\) 0 0
\(122\) 6.00000 0.543214
\(123\) 10.0000 0.901670
\(124\) 2.00000 0.179605
\(125\) −9.00000 −0.804984
\(126\) −2.00000 −0.178174
\(127\) 16.0000 1.41977 0.709885 0.704317i \(-0.248747\pi\)
0.709885 + 0.704317i \(0.248747\pi\)
\(128\) 3.00000 0.265165
\(129\) 0 0
\(130\) 1.00000 0.0877058
\(131\) 0 0 1.00000i \(-0.5\pi\)
1.00000i \(0.5\pi\)
\(132\) 0 0
\(133\) −12.0000 −1.04053
\(134\) −2.00000 −0.172774
\(135\) −4.00000 −0.344265
\(136\) 15.0000 1.28624
\(137\) −10.0000 −0.854358 −0.427179 0.904167i \(-0.640493\pi\)
−0.427179 + 0.904167i \(0.640493\pi\)
\(138\) −4.00000 −0.340503
\(139\) 2.00000 0.169638 0.0848189 0.996396i \(-0.472969\pi\)
0.0848189 + 0.996396i \(0.472969\pi\)
\(140\) −2.00000 −0.169031
\(141\) 4.00000 0.336861
\(142\) −12.0000 −1.00702
\(143\) 0 0
\(144\) −1.00000 −0.0833333
\(145\) −9.00000 −0.747409
\(146\) −2.00000 −0.165521
\(147\) −6.00000 −0.494872
\(148\) 3.00000 0.246598
\(149\) −17.0000 −1.39269 −0.696347 0.717705i \(-0.745193\pi\)
−0.696347 + 0.717705i \(0.745193\pi\)
\(150\) 8.00000 0.653197
\(151\) 16.0000 1.30206 0.651031 0.759051i \(-0.274337\pi\)
0.651031 + 0.759051i \(0.274337\pi\)
\(152\) −18.0000 −1.45999
\(153\) 5.00000 0.404226
\(154\) 0 0
\(155\) −2.00000 −0.160644
\(156\) 2.00000 0.160128
\(157\) 2.00000 0.159617 0.0798087 0.996810i \(-0.474569\pi\)
0.0798087 + 0.996810i \(0.474569\pi\)
\(158\) −10.0000 −0.795557
\(159\) 18.0000 1.42749
\(160\) −5.00000 −0.395285
\(161\) 4.00000 0.315244
\(162\) 11.0000 0.864242
\(163\) −2.00000 −0.156652 −0.0783260 0.996928i \(-0.524958\pi\)
−0.0783260 + 0.996928i \(0.524958\pi\)
\(164\) −5.00000 −0.390434
\(165\) 0 0
\(166\) 6.00000 0.465690
\(167\) −12.0000 −0.928588 −0.464294 0.885681i \(-0.653692\pi\)
−0.464294 + 0.885681i \(0.653692\pi\)
\(168\) 12.0000 0.925820
\(169\) −12.0000 −0.923077
\(170\) −5.00000 −0.383482
\(171\) −6.00000 −0.458831
\(172\) 0 0
\(173\) −6.00000 −0.456172 −0.228086 0.973641i \(-0.573247\pi\)
−0.228086 + 0.973641i \(0.573247\pi\)
\(174\) 18.0000 1.36458
\(175\) −8.00000 −0.604743
\(176\) 0 0
\(177\) 16.0000 1.20263
\(178\) 9.00000 0.674579
\(179\) 24.0000 1.79384 0.896922 0.442189i \(-0.145798\pi\)
0.896922 + 0.442189i \(0.145798\pi\)
\(180\) −1.00000 −0.0745356
\(181\) 1.00000 0.0743294 0.0371647 0.999309i \(-0.488167\pi\)
0.0371647 + 0.999309i \(0.488167\pi\)
\(182\) 2.00000 0.148250
\(183\) −12.0000 −0.887066
\(184\) 6.00000 0.442326
\(185\) −3.00000 −0.220564
\(186\) 4.00000 0.293294
\(187\) 0 0
\(188\) −2.00000 −0.145865
\(189\) −8.00000 −0.581914
\(190\) 6.00000 0.435286
\(191\) 8.00000 0.578860 0.289430 0.957199i \(-0.406534\pi\)
0.289430 + 0.957199i \(0.406534\pi\)
\(192\) 14.0000 1.01036
\(193\) 5.00000 0.359908 0.179954 0.983675i \(-0.442405\pi\)
0.179954 + 0.983675i \(0.442405\pi\)
\(194\) 13.0000 0.933346
\(195\) −2.00000 −0.143223
\(196\) 3.00000 0.214286
\(197\) 11.0000 0.783718 0.391859 0.920025i \(-0.371832\pi\)
0.391859 + 0.920025i \(0.371832\pi\)
\(198\) 0 0
\(199\) 24.0000 1.70131 0.850657 0.525720i \(-0.176204\pi\)
0.850657 + 0.525720i \(0.176204\pi\)
\(200\) −12.0000 −0.848528
\(201\) 4.00000 0.282138
\(202\) −10.0000 −0.703598
\(203\) −18.0000 −1.26335
\(204\) −10.0000 −0.700140
\(205\) 5.00000 0.349215
\(206\) −8.00000 −0.557386
\(207\) 2.00000 0.139010
\(208\) 1.00000 0.0693375
\(209\) 0 0
\(210\) −4.00000 −0.276026
\(211\) −12.0000 −0.826114 −0.413057 0.910705i \(-0.635539\pi\)
−0.413057 + 0.910705i \(0.635539\pi\)
\(212\) −9.00000 −0.618123
\(213\) 24.0000 1.64445
\(214\) 6.00000 0.410152
\(215\) 0 0
\(216\) −12.0000 −0.816497
\(217\) −4.00000 −0.271538
\(218\) −11.0000 −0.745014
\(219\) 4.00000 0.270295
\(220\) 0 0
\(221\) −5.00000 −0.336336
\(222\) 6.00000 0.402694
\(223\) −20.0000 −1.33930 −0.669650 0.742677i \(-0.733556\pi\)
−0.669650 + 0.742677i \(0.733556\pi\)
\(224\) −10.0000 −0.668153
\(225\) −4.00000 −0.266667
\(226\) 9.00000 0.598671
\(227\) 24.0000 1.59294 0.796468 0.604681i \(-0.206699\pi\)
