Properties

Label 6041.2.a.f.1.3
Level 6041
Weight 2
Character 6041.1
Self dual Yes
Analytic conductor 48.238
Analytic rank 0
Dimension 132
CM No

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Newspace parameters

Level: \( N \) = \( 6041 = 7 \cdot 863 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6041.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.2376278611\)
Analytic rank: \(0\)
Dimension: \(132\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.3
Character \(\chi\) = 6041.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.77966 q^{2}\) \(-1.97929 q^{3}\) \(+5.72652 q^{4}\) \(-3.34292 q^{5}\) \(+5.50177 q^{6}\) \(+1.00000 q^{7}\) \(-10.3585 q^{8}\) \(+0.917605 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.77966 q^{2}\) \(-1.97929 q^{3}\) \(+5.72652 q^{4}\) \(-3.34292 q^{5}\) \(+5.50177 q^{6}\) \(+1.00000 q^{7}\) \(-10.3585 q^{8}\) \(+0.917605 q^{9}\) \(+9.29218 q^{10}\) \(-6.19168 q^{11}\) \(-11.3345 q^{12}\) \(-4.77059 q^{13}\) \(-2.77966 q^{14}\) \(+6.61661 q^{15}\) \(+17.3400 q^{16}\) \(+6.95085 q^{17}\) \(-2.55063 q^{18}\) \(+5.45695 q^{19}\) \(-19.1433 q^{20}\) \(-1.97929 q^{21}\) \(+17.2108 q^{22}\) \(-5.40623 q^{23}\) \(+20.5025 q^{24}\) \(+6.17509 q^{25}\) \(+13.2606 q^{26}\) \(+4.12167 q^{27}\) \(+5.72652 q^{28}\) \(+1.50514 q^{29}\) \(-18.3920 q^{30}\) \(+6.57683 q^{31}\) \(-27.4824 q^{32}\) \(+12.2552 q^{33}\) \(-19.3210 q^{34}\) \(-3.34292 q^{35}\) \(+5.25469 q^{36}\) \(+2.34769 q^{37}\) \(-15.1685 q^{38}\) \(+9.44241 q^{39}\) \(+34.6275 q^{40}\) \(+3.44238 q^{41}\) \(+5.50177 q^{42}\) \(-10.2289 q^{43}\) \(-35.4568 q^{44}\) \(-3.06748 q^{45}\) \(+15.0275 q^{46}\) \(+4.97411 q^{47}\) \(-34.3210 q^{48}\) \(+1.00000 q^{49}\) \(-17.1647 q^{50}\) \(-13.7578 q^{51}\) \(-27.3189 q^{52}\) \(-0.487931 q^{53}\) \(-11.4569 q^{54}\) \(+20.6983 q^{55}\) \(-10.3585 q^{56}\) \(-10.8009 q^{57}\) \(-4.18379 q^{58}\) \(-1.04347 q^{59}\) \(+37.8902 q^{60}\) \(-11.8056 q^{61}\) \(-18.2814 q^{62}\) \(+0.917605 q^{63}\) \(+41.7118 q^{64}\) \(+15.9477 q^{65}\) \(-34.0652 q^{66}\) \(-7.29417 q^{67}\) \(+39.8042 q^{68}\) \(+10.7005 q^{69}\) \(+9.29218 q^{70}\) \(-0.563675 q^{71}\) \(-9.50499 q^{72}\) \(-13.1235 q^{73}\) \(-6.52579 q^{74}\) \(-12.2223 q^{75}\) \(+31.2494 q^{76}\) \(-6.19168 q^{77}\) \(-26.2467 q^{78}\) \(+2.20459 q^{79}\) \(-57.9662 q^{80}\) \(-10.9108 q^{81}\) \(-9.56864 q^{82}\) \(-16.2511 q^{83}\) \(-11.3345 q^{84}\) \(-23.2361 q^{85}\) \(+28.4328 q^{86}\) \(-2.97912 q^{87}\) \(+64.1364 q^{88}\) \(+1.00906 q^{89}\) \(+8.52655 q^{90}\) \(-4.77059 q^{91}\) \(-30.9589 q^{92}\) \(-13.0175 q^{93}\) \(-13.8263 q^{94}\) \(-18.2421 q^{95}\) \(+54.3958 q^{96}\) \(-3.71356 q^{97}\) \(-2.77966 q^{98}\) \(-5.68152 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(132q \) \(\mathstrut +\mathstrut 8q^{2} \) \(\mathstrut +\mathstrut 10q^{3} \) \(\mathstrut +\mathstrut 174q^{4} \) \(\mathstrut +\mathstrut 11q^{5} \) \(\mathstrut +\mathstrut 16q^{6} \) \(\mathstrut +\mathstrut 132q^{7} \) \(\mathstrut +\mathstrut 30q^{8} \) \(\mathstrut +\mathstrut 178q^{9} \) \(\mathstrut +\mathstrut 22q^{10} \) \(\mathstrut +\mathstrut 32q^{11} \) \(\mathstrut +\mathstrut 30q^{12} \) \(\mathstrut +\mathstrut 16q^{13} \) \(\mathstrut +\mathstrut 8q^{14} \) \(\mathstrut +\mathstrut 59q^{15} \) \(\mathstrut +\mathstrut 254q^{16} \) \(\mathstrut +\mathstrut 11q^{17} \) \(\mathstrut +\mathstrut 33q^{18} \) \(\mathstrut +\mathstrut 40q^{19} \) \(\mathstrut +\mathstrut 4q^{20} \) \(\mathstrut +\mathstrut 10q^{21} \) \(\mathstrut +\mathstrut 66q^{22} \) \(\mathstrut +\mathstrut 62q^{23} \) \(\mathstrut +\mathstrut 36q^{24} \) \(\mathstrut +\mathstrut 235q^{25} \) \(\mathstrut +\mathstrut 25q^{26} \) \(\mathstrut +\mathstrut 37q^{27} \) \(\mathstrut +\mathstrut 174q^{28} \) \(\mathstrut +\mathstrut 28q^{29} \) \(\mathstrut +\mathstrut 45q^{30} \) \(\mathstrut +\mathstrut 121q^{31} \) \(\mathstrut +\mathstrut 53q^{32} \) \(\mathstrut -\mathstrut 13q^{33} \) \(\mathstrut +\mathstrut 44q^{34} \) \(\mathstrut +\mathstrut 11q^{35} \) \(\mathstrut +\mathstrut 274q^{36} \) \(\mathstrut +\mathstrut 61q^{37} \) \(\mathstrut -\mathstrut 28q^{38} \) \(\mathstrut +\mathstrut 114q^{39} \) \(\mathstrut +\mathstrut 32q^{40} \) \(\mathstrut -\mathstrut q^{41} \) \(\mathstrut +\mathstrut 16q^{42} \) \(\mathstrut +\mathstrut 105q^{43} \) \(\mathstrut +\mathstrut 54q^{44} \) \(\mathstrut +\mathstrut 29q^{45} \) \(\mathstrut +\mathstrut 104q^{46} \) \(\mathstrut +\mathstrut 33q^{47} \) \(\mathstrut +\mathstrut 16q^{48} \) \(\mathstrut +\mathstrut 132q^{49} \) \(\mathstrut -\mathstrut 14q^{50} \) \(\mathstrut +\mathstrut 53q^{51} \) \(\mathstrut -\mathstrut 11q^{52} \) \(\mathstrut +\mathstrut 48q^{53} \) \(\mathstrut +\mathstrut 11q^{54} \) \(\mathstrut +\mathstrut 118q^{55} \) \(\mathstrut +\mathstrut 30q^{56} \) \(\mathstrut +\mathstrut 93q^{57} \) \(\mathstrut +\mathstrut 87q^{58} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut +\mathstrut 41q^{60} \) \(\mathstrut +\mathstrut 54q^{61} \) \(\mathstrut -\mathstrut 28q^{62} \) \(\mathstrut +\mathstrut 178q^{63} \) \(\mathstrut +\mathstrut 376q^{64} \) \(\mathstrut +\mathstrut 22q^{65} \) \(\mathstrut +\mathstrut 6q^{66} \) \(\mathstrut +\mathstrut 123q^{67} \) \(\mathstrut -\mathstrut 47q^{68} \) \(\mathstrut +\mathstrut 58q^{69} \) \(\mathstrut +\mathstrut 22q^{70} \) \(\mathstrut +\mathstrut 108q^{71} \) \(\mathstrut +\mathstrut 97q^{72} \) \(\mathstrut +\mathstrut q^{73} \) \(\mathstrut -\mathstrut 10q^{74} \) \(\mathstrut +\mathstrut 23q^{75} \) \(\mathstrut +\mathstrut 