Properties

Label 945.2.a.g.1.2
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 1.2
Root \(1.61803\)
Character \(\chi\) = 945.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.61803 q^{2}\) \(+0.618034 q^{4}\) \(-1.00000 q^{5}\) \(-1.00000 q^{7}\) \(-2.23607 q^{8}\) \(+O(q^{10})\) \(q\)\(+1.61803 q^{2}\) \(+0.618034 q^{4}\) \(-1.00000 q^{5}\) \(-1.00000 q^{7}\) \(-2.23607 q^{8}\) \(-1.61803 q^{10}\) \(-4.23607 q^{11}\) \(+1.38197 q^{13}\) \(-1.61803 q^{14}\) \(-4.85410 q^{16}\) \(-1.61803 q^{17}\) \(-7.09017 q^{19}\) \(-0.618034 q^{20}\) \(-6.85410 q^{22}\) \(-5.38197 q^{23}\) \(+1.00000 q^{25}\) \(+2.23607 q^{26}\) \(-0.618034 q^{28}\) \(+9.56231 q^{29}\) \(+6.70820 q^{31}\) \(-3.38197 q^{32}\) \(-2.61803 q^{34}\) \(+1.00000 q^{35}\) \(+6.70820 q^{37}\) \(-11.4721 q^{38}\) \(+2.23607 q^{40}\) \(-8.09017 q^{41}\) \(-9.94427 q^{43}\) \(-2.61803 q^{44}\) \(-8.70820 q^{46}\) \(-11.0000 q^{47}\) \(+1.00000 q^{49}\) \(+1.61803 q^{50}\) \(+0.854102 q^{52}\) \(+4.38197 q^{53}\) \(+4.23607 q^{55}\) \(+2.23607 q^{56}\) \(+15.4721 q^{58}\) \(-1.29180 q^{59}\) \(-13.8541 q^{61}\) \(+10.8541 q^{62}\) \(+4.23607 q^{64}\) \(-1.38197 q^{65}\) \(+11.3262 q^{67}\) \(-1.00000 q^{68}\) \(+1.61803 q^{70}\) \(-3.85410 q^{71}\) \(+13.9443 q^{73}\) \(+10.8541 q^{74}\) \(-4.38197 q^{76}\) \(+4.23607 q^{77}\) \(+5.61803 q^{79}\) \(+4.85410 q^{80}\) \(-13.0902 q^{82}\) \(-10.7082 q^{83}\) \(+1.61803 q^{85}\) \(-16.0902 q^{86}\) \(+9.47214 q^{88}\) \(-1.47214 q^{89}\) \(-1.38197 q^{91}\) \(-3.32624 q^{92}\) \(-17.7984 q^{94}\) \(+7.09017 q^{95}\) \(-3.32624 q^{97}\) \(+1.61803 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut +\mathstrut q^{2} \) \(\mathstrut -\mathstrut q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut q^{10} \) \(\mathstrut -\mathstrut 4q^{11} \) \(\mathstrut +\mathstrut 5q^{13} \) \(\mathstrut -\mathstrut q^{14} \) \(\mathstrut -\mathstrut 3q^{16} \) \(\mathstrut -\mathstrut q^{17} \) \(\mathstrut -\mathstrut 3q^{19} \) \(\mathstrut +\mathstrut q^{20} \) \(\mathstrut -\mathstrut 7q^{22} \) \(\mathstrut -\mathstrut 13q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut q^{28} \) \(\mathstrut -\mathstrut q^{29} \) \(\mathstrut -\mathstrut 9q^{32} \) \(\mathstrut -\mathstrut 3q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 14q^{38} \) \(\mathstrut -\mathstrut 5q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 3q^{44} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut -\mathstrut 22q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut +\mathstrut q^{50} \) \(\mathstrut -\mathstrut 5q^{52} \) \(\mathstrut +\mathstrut 11q^{53} \) \(\mathstrut +\mathstrut 4q^{55} \) \(\mathstrut +\mathstrut 22q^{58} \) \(\mathstrut -\mathstrut 16q^{59} \) \(\mathstrut -\mathstrut 21q^{61} \) \(\mathstrut +\mathstrut 15q^{62} \) \(\mathstrut +\mathstrut 4q^{64} \) \(\mathstrut -\mathstrut 5q^{65} \) \(\mathstrut +\mathstrut 7q^{67} \) \(\mathstrut -\mathstrut 2q^{68} \) \(\mathstrut +\mathstrut q^{70} \) \(\mathstrut -\mathstrut q^{71} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 15q^{74} \) \(\mathstrut -\mathstrut 11q^{76} \) \(\mathstrut +\mathstrut 4q^{77} \) \(\mathstrut +\mathstrut 9q^{79} \) \(\mathstrut +\mathstrut 3q^{80} \) \(\mathstrut -\mathstrut 15q^{82} \) \(\mathstrut -\mathstrut 8q^{83} \) \(\mathstrut +\mathstrut q^{85} \) \(\mathstrut -\mathstrut 21q^{86} \) \(\mathstrut +\mathstrut 10q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 5q^{91} \) \(\mathstrut +\mathstrut 9q^{92} \) \(\mathstrut -\mathstrut 11q^{94} \) \(\mathstrut +\mathstrut 3q^{95} \) \(\mathstrut +\mathstrut 9q^{97} \) \(\mathstrut +\mathstrut q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.61803 1.14412 0.572061 0.820211i \(-0.306144\pi\)
0.572061 + 0.820211i \(0.306144\pi\)
\(3\) 0 0
\(4\) 0.618034 0.309017
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −2.23607 −0.790569
\(9\) 0 0
\(10\) −1.61803 −0.511667
\(11\) −4.23607 −1.27722 −0.638611 0.769529i \(-0.720491\pi\)
−0.638611 + 0.769529i \(0.720491\pi\)
\(12\) 0 0
\(13\) 1.38197 0.383288 0.191644 0.981464i \(-0.438618\pi\)
0.191644 + 0.981464i \(0.438618\pi\)
\(14\) −1.61803 −0.432438
\(15\) 0 0
\(16\) −4.85410 −1.21353
\(17\) −1.61803 −0.392431 −0.196215 0.980561i \(-0.562865\pi\)
−0.196215 + 0.980561i \(0.562865\pi\)
\(18\) 0 0
\(19\) −7.09017 −1.62660 −0.813298 0.581847i \(-0.802330\pi\)
−0.813298 + 0.581847i \(0.802330\pi\)
\(20\) −0.618034 −0.138197
\(21\) 0 0
\(22\) −6.85410 −1.46130
\(23\) −5.38197 −1.12222 −0.561109 0.827742i \(-0.689625\pi\)
−0.561109 + 0.827742i \(0.689625\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) 2.23607 0.438529
\(27\) 0 0