0.796468 + 0.604681i \(0.206699\pi\)
\(228\) 12.0000 0.794719
\(229\) 9.00000 0.594737 0.297368 0.954763i \(-0.403891\pi\)
0.297368 + 0.954763i \(0.403891\pi\)
\(230\) −2.00000 −0.131876
\(231\) 0 0
\(232\) −27.0000 −1.77264
\(233\) 21.0000 1.37576 0.687878 0.725826i \(-0.258542\pi\)
0.687878 + 0.725826i \(0.258542\pi\)
\(234\) 1.00000 0.0653720
\(235\) 2.00000 0.130466
\(236\) −8.00000 −0.520756
\(237\) 20.0000 1.29914
\(238\) −10.0000 −0.648204
\(239\) −6.00000 −0.388108 −0.194054 0.980991i \(-0.562164\pi\)
−0.194054 + 0.980991i \(0.562164\pi\)
\(240\) −2.00000 −0.129099
\(241\) −22.0000 −1.41714 −0.708572 0.705638i \(-0.750660\pi\)
−0.708572 + 0.705638i \(0.750660\pi\)
\(242\) 0 0
\(243\) −10.0000 −0.641500
\(244\) 6.00000 0.384111
\(245\) −3.00000 −0.191663
\(246\) −10.0000 −0.637577
\(247\) 6.00000 0.381771
\(248\) −6.00000 −0.381000
\(249\) −12.0000 −0.760469
\(250\) 9.00000 0.569210
\(251\) −2.00000 −0.126239 −0.0631194 0.998006i \(-0.520105\pi\)
−0.0631194 + 0.998006i \(0.520105\pi\)
\(252\) −2.00000 −0.125988
\(253\) 0 0
\(254\) −16.0000 −1.00393
\(255\) 10.0000 0.626224
\(256\) −17.0000 −1.06250
\(257\) 19.0000 1.18519 0.592594 0.805502i \(-0.298104\pi\)
0.592594 + 0.805502i \(0.298104\pi\)
\(258\) 0 0
\(259\) −6.00000 −0.372822
\(260\) 1.00000 0.0620174
\(261\) −9.00000 −0.557086
\(262\) 0 0
\(263\) 22.0000 1.35658 0.678289 0.734795i \(-0.262722\pi\)
0.678289 + 0.734795i \(0.262722\pi\)
\(264\) 0 0
\(265\) 9.00000 0.552866
\(266\) 12.0000 0.735767
\(267\) −18.0000 −1.10158
\(268\) −2.00000 −0.122169
\(269\) 1.00000 0.0609711 0.0304855 0.999535i \(-0.490295\pi\)
0.0304855 + 0.999535i \(0.490295\pi\)
\(270\) 4.00000 0.243432
\(271\) −20.0000 −1.21491 −0.607457 0.794353i \(-0.707810\pi\)
−0.607457 + 0.794353i \(0.707810\pi\)
\(272\) −5.00000 −0.303170
\(273\) −4.00000 −0.242091
\(274\) 10.0000 0.604122
\(275\) 0 0
\(276\) −4.00000 −0.240772
\(277\) −1.00000 −0.0600842 −0.0300421 0.999549i \(-0.509564\pi\)
−0.0300421 + 0.999549i \(0.509564\pi\)
\(278\) −2.00000 −0.119952
\(279\) −2.00000 −0.119737
\(280\) 6.00000 0.358569
\(281\) −6.00000 −0.357930 −0.178965 0.983855i \(-0.557275\pi\)
−0.178965 + 0.983855i \(0.557275\pi\)
\(282\) −4.00000 −0.238197
\(283\) −28.0000 −1.66443 −0.832214 0.554455i \(-0.812927\pi\)
−0.832214 + 0.554455i \(0.812927\pi\)
\(284\) −12.0000 −0.712069
\(285\) −12.0000 −0.710819
\(286\) 0 0
\(287\) 10.0000 0.590281
\(288\) −5.00000 −0.294628
\(289\) 8.00000 0.470588
\(290\) 9.00000 0.528498
\(291\) −26.0000 −1.52415
\(292\) −2.00000 −0.117041
\(293\) −9.00000 −0.525786 −0.262893 0.964825i \(-0.584677\pi\)
−0.262893 + 0.964825i \(0.584677\pi\)
\(294\) 6.00000 0.349927
\(295\) 8.00000 0.465778
\(296\) −9.00000 −0.523114
\(297\) 0 0
\(298\) 17.0000 0.984784
\(299\) −2.00000 −0.115663
\(300\) 8.00000 0.461880
\(301\) 0 0
\(302\) −16.0000 −0.920697
\(303\) 20.0000 1.14897
\(304\) 6.00000 0.344124
\(305\) −6.00000 −0.343559
\(306\) −5.00000 −0.285831
\(307\) 22.0000 1.25561 0.627803 0.778372i \(-0.283954\pi\)
0.627803 + 0.778372i \(0.283954\pi\)
\(308\) 0 0
\(309\) 16.0000 0.910208
\(310\) 2.00000 0.113592
\(311\) 24.0000 1.36092 0.680458 0.732787i \(-0.261781\pi\)
0.680458 + 0.732787i \(0.261781\pi\)
\(312\) −6.00000 −0.339683
\(313\) 23.0000 1.30004 0.650018 0.759918i \(-0.274761\pi\)
0.650018 + 0.759918i \(0.274761\pi\)
\(314\) −2.00000 −0.112867
\(315\) 2.00000 0.112687
\(316\) −10.0000 −0.562544
\(317\) −2.00000 −0.112331 −0.0561656 0.998421i \(-0.517887\pi\)
−0.0561656 + 0.998421i \(0.517887\pi\)
\(318\) −18.0000 −1.00939
\(319\) 0 0
\(320\) 7.00000 0.391312
\(321\) −12.0000 −0.669775
\(322\) −4.00000 −0.222911
\(323\) −30.0000 −1.66924
\(324\) 11.0000 0.611111
\(325\) 4.00000 0.221880
\(326\) 2.00000 0.110770
\(327\) 22.0000 1.21660
\(328\) 15.0000 0.828236
\(329\) 4.00000 0.220527
\(330\) 0 0
\(331\) −20.0000 −1.09930 −0.549650 0.835395i \(-0.685239\pi\)
−0.549650 + 0.835395i \(0.685239\pi\)
\(332\) 6.00000 0.329293
\(333\) −3.00000 −0.164399
