Properties

Label 6036.2.a.g.1.14
Level 6036
Weight 2
Character 6036.1
Self dual Yes
Analytic conductor 48.198
Analytic rank 1
Dimension 15
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 6036 = 2^{2} \cdot 3 \cdot 503 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 6036.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(48.19770266\)
Analytic rank: \(1\)
Dimension: \(15\)
Coefficient field: \(\mathbb{Q}[x]/(x^{15} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{11}]\)
Coefficient ring index: \( 3 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.14
Root \(3.52096\)
Character \(\chi\) = 6036.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+1.00000 q^{3}\) \(+2.52096 q^{5}\) \(-1.02518 q^{7}\) \(+1.00000 q^{9}\) \(+O(q^{10})\) \(q\)\(+1.00000 q^{3}\) \(+2.52096 q^{5}\) \(-1.02518 q^{7}\) \(+1.00000 q^{9}\) \(-3.26772 q^{11}\) \(-2.87517 q^{13}\) \(+2.52096 q^{15}\) \(+0.377785 q^{17}\) \(-1.62078 q^{19}\) \(-1.02518 q^{21}\) \(-6.17692 q^{23}\) \(+1.35524 q^{25}\) \(+1.00000 q^{27}\) \(-5.77725 q^{29}\) \(+6.59306 q^{31}\) \(-3.26772 q^{33}\) \(-2.58443 q^{35}\) \(+2.04591 q^{37}\) \(-2.87517 q^{39}\) \(+1.64121 q^{41}\) \(-1.25813 q^{43}\) \(+2.52096 q^{45}\) \(+12.2278 q^{47}\) \(-5.94901 q^{49}\) \(+0.377785 q^{51}\) \(-8.59305 q^{53}\) \(-8.23780 q^{55}\) \(-1.62078 q^{57}\) \(-9.35721 q^{59}\) \(-1.13492 q^{61}\) \(-1.02518 q^{63}\) \(-7.24820 q^{65}\) \(+0.942111 q^{67}\) \(-6.17692 q^{69}\) \(+0.988908 q^{71}\) \(-12.7507 q^{73}\) \(+1.35524 q^{75}\) \(+3.34999 q^{77}\) \(-3.81707 q^{79}\) \(+1.00000 q^{81}\) \(+4.87138 q^{83}\) \(+0.952380 q^{85}\) \(-5.77725 q^{87}\) \(-16.9858 q^{89}\) \(+2.94756 q^{91}\) \(+6.59306 q^{93}\) \(-4.08593 q^{95}\) \(+5.17800 q^{97}\) \(-3.26772 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(15q \) \(\mathstrut +\mathstrut 15q^{3} \) \(\mathstrut -\mathstrut 11q^{5} \) \(\mathstrut -\mathstrut 4q^{7} \) \(\mathstrut +\mathstrut 15q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut -\mathstrut 14q^{13} \) \(\mathstrut -\mathstrut 11q^{15} \) \(\mathstrut -\mathstrut 5q^{17} \) \(\mathstrut +\mathstrut 3q^{19} \) \(\mathstrut -\mathstrut 4q^{21} \) \(\mathstrut -\mathstrut 32q^{23} \) \(\mathstrut +\mathstrut 2q^{25} \) \(\mathstrut +\mathstrut 15q^{27} \) \(\mathstrut -\mathstrut 23q^{29} \) \(\mathstrut -\mathstrut 13q^{31} \) \(\mathstrut -\mathstrut 5q^{33} \) \(\mathstrut -\mathstrut 16q^{35} \) \(\mathstrut -\mathstrut 10q^{37} \) \(\mathstrut -\mathstrut 14q^{39} \) \(\mathstrut -\mathstrut 14q^{41} \) \(\mathstrut +\mathstrut 4q^{43} \) \(\mathstrut -\mathstrut 11q^{45} \) \(\mathstrut -\mathstrut 20q^{47} \) \(\mathstrut -\mathstrut 9q^{49} \) \(\mathstrut -\mathstrut 5q^{51} \) \(\mathstrut -\mathstrut 30q^{53} \) \(\mathstrut -\mathstrut 10q^{55} \) \(\mathstrut +\mathstrut 3q^{57} \) \(\mathstrut -\mathstrut 14q^{59} \) \(\mathstrut -\mathstrut 38q^{61} \) \(\mathstrut -\mathstrut 4q^{63} \) \(\mathstrut -\mathstrut 24q^{65} \) \(\mathstrut -\mathstrut 8q^{67} \) \(\mathstrut -\mathstrut 32q^{69} \) \(\mathstrut -\mathstrut 41q^{71} \) \(\mathstrut -\mathstrut 19q^{73} \) \(\mathstrut +\mathstrut 2q^{75} \) \(\mathstrut -\mathstrut 39q^{77} \) \(\mathstrut -\mathstrut 27q^{79} \) \(\mathstrut +\mathstrut 15q^{81} \) \(\mathstrut -\mathstrut 17q^{83} \) \(\mathstrut -\mathstrut 6q^{85} \) \(\mathstrut -\mathstrut 23q^{87} \) \(\mathstrut -\mathstrut 23q^{89} \) \(\mathstrut +\mathstrut 4q^{91} \) \(\mathstrut -\mathstrut 13q^{93} \) \(\mathstrut -\mathstrut 30q^{95} \) \(\mathstrut -\mathstrut 18q^{97} \) \(\mathstrut -\mathstrut 5q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 1.00000 0.577350
\(4\) 0 0
\(5\) 2.52096 1.12741 0.563704 0.825977i \(-0.309376\pi\)
0.563704 + 0.825977i \(0.309376\pi\)
\(6\) 0 0
\(7\) −1.02518 −0.387480 −0.193740 0.981053i \(-0.562062\pi\)
−0.193740 + 0.981053i \(0.562062\pi\)
\(8\) 0 0
\(9\) 1.00000 0.333333
\(10\) 0 0
\(11\) −3.26772 −0.985255 −0.492628 0.870240i \(-0.663964\pi\)
−0.492628 + 0.870240i \(0.663964\pi\)
\(12\) 0 0
\(13\) −2.87517 −0.797430 −0.398715 0.917075i \(-0.630544\pi\)
−0.398715 + 0.917075i \(0.630544\pi\)
\(14\) 0 0
\(15\) 2.52096 0.650909
\(16\) 0 0
\(17\) 0.377785 0.0916263 0.0458131 0.998950i \(-0.485412\pi\)
0.0458131 + 0.998950i \(0.485412\pi\)
\(18\) 0 0
\(19\) −1.62078 −0.371833 −0.185917 0.982566i \(-0.559525\pi\)
