Properties

Label 8018.2.a.j.1.1
Level 8018
Weight 2
Character 8018.1
Self dual Yes
Analytic conductor 64.024
Analytic rank 0
Dimension 47
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8018 = 2 \cdot 19 \cdot 211 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8018.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0240523407\)
Analytic rank: \(0\)
Dimension: \(47\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 8018.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{2}\) \(-3.22214 q^{3}\) \(+1.00000 q^{4}\) \(+3.63661 q^{5}\) \(-3.22214 q^{6}\) \(-0.166372 q^{7}\) \(+1.00000 q^{8}\) \(+7.38220 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{2}\) \(-3.22214 q^{3}\) \(+1.00000 q^{4}\) \(+3.63661 q^{5}\) \(-3.22214 q^{6}\) \(-0.166372 q^{7}\) \(+1.00000 q^{8}\) \(+7.38220 q^{9}\) \(+3.63661 q^{10}\) \(+2.07117 q^{11}\) \(-3.22214 q^{12}\) \(+5.70273 q^{13}\) \(-0.166372 q^{14}\) \(-11.7177 q^{15}\) \(+1.00000 q^{16}\) \(-7.23099 q^{17}\) \(+7.38220 q^{18}\) \(-1.00000 q^{19}\) \(+3.63661 q^{20}\) \(+0.536074 q^{21}\) \(+2.07117 q^{22}\) \(-0.228368 q^{23}\) \(-3.22214 q^{24}\) \(+8.22492 q^{25}\) \(+5.70273 q^{26}\) \(-14.1201 q^{27}\) \(-0.166372 q^{28}\) \(+5.83954 q^{29}\) \(-11.7177 q^{30}\) \(-6.23393 q^{31}\) \(+1.00000 q^{32}\) \(-6.67361 q^{33}\) \(-7.23099 q^{34}\) \(-0.605029 q^{35}\) \(+7.38220 q^{36}\) \(+5.72120 q^{37}\) \(-1.00000 q^{38}\) \(-18.3750 q^{39}\) \(+3.63661 q^{40}\) \(+7.52149 q^{41}\) \(+0.536074 q^{42}\) \(+6.52032 q^{43}\) \(+2.07117 q^{44}\) \(+26.8462 q^{45}\) \(-0.228368 q^{46}\) \(+12.3649 q^{47}\) \(-3.22214 q^{48}\) \(-6.97232 q^{49}\) \(+8.22492 q^{50}\) \(+23.2993 q^{51}\) \(+5.70273 q^{52}\) \(-7.72094 q^{53}\) \(-14.1201 q^{54}\) \(+7.53204 q^{55}\) \(-0.166372 q^{56}\) \(+3.22214 q^{57}\) \(+5.83954 q^{58}\) \(+0.482122 q^{59}\) \(-11.7177 q^{60}\) \(+6.01579 q^{61}\) \(-6.23393 q^{62}\) \(-1.22819 q^{63}\) \(+1.00000 q^{64}\) \(+20.7386 q^{65}\) \(-6.67361 q^{66}\) \(+3.78945 q^{67}\) \(-7.23099 q^{68}\) \(+0.735834 q^{69}\) \(-0.605029 q^{70}\) \(+9.35881 q^{71}\) \(+7.38220 q^{72}\) \(-5.89786 q^{73}\) \(+5.72120 q^{74}\) \(-26.5019 q^{75}\) \(-1.00000 q^{76}\) \(-0.344584 q^{77}\) \(-18.3750 q^{78}\) \(-12.8417 q^{79}\) \(+3.63661 q^{80}\) \(+23.3503 q^{81}\) \(+7.52149 q^{82}\) \(-8.79057 q^{83}\) \(+0.536074 q^{84}\) \(-26.2963 q^{85}\) \(+6.52032 q^{86}\) \(-18.8158 q^{87}\) \(+2.07117 q^{88}\) \(+18.4932 q^{89}\) \(+26.8462 q^{90}\) \(-0.948774 q^{91}\) \(-0.228368 q^{92}\) \(+20.0866 q^{93}\) \(+12.3649 q^{94}\) \(-3.63661 q^{95}\) \(-3.22214 q^{96}\) \(-0.277043 q^{97}\) \(-6.97232 q^{98}\) \(+15.2898 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(47q \) \(\mathstrut +\mathstrut 47q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 47q^{4} \) \(\mathstrut +\mathstrut 15q^{5} \) \(\mathstrut +\mathstrut 10q^{6} \) \(\mathstrut +\mathstrut 47q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut 15q^{10} \) \(\mathstrut +\mathstrut 17q^{11} \) \(\mathstrut +\mathstrut 10q^{12} \) \(\mathstrut +\mathstrut 27q^{13} \) \(\mathstrut +\mathstrut 10q^{15} \) \(\mathstrut +\mathstrut 47q^{16} \) \(\mathstrut +\mathstrut 16q^{17} \) \(\mathstrut +\mathstrut 69q^{18} \) \(\mathstrut -\mathstrut 47q^{19} \) \(\mathstrut +\mathstrut 15q^{20} \) \(\mathstrut +\mathstrut 26q^{21} \) \(\mathstrut +\mathstrut 17q^{22} \) \(\mathstrut +\mathstrut 24q^{23} \) \(\mathstrut +\mathstrut 10q^{24} \) \(\mathstrut +\mathstrut 86q^{25} \) \(\mathstrut +\mathstrut 27q^{26} \) \(\mathstrut +\mathstrut 43q^{27} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 10q^{30} \) \(\mathstrut +\mathstrut 21q^{31} \) \(\mathstrut +\mathstrut 47q^{32} \) \(\mathstrut +\mathstrut 18q^{33} \) \(\mathstrut +\mathstrut 16q^{34} \) \(\mathstrut +\mathstrut 24q^{35} \) \(\mathstrut +\mathstrut 69q^{36} \) \(\mathstrut +\mathstrut 78q^{37} \) \(\mathstrut -\mathstrut 47q^{38} \) \(\mathstrut -\mathstrut 4q^{39} \) \(\mathstrut +\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 53q^{41} \) \(\mathstrut +\mathstrut 26q^{42} \) \(\mathstrut +\mathstrut 47q^{43} \) \(\mathstrut +\mathstrut 17q^{44} \) \(\mathstrut +\mathstrut 23q^{45} \) \(\mathstrut +\mathstrut 24q^{46} \) \(\mathstrut +\mathstrut 16q^{47} \) \(\mathstrut +\mathstrut 10q^{48} \) \(\mathstrut +\mathstrut 93q^{49} \) \(\mathstrut +\mathstrut 86q^{50} \) \(\mathstrut +\mathstrut 28q^{51} \) \(\mathstrut +\mathstrut 27q^{52} \) \(\mathstrut +\mathstrut 43q^{53} \) \(\mathstrut +\mathstrut 43q^{54} \) \(\mathstrut +\mathstrut 23q^{55} \) \(\mathstrut -\mathstrut 10q^{57} \) \(\mathstrut +\mathstrut 58q^{58} \) \(\mathstrut +\mathstrut 3q^{59} \) \(\mathstrut +\mathstrut 10q^{60} \) \(\mathstrut +\mathstrut 12q^{61} \) \(\mathstrut +\mathstrut 21q^{62} \) \(\mathstrut -\mathstrut 5q^{63} \) \(\mathstrut +\mathstrut 47q^{64} \) \(\mathstrut +\mathstrut 62q^{65} \) \(\mathstrut +\mathstrut 18q^{66} \) \(\mathstrut +\mathstrut 68q^{67} \) \(\mathstrut +\mathstrut 16q^{68} \) \(\mathstrut +\mathstrut 12q^{69} \) \(\mathstrut +\mathstrut 24q^{70} \) \(\mathstrut -\mathstrut 13q^{71} \) \(\mathstrut +\mathstrut 69q^{72} \) \(\mathstrut +\mathstrut 35q^{73} \) \(\mathstrut +\mathstrut 78q^{74} \) \(\mathstrut +\mathstrut 22q^{75} \) \(\mathstrut -\mathstrut 47q^{76} \) \(\mathstrut +\mathstrut 26q^{77} \) \(\mathstrut -\mathstrut 4q^{78} \) \(\mathstrut +\mathstrut 21q^{79} \) \(\mathstrut +\mathstrut 15q^{80} \) \(\mathstrut +\mathstrut 123q^{81} \) \(\mathstrut +\mathstrut 53q^{82} \) \(\mathstrut +\mathstrut 23q^{83} \) \(\mathstrut +\mathstrut 26q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut +\mathstrut 47q^{86} \) \(\mathstrut +\mathstrut 39q^{87} \) \(\mathstrut +\mathstrut 17q^{88} \) \(\mathstrut +\mathstrut 24q^{89} \) \(\mathstrut +\mathstrut 23q^{90} \) \(\mathstrut +\mathstrut 49q^{91} \) \(\mathstrut +\mathstrut 24q^{92} \) \(\mathstrut +\mathstrut 91q^{93} \) \(\mathstrut +\mathstrut 16q^{94} \) \(\mathstrut -\mathstrut 15q^{95} \) \(\mathstrut +\mathstrut 10q^{96} \) \(\mathstrut +\mathstrut 88q^{97} \) \(\mathstrut +\mathstrut 93q^{98} \) \(\mathstrut +\mathstrut 26q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 1.00000 0.707107
