Properties

Label 6003.2.a.t.1.1
Level 6003
Weight 2
Character 6003.1
Self dual Yes
Analytic conductor 47.934
Analytic rank 1
Dimension 22
CM No

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Newspace parameters

Level: \( N \) = \( 6003 = 3^{2} \cdot 23 \cdot 29 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6003.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(47.9341963334\)
Analytic rank: \(1\)
Dimension: \(22\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.1
Character \(\chi\) = 6003.1

$q$-expansion

\(f(q)\) \(=\) \(q-2.68779 q^{2} +5.22422 q^{4} -0.687677 q^{5} -3.46312 q^{7} -8.66603 q^{8} +O(q^{10})\) \(q-2.68779 q^{2} +5.22422 q^{4} -0.687677 q^{5} -3.46312 q^{7} -8.66603 q^{8} +1.84833 q^{10} +4.59608 q^{11} -5.14171 q^{13} +9.30814 q^{14} +12.8440 q^{16} +5.97345 q^{17} +2.27986 q^{19} -3.59258 q^{20} -12.3533 q^{22} +1.00000 q^{23} -4.52710 q^{25} +13.8198 q^{26} -18.0921 q^{28} +1.00000 q^{29} +1.71616 q^{31} -17.1900 q^{32} -16.0554 q^{34} +2.38151 q^{35} +1.76379 q^{37} -6.12779 q^{38} +5.95943 q^{40} +0.217203 q^{41} -10.2031 q^{43} +24.0109 q^{44} -2.68779 q^{46} -3.23531 q^{47} +4.99320 q^{49} +12.1679 q^{50} -26.8614 q^{52} -9.45848 q^{53} -3.16062 q^{55} +30.0115 q^{56} -2.68779 q^{58} -4.74278 q^{59} +0.257666 q^{61} -4.61267 q^{62} +20.5151 q^{64} +3.53584 q^{65} -12.3078 q^{67} +31.2066 q^{68} -6.40100 q^{70} +4.10541 q^{71} +3.50091 q^{73} -4.74070 q^{74} +11.9105 q^{76} -15.9168 q^{77} +12.8224 q^{79} -8.83255 q^{80} -0.583797 q^{82} +5.50862 q^{83} -4.10780 q^{85} +27.4238 q^{86} -39.8297 q^{88} +15.5057 q^{89} +17.8064 q^{91} +5.22422 q^{92} +8.69583 q^{94} -1.56781 q^{95} +18.9149 q^{97} -13.4207 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} + O(q^{10}) \) \( 22q - 3q^{2} + 17q^{4} - 6q^{7} - 6q^{8} - 12q^{10} - 28q^{13} - q^{14} + 3q^{16} - 10q^{17} - 8q^{19} - 11q^{22} + 22q^{23} + 11q^{26} - 21q^{28} + 22q^{29} - 18q^{31} + 5q^{32} - 33q^{34} + 2q^{35} - 28q^{37} + 14q^{38} - 30q^{40} - 10q^{41} - 14q^{43} + 37q^{44} - 3q^{46} - 18q^{47} + 2q^{49} + 7q^{50} - 57q^{52} + 20q^{53} - 42q^{55} - 2q^{56} - 3q^{58} - 20q^{59} - 38q^{61} + 4q^{62} - 24q^{64} + 12q^{65} - 50q^{67} + 11q^{68} - 48q^{70} + 12q^{71} - 46q^{73} - 6q^{74} - 16q^{76} - 14q^{77} - 20q^{79} - 58q^{80} - 42q^{82} + 22q^{83} - 66q^{85} + 22q^{86} - 68q^{88} - 14q^{89} - 16q^{91} + 17q^{92} - 27q^{94} - 20q^{95} - 48q^{97} - 28q^{98} + O(q^{100}) \)

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:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) −2.68779 −1.90056 −0.950278 0.311404i \(-0.899201\pi\)
−0.950278 + 0.311404i \(0.899201\pi\)
\(3\) 0 0
\(4\) 5.22422 2.61211
\(5\) −0.687677 −0.307539 −0.153769 0.988107i \(-0.549141\pi\)
−0.153769 + 0.988107i \(0.549141\pi\)
\(6\) 0 0
\(7\) −3.46312 −1.30894 −0.654468 0.756089i \(-0.727107\pi\)
−0.654468 + 0.756089i \(0.727107\pi\)
\(8\) −8.66603 −3.06390
\(9\) 0 0
\(10\) 1.84833 0.584494
\(11\) 4.59608 1.38577 0.692884 0.721049i \(-0.256340\pi\)
0.692884 + 0.721049i \(0.256340\pi\)
\(12\) 0 0
\(13\) −5.14171 −1.42605 −0.713027 0.701137i \(-0.752676\pi\)
−0.713027 + 0.701137i \(0.752676\pi\)
\(14\) 9.30814 2.48771
\(15\) 0 0
\(16\) 12.8440 3.21101
\(17\) 5.97345 1.44877 0.724387 0.689394i \(-0.242123\pi\)
0.724387 + 0.689394i \(0.242123\pi\)
\(18\) 0 0
\(19\) 2.27986 0.523036 0.261518 0.965199i \(-0.415777\pi\)
0.261518 + 0.965199i \(0.415777\pi\)
\(20\) −3.59258 −0.803324
\(21\) 0 0
\(22\) −12.3533 −2.63373
\(23\) 1.00000 0.208514
\(24\) 0 0
\(25\) −4.52710 −0.905420
\(26\) 13.8198 2.71029
\(27\) 0 0
\(28\) −18.0921 −3.41909
\(29\) 1.00000 0.185695
\(30\) 0 0
\(31\) 1.71616 0.308231 0.154115 0.988053i \(-0.450747\pi\)
0.154115 + 0.988053i \(0.450747\pi\)
\(32\) −17.1900 −3.03879
\(33\) 0 0
\(34\) −16.0554 −2.75347
\(35\) 2.38151 0.402548
\(36\) 0 0
\(37\) 1.76379 0.289965 0.144983 0.989434i \(-0.453687\pi\)
0.144983 + 0.989434i \(0.453687\pi\)
\(38\) −6.12779 −0.994059
\(39\) 0 0
\(40\) 5.95943 0.942268
\(41\) 0.217203 0.0339215 0.0169607 0.999856i \(-0.494601\pi\)
0.0169607 + 0.999856i \(0.494601\pi\)
\(42\) 0 0
\(43\) −10.2031 −1.55596 −0.777980 0.628289i \(-0.783756\pi\)
−0.777980 + 0.628289i \(0.783756\pi\)
\(44\) 24.0109 3.61978
\(45\) 0 0
\(46\) −2.68779 −0.396293
\(47\) −3.23531 −0.471918 −0.235959 0.971763i \(-0.575823\pi\)
−0.235959 + 0.971763i \(0.575823\pi\)
\(48\) 0 0
\(49\) 4.99320 0.713315
\(50\) 12.1679 1.72080
\(51\) 0 0
\(52\) −26.8614 −3.72501
\(53\) −9.45848 −1.29922 −0.649611 0.760267i \(-0.725068\pi\)
