Properties

Label 945.2.a.g.1.1
Level 945
Weight 2
Character 945.1
Self dual Yes
Analytic conductor 7.546
Analytic rank 1
Dimension 2
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 945 = 3^{3} \cdot 5 \cdot 7 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 945.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(7.54586299101\)
Analytic rank: \(1\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{10})^+\)
Coefficient ring: \(\Z[a_1, a_2]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Root \(-0.618034\)
Character \(\chi\) = 945.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.618034 q^{2}\) \(-1.61803 q^{4}\) \(-1.00000 q^{5}\) \(-1.00000 q^{7}\) \(+2.23607 q^{8}\) \(+O(q^{10})\) \(q\)\(-0.618034 q^{2}\) \(-1.61803 q^{4}\) \(-1.00000 q^{5}\) \(-1.00000 q^{7}\) \(+2.23607 q^{8}\) \(+0.618034 q^{10}\) \(+0.236068 q^{11}\) \(+3.61803 q^{13}\) \(+0.618034 q^{14}\) \(+1.85410 q^{16}\) \(+0.618034 q^{17}\) \(+4.09017 q^{19}\) \(+1.61803 q^{20}\) \(-0.145898 q^{22}\) \(-7.61803 q^{23}\) \(+1.00000 q^{25}\) \(-2.23607 q^{26}\) \(+1.61803 q^{28}\) \(-10.5623 q^{29}\) \(-6.70820 q^{31}\) \(-5.61803 q^{32}\) \(-0.381966 q^{34}\) \(+1.00000 q^{35}\) \(-6.70820 q^{37}\) \(-2.52786 q^{38}\) \(-2.23607 q^{40}\) \(+3.09017 q^{41}\) \(+7.94427 q^{43}\) \(-0.381966 q^{44}\) \(+4.70820 q^{46}\) \(-11.0000 q^{47}\) \(+1.00000 q^{49}\) \(-0.618034 q^{50}\) \(-5.85410 q^{52}\) \(+6.61803 q^{53}\) \(-0.236068 q^{55}\) \(-2.23607 q^{56}\) \(+6.52786 q^{58}\) \(-14.7082 q^{59}\) \(-7.14590 q^{61}\) \(+4.14590 q^{62}\) \(-0.236068 q^{64}\) \(-3.61803 q^{65}\) \(-4.32624 q^{67}\) \(-1.00000 q^{68}\) \(-0.618034 q^{70}\) \(+2.85410 q^{71}\) \(-3.94427 q^{73}\) \(+4.14590 q^{74}\) \(-6.61803 q^{76}\) \(-0.236068 q^{77}\) \(+3.38197 q^{79}\) \(-1.85410 q^{80}\) \(-1.90983 q^{82}\) \(+2.70820 q^{83}\) \(-0.618034 q^{85}\) \(-4.90983 q^{86}\) \(+0.527864 q^{88}\) \(+7.47214 q^{89}\) \(-3.61803 q^{91}\) \(+12.3262 q^{92}\) \(+6.79837 q^{94}\) \(-4.09017 q^{95}\) \(+12.3262 q^{97}\) \(-0.618034 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut q^{14} \) \(\mathstrut -\mathstrut 3q^{16} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut -\mathstrut 3q^{19} \) \(\mathstrut +\mathstrut q^{20} \) \(\mathstrut -\mathstrut 7q^{22} \) \(\mathstrut -\mathstrut 13q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut q^{28} \) \(\mathstrut -\mathstrut q^{29} \) \(\mathstrut -\mathstrut 9q^{32} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 5q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 3q^{44} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 22q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut q^{50} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 11q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 16q^{59} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 15q^{62} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut -\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 7q^{67} \) \(\mathstrut -\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut q^{70} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 11q^{76} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 15q^{82} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut q^{85} \) \(\mathstrut -\mathstrut 21q^{86} \) \(\mathstrut +\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 5q^{91} \) \(\mathstrut +\mathstrut 9q^{92} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut +\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 9q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.618034 −0.437016 −0.218508 0.975835i \(-0.570119\pi\)
−0.218508 + 0.975835i \(0.570119\pi\)
\(3\) 0 0
\(4\) −1.61803 −0.809017
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) 2.23607 0.790569
\(9\) 0 0
\(10\) 0.618034 0.195440
\(11\) 0.236068 0.0711772 0.0355886 0.999367i \(-0.488669\pi\)
0.0355886 + 0.999367i \(0.488669\pi\)
\(12\) 0 0
\(13\) 3.61803 1.00346 0.501731 0.865024i \(-0.332697\pi\)
0.501731 + 0.865024i \(0.332697\pi\)
\(14\) 0.618034 0.165177
\(15\) 0 0
\(16\) 1.85410 0.463525
\(17\) 0.618034 0.149895 0.0749476 0.997187i \(-0.476121\pi\)
0.0749476 + 0.997187i \(0.476121\pi\)
\(18\) 0 0
\(19\) 4.09017 0.938349 0.469175 0.883105i \(-0.344551\pi\)
0.469175 + 0.883105i \(0.344551\pi\)
\(20\) 1.61803 0.361803
\(21\) 0 0
\(22\) −0.145898 −0.0311056
\(23\) −7.61803 −1.58847 −0.794235 0.607611i \(-0.792128\pi\)
−0.794235 + 0.607611i \(0.792128\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −2.23607 −0.438529
\(27\) 0 0
\(28\) 1.61803 0.305780
\(29\) −10.5623 −1.96137 −0.980685 0.195591i \(-0.937337\pi\)
−0.980685 + 0.195591i \(0.937337\pi\)
\(30\) 0 0
