Properties

Label 4012.2.a.g.1.12
Level 4012
Weight 2
Character 4012.1
Self dual Yes
Analytic conductor 32.036
Analytic rank 1
Dimension 12
CM No
Inner twists 1

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Newspace parameters

Level: \( N \) = \( 4012 = 2^{2} \cdot 17 \cdot 59 \)
Weight: \( k \) = \( 2 \)
Character orbit: \([\chi]\) = 4012.a (trivial)

Newform invariants

Self dual: Yes
Analytic conductor: \(32.0359812909\)
Analytic rank: \(1\)
Dimension: \(12\)
Coefficient field: \(\mathbb{Q}[x]/(x^{12} - \cdots)\)
Coefficient ring: \(\Z[a_1, \ldots, a_{7}]\)
Coefficient ring index: \( 1 \)
Fricke sign: \(1\)
Sato-Tate group: $\mathrm{SU}(2)$

Embedding invariants

Embedding label 1.12
Root \(-2.86344\)
Character \(\chi\) = 4012.1

$q$-expansion

\(f(q)\) \(=\) \(q\)\(+2.86344 q^{3}\) \(-0.0527883 q^{5}\) \(-1.89476 q^{7}\) \(+5.19930 q^{9}\) \(+O(q^{10})\) \(q\)\(+2.86344 q^{3}\) \(-0.0527883 q^{5}\) \(-1.89476 q^{7}\) \(+5.19930 q^{9}\) \(-5.46657 q^{11}\) \(-0.847692 q^{13}\) \(-0.151156 q^{15}\) \(-1.00000 q^{17}\) \(+0.788998 q^{19}\) \(-5.42553 q^{21}\) \(+0.154474 q^{23}\) \(-4.99721 q^{25}\) \(+6.29755 q^{27}\) \(-3.17088 q^{29}\) \(-8.43776 q^{31}\) \(-15.6532 q^{33}\) \(+0.100021 q^{35}\) \(-3.87929 q^{37}\) \(-2.42732 q^{39}\) \(-1.73405 q^{41}\) \(-2.07545 q^{43}\) \(-0.274462 q^{45}\) \(+3.26225 q^{47}\) \(-3.40989 q^{49}\) \(-2.86344 q^{51}\) \(+2.52369 q^{53}\) \(+0.288571 q^{55}\) \(+2.25925 q^{57}\) \(+1.00000 q^{59}\) \(+8.67566 q^{61}\) \(-9.85141 q^{63}\) \(+0.0447482 q^{65}\) \(-6.26592 q^{67}\) \(+0.442328 q^{69}\) \(+1.81244 q^{71}\) \(+4.69077 q^{73}\) \(-14.3092 q^{75}\) \(+10.3578 q^{77}\) \(+3.52708 q^{79}\) \(+2.43479 q^{81}\) \(-6.16895 q^{83}\) \(+0.0527883 q^{85}\) \(-9.07962 q^{87}\) \(-8.42669 q^{89}\) \(+1.60617 q^{91}\) \(-24.1610 q^{93}\) \(-0.0416498 q^{95}\) \(+6.52415 q^{97}\) \(-28.4223 q^{99}\) \(+O(q^{100})\)
\(\operatorname{Tr}(f)(q)\) \(=\) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut +\mathstrut O(q^{10}) \) \(12q \) \(\mathstrut -\mathstrut 4q^{3} \) \(\mathstrut +\mathstrut 3q^{5} \) \(\mathstrut +\mathstrut 2q^{7} \) \(\mathstrut +\mathstrut 6q^{9} \) \(\mathstrut -\mathstrut 5q^{11} \) \(\mathstrut +\mathstrut 9q^{13} \) \(\mathstrut -\mathstrut 16q^{15} \) \(\mathstrut -\mathstrut 12q^{17} \) \(\mathstrut -\mathstrut 15q^{19} \) \(\mathstrut +\mathstrut 5q^{21} \) \(\mathstrut -\mathstrut 22q^{23} \) \(\mathstrut +\mathstrut 5q^{25} \) \(\mathstrut -\mathstrut 16q^{27} \) \(\mathstrut -\mathstrut 17q^{29} \) \(\mathstrut +\mathstrut 5q^{31} \) \(\mathstrut -\mathstrut 33q^{33} \) \(\mathstrut -\mathstrut 9q^{35} \) \(\mathstrut -\mathstrut 2q^{37} \) \(\mathstrut -\mathstrut 24q^{39} \) \(\mathstrut -\mathstrut 18q^{41} \) \(\mathstrut -\mathstrut 16q^{43} \) \(\mathstrut +\mathstrut 30q^{45} \) \(\mathstrut -\mathstrut 60q^{47} \) \(\mathstrut +\mathstrut 10q^{49} \) \(\mathstrut +\mathstrut 4q^{51} \) \(\mathstrut -\mathstrut 24q^{53} \) \(\mathstrut -\mathstrut q^{55} \) \(\mathstrut +\mathstrut 41q^{57} \) \(\mathstrut +\mathstrut 12q^{59} \) \(\mathstrut -\mathstrut 17q^{61} \) \(\mathstrut -\mathstrut 23q^{63} \) \(\mathstrut +\mathstrut 2q^{65} \) \(\mathstrut -\mathstrut 22q^{67} \) \(\mathstrut +\mathstrut 6q^{69} \) \(\mathstrut -\mathstrut 10q^{71} \) \(\mathstrut +\mathstrut 4q^{73} \) \(\mathstrut -\mathstrut 62q^{75} \) \(\mathstrut -\mathstrut 6q^{77} \) \(\mathstrut +\mathstrut 48q^{79} \) \(\mathstrut +\mathstrut 4q^{81} \) \(\mathstrut -\mathstrut 20q^{83} \) \(\mathstrut -\mathstrut 3q^{85} \) \(\mathstrut +\mathstrut 13q^{87} \) \(\mathstrut -\mathstrut 29q^{89} \) \(\mathstrut -\mathstrut 28q^{91} \) \(\mathstrut -\mathstrut 31q^{93} \) \(\mathstrut -\mathstrut 48q^{95} \) \(\mathstrut -\mathstrut 26q^{97} \) \(\mathstrut -\mathstrut 3q^{99} \) \(\mathstrut +\mathstrut O(q^{100}) \)

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
\(3\) 2.86344 1.65321 0.826604 0.562784i \(-0.190270\pi\)
0.826604 + 0.562784i \(0.190270\pi\)
\(4\) 0 0
\(5\) −0.0527883 −0.0236076 −0.0118038 0.999930i \(-0.503757\pi\)
−0.0118038 + 0.999930i \(0.503757\pi\)
\(6\) 0 0
\(7\) −1.89476 −0.716151 −0.358076 0.933693i \(-0.616567\pi\)
−0.358076 + 0.933693i \(0.616567\pi\)
\(8\) 0 0
\(9\) 5.19930 1.73310
\(10\) 0 0
\(11\) −5.46657 −1.64823 −0.824116 0.566421i \(-0.808328\pi\)
−0.824116 + 0.566421i \(0.808328\pi\)
\(12\) 0 0
\(13\) −0.847692 −0.235107 −0.117554 0.993067i \(-0.537505\pi\)