−0.649611 + 0.760267i \(0.725068\pi\)
\(54\) 0 0
\(55\) −3.16062 −0.426177
\(56\) 30.0115 4.01046
\(57\) 0 0
\(58\) −2.68779 −0.352924
\(59\) −4.74278 −0.617458 −0.308729 0.951150i \(-0.599904\pi\)
−0.308729 + 0.951150i \(0.599904\pi\)
\(60\) 0 0
\(61\) 0.257666 0.0329907 0.0164953 0.999864i \(-0.494749\pi\)
0.0164953 + 0.999864i \(0.494749\pi\)
\(62\) −4.61267 −0.585810
\(63\) 0 0
\(64\) 20.5151 2.56439
\(65\) 3.53584 0.438567
\(66\) 0 0
\(67\) −12.3078 −1.50364 −0.751818 0.659371i \(-0.770823\pi\)
−0.751818 + 0.659371i \(0.770823\pi\)
\(68\) 31.2066 3.78436
\(69\) 0 0
\(70\) −6.40100 −0.765065
\(71\) 4.10541 0.487222 0.243611 0.969873i \(-0.421668\pi\)
0.243611 + 0.969873i \(0.421668\pi\)
\(72\) 0 0
\(73\) 3.50091 0.409750 0.204875 0.978788i \(-0.434321\pi\)
0.204875 + 0.978788i \(0.434321\pi\)
\(74\) −4.74070 −0.551095
\(75\) 0 0
\(76\) 11.9105 1.36623
\(77\) −15.9168 −1.81388
\(78\) 0 0
\(79\) 12.8224 1.44263 0.721316 0.692606i \(-0.243537\pi\)
0.721316 + 0.692606i \(0.243537\pi\)
\(80\) −8.83255 −0.987509
\(81\) 0 0
\(82\) −0.583797 −0.0644696
\(83\) 5.50862 0.604649 0.302325 0.953205i \(-0.402237\pi\)
0.302325 + 0.953205i \(0.402237\pi\)
\(84\) 0 0
\(85\) −4.10780 −0.445554
\(86\) 27.4238 2.95719
\(87\) 0 0
\(88\) −39.8297 −4.24586
\(89\) 15.5057 1.64360 0.821799 0.569778i \(-0.192971\pi\)
0.821799 + 0.569778i \(0.192971\pi\)
\(90\) 0 0
\(91\) 17.8064 1.86661
\(92\) 5.22422 0.544663
\(93\) 0 0
\(94\) 8.69583 0.896906
\(95\) −1.56781 −0.160854
\(96\) 0 0
\(97\) 18.9149 1.92051 0.960256 0.279120i \(-0.0900429\pi\)
0.960256 + 0.279120i \(0.0900429\pi\)
\(98\) −13.4207 −1.35569
\(99\) 0 0
\(100\) −23.6506 −2.36506
\(101\) 10.8479 1.07940 0.539702 0.841856i \(-0.318537\pi\)
0.539702 + 0.841856i \(0.318537\pi\)
\(102\) 0 0
\(103\) 3.93386 0.387615 0.193807 0.981040i \(-0.437916\pi\)
0.193807 + 0.981040i \(0.437916\pi\)
\(104\) 44.5582 4.36929
\(105\) 0 0
\(106\) 25.4224 2.46924
\(107\) 4.74779 0.458986 0.229493 0.973310i \(-0.426293\pi\)
0.229493 + 0.973310i \(0.426293\pi\)
\(108\) 0 0
\(109\) −12.7331 −1.21961 −0.609806 0.792551i \(-0.708753\pi\)
−0.609806 + 0.792551i \(0.708753\pi\)
\(110\) 8.49507 0.809974
\(111\) 0 0
\(112\) −44.4804 −4.20301
\(113\) −9.80657 −0.922524 −0.461262 0.887264i \(-0.652603\pi\)
−0.461262 + 0.887264i \(0.652603\pi\)
\(114\) 0 0
\(115\) −0.687677 −0.0641262
\(116\) 5.22422 0.485057
\(117\) 0 0
\(118\) 12.7476 1.17351
\(119\) −20.6868 −1.89635
\(120\) 0 0
\(121\) 10.1239 0.920355
\(122\) −0.692551 −0.0627006
\(123\) 0 0
\(124\) 8.96558 0.805133
\(125\) 6.55157 0.585990
\(126\) 0 0
\(127\) 21.0846 1.87095 0.935476 0.353391i \(-0.114972\pi\)
0.935476 + 0.353391i \(0.114972\pi\)
\(128\) −20.7603 −1.83497
\(129\) 0 0
\(130\) −9.50359 −0.833520
\(131\) 2.04581 0.178743 0.0893715 0.995998i \(-0.471514\pi\)
0.0893715 + 0.995998i \(0.471514\pi\)
\(132\) 0 0
\(133\) −7.89544 −0.684621
\(134\) 33.0808 2.85774
\(135\) 0 0
\(136\) −51.7661 −4.43890
\(137\) 16.0616 1.37224 0.686118 0.727491i \(-0.259314\pi\)
0.686118 + 0.727491i \(0.259314\pi\)
\(138\) 0 0
\(139\) −9.16271 −0.777171 −0.388585 0.921413i \(-0.627036\pi\)
−0.388585 + 0.921413i \(0.627036\pi\)
\(140\) 12.4415 1.05150
\(141\) 0 0
\(142\) −11.0345 −0.925993
\(143\) −23.6317 −1.97618
\(144\) 0 0
\(145\) −0.687677 −0.0571085
\(146\) −9.40970 −0.778752
\(147\) 0 0
\(148\) 9.21443 0.757422
\(149\) −19.0418 −1.55997 −0.779984 0.625800i \(-0.784773\pi\)
−0.779984 + 0.625800i \(0.784773\pi\)
\(150\) 0 0
\(151\) 12.7520 1.03774 0.518870 0.854853i \(-0.326353\pi\)
0.518870 + 0.854853i \(0.326353\pi\)
\(152\) −19.7574 −1.60253
\(153\) 0 0
\(154\) 42.7809 3.44739
\(155\) −1.18016 −0.0947929
\(156\) 0 0
\(157\) −17.2736 −1.37858 −0.689290 0.724485i \(-0.742078\pi\)
−0.689290 + 0.724485i \(0.742078\pi\)
\(158\) −34.4639 −2.74180
\(159\) 0 0
\(160\) 11.8212 0.934546
\(161\) −3.46312 −0.272932
\(162\) 0 0
\(163\) −15.6701 −1.22737 −0.613687 0.789549i \(-0.710314\pi\)
−0.613687 + 0.789549i \(0.710314\pi\)
\(164\) 1.13472 0.0886066
\(165\) 0 0
\(166\) −14.8060 −1.14917
\(167\) −7.21984 −0.558688 −0.279344 0.960191i \(-0.590117\pi\)
−0.279344 + 0.960191i \(0.590117\pi\)
\(168\) 0 0
\(169\) 13.4372 1.03363
\(170\) 11.0409 0.846799
\(171\) 0 0
\(172\) −53.3033 −4.06434
\(173\) −21.9238 −1.66683 −0.833417 0.552644i \(-0.813619\pi\)
−0.833417 + 0.552644i \(0.813619\pi\)
\(174\) 0 0
\(175\) 15.6779 1.18514
\(176\) 59.0321 4.44972
\(177\) 0 0
\(178\) −41.6760 −3.12375
\(179\) −15.0851 −1.12751 −0.563757 0.825941i \(-0.690644\pi\)