\(28\) −0.618034 −0.116797
\(29\) 9.56231 1.77568 0.887838 0.460157i \(-0.152207\pi\)
0.887838 + 0.460157i \(0.152207\pi\)
\(30\) 0 0
\(31\) 6.70820 1.20483 0.602414 0.798183i \(-0.294205\pi\)
0.602414 + 0.798183i \(0.294205\pi\)
\(32\) −3.38197 −0.597853
\(33\) 0 0
\(34\) −2.61803 −0.448989
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) 6.70820 1.10282 0.551411 0.834234i \(-0.314090\pi\)
0.551411 + 0.834234i \(0.314090\pi\)
\(38\) −11.4721 −1.86103
\(39\) 0 0
\(40\) 2.23607 0.353553
\(41\) −8.09017 −1.26347 −0.631736 0.775183i \(-0.717657\pi\)
−0.631736 + 0.775183i \(0.717657\pi\)
\(42\) 0 0
\(43\) −9.94427 −1.51649 −0.758244 0.651971i \(-0.773942\pi\)
−0.758244 + 0.651971i \(0.773942\pi\)
\(44\) −2.61803 −0.394683
\(45\) 0 0
\(46\) −8.70820 −1.28395
\(47\) −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
\(50\) 1.61803 0.228825
\(51\) 0 0
\(52\) 0.854102 0.118443
\(53\) 4.38197 0.601909 0.300955 0.953638i \(-0.402695\pi\)
0.300955 + 0.953638i \(0.402695\pi\)
\(54\) 0 0
\(55\) 4.23607 0.571191
\(56\) 2.23607 0.298807
\(57\) 0 0
\(58\) 15.4721 2.03159
\(59\) −1.29180 −0.168178 −0.0840888 0.996458i \(-0.526798\pi\)
−0.0840888 + 0.996458i \(0.526798\pi\)
\(60\) 0 0
\(61\) −13.8541 −1.77384 −0.886918 0.461927i \(-0.847158\pi\)
−0.886918 + 0.461927i \(0.847158\pi\)
\(62\) 10.8541 1.37847
\(63\) 0 0
\(64\) 4.23607 0.529508
\(65\) −1.38197 −0.171412
\(66\) 0 0
\(67\) 11.3262 1.38372 0.691860 0.722032i \(-0.256791\pi\)
0.691860 + 0.722032i \(0.256791\pi\)
\(68\) −1.00000 −0.121268
\(69\) 0 0
\(70\) 1.61803 0.193392
\(71\) −3.85410 −0.457398 −0.228699 0.973497i \(-0.573447\pi\)
−0.228699 + 0.973497i \(0.573447\pi\)
\(72\) 0 0
\(73\) 13.9443 1.63205 0.816027 0.578014i \(-0.196172\pi\)
0.816027 + 0.578014i \(0.196172\pi\)
\(74\) 10.8541 1.26176
\(75\) 0 0
\(76\) −4.38197 −0.502646
\(77\) 4.23607 0.482745
\(78\) 0 0
\(79\) 5.61803 0.632078 0.316039 0.948746i \(-0.397647\pi\)
0.316039 + 0.948746i \(0.397647\pi\)
\(80\) 4.85410 0.542705
\(81\) 0 0
\(82\) −13.0902 −1.44557
\(83\) −10.7082 −1.17538 −0.587689 0.809087i \(-0.699962\pi\)
−0.587689 + 0.809087i \(0.699962\pi\)
\(84\) 0 0
\(85\) 1.61803 0.175500
\(86\) −16.0902 −1.73505
\(87\) 0 0
\(88\) 9.47214 1.00973
\(89\) −1.47214 −0.156046 −0.0780230 0.996952i \(-0.524861\pi\)
−0.0780230 + 0.996952i \(0.524861\pi\)
\(90\) 0 0
\(91\) −1.38197 −0.144869
\(92\) −3.32624 −0.346784
\(93\) 0 0
\(94\) −17.7984 −1.83576
\(95\) 7.09017 0.727436
\(96\) 0 0
\(97\) −3.32624 −0.337728 −0.168864 0.985639i \(-0.554010\pi\)
−0.168864 + 0.985639i \(0.554010\pi\)
\(98\) 1.61803 0.163446
\(99\) 0 0
\(100\) 0.618034 0.0618034
\(101\) −5.52786 −0.550043 −0.275022 0.961438i \(-0.588685\pi\)
−0.275022 + 0.961438i \(0.588685\pi\)
\(102\) 0 0
\(103\) 10.6180 1.04623 0.523113 0.852263i \(-0.324771\pi\)
0.523113 + 0.852263i \(0.324771\pi\)
\(104\) −3.09017 −0.303016
\(105\) 0 0
\(106\) 7.09017 0.688658
\(107\) 2.70820 0.261812 0.130906 0.991395i \(-0.458211\pi\)
0.130906 + 0.991395i \(0.458211\pi\)
\(108\) 0 0
\(109\) 12.5623 1.20325 0.601625 0.798778i \(-0.294520\pi\)
0.601625 + 0.798778i \(0.294520\pi\)
\(110\) 6.85410 0.653513
\(111\) 0 0
\(112\) 4.85410 0.458670
\(113\) −5.85410 −0.550708 −0.275354 0.961343i \(-0.588795\pi\)
−0.275354 + 0.961343i \(0.588795\pi\)
\(114\) 0 0
\(115\) 5.38197 0.501871
\(116\) 5.90983 0.548714
\(117\) 0 0
\(118\) −2.09017 −0.192416
\(119\) 1.61803 0.148325
\(120\) 0 0
\(121\) 6.94427 0.631297
\(122\) −22.4164 −2.02949
\(123\) 0 0
\(124\) 4.14590 0.372313
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 0.0901699 0.00800129 0.00400064 0.999992i \(-0.498727\pi\)
0.00400064 + 0.999992i \(0.498727\pi\)
\(128\) 13.6180 1.20368
\(129\) 0 0
\(130\) −2.23607 −0.196116
\(131\) −4.38197 −0.382854 −0.191427 0.981507i \(-0.561312\pi\)
−0.191427 + 0.981507i \(0.561312\pi\)
\(132\) 0 0
\(133\) 7.09017 0.614796
\(134\) 18.3262 1.58315
\(135\) 0 0
\(136\) 3.61803 0.310244
\(137\) −13.8885 −1.18658 −0.593289 0.804989i \(-0.702171\pi\)
−0.593289 + 0.804989i \(0.702171\pi\)
\(138\) 0 0
\(139\) 3.18034 0.269753 0.134876 0.990862i \(-0.456936\pi\)
0.134876 + 0.990862i \(0.456936\pi\)
\(140\) 0.618034 0.0522334
\(141\) 0 0
\(142\) −6.23607 −0.523319
\(143\) −5.85410 −0.489545
\(144\) 0 0
\(145\) −9.56231 −0.794106
\(146\) 22.5623 1.86727
\(147\) 0 0
\(148\) 4.14590 0.340791
\(149\) 15.7984 1.29425 0.647127 0.762383i \(-0.275971\pi\)
0.647127 + 0.762383i \(0.275971\pi\)
\(150\) 0 0
\(151\) −0.0557281 −0.00453509 −0.00226754 0.999997i \(-0.500722\pi\)
−0.00226754 + 0.999997i \(0.500722\pi\)
\(152\) 15.8541 1.28594
\(153\) 0 0
\(154\) 6.85410 0.552319
\(155\) −6.70820 −0.538816
\(156\) 0 0
\(157\) −5.23607 −0.417884 −0.208942 0.977928i \(-0.567002\pi\)
