Properties

Label 4015.2.a.h.1.17
Level 4015
Weight 2
Character 4015.1
Self dual Yes
Analytic conductor 32.060
Analytic rank 0
Dimension 37
CM No

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Newspace parameters

Level: \( N \) = \( 4015 = 5 \cdot 11 \cdot 73 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0599364115\)
Analytic rank: \(0\)
Dimension: \(37\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.17
Character \(\chi\) = 4015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-0.327392 q^{2}\) \(-2.36457 q^{3}\) \(-1.89281 q^{4}\) \(+1.00000 q^{5}\) \(+0.774141 q^{6}\) \(+2.46288 q^{7}\) \(+1.27448 q^{8}\) \(+2.59119 q^{9}\) \(+O(q^{10})\) \(q\)\(-0.327392 q^{2}\) \(-2.36457 q^{3}\) \(-1.89281 q^{4}\) \(+1.00000 q^{5}\) \(+0.774141 q^{6}\) \(+2.46288 q^{7}\) \(+1.27448 q^{8}\) \(+2.59119 q^{9}\) \(-0.327392 q^{10}\) \(+1.00000 q^{11}\) \(+4.47569 q^{12}\) \(-0.641298 q^{13}\) \(-0.806327 q^{14}\) \(-2.36457 q^{15}\) \(+3.36838 q^{16}\) \(-6.07665 q^{17}\) \(-0.848334 q^{18}\) \(+8.35139 q^{19}\) \(-1.89281 q^{20}\) \(-5.82365 q^{21}\) \(-0.327392 q^{22}\) \(+2.42427 q^{23}\) \(-3.01359 q^{24}\) \(+1.00000 q^{25}\) \(+0.209956 q^{26}\) \(+0.966665 q^{27}\) \(-4.66177 q^{28}\) \(+5.36357 q^{29}\) \(+0.774141 q^{30}\) \(+7.23441 q^{31}\) \(-3.65173 q^{32}\) \(-2.36457 q^{33}\) \(+1.98945 q^{34}\) \(+2.46288 q^{35}\) \(-4.90464 q^{36}\) \(-5.09224 q^{37}\) \(-2.73418 q^{38}\) \(+1.51639 q^{39}\) \(+1.27448 q^{40}\) \(-0.993086 q^{41}\) \(+1.90662 q^{42}\) \(+5.57472 q^{43}\) \(-1.89281 q^{44}\) \(+2.59119 q^{45}\) \(-0.793687 q^{46}\) \(+3.08560 q^{47}\) \(-7.96476 q^{48}\) \(-0.934228 q^{49}\) \(-0.327392 q^{50}\) \(+14.3687 q^{51}\) \(+1.21386 q^{52}\) \(+3.89942 q^{53}\) \(-0.316478 q^{54}\) \(+1.00000 q^{55}\) \(+3.13888 q^{56}\) \(-19.7474 q^{57}\) \(-1.75599 q^{58}\) \(-0.200959 q^{59}\) \(+4.47569 q^{60}\) \(-10.9562 q^{61}\) \(-2.36849 q^{62}\) \(+6.38178 q^{63}\) \(-5.54120 q^{64}\) \(-0.641298 q^{65}\) \(+0.774141 q^{66}\) \(-10.6466 q^{67}\) \(+11.5020 q^{68}\) \(-5.73236 q^{69}\) \(-0.806327 q^{70}\) \(-0.323595 q^{71}\) \(+3.30241 q^{72}\) \(+1.00000 q^{73}\) \(+1.66716 q^{74}\) \(-2.36457 q^{75}\) \(-15.8076 q^{76}\) \(+2.46288 q^{77}\) \(-0.496455 q^{78}\) \(-10.7550 q^{79}\) \(+3.36838 q^{80}\) \(-10.0593 q^{81}\) \(+0.325128 q^{82}\) \(+13.1546 q^{83}\) \(+11.0231 q^{84}\) \(-6.07665 q^{85}\) \(-1.82512 q^{86}\) \(-12.6825 q^{87}\) \(+1.27448 q^{88}\) \(+8.38454 q^{89}\) \(-0.848334 q^{90}\) \(-1.57944 q^{91}\) \(-4.58869 q^{92}\) \(-17.1063 q^{93}\) \(-1.01020 q^{94}\) \(+8.35139 q^{95}\) \(+8.63477 q^{96}\) \(-1.74254 q^{97}\) \(+0.305859 q^{98}\) \(+2.59119 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(37q \) \(\mathstrut +\mathstrut 5q^{2} \) \(\mathstrut +\mathstrut 3q^{3} \) \(\mathstrut +\mathstrut 43q^{4} \) \(\mathstrut +\mathstrut 37q^{5} \) \(\mathstrut +\mathstrut 9q^{6} \) \(\mathstrut +\mathstrut 6q^{7} \) \(\mathstrut +\mathstrut 12q^{8} \) \(\mathstrut +\mathstrut 50q^{9} \) \(\mathstrut +\mathstrut 5q^{10} \) \(\mathstrut +\mathstrut 37q^{11} \) \(\mathstrut +\mathstrut 6q^{12} \) \(\mathstrut +\mathstrut 11q^{13} \) \(\mathstrut +\mathstrut 11q^{14} \) \(\mathstrut +\mathstrut 3q^{15} \) \(\mathstrut +\mathstrut 43q^{16} \) \(\mathstrut +\mathstrut 38q^{17} \) \(\mathstrut +\mathstrut 11q^{18} \) \(\mathstrut +\mathstrut 34q^{19} \) \(\mathstrut +\mathstrut 43q^{20} \) \(\mathstrut +\mathstrut 39q^{21} \) \(\mathstrut +\mathstrut 5q^{22} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 25q^{24} \) \(\mathstrut +\mathstrut 37q^{25} \) \(\mathstrut -\mathstrut 9q^{26} \) \(\mathstrut +\mathstrut 3q^{27} \) \(\mathstrut +\mathstrut 14q^{28} \) \(\mathstrut +\mathstrut 58q^{29} \) \(\mathstrut +\mathstrut 9q^{30} \) \(\mathstrut +\mathstrut 8q^{31} \) \(\mathstrut +\mathstrut 14q^{32} \) \(\mathstrut +\mathstrut 3q^{33} \) \(\mathstrut +\mathstrut 8q^{34} \) \(\mathstrut +\mathstrut 6q^{35} \) \(\mathstrut +\mathstrut 20q^{36} \) \(\mathstrut +\mathstrut 2q^{37} \) \(\mathstrut +\mathstrut 15q^{38} \) \(\mathstrut +\mathstrut 14q^{39} \) \(\mathstrut +\mathstrut 12q^{40} \) \(\mathstrut +\mathstrut 62q^{41} \) \(\mathstrut -\mathstrut 13q^{42} \) \(\mathstrut +\mathstrut 30q^{43} \) \(\mathstrut +\mathstrut 43q^{44} \) \(\mathstrut +\mathstrut 50q^{45} \) \(\mathstrut +\mathstrut 31q^{46} \) \(\mathstrut +\mathstrut 5q^{47} \) \(\mathstrut -\mathstrut 25q^{48} \) \(\mathstrut +\mathstrut 59q^{49} \) \(\mathstrut +\mathstrut 5q^{50} \) \(\mathstrut +\mathstrut 23q^{51} \) \(\mathstrut -\mathstrut q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 13q^{54} \) \(\mathstrut +\mathstrut 37q^{55} \) \(\mathstrut +\mathstrut 22q^{56} \) \(\mathstrut +\mathstrut 5q^{57} \) \(\mathstrut -\mathstrut 40q^{58} \) \(\mathstrut +\mathstrut 15q^{59} \) \(\mathstrut +\mathstrut 6q^{60} \) \(\mathstrut +\mathstrut 57q^{61} \) \(\mathstrut +\mathstrut 20q^{62} \) \(\mathstrut -\mathstrut 29q^{63} \) \(\mathstrut +\mathstrut 10q^{64} \) \(\mathstrut +\mathstrut 11q^{65} \) \(\mathstrut +\mathstrut 9q^{66} \) \(\mathstrut -\mathstrut 14q^{67} \) \(\mathstrut +\mathstrut 53q^{68} \) \(\mathstrut +\mathstrut 24q^{69} \) \(\mathstrut +\mathstrut 11q^{70} \) \(\mathstrut +\mathstrut 8q^{71} \) \(\mathstrut +\mathstrut 15q^{72} \) \(\mathstrut +\mathstrut 37q^{73} \) \(\mathstrut +\mathstrut 7q^{74} \) \(\mathstrut +\mathstrut 3q^{75} \) \(\mathstrut +\mathstrut 59q^{76} \) \(\mathstrut +\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut q^{78} \) \(\mathstrut +\mathstrut 42q^{79} \) \(\mathstrut +\mathstrut 43q^{80} \) \(\mathstrut +\mathstrut 61q^{81} \) \(\mathstrut -\mathstrut 22q^{82} \) \(\mathstrut +\mathstrut 44q^{83} \) \(\mathstrut +\mathstrut 66q^{84} \) \(\mathstrut +\mathstrut 38q^{85} \) \(\mathstrut -\mathstrut q^{86} \) \(\mathstrut -\mathstrut 26q^{87} \) \(\mathstrut +\mathstrut 12q^{88} \) \(\mathstrut +\mathstrut 69q^{89} \) \(\mathstrut +\mathstrut 11q^{90} \) \(\mathstrut -\mathstrut 10q^{91} \) \(\mathstrut -\mathstrut 21q^{92} \) \(\mathstrut -\mathstrut 26q^{93} \) \(\mathstrut +\mathstrut 29q^{94} \) \(\mathstrut +\mathstrut 34q^{95} \) \(\mathstrut -\mathstrut 9q^{96} \) \(\mathstrut +\mathstrut 37q^{97} \) \(\mathstrut -\mathstrut 15q^{98} \) \(\mathstrut +\mathstrut 50q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −0.327392 −0.231501 −0.115751 0.993278i \(-0.536927\pi\)
