Properties

Label 945.2.a.b.1.2
Level 945
Weight 2
Character 945.1
Self dual Yes
Analytic conductor 7.546
Analytic rank 0
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: \(0\)
Dimension: \(2\)
Coefficient field: \(\Q(\zeta_{8})^+\)
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 \(1.41421\)
Character \(\chi\) = 945.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+0.414214 q^{2}\) \(-1.82843 q^{4}\) \(-1.00000 q^{5}\) \(-1.00000 q^{7}\) \(-1.58579 q^{8}\) \(+O(q^{10})\) \(q\)\(+0.414214 q^{2}\) \(-1.82843 q^{4}\) \(-1.00000 q^{5}\) \(-1.00000 q^{7}\) \(-1.58579 q^{8}\) \(-0.414214 q^{10}\) \(+2.41421 q^{11}\) \(-0.414214 q^{13}\) \(-0.414214 q^{14}\) \(+3.00000 q^{16}\) \(+0.828427 q^{17}\) \(+4.41421 q^{19}\) \(+1.82843 q^{20}\) \(+1.00000 q^{22}\) \(-4.82843 q^{23}\) \(+1.00000 q^{25}\) \(-0.171573 q^{26}\) \(+1.82843 q^{28}\) \(+4.00000 q^{29}\) \(+6.00000 q^{31}\) \(+4.41421 q^{32}\) \(+0.343146 q^{34}\) \(+1.00000 q^{35}\) \(+8.48528 q^{37}\) \(+1.82843 q^{38}\) \(+1.58579 q^{40}\) \(+2.17157 q^{41}\) \(+4.65685 q^{43}\) \(-4.41421 q^{44}\) \(-2.00000 q^{46}\) \(+9.48528 q^{47}\) \(+1.00000 q^{49}\) \(+0.414214 q^{50}\) \(+0.757359 q^{52}\) \(-8.89949 q^{53}\) \(-2.41421 q^{55}\) \(+1.58579 q^{56}\) \(+1.65685 q^{58}\) \(-10.4853 q^{59}\) \(+8.48528 q^{61}\) \(+2.48528 q^{62}\) \(-4.17157 q^{64}\) \(+0.414214 q^{65}\) \(+2.17157 q^{67}\) \(-1.51472 q^{68}\) \(+0.414214 q^{70}\) \(-2.00000 q^{71}\) \(+12.0711 q^{73}\) \(+3.51472 q^{74}\) \(-8.07107 q^{76}\) \(-2.41421 q^{77}\) \(+9.17157 q^{79}\) \(-3.00000 q^{80}\) \(+0.899495 q^{82}\) \(-9.48528 q^{83}\) \(-0.828427 q^{85}\) \(+1.92893 q^{86}\) \(-3.82843 q^{88}\) \(-2.65685 q^{89}\) \(+0.414214 q^{91}\) \(+8.82843 q^{92}\) \(+3.92893 q^{94}\) \(-4.41421 q^{95}\) \(-14.1421 q^{97}\) \(+0.414214 q^{98}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(2q \) \(\mathstrut -\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 2q^{4} \) \(\mathstrut -\mathstrut 2q^{5} \) \(\mathstrut -\mathstrut 2q^{7} \) \(\mathstrut -\mathstrut 6q^{8} \) \(\mathstrut +\mathstrut 2q^{10} \) \(\mathstrut +\mathstrut 2q^{11} \) \(\mathstrut +\mathstrut 2q^{13} \) \(\mathstrut +\mathstrut 2q^{14} \) \(\mathstrut +\mathstrut 6q^{16} \) \(\mathstrut -\mathstrut 4q^{17} \) \(\mathstrut +\mathstrut 6q^{19} \) \(\mathstrut -\mathstrut 2q^{20} \) \(\mathstrut +\mathstrut 2q^{22} \) \(\mathstrut -\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut -\mathstrut 6q^{26} \) \(\mathstrut -\mathstrut 2q^{28} \) \(\mathstrut +\mathstrut 8q^{29} \) \(\mathstrut +\mathstrut 12q^{31} \) \(\mathstrut +\mathstrut 6q^{32} \) \(\mathstrut +\mathstrut 12q^{34} \) \(\mathstrut +\mathstrut 2q^{35} \) \(\mathstrut -\mathstrut 2q^{38} \) \(\mathstrut +\mathstrut 6q^{40} \) \(\mathstrut +\mathstrut 10q^{41} \) \(\mathstrut -\mathstrut 2q^{43} \) \(\mathstrut -\mathstrut 6q^{44} \) \(\mathstrut -\mathstrut 4q^{46} \) \(\mathstrut +\mathstrut 2q^{47} \) \(\mathstrut +\mathstrut 2q^{49} \) \(\mathstrut -\mathstrut 2q^{50} \) \(\mathstrut +\mathstrut 10q^{52} \) \(\mathstrut +\mathstrut 2q^{53} \) \(\mathstrut -\mathstrut 2q^{55} \) \(\mathstrut +\mathstrut 6q^{56} \) \(\mathstrut -\mathstrut 8q^{58} \) \(\mathstrut -\mathstrut 4q^{59} \) \(\mathstrut -\mathstrut 12q^{62} \) \(\mathstrut -\mathstrut 14q^{64} \) \(\mathstrut -\mathstrut 2q^{65} \) \(\mathstrut +\mathstrut 10q^{67} \) \(\mathstrut -\mathstrut 20q^{68} \) \(\mathstrut -\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 4q^{71} \) \(\mathstrut +\mathstrut 10q^{73} \) \(\mathstrut +\mathstrut 24q^{74} \) \(\mathstrut -\mathstrut 2q^{76} \) \(\mathstrut -\mathstrut 2q^{77} \) \(\mathstrut +\mathstrut 24q^{79} \) \(\mathstrut -\mathstrut 6q^{80} \) \(\mathstrut -\mathstrut 18q^{82} \) \(\mathstrut -\mathstrut 2q^{83} \) \(\mathstrut +\mathstrut 4q^{85} \) \(\mathstrut +\mathstrut 18q^{86} \) \(\mathstrut -\mathstrut 2q^{88} \) \(\mathstrut +\mathstrut 6q^{89} \) \(\mathstrut -\mathstrut 2q^{91} \) \(\mathstrut +\mathstrut 12q^{92} \) \(\mathstrut +\mathstrut 22q^{94} \) \(\mathstrut -\mathstrut 6q^{95} \) \(\mathstrut -\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0.414214 0.292893 0.146447 0.989219i \(-0.453216\pi\)
0.146447 + 0.989219i \(0.453216\pi\)
\(3\) 0 0
\(4\) −1.82843 −0.914214
\(5\) −1.00000 −0.447214
\(6\) 0 0
\(7\) −1.00000 −0.377964
\(8\) −1.58579 −0.560660
\(9\) 0 0
\(10\) −0.414214 −0.130986
\(11\) 2.41421 0.727913 0.363956 0.931416i \(-0.381426\pi\)
0.363956 + 0.931416i \(0.381426\pi\)
\(12\) 0 0
\(13\) −0.414214 −0.114882 −0.0574411 0.998349i \(-0.518294\pi\)
−0.0574411 + 0.998349i \(0.518294\pi\)
\(14\) −0.414214 −0.110703
\(15\) 0 0
\(16\) 3.00000 0.750000
\(17\) 0.828427 0.200923 0.100462 0.994941i \(-0.467968\pi\)