\(31\) −6.70820 −1.20483 −0.602414 0.798183i \(-0.705795\pi\)
−0.602414 + 0.798183i \(0.705795\pi\)
\(32\) −5.61803 −0.993137
\(33\) 0 0
\(34\) −0.381966 −0.0655066
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) −6.70820 −1.10282 −0.551411 0.834234i \(-0.685910\pi\)
−0.551411 + 0.834234i \(0.685910\pi\)
\(38\) −2.52786 −0.410074
\(39\) 0 0
\(40\) −2.23607 −0.353553
\(41\) 3.09017 0.482603 0.241302 0.970450i \(-0.422426\pi\)
0.241302 + 0.970450i \(0.422426\pi\)
\(42\) 0 0
\(43\) 7.94427 1.21149 0.605745 0.795659i \(-0.292875\pi\)
0.605745 + 0.795659i \(0.292875\pi\)
\(44\) −0.381966 −0.0575835
\(45\) 0 0
\(46\) 4.70820 0.694187
\(47\) −11.0000 −1.60451 −0.802257 0.596978i \(-0.796368\pi\)
−0.802257 + 0.596978i \(0.796368\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) −0.618034 −0.0874032
\(51\) 0 0
\(52\) −5.85410 −0.811818
\(53\) 6.61803 0.909057 0.454528 0.890732i \(-0.349808\pi\)
0.454528 + 0.890732i \(0.349808\pi\)
\(54\) 0 0
\(55\) −0.236068 −0.0318314
\(56\) −2.23607 −0.298807
\(57\) 0 0
\(58\) 6.52786 0.857151
\(59\) −14.7082 −1.91485 −0.957423 0.288690i \(-0.906780\pi\)
−0.957423 + 0.288690i \(0.906780\pi\)
\(60\) 0 0
\(61\) −7.14590 −0.914938 −0.457469 0.889225i \(-0.651244\pi\)
−0.457469 + 0.889225i \(0.651244\pi\)
\(62\) 4.14590 0.526530
\(63\) 0 0
\(64\) −0.236068 −0.0295085
\(65\) −3.61803 −0.448762
\(66\) 0 0
\(67\) −4.32624 −0.528534 −0.264267 0.964450i \(-0.585130\pi\)
−0.264267 + 0.964450i \(0.585130\pi\)
\(68\) −1.00000 −0.121268
\(69\) 0 0
\(70\) −0.618034 −0.0738692
\(71\) 2.85410 0.338720 0.169360 0.985554i \(-0.445830\pi\)
0.169360 + 0.985554i \(0.445830\pi\)
\(72\) 0 0
\(73\) −3.94427 −0.461642 −0.230821 0.972996i \(-0.574141\pi\)
−0.230821 + 0.972996i \(0.574141\pi\)
\(74\) 4.14590 0.481951
\(75\) 0 0
\(76\) −6.61803 −0.759141
\(77\) −0.236068 −0.0269024
\(78\) 0 0
\(79\) 3.38197 0.380501 0.190250 0.981736i \(-0.439070\pi\)
0.190250 + 0.981736i \(0.439070\pi\)
\(80\) −1.85410 −0.207295
\(81\) 0 0
\(82\) −1.90983 −0.210905
\(83\) 2.70820 0.297264 0.148632 0.988893i \(-0.452513\pi\)
0.148632 + 0.988893i \(0.452513\pi\)
\(84\) 0 0
\(85\) −0.618034 −0.0670352
\(86\) −4.90983 −0.529441
\(87\) 0 0
\(88\) 0.527864 0.0562705
\(89\) 7.47214 0.792045 0.396022 0.918241i \(-0.370390\pi\)
0.396022 + 0.918241i \(0.370390\pi\)
\(90\) 0 0
\(91\) −3.61803 −0.379273
\(92\) 12.3262 1.28510
\(93\) 0 0
\(94\) 6.79837 0.701199
\(95\) −4.09017 −0.419643
\(96\) 0 0
\(97\) 12.3262 1.25154 0.625770 0.780008i \(-0.284785\pi\)
0.625770 + 0.780008i \(0.284785\pi\)
\(98\) −0.618034 −0.0624309
\(99\) 0 0
\(100\) −1.61803 −0.161803
\(101\) −14.4721 −1.44003 −0.720016 0.693958i \(-0.755865\pi\)
−0.720016 + 0.693958i \(0.755865\pi\)
\(102\) 0 0
\(103\) 8.38197 0.825900 0.412950 0.910754i \(-0.364498\pi\)
0.412950 + 0.910754i \(0.364498\pi\)
\(104\) 8.09017 0.793306
\(105\) 0 0
\(106\) −4.09017 −0.397272
\(107\) −10.7082 −1.03520 −0.517601 0.855622i \(-0.673175\pi\)
−0.517601 + 0.855622i \(0.673175\pi\)
\(108\) 0 0
\(109\) −7.56231 −0.724338 −0.362169 0.932113i \(-0.617964\pi\)
−0.362169 + 0.932113i \(0.617964\pi\)
\(110\) 0.145898 0.0139108
\(111\) 0 0
\(112\) −1.85410 −0.175196
\(113\) 0.854102 0.0803472 0.0401736 0.999193i \(-0.487209\pi\)
0.0401736 + 0.999193i \(0.487209\pi\)
\(114\) 0 0
\(115\) 7.61803 0.710385
\(116\) 17.0902 1.58678
\(117\) 0 0
\(118\) 9.09017 0.836818
\(119\) −0.618034 −0.0566551
\(120\) 0 0
\(121\) −10.9443 −0.994934
\(122\) 4.41641 0.399843
\(123\) 0 0
\(124\) 10.8541 0.974727
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) −11.0902 −0.984093 −0.492047 0.870569i \(-0.663751\pi\)
−0.492047 + 0.870569i \(0.663751\pi\)
\(128\) 11.3820 1.00603
\(129\) 0 0
\(130\) 2.23607 0.196116
\(131\) −6.61803 −0.578220 −0.289110 0.957296i \(-0.593359\pi\)
−0.289110 + 0.957296i \(0.593359\pi\)
\(132\) 0 0
\(133\) −4.09017 −0.354663
\(134\) 2.67376 0.230978
\(135\) 0 0
\(136\) 1.38197 0.118503
\(137\) 21.8885 1.87006 0.935032 0.354563i \(-0.115370\pi\)
0.935032 + 0.354563i \(0.115370\pi\)
\(138\) 0 0
\(139\) −19.1803 −1.62686 −0.813428 0.581666i \(-0.802401\pi\)
−0.813428 + 0.581666i \(0.802401\pi\)
\(140\) −1.61803 −0.136749
\(141\) 0 0
\(142\) −1.76393 −0.148026
\(143\) 0.854102 0.0714236
\(144\) 0 0
\(145\) 10.5623 0.877152
\(146\) 2.43769 0.201745
\(147\) 0 0
\(148\) 10.8541 0.892202
\(149\) −8.79837 −0.720791 −0.360395 0.932800i \(-0.617358\pi\)
−0.360395 + 0.932800i \(0.617358\pi\)
\(150\) 0 0
\(151\) −17.9443 −1.46028 −0.730142 0.683295i \(-0.760546\pi\)
−0.730142 + 0.683295i \(0.760546\pi\)
\(152\) 9.14590 0.741830
\(153\) 0 0
\(154\) 0.145898 0.0117568
\(155\) 6.70820 0.538816
\(156\) 0 0
\(157\) −0.763932 −0.0609684 −0.0304842 0.999535i \(-0.509705\pi\)