71q^{76} \) \(\mathstrut +\mathstrut 32q^{77} \) \(\mathstrut +\mathstrut 5q^{78} \) \(\mathstrut +\mathstrut 204q^{79} \) \(\mathstrut -\mathstrut 10q^{80} \) \(\mathstrut +\mathstrut 296q^{81} \) \(\mathstrut +\mathstrut 80q^{82} \) \(\mathstrut -\mathstrut 10q^{83} \) \(\mathstrut +\mathstrut 30q^{84} \) \(\mathstrut +\mathstrut 94q^{85} \) \(\mathstrut +\mathstrut 48q^{86} \) \(\mathstrut +\mathstrut 4q^{87} \) \(\mathstrut +\mathstrut 155q^{88} \) \(\mathstrut +\mathstrut q^{89} \) \(\mathstrut -\mathstrut 66q^{90} \) \(\mathstrut +\mathstrut 16q^{91} \) \(\mathstrut +\mathstrut 49q^{92} \) \(\mathstrut +\mathstrut 90q^{93} \) \(\mathstrut +\mathstrut 79q^{94} \) \(\mathstrut +\mathstrut 100q^{95} \) \(\mathstrut +\mathstrut q^{96} \) \(\mathstrut +\mathstrut 18q^{97} \) \(\mathstrut +\mathstrut 8q^{98} \) \(\mathstrut +\mathstrut 96q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.77966 −1.96552 −0.982759 0.184891i \(-0.940807\pi\)
−0.982759 + 0.184891i \(0.940807\pi\)
\(3\) −1.97929 −1.14275 −0.571373 0.820690i \(-0.693589\pi\)
−0.571373 + 0.820690i \(0.693589\pi\)
\(4\) 5.72652 2.86326
\(5\) −3.34292 −1.49500 −0.747499 0.664263i \(-0.768745\pi\)
−0.747499 + 0.664263i \(0.768745\pi\)
\(6\) 5.50177 2.24609
\(7\) 1.00000 0.377964
\(8\) −10.3585 −3.66227
\(9\) 0.917605 0.305868
\(10\) 9.29218 2.93844
\(11\) −6.19168 −1.86686 −0.933431 0.358756i \(-0.883201\pi\)
−0.933431 + 0.358756i \(0.883201\pi\)
\(12\) −11.3345 −3.27198
\(13\) −4.77059 −1.32312 −0.661562 0.749890i \(-0.730106\pi\)
−0.661562 + 0.749890i \(0.730106\pi\)
\(14\) −2.77966 −0.742896
\(15\) 6.61661 1.70840
\(16\) 17.3400 4.33500
\(17\) 6.95085 1.68583 0.842915 0.538047i \(-0.180838\pi\)
0.842915 + 0.538047i \(0.180838\pi\)
\(18\) −2.55063 −0.601190
\(19\) 5.45695 1.25191 0.625955 0.779859i \(-0.284709\pi\)
0.625955 + 0.779859i \(0.284709\pi\)
\(20\) −19.1433 −4.28057
\(21\) −1.97929 −0.431917
\(22\) 17.2108 3.66935
\(23\) −5.40623 −1.12728 −0.563639 0.826022i \(-0.690599\pi\)
−0.563639 + 0.826022i \(0.690599\pi\)
\(24\) 20.5025 4.18505
\(25\) 6.17509 1.23502
\(26\) 13.2606 2.60063
\(27\) 4.12167 0.793216
\(28\) 5.72652 1.08221
\(29\) 1.50514 0.279498 0.139749 0.990187i \(-0.455370\pi\)
0.139749 + 0.990187i \(0.455370\pi\)
\(30\) −18.3920 −3.35790
\(31\) 6.57683 1.18123 0.590617 0.806952i \(-0.298885\pi\)
0.590617 + 0.806952i \(0.298885\pi\)
\(32\) −27.4824 −4.85825
\(33\) 12.2552 2.13335
\(34\) −19.3210 −3.31353
\(35\) −3.34292 −0.565056
\(36\) 5.25469 0.875781
\(37\) 2.34769 0.385958 0.192979 0.981203i \(-0.438185\pi\)
0.192979 + 0.981203i \(0.438185\pi\)
\(38\) −15.1685 −2.46065
\(39\) 9.44241 1.51200
\(40\) 34.6275 5.47509
\(41\) 3.44238 0.537609 0.268804 0.963195i \(-0.413371\pi\)
0.268804 + 0.963195i \(0.413371\pi\)
\(42\) 5.50177 0.848941
\(43\) −10.2289 −1.55989 −0.779945 0.625848i \(-0.784753\pi\)
−0.779945 + 0.625848i \(0.784753\pi\)
\(44\) −35.4568 −5.34531
\(45\) −3.06748 −0.457273
\(46\) 15.0275 2.21568
\(47\) 4.97411 0.725548 0.362774 0.931877i \(-0.381830\pi\)
0.362774 + 0.931877i \(0.381830\pi\)
\(48\) −34.3210 −4.95381
\(49\) 1.00000 0.142857
\(50\) −17.1647 −2.42745
\(51\) −13.7578 −1.92648
\(52\) −27.3189 −3.78845
\(53\) −0.487931 −0.0670224 −0.0335112 0.999438i \(-0.510669\pi\)
−0.0335112 + 0.999438i \(0.510669\pi\)
\(54\) −11.4569 −1.55908
\(55\) 20.6983 2.79095
\(56\) −10.3585 −1.38421
\(57\) −10.8009 −1.43062
\(58\) −4.18379 −0.549359
\(59\) −1.04347 −0.135848 −0.0679241 0.997690i \(-0.521638\pi\)
−0.0679241 + 0.997690i \(0.521638\pi\)
\(60\) 37.8902 4.89160
\(61\) −11.8056 −1.51156 −0.755778 0.654828i \(-0.772741\pi\)
−0.755778 + 0.654828i \(0.772741\pi\)
\(62\) −18.2814 −2.32174
\(63\) 0.917605 0.115607
\(64\) 41.7118 5.21398
\(65\) 15.9477 1.97807
\(66\) −34.0652 −4.19314
\(67\) −7.29417 −0.891125 −0.445563 0.895251i \(-0.646996\pi\)
−0.445563 + 0.895251i \(0.646996\pi\)
\(68\) 39.8042 4.82697
\(69\) 10.7005 1.28819
\(70\) 9.29218 1.11063
\(71\) −0.563675 −0.0668959 −0.0334479 0.999440i \(-0.510649\pi\)
−0.0334479 + 0.999440i \(0.510649\pi\)
\(72\) −9.50499 −1.12017
\(73\) −13.1235 −1.53599 −0.767996 0.640455i \(-0.778746\pi\)
−0.767996 + 0.640455i \(0.778746\pi\)
\(74\) −6.52579 −0.758607
\(75\) −12.2223 −1.41131
\(76\) 31.2494 3.58455
\(77\) −6.19168 −0.705608
\(78\) −26.2467 −2.97185
\(79\) 2.20459 0.248036 0.124018 0.992280i \(-0.460422\pi\)
0.124018 + 0.992280i \(0.460422\pi\)
\(80\) −57.9662 −6.48082
\(81\) −10.9108 −1.21231
\(82\) −9.56864 −1.05668
\(83\) −16.2511 −1.78379 −0.891894 0.452244i \(-0.850623\pi\)
−0.891894 + 0.452244i \(0.850623\pi\)
\(84\) −11.3345 −1.23669
\(85\) −23.2361 −2.52031
\(86\) 28.4328 3.06599
\(87\) −2.97912 −0.319396
\(88\) 64.1364 6.83696
\(89\) 1.00906 0.106960 0.0534800 0.998569i \(-0.482969\pi\)
0.0534800 + 0.998569i \(0.482969\pi\)
\(90\) 8.52655 0.898777
\(91\) −4.77059 −0.500094
\(92\) −30.9589 −3.22769
\(93\) −13.0175 −1.34985
\(94\) −13.8263 −1.42608
\(95\) −18.2421 −1.87160
\(96\) 54.3958 5.55175
\(97\) −3.71356 −0.377055 −0.188527 0.982068i \(-0.560371\pi\)
−0.188527 + 0.982068i \(0.560371\pi\)
\(98\) −2.77966 −0.280788
\(99\) −5.68152 −0.571014
\(100\) 35.3618 3.53618
\(101\) −12.4218 −1.23602 −0.618009 0.786171i \(-0.712060\pi\)
−0.618009 + 0.786171i \(0.712060\pi\)
\(102\) 38.2420 3.78652
\(103\) 15.1733 1.49507 0.747534 0.664224i \(-0.231238\pi\)
0.747534 + 0.664224i \(0.231238\pi\)
\(104\) 49.4161 4.84564
\(105\) 6.61661 0.645715
\(106\) 1.35628 0.131734
\(107\) 3.95507 0.382351 0.191176 0.981556i \(-0.438770\pi\)
0.191176 + 0.981556i \(0.438770\pi\)
\(108\) 23.6028 2.27118
