Properties

Label 8048.2.a.v.1.5
Level 8048
Weight 2
Character 8048.1
Self dual Yes
Analytic conductor 64.264
Analytic rank 1
Dimension 28
CM No

Related objects

Downloads

Learn more about

Newspace parameters

Level: \( N \) = \( 8048 = 2^{4} \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 8048.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(64.2636035467\)
Analytic rank: \(1\)
Dimension: \(28\)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.5
Character \(\chi\) = 8048.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(-2.11208 q^{3}\) \(+2.26631 q^{5}\) \(+4.06526 q^{7}\) \(+1.46088 q^{9}\) \(+O(q^{10})\) \(q\)\(-2.11208 q^{3}\) \(+2.26631 q^{5}\) \(+4.06526 q^{7}\) \(+1.46088 q^{9}\) \(+1.00233 q^{11}\) \(-5.09690 q^{13}\) \(-4.78662 q^{15}\) \(+1.45394 q^{17}\) \(-6.53873 q^{19}\) \(-8.58614 q^{21}\) \(+4.54695 q^{23}\) \(+0.136156 q^{25}\) \(+3.25075 q^{27}\) \(-6.23661 q^{29}\) \(+10.1104 q^{31}\) \(-2.11699 q^{33}\) \(+9.21313 q^{35}\) \(+3.44313 q^{37}\) \(+10.7651 q^{39}\) \(-9.13103 q^{41}\) \(-2.78427 q^{43}\) \(+3.31079 q^{45}\) \(-6.12193 q^{47}\) \(+9.52632 q^{49}\) \(-3.07084 q^{51}\) \(-3.12167 q^{53}\) \(+2.27158 q^{55}\) \(+13.8103 q^{57}\) \(-2.23107 q^{59}\) \(-13.6990 q^{61}\) \(+5.93883 q^{63}\) \(-11.5512 q^{65}\) \(-14.1564 q^{67}\) \(-9.60351 q^{69}\) \(-13.8371 q^{71}\) \(+0.606303 q^{73}\) \(-0.287572 q^{75}\) \(+4.07472 q^{77}\) \(+14.1692 q^{79}\) \(-11.2485 q^{81}\) \(+6.43050 q^{83}\) \(+3.29508 q^{85}\) \(+13.1722 q^{87}\) \(+16.6860 q^{89}\) \(-20.7202 q^{91}\) \(-21.3540 q^{93}\) \(-14.8188 q^{95}\) \(-17.0100 q^{97}\) \(+1.46427 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(28q \) \(\mathstrut -\mathstrut 2q^{3} \) \(\mathstrut -\mathstrut 12q^{5} \) \(\mathstrut +\mathstrut 18q^{9} \) \(\mathstrut +\mathstrut 14q^{11} \) \(\mathstrut -\mathstrut 31q^{13} \) \(\mathstrut +\mathstrut 2q^{15} \) \(\mathstrut -\mathstrut 9q^{17} \) \(\mathstrut +\mathstrut 8q^{19} \) \(\mathstrut -\mathstrut 28q^{21} \) \(\mathstrut +\mathstrut 4q^{23} \) \(\mathstrut +\mathstrut 22q^{25} \) \(\mathstrut +\mathstrut 4q^{27} \) \(\mathstrut -\mathstrut 47q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 26q^{33} \) \(\mathstrut +\mathstrut 13q^{35} \) \(\mathstrut -\mathstrut 67q^{37} \) \(\mathstrut +\mathstrut 9q^{39} \) \(\mathstrut -\mathstrut 28q^{41} \) \(\mathstrut -\mathstrut 15q^{43} \) \(\mathstrut -\mathstrut 57q^{45} \) \(\mathstrut +\mathstrut 10q^{47} \) \(\mathstrut +\mathstrut 20q^{49} \) \(\mathstrut +\mathstrut 11q^{51} \) \(\mathstrut -\mathstrut 58q^{53} \) \(\mathstrut -\mathstrut 15q^{55} \) \(\mathstrut -\mathstrut 31q^{57} \) \(\mathstrut +\mathstrut 32q^{59} \) \(\mathstrut -\mathstrut 55q^{61} \) \(\mathstrut +\mathstrut 16q^{63} \) \(\mathstrut -\mathstrut 44q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut -\mathstrut 44q^{69} \) \(\mathstrut +\mathstrut 47q^{71} \) \(\mathstrut -\mathstrut 5q^{73} \) \(\mathstrut +\mathstrut 25q^{75} \) \(\mathstrut -\mathstrut 50q^{77} \) \(\mathstrut +\mathstrut 14q^{79} \) \(\mathstrut -\mathstrut 28q^{81} \) \(\mathstrut +\mathstrut 16q^{83} \) \(\mathstrut -\mathstrut 78q^{85} \) \(\mathstrut +\mathstrut 11q^{87} \) \(\mathstrut -\mathstrut 20q^{89} \) \(\mathstrut +\mathstrut 15q^{91} \) \(\mathstrut -\mathstrut 83q^{93} \) \(\mathstrut +\mathstrut 27q^{95} \) \(\mathstrut -\mathstrut 8q^{97} \) \(\mathstrut +\mathstrut 70q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

Coefficient data

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

Display \(a_p\) with \(p\) up to: 50 250 1000 (See \(a_n\) instead) (See \(a_n\) instead) (See \(a_n\) instead) Display \(a_n\) with \(n\) up to: 50 250 1000 (See only \(a_p\)) (See only \(a_p\)) (See only \(a_p\))
Significant digits:
\(n\) \(a_n\) \(a_n / n^{(k-1)/2}\) \( \alpha_n \) \( \theta_n \)
\(p\) \(a_p\) \(a_p / p^{(k-1)/2}\) \( \alpha_p\) \( \theta_p \)
\(2\) 0 0
\(3\) −2.11208 −1.21941 −0.609705 0.792629i \(-0.708712\pi\)
−0.609705 + 0.792629i \(0.708712\pi\)
\(4\) 0 0
\(5\) 2.26631 1.01352 0.506762 0.862086i \(-0.330842\pi\)
0.506762 + 0.862086i \(0.330842\pi\)
\(6\) 0 0
\(7\) 4.06526 1.53652 0.768261 0.640136i \(-0.221122\pi\)
0.768261 + 0.640136i \(0.221122\pi\)
\(8\) 0 0
\(9\) 1.46088 0.486958
\(10\) 0 0
\(11\) 1.00233 0.302213 0.151106 0.988517i \(-0.451716\pi\)
0.151106 + 0.988517i \(0.451716\pi\)
\(12\) 0 0