−0.0304842 + 0.999535i \(0.509705\pi\)
\(158\) −2.09017 −0.166285
\(159\) 0 0
\(160\) 5.61803 0.444145
\(161\) 7.61803 0.600385
\(162\) 0 0
\(163\) 14.9443 1.17053 0.585263 0.810844i \(-0.300991\pi\)
0.585263 + 0.810844i \(0.300991\pi\)
\(164\) −5.00000 −0.390434
\(165\) 0 0
\(166\) −1.67376 −0.129909
\(167\) −1.47214 −0.113917 −0.0569587 0.998377i \(-0.518140\pi\)
−0.0569587 + 0.998377i \(0.518140\pi\)
\(168\) 0 0
\(169\) 0.0901699 0.00693615
\(170\) 0.381966 0.0292955
\(171\) 0 0
\(172\) −12.8541 −0.980116
\(173\) −2.52786 −0.192190 −0.0960950 0.995372i \(-0.530635\pi\)
−0.0960950 + 0.995372i \(0.530635\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) 0.437694 0.0329924
\(177\) 0 0
\(178\) −4.61803 −0.346136
\(179\) 7.00000 0.523205 0.261602 0.965176i \(-0.415749\pi\)
0.261602 + 0.965176i \(0.415749\pi\)
\(180\) 0 0
\(181\) −10.5279 −0.782530 −0.391265 0.920278i \(-0.627962\pi\)
−0.391265 + 0.920278i \(0.627962\pi\)
\(182\) 2.23607 0.165748
\(183\) 0 0
\(184\) −17.0344 −1.25580
\(185\) 6.70820 0.493197
\(186\) 0 0
\(187\) 0.145898 0.0106691
\(188\) 17.7984 1.29808
\(189\) 0 0
\(190\) 2.52786 0.183391
\(191\) 5.79837 0.419556 0.209778 0.977749i \(-0.432726\pi\)
0.209778 + 0.977749i \(0.432726\pi\)
\(192\) 0 0
\(193\) 5.85410 0.421387 0.210694 0.977552i \(-0.432428\pi\)
0.210694 + 0.977552i \(0.432428\pi\)
\(194\) −7.61803 −0.546943
\(195\) 0 0
\(196\) −1.61803 −0.115574
\(197\) 10.5279 0.750079 0.375040 0.927009i \(-0.377629\pi\)
0.375040 + 0.927009i \(0.377629\pi\)
\(198\) 0 0
\(199\) −0.618034 −0.0438113 −0.0219056 0.999760i \(-0.506973\pi\)
−0.0219056 + 0.999760i \(0.506973\pi\)
\(200\) 2.23607 0.158114
\(201\) 0 0
\(202\) 8.94427 0.629317
\(203\) 10.5623 0.741329
\(204\) 0 0
\(205\) −3.09017 −0.215827
\(206\) −5.18034 −0.360931
\(207\) 0 0
\(208\) 6.70820 0.465130
\(209\) 0.965558 0.0667891
\(210\) 0 0
\(211\) 23.1246 1.59196 0.795982 0.605320i \(-0.206955\pi\)
0.795982 + 0.605320i \(0.206955\pi\)
\(212\) −10.7082 −0.735442
\(213\) 0 0
\(214\) 6.61803 0.452399
\(215\) −7.94427 −0.541795
\(216\) 0 0
\(217\) 6.70820 0.455383
\(218\) 4.67376 0.316547
\(219\) 0 0
\(220\) 0.381966 0.0257521
\(221\) 2.23607 0.150414
\(222\) 0 0
\(223\) −1.47214 −0.0985815 −0.0492908 0.998784i \(-0.515696\pi\)
−0.0492908 + 0.998784i \(0.515696\pi\)
\(224\) 5.61803 0.375371
\(225\) 0 0
\(226\) −0.527864 −0.0351130
\(227\) −27.5623 −1.82937 −0.914687 0.404162i \(-0.867563\pi\)
−0.914687 + 0.404162i \(0.867563\pi\)
\(228\) 0 0
\(229\) −0.0557281 −0.00368262 −0.00184131 0.999998i \(-0.500586\pi\)
−0.00184131 + 0.999998i \(0.500586\pi\)
\(230\) −4.70820 −0.310450
\(231\) 0 0
\(232\) −23.6180 −1.55060
\(233\) −5.90983 −0.387166 −0.193583 0.981084i \(-0.562011\pi\)
−0.193583 + 0.981084i \(0.562011\pi\)
\(234\) 0 0
\(235\) 11.0000 0.717561
\(236\) 23.7984 1.54914
\(237\) 0 0
\(238\) 0.381966 0.0247592
\(239\) 19.6525 1.27121 0.635606 0.772013i \(-0.280750\pi\)
0.635606 + 0.772013i \(0.280750\pi\)
\(240\) 0 0
\(241\) −5.38197 −0.346683 −0.173341 0.984862i \(-0.555456\pi\)
−0.173341 + 0.984862i \(0.555456\pi\)
\(242\) 6.76393 0.434802
\(243\) 0 0
\(244\) 11.5623 0.740201
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) 14.7984 0.941598
\(248\) −15.0000 −0.952501
\(249\) 0 0
\(250\) 0.618034 0.0390879
\(251\) 3.23607 0.204259 0.102129 0.994771i \(-0.467434\pi\)
0.102129 + 0.994771i \(0.467434\pi\)
\(252\) 0 0
\(253\) −1.79837 −0.113063
\(254\) 6.85410 0.430065
\(255\) 0 0
\(256\) −6.56231 −0.410144
\(257\) −8.94427 −0.557928 −0.278964 0.960302i \(-0.589991\pi\)
−0.278964 + 0.960302i \(0.589991\pi\)
\(258\) 0 0
\(259\) 6.70820 0.416828
\(260\) 5.85410 0.363056
\(261\) 0 0
\(262\) 4.09017 0.252692
\(263\) −11.7426 −0.724083 −0.362041 0.932162i \(-0.617920\pi\)
−0.362041 + 0.932162i \(0.617920\pi\)
\(264\) 0 0
\(265\) −6.61803 −0.406543
\(266\) 2.52786 0.154993
\(267\) 0 0
\(268\) 7.00000 0.427593
\(269\) 2.70820 0.165122 0.0825611 0.996586i \(-0.473690\pi\)
0.0825611 + 0.996586i \(0.473690\pi\)
\(270\) 0 0
\(271\) −4.43769 −0.269571 −0.134785 0.990875i \(-0.543034\pi\)
−0.134785 + 0.990875i \(0.543034\pi\)
\(272\) 1.14590 0.0694803
\(273\) 0 0
\(274\) −13.5279 −0.817248
\(275\) 0.236068 0.0142354
\(276\) 0 0
\(277\) 20.3262 1.22129 0.610643 0.791906i \(-0.290911\pi\)
0.610643 + 0.791906i \(0.290911\pi\)
\(278\) 11.8541 0.710962
\(279\) 0 0
\(280\) 2.23607 0.133631
\(281\) 11.3820 0.678991 0.339496 0.940608i \(-0.389744\pi\)
0.339496 + 0.940608i \(0.389744\pi\)
\(282\) 0 0
\(283\) 27.8541 1.65575 0.827877 0.560909i \(-0.189548\pi\)
0.827877 + 0.560909i \(0.189548\pi\)
\(284\) −4.61803 −0.274030
\(285\) 0 0
\(286\) −0.527864 −0.0312133
\(287\) −3.09017 −0.182407
\(288\) 0 0
\(289\) −16.6180 −0.977531