\(109\) 0.553679 0.0530328 0.0265164 0.999648i \(-0.491559\pi\)
0.0265164 + 0.999648i \(0.491559\pi\)
\(110\) −57.5342 −5.48567
\(111\) −4.64677 −0.441052
\(112\) 17.3400 1.63848
\(113\) −3.96232 −0.372744 −0.186372 0.982479i \(-0.559673\pi\)
−0.186372 + 0.982479i \(0.559673\pi\)
\(114\) 30.0229 2.81190
\(115\) 18.0726 1.68528
\(116\) 8.61924 0.800277
\(117\) −4.37752 −0.404702
\(118\) 2.90049 0.267012
\(119\) 6.95085 0.637184
\(120\) −68.5380 −6.25663
\(121\) 27.3369 2.48518
\(122\) 32.8157 2.97099
\(123\) −6.81347 −0.614350
\(124\) 37.6623 3.38218
\(125\) −3.92822 −0.351351
\(126\) −2.55063 −0.227228
\(127\) −4.95798 −0.439949 −0.219975 0.975506i \(-0.570597\pi\)
−0.219975 + 0.975506i \(0.570597\pi\)
\(128\) −60.9799 −5.38991
\(129\) 20.2460 1.78256
\(130\) −44.3292 −3.88793
\(131\) 9.81299 0.857365 0.428682 0.903455i \(-0.358978\pi\)
0.428682 + 0.903455i \(0.358978\pi\)
\(132\) 70.1794 6.10834
\(133\) 5.45695 0.473178
\(134\) 20.2753 1.75152
\(135\) −13.7784 −1.18586
\(136\) −72.0002 −6.17397
\(137\) 6.21435 0.530928 0.265464 0.964121i \(-0.414475\pi\)
0.265464 + 0.964121i \(0.414475\pi\)
\(138\) −29.7438 −2.53196
\(139\) −19.0566 −1.61636 −0.808179 0.588937i \(-0.799547\pi\)
−0.808179 + 0.588937i \(0.799547\pi\)
\(140\) −19.1433 −1.61790
\(141\) −9.84523 −0.829118
\(142\) 1.56682 0.131485
\(143\) 29.5380 2.47009
\(144\) 15.9113 1.32594
\(145\) −5.03157 −0.417849
\(146\) 36.4790 3.01902
\(147\) −1.97929 −0.163249
\(148\) 13.4441 1.10510
\(149\) −18.1028 −1.48304 −0.741521 0.670930i \(-0.765895\pi\)
−0.741521 + 0.670930i \(0.765895\pi\)
\(150\) 33.9739 2.77396
\(151\) −6.79550 −0.553010 −0.276505 0.961012i \(-0.589176\pi\)
−0.276505 + 0.961012i \(0.589176\pi\)
\(152\) −56.5257 −4.58484
\(153\) 6.37814 0.515642
\(154\) 17.2108 1.38688
\(155\) −21.9858 −1.76594
\(156\) 54.0722 4.32924
\(157\) −7.64318 −0.609992 −0.304996 0.952354i \(-0.598655\pi\)
−0.304996 + 0.952354i \(0.598655\pi\)
\(158\) −6.12802 −0.487519
\(159\) 0.965759 0.0765896
\(160\) 91.8714 7.26307
\(161\) −5.40623 −0.426071
\(162\) 30.3284 2.38282
\(163\) 20.1932 1.58165 0.790826 0.612042i \(-0.209651\pi\)
0.790826 + 0.612042i \(0.209651\pi\)
\(164\) 19.7128 1.53931
\(165\) −40.9680 −3.18935
\(166\) 45.1725 3.50607
\(167\) −16.7923 −1.29943 −0.649715 0.760178i \(-0.725112\pi\)
−0.649715 + 0.760178i \(0.725112\pi\)
\(168\) 20.5025 1.58180
\(169\) 9.75857 0.750659
\(170\) 64.5886 4.95372
\(171\) 5.00733 0.382920
\(172\) −58.5759 −4.46637
\(173\) −8.99218 −0.683663 −0.341831 0.939761i \(-0.611047\pi\)
−0.341831 + 0.939761i \(0.611047\pi\)
\(174\) 8.28096 0.627778
\(175\) 6.17509 0.466793
\(176\) −107.364 −8.09285
\(177\) 2.06533 0.155240
\(178\) −2.80484 −0.210232
\(179\) 10.2297 0.764607 0.382303 0.924037i \(-0.375131\pi\)
0.382303 + 0.924037i \(0.375131\pi\)
\(180\) −17.5660 −1.30929
\(181\) 18.1511 1.34916 0.674581 0.738201i \(-0.264324\pi\)
0.674581 + 0.738201i \(0.264324\pi\)
\(182\) 13.2606 0.982944
\(183\) 23.3668 1.72733
\(184\) 56.0003 4.12840
\(185\) −7.84813 −0.577006
\(186\) 36.1842 2.65315
\(187\) −43.0375 −3.14721
\(188\) 28.4843 2.07743
\(189\) 4.12167 0.299807
\(190\) 50.7070 3.67867
\(191\) −13.9354 −1.00833 −0.504165 0.863607i \(-0.668200\pi\)
−0.504165 + 0.863607i \(0.668200\pi\)
\(192\) −82.5599 −5.95825
\(193\) −15.9732 −1.14978 −0.574890 0.818231i \(-0.694955\pi\)
−0.574890 + 0.818231i \(0.694955\pi\)
\(194\) 10.3224 0.741108
\(195\) −31.5652 −2.26043
\(196\) 5.72652 0.409037
\(197\) −1.76439 −0.125708 −0.0628539 0.998023i \(-0.520020\pi\)
−0.0628539 + 0.998023i \(0.520020\pi\)
\(198\) 15.7927 1.12234
\(199\) 1.77239 0.125641 0.0628207 0.998025i \(-0.479990\pi\)
0.0628207 + 0.998025i \(0.479990\pi\)
\(200\) −63.9645 −4.52297
\(201\) 14.4373 1.01833
\(202\) 34.5285 2.42941
\(203\) 1.50514 0.105640
\(204\) −78.7842 −5.51600
\(205\) −11.5076 −0.803724
\(206\) −42.1766 −2.93858
\(207\) −4.96079 −0.344798
\(208\) −82.7221 −5.73575
\(209\) −33.7877 −2.33715
\(210\) −18.3920 −1.26917
\(211\) 5.21318 0.358890 0.179445 0.983768i \(-0.442570\pi\)
0.179445 + 0.983768i \(0.442570\pi\)
\(212\) −2.79415 −0.191903
\(213\) 1.11568 0.0764450
\(214\) −10.9938 −0.751518
\(215\) 34.1943 2.33203
\(216\) −42.6942 −2.90497
\(217\) 6.57683 0.446464
\(218\) −1.53904 −0.104237
\(219\) 25.9753 1.75525
\(220\) 118.529 7.99123
\(221\) −33.1597 −2.23056
\(222\) 12.9165 0.866895
\(223\) −28.4440 −1.90475 −0.952376 0.304926i \(-0.901368\pi\)
−0.952376 + 0.304926i \(0.901368\pi\)
\(224\) −27.4824 −1.83625
\(225\) 5.66629 0.377753
\(226\) 11.0139 0.732635
\(227\) −25.5923 −1.69862 −0.849312 0.527892i \(-0.822983\pi\)
−0.849312 + 0.527892i \(0.822983\pi\)
\(228\) −61.8517 −4.09623
\(229\) −6.29749 −0.416150 −0.208075 0.978113i \(-0.566720\pi\)
−0.208075 + 0.978113i \(0.566720\pi\)
\(230\) −50.2357 −3.31244
\(231\) 12.2552 0.806330
\(232\) −15.5910 −1.02360
\(233\) 8.65776 0.567188 0.283594 0.958944i \(-0.408473\pi\)
0.283594 + 0.958944i \(0.408473\pi\)
\(234\) 12.1680 0.795449
\(235\) −16.6280 −1.08469
\(236\) −5.97545 −0.388969
\(237\) −4.36353 −0.283442
\(238\) −19.3210 −1.25240
\(239\) 13.7734 0.890927 0.445463 0.895300i \(-0.353039\pi\)
0.445463 + 0.895300i \(0.353039\pi\)
\(240\) 114.732 7.40593
\(241\) −26.0178 −1.67595 −0.837977 0.545705i \(-0.816262\pi\)
−0.837977 + 0.545705i \(0.816262\pi\)
\(242\) −75.9874 −4.88466
\(243\) 9.23070 0.592150
\(244\) −67.6052 −4.32798
\(245\) −3.34292 −0.213571
\(246\) 18.9392 1.20752
\(247\) −26.0329 −1.65643
\(248\) −68.1259 −4.32600
\(249\) 32.1657 2.03842
\(250\) 10.9191 0.690586
\(251\) −24.2358 −1.52975 −0.764877 0.644177i \(-0.777200\pi\)