\(13\) −5.09690 −1.41363 −0.706813 0.707400i \(-0.749868\pi\)
−0.706813 + 0.707400i \(0.749868\pi\)
\(14\) 0 0
\(15\) −4.78662 −1.23590
\(16\) 0 0
\(17\) 1.45394 0.352633 0.176316 0.984334i \(-0.443582\pi\)
0.176316 + 0.984334i \(0.443582\pi\)
\(18\) 0 0
\(19\) −6.53873 −1.50009 −0.750044 0.661388i \(-0.769968\pi\)
−0.750044 + 0.661388i \(0.769968\pi\)
\(20\) 0 0
\(21\) −8.58614 −1.87365
\(22\) 0 0
\(23\) 4.54695 0.948104 0.474052 0.880497i \(-0.342791\pi\)
0.474052 + 0.880497i \(0.342791\pi\)
\(24\) 0 0
\(25\) 0.136156 0.0272311
\(26\) 0 0
\(27\) 3.25075 0.625608
\(28\) 0 0
\(29\) −6.23661 −1.15811 −0.579055 0.815288i \(-0.696578\pi\)
−0.579055 + 0.815288i \(0.696578\pi\)
\(30\) 0 0
\(31\) 10.1104 1.81588 0.907942 0.419095i \(-0.137653\pi\)
0.907942 + 0.419095i \(0.137653\pi\)
\(32\) 0 0
\(33\) −2.11699 −0.368521
\(34\) 0 0
\(35\) 9.21313 1.55730
\(36\) 0 0
\(37\) 3.44313 0.566047 0.283024 0.959113i \(-0.408663\pi\)
0.283024 + 0.959113i \(0.408663\pi\)
\(38\) 0 0
\(39\) 10.7651 1.72379
\(40\) 0 0
\(41\) −9.13103 −1.42603 −0.713013 0.701150i \(-0.752670\pi\)
−0.713013 + 0.701150i \(0.752670\pi\)
\(42\) 0 0
\(43\) −2.78427 −0.424597 −0.212299 0.977205i \(-0.568095\pi\)
−0.212299 + 0.977205i \(0.568095\pi\)
\(44\) 0 0
\(45\) 3.31079 0.493544
\(46\) 0 0
\(47\) −6.12193 −0.892976 −0.446488 0.894790i \(-0.647325\pi\)
−0.446488 + 0.894790i \(0.647325\pi\)
\(48\) 0 0
\(49\) 9.52632 1.36090
\(50\) 0 0
\(51\) −3.07084 −0.430004
\(52\) 0 0
\(53\) −3.12167 −0.428794 −0.214397 0.976747i \(-0.568779\pi\)
−0.214397 + 0.976747i \(0.568779\pi\)
\(54\) 0 0
\(55\) 2.27158 0.306300
\(56\) 0 0
\(57\) 13.8103 1.82922
\(58\) 0 0
\(59\) −2.23107 −0.290461 −0.145230 0.989398i \(-0.546392\pi\)
−0.145230 + 0.989398i \(0.546392\pi\)
\(60\) 0 0
\(61\) −13.6990 −1.75398 −0.876992 0.480506i \(-0.840453\pi\)
−0.876992 + 0.480506i \(0.840453\pi\)
\(62\) 0 0
\(63\) 5.93883 0.748223
\(64\) 0 0
\(65\) −11.5512 −1.43274
\(66\) 0 0
\(67\) −14.1564 −1.72948 −0.864742 0.502216i \(-0.832518\pi\)
−0.864742 + 0.502216i \(0.832518\pi\)
\(68\) 0 0
\(69\) −9.60351 −1.15613
\(70\) 0 0
\(71\) −13.8371 −1.64216 −0.821078 0.570816i \(-0.806627\pi\)
−0.821078 + 0.570816i \(0.806627\pi\)
\(72\) 0 0
\(73\) 0.606303 0.0709624 0.0354812 0.999370i \(-0.488704\pi\)
0.0354812 + 0.999370i \(0.488704\pi\)
\(74\) 0 0
\(75\) −0.287572 −0.0332059
\(76\) 0 0
\(77\) 4.07472 0.464357
\(78\) 0 0
\(79\) 14.1692 1.59416 0.797082 0.603871i \(-0.206376\pi\)
0.797082 + 0.603871i \(0.206376\pi\)
\(80\) 0 0
\(81\) −11.2485 −1.24983
\(82\) 0 0
\(83\) 6.43050 0.705839 0.352920 0.935654i \(-0.385189\pi\)
0.352920 + 0.935654i \(0.385189\pi\)
\(84\) 0 0
\(85\) 3.29508 0.357402
\(86\) 0 0
\(87\) 13.1722 1.41221
\(88\) 0 0
\(89\) 16.6860 1.76872 0.884358 0.466808i \(-0.154596\pi\)
0.884358 + 0.466808i \(0.154596\pi\)
\(90\) 0 0
\(91\) −20.7202 −2.17207
\(92\) 0 0
\(93\) −21.3540 −2.21431
\(94\) 0 0
\(95\) −14.8188 −1.52038
\(96\) 0 0
\(97\) −17.0100 −1.72710 −0.863552 0.504260i \(-0.831765\pi\)
−0.863552 + 0.504260i \(0.831765\pi\)
\(98\) 0 0
\(99\) 1.46427 0.147165
\(100\) 0 0
\(101\) −7.32097 −0.728463 −0.364232 0.931308i \(-0.618668\pi\)
−0.364232 + 0.931308i \(0.618668\pi\)
\(102\) 0 0
\(103\) −3.44714 −0.339657 −0.169828 0.985474i \(-0.554321\pi\)
−0.169828 + 0.985474i \(0.554321\pi\)
\(104\) 0 0
\(105\) −19.4589 −1.89899
\(106\) 0 0
\(107\) 5.62609 0.543895 0.271948 0.962312i \(-0.412332\pi\)
0.271948 + 0.962312i \(0.412332\pi\)
\(108\) 0 0
\(109\) −1.02306 −0.0979914 −0.0489957 0.998799i \(-0.515602\pi\)
−0.0489957 + 0.998799i \(0.515602\pi\)
\(110\) 0 0
\(111\) −7.27216 −0.690243
\(112\) 0 0
\(113\) −2.18647 −0.205686 −0.102843 0.994698i \(-0.532794\pi\)
−0.102843 + 0.994698i \(0.532794\pi\)
\(114\) 0 0
\(115\) 10.3048 0.960926
\(116\) 0 0
\(117\) −7.44594 −0.688377
\(118\) 0 0
\(119\) 5.91065 0.541828
\(120\) 0 0
\(121\) −9.99534 −0.908667
\(122\) 0 0
\(123\) 19.2854 1.73891
\(124\) 0 0
\(125\) −11.0230 −0.985925
\(126\) 0 0
\(127\) 12.8538 1.14059 0.570296 0.821439i \(-0.306829\pi\)
0.570296 + 0.821439i \(0.306829\pi\)
\(128\) 0 0
\(129\) 5.88060 0.517758
\(130\) 0 0
\(131\) 4.41645 0.385867 0.192933 0.981212i \(-0.438200\pi\)
0.192933 + 0.981212i \(0.438200\pi\)
\(132\) 0 0
\(133\) −26.5816 −2.30492
\(134\) 0 0
\(135\) 7.36721 0.634068
\(136\) 0 0
\(137\) −9.10428 −0.777831 −0.388915 0.921273i \(-0.627150\pi\)
−0.388915 + 0.921273i \(0.627150\pi\)
\(138\) 0 0