0.100462 + 0.994941i \(0.467968\pi\)
\(18\) 0 0
\(19\) 4.41421 1.01269 0.506345 0.862331i \(-0.330996\pi\)
0.506345 + 0.862331i \(0.330996\pi\)
\(20\) 1.82843 0.408849
\(21\) 0 0
\(22\) 1.00000 0.213201
\(23\) −4.82843 −1.00680 −0.503398 0.864054i \(-0.667917\pi\)
−0.503398 + 0.864054i \(0.667917\pi\)
\(24\) 0 0
\(25\) 1.00000 0.200000
\(26\) −0.171573 −0.0336482
\(27\) 0 0
\(28\) 1.82843 0.345540
\(29\) 4.00000 0.742781 0.371391 0.928477i \(-0.378881\pi\)
0.371391 + 0.928477i \(0.378881\pi\)
\(30\) 0 0
\(31\) 6.00000 1.07763 0.538816 0.842424i \(-0.318872\pi\)
0.538816 + 0.842424i \(0.318872\pi\)
\(32\) 4.41421 0.780330
\(33\) 0 0
\(34\) 0.343146 0.0588490
\(35\) 1.00000 0.169031
\(36\) 0 0
\(37\) 8.48528 1.39497 0.697486 0.716599i \(-0.254302\pi\)
0.697486 + 0.716599i \(0.254302\pi\)
\(38\) 1.82843 0.296610
\(39\) 0 0
\(40\) 1.58579 0.250735
\(41\) 2.17157 0.339143 0.169571 0.985518i \(-0.445762\pi\)
0.169571 + 0.985518i \(0.445762\pi\)
\(42\) 0 0
\(43\) 4.65685 0.710164 0.355082 0.934835i \(-0.384453\pi\)
0.355082 + 0.934835i \(0.384453\pi\)
\(44\) −4.41421 −0.665468
\(45\) 0 0
\(46\) −2.00000 −0.294884
\(47\) 9.48528 1.38357 0.691785 0.722103i \(-0.256824\pi\)
0.691785 + 0.722103i \(0.256824\pi\)
\(48\) 0 0
\(49\) 1.00000 0.142857
\(50\) 0.414214 0.0585786
\(51\) 0 0
\(52\) 0.757359 0.105027
\(53\) −8.89949 −1.22244 −0.611220 0.791461i \(-0.709321\pi\)
−0.611220 + 0.791461i \(0.709321\pi\)
\(54\) 0 0
\(55\) −2.41421 −0.325532
\(56\) 1.58579 0.211910
\(57\) 0 0
\(58\) 1.65685 0.217556
\(59\) −10.4853 −1.36507 −0.682534 0.730854i \(-0.739122\pi\)
−0.682534 + 0.730854i \(0.739122\pi\)
\(60\) 0 0
\(61\) 8.48528 1.08643 0.543214 0.839594i \(-0.317207\pi\)
0.543214 + 0.839594i \(0.317207\pi\)
\(62\) 2.48528 0.315631
\(63\) 0 0
\(64\) −4.17157 −0.521447
\(65\) 0.414214 0.0513769
\(66\) 0 0
\(67\) 2.17157 0.265300 0.132650 0.991163i \(-0.457651\pi\)
0.132650 + 0.991163i \(0.457651\pi\)
\(68\) −1.51472 −0.183687
\(69\) 0 0
\(70\) 0.414214 0.0495080
\(71\) −2.00000 −0.237356 −0.118678 0.992933i \(-0.537866\pi\)
−0.118678 + 0.992933i \(0.537866\pi\)
\(72\) 0 0
\(73\) 12.0711 1.41281 0.706406 0.707807i \(-0.250315\pi\)
0.706406 + 0.707807i \(0.250315\pi\)
\(74\) 3.51472 0.408578
\(75\) 0 0
\(76\) −8.07107 −0.925815
\(77\) −2.41421 −0.275125
\(78\) 0 0
\(79\) 9.17157 1.03188 0.515941 0.856624i \(-0.327442\pi\)
0.515941 + 0.856624i \(0.327442\pi\)
\(80\) −3.00000 −0.335410
\(81\) 0 0
\(82\) 0.899495 0.0993326
\(83\) −9.48528 −1.04114 −0.520572 0.853818i \(-0.674281\pi\)
−0.520572 + 0.853818i \(0.674281\pi\)
\(84\) 0 0
\(85\) −0.828427 −0.0898555
\(86\) 1.92893 0.208002
\(87\) 0 0
\(88\) −3.82843 −0.408112
\(89\) −2.65685 −0.281626 −0.140813 0.990036i \(-0.544972\pi\)
−0.140813 + 0.990036i \(0.544972\pi\)
\(90\) 0 0
\(91\) 0.414214 0.0434214
\(92\) 8.82843 0.920427
\(93\) 0 0
\(94\) 3.92893 0.405238
\(95\) −4.41421 −0.452889
\(96\) 0 0
\(97\) −14.1421 −1.43592 −0.717958 0.696086i \(-0.754923\pi\)
−0.717958 + 0.696086i \(0.754923\pi\)
\(98\) 0.414214 0.0418419
\(99\) 0 0
\(100\) −1.82843 −0.182843
\(101\) 14.1716 1.41012 0.705062 0.709146i \(-0.250919\pi\)
0.705062 + 0.709146i \(0.250919\pi\)
\(102\) 0 0
\(103\) 5.17157 0.509570 0.254785 0.966998i \(-0.417995\pi\)
0.254785 + 0.966998i \(0.417995\pi\)
\(104\) 0.656854 0.0644099
\(105\) 0 0
\(106\) −3.68629 −0.358044
\(107\) −6.48528 −0.626956 −0.313478 0.949595i \(-0.601494\pi\)
−0.313478 + 0.949595i \(0.601494\pi\)
\(108\) 0 0
\(109\) −13.4853 −1.29166 −0.645828 0.763483i \(-0.723488\pi\)
−0.645828 + 0.763483i \(0.723488\pi\)
\(110\) −1.00000 −0.0953463
\(111\) 0 0
\(112\) −3.00000 −0.283473
\(113\) −11.2426 −1.05762 −0.528809 0.848741i \(-0.677361\pi\)
−0.528809 + 0.848741i \(0.677361\pi\)
\(114\) 0 0
\(115\) 4.82843 0.450253
\(116\) −7.31371 −0.679061
\(117\) 0 0
\(118\) −4.34315 −0.399819
\(119\) −0.828427 −0.0759418
\(120\) 0 0
\(121\) −5.17157 −0.470143
\(122\) 3.51472 0.318208
\(123\) 0 0
\(124\) −10.9706 −0.985186
\(125\) −1.00000 −0.0894427
\(126\) 0 0
\(127\) 5.34315 0.474128 0.237064 0.971494i \(-0.423815\pi\)
0.237064 + 0.971494i \(0.423815\pi\)
\(128\) −10.5563 −0.933058
\(129\) 0 0
\(130\) 0.171573 0.0150479
\(131\) 16.1421 1.41034 0.705172 0.709036i \(-0.250870\pi\)
0.705172 + 0.709036i \(0.250870\pi\)
\(132\) 0 0
\(133\) −4.41421 −0.382761
\(134\) 0.899495 0.0777045
\(135\) 0 0
\(136\) −1.31371 −0.112650
\(137\) 5.58579 0.477226 0.238613 0.971115i \(-0.423307\pi\)
0.238613 + 0.971115i \(0.423307\pi\)
\(138\) 0 0
\(139\) −1.31371 −0.111427 −0.0557137 0.998447i \(-0.517743\pi\)
−0.0557137 + 0.998447i \(0.517743\pi\)
\(140\) −1.82843 −0.154530
\(141\) 0 0
\(142\) −0.828427 −0.0695201
\(143\) −1.00000 −0.0836242
\(144\) 0 0
\(145\) −4.00000 −0.332182
\(146\) 5.00000 0.413803