−0.115751 + 0.993278i \(0.536927\pi\)
\(3\) −2.36457 −1.36518 −0.682592 0.730799i \(-0.739148\pi\)
−0.682592 + 0.730799i \(0.739148\pi\)
\(4\) −1.89281 −0.946407
\(5\) 1.00000 0.447214
\(6\) 0.774141 0.316042
\(7\) 2.46288 0.930881 0.465440 0.885079i \(-0.345896\pi\)
0.465440 + 0.885079i \(0.345896\pi\)
\(8\) 1.27448 0.450595
\(9\) 2.59119 0.863729
\(10\) −0.327392 −0.103530
\(11\) 1.00000 0.301511
\(12\) 4.47569 1.29202
\(13\) −0.641298 −0.177864 −0.0889321 0.996038i \(-0.528345\pi\)
−0.0889321 + 0.996038i \(0.528345\pi\)
\(14\) −0.806327 −0.215500
\(15\) −2.36457 −0.610529
\(16\) 3.36838 0.842094
\(17\) −6.07665 −1.47380 −0.736902 0.675999i \(-0.763712\pi\)
−0.736902 + 0.675999i \(0.763712\pi\)
\(18\) −0.848334 −0.199954
\(19\) 8.35139 1.91594 0.957970 0.286869i \(-0.0926144\pi\)
0.957970 + 0.286869i \(0.0926144\pi\)
\(20\) −1.89281 −0.423246
\(21\) −5.82365 −1.27082
\(22\) −0.327392 −0.0698002
\(23\) 2.42427 0.505495 0.252748 0.967532i \(-0.418666\pi\)
0.252748 + 0.967532i \(0.418666\pi\)
\(24\) −3.01359 −0.615146
\(25\) 1.00000 0.200000
\(26\) 0.209956 0.0411757
\(27\) 0.966665 0.186035
\(28\) −4.66177 −0.880992
\(29\) 5.36357 0.995991 0.497995 0.867180i \(-0.334070\pi\)
0.497995 + 0.867180i \(0.334070\pi\)
\(30\) 0.774141 0.141338
\(31\) 7.23441 1.29934 0.649669 0.760217i \(-0.274907\pi\)
0.649669 + 0.760217i \(0.274907\pi\)
\(32\) −3.65173 −0.645541
\(33\) −2.36457 −0.411619
\(34\) 1.98945 0.341187
\(35\) 2.46288 0.416302
\(36\) −4.90464 −0.817440
\(37\) −5.09224 −0.837159 −0.418579 0.908180i \(-0.637472\pi\)
−0.418579 + 0.908180i \(0.637472\pi\)
\(38\) −2.73418 −0.443542
\(39\) 1.51639 0.242817
\(40\) 1.27448 0.201512
\(41\) −0.993086 −0.155094 −0.0775470 0.996989i \(-0.524709\pi\)
−0.0775470 + 0.996989i \(0.524709\pi\)
\(42\) 1.90662 0.294197
\(43\) 5.57472 0.850136 0.425068 0.905161i \(-0.360250\pi\)
0.425068 + 0.905161i \(0.360250\pi\)
\(44\) −1.89281 −0.285353
\(45\) 2.59119 0.386271
\(46\) −0.793687 −0.117023
\(47\) 3.08560 0.450081 0.225040 0.974349i \(-0.427749\pi\)
0.225040 + 0.974349i \(0.427749\pi\)
\(48\) −7.96476 −1.14961
\(49\) −0.934228 −0.133461
\(50\) −0.327392 −0.0463002
\(51\) 14.3687 2.01202
\(52\) 1.21386 0.168332
\(53\) 3.89942 0.535626 0.267813 0.963471i \(-0.413699\pi\)
0.267813 + 0.963471i \(0.413699\pi\)
\(54\) −0.316478 −0.0430672
\(55\) 1.00000 0.134840
\(56\) 3.13888 0.419451
\(57\) −19.7474 −2.61561
\(58\) −1.75599 −0.230573
\(59\) −0.200959 −0.0261627 −0.0130813 0.999914i \(-0.504164\pi\)
−0.0130813 + 0.999914i \(0.504164\pi\)
\(60\) 4.47569 0.577809
\(61\) −10.9562 −1.40280 −0.701400 0.712768i \(-0.747441\pi\)
−0.701400 + 0.712768i \(0.747441\pi\)
\(62\) −2.36849 −0.300798
\(63\) 6.38178 0.804029
\(64\) −5.54120 −0.692651
\(65\) −0.641298 −0.0795432
\(66\) 0.774141 0.0952902
\(67\) −10.6466 −1.30069 −0.650347 0.759637i \(-0.725376\pi\)
−0.650347 + 0.759637i \(0.725376\pi\)
\(68\) 11.5020 1.39482
\(69\) −5.73236 −0.690095
\(70\) −0.806327 −0.0963745
\(71\) −0.323595 −0.0384037 −0.0192018 0.999816i \(-0.506113\pi\)
−0.0192018 + 0.999816i \(0.506113\pi\)
\(72\) 3.30241 0.389192
\(73\) 1.00000 0.117041
\(74\) 1.66716 0.193803
\(75\) −2.36457 −0.273037
\(76\) −15.8076 −1.81326
\(77\) 2.46288 0.280671
\(78\) −0.496455 −0.0562125
\(79\) −10.7550 −1.21003 −0.605014 0.796215i \(-0.706832\pi\)
−0.605014 + 0.796215i \(0.706832\pi\)
\(80\) 3.36838 0.376596
\(81\) −10.0593 −1.11770
\(82\) 0.325128 0.0359044
\(83\) 13.1546 1.44391 0.721954 0.691941i \(-0.243244\pi\)
0.721954 + 0.691941i \(0.243244\pi\)
\(84\) 11.0231 1.20272
\(85\) −6.07665 −0.659106
\(86\) −1.82512 −0.196807
\(87\) −12.6825 −1.35971
\(88\) 1.27448 0.135860
\(89\) 8.38454 0.888760 0.444380 0.895838i \(-0.353424\pi\)
0.444380 + 0.895838i \(0.353424\pi\)
\(90\) −0.848334 −0.0894223
\(91\) −1.57944 −0.165570
\(92\) −4.58869 −0.478405
\(93\) −17.1063 −1.77384
\(94\) −1.01020 −0.104194
\(95\) 8.35139 0.856834
\(96\) 8.63477 0.881283
\(97\) −1.74254 −0.176928 −0.0884638 0.996079i \(-0.528196\pi\)
−0.0884638 + 0.996079i \(0.528196\pi\)
\(98\) 0.305859 0.0308964
\(99\) 2.59119 0.260424
\(100\) −1.89281 −0.189281
\(101\) −3.45766 −0.344050 −0.172025 0.985093i \(-0.555031\pi\)
−0.172025 + 0.985093i \(0.555031\pi\)
\(102\) −4.70419 −0.465784
\(103\) −15.8333 −1.56010 −0.780051 0.625716i \(-0.784807\pi\)
−0.780051 + 0.625716i \(0.784807\pi\)
\(104\) −0.817319 −0.0801447
\(105\) −5.82365 −0.568330
\(106\) −1.27664 −0.123998
\(107\) −6.58676 −0.636767 −0.318383 0.947962i \(-0.603140\pi\)
−0.318383 + 0.947962i \(0.603140\pi\)
\(108\) −1.82972 −0.176065
\(109\) 11.4360 1.09537 0.547687 0.836683i \(-0.315509\pi\)
0.547687 + 0.836683i \(0.315509\pi\)
\(110\) −0.327392 −0.0312156
\(111\) 12.0409 1.14288
\(112\) 8.29590 0.783889
\(113\) 2.18592 0.205634 0.102817 0.994700i \(-0.467214\pi\)
0.102817 + 0.994700i \(0.467214\pi\)
