Properties

Label 4028.2.a.d.1.18
Level 4028
Weight 2
Character 4028.1
Self dual Yes
Analytic conductor 32.164
Analytic rank 1
Dimension 19
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4028 = 2^{2} \cdot 19 \cdot 53 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4028.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.1637419342\)
Analytic rank: \(1\)
Dimension: \(19\)
Coefficient field: \(\mathbb{Q}[x]/(x^{19} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{5}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.18
Root \(-2.85652\)
Character \(\chi\) = 4028.1

$q$-expansion

\(f(q)\) \(=\) \(q+2.85652 q^{3} -0.0885731 q^{5} -1.03776 q^{7} +5.15970 q^{9} +O(q^{10})\) \(q+2.85652 q^{3} -0.0885731 q^{5} -1.03776 q^{7} +5.15970 q^{9} -3.21731 q^{11} -1.70422 q^{13} -0.253011 q^{15} -7.37063 q^{17} -1.00000 q^{19} -2.96439 q^{21} -8.03892 q^{23} -4.99215 q^{25} +6.16921 q^{27} +5.83179 q^{29} +4.90929 q^{31} -9.19032 q^{33} +0.0919179 q^{35} -4.56946 q^{37} -4.86813 q^{39} +4.12531 q^{41} -5.33634 q^{43} -0.457010 q^{45} -1.46858 q^{47} -5.92305 q^{49} -21.0543 q^{51} +1.00000 q^{53} +0.284967 q^{55} -2.85652 q^{57} +10.3962 q^{59} -9.61138 q^{61} -5.35455 q^{63} +0.150948 q^{65} +4.16429 q^{67} -22.9633 q^{69} -16.1829 q^{71} +7.73490 q^{73} -14.2602 q^{75} +3.33881 q^{77} +1.03842 q^{79} +2.14337 q^{81} +2.95170 q^{83} +0.652839 q^{85} +16.6586 q^{87} -3.28961 q^{89} +1.76858 q^{91} +14.0235 q^{93} +0.0885731 q^{95} -4.36984 q^{97} -16.6004 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} + O(q^{10}) \) \( 19q - 4q^{3} - 2q^{5} - 11q^{7} + 19q^{9} - 11q^{11} + q^{13} - 20q^{15} - q^{17} - 19q^{19} - 10q^{21} - 16q^{23} + 21q^{25} - 4q^{27} - 9q^{31} + 7q^{33} - 25q^{37} - 25q^{39} + q^{41} - 41q^{43} - 27q^{45} - 29q^{47} + 14q^{49} - 24q^{51} + 19q^{53} - 28q^{55} + 4q^{57} - 42q^{59} + q^{61} - 41q^{63} + 2q^{65} - 41q^{67} - 25q^{69} - 20q^{73} + 11q^{75} - 19q^{77} - 38q^{79} + 23q^{81} - 36q^{83} - 58q^{85} - 30q^{87} - 25q^{89} - 55q^{91} - 38q^{93} + 2q^{95} - 13q^{97} + q^{99} + O(q^{100}) \)

Coefficient data

For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) 2.85652 1.64921 0.824606 0.565708i \(-0.191397\pi\)
0.824606 + 0.565708i \(0.191397\pi\)
\(4\) 0 0
\(5\) −0.0885731 −0.0396111 −0.0198055 0.999804i \(-0.506305\pi\)
−0.0198055 + 0.999804i \(0.506305\pi\)
\(6\) 0 0
\(7\) −1.03776 −0.392238 −0.196119 0.980580i \(-0.562834\pi\)
−0.196119 + 0.980580i \(0.562834\pi\)
\(8\) 0 0
\(9\) 5.15970 1.71990
\(10\) 0 0
\(11\) −3.21731 −0.970057 −0.485028 0.874498i \(-0.661191\pi\)
−0.485028 + 0.874498i \(0.661191\pi\)
\(12\) 0 0
\(13\) −1.70422 −0.472665 −0.236333 0.971672i \(-0.575945\pi\)
−0.236333 + 0.971672i \(0.575945\pi\)
\(14\) 0 0
\(15\) −0.253011 −0.0653270
\(16\) 0 0
\(17\) −7.37063 −1.78764 −0.893820 0.448427i \(-0.851985\pi\)
−0.893820 + 0.448427i \(0.851985\pi\)
\(18\) 0 0
\(19\) −1.00000 −0.229416
\(20\) 0 0
\(21\) −2.96439 −0.646883
\(22\) 0 0
\(23\) −8.03892 −1.67623 −0.838115 0.545493i \(-0.816342\pi\)
−0.838115 + 0.545493i \(0.816342\pi\)
\(24\) 0 0
\(25\) −4.99215 −0.998431
\(26\) 0 0
\(27\) 6.16921 1.18726
\(28\) 0 0
\(29\) 5.83179 1.08294 0.541468 0.840721i \(-0.317869\pi\)
0.541468 + 0.840721i \(0.317869\pi\)
\(30\) 0 0
\(31\) 4.90929 0.881734 0.440867 0.897573i \(-0.354671\pi\)
0.440867 + 0.897573i \(0.354671\pi\)
\(32\) 0 0
\(33\) −9.19032 −1.59983
\(34\) 0 0
\(35\) 0.0919179 0.0155370
\(36\) 0 0
\(37\) −4.56946 −0.751214 −0.375607 0.926779i \(-0.622566\pi\)
−0.375607 + 0.926779i \(0.622566\pi\)
\(38\) 0 0
\(39\) −4.86813 −0.779525
\(40\) 0 0
\(41\) 4.12531 0.644265 0.322132 0.946695i \(-0.395600\pi\)
0.322132 + 0.946695i \(0.395600\pi\)
\(42\) 0 0
\(43\) −5.33634 −0.813784 −0.406892 0.913476i \(-0.633387\pi\)
−0.406892 + 0.913476i \(0.633387\pi\)
\(44\) 0 0
\(45\) −0.457010 −0.0681270
\(46\) 0 0
\(47\) −1.46858 −0.214215 −0.107107 0.994247i \(-0.534159\pi\)
−0.107107 + 0.994247i \(0.534159\pi\)
\(48\) 0 0
\(49\) −5.92305 −0.846149
\(50\) 0 0
\(51\) −21.0543 −2.94820
\(52\) 0 0
\(53\) 1.00000 0.137361
\(54\) 0 0
\(55\) 0.284967 0.0384250
\(56\) 0 0
\(57\) −2.85652 −0.378355
\(58\) 0 0
\(59\) 10.3962 1.35347 0.676733 0.736228i \(-0.263395\pi\)