\(147\) 0 0
\(148\) −15.5147 −1.27530
\(149\) 21.7990 1.78584 0.892921 0.450213i \(-0.148652\pi\)
0.892921 + 0.450213i \(0.148652\pi\)
\(150\) 0 0
\(151\) −0.686292 −0.0558496 −0.0279248 0.999610i \(-0.508890\pi\)
−0.0279248 + 0.999610i \(0.508890\pi\)
\(152\) −7.00000 −0.567775
\(153\) 0 0
\(154\) −1.00000 −0.0805823
\(155\) −6.00000 −0.481932
\(156\) 0 0
\(157\) 9.17157 0.731971 0.365986 0.930621i \(-0.380732\pi\)
0.365986 + 0.930621i \(0.380732\pi\)
\(158\) 3.79899 0.302231
\(159\) 0 0
\(160\) −4.41421 −0.348974
\(161\) 4.82843 0.380533
\(162\) 0 0
\(163\) 17.6569 1.38299 0.691496 0.722380i \(-0.256952\pi\)
0.691496 + 0.722380i \(0.256952\pi\)
\(164\) −3.97056 −0.310049
\(165\) 0 0
\(166\) −3.92893 −0.304944
\(167\) −11.3137 −0.875481 −0.437741 0.899101i \(-0.644221\pi\)
−0.437741 + 0.899101i \(0.644221\pi\)
\(168\) 0 0
\(169\) −12.8284 −0.986802
\(170\) −0.343146 −0.0263181
\(171\) 0 0
\(172\) −8.51472 −0.649241
\(173\) 7.31371 0.556051 0.278025 0.960574i \(-0.410320\pi\)
0.278025 + 0.960574i \(0.410320\pi\)
\(174\) 0 0
\(175\) −1.00000 −0.0755929
\(176\) 7.24264 0.545935
\(177\) 0 0
\(178\) −1.10051 −0.0824863
\(179\) −11.7279 −0.876586 −0.438293 0.898832i \(-0.644417\pi\)
−0.438293 + 0.898832i \(0.644417\pi\)
\(180\) 0 0
\(181\) −5.65685 −0.420471 −0.210235 0.977651i \(-0.567423\pi\)
−0.210235 + 0.977651i \(0.567423\pi\)
\(182\) 0.171573 0.0127178
\(183\) 0 0
\(184\) 7.65685 0.564471
\(185\) −8.48528 −0.623850
\(186\) 0 0
\(187\) 2.00000 0.146254
\(188\) −17.3431 −1.26488
\(189\) 0 0
\(190\) −1.82843 −0.132648
\(191\) 5.92893 0.429002 0.214501 0.976724i \(-0.431187\pi\)
0.214501 + 0.976724i \(0.431187\pi\)
\(192\) 0 0
\(193\) −22.4853 −1.61853 −0.809263 0.587447i \(-0.800133\pi\)
−0.809263 + 0.587447i \(0.800133\pi\)
\(194\) −5.85786 −0.420570
\(195\) 0 0
\(196\) −1.82843 −0.130602
\(197\) 6.89949 0.491569 0.245784 0.969325i \(-0.420955\pi\)
0.245784 + 0.969325i \(0.420955\pi\)
\(198\) 0 0
\(199\) 0.414214 0.0293628 0.0146814 0.999892i \(-0.495327\pi\)
0.0146814 + 0.999892i \(0.495327\pi\)
\(200\) −1.58579 −0.112132
\(201\) 0 0
\(202\) 5.87006 0.413016
\(203\) −4.00000 −0.280745
\(204\) 0 0
\(205\) −2.17157 −0.151669
\(206\) 2.14214 0.149250
\(207\) 0 0
\(208\) −1.24264 −0.0861616
\(209\) 10.6569 0.737150
\(210\) 0 0
\(211\) −14.4853 −0.997208 −0.498604 0.866830i \(-0.666154\pi\)
−0.498604 + 0.866830i \(0.666154\pi\)
\(212\) 16.2721 1.11757
\(213\) 0 0
\(214\) −2.68629 −0.183631
\(215\) −4.65685 −0.317595
\(216\) 0 0
\(217\) −6.00000 −0.407307
\(218\) −5.58579 −0.378317
\(219\) 0 0
\(220\) 4.41421 0.297606
\(221\) −0.343146 −0.0230825
\(222\) 0 0
\(223\) 5.65685 0.378811 0.189405 0.981899i \(-0.439344\pi\)
0.189405 + 0.981899i \(0.439344\pi\)
\(224\) −4.41421 −0.294937
\(225\) 0 0
\(226\) −4.65685 −0.309769
\(227\) 7.48528 0.496816 0.248408 0.968656i \(-0.420093\pi\)
0.248408 + 0.968656i \(0.420093\pi\)
\(228\) 0 0
\(229\) 17.6569 1.16680 0.583399 0.812186i \(-0.301722\pi\)
0.583399 + 0.812186i \(0.301722\pi\)
\(230\) 2.00000 0.131876
\(231\) 0 0
\(232\) −6.34315 −0.416448
\(233\) −16.5563 −1.08464 −0.542321 0.840171i \(-0.682454\pi\)
−0.542321 + 0.840171i \(0.682454\pi\)
\(234\) 0 0
\(235\) −9.48528 −0.618752
\(236\) 19.1716 1.24796
\(237\) 0 0
\(238\) −0.343146 −0.0222428
\(239\) 20.6274 1.33428 0.667138 0.744934i \(-0.267519\pi\)
0.667138 + 0.744934i \(0.267519\pi\)
\(240\) 0 0
\(241\) 23.7990 1.53303 0.766514 0.642228i \(-0.221990\pi\)
0.766514 + 0.642228i \(0.221990\pi\)
\(242\) −2.14214 −0.137702
\(243\) 0 0
\(244\) −15.5147 −0.993228
\(245\) −1.00000 −0.0638877
\(246\) 0 0
\(247\) −1.82843 −0.116340
\(248\) −9.51472 −0.604185
\(249\) 0 0
\(250\) −0.414214 −0.0261972
\(251\) 30.1421 1.90255 0.951277 0.308336i \(-0.0997723\pi\)
0.951277 + 0.308336i \(0.0997723\pi\)
\(252\) 0 0
\(253\) −11.6569 −0.732860
\(254\) 2.21320 0.138869
\(255\) 0 0
\(256\) 3.97056 0.248160
\(257\) −17.6569 −1.10140 −0.550702 0.834702i \(-0.685640\pi\)
−0.550702 + 0.834702i \(0.685640\pi\)
\(258\) 0 0
\(259\) −8.48528 −0.527250
\(260\) −0.757359 −0.0469694
\(261\) 0 0
\(262\) 6.68629 0.413080
\(263\) 7.65685 0.472142 0.236071 0.971736i \(-0.424140\pi\)
0.236071 + 0.971736i \(0.424140\pi\)
\(264\) 0 0
\(265\) 8.89949 0.546692
\(266\) −1.82843 −0.112108
\(267\) 0 0
\(268\) −3.97056 −0.242541
\(269\) 14.0000 0.853595 0.426798 0.904347i \(-0.359642\pi\)
0.426798 + 0.904347i \(0.359642\pi\)
\(270\) 0 0
\(271\) 21.2426 1.29040 0.645199 0.764014i \(-0.276774\pi\)
0.645199 + 0.764014i \(0.276774\pi\)
\(272\) 2.48528 0.150692
\(273\) 0 0
\(274\) 2.31371 0.139776
\(275\) 2.41421 0.145583
\(276\) 0 0
\(277\) −15.6569 −0.940729 −0.470365 0.882472i \(-0.655878\pi\)
−0.470365 + 0.882472i \(0.655878\pi\)
\(278\) −0.544156 −0.0326363
\(279\) 0 0