\(114\) 6.46515 0.605517
\(115\) 2.42427 0.226064
\(116\) −10.1522 −0.942613
\(117\) −1.66172 −0.153626
\(118\) 0.0657924 0.00605669
\(119\) −14.9661 −1.37194
\(120\) −3.01359 −0.275102
\(121\) 1.00000 0.0909091
\(122\) 3.58698 0.324750
\(123\) 2.34822 0.211732
\(124\) −13.6934 −1.22970
\(125\) 1.00000 0.0894427
\(126\) −2.08934 −0.186134
\(127\) 2.14448 0.190292 0.0951459 0.995463i \(-0.469668\pi\)
0.0951459 + 0.995463i \(0.469668\pi\)
\(128\) 9.11761 0.805890
\(129\) −13.1818 −1.16059
\(130\) 0.209956 0.0184143
\(131\) 13.2584 1.15839 0.579195 0.815189i \(-0.303367\pi\)
0.579195 + 0.815189i \(0.303367\pi\)
\(132\) 4.47569 0.389559
\(133\) 20.5685 1.78351
\(134\) 3.48562 0.301112
\(135\) 0.966665 0.0831973
\(136\) −7.74455 −0.664090
\(137\) 4.52897 0.386936 0.193468 0.981107i \(-0.438026\pi\)
0.193468 + 0.981107i \(0.438026\pi\)
\(138\) 1.87673 0.159758
\(139\) −18.8654 −1.60015 −0.800073 0.599903i \(-0.795206\pi\)
−0.800073 + 0.599903i \(0.795206\pi\)
\(140\) −4.66177 −0.393992
\(141\) −7.29611 −0.614443
\(142\) 0.105942 0.00889049
\(143\) −0.641298 −0.0536280
\(144\) 8.72809 0.727341
\(145\) 5.36357 0.445420
\(146\) −0.327392 −0.0270952
\(147\) 2.20905 0.182199
\(148\) 9.63866 0.792293
\(149\) 12.7596 1.04531 0.522653 0.852545i \(-0.324942\pi\)
0.522653 + 0.852545i \(0.324942\pi\)
\(150\) 0.774141 0.0632083
\(151\) 14.4526 1.17613 0.588066 0.808813i \(-0.299889\pi\)
0.588066 + 0.808813i \(0.299889\pi\)
\(152\) 10.6436 0.863314
\(153\) −15.7457 −1.27297
\(154\) −0.806327 −0.0649757
\(155\) 7.23441 0.581082
\(156\) −2.87025 −0.229804
\(157\) 1.71958 0.137237 0.0686187 0.997643i \(-0.478141\pi\)
0.0686187 + 0.997643i \(0.478141\pi\)
\(158\) 3.52109 0.280123
\(159\) −9.22044 −0.731228
\(160\) −3.65173 −0.288695
\(161\) 5.97068 0.470556
\(162\) 3.29334 0.258749
\(163\) 10.3229 0.808549 0.404275 0.914638i \(-0.367524\pi\)
0.404275 + 0.914638i \(0.367524\pi\)
\(164\) 1.87973 0.146782
\(165\) −2.36457 −0.184081
\(166\) −4.30672 −0.334266
\(167\) −19.0750 −1.47607 −0.738033 0.674765i \(-0.764245\pi\)
−0.738033 + 0.674765i \(0.764245\pi\)
\(168\) −7.42210 −0.572627
\(169\) −12.5887 −0.968364
\(170\) 1.98945 0.152584
\(171\) 21.6400 1.65485
\(172\) −10.5519 −0.804575
\(173\) 4.87923 0.370961 0.185480 0.982648i \(-0.440616\pi\)
0.185480 + 0.982648i \(0.440616\pi\)
\(174\) 4.15216 0.314775
\(175\) 2.46288 0.186176
\(176\) 3.36838 0.253901
\(177\) 0.475182 0.0357169
\(178\) −2.74503 −0.205749
\(179\) 7.09888 0.530595 0.265298 0.964167i \(-0.414530\pi\)
0.265298 + 0.964167i \(0.414530\pi\)
\(180\) −4.90464 −0.365570
\(181\) 4.60092 0.341984 0.170992 0.985272i \(-0.445303\pi\)
0.170992 + 0.985272i \(0.445303\pi\)
\(182\) 0.517096 0.0383297
\(183\) 25.9067 1.91508
\(184\) 3.08968 0.227774
\(185\) −5.09224 −0.374389
\(186\) 5.60045 0.410645
\(187\) −6.07665 −0.444369
\(188\) −5.84047 −0.425960
\(189\) 2.38078 0.173176
\(190\) −2.73418 −0.198358
\(191\) −7.01107 −0.507303 −0.253652 0.967296i \(-0.581632\pi\)
−0.253652 + 0.967296i \(0.581632\pi\)
\(192\) 13.1026 0.945596
\(193\) 10.9203 0.786061 0.393030 0.919525i \(-0.371427\pi\)
0.393030 + 0.919525i \(0.371427\pi\)
\(194\) 0.570492 0.0409589
\(195\) 1.51639 0.108591
\(196\) 1.76832 0.126309
\(197\) −5.70336 −0.406348 −0.203174 0.979143i \(-0.565126\pi\)
−0.203174 + 0.979143i \(0.565126\pi\)
\(198\) −0.848334 −0.0602885
\(199\) 17.4143 1.23447 0.617233 0.786780i \(-0.288253\pi\)
0.617233 + 0.786780i \(0.288253\pi\)
\(200\) 1.27448 0.0901191
\(201\) 25.1747 1.77569
\(202\) 1.13201 0.0796480
\(203\) 13.2098 0.927148
\(204\) −27.1972 −1.90419
\(205\) −0.993086 −0.0693601
\(206\) 5.18369 0.361165
\(207\) 6.28174 0.436611
\(208\) −2.16013 −0.149778
\(209\) 8.35139 0.577678
\(210\) 1.90662 0.131569
\(211\) 26.0862 1.79585 0.897924 0.440151i \(-0.145075\pi\)
0.897924 + 0.440151i \(0.145075\pi\)
\(212\) −7.38087 −0.506920
\(213\) 0.765163 0.0524281
\(214\) 2.15645 0.147412
\(215\) 5.57472 0.380192
\(216\) 1.23199 0.0838264
\(217\) 17.8175 1.20953
\(218\) −3.74407 −0.253580
\(219\) −2.36457 −0.159783
\(220\) −1.89281 −0.127614
\(221\) 3.89695 0.262137
\(222\) −3.94211 −0.264577
\(223\) −15.1221 −1.01265 −0.506326 0.862342i \(-0.668997\pi\)
−0.506326 + 0.862342i \(0.668997\pi\)
\(224\) −8.99377 −0.600922
\(225\) 2.59119 0.172746
\(226\) −0.715652 −0.0476045
\(227\) −15.3772 −1.02062 −0.510309 0.859991i \(-0.670469\pi\)
−0.510309 + 0.859991i \(0.670469\pi\)
\(228\) 37.3782 2.47543
\(229\) 28.8247 1.90479 0.952394 0.304871i \(-0.0986134\pi\)
0.952394 + 0.304871i \(0.0986134\pi\)
\(230\) −0.793687 −0.0523342
\(231\) −5.82365 −0.383168
\(232\) 6.83575 0.448789
\(233\) 21.3999 1.40195 0.700977 0.713183i \(-0.252747\pi\)
0.700977 + 0.713183i \(0.252747\pi\)
\(234\) 0.544035 0.0355647
\(235\) 3.08560 0.201282
\(236\) 0.380379 0.0247605
\(237\) 25.4308 1.65191
\(238\) 4.89977 0.317605
\(239\) −23.2103 −1.50135 −0.750676 0.660670i \(-0.770272\pi\)
−0.750676 + 0.660670i \(0.770272\pi\)
\(240\) −7.96476 −0.514123
\(241\) 15.7636 1.01543 0.507713 0.861526i \(-0.330491\pi\)
0.507713 + 0.861526i \(0.330491\pi\)
\(242\) −0.327392 −0.0210456
\(243\) 20.8859 1.33983
\(244\) 20.7381 1.32762
\(245\) −0.934228 −0.0596857
\(246\) −0.768788 −0.0490161
\(247\) −5.35573 −0.340777
\(248\) 9.22008 0.585476
\(249\) −31.1050 −1.97120
\(250\) −0.327392 −0.0207061
\(251\) 4.88454 0.308309 0.154155 0.988047i \(-0.450735\pi\)
0.154155 + 0.988047i \(0.450735\pi\)
\(252\) −12.0795 −0.760939
\(253\) 2.42427 0.152413
\(254\) −0.702085 −0.0440527
\(255\) 14.3687 0.899801
\(256\) 8.09738 0.506086
\(257\) 15.0578 0.939283 0.469641 0.882857i \(-0.344383\pi\)
0.469641 + 0.882857i \(0.344383\pi\)