\(139\) −13.5113 −1.14602 −0.573008 0.819549i \(-0.694224\pi\)
−0.573008 + 0.819549i \(0.694224\pi\)
\(140\) 0 0
\(141\) 12.9300 1.08890
\(142\) 0 0
\(143\) −5.10876 −0.427216
\(144\) 0 0
\(145\) −14.1341 −1.17377
\(146\) 0 0
\(147\) −20.1203 −1.65950
\(148\) 0 0
\(149\) 7.19494 0.589433 0.294716 0.955585i \(-0.404775\pi\)
0.294716 + 0.955585i \(0.404775\pi\)
\(150\) 0 0
\(151\) −10.9314 −0.889582 −0.444791 0.895634i \(-0.646722\pi\)
−0.444791 + 0.895634i \(0.646722\pi\)
\(152\) 0 0
\(153\) 2.12403 0.171717
\(154\) 0 0
\(155\) 22.9133 1.84044
\(156\) 0 0
\(157\) 9.72181 0.775885 0.387942 0.921684i \(-0.373186\pi\)
0.387942 + 0.921684i \(0.373186\pi\)
\(158\) 0 0
\(159\) 6.59321 0.522876
\(160\) 0 0
\(161\) 18.4845 1.45678
\(162\) 0 0
\(163\) 8.78257 0.687904 0.343952 0.938987i \(-0.388234\pi\)
0.343952 + 0.938987i \(0.388234\pi\)
\(164\) 0 0
\(165\) −4.79776 −0.373505
\(166\) 0 0
\(167\) −22.3161 −1.72687 −0.863436 0.504458i \(-0.831692\pi\)
−0.863436 + 0.504458i \(0.831692\pi\)
\(168\) 0 0
\(169\) 12.9784 0.998339
\(170\) 0 0
\(171\) −9.55228 −0.730481
\(172\) 0 0
\(173\) 17.9889 1.36767 0.683836 0.729635i \(-0.260310\pi\)
0.683836 + 0.729635i \(0.260310\pi\)
\(174\) 0 0
\(175\) 0.553508 0.0418413
\(176\) 0 0
\(177\) 4.71219 0.354190
\(178\) 0 0
\(179\) −15.9614 −1.19301 −0.596505 0.802609i \(-0.703445\pi\)
−0.596505 + 0.802609i \(0.703445\pi\)
\(180\) 0 0
\(181\) 8.14218 0.605204 0.302602 0.953117i \(-0.402145\pi\)
0.302602 + 0.953117i \(0.402145\pi\)
\(182\) 0 0
\(183\) 28.9335 2.13882
\(184\) 0 0
\(185\) 7.80320 0.573702
\(186\) 0 0
\(187\) 1.45733 0.106570
\(188\) 0 0
\(189\) 13.2151 0.961260
\(190\) 0 0
\(191\) −7.81409 −0.565407 −0.282704 0.959207i \(-0.591231\pi\)
−0.282704 + 0.959207i \(0.591231\pi\)
\(192\) 0 0
\(193\) −23.6828 −1.70473 −0.852363 0.522951i \(-0.824831\pi\)
−0.852363 + 0.522951i \(0.824831\pi\)
\(194\) 0 0
\(195\) 24.3969 1.74710
\(196\) 0 0
\(197\) −3.36345 −0.239636 −0.119818 0.992796i \(-0.538231\pi\)
−0.119818 + 0.992796i \(0.538231\pi\)
\(198\) 0 0
\(199\) 18.0958 1.28278 0.641389 0.767216i \(-0.278358\pi\)
0.641389 + 0.767216i \(0.278358\pi\)
\(200\) 0 0
\(201\) 29.8995 2.10895
\(202\) 0 0
\(203\) −25.3534 −1.77946
\(204\) 0 0
\(205\) −20.6937 −1.44531
\(206\) 0 0
\(207\) 6.64252 0.461687
\(208\) 0 0
\(209\) −6.55395 −0.453346
\(210\) 0 0
\(211\) −4.83062 −0.332554 −0.166277 0.986079i \(-0.553175\pi\)
−0.166277 + 0.986079i \(0.553175\pi\)
\(212\) 0 0
\(213\) 29.2249 2.00246
\(214\) 0 0
\(215\) −6.31002 −0.430340
\(216\) 0 0
\(217\) 41.1014 2.79015
\(218\) 0 0
\(219\) −1.28056 −0.0865322
\(220\) 0 0
\(221\) −7.41060 −0.498491
\(222\) 0 0
\(223\) 24.8400 1.66341 0.831705 0.555217i \(-0.187365\pi\)
0.831705 + 0.555217i \(0.187365\pi\)
\(224\) 0 0
\(225\) 0.198907 0.0132604
\(226\) 0 0
\(227\) −3.83084 −0.254262 −0.127131 0.991886i \(-0.540577\pi\)
−0.127131 + 0.991886i \(0.540577\pi\)
\(228\) 0 0
\(229\) 22.2951 1.47330 0.736651 0.676273i \(-0.236406\pi\)
0.736651 + 0.676273i \(0.236406\pi\)
\(230\) 0 0
\(231\) −8.60612 −0.566241
\(232\) 0 0
\(233\) 20.5463 1.34603 0.673017 0.739627i \(-0.264998\pi\)
0.673017 + 0.739627i \(0.264998\pi\)
\(234\) 0 0
\(235\) −13.8742 −0.905052
\(236\) 0 0
\(237\) −29.9266 −1.94394
\(238\) 0 0
\(239\) 22.2656 1.44024 0.720120 0.693849i \(-0.244087\pi\)
0.720120 + 0.693849i \(0.244087\pi\)
\(240\) 0 0
\(241\) 3.08389 0.198651 0.0993253 0.995055i \(-0.468332\pi\)
0.0993253 + 0.995055i \(0.468332\pi\)
\(242\) 0 0
\(243\) 14.0054 0.898446
\(244\) 0 0
\(245\) 21.5896 1.37931
\(246\) 0 0
\(247\) 33.3273 2.12056
\(248\) 0 0
\(249\) −13.5817 −0.860707
\(250\) 0 0
\(251\) −9.34145 −0.589627 −0.294814 0.955555i \(-0.595258\pi\)
−0.294814 + 0.955555i \(0.595258\pi\)
\(252\) 0 0
\(253\) 4.55753 0.286529
\(254\) 0 0
\(255\) −6.95947 −0.435819
\(256\) 0 0
\(257\) −4.88888 −0.304960 −0.152480 0.988307i \(-0.548726\pi\)
−0.152480 + 0.988307i \(0.548726\pi\)
\(258\) 0 0
\(259\) 13.9972 0.869744
\(260\) 0 0
\(261\) −9.11092 −0.563952
\(262\) 0 0
\(263\) 5.72421 0.352970 0.176485 0.984303i \(-0.443527\pi\)
0.176485 + 0.984303i \(0.443527\pi\)
\(264\) 0 0
\(265\) −7.07467 −0.434594
\(266\) 0 0
\(267\) −35.2422 −2.15679
\(268\) 0 0
\(269\) −16.5404 −1.00848 −0.504242 0.863562i \(-0.668228\pi\)
−0.504242 + 0.863562i \(0.668228\pi\)
\(270\) 0 0
\(271\) −3.11644 −0.189310 −0.0946550 0.995510i \(-0.530175\pi\)
−0.0946550 + 0.995510i \(0.530175\pi\)
\(272\) 0 0