−0.764877 + 0.644177i \(0.777200\pi\)
\(252\) 5.25469 0.331014
\(253\) 33.4737 2.10447
\(254\) 13.7815 0.864728
\(255\) 45.9911 2.88008
\(256\) 86.0799 5.38000
\(257\) 9.51267 0.593384 0.296692 0.954973i \(-0.404117\pi\)
0.296692 + 0.954973i \(0.404117\pi\)
\(258\) −56.2769 −3.50365
\(259\) 2.34769 0.145878
\(260\) 91.3248 5.66372
\(261\) 1.38113 0.0854897
\(262\) −27.2768 −1.68517
\(263\) 24.7176 1.52415 0.762076 0.647488i \(-0.224180\pi\)
0.762076 + 0.647488i \(0.224180\pi\)
\(264\) −126.945 −7.81291
\(265\) 1.63111 0.100198
\(266\) −15.1685 −0.930039
\(267\) −1.99722 −0.122228
\(268\) −41.7702 −2.55152
\(269\) 31.5595 1.92422 0.962110 0.272663i \(-0.0879044\pi\)
0.962110 + 0.272663i \(0.0879044\pi\)
\(270\) 38.2993 2.33082
\(271\) −15.9783 −0.970610 −0.485305 0.874345i \(-0.661292\pi\)
−0.485305 + 0.874345i \(0.661292\pi\)
\(272\) 120.528 7.30807
\(273\) 9.44241 0.571481
\(274\) −17.2738 −1.04355
\(275\) −38.2342 −2.30561
\(276\) 61.2768 3.68843
\(277\) −8.23691 −0.494908 −0.247454 0.968900i \(-0.579594\pi\)
−0.247454 + 0.968900i \(0.579594\pi\)
\(278\) 52.9708 3.17698
\(279\) 6.03493 0.361302
\(280\) 34.6275 2.06939
\(281\) 10.1158 0.603456 0.301728 0.953394i \(-0.402437\pi\)
0.301728 + 0.953394i \(0.402437\pi\)
\(282\) 27.3664 1.62965
\(283\) 7.96966 0.473747 0.236873 0.971541i \(-0.423877\pi\)
0.236873 + 0.971541i \(0.423877\pi\)
\(284\) −3.22789 −0.191540
\(285\) 36.1065 2.13877
\(286\) −82.1057 −4.85501
\(287\) 3.44238 0.203197
\(288\) −25.2180 −1.48599
\(289\) 31.3144 1.84202
\(290\) 13.9861 0.821290
\(291\) 7.35023 0.430878
\(292\) −75.1521 −4.39795
\(293\) 5.84491 0.341464 0.170732 0.985318i \(-0.445387\pi\)
0.170732 + 0.985318i \(0.445387\pi\)
\(294\) 5.50177 0.320870
\(295\) 3.48823 0.203093
\(296\) −24.3185 −1.41348
\(297\) −25.5201 −1.48083
\(298\) 50.3197 2.91494
\(299\) 25.7909 1.49153
\(300\) −69.9913 −4.04095
\(301\) −10.2289 −0.589583
\(302\) 18.8892 1.08695
\(303\) 24.5864 1.41245
\(304\) 94.6236 5.42703
\(305\) 39.4652 2.25977
\(306\) −17.7291 −1.01350
\(307\) 4.74578 0.270856 0.135428 0.990787i \(-0.456759\pi\)
0.135428 + 0.990787i \(0.456759\pi\)
\(308\) −35.4568 −2.02034
\(309\) −30.0324 −1.70848
\(310\) 61.1131 3.47099
\(311\) 27.0039 1.53125 0.765626 0.643285i \(-0.222429\pi\)
0.765626 + 0.643285i \(0.222429\pi\)
\(312\) −97.8089 −5.53734
\(313\) −4.28084 −0.241967 −0.120984 0.992654i \(-0.538605\pi\)
−0.120984 + 0.992654i \(0.538605\pi\)
\(314\) 21.2455 1.19895
\(315\) −3.06748 −0.172833
\(316\) 12.6246 0.710191
\(317\) −17.1471 −0.963078 −0.481539 0.876425i \(-0.659922\pi\)
−0.481539 + 0.876425i \(0.659922\pi\)
\(318\) −2.68448 −0.150538
\(319\) −9.31938 −0.521785
\(320\) −139.439 −7.79488
\(321\) −7.82825 −0.436931
\(322\) 15.0275 0.837450
\(323\) 37.9305 2.11051
\(324\) −62.4810 −3.47117
\(325\) −29.4588 −1.63408
\(326\) −56.1302 −3.10876
\(327\) −1.09589 −0.0606030
\(328\) −35.6578 −1.96887
\(329\) 4.97411 0.274232
\(330\) 113.877 6.26873
\(331\) −4.46118 −0.245209 −0.122604 0.992456i \(-0.539125\pi\)
−0.122604 + 0.992456i \(0.539125\pi\)
\(332\) −93.0622 −5.10745
\(333\) 2.15425 0.118052
\(334\) 46.6770 2.55405
\(335\) 24.3838 1.33223
\(336\) −34.3210 −1.87236
\(337\) −4.95466 −0.269898 −0.134949 0.990853i \(-0.543087\pi\)
−0.134949 + 0.990853i \(0.543087\pi\)
\(338\) −27.1255 −1.47543
\(339\) 7.84260 0.425952
\(340\) −133.062 −7.21631
\(341\) −40.7216 −2.20520
\(342\) −13.9187 −0.752636
\(343\) 1.00000 0.0539949
\(344\) 105.956 5.71274
\(345\) −35.7709 −1.92584
\(346\) 24.9952 1.34375
\(347\) −5.88572 −0.315962 −0.157981 0.987442i \(-0.550498\pi\)
−0.157981 + 0.987442i \(0.550498\pi\)
\(348\) −17.0600 −0.914513
\(349\) 4.55226 0.243677 0.121838 0.992550i \(-0.461121\pi\)
0.121838 + 0.992550i \(0.461121\pi\)
\(350\) −17.1647 −0.917489
\(351\) −19.6628 −1.04952
\(352\) 170.162 9.06968
\(353\) −21.2818 −1.13272 −0.566359 0.824159i \(-0.691648\pi\)
−0.566359 + 0.824159i \(0.691648\pi\)
\(354\) −5.74093 −0.305127
\(355\) 1.88432 0.100009
\(356\) 5.77840 0.306255
\(357\) −13.7578 −0.728139
\(358\) −28.4352 −1.50285
\(359\) 15.0025 0.791800 0.395900 0.918294i \(-0.370433\pi\)
0.395900 + 0.918294i \(0.370433\pi\)
\(360\) 31.7744 1.67466
\(361\) 10.7783 0.567281
\(362\) −50.4540 −2.65180
\(363\) −54.1078 −2.83992
\(364\) −27.3189 −1.43190
\(365\) 43.8708 2.29630
\(366\) −64.9519 −3.39509
\(367\) −12.3509 −0.644714 −0.322357 0.946618i \(-0.604475\pi\)
−0.322357 + 0.946618i \(0.604475\pi\)
\(368\) −93.7441 −4.88675
\(369\) 3.15874 0.164438
\(370\) 21.8152 1.13412
\(371\) −0.487931 −0.0253321
\(372\) −74.5449 −3.86497
\(373\) 12.0320 0.622991 0.311496 0.950248i \(-0.399170\pi\)
0.311496 + 0.950248i \(0.399170\pi\)
\(374\) 119.630 6.18590
\(375\) 7.77510 0.401504
\(376\) −51.5242 −2.65716
\(377\) −7.18043 −0.369811
\(378\) −11.4569 −0.589277
\(379\) −0.172165 −0.00884354 −0.00442177 0.999990i \(-0.501407\pi\)
−0.00442177 + 0.999990i \(0.501407\pi\)
\(380\) −104.464 −5.35889
\(381\) 9.81330 0.502750
\(382\) 38.7357 1.98189
\(383\) 2.84338 0.145290 0.0726450 0.997358i \(-0.476856\pi\)
0.0726450 + 0.997358i \(0.476856\pi\)
\(384\) 120.697 6.15930
\(385\) 20.6983 1.05488
\(386\) 44.4002 2.25991
\(387\) −9.38608 −0.477121
\(388\) −21.2658 −1.07961
\(389\) −30.1133 −1.52681 −0.763403 0.645923i \(-0.776473\pi\)
−0.763403 + 0.645923i \(0.776473\pi\)
\(390\) 87.7405 4.44291
\(391\) −37.5779 −1.90040
\(392\) −10.3585 −0.523182
\(393\) −19.4228 −0.979750
\(394\) 4.90441 0.247081
\(395\) −7.36976 −0.370813
\(396\) −32.5353 −1.63496
\(397\) −21.5186 −1.07999 −0.539995 0.841668i \(-0.681574\pi\)