\(258\) 4.31562 0.268678
\(259\) −12.5416 −0.779295
\(260\) 1.21386 0.0752803
\(261\) 13.8980 0.860266
\(262\) −4.34068 −0.268168
\(263\) 16.2991 1.00505 0.502524 0.864563i \(-0.332405\pi\)
0.502524 + 0.864563i \(0.332405\pi\)
\(264\) −3.01359 −0.185473
\(265\) 3.89942 0.239539
\(266\) −6.73395 −0.412885
\(267\) −19.8258 −1.21332
\(268\) 20.1521 1.23099
\(269\) 23.9598 1.46085 0.730426 0.682992i \(-0.239322\pi\)
0.730426 + 0.682992i \(0.239322\pi\)
\(270\) −0.316478 −0.0192603
\(271\) 13.9318 0.846295 0.423148 0.906061i \(-0.360925\pi\)
0.423148 + 0.906061i \(0.360925\pi\)
\(272\) −20.4685 −1.24108
\(273\) 3.73469 0.226034
\(274\) −1.48275 −0.0895762
\(275\) 1.00000 0.0603023
\(276\) 10.8503 0.653111
\(277\) −11.7456 −0.705723 −0.352861 0.935676i \(-0.614791\pi\)
−0.352861 + 0.935676i \(0.614791\pi\)
\(278\) 6.17639 0.370435
\(279\) 18.7457 1.12228
\(280\) 3.13888 0.187584
\(281\) −4.89579 −0.292058 −0.146029 0.989280i \(-0.546649\pi\)
−0.146029 + 0.989280i \(0.546649\pi\)
\(282\) 2.38869 0.142244
\(283\) −6.09546 −0.362338 −0.181169 0.983452i \(-0.557988\pi\)
−0.181169 + 0.983452i \(0.557988\pi\)
\(284\) 0.612505 0.0363455
\(285\) −19.7474 −1.16974
\(286\) 0.209956 0.0124150
\(287\) −2.44585 −0.144374
\(288\) −9.46232 −0.557573
\(289\) 19.9257 1.17210
\(290\) −1.75599 −0.103115
\(291\) 4.12035 0.241539
\(292\) −1.89281 −0.110769
\(293\) −2.88854 −0.168750 −0.0843750 0.996434i \(-0.526889\pi\)
−0.0843750 + 0.996434i \(0.526889\pi\)
\(294\) −0.723224 −0.0421793
\(295\) −0.200959 −0.0117003
\(296\) −6.48993 −0.377220
\(297\) 0.966665 0.0560916
\(298\) −4.17739 −0.241990
\(299\) −1.55468 −0.0899095
\(300\) 4.47569 0.258404
\(301\) 13.7298 0.791375
\(302\) −4.73165 −0.272276
\(303\) 8.17588 0.469692
\(304\) 28.1306 1.61340
\(305\) −10.9562 −0.627351
\(306\) 5.15503 0.294694
\(307\) −12.1863 −0.695511 −0.347756 0.937585i \(-0.613056\pi\)
−0.347756 + 0.937585i \(0.613056\pi\)
\(308\) −4.66177 −0.265629
\(309\) 37.4389 2.12983
\(310\) −2.36849 −0.134521
\(311\) 2.83566 0.160795 0.0803977 0.996763i \(-0.474381\pi\)
0.0803977 + 0.996763i \(0.474381\pi\)
\(312\) 1.93261 0.109412
\(313\) −8.16184 −0.461334 −0.230667 0.973033i \(-0.574091\pi\)
−0.230667 + 0.973033i \(0.574091\pi\)
\(314\) −0.562976 −0.0317706
\(315\) 6.38178 0.359573
\(316\) 20.3571 1.14518
\(317\) −6.90411 −0.387773 −0.193887 0.981024i \(-0.562109\pi\)
−0.193887 + 0.981024i \(0.562109\pi\)
\(318\) 3.01870 0.169280
\(319\) 5.36357 0.300302
\(320\) −5.54120 −0.309763
\(321\) 15.5749 0.869304
\(322\) −1.95475 −0.108934
\(323\) −50.7485 −2.82372
\(324\) 19.0404 1.05780
\(325\) −0.641298 −0.0355728
\(326\) −3.37962 −0.187180
\(327\) −27.0413 −1.49539
\(328\) −1.26566 −0.0698846
\(329\) 7.59945 0.418971
\(330\) 0.774141 0.0426151
\(331\) −22.3558 −1.22878 −0.614392 0.789001i \(-0.710599\pi\)
−0.614392 + 0.789001i \(0.710599\pi\)
\(332\) −24.8993 −1.36652
\(333\) −13.1949 −0.723078
\(334\) 6.24499 0.341711
\(335\) −10.6466 −0.581688
\(336\) −19.6162 −1.07015
\(337\) −10.0892 −0.549595 −0.274797 0.961502i \(-0.588611\pi\)
−0.274797 + 0.961502i \(0.588611\pi\)
\(338\) 4.12145 0.224177
\(339\) −5.16876 −0.280728
\(340\) 11.5020 0.623782
\(341\) 7.23441 0.391765
\(342\) −7.08477 −0.383100
\(343\) −19.5410 −1.05512
\(344\) 7.10484 0.383067
\(345\) −5.73236 −0.308620
\(346\) −1.59742 −0.0858778
\(347\) 25.6422 1.37655 0.688274 0.725451i \(-0.258369\pi\)
0.688274 + 0.725451i \(0.258369\pi\)
\(348\) 24.0057 1.28684
\(349\) −24.9774 −1.33701 −0.668505 0.743707i \(-0.733066\pi\)
−0.668505 + 0.743707i \(0.733066\pi\)
\(350\) −0.806327 −0.0431000
\(351\) −0.619920 −0.0330889
\(352\) −3.65173 −0.194638
\(353\) 7.78170 0.414178 0.207089 0.978322i \(-0.433601\pi\)
0.207089 + 0.978322i \(0.433601\pi\)
\(354\) −0.155571 −0.00826849
\(355\) −0.323595 −0.0171746
\(356\) −15.8704 −0.841129
\(357\) 35.3883 1.87295
\(358\) −2.32412 −0.122833
\(359\) 30.4828 1.60882 0.804411 0.594073i \(-0.202481\pi\)
0.804411 + 0.594073i \(0.202481\pi\)
\(360\) 3.30241 0.174052
\(361\) 50.7457 2.67083
\(362\) −1.50630 −0.0791696
\(363\) −2.36457 −0.124108
\(364\) 2.98959 0.156697
\(365\) 1.00000 0.0523424
\(366\) −8.48166 −0.443343
\(367\) 2.96163 0.154596 0.0772980 0.997008i \(-0.475371\pi\)
0.0772980 + 0.997008i \(0.475371\pi\)
\(368\) 8.16586 0.425675
\(369\) −2.57327 −0.133959
\(370\) 1.66716 0.0866714
\(371\) 9.60379 0.498604
\(372\) 32.3790 1.67877
\(373\) −0.746015 −0.0386272 −0.0193136 0.999813i \(-0.506148\pi\)
−0.0193136 + 0.999813i \(0.506148\pi\)
\(374\) 1.98945 0.102872
\(375\) −2.36457 −0.122106
\(376\) 3.93252 0.202804
\(377\) −3.43965 −0.177151
\(378\) −0.779448 −0.0400905
\(379\) 6.58248 0.338119 0.169060 0.985606i \(-0.445927\pi\)
0.169060 + 0.985606i \(0.445927\pi\)
\(380\) −15.8076 −0.810914
\(381\) −5.07077 −0.259783
\(382\) 2.29537 0.117441
\(383\) 26.6271 1.36058 0.680290 0.732943i \(-0.261854\pi\)
0.680290 + 0.732943i \(0.261854\pi\)
\(384\) −21.5592 −1.10019
\(385\) 2.46288 0.125520
\(386\) −3.57522 −0.181974
\(387\) 14.4451 0.734287
\(388\) 3.29830 0.167446
\(389\) −27.7437 −1.40666 −0.703330 0.710864i \(-0.748304\pi\)
−0.703330 + 0.710864i \(0.748304\pi\)
\(390\) −0.496455 −0.0251390
\(391\) −14.7315 −0.745002
\(392\) −1.19065 −0.0601370
\(393\) −31.3503 −1.58142
\(394\) 1.86723 0.0940699
\(395\) −10.7550 −0.541141
\(396\) −4.90464 −0.246467
\(397\) −0.366934 −0.0184159 −0.00920794 0.999958i \(-0.502931\pi\)
−0.00920794 + 0.999958i \(0.502931\pi\)
\(398\) −5.70130 −0.285780
\(399\) −48.6355 −2.43482
\(400\) 3.36838 0.168419
\(401\) 27.6164 1.37909 0.689547 0.724240i \(-0.257809\pi\)
0.689547 + 0.724240i \(0.257809\pi\)