\(273\) 43.7627 2.64864
\(274\) 0 0
\(275\) 0.136473 0.00822960
\(276\) 0 0
\(277\) −6.30954 −0.379103 −0.189552 0.981871i \(-0.560703\pi\)
−0.189552 + 0.981871i \(0.560703\pi\)
\(278\) 0 0
\(279\) 14.7701 0.884260
\(280\) 0 0
\(281\) −21.7959 −1.30023 −0.650117 0.759834i \(-0.725280\pi\)
−0.650117 + 0.759834i \(0.725280\pi\)
\(282\) 0 0
\(283\) −0.424595 −0.0252396 −0.0126198 0.999920i \(-0.504017\pi\)
−0.0126198 + 0.999920i \(0.504017\pi\)
\(284\) 0 0
\(285\) 31.2984 1.85396
\(286\) 0 0
\(287\) −37.1200 −2.19112
\(288\) 0 0
\(289\) −14.8861 −0.875650
\(290\) 0 0
\(291\) 35.9265 2.10605
\(292\) 0 0
\(293\) 9.78177 0.571457 0.285728 0.958311i \(-0.407764\pi\)
0.285728 + 0.958311i \(0.407764\pi\)
\(294\) 0 0
\(295\) −5.05629 −0.294389
\(296\) 0 0
\(297\) 3.25832 0.189067
\(298\) 0 0
\(299\) −23.1753 −1.34026
\(300\) 0 0
\(301\) −11.3188 −0.652404
\(302\) 0 0
\(303\) 15.4625 0.888295
\(304\) 0 0
\(305\) −31.0463 −1.77770
\(306\) 0 0
\(307\) −1.13123 −0.0645625 −0.0322813 0.999479i \(-0.510277\pi\)
−0.0322813 + 0.999479i \(0.510277\pi\)
\(308\) 0 0
\(309\) 7.28063 0.414181
\(310\) 0 0
\(311\) −10.9793 −0.622578 −0.311289 0.950315i \(-0.600761\pi\)
−0.311289 + 0.950315i \(0.600761\pi\)
\(312\) 0 0
\(313\) 19.4180 1.09757 0.548784 0.835964i \(-0.315091\pi\)
0.548784 + 0.835964i \(0.315091\pi\)
\(314\) 0 0
\(315\) 13.4592 0.758342
\(316\) 0 0
\(317\) 30.5541 1.71609 0.858043 0.513577i \(-0.171680\pi\)
0.858043 + 0.513577i \(0.171680\pi\)
\(318\) 0 0
\(319\) −6.25113 −0.349996
\(320\) 0 0
\(321\) −11.8828 −0.663230
\(322\) 0 0
\(323\) −9.50694 −0.528980
\(324\) 0 0
\(325\) −0.693972 −0.0384947
\(326\) 0 0
\(327\) 2.16078 0.119492
\(328\) 0 0
\(329\) −24.8872 −1.37208
\(330\) 0 0
\(331\) 8.49611 0.466989 0.233494 0.972358i \(-0.424984\pi\)
0.233494 + 0.972358i \(0.424984\pi\)
\(332\) 0 0
\(333\) 5.02998 0.275641
\(334\) 0 0
\(335\) −32.0829 −1.75287
\(336\) 0 0
\(337\) −7.03611 −0.383282 −0.191641 0.981465i \(-0.561381\pi\)
−0.191641 + 0.981465i \(0.561381\pi\)
\(338\) 0 0
\(339\) 4.61799 0.250815
\(340\) 0 0
\(341\) 10.1339 0.548784
\(342\) 0 0
\(343\) 10.2701 0.554535
\(344\) 0 0
\(345\) −21.7645 −1.17176
\(346\) 0 0
\(347\) −1.64781 −0.0884591 −0.0442295 0.999021i \(-0.514083\pi\)
−0.0442295 + 0.999021i \(0.514083\pi\)
\(348\) 0 0
\(349\) −20.2197 −1.08234 −0.541168 0.840915i \(-0.682018\pi\)
−0.541168 + 0.840915i \(0.682018\pi\)
\(350\) 0 0
\(351\) −16.5688 −0.884375
\(352\) 0 0
\(353\) −15.7630 −0.838982 −0.419491 0.907760i \(-0.637791\pi\)
−0.419491 + 0.907760i \(0.637791\pi\)
\(354\) 0 0
\(355\) −31.3590 −1.66437
\(356\) 0 0
\(357\) −12.4838 −0.660710
\(358\) 0 0
\(359\) −19.6558 −1.03739 −0.518697 0.854958i \(-0.673583\pi\)
−0.518697 + 0.854958i \(0.673583\pi\)
\(360\) 0 0
\(361\) 23.7550 1.25027
\(362\) 0 0
\(363\) 21.1109 1.10804
\(364\) 0 0
\(365\) 1.37407 0.0719221
\(366\) 0 0
\(367\) 27.9198 1.45740 0.728701 0.684832i \(-0.240125\pi\)
0.728701 + 0.684832i \(0.240125\pi\)
\(368\) 0 0
\(369\) −13.3393 −0.694416
\(370\) 0 0
\(371\) −12.6904 −0.658852
\(372\) 0 0
\(373\) 29.8859 1.54743 0.773717 0.633531i \(-0.218395\pi\)
0.773717 + 0.633531i \(0.218395\pi\)
\(374\) 0 0
\(375\) 23.2814 1.20225
\(376\) 0 0
\(377\) 31.7874 1.63713
\(378\) 0 0
\(379\) −24.0226 −1.23396 −0.616980 0.786979i \(-0.711644\pi\)
−0.616980 + 0.786979i \(0.711644\pi\)
\(380\) 0 0
\(381\) −27.1483 −1.39085
\(382\) 0 0
\(383\) −10.7433 −0.548958 −0.274479 0.961593i \(-0.588505\pi\)
−0.274479 + 0.961593i \(0.588505\pi\)
\(384\) 0 0
\(385\) 9.23457 0.470637
\(386\) 0 0
\(387\) −4.06747 −0.206761
\(388\) 0 0
\(389\) −17.5814 −0.891412 −0.445706 0.895179i \(-0.647047\pi\)
−0.445706 + 0.895179i \(0.647047\pi\)
\(390\) 0 0
\(391\) 6.61100 0.334332
\(392\) 0 0
\(393\) −9.32788 −0.470529
\(394\) 0 0
\(395\) 32.1119 1.61572
\(396\) 0 0
\(397\) 3.03562 0.152353 0.0761766 0.997094i \(-0.475729\pi\)
0.0761766 + 0.997094i \(0.475729\pi\)
\(398\) 0 0
\(399\) 56.1425 2.81064
\(400\) 0 0
\(401\) −24.3368 −1.21532 −0.607661 0.794197i \(-0.707892\pi\)
−0.607661 + 0.794197i \(0.707892\pi\)
\(402\) 0 0
\(403\) −51.5318 −2.56698
\(404\) 0 0
\(405\) −25.4925 −1.26673
\(406\) 0 0
\(407\) 3.45114 0.171067
\(408\) 0 0
\(409\) −32.4090 −1.60252 −0.801262 0.598314i \(-0.795838\pi\)
−0.801262 + 0.598314i \(0.795838\pi\)
\(410\) 0 0
\(411\) 19.2289 0.948494
\(412\) 0 0
\(413\) −9.06987 −0.446299
\(414\) 0 0
\(415\) 14.5735 0.715385
\(416\) 0 0
\(417\) 28.5370 1.39746