\(290\) −6.52786 −0.383329
\(291\) 0 0
\(292\) 6.38197 0.373476
\(293\) 19.7082 1.15137 0.575683 0.817673i \(-0.304736\pi\)
0.575683 + 0.817673i \(0.304736\pi\)
\(294\) 0 0
\(295\) 14.7082 0.856345
\(296\) −15.0000 −0.871857
\(297\) 0 0
\(298\) 5.43769 0.314997
\(299\) −27.5623 −1.59397
\(300\) 0 0
\(301\) −7.94427 −0.457900
\(302\) 11.0902 0.638168
\(303\) 0 0
\(304\) 7.58359 0.434949
\(305\) 7.14590 0.409173
\(306\) 0 0
\(307\) −7.41641 −0.423277 −0.211638 0.977348i \(-0.567880\pi\)
−0.211638 + 0.977348i \(0.567880\pi\)
\(308\) 0.381966 0.0217645
\(309\) 0 0
\(310\) −4.14590 −0.235471
\(311\) 1.32624 0.0752041 0.0376020 0.999293i \(-0.488028\pi\)
0.0376020 + 0.999293i \(0.488028\pi\)
\(312\) 0 0
\(313\) −0.819660 −0.0463299 −0.0231650 0.999732i \(-0.507374\pi\)
−0.0231650 + 0.999732i \(0.507374\pi\)
\(314\) 0.472136 0.0266442
\(315\) 0 0
\(316\) −5.47214 −0.307832
\(317\) 23.9443 1.34484 0.672422 0.740168i \(-0.265254\pi\)
0.672422 + 0.740168i \(0.265254\pi\)
\(318\) 0 0
\(319\) −2.49342 −0.139605
\(320\) 0.236068 0.0131966
\(321\) 0 0
\(322\) −4.70820 −0.262378
\(323\) 2.52786 0.140654
\(324\) 0 0
\(325\) 3.61803 0.200692
\(326\) −9.23607 −0.511538
\(327\) 0 0
\(328\) 6.90983 0.381532
\(329\) 11.0000 0.606450
\(330\) 0 0
\(331\) −25.1459 −1.38214 −0.691072 0.722786i \(-0.742861\pi\)
−0.691072 + 0.722786i \(0.742861\pi\)
\(332\) −4.38197 −0.240492
\(333\) 0 0
\(334\) 0.909830 0.0497837
\(335\) 4.32624 0.236368
\(336\) 0 0
\(337\) 10.7426 0.585189 0.292595 0.956237i \(-0.405481\pi\)
0.292595 + 0.956237i \(0.405481\pi\)
\(338\) −0.0557281 −0.00303121
\(339\) 0 0
\(340\) 1.00000 0.0542326
\(341\) −1.58359 −0.0857563
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 17.7639 0.957767
\(345\) 0 0
\(346\) 1.56231 0.0839901
\(347\) 17.2361 0.925281 0.462640 0.886546i \(-0.346902\pi\)
0.462640 + 0.886546i \(0.346902\pi\)
\(348\) 0 0
\(349\) −13.3607 −0.715181 −0.357590 0.933879i \(-0.616402\pi\)
−0.357590 + 0.933879i \(0.616402\pi\)
\(350\) 0.618034 0.0330353
\(351\) 0 0
\(352\) −1.32624 −0.0706887
\(353\) −27.3262 −1.45443 −0.727214 0.686410i \(-0.759185\pi\)
−0.727214 + 0.686410i \(0.759185\pi\)
\(354\) 0 0
\(355\) −2.85410 −0.151480
\(356\) −12.0902 −0.640778
\(357\) 0 0
\(358\) −4.32624 −0.228649
\(359\) −9.58359 −0.505803 −0.252901 0.967492i \(-0.581385\pi\)
−0.252901 + 0.967492i \(0.581385\pi\)
\(360\) 0 0
\(361\) −2.27051 −0.119501
\(362\) 6.50658 0.341978
\(363\) 0 0
\(364\) 5.85410 0.306838
\(365\) 3.94427 0.206453
\(366\) 0 0
\(367\) −8.14590 −0.425212 −0.212606 0.977138i \(-0.568195\pi\)
−0.212606 + 0.977138i \(0.568195\pi\)
\(368\) −14.1246 −0.736296
\(369\) 0 0
\(370\) −4.14590 −0.215535
\(371\) −6.61803 −0.343591
\(372\) 0 0
\(373\) 29.9787 1.55224 0.776119 0.630586i \(-0.217185\pi\)
0.776119 + 0.630586i \(0.217185\pi\)
\(374\) −0.0901699 −0.00466258
\(375\) 0 0
\(376\) −24.5967 −1.26848
\(377\) −38.2148 −1.96816
\(378\) 0 0
\(379\) −23.8885 −1.22707 −0.613536 0.789667i \(-0.710253\pi\)
−0.613536 + 0.789667i \(0.710253\pi\)
\(380\) 6.61803 0.339498
\(381\) 0 0
\(382\) −3.58359 −0.183353
\(383\) −19.6525 −1.00419 −0.502097 0.864811i \(-0.667438\pi\)
−0.502097 + 0.864811i \(0.667438\pi\)
\(384\) 0 0
\(385\) 0.236068 0.0120311
\(386\) −3.61803 −0.184153
\(387\) 0 0
\(388\) −19.9443 −1.01252
\(389\) −1.20163 −0.0609249 −0.0304624 0.999536i \(-0.509698\pi\)
−0.0304624 + 0.999536i \(0.509698\pi\)
\(390\) 0 0
\(391\) −4.70820 −0.238104
\(392\) 2.23607 0.112938
\(393\) 0 0
\(394\) −6.50658 −0.327797
\(395\) −3.38197 −0.170165
\(396\) 0 0
\(397\) 26.9443 1.35229 0.676147 0.736767i \(-0.263648\pi\)
0.676147 + 0.736767i \(0.263648\pi\)
\(398\) 0.381966 0.0191462
\(399\) 0 0
\(400\) 1.85410 0.0927051
\(401\) 19.6180 0.979678 0.489839 0.871813i \(-0.337056\pi\)
0.489839 + 0.871813i \(0.337056\pi\)
\(402\) 0 0
\(403\) −24.2705 −1.20900
\(404\) 23.4164 1.16501
\(405\) 0 0
\(406\) −6.52786 −0.323972
\(407\) −1.58359 −0.0784957
\(408\) 0 0
\(409\) −30.9443 −1.53010 −0.765048 0.643973i \(-0.777285\pi\)
−0.765048 + 0.643973i \(0.777285\pi\)
\(410\) 1.90983 0.0943198
\(411\) 0 0
\(412\) −13.5623 −0.668167
\(413\) 14.7082 0.723743
\(414\) 0 0
\(415\) −2.70820 −0.132941
\(416\) −20.3262 −0.996576
\(417\) 0 0
\(418\) −0.596748 −0.0291879
\(419\) 1.47214 0.0719185 0.0359593 0.999353i \(-0.488551\pi\)
0.0359593 + 0.999353i \(0.488551\pi\)
\(420\) 0 0
\(421\) 28.5623 1.39204 0.696021 0.718022i \(-0.254952\pi\)
0.696021 + 0.718022i \(0.254952\pi\)
\(422\) −14.2918 −0.695714
\(423\) 0 0
\(424\) 14.7984 0.718673
\(425\) 0.618034 0.0299791
\(426\) 0 0
\(427\) 7.14590 0.345814
\(428\) 17.3262 0.837495
\(429\) 0 0
\(430\) 4.90983 0.236773
\(431\) 25.4508 1.22592 0.612962 0.790112i \(-0.289978\pi\)