−0.117554 + 0.993067i \(0.537505\pi\)
\(14\) 0 0
\(15\) −0.151156 −0.0390283
\(16\) 0 0
\(17\) −1.00000 −0.242536
\(18\) 0 0
\(19\) 0.788998 0.181009 0.0905043 0.995896i \(-0.471152\pi\)
0.0905043 + 0.995896i \(0.471152\pi\)
\(20\) 0 0
\(21\) −5.42553 −1.18395
\(22\) 0 0
\(23\) 0.154474 0.0322101 0.0161051 0.999870i \(-0.494873\pi\)
0.0161051 + 0.999870i \(0.494873\pi\)
\(24\) 0 0
\(25\) −4.99721 −0.999443
\(26\) 0 0
\(27\) 6.29755 1.21196
\(28\) 0 0
\(29\) −3.17088 −0.588817 −0.294409 0.955680i \(-0.595123\pi\)
−0.294409 + 0.955680i \(0.595123\pi\)
\(30\) 0 0
\(31\) −8.43776 −1.51547 −0.757734 0.652564i \(-0.773693\pi\)
−0.757734 + 0.652564i \(0.773693\pi\)
\(32\) 0 0
\(33\) −15.6532 −2.72487
\(34\) 0 0
\(35\) 0.100021 0.0169066
\(36\) 0 0
\(37\) −3.87929 −0.637751 −0.318875 0.947797i \(-0.603305\pi\)
−0.318875 + 0.947797i \(0.603305\pi\)
\(38\) 0 0
\(39\) −2.42732 −0.388682
\(40\) 0 0
\(41\) −1.73405 −0.270813 −0.135406 0.990790i \(-0.543234\pi\)
−0.135406 + 0.990790i \(0.543234\pi\)
\(42\) 0 0
\(43\) −2.07545 −0.316503 −0.158251 0.987399i \(-0.550586\pi\)
−0.158251 + 0.987399i \(0.550586\pi\)
\(44\) 0 0
\(45\) −0.274462 −0.0409144
\(46\) 0 0
\(47\) 3.26225 0.475848 0.237924 0.971284i \(-0.423533\pi\)
0.237924 + 0.971284i \(0.423533\pi\)
\(48\) 0 0
\(49\) −3.40989 −0.487127
\(50\) 0 0
\(51\) −2.86344 −0.400962
\(52\) 0 0
\(53\) 2.52369 0.346655 0.173328 0.984864i \(-0.444548\pi\)
0.173328 + 0.984864i \(0.444548\pi\)
\(54\) 0 0
\(55\) 0.288571 0.0389109
\(56\) 0 0
\(57\) 2.25925 0.299245
\(58\) 0 0
\(59\) 1.00000 0.130189
\(60\) 0 0
\(61\) 8.67566 1.11080 0.555402 0.831582i \(-0.312564\pi\)
0.555402 + 0.831582i \(0.312564\pi\)
\(62\) 0 0
\(63\) −9.85141 −1.24116
\(64\) 0 0
\(65\) 0.0447482 0.00555033
\(66\) 0 0
\(67\) −6.26592 −0.765504 −0.382752 0.923851i \(-0.625024\pi\)
−0.382752 + 0.923851i \(0.625024\pi\)
\(68\) 0 0
\(69\) 0.442328 0.0532501
\(70\) 0 0
\(71\) 1.81244 0.215097 0.107548 0.994200i \(-0.465700\pi\)
0.107548 + 0.994200i \(0.465700\pi\)
\(72\) 0 0
\(73\) 4.69077 0.549013 0.274506 0.961585i \(-0.411486\pi\)
0.274506 + 0.961585i \(0.411486\pi\)
\(74\) 0 0
\(75\) −14.3092 −1.65229
\(76\) 0 0
\(77\) 10.3578 1.18038
\(78\) 0 0
\(79\) 3.52708 0.396827 0.198414 0.980118i \(-0.436421\pi\)
0.198414 + 0.980118i \(0.436421\pi\)
\(80\) 0 0
\(81\) 2.43479 0.270532
\(82\) 0 0
\(83\) −6.16895 −0.677131 −0.338565 0.940943i \(-0.609942\pi\)
−0.338565 + 0.940943i \(0.609942\pi\)
\(84\) 0 0
\(85\) 0.0527883 0.00572569
\(86\) 0 0
\(87\) −9.07962 −0.973438
\(88\) 0 0
\(89\) −8.42669 −0.893227 −0.446614 0.894727i \(-0.647370\pi\)
−0.446614 + 0.894727i \(0.647370\pi\)
\(90\) 0 0
\(91\) 1.60617 0.168373
\(92\) 0 0
\(93\) −24.1610 −2.50538
\(94\) 0 0
\(95\) −0.0416498 −0.00427318
\(96\) 0 0
\(97\) 6.52415 0.662427 0.331213 0.943556i \(-0.392542\pi\)
0.331213 + 0.943556i \(0.392542\pi\)
\(98\) 0 0
\(99\) −28.4223 −2.85655
\(100\) 0 0
\(101\) 8.32844 0.828711 0.414356 0.910115i \(-0.364007\pi\)
0.414356 + 0.910115i \(0.364007\pi\)
\(102\) 0 0
\(103\) 13.0925 1.29004 0.645020 0.764165i \(-0.276849\pi\)
0.645020 + 0.764165i \(0.276849\pi\)
\(104\) 0 0
\(105\) 0.286404 0.0279502
\(106\) 0 0
\(107\) −17.6204 −1.70343 −0.851713 0.524009i \(-0.824436\pi\)
−0.851713 + 0.524009i \(0.824436\pi\)
\(108\) 0 0
\(109\) −6.25149 −0.598785 −0.299392 0.954130i \(-0.596784\pi\)
−0.299392 + 0.954130i \(0.596784\pi\)
\(110\) 0 0
\(111\) −11.1081 −1.05434
\(112\) 0 0
\(113\) 9.41870 0.886037 0.443018 0.896513i \(-0.353908\pi\)
0.443018 + 0.896513i \(0.353908\pi\)
\(114\) 0 0
\(115\) −0.00815444 −0.000760405 0
\(116\) 0 0
\(117\) −4.40740 −0.407464
\(118\) 0 0
\(119\) 1.89476 0.173692
\(120\) 0 0
\(121\) 18.8833 1.71667
\(122\) 0 0
\(123\) −4.96534 −0.447710
\(124\) 0 0
\(125\) 0.527736 0.0472021
\(126\) 0 0
\(127\) −12.3046 −1.09186 −0.545928 0.837832i \(-0.683823\pi\)
−0.545928 + 0.837832i \(0.683823\pi\)
\(128\) 0 0
\(129\) −5.94292 −0.523245
\(130\) 0 0
\(131\) 9.85972 0.861448 0.430724 0.902484i \(-0.358258\pi\)
0.430724 + 0.902484i \(0.358258\pi\)
\(132\) 0 0
\(133\) −1.49496 −0.129630
\(134\) 0 0
\(135\) −0.332437 −0.0286116
\(136\) 0 0
\(137\) 0.947538 0.0809536 0.0404768 0.999180i \(-0.487112\pi\)
0.0404768 + 0.999180i \(0.487112\pi\)
\(138\) 0 0
\(139\) −14.0130 −1.18857 −0.594285 0.804254i \(-0.702565\pi\)
−0.594285 + 0.804254i \(0.702565\pi\)
\(140\) 0 0
\(141\) 9.34127 0.786677
\(142\) 0 0
\(143\) 4.63396 0.387512