0.676733 + 0.736228i \(0.263395\pi\)
\(60\) 0 0
\(61\) −9.61138 −1.23061 −0.615306 0.788289i \(-0.710967\pi\)
−0.615306 + 0.788289i \(0.710967\pi\)
\(62\) 0 0
\(63\) −5.35455 −0.674609
\(64\) 0 0
\(65\) 0.150948 0.0187228
\(66\) 0 0
\(67\) 4.16429 0.508749 0.254374 0.967106i \(-0.418130\pi\)
0.254374 + 0.967106i \(0.418130\pi\)
\(68\) 0 0
\(69\) −22.9633 −2.76446
\(70\) 0 0
\(71\) −16.1829 −1.92056 −0.960278 0.279044i \(-0.909982\pi\)
−0.960278 + 0.279044i \(0.909982\pi\)
\(72\) 0 0
\(73\) 7.73490 0.905301 0.452651 0.891688i \(-0.350478\pi\)
0.452651 + 0.891688i \(0.350478\pi\)
\(74\) 0 0
\(75\) −14.2602 −1.64662
\(76\) 0 0
\(77\) 3.33881 0.380493
\(78\) 0 0
\(79\) 1.03842 0.116832 0.0584159 0.998292i \(-0.481395\pi\)
0.0584159 + 0.998292i \(0.481395\pi\)
\(80\) 0 0
\(81\) 2.14337 0.238152
\(82\) 0 0
\(83\) 2.95170 0.323991 0.161996 0.986791i \(-0.448207\pi\)
0.161996 + 0.986791i \(0.448207\pi\)
\(84\) 0 0
\(85\) 0.652839 0.0708103
\(86\) 0 0
\(87\) 16.6586 1.78599
\(88\) 0 0
\(89\) −3.28961 −0.348698 −0.174349 0.984684i \(-0.555782\pi\)
−0.174349 + 0.984684i \(0.555782\pi\)
\(90\) 0 0
\(91\) 1.76858 0.185397
\(92\) 0 0
\(93\) 14.0235 1.45417
\(94\) 0 0
\(95\) 0.0885731 0.00908741
\(96\) 0 0
\(97\) −4.36984 −0.443690 −0.221845 0.975082i \(-0.571208\pi\)
−0.221845 + 0.975082i \(0.571208\pi\)
\(98\) 0 0
\(99\) −16.6004 −1.66840
\(100\) 0 0
\(101\) 12.0603 1.20004 0.600022 0.799984i \(-0.295159\pi\)
0.600022 + 0.799984i \(0.295159\pi\)
\(102\) 0 0
\(103\) −3.36874 −0.331932 −0.165966 0.986132i \(-0.553074\pi\)
−0.165966 + 0.986132i \(0.553074\pi\)
\(104\) 0 0
\(105\) 0.262565 0.0256237
\(106\) 0 0
\(107\) −6.33757 −0.612676 −0.306338 0.951923i \(-0.599104\pi\)
−0.306338 + 0.951923i \(0.599104\pi\)
\(108\) 0 0
\(109\) 9.26610 0.887531 0.443766 0.896143i \(-0.353642\pi\)
0.443766 + 0.896143i \(0.353642\pi\)
\(110\) 0 0
\(111\) −13.0527 −1.23891
\(112\) 0 0
\(113\) 14.2220 1.33790 0.668948 0.743309i \(-0.266745\pi\)
0.668948 + 0.743309i \(0.266745\pi\)
\(114\) 0 0
\(115\) 0.712032 0.0663973
\(116\) 0 0
\(117\) −8.79325 −0.812936
\(118\) 0 0
\(119\) 7.64897 0.701180
\(120\) 0 0
\(121\) −0.648889 −0.0589899
\(122\) 0 0
\(123\) 11.7840 1.06253
\(124\) 0 0
\(125\) 0.885036 0.0791600
\(126\) 0 0
\(127\) −7.75517 −0.688160 −0.344080 0.938940i \(-0.611809\pi\)
−0.344080 + 0.938940i \(0.611809\pi\)
\(128\) 0 0
\(129\) −15.2433 −1.34210
\(130\) 0 0
\(131\) 9.27890 0.810701 0.405351 0.914161i \(-0.367149\pi\)
0.405351 + 0.914161i \(0.367149\pi\)
\(132\) 0 0
\(133\) 1.03776 0.0899855
\(134\) 0 0
\(135\) −0.546426 −0.0470288
\(136\) 0 0
\(137\) 12.4985 1.06782 0.533909 0.845542i \(-0.320722\pi\)
0.533909 + 0.845542i \(0.320722\pi\)
\(138\) 0 0
\(139\) 16.7974 1.42474 0.712370 0.701804i \(-0.247622\pi\)
0.712370 + 0.701804i \(0.247622\pi\)
\(140\) 0 0
\(141\) −4.19503 −0.353286
\(142\) 0 0
\(143\) 5.48301 0.458512
\(144\) 0 0
\(145\) −0.516539 −0.0428962
\(146\) 0 0
\(147\) −16.9193 −1.39548
\(148\) 0 0
\(149\) 18.2187 1.49253 0.746265 0.665648i \(-0.231845\pi\)
0.746265 + 0.665648i \(0.231845\pi\)
\(150\) 0 0
\(151\) −6.79632 −0.553076 −0.276538 0.961003i \(-0.589187\pi\)
−0.276538 + 0.961003i \(0.589187\pi\)
\(152\) 0 0
\(153\) −38.0302 −3.07456
\(154\) 0 0
\(155\) −0.434831 −0.0349264
\(156\) 0 0
\(157\) −8.24443 −0.657977 −0.328989 0.944334i \(-0.606708\pi\)
−0.328989 + 0.944334i \(0.606708\pi\)
\(158\) 0 0
\(159\) 2.85652 0.226537
\(160\) 0 0
\(161\) 8.34250 0.657481
\(162\) 0 0
\(163\) −1.07188 −0.0839565 −0.0419782 0.999119i \(-0.513366\pi\)
−0.0419782 + 0.999119i \(0.513366\pi\)
\(164\) 0 0
\(165\) 0.814015 0.0633709
\(166\) 0 0
\(167\) −23.2284 −1.79747 −0.898735 0.438492i \(-0.855513\pi\)
−0.898735 + 0.438492i \(0.855513\pi\)
\(168\) 0 0
\(169\) −10.0956 −0.776588
\(170\) 0 0
\(171\) −5.15970 −0.394572
\(172\) 0 0
\(173\) −6.29216 −0.478384 −0.239192 0.970972i \(-0.576882\pi\)
−0.239192 + 0.970972i \(0.576882\pi\)
\(174\) 0 0
\(175\) 5.18068 0.391622
\(176\) 0 0
\(177\) 29.6969 2.23215
\(178\) 0 0
\(179\) 20.2652 1.51469 0.757347 0.653012i \(-0.226495\pi\)
0.757347 + 0.653012i \(0.226495\pi\)
\(180\) 0 0
\(181\) −8.39564 −0.624043 −0.312022 0.950075i \(-0.601006\pi\)