\(280\) −1.58579 −0.0947689
\(281\) −16.3431 −0.974950 −0.487475 0.873137i \(-0.662082\pi\)
−0.487475 + 0.873137i \(0.662082\pi\)
\(282\) 0 0
\(283\) 4.48528 0.266622 0.133311 0.991074i \(-0.457439\pi\)
0.133311 + 0.991074i \(0.457439\pi\)
\(284\) 3.65685 0.216994
\(285\) 0 0
\(286\) −0.414214 −0.0244930
\(287\) −2.17157 −0.128184
\(288\) 0 0
\(289\) −16.3137 −0.959630
\(290\) −1.65685 −0.0972938
\(291\) 0 0
\(292\) −22.0711 −1.29161
\(293\) 1.51472 0.0884908 0.0442454 0.999021i \(-0.485912\pi\)
0.0442454 + 0.999021i \(0.485912\pi\)
\(294\) 0 0
\(295\) 10.4853 0.610477
\(296\) −13.4558 −0.782105
\(297\) 0 0
\(298\) 9.02944 0.523061
\(299\) 2.00000 0.115663
\(300\) 0 0
\(301\) −4.65685 −0.268417
\(302\) −0.284271 −0.0163580
\(303\) 0 0
\(304\) 13.2426 0.759518
\(305\) −8.48528 −0.485866
\(306\) 0 0
\(307\) 2.48528 0.141843 0.0709213 0.997482i \(-0.477406\pi\)
0.0709213 + 0.997482i \(0.477406\pi\)
\(308\) 4.41421 0.251523
\(309\) 0 0
\(310\) −2.48528 −0.141154
\(311\) −25.6569 −1.45487 −0.727433 0.686178i \(-0.759287\pi\)
−0.727433 + 0.686178i \(0.759287\pi\)
\(312\) 0 0
\(313\) −9.38478 −0.530459 −0.265229 0.964185i \(-0.585448\pi\)
−0.265229 + 0.964185i \(0.585448\pi\)
\(314\) 3.79899 0.214389
\(315\) 0 0
\(316\) −16.7696 −0.943361
\(317\) −25.5858 −1.43704 −0.718520 0.695506i \(-0.755180\pi\)
−0.718520 + 0.695506i \(0.755180\pi\)
\(318\) 0 0
\(319\) 9.65685 0.540680
\(320\) 4.17157 0.233198
\(321\) 0 0
\(322\) 2.00000 0.111456
\(323\) 3.65685 0.203473
\(324\) 0 0
\(325\) −0.414214 −0.0229764
\(326\) 7.31371 0.405069
\(327\) 0 0
\(328\) −3.44365 −0.190144
\(329\) −9.48528 −0.522940
\(330\) 0 0
\(331\) 6.00000 0.329790 0.164895 0.986311i \(-0.447272\pi\)
0.164895 + 0.986311i \(0.447272\pi\)
\(332\) 17.3431 0.951829
\(333\) 0 0
\(334\) −4.68629 −0.256422
\(335\) −2.17157 −0.118646
\(336\) 0 0
\(337\) −16.6274 −0.905753 −0.452877 0.891573i \(-0.649602\pi\)
−0.452877 + 0.891573i \(0.649602\pi\)
\(338\) −5.31371 −0.289028
\(339\) 0 0
\(340\) 1.51472 0.0821472
\(341\) 14.4853 0.784422
\(342\) 0 0
\(343\) −1.00000 −0.0539949
\(344\) −7.38478 −0.398160
\(345\) 0 0
\(346\) 3.02944 0.162864
\(347\) −8.82843 −0.473935 −0.236967 0.971518i \(-0.576153\pi\)
−0.236967 + 0.971518i \(0.576153\pi\)
\(348\) 0 0
\(349\) 13.7990 0.738643 0.369321 0.929302i \(-0.379590\pi\)
0.369321 + 0.929302i \(0.379590\pi\)
\(350\) −0.414214 −0.0221406
\(351\) 0 0
\(352\) 10.6569 0.568012
\(353\) 2.14214 0.114014 0.0570072 0.998374i \(-0.481844\pi\)
0.0570072 + 0.998374i \(0.481844\pi\)
\(354\) 0 0
\(355\) 2.00000 0.106149
\(356\) 4.85786 0.257466
\(357\) 0 0
\(358\) −4.85786 −0.256746
\(359\) 30.6985 1.62020 0.810102 0.586289i \(-0.199412\pi\)
0.810102 + 0.586289i \(0.199412\pi\)
\(360\) 0 0
\(361\) 0.485281 0.0255411
\(362\) −2.34315 −0.123153
\(363\) 0 0
\(364\) −0.757359 −0.0396964
\(365\) −12.0711 −0.631829
\(366\) 0 0
\(367\) 26.0000 1.35719 0.678594 0.734513i \(-0.262589\pi\)
0.678594 + 0.734513i \(0.262589\pi\)
\(368\) −14.4853 −0.755097
\(369\) 0 0
\(370\) −3.51472 −0.182722
\(371\) 8.89949 0.462039
\(372\) 0 0
\(373\) −14.9706 −0.775146 −0.387573 0.921839i \(-0.626687\pi\)
−0.387573 + 0.921839i \(0.626687\pi\)
\(374\) 0.828427 0.0428369
\(375\) 0 0
\(376\) −15.0416 −0.775713
\(377\) −1.65685 −0.0853323
\(378\) 0 0
\(379\) −34.2843 −1.76106 −0.880532 0.473986i \(-0.842815\pi\)
−0.880532 + 0.473986i \(0.842815\pi\)
\(380\) 8.07107 0.414037
\(381\) 0 0
\(382\) 2.45584 0.125652
\(383\) −21.6569 −1.10661 −0.553307 0.832978i \(-0.686634\pi\)
−0.553307 + 0.832978i \(0.686634\pi\)
\(384\) 0 0
\(385\) 2.41421 0.123040
\(386\) −9.31371 −0.474055
\(387\) 0 0
\(388\) 25.8579 1.31273
\(389\) −5.31371 −0.269416 −0.134708 0.990885i \(-0.543010\pi\)
−0.134708 + 0.990885i \(0.543010\pi\)
\(390\) 0 0
\(391\) −4.00000 −0.202289
\(392\) −1.58579 −0.0800943
\(393\) 0 0
\(394\) 2.85786 0.143977
\(395\) −9.17157 −0.461472
\(396\) 0 0
\(397\) 9.17157 0.460308 0.230154 0.973154i \(-0.426077\pi\)
0.230154 + 0.973154i \(0.426077\pi\)
\(398\) 0.171573 0.00860017
\(399\) 0 0
\(400\) 3.00000 0.150000
\(401\) 33.7990 1.68784 0.843921 0.536468i \(-0.180242\pi\)
0.843921 + 0.536468i \(0.180242\pi\)
\(402\) 0 0
\(403\) −2.48528 −0.123801
\(404\) −25.9117 −1.28915
\(405\) 0 0
\(406\) −1.65685 −0.0822283
\(407\) 20.4853 1.01542
\(408\) 0 0
\(409\) 19.3137 0.955001 0.477501 0.878631i \(-0.341543\pi\)
0.477501 + 0.878631i \(0.341543\pi\)
\(410\) −0.899495 −0.0444229
\(411\) 0 0
\(412\) −9.45584 −0.465856
\(413\) 10.4853 0.515947
\(414\) 0 0
\(415\) 9.48528 0.465614
\(416\) −1.82843 −0.0896460
\(417\) 0 0
\(418\) 4.41421 0.215906
\(419\) 8.82843 0.431297 0.215648 0.976471i \(-0.430813\pi\)
0.215648 + 0.976471i \(0.430813\pi\)
\(420\) 0 0
\(421\) −7.00000 −0.341159 −0.170580 0.985344i \(-0.554564\pi\)