\(402\) −8.24200 −0.411073
\(403\) −4.63941 −0.231106
\(404\) 6.54471 0.325612
\(405\) −10.0593 −0.499851
\(406\) −4.32479 −0.214636
\(407\) −5.09224 −0.252413
\(408\) 18.3125 0.906605
\(409\) 23.3264 1.15342 0.576709 0.816950i \(-0.304337\pi\)
0.576709 + 0.816950i \(0.304337\pi\)
\(410\) 0.325128 0.0160569
\(411\) −10.7091 −0.528240
\(412\) 29.9695 1.47649
\(413\) −0.494938 −0.0243543
\(414\) −2.05659 −0.101076
\(415\) 13.1546 0.645735
\(416\) 2.34185 0.114819
\(417\) 44.6086 2.18449
\(418\) −2.73418 −0.133733
\(419\) −28.2163 −1.37846 −0.689229 0.724543i \(-0.742051\pi\)
−0.689229 + 0.724543i \(0.742051\pi\)
\(420\) 11.0231 0.537871
\(421\) 10.3554 0.504691 0.252346 0.967637i \(-0.418798\pi\)
0.252346 + 0.967637i \(0.418798\pi\)
\(422\) −8.54041 −0.415741
\(423\) 7.99536 0.388748
\(424\) 4.96971 0.241351
\(425\) −6.07665 −0.294761
\(426\) −0.250508 −0.0121372
\(427\) −26.9838 −1.30584
\(428\) 12.4675 0.602640
\(429\) 1.51639 0.0732122
\(430\) −1.82512 −0.0880150
\(431\) 11.9710 0.576625 0.288312 0.957536i \(-0.406906\pi\)
0.288312 + 0.957536i \(0.406906\pi\)
\(432\) 3.25609 0.156659
\(433\) 20.1829 0.969927 0.484963 0.874534i \(-0.338833\pi\)
0.484963 + 0.874534i \(0.338833\pi\)
\(434\) −5.83330 −0.280007
\(435\) −12.6825 −0.608081
\(436\) −21.6463 −1.03667
\(437\) 20.2460 0.968499
\(438\) 0.774141 0.0369899
\(439\) 0.532483 0.0254140 0.0127070 0.999919i \(-0.495955\pi\)
0.0127070 + 0.999919i \(0.495955\pi\)
\(440\) 1.27448 0.0607583
\(441\) −2.42076 −0.115274
\(442\) −1.27583 −0.0606850
\(443\) 25.8413 1.22776 0.613879 0.789400i \(-0.289608\pi\)
0.613879 + 0.789400i \(0.289608\pi\)
\(444\) −22.7913 −1.08163
\(445\) 8.38454 0.397465
\(446\) 4.95086 0.234430
\(447\) −30.1710 −1.42704
\(448\) −13.6473 −0.644775
\(449\) 25.4548 1.20129 0.600643 0.799518i \(-0.294911\pi\)
0.600643 + 0.799518i \(0.294911\pi\)
\(450\) −0.848334 −0.0399908
\(451\) −0.993086 −0.0467626
\(452\) −4.13754 −0.194613
\(453\) −34.1741 −1.60564
\(454\) 5.03436 0.236274
\(455\) −1.57944 −0.0740453
\(456\) −25.1676 −1.17858
\(457\) −20.7494 −0.970617 −0.485309 0.874343i \(-0.661293\pi\)
−0.485309 + 0.874343i \(0.661293\pi\)
\(458\) −9.43696 −0.440960
\(459\) −5.87409 −0.274179
\(460\) −4.58869 −0.213949
\(461\) 14.7332 0.686196 0.343098 0.939300i \(-0.388524\pi\)
0.343098 + 0.939300i \(0.388524\pi\)
\(462\) 1.90662 0.0887038
\(463\) −36.0823 −1.67689 −0.838443 0.544989i \(-0.816534\pi\)
−0.838443 + 0.544989i \(0.816534\pi\)
\(464\) 18.0665 0.838718
\(465\) −17.1063 −0.793284
\(466\) −7.00616 −0.324554
\(467\) 7.80516 0.361180 0.180590 0.983558i \(-0.442199\pi\)
0.180590 + 0.983558i \(0.442199\pi\)
\(468\) 3.14534 0.145393
\(469\) −26.2214 −1.21079
\(470\) −1.01020 −0.0465971
\(471\) −4.06606 −0.187354
\(472\) −0.256118 −0.0117888
\(473\) 5.57472 0.256326
\(474\) −8.32586 −0.382419
\(475\) 8.35139 0.383188
\(476\) 28.3280 1.29841
\(477\) 10.1041 0.462636
\(478\) 7.59888 0.347565
\(479\) 38.3255 1.75114 0.875569 0.483094i \(-0.160487\pi\)
0.875569 + 0.483094i \(0.160487\pi\)
\(480\) 8.63477 0.394122
\(481\) 3.26564 0.148900
\(482\) −5.16089 −0.235072
\(483\) −14.1181 −0.642396
\(484\) −1.89281 −0.0860370
\(485\) −1.74254 −0.0791245
\(486\) −6.83789 −0.310173
\(487\) 1.75485 0.0795197 0.0397598 0.999209i \(-0.487341\pi\)
0.0397598 + 0.999209i \(0.487341\pi\)
\(488\) −13.9634 −0.632095
\(489\) −24.4091 −1.10382
\(490\) 0.305859 0.0138173
\(491\) −26.6477 −1.20259 −0.601297 0.799026i \(-0.705349\pi\)
−0.601297 + 0.799026i \(0.705349\pi\)
\(492\) −4.44474 −0.200385
\(493\) −32.5926 −1.46790
\(494\) 1.75342 0.0788902
\(495\) 2.59119 0.116465
\(496\) 24.3682 1.09417
\(497\) −0.796975 −0.0357492
\(498\) 10.1835 0.456335
\(499\) −28.4960 −1.27566 −0.637829 0.770178i \(-0.720167\pi\)
−0.637829 + 0.770178i \(0.720167\pi\)
\(500\) −1.89281 −0.0846492
\(501\) 45.1041 2.01510
\(502\) −1.59916 −0.0713740
\(503\) −4.60256 −0.205218 −0.102609 0.994722i \(-0.532719\pi\)
−0.102609 + 0.994722i \(0.532719\pi\)
\(504\) 8.13343 0.362292
\(505\) −3.45766 −0.153864
\(506\) −0.793687 −0.0352837
\(507\) 29.7669 1.32200
\(508\) −4.05910 −0.180093
\(509\) 6.95620 0.308328 0.154164 0.988045i \(-0.450732\pi\)
0.154164 + 0.988045i \(0.450732\pi\)
\(510\) −4.70419 −0.208305
\(511\) 2.46288 0.108951
\(512\) −20.8862 −0.923050
\(513\) 8.07299 0.356431
\(514\) −4.92982 −0.217445
\(515\) −15.8333 −0.697699
\(516\) 24.9507 1.09839
\(517\) 3.08560 0.135704
\(518\) 4.10601 0.180408
\(519\) −11.5373 −0.506430
\(520\) −0.817319 −0.0358418
\(521\) −8.91754 −0.390685 −0.195342 0.980735i \(-0.562582\pi\)
−0.195342 + 0.980735i \(0.562582\pi\)
\(522\) −4.55010 −0.199153
\(523\) −17.4525 −0.763144 −0.381572 0.924339i \(-0.624617\pi\)
−0.381572 + 0.924339i \(0.624617\pi\)
\(524\) −25.0956 −1.09631
\(525\) −5.82365 −0.254165
\(526\) −5.33621 −0.232670
\(527\) −43.9610 −1.91497
\(528\) −7.96476 −0.346622
\(529\) −17.1229 −0.744474
\(530\) −1.27664 −0.0554536
\(531\) −0.520723 −0.0225975
\(532\) −38.9323 −1.68793
\(533\) 0.636864 0.0275856
\(534\) 6.49082 0.280885
\(535\) −6.58676 −0.284771
\(536\) −13.5689 −0.586087
\(537\) −16.7858 −0.724361
\(538\) −7.84423 −0.338189
\(539\) −0.934228 −0.0402401
\(540\) −1.82972 −0.0787385
\(541\) −29.6284 −1.27382 −0.636911 0.770937i \(-0.719788\pi\)
−0.636911 + 0.770937i \(0.719788\pi\)
\(542\) −4.56115 −0.195918
\(543\) −10.8792 −0.466871
\(544\) 22.1903 0.951402
\(545\) 11.4360 0.489866
\(546\) −1.22271 −0.0523271
\(547\) 5.42820 0.232093 0.116046 0.993244i \(-0.462978\pi\)
0.116046 + 0.993244i \(0.462978\pi\)
\(548\) −8.57251 −0.366199
\(549\) −28.3896 −1.21164
\(550\) −0.327392 −0.0139600
\(551\) 44.7933 1.90826