−0.539995 + 0.841668i \(0.681574\pi\)
\(398\) −4.92665 −0.246951
\(399\) −10.8009 −0.540722
\(400\) 107.076 5.35380
\(401\) 2.97108 0.148368 0.0741842 0.997245i \(-0.476365\pi\)
0.0741842 + 0.997245i \(0.476365\pi\)
\(402\) −40.1309 −2.00155
\(403\) −31.3754 −1.56292
\(404\) −71.1338 −3.53904
\(405\) 36.4739 1.81240
\(406\) −4.18379 −0.207638
\(407\) −14.5362 −0.720530
\(408\) 142.510 7.05528
\(409\) 5.28633 0.261392 0.130696 0.991422i \(-0.458279\pi\)
0.130696 + 0.991422i \(0.458279\pi\)
\(410\) 31.9872 1.57973
\(411\) −12.3000 −0.606715
\(412\) 86.8901 4.28077
\(413\) −1.04347 −0.0513458
\(414\) 13.7893 0.677708
\(415\) 54.3260 2.66676
\(416\) 131.107 6.42807
\(417\) 37.7186 1.84709
\(418\) 93.9184 4.59370
\(419\) −6.47399 −0.316275 −0.158138 0.987417i \(-0.550549\pi\)
−0.158138 + 0.987417i \(0.550549\pi\)
\(420\) 37.8902 1.84885
\(421\) 22.2759 1.08566 0.542830 0.839843i \(-0.317353\pi\)
0.542830 + 0.839843i \(0.317353\pi\)
\(422\) −14.4909 −0.705405
\(423\) 4.56427 0.221922
\(424\) 5.05422 0.245454
\(425\) 42.9221 2.08203
\(426\) −3.10121 −0.150254
\(427\) −11.8056 −0.571315
\(428\) 22.6488 1.09477
\(429\) −58.4644 −2.82269
\(430\) −95.0486 −4.58365
\(431\) −30.6431 −1.47603 −0.738014 0.674786i \(-0.764236\pi\)
−0.738014 + 0.674786i \(0.764236\pi\)
\(432\) 71.4698 3.43859
\(433\) −37.4271 −1.79863 −0.899316 0.437299i \(-0.855935\pi\)
−0.899316 + 0.437299i \(0.855935\pi\)
\(434\) −18.2814 −0.877533
\(435\) 9.95896 0.477496
\(436\) 3.17065 0.151847
\(437\) −29.5015 −1.41125
\(438\) −72.2026 −3.44997
\(439\) 2.97048 0.141773 0.0708865 0.997484i \(-0.477417\pi\)
0.0708865 + 0.997484i \(0.477417\pi\)
\(440\) −214.402 −10.2212
\(441\) 0.917605 0.0436955
\(442\) 92.1728 4.38421
\(443\) 4.06562 0.193163 0.0965816 0.995325i \(-0.469209\pi\)
0.0965816 + 0.995325i \(0.469209\pi\)
\(444\) −26.6098 −1.26285
\(445\) −3.37320 −0.159905
\(446\) 79.0648 3.74382
\(447\) 35.8308 1.69474
\(448\) 41.7118 1.97070
\(449\) −22.5341 −1.06345 −0.531725 0.846917i \(-0.678456\pi\)
−0.531725 + 0.846917i \(0.678456\pi\)
\(450\) −15.7504 −0.742480
\(451\) −21.3141 −1.00364
\(452\) −22.6903 −1.06726
\(453\) 13.4503 0.631950
\(454\) 71.1381 3.33867
\(455\) 15.9477 0.747639
\(456\) 111.881 5.23931
\(457\) −1.86633 −0.0873033 −0.0436517 0.999047i \(-0.513899\pi\)
−0.0436517 + 0.999047i \(0.513899\pi\)
\(458\) 17.5049 0.817950
\(459\) 28.6491 1.33723
\(460\) 103.493 4.82539
\(461\) 30.9483 1.44141 0.720703 0.693244i \(-0.243819\pi\)
0.720703 + 0.693244i \(0.243819\pi\)
\(462\) −34.0652 −1.58486
\(463\) 2.28236 0.106070 0.0530351 0.998593i \(-0.483110\pi\)
0.0530351 + 0.998593i \(0.483110\pi\)
\(464\) 26.0992 1.21163
\(465\) 43.5163 2.01802
\(466\) −24.0656 −1.11482
\(467\) 2.09724 0.0970489 0.0485244 0.998822i \(-0.484548\pi\)
0.0485244 + 0.998822i \(0.484548\pi\)
\(468\) −25.0680 −1.15877
\(469\) −7.29417 −0.336814
\(470\) 46.2203 2.13198
\(471\) 15.1281 0.697066
\(472\) 10.8087 0.497513
\(473\) 63.3340 2.91210
\(474\) 12.1291 0.557110
\(475\) 33.6972 1.54613
\(476\) 39.8042 1.82442
\(477\) −0.447728 −0.0205001
\(478\) −38.2854 −1.75113
\(479\) −15.4198 −0.704548 −0.352274 0.935897i \(-0.614592\pi\)
−0.352274 + 0.935897i \(0.614592\pi\)
\(480\) −181.841 −8.29985
\(481\) −11.1999 −0.510670
\(482\) 72.3207 3.29412
\(483\) 10.7005 0.486891
\(484\) 156.546 7.11571
\(485\) 12.4141 0.563696
\(486\) −25.6582 −1.16388
\(487\) −34.8612 −1.57971 −0.789855 0.613293i \(-0.789844\pi\)
−0.789855 + 0.613293i \(0.789844\pi\)
\(488\) 122.288 5.53573
\(489\) −39.9682 −1.80743
\(490\) 9.29218 0.419778
\(491\) 27.5227 1.24208 0.621042 0.783777i \(-0.286710\pi\)
0.621042 + 0.783777i \(0.286710\pi\)
\(492\) −39.0175 −1.75905
\(493\) 10.4620 0.471187
\(494\) 72.3627 3.25575
\(495\) 18.9928 0.853665
\(496\) 114.042 5.12065
\(497\) −0.563675 −0.0252843
\(498\) −89.4097 −4.00654
\(499\) 5.96452 0.267009 0.133504 0.991048i \(-0.457377\pi\)
0.133504 + 0.991048i \(0.457377\pi\)
\(500\) −22.4950 −1.00601
\(501\) 33.2370 1.48492
\(502\) 67.3675 3.00676
\(503\) −1.14699 −0.0511419 −0.0255709 0.999673i \(-0.508140\pi\)
−0.0255709 + 0.999673i \(0.508140\pi\)
\(504\) −9.50499 −0.423386
\(505\) 41.5251 1.84784
\(506\) −93.0455 −4.13638
\(507\) −19.3151 −0.857813
\(508\) −28.3920 −1.25969
\(509\) 11.8883 0.526939 0.263469 0.964668i \(-0.415133\pi\)
0.263469 + 0.964668i \(0.415133\pi\)
\(510\) −127.840 −5.66084
\(511\) −13.1235 −0.580550
\(512\) −117.313 −5.18456
\(513\) 22.4918 0.993036
\(514\) −26.4420 −1.16631
\(515\) −50.7230 −2.23512
\(516\) 115.939 5.10393
\(517\) −30.7981 −1.35450
\(518\) −6.52579 −0.286727
\(519\) 17.7982 0.781253
\(520\) −165.194 −7.24422
\(521\) −4.25156 −0.186264 −0.0931321 0.995654i \(-0.529688\pi\)
−0.0931321 + 0.995654i \(0.529688\pi\)
\(522\) −3.83907 −0.168032
\(523\) −17.5335 −0.766685 −0.383343 0.923606i \(-0.625227\pi\)
−0.383343 + 0.923606i \(0.625227\pi\)
\(524\) 56.1943 2.45486
\(525\) −12.2223 −0.533426
\(526\) −68.7065 −2.99575
\(527\) 45.7146 1.99136
\(528\) 212.505 9.24807
\(529\) 6.22734 0.270754
\(530\) −4.53394 −0.196942
\(531\) −0.957493 −0.0415517
\(532\) 31.2494 1.35483
\(533\) −16.4222 −0.711324
\(534\) 5.55161 0.240242
\(535\) −13.2215 −0.571614
\(536\) 75.5565 3.26354
\(537\) −20.2477 −0.873751
\(538\) −87.7249 −3.78209
\(539\) −6.19168 −0.266695
\(540\) −78.9023 −3.39541
\(541\) 45.7987 1.96904 0.984521 0.175268i \(-0.0560790\pi\)
0.984521 + 0.175268i \(0.0560790\pi\)
\(542\) 44.4142 1.90775
\(543\) −35.9264 −1.54175
\(544\) −191.026 −8.19018
\(545\) −1.85090 −0.0792839
\(546\) −26.2467 −1.12326
\(547\) −0.206296 −0.00882059 −0.00441030 0.999990i \(-0.501404\pi\)