\(144\) 0 0
\(145\) 0.167385 0.0139006
\(146\) 0 0
\(147\) −9.76402 −0.805323
\(148\) 0 0
\(149\) −12.9808 −1.06343 −0.531713 0.846924i \(-0.678452\pi\)
−0.531713 + 0.846924i \(0.678452\pi\)
\(150\) 0 0
\(151\) 10.4373 0.849377 0.424689 0.905339i \(-0.360384\pi\)
0.424689 + 0.905339i \(0.360384\pi\)
\(152\) 0 0
\(153\) −5.19930 −0.420338
\(154\) 0 0
\(155\) 0.445415 0.0357766
\(156\) 0 0
\(157\) 15.1671 1.21047 0.605234 0.796048i \(-0.293080\pi\)
0.605234 + 0.796048i \(0.293080\pi\)
\(158\) 0 0
\(159\) 7.22644 0.573094
\(160\) 0 0
\(161\) −0.292692 −0.0230673
\(162\) 0 0
\(163\) 2.52433 0.197721 0.0988603 0.995101i \(-0.468480\pi\)
0.0988603 + 0.995101i \(0.468480\pi\)
\(164\) 0 0
\(165\) 0.826305 0.0643278
\(166\) 0 0
\(167\) −19.2317 −1.48819 −0.744096 0.668073i \(-0.767119\pi\)
−0.744096 + 0.668073i \(0.767119\pi\)
\(168\) 0 0
\(169\) −12.2814 −0.944724
\(170\) 0 0
\(171\) 4.10223 0.313706
\(172\) 0 0
\(173\) 19.3075 1.46792 0.733962 0.679191i \(-0.237669\pi\)
0.733962 + 0.679191i \(0.237669\pi\)
\(174\) 0 0
\(175\) 9.46851 0.715752
\(176\) 0 0
\(177\) 2.86344 0.215229
\(178\) 0 0
\(179\) −23.7146 −1.77251 −0.886255 0.463198i \(-0.846702\pi\)
−0.886255 + 0.463198i \(0.846702\pi\)
\(180\) 0 0
\(181\) 7.64803 0.568474 0.284237 0.958754i \(-0.408260\pi\)
0.284237 + 0.958754i \(0.408260\pi\)
\(182\) 0 0
\(183\) 24.8422 1.83639
\(184\) 0 0
\(185\) 0.204781 0.0150558
\(186\) 0 0
\(187\) 5.46657 0.399755
\(188\) 0 0
\(189\) −11.9323 −0.867950
\(190\) 0 0
\(191\) −4.10952 −0.297354 −0.148677 0.988886i \(-0.547502\pi\)
−0.148677 + 0.988886i \(0.547502\pi\)
\(192\) 0 0
\(193\) 2.63181 0.189442 0.0947209 0.995504i \(-0.469804\pi\)
0.0947209 + 0.995504i \(0.469804\pi\)
\(194\) 0 0
\(195\) 0.128134 0.00917586
\(196\) 0 0
\(197\) −1.99260 −0.141967 −0.0709835 0.997477i \(-0.522614\pi\)
−0.0709835 + 0.997477i \(0.522614\pi\)
\(198\) 0 0
\(199\) 0.645571 0.0457633 0.0228817 0.999738i \(-0.492716\pi\)
0.0228817 + 0.999738i \(0.492716\pi\)
\(200\) 0 0
\(201\) −17.9421 −1.26554
\(202\) 0 0
\(203\) 6.00805 0.421682
\(204\) 0 0
\(205\) 0.0915374 0.00639325
\(206\) 0 0
\(207\) 0.803158 0.0558233
\(208\) 0 0
\(209\) −4.31311 −0.298344
\(210\) 0 0
\(211\) 20.7033 1.42528 0.712638 0.701532i \(-0.247500\pi\)
0.712638 + 0.701532i \(0.247500\pi\)
\(212\) 0 0
\(213\) 5.18981 0.355600
\(214\) 0 0
\(215\) 0.109559 0.00747188
\(216\) 0 0
\(217\) 15.9875 1.08530
\(218\) 0 0
\(219\) 13.4317 0.907632
\(220\) 0 0
\(221\) 0.847692 0.0570219
\(222\) 0 0
\(223\) −12.0087 −0.804161 −0.402080 0.915604i \(-0.631713\pi\)
−0.402080 + 0.915604i \(0.631713\pi\)
\(224\) 0 0
\(225\) −25.9820 −1.73213
\(226\) 0 0
\(227\) 14.2438 0.945392 0.472696 0.881226i \(-0.343281\pi\)
0.472696 + 0.881226i \(0.343281\pi\)
\(228\) 0 0
\(229\) −15.9843 −1.05627 −0.528136 0.849160i \(-0.677109\pi\)
−0.528136 + 0.849160i \(0.677109\pi\)
\(230\) 0 0
\(231\) 29.6590 1.95142
\(232\) 0 0
\(233\) −15.7786 −1.03369 −0.516845 0.856079i \(-0.672894\pi\)
−0.516845 + 0.856079i \(0.672894\pi\)
\(234\) 0 0
\(235\) −0.172209 −0.0112337
\(236\) 0 0
\(237\) 10.0996 0.656038
\(238\) 0 0
\(239\) −10.7711 −0.696727 −0.348364 0.937359i \(-0.613263\pi\)
−0.348364 + 0.937359i \(0.613263\pi\)
\(240\) 0 0
\(241\) −11.9469 −0.769565 −0.384782 0.923007i \(-0.625723\pi\)
−0.384782 + 0.923007i \(0.625723\pi\)
\(242\) 0 0
\(243\) −11.9208 −0.764719
\(244\) 0 0
\(245\) 0.180002 0.0114999
\(246\) 0 0
\(247\) −0.668827 −0.0425565
\(248\) 0 0
\(249\) −17.6644 −1.11944
\(250\) 0 0
\(251\) −10.8916 −0.687470 −0.343735 0.939067i \(-0.611692\pi\)
−0.343735 + 0.939067i \(0.611692\pi\)
\(252\) 0 0
\(253\) −0.844445 −0.0530898
\(254\) 0 0
\(255\) 0.151156 0.00946577
\(256\) 0 0
\(257\) −30.3817 −1.89516 −0.947579 0.319522i \(-0.896478\pi\)
−0.947579 + 0.319522i \(0.896478\pi\)
\(258\) 0 0
\(259\) 7.35031 0.456726
\(260\) 0 0
\(261\) −16.4863 −1.02048
\(262\) 0 0
\(263\) 14.2300 0.877457 0.438729 0.898620i \(-0.355429\pi\)
0.438729 + 0.898620i \(0.355429\pi\)
\(264\) 0 0
\(265\) −0.133221 −0.00818372
\(266\) 0 0
\(267\) −24.1293 −1.47669
\(268\) 0 0
\(269\) 21.2931 1.29826 0.649130 0.760677i \(-0.275133\pi\)
0.649130 + 0.760677i \(0.275133\pi\)
\(270\) 0 0
\(271\) 20.7841 1.26255 0.631273 0.775561i \(-0.282533\pi\)
0.631273 + 0.775561i \(0.282533\pi\)
\(272\) 0 0
\(273\) 4.59918 0.278355
\(274\) 0 0
\(275\) 27.3176 1.64731
\(276\) 0 0
\(277\) 19.6994 1.18362 0.591812 0.806076i \(-0.298413\pi\)
0.591812 + 0.806076i \(0.298413\pi\)