\(552\) −7.30575 −0.310953
\(553\) −26.4882 −1.12639
\(554\) 3.84541 0.163376
\(555\) 12.0409 0.511110
\(556\) 35.7088 1.51439
\(557\) −43.3884 −1.83842 −0.919212 0.393762i \(-0.871173\pi\)
−0.919212 + 0.393762i \(0.871173\pi\)
\(558\) −6.13720 −0.259808
\(559\) −3.57505 −0.151209
\(560\) 8.29590 0.350566
\(561\) 14.3687 0.606646
\(562\) 1.60284 0.0676118
\(563\) −32.9000 −1.38657 −0.693284 0.720665i \(-0.743837\pi\)
−0.693284 + 0.720665i \(0.743837\pi\)
\(564\) 13.8102 0.581514
\(565\) 2.18592 0.0919623
\(566\) 1.99561 0.0838816
\(567\) −24.7749 −1.04045
\(568\) −0.412414 −0.0173045
\(569\) −24.0786 −1.00943 −0.504714 0.863287i \(-0.668402\pi\)
−0.504714 + 0.863287i \(0.668402\pi\)
\(570\) 6.46515 0.270795
\(571\) 26.4741 1.10791 0.553953 0.832548i \(-0.313119\pi\)
0.553953 + 0.832548i \(0.313119\pi\)
\(572\) 1.21386 0.0507540
\(573\) 16.5782 0.692563
\(574\) 0.800751 0.0334227
\(575\) 2.42427 0.101099
\(576\) −14.3583 −0.598263
\(577\) 34.5156 1.43690 0.718452 0.695577i \(-0.244851\pi\)
0.718452 + 0.695577i \(0.244851\pi\)
\(578\) −6.52352 −0.271343
\(579\) −25.8218 −1.07312
\(580\) −10.1522 −0.421549
\(581\) 32.3983 1.34411
\(582\) −1.34897 −0.0559165
\(583\) 3.89942 0.161497
\(584\) 1.27448 0.0527382
\(585\) −1.66172 −0.0687038
\(586\) 0.945683 0.0390658
\(587\) 37.2797 1.53870 0.769350 0.638828i \(-0.220580\pi\)
0.769350 + 0.638828i \(0.220580\pi\)
\(588\) −4.18132 −0.172435
\(589\) 60.4174 2.48945
\(590\) 0.0657924 0.00270863
\(591\) 13.4860 0.554739
\(592\) −17.1526 −0.704966
\(593\) 26.6379 1.09389 0.546944 0.837169i \(-0.315791\pi\)
0.546944 + 0.837169i \(0.315791\pi\)
\(594\) −0.316478 −0.0129853
\(595\) −14.9661 −0.613549
\(596\) −24.1516 −0.989286
\(597\) −41.1773 −1.68527
\(598\) 0.508990 0.0208141
\(599\) 43.8011 1.78966 0.894832 0.446404i \(-0.147296\pi\)
0.894832 + 0.446404i \(0.147296\pi\)
\(600\) −3.01359 −0.123029
\(601\) −47.8903 −1.95349 −0.976743 0.214412i \(-0.931217\pi\)
−0.976743 + 0.214412i \(0.931217\pi\)
\(602\) −4.49504 −0.183204
\(603\) −27.5874 −1.12345
\(604\) −27.3560 −1.11310
\(605\) 1.00000 0.0406558
\(606\) −2.67672 −0.108734
\(607\) −0.500138 −0.0203000 −0.0101500 0.999948i \(-0.503231\pi\)
−0.0101500 + 0.999948i \(0.503231\pi\)
\(608\) −30.4970 −1.23682
\(609\) −31.2356 −1.26573
\(610\) 3.58698 0.145232
\(611\) −1.97879 −0.0800532
\(612\) 29.8038 1.20475
\(613\) 31.3670 1.26690 0.633450 0.773784i \(-0.281638\pi\)
0.633450 + 0.773784i \(0.281638\pi\)
\(614\) 3.98971 0.161012
\(615\) 2.34822 0.0946893
\(616\) 3.13888 0.126469
\(617\) −27.1936 −1.09477 −0.547386 0.836880i \(-0.684377\pi\)
−0.547386 + 0.836880i \(0.684377\pi\)
\(618\) −12.2572 −0.493057
\(619\) 42.6195 1.71302 0.856511 0.516130i \(-0.172628\pi\)
0.856511 + 0.516130i \(0.172628\pi\)
\(620\) −13.6934 −0.549940
\(621\) 2.34346 0.0940397
\(622\) −0.928371 −0.0372243
\(623\) 20.6501 0.827329
\(624\) 5.10778 0.204475
\(625\) 1.00000 0.0400000
\(626\) 2.67212 0.106799
\(627\) −19.7474 −0.788637
\(628\) −3.25484 −0.129882
\(629\) 30.9438 1.23381
\(630\) −2.08934 −0.0832414
\(631\) −14.5786 −0.580366 −0.290183 0.956971i \(-0.593716\pi\)
−0.290183 + 0.956971i \(0.593716\pi\)
\(632\) −13.7069 −0.545233
\(633\) −61.6826 −2.45166
\(634\) 2.26035 0.0897699
\(635\) 2.14448 0.0851010
\(636\) 17.4526 0.692040
\(637\) 0.599119 0.0237380
\(638\) −1.75599 −0.0695203
\(639\) −0.838495 −0.0331704
\(640\) 9.11761 0.360405
\(641\) 39.1527 1.54644 0.773219 0.634139i \(-0.218645\pi\)
0.773219 + 0.634139i \(0.218645\pi\)
\(642\) −5.09908 −0.201245
\(643\) 25.0115 0.986358 0.493179 0.869928i \(-0.335835\pi\)
0.493179 + 0.869928i \(0.335835\pi\)
\(644\) −11.3014 −0.445338
\(645\) −13.1818 −0.519033
\(646\) 16.6146 0.653695
\(647\) −12.8263 −0.504253 −0.252127 0.967694i \(-0.581130\pi\)
−0.252127 + 0.967694i \(0.581130\pi\)
\(648\) −12.8203 −0.503631
\(649\) −0.200959 −0.00788834
\(650\) 0.209956 0.00823515
\(651\) −42.1307 −1.65123
\(652\) −19.5393 −0.765217
\(653\) −29.0871 −1.13827 −0.569133 0.822245i \(-0.692721\pi\)
−0.569133 + 0.822245i \(0.692721\pi\)
\(654\) 8.85310 0.346184
\(655\) 13.2584 0.518047
\(656\) −3.34509 −0.130604
\(657\) 2.59119 0.101092
\(658\) −2.48800 −0.0969923
\(659\) −23.4984 −0.915366 −0.457683 0.889115i \(-0.651321\pi\)
−0.457683 + 0.889115i \(0.651321\pi\)
\(660\) 4.47569 0.174216
\(661\) 18.5339 0.720886 0.360443 0.932781i \(-0.382626\pi\)
0.360443 + 0.932781i \(0.382626\pi\)
\(662\) 7.31910 0.284465
\(663\) −9.21460 −0.357865
\(664\) 16.7653 0.650618
\(665\) 20.5685 0.797610
\(666\) 4.31992 0.167393
\(667\) 13.0028 0.503469
\(668\) 36.1054 1.39696
\(669\) 35.7573 1.38246
\(670\) 3.48562 0.134661
\(671\) −10.9562 −0.422960
\(672\) 21.2664 0.820369
\(673\) −15.2624 −0.588321 −0.294160 0.955756i \(-0.595040\pi\)
−0.294160 + 0.955756i \(0.595040\pi\)
\(674\) 3.30313 0.127232
\(675\) 0.966665 0.0372070
\(676\) 23.8281 0.916467
\(677\) −36.4187 −1.39969 −0.699843 0.714297i \(-0.746747\pi\)
−0.699843 + 0.714297i \(0.746747\pi\)
\(678\) 1.69221 0.0649889
\(679\) −4.29165 −0.164699
\(680\) −7.74455 −0.296990
\(681\) 36.3603 1.39333
\(682\) −2.36849 −0.0906941
\(683\) 1.68988 0.0646615 0.0323307 0.999477i \(-0.489707\pi\)
0.0323307 + 0.999477i \(0.489707\pi\)
\(684\) −40.9605 −1.56617
\(685\) 4.52897 0.173043
\(686\) 6.39758 0.244261
\(687\) −68.1579 −2.60039
\(688\) 18.7777 0.715895
\(689\) −2.50069 −0.0952686
\(690\) 1.87673 0.0714458
\(691\) −8.73047 −0.332123 −0.166061 0.986115i \(-0.553105\pi\)
−0.166061 + 0.986115i \(0.553105\pi\)
\(692\) −9.23547 −0.351080
\(693\) 6.38178 0.242424
\(694\) −8.39506 −0.318672
\(695\) −18.8654 −0.715607
\(696\) −16.1636 −0.612679
\(697\) 6.03464 0.228578
