Properties

Label 8015.2.a.l.1.15
Level 8015
Weight 2
Character 8015.1
Self dual Yes
Analytic conductor 64.000
Analytic rank 0
Dimension 62
CM No

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Newspace parameters

Level: \( N \) = \( 8015 = 5 \cdot 7 \cdot 229 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8015.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.0000972201\)
Analytic rank: \(0\)
Dimension: \(62\)
Fricke sign: \(-1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.15
Character \(\chi\) = 8015.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-1.54368 q^{2}\) \(+0.772565 q^{3}\) \(+0.382940 q^{4}\) \(-1.00000 q^{5}\) \(-1.19259 q^{6}\) \(-1.00000 q^{7}\) \(+2.49622 q^{8}\) \(-2.40314 q^{9}\) \(+O(q^{10})\) \(q\)\(-1.54368 q^{2}\) \(+0.772565 q^{3}\) \(+0.382940 q^{4}\) \(-1.00000 q^{5}\) \(-1.19259 q^{6}\) \(-1.00000 q^{7}\) \(+2.49622 q^{8}\) \(-2.40314 q^{9}\) \(+1.54368 q^{10}\) \(+5.00484 q^{11}\) \(+0.295846 q^{12}\) \(-5.25397 q^{13}\) \(+1.54368 q^{14}\) \(-0.772565 q^{15}\) \(-4.61924 q^{16}\) \(+4.80207 q^{17}\) \(+3.70968 q^{18}\) \(+8.27223 q^{19}\) \(-0.382940 q^{20}\) \(-0.772565 q^{21}\) \(-7.72586 q^{22}\) \(+5.61714 q^{23}\) \(+1.92849 q^{24}\) \(+1.00000 q^{25}\) \(+8.11043 q^{26}\) \(-4.17428 q^{27}\) \(-0.382940 q^{28}\) \(-1.77847 q^{29}\) \(+1.19259 q^{30}\) \(-8.75809 q^{31}\) \(+2.13817 q^{32}\) \(+3.86656 q^{33}\) \(-7.41285 q^{34}\) \(+1.00000 q^{35}\) \(-0.920260 q^{36}\) \(+12.0820 q^{37}\) \(-12.7697 q^{38}\) \(-4.05903 q^{39}\) \(-2.49622 q^{40}\) \(+8.03675 q^{41}\) \(+1.19259 q^{42}\) \(-7.64728 q^{43}\) \(+1.91655 q^{44}\) \(+2.40314 q^{45}\) \(-8.67105 q^{46}\) \(-5.23408 q^{47}\) \(-3.56866 q^{48}\) \(+1.00000 q^{49}\) \(-1.54368 q^{50}\) \(+3.70991 q^{51}\) \(-2.01195 q^{52}\) \(+9.75944 q^{53}\) \(+6.44374 q^{54}\) \(-5.00484 q^{55}\) \(-2.49622 q^{56}\) \(+6.39083 q^{57}\) \(+2.74539 q^{58}\) \(+8.20919 q^{59}\) \(-0.295846 q^{60}\) \(-1.84675 q^{61}\) \(+13.5197 q^{62}\) \(+2.40314 q^{63}\) \(+5.93782 q^{64}\) \(+5.25397 q^{65}\) \(-5.96873 q^{66}\) \(-5.46181 q^{67}\) \(+1.83890 q^{68}\) \(+4.33960 q^{69}\) \(-1.54368 q^{70}\) \(-6.45927 q^{71}\) \(-5.99877 q^{72}\) \(-3.63322 q^{73}\) \(-18.6507 q^{74}\) \(+0.772565 q^{75}\) \(+3.16777 q^{76}\) \(-5.00484 q^{77}\) \(+6.26583 q^{78}\) \(-15.3203 q^{79}\) \(+4.61924 q^{80}\) \(+3.98453 q^{81}\) \(-12.4061 q^{82}\) \(+11.6486 q^{83}\) \(-0.295846 q^{84}\) \(-4.80207 q^{85}\) \(+11.8049 q^{86}\) \(-1.37398 q^{87}\) \(+12.4932 q^{88}\) \(+6.69176 q^{89}\) \(-3.70968 q^{90}\) \(+5.25397 q^{91}\) \(+2.15103 q^{92}\) \(-6.76619 q^{93}\) \(+8.07973 q^{94}\) \(-8.27223 q^{95}\) \(+1.65188 q^{96}\) \(-16.4107 q^{97}\) \(-1.54368 q^{98}\) \(-12.0274 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(62q \) \(\mathstrut +\mathstrut 2q^{2} \) \(\mathstrut +\mathstrut 11q^{3} \) \(\mathstrut +\mathstrut 64q^{4} \) \(\mathstrut -\mathstrut 62q^{5} \) \(\mathstrut +\mathstrut 3q^{6} \) \(\mathstrut -\mathstrut 62q^{7} \) \(\mathstrut +\mathstrut 15q^{8} \) \(\mathstrut +\mathstrut 69q^{9} \) \(\mathstrut -\mathstrut 2q^{10} \) \(\mathstrut -\mathstrut 13q^{11} \) \(\mathstrut +\mathstrut 37q^{12} \) \(\mathstrut +\mathstrut 31q^{13} \) \(\mathstrut -\mathstrut 2q^{14} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut +\mathstrut 64q^{16} \) \(\mathstrut +\mathstrut 30q^{17} \) \(\mathstrut +\mathstrut 18q^{18} \) \(\mathstrut +\mathstrut 20q^{19} \) \(\mathstrut -\mathstrut 64q^{20} \) \(\mathstrut -\mathstrut 11q^{21} \) \(\mathstrut +\mathstrut 7q^{22} \) \(\mathstrut +\mathstrut 29q^{24} \) \(\mathstrut +\mathstrut 62q^{25} \) \(\mathstrut +\mathstrut 59q^{27} \) \(\mathstrut -\mathstrut 64q^{28} \) \(\mathstrut -\mathstrut 29q^{29} \) \(\mathstrut -\mathstrut 3q^{30} \) \(\mathstrut +\mathstrut 20q^{31} \) \(\mathstrut +\mathstrut 22q^{32} \) \(\mathstrut +\mathstrut 72q^{33} \) \(\mathstrut +\mathstrut 13q^{34} \) \(\mathstrut +\mathstrut 62q^{35} \) \(\mathstrut +\mathstrut 53q^{36} \) \(\mathstrut +\mathstrut 35q^{37} \) \(\mathstrut +\mathstrut 34q^{38} \) \(\mathstrut -\mathstrut 6q^{39} \) \(\mathstrut -\mathstrut 15q^{40} \) \(\mathstrut +\mathstrut 13q^{41} \) \(\mathstrut -\mathstrut 3q^{42} \) \(\mathstrut -\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 44q^{44} \) \(\mathstrut -\mathstrut 69q^{45} \) \(\mathstrut -\mathstrut 19q^{46} \) \(\mathstrut +\mathstrut 58q^{47} \) \(\mathstrut +\mathstrut 64q^{48} \) \(\mathstrut +\mathstrut 62q^{49} \) \(\mathstrut +\mathstrut 2q^{50} \) \(\mathstrut -\mathstrut 30q^{51} \) \(\mathstrut +\mathstrut 82q^{52} \) \(\mathstrut +\mathstrut 18q^{53} \) \(\mathstrut +\mathstrut 22q^{54} \) \(\mathstrut +\mathstrut 13q^{55} \) \(\mathstrut -\mathstrut 15q^{56} \) \(\mathstrut +\mathstrut 21q^{57} \) \(\mathstrut +\mathstrut 18q^{58} \) \(\mathstrut -\mathstrut 11q^{59} \) \(\mathstrut -\mathstrut 37q^{60} \) \(\mathstrut +\mathstrut 24q^{61} \) \(\mathstrut +\mathstrut 48q^{62} \) \(\mathstrut -\mathstrut 69q^{63} \) \(\mathstrut +\mathstrut 65q^{64} \) \(\mathstrut -\mathstrut 31q^{65} \) \(\mathstrut +\mathstrut 25q^{66} \) \(\mathstrut -\mathstrut 6q^{67} \) \(\mathstrut +\mathstrut 65q^{68} \) \(\mathstrut +\mathstrut 27q^{69} \) \(\mathstrut +\mathstrut 2q^{70} \) \(\mathstrut -\mathstrut 35q^{71} \) \(\mathstrut +\mathstrut 53q^{72} \) \(\mathstrut +\mathstrut 116q^{73} \) \(\mathstrut -\mathstrut 69q^{74} \) \(\mathstrut +\mathstrut 11q^{75} \) \(\mathstrut +\mathstrut 65q^{76} \) \(\mathstrut +\mathstrut 13q^{77} \) \(\mathstrut +\mathstrut 102q^{78} \) \(\mathstrut -\mathstrut 83q^{79} \) \(\mathstrut -\mathstrut 64q^{80} \) \(\mathstrut +\mathstrut 126q^{81} \) \(\mathstrut +\mathstrut 71q^{82} \) \(\mathstrut +\mathstrut 84q^{83} \) \(\mathstrut -\mathstrut 37q^{84} \) \(\mathstrut -\mathstrut 30q^{85} \) \(\mathstrut +\mathstrut 24q^{86} \) \(\mathstrut +\mathstrut 49q^{87} \) \(\mathstrut +\mathstrut 20q^{88} \) \(\mathstrut -\mathstrut 16q^{89} \) \(\mathstrut -\mathstrut 18q^{90} \) \(\mathstrut -\mathstrut 31q^{91} \) \(\mathstrut +\mathstrut 19q^{92} \) \(\mathstrut +\mathstrut 65q^{93} \) \(\mathstrut +\mathstrut 54q^{94} \) \(\mathstrut -\mathstrut 20q^{95} \) \(\mathstrut +\mathstrut 17q^{96} \) \(\mathstrut +\mathstrut 155q^{97} \) \(\mathstrut +\mathstrut 2q^{98} \) \(\mathstrut +\mathstrut 6q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −1.54368 −1.09154 −0.545772 0.837933i \(-0.683764\pi\)
−0.545772 + 0.837933i \(0.683764\pi\)
\(3\) 0.772565 0.446041 0.223020 0.974814i \(-0.428408\pi\)
0.223020 + 0.974814i \(0.428408\pi\)
\(4\) 0.382940 0.191470
\(5\) −1.00000 −0.447214
\(6\) −1.19259 −0.486873
\(7\) −1.00000 −0.377964
\(8\) 2.49622 0.882547
\(9\) −2.40314 −0.801048
\(10\) 1.54368 0.488154
\(11\) 5.00484 1.50902 0.754508 0.656291i \(-0.227876\pi\)
0.754508 + 0.656291i \(0.227876\pi\)
\(12\) 0.295846 0.0854034
\(13\) −5.25397 −1.45719 −0.728594 0.684946i \(-0.759826\pi\)
−0.728594 + 0.684946i \(0.759826\pi\)
\(14\) 1.54368 0.412565
\(15\) −0.772565 −0.199475
\(16\) −4.61924 −1.15481
\(17\) 4.80207 1.16467 0.582336 0.812948i \(-0.302139\pi\)
0.582336 + 0.812948i \(0.302139\pi\)
\(18\) 3.70968 0.874380
\(19\) 8.27223 1.89778 0.948890 0.315607i \(-0.102208\pi\)
0.948890 + 0.315607i \(0.102208\pi\)
\(20\) −0.382940 −0.0856280
\(21\) −0.772565 −0.168587
\(22\) −7.72586 −1.64716
\(23\) 5.61714 1.17125 0.585627 0.810581i \(-0.300848\pi\)
0.585627 + 0.810581i \(0.300848\pi\)
\(24\) 1.92849 0.393652
\(25\) 1.00000 0.200000
\(26\) 8.11043 1.59059
\(27\) −4.17428 −0.803340
\(28\) −0.382940 −0.0723689
\(29\) −1.77847 −0.330254 −0.165127 0.986272i \(-0.552803\pi\)
−0.165127 + 0.986272i \(0.552803\pi\)
\(30\) 1.19259 0.217736
\(31\) −8.75809 −1.57300 −0.786499 0.617591i \(-0.788109\pi\)
−0.786499 + 0.617591i \(0.788109\pi\)
\(32\) 2.13817 0.377979
\(33\) 3.86656 0.673082
\(34\) −7.41285 −1.27129
\(35\) 1.00000 0.169031
\(36\) −0.920260 −0.153377
\(37\) 12.0820 1.98627 0.993136 0.116964i \(-0.0373163\pi\)
0.993136 + 0.116964i \(0.0373163\pi\)
\(38\) −12.7697 −2.07151
\(39\) −4.05903 −0.649965
\(40\) −2.49622 −0.394687
\(41\) 8.03675 1.25513 0.627565 0.778564i \(-0.284052\pi\)
0.627565 + 0.778564i \(0.284052\pi\)
\(42\) 1.19259 0.184021
\(43\) −7.64728 −1.16620 −0.583100 0.812400i \(-0.698160\pi\)
−0.583100 + 0.812400i \(0.698160\pi\)
\(44\) 1.91655 0.288931
\(45\) 2.40314 0.358239
\(46\) −8.67105 −1.27848
\(47\) −5.23408 −0.763469 −0.381734 0.924272i \(-0.624673\pi\)
−0.381734 + 0.924272i \(0.624673\pi\)
\(48\) −3.56866 −0.515092
\(49\) 1.00000 0.142857
\(50\) −1.54368 −0.218309
\(51\) 3.70991 0.519491
\(52\) −2.01195 −0.279008
\(53\) 9.75944 1.34056 0.670281 0.742108i \(-0.266174\pi\)
0.670281 + 0.742108i \(0.266174\pi\)
\(54\) 6.44374 0.876882
\(55\) −5.00484 −0.674853
\(56\) −2.49622 −0.333571
\(57\) 6.39083 0.846487
\(58\) 2.74539 0.360487
\(59\) 8.20919 1.06875 0.534373 0.845249i \(-0.320548\pi\)
0.534373 + 0.845249i \(0.320548\pi\)
\(60\) −0.295846 −0.0381936
\(61\) −1.84675 −0.236452 −0.118226 0.992987i \(-0.537721\pi\)
−0.118226 + 0.992987i \(0.537721\pi\)
\(62\) 13.5197 1.71700
\(63\) 2.40314 0.302768
\(64\) 5.93782 0.742228
\(65\) 5.25397 0.651674
\(66\) −5.96873 −0.734700
\(67\) −5.46181 −0.667267 −0.333633 0.942703i \(-0.608275\pi\)
−0.333633 + 0.942703i \(0.608275\pi\)
\(68\) 1.83890 0.223000
\(69\) 4.33960 0.522427
\(70\) −1.54368 −0.184505
\(71\) −6.45927 −0.766575 −0.383287 0.923629i \(-0.625208\pi\)
−0.383287 + 0.923629i \(0.625208\pi\)
\(72\) −5.99877 −0.706962
\(73\) −3.63322 −0.425237 −0.212618 0.977135i \(-0.568199\pi\)
−0.212618 + 0.977135i \(0.568199\pi\)
\(74\) −18.6507 −2.16811
\(75\) 0.772565 0.0892081
\(76\) 3.16777 0.363368
\(77\) −5.00484 −0.570355
\(78\) 6.26583 0.709466
\(79\) −15.3203 −1.72367 −0.861836 0.507187i \(-0.830685\pi\)
−0.861836 + 0.507187i \(0.830685\pi\)
\(80\) 4.61924 0.516446
\(81\) 3.98453 0.442725
\(82\) −12.4061 −1.37003
\(83\) 11.6486 1.27860 0.639301 0.768956i \(-0.279224\pi\)
0.639301 + 0.768956i \(0.279224\pi\)
\(84\) −0.295846 −0.0322795
\(85\) −4.80207 −0.520858
\(86\) 11.8049 1.27296
\(87\) −1.37398 −0.147307
\(88\) 12.4932 1.33178
\(89\) 6.69176 0.709325 0.354662 0.934994i \(-0.384596\pi\)
0.354662 + 0.934994i \(0.384596\pi\)
\(90\) −3.70968 −0.391034
\(91\) 5.25397 0.550765
\(92\) 2.15103 0.224260
\(93\) −6.76619 −0.701621
\(94\) 8.07973 0.833361
\(95\) −8.27223 −0.848713
\(96\) 1.65188 0.168594
\(97\) −16.4107 −1.66626 −0.833128 0.553081i \(-0.813452\pi\)
−0.833128 + 0.553081i \(0.813452\pi\)
\(98\) −1.54368 −0.155935
\(99\) −12.0274 −1.20879
\(100\) 0.382940 0.0382940
\(101\) −13.4452 −1.33785 −0.668924 0.743331i \(-0.733245\pi\)
−0.668924 + 0.743331i \(0.733245\pi\)
\(102\) −5.72691 −0.567048
\(103\) 8.60526 0.847901 0.423951 0.905685i \(-0.360643\pi\)
0.423951 + 0.905685i \(0.360643\pi\)
\(104\) −13.1150 −1.28604
\(105\) 0.772565 0.0753946
\(106\) −15.0654 −1.46328
\(107\) 7.89268 0.763014 0.381507 0.924366i \(-0.375405\pi\)
0.381507 + 0.924366i \(0.375405\pi\)
\(108\) −1.59850 −0.153816
\(109\) −13.5644 −1.29923 −0.649615 0.760264i \(-0.725070\pi\)
−0.649615 + 0.760264i \(0.725070\pi\)
\(110\) 7.72586 0.736632
\(111\) 9.33415 0.885958