−0.563757 + 0.825941i \(0.690644\pi\)
\(180\) 0 0
\(181\) −12.6056 −0.936969 −0.468484 0.883472i \(-0.655200\pi\)
−0.468484 + 0.883472i \(0.655200\pi\)
\(182\) −47.8598 −3.54760
\(183\) 0 0
\(184\) −8.66603 −0.638868
\(185\) −1.21292 −0.0891755
\(186\) 0 0
\(187\) 27.4544 2.00767
\(188\) −16.9020 −1.23270
\(189\) 0 0
\(190\) 4.21394 0.305712
\(191\) −5.43046 −0.392934 −0.196467 0.980510i \(-0.562947\pi\)
−0.196467 + 0.980510i \(0.562947\pi\)
\(192\) 0 0
\(193\) 20.8624 1.50171 0.750856 0.660466i \(-0.229641\pi\)
0.750856 + 0.660466i \(0.229641\pi\)
\(194\) −50.8392 −3.65004
\(195\) 0 0
\(196\) 26.0856 1.86326
\(197\) 8.43033 0.600636 0.300318 0.953839i \(-0.402907\pi\)
0.300318 + 0.953839i \(0.402907\pi\)
\(198\) 0 0
\(199\) −18.0862 −1.28209 −0.641047 0.767502i \(-0.721500\pi\)
−0.641047 + 0.767502i \(0.721500\pi\)
\(200\) 39.2320 2.77412
\(201\) 0 0
\(202\) −29.1568 −2.05147
\(203\) −3.46312 −0.243063
\(204\) 0 0
\(205\) −0.149366 −0.0104322
\(206\) −10.5734 −0.736683
\(207\) 0 0
\(208\) −66.0403 −4.57907
\(209\) 10.4784 0.724808
\(210\) 0 0
\(211\) −5.36796 −0.369545 −0.184773 0.982781i \(-0.559155\pi\)
−0.184773 + 0.982781i \(0.559155\pi\)
\(212\) −49.4132 −3.39371
\(213\) 0 0
\(214\) −12.7611 −0.872328
\(215\) 7.01645 0.478518
\(216\) 0 0
\(217\) −5.94326 −0.403455
\(218\) 34.2240 2.31794
\(219\) 0 0
\(220\) −16.5118 −1.11322
\(221\) −30.7137 −2.06603
\(222\) 0 0
\(223\) 13.0007 0.870588 0.435294 0.900288i \(-0.356644\pi\)
0.435294 + 0.900288i \(0.356644\pi\)
\(224\) 59.5311 3.97759
\(225\) 0 0
\(226\) 26.3580 1.75331
\(227\) 20.0165 1.32854 0.664271 0.747492i \(-0.268742\pi\)
0.664271 + 0.747492i \(0.268742\pi\)
\(228\) 0 0
\(229\) −20.8501 −1.37781 −0.688905 0.724851i \(-0.741908\pi\)
−0.688905 + 0.724851i \(0.741908\pi\)
\(230\) 1.84833 0.121875
\(231\) 0 0
\(232\) −8.66603 −0.568953
\(233\) 26.7760 1.75416 0.877078 0.480348i \(-0.159490\pi\)
0.877078 + 0.480348i \(0.159490\pi\)
\(234\) 0 0
\(235\) 2.22485 0.145133
\(236\) −24.7773 −1.61287
\(237\) 0 0
\(238\) 55.6017 3.60412
\(239\) −2.28068 −0.147525 −0.0737624 0.997276i \(-0.523501\pi\)
−0.0737624 + 0.997276i \(0.523501\pi\)
\(240\) 0 0
\(241\) 13.3485 0.859853 0.429926 0.902864i \(-0.358539\pi\)
0.429926 + 0.902864i \(0.358539\pi\)
\(242\) −27.2110 −1.74919
\(243\) 0 0
\(244\) 1.34610 0.0861753
\(245\) −3.43371 −0.219372
\(246\) 0 0
\(247\) −11.7224 −0.745878
\(248\) −14.8723 −0.944390
\(249\) 0 0
\(250\) −17.6092 −1.11371
\(251\) 6.58893 0.415889 0.207945 0.978141i \(-0.433323\pi\)
0.207945 + 0.978141i \(0.433323\pi\)
\(252\) 0 0
\(253\) 4.59608 0.288953
\(254\) −56.6709 −3.55585
\(255\) 0 0
\(256\) 14.7691 0.923067
\(257\) 6.96581 0.434515 0.217257 0.976114i \(-0.430289\pi\)
0.217257 + 0.976114i \(0.430289\pi\)
\(258\) 0 0
\(259\) −6.10822 −0.379546
\(260\) 18.4720 1.14558
\(261\) 0 0
\(262\) −5.49870 −0.339711
\(263\) 26.9584 1.66233 0.831164 0.556027i \(-0.187675\pi\)
0.831164 + 0.556027i \(0.187675\pi\)
\(264\) 0 0
\(265\) 6.50438 0.399561
\(266\) 21.2213 1.30116
\(267\) 0 0
\(268\) −64.2986 −3.92766
\(269\) 15.4844 0.944098 0.472049 0.881572i \(-0.343515\pi\)
0.472049 + 0.881572i \(0.343515\pi\)
\(270\) 0 0
\(271\) −18.6202 −1.13110 −0.565548 0.824716i \(-0.691335\pi\)
−0.565548 + 0.824716i \(0.691335\pi\)
\(272\) 76.7231 4.65202
\(273\) 0 0
\(274\) −43.1702 −2.60801
\(275\) −20.8069 −1.25470
\(276\) 0 0
\(277\) 14.4460 0.867976 0.433988 0.900919i \(-0.357106\pi\)
0.433988 + 0.900919i \(0.357106\pi\)
\(278\) 24.6274 1.47706
\(279\) 0 0
\(280\) −20.6382 −1.23337
\(281\) −21.8021 −1.30061 −0.650303 0.759675i \(-0.725358\pi\)
−0.650303 + 0.759675i \(0.725358\pi\)
\(282\) 0 0
\(283\) 7.24549 0.430700 0.215350 0.976537i \(-0.430911\pi\)
0.215350 + 0.976537i \(0.430911\pi\)
\(284\) 21.4476 1.27268
\(285\) 0 0
\(286\) 63.5170 3.75584
\(287\) −0.752202 −0.0444011
\(288\) 0 0
\(289\) 18.6821 1.09894
\(290\) 1.84833 0.108538
\(291\) 0 0
\(292\) 18.2895 1.07031
\(293\) −6.89562 −0.402847 −0.201423 0.979504i \(-0.564557\pi\)
−0.201423 + 0.979504i \(0.564557\pi\)
\(294\) 0 0
\(295\) 3.26150 0.189892
\(296\) −15.2851 −0.888426
\(297\) 0 0
\(298\) 51.1805 2.96480
\(299\) −5.14171 −0.297353
\(300\) 0 0
\(301\) 35.3346 2.03665
\(302\) −34.2746 −1.97228
\(303\) 0 0
\(304\) 29.2826 1.67947
\(305\) −0.177191 −0.0101459
\(306\) 0 0
\(307\) 3.63268 0.207328 0.103664 0.994612i \(-0.466943\pi\)
0.103664 + 0.994612i \(0.466943\pi\)
\(308\) −83.1527 −4.73806
\(309\) 0 0
\(310\) 3.17203 0.180159
\(311\) −28.6581 −1.62505 −0.812527 0.582923i \(-0.801909\pi\)