\(698\) 8.17741 0.309519
\(699\) −50.6016 −1.91393
\(700\) −4.66177 −0.176198
\(701\) −26.8542 −1.01427 −0.507135 0.861867i \(-0.669295\pi\)
−0.507135 + 0.861867i \(0.669295\pi\)
\(702\) 0.202957 0.00766012
\(703\) −42.5272 −1.60395
\(704\) −5.54120 −0.208842
\(705\) −7.29611 −0.274787
\(706\) −2.54767 −0.0958827
\(707\) −8.51580 −0.320270
\(708\) −0.899432 −0.0338027
\(709\) 35.9422 1.34984 0.674919 0.737892i \(-0.264178\pi\)
0.674919 + 0.737892i \(0.264178\pi\)
\(710\) 0.105942 0.00397595
\(711\) −27.8681 −1.04514
\(712\) 10.6859 0.400471
\(713\) 17.5382 0.656810
\(714\) −11.5858 −0.433589
\(715\) −0.641298 −0.0239832
\(716\) −13.4369 −0.502159
\(717\) 54.8825 2.04962
\(718\) −9.97984 −0.372444
\(719\) 32.7152 1.22007 0.610036 0.792374i \(-0.291155\pi\)
0.610036 + 0.792374i \(0.291155\pi\)
\(720\) 8.72809 0.325277
\(721\) −38.9955 −1.45227
\(722\) −16.6137 −0.618299
\(723\) −37.2742 −1.38624
\(724\) −8.70869 −0.323656
\(725\) 5.36357 0.199198
\(726\) 0.774141 0.0287311
\(727\) −17.9525 −0.665820 −0.332910 0.942959i \(-0.608031\pi\)
−0.332910 + 0.942959i \(0.608031\pi\)
\(728\) −2.01296 −0.0746052
\(729\) −19.2083 −0.711419
\(730\) −0.327392 −0.0121173
\(731\) −33.8756 −1.25293
\(732\) −49.0366 −1.81245
\(733\) 41.1438 1.51968 0.759840 0.650110i \(-0.225277\pi\)
0.759840 + 0.650110i \(0.225277\pi\)
\(734\) −0.969614 −0.0357891
\(735\) 2.20905 0.0814819
\(736\) −8.85279 −0.326318
\(737\) −10.6466 −0.392174
\(738\) 0.842468 0.0310117
\(739\) 11.4091 0.419692 0.209846 0.977734i \(-0.432704\pi\)
0.209846 + 0.977734i \(0.432704\pi\)
\(740\) 9.63866 0.354324
\(741\) 12.6640 0.465223
\(742\) −3.14420 −0.115427
\(743\) 10.8685 0.398725 0.199362 0.979926i \(-0.436113\pi\)
0.199362 + 0.979926i \(0.436113\pi\)
\(744\) −21.8015 −0.799283
\(745\) 12.7596 0.467475
\(746\) 0.244239 0.00894224
\(747\) 34.0861 1.24715
\(748\) 11.5020 0.420554
\(749\) −16.2224 −0.592754
\(750\) 0.774141 0.0282676
\(751\) −14.7036 −0.536541 −0.268271 0.963344i \(-0.586452\pi\)
−0.268271 + 0.963344i \(0.586452\pi\)
\(752\) 10.3935 0.379010
\(753\) −11.5498 −0.420899
\(754\) 1.12611 0.0410106
\(755\) 14.4526 0.525983
\(756\) −4.50637 −0.163895
\(757\) 12.3967 0.450565 0.225282 0.974294i \(-0.427670\pi\)
0.225282 + 0.974294i \(0.427670\pi\)
\(758\) −2.15505 −0.0782750
\(759\) −5.73236 −0.208071
\(760\) 10.6436 0.386086
\(761\) 25.8774 0.938053 0.469027 0.883184i \(-0.344605\pi\)
0.469027 + 0.883184i \(0.344605\pi\)
\(762\) 1.66013 0.0601401
\(763\) 28.1656 1.01966
\(764\) 13.2707 0.480116
\(765\) −15.7457 −0.569289
\(766\) −8.71749 −0.314976
\(767\) 0.128875 0.00465340
\(768\) −19.1468 −0.690901
\(769\) −36.7336 −1.32465 −0.662323 0.749218i \(-0.730429\pi\)
−0.662323 + 0.749218i \(0.730429\pi\)
\(770\) −0.806327 −0.0290580
\(771\) −35.6053 −1.28229
\(772\) −20.6701 −0.743934
\(773\) −50.3884 −1.81235 −0.906173 0.422907i \(-0.861010\pi\)
−0.906173 + 0.422907i \(0.861010\pi\)
\(774\) −4.72922 −0.169988
\(775\) 7.23441 0.259868
\(776\) −2.22082 −0.0797228
\(777\) 29.6554 1.06388
\(778\) 9.08305 0.325643
\(779\) −8.29364 −0.297151
\(780\) −2.87025 −0.102772
\(781\) −0.323595 −0.0115791
\(782\) 4.82296 0.172469
\(783\) 5.18478 0.185289
\(784\) −3.14683 −0.112387
\(785\) 1.71958 0.0613744
\(786\) 10.2638 0.366099
\(787\) 36.6300 1.30572 0.652859 0.757479i \(-0.273569\pi\)
0.652859 + 0.757479i \(0.273569\pi\)
\(788\) 10.7954 0.384570
\(789\) −38.5405 −1.37208
\(790\) 3.52109 0.125275
\(791\) 5.38365 0.191421
\(792\) 3.30241 0.117346
\(793\) 7.02620 0.249508
\(794\) 0.120131 0.00426329
\(795\) −9.22044 −0.327015
\(796\) −32.9620 −1.16831
\(797\) 26.3137 0.932080 0.466040 0.884764i \(-0.345680\pi\)
0.466040 + 0.884764i \(0.345680\pi\)
\(798\) 15.9229 0.563664
\(799\) −18.7501 −0.663331
\(800\) −3.65173 −0.129108
\(801\) 21.7259 0.767648
\(802\) −9.04137 −0.319262
\(803\) 1.00000 0.0352892
\(804\) −47.6511 −1.68052
\(805\) 5.97068 0.210439
\(806\) 1.51891 0.0535012
\(807\) −56.6545 −1.99433
\(808\) −4.40671 −0.155027
\(809\) 39.1233 1.37550 0.687751 0.725947i \(-0.258598\pi\)
0.687751 + 0.725947i \(0.258598\pi\)
\(810\) 3.29334 0.115716
\(811\) 5.79807 0.203598 0.101799 0.994805i \(-0.467540\pi\)
0.101799 + 0.994805i \(0.467540\pi\)
\(812\) −25.0038 −0.877460
\(813\) −32.9427 −1.15535
\(814\) 1.66716 0.0584338
\(815\) 10.3229 0.361594
\(816\) 48.3991 1.69431
\(817\) 46.5566 1.62881
\(818\) −7.63689 −0.267018
\(819\) −4.09262 −0.143008
\(820\) 1.87973 0.0656429
\(821\) −3.76985 −0.131569 −0.0657843 0.997834i \(-0.520955\pi\)
−0.0657843 + 0.997834i \(0.520955\pi\)
\(822\) 3.50606 0.122288
\(823\) −21.5281 −0.750421 −0.375210 0.926940i \(-0.622430\pi\)
−0.375210 + 0.926940i \(0.622430\pi\)
\(824\) −20.1792 −0.702974
\(825\) −2.36457 −0.0823237
\(826\) 0.162039 0.00563805
\(827\) 9.66591 0.336117 0.168058 0.985777i \(-0.446250\pi\)
0.168058 + 0.985777i \(0.446250\pi\)
\(828\) −11.8902 −0.413212
\(829\) 17.5613 0.609929 0.304965 0.952364i \(-0.401355\pi\)
0.304965 + 0.952364i \(0.401355\pi\)
\(830\) −4.30672 −0.149488
\(831\) 27.7732 0.963442
\(832\) 3.55356 0.123198
\(833\) 5.67698 0.196696
\(834\) −14.6045 −0.505713
\(835\) −19.0750 −0.660117
\(836\) −15.8076 −0.546718
\(837\) 6.99325 0.241722
\(838\) 9.23780 0.319115
\(839\) −14.8219 −0.511708 −0.255854 0.966715i \(-0.582357\pi\)
−0.255854 + 0.966715i \(0.582357\pi\)
\(840\) −7.42210 −0.256087
\(841\) −0.232084 −0.00800289
\(842\) −3.39027 −0.116837
\(843\) 11.5764 0.398714
\(844\) −49.3763 −1.69960
\(845\) −12.5887 −0.433066
\(846\) −2.61762 −0.0899956
\(847\) 2.46288 0.0846255
\(848\) 13.1347 0.451047
\(849\) 14.4131 0.494658
\(850\) 1.98945 0.0682375