\(112\) 4.61924 0.436477
\(113\) 19.5903 1.84290 0.921448 0.388501i \(-0.127007\pi\)
0.921448 + 0.388501i \(0.127007\pi\)
\(114\) −9.86539 −0.923978
\(115\) −5.61714 −0.523801
\(116\) −0.681048 −0.0632337
\(117\) 12.6260 1.16728
\(118\) −12.6723 −1.16658
\(119\) −4.80207 −0.440205
\(120\) −1.92849 −0.176046
\(121\) 14.0484 1.27713
\(122\) 2.85078 0.258098
\(123\) 6.20891 0.559839
\(124\) −3.35382 −0.301182
\(125\) −1.00000 −0.0894427
\(126\) −3.70968 −0.330484
\(127\) −20.8548 −1.85056 −0.925281 0.379282i \(-0.876171\pi\)
−0.925281 + 0.379282i \(0.876171\pi\)
\(128\) −13.4424 −1.18815
\(129\) −5.90802 −0.520172
\(130\) −8.11043 −0.711332
\(131\) 4.08628 0.357020 0.178510 0.983938i \(-0.442872\pi\)
0.178510 + 0.983938i \(0.442872\pi\)
\(132\) 1.48066 0.128875
\(133\) −8.27223 −0.717293
\(134\) 8.43128 0.728352
\(135\) 4.17428 0.359265
\(136\) 11.9870 1.02788
\(137\) 8.21971 0.702257 0.351128 0.936327i \(-0.385798\pi\)
0.351128 + 0.936327i \(0.385798\pi\)
\(138\) −6.69895 −0.570252
\(139\) 12.0164 1.01921 0.509607 0.860407i \(-0.329791\pi\)
0.509607 + 0.860407i \(0.329791\pi\)
\(140\) 0.382940 0.0323643
\(141\) −4.04367 −0.340538
\(142\) 9.97103 0.836751
\(143\) −26.2953 −2.19892
\(144\) 11.1007 0.925057
\(145\) 1.77847 0.147694
\(146\) 5.60853 0.464165
\(147\) 0.772565 0.0637201
\(148\) 4.62669 0.380312
\(149\) −22.5174 −1.84470 −0.922350 0.386356i \(-0.873734\pi\)
−0.922350 + 0.386356i \(0.873734\pi\)
\(150\) −1.19259 −0.0973746
\(151\) 3.15924 0.257095 0.128548 0.991703i \(-0.458968\pi\)
0.128548 + 0.991703i \(0.458968\pi\)
\(152\) 20.6493 1.67488
\(153\) −11.5401 −0.932959
\(154\) 7.72586 0.622568
\(155\) 8.75809 0.703466
\(156\) −1.55436 −0.124449
\(157\) −21.0994 −1.68391 −0.841957 0.539545i \(-0.818596\pi\)
−0.841957 + 0.539545i \(0.818596\pi\)
\(158\) 23.6496 1.88146
\(159\) 7.53980 0.597945
\(160\) −2.13817 −0.169038
\(161\) −5.61714 −0.442692
\(162\) −6.15083 −0.483255
\(163\) −4.75648 −0.372556 −0.186278 0.982497i \(-0.559643\pi\)
−0.186278 + 0.982497i \(0.559643\pi\)
\(164\) 3.07759 0.240320
\(165\) −3.86656 −0.301012
\(166\) −17.9817 −1.39565
\(167\) 10.1412 0.784753 0.392376 0.919805i \(-0.371653\pi\)
0.392376 + 0.919805i \(0.371653\pi\)
\(168\) −1.92849 −0.148786
\(169\) 14.6042 1.12340
\(170\) 7.41285 0.568539
\(171\) −19.8794 −1.52021
\(172\) −2.92845 −0.223292
\(173\) 11.1150 0.845061 0.422531 0.906349i \(-0.361142\pi\)
0.422531 + 0.906349i \(0.361142\pi\)
\(174\) 2.12099 0.160792
\(175\) −1.00000 −0.0755929
\(176\) −23.1185 −1.74263
\(177\) 6.34213 0.476704
\(178\) −10.3299 −0.774260
\(179\) 12.9892 0.970859 0.485430 0.874276i \(-0.338663\pi\)
0.485430 + 0.874276i \(0.338663\pi\)
\(180\) 0.920260 0.0685921
\(181\) 18.2693 1.35794 0.678972 0.734164i \(-0.262426\pi\)
0.678972 + 0.734164i \(0.262426\pi\)
\(182\) −8.11043 −0.601185
\(183\) −1.42673 −0.105467
\(184\) 14.0216 1.03369
\(185\) −12.0820 −0.888288
\(186\) 10.4448 0.765851
\(187\) 24.0336 1.75751
\(188\) −2.00434 −0.146181
\(189\) 4.17428 0.303634
\(190\) 12.7697 0.926408
\(191\) −18.8628 −1.36486 −0.682431 0.730950i \(-0.739077\pi\)
−0.682431 + 0.730950i \(0.739077\pi\)
\(192\) 4.58735 0.331064
\(193\) 11.8213 0.850918 0.425459 0.904978i \(-0.360113\pi\)
0.425459 + 0.904978i \(0.360113\pi\)
\(194\) 25.3328 1.81879
\(195\) 4.05903 0.290673
\(196\) 0.382940 0.0273529
\(197\) 0.733407 0.0522531 0.0261265 0.999659i \(-0.491683\pi\)
0.0261265 + 0.999659i \(0.491683\pi\)
\(198\) 18.5663 1.31945
\(199\) −10.8067 −0.766067 −0.383034 0.923734i \(-0.625121\pi\)
−0.383034 + 0.923734i \(0.625121\pi\)
\(200\) 2.49622 0.176509
\(201\) −4.21961 −0.297628
\(202\) 20.7551 1.46032
\(203\) 1.77847 0.124824
\(204\) 1.42067 0.0994670
\(205\) −8.03675 −0.561311
\(206\) −13.2837 −0.925522
\(207\) −13.4988 −0.938231
\(208\) 24.2693 1.68277
\(209\) 41.4012 2.86378
\(210\) −1.19259 −0.0822966
\(211\) 1.14022 0.0784959 0.0392479 0.999230i \(-0.487504\pi\)
0.0392479 + 0.999230i \(0.487504\pi\)
\(212\) 3.73728 0.256677
\(213\) −4.99021 −0.341923
\(214\) −12.1838 −0.832864
\(215\) 7.64728 0.521540
\(216\) −10.4199 −0.708985
\(217\) 8.75809 0.594538
\(218\) 20.9390 1.41817
\(219\) −2.80690 −0.189673
\(220\) −1.91655 −0.129214
\(221\) −25.2299 −1.69715
\(222\) −14.4089 −0.967063
\(223\) 11.9786 0.802147 0.401073 0.916046i \(-0.368637\pi\)
0.401073 + 0.916046i \(0.368637\pi\)
\(224\) −2.13817 −0.142863
\(225\) −2.40314 −0.160210
\(226\) −30.2410 −2.01160
\(227\) 24.2112 1.60696 0.803479 0.595334i \(-0.202980\pi\)
0.803479 + 0.595334i \(0.202980\pi\)
\(228\) 2.44731 0.162077
\(229\) 1.00000 0.0660819
\(230\) 8.67105 0.571752
\(231\) −3.86656 −0.254401
\(232\) −4.43945 −0.291464
\(233\) 20.7067 1.35654 0.678269 0.734814i \(-0.262730\pi\)
0.678269 + 0.734814i \(0.262730\pi\)
\(234\) −19.4905 −1.27414
\(235\) 5.23408 0.341434
\(236\) 3.14363 0.204633
\(237\) −11.8359 −0.768827
\(238\) 7.41285 0.480503
\(239\) 11.9296 0.771660 0.385830 0.922570i \(-0.373915\pi\)
0.385830 + 0.922570i \(0.373915\pi\)
\(240\) 3.56866 0.230356
\(241\) 12.1920 0.785358 0.392679 0.919676i \(-0.371548\pi\)
0.392679 + 0.919676i \(0.371548\pi\)
\(242\) −21.6862 −1.39404
\(243\) 15.6011 1.00081
\(244\) −0.707193 −0.0452734
\(245\) −1.00000 −0.0638877
\(246\) −9.58455 −0.611089
\(247\) −43.4620 −2.76542
\(248\) −21.8621 −1.38824
\(249\) 8.99932 0.570309
\(250\) 1.54368 0.0976307
\(251\) 0.768976 0.0485373 0.0242687 0.999705i \(-0.492274\pi\)
0.0242687 + 0.999705i \(0.492274\pi\)
\(252\) 0.920260 0.0579709
\(253\) 28.1129 1.76744
\(254\) 32.1930 2.01997
\(255\) −3.70991 −0.232324
\(256\) 8.87513 0.554696