\(3\) −3.22214 −1.86030 −0.930152 0.367174i \(-0.880325\pi\)
−0.930152 + 0.367174i \(0.880325\pi\)
\(4\) 1.00000 0.500000
\(5\) 3.63661 1.62634 0.813170 0.582026i \(-0.197740\pi\)
0.813170 + 0.582026i \(0.197740\pi\)
\(6\) −3.22214 −1.31543
\(7\) −0.166372 −0.0628827 −0.0314413 0.999506i \(-0.510010\pi\)
−0.0314413 + 0.999506i \(0.510010\pi\)
\(8\) 1.00000 0.353553
\(9\) 7.38220 2.46073
\(10\) 3.63661 1.15000
\(11\) 2.07117 0.624481 0.312241 0.950003i \(-0.398920\pi\)
0.312241 + 0.950003i \(0.398920\pi\)
\(12\) −3.22214 −0.930152
\(13\) 5.70273 1.58165 0.790827 0.612040i \(-0.209651\pi\)
0.790827 + 0.612040i \(0.209651\pi\)
\(14\) −0.166372 −0.0444648
\(15\) −11.7177 −3.02549
\(16\) 1.00000 0.250000
\(17\) −7.23099 −1.75377 −0.876886 0.480699i \(-0.840383\pi\)
−0.876886 + 0.480699i \(0.840383\pi\)
\(18\) 7.38220 1.74000
\(19\) −1.00000 −0.229416
\(20\) 3.63661 0.813170
\(21\) 0.536074 0.116981
\(22\) 2.07117 0.441575
\(23\) −0.228368 −0.0476180 −0.0238090 0.999717i \(-0.507579\pi\)
−0.0238090 + 0.999717i \(0.507579\pi\)
\(24\) −3.22214 −0.657717
\(25\) 8.22492 1.64498
\(26\) 5.70273 1.11840
\(27\) −14.1201 −2.71741
\(28\) −0.166372 −0.0314413
\(29\) 5.83954 1.08437 0.542187 0.840258i \(-0.317596\pi\)
0.542187 + 0.840258i \(0.317596\pi\)
\(30\) −11.7177 −2.13934
\(31\) −6.23393 −1.11965 −0.559824 0.828612i \(-0.689131\pi\)
−0.559824 + 0.828612i \(0.689131\pi\)
\(32\) 1.00000 0.176777
\(33\) −6.67361 −1.16173
\(34\) −7.23099 −1.24010
\(35\) −0.605029 −0.102269
\(36\) 7.38220 1.23037
\(37\) 5.72120 0.940559 0.470280 0.882518i \(-0.344153\pi\)
0.470280 + 0.882518i \(0.344153\pi\)
\(38\) −1.00000 −0.162221
\(39\) −18.3750 −2.94236
\(40\) 3.63661 0.574998
\(41\) 7.52149 1.17466 0.587330 0.809348i \(-0.300179\pi\)
0.587330 + 0.809348i \(0.300179\pi\)
\(42\) 0.536074 0.0827180
\(43\) 6.52032 0.994340 0.497170 0.867653i \(-0.334373\pi\)
0.497170 + 0.867653i \(0.334373\pi\)
\(44\) 2.07117 0.312241
\(45\) 26.8462 4.00199
\(46\) −0.228368 −0.0336710
\(47\) 12.3649 1.80360 0.901800 0.432154i \(-0.142246\pi\)
0.901800 + 0.432154i \(0.142246\pi\)
\(48\) −3.22214 −0.465076
\(49\) −6.97232 −0.996046
\(50\) 8.22492 1.16318
\(51\) 23.2993 3.26255
\(52\) 5.70273 0.790827
\(53\) −7.72094 −1.06055 −0.530276 0.847825i \(-0.677912\pi\)
−0.530276 + 0.847825i \(0.677912\pi\)
\(54\) −14.1201 −1.92150
\(55\) 7.53204 1.01562
\(56\) −0.166372 −0.0222324
\(57\) 3.22214 0.426783
\(58\) 5.83954 0.766769
\(59\) 0.482122 0.0627669 0.0313835 0.999507i \(-0.490009\pi\)
0.0313835 + 0.999507i \(0.490009\pi\)
\(60\) −11.7177 −1.51274
\(61\) 6.01579 0.770242 0.385121 0.922866i \(-0.374160\pi\)
0.385121 + 0.922866i \(0.374160\pi\)
\(62\) −6.23393 −0.791710
\(63\) −1.22819 −0.154737
\(64\) 1.00000 0.125000
\(65\) 20.7386 2.57231
\(66\) −6.67361 −0.821464
\(67\) 3.78945 0.462955 0.231477 0.972840i \(-0.425644\pi\)
0.231477 + 0.972840i \(0.425644\pi\)
\(68\) −7.23099 −0.876886
\(69\) 0.735834 0.0885841
\(70\) −0.605029 −0.0723148
\(71\) 9.35881 1.11069 0.555343 0.831621i \(-0.312587\pi\)
0.555343 + 0.831621i \(0.312587\pi\)
\(72\) 7.38220 0.870001
\(73\) −5.89786 −0.690293 −0.345146 0.938549i \(-0.612171\pi\)
−0.345146 + 0.938549i \(0.612171\pi\)
\(74\) 5.72120 0.665076
\(75\) −26.5019 −3.06017
\(76\) −1.00000 −0.114708
\(77\) −0.344584 −0.0392690
\(78\) −18.3750 −2.08056
\(79\) −12.8417 −1.44480 −0.722400 0.691475i \(-0.756961\pi\)
−0.722400 + 0.691475i \(0.756961\pi\)
\(80\) 3.63661 0.406585
\(81\) 23.3503 2.59448
\(82\) 7.52149 0.830610
\(83\) −8.79057 −0.964890 −0.482445 0.875926i \(-0.660251\pi\)
−0.482445 + 0.875926i \(0.660251\pi\)
\(84\) 0.536074 0.0584905
\(85\) −26.2963 −2.85223
\(86\) 6.52032 0.703105
\(87\) −18.8158 −2.01727
\(88\) 2.07117 0.220788
\(89\) 18.4932 1.96028 0.980140 0.198309i \(-0.0635448\pi\)
0.980140 + 0.198309i \(0.0635448\pi\)
\(90\) 26.8462 2.82984
\(91\) −0.948774 −0.0994586
\(92\) −0.228368 −0.0238090
\(93\) 20.0866 2.08289
\(94\) 12.3649 1.27534
\(95\) −3.63661 −0.373108
\(96\) −3.22214 −0.328859
\(97\) −0.277043 −0.0281295 −0.0140647 0.999901i \(-0.504477\pi\)
−0.0140647 + 0.999901i \(0.504477\pi\)
\(98\) −6.97232 −0.704311
\(99\) 15.2898 1.53668
\(100\) 8.22492 0.822492
\(101\) −11.4514 −1.13946 −0.569731 0.821832i \(-0.692952\pi\)
−0.569731 + 0.821832i \(0.692952\pi\)
\(102\) 23.2993 2.30697
\(103\) 6.03457 0.594604 0.297302 0.954784i \(-0.403913\pi\)
0.297302 + 0.954784i \(0.403913\pi\)
\(104\) 5.70273 0.559199
\(105\) 1.94949 0.190251
\(106\) −7.72094 −0.749924
\(107\) 4.23441 0.409356 0.204678 0.978829i \(-0.434385\pi\)
0.204678 + 0.978829i \(0.434385\pi\)
\(108\) −14.1201 −1.35871
\(109\) −7.88401 −0.755151 −0.377576 0.925979i \(-0.623242\pi\)
−0.377576 + 0.925979i \(0.623242\pi\)
\(110\) 7.53204 0.718151
\(111\) −18.4345 −1.74973
\(112\) −0.166372 −0.0157207
\(113\) 18.4543 1.73603 0.868017 0.496535i \(-0.165395\pi\)
0.868017 + 0.496535i \(0.165395\pi\)
\(114\) 3.22214 0.301781