−0.208942 + 0.977928i \(0.567002\pi\)
\(158\) 9.09017 0.723175
\(159\) 0 0
\(160\) 3.38197 0.267368
\(161\) 5.38197 0.424158
\(162\) 0 0
\(163\) −2.94427 −0.230613 −0.115307 0.993330i \(-0.536785\pi\)
−0.115307 + 0.993330i \(0.536785\pi\)
\(164\) −5.00000 −0.390434
\(165\) 0 0
\(166\) −17.3262 −1.34478
\(167\) 7.47214 0.578211 0.289106 0.957297i \(-0.406642\pi\)
0.289106 + 0.957297i \(0.406642\pi\)
\(168\) 0 0
\(169\) −11.0902 −0.853090
\(170\) 2.61803 0.200794
\(171\) 0 0
\(172\) −6.14590 −0.468620
\(173\) −11.4721 −0.872210 −0.436105 0.899896i \(-0.643642\pi\)
−0.436105 + 0.899896i \(0.643642\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) 20.5623 1.54994
\(177\) 0 0
\(178\) −2.38197 −0.178536
\(179\) 7.00000 0.523205 0.261602 0.965176i \(-0.415749\pi\)
0.261602 + 0.965176i \(0.415749\pi\)
\(180\) 0 0
\(181\) −19.4721 −1.44735 −0.723676 0.690140i \(-0.757549\pi\)
−0.723676 + 0.690140i \(0.757549\pi\)
\(182\) −2.23607 −0.165748
\(183\) 0 0
\(184\) 12.0344 0.887191
\(185\) −6.70820 −0.493197
\(186\) 0 0
\(187\) 6.85410 0.501222
\(188\) −6.79837 −0.495822
\(189\) 0 0
\(190\) 11.4721 0.832276
\(191\) −18.7984 −1.36020 −0.680101 0.733118i \(-0.738064\pi\)
−0.680101 + 0.733118i \(0.738064\pi\)
\(192\) 0 0
\(193\) −0.854102 −0.0614796 −0.0307398 0.999527i \(-0.509786\pi\)
−0.0307398 + 0.999527i \(0.509786\pi\)
\(194\) −5.38197 −0.386403
\(195\) 0 0
\(196\) 0.618034 0.0441453
\(197\) 19.4721 1.38733 0.693666 0.720297i \(-0.255994\pi\)
0.693666 + 0.720297i \(0.255994\pi\)
\(198\) 0 0
\(199\) 1.61803 0.114699 0.0573497 0.998354i \(-0.481735\pi\)
0.0573497 + 0.998354i \(0.481735\pi\)
\(200\) −2.23607 −0.158114
\(201\) 0 0
\(202\) −8.94427 −0.629317
\(203\) −9.56231 −0.671142
\(204\) 0 0
\(205\) 8.09017 0.565042
\(206\) 17.1803 1.19701
\(207\) 0 0
\(208\) −6.70820 −0.465130
\(209\) 30.0344 2.07753
\(210\) 0 0
\(211\) −17.1246 −1.17891 −0.589453 0.807802i \(-0.700657\pi\)
−0.589453 + 0.807802i \(0.700657\pi\)
\(212\) 2.70820 0.186000
\(213\) 0 0
\(214\) 4.38197 0.299545
\(215\) 9.94427 0.678194
\(216\) 0 0
\(217\) −6.70820 −0.455383
\(218\) 20.3262 1.37667
\(219\) 0 0
\(220\) 2.61803 0.176508
\(221\) −2.23607 −0.150414
\(222\) 0 0
\(223\) 7.47214 0.500371 0.250186 0.968198i \(-0.419508\pi\)
0.250186 + 0.968198i \(0.419508\pi\)
\(224\) 3.38197 0.225967
\(225\) 0 0
\(226\) −9.47214 −0.630077
\(227\) −7.43769 −0.493657 −0.246829 0.969059i \(-0.579388\pi\)
−0.246829 + 0.969059i \(0.579388\pi\)
\(228\) 0 0
\(229\) −17.9443 −1.18579 −0.592895 0.805279i \(-0.702015\pi\)
−0.592895 + 0.805279i \(0.702015\pi\)
\(230\) 8.70820 0.574202
\(231\) 0 0
\(232\) −21.3820 −1.40379
\(233\) −17.0902 −1.11961 −0.559807 0.828623i \(-0.689125\pi\)
−0.559807 + 0.828623i \(0.689125\pi\)
\(234\) 0 0
\(235\) 11.0000 0.717561
\(236\) −0.798374 −0.0519697
\(237\) 0 0
\(238\) 2.61803 0.169702
\(239\) −11.6525 −0.753736 −0.376868 0.926267i \(-0.622999\pi\)
−0.376868 + 0.926267i \(0.622999\pi\)
\(240\) 0 0
\(241\) −7.61803 −0.490721 −0.245360 0.969432i \(-0.578906\pi\)
−0.245360 + 0.969432i \(0.578906\pi\)
\(242\) 11.2361 0.722282
\(243\) 0 0
\(244\) −8.56231 −0.548145
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) −9.79837 −0.623456
\(248\) −15.0000 −0.952501
\(249\) 0 0
\(250\) −1.61803 −0.102333
\(251\) −1.23607 −0.0780199 −0.0390100 0.999239i \(-0.512420\pi\)
−0.0390100 + 0.999239i \(0.512420\pi\)
\(252\) 0 0
\(253\) 22.7984 1.43332
\(254\) 0.145898 0.00915446
\(255\) 0 0
\(256\) 13.5623 0.847644
\(257\) 8.94427 0.557928 0.278964 0.960302i \(-0.410009\pi\)
0.278964 + 0.960302i \(0.410009\pi\)
\(258\) 0 0
\(259\) −6.70820 −0.416828
\(260\) −0.854102 −0.0529692
\(261\) 0 0
\(262\) −7.09017 −0.438032
\(263\) 30.7426 1.89567 0.947836 0.318757i \(-0.103265\pi\)
0.947836 + 0.318757i \(0.103265\pi\)
\(264\) 0 0
\(265\) −4.38197 −0.269182
\(266\) 11.4721 0.703402
\(267\) 0 0
\(268\) 7.00000 0.427593
\(269\) −10.7082 −0.652891 −0.326445 0.945216i \(-0.605851\pi\)
−0.326445 + 0.945216i \(0.605851\pi\)
\(270\) 0 0
\(271\) −24.5623 −1.49205 −0.746027 0.665916i \(-0.768041\pi\)
−0.746027 + 0.665916i \(0.768041\pi\)
\(272\) 7.85410 0.476225
\(273\) 0 0
\(274\) −22.4721 −1.35759
\(275\) −4.23607 −0.255445
\(276\) 0 0
\(277\) 4.67376 0.280819 0.140410 0.990094i \(-0.455158\pi\)
0.140410 + 0.990094i \(0.455158\pi\)
\(278\) 5.14590 0.308630
\(279\) 0 0
\(280\) −2.23607 −0.133631
\(281\) 13.6180 0.812384 0.406192 0.913788i \(-0.366856\pi\)
0.406192 + 0.913788i \(0.366856\pi\)
\(282\) 0 0
\(283\) 21.1459 1.25699 0.628497 0.777812i \(-0.283671\pi\)
0.628497 + 0.777812i \(0.283671\pi\)
\(284\) −2.38197 −0.141344
\(285\) 0 0
\(286\) −9.47214 −0.560099
\(287\) 8.09017 0.477548