\(257\) −25.8132 −1.61018 −0.805091 0.593151i \(-0.797884\pi\)
−0.805091 + 0.593151i \(0.797884\pi\)
\(258\) 9.12008 0.567792
\(259\) −12.0820 −0.750740
\(260\) 2.01195 0.124776
\(261\) 4.27392 0.264549
\(262\) −6.30789 −0.389703
\(263\) −7.30670 −0.450550 −0.225275 0.974295i \(-0.572328\pi\)
−0.225275 + 0.974295i \(0.572328\pi\)
\(264\) 9.65179 0.594027
\(265\) −9.75944 −0.599517
\(266\) 12.7697 0.782958
\(267\) 5.16982 0.316388
\(268\) −2.09155 −0.127762
\(269\) 13.7179 0.836396 0.418198 0.908356i \(-0.362662\pi\)
0.418198 + 0.908356i \(0.362662\pi\)
\(270\) −6.44374 −0.392154
\(271\) 3.82091 0.232104 0.116052 0.993243i \(-0.462976\pi\)
0.116052 + 0.993243i \(0.462976\pi\)
\(272\) −22.1819 −1.34498
\(273\) 4.05903 0.245664
\(274\) −12.6886 −0.766545
\(275\) 5.00484 0.301803
\(276\) 1.66181 0.100029
\(277\) 10.6675 0.640946 0.320473 0.947258i \(-0.396158\pi\)
0.320473 + 0.947258i \(0.396158\pi\)
\(278\) −18.5494 −1.11252
\(279\) 21.0469 1.26005
\(280\) 2.49622 0.149178
\(281\) −7.45763 −0.444885 −0.222442 0.974946i \(-0.571403\pi\)
−0.222442 + 0.974946i \(0.571403\pi\)
\(282\) 6.24212 0.371713
\(283\) −5.34808 −0.317910 −0.158955 0.987286i \(-0.550813\pi\)
−0.158955 + 0.987286i \(0.550813\pi\)
\(284\) −2.47351 −0.146776
\(285\) −6.39083 −0.378560
\(286\) 40.5914 2.40022
\(287\) −8.03675 −0.474394
\(288\) −5.13834 −0.302780
\(289\) 6.05987 0.356463
\(290\) −2.74539 −0.161215
\(291\) −12.6783 −0.743218
\(292\) −1.39131 −0.0814201
\(293\) −11.4990 −0.671777 −0.335889 0.941902i \(-0.609037\pi\)
−0.335889 + 0.941902i \(0.609037\pi\)
\(294\) −1.19259 −0.0695533
\(295\) −8.20919 −0.477958
\(296\) 30.1594 1.75298
\(297\) −20.8916 −1.21225
\(298\) 34.7596 2.01357
\(299\) −29.5123 −1.70674
\(300\) 0.295846 0.0170807
\(301\) 7.64728 0.440782
\(302\) −4.87685 −0.280631
\(303\) −10.3873 −0.596734
\(304\) −38.2114 −2.19157
\(305\) 1.84675 0.105744
\(306\) 17.8141 1.01837
\(307\) −11.2256 −0.640677 −0.320339 0.947303i \(-0.603797\pi\)
−0.320339 + 0.947303i \(0.603797\pi\)
\(308\) −1.91655 −0.109206
\(309\) 6.64812 0.378198
\(310\) −13.5197 −0.767865
\(311\) −5.12149 −0.290413 −0.145206 0.989401i \(-0.546385\pi\)
−0.145206 + 0.989401i \(0.546385\pi\)
\(312\) −10.1322 −0.573624
\(313\) −6.11628 −0.345713 −0.172856 0.984947i \(-0.555300\pi\)
−0.172856 + 0.984947i \(0.555300\pi\)
\(314\) 32.5706 1.83807
\(315\) −2.40314 −0.135402
\(316\) −5.86677 −0.330031
\(317\) 29.6063 1.66286 0.831428 0.555632i \(-0.187524\pi\)
0.831428 + 0.555632i \(0.187524\pi\)
\(318\) −11.6390 −0.652684
\(319\) −8.90097 −0.498359
\(320\) −5.93782 −0.331934
\(321\) 6.09761 0.340335
\(322\) 8.67105 0.483219
\(323\) 39.7238 2.21029
\(324\) 1.52584 0.0847687
\(325\) −5.25397 −0.291438
\(326\) 7.34247 0.406662
\(327\) −10.4793 −0.579509
\(328\) 20.0615 1.10771
\(329\) 5.23408 0.288564
\(330\) 5.96873 0.328568
\(331\) −15.3387 −0.843093 −0.421546 0.906807i \(-0.638513\pi\)
−0.421546 + 0.906807i \(0.638513\pi\)
\(332\) 4.46073 0.244814
\(333\) −29.0348 −1.59110
\(334\) −15.6548 −0.856593
\(335\) 5.46181 0.298411
\(336\) 3.56866 0.194686
\(337\) −22.6846 −1.23571 −0.617854 0.786293i \(-0.711998\pi\)
−0.617854 + 0.786293i \(0.711998\pi\)
\(338\) −22.5441 −1.22624
\(339\) 15.1347 0.822007
\(340\) −1.83890 −0.0997286
\(341\) −43.8328 −2.37368
\(342\) 30.6873 1.65938
\(343\) −1.00000 −0.0539949
\(344\) −19.0893 −1.02923
\(345\) −4.33960 −0.233636
\(346\) −17.1580 −0.922422
\(347\) 9.63092 0.517015 0.258508 0.966009i \(-0.416769\pi\)
0.258508 + 0.966009i \(0.416769\pi\)
\(348\) −0.526154 −0.0282048
\(349\) 12.4938 0.668776 0.334388 0.942436i \(-0.391470\pi\)
0.334388 + 0.942436i \(0.391470\pi\)
\(350\) 1.54368 0.0825130
\(351\) 21.9315 1.17062
\(352\) 10.7012 0.570377
\(353\) 4.33741 0.230857 0.115428 0.993316i \(-0.463176\pi\)
0.115428 + 0.993316i \(0.463176\pi\)
\(354\) −9.79021 −0.520344
\(355\) 6.45927 0.342823
\(356\) 2.56254 0.135814
\(357\) −3.70991 −0.196349
\(358\) −20.0512 −1.05974
\(359\) 10.7235 0.565967 0.282983 0.959125i \(-0.408676\pi\)
0.282983 + 0.959125i \(0.408676\pi\)
\(360\) 5.99877 0.316163
\(361\) 49.4298 2.60157
\(362\) −28.2019 −1.48226
\(363\) 10.8533 0.569652
\(364\) 2.01195 0.105455
\(365\) 3.63322 0.190172
\(366\) 2.20241 0.115122
\(367\) 4.29139 0.224009 0.112004 0.993708i \(-0.464273\pi\)
0.112004 + 0.993708i \(0.464273\pi\)
\(368\) −25.9469 −1.35258
\(369\) −19.3135 −1.00542
\(370\) 18.6507 0.969606
\(371\) −9.75944 −0.506685
\(372\) −2.59105 −0.134339
\(373\) −11.6324 −0.602304 −0.301152 0.953576i \(-0.597371\pi\)
−0.301152 + 0.953576i \(0.597371\pi\)
\(374\) −37.1001 −1.91840
\(375\) −0.772565 −0.0398951
\(376\) −13.0654 −0.673797
\(377\) 9.34403 0.481242
\(378\) −6.44374 −0.331430
\(379\) −3.70016 −0.190064 −0.0950322 0.995474i \(-0.530295\pi\)
−0.0950322 + 0.995474i \(0.530295\pi\)
\(380\) −3.16777 −0.162503
\(381\) −16.1117 −0.825426
\(382\) 29.1180 1.48981
\(383\) 35.6531 1.82179 0.910894 0.412640i \(-0.135393\pi\)
0.910894 + 0.412640i \(0.135393\pi\)
\(384\) −10.3852 −0.529965
\(385\) 5.00484 0.255070
\(386\) −18.2483 −0.928816
\(387\) 18.3775 0.934182
\(388\) −6.28432 −0.319038
\(389\) −11.3836 −0.577173 −0.288587 0.957454i \(-0.593185\pi\)
−0.288587 + 0.957454i \(0.593185\pi\)
\(390\) −6.26583 −0.317283
\(391\) 26.9739 1.36413
\(392\) 2.49622 0.126078
\(393\) 3.15691 0.159245
\(394\) −1.13214 −0.0570366
\(395\) 15.3203 0.770849
\(396\) −4.60575 −0.231448
\(397\) 4.52813 0.227260 0.113630 0.993523i \(-0.463752\pi\)
0.113630 + 0.993523i \(0.463752\pi\)
\(398\) 16.6821 0.836197
\(399\) −6.39083 −0.319942
\(400\) −4.61924 −0.230962
\(401\) −32.4889 −1.62242 −0.811208 0.584758i \(-0.801190\pi\)