0.612962 + 0.790112i \(0.289978\pi\)
\(432\) 0 0
\(433\) 30.2148 1.45203 0.726015 0.687679i \(-0.241370\pi\)
0.726015 + 0.687679i \(0.241370\pi\)
\(434\) −4.14590 −0.199009
\(435\) 0 0
\(436\) 12.2361 0.586001
\(437\) −31.1591 −1.49054
\(438\) 0 0
\(439\) 24.7082 1.17926 0.589629 0.807674i \(-0.299274\pi\)
0.589629 + 0.807674i \(0.299274\pi\)
\(440\) −0.527864 −0.0251649
\(441\) 0 0
\(442\) −1.38197 −0.0657334
\(443\) −19.6869 −0.935354 −0.467677 0.883900i \(-0.654909\pi\)
−0.467677 + 0.883900i \(0.654909\pi\)
\(444\) 0 0
\(445\) −7.47214 −0.354213
\(446\) 0.909830 0.0430817
\(447\) 0 0
\(448\) 0.236068 0.0111532
\(449\) −11.5279 −0.544034 −0.272017 0.962293i \(-0.587691\pi\)
−0.272017 + 0.962293i \(0.587691\pi\)
\(450\) 0 0
\(451\) 0.729490 0.0343504
\(452\) −1.38197 −0.0650022
\(453\) 0 0
\(454\) 17.0344 0.799466
\(455\) 3.61803 0.169616
\(456\) 0 0
\(457\) 1.67376 0.0782953 0.0391476 0.999233i \(-0.487536\pi\)
0.0391476 + 0.999233i \(0.487536\pi\)
\(458\) 0.0344419 0.00160936
\(459\) 0 0
\(460\) −12.3262 −0.574714
\(461\) −1.79837 −0.0837586 −0.0418793 0.999123i \(-0.513334\pi\)
−0.0418793 + 0.999123i \(0.513334\pi\)
\(462\) 0 0
\(463\) 1.61803 0.0751964 0.0375982 0.999293i \(-0.488029\pi\)
0.0375982 + 0.999293i \(0.488029\pi\)
\(464\) −19.5836 −0.909145
\(465\) 0 0
\(466\) 3.65248 0.169198
\(467\) 0.944272 0.0436957 0.0218478 0.999761i \(-0.493045\pi\)
0.0218478 + 0.999761i \(0.493045\pi\)
\(468\) 0 0
\(469\) 4.32624 0.199767
\(470\) −6.79837 −0.313586
\(471\) 0 0
\(472\) −32.8885 −1.51382
\(473\) 1.87539 0.0862304
\(474\) 0 0
\(475\) 4.09017 0.187670
\(476\) 1.00000 0.0458349
\(477\) 0 0
\(478\) −12.1459 −0.555540
\(479\) −37.0902 −1.69469 −0.847347 0.531040i \(-0.821801\pi\)
−0.847347 + 0.531040i \(0.821801\pi\)
\(480\) 0 0
\(481\) −24.2705 −1.10664
\(482\) 3.32624 0.151506
\(483\) 0 0
\(484\) 17.7082 0.804918
\(485\) −12.3262 −0.559706
\(486\) 0 0
\(487\) −24.4721 −1.10894 −0.554469 0.832204i \(-0.687079\pi\)
−0.554469 + 0.832204i \(0.687079\pi\)
\(488\) −15.9787 −0.723322
\(489\) 0 0
\(490\) 0.618034 0.0279199
\(491\) −18.5066 −0.835190 −0.417595 0.908633i \(-0.637127\pi\)
−0.417595 + 0.908633i \(0.637127\pi\)
\(492\) 0 0
\(493\) −6.52786 −0.294000
\(494\) −9.14590 −0.411493
\(495\) 0 0
\(496\) −12.4377 −0.558469
\(497\) −2.85410 −0.128024
\(498\) 0 0
\(499\) −41.3607 −1.85156 −0.925779 0.378065i \(-0.876590\pi\)
−0.925779 + 0.378065i \(0.876590\pi\)
\(500\) 1.61803 0.0723607
\(501\) 0 0
\(502\) −2.00000 −0.0892644
\(503\) −42.0902 −1.87671 −0.938354 0.345676i \(-0.887650\pi\)
−0.938354 + 0.345676i \(0.887650\pi\)
\(504\) 0 0
\(505\) 14.4721 0.644002
\(506\) 1.11146 0.0494103
\(507\) 0 0
\(508\) 17.9443 0.796148
\(509\) 30.3050 1.34324 0.671622 0.740894i \(-0.265598\pi\)
0.671622 + 0.740894i \(0.265598\pi\)
\(510\) 0 0
\(511\) 3.94427 0.174484
\(512\) −18.7082 −0.826794
\(513\) 0 0
\(514\) 5.52786 0.243824
\(515\) −8.38197 −0.369354
\(516\) 0 0
\(517\) −2.59675 −0.114205
\(518\) −4.14590 −0.182160
\(519\) 0 0
\(520\) −8.09017 −0.354777
\(521\) −33.8328 −1.48224 −0.741121 0.671371i \(-0.765706\pi\)
−0.741121 + 0.671371i \(0.765706\pi\)
\(522\) 0 0
\(523\) −25.7984 −1.12808 −0.564042 0.825746i \(-0.690754\pi\)
−0.564042 + 0.825746i \(0.690754\pi\)
\(524\) 10.7082 0.467790
\(525\) 0 0
\(526\) 7.25735 0.316436
\(527\) −4.14590 −0.180598
\(528\) 0 0
\(529\) 35.0344 1.52324
\(530\) 4.09017 0.177666
\(531\) 0 0
\(532\) 6.61803 0.286928
\(533\) 11.1803 0.484274
\(534\) 0 0
\(535\) 10.7082 0.462956
\(536\) −9.67376 −0.417843
\(537\) 0 0
\(538\) −1.67376 −0.0721610
\(539\) 0.236068 0.0101682
\(540\) 0 0
\(541\) 24.5066 1.05362 0.526810 0.849983i \(-0.323388\pi\)
0.526810 + 0.849983i \(0.323388\pi\)
\(542\) 2.74265 0.117807
\(543\) 0 0
\(544\) −3.47214 −0.148867
\(545\) 7.56231 0.323934
\(546\) 0 0
\(547\) −25.3607 −1.08434 −0.542172 0.840267i \(-0.682398\pi\)
−0.542172 + 0.840267i \(0.682398\pi\)
\(548\) −35.4164 −1.51291
\(549\) 0 0
\(550\) −0.145898 −0.00622111
\(551\) −43.2016 −1.84045
\(552\) 0 0
\(553\) −3.38197 −0.143816
\(554\) −12.5623 −0.533721
\(555\) 0 0
\(556\) 31.0344 1.31615
\(557\) −7.79837 −0.330428 −0.165214 0.986258i \(-0.552831\pi\)
−0.165214 + 0.986258i \(0.552831\pi\)
\(558\) 0 0
\(559\) 28.7426 1.21568
\(560\) 1.85410 0.0783501
\(561\) 0 0
\(562\) −7.03444 −0.296730
\(563\) 38.6869 1.63046 0.815230 0.579138i \(-0.196611\pi\)
0.815230 + 0.579138i \(0.196611\pi\)
\(564\) 0 0
\(565\) −0.854102 −0.0359323
\(566\) −17.2148 −0.723591
\(567\) 0 0
\(568\) 6.38197 0.267781
\(569\) 42.2361 1.77063 0.885314 0.464994i \(-0.153943\pi\)
0.885314 + 0.464994i \(0.153943\pi\)
\(570\) 0 0
\(571\) 43.7426 1.83057 0.915286 0.402804i \(-0.131964\pi\)