−0.312022 + 0.950075i \(0.601006\pi\)
\(182\) 0 0
\(183\) −27.4551 −2.02954
\(184\) 0 0
\(185\) 0.404731 0.0297564
\(186\) 0 0
\(187\) 23.7136 1.73411
\(188\) 0 0
\(189\) −6.40218 −0.465690
\(190\) 0 0
\(191\) −3.03597 −0.219675 −0.109838 0.993950i \(-0.535033\pi\)
−0.109838 + 0.993950i \(0.535033\pi\)
\(192\) 0 0
\(193\) 12.1680 0.875873 0.437937 0.899006i \(-0.355709\pi\)
0.437937 + 0.899006i \(0.355709\pi\)
\(194\) 0 0
\(195\) 0.431185 0.0308778
\(196\) 0 0
\(197\) −5.33865 −0.380363 −0.190182 0.981749i \(-0.560908\pi\)
−0.190182 + 0.981749i \(0.560908\pi\)
\(198\) 0 0
\(199\) 14.2965 1.01345 0.506727 0.862107i \(-0.330855\pi\)
0.506727 + 0.862107i \(0.330855\pi\)
\(200\) 0 0
\(201\) 11.8954 0.839034
\(202\) 0 0
\(203\) −6.05202 −0.424768
\(204\) 0 0
\(205\) −0.365391 −0.0255200
\(206\) 0 0
\(207\) −41.4784 −2.88295
\(208\) 0 0
\(209\) 3.21731 0.222546
\(210\) 0 0
\(211\) −22.9466 −1.57971 −0.789853 0.613296i \(-0.789843\pi\)
−0.789853 + 0.613296i \(0.789843\pi\)
\(212\) 0 0
\(213\) −46.2267 −3.16740
\(214\) 0 0
\(215\) 0.472656 0.0322349
\(216\) 0 0
\(217\) −5.09468 −0.345849
\(218\) 0 0
\(219\) 22.0949 1.49303
\(220\) 0 0
\(221\) 12.5612 0.844955
\(222\) 0 0
\(223\) −26.4394 −1.77051 −0.885256 0.465104i \(-0.846017\pi\)
−0.885256 + 0.465104i \(0.846017\pi\)
\(224\) 0 0
\(225\) −25.7580 −1.71720
\(226\) 0 0
\(227\) −13.9138 −0.923493 −0.461747 0.887012i \(-0.652777\pi\)
−0.461747 + 0.887012i \(0.652777\pi\)
\(228\) 0 0
\(229\) −9.45337 −0.624696 −0.312348 0.949968i \(-0.601116\pi\)
−0.312348 + 0.949968i \(0.601116\pi\)
\(230\) 0 0
\(231\) 9.53738 0.627513
\(232\) 0 0
\(233\) −3.77299 −0.247177 −0.123589 0.992334i \(-0.539440\pi\)
−0.123589 + 0.992334i \(0.539440\pi\)
\(234\) 0 0
\(235\) 0.130077 0.00848528
\(236\) 0 0
\(237\) 2.96628 0.192680
\(238\) 0 0
\(239\) 21.3884 1.38350 0.691752 0.722135i \(-0.256839\pi\)
0.691752 + 0.722135i \(0.256839\pi\)
\(240\) 0 0
\(241\) −10.8013 −0.695771 −0.347885 0.937537i \(-0.613100\pi\)
−0.347885 + 0.937537i \(0.613100\pi\)
\(242\) 0 0
\(243\) −12.3850 −0.794501
\(244\) 0 0
\(245\) 0.524622 0.0335169
\(246\) 0 0
\(247\) 1.70422 0.108437
\(248\) 0 0
\(249\) 8.43159 0.534330
\(250\) 0 0
\(251\) 28.4478 1.79561 0.897803 0.440396i \(-0.145162\pi\)
0.897803 + 0.440396i \(0.145162\pi\)
\(252\) 0 0
\(253\) 25.8637 1.62604
\(254\) 0 0
\(255\) 1.86485 0.116781
\(256\) 0 0
\(257\) −5.27628 −0.329125 −0.164563 0.986367i \(-0.552621\pi\)
−0.164563 + 0.986367i \(0.552621\pi\)
\(258\) 0 0
\(259\) 4.74202 0.294655
\(260\) 0 0
\(261\) 30.0902 1.86254
\(262\) 0 0
\(263\) −1.58348 −0.0976416 −0.0488208 0.998808i \(-0.515546\pi\)
−0.0488208 + 0.998808i \(0.515546\pi\)
\(264\) 0 0
\(265\) −0.0885731 −0.00544100
\(266\) 0 0
\(267\) −9.39682 −0.575076
\(268\) 0 0
\(269\) 4.60812 0.280962 0.140481 0.990083i \(-0.455135\pi\)
0.140481 + 0.990083i \(0.455135\pi\)
\(270\) 0 0
\(271\) 3.79800 0.230712 0.115356 0.993324i \(-0.463199\pi\)
0.115356 + 0.993324i \(0.463199\pi\)
\(272\) 0 0
\(273\) 5.05197 0.305759
\(274\) 0 0
\(275\) 16.0613 0.968535
\(276\) 0 0
\(277\) −12.4205 −0.746278 −0.373139 0.927775i \(-0.621719\pi\)
−0.373139 + 0.927775i \(0.621719\pi\)
\(278\) 0 0
\(279\) 25.3304 1.51649
\(280\) 0 0
\(281\) −1.97777 −0.117984 −0.0589920 0.998258i \(-0.518789\pi\)
−0.0589920 + 0.998258i \(0.518789\pi\)
\(282\) 0 0
\(283\) −3.55942 −0.211585 −0.105793 0.994388i \(-0.533738\pi\)
−0.105793 + 0.994388i \(0.533738\pi\)
\(284\) 0 0
\(285\) 0.253011 0.0149871
\(286\) 0 0
\(287\) −4.28110 −0.252705
\(288\) 0 0
\(289\) 37.3261 2.19565
\(290\) 0 0
\(291\) −12.4825 −0.731739
\(292\) 0 0
\(293\) 5.16113 0.301516 0.150758 0.988571i \(-0.451829\pi\)
0.150758 + 0.988571i \(0.451829\pi\)
\(294\) 0 0
\(295\) −0.920821 −0.0536123
\(296\) 0 0
\(297\) −19.8483 −1.15171
\(298\) 0 0
\(299\) 13.7001 0.792296
\(300\) 0 0
\(301\) 5.53786 0.319197
\(302\) 0 0
\(303\) 34.4504 1.97913
\(304\) 0 0
\(305\) 0.851310 0.0487458
\(306\) 0 0
\(307\) −14.4802 −0.826431 −0.413215 0.910633i \(-0.635594\pi\)
−0.413215 + 0.910633i \(0.635594\pi\)
\(308\) 0 0
\(309\) −9.62286 −0.547425
\(310\) 0 0
\(311\) 9.49798 0.538581 0.269290 0.963059i \(-0.413211\pi\)
0.269290 + 0.963059i \(0.413211\pi\)
\(312\) 0 0