−0.811208 + 0.584758i \(0.801190\pi\)
\(402\) 6.51371 0.324874
\(403\) 46.0147 2.29215
\(404\) −5.14871 −0.256158
\(405\) −3.98453 −0.197993
\(406\) −2.74539 −0.136251
\(407\) 60.4686 2.99732
\(408\) 9.26075 0.458475
\(409\) −9.13004 −0.451452 −0.225726 0.974191i \(-0.572475\pi\)
−0.225726 + 0.974191i \(0.572475\pi\)
\(410\) 12.4061 0.612696
\(411\) 6.35026 0.313235
\(412\) 3.29530 0.162348
\(413\) −8.20919 −0.403948
\(414\) 20.8378 1.02412
\(415\) −11.6486 −0.571808
\(416\) −11.2339 −0.550787
\(417\) 9.28342 0.454611
\(418\) −63.9101 −3.12594
\(419\) 32.2584 1.57593 0.787963 0.615723i \(-0.211136\pi\)
0.787963 + 0.615723i \(0.211136\pi\)
\(420\) 0.295846 0.0144358
\(421\) 25.2314 1.22970 0.614852 0.788643i \(-0.289216\pi\)
0.614852 + 0.788643i \(0.289216\pi\)
\(422\) −1.76013 −0.0856818
\(423\) 12.5782 0.611575
\(424\) 24.3617 1.18311
\(425\) 4.80207 0.232935
\(426\) 7.70327 0.373225
\(427\) 1.84675 0.0893704
\(428\) 3.02242 0.146094
\(429\) −20.3148 −0.980808
\(430\) −11.8049 −0.569285
\(431\) −6.70188 −0.322818 −0.161409 0.986888i \(-0.551604\pi\)
−0.161409 + 0.986888i \(0.551604\pi\)
\(432\) 19.2820 0.927705
\(433\) 23.5221 1.13040 0.565200 0.824954i \(-0.308799\pi\)
0.565200 + 0.824954i \(0.308799\pi\)
\(434\) −13.5197 −0.648965
\(435\) 1.37398 0.0658775
\(436\) −5.19433 −0.248763
\(437\) 46.4663 2.22278
\(438\) 4.33295 0.207036
\(439\) 17.6896 0.844281 0.422140 0.906530i \(-0.361279\pi\)
0.422140 + 0.906530i \(0.361279\pi\)
\(440\) −12.4932 −0.595589
\(441\) −2.40314 −0.114435
\(442\) 38.9468 1.85251
\(443\) 22.4149 1.06496 0.532482 0.846442i \(-0.321260\pi\)
0.532482 + 0.846442i \(0.321260\pi\)
\(444\) 3.57442 0.169634
\(445\) −6.69176 −0.317220
\(446\) −18.4911 −0.875579
\(447\) −17.3962 −0.822811
\(448\) −5.93782 −0.280536
\(449\) 16.8379 0.794631 0.397316 0.917682i \(-0.369942\pi\)
0.397316 + 0.917682i \(0.369942\pi\)
\(450\) 3.70968 0.174876
\(451\) 40.2226 1.89401
\(452\) 7.50190 0.352859
\(453\) 2.44072 0.114675
\(454\) −37.3744 −1.75407
\(455\) −5.25397 −0.246310
\(456\) 15.9529 0.747064
\(457\) −32.2195 −1.50716 −0.753582 0.657354i \(-0.771676\pi\)
−0.753582 + 0.657354i \(0.771676\pi\)
\(458\) −1.54368 −0.0721313
\(459\) −20.0452 −0.935629
\(460\) −2.15103 −0.100292
\(461\) 33.2163 1.54704 0.773518 0.633774i \(-0.218495\pi\)
0.773518 + 0.633774i \(0.218495\pi\)
\(462\) 5.96873 0.277690
\(463\) 22.8945 1.06400 0.531998 0.846746i \(-0.321441\pi\)
0.531998 + 0.846746i \(0.321441\pi\)
\(464\) 8.21518 0.381380
\(465\) 6.76619 0.313775
\(466\) −31.9644 −1.48072
\(467\) −3.90717 −0.180802 −0.0904011 0.995905i \(-0.528815\pi\)
−0.0904011 + 0.995905i \(0.528815\pi\)
\(468\) 4.83501 0.223499
\(469\) 5.46181 0.252203
\(470\) −8.07973 −0.372690
\(471\) −16.3006 −0.751093
\(472\) 20.4919 0.943218
\(473\) −38.2734 −1.75981
\(474\) 18.2709 0.839210
\(475\) 8.27223 0.379556
\(476\) −1.83890 −0.0842861
\(477\) −23.4533 −1.07385
\(478\) −18.4154 −0.842302
\(479\) 10.6615 0.487138 0.243569 0.969884i \(-0.421682\pi\)
0.243569 + 0.969884i \(0.421682\pi\)
\(480\) −1.65188 −0.0753976
\(481\) −63.4785 −2.89437
\(482\) −18.8206 −0.857253
\(483\) −4.33960 −0.197459
\(484\) 5.37971 0.244532
\(485\) 16.4107 0.745172
\(486\) −24.0831 −1.09243
\(487\) −12.5384 −0.568170 −0.284085 0.958799i \(-0.591690\pi\)
−0.284085 + 0.958799i \(0.591690\pi\)
\(488\) −4.60988 −0.208680
\(489\) −3.67469 −0.166175
\(490\) 1.54368 0.0697362
\(491\) −5.27132 −0.237891 −0.118946 0.992901i \(-0.537951\pi\)
−0.118946 + 0.992901i \(0.537951\pi\)
\(492\) 2.37764 0.107192
\(493\) −8.54034 −0.384638
\(494\) 67.0913 3.01858
\(495\) 12.0274 0.540589
\(496\) 40.4557 1.81651
\(497\) 6.45927 0.289738
\(498\) −13.8920 −0.622517
\(499\) −15.4739 −0.692707 −0.346353 0.938104i \(-0.612580\pi\)
−0.346353 + 0.938104i \(0.612580\pi\)
\(500\) −0.382940 −0.0171256
\(501\) 7.83477 0.350032
\(502\) −1.18705 −0.0529807
\(503\) 21.4126 0.954741 0.477371 0.878702i \(-0.341590\pi\)
0.477371 + 0.878702i \(0.341590\pi\)
\(504\) 5.99877 0.267207
\(505\) 13.4452 0.598304
\(506\) −43.3972 −1.92924
\(507\) 11.2827 0.501080
\(508\) −7.98613 −0.354327
\(509\) −9.27872 −0.411272 −0.205636 0.978629i \(-0.565926\pi\)
−0.205636 + 0.978629i \(0.565926\pi\)
\(510\) 5.72691 0.253592
\(511\) 3.63322 0.160724
\(512\) 13.1845 0.582679
\(513\) −34.5306 −1.52456
\(514\) 39.8472 1.75759
\(515\) −8.60526 −0.379193
\(516\) −2.26242 −0.0995974
\(517\) −26.1957 −1.15209
\(518\) 18.6507 0.819467
\(519\) 8.58709 0.376932
\(520\) 13.1150 0.575133
\(521\) 14.9905 0.656748 0.328374 0.944548i \(-0.393499\pi\)
0.328374 + 0.944548i \(0.393499\pi\)
\(522\) −6.59756 −0.288767
\(523\) 23.8618 1.04340 0.521702 0.853128i \(-0.325297\pi\)
0.521702 + 0.853128i \(0.325297\pi\)
\(524\) 1.56480 0.0683586
\(525\) −0.772565 −0.0337175
\(526\) 11.2792 0.491796
\(527\) −42.0569 −1.83203
\(528\) −17.8606 −0.777282
\(529\) 8.55224 0.371837
\(530\) 15.0654 0.654400
\(531\) −19.7279 −0.856116
\(532\) −3.16777 −0.137340
\(533\) −42.2248 −1.82896
\(534\) −7.98053 −0.345351
\(535\) −7.89268 −0.341230
\(536\) −13.6339 −0.588894
\(537\) 10.0350 0.433043
\(538\) −21.1760 −0.912964
\(539\) 5.00484 0.215574
\(540\) 1.59850 0.0687884
\(541\) 16.6714 0.716760 0.358380 0.933576i \(-0.383329\pi\)
0.358380 + 0.933576i \(0.383329\pi\)
\(542\) −5.89826 −0.253352
\(543\) 14.1142 0.605698
\(544\) 10.2677 0.440222
\(545\) 13.5644 0.581033
\(546\) −6.26583 −0.268153
\(547\) 44.9582 1.92228 0.961138 0.276069i \(-0.0890318\pi\)
0.961138 + 0.276069i \(0.0890318\pi\)
\(548\) 3.14765 0.134461
\(549\) 4.43800 0.189409
\(550\) −7.72586 −0.329432
\(551\) −14.7119 −0.626749