\(115\) −0.830485 −0.0774431
\(116\) 5.83954 0.542187
\(117\) 42.0987 3.89203
\(118\) 0.482122 0.0443829
\(119\) 1.20303 0.110282
\(120\) −11.7177 −1.06967
\(121\) −6.71025 −0.610023
\(122\) 6.01579 0.544644
\(123\) −24.2353 −2.18522
\(124\) −6.23393 −0.559824
\(125\) 11.7278 1.04896
\(126\) −1.22819 −0.109416
\(127\) 10.6436 0.944468 0.472234 0.881473i \(-0.343448\pi\)
0.472234 + 0.881473i \(0.343448\pi\)
\(128\) 1.00000 0.0883883
\(129\) −21.0094 −1.84978
\(130\) 20.7386 1.81890
\(131\) −21.8119 −1.90571 −0.952856 0.303423i \(-0.901871\pi\)
−0.952856 + 0.303423i \(0.901871\pi\)
\(132\) −6.67361 −0.580863
\(133\) 0.166372 0.0144263
\(134\) 3.78945 0.327359
\(135\) −51.3492 −4.41944
\(136\) −7.23099 −0.620052
\(137\) 11.1022 0.948525 0.474262 0.880384i \(-0.342715\pi\)
0.474262 + 0.880384i \(0.342715\pi\)
\(138\) 0.735834 0.0626384
\(139\) 4.76970 0.404561 0.202280 0.979328i \(-0.435165\pi\)
0.202280 + 0.979328i \(0.435165\pi\)
\(140\) −0.605029 −0.0511343
\(141\) −39.8413 −3.35525
\(142\) 9.35881 0.785374
\(143\) 11.8113 0.987713
\(144\) 7.38220 0.615183
\(145\) 21.2361 1.76356
\(146\) −5.89786 −0.488111
\(147\) 22.4658 1.85295
\(148\) 5.72120 0.470280
\(149\) −20.5731 −1.68541 −0.842707 0.538373i \(-0.819039\pi\)
−0.842707 + 0.538373i \(0.819039\pi\)
\(150\) −26.5019 −2.16387
\(151\) −21.4671 −1.74696 −0.873482 0.486856i \(-0.838144\pi\)
−0.873482 + 0.486856i \(0.838144\pi\)
\(152\) −1.00000 −0.0811107
\(153\) −53.3806 −4.31557
\(154\) −0.344584 −0.0277674
\(155\) −22.6704 −1.82093
\(156\) −18.3750 −1.47118
\(157\) −0.00441305 −0.000352200 0 −0.000176100 1.00000i \(-0.500056\pi\)
−0.000176100 1.00000i \(0.500056\pi\)
\(158\) −12.8417 −1.02163
\(159\) 24.8780 1.97295
\(160\) 3.63661 0.287499
\(161\) 0.0379940 0.00299435
\(162\) 23.3503 1.83457
\(163\) 2.00586 0.157111 0.0785557 0.996910i \(-0.474969\pi\)
0.0785557 + 0.996910i \(0.474969\pi\)
\(164\) 7.52149 0.587330
\(165\) −24.2693 −1.88936
\(166\) −8.79057 −0.682280
\(167\) −13.2659 −1.02655 −0.513275 0.858224i \(-0.671568\pi\)
−0.513275 + 0.858224i \(0.671568\pi\)
\(168\) 0.536074 0.0413590
\(169\) 19.5212 1.50163
\(170\) −26.2963 −2.01683
\(171\) −7.38220 −0.564531
\(172\) 6.52032 0.497170
\(173\) −15.3425 −1.16647 −0.583235 0.812303i \(-0.698213\pi\)
−0.583235 + 0.812303i \(0.698213\pi\)
\(174\) −18.8158 −1.42642
\(175\) −1.36840 −0.103441
\(176\) 2.07117 0.156120
\(177\) −1.55347 −0.116766
\(178\) 18.4932 1.38613
\(179\) −2.25927 −0.168866 −0.0844328 0.996429i \(-0.526908\pi\)
−0.0844328 + 0.996429i \(0.526908\pi\)
\(180\) 26.8462 2.00100
\(181\) 24.2192 1.80020 0.900101 0.435682i \(-0.143493\pi\)
0.900101 + 0.435682i \(0.143493\pi\)
\(182\) −0.948774 −0.0703278
\(183\) −19.3837 −1.43289
\(184\) −0.228368 −0.0168355
\(185\) 20.8058 1.52967
\(186\) 20.0866 1.47282
\(187\) −14.9766 −1.09520
\(188\) 12.3649 0.901800
\(189\) 2.34918 0.170878
\(190\) −3.63661 −0.263827
\(191\) −9.10558 −0.658856 −0.329428 0.944181i \(-0.606856\pi\)
−0.329428 + 0.944181i \(0.606856\pi\)
\(192\) −3.22214 −0.232538
\(193\) 11.3800 0.819151 0.409576 0.912276i \(-0.365677\pi\)
0.409576 + 0.912276i \(0.365677\pi\)
\(194\) −0.277043 −0.0198906
\(195\) −66.8227 −4.78528
\(196\) −6.97232 −0.498023
\(197\) 6.15634 0.438621 0.219311 0.975655i \(-0.429619\pi\)
0.219311 + 0.975655i \(0.429619\pi\)
\(198\) 15.2898 1.08660
\(199\) −7.22831 −0.512401 −0.256201 0.966624i \(-0.582471\pi\)
−0.256201 + 0.966624i \(0.582471\pi\)
\(200\) 8.22492 0.581590
\(201\) −12.2101 −0.861237
\(202\) −11.4514 −0.805721
\(203\) −0.971535 −0.0681884
\(204\) 23.2993 1.63128
\(205\) 27.3527 1.91040
\(206\) 6.03457 0.420448
\(207\) −1.68586 −0.117175
\(208\) 5.70273 0.395413
\(209\) −2.07117 −0.143266
\(210\) 1.94949 0.134528
\(211\) −1.00000 −0.0688428
\(212\) −7.72094 −0.530276
\(213\) −30.1554 −2.06622
\(214\) 4.23441 0.289459
\(215\) 23.7119 1.61714
\(216\) −14.1201 −0.960750
\(217\) 1.03715 0.0704064
\(218\) −7.88401 −0.533973
\(219\) 19.0038 1.28415
\(220\) 7.53204 0.507810
\(221\) −41.2364 −2.77386
\(222\) −18.4345 −1.23724
\(223\) 15.2766 1.02300 0.511498 0.859285i \(-0.329091\pi\)
0.511498 + 0.859285i \(0.329091\pi\)
\(224\) −0.166372 −0.0111162
\(225\) 60.7180 4.04787
\(226\) 18.4543 1.22756
\(227\) −8.74809 −0.580631 −0.290316 0.956931i \(-0.593760\pi\)
−0.290316 + 0.956931i \(0.593760\pi\)
\(228\) 3.22214 0.213392
\(229\) 2.49445 0.164838 0.0824191 0.996598i \(-0.473735\pi\)
0.0824191 + 0.996598i \(0.473735\pi\)
\(230\) −0.830485 −0.0547606
\(231\) 1.11030 0.0730524
\(232\) 5.83954 0.383384
\(233\) 19.4011 1.27101 0.635504 0.772097i \(-0.280792\pi\)
0.635504 + 0.772097i \(0.280792\pi\)
\(234\) 42.0987 2.75208
\(235\) 44.9661 2.93327
\(236\) 0.482122 0.0313835
\(237\) 41.3777 2.68777
\(238\) 1.20303 0.0779810
\(239\) 11.1721 0.722663 0.361331 0.932438i \(-0.382322\pi\)
0.361331 + 0.932438i \(0.382322\pi\)
\(240\) −11.7177 −0.756372
\(241\) 26.8890 1.73207 0.866037 0.499980i \(-0.166659\pi\)
0.866037 + 0.499980i \(0.166659\pi\)
\(242\) −6.71025 −0.431351
\(243\) −32.8778 −2.10911
\(244\) 6.01579 0.385121
\(245\) −25.3556 −1.61991
\(246\) −24.2353 −1.54519
\(247\) −5.70273 −0.362856
\(248\) −6.23393 −0.395855
\(249\) 28.3245 1.79499
\(250\) 11.7278 0.741729
\(251\) −3.96443 −0.250232 −0.125116 0.992142i \(-0.539930\pi\)
−0.125116 + 0.992142i \(0.539930\pi\)
\(252\) −1.22819 −0.0773687
\(253\) −0.472989 −0.0297366
\(254\) 10.6436 0.667840
\(255\) 84.7303 5.30602
\(256\) 1.00000 0.0625000
\(257\) −16.9574 −1.05778 −0.528888 0.848691i \(-0.677391\pi\)
−0.528888 + 0.848691i \(0.677391\pi\)
\(258\) −21.0094 −1.30799
\(259\) −0.951846 −0.0591448