\(313\) −20.4175 −1.15406 −0.577032 0.816722i \(-0.695789\pi\)
−0.577032 + 0.816722i \(0.695789\pi\)
\(314\) 0 0
\(315\) 0.474268 0.0267220
\(316\) 0 0
\(317\) −7.90019 −0.443719 −0.221859 0.975079i \(-0.571213\pi\)
−0.221859 + 0.975079i \(0.571213\pi\)
\(318\) 0 0
\(319\) −18.7627 −1.05051
\(320\) 0 0
\(321\) −18.1034 −1.01043
\(322\) 0 0
\(323\) 7.37063 0.410113
\(324\) 0 0
\(325\) 8.50772 0.471923
\(326\) 0 0
\(327\) 26.4688 1.46373
\(328\) 0 0
\(329\) 1.52404 0.0840232
\(330\) 0 0
\(331\) 23.0082 1.26464 0.632322 0.774706i \(-0.282102\pi\)
0.632322 + 0.774706i \(0.282102\pi\)
\(332\) 0 0
\(333\) −23.5770 −1.29201
\(334\) 0 0
\(335\) −0.368844 −0.0201521
\(336\) 0 0
\(337\) 9.00185 0.490362 0.245181 0.969477i \(-0.421153\pi\)
0.245181 + 0.969477i \(0.421153\pi\)
\(338\) 0 0
\(339\) 40.6255 2.20648
\(340\) 0 0
\(341\) −15.7947 −0.855332
\(342\) 0 0
\(343\) 13.4111 0.724130
\(344\) 0 0
\(345\) 2.03393 0.109503
\(346\) 0 0
\(347\) 9.39084 0.504127 0.252063 0.967711i \(-0.418891\pi\)
0.252063 + 0.967711i \(0.418891\pi\)
\(348\) 0 0
\(349\) −27.8648 −1.49157 −0.745785 0.666187i \(-0.767925\pi\)
−0.745785 + 0.666187i \(0.767925\pi\)
\(350\) 0 0
\(351\) −10.5137 −0.561179
\(352\) 0 0
\(353\) −19.2736 −1.02583 −0.512914 0.858440i \(-0.671434\pi\)
−0.512914 + 0.858440i \(0.671434\pi\)
\(354\) 0 0
\(355\) 1.43337 0.0760753
\(356\) 0 0
\(357\) 21.8494 1.15639
\(358\) 0 0
\(359\) −9.90579 −0.522807 −0.261404 0.965230i \(-0.584185\pi\)
−0.261404 + 0.965230i \(0.584185\pi\)
\(360\) 0 0
\(361\) 1.00000 0.0526316
\(362\) 0 0
\(363\) −1.85356 −0.0972868
\(364\) 0 0
\(365\) −0.685104 −0.0358600
\(366\) 0 0
\(367\) 7.46826 0.389840 0.194920 0.980819i \(-0.437555\pi\)
0.194920 + 0.980819i \(0.437555\pi\)
\(368\) 0 0
\(369\) 21.2853 1.10807
\(370\) 0 0
\(371\) −1.03776 −0.0538780
\(372\) 0 0
\(373\) −13.0939 −0.677974 −0.338987 0.940791i \(-0.610084\pi\)
−0.338987 + 0.940791i \(0.610084\pi\)
\(374\) 0 0
\(375\) 2.52812 0.130552
\(376\) 0 0
\(377\) −9.93864 −0.511866
\(378\) 0 0
\(379\) 26.3309 1.35253 0.676264 0.736659i \(-0.263598\pi\)
0.676264 + 0.736659i \(0.263598\pi\)
\(380\) 0 0
\(381\) −22.1528 −1.13492
\(382\) 0 0
\(383\) −31.8993 −1.62998 −0.814990 0.579475i \(-0.803258\pi\)
−0.814990 + 0.579475i \(0.803258\pi\)
\(384\) 0 0
\(385\) −0.295729 −0.0150717
\(386\) 0 0
\(387\) −27.5339 −1.39963
\(388\) 0 0
\(389\) −34.0638 −1.72710 −0.863550 0.504263i \(-0.831764\pi\)
−0.863550 + 0.504263i \(0.831764\pi\)
\(390\) 0 0
\(391\) 59.2519 2.99650
\(392\) 0 0
\(393\) 26.5054 1.33702
\(394\) 0 0
\(395\) −0.0919764 −0.00462783
\(396\) 0 0
\(397\) 2.76277 0.138659 0.0693296 0.997594i \(-0.477914\pi\)
0.0693296 + 0.997594i \(0.477914\pi\)
\(398\) 0 0
\(399\) 2.96439 0.148405
\(400\) 0 0
\(401\) 12.3761 0.618031 0.309016 0.951057i \(-0.400000\pi\)
0.309016 + 0.951057i \(0.400000\pi\)
\(402\) 0 0
\(403\) −8.36649 −0.416765
\(404\) 0 0
\(405\) −0.189845 −0.00943347
\(406\) 0 0
\(407\) 14.7014 0.728721
\(408\) 0 0
\(409\) −12.9713 −0.641390 −0.320695 0.947183i \(-0.603916\pi\)
−0.320695 + 0.947183i \(0.603916\pi\)
\(410\) 0 0
\(411\) 35.7022 1.76106
\(412\) 0 0
\(413\) −10.7888 −0.530881
\(414\) 0 0
\(415\) −0.261441 −0.0128336
\(416\) 0 0
\(417\) 47.9822 2.34970
\(418\) 0 0
\(419\) −33.5359 −1.63833 −0.819167 0.573555i \(-0.805564\pi\)
−0.819167 + 0.573555i \(0.805564\pi\)
\(420\) 0 0
\(421\) 13.6229 0.663940 0.331970 0.943290i \(-0.392287\pi\)
0.331970 + 0.943290i \(0.392287\pi\)
\(422\) 0 0
\(423\) −7.57744 −0.368428
\(424\) 0 0
\(425\) 36.7953 1.78483
\(426\) 0 0
\(427\) 9.97434 0.482692
\(428\) 0 0
\(429\) 15.6623 0.756183
\(430\) 0 0
\(431\) −29.7866 −1.43477 −0.717385 0.696677i \(-0.754661\pi\)
−0.717385 + 0.696677i \(0.754661\pi\)
\(432\) 0 0
\(433\) 21.1599 1.01688 0.508440 0.861098i \(-0.330223\pi\)
0.508440 + 0.861098i \(0.330223\pi\)
\(434\) 0 0
\(435\) −1.47550 −0.0707450
\(436\) 0 0
\(437\) 8.03892 0.384554
\(438\) 0 0
\(439\) −16.0324 −0.765184 −0.382592 0.923917i \(-0.624968\pi\)
−0.382592 + 0.923917i \(0.624968\pi\)
\(440\) 0 0
\(441\) −30.5611 −1.45529
\(442\) 0 0
\(443\) 3.35806 0.159546 0.0797731 0.996813i \(-0.474580\pi\)
0.0797731 + 0.996813i \(0.474580\pi\)
\(444\) 0 0
\(445\) 0.291371 0.0138123
\(446\) 0 0