\(552\) 10.8326 0.461066
\(553\) 15.3203 0.651487
\(554\) −16.4671 −0.699621
\(555\) −9.33415 −0.396212
\(556\) 4.60155 0.195149
\(557\) −44.8853 −1.90185 −0.950926 0.309417i \(-0.899866\pi\)
−0.950926 + 0.309417i \(0.899866\pi\)
\(558\) −32.4897 −1.37540
\(559\) 40.1786 1.69937
\(560\) −4.61924 −0.195198
\(561\) 18.5675 0.783921
\(562\) 11.5122 0.485612
\(563\) −5.89713 −0.248534 −0.124267 0.992249i \(-0.539658\pi\)
−0.124267 + 0.992249i \(0.539658\pi\)
\(564\) −1.54848 −0.0652028
\(565\) −19.5903 −0.824168
\(566\) 8.25571 0.347013
\(567\) −3.98453 −0.167334
\(568\) −16.1238 −0.676538
\(569\) −22.1579 −0.928907 −0.464454 0.885597i \(-0.653749\pi\)
−0.464454 + 0.885597i \(0.653749\pi\)
\(570\) 9.86539 0.413216
\(571\) 28.6864 1.20049 0.600245 0.799816i \(-0.295070\pi\)
0.600245 + 0.799816i \(0.295070\pi\)
\(572\) −10.0695 −0.421027
\(573\) −14.5727 −0.608784
\(574\) 12.4061 0.517823
\(575\) 5.61714 0.234251
\(576\) −14.2694 −0.594560
\(577\) 24.7114 1.02875 0.514375 0.857565i \(-0.328024\pi\)
0.514375 + 0.857565i \(0.328024\pi\)
\(578\) −9.35449 −0.389095
\(579\) 9.13275 0.379544
\(580\) 0.681048 0.0282790
\(581\) −11.6486 −0.483266
\(582\) 19.5713 0.811255
\(583\) 48.8444 2.02293
\(584\) −9.06932 −0.375291
\(585\) −12.6260 −0.522022
\(586\) 17.7507 0.733275
\(587\) 1.74344 0.0719595 0.0359798 0.999353i \(-0.488545\pi\)
0.0359798 + 0.999353i \(0.488545\pi\)
\(588\) 0.295846 0.0122005
\(589\) −72.4489 −2.98521
\(590\) 12.6723 0.521712
\(591\) 0.566605 0.0233070
\(592\) −55.8097 −2.29377
\(593\) −19.7363 −0.810474 −0.405237 0.914212i \(-0.632811\pi\)
−0.405237 + 0.914212i \(0.632811\pi\)
\(594\) 32.2499 1.32323
\(595\) 4.80207 0.196866
\(596\) −8.62282 −0.353205
\(597\) −8.34888 −0.341697
\(598\) 45.5574 1.86298
\(599\) −8.34568 −0.340995 −0.170498 0.985358i \(-0.554538\pi\)
−0.170498 + 0.985358i \(0.554538\pi\)
\(600\) 1.92849 0.0787303
\(601\) −0.894415 −0.0364840 −0.0182420 0.999834i \(-0.505807\pi\)
−0.0182420 + 0.999834i \(0.505807\pi\)
\(602\) −11.8049 −0.481133
\(603\) 13.1255 0.534513
\(604\) 1.20980 0.0492260
\(605\) −14.0484 −0.571150
\(606\) 16.0346 0.651362
\(607\) 13.2559 0.538042 0.269021 0.963134i \(-0.413300\pi\)
0.269021 + 0.963134i \(0.413300\pi\)
\(608\) 17.6875 0.717322
\(609\) 1.37398 0.0556767
\(610\) −2.85078 −0.115425
\(611\) 27.4997 1.11252
\(612\) −4.41915 −0.178634
\(613\) 33.3017 1.34504 0.672521 0.740078i \(-0.265211\pi\)
0.672521 + 0.740078i \(0.265211\pi\)
\(614\) 17.3287 0.699328
\(615\) −6.20891 −0.250367
\(616\) −12.4932 −0.503364
\(617\) −16.4131 −0.660768 −0.330384 0.943847i \(-0.607178\pi\)
−0.330384 + 0.943847i \(0.607178\pi\)
\(618\) −10.2626 −0.412820
\(619\) 2.77843 0.111675 0.0558373 0.998440i \(-0.482217\pi\)
0.0558373 + 0.998440i \(0.482217\pi\)
\(620\) 3.35382 0.134693
\(621\) −23.4475 −0.940916
\(622\) 7.90593 0.316999
\(623\) −6.69176 −0.268100
\(624\) 18.7496 0.750585
\(625\) 1.00000 0.0400000
\(626\) 9.44157 0.377361
\(627\) 31.9851 1.27736
\(628\) −8.07979 −0.322419
\(629\) 58.0187 2.31336
\(630\) 3.70968 0.147797
\(631\) −40.1668 −1.59901 −0.799507 0.600657i \(-0.794906\pi\)
−0.799507 + 0.600657i \(0.794906\pi\)
\(632\) −38.2429 −1.52122
\(633\) 0.880893 0.0350123
\(634\) −45.7026 −1.81508
\(635\) 20.8548 0.827597
\(636\) 2.88729 0.114489
\(637\) −5.25397 −0.208170
\(638\) 13.7402 0.543981
\(639\) 15.5226 0.614063
\(640\) 13.4424 0.531359
\(641\) −13.9647 −0.551571 −0.275785 0.961219i \(-0.588938\pi\)
−0.275785 + 0.961219i \(0.588938\pi\)
\(642\) −9.41274 −0.371491
\(643\) 27.7021 1.09247 0.546233 0.837633i \(-0.316061\pi\)
0.546233 + 0.837633i \(0.316061\pi\)
\(644\) −2.15103 −0.0847623
\(645\) 5.90802 0.232628
\(646\) −61.3208 −2.41263
\(647\) −33.5077 −1.31732 −0.658662 0.752439i \(-0.728877\pi\)
−0.658662 + 0.752439i \(0.728877\pi\)
\(648\) 9.94626 0.390726
\(649\) 41.0857 1.61275
\(650\) 8.11043 0.318117
\(651\) 6.76619 0.265188
\(652\) −1.82145 −0.0713333
\(653\) 33.7729 1.32164 0.660818 0.750546i \(-0.270210\pi\)
0.660818 + 0.750546i \(0.270210\pi\)
\(654\) 16.1767 0.632560
\(655\) −4.08628 −0.159664
\(656\) −37.1236 −1.44943
\(657\) 8.73116 0.340635
\(658\) −8.07973 −0.314981
\(659\) −36.2708 −1.41291 −0.706455 0.707758i \(-0.749707\pi\)
−0.706455 + 0.707758i \(0.749707\pi\)
\(660\) −1.48066 −0.0576347
\(661\) −24.1701 −0.940108 −0.470054 0.882638i \(-0.655766\pi\)
−0.470054 + 0.882638i \(0.655766\pi\)
\(662\) 23.6780 0.920273
\(663\) −19.4917 −0.756997
\(664\) 29.0775 1.12843
\(665\) 8.27223 0.320783
\(666\) 44.8204 1.73676
\(667\) −9.98992 −0.386811
\(668\) 3.88349 0.150257
\(669\) 9.25425 0.357790
\(670\) −8.43128 −0.325729
\(671\) −9.24267 −0.356809
\(672\) −1.65188 −0.0637226
\(673\) −36.6169 −1.41148 −0.705738 0.708473i \(-0.749384\pi\)
−0.705738 + 0.708473i \(0.749384\pi\)
\(674\) 35.0177 1.34883
\(675\) −4.17428 −0.160668
\(676\) 5.59252 0.215097
\(677\) 14.9806 0.575752 0.287876 0.957668i \(-0.407051\pi\)
0.287876 + 0.957668i \(0.407051\pi\)
\(678\) −23.3632 −0.897257
\(679\) 16.4107 0.629785
\(680\) −11.9870 −0.459681
\(681\) 18.7048 0.716768
\(682\) 67.6638 2.59098
\(683\) −2.93032 −0.112126 −0.0560628 0.998427i \(-0.517855\pi\)
−0.0560628 + 0.998427i \(0.517855\pi\)
\(684\) −7.61260 −0.291075
\(685\) −8.21971 −0.314059
\(686\) 1.54368 0.0589379
\(687\) 0.772565 0.0294752
\(688\) 35.3246 1.34674
\(689\) −51.2757 −1.95345
\(690\) 6.69895 0.255025
\(691\) 18.3032 0.696286 0.348143 0.937441i \(-0.386812\pi\)
0.348143 + 0.937441i \(0.386812\pi\)
\(692\) 4.25640 0.161804
\(693\) 12.0274 0.456881
\(694\) −14.8670 −0.564345
\(695\) −12.0164 −0.455806
\(696\) −3.42977 −0.130005
\(697\) 38.5930 1.46182