\(288\) 0 0
\(289\) −14.3820 −0.845998
\(290\) −15.4721 −0.908555
\(291\) 0 0
\(292\) 8.61803 0.504332
\(293\) 6.29180 0.367571 0.183785 0.982966i \(-0.441165\pi\)
0.183785 + 0.982966i \(0.441165\pi\)
\(294\) 0 0
\(295\) 1.29180 0.0752113
\(296\) −15.0000 −0.871857
\(297\) 0 0
\(298\) 25.5623 1.48078
\(299\) −7.43769 −0.430133
\(300\) 0 0
\(301\) 9.94427 0.573178
\(302\) −0.0901699 −0.00518870
\(303\) 0 0
\(304\) 34.4164 1.97392
\(305\) 13.8541 0.793284
\(306\) 0 0
\(307\) 19.4164 1.10815 0.554076 0.832466i \(-0.313072\pi\)
0.554076 + 0.832466i \(0.313072\pi\)
\(308\) 2.61803 0.149176
\(309\) 0 0
\(310\) −10.8541 −0.616472
\(311\) −14.3262 −0.812366 −0.406183 0.913792i \(-0.633141\pi\)
−0.406183 + 0.913792i \(0.633141\pi\)
\(312\) 0 0
\(313\) −23.1803 −1.31023 −0.655115 0.755529i \(-0.727380\pi\)
−0.655115 + 0.755529i \(0.727380\pi\)
\(314\) −8.47214 −0.478110
\(315\) 0 0
\(316\) 3.47214 0.195323
\(317\) 6.05573 0.340124 0.170062 0.985433i \(-0.445603\pi\)
0.170062 + 0.985433i \(0.445603\pi\)
\(318\) 0 0
\(319\) −40.5066 −2.26793
\(320\) −4.23607 −0.236803
\(321\) 0 0
\(322\) 8.70820 0.485289
\(323\) 11.4721 0.638327
\(324\) 0 0
\(325\) 1.38197 0.0766577
\(326\) −4.76393 −0.263850
\(327\) 0 0
\(328\) 18.0902 0.998863
\(329\) 11.0000 0.606450
\(330\) 0 0
\(331\) −31.8541 −1.75086 −0.875430 0.483345i \(-0.839422\pi\)
−0.875430 + 0.483345i \(0.839422\pi\)
\(332\) −6.61803 −0.363212
\(333\) 0 0
\(334\) 12.0902 0.661545
\(335\) −11.3262 −0.618818
\(336\) 0 0
\(337\) −31.7426 −1.72913 −0.864566 0.502519i \(-0.832407\pi\)
−0.864566 + 0.502519i \(0.832407\pi\)
\(338\) −17.9443 −0.976040
\(339\) 0 0
\(340\) 1.00000 0.0542326
\(341\) −28.4164 −1.53883
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) 22.2361 1.19889
\(345\) 0 0
\(346\) −18.5623 −0.997916
\(347\) 12.7639 0.685204 0.342602 0.939481i \(-0.388692\pi\)
0.342602 + 0.939481i \(0.388692\pi\)
\(348\) 0 0
\(349\) 31.3607 1.67870 0.839349 0.543592i \(-0.182936\pi\)
0.839349 + 0.543592i \(0.182936\pi\)
\(350\) −1.61803 −0.0864876
\(351\) 0 0
\(352\) 14.3262 0.763591
\(353\) −11.6738 −0.621332 −0.310666 0.950519i \(-0.600552\pi\)
−0.310666 + 0.950519i \(0.600552\pi\)
\(354\) 0 0
\(355\) 3.85410 0.204554
\(356\) −0.909830 −0.0482209
\(357\) 0 0
\(358\) 11.3262 0.598610
\(359\) −36.4164 −1.92198 −0.960992 0.276575i \(-0.910800\pi\)
−0.960992 + 0.276575i \(0.910800\pi\)
\(360\) 0 0
\(361\) 31.2705 1.64582
\(362\) −31.5066 −1.65595
\(363\) 0 0
\(364\) −0.854102 −0.0447671
\(365\) −13.9443 −0.729877
\(366\) 0 0
\(367\) −14.8541 −0.775378 −0.387689 0.921790i \(-0.626727\pi\)
−0.387689 + 0.921790i \(0.626727\pi\)
\(368\) 26.1246 1.36184
\(369\) 0 0
\(370\) −10.8541 −0.564278
\(371\) −4.38197 −0.227500
\(372\) 0 0
\(373\) −16.9787 −0.879124 −0.439562 0.898212i \(-0.644866\pi\)
−0.439562 + 0.898212i \(0.644866\pi\)
\(374\) 11.0902 0.573459
\(375\) 0 0
\(376\) 24.5967 1.26848
\(377\) 13.2148 0.680596
\(378\) 0 0
\(379\) 11.8885 0.610673 0.305337 0.952244i \(-0.401231\pi\)
0.305337 + 0.952244i \(0.401231\pi\)
\(380\) 4.38197 0.224790
\(381\) 0 0
\(382\) −30.4164 −1.55624
\(383\) 11.6525 0.595414 0.297707 0.954657i \(-0.403778\pi\)
0.297707 + 0.954657i \(0.403778\pi\)
\(384\) 0 0
\(385\) −4.23607 −0.215890
\(386\) −1.38197 −0.0703402
\(387\) 0 0
\(388\) −2.05573 −0.104364
\(389\) −25.7984 −1.30803 −0.654015 0.756482i \(-0.726917\pi\)
−0.654015 + 0.756482i \(0.726917\pi\)
\(390\) 0 0
\(391\) 8.70820 0.440393
\(392\) −2.23607 −0.112938
\(393\) 0 0
\(394\) 31.5066 1.58728
\(395\) −5.61803 −0.282674
\(396\) 0 0
\(397\) 9.05573 0.454494 0.227247 0.973837i \(-0.427028\pi\)
0.227247 + 0.973837i \(0.427028\pi\)
\(398\) 2.61803 0.131230
\(399\) 0 0
\(400\) −4.85410 −0.242705
\(401\) 17.3820 0.868014 0.434007 0.900910i \(-0.357099\pi\)
0.434007 + 0.900910i \(0.357099\pi\)
\(402\) 0 0
\(403\) 9.27051 0.461797
\(404\) −3.41641 −0.169973
\(405\) 0 0
\(406\) −15.4721 −0.767869
\(407\) −28.4164 −1.40855
\(408\) 0 0
\(409\) −13.0557 −0.645564 −0.322782 0.946473i \(-0.604618\pi\)
−0.322782 + 0.946473i \(0.604618\pi\)
\(410\) 13.0902 0.646477
\(411\) 0 0
\(412\) 6.56231 0.323302
\(413\) 1.29180 0.0635651
\(414\) 0 0
\(415\) 10.7082 0.525645
\(416\) −4.67376 −0.229150
\(417\) 0 0
\(418\) 48.5967 2.37694
\(419\) −7.47214 −0.365038 −0.182519 0.983202i \(-0.558425\pi\)
−0.182519 + 0.983202i \(0.558425\pi\)
\(420\) 0 0
\(421\) 8.43769 0.411228 0.205614 0.978633i \(-0.434081\pi\)
0.205614 + 0.978633i \(0.434081\pi\)
\(422\) −27.7082 −1.34881
\(423\) 0 0
\(424\) −9.79837 −0.475851
\(425\) −1.61803 −0.0784862
\(426\) 0 0
\(427\) 13.8541 0.670447
\(428\) 1.67376 0.0809043
\(429\) 0 0
\(430\) 16.0902 0.775937