\(447\) 52.0419 2.46150
\(448\) 0 0
\(449\) −39.1830 −1.84916 −0.924581 0.380986i \(-0.875585\pi\)
−0.924581 + 0.380986i \(0.875585\pi\)
\(450\) 0 0
\(451\) −13.2724 −0.624973
\(452\) 0 0
\(453\) −19.4138 −0.912140
\(454\) 0 0
\(455\) −0.156648 −0.00734378
\(456\) 0 0
\(457\) 30.2503 1.41505 0.707524 0.706689i \(-0.249812\pi\)
0.707524 + 0.706689i \(0.249812\pi\)
\(458\) 0 0
\(459\) −45.4709 −2.12240
\(460\) 0 0
\(461\) 14.3657 0.669079 0.334540 0.942382i \(-0.391419\pi\)
0.334540 + 0.942382i \(0.391419\pi\)
\(462\) 0 0
\(463\) −13.1330 −0.610344 −0.305172 0.952297i \(-0.598714\pi\)
−0.305172 + 0.952297i \(0.598714\pi\)
\(464\) 0 0
\(465\) −1.24210 −0.0576011
\(466\) 0 0
\(467\) −21.0546 −0.974289 −0.487145 0.873321i \(-0.661962\pi\)
−0.487145 + 0.873321i \(0.661962\pi\)
\(468\) 0 0
\(469\) −4.32155 −0.199550
\(470\) 0 0
\(471\) −23.5504 −1.08514
\(472\) 0 0
\(473\) 17.1687 0.789417
\(474\) 0 0
\(475\) 4.99215 0.229056
\(476\) 0 0
\(477\) 5.15970 0.236246
\(478\) 0 0
\(479\) 18.5659 0.848300 0.424150 0.905592i \(-0.360573\pi\)
0.424150 + 0.905592i \(0.360573\pi\)
\(480\) 0 0
\(481\) 7.78736 0.355073
\(482\) 0 0
\(483\) 23.8305 1.08433
\(484\) 0 0
\(485\) 0.387050 0.0175750
\(486\) 0 0
\(487\) 10.5515 0.478132 0.239066 0.971003i \(-0.423159\pi\)
0.239066 + 0.971003i \(0.423159\pi\)
\(488\) 0 0
\(489\) −3.06186 −0.138462
\(490\) 0 0
\(491\) 30.9409 1.39634 0.698171 0.715931i \(-0.253997\pi\)
0.698171 + 0.715931i \(0.253997\pi\)
\(492\) 0 0
\(493\) −42.9839 −1.93590
\(494\) 0 0
\(495\) 1.47035 0.0660871
\(496\) 0 0
\(497\) 16.7940 0.753315
\(498\) 0 0
\(499\) −7.86676 −0.352165 −0.176082 0.984375i \(-0.556342\pi\)
−0.176082 + 0.984375i \(0.556342\pi\)
\(500\) 0 0
\(501\) −66.3525 −2.96441
\(502\) 0 0
\(503\) −36.8432 −1.64275 −0.821377 0.570385i \(-0.806794\pi\)
−0.821377 + 0.570385i \(0.806794\pi\)
\(504\) 0 0
\(505\) −1.06822 −0.0475350
\(506\) 0 0
\(507\) −28.8384 −1.28076
\(508\) 0 0
\(509\) 14.0462 0.622586 0.311293 0.950314i \(-0.399238\pi\)
0.311293 + 0.950314i \(0.399238\pi\)
\(510\) 0 0
\(511\) −8.02700 −0.355093
\(512\) 0 0
\(513\) −6.16921 −0.272377
\(514\) 0 0
\(515\) 0.298379 0.0131482
\(516\) 0 0
\(517\) 4.72489 0.207801
\(518\) 0 0
\(519\) −17.9737 −0.788956
\(520\) 0 0
\(521\) 28.8705 1.26484 0.632419 0.774626i \(-0.282062\pi\)
0.632419 + 0.774626i \(0.282062\pi\)
\(522\) 0 0
\(523\) 7.42273 0.324573 0.162287 0.986744i \(-0.448113\pi\)
0.162287 + 0.986744i \(0.448113\pi\)
\(524\) 0 0
\(525\) 14.7987 0.645868
\(526\) 0 0
\(527\) −36.1845 −1.57622
\(528\) 0 0
\(529\) 41.6242 1.80975
\(530\) 0 0
\(531\) 53.6411 2.32783
\(532\) 0 0
\(533\) −7.03043 −0.304522
\(534\) 0 0
\(535\) 0.561338 0.0242688
\(536\) 0 0
\(537\) 57.8880 2.49805
\(538\) 0 0
\(539\) 19.0563 0.820813
\(540\) 0 0
\(541\) −14.9867 −0.644328 −0.322164 0.946684i \(-0.604410\pi\)
−0.322164 + 0.946684i \(0.604410\pi\)
\(542\) 0 0
\(543\) −23.9823 −1.02918
\(544\) 0 0
\(545\) −0.820727 −0.0351561
\(546\) 0 0
\(547\) 6.85339 0.293030 0.146515 0.989208i \(-0.453194\pi\)
0.146515 + 0.989208i \(0.453194\pi\)
\(548\) 0 0
\(549\) −49.5918 −2.11653
\(550\) 0 0
\(551\) −5.83179 −0.248442
\(552\) 0 0
\(553\) −1.07764 −0.0458258
\(554\) 0 0
\(555\) 1.15612 0.0490746
\(556\) 0 0
\(557\) −2.71004 −0.114828 −0.0574139 0.998350i \(-0.518285\pi\)
−0.0574139 + 0.998350i \(0.518285\pi\)
\(558\) 0 0
\(559\) 9.09429 0.384647
\(560\) 0 0
\(561\) 67.7384 2.85992
\(562\) 0 0
\(563\) −2.10309 −0.0886348 −0.0443174 0.999018i \(-0.514111\pi\)
−0.0443174 + 0.999018i \(0.514111\pi\)
\(564\) 0 0
\(565\) −1.25969 −0.0529955
\(566\) 0 0
\(567\) −2.22431 −0.0934124
\(568\) 0 0
\(569\) 6.39698 0.268175 0.134088 0.990969i \(-0.457190\pi\)
0.134088 + 0.990969i \(0.457190\pi\)
\(570\) 0 0
\(571\) 1.82945 0.0765599 0.0382800 0.999267i \(-0.487812\pi\)
0.0382800 + 0.999267i \(0.487812\pi\)
\(572\) 0 0
\(573\) −8.67231 −0.362291
\(574\) 0 0
\(575\) 40.1315 1.67360
\(576\) 0 0
\(577\) 8.85154 0.368494 0.184247 0.982880i \(-0.441015\pi\)
0.184247 + 0.982880i \(0.441015\pi\)
\(578\) 0 0
\(579\) 34.7582 1.44450
\(580\) 0 0
\(581\) −3.06317 −0.127082
\(582\) 0 0
\(583\) −3.21731 −0.133248
\(584\) 0 0
\(585\) 0.778845 0.0322013
\(586\) 0 0