\(260\) 20.7386 1.28615
\(261\) 43.1086 2.66836
\(262\) −21.8119 −1.34754
\(263\) 25.6336 1.58063 0.790317 0.612698i \(-0.209916\pi\)
0.790317 + 0.612698i \(0.209916\pi\)
\(264\) −6.67361 −0.410732
\(265\) −28.0780 −1.72482
\(266\) 0.166372 0.0102009
\(267\) −59.5878 −3.64672
\(268\) 3.78945 0.231477
\(269\) 4.39484 0.267958 0.133979 0.990984i \(-0.457224\pi\)
0.133979 + 0.990984i \(0.457224\pi\)
\(270\) −51.3492 −3.12501
\(271\) −28.4547 −1.72850 −0.864250 0.503063i \(-0.832206\pi\)
−0.864250 + 0.503063i \(0.832206\pi\)
\(272\) −7.23099 −0.438443
\(273\) 3.05709 0.185023
\(274\) 11.1022 0.670708
\(275\) 17.0352 1.02726
\(276\) 0.735834 0.0442920
\(277\) 12.4980 0.750934 0.375467 0.926836i \(-0.377482\pi\)
0.375467 + 0.926836i \(0.377482\pi\)
\(278\) 4.76970 0.286068
\(279\) −46.0201 −2.75515
\(280\) −0.605029 −0.0361574
\(281\) 17.9288 1.06954 0.534772 0.844996i \(-0.320397\pi\)
0.534772 + 0.844996i \(0.320397\pi\)
\(282\) −39.8413 −2.37252
\(283\) −6.42188 −0.381741 −0.190871 0.981615i \(-0.561131\pi\)
−0.190871 + 0.981615i \(0.561131\pi\)
\(284\) 9.35881 0.555343
\(285\) 11.7177 0.694095
\(286\) 11.8113 0.698419
\(287\) −1.25136 −0.0738657
\(288\) 7.38220 0.435000
\(289\) 35.2872 2.07572
\(290\) 21.2361 1.24703
\(291\) 0.892673 0.0523294
\(292\) −5.89786 −0.345146
\(293\) 16.2537 0.949552 0.474776 0.880107i \(-0.342529\pi\)
0.474776 + 0.880107i \(0.342529\pi\)
\(294\) 22.4658 1.31023
\(295\) 1.75329 0.102080
\(296\) 5.72120 0.332538
\(297\) −29.2451 −1.69697
\(298\) −20.5731 −1.19177
\(299\) −1.30232 −0.0753152
\(300\) −26.5019 −1.53009
\(301\) −1.08480 −0.0625267
\(302\) −21.4671 −1.23529
\(303\) 36.8982 2.11974
\(304\) −1.00000 −0.0573539
\(305\) 21.8771 1.25268
\(306\) −53.3806 −3.05157
\(307\) −3.70255 −0.211316 −0.105658 0.994403i \(-0.533695\pi\)
−0.105658 + 0.994403i \(0.533695\pi\)
\(308\) −0.344584 −0.0196345
\(309\) −19.4442 −1.10614
\(310\) −22.6704 −1.28759
\(311\) −27.9777 −1.58647 −0.793236 0.608914i \(-0.791605\pi\)
−0.793236 + 0.608914i \(0.791605\pi\)
\(312\) −18.3750 −1.04028
\(313\) −8.95845 −0.506361 −0.253181 0.967419i \(-0.581477\pi\)
−0.253181 + 0.967419i \(0.581477\pi\)
\(314\) −0.00441305 −0.000249043 0
\(315\) −4.46645 −0.251656
\(316\) −12.8417 −0.722400
\(317\) 6.92826 0.389130 0.194565 0.980890i \(-0.437670\pi\)
0.194565 + 0.980890i \(0.437670\pi\)
\(318\) 24.8780 1.39509
\(319\) 12.0947 0.677172
\(320\) 3.63661 0.203293
\(321\) −13.6439 −0.761527
\(322\) 0.0379940 0.00211732
\(323\) 7.23099 0.402343
\(324\) 23.3503 1.29724
\(325\) 46.9045 2.60179
\(326\) 2.00586 0.111095
\(327\) 25.4034 1.40481
\(328\) 7.52149 0.415305
\(329\) −2.05716 −0.113415
\(330\) −24.2693 −1.33598
\(331\) 4.13486 0.227272 0.113636 0.993522i \(-0.463750\pi\)
0.113636 + 0.993522i \(0.463750\pi\)
\(332\) −8.79057 −0.482445
\(333\) 42.2350 2.31447
\(334\) −13.2659 −0.725880
\(335\) 13.7807 0.752922
\(336\) 0.536074 0.0292452
\(337\) 19.9193 1.08507 0.542536 0.840032i \(-0.317464\pi\)
0.542536 + 0.840032i \(0.317464\pi\)
\(338\) 19.5212 1.06181
\(339\) −59.4623 −3.22955
\(340\) −26.2963 −1.42612
\(341\) −12.9115 −0.699199
\(342\) −7.38220 −0.399184
\(343\) 2.32460 0.125517
\(344\) 6.52032 0.351552
\(345\) 2.67594 0.144068
\(346\) −15.3425 −0.824819
\(347\) 20.7244 1.11255 0.556273 0.830999i \(-0.312231\pi\)
0.556273 + 0.830999i \(0.312231\pi\)
\(348\) −18.8158 −1.00863
\(349\) −26.0662 −1.39529 −0.697646 0.716443i \(-0.745769\pi\)
−0.697646 + 0.716443i \(0.745769\pi\)
\(350\) −1.36840 −0.0731438
\(351\) −80.5230 −4.29800
\(352\) 2.07117 0.110394
\(353\) 1.39788 0.0744016 0.0372008 0.999308i \(-0.488156\pi\)
0.0372008 + 0.999308i \(0.488156\pi\)
\(354\) −1.55347 −0.0825658
\(355\) 34.0343 1.80635
\(356\) 18.4932 0.980140
\(357\) −3.87634 −0.205158
\(358\) −2.25927 −0.119406
\(359\) −22.8375 −1.20532 −0.602659 0.797999i \(-0.705892\pi\)
−0.602659 + 0.797999i \(0.705892\pi\)
\(360\) 26.8462 1.41492
\(361\) 1.00000 0.0526316
\(362\) 24.2192 1.27293
\(363\) 21.6214 1.13483
\(364\) −0.948774 −0.0497293
\(365\) −21.4482 −1.12265
\(366\) −19.3837 −1.01320
\(367\) 9.42875 0.492177 0.246088 0.969247i \(-0.420855\pi\)
0.246088 + 0.969247i \(0.420855\pi\)
\(368\) −0.228368 −0.0119045
\(369\) 55.5252 2.89052
\(370\) 20.8058 1.08164
\(371\) 1.28455 0.0666903
\(372\) 20.0866 1.04144
\(373\) −28.3229 −1.46650 −0.733252 0.679957i \(-0.761998\pi\)
−0.733252 + 0.679957i \(0.761998\pi\)
\(374\) −14.9766 −0.774422
\(375\) −37.7886 −1.95139
\(376\) 12.3649 0.637669
\(377\) 33.3013 1.71510
\(378\) 2.34918 0.120829
\(379\) 1.54112 0.0791618 0.0395809 0.999216i \(-0.487398\pi\)
0.0395809 + 0.999216i \(0.487398\pi\)
\(380\) −3.63661 −0.186554
\(381\) −34.2953 −1.75700
\(382\) −9.10558 −0.465882
\(383\) 21.3437 1.09061 0.545306 0.838237i \(-0.316413\pi\)
0.545306 + 0.838237i \(0.316413\pi\)
\(384\) −3.22214 −0.164429
\(385\) −1.25312 −0.0638649
\(386\) 11.3800 0.579227
\(387\) 48.1343 2.44681
\(388\) −0.277043 −0.0140647
\(389\) 39.0171 1.97825 0.989124 0.147086i \(-0.0469894\pi\)
0.989124 + 0.147086i \(0.0469894\pi\)
\(390\) −66.8227 −3.38370
\(391\) 1.65133 0.0835112
\(392\) −6.97232 −0.352155
\(393\) 70.2810 3.54521
\(394\) 6.15634 0.310152
\(395\) −46.7001 −2.34974
\(396\) 15.2898 0.768341
\(397\) −13.2985 −0.667430 −0.333715 0.942674i \(-0.608302\pi\)
−0.333715 + 0.942674i \(0.608302\pi\)
\(398\) −7.22831 −0.362322
\(399\) −0.536074 −0.0268373
\(400\) 8.22492 0.411246
\(401\) −10.6083 −0.529753 −0.264876 0.964282i \(-0.585331\pi\)
−0.264876 + 0.964282i \(0.585331\pi\)
\(402\) −12.2101 −0.608987
\(403\) −35.5504 −1.77089
\(404\) −11.4514 −0.569731