0.915286 + 0.402804i \(0.131964\pi\)
\(572\) −1.38197 −0.0577829
\(573\) 0 0
\(574\) 1.90983 0.0797148
\(575\) −7.61803 −0.317694
\(576\) 0 0
\(577\) −18.1246 −0.754537 −0.377269 0.926104i \(-0.623137\pi\)
−0.377269 + 0.926104i \(0.623137\pi\)
\(578\) 10.2705 0.427197
\(579\) 0 0
\(580\) −17.0902 −0.709631
\(581\) −2.70820 −0.112355
\(582\) 0 0
\(583\) 1.56231 0.0647041
\(584\) −8.81966 −0.364960
\(585\) 0 0
\(586\) −12.1803 −0.503165
\(587\) 31.7984 1.31246 0.656230 0.754561i \(-0.272150\pi\)
0.656230 + 0.754561i \(0.272150\pi\)
\(588\) 0 0
\(589\) −27.4377 −1.13055
\(590\) −9.09017 −0.374236
\(591\) 0 0
\(592\) −12.4377 −0.511186
\(593\) −28.3050 −1.16235 −0.581173 0.813780i \(-0.697406\pi\)
−0.581173 + 0.813780i \(0.697406\pi\)
\(594\) 0 0
\(595\) 0.618034 0.0253369
\(596\) 14.2361 0.583132
\(597\) 0 0
\(598\) 17.0344 0.696590
\(599\) 21.0557 0.860314 0.430157 0.902754i \(-0.358458\pi\)
0.430157 + 0.902754i \(0.358458\pi\)
\(600\) 0 0
\(601\) −23.7984 −0.970756 −0.485378 0.874304i \(-0.661318\pi\)
−0.485378 + 0.874304i \(0.661318\pi\)
\(602\) 4.90983 0.200110
\(603\) 0 0
\(604\) 29.0344 1.18139
\(605\) 10.9443 0.444948
\(606\) 0 0
\(607\) −2.41641 −0.0980790 −0.0490395 0.998797i \(-0.515616\pi\)
−0.0490395 + 0.998797i \(0.515616\pi\)
\(608\) −22.9787 −0.931910
\(609\) 0 0
\(610\) −4.41641 −0.178815
\(611\) −39.7984 −1.61007
\(612\) 0 0
\(613\) −20.7082 −0.836396 −0.418198 0.908356i \(-0.637338\pi\)
−0.418198 + 0.908356i \(0.637338\pi\)
\(614\) 4.58359 0.184979
\(615\) 0 0
\(616\) −0.527864 −0.0212682
\(617\) 13.2016 0.531477 0.265739 0.964045i \(-0.414384\pi\)
0.265739 + 0.964045i \(0.414384\pi\)
\(618\) 0 0
\(619\) 19.5410 0.785420 0.392710 0.919662i \(-0.371538\pi\)
0.392710 + 0.919662i \(0.371538\pi\)
\(620\) −10.8541 −0.435911
\(621\) 0 0
\(622\) −0.819660 −0.0328654
\(623\) −7.47214 −0.299365
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) 0.506578 0.0202469
\(627\) 0 0
\(628\) 1.23607 0.0493245
\(629\) −4.14590 −0.165308
\(630\) 0 0
\(631\) 6.11146 0.243293 0.121647 0.992573i \(-0.461183\pi\)
0.121647 + 0.992573i \(0.461183\pi\)
\(632\) 7.56231 0.300812
\(633\) 0 0
\(634\) −14.7984 −0.587719
\(635\) 11.0902 0.440100
\(636\) 0 0
\(637\) 3.61803 0.143352
\(638\) 1.54102 0.0610096
\(639\) 0 0
\(640\) −11.3820 −0.449912
\(641\) 34.2705 1.35360 0.676802 0.736165i \(-0.263365\pi\)
0.676802 + 0.736165i \(0.263365\pi\)
\(642\) 0 0
\(643\) −0.742646 −0.0292871 −0.0146435 0.999893i \(-0.504661\pi\)
−0.0146435 + 0.999893i \(0.504661\pi\)
\(644\) −12.3262 −0.485722
\(645\) 0 0
\(646\) −1.56231 −0.0614681
\(647\) 30.9443 1.21654 0.608272 0.793728i \(-0.291863\pi\)
0.608272 + 0.793728i \(0.291863\pi\)
\(648\) 0 0
\(649\) −3.47214 −0.136293
\(650\) −2.23607 −0.0877058
\(651\) 0 0
\(652\) −24.1803 −0.946975
\(653\) 23.0344 0.901407 0.450704 0.892674i \(-0.351173\pi\)
0.450704 + 0.892674i \(0.351173\pi\)
\(654\) 0 0
\(655\) 6.61803 0.258588
\(656\) 5.72949 0.223699
\(657\) 0 0
\(658\) −6.79837 −0.265028
\(659\) 5.23607 0.203968 0.101984 0.994786i \(-0.467481\pi\)
0.101984 + 0.994786i \(0.467481\pi\)
\(660\) 0 0
\(661\) 35.2148 1.36970 0.684848 0.728686i \(-0.259869\pi\)
0.684848 + 0.728686i \(0.259869\pi\)
\(662\) 15.5410 0.604019
\(663\) 0 0
\(664\) 6.05573 0.235008
\(665\) 4.09017 0.158610
\(666\) 0 0
\(667\) 80.4640 3.11558
\(668\) 2.38197 0.0921610
\(669\) 0 0
\(670\) −2.67376 −0.103296
\(671\) −1.68692 −0.0651227
\(672\) 0 0
\(673\) −37.5279 −1.44659 −0.723296 0.690538i \(-0.757374\pi\)
−0.723296 + 0.690538i \(0.757374\pi\)
\(674\) −6.63932 −0.255737
\(675\) 0 0
\(676\) −0.145898 −0.00561146
\(677\) −13.6525 −0.524707 −0.262354 0.964972i \(-0.584499\pi\)
−0.262354 + 0.964972i \(0.584499\pi\)
\(678\) 0 0
\(679\) −12.3262 −0.473038
\(680\) −1.38197 −0.0529960
\(681\) 0 0
\(682\) 0.978714 0.0374769
\(683\) −3.97871 −0.152241 −0.0761206 0.997099i \(-0.524253\pi\)
−0.0761206 + 0.997099i \(0.524253\pi\)
\(684\) 0 0
\(685\) −21.8885 −0.836318
\(686\) 0.618034 0.0235966
\(687\) 0 0
\(688\) 14.7295 0.561557
\(689\) 23.9443 0.912204
\(690\) 0 0
\(691\) −39.4721 −1.50159 −0.750795 0.660535i \(-0.770330\pi\)
−0.750795 + 0.660535i \(0.770330\pi\)
\(692\) 4.09017 0.155485
\(693\) 0 0
\(694\) −10.6525 −0.404362
\(695\) 19.1803 0.727552
\(696\) 0 0
\(697\) 1.90983 0.0723400
\(698\) 8.25735 0.312545
\(699\) 0 0
\(700\) 1.61803 0.0611559
\(701\) 28.8885 1.09111 0.545553 0.838077i \(-0.316320\pi\)
0.545553 + 0.838077i \(0.316320\pi\)
\(702\) 0 0
\(703\) −27.4377 −1.03483
\(704\) −0.0557281 −0.00210033
\(705\) 0 0
\(706\) 16.8885 0.635609
\(707\) 14.4721 0.544281
\(708\) 0 0
\(709\) 39.5967 1.48709 0.743544 0.668688i \(-0.233144\pi\)
0.743544 + 0.668688i \(0.233144\pi\)
\(710\) 1.76393 0.0661992