−0.812527 + 0.582923i \(0.801909\pi\)
\(312\) 0 0
\(313\) −22.6141 −1.27823 −0.639114 0.769112i \(-0.720699\pi\)
−0.639114 + 0.769112i \(0.720699\pi\)
\(314\) 46.4277 2.62007
\(315\) 0 0
\(316\) 66.9870 3.76831
\(317\) −10.9269 −0.613714 −0.306857 0.951756i \(-0.599277\pi\)
−0.306857 + 0.951756i \(0.599277\pi\)
\(318\) 0 0
\(319\) 4.59608 0.257331
\(320\) −14.1078 −0.788648
\(321\) 0 0
\(322\) 9.30814 0.518723
\(323\) 13.6186 0.757761
\(324\) 0 0
\(325\) 23.2770 1.29118
\(326\) 42.1179 2.33269
\(327\) 0 0
\(328\) −1.88229 −0.103932
\(329\) 11.2043 0.617711
\(330\) 0 0
\(331\) −17.2545 −0.948394 −0.474197 0.880419i \(-0.657262\pi\)
−0.474197 + 0.880419i \(0.657262\pi\)
\(332\) 28.7782 1.57941
\(333\) 0 0
\(334\) 19.4054 1.06182
\(335\) 8.46379 0.462426
\(336\) 0 0
\(337\) 19.5276 1.06374 0.531868 0.846827i \(-0.321490\pi\)
0.531868 + 0.846827i \(0.321490\pi\)
\(338\) −36.1164 −1.96447
\(339\) 0 0
\(340\) −21.4601 −1.16384
\(341\) 7.88759 0.427137
\(342\) 0 0
\(343\) 6.94978 0.375253
\(344\) 88.4205 4.76731
\(345\) 0 0
\(346\) 58.9265 3.16791
\(347\) −32.7192 −1.75646 −0.878229 0.478240i \(-0.841275\pi\)
−0.878229 + 0.478240i \(0.841275\pi\)
\(348\) 0 0
\(349\) −1.17233 −0.0627536 −0.0313768 0.999508i \(-0.509989\pi\)
−0.0313768 + 0.999508i \(0.509989\pi\)
\(350\) −42.1389 −2.25242
\(351\) 0 0
\(352\) −79.0066 −4.21107
\(353\) −7.39875 −0.393796 −0.196898 0.980424i \(-0.563087\pi\)
−0.196898 + 0.980424i \(0.563087\pi\)
\(354\) 0 0
\(355\) −2.82319 −0.149840
\(356\) 81.0050 4.29326
\(357\) 0 0
\(358\) 40.5456 2.14290
\(359\) −13.9250 −0.734932 −0.367466 0.930037i \(-0.619775\pi\)
−0.367466 + 0.930037i \(0.619775\pi\)
\(360\) 0 0
\(361\) −13.8022 −0.726433
\(362\) 33.8813 1.78076
\(363\) 0 0
\(364\) 93.0244 4.87580
\(365\) −2.40749 −0.126014
\(366\) 0 0
\(367\) −23.7137 −1.23784 −0.618922 0.785452i \(-0.712430\pi\)
−0.618922 + 0.785452i \(0.712430\pi\)
\(368\) 12.8440 0.669541
\(369\) 0 0
\(370\) 3.26007 0.169483
\(371\) 32.7559 1.70060
\(372\) 0 0
\(373\) −4.03710 −0.209033 −0.104517 0.994523i \(-0.533330\pi\)
−0.104517 + 0.994523i \(0.533330\pi\)
\(374\) −73.7917 −3.81568
\(375\) 0 0
\(376\) 28.0373 1.44591
\(377\) −5.14171 −0.264812
\(378\) 0 0
\(379\) −24.0642 −1.23610 −0.618048 0.786141i \(-0.712076\pi\)
−0.618048 + 0.786141i \(0.712076\pi\)
\(380\) −8.19058 −0.420168
\(381\) 0 0
\(382\) 14.5959 0.746794
\(383\) 1.24183 0.0634545 0.0317273 0.999497i \(-0.489899\pi\)
0.0317273 + 0.999497i \(0.489899\pi\)
\(384\) 0 0
\(385\) 10.9456 0.557839
\(386\) −56.0739 −2.85409
\(387\) 0 0
\(388\) 98.8153 5.01659
\(389\) −25.7280 −1.30446 −0.652231 0.758020i \(-0.726167\pi\)
−0.652231 + 0.758020i \(0.726167\pi\)
\(390\) 0 0
\(391\) 5.97345 0.302090
\(392\) −43.2712 −2.18553
\(393\) 0 0
\(394\) −22.6590 −1.14154
\(395\) −8.81767 −0.443665
\(396\) 0 0
\(397\) −21.6301 −1.08559 −0.542793 0.839867i \(-0.682633\pi\)
−0.542793 + 0.839867i \(0.682633\pi\)
\(398\) 48.6118 2.43669
\(399\) 0 0
\(400\) −58.1462 −2.90731
\(401\) −5.76638 −0.287959 −0.143980 0.989581i \(-0.545990\pi\)
−0.143980 + 0.989581i \(0.545990\pi\)
\(402\) 0 0
\(403\) −8.82399 −0.439554
\(404\) 56.6717 2.81952
\(405\) 0 0
\(406\) 9.30814 0.461955
\(407\) 8.10652 0.401825
\(408\) 0 0
\(409\) −17.2558 −0.853245 −0.426623 0.904430i \(-0.640297\pi\)
−0.426623 + 0.904430i \(0.640297\pi\)
\(410\) 0.401464 0.0198269
\(411\) 0 0
\(412\) 20.5513 1.01249
\(413\) 16.4248 0.808213
\(414\) 0 0
\(415\) −3.78815 −0.185953
\(416\) 88.3861 4.33349
\(417\) 0 0
\(418\) −28.1638 −1.37754
\(419\) −0.0725445 −0.00354403 −0.00177202 0.999998i \(-0.500564\pi\)
−0.00177202 + 0.999998i \(0.500564\pi\)
\(420\) 0 0
\(421\) −1.44894 −0.0706170 −0.0353085 0.999376i \(-0.511241\pi\)
−0.0353085 + 0.999376i \(0.511241\pi\)
\(422\) 14.4279 0.702342
\(423\) 0 0
\(424\) 81.9674 3.98069
\(425\) −27.0424 −1.31175
\(426\) 0 0
\(427\) −0.892327 −0.0431827
\(428\) 24.8035 1.19892
\(429\) 0 0
\(430\) −18.8587 −0.909449
\(431\) −13.1784 −0.634782 −0.317391 0.948295i \(-0.602807\pi\)
−0.317391 + 0.948295i \(0.602807\pi\)
\(432\) 0 0
\(433\) −38.6226 −1.85608 −0.928042 0.372476i \(-0.878509\pi\)
−0.928042 + 0.372476i \(0.878509\pi\)
\(434\) 15.9742 0.766788
\(435\) 0 0
\(436\) −66.5206 −3.18576
\(437\) 2.27986 0.109061
\(438\) 0 0
\(439\) −14.4449 −0.689417 −0.344708 0.938710i \(-0.612022\pi\)
−0.344708 + 0.938710i \(0.612022\pi\)
\(440\) 27.3900 1.30577
\(441\) 0 0
\(442\) 82.5521 3.92660
\(443\) 7.89171 0.374946 0.187473 0.982270i \(-0.439970\pi\)
0.187473 + 0.982270i \(0.439970\pi\)