−0.170580 + 0.985344i \(0.554564\pi\)
\(422\) −6.00000 −0.292075
\(423\) 0 0
\(424\) 14.1127 0.685373
\(425\) 0.828427 0.0401846
\(426\) 0 0
\(427\) −8.48528 −0.410632
\(428\) 11.8579 0.573172
\(429\) 0 0
\(430\) −1.92893 −0.0930214
\(431\) 33.5858 1.61777 0.808885 0.587967i \(-0.200071\pi\)
0.808885 + 0.587967i \(0.200071\pi\)
\(432\) 0 0
\(433\) 23.8701 1.14712 0.573561 0.819163i \(-0.305562\pi\)
0.573561 + 0.819163i \(0.305562\pi\)
\(434\) −2.48528 −0.119297
\(435\) 0 0
\(436\) 24.6569 1.18085
\(437\) −21.3137 −1.01957
\(438\) 0 0
\(439\) 19.2426 0.918401 0.459201 0.888333i \(-0.348136\pi\)
0.459201 + 0.888333i \(0.348136\pi\)
\(440\) 3.82843 0.182513
\(441\) 0 0
\(442\) −0.142136 −0.00676070
\(443\) −40.9706 −1.94657 −0.973285 0.229600i \(-0.926258\pi\)
−0.973285 + 0.229600i \(0.926258\pi\)
\(444\) 0 0
\(445\) 2.65685 0.125947
\(446\) 2.34315 0.110951
\(447\) 0 0
\(448\) 4.17157 0.197088
\(449\) 16.8284 0.794183 0.397091 0.917779i \(-0.370020\pi\)
0.397091 + 0.917779i \(0.370020\pi\)
\(450\) 0 0
\(451\) 5.24264 0.246866
\(452\) 20.5563 0.966889
\(453\) 0 0
\(454\) 3.10051 0.145514
\(455\) −0.414214 −0.0194186
\(456\) 0 0
\(457\) −1.85786 −0.0869072 −0.0434536 0.999055i \(-0.513836\pi\)
−0.0434536 + 0.999055i \(0.513836\pi\)
\(458\) 7.31371 0.341747
\(459\) 0 0
\(460\) −8.82843 −0.411628
\(461\) −31.6274 −1.47304 −0.736518 0.676418i \(-0.763531\pi\)
−0.736518 + 0.676418i \(0.763531\pi\)
\(462\) 0 0
\(463\) 11.3431 0.527161 0.263580 0.964637i \(-0.415097\pi\)
0.263580 + 0.964637i \(0.415097\pi\)
\(464\) 12.0000 0.557086
\(465\) 0 0
\(466\) −6.85786 −0.317684
\(467\) 9.65685 0.446866 0.223433 0.974719i \(-0.428274\pi\)
0.223433 + 0.974719i \(0.428274\pi\)
\(468\) 0 0
\(469\) −2.17157 −0.100274
\(470\) −3.92893 −0.181228
\(471\) 0 0
\(472\) 16.6274 0.765339
\(473\) 11.2426 0.516937
\(474\) 0 0
\(475\) 4.41421 0.202538
\(476\) 1.51472 0.0694270
\(477\) 0 0
\(478\) 8.54416 0.390801
\(479\) −2.14214 −0.0978767 −0.0489383 0.998802i \(-0.515584\pi\)
−0.0489383 + 0.998802i \(0.515584\pi\)
\(480\) 0 0
\(481\) −3.51472 −0.160257
\(482\) 9.85786 0.449013
\(483\) 0 0
\(484\) 9.45584 0.429811
\(485\) 14.1421 0.642161
\(486\) 0 0
\(487\) 7.68629 0.348299 0.174150 0.984719i \(-0.444282\pi\)
0.174150 + 0.984719i \(0.444282\pi\)
\(488\) −13.4558 −0.609117
\(489\) 0 0
\(490\) −0.414214 −0.0187123
\(491\) −32.6274 −1.47245 −0.736227 0.676734i \(-0.763395\pi\)
−0.736227 + 0.676734i \(0.763395\pi\)
\(492\) 0 0
\(493\) 3.31371 0.149242
\(494\) −0.757359 −0.0340752
\(495\) 0 0
\(496\) 18.0000 0.808224
\(497\) 2.00000 0.0897123
\(498\) 0 0
\(499\) 39.7990 1.78165 0.890824 0.454349i \(-0.150128\pi\)
0.890824 + 0.454349i \(0.150128\pi\)
\(500\) 1.82843 0.0817697
\(501\) 0 0
\(502\) 12.4853 0.557245
\(503\) −9.62742 −0.429265 −0.214633 0.976695i \(-0.568855\pi\)
−0.214633 + 0.976695i \(0.568855\pi\)
\(504\) 0 0
\(505\) −14.1716 −0.630627
\(506\) −4.82843 −0.214650
\(507\) 0 0
\(508\) −9.76955 −0.433454
\(509\) −15.6569 −0.693978 −0.346989 0.937869i \(-0.612796\pi\)
−0.346989 + 0.937869i \(0.612796\pi\)
\(510\) 0 0
\(511\) −12.0711 −0.533993
\(512\) 22.7574 1.00574
\(513\) 0 0
\(514\) −7.31371 −0.322594
\(515\) −5.17157 −0.227887
\(516\) 0 0
\(517\) 22.8995 1.00712
\(518\) −3.51472 −0.154428
\(519\) 0 0
\(520\) −0.656854 −0.0288050
\(521\) −10.5147 −0.460658 −0.230329 0.973113i \(-0.573980\pi\)
−0.230329 + 0.973113i \(0.573980\pi\)
\(522\) 0 0
\(523\) 26.8284 1.17313 0.586563 0.809904i \(-0.300481\pi\)
0.586563 + 0.809904i \(0.300481\pi\)
\(524\) −29.5147 −1.28936
\(525\) 0 0
\(526\) 3.17157 0.138287
\(527\) 4.97056 0.216521
\(528\) 0 0
\(529\) 0.313708 0.0136395
\(530\) 3.68629 0.160122
\(531\) 0 0
\(532\) 8.07107 0.349925
\(533\) −0.899495 −0.0389615
\(534\) 0 0
\(535\) 6.48528 0.280383
\(536\) −3.44365 −0.148743
\(537\) 0 0
\(538\) 5.79899 0.250012
\(539\) 2.41421 0.103988
\(540\) 0 0
\(541\) 17.6274 0.757862 0.378931 0.925425i \(-0.376292\pi\)
0.378931 + 0.925425i \(0.376292\pi\)
\(542\) 8.79899 0.377949
\(543\) 0 0
\(544\) 3.65685 0.156786
\(545\) 13.4853 0.577646
\(546\) 0 0
\(547\) 16.2843 0.696265 0.348133 0.937445i \(-0.386816\pi\)
0.348133 + 0.937445i \(0.386816\pi\)
\(548\) −10.2132 −0.436286
\(549\) 0 0
\(550\) 1.00000 0.0426401
\(551\) 17.6569 0.752207
\(552\) 0 0
\(553\) −9.17157 −0.390015
\(554\) −6.48528 −0.275533
\(555\) 0 0
\(556\) 2.40202 0.101868
\(557\) −4.20101 −0.178003 −0.0890013 0.996032i \(-0.528368\pi\)
−0.0890013 + 0.996032i \(0.528368\pi\)
\(558\) 0 0
\(559\) −1.92893 −0.0815851
\(560\) 3.00000 0.126773
\(561\) 0 0
\(562\) −6.76955 −0.285556
\(563\) 5.97056 0.251629 0.125815 0.992054i \(-0.459846\pi\)
0.125815 + 0.992054i \(0.459846\pi\)
\(564\) 0 0
\(565\) 11.2426 0.472981
\(566\) 1.85786 0.0780919
\(567\) 0 0