\(587\) −11.8109 −0.487490 −0.243745 0.969839i \(-0.578376\pi\)
−0.243745 + 0.969839i \(0.578376\pi\)
\(588\) 0 0
\(589\) −4.90929 −0.202284
\(590\) 0 0
\(591\) −15.2500 −0.627299
\(592\) 0 0
\(593\) −27.1874 −1.11645 −0.558226 0.829689i \(-0.688518\pi\)
−0.558226 + 0.829689i \(0.688518\pi\)
\(594\) 0 0
\(595\) −0.677493 −0.0277745
\(596\) 0 0
\(597\) 40.8383 1.67140
\(598\) 0 0
\(599\) −14.3426 −0.586025 −0.293012 0.956109i \(-0.594658\pi\)
−0.293012 + 0.956109i \(0.594658\pi\)
\(600\) 0 0
\(601\) 38.3965 1.56622 0.783112 0.621881i \(-0.213631\pi\)
0.783112 + 0.621881i \(0.213631\pi\)
\(602\) 0 0
\(603\) 21.4865 0.874996
\(604\) 0 0
\(605\) 0.0574741 0.00233665
\(606\) 0 0
\(607\) 11.9277 0.484130 0.242065 0.970260i \(-0.422175\pi\)
0.242065 + 0.970260i \(0.422175\pi\)
\(608\) 0 0
\(609\) −17.2877 −0.700533
\(610\) 0 0
\(611\) 2.50279 0.101252
\(612\) 0 0
\(613\) −20.0479 −0.809727 −0.404864 0.914377i \(-0.632681\pi\)
−0.404864 + 0.914377i \(0.632681\pi\)
\(614\) 0 0
\(615\) −1.04375 −0.0420879
\(616\) 0 0
\(617\) 20.9788 0.844574 0.422287 0.906462i \(-0.361227\pi\)
0.422287 + 0.906462i \(0.361227\pi\)
\(618\) 0 0
\(619\) −12.2131 −0.490884 −0.245442 0.969411i \(-0.578933\pi\)
−0.245442 + 0.969411i \(0.578933\pi\)
\(620\) 0 0
\(621\) −49.5938 −1.99013
\(622\) 0 0
\(623\) 3.41383 0.136772
\(624\) 0 0
\(625\) 24.8824 0.995295
\(626\) 0 0
\(627\) 9.19032 0.367026
\(628\) 0 0
\(629\) 33.6798 1.34290
\(630\) 0 0
\(631\) −37.2634 −1.48343 −0.741716 0.670714i \(-0.765988\pi\)
−0.741716 + 0.670714i \(0.765988\pi\)
\(632\) 0 0
\(633\) −65.5473 −2.60527
\(634\) 0 0
\(635\) 0.686900 0.0272588
\(636\) 0 0
\(637\) 10.0942 0.399945
\(638\) 0 0
\(639\) −83.4988 −3.30316
\(640\) 0 0
\(641\) −20.8250 −0.822537 −0.411268 0.911514i \(-0.634914\pi\)
−0.411268 + 0.911514i \(0.634914\pi\)
\(642\) 0 0
\(643\) −50.0434 −1.97352 −0.986759 0.162193i \(-0.948143\pi\)
−0.986759 + 0.162193i \(0.948143\pi\)
\(644\) 0 0
\(645\) 1.35015 0.0531621
\(646\) 0 0
\(647\) 17.6868 0.695340 0.347670 0.937617i \(-0.386973\pi\)
0.347670 + 0.937617i \(0.386973\pi\)
\(648\) 0 0
\(649\) −33.4478 −1.31294
\(650\) 0 0
\(651\) −14.5530 −0.570379
\(652\) 0 0
\(653\) 39.0964 1.52996 0.764981 0.644053i \(-0.222749\pi\)
0.764981 + 0.644053i \(0.222749\pi\)
\(654\) 0 0
\(655\) −0.821861 −0.0321128
\(656\) 0 0
\(657\) 39.9097 1.55703
\(658\) 0 0
\(659\) −7.52628 −0.293182 −0.146591 0.989197i \(-0.546830\pi\)
−0.146591 + 0.989197i \(0.546830\pi\)
\(660\) 0 0
\(661\) −44.7980 −1.74244 −0.871220 0.490893i \(-0.836671\pi\)
−0.871220 + 0.490893i \(0.836671\pi\)
\(662\) 0 0
\(663\) 35.8812 1.39351
\(664\) 0 0
\(665\) −0.0919179 −0.00356442
\(666\) 0 0
\(667\) −46.8813 −1.81525
\(668\) 0 0
\(669\) −75.5246 −2.91995
\(670\) 0 0
\(671\) 30.9228 1.19376
\(672\) 0 0
\(673\) 8.93385 0.344375 0.172187 0.985064i \(-0.444917\pi\)
0.172187 + 0.985064i \(0.444917\pi\)
\(674\) 0 0
\(675\) −30.7976 −1.18540
\(676\) 0 0
\(677\) 40.3985 1.55264 0.776320 0.630339i \(-0.217084\pi\)
0.776320 + 0.630339i \(0.217084\pi\)
\(678\) 0 0
\(679\) 4.53486 0.174032
\(680\) 0 0
\(681\) −39.7451 −1.52304
\(682\) 0 0
\(683\) 27.7635 1.06234 0.531171 0.847264i \(-0.321752\pi\)
0.531171 + 0.847264i \(0.321752\pi\)
\(684\) 0 0
\(685\) −1.10703 −0.0422974
\(686\) 0 0
\(687\) −27.0037 −1.03026
\(688\) 0 0
\(689\) −1.70422 −0.0649255
\(690\) 0 0
\(691\) −29.5104 −1.12263 −0.561315 0.827602i \(-0.689704\pi\)
−0.561315 + 0.827602i \(0.689704\pi\)
\(692\) 0 0
\(693\) 17.2273 0.654409
\(694\) 0 0
\(695\) −1.48780 −0.0564355
\(696\) 0 0
\(697\) −30.4061 −1.15171
\(698\) 0 0
\(699\) −10.7776 −0.407647
\(700\) 0 0
\(701\) −19.0356 −0.718966 −0.359483 0.933152i \(-0.617047\pi\)
−0.359483 + 0.933152i \(0.617047\pi\)
\(702\) 0 0
\(703\) 4.56946 0.172340
\(704\) 0 0
\(705\) 0.371567 0.0139940
\(706\) 0 0
\(707\) −12.5157 −0.470702
\(708\) 0 0
\(709\) 10.2727 0.385798 0.192899 0.981219i \(-0.438211\pi\)
0.192899 + 0.981219i \(0.438211\pi\)
\(710\) 0 0
\(711\) 5.35795 0.200939
\(712\) 0 0
\(713\) −39.4654 −1.47799
\(714\) 0 0
\(715\) −0.485647 −0.0181622
\(716\) 0 0
\(717\) 61.0965 2.28169
\(718\) 0 0
\(719\) −52.4911 −1.95759 −0.978794 0.204847i \(-0.934330\pi\)
−0.978794 + 0.204847i \(0.934330\pi\)
\(720\) 0 0