\(278\) 0 0
\(279\) −43.8704 −2.62645
\(280\) 0 0
\(281\) −6.48240 −0.386708 −0.193354 0.981129i \(-0.561937\pi\)
−0.193354 + 0.981129i \(0.561937\pi\)
\(282\) 0 0
\(283\) 8.14828 0.484365 0.242183 0.970231i \(-0.422137\pi\)
0.242183 + 0.970231i \(0.422137\pi\)
\(284\) 0 0
\(285\) −0.119262 −0.00706446
\(286\) 0 0
\(287\) 3.28560 0.193943
\(288\) 0 0
\(289\) 1.00000 0.0588235
\(290\) 0 0
\(291\) 18.6815 1.09513
\(292\) 0 0
\(293\) −14.0823 −0.822698 −0.411349 0.911478i \(-0.634942\pi\)
−0.411349 + 0.911478i \(0.634942\pi\)
\(294\) 0 0
\(295\) −0.0527883 −0.00307345
\(296\) 0 0
\(297\) −34.4260 −1.99760
\(298\) 0 0
\(299\) −0.130947 −0.00757285
\(300\) 0 0
\(301\) 3.93247 0.226664
\(302\) 0 0
\(303\) 23.8480 1.37003
\(304\) 0 0
\(305\) −0.457973 −0.0262235
\(306\) 0 0
\(307\) 18.6142 1.06237 0.531184 0.847256i \(-0.321747\pi\)
0.531184 + 0.847256i \(0.321747\pi\)
\(308\) 0 0
\(309\) 37.4896 2.13271
\(310\) 0 0
\(311\) 21.9495 1.24464 0.622321 0.782762i \(-0.286190\pi\)
0.622321 + 0.782762i \(0.286190\pi\)
\(312\) 0 0
\(313\) 20.9389 1.18354 0.591770 0.806107i \(-0.298430\pi\)
0.591770 + 0.806107i \(0.298430\pi\)
\(314\) 0 0
\(315\) 0.520039 0.0293009
\(316\) 0 0
\(317\) −5.95193 −0.334294 −0.167147 0.985932i \(-0.553455\pi\)
−0.167147 + 0.985932i \(0.553455\pi\)
\(318\) 0 0
\(319\) 17.3338 0.970507
\(320\) 0 0
\(321\) −50.4549 −2.81612
\(322\) 0 0
\(323\) −0.788998 −0.0439010
\(324\) 0 0
\(325\) 4.23610 0.234976
\(326\) 0 0
\(327\) −17.9008 −0.989916
\(328\) 0 0
\(329\) −6.18118 −0.340780
\(330\) 0 0
\(331\) −25.2684 −1.38888 −0.694439 0.719551i \(-0.744348\pi\)
−0.694439 + 0.719551i \(0.744348\pi\)
\(332\) 0 0
\(333\) −20.1696 −1.10528
\(334\) 0 0
\(335\) 0.330767 0.0180717
\(336\) 0 0
\(337\) 1.18871 0.0647532 0.0323766 0.999476i \(-0.489692\pi\)
0.0323766 + 0.999476i \(0.489692\pi\)
\(338\) 0 0
\(339\) 26.9699 1.46480
\(340\) 0 0
\(341\) 46.1256 2.49784
\(342\) 0 0
\(343\) 19.7242 1.06501
\(344\) 0 0
\(345\) −0.0233498 −0.00125711
\(346\) 0 0
\(347\) −1.06996 −0.0574386 −0.0287193 0.999588i \(-0.509143\pi\)
−0.0287193 + 0.999588i \(0.509143\pi\)
\(348\) 0 0
\(349\) −15.7638 −0.843816 −0.421908 0.906639i \(-0.638640\pi\)
−0.421908 + 0.906639i \(0.638640\pi\)
\(350\) 0 0
\(351\) −5.33839 −0.284942
\(352\) 0 0
\(353\) 30.2569 1.61041 0.805207 0.592994i \(-0.202054\pi\)
0.805207 + 0.592994i \(0.202054\pi\)
\(354\) 0 0
\(355\) −0.0956755 −0.00507793
\(356\) 0 0
\(357\) 5.42553 0.287149
\(358\) 0 0
\(359\) 5.93716 0.313351 0.156676 0.987650i \(-0.449922\pi\)
0.156676 + 0.987650i \(0.449922\pi\)
\(360\) 0 0
\(361\) −18.3775 −0.967236
\(362\) 0 0
\(363\) 54.0713 2.83801
\(364\) 0 0
\(365\) −0.247617 −0.0129609
\(366\) 0 0
\(367\) −18.3281 −0.956720 −0.478360 0.878164i \(-0.658768\pi\)
−0.478360 + 0.878164i \(0.658768\pi\)
\(368\) 0 0
\(369\) −9.01583 −0.469345
\(370\) 0 0
\(371\) −4.78178 −0.248258
\(372\) 0 0
\(373\) 4.39637 0.227636 0.113818 0.993502i \(-0.463692\pi\)
0.113818 + 0.993502i \(0.463692\pi\)
\(374\) 0 0
\(375\) 1.51114 0.0780349
\(376\) 0 0
\(377\) 2.68793 0.138435
\(378\) 0 0
\(379\) 12.2502 0.629250 0.314625 0.949216i \(-0.398121\pi\)
0.314625 + 0.949216i \(0.398121\pi\)
\(380\) 0 0
\(381\) −35.2335 −1.80506
\(382\) 0 0
\(383\) −27.6073 −1.41067 −0.705333 0.708876i \(-0.749203\pi\)
−0.705333 + 0.708876i \(0.749203\pi\)
\(384\) 0 0
\(385\) −0.546772 −0.0278661
\(386\) 0 0
\(387\) −10.7909 −0.548530
\(388\) 0 0
\(389\) −1.25576 −0.0636696 −0.0318348 0.999493i \(-0.510135\pi\)
−0.0318348 + 0.999493i \(0.510135\pi\)
\(390\) 0 0
\(391\) −0.154474 −0.00781211
\(392\) 0 0
\(393\) 28.2327 1.42415
\(394\) 0 0
\(395\) −0.186188 −0.00936815
\(396\) 0 0
\(397\) 28.6324 1.43702 0.718510 0.695517i \(-0.244825\pi\)
0.718510 + 0.695517i \(0.244825\pi\)
\(398\) 0 0
\(399\) −4.28073 −0.214305
\(400\) 0 0
\(401\) 1.53912 0.0768599 0.0384300 0.999261i \(-0.487764\pi\)
0.0384300 + 0.999261i \(0.487764\pi\)
\(402\) 0 0
\(403\) 7.15263 0.356298
\(404\) 0 0
\(405\) −0.128528 −0.00638662
\(406\) 0 0
\(407\) 21.2064 1.05116
\(408\) 0 0
\(409\) 1.84451 0.0912052 0.0456026 0.998960i \(-0.485479\pi\)
0.0456026 + 0.998960i \(0.485479\pi\)
\(410\) 0 0
\(411\) 2.71322 0.133833
\(412\) 0 0
\(413\) −1.89476 −0.0932350
\(414\) 0 0
\(415\) 0.325648 0.0159855
\(416\) 0 0
\(417\) −40.1255 −1.96496
\(418\) 0 0
\(419\) −11.9843 −0.585474 −0.292737 0.956193i \(-0.594566\pi\)
−0.292737 + 0.956193i \(0.594566\pi\)
\(420\) 0 0