\(568\) 3.17157 0.133076
\(569\) −31.3137 −1.31274 −0.656369 0.754440i \(-0.727909\pi\)
−0.656369 + 0.754440i \(0.727909\pi\)
\(570\) 0 0
\(571\) −4.20101 −0.175807 −0.0879034 0.996129i \(-0.528017\pi\)
−0.0879034 + 0.996129i \(0.528017\pi\)
\(572\) 1.82843 0.0764504
\(573\) 0 0
\(574\) −0.899495 −0.0375442
\(575\) −4.82843 −0.201359
\(576\) 0 0
\(577\) −19.7279 −0.821284 −0.410642 0.911797i \(-0.634695\pi\)
−0.410642 + 0.911797i \(0.634695\pi\)
\(578\) −6.75736 −0.281069
\(579\) 0 0
\(580\) 7.31371 0.303685
\(581\) 9.48528 0.393516
\(582\) 0 0
\(583\) −21.4853 −0.889829
\(584\) −19.1421 −0.792107
\(585\) 0 0
\(586\) 0.627417 0.0259184
\(587\) −35.3137 −1.45755 −0.728776 0.684752i \(-0.759911\pi\)
−0.728776 + 0.684752i \(0.759911\pi\)
\(588\) 0 0
\(589\) 26.4853 1.09131
\(590\) 4.34315 0.178804
\(591\) 0 0
\(592\) 25.4558 1.04623
\(593\) 38.1421 1.56631 0.783155 0.621827i \(-0.213609\pi\)
0.783155 + 0.621827i \(0.213609\pi\)
\(594\) 0 0
\(595\) 0.828427 0.0339622
\(596\) −39.8579 −1.63264
\(597\) 0 0
\(598\) 0.828427 0.0338769
\(599\) −24.8995 −1.01737 −0.508683 0.860954i \(-0.669867\pi\)
−0.508683 + 0.860954i \(0.669867\pi\)
\(600\) 0 0
\(601\) −20.6274 −0.841410 −0.420705 0.907198i \(-0.638217\pi\)
−0.420705 + 0.907198i \(0.638217\pi\)
\(602\) −1.92893 −0.0786174
\(603\) 0 0
\(604\) 1.25483 0.0510585
\(605\) 5.17157 0.210254
\(606\) 0 0
\(607\) 23.5147 0.954433 0.477216 0.878786i \(-0.341646\pi\)
0.477216 + 0.878786i \(0.341646\pi\)
\(608\) 19.4853 0.790233
\(609\) 0 0
\(610\) −3.51472 −0.142307
\(611\) −3.92893 −0.158948
\(612\) 0 0
\(613\) −29.9411 −1.20931 −0.604655 0.796487i \(-0.706689\pi\)
−0.604655 + 0.796487i \(0.706689\pi\)
\(614\) 1.02944 0.0415447
\(615\) 0 0
\(616\) 3.82843 0.154252
\(617\) 48.7696 1.96339 0.981694 0.190464i \(-0.0609993\pi\)
0.981694 + 0.190464i \(0.0609993\pi\)
\(618\) 0 0
\(619\) 16.2132 0.651664 0.325832 0.945428i \(-0.394356\pi\)
0.325832 + 0.945428i \(0.394356\pi\)
\(620\) 10.9706 0.440588
\(621\) 0 0
\(622\) −10.6274 −0.426121
\(623\) 2.65685 0.106445
\(624\) 0 0
\(625\) 1.00000 0.0400000
\(626\) −3.88730 −0.155368
\(627\) 0 0
\(628\) −16.7696 −0.669178
\(629\) 7.02944 0.280282
\(630\) 0 0
\(631\) 46.6274 1.85621 0.928104 0.372321i \(-0.121438\pi\)
0.928104 + 0.372321i \(0.121438\pi\)
\(632\) −14.5442 −0.578535
\(633\) 0 0
\(634\) −10.5980 −0.420900
\(635\) −5.34315 −0.212036
\(636\) 0 0
\(637\) −0.414214 −0.0164117
\(638\) 4.00000 0.158362
\(639\) 0 0
\(640\) 10.5563 0.417276
\(641\) −16.4853 −0.651129 −0.325565 0.945520i \(-0.605554\pi\)
−0.325565 + 0.945520i \(0.605554\pi\)
\(642\) 0 0
\(643\) −44.7696 −1.76554 −0.882769 0.469807i \(-0.844324\pi\)
−0.882769 + 0.469807i \(0.844324\pi\)
\(644\) −8.82843 −0.347889
\(645\) 0 0
\(646\) 1.51472 0.0595958
\(647\) 36.6569 1.44113 0.720565 0.693388i \(-0.243883\pi\)
0.720565 + 0.693388i \(0.243883\pi\)
\(648\) 0 0
\(649\) −25.3137 −0.993650
\(650\) −0.171573 −0.00672964
\(651\) 0 0
\(652\) −32.2843 −1.26435
\(653\) 47.7990 1.87052 0.935260 0.353963i \(-0.115166\pi\)
0.935260 + 0.353963i \(0.115166\pi\)
\(654\) 0 0
\(655\) −16.1421 −0.630725
\(656\) 6.51472 0.254357
\(657\) 0 0
\(658\) −3.92893 −0.153166
\(659\) 23.6569 0.921540 0.460770 0.887520i \(-0.347573\pi\)
0.460770 + 0.887520i \(0.347573\pi\)
\(660\) 0 0
\(661\) −47.7990 −1.85917 −0.929583 0.368614i \(-0.879832\pi\)
−0.929583 + 0.368614i \(0.879832\pi\)
\(662\) 2.48528 0.0965932
\(663\) 0 0
\(664\) 15.0416 0.583728
\(665\) 4.41421 0.171176
\(666\) 0 0
\(667\) −19.3137 −0.747830
\(668\) 20.6863 0.800377
\(669\) 0 0
\(670\) −0.899495 −0.0347505
\(671\) 20.4853 0.790826
\(672\) 0 0
\(673\) 8.82843 0.340311 0.170155 0.985417i \(-0.445573\pi\)
0.170155 + 0.985417i \(0.445573\pi\)
\(674\) −6.88730 −0.265289
\(675\) 0 0
\(676\) 23.4558 0.902148
\(677\) −42.1421 −1.61965 −0.809827 0.586669i \(-0.800439\pi\)
−0.809827 + 0.586669i \(0.800439\pi\)
\(678\) 0 0
\(679\) 14.1421 0.542725
\(680\) 1.31371 0.0503784
\(681\) 0 0
\(682\) 6.00000 0.229752
\(683\) 32.4853 1.24301 0.621507 0.783408i \(-0.286521\pi\)
0.621507 + 0.783408i \(0.286521\pi\)
\(684\) 0 0
\(685\) −5.58579 −0.213422
\(686\) −0.414214 −0.0158147
\(687\) 0 0
\(688\) 13.9706 0.532623
\(689\) 3.68629 0.140437
\(690\) 0 0
\(691\) −2.55635 −0.0972481 −0.0486241 0.998817i \(-0.515484\pi\)
−0.0486241 + 0.998817i \(0.515484\pi\)
\(692\) −13.3726 −0.508349
\(693\) 0 0
\(694\) −3.65685 −0.138812
\(695\) 1.31371 0.0498318
\(696\) 0 0
\(697\) 1.79899 0.0681416
\(698\) 5.71573 0.216344
\(699\) 0 0
\(700\) 1.82843 0.0691080
\(701\) −39.6569 −1.49782 −0.748909 0.662672i \(-0.769422\pi\)
−0.748909 + 0.662672i \(0.769422\pi\)
\(702\) 0 0
\(703\) 37.4558 1.41267
\(704\) −10.0711 −0.379568
\(705\) 0 0
\(706\) 0.887302 0.0333940
\(707\) −14.1716 −0.532977