\(721\) 3.49595 0.130196
\(722\) 0 0
\(723\) −30.8540 −1.14747
\(724\) 0 0
\(725\) −29.1132 −1.08124
\(726\) 0 0
\(727\) −44.1990 −1.63925 −0.819624 0.572901i \(-0.805818\pi\)
−0.819624 + 0.572901i \(0.805818\pi\)
\(728\) 0 0
\(729\) −41.8082 −1.54845
\(730\) 0 0
\(731\) 39.3322 1.45475
\(732\) 0 0
\(733\) 48.7174 1.79942 0.899709 0.436489i \(-0.143778\pi\)
0.899709 + 0.436489i \(0.143778\pi\)
\(734\) 0 0
\(735\) 1.49859 0.0552764
\(736\) 0 0
\(737\) −13.3978 −0.493515
\(738\) 0 0
\(739\) −11.3238 −0.416552 −0.208276 0.978070i \(-0.566785\pi\)
−0.208276 + 0.978070i \(0.566785\pi\)
\(740\) 0 0
\(741\) 4.86813 0.178835
\(742\) 0 0
\(743\) 9.69013 0.355496 0.177748 0.984076i \(-0.443119\pi\)
0.177748 + 0.984076i \(0.443119\pi\)
\(744\) 0 0
\(745\) −1.61368 −0.0591208
\(746\) 0 0
\(747\) 15.2299 0.557232
\(748\) 0 0
\(749\) 6.57690 0.240315
\(750\) 0 0
\(751\) −13.1889 −0.481268 −0.240634 0.970616i \(-0.577355\pi\)
−0.240634 + 0.970616i \(0.577355\pi\)
\(752\) 0 0
\(753\) 81.2615 2.96134
\(754\) 0 0
\(755\) 0.601971 0.0219080
\(756\) 0 0
\(757\) −19.6045 −0.712537 −0.356269 0.934384i \(-0.615951\pi\)
−0.356269 + 0.934384i \(0.615951\pi\)
\(758\) 0 0
\(759\) 73.8802 2.68168
\(760\) 0 0
\(761\) −35.1170 −1.27299 −0.636494 0.771281i \(-0.719616\pi\)
−0.636494 + 0.771281i \(0.719616\pi\)
\(762\) 0 0
\(763\) −9.61602 −0.348123
\(764\) 0 0
\(765\) 3.36845 0.121787
\(766\) 0 0
\(767\) −17.7173 −0.639736
\(768\) 0 0
\(769\) 8.63677 0.311450 0.155725 0.987800i \(-0.450229\pi\)
0.155725 + 0.987800i \(0.450229\pi\)
\(770\) 0 0
\(771\) −15.0718 −0.542797
\(772\) 0 0
\(773\) −20.2541 −0.728489 −0.364245 0.931303i \(-0.618673\pi\)
−0.364245 + 0.931303i \(0.618673\pi\)
\(774\) 0 0
\(775\) −24.5079 −0.880350
\(776\) 0 0
\(777\) 13.5457 0.485948
\(778\) 0 0
\(779\) −4.12531 −0.147804
\(780\) 0 0
\(781\) 52.0655 1.86305
\(782\) 0 0
\(783\) 35.9775 1.28573
\(784\) 0 0
\(785\) 0.730235 0.0260632
\(786\) 0 0
\(787\) 2.56732 0.0915152 0.0457576 0.998953i \(-0.485430\pi\)
0.0457576 + 0.998953i \(0.485430\pi\)
\(788\) 0 0
\(789\) −4.52324 −0.161032
\(790\) 0 0
\(791\) −14.7591 −0.524774
\(792\) 0 0
\(793\) 16.3799 0.581667
\(794\) 0 0
\(795\) −0.253011 −0.00897336
\(796\) 0 0
\(797\) −24.0570 −0.852142 −0.426071 0.904690i \(-0.640103\pi\)
−0.426071 + 0.904690i \(0.640103\pi\)
\(798\) 0 0
\(799\) 10.8244 0.382939
\(800\) 0 0
\(801\) −16.9734 −0.599724
\(802\) 0 0
\(803\) −24.8856 −0.878194
\(804\) 0 0
\(805\) −0.738921 −0.0260435
\(806\) 0 0
\(807\) 13.1632 0.463365
\(808\) 0 0
\(809\) 27.9163 0.981486 0.490743 0.871304i \(-0.336725\pi\)
0.490743 + 0.871304i \(0.336725\pi\)
\(810\) 0 0
\(811\) −35.9634 −1.26285 −0.631423 0.775439i \(-0.717529\pi\)
−0.631423 + 0.775439i \(0.717529\pi\)
\(812\) 0 0
\(813\) 10.8491 0.380493
\(814\) 0 0
\(815\) 0.0949401 0.00332561
\(816\) 0 0
\(817\) 5.33634 0.186695
\(818\) 0 0
\(819\) 9.12531 0.318864
\(820\) 0 0
\(821\) 48.3921 1.68889 0.844447 0.535639i \(-0.179929\pi\)
0.844447 + 0.535639i \(0.179929\pi\)
\(822\) 0 0
\(823\) −36.2755 −1.26449 −0.632243 0.774770i \(-0.717866\pi\)
−0.632243 + 0.774770i \(0.717866\pi\)
\(824\) 0 0
\(825\) 45.8795 1.59732
\(826\) 0 0
\(827\) 9.80648 0.341005 0.170502 0.985357i \(-0.445461\pi\)
0.170502 + 0.985357i \(0.445461\pi\)
\(828\) 0 0
\(829\) 28.5270 0.990784 0.495392 0.868669i \(-0.335024\pi\)
0.495392 + 0.868669i \(0.335024\pi\)
\(830\) 0 0
\(831\) −35.4795 −1.23077
\(832\) 0 0
\(833\) 43.6566 1.51261
\(834\) 0 0
\(835\) 2.05741 0.0711997
\(836\) 0 0
\(837\) 30.2864 1.04685
\(838\) 0 0
\(839\) 3.84903 0.132883 0.0664417 0.997790i \(-0.478835\pi\)
0.0664417 + 0.997790i \(0.478835\pi\)
\(840\) 0 0
\(841\) 5.00974 0.172749
\(842\) 0 0
\(843\) −5.64955 −0.194581
\(844\) 0 0
\(845\) 0.894202 0.0307615
\(846\) 0 0
\(847\) 0.673394 0.0231381
\(848\) 0 0
\(849\) −10.1675 −0.348949
\(850\) 0 0
\(851\) 36.7335 1.25921
\(852\) 0 0
\(853\) 29.5811 1.01284 0.506419 0.862287i \(-0.330969\pi\)
0.506419 + 0.862287i \(0.330969\pi\)
\(854\) 0 0
\(855\) 0.457010 0.0156294
\(856\) 0 0
\(857\) 47.9147 1.63673 0.818367 0.574696i \(-0.194880\pi\)
0.818367 + 0.574696i \(0.194880\pi\)
\(858\) 0 0
\(859\) 25.9344 0.884869 0.442435 0.896801i \(-0.354115\pi\)