−0.00441030 + 0.999990i \(0.501404\pi\)
\(548\) 35.5866 1.52018
\(549\) −10.8329 −0.462337
\(550\) 106.278 4.53171
\(551\) 8.21350 0.349907
\(552\) −110.841 −4.71771
\(553\) 2.20459 0.0937487
\(554\) 22.8958 0.972750
\(555\) 15.5338 0.659371
\(556\) −109.128 −4.62805
\(557\) −41.0407 −1.73895 −0.869476 0.493975i \(-0.835543\pi\)
−0.869476 + 0.493975i \(0.835543\pi\)
\(558\) −16.7751 −0.710145
\(559\) 48.7978 2.06393
\(560\) −57.9662 −2.44952
\(561\) 85.1838 3.59646
\(562\) −28.1184 −1.18610
\(563\) 17.9057 0.754637 0.377318 0.926084i \(-0.376846\pi\)
0.377318 + 0.926084i \(0.376846\pi\)
\(564\) −56.3789 −2.37398
\(565\) 13.2457 0.557251
\(566\) −22.1530 −0.931158
\(567\) −10.9108 −0.458211
\(568\) 5.83881 0.244991
\(569\) 20.5517 0.861573 0.430787 0.902454i \(-0.358236\pi\)
0.430787 + 0.902454i \(0.358236\pi\)
\(570\) −100.364 −4.20379
\(571\) 33.0094 1.38140 0.690701 0.723140i \(-0.257302\pi\)
0.690701 + 0.723140i \(0.257302\pi\)
\(572\) 169.150 7.07252
\(573\) 27.5822 1.15227
\(574\) −9.56864 −0.399387
\(575\) −33.3840 −1.39221
\(576\) 38.2750 1.59479
\(577\) 29.4541 1.22619 0.613094 0.790010i \(-0.289925\pi\)
0.613094 + 0.790010i \(0.289925\pi\)
\(578\) −87.0434 −3.62053
\(579\) 31.6157 1.31391
\(580\) −28.8134 −1.19641
\(581\) −16.2511 −0.674209
\(582\) −20.4312 −0.846898
\(583\) 3.02111 0.125122
\(584\) 135.940 5.62522
\(585\) 14.6337 0.605029
\(586\) −16.2469 −0.671153
\(587\) 36.8284 1.52007 0.760035 0.649883i \(-0.225182\pi\)
0.760035 + 0.649883i \(0.225182\pi\)
\(588\) −11.3345 −0.467426
\(589\) 35.8894 1.47880
\(590\) −9.69610 −0.399182
\(591\) 3.49225 0.143652
\(592\) 40.7090 1.67313
\(593\) −9.34275 −0.383661 −0.191830 0.981428i \(-0.561442\pi\)
−0.191830 + 0.981428i \(0.561442\pi\)
\(594\) 70.9372 2.91059
\(595\) −23.2361 −0.952588
\(596\) −103.666 −4.24633
\(597\) −3.50808 −0.143576
\(598\) −71.6901 −2.93163
\(599\) 6.60359 0.269815 0.134908 0.990858i \(-0.456926\pi\)
0.134908 + 0.990858i \(0.456926\pi\)
\(600\) 126.604 5.16861
\(601\) −33.3652 −1.36100 −0.680498 0.732750i \(-0.738237\pi\)
−0.680498 + 0.732750i \(0.738237\pi\)
\(602\) 28.4328 1.15884
\(603\) −6.69317 −0.272567
\(604\) −38.9146 −1.58341
\(605\) −91.3851 −3.71533
\(606\) −68.3420 −2.77620
\(607\) 9.80090 0.397806 0.198903 0.980019i \(-0.436262\pi\)
0.198903 + 0.980019i \(0.436262\pi\)
\(608\) −149.970 −6.08210
\(609\) −2.97912 −0.120720
\(610\) −109.700 −4.44162
\(611\) −23.7295 −0.959991
\(612\) 36.5246 1.47642
\(613\) −2.04850 −0.0827382 −0.0413691 0.999144i \(-0.513172\pi\)
−0.0413691 + 0.999144i \(0.513172\pi\)
\(614\) −13.1917 −0.532372
\(615\) 22.7769 0.918452
\(616\) 64.1364 2.58413
\(617\) 21.1575 0.851768 0.425884 0.904778i \(-0.359963\pi\)
0.425884 + 0.904778i \(0.359963\pi\)
\(618\) 83.4799 3.35805
\(619\) 14.1691 0.569506 0.284753 0.958601i \(-0.408088\pi\)
0.284753 + 0.958601i \(0.408088\pi\)
\(620\) −125.902 −5.05635
\(621\) −22.2827 −0.894174
\(622\) −75.0618 −3.00970
\(623\) 1.00906 0.0404271
\(624\) 163.731 6.55450
\(625\) −17.7437 −0.709749
\(626\) 11.8993 0.475591
\(627\) 66.8758 2.67076
\(628\) −43.7688 −1.74657
\(629\) 16.3185 0.650659
\(630\) 8.52655 0.339706
\(631\) −22.2323 −0.885055 −0.442527 0.896755i \(-0.645918\pi\)
−0.442527 + 0.896755i \(0.645918\pi\)
\(632\) −22.8362 −0.908375
\(633\) −10.3184 −0.410120
\(634\) 47.6632 1.89295
\(635\) 16.5741 0.657723
\(636\) 5.53044 0.219296
\(637\) −4.77059 −0.189018
\(638\) 25.9047 1.02558
\(639\) −0.517231 −0.0204613
\(640\) 203.851 8.05791
\(641\) −6.35933 −0.251178 −0.125589 0.992082i \(-0.540082\pi\)
−0.125589 + 0.992082i \(0.540082\pi\)
\(642\) 21.7599 0.858795
\(643\) 11.6601 0.459830 0.229915 0.973211i \(-0.426155\pi\)
0.229915 + 0.973211i \(0.426155\pi\)
\(644\) −30.9589 −1.21995
\(645\) −67.6806 −2.66492
\(646\) −105.434 −4.14824
\(647\) 10.4861 0.412252 0.206126 0.978525i \(-0.433914\pi\)
0.206126 + 0.978525i \(0.433914\pi\)
\(648\) 113.019 4.43982
\(649\) 6.46083 0.253610
\(650\) 81.8856 3.21182
\(651\) −13.0175 −0.510195
\(652\) 115.637 4.52868
\(653\) −12.2095 −0.477793 −0.238897 0.971045i \(-0.576786\pi\)
−0.238897 + 0.971045i \(0.576786\pi\)
\(654\) 3.04621 0.119116
\(655\) −32.8040 −1.28176
\(656\) 59.6908 2.33053
\(657\) −12.0422 −0.469812
\(658\) −13.8263 −0.539007
\(659\) 32.8898 1.28121 0.640603 0.767872i \(-0.278684\pi\)
0.640603 + 0.767872i \(0.278684\pi\)
\(660\) −234.604 −9.13195
\(661\) 24.1826 0.940595 0.470298 0.882508i \(-0.344147\pi\)
0.470298 + 0.882508i \(0.344147\pi\)
\(662\) 12.4006 0.481962
\(663\) 65.6328 2.54897
\(664\) 168.336 6.53272
\(665\) −18.2421 −0.707400
\(666\) −5.98810 −0.232034
\(667\) −8.13716 −0.315072
\(668\) −96.1617 −3.72061
\(669\) 56.2991 2.17665
\(670\) −67.7788 −2.61852
\(671\) 73.0967 2.82187
\(672\) 54.3958 2.09836
\(673\) −1.75396 −0.0676103 −0.0338051 0.999428i \(-0.510763\pi\)
−0.0338051 + 0.999428i \(0.510763\pi\)
\(674\) 13.7723 0.530489
\(675\) 25.4517 0.979636
\(676\) 55.8826 2.14933
\(677\) 30.6664 1.17860 0.589302 0.807913i \(-0.299403\pi\)
0.589302 + 0.807913i \(0.299403\pi\)
\(678\) −21.7998 −0.837216
\(679\) −3.71356 −0.142513
\(680\) 240.691 9.23007
\(681\) 50.6548 1.94110
\(682\) 113.192 4.33436
\(683\) −29.6528 −1.13463 −0.567316 0.823500i \(-0.692018\pi\)
−0.567316 + 0.823500i \(0.692018\pi\)
\(684\) 28.6746 1.09640
\(685\) −20.7740 −0.793736
\(686\) −2.77966 −0.106128
\(687\) 12.4646 0.475553
\(688\) −177.369 −6.76212
\(689\) 2.32772 0.0886791
\(690\) 99.4311 3.78528
\(691\) 32.8988 1.25153 0.625765 0.780012i \(-0.284787\pi\)
0.625765 + 0.780012i \(0.284787\pi\)