\(431\) −30.4508 −1.46677 −0.733383 0.679816i \(-0.762060\pi\)
−0.733383 + 0.679816i \(0.762060\pi\)
\(432\) 0 0
\(433\) −21.2148 −1.01952 −0.509759 0.860317i \(-0.670265\pi\)
−0.509759 + 0.860317i \(0.670265\pi\)
\(434\) −10.8541 −0.521014
\(435\) 0 0
\(436\) 7.76393 0.371825
\(437\) 38.1591 1.82540
\(438\) 0 0
\(439\) 11.2918 0.538928 0.269464 0.963010i \(-0.413153\pi\)
0.269464 + 0.963010i \(0.413153\pi\)
\(440\) −9.47214 −0.451566
\(441\) 0 0
\(442\) −3.61803 −0.172092
\(443\) 40.6869 1.93309 0.966547 0.256490i \(-0.0825661\pi\)
0.966547 + 0.256490i \(0.0825661\pi\)
\(444\) 0 0
\(445\) 1.47214 0.0697859
\(446\) 12.0902 0.572486
\(447\) 0 0
\(448\) −4.23607 −0.200135
\(449\) −20.4721 −0.966140 −0.483070 0.875582i \(-0.660478\pi\)
−0.483070 + 0.875582i \(0.660478\pi\)
\(450\) 0 0
\(451\) 34.2705 1.61374
\(452\) −3.61803 −0.170178
\(453\) 0 0
\(454\) −12.0344 −0.564804
\(455\) 1.38197 0.0647876
\(456\) 0 0
\(457\) 17.3262 0.810487 0.405244 0.914209i \(-0.367187\pi\)
0.405244 + 0.914209i \(0.367187\pi\)
\(458\) −29.0344 −1.35669
\(459\) 0 0
\(460\) 3.32624 0.155087
\(461\) 22.7984 1.06183 0.530913 0.847426i \(-0.321849\pi\)
0.530913 + 0.847426i \(0.321849\pi\)
\(462\) 0 0
\(463\) −0.618034 −0.0287225 −0.0143612 0.999897i \(-0.504571\pi\)
−0.0143612 + 0.999897i \(0.504571\pi\)
\(464\) −46.4164 −2.15483
\(465\) 0 0
\(466\) −27.6525 −1.28098
\(467\) −16.9443 −0.784087 −0.392044 0.919947i \(-0.628232\pi\)
−0.392044 + 0.919947i \(0.628232\pi\)
\(468\) 0 0
\(469\) −11.3262 −0.522997
\(470\) 17.7984 0.820978
\(471\) 0 0
\(472\) 2.88854 0.132956
\(473\) 42.1246 1.93689
\(474\) 0 0
\(475\) −7.09017 −0.325319
\(476\) 1.00000 0.0458349
\(477\) 0 0
\(478\) −18.8541 −0.862367
\(479\) −25.9098 −1.18385 −0.591925 0.805993i \(-0.701632\pi\)
−0.591925 + 0.805993i \(0.701632\pi\)
\(480\) 0 0
\(481\) 9.27051 0.422699
\(482\) −12.3262 −0.561445
\(483\) 0 0
\(484\) 4.29180 0.195082
\(485\) 3.32624 0.151037
\(486\) 0 0
\(487\) −15.5279 −0.703635 −0.351817 0.936069i \(-0.614436\pi\)
−0.351817 + 0.936069i \(0.614436\pi\)
\(488\) 30.9787 1.40234
\(489\) 0 0
\(490\) −1.61803 −0.0730953
\(491\) 19.5066 0.880320 0.440160 0.897919i \(-0.354922\pi\)
0.440160 + 0.897919i \(0.354922\pi\)
\(492\) 0 0
\(493\) −15.4721 −0.696830
\(494\) −15.8541 −0.713310
\(495\) 0 0
\(496\) −32.5623 −1.46209
\(497\) 3.85410 0.172880
\(498\) 0 0
\(499\) 3.36068 0.150445 0.0752223 0.997167i \(-0.476033\pi\)
0.0752223 + 0.997167i \(0.476033\pi\)
\(500\) −0.618034 −0.0276393
\(501\) 0 0
\(502\) −2.00000 −0.0892644
\(503\) −30.9098 −1.37820 −0.689101 0.724666i \(-0.741994\pi\)
−0.689101 + 0.724666i \(0.741994\pi\)
\(504\) 0 0
\(505\) 5.52786 0.245987
\(506\) 36.8885 1.63990
\(507\) 0 0
\(508\) 0.0557281 0.00247253
\(509\) −32.3050 −1.43189 −0.715946 0.698156i \(-0.754004\pi\)
−0.715946 + 0.698156i \(0.754004\pi\)
\(510\) 0 0
\(511\) −13.9443 −0.616858
\(512\) −5.29180 −0.233867
\(513\) 0 0
\(514\) 14.4721 0.638339
\(515\) −10.6180 −0.467886
\(516\) 0 0
\(517\) 46.5967 2.04932
\(518\) −10.8541 −0.476902
\(519\) 0 0
\(520\) 3.09017 0.135513
\(521\) 19.8328 0.868891 0.434446 0.900698i \(-0.356944\pi\)
0.434446 + 0.900698i \(0.356944\pi\)
\(522\) 0 0
\(523\) −1.20163 −0.0525434 −0.0262717 0.999655i \(-0.508364\pi\)
−0.0262717 + 0.999655i \(0.508364\pi\)
\(524\) −2.70820 −0.118308
\(525\) 0 0
\(526\) 49.7426 2.16888
\(527\) −10.8541 −0.472812
\(528\) 0 0
\(529\) 5.96556 0.259372
\(530\) −7.09017 −0.307977
\(531\) 0 0
\(532\) 4.38197 0.189982
\(533\) −11.1803 −0.484274
\(534\) 0 0
\(535\) −2.70820 −0.117086
\(536\) −25.3262 −1.09393
\(537\) 0 0
\(538\) −17.3262 −0.746987
\(539\) −4.23607 −0.182460
\(540\) 0 0
\(541\) −13.5066 −0.580693 −0.290347 0.956922i \(-0.593771\pi\)
−0.290347 + 0.956922i \(0.593771\pi\)
\(542\) −39.7426 −1.70709
\(543\) 0 0
\(544\) 5.47214 0.234616
\(545\) −12.5623 −0.538110
\(546\) 0 0
\(547\) 19.3607 0.827803 0.413901 0.910322i \(-0.364166\pi\)
0.413901 + 0.910322i \(0.364166\pi\)
\(548\) −8.58359 −0.366673
\(549\) 0 0
\(550\) −6.85410 −0.292260
\(551\) −67.7984 −2.88831
\(552\) 0 0
\(553\) −5.61803 −0.238903
\(554\) 7.56231 0.321292
\(555\) 0 0
\(556\) 1.96556 0.0833582
\(557\) 16.7984 0.711770 0.355885 0.934530i \(-0.384179\pi\)
0.355885 + 0.934530i \(0.384179\pi\)
\(558\) 0 0
\(559\) −13.7426 −0.581252
\(560\) −4.85410 −0.205123
\(561\) 0 0
\(562\) 22.0344 0.929467
\(563\) −21.6869 −0.913995 −0.456997 0.889468i \(-0.651075\pi\)
−0.456997 + 0.889468i \(0.651075\pi\)
\(564\) 0 0
\(565\) 5.85410 0.246284
\(566\) 34.2148 1.43815
\(567\) 0 0
\(568\) 8.61803 0.361605
\(569\) 37.7639 1.58315 0.791573 0.611074i \(-0.209262\pi\)
0.791573 + 0.611074i \(0.209262\pi\)
\(570\) 0 0
\(571\) 1.25735 0.0526186 0.0263093 0.999654i \(-0.491625\pi\)