0.442435 + 0.896801i \(0.354115\pi\)
\(860\) 0 0
\(861\) −12.2290 −0.416764
\(862\) 0 0
\(863\) 33.4891 1.13998 0.569991 0.821651i \(-0.306947\pi\)
0.569991 + 0.821651i \(0.306947\pi\)
\(864\) 0 0
\(865\) 0.557316 0.0189493
\(866\) 0 0
\(867\) 106.623 3.62110
\(868\) 0 0
\(869\) −3.34094 −0.113333
\(870\) 0 0
\(871\) −7.09685 −0.240468
\(872\) 0 0
\(873\) −22.5471 −0.763102
\(874\) 0 0
\(875\) −0.918458 −0.0310496
\(876\) 0 0
\(877\) −40.3017 −1.36089 −0.680445 0.732799i \(-0.738214\pi\)
−0.680445 + 0.732799i \(0.738214\pi\)
\(878\) 0 0
\(879\) 14.7429 0.497264
\(880\) 0 0
\(881\) 30.1204 1.01478 0.507390 0.861716i \(-0.330610\pi\)
0.507390 + 0.861716i \(0.330610\pi\)
\(882\) 0 0
\(883\) −42.0269 −1.41432 −0.707159 0.707054i \(-0.750024\pi\)
−0.707159 + 0.707054i \(0.750024\pi\)
\(884\) 0 0
\(885\) −2.63034 −0.0884180
\(886\) 0 0
\(887\) −3.57071 −0.119893 −0.0599464 0.998202i \(-0.519093\pi\)
−0.0599464 + 0.998202i \(0.519093\pi\)
\(888\) 0 0
\(889\) 8.04804 0.269923
\(890\) 0 0
\(891\) −6.89590 −0.231021
\(892\) 0 0
\(893\) 1.46858 0.0491443
\(894\) 0 0
\(895\) −1.79495 −0.0599987
\(896\) 0 0
\(897\) 39.1345 1.30666
\(898\) 0 0
\(899\) 28.6299 0.954861
\(900\) 0 0
\(901\) −7.37063 −0.245551
\(902\) 0 0
\(903\) 15.8190 0.526423
\(904\) 0 0
\(905\) 0.743628 0.0247190
\(906\) 0 0
\(907\) 3.83728 0.127415 0.0637075 0.997969i \(-0.479708\pi\)
0.0637075 + 0.997969i \(0.479708\pi\)
\(908\) 0 0
\(909\) 62.2274 2.06395
\(910\) 0 0
\(911\) −56.0715 −1.85773 −0.928865 0.370417i \(-0.879215\pi\)
−0.928865 + 0.370417i \(0.879215\pi\)
\(912\) 0 0
\(913\) −9.49655 −0.314290
\(914\) 0 0
\(915\) 2.43178 0.0803922
\(916\) 0 0
\(917\) −9.62931 −0.317988
\(918\) 0 0
\(919\) −17.4512 −0.575662 −0.287831 0.957681i \(-0.592934\pi\)
−0.287831 + 0.957681i \(0.592934\pi\)
\(920\) 0 0
\(921\) −41.3630 −1.36296
\(922\) 0 0
\(923\) 27.5792 0.907780
\(924\) 0 0
\(925\) 22.8114 0.750036
\(926\) 0 0
\(927\) −17.3817 −0.570889
\(928\) 0 0
\(929\) 18.2513 0.598805 0.299403 0.954127i \(-0.403213\pi\)
0.299403 + 0.954127i \(0.403213\pi\)
\(930\) 0 0
\(931\) 5.92305 0.194120
\(932\) 0 0
\(933\) 27.1311 0.888234
\(934\) 0 0
\(935\) −2.10039 −0.0686900
\(936\) 0 0
\(937\) 31.0007 1.01275 0.506374 0.862314i \(-0.330985\pi\)
0.506374 + 0.862314i \(0.330985\pi\)
\(938\) 0 0
\(939\) −58.3229 −1.90329
\(940\) 0 0
\(941\) −9.79842 −0.319419 −0.159710 0.987164i \(-0.551056\pi\)
−0.159710 + 0.987164i \(0.551056\pi\)
\(942\) 0 0
\(943\) −33.1630 −1.07994
\(944\) 0 0
\(945\) 0.567061 0.0184465
\(946\) 0 0
\(947\) 26.3777 0.857159 0.428579 0.903504i \(-0.359014\pi\)
0.428579 + 0.903504i \(0.359014\pi\)
\(948\) 0 0
\(949\) −13.1820 −0.427904
\(950\) 0 0
\(951\) −22.5670 −0.731786
\(952\) 0 0
\(953\) −6.36599 −0.206215 −0.103107 0.994670i \(-0.532879\pi\)
−0.103107 + 0.994670i \(0.532879\pi\)
\(954\) 0 0
\(955\) 0.268905 0.00870157
\(956\) 0 0
\(957\) −53.5960 −1.73251
\(958\) 0 0
\(959\) −12.9705 −0.418839
\(960\) 0 0
\(961\) −6.89891 −0.222546
\(962\) 0 0
\(963\) −32.6999 −1.05374
\(964\) 0 0
\(965\) −1.07776 −0.0346943
\(966\) 0 0
\(967\) 16.1282 0.518647 0.259323 0.965791i \(-0.416500\pi\)
0.259323 + 0.965791i \(0.416500\pi\)
\(968\) 0 0
\(969\) 21.0543 0.676362
\(970\) 0 0
\(971\) 50.3086 1.61448 0.807239 0.590224i \(-0.200961\pi\)
0.807239 + 0.590224i \(0.200961\pi\)
\(972\) 0 0
\(973\) −17.4318 −0.558837
\(974\) 0 0
\(975\) 24.3025 0.778302
\(976\) 0 0
\(977\) −41.1982 −1.31805 −0.659024 0.752122i \(-0.729031\pi\)
−0.659024 + 0.752122i \(0.729031\pi\)
\(978\) 0 0
\(979\) 10.5837 0.338256
\(980\) 0 0
\(981\) 47.8102 1.52646
\(982\) 0 0
\(983\) −20.8963 −0.666487 −0.333244 0.942841i \(-0.608143\pi\)
−0.333244 + 0.942841i \(0.608143\pi\)
\(984\) 0 0
\(985\) 0.472861 0.0150666
\(986\) 0 0
\(987\) 4.35345 0.138572
\(988\) 0 0
\(989\) 42.8984 1.36409
\(990\) 0 0
\(991\) −13.2955 −0.422345 −0.211173 0.977449i \(-0.567728\pi\)
−0.211173 + 0.977449i \(0.567728\pi\)
\(992\) 0 0
\(993\) 65.7233 2.08567
\(994\) 0 0
\(995\) −1.26629 −0.0401440
\(996\) 0 0
\(997\) 47.2409 1.49613 0.748067 0.663623i \(-0.230982\pi\)
0.748067 + 0.663623i \(0.230982\pi\)
\(998\) 0 0
\(999\) −28.1899 −0.891891
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 \(a_p\))