\(444\) 0 0
\(445\) −10.6629 −0.505469
\(446\) −34.9430 −1.65460
\(447\) 0 0
\(448\) −71.0463 −3.35662
\(449\) −0.0225254 −0.00106304 −0.000531521 1.00000i \(-0.500169\pi\)
−0.000531521 1.00000i \(0.500169\pi\)
\(450\) 0 0
\(451\) 0.998283 0.0470073
\(452\) −51.2317 −2.40973
\(453\) 0 0
\(454\) −53.8002 −2.52497
\(455\) −12.2450 −0.574056
\(456\) 0 0
\(457\) −33.7655 −1.57948 −0.789742 0.613439i \(-0.789786\pi\)
−0.789742 + 0.613439i \(0.789786\pi\)
\(458\) 56.0406 2.61860
\(459\) 0 0
\(460\) −3.59258 −0.167505
\(461\) 16.2703 0.757783 0.378892 0.925441i \(-0.376305\pi\)
0.378892 + 0.925441i \(0.376305\pi\)
\(462\) 0 0
\(463\) −16.5955 −0.771260 −0.385630 0.922653i \(-0.626016\pi\)
−0.385630 + 0.922653i \(0.626016\pi\)
\(464\) 12.8440 0.596269
\(465\) 0 0
\(466\) −71.9683 −3.33387
\(467\) 24.7206 1.14393 0.571967 0.820277i \(-0.306180\pi\)
0.571967 + 0.820277i \(0.306180\pi\)
\(468\) 0 0
\(469\) 42.6234 1.96816
\(470\) −5.97992 −0.275833
\(471\) 0 0
\(472\) 41.1011 1.89183
\(473\) −46.8943 −2.15620
\(474\) 0 0
\(475\) −10.3212 −0.473568
\(476\) −108.072 −4.95348
\(477\) 0 0
\(478\) 6.12998 0.280379
\(479\) 17.0459 0.778849 0.389424 0.921058i \(-0.372674\pi\)
0.389424 + 0.921058i \(0.372674\pi\)
\(480\) 0 0
\(481\) −9.06890 −0.413506
\(482\) −35.8780 −1.63420
\(483\) 0 0
\(484\) 52.8895 2.40407
\(485\) −13.0073 −0.590631
\(486\) 0 0
\(487\) 9.44988 0.428215 0.214108 0.976810i \(-0.431316\pi\)
0.214108 + 0.976810i \(0.431316\pi\)
\(488\) −2.23294 −0.101080
\(489\) 0 0
\(490\) 9.22910 0.416928
\(491\) −9.10839 −0.411056 −0.205528 0.978651i \(-0.565891\pi\)
−0.205528 + 0.978651i \(0.565891\pi\)
\(492\) 0 0
\(493\) 5.97345 0.269030
\(494\) 31.5073 1.41758
\(495\) 0 0
\(496\) 22.0424 0.989732
\(497\) −14.2175 −0.637743
\(498\) 0 0
\(499\) 11.3259 0.507016 0.253508 0.967333i \(-0.418416\pi\)
0.253508 + 0.967333i \(0.418416\pi\)
\(500\) 34.2268 1.53067
\(501\) 0 0
\(502\) −17.7097 −0.790421
\(503\) −12.6017 −0.561880 −0.280940 0.959725i \(-0.590646\pi\)
−0.280940 + 0.959725i \(0.590646\pi\)
\(504\) 0 0
\(505\) −7.45983 −0.331958
\(506\) −12.3533 −0.549171
\(507\) 0 0
\(508\) 110.150 4.88713
\(509\) 33.1311 1.46851 0.734254 0.678875i \(-0.237532\pi\)
0.734254 + 0.678875i \(0.237532\pi\)
\(510\) 0 0
\(511\) −12.1241 −0.536337
\(512\) 1.82437 0.0806266
\(513\) 0 0
\(514\) −18.7226 −0.825820
\(515\) −2.70522 −0.119206
\(516\) 0 0
\(517\) −14.8697 −0.653969
\(518\) 16.4176 0.721349
\(519\) 0 0
\(520\) −30.6417 −1.34373
\(521\) 23.0329 1.00909 0.504546 0.863385i \(-0.331660\pi\)
0.504546 + 0.863385i \(0.331660\pi\)
\(522\) 0 0
\(523\) −0.588330 −0.0257259 −0.0128629 0.999917i \(-0.504095\pi\)
−0.0128629 + 0.999917i \(0.504095\pi\)
\(524\) 10.6877 0.466896
\(525\) 0 0
\(526\) −72.4586 −3.15935
\(527\) 10.2514 0.446557
\(528\) 0 0
\(529\) 1.00000 0.0434783
\(530\) −17.4824 −0.759387
\(531\) 0 0
\(532\) −41.2475 −1.78831
\(533\) −1.11680 −0.0483739
\(534\) 0 0
\(535\) −3.26494 −0.141156
\(536\) 106.660 4.60700
\(537\) 0 0
\(538\) −41.6187 −1.79431
\(539\) 22.9491 0.988490
\(540\) 0 0
\(541\) 8.17964 0.351670 0.175835 0.984420i \(-0.443737\pi\)
0.175835 + 0.984420i \(0.443737\pi\)
\(542\) 50.0472 2.14971
\(543\) 0 0
\(544\) −102.684 −4.40252
\(545\) 8.75627 0.375078
\(546\) 0 0
\(547\) −25.2950 −1.08153 −0.540767 0.841172i \(-0.681866\pi\)
−0.540767 + 0.841172i \(0.681866\pi\)
\(548\) 83.9093 3.58443
\(549\) 0 0
\(550\) 55.9246 2.38463
\(551\) 2.27986 0.0971254
\(552\) 0 0
\(553\) −44.4055 −1.88831
\(554\) −38.8278 −1.64964
\(555\) 0 0
\(556\) −47.8680 −2.03006
\(557\) −19.3382 −0.819385 −0.409693 0.912224i \(-0.634364\pi\)
−0.409693 + 0.912224i \(0.634364\pi\)
\(558\) 0 0
\(559\) 52.4615 2.21888
\(560\) 30.5882 1.29259
\(561\) 0 0
\(562\) 58.5996 2.47187
\(563\) −33.8682 −1.42737 −0.713687 0.700465i \(-0.752976\pi\)
−0.713687 + 0.700465i \(0.752976\pi\)
\(564\) 0 0
\(565\) 6.74375 0.283712
\(566\) −19.4744 −0.818569
\(567\) 0 0
\(568\) −35.5776 −1.49280
\(569\) 41.3111 1.73185 0.865926 0.500171i \(-0.166730\pi\)
0.865926 + 0.500171i \(0.166730\pi\)
\(570\) 0 0
\(571\) 6.63809 0.277795 0.138898 0.990307i \(-0.455644\pi\)
0.138898 + 0.990307i \(0.455644\pi\)
\(572\) −123.457 −5.16200
\(573\) 0 0
\(574\) 2.02176 0.0843867
\(575\) −4.52710 −0.188793
\(576\) 0 0
\(577\) −20.9868 −0.873694 −0.436847 0.899536i \(-0.643905\pi\)
−0.436847 + 0.899536i \(0.643905\pi\)
\(578\) −50.2135 −2.08861
\(579\) 0 0
\(580\) −3.59258 −0.149174
\(581\) −19.0770 −0.791448
\(582\) 0 0
\(583\) −43.4719 −1.80042
\(584\) −30.3389 −1.25543