\(698\) −19.2863 −0.729999
\(699\) 15.9972 0.605071
\(700\) −0.382940 −0.0144738
\(701\) 21.6409 0.817364 0.408682 0.912677i \(-0.365989\pi\)
0.408682 + 0.912677i \(0.365989\pi\)
\(702\) −33.8552 −1.27778
\(703\) 99.9453 3.76951
\(704\) 29.7179 1.12003
\(705\) 4.04367 0.152293
\(706\) −6.69556 −0.251991
\(707\) 13.4452 0.505659
\(708\) 2.42866 0.0912745
\(709\) 13.7434 0.516144 0.258072 0.966126i \(-0.416913\pi\)
0.258072 + 0.966126i \(0.416913\pi\)
\(710\) −9.97103 −0.374206
\(711\) 36.8169 1.38074
\(712\) 16.7041 0.626012
\(713\) −49.1954 −1.84238
\(714\) 5.72691 0.214324
\(715\) 26.2953 0.983387
\(716\) 4.97409 0.185890
\(717\) 9.21638 0.344192
\(718\) −16.5537 −0.617778
\(719\) 52.4084 1.95450 0.977252 0.212080i \(-0.0680239\pi\)
0.977252 + 0.212080i \(0.0680239\pi\)
\(720\) −11.1007 −0.413698
\(721\) −8.60526 −0.320476
\(722\) −76.3037 −2.83973
\(723\) 9.41914 0.350301
\(724\) 6.99604 0.260006
\(725\) −1.77847 −0.0660508
\(726\) −16.7540 −0.621800
\(727\) −30.6162 −1.13549 −0.567746 0.823204i \(-0.692184\pi\)
−0.567746 + 0.823204i \(0.692184\pi\)
\(728\) 13.1150 0.486076
\(729\) 0.0993089 0.00367811
\(730\) −5.60853 −0.207581
\(731\) −36.7228 −1.35824
\(732\) −0.546353 −0.0201938
\(733\) 16.9972 0.627805 0.313903 0.949455i \(-0.398363\pi\)
0.313903 + 0.949455i \(0.398363\pi\)
\(734\) −6.62452 −0.244515
\(735\) −0.772565 −0.0284965
\(736\) 12.0104 0.442710
\(737\) −27.3355 −1.00692
\(738\) 29.8138 1.09746
\(739\) −33.3626 −1.22726 −0.613632 0.789592i \(-0.710292\pi\)
−0.613632 + 0.789592i \(0.710292\pi\)
\(740\) −4.62669 −0.170081
\(741\) −33.5772 −1.23349
\(742\) 15.0654 0.553069
\(743\) 34.7756 1.27579 0.637897 0.770122i \(-0.279805\pi\)
0.637897 + 0.770122i \(0.279805\pi\)
\(744\) −16.8899 −0.619214
\(745\) 22.5174 0.824975
\(746\) 17.9567 0.657441
\(747\) −27.9933 −1.02422
\(748\) 9.20343 0.336511
\(749\) −7.89268 −0.288392
\(750\) 1.19259 0.0435473
\(751\) −10.7450 −0.392092 −0.196046 0.980595i \(-0.562810\pi\)
−0.196046 + 0.980595i \(0.562810\pi\)
\(752\) 24.1775 0.881661
\(753\) 0.594084 0.0216496
\(754\) −14.4242 −0.525297
\(755\) −3.15924 −0.114977
\(756\) 1.59850 0.0581368
\(757\) 38.9751 1.41658 0.708288 0.705924i \(-0.249468\pi\)
0.708288 + 0.705924i \(0.249468\pi\)
\(758\) 5.71185 0.207464
\(759\) 21.7190 0.788351
\(760\) −20.6493 −0.749029
\(761\) −3.65362 −0.132444 −0.0662219 0.997805i \(-0.521095\pi\)
−0.0662219 + 0.997805i \(0.521095\pi\)
\(762\) 24.8712 0.900989
\(763\) 13.5644 0.491063
\(764\) −7.22331 −0.261330
\(765\) 11.5401 0.417232
\(766\) −55.0369 −1.98856
\(767\) −43.1308 −1.55736
\(768\) 6.85662 0.247417
\(769\) 8.89807 0.320873 0.160436 0.987046i \(-0.448710\pi\)
0.160436 + 0.987046i \(0.448710\pi\)
\(770\) −7.72586 −0.278421
\(771\) −19.9424 −0.718206
\(772\) 4.52686 0.162925
\(773\) 18.0636 0.649703 0.324851 0.945765i \(-0.394686\pi\)
0.324851 + 0.945765i \(0.394686\pi\)
\(774\) −28.3690 −1.01970
\(775\) −8.75809 −0.314600
\(776\) −40.9647 −1.47055
\(777\) −9.33415 −0.334861
\(778\) 17.5727 0.630010
\(779\) 66.4818 2.38196
\(780\) 1.55436 0.0556552
\(781\) −32.3276 −1.15677
\(782\) −41.6390 −1.48901
\(783\) 7.42384 0.265306
\(784\) −4.61924 −0.164973
\(785\) 21.0994 0.753069
\(786\) −4.87326 −0.173823
\(787\) −12.9589 −0.461934 −0.230967 0.972962i \(-0.574189\pi\)
−0.230967 + 0.972962i \(0.574189\pi\)
\(788\) 0.280851 0.0100049
\(789\) −5.64490 −0.200964
\(790\) −23.6496 −0.841417
\(791\) −19.5903 −0.696549
\(792\) −30.0229 −1.06682
\(793\) 9.70275 0.344555
\(794\) −6.98998 −0.248065
\(795\) −7.53980 −0.267409
\(796\) −4.13832 −0.146679
\(797\) 44.8698 1.58937 0.794685 0.607021i \(-0.207636\pi\)
0.794685 + 0.607021i \(0.207636\pi\)
\(798\) 9.86539 0.349231
\(799\) −25.1344 −0.889192
\(800\) 2.13817 0.0755959
\(801\) −16.0813 −0.568203
\(802\) 50.1523 1.77094
\(803\) −18.1837 −0.641689
\(804\) −1.61586 −0.0569869
\(805\) 5.61714 0.197978
\(806\) −71.0318 −2.50199
\(807\) 10.5980 0.373067
\(808\) −33.5622 −1.18071
\(809\) 8.86536 0.311690 0.155845 0.987782i \(-0.450190\pi\)
0.155845 + 0.987782i \(0.450190\pi\)
\(810\) 6.15083 0.216118
\(811\) −1.93965 −0.0681103 −0.0340552 0.999420i \(-0.510842\pi\)
−0.0340552 + 0.999420i \(0.510842\pi\)
\(812\) 0.681048 0.0239001
\(813\) 2.95190 0.103528
\(814\) −93.3440 −3.27171
\(815\) 4.75648 0.166612
\(816\) −17.1370 −0.599913
\(817\) −63.2601 −2.21319
\(818\) 14.0938 0.492780
\(819\) −12.6260 −0.441189
\(820\) −3.07759 −0.107474
\(821\) 24.8041 0.865668 0.432834 0.901474i \(-0.357514\pi\)
0.432834 + 0.901474i \(0.357514\pi\)
\(822\) −9.80275 −0.341910
\(823\) 45.2408 1.57700 0.788498 0.615038i \(-0.210859\pi\)
0.788498 + 0.615038i \(0.210859\pi\)
\(824\) 21.4806 0.748312
\(825\) 3.86656 0.134616
\(826\) 12.6723 0.440927
\(827\) −44.4744 −1.54653 −0.773264 0.634085i \(-0.781377\pi\)
−0.773264 + 0.634085i \(0.781377\pi\)
\(828\) −5.16923 −0.179643
\(829\) −0.0461342 −0.00160231 −0.000801153 1.00000i \(-0.500255\pi\)
−0.000801153 1.00000i \(0.500255\pi\)
\(830\) 17.9817 0.624155
\(831\) 8.24131 0.285888
\(832\) −31.1971 −1.08157
\(833\) 4.80207 0.166382
\(834\) −14.3306 −0.496228
\(835\) −10.1412 −0.350952
\(836\) 15.8542 0.548328
\(837\) 36.5587 1.26365
\(838\) −49.7965 −1.72019
\(839\) −38.4112 −1.32610 −0.663052 0.748574i \(-0.730739\pi\)
−0.663052 + 0.748574i \(0.730739\pi\)
\(840\) 1.92849 0.0665393
\(841\) −25.8370 −0.890932
\(842\) −38.9492 −1.34228
\(843\) −5.76150 −0.198437
\(844\) 0.436635 0.0150296
\(845\) −14.6042 −0.502398
\(846\) −19.4168 −0.667562
\(847\) −14.0484 −0.482710
\(848\) −45.0811 −1.54809
\(849\) −4.13174 −0.141801
\(850\) −7.41285 −0.254259