\(708\) 0 0
\(709\) −43.6274 −1.63846 −0.819231 0.573464i \(-0.805599\pi\)
−0.819231 + 0.573464i \(0.805599\pi\)
\(710\) 0.828427 0.0310903
\(711\) 0 0
\(712\) 4.21320 0.157896
\(713\) −28.9706 −1.08496
\(714\) 0 0
\(715\) 1.00000 0.0373979
\(716\) 21.4437 0.801387
\(717\) 0 0
\(718\) 12.7157 0.474547
\(719\) −3.79899 −0.141678 −0.0708392 0.997488i \(-0.522568\pi\)
−0.0708392 + 0.997488i \(0.522568\pi\)
\(720\) 0 0
\(721\) −5.17157 −0.192599
\(722\) 0.201010 0.00748082
\(723\) 0 0
\(724\) 10.3431 0.384400
\(725\) 4.00000 0.148556
\(726\) 0 0
\(727\) −48.0833 −1.78331 −0.891655 0.452716i \(-0.850455\pi\)
−0.891655 + 0.452716i \(0.850455\pi\)
\(728\) −0.656854 −0.0243446
\(729\) 0 0
\(730\) −5.00000 −0.185058
\(731\) 3.85786 0.142688
\(732\) 0 0
\(733\) −32.7574 −1.20992 −0.604960 0.796256i \(-0.706811\pi\)
−0.604960 + 0.796256i \(0.706811\pi\)
\(734\) 10.7696 0.397511
\(735\) 0 0
\(736\) −21.3137 −0.785634
\(737\) 5.24264 0.193115
\(738\) 0 0
\(739\) −40.8284 −1.50190 −0.750949 0.660360i \(-0.770404\pi\)
−0.750949 + 0.660360i \(0.770404\pi\)
\(740\) 15.5147 0.570332
\(741\) 0 0
\(742\) 3.68629 0.135328
\(743\) −0.343146 −0.0125888 −0.00629440 0.999980i \(-0.502004\pi\)
−0.00629440 + 0.999980i \(0.502004\pi\)
\(744\) 0 0
\(745\) −21.7990 −0.798653
\(746\) −6.20101 −0.227035
\(747\) 0 0
\(748\) −3.65685 −0.133708
\(749\) 6.48528 0.236967
\(750\) 0 0
\(751\) −15.1716 −0.553619 −0.276809 0.960925i \(-0.589277\pi\)
−0.276809 + 0.960925i \(0.589277\pi\)
\(752\) 28.4558 1.03768
\(753\) 0 0
\(754\) −0.686292 −0.0249933
\(755\) 0.686292 0.0249767
\(756\) 0 0
\(757\) −21.5147 −0.781966 −0.390983 0.920398i \(-0.627865\pi\)
−0.390983 + 0.920398i \(0.627865\pi\)
\(758\) −14.2010 −0.515804
\(759\) 0 0
\(760\) 7.00000 0.253917
\(761\) −20.6274 −0.747743 −0.373872 0.927480i \(-0.621970\pi\)
−0.373872 + 0.927480i \(0.621970\pi\)
\(762\) 0 0
\(763\) 13.4853 0.488200
\(764\) −10.8406 −0.392200
\(765\) 0 0
\(766\) −8.97056 −0.324120
\(767\) 4.34315 0.156822
\(768\) 0 0
\(769\) −26.7696 −0.965335 −0.482667 0.875804i \(-0.660332\pi\)
−0.482667 + 0.875804i \(0.660332\pi\)
\(770\) 1.00000 0.0360375
\(771\) 0 0
\(772\) 41.1127 1.47968
\(773\) 15.8579 0.570368 0.285184 0.958473i \(-0.407945\pi\)
0.285184 + 0.958473i \(0.407945\pi\)
\(774\) 0 0
\(775\) 6.00000 0.215526
\(776\) 22.4264 0.805061
\(777\) 0 0
\(778\) −2.20101 −0.0789100
\(779\) 9.58579 0.343446
\(780\) 0 0
\(781\) −4.82843 −0.172775
\(782\) −1.65685 −0.0592490
\(783\) 0 0
\(784\) 3.00000 0.107143
\(785\) −9.17157 −0.327347
\(786\) 0 0
\(787\) −35.7990 −1.27610 −0.638048 0.769997i \(-0.720258\pi\)
−0.638048 + 0.769997i \(0.720258\pi\)
\(788\) −12.6152 −0.449399
\(789\) 0 0
\(790\) −3.79899 −0.135162
\(791\) 11.2426 0.399742
\(792\) 0 0
\(793\) −3.51472 −0.124811
\(794\) 3.79899 0.134821
\(795\) 0 0
\(796\) −0.757359 −0.0268439
\(797\) −16.0000 −0.566749 −0.283375 0.959009i \(-0.591454\pi\)
−0.283375 + 0.959009i \(0.591454\pi\)
\(798\) 0 0
\(799\) 7.85786 0.277991
\(800\) 4.41421 0.156066
\(801\) 0 0
\(802\) 14.0000 0.494357
\(803\) 29.1421 1.02840
\(804\) 0 0
\(805\) −4.82843 −0.170180
\(806\) −1.02944 −0.0362604
\(807\) 0 0
\(808\) −22.4731 −0.790600
\(809\) 44.0833 1.54988 0.774942 0.632032i \(-0.217779\pi\)
0.774942 + 0.632032i \(0.217779\pi\)
\(810\) 0 0
\(811\) 17.3848 0.610462 0.305231 0.952278i \(-0.401266\pi\)
0.305231 + 0.952278i \(0.401266\pi\)
\(812\) 7.31371 0.256661
\(813\) 0 0
\(814\) 8.48528 0.297409
\(815\) −17.6569 −0.618493
\(816\) 0 0
\(817\) 20.5563 0.719176
\(818\) 8.00000 0.279713
\(819\) 0 0
\(820\) 3.97056 0.138658
\(821\) −42.9706 −1.49968 −0.749841 0.661618i \(-0.769870\pi\)
−0.749841 + 0.661618i \(0.769870\pi\)
\(822\) 0 0
\(823\) −27.2843 −0.951070 −0.475535 0.879697i \(-0.657745\pi\)
−0.475535 + 0.879697i \(0.657745\pi\)
\(824\) −8.20101 −0.285696
\(825\) 0 0
\(826\) 4.34315 0.151117
\(827\) −19.5147 −0.678593 −0.339297 0.940679i \(-0.610189\pi\)
−0.339297 + 0.940679i \(0.610189\pi\)
\(828\) 0 0
\(829\) −26.8284 −0.931790 −0.465895 0.884840i \(-0.654268\pi\)
−0.465895 + 0.884840i \(0.654268\pi\)
\(830\) 3.92893 0.136375
\(831\) 0 0
\(832\) 1.72792 0.0599049
\(833\) 0.828427 0.0287033
\(834\) 0 0
\(835\) 11.3137 0.391527
\(836\) −19.4853 −0.673913
\(837\) 0 0
\(838\) 3.65685 0.126324
\(839\) −13.7990 −0.476394 −0.238197 0.971217i \(-0.576556\pi\)
−0.238197 + 0.971217i \(0.576556\pi\)
\(840\) 0 0
\(841\) −13.0000 −0.448276
\(842\) −2.89949 −0.0999232
\(843\) 0 0
\(844\) 26.4853 0.911661
\(845\) 12.8284 0.441311
\(846\) 0 0
\(847\) 5.17157 0.177697
\(848\) −26.6985 −0.916830
\(849\) 0 0
\(850\) 0.343146 0.0117698
\(851\) −40.9706 −1.40445
\(852\) 0 0
\(853\) 12.4853 0.427488 0.213744 0.976890i \(-0.431434\pi\)
0.213744 + 0.976890i \(0.431434\pi\)
\(854\) −3.51472 −0.120271