\(418\) 0 0
\(419\) 22.9156 1.11950 0.559749 0.828662i \(-0.310897\pi\)
0.559749 + 0.828662i \(0.310897\pi\)
\(420\) 0 0
\(421\) −14.6625 −0.714606 −0.357303 0.933989i \(-0.616304\pi\)
−0.357303 + 0.933989i \(0.616304\pi\)
\(422\) 0 0
\(423\) −8.94338 −0.434842
\(424\) 0 0
\(425\) 0.197963 0.00960259
\(426\) 0 0
\(427\) −55.6902 −2.69504
\(428\) 0 0
\(429\) 10.7901 0.520951
\(430\) 0 0
\(431\) 12.0617 0.580989 0.290495 0.956877i \(-0.406180\pi\)
0.290495 + 0.956877i \(0.406180\pi\)
\(432\) 0 0
\(433\) −32.4757 −1.56068 −0.780341 0.625354i \(-0.784955\pi\)
−0.780341 + 0.625354i \(0.784955\pi\)
\(434\) 0 0
\(435\) 29.8523 1.43131
\(436\) 0 0
\(437\) −29.7313 −1.42224
\(438\) 0 0
\(439\) −15.8820 −0.758008 −0.379004 0.925395i \(-0.623733\pi\)
−0.379004 + 0.925395i \(0.623733\pi\)
\(440\) 0 0
\(441\) 13.9168 0.662703
\(442\) 0 0
\(443\) −19.8338 −0.942334 −0.471167 0.882044i \(-0.656167\pi\)
−0.471167 + 0.882044i \(0.656167\pi\)
\(444\) 0 0
\(445\) 37.8157 1.79264
\(446\) 0 0
\(447\) −15.1963 −0.718759
\(448\) 0 0
\(449\) −20.1451 −0.950705 −0.475352 0.879796i \(-0.657679\pi\)
−0.475352 + 0.879796i \(0.657679\pi\)
\(450\) 0 0
\(451\) −9.15227 −0.430964
\(452\) 0 0
\(453\) 23.0879 1.08476
\(454\) 0 0
\(455\) −46.9584 −2.20144
\(456\) 0 0
\(457\) 29.8675 1.39714 0.698572 0.715540i \(-0.253819\pi\)
0.698572 + 0.715540i \(0.253819\pi\)
\(458\) 0 0
\(459\) 4.72640 0.220610
\(460\) 0 0
\(461\) 26.1591 1.21835 0.609176 0.793035i \(-0.291500\pi\)
0.609176 + 0.793035i \(0.291500\pi\)
\(462\) 0 0
\(463\) −19.3246 −0.898090 −0.449045 0.893509i \(-0.648236\pi\)
−0.449045 + 0.893509i \(0.648236\pi\)
\(464\) 0 0
\(465\) −48.3947 −2.24425
\(466\) 0 0
\(467\) 5.38944 0.249393 0.124697 0.992195i \(-0.460204\pi\)
0.124697 + 0.992195i \(0.460204\pi\)
\(468\) 0 0
\(469\) −57.5496 −2.65739
\(470\) 0 0
\(471\) −20.5332 −0.946121
\(472\) 0 0
\(473\) −2.79075 −0.128319
\(474\) 0 0
\(475\) −0.890286 −0.0408491
\(476\) 0 0
\(477\) −4.56037 −0.208805
\(478\) 0 0
\(479\) 3.08980 0.141177 0.0705884 0.997506i \(-0.477512\pi\)
0.0705884 + 0.997506i \(0.477512\pi\)
\(480\) 0 0
\(481\) −17.5493 −0.800179
\(482\) 0 0
\(483\) −39.0407 −1.77641
\(484\) 0 0
\(485\) −38.5499 −1.75046
\(486\) 0 0
\(487\) −11.5620 −0.523923 −0.261961 0.965078i \(-0.584369\pi\)
−0.261961 + 0.965078i \(0.584369\pi\)
\(488\) 0 0
\(489\) −18.5495 −0.838836
\(490\) 0 0
\(491\) −22.2460 −1.00395 −0.501975 0.864882i \(-0.667393\pi\)
−0.501975 + 0.864882i \(0.667393\pi\)
\(492\) 0 0
\(493\) −9.06768 −0.408388
\(494\) 0 0
\(495\) 3.31850 0.149155
\(496\) 0 0
\(497\) −56.2512 −2.52321
\(498\) 0 0
\(499\) −41.1617 −1.84265 −0.921326 0.388792i \(-0.872892\pi\)
−0.921326 + 0.388792i \(0.872892\pi\)
\(500\) 0 0
\(501\) 47.1334 2.10576
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) −16.5916 −0.738315
\(506\) 0 0
\(507\) −27.4114 −1.21738
\(508\) 0 0
\(509\) 32.0313 1.41976 0.709881 0.704322i \(-0.248749\pi\)
0.709881 + 0.704322i \(0.248749\pi\)
\(510\) 0 0
\(511\) 2.46478 0.109035
\(512\) 0 0
\(513\) −21.2558 −0.938467
\(514\) 0 0
\(515\) −7.81229 −0.344250
\(516\) 0 0
\(517\) −6.13618 −0.269869
\(518\) 0 0
\(519\) −37.9940 −1.66775
\(520\) 0 0
\(521\) −21.5660 −0.944823 −0.472412 0.881378i \(-0.656616\pi\)
−0.472412 + 0.881378i \(0.656616\pi\)
\(522\) 0 0
\(523\) 27.0448 1.18259 0.591294 0.806456i \(-0.298617\pi\)
0.591294 + 0.806456i \(0.298617\pi\)
\(524\) 0 0
\(525\) −1.16905 −0.0510216
\(526\) 0 0
\(527\) 14.7000 0.640340
\(528\) 0 0
\(529\) −2.32529 −0.101099
\(530\) 0 0
\(531\) −3.25931 −0.141442
\(532\) 0 0
\(533\) 46.5399 2.01587
\(534\) 0 0
\(535\) 12.7505 0.551251
\(536\) 0 0
\(537\) 33.7117 1.45477
\(538\) 0 0
\(539\) 9.54849 0.411282
\(540\) 0 0
\(541\) 28.7357 1.23545 0.617723 0.786396i \(-0.288055\pi\)
0.617723 + 0.786396i \(0.288055\pi\)
\(542\) 0 0
\(543\) −17.1969 −0.737991
\(544\) 0 0
\(545\) −2.31857 −0.0993167
\(546\) 0 0
\(547\) 16.5139 0.706083 0.353041 0.935608i \(-0.385148\pi\)
0.353041 + 0.935608i \(0.385148\pi\)
\(548\) 0 0
\(549\) −20.0126 −0.854117
\(550\) 0 0
\(551\) 40.7796 1.73727
\(552\) 0 0
\(553\) 57.6016 2.44947
\(554\) 0 0
\(555\) −16.4810 −0.699578
\(556\) 0 0
\(557\) −30.5389 −1.29397 −0.646986 0.762502i \(-0.723971\pi\)
−0.646986 + 0.762502i \(0.723971\pi\)
\(558\) 0 0
\(559\) 14.1912 0.600222
\(560\) 0 0
\(561\) −3.07798 −0.129953
\(562\) 0 0
\(563\) −27.7696 −1.17035 −0.585174 0.810908i \(-0.698974\pi\)