\(334\) 12.0000 0.656611
\(335\) 2.00000 0.109272
\(336\) −4.00000 −0.218218
\(337\) 13.0000 0.708155 0.354078 0.935216i \(-0.384795\pi\)
0.354078 + 0.935216i \(0.384795\pi\)
\(338\) 12.0000 0.652714
\(339\) −18.0000 −0.977626
\(340\) −5.00000 −0.271163
\(341\) 0 0
\(342\) 6.00000 0.324443
\(343\) −20.0000 −1.07990
\(344\) 0 0
\(345\) 4.00000 0.215353
\(346\) 6.00000 0.322562
\(347\) −28.0000 −1.50312 −0.751559 0.659665i \(-0.770698\pi\)
−0.751559 + 0.659665i \(0.770698\pi\)
\(348\) 18.0000 0.964901
\(349\) 27.0000 1.44528 0.722638 0.691226i \(-0.242929\pi\)
0.722638 + 0.691226i \(0.242929\pi\)
\(350\) 8.00000 0.427618
\(351\) 4.00000 0.213504
\(352\) 0 0
\(353\) −9.00000 −0.479022 −0.239511 0.970894i \(-0.576987\pi\)
−0.239511 + 0.970894i \(0.576987\pi\)
\(354\) −16.0000 −0.850390
\(355\) 12.0000 0.636894
\(356\) 9.00000 0.476999
\(357\) 20.0000 1.05851
\(358\) −24.0000 −1.26844
\(359\) 2.00000 0.105556 0.0527780 0.998606i \(-0.483192\pi\)
0.0527780 + 0.998606i \(0.483192\pi\)
\(360\) 3.00000 0.158114
\(361\) 17.0000 0.894737
\(362\) −1.00000 −0.0525588
\(363\) 0 0
\(364\) 2.00000 0.104828
\(365\) 2.00000 0.104685
\(366\) 12.0000 0.627250
\(367\) −14.0000 −0.730794 −0.365397 0.930852i \(-0.619067\pi\)
−0.365397 + 0.930852i \(0.619067\pi\)
\(368\) −2.00000 −0.104257
\(369\) 5.00000 0.260290
\(370\) 3.00000 0.155963
\(371\) 18.0000 0.934513
\(372\) 4.00000 0.207390
\(373\) −22.0000 −1.13912 −0.569558 0.821951i \(-0.692886\pi\)
−0.569558 + 0.821951i \(0.692886\pi\)
\(374\) 0 0
\(375\) −18.0000 −0.929516
\(376\) 6.00000 0.309426
\(377\) 9.00000 0.463524
\(378\) 8.00000 0.411476
\(379\) −32.0000 −1.64373 −0.821865 0.569683i \(-0.807066\pi\)
−0.821865 + 0.569683i \(0.807066\pi\)
\(380\) 6.00000 0.307794
\(381\) 32.0000 1.63941
\(382\) −8.00000 −0.409316
\(383\) 20.0000 1.02195 0.510976 0.859595i \(-0.329284\pi\)
0.510976 + 0.859595i \(0.329284\pi\)
\(384\) 6.00000 0.306186
\(385\) 0 0
\(386\) −5.00000 −0.254493
\(387\) 0 0
\(388\) 13.0000 0.659975
\(389\) −3.00000 −0.152106 −0.0760530 0.997104i \(-0.524232\pi\)
−0.0760530 + 0.997104i \(0.524232\pi\)
\(390\) 2.00000 0.101274
\(391\) 10.0000 0.505722
\(392\) −9.00000 −0.454569
\(393\) 0 0
\(394\) −11.0000 −0.554172
\(395\) 10.0000 0.503155
\(396\) 0 0
\(397\) 13.0000 0.652451 0.326226 0.945292i \(-0.394223\pi\)
0.326226 + 0.945292i \(0.394223\pi\)
\(398\) −24.0000 −1.20301
\(399\) −24.0000 −1.20150
\(400\) 4.00000 0.200000
\(401\) 23.0000 1.14857 0.574283 0.818657i \(-0.305281\pi\)
0.574283 + 0.818657i \(0.305281\pi\)
\(402\) −4.00000 −0.199502
\(403\) 2.00000 0.0996271
\(404\) −10.0000 −0.497519
\(405\) −11.0000 −0.546594
\(406\) 18.0000 0.893325
\(407\) 0 0
\(408\) 30.0000 1.48522
\(409\) 21.0000 1.03838 0.519192 0.854658i \(-0.326233\pi\)
0.519192 + 0.854658i \(0.326233\pi\)
\(410\) −5.00000 −0.246932
\(411\) −20.0000 −0.986527
\(412\) −8.00000 −0.394132
\(413\) 16.0000 0.787309
\(414\) −2.00000 −0.0982946
\(415\) −6.00000 −0.294528
\(416\) 5.00000 0.245145
\(417\) 4.00000 0.195881
\(418\) 0 0
\(419\) 2.00000 0.0977064 0.0488532 0.998806i \(-0.484443\pi\)
0.0488532 + 0.998806i \(0.484443\pi\)
\(420\) −4.00000 −0.195180
\(421\) 13.0000 0.633581 0.316791 0.948495i \(-0.397395\pi\)
0.316791 + 0.948495i \(0.397395\pi\)
\(422\) 12.0000 0.584151
\(423\) 2.00000 0.0972433
\(424\) 27.0000 1.31124
\(425\) −20.0000 −0.970143
\(426\) −24.0000 −1.16280
\(427\) −12.0000 −0.580721
\(428\) 6.00000 0.290021
\(429\) 0 0
\(430\) 0 0
\(431\) −12.0000 −0.578020 −0.289010 0.957326i \(-0.593326\pi\)
−0.289010 + 0.957326i \(0.593326\pi\)
\(432\) 4.00000 0.192450
\(433\) 19.0000 0.913082 0.456541 0.889702i \(-0.349088\pi\)
0.456541 + 0.889702i \(0.349088\pi\)
\(434\) 4.00000 0.192006
\(435\) −18.0000 −0.863034
\(436\) −11.0000 −0.526804
\(437\) −12.0000 −0.574038
\(438\) −4.00000 −0.191127
\(439\) −22.0000 −1.05000 −0.525001 0.851101i \(-0.675935\pi\)
−0.525001 + 0.851101i \(0.675935\pi\)
\(440\) 0 0
\(441\) −3.00000 −0.142857