\(855\) 0 0
\(856\) 10.2843 0.351509
\(857\) 5.31371 0.181513 0.0907564 0.995873i \(-0.471072\pi\)
0.0907564 + 0.995873i \(0.471072\pi\)
\(858\) 0 0
\(859\) 32.3553 1.10395 0.551975 0.833861i \(-0.313874\pi\)
0.551975 + 0.833861i \(0.313874\pi\)
\(860\) 8.51472 0.290349
\(861\) 0 0
\(862\) 13.9117 0.473834
\(863\) 28.3431 0.964812 0.482406 0.875948i \(-0.339763\pi\)
0.482406 + 0.875948i \(0.339763\pi\)
\(864\) 0 0
\(865\) −7.31371 −0.248674
\(866\) 9.88730 0.335984
\(867\) 0 0
\(868\) 10.9706 0.372365
\(869\) 22.1421 0.751121
\(870\) 0 0
\(871\) −0.899495 −0.0304782
\(872\) 21.3848 0.724180
\(873\) 0 0
\(874\) −8.82843 −0.298626
\(875\) 1.00000 0.0338062
\(876\) 0 0
\(877\) −29.1716 −0.985054 −0.492527 0.870297i \(-0.663927\pi\)
−0.492527 + 0.870297i \(0.663927\pi\)
\(878\) 7.97056 0.268993
\(879\) 0 0
\(880\) −7.24264 −0.244149
\(881\) 4.34315 0.146324 0.0731621 0.997320i \(-0.476691\pi\)
0.0731621 + 0.997320i \(0.476691\pi\)
\(882\) 0 0
\(883\) 13.6569 0.459590 0.229795 0.973239i \(-0.426194\pi\)
0.229795 + 0.973239i \(0.426194\pi\)
\(884\) 0.627417 0.0211023
\(885\) 0 0
\(886\) −16.9706 −0.570137
\(887\) −55.7696 −1.87256 −0.936279 0.351257i \(-0.885754\pi\)
−0.936279 + 0.351257i \(0.885754\pi\)
\(888\) 0 0
\(889\) −5.34315 −0.179203
\(890\) 1.10051 0.0368890
\(891\) 0 0
\(892\) −10.3431 −0.346314
\(893\) 41.8701 1.40113
\(894\) 0 0
\(895\) 11.7279 0.392021
\(896\) 10.5563 0.352663
\(897\) 0 0
\(898\) 6.97056 0.232611
\(899\) 24.0000 0.800445
\(900\) 0 0
\(901\) −7.37258 −0.245616
\(902\) 2.17157 0.0723055
\(903\) 0 0
\(904\) 17.8284 0.592965
\(905\) 5.65685 0.188040
\(906\) 0 0
\(907\) −43.4853 −1.44391 −0.721953 0.691943i \(-0.756755\pi\)
−0.721953 + 0.691943i \(0.756755\pi\)
\(908\) −13.6863 −0.454196
\(909\) 0 0
\(910\) −0.171573 −0.00568759
\(911\) −46.8406 −1.55190 −0.775949 0.630795i \(-0.782729\pi\)
−0.775949 + 0.630795i \(0.782729\pi\)
\(912\) 0 0
\(913\) −22.8995 −0.757863
\(914\) −0.769553 −0.0254545
\(915\) 0 0
\(916\) −32.2843 −1.06670
\(917\) −16.1421 −0.533060
\(918\) 0 0
\(919\) −36.7696 −1.21292 −0.606458 0.795116i \(-0.707410\pi\)
−0.606458 + 0.795116i \(0.707410\pi\)
\(920\) −7.65685 −0.252439
\(921\) 0 0
\(922\) −13.1005 −0.431442
\(923\) 0.828427 0.0272680
\(924\) 0 0
\(925\) 8.48528 0.278994
\(926\) 4.69848 0.154402
\(927\) 0 0
\(928\) 17.6569 0.579615
\(929\) −43.9706 −1.44263 −0.721314 0.692609i \(-0.756461\pi\)
−0.721314 + 0.692609i \(0.756461\pi\)
\(930\) 0 0
\(931\) 4.41421 0.144670
\(932\) 30.2721 0.991595
\(933\) 0 0
\(934\) 4.00000 0.130884
\(935\) −2.00000 −0.0654070
\(936\) 0 0
\(937\) −0.899495 −0.0293852 −0.0146926 0.999892i \(-0.504677\pi\)
−0.0146926 + 0.999892i \(0.504677\pi\)
\(938\) −0.899495 −0.0293696
\(939\) 0 0
\(940\) 17.3431 0.565671
\(941\) −26.3137 −0.857802 −0.428901 0.903351i \(-0.641099\pi\)
−0.428901 + 0.903351i \(0.641099\pi\)
\(942\) 0 0
\(943\) −10.4853 −0.341448
\(944\) −31.4558 −1.02380
\(945\) 0 0
\(946\) 4.65685 0.151407
\(947\) −41.4558 −1.34713 −0.673567 0.739126i \(-0.735239\pi\)
−0.673567 + 0.739126i \(0.735239\pi\)
\(948\) 0 0
\(949\) −5.00000 −0.162307
\(950\) 1.82843 0.0593220
\(951\) 0 0
\(952\) 1.31371 0.0425775
\(953\) 17.8579 0.578473 0.289236 0.957258i \(-0.406599\pi\)
0.289236 + 0.957258i \(0.406599\pi\)
\(954\) 0 0
\(955\) −5.92893 −0.191856
\(956\) −37.7157 −1.21981
\(957\) 0 0
\(958\) −0.887302 −0.0286674
\(959\) −5.58579 −0.180374
\(960\) 0 0
\(961\) 5.00000 0.161290
\(962\) −1.45584 −0.0469383
\(963\) 0 0
\(964\) −43.5147 −1.40151
\(965\) 22.4853 0.723827
\(966\) 0 0
\(967\) 8.17157 0.262780 0.131390 0.991331i \(-0.458056\pi\)
0.131390 + 0.991331i \(0.458056\pi\)
\(968\) 8.20101 0.263590
\(969\) 0 0
\(970\) 5.85786 0.188085
\(971\) 37.4558 1.20202 0.601008 0.799243i \(-0.294766\pi\)
0.601008 + 0.799243i \(0.294766\pi\)
\(972\) 0 0
\(973\) 1.31371 0.0421156
\(974\) 3.18377 0.102014
\(975\) 0 0
\(976\) 25.4558 0.814822
\(977\) −21.5269 −0.688707 −0.344353 0.938840i \(-0.611902\pi\)
−0.344353 + 0.938840i \(0.611902\pi\)
\(978\) 0 0
\(979\) −6.41421 −0.204999
\(980\) 1.82843 0.0584070
\(981\) 0 0
\(982\) −13.5147 −0.431272
\(983\) 36.9706 1.17918 0.589589 0.807703i \(-0.299290\pi\)
0.589589 + 0.807703i \(0.299290\pi\)
\(984\) 0 0
\(985\) −6.89949 −0.219836
\(986\) 1.37258 0.0437119
\(987\) 0 0
\(988\) 3.34315 0.106360
\(989\) −22.4853 −0.714990
\(990\) 0 0
\(991\) 28.8284 0.915765 0.457883 0.889013i \(-0.348608\pi\)
0.457883 + 0.889013i \(0.348608\pi\)
\(992\) 26.4853 0.840909
\(993\) 0 0
\(994\) 0.828427 0.0262761
\(995\) −0.414214 −0.0131315
\(996\) 0 0
\(997\) −48.4853 −1.53554 −0.767772 0.640723i \(-0.778635\pi\)
−0.767772 + 0.640723i \(0.778635\pi\)
\(998\) 16.4853 0.521832
\(999\) 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 \(a_p\))