−0.185917 + 0.982566i \(0.559525\pi\)
\(20\) 0 0
\(21\) −1.02518 −0.223712
\(22\) 0 0
\(23\) −6.17692 −1.28798 −0.643989 0.765035i \(-0.722722\pi\)
−0.643989 + 0.765035i \(0.722722\pi\)
\(24\) 0 0
\(25\) 1.35524 0.271048
\(26\) 0 0
\(27\) 1.00000 0.192450
\(28\) 0 0
\(29\) −5.77725 −1.07281 −0.536404 0.843961i \(-0.680218\pi\)
−0.536404 + 0.843961i \(0.680218\pi\)
\(30\) 0 0
\(31\) 6.59306 1.18415 0.592074 0.805883i \(-0.298309\pi\)
0.592074 + 0.805883i \(0.298309\pi\)
\(32\) 0 0
\(33\) −3.26772 −0.568837
\(34\) 0 0
\(35\) −2.58443 −0.436848
\(36\) 0 0
\(37\) 2.04591 0.336345 0.168172 0.985758i \(-0.446213\pi\)
0.168172 + 0.985758i \(0.446213\pi\)
\(38\) 0 0
\(39\) −2.87517 −0.460396
\(40\) 0 0
\(41\) 1.64121 0.256313 0.128157 0.991754i \(-0.459094\pi\)
0.128157 + 0.991754i \(0.459094\pi\)
\(42\) 0 0
\(43\) −1.25813 −0.191863 −0.0959316 0.995388i \(-0.530583\pi\)
−0.0959316 + 0.995388i \(0.530583\pi\)
\(44\) 0 0
\(45\) 2.52096 0.375803
\(46\) 0 0
\(47\) 12.2278 1.78361 0.891803 0.452424i \(-0.149440\pi\)
0.891803 + 0.452424i \(0.149440\pi\)
\(48\) 0 0
\(49\) −5.94901 −0.849859
\(50\) 0 0
\(51\) 0.377785 0.0529004
\(52\) 0 0
\(53\) −8.59305 −1.18035 −0.590173 0.807277i \(-0.700941\pi\)
−0.590173 + 0.807277i \(0.700941\pi\)
\(54\) 0 0
\(55\) −8.23780 −1.11078
\(56\) 0 0
\(57\) −1.62078 −0.214678
\(58\) 0 0
\(59\) −9.35721 −1.21820 −0.609102 0.793092i \(-0.708470\pi\)
−0.609102 + 0.793092i \(0.708470\pi\)
\(60\) 0 0
\(61\) −1.13492 −0.145311 −0.0726555 0.997357i \(-0.523147\pi\)
−0.0726555 + 0.997357i \(0.523147\pi\)
\(62\) 0 0
\(63\) −1.02518 −0.129160
\(64\) 0 0
\(65\) −7.24820 −0.899029
\(66\) 0 0
\(67\) 0.942111 0.115097 0.0575486 0.998343i \(-0.481672\pi\)
0.0575486 + 0.998343i \(0.481672\pi\)
\(68\) 0 0
\(69\) −6.17692 −0.743614
\(70\) 0 0
\(71\) 0.988908 0.117362 0.0586809 0.998277i \(-0.481311\pi\)
0.0586809 + 0.998277i \(0.481311\pi\)
\(72\) 0 0
\(73\) −12.7507 −1.49236 −0.746178 0.665747i \(-0.768113\pi\)
−0.746178 + 0.665747i \(0.768113\pi\)
\(74\) 0 0
\(75\) 1.35524 0.156490
\(76\) 0 0
\(77\) 3.34999 0.381767
\(78\) 0 0
\(79\) −3.81707 −0.429454 −0.214727 0.976674i \(-0.568886\pi\)
−0.214727 + 0.976674i \(0.568886\pi\)
\(80\) 0 0
\(81\) 1.00000 0.111111
\(82\) 0 0
\(83\) 4.87138 0.534703 0.267352 0.963599i \(-0.413851\pi\)
0.267352 + 0.963599i \(0.413851\pi\)
\(84\) 0 0
\(85\) 0.952380 0.103300
\(86\) 0 0
\(87\) −5.77725 −0.619386
\(88\) 0 0
\(89\) −16.9858 −1.80049 −0.900246 0.435382i \(-0.856613\pi\)
−0.900246 + 0.435382i \(0.856613\pi\)
\(90\) 0 0
\(91\) 2.94756 0.308988
\(92\) 0 0
\(93\) 6.59306 0.683668
\(94\) 0 0
\(95\) −4.08593 −0.419208
\(96\) 0 0
\(97\) 5.17800 0.525746 0.262873 0.964830i \(-0.415330\pi\)
0.262873 + 0.964830i \(0.415330\pi\)
\(98\) 0 0
\(99\) −3.26772 −0.328418
\(100\) 0 0
\(101\) 8.78904 0.874542 0.437271 0.899330i \(-0.355945\pi\)
0.437271 + 0.899330i \(0.355945\pi\)
\(102\) 0 0
\(103\) −16.6235 −1.63796 −0.818980 0.573822i \(-0.805460\pi\)
−0.818980 + 0.573822i \(0.805460\pi\)
\(104\) 0 0
\(105\) −2.58443 −0.252214
\(106\) 0 0
\(107\) 1.66433 0.160897 0.0804486 0.996759i \(-0.474365\pi\)
0.0804486 + 0.996759i \(0.474365\pi\)
\(108\) 0 0
\(109\) −17.7496 −1.70010 −0.850050 0.526702i \(-0.823428\pi\)
−0.850050 + 0.526702i \(0.823428\pi\)
\(110\) 0 0
\(111\) 2.04591 0.194189
\(112\) 0 0
\(113\) −4.24845 −0.399661 −0.199830 0.979831i \(-0.564039\pi\)
−0.199830 + 0.979831i \(0.564039\pi\)
\(114\) 0 0
\(115\) −15.5718 −1.45208
\(116\) 0 0
\(117\) −2.87517 −0.265810
\(118\) 0 0
\(119\) −0.387296 −0.0355034
\(120\) 0 0
\(121\) −0.321992 −0.0292720
\(122\) 0 0
\(123\) 1.64121 0.147983
\(124\) 0 0
\(125\) −9.18830 −0.821826
\(126\) 0 0
\(127\) 10.3085 0.914731 0.457365 0.889279i \(-0.348793\pi\)
0.457365 + 0.889279i \(0.348793\pi\)
\(128\) 0 0
\(129\) −1.25813 −0.110772
\(130\) 0 0
\(131\) 8.88317 0.776126 0.388063 0.921633i \(-0.373144\pi\)
0.388063 + 0.921633i \(0.373144\pi\)
\(132\) 0 0
\(133\) 1.66159 0.144078
\(134\) 0 0
\(135\) 2.52096 0.216970
\(136\) 0 0
\(137\) −11.0387 −0.943097 −0.471549 0.881840i \(-0.656305\pi\)
−0.471549 + 0.881840i \(0.656305\pi\)
\(138\) 0 0
\(139\) 10.0393 0.851520 0.425760 0.904836i \(-0.360007\pi\)
0.425760 + 0.904836i \(0.360007\pi\)
\(140\) 0 0
\(141\) 12.2278 1.02977
\(142\) 0 0
\(143\) 9.39527 0.785672
\(144\) 0 0
\(145\) −14.5642 −1.20949
\(146\) 0 0
\(147\) −5.94901 −0.490666
\(148\) 0 0