\(442\) 5.00000 0.237826
\(443\) −20.0000 −0.950229 −0.475114 0.879924i \(-0.657593\pi\)
−0.475114 + 0.879924i \(0.657593\pi\)
\(444\) 6.00000 0.284747
\(445\) −9.00000 −0.426641
\(446\) 20.0000 0.947027
\(447\) −34.0000 −1.60814
\(448\) 14.0000 0.661438
\(449\) −13.0000 −0.613508 −0.306754 0.951789i \(-0.599243\pi\)
−0.306754 + 0.951789i \(0.599243\pi\)
\(450\) 4.00000 0.188562
\(451\) 0 0
\(452\) 9.00000 0.423324
\(453\) 32.0000 1.50349
\(454\) −24.0000 −1.12638
\(455\) −2.00000 −0.0937614
\(456\) −36.0000 −1.68585
\(457\) −39.0000 −1.82434 −0.912172 0.409809i \(-0.865595\pi\)
−0.912172 + 0.409809i \(0.865595\pi\)
\(458\) −9.00000 −0.420542
\(459\) −20.0000 −0.933520
\(460\) −2.00000 −0.0932505
\(461\) −33.0000 −1.53696 −0.768482 0.639872i \(-0.778987\pi\)
−0.768482 + 0.639872i \(0.778987\pi\)
\(462\) 0 0
\(463\) −20.0000 −0.929479 −0.464739 0.885448i \(-0.653852\pi\)
−0.464739 + 0.885448i \(0.653852\pi\)
\(464\) 9.00000 0.417815
\(465\) −4.00000 −0.185496
\(466\) −21.0000 −0.972806
\(467\) 12.0000 0.555294 0.277647 0.960683i \(-0.410445\pi\)
0.277647 + 0.960683i \(0.410445\pi\)
\(468\) 1.00000 0.0462250
\(469\) 4.00000 0.184703
\(470\) −2.00000 −0.0922531
\(471\) 4.00000 0.184310
\(472\) 24.0000 1.10469
\(473\) 0 0
\(474\) −20.0000 −0.918630
\(475\) 24.0000 1.10120
\(476\) −10.0000 −0.458349
\(477\) 9.00000 0.412082
\(478\) 6.00000 0.274434
\(479\) 16.0000 0.731059 0.365529 0.930800i \(-0.380888\pi\)
0.365529 + 0.930800i \(0.380888\pi\)
\(480\) −10.0000 −0.456435
\(481\) 3.00000 0.136788
\(482\) 22.0000 1.00207
\(483\) 8.00000 0.364013
\(484\) 0 0
\(485\) −13.0000 −0.590300
\(486\) 10.0000 0.453609
\(487\) 2.00000 0.0906287 0.0453143 0.998973i \(-0.485571\pi\)
0.0453143 + 0.998973i \(0.485571\pi\)
\(488\) −18.0000 −0.814822
\(489\) −4.00000 −0.180886
\(490\) 3.00000 0.135526
\(491\) 2.00000 0.0902587 0.0451294 0.998981i \(-0.485630\pi\)
0.0451294 + 0.998981i \(0.485630\pi\)
\(492\) −10.0000 −0.450835
\(493\) −45.0000 −2.02670
\(494\) −6.00000 −0.269953
\(495\) 0 0
\(496\) 2.00000 0.0898027
\(497\) 24.0000 1.07655
\(498\) 12.0000 0.537733
\(499\) 8.00000 0.358129 0.179065 0.983837i \(-0.442693\pi\)
0.179065 + 0.983837i \(0.442693\pi\)
\(500\) 9.00000 0.402492
\(501\) −24.0000 −1.07224
\(502\) 2.00000 0.0892644
\(503\) 38.0000 1.69434 0.847168 0.531325i \(-0.178306\pi\)
0.847168 + 0.531325i \(0.178306\pi\)
\(504\) 6.00000 0.267261
\(505\) 10.0000 0.444994
\(506\) 0 0
\(507\) −24.0000 −1.06588
\(508\) −16.0000 −0.709885
\(509\) −42.0000 −1.86162 −0.930809 0.365507i \(-0.880896\pi\)
−0.930809 + 0.365507i \(0.880896\pi\)
\(510\) −10.0000 −0.442807
\(511\) 4.00000 0.176950
\(512\) 11.0000 0.486136
\(513\) 24.0000 1.05963
\(514\) −19.0000 −0.838054
\(515\) 8.00000 0.352522
\(516\) 0 0
\(517\) 0 0
\(518\) 6.00000 0.263625
\(519\) −12.0000 −0.526742
\(520\) −3.00000 −0.131559
\(521\) 30.0000 1.31432 0.657162 0.753749i \(-0.271757\pi\)
0.657162 + 0.753749i \(0.271757\pi\)
\(522\) 9.00000 0.393919
\(523\) 16.0000 0.699631 0.349816 0.936819i \(-0.386244\pi\)
0.349816 + 0.936819i \(0.386244\pi\)
\(524\) 0 0
\(525\) −16.0000 −0.698297
\(526\) −22.0000 −0.959246
\(527\) −10.0000 −0.435607
\(528\) 0 0
\(529\) −19.0000 −0.826087
\(530\) −9.00000 −0.390935
\(531\) 8.00000 0.347170
\(532\) 12.0000 0.520266
\(533\) −5.00000 −0.216574
\(534\) 18.0000 0.778936
\(535\) −6.00000 −0.259403
\(536\) 6.00000 0.259161
\(537\) 48.0000 2.07135
\(538\) −1.00000 −0.0431131
\(539\) 0 0
\(540\) 4.00000 0.172133
\(541\) −34.0000 −1.46177 −0.730887 0.682498i \(-0.760893\pi\)
−0.730887 + 0.682498i \(0.760893\pi\)
\(542\) 20.0000 0.859074
\(543\) 2.00000 0.0858282
\(544\) −25.0000 −1.07187
\(545\) 11.0000 0.471188
\(546\) 4.00000 0.171184
\(547\) 16.0000 0.684111 0.342055 0.939680i \(-0.388877\pi\)
0.342055 + 0.939680i \(0.388877\pi\)
\(548\) 10.0000 0.427179
\(549\) −6.00000 −0.256074
\(550\) 0 0
\(551\) 54.0000 2.30048
\(552\) 12.0000 0.510754
\(553\) 20.0000 0.850487
\(554\) 1.00000 0.0424859