0.0263093 + 0.999654i \(0.491625\pi\)
\(572\) −3.61803 −0.151278
\(573\) 0 0
\(574\) 13.0902 0.546373
\(575\) −5.38197 −0.224443
\(576\) 0 0
\(577\) 22.1246 0.921060 0.460530 0.887644i \(-0.347659\pi\)
0.460530 + 0.887644i \(0.347659\pi\)
\(578\) −23.2705 −0.967926
\(579\) 0 0
\(580\) −5.90983 −0.245392
\(581\) 10.7082 0.444251
\(582\) 0 0
\(583\) −18.5623 −0.768772
\(584\) −31.1803 −1.29025
\(585\) 0 0
\(586\) 10.1803 0.420546
\(587\) 7.20163 0.297243 0.148621 0.988894i \(-0.452516\pi\)
0.148621 + 0.988894i \(0.452516\pi\)
\(588\) 0 0
\(589\) −47.5623 −1.95977
\(590\) 2.09017 0.0860509
\(591\) 0 0
\(592\) −32.5623 −1.33830
\(593\) 34.3050 1.40874 0.704368 0.709835i \(-0.251231\pi\)
0.704368 + 0.709835i \(0.251231\pi\)
\(594\) 0 0
\(595\) −1.61803 −0.0663329
\(596\) 9.76393 0.399946
\(597\) 0 0
\(598\) −12.0344 −0.492125
\(599\) 38.9443 1.59122 0.795610 0.605809i \(-0.207151\pi\)
0.795610 + 0.605809i \(0.207151\pi\)
\(600\) 0 0
\(601\) 0.798374 0.0325663 0.0162832 0.999867i \(-0.494817\pi\)
0.0162832 + 0.999867i \(0.494817\pi\)
\(602\) 16.0902 0.655786
\(603\) 0 0
\(604\) −0.0344419 −0.00140142
\(605\) −6.94427 −0.282325
\(606\) 0 0
\(607\) 24.4164 0.991031 0.495516 0.868599i \(-0.334979\pi\)
0.495516 + 0.868599i \(0.334979\pi\)
\(608\) 23.9787 0.972465
\(609\) 0 0
\(610\) 22.4164 0.907614
\(611\) −15.2016 −0.614992
\(612\) 0 0
\(613\) −7.29180 −0.294513 −0.147256 0.989098i \(-0.547044\pi\)
−0.147256 + 0.989098i \(0.547044\pi\)
\(614\) 31.4164 1.26786
\(615\) 0 0
\(616\) −9.47214 −0.381643
\(617\) 37.7984 1.52171 0.760853 0.648925i \(-0.224781\pi\)
0.760853 + 0.648925i \(0.224781\pi\)
\(618\) 0 0
\(619\) −47.5410 −1.91083 −0.955417 0.295258i \(-0.904594\pi\)
−0.955417 + 0.295258i \(0.904594\pi\)
\(620\) −4.14590 −0.166503
\(621\) 0 0
\(622\) −23.1803 −0.929447
\(623\) 1.47214 0.0589799
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −37.5066 −1.49906
\(627\) 0 0
\(628\) −3.23607 −0.129133
\(629\) −10.8541 −0.432781
\(630\) 0 0
\(631\) 41.8885 1.66756 0.833778 0.552099i \(-0.186173\pi\)
0.833778 + 0.552099i \(0.186173\pi\)
\(632\) −12.5623 −0.499702
\(633\) 0 0
\(634\) 9.79837 0.389143
\(635\) −0.0901699 −0.00357829
\(636\) 0 0
\(637\) 1.38197 0.0547555
\(638\) −65.5410 −2.59479
\(639\) 0 0
\(640\) −13.6180 −0.538300
\(641\) 0.729490 0.0288131 0.0144066 0.999896i \(-0.495414\pi\)
0.0144066 + 0.999896i \(0.495414\pi\)
\(642\) 0 0
\(643\) 41.7426 1.64617 0.823085 0.567919i \(-0.192251\pi\)
0.823085 + 0.567919i \(0.192251\pi\)
\(644\) 3.32624 0.131072
\(645\) 0 0
\(646\) 18.5623 0.730324
\(647\) 13.0557 0.513274 0.256637 0.966508i \(-0.417386\pi\)
0.256637 + 0.966508i \(0.417386\pi\)
\(648\) 0 0
\(649\) 5.47214 0.214800
\(650\) 2.23607 0.0877058
\(651\) 0 0
\(652\) −1.81966 −0.0712634
\(653\) −6.03444 −0.236146 −0.118073 0.993005i \(-0.537672\pi\)
−0.118073 + 0.993005i \(0.537672\pi\)
\(654\) 0 0
\(655\) 4.38197 0.171218
\(656\) 39.2705 1.53326
\(657\) 0 0
\(658\) 17.7984 0.693853
\(659\) 0.763932 0.0297586 0.0148793 0.999889i \(-0.495264\pi\)
0.0148793 + 0.999889i \(0.495264\pi\)
\(660\) 0 0
\(661\) −16.2148 −0.630682 −0.315341 0.948978i \(-0.602119\pi\)
−0.315341 + 0.948978i \(0.602119\pi\)
\(662\) −51.5410 −2.00320
\(663\) 0 0
\(664\) 23.9443 0.929218
\(665\) −7.09017 −0.274945
\(666\) 0 0
\(667\) −51.4640 −1.99269
\(668\) 4.61803 0.178677
\(669\) 0 0
\(670\) −18.3262 −0.708004
\(671\) 58.6869 2.26558
\(672\) 0 0
\(673\) −46.4721 −1.79137 −0.895685 0.444690i \(-0.853314\pi\)
−0.895685 + 0.444690i \(0.853314\pi\)
\(674\) −51.3607 −1.97834
\(675\) 0 0
\(676\) −6.85410 −0.263619
\(677\) 17.6525 0.678440 0.339220 0.940707i \(-0.389837\pi\)
0.339220 + 0.940707i \(0.389837\pi\)
\(678\) 0 0
\(679\) 3.32624 0.127649
\(680\) −3.61803 −0.138745
\(681\) 0 0
\(682\) −45.9787 −1.76062
\(683\) 42.9787 1.64453 0.822267 0.569101i \(-0.192709\pi\)
0.822267 + 0.569101i \(0.192709\pi\)
\(684\) 0 0
\(685\) 13.8885 0.530654
\(686\) −1.61803 −0.0617768
\(687\) 0 0
\(688\) 48.2705 1.84030
\(689\) 6.05573 0.230705
\(690\) 0 0
\(691\) −30.5279 −1.16133 −0.580667 0.814141i \(-0.697208\pi\)
−0.580667 + 0.814141i \(0.697208\pi\)
\(692\) −7.09017 −0.269528
\(693\) 0 0
\(694\) 20.6525 0.783957
\(695\) −3.18034 −0.120637
\(696\) 0 0
\(697\) 13.0902 0.495826
\(698\) 50.7426 1.92064
\(699\) 0 0
\(700\) −0.618034 −0.0233595
\(701\) −6.88854 −0.260177 −0.130088 0.991502i \(-0.541526\pi\)
−0.130088 + 0.991502i \(0.541526\pi\)
\(702\) 0 0
\(703\) −47.5623 −1.79385
\(704\) −17.9443 −0.676300
\(705\) 0 0
\(706\) −18.8885 −0.710880
\(707\) 5.52786 0.207897
\(708\) 0 0
\(709\) −9.59675 −0.360413 −0.180207 0.983629i \(-0.557677\pi\)
−0.180207 + 0.983629i \(0.557677\pi\)