\(585\) 0 0
\(586\) 18.5340 0.765632
\(587\) −25.7439 −1.06257 −0.531283 0.847195i \(-0.678290\pi\)
−0.531283 + 0.847195i \(0.678290\pi\)
\(588\) 0 0
\(589\) 3.91260 0.161216
\(590\) −8.76624 −0.360900
\(591\) 0 0
\(592\) 22.6542 0.931081
\(593\) 30.7966 1.26466 0.632332 0.774697i \(-0.282098\pi\)
0.632332 + 0.774697i \(0.282098\pi\)
\(594\) 0 0
\(595\) 14.2258 0.583201
\(596\) −99.4787 −4.07481
\(597\) 0 0
\(598\) 13.8198 0.565135
\(599\) −6.10728 −0.249537 −0.124768 0.992186i \(-0.539819\pi\)
−0.124768 + 0.992186i \(0.539819\pi\)
\(600\) 0 0
\(601\) −11.2448 −0.458685 −0.229343 0.973346i \(-0.573658\pi\)
−0.229343 + 0.973346i \(0.573658\pi\)
\(602\) −94.9720 −3.87077
\(603\) 0 0
\(604\) 66.6190 2.71069
\(605\) −6.96198 −0.283045
\(606\) 0 0
\(607\) −7.27827 −0.295416 −0.147708 0.989031i \(-0.547190\pi\)
−0.147708 + 0.989031i \(0.547190\pi\)
\(608\) −39.1909 −1.58940
\(609\) 0 0
\(610\) 0.476251 0.0192829
\(611\) 16.6350 0.672981
\(612\) 0 0
\(613\) −15.4067 −0.622269 −0.311134 0.950366i \(-0.600709\pi\)
−0.311134 + 0.950366i \(0.600709\pi\)
\(614\) −9.76389 −0.394039
\(615\) 0 0
\(616\) 137.935 5.55756
\(617\) 18.9132 0.761417 0.380708 0.924695i \(-0.375680\pi\)
0.380708 + 0.924695i \(0.375680\pi\)
\(618\) 0 0
\(619\) −7.27806 −0.292530 −0.146265 0.989245i \(-0.546725\pi\)
−0.146265 + 0.989245i \(0.546725\pi\)
\(620\) −6.16543 −0.247609
\(621\) 0 0
\(622\) 77.0271 3.08851
\(623\) −53.6980 −2.15136
\(624\) 0 0
\(625\) 18.1301 0.725206
\(626\) 60.7821 2.42934
\(627\) 0 0
\(628\) −90.2409 −3.60100
\(629\) 10.5359 0.420094
\(630\) 0 0
\(631\) −5.52403 −0.219908 −0.109954 0.993937i \(-0.535070\pi\)
−0.109954 + 0.993937i \(0.535070\pi\)
\(632\) −111.119 −4.42009
\(633\) 0 0
\(634\) 29.3691 1.16640
\(635\) −14.4994 −0.575390
\(636\) 0 0
\(637\) −25.6736 −1.01723
\(638\) −12.3533 −0.489071
\(639\) 0 0
\(640\) 14.2764 0.564323
\(641\) −43.0502 −1.70038 −0.850189 0.526477i \(-0.823513\pi\)
−0.850189 + 0.526477i \(0.823513\pi\)
\(642\) 0 0
\(643\) −8.00495 −0.315685 −0.157842 0.987464i \(-0.550454\pi\)
−0.157842 + 0.987464i \(0.550454\pi\)
\(644\) −18.0921 −0.712929
\(645\) 0 0
\(646\) −36.6040 −1.44017
\(647\) −34.1726 −1.34346 −0.671732 0.740794i \(-0.734449\pi\)
−0.671732 + 0.740794i \(0.734449\pi\)
\(648\) 0 0
\(649\) −21.7982 −0.855654
\(650\) −62.5638 −2.45395
\(651\) 0 0
\(652\) −81.8639 −3.20604
\(653\) 15.0216 0.587839 0.293920 0.955830i \(-0.405040\pi\)
0.293920 + 0.955830i \(0.405040\pi\)
\(654\) 0 0
\(655\) −1.40685 −0.0549703
\(656\) 2.78977 0.108922
\(657\) 0 0
\(658\) −30.1147 −1.17399
\(659\) −43.8463 −1.70801 −0.854005 0.520265i \(-0.825833\pi\)
−0.854005 + 0.520265i \(0.825833\pi\)
\(660\) 0 0
\(661\) 11.7036 0.455218 0.227609 0.973753i \(-0.426909\pi\)
0.227609 + 0.973753i \(0.426909\pi\)
\(662\) 46.3765 1.80247
\(663\) 0 0
\(664\) −47.7378 −1.85259
\(665\) 5.42951 0.210547
\(666\) 0 0
\(667\) 1.00000 0.0387202
\(668\) −37.7180 −1.45935
\(669\) 0 0
\(670\) −22.7489 −0.878866
\(671\) 1.18425 0.0457175
\(672\) 0 0
\(673\) −27.5495 −1.06196 −0.530978 0.847386i \(-0.678175\pi\)
−0.530978 + 0.847386i \(0.678175\pi\)
\(674\) −52.4861 −2.02169
\(675\) 0 0
\(676\) 70.1989 2.69996
\(677\) −20.1222 −0.773358 −0.386679 0.922214i \(-0.626378\pi\)
−0.386679 + 0.922214i \(0.626378\pi\)
\(678\) 0 0
\(679\) −65.5044 −2.51383
\(680\) 35.5983 1.36513
\(681\) 0 0
\(682\) −21.2002 −0.811797
\(683\) 13.2484 0.506936 0.253468 0.967344i \(-0.418429\pi\)
0.253468 + 0.967344i \(0.418429\pi\)
\(684\) 0 0
\(685\) −11.0452 −0.422015
\(686\) −18.6795 −0.713188
\(687\) 0 0
\(688\) −131.049 −4.99620
\(689\) 48.6328 1.85276
\(690\) 0 0
\(691\) 40.4059 1.53711 0.768557 0.639782i \(-0.220975\pi\)
0.768557 + 0.639782i \(0.220975\pi\)
\(692\) −114.535 −4.35395
\(693\) 0 0
\(694\) 87.9424 3.33825
\(695\) 6.30098 0.239010
\(696\) 0 0
\(697\) 1.29745 0.0491445
\(698\) 3.15099 0.119267
\(699\) 0 0
\(700\) 81.9048 3.09571
\(701\) −21.7925 −0.823093 −0.411546 0.911389i \(-0.635011\pi\)
−0.411546 + 0.911389i \(0.635011\pi\)
\(702\) 0 0
\(703\) 4.02120 0.151662
\(704\) 94.2890 3.55365
\(705\) 0 0
\(706\) 19.8863 0.748431
\(707\) −37.5675 −1.41287
\(708\) 0 0
\(709\) −39.1893 −1.47179 −0.735893 0.677097i \(-0.763238\pi\)
−0.735893 + 0.677097i \(0.763238\pi\)
\(710\) 7.58816 0.284778
\(711\) 0 0
\(712\) −134.373 −5.03582
\(713\) 1.71616 0.0642706
\(714\) 0 0
\(715\) 16.2510 0.607752
\(716\) −78.8079 −2.94519
\(717\) 0 0
\(718\) 37.4274 1.39678
\(719\) −11.5706 −0.431509 −0.215754 0.976448i \(-0.569221\pi\)