\(405\) 84.9159 4.21950
\(406\) −0.971535 −0.0482165
\(407\) 11.8496 0.587362
\(408\) 23.2993 1.15349
\(409\) 0.966613 0.0477959 0.0238980 0.999714i \(-0.492392\pi\)
0.0238980 + 0.999714i \(0.492392\pi\)
\(410\) 27.3527 1.35085
\(411\) −35.7729 −1.76454
\(412\) 6.03457 0.297302
\(413\) −0.0802116 −0.00394695
\(414\) −1.68586 −0.0828555
\(415\) −31.9678 −1.56924
\(416\) 5.70273 0.279599
\(417\) −15.3687 −0.752606
\(418\) −2.07117 −0.101304
\(419\) −29.3560 −1.43414 −0.717068 0.697003i \(-0.754516\pi\)
−0.717068 + 0.697003i \(0.754516\pi\)
\(420\) 1.94949 0.0951254
\(421\) −36.4142 −1.77472 −0.887360 0.461077i \(-0.847463\pi\)
−0.887360 + 0.461077i \(0.847463\pi\)
\(422\) −1.00000 −0.0486792
\(423\) 91.2799 4.43818
\(424\) −7.72094 −0.374962
\(425\) −59.4743 −2.88493
\(426\) −30.1554 −1.46103
\(427\) −1.00086 −0.0484349
\(428\) 4.23441 0.204678
\(429\) −38.0578 −1.83745
\(430\) 23.7119 1.14349
\(431\) 0.860803 0.0414634 0.0207317 0.999785i \(-0.493400\pi\)
0.0207317 + 0.999785i \(0.493400\pi\)
\(432\) −14.1201 −0.679353
\(433\) 37.1074 1.78327 0.891635 0.452755i \(-0.149559\pi\)
0.891635 + 0.452755i \(0.149559\pi\)
\(434\) 1.03715 0.0497848
\(435\) −68.4258 −3.28076
\(436\) −7.88401 −0.377576
\(437\) 0.228368 0.0109243
\(438\) 19.0038 0.908034
\(439\) 29.1117 1.38943 0.694713 0.719287i \(-0.255531\pi\)
0.694713 + 0.719287i \(0.255531\pi\)
\(440\) 7.53204 0.359076
\(441\) −51.4711 −2.45100
\(442\) −41.2364 −1.96141
\(443\) −1.04138 −0.0494776 −0.0247388 0.999694i \(-0.507875\pi\)
−0.0247388 + 0.999694i \(0.507875\pi\)
\(444\) −18.4345 −0.874863
\(445\) 67.2527 3.18808
\(446\) 15.2766 0.723367
\(447\) 66.2894 3.13538
\(448\) −0.166372 −0.00786033
\(449\) −8.59234 −0.405497 −0.202749 0.979231i \(-0.564987\pi\)
−0.202749 + 0.979231i \(0.564987\pi\)
\(450\) 60.7180 2.86228
\(451\) 15.5783 0.733553
\(452\) 18.4543 0.868017
\(453\) 69.1699 3.24989
\(454\) −8.74809 −0.410568
\(455\) −3.45032 −0.161753
\(456\) 3.22214 0.150891
\(457\) −29.8356 −1.39565 −0.697825 0.716269i \(-0.745848\pi\)
−0.697825 + 0.716269i \(0.745848\pi\)
\(458\) 2.49445 0.116558
\(459\) 102.102 4.76572
\(460\) −0.830485 −0.0387216
\(461\) 7.70245 0.358739 0.179369 0.983782i \(-0.442594\pi\)
0.179369 + 0.983782i \(0.442594\pi\)
\(462\) 1.11030 0.0516558
\(463\) 6.07997 0.282560 0.141280 0.989970i \(-0.454878\pi\)
0.141280 + 0.989970i \(0.454878\pi\)
\(464\) 5.83954 0.271094
\(465\) 73.0472 3.38748
\(466\) 19.4011 0.898739
\(467\) 39.1068 1.80965 0.904823 0.425788i \(-0.140003\pi\)
0.904823 + 0.425788i \(0.140003\pi\)
\(468\) 42.0987 1.94601
\(469\) −0.630458 −0.0291118
\(470\) 44.9661 2.07413
\(471\) 0.0142195 0.000655199 0
\(472\) 0.482122 0.0221915
\(473\) 13.5047 0.620947
\(474\) 41.3777 1.90054
\(475\) −8.22492 −0.377385
\(476\) 1.20303 0.0551409
\(477\) −56.9975 −2.60974
\(478\) 11.1721 0.511000
\(479\) −26.4905 −1.21038 −0.605191 0.796081i \(-0.706903\pi\)
−0.605191 + 0.796081i \(0.706903\pi\)
\(480\) −11.7177 −0.534836
\(481\) 32.6265 1.48764
\(482\) 26.8890 1.22476
\(483\) −0.122422 −0.00557040
\(484\) −6.71025 −0.305011
\(485\) −1.00750 −0.0457481
\(486\) −32.8778 −1.49137
\(487\) −20.9713 −0.950303 −0.475151 0.879904i \(-0.657607\pi\)
−0.475151 + 0.879904i \(0.657607\pi\)
\(488\) 6.01579 0.272322
\(489\) −6.46318 −0.292275
\(490\) −25.3556 −1.14545
\(491\) −0.745349 −0.0336371 −0.0168186 0.999859i \(-0.505354\pi\)
−0.0168186 + 0.999859i \(0.505354\pi\)
\(492\) −24.2353 −1.09261
\(493\) −42.2256 −1.90175
\(494\) −5.70273 −0.256578
\(495\) 55.6030 2.49917
\(496\) −6.23393 −0.279912
\(497\) −1.55704 −0.0698429
\(498\) 28.3245 1.26925
\(499\) 20.7046 0.926867 0.463433 0.886132i \(-0.346617\pi\)
0.463433 + 0.886132i \(0.346617\pi\)
\(500\) 11.7278 0.524482
\(501\) 42.7448 1.90970
\(502\) −3.96443 −0.176941
\(503\) −26.6368 −1.18768 −0.593838 0.804585i \(-0.702388\pi\)
−0.593838 + 0.804585i \(0.702388\pi\)
\(504\) −1.22819 −0.0547080
\(505\) −41.6444 −1.85315
\(506\) −0.472989 −0.0210269
\(507\) −62.8999 −2.79348
\(508\) 10.6436 0.472234
\(509\) −36.5215 −1.61879 −0.809393 0.587267i \(-0.800204\pi\)
−0.809393 + 0.587267i \(0.800204\pi\)
\(510\) 84.7303 3.75192
\(511\) 0.981238 0.0434074
\(512\) 1.00000 0.0441942
\(513\) 14.1201 0.623417
\(514\) −16.9574 −0.747961
\(515\) 21.9454 0.967028
\(516\) −21.0094 −0.924888
\(517\) 25.6097 1.12631
\(518\) −0.951846 −0.0418217
\(519\) 49.4358 2.16999
\(520\) 20.7386 0.909448
\(521\) 10.6442 0.466330 0.233165 0.972437i \(-0.425092\pi\)
0.233165 + 0.972437i \(0.425092\pi\)
\(522\) 43.1086 1.88681
\(523\) 4.05160 0.177164 0.0885821 0.996069i \(-0.471766\pi\)
0.0885821 + 0.996069i \(0.471766\pi\)
\(524\) −21.8119 −0.952856
\(525\) 4.40916 0.192432
\(526\) 25.6336 1.11768
\(527\) 45.0775 1.96361
\(528\) −6.67361 −0.290431
\(529\) −22.9478 −0.997733
\(530\) −28.0780 −1.21963
\(531\) 3.55912 0.154453
\(532\) 0.166372 0.00721314
\(533\) 42.8930 1.85790
\(534\) −59.5878 −2.57862
\(535\) 15.3989 0.665753
\(536\) 3.78945 0.163679
\(537\) 7.27968 0.314141
\(538\) 4.39484 0.189475
\(539\) −14.4409 −0.622012
\(540\) −51.3492 −2.20972
\(541\) 33.7191 1.44970 0.724848 0.688909i \(-0.241910\pi\)
0.724848 + 0.688909i \(0.241910\pi\)
\(542\) −28.4547 −1.22223
\(543\) −78.0378 −3.34892
\(544\) −7.23099 −0.310026
\(545\) −28.6711 −1.22813
\(546\) 3.05709 0.130831
\(547\) 17.2693 0.738382 0.369191 0.929353i \(-0.379635\pi\)
0.369191 + 0.929353i \(0.379635\pi\)
\(548\) 11.1022 0.474262
\(549\) 44.4097 1.89536
\(550\) 17.0352 0.726384
\(551\) −5.83954 −0.248773
\(552\) 0.735834 0.0313192
\(553\) 2.13649 0.0908529
\(554\) 12.4980 0.530991