\(149\) 4.47326 0.366463 0.183232 0.983070i \(-0.441344\pi\)
0.183232 + 0.983070i \(0.441344\pi\)
\(150\) 0 0
\(151\) 18.6111 1.51455 0.757275 0.653096i \(-0.226530\pi\)
0.757275 + 0.653096i \(0.226530\pi\)
\(152\) 0 0
\(153\) 0.377785 0.0305421
\(154\) 0 0
\(155\) 16.6208 1.33502
\(156\) 0 0
\(157\) −14.3876 −1.14826 −0.574128 0.818766i \(-0.694659\pi\)
−0.574128 + 0.818766i \(0.694659\pi\)
\(158\) 0 0
\(159\) −8.59305 −0.681473
\(160\) 0 0
\(161\) 6.33243 0.499066
\(162\) 0 0
\(163\) −4.81245 −0.376940 −0.188470 0.982079i \(-0.560353\pi\)
−0.188470 + 0.982079i \(0.560353\pi\)
\(164\) 0 0
\(165\) −8.23780 −0.641312
\(166\) 0 0
\(167\) 0.760554 0.0588534 0.0294267 0.999567i \(-0.490632\pi\)
0.0294267 + 0.999567i \(0.490632\pi\)
\(168\) 0 0
\(169\) −4.73337 −0.364106
\(170\) 0 0
\(171\) −1.62078 −0.123944
\(172\) 0 0
\(173\) −10.1595 −0.772410 −0.386205 0.922413i \(-0.626214\pi\)
−0.386205 + 0.922413i \(0.626214\pi\)
\(174\) 0 0
\(175\) −1.38936 −0.105026
\(176\) 0 0
\(177\) −9.35721 −0.703331
\(178\) 0 0
\(179\) 17.1094 1.27882 0.639409 0.768867i \(-0.279179\pi\)
0.639409 + 0.768867i \(0.279179\pi\)
\(180\) 0 0
\(181\) 3.61105 0.268407 0.134203 0.990954i \(-0.457152\pi\)
0.134203 + 0.990954i \(0.457152\pi\)
\(182\) 0 0
\(183\) −1.13492 −0.0838954
\(184\) 0 0
\(185\) 5.15765 0.379198
\(186\) 0 0
\(187\) −1.23450 −0.0902753
\(188\) 0 0
\(189\) −1.02518 −0.0745706
\(190\) 0 0
\(191\) 0.296153 0.0214289 0.0107144 0.999943i \(-0.496589\pi\)
0.0107144 + 0.999943i \(0.496589\pi\)
\(192\) 0 0
\(193\) 14.8084 1.06593 0.532966 0.846137i \(-0.321077\pi\)
0.532966 + 0.846137i \(0.321077\pi\)
\(194\) 0 0
\(195\) −7.24820 −0.519054
\(196\) 0 0
\(197\) −19.2880 −1.37421 −0.687105 0.726558i \(-0.741119\pi\)
−0.687105 + 0.726558i \(0.741119\pi\)
\(198\) 0 0
\(199\) −15.1845 −1.07640 −0.538201 0.842817i \(-0.680896\pi\)
−0.538201 + 0.842817i \(0.680896\pi\)
\(200\) 0 0
\(201\) 0.942111 0.0664514
\(202\) 0 0
\(203\) 5.92270 0.415692
\(204\) 0 0
\(205\) 4.13742 0.288970
\(206\) 0 0
\(207\) −6.17692 −0.429326
\(208\) 0 0
\(209\) 5.29627 0.366351
\(210\) 0 0
\(211\) −22.1254 −1.52317 −0.761587 0.648063i \(-0.775579\pi\)
−0.761587 + 0.648063i \(0.775579\pi\)
\(212\) 0 0
\(213\) 0.988908 0.0677589
\(214\) 0 0
\(215\) −3.17170 −0.216308
\(216\) 0 0
\(217\) −6.75905 −0.458834
\(218\) 0 0
\(219\) −12.7507 −0.861612
\(220\) 0 0
\(221\) −1.08620 −0.0730655
\(222\) 0 0
\(223\) −18.7967 −1.25872 −0.629359 0.777115i \(-0.716683\pi\)
−0.629359 + 0.777115i \(0.716683\pi\)
\(224\) 0 0
\(225\) 1.35524 0.0903493
\(226\) 0 0
\(227\) −10.1902 −0.676350 −0.338175 0.941083i \(-0.609810\pi\)
−0.338175 + 0.941083i \(0.609810\pi\)
\(228\) 0 0
\(229\) 8.80690 0.581976 0.290988 0.956727i \(-0.406016\pi\)
0.290988 + 0.956727i \(0.406016\pi\)
\(230\) 0 0
\(231\) 3.34999 0.220413
\(232\) 0 0
\(233\) −11.6965 −0.766263 −0.383131 0.923694i \(-0.625154\pi\)
−0.383131 + 0.923694i \(0.625154\pi\)
\(234\) 0 0
\(235\) 30.8258 2.01085
\(236\) 0 0
\(237\) −3.81707 −0.247945
\(238\) 0 0
\(239\) −23.7646 −1.53721 −0.768603 0.639725i \(-0.779048\pi\)
−0.768603 + 0.639725i \(0.779048\pi\)
\(240\) 0 0
\(241\) 4.06074 0.261575 0.130788 0.991410i \(-0.458249\pi\)
0.130788 + 0.991410i \(0.458249\pi\)
\(242\) 0 0
\(243\) 1.00000 0.0641500
\(244\) 0 0
\(245\) −14.9972 −0.958138
\(246\) 0 0
\(247\) 4.66004 0.296511
\(248\) 0 0
\(249\) 4.87138 0.308711
\(250\) 0 0
\(251\) 29.8288 1.88278 0.941388 0.337326i \(-0.109522\pi\)
0.941388 + 0.337326i \(0.109522\pi\)
\(252\) 0 0
\(253\) 20.1845 1.26899
\(254\) 0 0
\(255\) 0.952380 0.0596404
\(256\) 0 0
\(257\) −0.936638 −0.0584258 −0.0292129 0.999573i \(-0.509300\pi\)
−0.0292129 + 0.999573i \(0.509300\pi\)
\(258\) 0 0
\(259\) −2.09741 −0.130327
\(260\) 0 0
\(261\) −5.77725 −0.357603
\(262\) 0 0
\(263\) −3.88139 −0.239337 −0.119668 0.992814i \(-0.538183\pi\)
−0.119668 + 0.992814i \(0.538183\pi\)
\(264\) 0 0
\(265\) −21.6627 −1.33073
\(266\) 0 0
\(267\) −16.9858 −1.03951
\(268\) 0 0
\(269\) 32.5695 1.98580 0.992898 0.118971i \(-0.0379596\pi\)
0.992898 + 0.118971i \(0.0379596\pi\)
\(270\) 0 0
\(271\) 23.0539 1.40042 0.700211 0.713936i \(-0.253089\pi\)
0.700211 + 0.713936i \(0.253089\pi\)
\(272\) 0 0
\(273\) 2.94756 0.178395
\(274\) 0 0
\(275\) −4.42854 −0.267051
\(276\) 0 0
\(277\) 24.4849 1.47115 0.735577 0.677442i \(-0.236911\pi\)
0.735577 + 0.677442i \(0.236911\pi\)
\(278\) 0 0
\(279\) 6.59306 0.394716
\(280\) 0 0