−0.585174 + 0.810908i \(0.698974\pi\)
\(564\) 0 0
\(565\) −4.95521 −0.208467
\(566\) 0 0
\(567\) −45.7279 −1.92039
\(568\) 0 0
\(569\) 6.01578 0.252194 0.126097 0.992018i \(-0.459755\pi\)
0.126097 + 0.992018i \(0.459755\pi\)
\(570\) 0 0
\(571\) 13.6672 0.571956 0.285978 0.958236i \(-0.407682\pi\)
0.285978 + 0.958236i \(0.407682\pi\)
\(572\) 0 0
\(573\) 16.5040 0.689463
\(574\) 0 0
\(575\) 0.619093 0.0258179
\(576\) 0 0
\(577\) −23.8180 −0.991555 −0.495778 0.868449i \(-0.665117\pi\)
−0.495778 + 0.868449i \(0.665117\pi\)
\(578\) 0 0
\(579\) 50.0199 2.07876
\(580\) 0 0
\(581\) 26.1416 1.08454
\(582\) 0 0
\(583\) −3.12893 −0.129587
\(584\) 0 0
\(585\) −16.8748 −0.697687
\(586\) 0 0
\(587\) −40.5651 −1.67430 −0.837151 0.546972i \(-0.815780\pi\)
−0.837151 + 0.546972i \(0.815780\pi\)
\(588\) 0 0
\(589\) −66.1093 −2.72399
\(590\) 0 0
\(591\) 7.10388 0.292215
\(592\) 0 0
\(593\) 10.2283 0.420028 0.210014 0.977698i \(-0.432649\pi\)
0.210014 + 0.977698i \(0.432649\pi\)
\(594\) 0 0
\(595\) 13.3954 0.549156
\(596\) 0 0
\(597\) −38.2198 −1.56423
\(598\) 0 0
\(599\) 42.5115 1.73697 0.868486 0.495714i \(-0.165094\pi\)
0.868486 + 0.495714i \(0.165094\pi\)
\(600\) 0 0
\(601\) 15.7198 0.641223 0.320612 0.947211i \(-0.396112\pi\)
0.320612 + 0.947211i \(0.396112\pi\)
\(602\) 0 0
\(603\) −20.6808 −0.842187
\(604\) 0 0
\(605\) −22.6525 −0.920956
\(606\) 0 0
\(607\) −15.9609 −0.647832 −0.323916 0.946086i \(-0.605000\pi\)
−0.323916 + 0.946086i \(0.605000\pi\)
\(608\) 0 0
\(609\) 53.5485 2.16989
\(610\) 0 0
\(611\) 31.2029 1.26233
\(612\) 0 0
\(613\) −2.46409 −0.0995238 −0.0497619 0.998761i \(-0.515846\pi\)
−0.0497619 + 0.998761i \(0.515846\pi\)
\(614\) 0 0
\(615\) 43.7068 1.76243
\(616\) 0 0
\(617\) 5.72545 0.230498 0.115249 0.993337i \(-0.463233\pi\)
0.115249 + 0.993337i \(0.463233\pi\)
\(618\) 0 0
\(619\) 5.54382 0.222825 0.111412 0.993774i \(-0.464463\pi\)
0.111412 + 0.993774i \(0.464463\pi\)
\(620\) 0 0
\(621\) 14.7810 0.593141
\(622\) 0 0
\(623\) 67.8331 2.71767
\(624\) 0 0
\(625\) −25.6622 −1.02649
\(626\) 0 0
\(627\) 13.8425 0.552814
\(628\) 0 0
\(629\) 5.00611 0.199607
\(630\) 0 0
\(631\) 14.2290 0.566448 0.283224 0.959054i \(-0.408596\pi\)
0.283224 + 0.959054i \(0.408596\pi\)
\(632\) 0 0
\(633\) 10.2027 0.405519
\(634\) 0 0
\(635\) 29.1307 1.15602
\(636\) 0 0
\(637\) −48.5547 −1.92381
\(638\) 0 0
\(639\) −20.2142 −0.799662
\(640\) 0 0
\(641\) −22.9795 −0.907636 −0.453818 0.891094i \(-0.649938\pi\)
−0.453818 + 0.891094i \(0.649938\pi\)
\(642\) 0 0
\(643\) −42.2301 −1.66539 −0.832696 0.553730i \(-0.813204\pi\)
−0.832696 + 0.553730i \(0.813204\pi\)
\(644\) 0 0
\(645\) 13.3273 0.524760
\(646\) 0 0
\(647\) 44.3781 1.74468 0.872341 0.488898i \(-0.162601\pi\)
0.872341 + 0.488898i \(0.162601\pi\)
\(648\) 0 0
\(649\) −2.23626 −0.0877809
\(650\) 0 0
\(651\) −86.8095 −3.40233
\(652\) 0 0
\(653\) 15.9984 0.626065 0.313032 0.949742i \(-0.398655\pi\)
0.313032 + 0.949742i \(0.398655\pi\)
\(654\) 0 0
\(655\) 10.0090 0.391085
\(656\) 0 0
\(657\) 0.885733 0.0345558
\(658\) 0 0
\(659\) 4.85181 0.189000 0.0944998 0.995525i \(-0.469875\pi\)
0.0944998 + 0.995525i \(0.469875\pi\)
\(660\) 0 0
\(661\) 51.1792 1.99064 0.995321 0.0966234i \(-0.0308042\pi\)
0.995321 + 0.0966234i \(0.0308042\pi\)
\(662\) 0 0
\(663\) 15.6518 0.607864
\(664\) 0 0
\(665\) −60.2422 −2.33609
\(666\) 0 0
\(667\) −28.3575 −1.09801
\(668\) 0 0
\(669\) −52.4641 −2.02838
\(670\) 0 0
\(671\) −13.7309 −0.530076
\(672\) 0 0
\(673\) −24.8027 −0.956075 −0.478038 0.878339i \(-0.658652\pi\)
−0.478038 + 0.878339i \(0.658652\pi\)
\(674\) 0 0
\(675\) 0.442608 0.0170360
\(676\) 0 0
\(677\) −13.0820 −0.502781 −0.251391 0.967886i \(-0.580888\pi\)
−0.251391 + 0.967886i \(0.580888\pi\)
\(678\) 0 0
\(679\) −69.1500 −2.65374
\(680\) 0 0
\(681\) 8.09104 0.310049
\(682\) 0 0
\(683\) −13.8577 −0.530249 −0.265125 0.964214i \(-0.585413\pi\)
−0.265125 + 0.964214i \(0.585413\pi\)
\(684\) 0 0
\(685\) −20.6331 −0.788350
\(686\) 0 0
\(687\) −47.0890 −1.79656
\(688\) 0 0
\(689\) 15.9108 0.606155
\(690\) 0 0
\(691\) 4.85400 0.184655 0.0923275 0.995729i \(-0.470569\pi\)
0.0923275 + 0.995729i \(0.470569\pi\)
\(692\) 0 0
\(693\) 5.95265 0.226123
\(694\) 0 0
\(695\) −30.6209 −1.16152
\(696\) 0 0
\(697\) −13.2760 −0.502864
\(698\) 0 0
\(699\) −43.3954 −1.64137
\(700\) 0 0
\(701\) −26.4296 −0.998233 −0.499116 0.866535i \(-0.666342\pi\)
−0.499116 + 0.866535i \(0.666342\pi\)
\(702\) 0 0
\(703\) −22.5137 −0.849121