\(421\) 5.13894 0.250456 0.125228 0.992128i \(-0.460034\pi\)
0.125228 + 0.992128i \(0.460034\pi\)
\(422\) 0 0
\(423\) 16.9614 0.824692
\(424\) 0 0
\(425\) 4.99721 0.242400
\(426\) 0 0
\(427\) −16.4383 −0.795504
\(428\) 0 0
\(429\) 13.2691 0.640637
\(430\) 0 0
\(431\) 34.1372 1.64433 0.822166 0.569247i \(-0.192765\pi\)
0.822166 + 0.569247i \(0.192765\pi\)
\(432\) 0 0
\(433\) 0.887422 0.0426468 0.0213234 0.999773i \(-0.493212\pi\)
0.0213234 + 0.999773i \(0.493212\pi\)
\(434\) 0 0
\(435\) 0.479298 0.0229806
\(436\) 0 0
\(437\) 0.121880 0.00583031
\(438\) 0 0
\(439\) −2.96442 −0.141484 −0.0707420 0.997495i \(-0.522537\pi\)
−0.0707420 + 0.997495i \(0.522537\pi\)
\(440\) 0 0
\(441\) −17.7290 −0.844240
\(442\) 0 0
\(443\) 5.19805 0.246967 0.123483 0.992347i \(-0.460593\pi\)
0.123483 + 0.992347i \(0.460593\pi\)
\(444\) 0 0
\(445\) 0.444830 0.0210870
\(446\) 0 0
\(447\) −37.1697 −1.75807
\(448\) 0 0
\(449\) −3.06611 −0.144699 −0.0723494 0.997379i \(-0.523050\pi\)
−0.0723494 + 0.997379i \(0.523050\pi\)
\(450\) 0 0
\(451\) 9.47929 0.446362
\(452\) 0 0
\(453\) 29.8867 1.40420
\(454\) 0 0
\(455\) −0.0847870 −0.00397488
\(456\) 0 0
\(457\) −0.551155 −0.0257819 −0.0128910 0.999917i \(-0.504103\pi\)
−0.0128910 + 0.999917i \(0.504103\pi\)
\(458\) 0 0
\(459\) −6.29755 −0.293945
\(460\) 0 0
\(461\) 5.61995 0.261747 0.130874 0.991399i \(-0.458222\pi\)
0.130874 + 0.991399i \(0.458222\pi\)
\(462\) 0 0
\(463\) −32.8869 −1.52839 −0.764193 0.644988i \(-0.776862\pi\)
−0.764193 + 0.644988i \(0.776862\pi\)
\(464\) 0 0
\(465\) 1.27542 0.0591462
\(466\) 0 0
\(467\) 11.0984 0.513571 0.256785 0.966468i \(-0.417337\pi\)
0.256785 + 0.966468i \(0.417337\pi\)
\(468\) 0 0
\(469\) 11.8724 0.548216
\(470\) 0 0
\(471\) 43.4301 2.00115
\(472\) 0 0
\(473\) 11.3456 0.521670
\(474\) 0 0
\(475\) −3.94279 −0.180908
\(476\) 0 0
\(477\) 13.1214 0.600788
\(478\) 0 0
\(479\) 4.18647 0.191285 0.0956424 0.995416i \(-0.469509\pi\)
0.0956424 + 0.995416i \(0.469509\pi\)
\(480\) 0 0
\(481\) 3.28844 0.149940
\(482\) 0 0
\(483\) −0.838105 −0.0381351
\(484\) 0 0
\(485\) −0.344399 −0.0156383
\(486\) 0 0
\(487\) −21.4694 −0.972873 −0.486437 0.873716i \(-0.661704\pi\)
−0.486437 + 0.873716i \(0.661704\pi\)
\(488\) 0 0
\(489\) 7.22827 0.326874
\(490\) 0 0
\(491\) −16.2213 −0.732055 −0.366027 0.930604i \(-0.619282\pi\)
−0.366027 + 0.930604i \(0.619282\pi\)
\(492\) 0 0
\(493\) 3.17088 0.142809
\(494\) 0 0
\(495\) 1.50036 0.0674363
\(496\) 0 0
\(497\) −3.43413 −0.154042
\(498\) 0 0
\(499\) −0.627481 −0.0280899 −0.0140450 0.999901i \(-0.504471\pi\)
−0.0140450 + 0.999901i \(0.504471\pi\)
\(500\) 0 0
\(501\) −55.0687 −2.46029
\(502\) 0 0
\(503\) −17.3264 −0.772548 −0.386274 0.922384i \(-0.626238\pi\)
−0.386274 + 0.922384i \(0.626238\pi\)
\(504\) 0 0
\(505\) −0.439644 −0.0195639
\(506\) 0 0
\(507\) −35.1671 −1.56183
\(508\) 0 0
\(509\) −39.4755 −1.74972 −0.874861 0.484374i \(-0.839047\pi\)
−0.874861 + 0.484374i \(0.839047\pi\)
\(510\) 0 0
\(511\) −8.88787 −0.393176
\(512\) 0 0
\(513\) 4.96876 0.219376
\(514\) 0 0
\(515\) −0.691130 −0.0304548
\(516\) 0 0
\(517\) −17.8333 −0.784309
\(518\) 0 0
\(519\) 55.2859 2.42678
\(520\) 0 0
\(521\) 32.9170 1.44212 0.721061 0.692872i \(-0.243655\pi\)
0.721061 + 0.692872i \(0.243655\pi\)
\(522\) 0 0
\(523\) 16.6615 0.728555 0.364277 0.931290i \(-0.381316\pi\)
0.364277 + 0.931290i \(0.381316\pi\)
\(524\) 0 0
\(525\) 27.1125 1.18329
\(526\) 0 0
\(527\) 8.43776 0.367555
\(528\) 0 0
\(529\) −22.9761 −0.998963
\(530\) 0 0
\(531\) 5.19930 0.225630
\(532\) 0 0
\(533\) 1.46994 0.0636701
\(534\) 0 0
\(535\) 0.930149 0.0402139
\(536\) 0 0
\(537\) −67.9053 −2.93033
\(538\) 0 0
\(539\) 18.6404 0.802899
\(540\) 0 0
\(541\) 13.1812 0.566706 0.283353 0.959016i \(-0.408553\pi\)
0.283353 + 0.959016i \(0.408553\pi\)
\(542\) 0 0
\(543\) 21.8997 0.939806
\(544\) 0 0
\(545\) 0.330006 0.0141359
\(546\) 0 0
\(547\) 26.1225 1.11692 0.558458 0.829533i \(-0.311393\pi\)
0.558458 + 0.829533i \(0.311393\pi\)
\(548\) 0 0
\(549\) 45.1073 1.92513
\(550\) 0 0
\(551\) −2.50182 −0.106581
\(552\) 0 0
\(553\) −6.68296 −0.284188
\(554\) 0 0
\(555\) 0.586378 0.0248904
\(556\) 0 0
\(557\) −9.96106 −0.422064 −0.211032 0.977479i \(-0.567682\pi\)
−0.211032 + 0.977479i \(0.567682\pi\)
\(558\) 0 0
\(559\) 1.75934 0.0744121
\(560\) 0 0
\(561\) 15.6532 0.660878
\(562\) 0 0
\(563\) −23.7366 −1.00038 −0.500189 0.865916i \(-0.666736\pi\)
−0.500189 + 0.865916i \(0.666736\pi\)
\(564\) 0 0
\(565\) −0.497197 −0.0209172
\(566\) 0 0