\(692\) −51.4939 −1.95750
\(693\) −5.68152 −0.215823
\(694\) 16.3603 0.621029
\(695\) 63.7045 2.41645
\(696\) 30.8592 1.16971
\(697\) 23.9275 0.906317
\(698\) −12.6537 −0.478951
\(699\) −17.1362 −0.648152
\(700\) 35.3618 1.33655
\(701\) 10.3374 0.390437 0.195218 0.980760i \(-0.437458\pi\)
0.195218 + 0.980760i \(0.437458\pi\)
\(702\) 54.6560 2.06286
\(703\) 12.8112 0.483185
\(704\) −258.266 −9.73378
\(705\) 32.9118 1.23953
\(706\) 59.1563 2.22638
\(707\) −12.4218 −0.467171
\(708\) 11.8272 0.444492
\(709\) 46.3400 1.74033 0.870167 0.492757i \(-0.164011\pi\)
0.870167 + 0.492757i \(0.164011\pi\)
\(710\) −5.23776 −0.196570
\(711\) 2.02294 0.0758663
\(712\) −10.4523 −0.391717
\(713\) −35.5559 −1.33158
\(714\) 38.2420 1.43117
\(715\) −98.7431 −3.69278
\(716\) 58.5808 2.18927
\(717\) −27.2616 −1.01810
\(718\) −41.7018 −1.55630
\(719\) −24.2676 −0.905030 −0.452515 0.891757i \(-0.649473\pi\)
−0.452515 + 0.891757i \(0.649473\pi\)
\(720\) −53.1901 −1.98228
\(721\) 15.1733 0.565083
\(722\) −29.9601 −1.11500
\(723\) 51.4969 1.91519
\(724\) 103.943 3.86300
\(725\) 9.29440 0.345185
\(726\) 150.401 5.58192
\(727\) −32.4213 −1.20244 −0.601220 0.799083i \(-0.705319\pi\)
−0.601220 + 0.799083i \(0.705319\pi\)
\(728\) 49.4161 1.83148
\(729\) 14.4622 0.535636
\(730\) −121.946 −4.51343
\(731\) −71.0995 −2.62971
\(732\) 133.811 4.94578
\(733\) −17.3482 −0.640770 −0.320385 0.947288i \(-0.603812\pi\)
−0.320385 + 0.947288i \(0.603812\pi\)
\(734\) 34.3314 1.26720
\(735\) 6.61661 0.244057
\(736\) 148.576 5.47659
\(737\) 45.1632 1.66361
\(738\) −8.78024 −0.323205
\(739\) −25.6340 −0.942961 −0.471481 0.881876i \(-0.656280\pi\)
−0.471481 + 0.881876i \(0.656280\pi\)
\(740\) −44.9425 −1.65212
\(741\) 51.5268 1.89288
\(742\) 1.35628 0.0497907
\(743\) −14.1137 −0.517783 −0.258891 0.965906i \(-0.583357\pi\)
−0.258891 + 0.965906i \(0.583357\pi\)
\(744\) 134.841 4.94352
\(745\) 60.5162 2.21714
\(746\) −33.4448 −1.22450
\(747\) −14.9121 −0.545604
\(748\) −246.455 −9.01129
\(749\) 3.95507 0.144515
\(750\) −21.6122 −0.789164
\(751\) −18.5451 −0.676719 −0.338360 0.941017i \(-0.609872\pi\)
−0.338360 + 0.941017i \(0.609872\pi\)
\(752\) 86.2511 3.14525
\(753\) 47.9699 1.74812
\(754\) 19.9592 0.726870
\(755\) 22.7168 0.826749
\(756\) 23.6028 0.858427
\(757\) 28.9796 1.05328 0.526641 0.850088i \(-0.323451\pi\)
0.526641 + 0.850088i \(0.323451\pi\)
\(758\) 0.478561 0.0173821
\(759\) −66.2542 −2.40488
\(760\) 188.961 6.85432
\(761\) −40.7998 −1.47899 −0.739495 0.673162i \(-0.764936\pi\)
−0.739495 + 0.673162i \(0.764936\pi\)
\(762\) −27.2776 −0.988165
\(763\) 0.553679 0.0200445
\(764\) −79.8013 −2.88711
\(765\) −21.3216 −0.770884
\(766\) −7.90364 −0.285570
\(767\) 4.97797 0.179744
\(768\) −170.378 −6.14797
\(769\) −19.0973 −0.688668 −0.344334 0.938847i \(-0.611895\pi\)
−0.344334 + 0.938847i \(0.611895\pi\)
\(770\) −57.5342 −2.07339
\(771\) −18.8284 −0.678087
\(772\) −91.4711 −3.29212
\(773\) −6.93671 −0.249496 −0.124748 0.992188i \(-0.539812\pi\)
−0.124748 + 0.992188i \(0.539812\pi\)
\(774\) 26.0901 0.937790
\(775\) 40.6125 1.45884
\(776\) 38.4668 1.38088
\(777\) −4.64677 −0.166702
\(778\) 83.7048 3.00096
\(779\) 18.7849 0.673038
\(780\) −180.759 −6.47220
\(781\) 3.49009 0.124885
\(782\) 104.454 3.73526
\(783\) 6.20371 0.221703
\(784\) 17.3400 0.619286
\(785\) 25.5505 0.911937
\(786\) 53.9888 1.92572
\(787\) −39.9308 −1.42338 −0.711689 0.702494i \(-0.752070\pi\)
−0.711689 + 0.702494i \(0.752070\pi\)
\(788\) −10.1038 −0.359934
\(789\) −48.9234 −1.74172
\(790\) 20.4854 0.728840
\(791\) −3.96232 −0.140884
\(792\) 58.8519 2.09121
\(793\) 56.3199 1.99998
\(794\) 59.8146 2.12274
\(795\) −3.22845 −0.114501
\(796\) 10.1496 0.359744
\(797\) −38.3478 −1.35835 −0.679175 0.733977i \(-0.737662\pi\)
−0.679175 + 0.733977i \(0.737662\pi\)
\(798\) 30.0229 1.06280
\(799\) 34.5743 1.22315
\(800\) −169.706 −6.00002
\(801\) 0.925918 0.0327157
\(802\) −8.25859 −0.291621
\(803\) 81.2567 2.86749
\(804\) 82.6756 2.91574
\(805\) 18.0726 0.636975
\(806\) 87.2130 3.07195
\(807\) −62.4656 −2.19889
\(808\) 128.671 4.52663
\(809\) −35.0181 −1.23117 −0.615585 0.788071i \(-0.711080\pi\)
−0.615585 + 0.788071i \(0.711080\pi\)
\(810\) −101.385 −3.56231
\(811\) −7.23577 −0.254082 −0.127041 0.991897i \(-0.540548\pi\)
−0.127041 + 0.991897i \(0.540548\pi\)
\(812\) 8.61924 0.302476
\(813\) 31.6257 1.10916
\(814\) 40.4056 1.41622
\(815\) −67.5041 −2.36456
\(816\) −238.560 −8.35127
\(817\) −55.8185 −1.95284
\(818\) −14.6942 −0.513772
\(819\) −4.37752 −0.152963
\(820\) −65.8984 −2.30127
\(821\) −7.16809 −0.250168 −0.125084 0.992146i \(-0.539920\pi\)
−0.125084 + 0.992146i \(0.539920\pi\)
\(822\) 34.1899 1.19251
\(823\) −10.3114 −0.359433 −0.179716 0.983718i \(-0.557518\pi\)
−0.179716 + 0.983718i \(0.557518\pi\)
\(824\) −157.172 −5.47535
\(825\) 75.6767 2.63472
\(826\) 2.90049 0.100921
\(827\) −11.5523 −0.401713 −0.200857 0.979621i \(-0.564373\pi\)
−0.200857 + 0.979621i \(0.564373\pi\)
\(828\) −28.4080 −0.987248
\(829\) 8.47299 0.294279 0.147140 0.989116i \(-0.452993\pi\)
0.147140 + 0.989116i \(0.452993\pi\)
\(830\) −151.008 −5.24156
\(831\) 16.3033 0.565554
\(832\) −198.990 −6.89874
\(833\) 6.95085 0.240833
\(834\) −104.845 −3.63048
\(835\) 56.1354 1.94265
\(836\) −193.486 −6.69186
\(837\) 27.1075 0.936973
\(838\) 17.9955 0.621645
\(839\) 39.9674 1.37983 0.689914 0.723891i \(-0.257648\pi\)
0.689914 + 0.723891i \(0.257648\pi\)
\(840\) −68.5380 −2.36479
\(841\) −26.7345 −0.921881
\(842\) −61.9194 −2.13388
\(843\) −20.0221 −0.689597
\(844\) 29.8534 1.02760
\(845\) −32.6221 −1.12223
\(846\) −12.6871 −0.436192
\(847\) 27.3369 0.939308