\(281\) 11.0539 0.659418 0.329709 0.944083i \(-0.393049\pi\)
0.329709 + 0.944083i \(0.393049\pi\)
\(282\) 0 0
\(283\) 17.3703 1.03256 0.516278 0.856421i \(-0.327317\pi\)
0.516278 + 0.856421i \(0.327317\pi\)
\(284\) 0 0
\(285\) −4.08593 −0.242030
\(286\) 0 0
\(287\) −1.68253 −0.0993164
\(288\) 0 0
\(289\) −16.8573 −0.991605
\(290\) 0 0
\(291\) 5.17800 0.303540
\(292\) 0 0
\(293\) 2.92081 0.170636 0.0853178 0.996354i \(-0.472809\pi\)
0.0853178 + 0.996354i \(0.472809\pi\)
\(294\) 0 0
\(295\) −23.5891 −1.37341
\(296\) 0 0
\(297\) −3.26772 −0.189612
\(298\) 0 0
\(299\) 17.7597 1.02707
\(300\) 0 0
\(301\) 1.28981 0.0743432
\(302\) 0 0
\(303\) 8.78904 0.504917
\(304\) 0 0
\(305\) −2.86108 −0.163825
\(306\) 0 0
\(307\) 23.5812 1.34585 0.672925 0.739711i \(-0.265038\pi\)
0.672925 + 0.739711i \(0.265038\pi\)
\(308\) 0 0
\(309\) −16.6235 −0.945677
\(310\) 0 0
\(311\) −15.0568 −0.853793 −0.426896 0.904301i \(-0.640393\pi\)
−0.426896 + 0.904301i \(0.640393\pi\)
\(312\) 0 0
\(313\) 17.4291 0.985153 0.492577 0.870269i \(-0.336055\pi\)
0.492577 + 0.870269i \(0.336055\pi\)
\(314\) 0 0
\(315\) −2.58443 −0.145616
\(316\) 0 0
\(317\) −6.21009 −0.348794 −0.174397 0.984675i \(-0.555798\pi\)
−0.174397 + 0.984675i \(0.555798\pi\)
\(318\) 0 0
\(319\) 18.8785 1.05699
\(320\) 0 0
\(321\) 1.66433 0.0928941
\(322\) 0 0
\(323\) −0.612307 −0.0340697
\(324\) 0 0
\(325\) −3.89655 −0.216142
\(326\) 0 0
\(327\) −17.7496 −0.981553
\(328\) 0 0
\(329\) −12.5356 −0.691112
\(330\) 0 0
\(331\) −16.0705 −0.883314 −0.441657 0.897184i \(-0.645609\pi\)
−0.441657 + 0.897184i \(0.645609\pi\)
\(332\) 0 0
\(333\) 2.04591 0.112115
\(334\) 0 0
\(335\) 2.37502 0.129761
\(336\) 0 0
\(337\) 16.0344 0.873447 0.436724 0.899596i \(-0.356139\pi\)
0.436724 + 0.899596i \(0.356139\pi\)
\(338\) 0 0
\(339\) −4.24845 −0.230744
\(340\) 0 0
\(341\) −21.5443 −1.16669
\(342\) 0 0
\(343\) 13.2750 0.716784
\(344\) 0 0
\(345\) −15.5718 −0.838356
\(346\) 0 0
\(347\) 32.1269 1.72466 0.862331 0.506345i \(-0.169004\pi\)
0.862331 + 0.506345i \(0.169004\pi\)
\(348\) 0 0
\(349\) 16.0352 0.858345 0.429173 0.903223i \(-0.358805\pi\)
0.429173 + 0.903223i \(0.358805\pi\)
\(350\) 0 0
\(351\) −2.87517 −0.153465
\(352\) 0 0
\(353\) −23.0322 −1.22588 −0.612940 0.790129i \(-0.710013\pi\)
−0.612940 + 0.790129i \(0.710013\pi\)
\(354\) 0 0
\(355\) 2.49300 0.132315
\(356\) 0 0
\(357\) −0.387296 −0.0204979
\(358\) 0 0
\(359\) −10.1002 −0.533067 −0.266533 0.963826i \(-0.585878\pi\)
−0.266533 + 0.963826i \(0.585878\pi\)
\(360\) 0 0
\(361\) −16.3731 −0.861740
\(362\) 0 0
\(363\) −0.321992 −0.0169002
\(364\) 0 0
\(365\) −32.1440 −1.68249
\(366\) 0 0
\(367\) 9.20738 0.480622 0.240311 0.970696i \(-0.422751\pi\)
0.240311 + 0.970696i \(0.422751\pi\)
\(368\) 0 0
\(369\) 1.64121 0.0854378
\(370\) 0 0
\(371\) 8.80939 0.457361
\(372\) 0 0
\(373\) 21.8720 1.13249 0.566244 0.824237i \(-0.308396\pi\)
0.566244 + 0.824237i \(0.308396\pi\)
\(374\) 0 0
\(375\) −9.18830 −0.474482
\(376\) 0 0
\(377\) 16.6106 0.855490
\(378\) 0 0
\(379\) 33.3983 1.71556 0.857779 0.514019i \(-0.171844\pi\)
0.857779 + 0.514019i \(0.171844\pi\)
\(380\) 0 0
\(381\) 10.3085 0.528120
\(382\) 0 0
\(383\) 20.2461 1.03453 0.517264 0.855826i \(-0.326950\pi\)
0.517264 + 0.855826i \(0.326950\pi\)
\(384\) 0 0
\(385\) 8.44519 0.430407
\(386\) 0 0
\(387\) −1.25813 −0.0639544
\(388\) 0 0
\(389\) −32.2980 −1.63758 −0.818788 0.574096i \(-0.805354\pi\)
−0.818788 + 0.574096i \(0.805354\pi\)
\(390\) 0 0
\(391\) −2.33355 −0.118013
\(392\) 0 0
\(393\) 8.88317 0.448097
\(394\) 0 0
\(395\) −9.62268 −0.484170
\(396\) 0 0
\(397\) 16.3523 0.820697 0.410348 0.911929i \(-0.365407\pi\)
0.410348 + 0.911929i \(0.365407\pi\)
\(398\) 0 0
\(399\) 1.66159 0.0831835
\(400\) 0 0
\(401\) −27.6189 −1.37922 −0.689612 0.724179i \(-0.742219\pi\)
−0.689612 + 0.724179i \(0.742219\pi\)
\(402\) 0 0
\(403\) −18.9562 −0.944275
\(404\) 0 0
\(405\) 2.52096 0.125268
\(406\) 0 0
\(407\) −6.68545 −0.331385
\(408\) 0 0
\(409\) −3.45875 −0.171024 −0.0855121 0.996337i \(-0.527253\pi\)
−0.0855121 + 0.996337i \(0.527253\pi\)
\(410\) 0 0
\(411\) −11.0387 −0.544498
\(412\) 0 0
\(413\) 9.59279 0.472030
\(414\) 0 0
\(415\) 12.2806 0.602828
\(416\) 0 0
\(417\) 10.0393 0.491625
\(418\) 0 0
\(419\) 6.45922 0.315553 0.157777 0.987475i \(-0.449567\pi\)
0.157777 + 0.987475i \(0.449567\pi\)
\(420\) 0 0
\(421\) −32.0739 −1.56319 −0.781593 0.623789i \(-0.785593\pi\)
−0.781593 + 0.623789i \(0.785593\pi\)