\(567\) −4.61333 −0.193742
\(568\) 0 0
\(569\) −1.60597 −0.0673259 −0.0336629 0.999433i \(-0.510717\pi\)
−0.0336629 + 0.999433i \(0.510717\pi\)
\(570\) 0 0
\(571\) −24.8605 −1.04038 −0.520191 0.854050i \(-0.674139\pi\)
−0.520191 + 0.854050i \(0.674139\pi\)
\(572\) 0 0
\(573\) −11.7674 −0.491589
\(574\) 0 0
\(575\) −0.771942 −0.0321922
\(576\) 0 0
\(577\) 36.4075 1.51566 0.757832 0.652450i \(-0.226259\pi\)
0.757832 + 0.652450i \(0.226259\pi\)
\(578\) 0 0
\(579\) 7.53603 0.313187
\(580\) 0 0
\(581\) 11.6887 0.484928
\(582\) 0 0
\(583\) −13.7959 −0.571368
\(584\) 0 0
\(585\) 0.232659 0.00961927
\(586\) 0 0
\(587\) −27.0522 −1.11656 −0.558282 0.829651i \(-0.688539\pi\)
−0.558282 + 0.829651i \(0.688539\pi\)
\(588\) 0 0
\(589\) −6.65738 −0.274312
\(590\) 0 0
\(591\) −5.70570 −0.234701
\(592\) 0 0
\(593\) −18.5883 −0.763332 −0.381666 0.924300i \(-0.624649\pi\)
−0.381666 + 0.924300i \(0.624649\pi\)
\(594\) 0 0
\(595\) −0.100021 −0.00410046
\(596\) 0 0
\(597\) 1.84856 0.0756563
\(598\) 0 0
\(599\) −1.63500 −0.0668042 −0.0334021 0.999442i \(-0.510634\pi\)
−0.0334021 + 0.999442i \(0.510634\pi\)
\(600\) 0 0
\(601\) 15.9325 0.649900 0.324950 0.945731i \(-0.394653\pi\)
0.324950 + 0.945731i \(0.394653\pi\)
\(602\) 0 0
\(603\) −32.5784 −1.32669
\(604\) 0 0
\(605\) −0.996819 −0.0405265
\(606\) 0 0
\(607\) −2.17386 −0.0882344 −0.0441172 0.999026i \(-0.514047\pi\)
−0.0441172 + 0.999026i \(0.514047\pi\)
\(608\) 0 0
\(609\) 17.2037 0.697129
\(610\) 0 0
\(611\) −2.76539 −0.111876
\(612\) 0 0
\(613\) 32.9154 1.32944 0.664720 0.747092i \(-0.268551\pi\)
0.664720 + 0.747092i \(0.268551\pi\)
\(614\) 0 0
\(615\) 0.262112 0.0105694
\(616\) 0 0
\(617\) 9.20165 0.370444 0.185222 0.982697i \(-0.440700\pi\)
0.185222 + 0.982697i \(0.440700\pi\)
\(618\) 0 0
\(619\) 24.8989 1.00077 0.500386 0.865802i \(-0.333191\pi\)
0.500386 + 0.865802i \(0.333191\pi\)
\(620\) 0 0
\(621\) 0.972811 0.0390375
\(622\) 0 0
\(623\) 15.9665 0.639686
\(624\) 0 0
\(625\) 24.9582 0.998328
\(626\) 0 0
\(627\) −12.3503 −0.493225
\(628\) 0 0
\(629\) 3.87929 0.154677
\(630\) 0 0
\(631\) −36.0425 −1.43483 −0.717414 0.696647i \(-0.754674\pi\)
−0.717414 + 0.696647i \(0.754674\pi\)
\(632\) 0 0
\(633\) 59.2827 2.35628
\(634\) 0 0
\(635\) 0.649538 0.0257761
\(636\) 0 0
\(637\) 2.89054 0.114527
\(638\) 0 0
\(639\) 9.42340 0.372784
\(640\) 0 0
\(641\) −12.4524 −0.491840 −0.245920 0.969290i \(-0.579090\pi\)
−0.245920 + 0.969290i \(0.579090\pi\)
\(642\) 0 0
\(643\) −37.7762 −1.48975 −0.744875 0.667204i \(-0.767491\pi\)
−0.744875 + 0.667204i \(0.767491\pi\)
\(644\) 0 0
\(645\) 0.313717 0.0123526
\(646\) 0 0
\(647\) 1.46180 0.0574692 0.0287346 0.999587i \(-0.490852\pi\)
0.0287346 + 0.999587i \(0.490852\pi\)
\(648\) 0 0
\(649\) −5.46657 −0.214581
\(650\) 0 0
\(651\) 45.7793 1.79423
\(652\) 0 0
\(653\) −14.0750 −0.550797 −0.275398 0.961330i \(-0.588810\pi\)
−0.275398 + 0.961330i \(0.588810\pi\)
\(654\) 0 0
\(655\) −0.520478 −0.0203368
\(656\) 0 0
\(657\) 24.3887 0.951493
\(658\) 0 0
\(659\) −26.1024 −1.01680 −0.508402 0.861120i \(-0.669764\pi\)
−0.508402 + 0.861120i \(0.669764\pi\)
\(660\) 0 0
\(661\) −10.0745 −0.391852 −0.195926 0.980619i \(-0.562771\pi\)
−0.195926 + 0.980619i \(0.562771\pi\)
\(662\) 0 0
\(663\) 2.42732 0.0942692
\(664\) 0 0
\(665\) 0.0789164 0.00306025
\(666\) 0 0
\(667\) −0.489820 −0.0189659
\(668\) 0 0
\(669\) −34.3861 −1.32945
\(670\) 0 0
\(671\) −47.4261 −1.83086
\(672\) 0 0
\(673\) −25.3846 −0.978504 −0.489252 0.872143i \(-0.662730\pi\)
−0.489252 + 0.872143i \(0.662730\pi\)
\(674\) 0 0
\(675\) −31.4702 −1.21129
\(676\) 0 0
\(677\) −5.67609 −0.218150 −0.109075 0.994034i \(-0.534789\pi\)
−0.109075 + 0.994034i \(0.534789\pi\)
\(678\) 0 0
\(679\) −12.3617 −0.474398
\(680\) 0 0
\(681\) 40.7862 1.56293
\(682\) 0 0
\(683\) −36.4544 −1.39489 −0.697445 0.716639i \(-0.745680\pi\)
−0.697445 + 0.716639i \(0.745680\pi\)
\(684\) 0 0
\(685\) −0.0500189 −0.00191112
\(686\) 0 0
\(687\) −45.7701 −1.74624
\(688\) 0 0
\(689\) −2.13931 −0.0815013
\(690\) 0 0
\(691\) 7.13483 0.271422 0.135711 0.990748i \(-0.456668\pi\)
0.135711 + 0.990748i \(0.456668\pi\)
\(692\) 0 0
\(693\) 53.8534 2.04572
\(694\) 0 0
\(695\) 0.739725 0.0280594
\(696\) 0 0
\(697\) 1.73405 0.0656818
\(698\) 0 0
\(699\) −45.1811 −1.70891
\(700\) 0 0
\(701\) −38.7241 −1.46259 −0.731295 0.682062i \(-0.761084\pi\)
−0.731295 + 0.682062i \(0.761084\pi\)
\(702\) 0 0
\(703\) −3.06075 −0.115438
\(704\) 0 0
\(705\) −0.493110 −0.0185716
\(706\) 0 0