\(704\) 0 0
\(705\) 29.3034 1.10363
\(706\) 0 0
\(707\) −29.7616 −1.11930
\(708\) 0 0
\(709\) −3.89825 −0.146402 −0.0732010 0.997317i \(-0.523321\pi\)
−0.0732010 + 0.997317i \(0.523321\pi\)
\(710\) 0 0
\(711\) 20.6995 0.776292
\(712\) 0 0
\(713\) 45.9715 1.72165
\(714\) 0 0
\(715\) −11.5780 −0.432994
\(716\) 0 0
\(717\) −47.0266 −1.75624
\(718\) 0 0
\(719\) 2.53133 0.0944026 0.0472013 0.998885i \(-0.484970\pi\)
0.0472013 + 0.998885i \(0.484970\pi\)
\(720\) 0 0
\(721\) −14.0135 −0.521891
\(722\) 0 0
\(723\) −6.51341 −0.242236
\(724\) 0 0
\(725\) −0.849151 −0.0315367
\(726\) 0 0
\(727\) −5.56956 −0.206564 −0.103282 0.994652i \(-0.532934\pi\)
−0.103282 + 0.994652i \(0.532934\pi\)
\(728\) 0 0
\(729\) 4.16492 0.154256
\(730\) 0 0
\(731\) −4.04817 −0.149727
\(732\) 0 0
\(733\) 15.1483 0.559516 0.279758 0.960071i \(-0.409746\pi\)
0.279758 + 0.960071i \(0.409746\pi\)
\(734\) 0 0
\(735\) −45.5989 −1.68194
\(736\) 0 0
\(737\) −14.1894 −0.522673
\(738\) 0 0
\(739\) 43.6156 1.60443 0.802213 0.597038i \(-0.203656\pi\)
0.802213 + 0.597038i \(0.203656\pi\)
\(740\) 0 0
\(741\) −70.3898 −2.58584
\(742\) 0 0
\(743\) 47.4032 1.73905 0.869527 0.493885i \(-0.164424\pi\)
0.869527 + 0.493885i \(0.164424\pi\)
\(744\) 0 0
\(745\) 16.3060 0.597404
\(746\) 0 0
\(747\) 9.39416 0.343714
\(748\) 0 0
\(749\) 22.8715 0.835707
\(750\) 0 0
\(751\) −14.1780 −0.517364 −0.258682 0.965963i \(-0.583288\pi\)
−0.258682 + 0.965963i \(0.583288\pi\)
\(752\) 0 0
\(753\) 19.7299 0.718997
\(754\) 0 0
\(755\) −24.7739 −0.901613
\(756\) 0 0
\(757\) −41.6574 −1.51406 −0.757032 0.653377i \(-0.773352\pi\)
−0.757032 + 0.653377i \(0.773352\pi\)
\(758\) 0 0
\(759\) −9.62585 −0.349396
\(760\) 0 0
\(761\) −30.2244 −1.09563 −0.547817 0.836598i \(-0.684541\pi\)
−0.547817 + 0.836598i \(0.684541\pi\)
\(762\) 0 0
\(763\) −4.15901 −0.150566
\(764\) 0 0
\(765\) 4.81370 0.174040
\(766\) 0 0
\(767\) 11.3715 0.410603
\(768\) 0 0
\(769\) −7.00069 −0.252451 −0.126226 0.992002i \(-0.540286\pi\)
−0.126226 + 0.992002i \(0.540286\pi\)
\(770\) 0 0
\(771\) 10.3257 0.371871
\(772\) 0 0
\(773\) −38.7751 −1.39464 −0.697322 0.716758i \(-0.745625\pi\)
−0.697322 + 0.716758i \(0.745625\pi\)
\(774\) 0 0
\(775\) 1.37659 0.0494486
\(776\) 0 0
\(777\) −29.5632 −1.06057
\(778\) 0 0
\(779\) 59.7054 2.13917
\(780\) 0 0
\(781\) −13.8693 −0.496281
\(782\) 0 0
\(783\) −20.2737 −0.724523
\(784\) 0 0
\(785\) 22.0326 0.786378
\(786\) 0 0
\(787\) −37.1123 −1.32291 −0.661455 0.749984i \(-0.730061\pi\)
−0.661455 + 0.749984i \(0.730061\pi\)
\(788\) 0 0
\(789\) −12.0900 −0.430415
\(790\) 0 0
\(791\) −8.88855 −0.316041
\(792\) 0 0
\(793\) 69.8227 2.47948
\(794\) 0 0
\(795\) 14.9423 0.529947
\(796\) 0 0
\(797\) −45.0577 −1.59603 −0.798013 0.602641i \(-0.794115\pi\)
−0.798013 + 0.602641i \(0.794115\pi\)
\(798\) 0 0
\(799\) −8.90093 −0.314892
\(800\) 0 0
\(801\) 24.3762 0.861292
\(802\) 0 0
\(803\) 0.607714 0.0214458
\(804\) 0 0
\(805\) 41.8916 1.47648
\(806\) 0 0
\(807\) 34.9345 1.22975
\(808\) 0 0
\(809\) 52.2972 1.83867 0.919335 0.393475i \(-0.128727\pi\)
0.919335 + 0.393475i \(0.128727\pi\)
\(810\) 0 0
\(811\) 51.0213 1.79160 0.895799 0.444459i \(-0.146604\pi\)
0.895799 + 0.444459i \(0.146604\pi\)
\(812\) 0 0
\(813\) 6.58216 0.230846
\(814\) 0 0
\(815\) 19.9040 0.697207
\(816\) 0 0
\(817\) 18.2056 0.636934
\(818\) 0 0
\(819\) −30.2697 −1.05771
\(820\) 0 0
\(821\) −22.6715 −0.791242 −0.395621 0.918414i \(-0.629471\pi\)
−0.395621 + 0.918414i \(0.629471\pi\)
\(822\) 0 0
\(823\) −36.8627 −1.28495 −0.642477 0.766305i \(-0.722093\pi\)
−0.642477 + 0.766305i \(0.722093\pi\)
\(824\) 0 0
\(825\) −0.288241 −0.0100353
\(826\) 0 0
\(827\) 13.5507 0.471202 0.235601 0.971850i \(-0.424294\pi\)
0.235601 + 0.971850i \(0.424294\pi\)
\(828\) 0 0
\(829\) 12.5840 0.437060 0.218530 0.975830i \(-0.429874\pi\)
0.218530 + 0.975830i \(0.429874\pi\)
\(830\) 0 0
\(831\) 13.3262 0.462282
\(832\) 0 0
\(833\) 13.8507 0.479899
\(834\) 0 0
\(835\) −50.5752 −1.75023
\(836\) 0 0
\(837\) 32.8665 1.13603
\(838\) 0 0
\(839\) 40.1777 1.38709 0.693545 0.720414i \(-0.256048\pi\)
0.693545 + 0.720414i \(0.256048\pi\)
\(840\) 0 0
\(841\) 9.89537 0.341220
\(842\) 0 0
\(843\) 46.0346 1.58552
\(844\) 0 0
\(845\) 29.4131 1.01184
\(846\) 0 0
\(847\) −40.6336 −1.39619
\(848\) 0 0
\(849\) 0.896779 0.0307774
\(850\) 0 0
\(851\) 15.6557 0.536671
\(852\) 0 0
\(853\) −8.72638 −0.298786 −0.149393 0.988778i \(-0.547732\pi\)
−0.149393 + 0.988778i \(0.547732\pi\)