\(555\) −6.00000 −0.254686
\(556\) −2.00000 −0.0848189
\(557\) 2.00000 0.0847427 0.0423714 0.999102i \(-0.486509\pi\)
0.0423714 + 0.999102i \(0.486509\pi\)
\(558\) 2.00000 0.0846668
\(559\) 0 0
\(560\) −2.00000 −0.0845154
\(561\) 0 0
\(562\) 6.00000 0.253095
\(563\) −34.0000 −1.43293 −0.716465 0.697623i \(-0.754241\pi\)
−0.716465 + 0.697623i \(0.754241\pi\)
\(564\) −4.00000 −0.168430
\(565\) −9.00000 −0.378633
\(566\) 28.0000 1.17693
\(567\) −22.0000 −0.923913
\(568\) 36.0000 1.51053
\(569\) −6.00000 −0.251533 −0.125767 0.992060i \(-0.540139\pi\)
−0.125767 + 0.992060i \(0.540139\pi\)
\(570\) 12.0000 0.502625
\(571\) 22.0000 0.920671 0.460336 0.887745i \(-0.347729\pi\)
0.460336 + 0.887745i \(0.347729\pi\)
\(572\) 0 0
\(573\) 16.0000 0.668410
\(574\) −10.0000 −0.417392
\(575\) −8.00000 −0.333623
\(576\) 7.00000 0.291667
\(577\) −21.0000 −0.874241 −0.437121 0.899403i \(-0.644002\pi\)
−0.437121 + 0.899403i \(0.644002\pi\)
\(578\) −8.00000 −0.332756
\(579\) 10.0000 0.415586
\(580\) 9.00000 0.373705
\(581\) −12.0000 −0.497844
\(582\) 26.0000 1.07773
\(583\) 0 0
\(584\) 6.00000 0.248282
\(585\) −1.00000 −0.0413449
\(586\) 9.00000 0.371787
\(587\) −14.0000 −0.577842 −0.288921 0.957353i \(-0.593296\pi\)
−0.288921 + 0.957353i \(0.593296\pi\)
\(588\) 6.00000 0.247436
\(589\) 12.0000 0.494451
\(590\) −8.00000 −0.329355
\(591\) 22.0000 0.904959
\(592\) 3.00000 0.123299
\(593\) −11.0000 −0.451716 −0.225858 0.974160i \(-0.572519\pi\)
−0.225858 + 0.974160i \(0.572519\pi\)
\(594\) 0 0
\(595\) 10.0000 0.409960
\(596\) 17.0000 0.696347
\(597\) 48.0000 1.96451
\(598\) 2.00000 0.0817861
\(599\) 34.0000 1.38920 0.694601 0.719395i \(-0.255581\pi\)
0.694601 + 0.719395i \(0.255581\pi\)
\(600\) −24.0000 −0.979796
\(601\) 13.0000 0.530281 0.265141 0.964210i \(-0.414582\pi\)
0.265141 + 0.964210i \(0.414582\pi\)
\(602\) 0 0
\(603\) 2.00000 0.0814463
\(604\) −16.0000 −0.651031
\(605\) 0 0
\(606\) −20.0000 −0.812444
\(607\) 10.0000 0.405887 0.202944 0.979190i \(-0.434949\pi\)
0.202944 + 0.979190i \(0.434949\pi\)
\(608\) 30.0000 1.21666
\(609\) −36.0000 −1.45879
\(610\) 6.00000 0.242933
\(611\) −2.00000 −0.0809113
\(612\) −5.00000 −0.202113
\(613\) −17.0000 −0.686624 −0.343312 0.939222i \(-0.611549\pi\)
−0.343312 + 0.939222i \(0.611549\pi\)
\(614\) −22.0000 −0.887848
\(615\) 10.0000 0.403239
\(616\) 0 0
\(617\) −9.00000 −0.362326 −0.181163 0.983453i \(-0.557986\pi\)
−0.181163 + 0.983453i \(0.557986\pi\)
\(618\) −16.0000 −0.643614
\(619\) 2.00000 0.0803868 0.0401934 0.999192i \(-0.487203\pi\)
0.0401934 + 0.999192i \(0.487203\pi\)
\(620\) 2.00000 0.0803219
\(621\) −8.00000 −0.321029
\(622\) −24.0000 −0.962312
\(623\) −18.0000 −0.721155
\(624\) 2.00000 0.0800641
\(625\) 11.0000 0.440000
\(626\) −23.0000 −0.919265
\(627\) 0 0
\(628\) −2.00000 −0.0798087
\(629\) −15.0000 −0.598089
\(630\) −2.00000 −0.0796819
\(631\) −14.0000 −0.557331 −0.278666 0.960388i \(-0.589892\pi\)
−0.278666 + 0.960388i \(0.589892\pi\)
\(632\) 30.0000 1.19334
\(633\) −24.0000 −0.953914
\(634\) 2.00000 0.0794301
\(635\) 16.0000 0.634941
\(636\) −18.0000 −0.713746
\(637\) 3.00000 0.118864
\(638\) 0 0
\(639\) 12.0000 0.474713
\(640\) 3.00000 0.118585
\(641\) −9.00000 −0.355479 −0.177739 0.984078i \(-0.556878\pi\)
−0.177739 + 0.984078i \(0.556878\pi\)
\(642\) 12.0000 0.473602
\(643\) −10.0000 −0.394362 −0.197181 0.980367i \(-0.563179\pi\)
−0.197181 + 0.980367i \(0.563179\pi\)
\(644\) −4.00000 −0.157622
\(645\) 0 0
\(646\) 30.0000 1.18033
\(647\) 20.0000 0.786281 0.393141 0.919478i \(-0.371389\pi\)
0.393141 + 0.919478i \(0.371389\pi\)
\(648\) −33.0000 −1.29636
\(649\) 0 0
\(650\) −4.00000 −0.156893
\(651\) −8.00000 −0.313545
\(652\) 2.00000 0.0783260
\(653\) −14.0000 −0.547862 −0.273931 0.961749i \(-0.588324\pi\)
−0.273931 + 0.961749i \(0.588324\pi\)
\(654\) −22.0000 −0.860268
\(655\) 0 0
\(656\) −5.00000 −0.195217
\(657\) 2.00000 0.0780274
\(658\) −4.00000 −0.155936
\(659\) −22.0000 −0.856998 −0.428499 0.903542i \(-0.640958\pi\)