\(422\) 0 0
\(423\) 12.2278 0.594535
\(424\) 0 0
\(425\) 0.511989 0.0248351
\(426\) 0 0
\(427\) 1.16349 0.0563052
\(428\) 0 0
\(429\) 9.39527 0.453608
\(430\) 0 0
\(431\) −21.9616 −1.05785 −0.528926 0.848668i \(-0.677405\pi\)
−0.528926 + 0.848668i \(0.677405\pi\)
\(432\) 0 0
\(433\) 20.1059 0.966226 0.483113 0.875558i \(-0.339506\pi\)
0.483113 + 0.875558i \(0.339506\pi\)
\(434\) 0 0
\(435\) −14.5642 −0.698301
\(436\) 0 0
\(437\) 10.0115 0.478913
\(438\) 0 0
\(439\) −0.533793 −0.0254766 −0.0127383 0.999919i \(-0.504055\pi\)
−0.0127383 + 0.999919i \(0.504055\pi\)
\(440\) 0 0
\(441\) −5.94901 −0.283286
\(442\) 0 0
\(443\) −33.0425 −1.56989 −0.784947 0.619563i \(-0.787310\pi\)
−0.784947 + 0.619563i \(0.787310\pi\)
\(444\) 0 0
\(445\) −42.8205 −2.02989
\(446\) 0 0
\(447\) 4.47326 0.211578
\(448\) 0 0
\(449\) −18.1673 −0.857366 −0.428683 0.903455i \(-0.641022\pi\)
−0.428683 + 0.903455i \(0.641022\pi\)
\(450\) 0 0
\(451\) −5.36301 −0.252534
\(452\) 0 0
\(453\) 18.6111 0.874426
\(454\) 0 0
\(455\) 7.43068 0.348356
\(456\) 0 0
\(457\) 23.1718 1.08393 0.541965 0.840401i \(-0.317680\pi\)
0.541965 + 0.840401i \(0.317680\pi\)
\(458\) 0 0
\(459\) 0.377785 0.0176335
\(460\) 0 0
\(461\) −10.8369 −0.504725 −0.252363 0.967633i \(-0.581208\pi\)
−0.252363 + 0.967633i \(0.581208\pi\)
\(462\) 0 0
\(463\) −5.90221 −0.274299 −0.137149 0.990550i \(-0.543794\pi\)
−0.137149 + 0.990550i \(0.543794\pi\)
\(464\) 0 0
\(465\) 16.6208 0.770773
\(466\) 0 0
\(467\) −16.2479 −0.751864 −0.375932 0.926647i \(-0.622677\pi\)
−0.375932 + 0.926647i \(0.622677\pi\)
\(468\) 0 0
\(469\) −0.965830 −0.0445979
\(470\) 0 0
\(471\) −14.3876 −0.662946
\(472\) 0 0
\(473\) 4.11122 0.189034
\(474\) 0 0
\(475\) −2.19655 −0.100785
\(476\) 0 0
\(477\) −8.59305 −0.393449
\(478\) 0 0
\(479\) 20.2545 0.925452 0.462726 0.886501i \(-0.346871\pi\)
0.462726 + 0.886501i \(0.346871\pi\)
\(480\) 0 0
\(481\) −5.88233 −0.268211
\(482\) 0 0
\(483\) 6.33243 0.288136
\(484\) 0 0
\(485\) 13.0535 0.592730
\(486\) 0 0
\(487\) −6.32264 −0.286506 −0.143253 0.989686i \(-0.545756\pi\)
−0.143253 + 0.989686i \(0.545756\pi\)
\(488\) 0 0
\(489\) −4.81245 −0.217627
\(490\) 0 0
\(491\) 22.0921 0.997002 0.498501 0.866889i \(-0.333884\pi\)
0.498501 + 0.866889i \(0.333884\pi\)
\(492\) 0 0
\(493\) −2.18256 −0.0982975
\(494\) 0 0
\(495\) −8.23780 −0.370261
\(496\) 0 0
\(497\) −1.01381 −0.0454754
\(498\) 0 0
\(499\) −26.8788 −1.20326 −0.601631 0.798774i \(-0.705482\pi\)
−0.601631 + 0.798774i \(0.705482\pi\)
\(500\) 0 0
\(501\) 0.760554 0.0339790
\(502\) 0 0
\(503\) −1.00000 −0.0445878
\(504\) 0 0
\(505\) 22.1568 0.985965
\(506\) 0 0
\(507\) −4.73337 −0.210216
\(508\) 0 0
\(509\) 40.8050 1.80865 0.904325 0.426845i \(-0.140375\pi\)
0.904325 + 0.426845i \(0.140375\pi\)
\(510\) 0 0
\(511\) 13.0717 0.578258
\(512\) 0 0
\(513\) −1.62078 −0.0715594
\(514\) 0 0
\(515\) −41.9071 −1.84665
\(516\) 0 0
\(517\) −39.9570 −1.75731
\(518\) 0 0
\(519\) −10.1595 −0.445951
\(520\) 0 0
\(521\) 26.1863 1.14724 0.573621 0.819121i \(-0.305538\pi\)
0.573621 + 0.819121i \(0.305538\pi\)
\(522\) 0 0
\(523\) 32.3042 1.41256 0.706282 0.707930i \(-0.250371\pi\)
0.706282 + 0.707930i \(0.250371\pi\)
\(524\) 0 0
\(525\) −1.38936 −0.0606366
\(526\) 0 0
\(527\) 2.49076 0.108499
\(528\) 0 0
\(529\) 15.1543 0.658885
\(530\) 0 0
\(531\) −9.35721 −0.406068
\(532\) 0 0
\(533\) −4.71876 −0.204392
\(534\) 0 0
\(535\) 4.19572 0.181397
\(536\) 0 0
\(537\) 17.1094 0.738326
\(538\) 0 0
\(539\) 19.4397 0.837328
\(540\) 0 0
\(541\) −15.2223 −0.654458 −0.327229 0.944945i \(-0.606115\pi\)
−0.327229 + 0.944945i \(0.606115\pi\)
\(542\) 0 0
\(543\) 3.61105 0.154965
\(544\) 0 0
\(545\) −44.7459 −1.91671
\(546\) 0 0
\(547\) −22.6856 −0.969966 −0.484983 0.874524i \(-0.661174\pi\)
−0.484983 + 0.874524i \(0.661174\pi\)
\(548\) 0 0
\(549\) −1.13492 −0.0484370
\(550\) 0 0
\(551\) 9.36368 0.398906
\(552\) 0 0
\(553\) 3.91317 0.166405
\(554\) 0 0
\(555\) 5.15765 0.218930
\(556\) 0 0
\(557\) 1.53786 0.0651614 0.0325807 0.999469i \(-0.489627\pi\)
0.0325807 + 0.999469i \(0.489627\pi\)
\(558\) 0 0
\(559\) 3.61735 0.152998
\(560\) 0 0
\(561\) −1.23450 −0.0521204
\(562\) 0 0
\(563\) −36.8937 −1.55488 −0.777442 0.628954i \(-0.783483\pi\)
−0.777442 + 0.628954i \(0.783483\pi\)
\(564\) 0 0
\(565\) −10.7102 −0.450581
\(566\) 0 0
\(567\) −1.02518 −0.0430534
\(568\) 0 0
\(569\) 2.39067 0.100222 0.0501110 0.998744i \(-0.484042\pi\)