\(711\) 0 0
\(712\) 16.7082 0.626166
\(713\) 51.1033 1.91383
\(714\) 0 0
\(715\) −0.854102 −0.0319416
\(716\) −11.3262 −0.423281
\(717\) 0 0
\(718\) 5.92299 0.221044
\(719\) −42.0344 −1.56762 −0.783810 0.621001i \(-0.786726\pi\)
−0.783810 + 0.621001i \(0.786726\pi\)
\(720\) 0 0
\(721\) −8.38197 −0.312161
\(722\) 1.40325 0.0522236
\(723\) 0 0
\(724\) 17.0344 0.633080
\(725\) −10.5623 −0.392274
\(726\) 0 0
\(727\) 44.4508 1.64859 0.824295 0.566160i \(-0.191572\pi\)
0.824295 + 0.566160i \(0.191572\pi\)
\(728\) −8.09017 −0.299842
\(729\) 0 0
\(730\) −2.43769 −0.0902231
\(731\) 4.90983 0.181597
\(732\) 0 0
\(733\) −9.56231 −0.353192 −0.176596 0.984283i \(-0.556509\pi\)
−0.176596 + 0.984283i \(0.556509\pi\)
\(734\) 5.03444 0.185825
\(735\) 0 0
\(736\) 42.7984 1.57757
\(737\) −1.02129 −0.0376196
\(738\) 0 0
\(739\) 10.6525 0.391858 0.195929 0.980618i \(-0.437228\pi\)
0.195929 + 0.980618i \(0.437228\pi\)
\(740\) −10.8541 −0.399005
\(741\) 0 0
\(742\) 4.09017 0.150155
\(743\) −12.3262 −0.452206 −0.226103 0.974103i \(-0.572599\pi\)
−0.226103 + 0.974103i \(0.572599\pi\)
\(744\) 0 0
\(745\) 8.79837 0.322347
\(746\) −18.5279 −0.678353
\(747\) 0 0
\(748\) −0.236068 −0.00863150
\(749\) 10.7082 0.391269
\(750\) 0 0
\(751\) −12.1115 −0.441953 −0.220977 0.975279i \(-0.570924\pi\)
−0.220977 + 0.975279i \(0.570924\pi\)
\(752\) −20.3951 −0.743734
\(753\) 0 0
\(754\) 23.6180 0.860118
\(755\) 17.9443 0.653059
\(756\) 0 0
\(757\) −27.2705 −0.991164 −0.495582 0.868561i \(-0.665045\pi\)
−0.495582 + 0.868561i \(0.665045\pi\)
\(758\) 14.7639 0.536250
\(759\) 0 0
\(760\) −9.14590 −0.331757
\(761\) 39.0344 1.41500 0.707499 0.706715i \(-0.249824\pi\)
0.707499 + 0.706715i \(0.249824\pi\)
\(762\) 0 0
\(763\) 7.56231 0.273774
\(764\) −9.38197 −0.339428
\(765\) 0 0
\(766\) 12.1459 0.438849
\(767\) −53.2148 −1.92147
\(768\) 0 0
\(769\) −26.5967 −0.959103 −0.479552 0.877514i \(-0.659201\pi\)
−0.479552 + 0.877514i \(0.659201\pi\)
\(770\) −0.145898 −0.00525780
\(771\) 0 0
\(772\) −9.47214 −0.340910
\(773\) 33.3262 1.19866 0.599331 0.800502i \(-0.295433\pi\)
0.599331 + 0.800502i \(0.295433\pi\)
\(774\) 0 0
\(775\) −6.70820 −0.240966
\(776\) 27.5623 0.989429
\(777\) 0 0
\(778\) 0.742646 0.0266251
\(779\) 12.6393 0.452851
\(780\) 0 0
\(781\) 0.673762 0.0241091
\(782\) 2.90983 0.104055
\(783\) 0 0
\(784\) 1.85410 0.0662179
\(785\) 0.763932 0.0272659
\(786\) 0 0
\(787\) 1.23607 0.0440611 0.0220305 0.999757i \(-0.492987\pi\)
0.0220305 + 0.999757i \(0.492987\pi\)
\(788\) −17.0344 −0.606827
\(789\) 0 0
\(790\) 2.09017 0.0743649
\(791\) −0.854102 −0.0303684
\(792\) 0 0
\(793\) −25.8541 −0.918106
\(794\) −16.6525 −0.590974
\(795\) 0 0
\(796\) 1.00000 0.0354441
\(797\) 36.6869 1.29952 0.649759 0.760141i \(-0.274870\pi\)
0.649759 + 0.760141i \(0.274870\pi\)
\(798\) 0 0
\(799\) −6.79837 −0.240509
\(800\) −5.61803 −0.198627
\(801\) 0 0
\(802\) −12.1246 −0.428135
\(803\) −0.931116 −0.0328584
\(804\) 0 0
\(805\) −7.61803 −0.268500
\(806\) 15.0000 0.528352
\(807\) 0 0
\(808\) −32.3607 −1.13844
\(809\) 51.3607 1.80575 0.902873 0.429908i \(-0.141454\pi\)
0.902873 + 0.429908i \(0.141454\pi\)
\(810\) 0 0
\(811\) −7.32624 −0.257259 −0.128630 0.991693i \(-0.541058\pi\)
−0.128630 + 0.991693i \(0.541058\pi\)
\(812\) −17.0902 −0.599747
\(813\) 0 0
\(814\) 0.978714 0.0343039
\(815\) −14.9443 −0.523475
\(816\) 0 0
\(817\) 32.4934 1.13680
\(818\) 19.1246 0.668676
\(819\) 0 0
\(820\) 5.00000 0.174608
\(821\) 56.4164 1.96895 0.984473 0.175535i \(-0.0561657\pi\)
0.984473 + 0.175535i \(0.0561657\pi\)
\(822\) 0 0
\(823\) −20.0557 −0.699099 −0.349549 0.936918i \(-0.613665\pi\)
−0.349549 + 0.936918i \(0.613665\pi\)
\(824\) 18.7426 0.652931
\(825\) 0 0
\(826\) −9.09017 −0.316287
\(827\) −55.5410 −1.93135 −0.965675 0.259752i \(-0.916359\pi\)
−0.965675 + 0.259752i \(0.916359\pi\)
\(828\) 0 0
\(829\) 31.3607 1.08920 0.544601 0.838695i \(-0.316681\pi\)
0.544601 + 0.838695i \(0.316681\pi\)
\(830\) 1.67376 0.0580971
\(831\) 0 0
\(832\) −0.854102 −0.0296107
\(833\) 0.618034 0.0214136
\(834\) 0 0
\(835\) 1.47214 0.0509454
\(836\) −1.56231 −0.0540335
\(837\) 0 0
\(838\) −0.909830 −0.0314296
\(839\) −2.61803 −0.0903846 −0.0451923 0.998978i \(-0.514390\pi\)
−0.0451923 + 0.998978i \(0.514390\pi\)
\(840\) 0 0
\(841\) 82.5623 2.84698
\(842\) −17.6525 −0.608344
\(843\) 0 0
\(844\) −37.4164 −1.28793
\(845\) −0.0901699 −0.00310194
\(846\) 0 0
\(847\) 10.9443 0.376050
\(848\) 12.2705 0.421371
\(849\) 0 0
\(850\) −0.381966 −0.0131013
\(851\) 51.1033 1.75180
\(852\) 0 0
\(853\) −55.8328 −1.91168 −0.955840 0.293889i \(-0.905050\pi\)
−0.955840 + 0.293889i \(0.905050\pi\)
\(854\) −4.41641 −0.151126
\(855\) 0 0
\(856\) −23.9443 −0.818398
\(857\) 21.7639 0.743442 0.371721 0.928345i \(-0.378768\pi\)