\(707\) −15.7804 −0.593483
\(708\) 0 0
\(709\) −0.389087 −0.0146125 −0.00730623 0.999973i \(-0.502326\pi\)
−0.00730623 + 0.999973i \(0.502326\pi\)
\(710\) 0 0
\(711\) 18.3383 0.687740
\(712\) 0 0
\(713\) −1.30342 −0.0488134
\(714\) 0 0
\(715\) −0.244619 −0.00914823
\(716\) 0 0
\(717\) −30.8425 −1.15184
\(718\) 0 0
\(719\) 17.4702 0.651529 0.325765 0.945451i \(-0.394378\pi\)
0.325765 + 0.945451i \(0.394378\pi\)
\(720\) 0 0
\(721\) −24.8071 −0.923864
\(722\) 0 0
\(723\) −34.2091 −1.27225
\(724\) 0 0
\(725\) 15.8456 0.588489
\(726\) 0 0
\(727\) −39.3193 −1.45827 −0.729137 0.684368i \(-0.760078\pi\)
−0.729137 + 0.684368i \(0.760078\pi\)
\(728\) 0 0
\(729\) −41.4388 −1.53477
\(730\) 0 0
\(731\) 2.07545 0.0767632
\(732\) 0 0
\(733\) 17.0681 0.630425 0.315213 0.949021i \(-0.397924\pi\)
0.315213 + 0.949021i \(0.397924\pi\)
\(734\) 0 0
\(735\) 0.515426 0.0190118
\(736\) 0 0
\(737\) 34.2531 1.26173
\(738\) 0 0
\(739\) −16.7465 −0.616030 −0.308015 0.951382i \(-0.599665\pi\)
−0.308015 + 0.951382i \(0.599665\pi\)
\(740\) 0 0
\(741\) −1.91515 −0.0703547
\(742\) 0 0
\(743\) 17.9666 0.659131 0.329565 0.944133i \(-0.393098\pi\)
0.329565 + 0.944133i \(0.393098\pi\)
\(744\) 0 0
\(745\) 0.685233 0.0251050
\(746\) 0 0
\(747\) −32.0742 −1.17353
\(748\) 0 0
\(749\) 33.3863 1.21991
\(750\) 0 0
\(751\) −36.7108 −1.33959 −0.669797 0.742544i \(-0.733619\pi\)
−0.669797 + 0.742544i \(0.733619\pi\)
\(752\) 0 0
\(753\) −31.1874 −1.13653
\(754\) 0 0
\(755\) −0.550968 −0.0200518
\(756\) 0 0
\(757\) 10.3431 0.375926 0.187963 0.982176i \(-0.439812\pi\)
0.187963 + 0.982176i \(0.439812\pi\)
\(758\) 0 0
\(759\) −2.41802 −0.0877685
\(760\) 0 0
\(761\) 2.86805 0.103967 0.0519834 0.998648i \(-0.483446\pi\)
0.0519834 + 0.998648i \(0.483446\pi\)
\(762\) 0 0
\(763\) 11.8451 0.428820
\(764\) 0 0
\(765\) 0.274462 0.00992319
\(766\) 0 0
\(767\) −0.847692 −0.0306084
\(768\) 0 0
\(769\) −0.874132 −0.0315220 −0.0157610 0.999876i \(-0.505017\pi\)
−0.0157610 + 0.999876i \(0.505017\pi\)
\(770\) 0 0
\(771\) −86.9962 −3.13309
\(772\) 0 0
\(773\) 12.1205 0.435945 0.217973 0.975955i \(-0.430056\pi\)
0.217973 + 0.975955i \(0.430056\pi\)
\(774\) 0 0
\(775\) 42.1653 1.51462
\(776\) 0 0
\(777\) 21.0472 0.755063
\(778\) 0 0
\(779\) −1.36816 −0.0490194
\(780\) 0 0
\(781\) −9.90782 −0.354530
\(782\) 0 0
\(783\) −19.9688 −0.713626
\(784\) 0 0
\(785\) −0.800646 −0.0285763
\(786\) 0 0
\(787\) −17.8117 −0.634918 −0.317459 0.948272i \(-0.602830\pi\)
−0.317459 + 0.948272i \(0.602830\pi\)
\(788\) 0 0
\(789\) 40.7467 1.45062
\(790\) 0 0
\(791\) −17.8462 −0.634536
\(792\) 0 0
\(793\) −7.35429 −0.261158
\(794\) 0 0
\(795\) −0.381471 −0.0135294
\(796\) 0 0
\(797\) 18.6229 0.659656 0.329828 0.944041i \(-0.393009\pi\)
0.329828 + 0.944041i \(0.393009\pi\)
\(798\) 0 0
\(799\) −3.26225 −0.115410
\(800\) 0 0
\(801\) −43.8128 −1.54805
\(802\) 0 0
\(803\) −25.6424 −0.904900
\(804\) 0 0
\(805\) 0.0154507 0.000544565 0
\(806\) 0 0
\(807\) 60.9714 2.14629
\(808\) 0 0
\(809\) −10.1096 −0.355433 −0.177717 0.984082i \(-0.556871\pi\)
−0.177717 + 0.984082i \(0.556871\pi\)
\(810\) 0 0
\(811\) 5.73415 0.201353 0.100677 0.994919i \(-0.467899\pi\)
0.100677 + 0.994919i \(0.467899\pi\)
\(812\) 0 0
\(813\) 59.5141 2.08725
\(814\) 0 0
\(815\) −0.133255 −0.00466772
\(816\) 0 0
\(817\) −1.63752 −0.0572897
\(818\) 0 0
\(819\) 8.35096 0.291806
\(820\) 0 0
\(821\) 23.2314 0.810782 0.405391 0.914143i \(-0.367135\pi\)
0.405391 + 0.914143i \(0.367135\pi\)
\(822\) 0 0
\(823\) 41.0816 1.43202 0.716008 0.698092i \(-0.245968\pi\)
0.716008 + 0.698092i \(0.245968\pi\)
\(824\) 0 0
\(825\) 78.2223 2.72335
\(826\) 0 0
\(827\) 28.3794 0.986849 0.493425 0.869789i \(-0.335745\pi\)
0.493425 + 0.869789i \(0.335745\pi\)
\(828\) 0 0
\(829\) −8.22836 −0.285783 −0.142891 0.989738i \(-0.545640\pi\)
−0.142891 + 0.989738i \(0.545640\pi\)
\(830\) 0 0
\(831\) 56.4082 1.95678
\(832\) 0 0
\(833\) 3.40989 0.118146
\(834\) 0 0
\(835\) 1.01521 0.0351327
\(836\) 0 0
\(837\) −53.1373 −1.83669
\(838\) 0 0
\(839\) 46.5697 1.60776 0.803882 0.594788i \(-0.202764\pi\)
0.803882 + 0.594788i \(0.202764\pi\)
\(840\) 0 0
\(841\) −18.9455 −0.653294
\(842\) 0 0
\(843\) −18.5620 −0.639308
\(844\) 0 0
\(845\) 0.648315 0.0223027
\(846\) 0 0
\(847\) −35.7794 −1.22939
\(848\) 0 0
\(849\) 23.3321 0.800757
\(850\) 0 0
\(851\) −0.599251 −0.0205420
\(852\) 0 0
\(853\) 41.4311 1.41857 0.709286 0.704920i \(-0.249017\pi\)
0.709286 + 0.704920i \(0.249017\pi\)
\(854\) 0 0