−0.428499 + 0.903542i \(0.640958\pi\)
\(660\) 0 0
\(661\) 13.0000 0.505641 0.252821 0.967513i \(-0.418642\pi\)
0.252821 + 0.967513i \(0.418642\pi\)
\(662\) 20.0000 0.777322
\(663\) −10.0000 −0.388368
\(664\) −18.0000 −0.698535
\(665\) −12.0000 −0.465340
\(666\) 3.00000 0.116248
\(667\) −18.0000 −0.696963
\(668\) 12.0000 0.464294
\(669\) −40.0000 −1.54649
\(670\) −2.00000 −0.0772667
\(671\) 0 0
\(672\) −20.0000 −0.771517
\(673\) 10.0000 0.385472 0.192736 0.981251i \(-0.438264\pi\)
0.192736 + 0.981251i \(0.438264\pi\)
\(674\) −13.0000 −0.500741
\(675\) 16.0000 0.615840
\(676\) 12.0000 0.461538
\(677\) 27.0000 1.03769 0.518847 0.854867i \(-0.326361\pi\)
0.518847 + 0.854867i \(0.326361\pi\)
\(678\) 18.0000 0.691286
\(679\) −26.0000 −0.997788
\(680\) 15.0000 0.575224
\(681\) 48.0000 1.83936
\(682\) 0 0
\(683\) 2.00000 0.0765279 0.0382639 0.999268i \(-0.487817\pi\)
0.0382639 + 0.999268i \(0.487817\pi\)
\(684\) 6.00000 0.229416
\(685\) −10.0000 −0.382080
\(686\) 20.0000 0.763604
\(687\) 18.0000 0.686743
\(688\) 0 0
\(689\) −9.00000 −0.342873
\(690\) −4.00000 −0.152277
\(691\) 20.0000 0.760836 0.380418 0.924815i \(-0.375780\pi\)
0.380418 + 0.924815i \(0.375780\pi\)
\(692\) 6.00000 0.228086
\(693\) 0 0
\(694\) 28.0000 1.06287
\(695\) 2.00000 0.0758643
\(696\) −54.0000 −2.04686
\(697\) 25.0000 0.946943
\(698\) −27.0000 −1.02197
\(699\) 42.0000 1.58859
\(700\) 8.00000 0.302372
\(701\) −17.0000 −0.642081 −0.321041 0.947065i \(-0.604033\pi\)
−0.321041 + 0.947065i \(0.604033\pi\)
\(702\) −4.00000 −0.150970
\(703\) 18.0000 0.678883
\(704\) 0 0
\(705\) 4.00000 0.150649
\(706\) 9.00000 0.338719
\(707\) 20.0000 0.752177
\(708\) −16.0000 −0.601317
\(709\) −10.0000 −0.375558 −0.187779 0.982211i \(-0.560129\pi\)
−0.187779 + 0.982211i \(0.560129\pi\)
\(710\) −12.0000 −0.450352
\(711\) 10.0000 0.375029
\(712\) −27.0000 −1.01187
\(713\) −4.00000 −0.149801
\(714\) −20.0000 −0.748481
\(715\) 0 0
\(716\) −24.0000 −0.896922
\(717\) −12.0000 −0.448148
\(718\) −2.00000 −0.0746393
\(719\) 30.0000 1.11881 0.559406 0.828894i \(-0.311029\pi\)
0.559406 + 0.828894i \(0.311029\pi\)
\(720\) −1.00000 −0.0372678
\(721\) 16.0000 0.595871
\(722\) −17.0000 −0.632674
\(723\) −44.0000 −1.63638
\(724\) −1.00000 −0.0371647
\(725\) 36.0000 1.33701
\(726\) 0 0
\(727\) −42.0000 −1.55769 −0.778847 0.627214i \(-0.784195\pi\)
−0.778847 + 0.627214i \(0.784195\pi\)
\(728\) −6.00000 −0.222375
\(729\) 13.0000 0.481481
\(730\) −2.00000 −0.0740233
\(731\) 0 0
\(732\) 12.0000 0.443533
\(733\) −9.00000 −0.332423 −0.166211 0.986090i \(-0.553153\pi\)
−0.166211 + 0.986090i \(0.553153\pi\)
\(734\) 14.0000 0.516749
\(735\) −6.00000 −0.221313
\(736\) −10.0000 −0.368605
\(737\) 0 0
\(738\) −5.00000 −0.184053
\(739\) 10.0000 0.367856 0.183928 0.982940i \(-0.441119\pi\)
0.183928 + 0.982940i \(0.441119\pi\)
\(740\) 3.00000 0.110282
\(741\) 12.0000 0.440831
\(742\) −18.0000 −0.660801
\(743\) 38.0000 1.39408 0.697042 0.717030i \(-0.254499\pi\)
0.697042 + 0.717030i \(0.254499\pi\)
\(744\) −12.0000 −0.439941
\(745\) −17.0000 −0.622832
\(746\) 22.0000 0.805477
\(747\) −6.00000 −0.219529
\(748\) 0 0
\(749\) −12.0000 −0.438470
\(750\) 18.0000 0.657267
\(751\) −20.0000 −0.729810 −0.364905 0.931045i \(-0.618899\pi\)
−0.364905 + 0.931045i \(0.618899\pi\)
\(752\) −2.00000 −0.0729325
\(753\) −4.00000 −0.145768
\(754\) −9.00000 −0.327761
\(755\) 16.0000 0.582300
\(756\) 8.00000 0.290957
\(757\) 53.0000 1.92632 0.963159 0.268933i \(-0.0866710\pi\)
0.963159 + 0.268933i \(0.0866710\pi\)
\(758\) 32.0000 1.16229
\(759\) 0 0
\(760\) −18.0000 −0.652929
\(761\) 21.0000 0.761249 0.380625 0.924730i \(-0.375709\pi\)
0.380625 + 0.924730i \(0.375709\pi\)
\(762\) −32.0000 −1.15924
\(763\) 22.0000 0.796453
\(764\) −8.00000 −0.289430
\(765\) 5.00000 0.180775
\(766\) −20.0000 −0.722629
\(767\) −8.00000 −0.288863
\(768\) −34.0000 −1.22687
\(769\) −11.0000 −0.396670 −0.198335 0.980134i \(-0.563553\pi\)
−0.198335 + 0.980134i \(0.563553\pi\)
\(770\) 0 0