\(710\) 6.23607 0.234035
\(711\) 0 0
\(712\) 3.29180 0.123365
\(713\) −36.1033 −1.35208
\(714\) 0 0
\(715\) 5.85410 0.218931
\(716\) 4.32624 0.161679
\(717\) 0 0
\(718\) −58.9230 −2.19899
\(719\) −12.9656 −0.483534 −0.241767 0.970334i \(-0.577727\pi\)
−0.241767 + 0.970334i \(0.577727\pi\)
\(720\) 0 0
\(721\) −10.6180 −0.395436
\(722\) 50.5967 1.88302
\(723\) 0 0
\(724\) −12.0344 −0.447257
\(725\) 9.56231 0.355135
\(726\) 0 0
\(727\) −11.4508 −0.424689 −0.212344 0.977195i \(-0.568110\pi\)
−0.212344 + 0.977195i \(0.568110\pi\)
\(728\) 3.09017 0.114529
\(729\) 0 0
\(730\) −22.5623 −0.835068
\(731\) 16.0902 0.595116
\(732\) 0 0
\(733\) 10.5623 0.390128 0.195064 0.980791i \(-0.437509\pi\)
0.195064 + 0.980791i \(0.437509\pi\)
\(734\) −24.0344 −0.887127
\(735\) 0 0
\(736\) 18.2016 0.670921
\(737\) −47.9787 −1.76732
\(738\) 0 0
\(739\) −20.6525 −0.759714 −0.379857 0.925045i \(-0.624027\pi\)
−0.379857 + 0.925045i \(0.624027\pi\)
\(740\) −4.14590 −0.152406
\(741\) 0 0
\(742\) −7.09017 −0.260288
\(743\) 3.32624 0.122028 0.0610139 0.998137i \(-0.480567\pi\)
0.0610139 + 0.998137i \(0.480567\pi\)
\(744\) 0 0
\(745\) −15.7984 −0.578808
\(746\) −27.4721 −1.00583
\(747\) 0 0
\(748\) 4.23607 0.154886
\(749\) −2.70820 −0.0989556
\(750\) 0 0
\(751\) −47.8885 −1.74748 −0.873739 0.486395i \(-0.838312\pi\)
−0.873739 + 0.486395i \(0.838312\pi\)
\(752\) 53.3951 1.94712
\(753\) 0 0
\(754\) 21.3820 0.778685
\(755\) 0.0557281 0.00202815
\(756\) 0 0
\(757\) 6.27051 0.227906 0.113953 0.993486i \(-0.463649\pi\)
0.113953 + 0.993486i \(0.463649\pi\)
\(758\) 19.2361 0.698685
\(759\) 0 0
\(760\) −15.8541 −0.575089
\(761\) 9.96556 0.361251 0.180626 0.983552i \(-0.442188\pi\)
0.180626 + 0.983552i \(0.442188\pi\)
\(762\) 0 0
\(763\) −12.5623 −0.454786
\(764\) −11.6180 −0.420326
\(765\) 0 0
\(766\) 18.8541 0.681226
\(767\) −1.78522 −0.0644605
\(768\) 0 0
\(769\) 22.5967 0.814860 0.407430 0.913237i \(-0.366425\pi\)
0.407430 + 0.913237i \(0.366425\pi\)
\(770\) −6.85410 −0.247005
\(771\) 0 0
\(772\) −0.527864 −0.0189982
\(773\) 17.6738 0.635681 0.317841 0.948144i \(-0.397042\pi\)
0.317841 + 0.948144i \(0.397042\pi\)
\(774\) 0 0
\(775\) 6.70820 0.240966
\(776\) 7.43769 0.266998
\(777\) 0 0
\(778\) −41.7426 −1.49655
\(779\) 57.3607 2.05516
\(780\) 0 0
\(781\) 16.3262 0.584199
\(782\) 14.0902 0.503863
\(783\) 0 0
\(784\) −4.85410 −0.173361
\(785\) 5.23607 0.186883
\(786\) 0 0
\(787\) −3.23607 −0.115353 −0.0576767 0.998335i \(-0.518369\pi\)
−0.0576767 + 0.998335i \(0.518369\pi\)
\(788\) 12.0344 0.428709
\(789\) 0 0
\(790\) −9.09017 −0.323414
\(791\) 5.85410 0.208148
\(792\) 0 0
\(793\) −19.1459 −0.679891
\(794\) 14.6525 0.519997
\(795\) 0 0
\(796\) 1.00000 0.0354441
\(797\) −23.6869 −0.839034 −0.419517 0.907748i \(-0.637800\pi\)
−0.419517 + 0.907748i \(0.637800\pi\)
\(798\) 0 0
\(799\) 17.7984 0.629661
\(800\) −3.38197 −0.119571
\(801\) 0 0
\(802\) 28.1246 0.993115
\(803\) −59.0689 −2.08450
\(804\) 0 0
\(805\) −5.38197 −0.189689
\(806\) 15.0000 0.528352
\(807\) 0 0
\(808\) 12.3607 0.434847
\(809\) 6.63932 0.233426 0.116713 0.993166i \(-0.462764\pi\)
0.116713 + 0.993166i \(0.462764\pi\)
\(810\) 0 0
\(811\) 8.32624 0.292374 0.146187 0.989257i \(-0.453300\pi\)
0.146187 + 0.989257i \(0.453300\pi\)
\(812\) −5.90983 −0.207394
\(813\) 0 0
\(814\) −45.9787 −1.61155
\(815\) 2.94427 0.103133
\(816\) 0 0
\(817\) 70.5066 2.46671
\(818\) −21.1246 −0.738605
\(819\) 0 0
\(820\) 5.00000 0.174608
\(821\) 29.5836 1.03247 0.516237 0.856446i \(-0.327332\pi\)
0.516237 + 0.856446i \(0.327332\pi\)
\(822\) 0 0
\(823\) −37.9443 −1.32265 −0.661327 0.750098i \(-0.730006\pi\)
−0.661327 + 0.750098i \(0.730006\pi\)
\(824\) −23.7426 −0.827114
\(825\) 0 0
\(826\) 2.09017 0.0727263
\(827\) 11.5410 0.401321 0.200660 0.979661i \(-0.435691\pi\)
0.200660 + 0.979661i \(0.435691\pi\)
\(828\) 0 0
\(829\) −13.3607 −0.464036 −0.232018 0.972712i \(-0.574533\pi\)
−0.232018 + 0.972712i \(0.574533\pi\)
\(830\) 17.3262 0.601402
\(831\) 0 0
\(832\) 5.85410 0.202954
\(833\) −1.61803 −0.0560616
\(834\) 0 0
\(835\) −7.47214 −0.258584
\(836\) 18.5623 0.641991
\(837\) 0 0
\(838\) −12.0902 −0.417648
\(839\) −0.381966 −0.0131869 −0.00659347 0.999978i \(-0.502099\pi\)
−0.00659347 + 0.999978i \(0.502099\pi\)
\(840\) 0 0
\(841\) 62.4377 2.15302
\(842\) 13.6525 0.470495
\(843\) 0 0
\(844\) −10.5836 −0.364302
\(845\) 11.0902 0.381513
\(846\) 0 0
\(847\) −6.94427 −0.238608
\(848\) −21.2705 −0.730432
\(849\) 0 0
\(850\) −2.61803 −0.0897978
\(851\) −36.1033 −1.23761
\(852\) 0 0
\(853\) −2.16718 −0.0742030 −0.0371015 0.999312i \(-0.511812\pi\)
−0.0371015 + 0.999312i \(0.511812\pi\)
\(854\) 22.4164 0.767074
\(855\) 0 0
\(856\) −6.05573 −0.206981