0.371721 + 0.928345i \(0.378768\pi\)
\(858\) 0 0
\(859\) −27.5967 −0.941589 −0.470794 0.882243i \(-0.656033\pi\)
−0.470794 + 0.882243i \(0.656033\pi\)
\(860\) 12.8541 0.438321
\(861\) 0 0
\(862\) −15.7295 −0.535749
\(863\) −19.7771 −0.673220 −0.336610 0.941644i \(-0.609280\pi\)
−0.336610 + 0.941644i \(0.609280\pi\)
\(864\) 0 0
\(865\) 2.52786 0.0859500
\(866\) −18.6738 −0.634560
\(867\) 0 0
\(868\) −10.8541 −0.368412
\(869\) 0.798374 0.0270830
\(870\) 0 0
\(871\) −15.6525 −0.530364
\(872\) −16.9098 −0.572639
\(873\) 0 0
\(874\) 19.2574 0.651390
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) 10.0557 0.339558 0.169779 0.985482i \(-0.445695\pi\)
0.169779 + 0.985482i \(0.445695\pi\)
\(878\) −15.2705 −0.515355
\(879\) 0 0
\(880\) −0.437694 −0.0147547
\(881\) −20.1115 −0.677572 −0.338786 0.940863i \(-0.610016\pi\)
−0.338786 + 0.940863i \(0.610016\pi\)
\(882\) 0 0
\(883\) 11.6525 0.392137 0.196069 0.980590i \(-0.437182\pi\)
0.196069 + 0.980590i \(0.437182\pi\)
\(884\) −3.61803 −0.121688
\(885\) 0 0
\(886\) 12.1672 0.408765
\(887\) 19.2361 0.645884 0.322942 0.946419i \(-0.395328\pi\)
0.322942 + 0.946419i \(0.395328\pi\)
\(888\) 0 0
\(889\) 11.0902 0.371952
\(890\) 4.61803 0.154797
\(891\) 0 0
\(892\) 2.38197 0.0797541
\(893\) −44.9919 −1.50560
\(894\) 0 0
\(895\) −7.00000 −0.233984
\(896\) −11.3820 −0.380245
\(897\) 0 0
\(898\) 7.12461 0.237751
\(899\) 70.8541 2.36312
\(900\) 0 0
\(901\) 4.09017 0.136263
\(902\) −0.450850 −0.0150117
\(903\) 0 0
\(904\) 1.90983 0.0635200
\(905\) 10.5279 0.349958
\(906\) 0 0
\(907\) 14.8541 0.493222 0.246611 0.969115i \(-0.420683\pi\)
0.246611 + 0.969115i \(0.420683\pi\)
\(908\) 44.5967 1.48000
\(909\) 0 0
\(910\) −2.23607 −0.0741249
\(911\) −52.3607 −1.73479 −0.867393 0.497623i \(-0.834206\pi\)
−0.867393 + 0.497623i \(0.834206\pi\)
\(912\) 0 0
\(913\) 0.639320 0.0211584
\(914\) −1.03444 −0.0342163
\(915\) 0 0
\(916\) 0.0901699 0.00297930
\(917\) 6.61803 0.218547
\(918\) 0 0
\(919\) −27.1591 −0.895895 −0.447947 0.894060i \(-0.647845\pi\)
−0.447947 + 0.894060i \(0.647845\pi\)
\(920\) 17.0344 0.561609
\(921\) 0 0
\(922\) 1.11146 0.0366039
\(923\) 10.3262 0.339892
\(924\) 0 0
\(925\) −6.70820 −0.220564
\(926\) −1.00000 −0.0328620
\(927\) 0 0
\(928\) 59.3394 1.94791
\(929\) −30.1033 −0.987658 −0.493829 0.869559i \(-0.664403\pi\)
−0.493829 + 0.869559i \(0.664403\pi\)
\(930\) 0 0
\(931\) 4.09017 0.134050
\(932\) 9.56231 0.313224
\(933\) 0 0
\(934\) −0.583592 −0.0190957
\(935\) −0.145898 −0.00477138
\(936\) 0 0
\(937\) 9.05573 0.295838 0.147919 0.988999i \(-0.452743\pi\)
0.147919 + 0.988999i \(0.452743\pi\)
\(938\) −2.67376 −0.0873014
\(939\) 0 0
\(940\) −17.7984 −0.580519
\(941\) 50.2361 1.63765 0.818825 0.574044i \(-0.194626\pi\)
0.818825 + 0.574044i \(0.194626\pi\)
\(942\) 0 0
\(943\) −23.5410 −0.766601
\(944\) −27.2705 −0.887579
\(945\) 0 0
\(946\) −1.15905 −0.0376841
\(947\) 25.5623 0.830663 0.415332 0.909670i \(-0.363666\pi\)
0.415332 + 0.909670i \(0.363666\pi\)
\(948\) 0 0
\(949\) −14.2705 −0.463240
\(950\) −2.52786 −0.0820147
\(951\) 0 0
\(952\) −1.38197 −0.0447898
\(953\) 4.34752 0.140830 0.0704151 0.997518i \(-0.477568\pi\)
0.0704151 + 0.997518i \(0.477568\pi\)
\(954\) 0 0
\(955\) −5.79837 −0.187631
\(956\) −31.7984 −1.02843
\(957\) 0 0
\(958\) 22.9230 0.740608
\(959\) −21.8885 −0.706818
\(960\) 0 0
\(961\) 14.0000 0.451613
\(962\) 15.0000 0.483619
\(963\) 0 0
\(964\) 8.70820 0.280472
\(965\) −5.85410 −0.188450
\(966\) 0 0
\(967\) −17.4721 −0.561866 −0.280933 0.959727i \(-0.590644\pi\)
−0.280933 + 0.959727i \(0.590644\pi\)
\(968\) −24.4721 −0.786564
\(969\) 0 0
\(970\) 7.61803 0.244600
\(971\) 58.2492 1.86931 0.934653 0.355560i \(-0.115710\pi\)
0.934653 + 0.355560i \(0.115710\pi\)
\(972\) 0 0
\(973\) 19.1803 0.614893
\(974\) 15.1246 0.484624
\(975\) 0 0
\(976\) −13.2492 −0.424097
\(977\) 30.3607 0.971324 0.485662 0.874147i \(-0.338579\pi\)
0.485662 + 0.874147i \(0.338579\pi\)
\(978\) 0 0
\(979\) 1.76393 0.0563755
\(980\) 1.61803 0.0516862
\(981\) 0 0
\(982\) 11.4377 0.364991
\(983\) −0.0212862 −0.000678925 0 −0.000339463 1.00000i \(-0.500108\pi\)
−0.000339463 1.00000i \(0.500108\pi\)
\(984\) 0 0
\(985\) −10.5279 −0.335446
\(986\) 4.03444 0.128483
\(987\) 0 0
\(988\) −23.9443 −0.761769
\(989\) −60.5197 −1.92442
\(990\) 0 0
\(991\) −7.11146 −0.225903 −0.112951 0.993601i \(-0.536030\pi\)
−0.112951 + 0.993601i \(0.536030\pi\)
\(992\) 37.6869 1.19656
\(993\) 0 0
\(994\) 1.76393 0.0559485
\(995\) 0.618034 0.0195930
\(996\) 0 0
\(997\) 1.29180 0.0409116 0.0204558 0.999791i \(-0.493488\pi\)
0.0204558 + 0.999791i \(0.493488\pi\)
\(998\) 25.5623 0.809161
\(999\) 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 \(a_p\))