−0.215754 + 0.976448i \(0.569221\pi\)
\(720\) 0 0
\(721\) −13.6234 −0.507363
\(722\) 37.0975 1.38063
\(723\) 0 0
\(724\) −65.8546 −2.44747
\(725\) −4.52710 −0.168132
\(726\) 0 0
\(727\) −17.8413 −0.661699 −0.330849 0.943684i \(-0.607335\pi\)
−0.330849 + 0.943684i \(0.607335\pi\)
\(728\) −154.310 −5.71913
\(729\) 0 0
\(730\) 6.47084 0.239496
\(731\) −60.9477 −2.25423
\(732\) 0 0
\(733\) −28.5426 −1.05425 −0.527123 0.849789i \(-0.676729\pi\)
−0.527123 + 0.849789i \(0.676729\pi\)
\(734\) 63.7374 2.35259
\(735\) 0 0
\(736\) −17.1900 −0.633632
\(737\) −56.5675 −2.08369
\(738\) 0 0
\(739\) 51.0985 1.87969 0.939845 0.341602i \(-0.110970\pi\)
0.939845 + 0.341602i \(0.110970\pi\)
\(740\) −6.33655 −0.232936
\(741\) 0 0
\(742\) −88.0409 −3.23208
\(743\) 2.05369 0.0753425 0.0376713 0.999290i \(-0.488006\pi\)
0.0376713 + 0.999290i \(0.488006\pi\)
\(744\) 0 0
\(745\) 13.0946 0.479750
\(746\) 10.8509 0.397279
\(747\) 0 0
\(748\) 143.428 5.24424
\(749\) −16.4422 −0.600783
\(750\) 0 0
\(751\) 27.4583 1.00197 0.500984 0.865456i \(-0.332971\pi\)
0.500984 + 0.865456i \(0.332971\pi\)
\(752\) −41.5544 −1.51533
\(753\) 0 0
\(754\) 13.8198 0.503289
\(755\) −8.76922 −0.319145
\(756\) 0 0
\(757\) 12.5724 0.456951 0.228475 0.973550i \(-0.426626\pi\)
0.228475 + 0.973550i \(0.426626\pi\)
\(758\) 64.6796 2.34927
\(759\) 0 0
\(760\) 13.5867 0.492841
\(761\) −16.8228 −0.609825 −0.304912 0.952380i \(-0.598627\pi\)
−0.304912 + 0.952380i \(0.598627\pi\)
\(762\) 0 0
\(763\) 44.0963 1.59639
\(764\) −28.3699 −1.02639
\(765\) 0 0
\(766\) −3.33778 −0.120599
\(767\) 24.3860 0.880528
\(768\) 0 0
\(769\) 39.6902 1.43127 0.715633 0.698477i \(-0.246139\pi\)
0.715633 + 0.698477i \(0.246139\pi\)
\(770\) −29.4195 −1.06020
\(771\) 0 0
\(772\) 108.990 3.92264
\(773\) 25.9789 0.934398 0.467199 0.884152i \(-0.345263\pi\)
0.467199 + 0.884152i \(0.345263\pi\)
\(774\) 0 0
\(775\) −7.76922 −0.279079
\(776\) −163.917 −5.88426
\(777\) 0 0
\(778\) 69.1516 2.47920
\(779\) 0.495194 0.0177422
\(780\) 0 0
\(781\) 18.8688 0.675177
\(782\) −16.0554 −0.574139
\(783\) 0 0
\(784\) 64.1329 2.29046
\(785\) 11.8786 0.423967
\(786\) 0 0
\(787\) −35.2024 −1.25483 −0.627415 0.778685i \(-0.715887\pi\)
−0.627415 + 0.778685i \(0.715887\pi\)
\(788\) 44.0419 1.56893
\(789\) 0 0
\(790\) 23.7001 0.843210
\(791\) 33.9613 1.20753
\(792\) 0 0
\(793\) −1.32484 −0.0470465
\(794\) 58.1373 2.06322
\(795\) 0 0
\(796\) −94.4861 −3.34897
\(797\) 33.9033 1.20092 0.600458 0.799656i \(-0.294985\pi\)
0.600458 + 0.799656i \(0.294985\pi\)
\(798\) 0 0
\(799\) −19.3259 −0.683702
\(800\) 77.8209 2.75139
\(801\) 0 0
\(802\) 15.4988 0.547283
\(803\) 16.0904 0.567819
\(804\) 0 0
\(805\) 2.38151 0.0839371
\(806\) 23.7170 0.835397
\(807\) 0 0
\(808\) −94.0080 −3.30719
\(809\) −35.0829 −1.23345 −0.616725 0.787179i \(-0.711541\pi\)
−0.616725 + 0.787179i \(0.711541\pi\)
\(810\) 0 0
\(811\) 48.8056 1.71379 0.856897 0.515487i \(-0.172389\pi\)
0.856897 + 0.515487i \(0.172389\pi\)
\(812\) −18.0921 −0.634908
\(813\) 0 0
\(814\) −21.7886 −0.763691
\(815\) 10.7759 0.377465
\(816\) 0 0
\(817\) −23.2617 −0.813824
\(818\) 46.3800 1.62164
\(819\) 0 0
\(820\) −0.780320 −0.0272499
\(821\) −48.5225 −1.69345 −0.846724 0.532033i \(-0.821428\pi\)
−0.846724 + 0.532033i \(0.821428\pi\)
\(822\) 0 0
\(823\) −2.03604 −0.0709717 −0.0354859 0.999370i \(-0.511298\pi\)
−0.0354859 + 0.999370i \(0.511298\pi\)
\(824\) −34.0909 −1.18761
\(825\) 0 0
\(826\) −44.1465 −1.53605
\(827\) −12.7928 −0.444849 −0.222425 0.974950i \(-0.571397\pi\)
−0.222425 + 0.974950i \(0.571397\pi\)
\(828\) 0 0
\(829\) −47.1565 −1.63781 −0.818907 0.573926i \(-0.805420\pi\)
−0.818907 + 0.573926i \(0.805420\pi\)
\(830\) 10.1818 0.353414
\(831\) 0 0
\(832\) −105.483 −3.65696
\(833\) 29.8266 1.03343
\(834\) 0 0
\(835\) 4.96492 0.171818
\(836\) 54.7416 1.89328
\(837\) 0 0
\(838\) 0.194984 0.00673563
\(839\) 0.628748 0.0217068 0.0108534 0.999941i \(-0.496545\pi\)
0.0108534 + 0.999941i \(0.496545\pi\)
\(840\) 0 0
\(841\) 1.00000 0.0344828
\(842\) 3.89445 0.134212
\(843\) 0 0
\(844\) −28.0434 −0.965293
\(845\) −9.24045 −0.317881
\(846\) 0 0
\(847\) −35.0603 −1.20469
\(848\) −121.485 −4.17181
\(849\) 0 0
\(850\) 72.6843 2.49305
\(851\) 1.76379 0.0604620
\(852\) 0 0
\(853\) −26.8985 −0.920986 −0.460493 0.887663i \(-0.652327\pi\)
−0.460493 + 0.887663i \(0.652327\pi\)
\(854\) 2.39839 0.0820711
\(855\) 0 0
\(856\) −41.1444 −1.40629
\(857\) 22.5856 0.771510 0.385755 0.922601i \(-0.373941\pi\)
0.385755 + 0.922601i \(0.373941\pi\)
\(858\) 0 0
\(859\) −22.6647 −0.773308 −0.386654 0.922225i \(-0.626369\pi\)