\(851\) 67.8664 2.32643
\(852\) −1.91095 −0.0654681
\(853\) 0.525120 0.0179797 0.00898987 0.999960i \(-0.497138\pi\)
0.00898987 + 0.999960i \(0.497138\pi\)
\(854\) −2.85078 −0.0975517
\(855\) 19.8794 0.679860
\(856\) 19.7019 0.673396
\(857\) 1.62314 0.0554456 0.0277228 0.999616i \(-0.491174\pi\)
0.0277228 + 0.999616i \(0.491174\pi\)
\(858\) 31.3595 1.07060
\(859\) −2.39104 −0.0815811 −0.0407906 0.999168i \(-0.512988\pi\)
−0.0407906 + 0.999168i \(0.512988\pi\)
\(860\) 2.92845 0.0998594
\(861\) −6.20891 −0.211599
\(862\) 10.3455 0.352371
\(863\) −26.3843 −0.898132 −0.449066 0.893499i \(-0.648243\pi\)
−0.449066 + 0.893499i \(0.648243\pi\)
\(864\) −8.92534 −0.303646
\(865\) −11.1150 −0.377923
\(866\) −36.3105 −1.23388
\(867\) 4.68164 0.158997
\(868\) 3.35382 0.113836
\(869\) −76.6758 −2.60105
\(870\) −2.12099 −0.0719083
\(871\) 28.6962 0.972333
\(872\) −33.8596 −1.14663
\(873\) 39.4373 1.33475
\(874\) −71.7289 −2.42627
\(875\) 1.00000 0.0338062
\(876\) −1.07488 −0.0363167
\(877\) 37.8030 1.27652 0.638259 0.769822i \(-0.279655\pi\)
0.638259 + 0.769822i \(0.279655\pi\)
\(878\) −27.3071 −0.921570
\(879\) −8.88371 −0.299640
\(880\) 23.1185 0.779326
\(881\) −24.0587 −0.810559 −0.405279 0.914193i \(-0.632826\pi\)
−0.405279 + 0.914193i \(0.632826\pi\)
\(882\) 3.70968 0.124911
\(883\) 49.5406 1.66717 0.833587 0.552389i \(-0.186284\pi\)
0.833587 + 0.552389i \(0.186284\pi\)
\(884\) −9.66154 −0.324953
\(885\) −6.34213 −0.213188
\(886\) −34.6014 −1.16246
\(887\) 47.2735 1.58729 0.793645 0.608381i \(-0.208181\pi\)
0.793645 + 0.608381i \(0.208181\pi\)
\(888\) 23.3001 0.781899
\(889\) 20.8548 0.699447
\(890\) 10.3299 0.346260
\(891\) 19.9419 0.668080
\(892\) 4.58709 0.153587
\(893\) −43.2975 −1.44890
\(894\) 26.8541 0.898135
\(895\) −12.9892 −0.434181
\(896\) 13.4424 0.449080
\(897\) −22.8001 −0.761274
\(898\) −25.9923 −0.867376
\(899\) 15.5760 0.519489
\(900\) −0.920260 −0.0306753
\(901\) 46.8655 1.56132
\(902\) −62.0908 −2.06740
\(903\) 5.90802 0.196607
\(904\) 48.9016 1.62644
\(905\) −18.2693 −0.607291
\(906\) −3.76768 −0.125173
\(907\) −27.1777 −0.902422 −0.451211 0.892417i \(-0.649008\pi\)
−0.451211 + 0.892417i \(0.649008\pi\)
\(908\) 9.27146 0.307684
\(909\) 32.3107 1.07168
\(910\) 8.11043 0.268858
\(911\) −33.0610 −1.09536 −0.547679 0.836688i \(-0.684489\pi\)
−0.547679 + 0.836688i \(0.684489\pi\)
\(912\) −29.5208 −0.977531
\(913\) 58.2995 1.92943
\(914\) 49.7365 1.64514
\(915\) 1.42673 0.0471663
\(916\) 0.382940 0.0126527
\(917\) −4.08628 −0.134941
\(918\) 30.9433 1.02128
\(919\) 47.9650 1.58222 0.791109 0.611675i \(-0.209504\pi\)
0.791109 + 0.611675i \(0.209504\pi\)
\(920\) −14.0216 −0.462279
\(921\) −8.67249 −0.285768
\(922\) −51.2752 −1.68866
\(923\) 33.9368 1.11704
\(924\) −1.48066 −0.0487102
\(925\) 12.0820 0.397254
\(926\) −35.3417 −1.16140
\(927\) −20.6797 −0.679209
\(928\) −3.80268 −0.124829
\(929\) 15.3071 0.502210 0.251105 0.967960i \(-0.419206\pi\)
0.251105 + 0.967960i \(0.419206\pi\)
\(930\) −10.4448 −0.342499
\(931\) 8.27223 0.271111
\(932\) 7.92941 0.259736
\(933\) −3.95668 −0.129536
\(934\) 6.03141 0.197354
\(935\) −24.0336 −0.785983
\(936\) 31.5173 1.03018
\(937\) 12.8824 0.420851 0.210426 0.977610i \(-0.432515\pi\)
0.210426 + 0.977610i \(0.432515\pi\)
\(938\) −8.43128 −0.275291
\(939\) −4.72523 −0.154202
\(940\) 2.00434 0.0653743
\(941\) −16.0699 −0.523864 −0.261932 0.965086i \(-0.584360\pi\)
−0.261932 + 0.965086i \(0.584360\pi\)
\(942\) 25.1629 0.819852
\(943\) 45.1435 1.47008
\(944\) −37.9202 −1.23420
\(945\) −4.17428 −0.135789
\(946\) 59.0818 1.92092
\(947\) −29.8896 −0.971281 −0.485641 0.874158i \(-0.661414\pi\)
−0.485641 + 0.874158i \(0.661414\pi\)
\(948\) −4.53246 −0.147207
\(949\) 19.0888 0.619650
\(950\) −12.7697 −0.414302
\(951\) 22.8728 0.741701
\(952\) −11.9870 −0.388501
\(953\) 36.4466 1.18062 0.590311 0.807176i \(-0.299005\pi\)
0.590311 + 0.807176i \(0.299005\pi\)
\(954\) 36.2044 1.17216
\(955\) 18.8628 0.610385
\(956\) 4.56831 0.147750
\(957\) −6.87657 −0.222288
\(958\) −16.4580 −0.531733
\(959\) −8.21971 −0.265428
\(960\) −4.58735 −0.148056
\(961\) 45.7041 1.47433
\(962\) 97.9904 3.15934
\(963\) −18.9672 −0.611211
\(964\) 4.66882 0.150372
\(965\) −11.8213 −0.380542
\(966\) 6.69895 0.215535
\(967\) 36.7951 1.18325 0.591625 0.806213i \(-0.298486\pi\)
0.591625 + 0.806213i \(0.298486\pi\)
\(968\) 35.0680 1.12713
\(969\) 30.6892 0.985880
\(970\) −25.3328 −0.813389
\(971\) −5.50229 −0.176577 −0.0882885 0.996095i \(-0.528140\pi\)
−0.0882885 + 0.996095i \(0.528140\pi\)
\(972\) 5.97430 0.191626
\(973\) −12.0164 −0.385227
\(974\) 19.3553 0.620183
\(975\) −4.05903 −0.129993
\(976\) 8.53056 0.273057
\(977\) 17.2110 0.550628 0.275314 0.961354i \(-0.411218\pi\)
0.275314 + 0.961354i \(0.411218\pi\)
\(978\) 5.67253 0.181388
\(979\) 33.4912 1.07038
\(980\) −0.382940 −0.0122326
\(981\) 32.5971 1.04074
\(982\) 8.13722 0.259669
\(983\) 37.0276 1.18100 0.590499 0.807038i \(-0.298931\pi\)
0.590499 + 0.807038i \(0.298931\pi\)
\(984\) 15.4988 0.494084
\(985\) −0.733407 −0.0233683
\(986\) 13.1835 0.419849
\(987\) 4.04367 0.128711
\(988\) −16.6433 −0.529495
\(989\) −42.9559 −1.36592
\(990\) −18.5663 −0.590077
\(991\) −2.56309 −0.0814192 −0.0407096 0.999171i \(-0.512962\pi\)
−0.0407096 + 0.999171i \(0.512962\pi\)
\(992\) −18.7263 −0.594561
\(993\) −11.8502 −0.376054
\(994\) −9.97103 −0.316262
\(995\) 10.8067 0.342596
\(996\) 3.44620 0.109197
\(997\) 38.4010 1.21617 0.608086 0.793871i \(-0.291938\pi\)
0.608086 + 0.793871i \(0.291938\pi\)
\(998\) 23.8867 0.756120
\(999\) −50.4337 −1.59565
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 \(a_p\))