\(851\) −12.3450 −0.423180
\(852\) −1.44831 −0.0496183
\(853\) −17.0110 −0.582445 −0.291223 0.956655i \(-0.594062\pi\)
−0.291223 + 0.956655i \(0.594062\pi\)
\(854\) 8.83429 0.302303
\(855\) 21.6400 0.740073
\(856\) −8.39467 −0.286924
\(857\) 34.9627 1.19430 0.597152 0.802128i \(-0.296299\pi\)
0.597152 + 0.802128i \(0.296299\pi\)
\(858\) −0.496455 −0.0169487
\(859\) 35.1109 1.19797 0.598985 0.800760i \(-0.295571\pi\)
0.598985 + 0.800760i \(0.295571\pi\)
\(860\) −10.5519 −0.359817
\(861\) 5.78338 0.197097
\(862\) −3.91922 −0.133489
\(863\) 31.4924 1.07201 0.536006 0.844214i \(-0.319932\pi\)
0.536006 + 0.844214i \(0.319932\pi\)
\(864\) −3.53000 −0.120093
\(865\) 4.87923 0.165899
\(866\) −6.60771 −0.224539
\(867\) −47.1157 −1.60013
\(868\) −33.7252 −1.14471
\(869\) −10.7550 −0.364837
\(870\) 4.15216 0.140771
\(871\) 6.82767 0.231347
\(872\) 14.5750 0.493570
\(873\) −4.51524 −0.152818
\(874\) −6.62839 −0.224208
\(875\) 2.46288 0.0832605
\(876\) 4.47569 0.151220
\(877\) −12.9989 −0.438941 −0.219471 0.975619i \(-0.570433\pi\)
−0.219471 + 0.975619i \(0.570433\pi\)
\(878\) −0.174331 −0.00588338
\(879\) 6.83014 0.230375
\(880\) 3.36838 0.113548
\(881\) 18.5787 0.625933 0.312966 0.949764i \(-0.398677\pi\)
0.312966 + 0.949764i \(0.398677\pi\)
\(882\) 0.792538 0.0266861
\(883\) −37.9881 −1.27840 −0.639201 0.769040i \(-0.720735\pi\)
−0.639201 + 0.769040i \(0.720735\pi\)
\(884\) −7.37620 −0.248088
\(885\) 0.475182 0.0159731
\(886\) −8.46023 −0.284227
\(887\) 14.5261 0.487738 0.243869 0.969808i \(-0.421583\pi\)
0.243869 + 0.969808i \(0.421583\pi\)
\(888\) 15.3459 0.514975
\(889\) 5.28159 0.177139
\(890\) −2.74503 −0.0920137
\(891\) −10.0593 −0.337000
\(892\) 28.6234 0.958381
\(893\) 25.7690 0.862328
\(894\) 9.87773 0.330361
\(895\) 7.09888 0.237289
\(896\) 22.4556 0.750188
\(897\) 3.67615 0.122743
\(898\) −8.33369 −0.278099
\(899\) 38.8023 1.29413
\(900\) −4.90464 −0.163488
\(901\) −23.6954 −0.789408
\(902\) 0.325128 0.0108256
\(903\) −32.4652 −1.08037
\(904\) 2.78590 0.0926577
\(905\) 4.60092 0.152940
\(906\) 11.1883 0.371707
\(907\) −43.7140 −1.45150 −0.725750 0.687959i \(-0.758507\pi\)
−0.725750 + 0.687959i \(0.758507\pi\)
\(908\) 29.1061 0.965920
\(909\) −8.95945 −0.297166
\(910\) 0.517096 0.0171416
\(911\) −22.0078 −0.729152 −0.364576 0.931174i \(-0.618786\pi\)
−0.364576 + 0.931174i \(0.618786\pi\)
\(912\) −66.5168 −2.20259
\(913\) 13.1546 0.435355
\(914\) 6.79319 0.224699
\(915\) 25.9067 0.856450
\(916\) −54.5597 −1.80270
\(917\) 32.6538 1.07832
\(918\) 1.92313 0.0634727
\(919\) −37.4451 −1.23520 −0.617600 0.786492i \(-0.711895\pi\)
−0.617600 + 0.786492i \(0.711895\pi\)
\(920\) 3.08968 0.101864
\(921\) 28.8154 0.949501
\(922\) −4.82355 −0.158855
\(923\) 0.207521 0.00683063
\(924\) 11.0231 0.362633
\(925\) −5.09224 −0.167432
\(926\) 11.8130 0.388201
\(927\) −41.0271 −1.34751
\(928\) −19.5863 −0.642953
\(929\) −26.9397 −0.883863 −0.441932 0.897049i \(-0.645707\pi\)
−0.441932 + 0.897049i \(0.645707\pi\)
\(930\) 5.60045 0.183646
\(931\) −7.80210 −0.255704
\(932\) −40.5061 −1.32682
\(933\) −6.70511 −0.219515
\(934\) −2.55535 −0.0836135
\(935\) −6.07665 −0.198728
\(936\) −2.11783 −0.0692234
\(937\) −0.290083 −0.00947661 −0.00473831 0.999989i \(-0.501508\pi\)
−0.00473831 + 0.999989i \(0.501508\pi\)
\(938\) 8.58467 0.280299
\(939\) 19.2992 0.629806
\(940\) −5.84047 −0.190495
\(941\) 12.8927 0.420292 0.210146 0.977670i \(-0.432606\pi\)
0.210146 + 0.977670i \(0.432606\pi\)
\(942\) 1.33120 0.0433727
\(943\) −2.40751 −0.0783993
\(944\) −0.676906 −0.0220314
\(945\) 2.38078 0.0774467
\(946\) −1.82512 −0.0593397
\(947\) −14.2277 −0.462337 −0.231168 0.972914i \(-0.574255\pi\)
−0.231168 + 0.972914i \(0.574255\pi\)
\(948\) −48.1359 −1.56338
\(949\) −0.641298 −0.0208174
\(950\) −2.73418 −0.0887084
\(951\) 16.3252 0.529382
\(952\) −19.0739 −0.618188
\(953\) 26.5061 0.858618 0.429309 0.903158i \(-0.358757\pi\)
0.429309 + 0.903158i \(0.358757\pi\)
\(954\) −3.30801 −0.107101
\(955\) −7.01107 −0.226873
\(956\) 43.9329 1.42089
\(957\) −12.6825 −0.409968
\(958\) −12.5475 −0.405390
\(959\) 11.1543 0.360192
\(960\) 13.1026 0.422883
\(961\) 21.3367 0.688280
\(962\) −1.06915 −0.0344706
\(963\) −17.0675 −0.549994
\(964\) −29.8377 −0.961006
\(965\) 10.9203 0.351537
\(966\) 4.62215 0.148715
\(967\) 34.5708 1.11172 0.555861 0.831275i \(-0.312389\pi\)
0.555861 + 0.831275i \(0.312389\pi\)
\(968\) 1.27448 0.0409632
\(969\) 119.998 3.85490
\(970\) 0.570492 0.0183174
\(971\) −19.9766 −0.641080 −0.320540 0.947235i \(-0.603864\pi\)
−0.320540 + 0.947235i \(0.603864\pi\)
\(972\) −39.5332 −1.26803
\(973\) −46.4633 −1.48954
\(974\) −0.574523 −0.0184089
\(975\) 1.51639 0.0485635
\(976\) −36.9047 −1.18129
\(977\) 13.4085 0.428975 0.214488 0.976727i \(-0.431192\pi\)
0.214488 + 0.976727i \(0.431192\pi\)
\(978\) 7.99135 0.255535
\(979\) 8.38454 0.267971
\(980\) 1.76832 0.0564869
\(981\) 29.6329 0.946106
\(982\) 8.72424 0.278402
\(983\) 14.5455 0.463928 0.231964 0.972724i \(-0.425485\pi\)
0.231964 + 0.972724i \(0.425485\pi\)
\(984\) 2.99275 0.0954054
\(985\) −5.70336 −0.181724
\(986\) 10.6705 0.339819
\(987\) −17.9694 −0.571973
\(988\) 10.1374 0.322514
\(989\) 13.5146 0.429740
\(990\) −0.848334 −0.0269618
\(991\) 34.9445 1.11005 0.555024 0.831834i \(-0.312709\pi\)
0.555024 + 0.831834i \(0.312709\pi\)
\(992\) −26.4181 −0.838776
\(993\) 52.8618 1.67752
\(994\) 0.260923 0.00827598
\(995\) 17.4143 0.552070
\(996\) 58.8760 1.86556
\(997\) −14.0164 −0.443903 −0.221952 0.975058i \(-0.571243\pi\)
−0.221952 + 0.975058i \(0.571243\pi\)
\(998\) 9.32937 0.295316
\(999\) −4.92249 −0.155741
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 \(a_p\))