\(771\) 38.0000 1.36854
\(772\) −5.00000 −0.179954
\(773\) −42.0000 −1.51064 −0.755318 0.655359i \(-0.772517\pi\)
−0.755318 + 0.655359i \(0.772517\pi\)
\(774\) 0 0
\(775\) 8.00000 0.287368
\(776\) −39.0000 −1.40002
\(777\) −12.0000 −0.430498
\(778\) 3.00000 0.107555
\(779\) −30.0000 −1.07486
\(780\) 2.00000 0.0716115
\(781\) 0 0
\(782\) −10.0000 −0.357599
\(783\) 36.0000 1.28654
\(784\) 3.00000 0.107143
\(785\) 2.00000 0.0713831
\(786\) 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
\(789\) 44.0000 1.56644
\(790\) −10.0000 −0.355784
\(791\) −18.0000 −0.640006
\(792\) 0 0
\(793\) 6.00000 0.213066
\(794\) −13.0000 −0.461353
\(795\) 18.0000 0.638394
\(796\) −24.0000 −0.850657
\(797\) −10.0000 −0.354218 −0.177109 0.984191i \(-0.556675\pi\)
−0.177109 + 0.984191i \(0.556675\pi\)
\(798\) 24.0000 0.849591
\(799\) 10.0000 0.353775
\(800\) 20.0000 0.707107
\(801\) −9.00000 −0.317999
\(802\) −23.0000 −0.812158
\(803\) 0 0
\(804\) −4.00000 −0.141069
\(805\) 4.00000 0.140981
\(806\) −2.00000 −0.0704470
\(807\) 2.00000 0.0704033
\(808\) 30.0000 1.05540
\(809\) −6.00000 −0.210949 −0.105474 0.994422i \(-0.533636\pi\)
−0.105474 + 0.994422i \(0.533636\pi\)
\(810\) 11.0000 0.386501
\(811\) −28.0000 −0.983213 −0.491606 0.870817i \(-0.663590\pi\)
−0.491606 + 0.870817i \(0.663590\pi\)
\(812\) 18.0000 0.631676
\(813\) −40.0000 −1.40286
\(814\) 0 0
\(815\) −2.00000 −0.0700569
\(816\) −10.0000 −0.350070
\(817\) 0 0
\(818\) −21.0000 −0.734248
\(819\) −2.00000 −0.0698857
\(820\) −5.00000 −0.174608
\(821\) 2.00000 0.0698005 0.0349002 0.999391i \(-0.488889\pi\)
0.0349002 + 0.999391i \(0.488889\pi\)
\(822\) 20.0000 0.697580
\(823\) −24.0000 −0.836587 −0.418294 0.908312i \(-0.637372\pi\)
−0.418294 + 0.908312i \(0.637372\pi\)
\(824\) 24.0000 0.836080
\(825\) 0 0
\(826\) −16.0000 −0.556711
\(827\) 10.0000 0.347734 0.173867 0.984769i \(-0.444374\pi\)
0.173867 + 0.984769i \(0.444374\pi\)
\(828\) −2.00000 −0.0695048
\(829\) −47.0000 −1.63238 −0.816189 0.577785i \(-0.803917\pi\)
−0.816189 + 0.577785i \(0.803917\pi\)
\(830\) 6.00000 0.208263
\(831\) −2.00000 −0.0693792
\(832\) −7.00000 −0.242681
\(833\) −15.0000 −0.519719
\(834\) −4.00000 −0.138509
\(835\) −12.0000 −0.415277
\(836\) 0 0
\(837\) 8.00000 0.276520
\(838\) −2.00000 −0.0690889
\(839\) 46.0000 1.58810 0.794048 0.607855i \(-0.207970\pi\)
0.794048 + 0.607855i \(0.207970\pi\)
\(840\) 12.0000 0.414039
\(841\) 52.0000 1.79310
\(842\) −13.0000 −0.448010
\(843\) −12.0000 −0.413302
\(844\) 12.0000 0.413057
\(845\) −12.0000 −0.412813
\(846\) −2.00000 −0.0687614
\(847\) 0 0
\(848\) −9.00000 −0.309061
\(849\) −56.0000 −1.92192
\(850\) 20.0000 0.685994
\(851\) −6.00000 −0.205677
\(852\) −24.0000 −0.822226
\(853\) −17.0000 −0.582069 −0.291034 0.956713i \(-0.593999\pi\)
−0.291034 + 0.956713i \(0.593999\pi\)
\(854\) 12.0000 0.410632
\(855\) −6.00000 −0.205196
\(856\) −18.0000 −0.615227
\(857\) 22.0000 0.751506 0.375753 0.926720i \(-0.377384\pi\)
0.375753 + 0.926720i \(0.377384\pi\)
\(858\) 0 0
\(859\) 24.0000 0.818869 0.409435 0.912339i \(-0.365726\pi\)
0.409435 + 0.912339i \(0.365726\pi\)
\(860\) 0 0
\(861\) 20.0000 0.681598
\(862\) 12.0000 0.408722
\(863\) −54.0000 −1.83818 −0.919091 0.394046i \(-0.871075\pi\)
−0.919091 + 0.394046i \(0.871075\pi\)
\(864\) 20.0000 0.680414
\(865\) −6.00000 −0.204006
\(866\) −19.0000 −0.645646
\(867\) 16.0000 0.543388
\(868\) 4.00000 0.135769
\(869\) 0 0
\(870\) 18.0000 0.610257
\(871\) −2.00000 −0.0677674
\(872\) 33.0000 1.11752
\(873\) −13.0000 −0.439983
\(874\) 12.0000 0.405906
\(875\) −18.0000 −0.608511
\(876\) −4.00000 −0.135147
\(877\) 27.0000 0.911725 0.455863 0.890050i \(-0.349331\pi\)
0.455863 + 0.890050i \(0.349331\pi\)
\(878\) 22.0000 0.742464
\(879\) −18.0000 −0.607125
\(880\) 0 0
\(881\) 35.0000 1.17918 0.589590 0.807703i \(-0.299289\pi\)
0.589590 + 0.807703i \(0.299289\pi\)
\(882\) 3.00000 0.101015
\(883\) −20.0000 −0.673054 −0.336527 0.941674i \(-0.609252\pi\)
−0.336527 + 0.941674i \(0.609252\pi\)