\(555\) −67.0391 −2.84565
\(556\) 4.76970 0.202280
\(557\) −14.9135 −0.631903 −0.315952 0.948775i \(-0.602324\pi\)
−0.315952 + 0.948775i \(0.602324\pi\)
\(558\) −46.0201 −1.94819
\(559\) 37.1837 1.57270
\(560\) −0.605029 −0.0255672
\(561\) 48.2568 2.03740
\(562\) 17.9288 0.756282
\(563\) 24.7547 1.04329 0.521643 0.853164i \(-0.325319\pi\)
0.521643 + 0.853164i \(0.325319\pi\)
\(564\) −39.8413 −1.67762
\(565\) 67.1110 2.82338
\(566\) −6.42188 −0.269932
\(567\) −3.88483 −0.163148
\(568\) 9.35881 0.392687
\(569\) 11.2476 0.471522 0.235761 0.971811i \(-0.424242\pi\)
0.235761 + 0.971811i \(0.424242\pi\)
\(570\) 11.7177 0.490799
\(571\) 46.9145 1.96331 0.981655 0.190667i \(-0.0610650\pi\)
0.981655 + 0.190667i \(0.0610650\pi\)
\(572\) 11.8113 0.493857
\(573\) 29.3395 1.22567
\(574\) −1.25136 −0.0522309
\(575\) −1.87831 −0.0783309
\(576\) 7.38220 0.307592
\(577\) −13.1173 −0.546081 −0.273040 0.962003i \(-0.588029\pi\)
−0.273040 + 0.962003i \(0.588029\pi\)
\(578\) 35.2872 1.46775
\(579\) −36.6680 −1.52387
\(580\) 21.2361 0.881781
\(581\) 1.46250 0.0606748
\(582\) 0.892673 0.0370025
\(583\) −15.9914 −0.662295
\(584\) −5.89786 −0.244055
\(585\) 153.097 6.32976
\(586\) 16.2537 0.671434
\(587\) 38.1722 1.57553 0.787767 0.615974i \(-0.211237\pi\)
0.787767 + 0.615974i \(0.211237\pi\)
\(588\) 22.4658 0.926474
\(589\) 6.23393 0.256865
\(590\) 1.75329 0.0721818
\(591\) −19.8366 −0.815969
\(592\) 5.72120 0.235140
\(593\) −22.5728 −0.926952 −0.463476 0.886109i \(-0.653398\pi\)
−0.463476 + 0.886109i \(0.653398\pi\)
\(594\) −29.2451 −1.19994
\(595\) 4.37496 0.179356
\(596\) −20.5731 −0.842707
\(597\) 23.2906 0.953222
\(598\) −1.30232 −0.0532559
\(599\) 19.7584 0.807305 0.403652 0.914912i \(-0.367740\pi\)
0.403652 + 0.914912i \(0.367740\pi\)
\(600\) −26.5019 −1.08193
\(601\) −35.4575 −1.44634 −0.723171 0.690669i \(-0.757316\pi\)
−0.723171 + 0.690669i \(0.757316\pi\)
\(602\) −1.08480 −0.0442131
\(603\) 27.9745 1.13921
\(604\) −21.4671 −0.873482
\(605\) −24.4026 −0.992105
\(606\) 36.8982 1.49889
\(607\) 37.3812 1.51726 0.758629 0.651523i \(-0.225870\pi\)
0.758629 + 0.651523i \(0.225870\pi\)
\(608\) −1.00000 −0.0405554
\(609\) 3.13042 0.126851
\(610\) 21.8771 0.885776
\(611\) 70.5135 2.85267
\(612\) −53.3806 −2.15778
\(613\) −27.2688 −1.10137 −0.550687 0.834712i \(-0.685634\pi\)
−0.550687 + 0.834712i \(0.685634\pi\)
\(614\) −3.70255 −0.149423
\(615\) −88.1344 −3.55392
\(616\) −0.344584 −0.0138837
\(617\) −4.00168 −0.161102 −0.0805508 0.996751i \(-0.525668\pi\)
−0.0805508 + 0.996751i \(0.525668\pi\)
\(618\) −19.4442 −0.782162
\(619\) 16.7364 0.672694 0.336347 0.941738i \(-0.390809\pi\)
0.336347 + 0.941738i \(0.390809\pi\)
\(620\) −22.6704 −0.910464
\(621\) 3.22458 0.129398
\(622\) −27.9777 −1.12181
\(623\) −3.07675 −0.123268
\(624\) −18.3750 −0.735589
\(625\) 1.52471 0.0609885
\(626\) −8.95845 −0.358052
\(627\) 6.67361 0.266518
\(628\) −0.00441305 −0.000176100 0
\(629\) −41.3699 −1.64953
\(630\) −4.46645 −0.177948
\(631\) 29.1570 1.16072 0.580361 0.814359i \(-0.302911\pi\)
0.580361 + 0.814359i \(0.302911\pi\)
\(632\) −12.8417 −0.510814
\(633\) 3.22214 0.128069
\(634\) 6.92826 0.275156
\(635\) 38.7067 1.53603
\(636\) 24.8780 0.986475
\(637\) −39.7613 −1.57540
\(638\) 12.0947 0.478833
\(639\) 69.0886 2.73310
\(640\) 3.63661 0.143750
\(641\) −22.9321 −0.905764 −0.452882 0.891570i \(-0.649604\pi\)
−0.452882 + 0.891570i \(0.649604\pi\)
\(642\) −13.6439 −0.538481
\(643\) −19.0285 −0.750410 −0.375205 0.926942i \(-0.622428\pi\)
−0.375205 + 0.926942i \(0.622428\pi\)
\(644\) 0.0379940 0.00149717
\(645\) −76.4030 −3.00837
\(646\) 7.23099 0.284499
\(647\) −12.0515 −0.473792 −0.236896 0.971535i \(-0.576130\pi\)
−0.236896 + 0.971535i \(0.576130\pi\)
\(648\) 23.3503 0.917286
\(649\) 0.998557 0.0391968
\(650\) 46.9045 1.83975
\(651\) −3.34185 −0.130977
\(652\) 2.00586 0.0785557
\(653\) 34.0611 1.33291 0.666456 0.745544i \(-0.267810\pi\)
0.666456 + 0.745544i \(0.267810\pi\)
\(654\) 25.4034 0.993352
\(655\) −79.3212 −3.09934
\(656\) 7.52149 0.293665
\(657\) −43.5392 −1.69863
\(658\) −2.05716 −0.0801966
\(659\) 12.1607 0.473715 0.236857 0.971544i \(-0.423883\pi\)
0.236857 + 0.971544i \(0.423883\pi\)
\(660\) −24.2693 −0.944681
\(661\) 42.2494 1.64331 0.821656 0.569983i \(-0.193050\pi\)
0.821656 + 0.569983i \(0.193050\pi\)
\(662\) 4.13486 0.160706
\(663\) 132.869 5.16022
\(664\) −8.79057 −0.341140
\(665\) 0.605029 0.0234620
\(666\) 42.2350 1.63657
\(667\) −1.33356 −0.0516358
\(668\) −13.2659 −0.513275
\(669\) −49.2233 −1.90308
\(670\) 13.7807 0.532397
\(671\) 12.4597 0.481002
\(672\) 0.536074 0.0206795
\(673\) −39.3268 −1.51594 −0.757968 0.652292i \(-0.773808\pi\)
−0.757968 + 0.652292i \(0.773808\pi\)
\(674\) 19.9193 0.767262
\(675\) −116.137 −4.47010
\(676\) 19.5212 0.750813
\(677\) 23.4604 0.901657 0.450829 0.892610i \(-0.351129\pi\)
0.450829 + 0.892610i \(0.351129\pi\)
\(678\) −59.4623 −2.28364
\(679\) 0.0460922 0.00176886
\(680\) −26.2963 −1.00842
\(681\) 28.1876 1.08015
\(682\) −12.9115 −0.494408
\(683\) −16.8660 −0.645361 −0.322680 0.946508i \(-0.604584\pi\)
−0.322680 + 0.946508i \(0.604584\pi\)
\(684\) −7.38220 −0.282266
\(685\) 40.3743 1.54262
\(686\) 2.32460 0.0887537
\(687\) −8.03749 −0.306649
\(688\) 6.52032 0.248585
\(689\) −44.0304 −1.67743
\(690\) 2.67594 0.101871
\(691\) 7.19988 0.273896 0.136948 0.990578i \(-0.456271\pi\)
0.136948 + 0.990578i \(0.456271\pi\)
\(692\) −15.3425 −0.583235
\(693\) −2.54379 −0.0966307
\(694\) 20.7244 0.786689
\(695\) 17.3455 0.657954
\(696\) −18.8158 −0.713212
\(697\) −54.3878 −2.06008
\(698\) −26.0662 −0.986621
\(699\) −62.5131 −2.36446