0.0501110 + 0.998744i \(0.484042\pi\)
\(570\) 0 0
\(571\) 13.1095 0.548616 0.274308 0.961642i \(-0.411551\pi\)
0.274308 + 0.961642i \(0.411551\pi\)
\(572\) 0 0
\(573\) 0.296153 0.0123720
\(574\) 0 0
\(575\) −8.37120 −0.349103
\(576\) 0 0
\(577\) −5.33586 −0.222135 −0.111067 0.993813i \(-0.535427\pi\)
−0.111067 + 0.993813i \(0.535427\pi\)
\(578\) 0 0
\(579\) 14.8084 0.615416
\(580\) 0 0
\(581\) −4.99402 −0.207187
\(582\) 0 0
\(583\) 28.0797 1.16294
\(584\) 0 0
\(585\) −7.24820 −0.299676
\(586\) 0 0
\(587\) 9.35300 0.386040 0.193020 0.981195i \(-0.438172\pi\)
0.193020 + 0.981195i \(0.438172\pi\)
\(588\) 0 0
\(589\) −10.6859 −0.440306
\(590\) 0 0
\(591\) −19.2880 −0.793401
\(592\) 0 0
\(593\) −1.61989 −0.0665208 −0.0332604 0.999447i \(-0.510589\pi\)
−0.0332604 + 0.999447i \(0.510589\pi\)
\(594\) 0 0
\(595\) −0.976358 −0.0400268
\(596\) 0 0
\(597\) −15.1845 −0.621461
\(598\) 0 0
\(599\) −6.44660 −0.263401 −0.131700 0.991290i \(-0.542044\pi\)
−0.131700 + 0.991290i \(0.542044\pi\)
\(600\) 0 0
\(601\) −12.9643 −0.528824 −0.264412 0.964410i \(-0.585178\pi\)
−0.264412 + 0.964410i \(0.585178\pi\)
\(602\) 0 0
\(603\) 0.942111 0.0383657
\(604\) 0 0
\(605\) −0.811729 −0.0330015
\(606\) 0 0
\(607\) −12.4087 −0.503654 −0.251827 0.967772i \(-0.581031\pi\)
−0.251827 + 0.967772i \(0.581031\pi\)
\(608\) 0 0
\(609\) 5.92270 0.240000
\(610\) 0 0
\(611\) −35.1570 −1.42230
\(612\) 0 0
\(613\) 1.41520 0.0571593 0.0285796 0.999592i \(-0.490902\pi\)
0.0285796 + 0.999592i \(0.490902\pi\)
\(614\) 0 0
\(615\) 4.13742 0.166837
\(616\) 0 0
\(617\) −15.0686 −0.606638 −0.303319 0.952889i \(-0.598095\pi\)
−0.303319 + 0.952889i \(0.598095\pi\)
\(618\) 0 0
\(619\) −7.87864 −0.316669 −0.158335 0.987386i \(-0.550612\pi\)
−0.158335 + 0.987386i \(0.550612\pi\)
\(620\) 0 0
\(621\) −6.17692 −0.247871
\(622\) 0 0
\(623\) 17.4134 0.697655
\(624\) 0 0
\(625\) −29.9395 −1.19758
\(626\) 0 0
\(627\) 5.29627 0.211513
\(628\) 0 0
\(629\) 0.772912 0.0308180
\(630\) 0 0
\(631\) −8.63840 −0.343889 −0.171945 0.985107i \(-0.555005\pi\)
−0.171945 + 0.985107i \(0.555005\pi\)
\(632\) 0 0
\(633\) −22.1254 −0.879405
\(634\) 0 0
\(635\) 25.9873 1.03127
\(636\) 0 0
\(637\) 17.1045 0.677703
\(638\) 0 0
\(639\) 0.988908 0.0391206
\(640\) 0 0
\(641\) 33.1040 1.30753 0.653764 0.756699i \(-0.273189\pi\)
0.653764 + 0.756699i \(0.273189\pi\)
\(642\) 0 0
\(643\) −22.1720 −0.874377 −0.437188 0.899370i \(-0.644026\pi\)
−0.437188 + 0.899370i \(0.644026\pi\)
\(644\) 0 0
\(645\) −3.17170 −0.124886
\(646\) 0 0
\(647\) −5.66692 −0.222790 −0.111395 0.993776i \(-0.535532\pi\)
−0.111395 + 0.993776i \(0.535532\pi\)
\(648\) 0 0
\(649\) 30.5767 1.20024
\(650\) 0 0
\(651\) −6.75905 −0.264908
\(652\) 0 0
\(653\) −13.2652 −0.519108 −0.259554 0.965729i \(-0.583576\pi\)
−0.259554 + 0.965729i \(0.583576\pi\)
\(654\) 0 0
\(655\) 22.3941 0.875010
\(656\) 0 0
\(657\) −12.7507 −0.497452
\(658\) 0 0
\(659\) −41.7765 −1.62738 −0.813692 0.581297i \(-0.802545\pi\)
−0.813692 + 0.581297i \(0.802545\pi\)
\(660\) 0 0
\(661\) −21.9461 −0.853605 −0.426802 0.904345i \(-0.640360\pi\)
−0.426802 + 0.904345i \(0.640360\pi\)
\(662\) 0 0
\(663\) −1.08620 −0.0421844
\(664\) 0 0
\(665\) 4.18880 0.162435
\(666\) 0 0
\(667\) 35.6856 1.38175
\(668\) 0 0
\(669\) −18.7967 −0.726721
\(670\) 0 0
\(671\) 3.70859 0.143168
\(672\) 0 0
\(673\) −0.398443 −0.0153589 −0.00767943 0.999971i \(-0.502444\pi\)
−0.00767943 + 0.999971i \(0.502444\pi\)
\(674\) 0 0
\(675\) 1.35524 0.0521632
\(676\) 0 0
\(677\) −27.1248 −1.04249 −0.521246 0.853407i \(-0.674533\pi\)
−0.521246 + 0.853407i \(0.674533\pi\)
\(678\) 0 0
\(679\) −5.30836 −0.203716
\(680\) 0 0
\(681\) −10.1902 −0.390491
\(682\) 0 0
\(683\) −0.255415 −0.00977319 −0.00488660 0.999988i \(-0.501555\pi\)
−0.00488660 + 0.999988i \(0.501555\pi\)
\(684\) 0 0
\(685\) −27.8281 −1.06326
\(686\) 0 0
\(687\) 8.80690 0.336004
\(688\) 0 0
\(689\) 24.7065 0.941244
\(690\) 0 0
\(691\) 11.6261 0.442279 0.221140 0.975242i \(-0.429022\pi\)
0.221140 + 0.975242i \(0.429022\pi\)
\(692\) 0 0
\(693\) 3.34999 0.127256
\(694\) 0 0
\(695\) 25.3086 0.960010
\(696\) 0 0
\(697\) 0.620023 0.0234850
\(698\) 0 0
\(699\) −11.6965 −0.442402
\(700\) 0 0
\(701\) 12.8197 0.484193 0.242097 0.970252i \(-0.422165\pi\)
0.242097 + 0.970252i \(0.422165\pi\)
\(702\) 0 0
\(703\) −3.31597 −0.125064
\(704\) 0 0
\(705\) 30.8258 1.16097
\(706\) 0 0
\(707\) −9.01032 −0.338868
\(708\) 0 0