\(848\) −8.46072 −0.290542
\(849\) −15.7743 −0.541372
\(850\) −119.309 −4.09227
\(851\) −12.6922 −0.435082
\(852\) 6.38895 0.218882
\(853\) 48.7968 1.67077 0.835385 0.549665i \(-0.185245\pi\)
0.835385 + 0.549665i \(0.185245\pi\)
\(854\) 32.8157 1.12293
\(855\) −16.7391 −0.572464
\(856\) −40.9685 −1.40027
\(857\) 22.9315 0.783325 0.391662 0.920109i \(-0.371900\pi\)
0.391662 + 0.920109i \(0.371900\pi\)
\(858\) 162.511 5.54804
\(859\) 21.8748 0.746359 0.373179 0.927759i \(-0.378268\pi\)
0.373179 + 0.927759i \(0.378268\pi\)
\(860\) 195.814 6.67721
\(861\) −6.81347 −0.232203
\(862\) 85.1776 2.90116
\(863\) −1.00000 −0.0340404
\(864\) −113.273 −3.85364
\(865\) 30.0601 1.02207
\(866\) 104.035 3.53524
\(867\) −61.9803 −2.10496
\(868\) 37.6623 1.27834
\(869\) −13.6501 −0.463049
\(870\) −27.6825 −0.938526
\(871\) 34.7975 1.17907
\(872\) −5.73527 −0.194221
\(873\) −3.40758 −0.115329
\(874\) 82.0043 2.77384
\(875\) −3.92822 −0.132798
\(876\) 148.748 5.02574
\(877\) −24.2205 −0.817868 −0.408934 0.912564i \(-0.634099\pi\)
−0.408934 + 0.912564i \(0.634099\pi\)
\(878\) −8.25692 −0.278658
\(879\) −11.5688 −0.390206
\(880\) 358.908 12.0988
\(881\) 1.47634 0.0497390 0.0248695 0.999691i \(-0.492083\pi\)
0.0248695 + 0.999691i \(0.492083\pi\)
\(882\) −2.55063 −0.0858843
\(883\) −23.4755 −0.790013 −0.395007 0.918678i \(-0.629258\pi\)
−0.395007 + 0.918678i \(0.629258\pi\)
\(884\) −189.890 −6.38668
\(885\) −6.90424 −0.232083
\(886\) −11.3010 −0.379666
\(887\) 47.2922 1.58792 0.793958 0.607973i \(-0.208017\pi\)
0.793958 + 0.607973i \(0.208017\pi\)
\(888\) 48.1334 1.61525
\(889\) −4.95798 −0.166285
\(890\) 9.37636 0.314296
\(891\) 67.5563 2.26322
\(892\) −162.885 −5.45380
\(893\) 27.1435 0.908322
\(894\) −99.5976 −3.33104
\(895\) −34.1972 −1.14309
\(896\) −60.9799 −2.03720
\(897\) −51.0478 −1.70444
\(898\) 62.6372 2.09023
\(899\) 9.89908 0.330153
\(900\) 32.4481 1.08160
\(901\) −3.39154 −0.112988
\(902\) 59.2460 1.97268
\(903\) 20.2460 0.673743
\(904\) 41.0436 1.36509
\(905\) −60.6777 −2.01699
\(906\) −37.3873 −1.24211
\(907\) 7.54661 0.250581 0.125291 0.992120i \(-0.460014\pi\)
0.125291 + 0.992120i \(0.460014\pi\)
\(908\) −146.555 −4.86360
\(909\) −11.3983 −0.378059
\(910\) −44.3292 −1.46950
\(911\) −40.8777 −1.35434 −0.677170 0.735827i \(-0.736794\pi\)
−0.677170 + 0.735827i \(0.736794\pi\)
\(912\) −187.288 −6.20172
\(913\) 100.622 3.33009
\(914\) 5.18777 0.171596
\(915\) −78.1133 −2.58235
\(916\) −36.0627 −1.19154
\(917\) 9.81299 0.324053
\(918\) −79.6349 −2.62834
\(919\) −48.0843 −1.58615 −0.793077 0.609121i \(-0.791522\pi\)
−0.793077 + 0.609121i \(0.791522\pi\)
\(920\) −187.204 −6.17194
\(921\) −9.39329 −0.309519
\(922\) −86.0258 −2.83311
\(923\) 2.68906 0.0885116
\(924\) 70.1794 2.30873
\(925\) 14.4972 0.476665
\(926\) −6.34419 −0.208483
\(927\) 13.9231 0.457294
\(928\) −41.3650 −1.35787
\(929\) 0.944216 0.0309787 0.0154894 0.999880i \(-0.495069\pi\)
0.0154894 + 0.999880i \(0.495069\pi\)
\(930\) −120.961 −3.96646
\(931\) 5.45695 0.178844
\(932\) 49.5788 1.62401
\(933\) −53.4487 −1.74983
\(934\) −5.82963 −0.190751
\(935\) 143.871 4.70507
\(936\) 45.3444 1.48213
\(937\) 30.4214 0.993823 0.496912 0.867801i \(-0.334467\pi\)
0.496912 + 0.867801i \(0.334467\pi\)
\(938\) 20.2753 0.662013
\(939\) 8.47304 0.276507
\(940\) −95.2208 −3.10576
\(941\) −0.250786 −0.00817539 −0.00408769 0.999992i \(-0.501301\pi\)
−0.00408769 + 0.999992i \(0.501301\pi\)
\(942\) −42.0510 −1.37010
\(943\) −18.6103 −0.606034
\(944\) −18.0938 −0.588902
\(945\) −13.7784 −0.448211
\(946\) −176.047 −5.72378
\(947\) 43.2058 1.40400 0.702001 0.712176i \(-0.252290\pi\)
0.702001 + 0.712176i \(0.252290\pi\)
\(948\) −24.9879 −0.811568
\(949\) 62.6070 2.03231
\(950\) −93.6667 −3.03895
\(951\) 33.9392 1.10055
\(952\) −72.0002 −2.33354
\(953\) 12.0748 0.391141 0.195570 0.980690i \(-0.437344\pi\)
0.195570 + 0.980690i \(0.437344\pi\)
\(954\) 1.24453 0.0402932
\(955\) 46.5849 1.50745
\(956\) 78.8736 2.55096
\(957\) 18.4458 0.596268
\(958\) 42.8618 1.38480
\(959\) 6.21435 0.200672
\(960\) 275.991 8.90757
\(961\) 12.2547 0.395312
\(962\) 31.1319 1.00373
\(963\) 3.62920 0.116949
\(964\) −148.992 −4.79870
\(965\) 53.3972 1.71892
\(966\) −29.7438 −0.956992
\(967\) −1.52583 −0.0490673 −0.0245336 0.999699i \(-0.507810\pi\)
−0.0245336 + 0.999699i \(0.507810\pi\)
\(968\) −283.169 −9.10139
\(969\) −75.0756 −2.41177
\(970\) −34.5071 −1.10795
\(971\) −16.4589 −0.528191 −0.264095 0.964497i \(-0.585073\pi\)
−0.264095 + 0.964497i \(0.585073\pi\)
\(972\) 52.8598 1.69548
\(973\) −19.0566 −0.610926
\(974\) 96.9023 3.10495
\(975\) 58.3077 1.86734
\(976\) −204.710 −6.55260
\(977\) −29.3602 −0.939315 −0.469657 0.882849i \(-0.655623\pi\)
−0.469657 + 0.882849i \(0.655623\pi\)
\(978\) 111.098 3.55253
\(979\) −6.24777 −0.199680
\(980\) −19.1433 −0.611510
\(981\) 0.508059 0.0162211
\(982\) −76.5039 −2.44134
\(983\) 30.8785 0.984872 0.492436 0.870349i \(-0.336107\pi\)
0.492436 + 0.870349i \(0.336107\pi\)
\(984\) 70.5772 2.24992
\(985\) 5.89822 0.187933
\(986\) −29.0809 −0.926126
\(987\) −9.84523 −0.313377
\(988\) −149.078 −4.74280
\(989\) 55.2997 1.75843
\(990\) −52.7937 −1.67789
\(991\) 38.0520 1.20876 0.604381 0.796695i \(-0.293420\pi\)
0.604381 + 0.796695i \(0.293420\pi\)
\(992\) −180.747 −5.73873
\(993\) 8.82999 0.280211
\(994\) 1.56682 0.0496967
\(995\) −5.92496 −0.187834
\(996\) 184.197 5.83652
\(997\) −4.21961 −0.133636 −0.0668181 0.997765i \(-0.521285\pi\)
−0.0668181 + 0.997765i \(0.521285\pi\)
\(998\) −16.5794 −0.524810
\(999\) 9.67641 0.306148
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 \(a_p\))