\(700\) −1.36840 −0.0517205
\(701\) −32.8059 −1.23906 −0.619530 0.784973i \(-0.712677\pi\)
−0.619530 + 0.784973i \(0.712677\pi\)
\(702\) −80.5230 −3.03915
\(703\) −5.72120 −0.215779
\(704\) 2.07117 0.0780602
\(705\) −144.887 −5.45677
\(706\) 1.39788 0.0526099
\(707\) 1.90520 0.0716523
\(708\) −1.55347 −0.0583828
\(709\) −25.6674 −0.963958 −0.481979 0.876183i \(-0.660082\pi\)
−0.481979 + 0.876183i \(0.660082\pi\)
\(710\) 34.0343 1.27729
\(711\) −94.7998 −3.55527
\(712\) 18.4932 0.693063
\(713\) 1.42363 0.0533154
\(714\) −3.87634 −0.145068
\(715\) 42.9532 1.60636
\(716\) −2.25927 −0.0844328
\(717\) −35.9981 −1.34437
\(718\) −22.8375 −0.852289
\(719\) 47.6643 1.77758 0.888790 0.458315i \(-0.151547\pi\)
0.888790 + 0.458315i \(0.151547\pi\)
\(720\) 26.8462 1.00050
\(721\) −1.00398 −0.0373903
\(722\) 1.00000 0.0372161
\(723\) −86.6402 −3.22218
\(724\) 24.2192 0.900101
\(725\) 48.0297 1.78378
\(726\) 21.6214 0.802445
\(727\) 19.6241 0.727817 0.363909 0.931435i \(-0.381442\pi\)
0.363909 + 0.931435i \(0.381442\pi\)
\(728\) −0.948774 −0.0351639
\(729\) 35.8859 1.32911
\(730\) −21.4482 −0.793834
\(731\) −47.1484 −1.74385
\(732\) −19.3837 −0.716443
\(733\) −1.73534 −0.0640963 −0.0320481 0.999486i \(-0.510203\pi\)
−0.0320481 + 0.999486i \(0.510203\pi\)
\(734\) 9.42875 0.348022
\(735\) 81.6994 3.01353
\(736\) −0.228368 −0.00841776
\(737\) 7.84860 0.289107
\(738\) 55.5252 2.04391
\(739\) −16.7922 −0.617712 −0.308856 0.951109i \(-0.599946\pi\)
−0.308856 + 0.951109i \(0.599946\pi\)
\(740\) 20.8058 0.764835
\(741\) 18.3750 0.675023
\(742\) 1.28455 0.0471572
\(743\) −12.8351 −0.470875 −0.235437 0.971890i \(-0.575652\pi\)
−0.235437 + 0.971890i \(0.575652\pi\)
\(744\) 20.0866 0.736411
\(745\) −74.8163 −2.74106
\(746\) −28.3229 −1.03697
\(747\) −64.8937 −2.37434
\(748\) −14.9766 −0.547599
\(749\) −0.704487 −0.0257414
\(750\) −37.7886 −1.37984
\(751\) 26.4604 0.965554 0.482777 0.875743i \(-0.339628\pi\)
0.482777 + 0.875743i \(0.339628\pi\)
\(752\) 12.3649 0.450900
\(753\) 12.7739 0.465508
\(754\) 33.3013 1.21276
\(755\) −78.0673 −2.84116
\(756\) 2.34918 0.0854390
\(757\) 12.0402 0.437610 0.218805 0.975769i \(-0.429784\pi\)
0.218805 + 0.975769i \(0.429784\pi\)
\(758\) 1.54112 0.0559758
\(759\) 1.52404 0.0553191
\(760\) −3.63661 −0.131914
\(761\) −14.2388 −0.516157 −0.258079 0.966124i \(-0.583089\pi\)
−0.258079 + 0.966124i \(0.583089\pi\)
\(762\) −34.2953 −1.24239
\(763\) 1.31168 0.0474859
\(764\) −9.10558 −0.329428
\(765\) −194.124 −7.01858
\(766\) 21.3437 0.771179
\(767\) 2.74941 0.0992755
\(768\) −3.22214 −0.116269
\(769\) −8.21118 −0.296103 −0.148051 0.988980i \(-0.547300\pi\)
−0.148051 + 0.988980i \(0.547300\pi\)
\(770\) −1.25312 −0.0451593
\(771\) 54.6393 1.96779
\(772\) 11.3800 0.409576
\(773\) −27.9692 −1.00598 −0.502990 0.864292i \(-0.667767\pi\)
−0.502990 + 0.864292i \(0.667767\pi\)
\(774\) 48.1343 1.73015
\(775\) −51.2736 −1.84180
\(776\) −0.277043 −0.00994528
\(777\) 3.06698 0.110027
\(778\) 39.0171 1.39883
\(779\) −7.52149 −0.269485
\(780\) −66.8227 −2.39264
\(781\) 19.3837 0.693603
\(782\) 1.65133 0.0590513
\(783\) −82.4547 −2.94669
\(784\) −6.97232 −0.249011
\(785\) −0.0160485 −0.000572797 0
\(786\) 70.2810 2.50684
\(787\) 17.7545 0.632881 0.316440 0.948612i \(-0.397512\pi\)
0.316440 + 0.948612i \(0.397512\pi\)
\(788\) 6.15634 0.219311
\(789\) −82.5950 −2.94046
\(790\) −46.7001 −1.66152
\(791\) −3.07027 −0.109166
\(792\) 15.2898 0.543299
\(793\) 34.3064 1.21826
\(794\) −13.2985 −0.471945
\(795\) 90.4714 3.20869
\(796\) −7.22831 −0.256201
\(797\) 32.0727 1.13607 0.568037 0.823003i \(-0.307703\pi\)
0.568037 + 0.823003i \(0.307703\pi\)
\(798\) −0.536074 −0.0189768
\(799\) −89.4101 −3.16310
\(800\) 8.22492 0.290795
\(801\) 136.521 4.82373
\(802\) −10.6083 −0.374592
\(803\) −12.2155 −0.431075
\(804\) −12.2101 −0.430619
\(805\) 0.138169 0.00486983
\(806\) −35.5504 −1.25221
\(807\) −14.1608 −0.498484
\(808\) −11.4514 −0.402860
\(809\) 29.0467 1.02123 0.510615 0.859810i \(-0.329418\pi\)
0.510615 + 0.859810i \(0.329418\pi\)
\(810\) 84.9159 2.98364
\(811\) 38.5610 1.35406 0.677029 0.735956i \(-0.263267\pi\)
0.677029 + 0.735956i \(0.263267\pi\)
\(812\) −0.971535 −0.0340942
\(813\) 91.6851 3.21554
\(814\) 11.8496 0.415327
\(815\) 7.29454 0.255517
\(816\) 23.2993 0.815638
\(817\) −6.52032 −0.228117
\(818\) 0.966613 0.0337968
\(819\) −7.00404 −0.244741
\(820\) 27.3527 0.955198
\(821\) 26.7207 0.932560 0.466280 0.884637i \(-0.345594\pi\)
0.466280 + 0.884637i \(0.345594\pi\)
\(822\) −35.7729 −1.24772
\(823\) −17.9214 −0.624702 −0.312351 0.949967i \(-0.601116\pi\)
−0.312351 + 0.949967i \(0.601116\pi\)
\(824\) 6.03457 0.210224
\(825\) −54.8899 −1.91102
\(826\) −0.0802116 −0.00279092
\(827\) 3.62102 0.125915 0.0629576 0.998016i \(-0.479947\pi\)
0.0629576 + 0.998016i \(0.479947\pi\)
\(828\) −1.68586 −0.0585877
\(829\) −38.2443 −1.32828 −0.664139 0.747609i \(-0.731202\pi\)
−0.664139 + 0.747609i \(0.731202\pi\)
\(830\) −31.9678 −1.10962
\(831\) −40.2705 −1.39697
\(832\) 5.70273 0.197707
\(833\) 50.4168 1.74684
\(834\) −15.3687 −0.532173
\(835\) −48.2430 −1.66952
\(836\) −2.07117 −0.0716329
\(837\) 88.0236 3.04254
\(838\) −29.3560 −1.01409
\(839\) −36.4415 −1.25810 −0.629049 0.777365i \(-0.716556\pi\)
−0.629049 + 0.777365i \(0.716556\pi\)
\(840\) 1.94949 0.0672638
\(841\) 5.10018 0.175868
\(842\) −36.4142 −1.25492
\(843\) −57.7693 −1.98968
\(844\) −1.00000 −0.0344214
\(845\) 70.9908 2.44216
\(846\) 91.2799 3.13827
\(847\) 1.11640 0.0383599
\(848\) −7.72094 −0.265138
\(849\) 20.6922 0.710155
\(850\) −59.4743 −2.03995
\(851\) −1.30654 −0.0447876