\(855\) −0.216550 −0.00740585
\(856\) 0 0
\(857\) −26.4815 −0.904590 −0.452295 0.891868i \(-0.649395\pi\)
−0.452295 + 0.891868i \(0.649395\pi\)
\(858\) 0 0
\(859\) −28.2438 −0.963665 −0.481833 0.876263i \(-0.660029\pi\)
−0.481833 + 0.876263i \(0.660029\pi\)
\(860\) 0 0
\(861\) 9.40813 0.320628
\(862\) 0 0
\(863\) −45.2780 −1.54128 −0.770640 0.637270i \(-0.780064\pi\)
−0.770640 + 0.637270i \(0.780064\pi\)
\(864\) 0 0
\(865\) −1.01921 −0.0346542
\(866\) 0 0
\(867\) 2.86344 0.0972476
\(868\) 0 0
\(869\) −19.2810 −0.654063
\(870\) 0 0
\(871\) 5.31157 0.179976
\(872\) 0 0
\(873\) 33.9210 1.14805
\(874\) 0 0
\(875\) −0.999932 −0.0338039
\(876\) 0 0
\(877\) −12.8422 −0.433650 −0.216825 0.976210i \(-0.569570\pi\)
−0.216825 + 0.976210i \(0.569570\pi\)
\(878\) 0 0
\(879\) −40.3239 −1.36009
\(880\) 0 0
\(881\) 37.2730 1.25576 0.627879 0.778311i \(-0.283923\pi\)
0.627879 + 0.778311i \(0.283923\pi\)
\(882\) 0 0
\(883\) 47.5646 1.60068 0.800338 0.599549i \(-0.204654\pi\)
0.800338 + 0.599549i \(0.204654\pi\)
\(884\) 0 0
\(885\) −0.151156 −0.00508106
\(886\) 0 0
\(887\) −47.6135 −1.59871 −0.799353 0.600862i \(-0.794824\pi\)
−0.799353 + 0.600862i \(0.794824\pi\)
\(888\) 0 0
\(889\) 23.3142 0.781934
\(890\) 0 0
\(891\) −13.3099 −0.445899
\(892\) 0 0
\(893\) 2.57391 0.0861326
\(894\) 0 0
\(895\) 1.25185 0.0418448
\(896\) 0 0
\(897\) −0.374958 −0.0125195
\(898\) 0 0
\(899\) 26.7551 0.892333
\(900\) 0 0
\(901\) −2.52369 −0.0840763
\(902\) 0 0
\(903\) 11.2604 0.374723
\(904\) 0 0
\(905\) −0.403727 −0.0134203
\(906\) 0 0
\(907\) −20.1581 −0.669339 −0.334669 0.942336i \(-0.608625\pi\)
−0.334669 + 0.942336i \(0.608625\pi\)
\(908\) 0 0
\(909\) 43.3020 1.43624
\(910\) 0 0
\(911\) 44.8639 1.48641 0.743203 0.669066i \(-0.233306\pi\)
0.743203 + 0.669066i \(0.233306\pi\)
\(912\) 0 0
\(913\) 33.7230 1.11607
\(914\) 0 0
\(915\) −1.31138 −0.0433529
\(916\) 0 0
\(917\) −18.6818 −0.616927
\(918\) 0 0
\(919\) 41.5002 1.36896 0.684482 0.729030i \(-0.260028\pi\)
0.684482 + 0.729030i \(0.260028\pi\)
\(920\) 0 0
\(921\) 53.3007 1.75632
\(922\) 0 0
\(923\) −1.53639 −0.0505709
\(924\) 0 0
\(925\) 19.3856 0.637395
\(926\) 0 0
\(927\) 68.0717 2.23577
\(928\) 0 0
\(929\) −39.8060 −1.30599 −0.652996 0.757361i \(-0.726488\pi\)
−0.652996 + 0.757361i \(0.726488\pi\)
\(930\) 0 0
\(931\) −2.69040 −0.0881742
\(932\) 0 0
\(933\) 62.8511 2.05765
\(934\) 0 0
\(935\) −0.288571 −0.00943727
\(936\) 0 0
\(937\) 1.58085 0.0516440 0.0258220 0.999667i \(-0.491780\pi\)
0.0258220 + 0.999667i \(0.491780\pi\)
\(938\) 0 0
\(939\) 59.9574 1.95664
\(940\) 0 0
\(941\) 29.3211 0.955840 0.477920 0.878403i \(-0.341391\pi\)
0.477920 + 0.878403i \(0.341391\pi\)
\(942\) 0 0
\(943\) −0.267866 −0.00872292
\(944\) 0 0
\(945\) 0.629888 0.0204903
\(946\) 0 0
\(947\) −29.0724 −0.944725 −0.472363 0.881404i \(-0.656599\pi\)
−0.472363 + 0.881404i \(0.656599\pi\)
\(948\) 0 0
\(949\) −3.97632 −0.129077
\(950\) 0 0
\(951\) −17.0430 −0.552657
\(952\) 0 0
\(953\) 2.02910 0.0657291 0.0328646 0.999460i \(-0.489537\pi\)
0.0328646 + 0.999460i \(0.489537\pi\)
\(954\) 0 0
\(955\) 0.216934 0.00701983
\(956\) 0 0
\(957\) 49.6344 1.60445
\(958\) 0 0
\(959\) −1.79535 −0.0579750
\(960\) 0 0
\(961\) 40.1959 1.29664
\(962\) 0 0
\(963\) −91.6135 −2.95220
\(964\) 0 0
\(965\) −0.138929 −0.00447227
\(966\) 0 0
\(967\) 5.57318 0.179221 0.0896107 0.995977i \(-0.471438\pi\)
0.0896107 + 0.995977i \(0.471438\pi\)
\(968\) 0 0
\(969\) −2.25925 −0.0725775
\(970\) 0 0
\(971\) −12.7199 −0.408201 −0.204100 0.978950i \(-0.565427\pi\)
−0.204100 + 0.978950i \(0.565427\pi\)
\(972\) 0 0
\(973\) 26.5513 0.851197
\(974\) 0 0
\(975\) 12.1298 0.388465
\(976\) 0 0
\(977\) 1.65484 0.0529431 0.0264716 0.999650i \(-0.491573\pi\)
0.0264716 + 0.999650i \(0.491573\pi\)
\(978\) 0 0
\(979\) 46.0650 1.47225
\(980\) 0 0
\(981\) −32.5034 −1.03775
\(982\) 0 0
\(983\) 14.8741 0.474411 0.237206 0.971459i \(-0.423768\pi\)
0.237206 + 0.971459i \(0.423768\pi\)
\(984\) 0 0
\(985\) 0.105186 0.00335151
\(986\) 0 0
\(987\) −17.6994 −0.563380
\(988\) 0 0
\(989\) −0.320603 −0.0101946
\(990\) 0 0
\(991\) 34.2475 1.08791 0.543953 0.839116i \(-0.316927\pi\)
0.543953 + 0.839116i \(0.316927\pi\)
\(992\) 0 0
\(993\) −72.3547 −2.29611
\(994\) 0 0
\(995\) −0.0340786 −0.00108036
\(996\) 0 0
\(997\) 4.67522 0.148066 0.0740328 0.997256i \(-0.476413\pi\)
0.0740328 + 0.997256i \(0.476413\pi\)
\(998\) 0 0
\(999\) −24.4300 −0.772931
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 \(a_p\))