\(854\) 0 0
\(855\) −21.6484 −0.740360
\(856\) 0 0
\(857\) 34.4294 1.17609 0.588044 0.808829i \(-0.299898\pi\)
0.588044 + 0.808829i \(0.299898\pi\)
\(858\) 0 0
\(859\) −20.9612 −0.715188 −0.357594 0.933877i \(-0.616403\pi\)
−0.357594 + 0.933877i \(0.616403\pi\)
\(860\) 0 0
\(861\) 78.4003 2.67188
\(862\) 0 0
\(863\) −57.0318 −1.94138 −0.970692 0.240327i \(-0.922745\pi\)
−0.970692 + 0.240327i \(0.922745\pi\)
\(864\) 0 0
\(865\) 40.7685 1.38617
\(866\) 0 0
\(867\) 31.4405 1.06778
\(868\) 0 0
\(869\) 14.2022 0.481777
\(870\) 0 0
\(871\) 72.1540 2.44484
\(872\) 0 0
\(873\) −24.8495 −0.841028
\(874\) 0 0
\(875\) −44.8112 −1.51490
\(876\) 0 0
\(877\) −38.0437 −1.28465 −0.642323 0.766434i \(-0.722029\pi\)
−0.642323 + 0.766434i \(0.722029\pi\)
\(878\) 0 0
\(879\) −20.6599 −0.696840
\(880\) 0 0
\(881\) 35.7757 1.20531 0.602657 0.798000i \(-0.294109\pi\)
0.602657 + 0.798000i \(0.294109\pi\)
\(882\) 0 0
\(883\) 26.1190 0.878976 0.439488 0.898248i \(-0.355160\pi\)
0.439488 + 0.898248i \(0.355160\pi\)
\(884\) 0 0
\(885\) 10.6793 0.358980
\(886\) 0 0
\(887\) 6.17839 0.207450 0.103725 0.994606i \(-0.466924\pi\)
0.103725 + 0.994606i \(0.466924\pi\)
\(888\) 0 0
\(889\) 52.2541 1.75254
\(890\) 0 0
\(891\) −11.2746 −0.377715
\(892\) 0 0
\(893\) 40.0297 1.33954
\(894\) 0 0
\(895\) −36.1735 −1.20915
\(896\) 0 0
\(897\) 48.9481 1.63433
\(898\) 0 0
\(899\) −63.0548 −2.10299
\(900\) 0 0
\(901\) −4.53873 −0.151207
\(902\) 0 0
\(903\) 23.9062 0.795547
\(904\) 0 0
\(905\) 18.4527 0.613388
\(906\) 0 0
\(907\) −43.7016 −1.45109 −0.725544 0.688176i \(-0.758412\pi\)
−0.725544 + 0.688176i \(0.758412\pi\)
\(908\) 0 0
\(909\) −10.6950 −0.354731
\(910\) 0 0
\(911\) −16.3022 −0.540116 −0.270058 0.962844i \(-0.587043\pi\)
−0.270058 + 0.962844i \(0.587043\pi\)
\(912\) 0 0
\(913\) 6.44546 0.213314
\(914\) 0 0
\(915\) 65.5722 2.16775
\(916\) 0 0
\(917\) 17.9540 0.592893
\(918\) 0 0
\(919\) 50.9542 1.68083 0.840413 0.541947i \(-0.182313\pi\)
0.840413 + 0.541947i \(0.182313\pi\)
\(920\) 0 0
\(921\) 2.38924 0.0787281
\(922\) 0 0
\(923\) 70.5261 2.32140
\(924\) 0 0
\(925\) 0.468802 0.0154141
\(926\) 0 0
\(927\) −5.03584 −0.165399
\(928\) 0 0
\(929\) −15.0110 −0.492494 −0.246247 0.969207i \(-0.579197\pi\)
−0.246247 + 0.969207i \(0.579197\pi\)
\(930\) 0 0
\(931\) −62.2901 −2.04147
\(932\) 0 0
\(933\) 23.1891 0.759177
\(934\) 0 0
\(935\) 3.30275 0.108011
\(936\) 0 0
\(937\) −26.8600 −0.877477 −0.438738 0.898615i \(-0.644575\pi\)
−0.438738 + 0.898615i \(0.644575\pi\)
\(938\) 0 0
\(939\) −41.0123 −1.33838
\(940\) 0 0
\(941\) −38.5130 −1.25549 −0.627744 0.778420i \(-0.716021\pi\)
−0.627744 + 0.778420i \(0.716021\pi\)
\(942\) 0 0
\(943\) −41.5183 −1.35202
\(944\) 0 0
\(945\) 29.9496 0.974260
\(946\) 0 0
\(947\) 46.6430 1.51569 0.757846 0.652433i \(-0.226252\pi\)
0.757846 + 0.652433i \(0.226252\pi\)
\(948\) 0 0
\(949\) −3.09027 −0.100314
\(950\) 0 0
\(951\) −64.5326 −2.09261
\(952\) 0 0
\(953\) 45.0755 1.46014 0.730070 0.683373i \(-0.239488\pi\)
0.730070 + 0.683373i \(0.239488\pi\)
\(954\) 0 0
\(955\) −17.7091 −0.573054
\(956\) 0 0
\(957\) 13.2029 0.426788
\(958\) 0 0
\(959\) −37.0112 −1.19515
\(960\) 0 0
\(961\) 71.2205 2.29744
\(962\) 0 0
\(963\) 8.21902 0.264854
\(964\) 0 0
\(965\) −53.6725 −1.72778
\(966\) 0 0
\(967\) −17.5880 −0.565591 −0.282795 0.959180i \(-0.591262\pi\)
−0.282795 + 0.959180i \(0.591262\pi\)
\(968\) 0 0
\(969\) 20.0794 0.645043
\(970\) 0 0
\(971\) −28.5401 −0.915895 −0.457948 0.888979i \(-0.651415\pi\)
−0.457948 + 0.888979i \(0.651415\pi\)
\(972\) 0 0
\(973\) −54.9271 −1.76088
\(974\) 0 0
\(975\) 1.46572 0.0469407
\(976\) 0 0
\(977\) 20.4418 0.653992 0.326996 0.945026i \(-0.393964\pi\)
0.326996 + 0.945026i \(0.393964\pi\)
\(978\) 0 0
\(979\) 16.7249 0.534529
\(980\) 0 0
\(981\) −1.49456 −0.0477178
\(982\) 0 0
\(983\) 12.8951 0.411291 0.205645 0.978627i \(-0.434071\pi\)
0.205645 + 0.978627i \(0.434071\pi\)
\(984\) 0 0
\(985\) −7.62263 −0.242877
\(986\) 0 0
\(987\) 52.5638 1.67312
\(988\) 0 0
\(989\) −12.6599 −0.402562
\(990\) 0 0
\(991\) −40.3531 −1.28186 −0.640929 0.767600i \(-0.721451\pi\)
−0.640929 + 0.767600i \(0.721451\pi\)
\(992\) 0 0
\(993\) −17.9445 −0.569450
\(994\) 0 0
\(995\) 41.0107 1.30013
\(996\) 0 0
\(997\) 26.4183 0.836677 0.418339 0.908291i \(-0.362613\pi\)
0.418339 + 0.908291i \(0.362613\pi\)
\(998\) 0 0
\(999\) 11.1928 0.354123
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 \(a_p\))