\(852\) −30.1554 −1.03311
\(853\) −35.4911 −1.21519 −0.607596 0.794247i \(-0.707866\pi\)
−0.607596 + 0.794247i \(0.707866\pi\)
\(854\) −1.00086 −0.0342486
\(855\) −26.8462 −0.918120
\(856\) 4.23441 0.144729
\(857\) −30.3521 −1.03681 −0.518404 0.855136i \(-0.673474\pi\)
−0.518404 + 0.855136i \(0.673474\pi\)
\(858\) −38.0578 −1.29927
\(859\) 31.1219 1.06186 0.530932 0.847414i \(-0.321842\pi\)
0.530932 + 0.847414i \(0.321842\pi\)
\(860\) 23.7119 0.808568
\(861\) 4.03207 0.137413
\(862\) 0.860803 0.0293191
\(863\) 46.2824 1.57547 0.787736 0.616012i \(-0.211253\pi\)
0.787736 + 0.616012i \(0.211253\pi\)
\(864\) −14.1201 −0.480375
\(865\) −55.7948 −1.89708
\(866\) 37.1074 1.26096
\(867\) −113.700 −3.86146
\(868\) 1.03715 0.0352032
\(869\) −26.5973 −0.902251
\(870\) −68.4258 −2.31985
\(871\) 21.6102 0.732234
\(872\) −7.88401 −0.266986
\(873\) −2.04519 −0.0692192
\(874\) 0.228368 0.00772467
\(875\) −1.95117 −0.0659616
\(876\) 19.0038 0.642077
\(877\) −32.5052 −1.09762 −0.548812 0.835946i \(-0.684920\pi\)
−0.548812 + 0.835946i \(0.684920\pi\)
\(878\) 29.1117 0.982472
\(879\) −52.3718 −1.76646
\(880\) 7.53204 0.253905
\(881\) 21.1923 0.713987 0.356993 0.934107i \(-0.383802\pi\)
0.356993 + 0.934107i \(0.383802\pi\)
\(882\) −51.4711 −1.73312
\(883\) −12.6059 −0.424224 −0.212112 0.977245i \(-0.568034\pi\)
−0.212112 + 0.977245i \(0.568034\pi\)
\(884\) −41.2364 −1.38693
\(885\) −5.64935 −0.189901
\(886\) −1.04138 −0.0349860
\(887\) −35.5370 −1.19321 −0.596607 0.802533i \(-0.703485\pi\)
−0.596607 + 0.802533i \(0.703485\pi\)
\(888\) −18.4345 −0.618622
\(889\) −1.77080 −0.0593907
\(890\) 67.2527 2.25431
\(891\) 48.3625 1.62020
\(892\) 15.2766 0.511498
\(893\) −12.3649 −0.413774
\(894\) 66.2894 2.21705
\(895\) −8.21607 −0.274633
\(896\) −0.166372 −0.00555809
\(897\) 4.19627 0.140109
\(898\) −8.59234 −0.286730
\(899\) −36.4033 −1.21412
\(900\) 60.7180 2.02393
\(901\) 55.8300 1.85997
\(902\) 15.5783 0.518700
\(903\) 3.49538 0.116319
\(904\) 18.4543 0.613780
\(905\) 88.0759 2.92774
\(906\) 69.1699 2.29802
\(907\) 29.9396 0.994127 0.497064 0.867714i \(-0.334412\pi\)
0.497064 + 0.867714i \(0.334412\pi\)
\(908\) −8.74809 −0.290316
\(909\) −84.5369 −2.80391
\(910\) −3.45032 −0.114377
\(911\) 41.4920 1.37469 0.687345 0.726331i \(-0.258776\pi\)
0.687345 + 0.726331i \(0.258776\pi\)
\(912\) 3.22214 0.106696
\(913\) −18.2068 −0.602556
\(914\) −29.8356 −0.986873
\(915\) −70.4910 −2.33036
\(916\) 2.49445 0.0824191
\(917\) 3.62888 0.119836
\(918\) 102.102 3.36987
\(919\) 2.59227 0.0855112 0.0427556 0.999086i \(-0.486386\pi\)
0.0427556 + 0.999086i \(0.486386\pi\)
\(920\) −0.830485 −0.0273803
\(921\) 11.9301 0.393112
\(922\) 7.70245 0.253667
\(923\) 53.3708 1.75672
\(924\) 1.11030 0.0365262
\(925\) 47.0564 1.54720
\(926\) 6.07997 0.199800
\(927\) 44.5484 1.46316
\(928\) 5.83954 0.191692
\(929\) 44.8445 1.47130 0.735649 0.677363i \(-0.236877\pi\)
0.735649 + 0.677363i \(0.236877\pi\)
\(930\) 73.0472 2.39531
\(931\) 6.97232 0.228509
\(932\) 19.4011 0.635504
\(933\) 90.1483 2.95132
\(934\) 39.1068 1.27961
\(935\) −54.4640 −1.78116
\(936\) 42.0987 1.37604
\(937\) −22.7086 −0.741859 −0.370929 0.928661i \(-0.620961\pi\)
−0.370929 + 0.928661i \(0.620961\pi\)
\(938\) −0.630458 −0.0205852
\(939\) 28.8654 0.941987
\(940\) 44.9661 1.46663
\(941\) −36.0263 −1.17443 −0.587213 0.809433i \(-0.699775\pi\)
−0.587213 + 0.809433i \(0.699775\pi\)
\(942\) 0.0142195 0.000463296 0
\(943\) −1.71767 −0.0559350
\(944\) 0.482122 0.0156917
\(945\) 8.54306 0.277906
\(946\) 13.5047 0.439076
\(947\) 11.9502 0.388328 0.194164 0.980969i \(-0.437801\pi\)
0.194164 + 0.980969i \(0.437801\pi\)
\(948\) 41.3777 1.34388
\(949\) −33.6339 −1.09180
\(950\) −8.22492 −0.266852
\(951\) −22.3238 −0.723900
\(952\) 1.20303 0.0389905
\(953\) −10.8019 −0.349906 −0.174953 0.984577i \(-0.555977\pi\)
−0.174953 + 0.984577i \(0.555977\pi\)
\(954\) −56.9975 −1.84536
\(955\) −33.1134 −1.07152
\(956\) 11.1721 0.361331
\(957\) −38.9708 −1.25975
\(958\) −26.4905 −0.855869
\(959\) −1.84709 −0.0596457
\(960\) −11.7177 −0.378186
\(961\) 7.86191 0.253610
\(962\) 32.6265 1.05192
\(963\) 31.2593 1.00732
\(964\) 26.8890 0.866037
\(965\) 41.3846 1.33222
\(966\) −0.122422 −0.00393887
\(967\) 5.12018 0.164654 0.0823269 0.996605i \(-0.473765\pi\)
0.0823269 + 0.996605i \(0.473765\pi\)
\(968\) −6.71025 −0.215676
\(969\) −23.2993 −0.748480
\(970\) −1.00750 −0.0323488
\(971\) −8.05833 −0.258604 −0.129302 0.991605i \(-0.541274\pi\)
−0.129302 + 0.991605i \(0.541274\pi\)
\(972\) −32.8778 −1.05455
\(973\) −0.793544 −0.0254399
\(974\) −20.9713 −0.671965
\(975\) −151.133 −4.84013
\(976\) 6.01579 0.192561
\(977\) −61.5604 −1.96949 −0.984746 0.173997i \(-0.944332\pi\)
−0.984746 + 0.173997i \(0.944332\pi\)
\(978\) −6.46318 −0.206670
\(979\) 38.3026 1.22416
\(980\) −25.3556 −0.809955
\(981\) −58.2014 −1.85823
\(982\) −0.745349 −0.0237850
\(983\) −3.44294 −0.109813 −0.0549064 0.998492i \(-0.517486\pi\)
−0.0549064 + 0.998492i \(0.517486\pi\)
\(984\) −24.2353 −0.772594
\(985\) 22.3882 0.713348
\(986\) −42.2256 −1.34474
\(987\) 6.62848 0.210987
\(988\) −5.70273 −0.181428
\(989\) −1.48903 −0.0473485
\(990\) 55.6030 1.76718
\(991\) −18.3113 −0.581678 −0.290839 0.956772i \(-0.593934\pi\)
−0.290839 + 0.956772i \(0.593934\pi\)
\(992\) −6.23393 −0.197928
\(993\) −13.3231 −0.422796
\(994\) −1.55704 −0.0493864
\(995\) −26.2865 −0.833339
\(996\) 28.3245 0.897495
\(997\) 20.3614 0.644853 0.322426 0.946595i \(-0.395502\pi\)
0.322426 + 0.946595i \(0.395502\pi\)
\(998\) 20.7046 0.655394
\(999\) −80.7838 −2.55588
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 \(a_p\))