−0.386654 + 0.922225i \(0.626369\pi\)
\(860\) 36.6555 1.24994
\(861\) 0 0
\(862\) 35.4208 1.20644
\(863\) 16.0538 0.546478 0.273239 0.961946i \(-0.411905\pi\)
0.273239 + 0.961946i \(0.411905\pi\)
\(864\) 0 0
\(865\) 15.0765 0.512616
\(866\) 103.809 3.52759
\(867\) 0 0
\(868\) −31.0489 −1.05387
\(869\) 58.9327 1.99916
\(870\) 0 0
\(871\) 63.2831 2.14427
\(872\) 110.346 3.73677
\(873\) 0 0
\(874\) −6.12779 −0.207276
\(875\) −22.6889 −0.767024
\(876\) 0 0
\(877\) −23.5671 −0.795805 −0.397903 0.917428i \(-0.630262\pi\)
−0.397903 + 0.917428i \(0.630262\pi\)
\(878\) 38.8248 1.31028
\(879\) 0 0
\(880\) −40.5950 −1.36846
\(881\) −3.08556 −0.103955 −0.0519775 0.998648i \(-0.516552\pi\)
−0.0519775 + 0.998648i \(0.516552\pi\)
\(882\) 0 0
\(883\) −7.53587 −0.253602 −0.126801 0.991928i \(-0.540471\pi\)
−0.126801 + 0.991928i \(0.540471\pi\)
\(884\) −160.455 −5.39670
\(885\) 0 0
\(886\) −21.2113 −0.712606
\(887\) 8.48441 0.284879 0.142439 0.989804i \(-0.454505\pi\)
0.142439 + 0.989804i \(0.454505\pi\)
\(888\) 0 0
\(889\) −73.0183 −2.44896
\(890\) 28.6596 0.960672
\(891\) 0 0
\(892\) 67.9183 2.27407
\(893\) −7.37606 −0.246830
\(894\) 0 0
\(895\) 10.3737 0.346754
\(896\) 71.8953 2.40185
\(897\) 0 0
\(898\) 0.0605437 0.00202037
\(899\) 1.71616 0.0572371
\(900\) 0 0
\(901\) −56.4997 −1.88228
\(902\) −2.68318 −0.0893400
\(903\) 0 0
\(904\) 84.9840 2.82652
\(905\) 8.66860 0.288154
\(906\) 0 0
\(907\) 46.4640 1.54281 0.771405 0.636344i \(-0.219554\pi\)
0.771405 + 0.636344i \(0.219554\pi\)
\(908\) 104.571 3.47030
\(909\) 0 0
\(910\) 32.9121 1.09102
\(911\) −23.9669 −0.794060 −0.397030 0.917806i \(-0.629959\pi\)
−0.397030 + 0.917806i \(0.629959\pi\)
\(912\) 0 0
\(913\) 25.3180 0.837904
\(914\) 90.7547 3.00190
\(915\) 0 0
\(916\) −108.925 −3.59899
\(917\) −7.08488 −0.233963
\(918\) 0 0
\(919\) 28.2588 0.932172 0.466086 0.884739i \(-0.345664\pi\)
0.466086 + 0.884739i \(0.345664\pi\)
\(920\) 5.95943 0.196477
\(921\) 0 0
\(922\) −43.7311 −1.44021
\(923\) −21.1088 −0.694805
\(924\) 0 0
\(925\) −7.98486 −0.262541
\(926\) 44.6053 1.46582
\(927\) 0 0
\(928\) −17.1900 −0.564290
\(929\) 11.4877 0.376901 0.188450 0.982083i \(-0.439654\pi\)
0.188450 + 0.982083i \(0.439654\pi\)
\(930\) 0 0
\(931\) 11.3838 0.373090
\(932\) 139.884 4.58205
\(933\) 0 0
\(934\) −66.4439 −2.17411
\(935\) −18.8798 −0.617434
\(936\) 0 0
\(937\) −21.1049 −0.689467 −0.344734 0.938701i \(-0.612031\pi\)
−0.344734 + 0.938701i \(0.612031\pi\)
\(938\) −114.563 −3.74060
\(939\) 0 0
\(940\) 11.6231 0.379103
\(941\) −41.1147 −1.34030 −0.670151 0.742225i \(-0.733771\pi\)
−0.670151 + 0.742225i \(0.733771\pi\)
\(942\) 0 0
\(943\) 0.217203 0.00707312
\(944\) −60.9165 −1.98266
\(945\) 0 0
\(946\) 126.042 4.09798
\(947\) 44.3513 1.44122 0.720611 0.693339i \(-0.243861\pi\)
0.720611 + 0.693339i \(0.243861\pi\)
\(948\) 0 0
\(949\) −18.0006 −0.584326
\(950\) 27.7411 0.900041
\(951\) 0 0
\(952\) 179.272 5.81024
\(953\) 41.1340 1.33246 0.666231 0.745746i \(-0.267907\pi\)
0.666231 + 0.745746i \(0.267907\pi\)
\(954\) 0 0
\(955\) 3.73440 0.120842
\(956\) −11.9148 −0.385351
\(957\) 0 0
\(958\) −45.8159 −1.48024
\(959\) −55.6233 −1.79617
\(960\) 0 0
\(961\) −28.0548 −0.904994
\(962\) 24.3753 0.785892
\(963\) 0 0
\(964\) 69.7355 2.24603
\(965\) −14.3466 −0.461834
\(966\) 0 0
\(967\) 9.08667 0.292207 0.146104 0.989269i \(-0.453327\pi\)
0.146104 + 0.989269i \(0.453327\pi\)
\(968\) −87.7341 −2.81988
\(969\) 0 0
\(970\) 34.9609 1.12253
\(971\) −48.2330 −1.54787 −0.773935 0.633265i \(-0.781714\pi\)
−0.773935 + 0.633265i \(0.781714\pi\)
\(972\) 0 0
\(973\) 31.7316 1.01727
\(974\) −25.3993 −0.813846
\(975\) 0 0
\(976\) 3.30946 0.105933
\(977\) −18.0712 −0.578148 −0.289074 0.957307i \(-0.593347\pi\)
−0.289074 + 0.957307i \(0.593347\pi\)
\(978\) 0 0
\(979\) 71.2652 2.27765
\(980\) −17.9385 −0.573023
\(981\) 0 0
\(982\) 24.4814 0.781234
\(983\) 3.85948 0.123098 0.0615491 0.998104i \(-0.480396\pi\)
0.0615491 + 0.998104i \(0.480396\pi\)
\(984\) 0 0
\(985\) −5.79734 −0.184719
\(986\) −16.0554 −0.511307
\(987\) 0 0
\(988\) −61.2404 −1.94832
\(989\) −10.2031 −0.324440
\(990\) 0 0
\(991\) −37.8631 −1.20276 −0.601381 0.798963i \(-0.705382\pi\)
−0.601381 + 0.798963i \(0.705382\pi\)
\(992\) −29.5008 −0.936651
\(993\) 0 0
\(994\) 38.2137 1.21207
\(995\) 12.4374 0.394293
\(996\) 0 0
\(997\) −55.9892 −1.77320 −0.886598 0.462541i \(-0.846938\pi\)
−0.886598 + 0.462541i \(0.846938\pi\)
\(998\) −30.4416 −0.963612
\(999\) 0 0
Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))