\(857\) 26.2361 0.896207 0.448104 0.893982i \(-0.352100\pi\)
0.448104 + 0.893982i \(0.352100\pi\)
\(858\) 0 0
\(859\) 21.5967 0.736872 0.368436 0.929653i \(-0.379893\pi\)
0.368436 + 0.929653i \(0.379893\pi\)
\(860\) 6.14590 0.209573
\(861\) 0 0
\(862\) −49.2705 −1.67816
\(863\) 51.7771 1.76251 0.881256 0.472639i \(-0.156698\pi\)
0.881256 + 0.472639i \(0.156698\pi\)
\(864\) 0 0
\(865\) 11.4721 0.390064
\(866\) −34.3262 −1.16645
\(867\) 0 0
\(868\) −4.14590 −0.140721
\(869\) −23.7984 −0.807305
\(870\) 0 0
\(871\) 15.6525 0.530364
\(872\) −28.0902 −0.951253
\(873\) 0 0
\(874\) 61.7426 2.08848
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) 27.9443 0.943611 0.471806 0.881703i \(-0.343602\pi\)
0.471806 + 0.881703i \(0.343602\pi\)
\(878\) 18.2705 0.616600
\(879\) 0 0
\(880\) −20.5623 −0.693155
\(881\) −55.8885 −1.88293 −0.941466 0.337107i \(-0.890552\pi\)
−0.941466 + 0.337107i \(0.890552\pi\)
\(882\) 0 0
\(883\) −19.6525 −0.661358 −0.330679 0.943743i \(-0.607278\pi\)
−0.330679 + 0.943743i \(0.607278\pi\)
\(884\) −1.38197 −0.0464805
\(885\) 0 0
\(886\) 65.8328 2.21170
\(887\) 14.7639 0.495724 0.247862 0.968795i \(-0.420272\pi\)
0.247862 + 0.968795i \(0.420272\pi\)
\(888\) 0 0
\(889\) −0.0901699 −0.00302420
\(890\) 2.38197 0.0798437
\(891\) 0 0
\(892\) 4.61803 0.154623
\(893\) 77.9919 2.60990
\(894\) 0 0
\(895\) −7.00000 −0.233984
\(896\) −13.6180 −0.454947
\(897\) 0 0
\(898\) −33.1246 −1.10538
\(899\) 64.1459 2.13939
\(900\) 0 0
\(901\) −7.09017 −0.236208
\(902\) 55.4508 1.84631
\(903\) 0 0
\(904\) 13.0902 0.435373
\(905\) 19.4721 0.647276
\(906\) 0 0
\(907\) 8.14590 0.270480 0.135240 0.990813i \(-0.456819\pi\)
0.135240 + 0.990813i \(0.456819\pi\)
\(908\) −4.59675 −0.152548
\(909\) 0 0
\(910\) 2.23607 0.0741249
\(911\) −7.63932 −0.253102 −0.126551 0.991960i \(-0.540391\pi\)
−0.126551 + 0.991960i \(0.540391\pi\)
\(912\) 0 0
\(913\) 45.3607 1.50122
\(914\) 28.0344 0.927297
\(915\) 0 0
\(916\) −11.0902 −0.366430
\(917\) 4.38197 0.144705
\(918\) 0 0
\(919\) 42.1591 1.39070 0.695349 0.718672i \(-0.255250\pi\)
0.695349 + 0.718672i \(0.255250\pi\)
\(920\) −12.0344 −0.396764
\(921\) 0 0
\(922\) 36.8885 1.21486
\(923\) −5.32624 −0.175315
\(924\) 0 0
\(925\) 6.70820 0.220564
\(926\) −1.00000 −0.0328620
\(927\) 0 0
\(928\) −32.3394 −1.06159
\(929\) 57.1033 1.87350 0.936750 0.350000i \(-0.113818\pi\)
0.936750 + 0.350000i \(0.113818\pi\)
\(930\) 0 0
\(931\) −7.09017 −0.232371
\(932\) −10.5623 −0.345980
\(933\) 0 0
\(934\) −27.4164 −0.897092
\(935\) −6.85410 −0.224153
\(936\) 0 0
\(937\) 26.9443 0.880231 0.440115 0.897941i \(-0.354937\pi\)
0.440115 + 0.897941i \(0.354937\pi\)
\(938\) −18.3262 −0.598373
\(939\) 0 0
\(940\) 6.79837 0.221739
\(941\) 45.7639 1.49186 0.745931 0.666023i \(-0.232005\pi\)
0.745931 + 0.666023i \(0.232005\pi\)
\(942\) 0 0
\(943\) 43.5410 1.41789
\(944\) 6.27051 0.204088
\(945\) 0 0
\(946\) 68.1591 2.21604
\(947\) 5.43769 0.176701 0.0883507 0.996089i \(-0.471840\pi\)
0.0883507 + 0.996089i \(0.471840\pi\)
\(948\) 0 0
\(949\) 19.2705 0.625547
\(950\) −11.4721 −0.372205
\(951\) 0 0
\(952\) −3.61803 −0.117261
\(953\) 35.6525 1.15490 0.577448 0.816427i \(-0.304048\pi\)
0.577448 + 0.816427i \(0.304048\pi\)
\(954\) 0 0
\(955\) 18.7984 0.608301
\(956\) −7.20163 −0.232917
\(957\) 0 0
\(958\) −41.9230 −1.35447
\(959\) 13.8885 0.448484
\(960\) 0 0
\(961\) 14.0000 0.451613
\(962\) 15.0000 0.483619
\(963\) 0 0
\(964\) −4.70820 −0.151641
\(965\) 0.854102 0.0274945
\(966\) 0 0
\(967\) −8.52786 −0.274238 −0.137119 0.990555i \(-0.543784\pi\)
−0.137119 + 0.990555i \(0.543784\pi\)
\(968\) −15.5279 −0.499084
\(969\) 0 0
\(970\) 5.38197 0.172805
\(971\) −22.2492 −0.714012 −0.357006 0.934102i \(-0.616202\pi\)
−0.357006 + 0.934102i \(0.616202\pi\)
\(972\) 0 0
\(973\) −3.18034 −0.101957
\(974\) −25.1246 −0.805044
\(975\) 0 0
\(976\) 67.2492 2.15260
\(977\) −14.3607 −0.459439 −0.229719 0.973257i \(-0.573781\pi\)
−0.229719 + 0.973257i \(0.573781\pi\)
\(978\) 0 0
\(979\) 6.23607 0.199306
\(980\) −0.618034 −0.0197424
\(981\) 0 0
\(982\) 31.5623 1.00719
\(983\) −46.9787 −1.49839 −0.749194 0.662350i \(-0.769559\pi\)
−0.749194 + 0.662350i \(0.769559\pi\)
\(984\) 0 0
\(985\) −19.4721 −0.620434
\(986\) −25.0344 −0.797259
\(987\) 0 0
\(988\) −6.05573 −0.192658
\(989\) 53.5197 1.70183
\(990\) 0 0
\(991\) −42.8885 −1.36240 −0.681200 0.732098i \(-0.738541\pi\)
−0.681200 + 0.732098i \(0.738541\pi\)
\(992\) −22.6869 −0.720310
\(993\) 0 0
\(994\) 6.23607 0.197796
\(995\) −1.61803 −0.0512951
\(996\) 0 0
\(997\) 14.7082 0.465813 0.232907 0.972499i \(-0.425176\pi\)
0.232907 + 0.972499i \(0.425176\pi\)
\(998\) 5.43769 0.172127
\(999\) 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 \(a_p\))