\(709\) 32.8398 1.23333 0.616663 0.787227i \(-0.288484\pi\)
0.616663 + 0.787227i \(0.288484\pi\)
\(710\) 0 0
\(711\) −3.81707 −0.143151
\(712\) 0 0
\(713\) −40.7248 −1.52516
\(714\) 0 0
\(715\) 23.6851 0.885773
\(716\) 0 0
\(717\) −23.7646 −0.887507
\(718\) 0 0
\(719\) −20.3717 −0.759735 −0.379867 0.925041i \(-0.624030\pi\)
−0.379867 + 0.925041i \(0.624030\pi\)
\(720\) 0 0
\(721\) 17.0420 0.634677
\(722\) 0 0
\(723\) 4.06074 0.151021
\(724\) 0 0
\(725\) −7.82956 −0.290782
\(726\) 0 0
\(727\) −24.8350 −0.921078 −0.460539 0.887640i \(-0.652344\pi\)
−0.460539 + 0.887640i \(0.652344\pi\)
\(728\) 0 0
\(729\) 1.00000 0.0370370
\(730\) 0 0
\(731\) −0.475303 −0.0175797
\(732\) 0 0
\(733\) 23.4421 0.865853 0.432927 0.901429i \(-0.357481\pi\)
0.432927 + 0.901429i \(0.357481\pi\)
\(734\) 0 0
\(735\) −14.9972 −0.553181
\(736\) 0 0
\(737\) −3.07856 −0.113400
\(738\) 0 0
\(739\) −13.3235 −0.490114 −0.245057 0.969509i \(-0.578807\pi\)
−0.245057 + 0.969509i \(0.578807\pi\)
\(740\) 0 0
\(741\) 4.66004 0.171191
\(742\) 0 0
\(743\) −34.6296 −1.27044 −0.635218 0.772333i \(-0.719090\pi\)
−0.635218 + 0.772333i \(0.719090\pi\)
\(744\) 0 0
\(745\) 11.2769 0.413154
\(746\) 0 0
\(747\) 4.87138 0.178234
\(748\) 0 0
\(749\) −1.70624 −0.0623445
\(750\) 0 0
\(751\) 20.2014 0.737158 0.368579 0.929596i \(-0.379844\pi\)
0.368579 + 0.929596i \(0.379844\pi\)
\(752\) 0 0
\(753\) 29.8288 1.08702
\(754\) 0 0
\(755\) 46.9179 1.70752
\(756\) 0 0
\(757\) 35.8622 1.30343 0.651716 0.758463i \(-0.274049\pi\)
0.651716 + 0.758463i \(0.274049\pi\)
\(758\) 0 0
\(759\) 20.1845 0.732650
\(760\) 0 0
\(761\) 14.8328 0.537690 0.268845 0.963184i \(-0.413358\pi\)
0.268845 + 0.963184i \(0.413358\pi\)
\(762\) 0 0
\(763\) 18.1964 0.658755
\(764\) 0 0
\(765\) 0.952380 0.0344334
\(766\) 0 0
\(767\) 26.9036 0.971433
\(768\) 0 0
\(769\) 1.01654 0.0366574 0.0183287 0.999832i \(-0.494165\pi\)
0.0183287 + 0.999832i \(0.494165\pi\)
\(770\) 0 0
\(771\) −0.936638 −0.0337322
\(772\) 0 0
\(773\) −17.5917 −0.632731 −0.316365 0.948637i \(-0.602463\pi\)
−0.316365 + 0.948637i \(0.602463\pi\)
\(774\) 0 0
\(775\) 8.93517 0.320961
\(776\) 0 0
\(777\) −2.09741 −0.0752443
\(778\) 0 0
\(779\) −2.66004 −0.0953059
\(780\) 0 0
\(781\) −3.23148 −0.115631
\(782\) 0 0
\(783\) −5.77725 −0.206462
\(784\) 0 0
\(785\) −36.2706 −1.29455
\(786\) 0 0
\(787\) 49.1247 1.75111 0.875553 0.483121i \(-0.160497\pi\)
0.875553 + 0.483121i \(0.160497\pi\)
\(788\) 0 0
\(789\) −3.88139 −0.138181
\(790\) 0 0
\(791\) 4.35541 0.154861
\(792\) 0 0
\(793\) 3.26308 0.115875
\(794\) 0 0
\(795\) −21.6627 −0.768298
\(796\) 0 0
\(797\) 30.3445 1.07486 0.537429 0.843309i \(-0.319396\pi\)
0.537429 + 0.843309i \(0.319396\pi\)
\(798\) 0 0
\(799\) 4.61947 0.163425
\(800\) 0 0
\(801\) −16.9858 −0.600164
\(802\) 0 0
\(803\) 41.6657 1.47035
\(804\) 0 0
\(805\) 15.9638 0.562650
\(806\) 0 0
\(807\) 32.5695 1.14650
\(808\) 0 0
\(809\) 15.0475 0.529040 0.264520 0.964380i \(-0.414786\pi\)
0.264520 + 0.964380i \(0.414786\pi\)
\(810\) 0 0
\(811\) −31.4681 −1.10499 −0.552497 0.833515i \(-0.686325\pi\)
−0.552497 + 0.833515i \(0.686325\pi\)
\(812\) 0 0
\(813\) 23.0539 0.808534
\(814\) 0 0
\(815\) −12.1320 −0.424965
\(816\) 0 0
\(817\) 2.03916 0.0713412
\(818\) 0 0
\(819\) 2.94756 0.102996
\(820\) 0 0
\(821\) −42.1869 −1.47233 −0.736167 0.676800i \(-0.763366\pi\)
−0.736167 + 0.676800i \(0.763366\pi\)
\(822\) 0 0
\(823\) −0.0254204 −0.000886100 0 −0.000443050 1.00000i \(-0.500141\pi\)
−0.000443050 1.00000i \(0.500141\pi\)
\(824\) 0 0
\(825\) −4.42854 −0.154182
\(826\) 0 0
\(827\) −23.6664 −0.822961 −0.411480 0.911419i \(-0.634988\pi\)
−0.411480 + 0.911419i \(0.634988\pi\)
\(828\) 0 0
\(829\) 45.0883 1.56598 0.782990 0.622034i \(-0.213694\pi\)
0.782990 + 0.622034i \(0.213694\pi\)
\(830\) 0 0
\(831\) 24.4849 0.849371
\(832\) 0 0
\(833\) −2.24745 −0.0778694
\(834\) 0 0
\(835\) 1.91733 0.0663518
\(836\) 0 0
\(837\) 6.59306 0.227889
\(838\) 0 0
\(839\) −11.7537 −0.405782 −0.202891 0.979201i \(-0.565034\pi\)
−0.202891 + 0.979201i \(0.565034\pi\)
\(840\) 0 0
\(841\) 4.37664 0.150919
\(842\) 0 0
\(843\) 11.0539 0.380715
\(844\) 0 0
\(845\) −11.9326 −0.410495
\(846\) 0 0
\(847\) 0.330099 0.0113423
\(848\) 0 0
\(849\) 17.3703 0.596147
\(850\) 0 0
\(851\) −12.6374 −0.433204
\(852\) 0 0
\(853\) 17.4368 0.597026 0.298513 0.954406i \(-0.403509\pi\)
0.298513 + 0.954406i \(0.403509\pi\)
\(854\) 0 0
\(855\) −4.08593 −0.139736
\(856\) 0 0