\(884\) 5.00000 0.168168
\(885\) 16.0000 0.537834
\(886\) 20.0000 0.671913
\(887\) 46.0000 1.54453 0.772264 0.635301i \(-0.219124\pi\)
0.772264 + 0.635301i \(0.219124\pi\)
\(888\) −18.0000 −0.604040
\(889\) 32.0000 1.07325
\(890\) 9.00000 0.301681
\(891\) 0 0
\(892\) 20.0000 0.669650
\(893\) −12.0000 −0.401565
\(894\) 34.0000 1.13713
\(895\) 24.0000 0.802232
\(896\) 6.00000 0.200446
\(897\) −4.00000 −0.133556
\(898\) 13.0000 0.433816
\(899\) 18.0000 0.600334
\(900\) 4.00000 0.133333
\(901\) 45.0000 1.49917
\(902\) 0 0
\(903\) 0 0
\(904\) −27.0000 −0.898007
\(905\) 1.00000 0.0332411
\(906\) −32.0000 −1.06313
\(907\) 12.0000 0.398453 0.199227 0.979953i \(-0.436157\pi\)
0.199227 + 0.979953i \(0.436157\pi\)
\(908\) −24.0000 −0.796468
\(909\) 10.0000 0.331679
\(910\) 2.00000 0.0662994
\(911\) −24.0000 −0.795155 −0.397578 0.917568i \(-0.630149\pi\)
−0.397578 + 0.917568i \(0.630149\pi\)
\(912\) 12.0000 0.397360
\(913\) 0 0
\(914\) 39.0000 1.29001
\(915\) −12.0000 −0.396708
\(916\) −9.00000 −0.297368
\(917\) 0 0
\(918\) 20.0000 0.660098
\(919\) −28.0000 −0.923635 −0.461817 0.886975i \(-0.652802\pi\)
−0.461817 + 0.886975i \(0.652802\pi\)
\(920\) 6.00000 0.197814
\(921\) 44.0000 1.44985
\(922\) 33.0000 1.08680
\(923\) −12.0000 −0.394985
\(924\) 0 0
\(925\) 12.0000 0.394558
\(926\) 20.0000 0.657241
\(927\) 8.00000 0.262754
\(928\) 45.0000 1.47720
\(929\) −21.0000 −0.688988 −0.344494 0.938789i \(-0.611949\pi\)
−0.344494 + 0.938789i \(0.611949\pi\)
\(930\) 4.00000 0.131165
\(931\) 18.0000 0.589926
\(932\) −21.0000 −0.687878
\(933\) 48.0000 1.57145
\(934\) −12.0000 −0.392652
\(935\) 0 0
\(936\) −3.00000 −0.0980581
\(937\) −23.0000 −0.751377 −0.375689 0.926746i \(-0.622594\pi\)
−0.375689 + 0.926746i \(0.622594\pi\)
\(938\) −4.00000 −0.130605
\(939\) 46.0000 1.50115
\(940\) −2.00000 −0.0652328
\(941\) 27.0000 0.880175 0.440087 0.897955i \(-0.354947\pi\)
0.440087 + 0.897955i \(0.354947\pi\)
\(942\) −4.00000 −0.130327
\(943\) 10.0000 0.325645
\(944\) −8.00000 −0.260378
\(945\) −8.00000 −0.260240
\(946\) 0 0
\(947\) −42.0000 −1.36482 −0.682408 0.730971i \(-0.739067\pi\)
−0.682408 + 0.730971i \(0.739067\pi\)
\(948\) −20.0000 −0.649570
\(949\) −2.00000 −0.0649227
\(950\) −24.0000 −0.778663
\(951\) −4.00000 −0.129709
\(952\) 30.0000 0.972306
\(953\) −31.0000 −1.00419 −0.502094 0.864813i \(-0.667437\pi\)
−0.502094 + 0.864813i \(0.667437\pi\)
\(954\) −9.00000 −0.291386
\(955\) 8.00000 0.258874
\(956\) 6.00000 0.194054
\(957\) 0 0
\(958\) −16.0000 −0.516937
\(959\) −20.0000 −0.645834
\(960\) 14.0000 0.451848
\(961\) −27.0000 −0.870968
\(962\) −3.00000 −0.0967239
\(963\) −6.00000 −0.193347
\(964\) 22.0000 0.708572
\(965\) 5.00000 0.160956
\(966\) −8.00000 −0.257396
\(967\) −22.0000 −0.707472 −0.353736 0.935345i \(-0.615089\pi\)
−0.353736 + 0.935345i \(0.615089\pi\)
\(968\) 0 0
\(969\) −60.0000 −1.92748
\(970\) 13.0000 0.417405
\(971\) 2.00000 0.0641831 0.0320915 0.999485i \(-0.489783\pi\)
0.0320915 + 0.999485i \(0.489783\pi\)
\(972\) 10.0000 0.320750
\(973\) 4.00000 0.128234
\(974\) −2.00000 −0.0640841
\(975\) 8.00000 0.256205
\(976\) 6.00000 0.192055
\(977\) −57.0000 −1.82359 −0.911796 0.410644i \(-0.865304\pi\)
−0.911796 + 0.410644i \(0.865304\pi\)
\(978\) 4.00000 0.127906
\(979\) 0 0
\(980\) 3.00000 0.0958315
\(981\) 11.0000 0.351203
\(982\) −2.00000 −0.0638226
\(983\) −36.0000 −1.14822 −0.574111 0.818778i \(-0.694652\pi\)
−0.574111 + 0.818778i \(0.694652\pi\)
\(984\) 30.0000 0.956365
\(985\) 11.0000 0.350489
\(986\) 45.0000 1.43309
\(987\) 8.00000 0.254643
\(988\) −6.00000 −0.190885
\(989\) 0 0
\(990\) 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
\(993\) −40.0000 −1.26936
\(994\) −24.0000 −0.761234
\(995\) 24.0000 0.760851
\(996\) 12.0000 0.380235
\(997\) −53.0000 −1.67853 −0.839263 0.543725i \(-0.817013\pi\)
−0.839263 + 0.543725i \(0.817013\pi\)
\(998\) −8.00000 −0.253236
\(999\) 12.0000 0.379663
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 \(a_p\))