\(857\) −9.57857 −0.327198 −0.163599 0.986527i \(-0.552310\pi\)
−0.163599 + 0.986527i \(0.552310\pi\)
\(858\) 0 0
\(859\) −12.8356 −0.437944 −0.218972 0.975731i \(-0.570270\pi\)
−0.218972 + 0.975731i \(0.570270\pi\)
\(860\) 0 0
\(861\) −1.68253 −0.0573403
\(862\) 0 0
\(863\) −11.5875 −0.394443 −0.197221 0.980359i \(-0.563192\pi\)
−0.197221 + 0.980359i \(0.563192\pi\)
\(864\) 0 0
\(865\) −25.6116 −0.870821
\(866\) 0 0
\(867\) −16.8573 −0.572503
\(868\) 0 0
\(869\) 12.4731 0.423122
\(870\) 0 0
\(871\) −2.70873 −0.0917819
\(872\) 0 0
\(873\) 5.17800 0.175249
\(874\) 0 0
\(875\) 9.41963 0.318441
\(876\) 0 0
\(877\) −3.17868 −0.107336 −0.0536682 0.998559i \(-0.517091\pi\)
−0.0536682 + 0.998559i \(0.517091\pi\)
\(878\) 0 0
\(879\) 2.92081 0.0985165
\(880\) 0 0
\(881\) 33.9054 1.14230 0.571150 0.820845i \(-0.306497\pi\)
0.571150 + 0.820845i \(0.306497\pi\)
\(882\) 0 0
\(883\) 30.7707 1.03552 0.517758 0.855527i \(-0.326767\pi\)
0.517758 + 0.855527i \(0.326767\pi\)
\(884\) 0 0
\(885\) −23.5891 −0.792940
\(886\) 0 0
\(887\) 23.4377 0.786962 0.393481 0.919333i \(-0.371271\pi\)
0.393481 + 0.919333i \(0.371271\pi\)
\(888\) 0 0
\(889\) −10.5680 −0.354440
\(890\) 0 0
\(891\) −3.26772 −0.109473
\(892\) 0 0
\(893\) −19.8186 −0.663204
\(894\) 0 0
\(895\) 43.1322 1.44175
\(896\) 0 0
\(897\) 17.7597 0.592980
\(898\) 0 0
\(899\) −38.0898 −1.27036
\(900\) 0 0
\(901\) −3.24632 −0.108151
\(902\) 0 0
\(903\) 1.28981 0.0429221
\(904\) 0 0
\(905\) 9.10330 0.302604
\(906\) 0 0
\(907\) 23.7964 0.790148 0.395074 0.918649i \(-0.370719\pi\)
0.395074 + 0.918649i \(0.370719\pi\)
\(908\) 0 0
\(909\) 8.78904 0.291514
\(910\) 0 0
\(911\) −39.6175 −1.31259 −0.656293 0.754506i \(-0.727877\pi\)
−0.656293 + 0.754506i \(0.727877\pi\)
\(912\) 0 0
\(913\) −15.9183 −0.526819
\(914\) 0 0
\(915\) −2.86108 −0.0945843
\(916\) 0 0
\(917\) −9.10681 −0.300734
\(918\) 0 0
\(919\) 35.2164 1.16168 0.580840 0.814018i \(-0.302724\pi\)
0.580840 + 0.814018i \(0.302724\pi\)
\(920\) 0 0
\(921\) 23.5812 0.777027
\(922\) 0 0
\(923\) −2.84328 −0.0935878
\(924\) 0 0
\(925\) 2.77269 0.0911655
\(926\) 0 0
\(927\) −16.6235 −0.545987
\(928\) 0 0
\(929\) −24.0219 −0.788134 −0.394067 0.919082i \(-0.628932\pi\)
−0.394067 + 0.919082i \(0.628932\pi\)
\(930\) 0 0
\(931\) 9.64206 0.316006
\(932\) 0 0
\(933\) −15.0568 −0.492938
\(934\) 0 0
\(935\) −3.11211 −0.101777
\(936\) 0 0
\(937\) 28.3384 0.925775 0.462888 0.886417i \(-0.346813\pi\)
0.462888 + 0.886417i \(0.346813\pi\)
\(938\) 0 0
\(939\) 17.4291 0.568778
\(940\) 0 0
\(941\) −31.7155 −1.03390 −0.516948 0.856017i \(-0.672932\pi\)
−0.516948 + 0.856017i \(0.672932\pi\)
\(942\) 0 0
\(943\) −10.1376 −0.330126
\(944\) 0 0
\(945\) −2.58443 −0.0840715
\(946\) 0 0
\(947\) −41.0291 −1.33327 −0.666634 0.745385i \(-0.732266\pi\)
−0.666634 + 0.745385i \(0.732266\pi\)
\(948\) 0 0
\(949\) 36.6605 1.19005
\(950\) 0 0
\(951\) −6.21009 −0.201376
\(952\) 0 0
\(953\) 42.8897 1.38933 0.694667 0.719332i \(-0.255552\pi\)
0.694667 + 0.719332i \(0.255552\pi\)
\(954\) 0 0
\(955\) 0.746590 0.0241591
\(956\) 0 0
\(957\) 18.8785 0.610254
\(958\) 0 0
\(959\) 11.3166 0.365432
\(960\) 0 0
\(961\) 12.4684 0.402207
\(962\) 0 0
\(963\) 1.66433 0.0536324
\(964\) 0 0
\(965\) 37.3314 1.20174
\(966\) 0 0
\(967\) −45.9167 −1.47658 −0.738291 0.674482i \(-0.764367\pi\)
−0.738291 + 0.674482i \(0.764367\pi\)
\(968\) 0 0
\(969\) −0.612307 −0.0196701
\(970\) 0 0
\(971\) −37.6867 −1.20942 −0.604712 0.796444i \(-0.706712\pi\)
−0.604712 + 0.796444i \(0.706712\pi\)
\(972\) 0 0
\(973\) −10.2920 −0.329947
\(974\) 0 0
\(975\) −3.89655 −0.124789
\(976\) 0 0
\(977\) −5.87111 −0.187834 −0.0939168 0.995580i \(-0.529939\pi\)
−0.0939168 + 0.995580i \(0.529939\pi\)
\(978\) 0 0
\(979\) 55.5049 1.77394
\(980\) 0 0
\(981\) −17.7496 −0.566700
\(982\) 0 0
\(983\) −33.7567 −1.07667 −0.538336 0.842731i \(-0.680947\pi\)
−0.538336 + 0.842731i \(0.680947\pi\)
\(984\) 0 0
\(985\) −48.6242 −1.54930
\(986\) 0 0
\(987\) −12.5356 −0.399014
\(988\) 0 0
\(989\) 7.77138 0.247115
\(990\) 0 0
\(991\) 43.4635 1.38066 0.690332 0.723493i \(-0.257464\pi\)
0.690332 + 0.723493i \(0.257464\pi\)
\(992\) 0 0
\(993\) −16.0705 −0.509982
\(994\) 0 0
\(995\) −38.2796 −1.21354
\(996\) 0 0
\(997\) 11.9207 0.377532 0.188766 0.982022i \(-0.439551\pi\)
0.188766 + 0.982022i \(0.439551\pi\)
\(998\) 0 0
\(999\) 2.04591 0.0647296
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 \(a_p\))